International Geophysics Series Edited by J. VAN MIEGHEM
Royal Belgian Meteorological Institute Uccle, Belgium Volume 1 Volume 2 Volume 3 Volume 4 Volume 5 Volume 6 Volume 7
BENO GUTENBERG. Physics of the Earth's Interior. 1959 JOSEPH W. CHAMBERLAIN. Physics of the Aurora and Airglow. 1961 S. K. RUNCORN (ed.). Continental Drift. 1962 C. E. JUNGE. Air Chemistry and Radioactivity. 1963 ROBERT G. FLEAGLE AND JOOST A. BuSINGER. An Introduction to Atmospheric Physics. 1963 L. DUFOUR AND R. DEFAY. Thermodynamics of Clouds. 1963 H. U. ROLL. Physics of the Marine Atmosphere. 1965
IN PREPARATION RICHARD A. CRAIG
.
The Upper Atmosphere: Meteorology and Physics
COPYRIGHT
© 1965, BY ACADEMIC
PRESS INC.
ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS. WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS.
ACADEMIC PRESS INC.
111 Fifth Avenue, New York, New York 10003
United Kingdom Edition published by ACADEMIC PRESS INC. (LONDON) LTD.
Berkeley Square House. London W.l
LIBRARY OF CONGRESS CATALOG CARD NUMBER:
PRINTED IN THE UNITED STATES OF AMERICA
64-21673
Preface Although a sufficient number of books exist that treat maritime meteorology as an applied science, I doubt that there is any book available that considers the subject as a pure science. In view of the particular emphasis now placed on the development of marine sciences, it is felt that works dealing with the physical approach are needed. It is hoped that this volume will fill this need and will prove useful not only to meteorologists and oceanographers but also to scientists working in the fields of atmospheric physics and geophysics. In this volume, marine atmosphere is regarded as that part of the atmosphere which has the sea surface as its lower boundary and which receives its peculiar characteristics from interaction with the ocean. The main object of this monograph is to discuss the influence exerted by the sea surface on the properties of the atmosphere as well as on atmospheric processes of small and medium scale. Particular consideration is given to the exchange occurring in the boundary layer between ocean and atmosphere. The discussions include the flow characteristics and thermodynamics, as well as the chemistry, electricity, and radioactivity, of the marine atmosphere. The particular difficulties inherent in meteorological measurements at sea are considered in an opening section. Emphasis is placed on the physical approach rather than on geographical aspects and those of application. The discussion of the empirical facts, regarded as fundamental, is followed by a theoretical interpretation. The extent of the representation and the details given therein are dependent on the amount of information available to me in the literature published up to 1961, and in some 1962 and 1963 publications. About 600 papers and books were consulted. It is interesting to note that the number of works published in the decade 1950-1960 is almost three times greater than the total number published in the previous five decades. I wish to acknowledge the support I received from the German Federal Ministry of Transport and from the German Weather Service who granted me additional leave for writing this monograph. I have had the advantage of working with a group of scientists who are particularly distinguished in the field of maritime meteorology and v
vi
PREFACE
thus I feel extremely indebted to my colleagues in the Seewetteramt who offered me helpful suggestions and constructive criticism. I am appreciative of the help of my secretary, Mrs. Franziska Petsch, who typed the manuscript with considerable devotion and reliability. Further, I am very much obliged to the Publisher for valuable assistance. Finally I want to address my sincerest thanks to my wife who never failed to encourage me in spite of the fact that I had to do the writing during my spare time. Without her understanding and her continuous linguistic assistance this book would never have been written. Hamburg November, 1964
H. U.
ROLL
Harmonious in their action, the air and sea are obedient to law and subject to order in all their movements; when we consult them in the performance of their manifold and marvelous offices, they teach us lessons concerning the wonders of the deep, the mysteries of the sky, the greatness, and the wisdom, and goodness of the Creator, which make us wiser and better men. M. F. Maury, The Physical Geography of the Sea, 1858.
1. Introduction and Basic Principles Since the very first meteorological observations and investigations at sea, maritime meteorology has mostly been considered and treated as an applied science, its chief purpose being to benefit shipping, fishing, and marine aviation. For this reason books dealing with this subject have generally been written with the intention of furnishing seamen with the necessary basic knowledge of meteorological phenomena and processes at sea as well as giving them some guidance on how to use the information received from the weather services with regard to improving both the security and economy of marine navigation. It goes without saying that any publication issued for this purpose must try to deal with the subject in a manner as elementary as possible and as practical as necessary. Neither is there a need to give a detailed and comprehensive account of the state of knowledge maritime meteorological science has reached so far, nor is it essential to discuss the inherent physical problems which have not yet been settled. For maritime application it is fully sufficient to restrict the treatment to describing the well-known facts and explaining those maritime meteorological phenomena, processes, and procedures which are of importance to shipping and flying. Looking back to the old days when Maury initiated the development of modern maritime meteorology, we notice a long line of excellent textbooks which have served and are still serving the purpose mentioned above. There is hardly a maritime country which has not tried to comply with the marine requirements in this way. Moreover, maritime interests and needs are still vivid and strong, which may be gathered from the fact that France, Germany, The Netherlands, 1
2
I
INTRODUCTION AND BASIC PRINCIPLES
Poland, the Union of Soviet Socialist Republics, the United Kingdom, and the United States of America, among others, have published textbooks on maritime meteorology for the use of mariners within the past ten years. (Titles and names of authors are given at the beginning of the list of references.) Having this in mind, I hope everybody will agree that there is no pronounced necessity for an additional publication of this kind, i.e., a meteorological textbook for mariners. But there are other aspects which should be dealt with. Turning to a more scientific approach and dropping the matter of application to shipping and flying, we should ask which publications of this kind are available at present. The result will be that there is a considerable number of monographs and handbooks chiefly devoted to general meteorology and/or oceanography and containing more or less detailed and complete sections on maritime meteorology. As an example of the first type, there may be mentioned Byers' widely known General Meteorology (1959), which-within a comprehensive treatment of all the important modern topics of meteorology -also deals with certain maritime meteorological problems such as energy exchange between ocean and atmosphere or tropical cyclones. The second type, giving a representation of oceanography from a purely scientific viewpoint and including maritime meteorology, is, of course, much more frequent than the first. Starting with the classical book by Maury (1858), where the modern concept of considering ocean and atmosphere as a whole certainly has its source, we meet with numerous relevant publications, of which only the books by Berget (1931), Bigelow (1931), Shoulejkin (1953) and Sverdrup (1943a) will be mentioned here. In each of these four publications attention is paid to the problems of maritime meteorology, although there are certain differences as to putting the question and handling the subject. Berget's contribution originates from lectures given on physical oceanography (without any references to other papers and publications). It contains a discussion of ocean and atmosphere which, however, must now be considered as superseded by new results. In Bigelow's book the chapter dealing with the relations between oceanography and meteorology, especially the section on seasonal weather forecasting on the basis of oceanographic data, may be of interest to meteorologists even today. Shoulejkin's work covers many meteorological aspects, although it is principally concerned with the physics of the sea. Sverdrup, finally, presented us with a treatment of oceanography that distinguished itself by a new tendency especially welcome to meteorologists: It was written particularly for them;
1
INTRODUCTION AND BASIC PRINCIPLES
3
they now can obtain information from it on the findings in physical oceanography that have bearing upon problems of the atmosphere. Taking these contributions into consideration we may state that they do not provide a complete scientific treatment of what we now understand by maritime meteorology. According to the International Meteorological Vocabulary-(World Meteorological Organization, 1959) maritime meteorology is defined as follows: "Branch of meteorology which is concerned with the study of atmospheric phenomena above the oceans, their influence on shallow and deep sea water, and the influence of the ocean surface on atmospheric phenomena." This definition clearly comprises more than the books on oceanography mentioned above contain. They are more or less restricted to describing the energy exchange between ocean and atmosphere or at least certain parts of it. A complete treatment of marine meteorology should, however, aim at investigating and characterizing all the atmospheric phenomena occurring above the sea and controlled by the sea surface as lower boundary of the air flow. Thus maritime meteorology is going to emerge from the "inferior regions" of applied science in order to enter the "sacred realm" of pure science. I realize quite well that this interpretation is liable to meet with criticism. The statement of Donn should be mentioned here. He said in the Preface to his excellent book Meteorology with Marine Applications (1951) that there is only one meteorology dealing with the atmosphere as a whole and that, consequently, there does not exist a marine meteorology, or any other kind, these being merely applications of the pure science to different fields of human endeavor. Nevertheless it is my opinion that there is evidence enough for the existence of a marine meteorology as a pure science. When we look at the known data on oceans we notice that there is not a small but rather a large number of meteorological phenomena that are closely related to or dependent on the sea surface and which do not occur on land. Without intending to be complete I would like to refer to such problems as the energy exchange between sea and atmosphere, which manifests itself not only in small-scale processes as, e.g., wind stress, heat transfer, and evaporation, but also extends its influence to phenomena of medium and large scale, eventually affecting the whole system of oceanic and atmospheric circulation and thermal interaction. Furthermore, there are the numerous problems connected with tropical cyclones, which originate at sea and spend the greatest
4
1
INTRODUCTION AND BASIC PRINCIPLES
part of their life history there, too. Even when summarizing meteorological data by means of statistical methods we encounter fundamental differences between land and sea not only with regard to the behavior of the climatological elements themselves but also as far as the methods and procedures used therein are concerned. Taking all these experiences together I feel we must agree that there exist special atmospheric phenomena at sea that have no analogs or that differ from similar processes on land. Therefore, particular studies must be carried out that form a special branch of basic research on meteorology. Certainly it would be clarifying to use another name for this pure science than the traditional phrase "maritime meteorology" which has already been used for the applications of this science to shipping. Therefore, we suggest referring to this part of meteorology as "physics of the marine atmosphere," indicating the intention of dealing with the subject from a purely scientific viewpoint and neglecting the traditional shipping aspect. A similar procedure is pursued in other fields of meteorology, e.g., the word "micrometeorology" is used for the basic studies and "agricultural meteorology" for the applied science. So the question is raised of where to fix the border lines of the "marine atmosphere." It is obvious that the sea surface forms the lower boundary, but the determination of the upper boundary is not so self-evident and clear. If we restrict the marine atmosphere to the layer affected by surface friction, a height of, say, 1500 meters might perhaps be sufficient. But there can also be observed at sea atmospheric processes which extend to much greater heights. Therefore, a general upper limit cannot be fixed. It will depend on the special problem under study. In principle all atmospheric properties, phenomena, and processes substantially influenced by the sea surface as lower boundary and investigated by meteorological measurements at sea should be considered as belonging to the marine atmosphere. With regard to the horizontal boundaries of the marine atmosphere, circumstances are even more difficult. Of course, the coast lines are clearly defined and sufficiently known. The difficulty is that the atmosphere does not respect these boundaries and that an intense and frequent exchange of air masses takes place across the coast lines, affecting weather and climate over large continental and maritime areas. The processes involved depend to some extent on the geographical situation and, consequently, call for a climatological treatment. The physical core of the problem in question, i.e., the modification of air masses by the sea surface, can, however, be studied in a general way.
I
INTRODUCTION AND BASIC PRINCIPLES
5
Apart from the connections the marine atmosphere has with meteorological processes on the continents there exist relations to other physical and biological phenomena. In the first place the interaction of ocean and atmosphere is considered important. Further, reference is made to the propagation of visible light, of radio, radar, and sound waves at sea, which strongly depend on meteorological conditions. Moreover we should mention the relations between meteorological disturbances and "atmospherics" as well as seismic waves originating from them. Expanding finally into the field of biology, we have come to believe that meteorological phenomena also affect certain parts of oceanic life. With respect to those relations, I would like to state that they belong to the physics of the marine atmosphere only as far as they have a bearing on the physical processes occurring in it. Primarily this is the case with the oceanic influence on the marine atmosphere. Originally I intended to attempt a review of the present state of our knowledge with regard to the physics of the marine atmosphere within the scope outlined above, i.e., including the interaction of air and sea, but leaving out the relations of other physical and biological processes within and above the oceans as well as the application to human activities such as shipping, fishing, and marine aviation. But realizing the considerable number of problems involved I had to confine myself to describing some basic concepts of the physics of the marine atmosphere. Regarding the characteristic features of that science, which were roughly sketched above, those fundamentals must necessarily and primarily comprise the influences exerted by the sea surface on the properties of the atmosphere and on atmospheric processes of small and medium scale. Thus this monograph is mainly concerned with maritime boundary layer problems which form an essential part of all physical processes in the marine atmosphere. The representation of the large-scale phenomena observed at sea must be left to further efforts which, I hope, will be undertaken by a scientist who can approach this work with more authority than I. In order to be as complete as possible within these limits I have laid stress on the inclusion of numerous references. They are to inform the scientific reader-especially the scientist working in that branch, or related branches, of geophysics to whom this monograph is addressed in particular-of the broad spectrum of scientific activity in this important field of the physics of the earth.
2. Meteorological Observations and Measurements at Sea 2.1
BASIC PROBLEMS
In maritime meteorology, as in any branch of natural science, suitable measurements are required as a basis for empirical investigations and as a touchstone for theoretical studies. Owing to the vastness, enormous energy, and variety of influencing forces by which the atmospheric processes are distinguished from others, there are at present only very few opportunities for enlarging our knowledge by experiments under completely controlled conditions. Therefore, the classical physical approach characterized by separating, dimensioning, and controlling the acting forces, and by measuring their effects, is generally not adaptable to meteorology. Meteorologists are rather forced to execute field measurements which must be representative, dense in time and space, and complete with regard to the influencing factors, all to such a degree as to achieve the success that is expected. These requirements can be fixed and written down much more easily than they can be fulfilled. This is especially true for meteorological measurements at sea. On the oceans it is very difficult to meet even a primary demand which can be easily provided for on land, namely, a fixed site for measuring. Even if we succeed in keeping a floating observing station always at the same point, movements of this float caused by the waves will raise new difficulties. Of course, these two handicaps could be overcome by using fixed constructions erected from the bottom of the sea (e.g., lighthouses, Texas towers) as bases for meteorological measurements. Since such maritime structures are only possible in shallow waters (in tidal flats or on the continental shelf), it is only in coastal waters that they can serve as useful and, therefore, welcome additional sites for meteorological activity. In view of the necessity of gathering meteorological data from deep sea areas also, we have to 6
2.1
BASIC PROBLEMS
7
face the difficulties inevitably connected with the use of floating bases for measuring. From the purely methodical viewpoint five possibilities are available at present. We can use anchored ships, drifting ships, moving ships, anchored buoys, or drifting buoys for obtaining meteorological observations near the sea surface. All of them have the disadvantage that they are exposed to the action of ocean waves, and consequently, make irregular motions. Taking a ship as base means further disadvantages. The body of the ship causes a considerable disturbance of the air flow and, furthermore, forms a source of convective and radiative heat. Therefore, it is to be expected that errors will occur in meteorological measurements on shipboard, owing partly to the presence of the ship and partly to its irregular movements in the seaway. The amount of these errors is very difficult to estimate and not exactly known. It will depend on various factors (size of the ship, site of measurement, apparent wind, sea spray, sea conditions, and others). There is some evidence (Dietrich, 1950; Hay, 1956a) that these errors are larger with ships under way than with anchored ships, e.g., lightships. However, in comparing humidity observations made on merchant ships and on ocean station vessels, Brown (1952) found satisfactory agreement between the corresponding monthly averages. The disturbing influence of the ship can be removed if the measuring equipment is installed on a buoy, whereas the disturbing effect of wave motion cannot. In spite of the latter handicap and although the construction and operation of telemetering and reporting buoys offer severe technical and economic difficulties, automatic ocean-based weather stations are to be considered as promising progress and will perhaps form an important part of the future meteorological network at sea. As long as the use of automatic weather buoys is still in the development and trial stage, measurements made on anchored, on drifting, and on steaming ships will constitute the bulk of maritime weather data. All these considerations refer to meteorological measurements near the surface of the sea. As regards aerological observations it should be stated here that these are not as dependent on sea conditions as the surface observations. On principle, the same methods may be used at sea as over land. This is true, above all, if land-based airplanes serve for weather reconnaissance purposes. Radiosonde and radar wind techniques need certain adaptations to the special requirements aboard ship.
8
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
2.2
OPERATIONAL QUESTIONS
The principal difficulties connected with meteorological measurements at sea having been indicated, detailed consideration will now be given to the question of what bases and procedures are available for executing such measurements. We had better clarify this matter first before entering into a discussion of maritime meteorological instruments and observation methods, since the use of these devices will depend strongly on the operational systems available. 2.2.1 Mobile Stations Meteorological stations established on ship or aircraft whose motions are determined by man are defined as "mobile" stations.
2.2.1.1 Merchant Ships and Trawlers. In view of the vastness of the oceanic regions it seems quite hopeless that sufficient control of : maritime weather can be achieved through the use of only those observing stations managed by scientific institutions or weather services. The only possibility of getting meteorological observations from the sea somewhat regularly has been to ask the captains and officers of merchant ships for cooperation. This is a very natural request, since the chief practical aim of marine meteorology is to render assistance to shipping and fishing. This scheme of mutual assistance came into being at the very beginning of modern meteorological activity at sea more than 100 years ago. It is again Maury to whom is due the credit that the cooperation between shipping and maritime meteorology was started, organized, and coordinated internationally. From the first international conference at Brussels in 1853 onward, this scheme of mutual assistance has been further developed, especially by the Commission for Maritime Meteorology of the IMO (International Meteorological Organization), and later by that of the WMO (World Meteorological Organization). At present a fleet of 4000 ships under the flags of all seafaring nations is taking part in the weather-observing network at sea. These ships are classified into "selected ships," making full observations, "supplementary ships," sending weather messages in abbreviated form, and "auxiliary ships," which make additional observations by means of noncertified instruments of their own. In order to supply the seamen with the necessary meteorological knowledge, care has been taken that basic instruction in meteorology is included in the training curriculum at navigation schools. Furthermore, meteorological liaison officers in ports are prepared to check the meteorological
2.2
OPERATIONAL QUESTIONS
9
instruments on shipboard, to contact the weather observers on merchant vessels, and to give them any advice they may need. This traditional system, which has proved very useful for more than a century, may be characterized with regard to its effectiveness as follows: Advantages: It is an ideal system of cooperation on a nonprofit basis, devoted only to the security of life at sea. Since the meteorological observations are made by the ships' officers voluntarily and without payment, the weather services are merely charged with the cost of the instruments and for the transmission of coded weather messages. Therefore, the scheme is less expensive by far than it would be if meteorological services had to pay for every observation, or had to do the observing with their own personnel. Disadvantages: The observations are made not by specialists but by meteorological laymen who have received only brief training. Therefore, detailed checking of the observations is indispensable. Since the ships' officers do the observing work in addition to their other duties, only the limited routine observations and no special data can be expected from them. The instruments used must be robust, easy to maintain, and, also, easy to remove if observing is discontinued. Expensive installations are not feasible in general; they are possible only in cases in which the shipowners are willing to take over the costs. The observations from merchant vessels are more or less confined to the main sea routes. In order to extend the observations to other areas several countries have successfully recruited weather observers on trawlers, who furnish additional reports from the fishing grounds. A distribution picked at random is given in Fig. 1. It clearly shows that a sufficiently dense and quasiuniform coverage is attained only in certain parts of the North Atlantic Ocean and its adjacent seas. A similar random sample taken at a later date resulted in about 44 per cent of all observations being located in the North Atlantic. While 89 per cent were allotted to the northern hemisphere, only 11 per cent originated from the vast seas of the southern half of the globe. For climatological purposes a certain improvement of coverage can be achieved by taking meteorological observations from the log books of sailing ships, since the former sailing routes differed considerably from the tracks followed by modern powered shipping. 2.2.1.2 Special Ships. An important supplement to the scheme of voluntarily observing merchant vessels and trawlers is provided by
I
I
I
I
\
,
I
I
I
I
I
i~n--r;-r Uif
I
I
I
I! r b
I ---;--t--r-r-
I
I
-
y,
II I' Tl~ I I II I ;! - lII
hi
I .-
r-t-r-t-t
I I
! I
I',
FIG, 1. Distribution of ships making meteorological observations at 1200 GMT, November 1, 1957; total number 937. (From World Meteorological Organization, 1961.)
2.2
OPERATIONAL QUESTIONS
11
special ships which undertake scientific investigations or fulfil other duties at sea. Under this heading belong the following marine activities: Voyages and expeditions of research vessels with complete scientific outfit and collecting data and carrying out investigations for oceanography, maritime geology, biology, and/or meteorology. Expeditions of whaling factories making similar measurements incidentally, and to a smaller extent, than the above. Cruises of fishery protection vessels, coast guard cutters, ice breakers, and other special ships fitted out with meteorological equipment and staffed with experienced personnel. Voyages of transports, freighters, and tankers with radiosonde, pilot balloon, or radar wind equipment, and with the meteorological experts to make aerological measurements. Although all these undertakings were not, and are not now, carried out primarily for meteorological studies, and, consequently, the course, speed, and stops of the ships have almost never been determined by meteorological interests, they have contributed enormously to our knowledge of marine meteorology. An important advantage is that on research vessels and other special ships the handicaps of instrumentation mentioned before for merchant ships do not occur, since in general here it is possible to install the necessary meteorological equipment even if certain alterations in the ship's hull or superstructure are required.
2.2.1.3 Air-Borne Meteorological Reconnaissance. During World War II when meteorological observations were kept secret, weather reconnaissance flights over meteorologically unknown areas were regularly executed by both sides and supplied very useful, sometimes even vital, information. Since the war this technique has been successfully employed in polar meteorology and for detecting and tracking tropical cyclones. In the latter case especially, great advances in marine meteorological knowledge have been achieved. It is one unwelcome by-product of effective maritime storm-warning activity that the regions covered by tropical cyclones are nearly deserted, as all the ships do their best to avoid these dangerous areas. The consequence is that almost no surface weather observations are received at the maritime forecast centers from the regions in question. In this situation meteorological observations and measurements collected by aircraft are not only a necessary and useful substitute but, more than that, they furnish exact data on the location, the horizontal and vertical structure, and the
12
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
movement of tropical cyclones-and this is much more than could be obtained from ships' reports. These airplanes are flying laboratories; they carry air-borne equipment specially developed for measuring winds, atmospheric pressure, air temperature and humidity, sea surface temperature, electric field, icing, turbulence, cloud-physics parameters, clouds, and other elements during hurricane reconnaissance flights (Hilleary and Christensen, 1957). The airplanes even penetrate the circular area of hurricane winds, thus reaching the "eye" of the cyclone, whereby they get the exact position of the center and are able to measure the minimum pressure at sea level by dropsonde. Releasing a tracer balloon, which is kept within the center by the cyclone's circulation, may then help in locating the moving cyclone for a certain time. The information provided by such ingenious and elaborate techniques is of great importance not only for the stormwarning service but also for research purposes. In recent years camera-carrying rockets and satellites have been launched successfully, offering us a foretaste of what maritime meteorology can expect from such new devices. At this stage of development it is rather difficult to estimate the real extent of the meteorological progress that will be reached in this way. Certainly these photographs will at least provide us regularly with global representations of cloud distribution, which will help us to detect disturbances in the so-called "sparse areas" of the oceans where there is no sea traffic, and which will give us new insight into atmospheric circulation patterns. Moreover, suitably instrumented rockets and satellites may be very useful tools for measuring and controlling the radiation budget of the earth. 2.2.2 Fixed Stations Meteorological stations operating more or less at the same location are referred to as fixed stations. 2.2.2.1 Fixed Constructions. Although lighthouses, Texas towers, and similar fixed maritime structures are erected in tidal waters or on the continental shelf and, consequently, belong more or less to the coastal zone, they may render good service not only to coastal meteorology but also to maritime meteorology in general. They represent the sole carriers of instruments in marine meteorology that are not liable to fluctuations in space and time, if seismic influences are left aside. Therefore, such maritime constructions are the most suitable bases for investigations of meteorological fluctuations at sea, e.g., wind structure, oscillations of air temperature, and humidity. Of
2.2
OPERATIONAL QUESTIONS
13
course, special care must be taken that the records of meteorological elements are truly representative of maritime conditions and not influenced by the land or the construction itself. 2.2.2.2 Lightships. Lightships are anchored ships with special nautical duties, including meteorological observations. Comparing them with merchant ships as far as weather observing is concerned, we may state that they offer the following advantages: (a) They are special ships managed by the government. Therefore, it is comparatively easy to equip them with additional instruments for research purposes. (b) Their position is more or less fixed, a fact enabling us to install recording instruments on shipboard (e.g., for mean wind speed), if the influence of the ship's movement is not decisive or can be ruled out. Since the observers on lightships are usually thoroughly experienced men and the instruments are under continuous control, the observations are, in general, of a high standard. In certain maritime countries meteorological observations on lightships have a fairly long tradition and may even be used for studies of climatic change. 2.2.2.3 Ocean Weather Stations. In all arrangements mentioned so far and concerned with ships, meteorological observing and measuring was considered as an additional and secondary task, the primary duties being shipping, fishing, whaling, oceanographic research, fishery protection, ice breaking, etc. Maritime meteorology was admitted or sometimes invited to take part-more or less as a guestand tried to do its best in utilizing the existing conditions for its own purposes, without having the opportunity of adapting these conditions to meteorological requirements. The situation changed gradually with the development of marine aviation which urgently needed meteorological information to an extent not available from mobile ships' stations. The first forerunners of the weather ships of today appeared in the early thirties when some countries, e.g., France and Germany, started to operate suitably converted merchant vessels in order to render assistance to Atlantic flying. Within the duties of these ships, meteorological and aerological measurements formed an important, if not the principal, part. The demand for such meteorological information increased rapidly during and after World War II, thus leading at first to a variable scheme of weather ships according to wartime emergencies and finally
14
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
in 1946 to an international agreement for the North Atlantic. A fixed network of thirteen ocean stations was established by the International Civil Aviation Organization. This agreement was amended-mostly for economic reasons, in 1949 and 1954-reducing the number of stations to ten and finally to nine. Twenty-one ships are now engaged in this service, among them nine from the U.S.A., four from the U.K., three from France, two each from Holland and Norway, and one from Canada. Other nonoperating states contribute in cash. The share of each country depends on the number of its transatlantic crossings. In the North Pacific three ocean stations are operating. A Dutch weather ship was transitorily stationed in the Indian Ocean. The locations of the twelve weather ships of today may be seen on the map (Fig. 2). This representation clearly shows that the vast ocean areas of the southern hemisphere are not covered by a similar observing system. It will be a future task to find an adequate and economical solution for this region. The types of ships used for ocean station work are coast guard cutters (U.S.A.) or converted corvettes or frigates (U.K., Holland, Norway). In France two newly built vessels came into service in 1959. Since these ships are comparatively small and have to perform continuous duties frequently in regions of bad weather, ships and crews are subject to a heavy strain. The meteorological work of the ocean stations comprises an hourly routine program of surface observations as well as upper air ascents with radiosonde and radar wind techniques four times per day. In addition, scientific investigations, e.g., recording ocean waves, studies of boundary layer problems, and radiation measurements, are carried out according to circumstances. On two new U.S.S.R. weather ships, which are cruising or occupying stations in the North and Central Pacific, meteorological rockets are used to get upper air data up to a height of 80 km. For maritime meteorology the important state of progress reached with the ocean station network is due to the fact that the locations assigned, i.e., positions within a square of 10 nautical miles around the designated stations, are maintained whenever practicable, and that interruptions of observing routine will only happen in case of emergency (such as air-sea rescue work). Therefore, complete series of meteorological observations, which were not possible before, can be obtained for fixed locations in the oceans over long periods. The weather ships' data constitute material of eminent value for nearly all studies in maritime meteorology. Their
FIG.
2. Map indicating the positions of the ocean stations.
16
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
importance will even be increased in future years when the available period, which now comprises 14-17 years, will be longer. 2.2.2.4 Floating Automatic Weather Stations. As already mentioned in Section 2.1 the great advantage of automatic weather buoys is that their disturbing effect on meteorological measurements may be much smaller than that of ships. Furthermore, there is a serious lack of meteorological information from certain parts of the oceans which are not fishing grounds, not crossed regularly by merchant ships, and not controlled by meteorological reconnaissance flights, and where establishing an ocean weather station is not considered feasible for economic reasons. In those areas floating automatic weather stations could render good service to marine meteorology. Several types of such weather buoys have been developed by the U.S. National Bureau of Standards (1956) after similar attempts had been made by other countries during World War II. The so-called Marine Automatic Meteorological Observing Station (MAMOS) can be anchored. Therefore it may be considered as a fixed station. It is a boat type of hull, 20 feet long anJ 10 feet wide, made of aluminum and nonmagnetic alloys; it has two masts and wind powered batteries; and it can be anchored even in water 12,000 feet deep if necessary (Fig. 3). It sends out coded broadcasts of air and water temperature, barometric pressure, and wind direction and speed at intervals of 6 hours with a nighttime range of 1500 nautical miles, the daytime range, however, being much less. The station can be left unattended for several months. Field tests have been conducted during the past few years in the Gulf of Mexico (U.S. Weather Bureau, 1959) to determine the durability of moorings, rigidity and performance of the station, and the effectiveness of the broadcasts. Encouraging results have been obtained. During the 1960 tests the automatic station broadcasts alerted forecasters to the development of hurricane Ethel, permitting warnings to be issued several hours earlier than would have been possible without such reports. The automatic station has survived hurricane winds and has been at its station up to 8 months before being returned to port for servicing. The tests were continued during the 1961 hurricane season, when the buoy experienced winds exceeding 100 knots as the center of hurricane Carla passed the station at a distance of less than 100 miles. Though some difficulty arose from high seas, extremely low pressure, and blowing spray, the moorings and the transmitter withstood the ordeal. In the future these weather buoys are expected to be equipped with solar cells for recharging the storage
2.2
17
OPERATIONAL QUESTIONS
AUTOMATIC WEATHER STATION
3/.
INCH CHAIN
THIMBLED' EYE AND SHACKLE
1875 FATHOMS
3/.
INCH DACRON CABLE (5,000 FEET)
3/.
INCH POLYPROPYLENE CABLE (1V.OOO FEET)
THIMBLED EYE AND SHACKLE
3/.
INCH CHAIN
500 POUND MUSHROOM ANCHOR
FIG. 3. Boat type of automatic weather station with deep-water slack-line anchorage. (From Corwin et al., 1959.)
18
2
METEOROLOGICAL OBSER VAnONS AND MEASUREMENTS
l-- --------------------~8
EN
Mast of aluminum
E u
o L[) r--
E
r
Buoy
u
o L[)
~ o
o
L[)
x
c
E
I
r. FIG. 4. Buoy for recording the vertical distributions of wind speed, temperature, and humidity near the sea surface. (From Brocks, 1959a.)
2.2
OPERATIONAL QUESTIONS
19
batteries which are now energized by wind driven chargers. With such an outfit these stations are supposed to operate for one year or more without any servicing. In addition to automatic weather buoys used for synoptic observations, special meteorological buoys have been constructed for scientific investigations, e.g., for air-sea transfer studies, in particular for recording the vertical wind, temperature, and humidity distributions in the first few meters above the sea surface (Shoulejkin, 1928; Brocks, 1959a, Fig. 4; Deardorff, 1962). Such studies require very accurate measurements taken in an airflow not disturbed by any obstructions and, therefore, they cannot be carried out on, or in the neighborhood of, a ship. 2.2.3 Drifting Stations Meteorological stations, established on bases whose motions are not determined by man but by natural forces, are defined as "drifting stations." 2.2.3.1 Drifting Stations in Air. The constant-level balloon technique, called "Transosonde," should be mentioned here. It collects upper-air meteorological data such as wind, atmospheric pressure, air temperature, and humidity during transoceanic flights and may serve to supply welcome information from oceanic areas (Corwin et al., 1959). 2.2.3.2 Drifting Stations in Water. The U.S. Navy has been developing three types of free-floating automatic weather stations (Corwin et al., 1959), all of which are able to transmit the following data: station identification, wind speed and direction, barometric pressure, air and sea temperature. (a) The "Transobuoy" was constructed as a means of gathering meteorological data on a transoceanic scale. It is 10 ft long, weighs about 600 lb, carries a 25-ft whip antenna, and can broadcast daytime transmissions from over 1000 to 2000 miles, while nighttime transmissions can be heard up to 4000 miles. It is expected to operate for approximately 6 months, transmitting coded radio signals of 3 minutes' duration on a 6-hour schedule. During preliminary testing the messages were received over a 10-day period at distances of up to 5000 miles. (b) The "Parachute Weather Buoy" is designed to be put into action by parachute in areas from where no weather information is available. Its characteristic feature is that it can be delivered and placed exactly at the desired location by aircraft in a comparatively
20
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
short time. It is 10 ft long, weighs about 350 lb, has a 12-ft parachuteerected, telescoping antenna, and will operate for 2 months on a 6-hour schedule. Tests have indicated that parachute delivery of the buoy can be accomplished without damage to the equipment. (c) The "Hurricane Monitoring Buoy" was developed as an expendable automatic weather reporting instrument for tactical use in connection with forecasting tropical storms. It consists of a cylindrical buoy 6 ft in length supporting a 9-ft instrumented mast and a 7-ft whip antenna (Fig. 5). Furthermore, it carries an 8-ft counterpoise, thus making the overall length 30 ft. The buoy telemetered meteorological data every 6 hours for 2 months with a reliable operation range of from 800 to 1000 miles. Such buoys proved very useful during the 1955 and 1956 hurricane seasons. If we compare the drifting buoys with the anchored buoy MAMaS described in Section 2.2.2.4 it can be stated that the latter offers several advantages over the free floating buoys, among which there is the possibility of installing additional sensors for other quantities and of wind driven, thermo-electric, or nuclear power generators to enlarge the operation period. In addition, the problem of locating the buoy is eliminated. Although securing reliable operation of such buoys must be considered as very noteworthy progress in marine-meteorological observing technique, the full benefit of these devices will also depend on the quality of the measurements themselves, especially when severe weather conditions hamper the performance of the buoy. Bearing in mind that the measuring heads are very near the sea surface we may ask what disturbing influences are to be expected, for instance, on wind and temperature data from wave motion and sea spray. Up to now no information has been available with regard to these questions. 2.2.3.3 Drifting Stations on Sea Ice. Meteorological stations on drifting ice, as operated by the U.S.A. and the U.S.S.R. in the Arctic Ocean, must also be considered as maritime stations. On the basis of the experience gained from the famous drift of Nansen's polar vessel Fram from 1893 to 1896 and similar later expeditions (e.g., the Norwegian Maud 1918-25), in 1937 the U.S.S.R. established by airplane the first drifting station near the North Pole, which was then rescued near Scoresby Sound in East Greenland 9 months later. Further similar expeditions followed and in April 1959 the eighth Pole station was set up (Polar Record, 1959a). Reference should also be made to the drift of the Russian icebreaker Sedov 1937-40.
2.2
OPERATIONAL QUESTIONS
21
FIG. 5. Hurricane monitoring buoy measuring and transmitting station identification, atmospheric pressure, wind direction and speed, and air and sea temperature. (Official U.S. Navy Photo.)
22
2 METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
In addition to these manned ice stations, automatic weather stations measuring wind direction and speed, air temperature, and atmospheric pressure, were established on the polar ice by U.S.S.R. airplanes. There were 30 of these in the spring of 1959 (Polar Record, 1959b). The U.S.A. has been operating drifting stations on so-called "ice islands" in the North Polar Sea from 1952 onward; two stations, named "A" and "B," were set up as a contribution to the International Geophysical Year (Groen, 1960). At all manned stations surface weather observations and, to some extent, also aerological ascents were carried out according to international schedules. In addition to this routine service, micrometeoro logical investigations, as well as radiation measurements, were executed in order to study the thermal balance of the pack ice (Larsson, 1959). 2.3.
REVIEW OF INSTRUMENTS AND METHODS
Now that the operational considerations for meteorological measurements at sea have been described in some detail, we will discuss the meteorological instruments and methods themselves. It is not intended to give a thorough description of the different types involved; we shall rather confine ourselves to dealing with the particular aspects of maritime measurements, supposing that the principal facts on the relevant instruments and methods are known. Only those procedures that are used for routine observations at sea will be considered whereas special techniques developed for research purposes will not be dealt with here. These will be mentioned in the relevant sections of this monograph if necessary. A detailed discussion of meteorological instruments for use on ship-board has recently been published by Hahne (1963). 2.3.1 Surface Observations 2.3.1.1 Wind. The observation of wind speed and direction is usually made either by visual estimates or by means of anemometers or anemographs. Visual estimates are normally based upon the appearance of the sea surface under the action of the present wind. This traditional method is widely used at sea, as only special ships have anemometers at their disposal. The wind speed is estimated in the numbers 0-12 of the Beaufort scale using sea surface specifications attached to these numbers. These descriptive terms applied to the different Beaufort numbers
2.3
REVIEW OF INSTRUMENTS AND METHODS
23
originate from Petersen (1927). He transformed the specifications, originally given by Admiral Beaufort, and referring to the speed and sails of a full-rigged frigate at the beginning of the nineteenth century, into descriptions of the sea surface, basing these upon his long experience as a captain of sailing ships. Later on these specifications were slightly amended with regard to the requirements of modern shipping. There were many efforts to determine the correct wind speed equivalents pertaining to these Beaufort numbers. The values published by Verploegh (1956) are based on the results of all comparative studies so far available from the sea and may, therefore, be considered as the most suitable ones at present. They are given in Table I together with the specifications of the Beaufort numbers. It should be noted that these wind speed equivalents are valid for a height of 10 meters above sea level under indifferent atmospheric stability. Marked deviations from these equivalents may occur with other thermal stabilities (Roll, 1953-1954; Brooks and Brooks, 1958), winds colder than the sea producing higher and steeper waves than warm winds. Since the high Beaufort numbers, above and including 10, are based on comparatively rare cases, the relevant equivalents may not be considered as well established as those for the lower wind forces. The wind direction is obtained by observing the motion of wind driven waves. Estimating the wind visually is a matter of experience. Several disturbing effects have to be taken into account, e.g., the "lag" between the wind increasing and the sea getting up, and the influences of fetch, depth, swell, heavy rain, and tidal currents on the appearance of the sea. As shown by Otto (1961), the tidal effect, particularly in cases of low wind velocities, causes the estimation of an apparent wind force which corresponds to the air speed relative to that of the water. Even the plankton content may influence wind estimates at sea since the foaming of the sea water depends on it. Seilkopf(1955-l956) has found that in sea areas rich in plankton the foaming (as taken from estimated wind forces greater than 3 Beaufort) observed with smaller wind speeds is the same as that with higher wind speeds in areas poor in plankton. Consequently, there is a certain tendency to overestimate wind speeds in regions with high plankton content. When the sea surface is invisible, e.g., at night, estimation becomes questionable. To meet this difficulty Graham Millar and Macphail (1951) proposed a scale for estimating apparent wind from on board ship basing their conclusion on wind effects on persons, rigging, flags, and smoke plumes, but, so far, little use seems to have been made of this method.
TABLE I WIND SPEED EQUIVALENTSa AND SPECIFICATIONS FOR THE BEAUFORT NUMBERS OF WIND FORCE
Wind speed equivalents Beaufort number
knots
Descriptive term
Mean
meters/sec
Limits
Mean
Specifications
Limits
0 1
Calm Light air
0 3
<1 1-4
0 1.5
<0.6 0.7-2.3
2
Light breeze
7
5-8
3.4
2.4-4.4
3
Gentle breeze
11
9-12
5.6
4.5-6.6
4
Moderate breeze
15
13-16
7.8
6.7-8.9
5
Fresh breeze
19
17-21
10.2
9.0-11.3
6
Strong breeze
24
22-26
12.6
11.4-13.8
7
Near gale
29
27-31
15.1
13.9-16.4
Sea like a mirror Ripples with the appearance of scales are formed, but without foam crests Small wavelets, still short but more pronounced; crests have a glassy appearance and do not break Large wavelets; crests begin to break; foam of glassy appearance; perhaps scattered white horses Small waves, becoming longer; fairly frequent white horses Moderate waves, taking a more pronounced long form; many white horses are formed (chance of some spray) Large waves begin to form; the white foam crests are more extensive everywhere (probably some spray) Sea heaps up and white foam from breaking waves begins to be blown in streaks along the direction of the wind
a
8
Gale
34
32-36
17.7
16.5-19.0
9
Strong gale
39
37-42
20.4
19.1-21.8
10
Storm
45
43-48
23.3
21.9-24.8
11
Violent storm
52
49-55
26.5
24.9-28.2
12
Hurricane
Verploegh (1956).
>55
>28.2
Moderately high waves of greater length; edges of crests begin to break into the spindrift; the foam is blown in well-marked streaks along the direction of the wind High waves; dense streaks of foam along the direction of the wind; crests of waves begin to topple, tumble, and roll over; spray may affect visibility Very high waves with long overhanging crests; the resulting foam, in great patches, is blown in dense white streaks along the direction of the wind; on the whole, the surface of the sea takes a white appearance; the tumbling of the sea becomes heavy and shock-like; visibility affected Exceptionally high waves (small- and mediumsize ships might for a time be lost to view behind the waves); the sea is completely covered with long white patches of foam lying along the direction of the wind; everywhere the edges of the wave crests are blown into froth; visibility affected The air is filled with foam and spray; sea completely white with driving spray; visibility very seriously affected
26
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
Measuring wind on board ship meets with certain difficulties, by which such measurements are restricted more or less to special ships. The instruments used should give both wind speed and direction. They should have a proper exposure and be capable of minimizing roll effects. With regard to the exposure of wind measuring instruments, the disturbance of the air flow produced by the superstructure of the ship must be taken into account. The obstruction of the air flow by the ship's hull is by no means negligible even with small vessels. Deacon et al. (1956), who studied this subject in the case of a small diesel schooner, obtained hull effect corrections ranging between 1 and 12 per cent. Similar values were reported by Brocks (1959a). Therefore, the position of the instrument should be as far forward and as high as practicable. The top of the foremast is generally thought to be the best site for an anemometer. Naturally, such an installation requires a distant reading instrument. This is the reason that anemometers are very rarely found on merchant vessels. Hand anemometers are no substitutes since they can hardly be given a representative exposure on board. Only an observer who knows the distribution and structure of the air flow over the ship under different conditions may be able to choose a place for measuring where he will arrive at satisfactory results. Some hints as to the errors caused by the ship's movement can be found in papers of Sanuki and Kimura (1954, 1955), who tackled this problem empirically by wind tunnel investigations. They arrived at the result that the readings of cup anemometers were increased by about 10 to 25 per cent by pitching and rolling motion. An increase was also reported by Ogata et al. (1958b) but it amounted only to from 2 to 3 per cent at a height of 11 meters. A more theoretical treatment of this subject was given by Langmaack (1938), who computed the wind speed error caused by the rolling of the ship by taking into account the angle between the wind direction and the direction of the ship's oscillation as well as the relation between the maximum velocity of the oscillating anemometer and the true wind speed. To correct the values given by a cup anemometer for the rolling effect Deacon et al. (1956) suggested the following formula (2.1) where u- = recorded wind speed, u- = corrected wind speed, h = anemometer height above the axis of roll, z/; = root mean square rolling amplitude, and T r = root mean square rolling period.
2.3
REVIEW OF INSTRUMENTS AND METHODS
27
Wind measuring equipment particularly developed for use on shipboard was described by Hohne (1960). On a moving ship it is only the apparent or relative wind that is given by such measurements. The true wind is obtained from it by allowing for the ship's course and speed. This can be done automatically by a computer, to be sure, but the amount of equipment needed for this simple correction would be considerable and is, at present, almost prohibitive for merchant vessels (Bell, 1951; Bell and Langham, 1952). The wind data generally refer to a period of 10 minutes. They are, therefore, mean values. The accuracy obtained in measuring mean wind at sea under fair conditions is estimated at present to be ± 5° in direction and ± 1 knot in speed. The approximate maximum error under bad conditions at sea may reach ± 15° and 5 knots, respectively. Since the influence of the ship's movements on measurements of instantaneous wind vector is very difficult to estimate and to compensate, only few possibilities can be seen at present for the use of anemographs for obtaining representative wind records on shipboard. An examination of wind records gained on British weather ships made it clear that a large proportion of the apparent gustiness was actually caused by the rolling of the ship. Therefore, investigations of wind structure at sea can only be carried out on fixed constructions or stabilized buoys.
2.3.1.2 Atmospheric Pressure. Pressure may be measured by either precision aneroid or mercury barometers. The main difficulties arising with barometric measurements on shipboard are caused by the effects of the wind and by the movement of the ship. The influence of the first source of error may be reduced by enclosing the instrument in a chamber connected with a static pressure vent. The second disturbing effect is particularly bothersome with mercury barometers. Certainly, the pressure variations caused by the lifting and sinking of the barometer in a rolling and pitching vessel are of less importance, since these marine barometers have an appropriate lag in order to reduce the pumping of the mercury column. Much higher errors may arise from the varying accelerations to which the barometer is subjected by the movement of the ship. Since the instrument is mounted in gimbals and can swing freely it will execute more or less regular oscillations due to the movement of the ship in the seaway. A barometer which is oscillating for 15 minutes or more
28
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
with an amplitude of about 10° may read as much as 4 mb too high. This error would, however, be reduced to about 0.2 mb if the amplitude of the swing were only 2°. This difficulty and, furthermore, the necessity of applying four corrections (index error, temperature of the instrument, latitude, reduction to sea level) to mercury barometer data are the reasons that such instruments are gradually losing importance in routine meteorological work at sea. Now that the instrument industry has succeeded in constructing aneroid barometers that are sufficiently reliable and will also remain so for some time, these handy barometers may be considered as standard instruments for the use on shipboard, especially as far as merchant vessels are concerned. Aneroid barometers and barographs specially adapted for maritime purposes are distinguished by a builtin damping device and a relatively powerful control exerted by the actuating element in order to avoid frictional errors. They should be mounted on shock-absorbing material in a position where they are least likely to be affected by concussion, vibration, or movement of the ship. The best results are generally obtained from a position as near to the center of flotation as possible. Since nearly all aneroid barometers are compensated for temperature, corrections have to be applied only with regard to scale error and reduction to sea level, which in most cases can be allowed for by adequate adjustment during calibration. The accuracy of atmospheric pressure data obtained at sea may be estimated to ± 0.5 mb. Under bad conditions at sea, especially if no damping device is provided, the approximate maximum error may reach ± 3 mb.
2.3.1.3 Air Temperature and Humidity. In merchant vessels temperature and humidity observations are usually made by means of well-ventilated psychrometers with direct reading. Ventilation may be operated manually, electrically, or by clockwork. Special care must be taken that psychrometers are well exposed in an air flow that is not affected by the ship, such as is the case at the windward side of the bridge. Furthermore, they must be protected against radiation, precipitation, and sea spray. Exposure in a fixed single screen is not suitable. According to Walden (1952, 1953-1954) the increase in the air temperature measured in a fixed screen of an old-fashioned (varnished!) type on sailing vessels against the temperature value obtained from aspirated psychrometer readings to the windward side was as follows:
2.3
REVIEW OF INSTRUMENTS AND METHODS
29
Averaged over all hours and conditions +O.9°C Averaged around the daily maximum +2.7°C Averaged with screen in full sunshine +4.5°C Averaged at the daily maximum with screen in full sunshine Single cases with screen in full sunshine and ventilation speed near the screen below 1 knot up to + l1.3°C We should take note from these values that great caution is necessary when conclusions are drawn from temperature observations in old log books. If a screen is still used for temperature and humidity measurements, it should be at least a portable one and hung to the windward side. Although temperature 'and humidity measurements obtained by operating ventilated psychrometers at windward generally seem to be fairly satisfactory for routine purposes, it is rather certain-and it can be proved by comparative measurements-that the disturbing effect of the ship, manifesting itself by conductive and radiative heating, is not completely removed if observations are made quite near to the superstructure of the ship, e.g., on the bridge. Real improvement can only be made if the measuring head is installed as far away from the ship's hull as possible, i.e., on the top of the mast. Such exposure necessarily requires distant reading equipment which confines measurements of this kind more or less to weather ships, lightships, research ships, and other ships with special meteorological tasks and equipment. Some information on the differences between "conventional" readings of air temperature on the bridge or elsewhere near the superstructure of a vessel and measurements obtained on the mast is given in the following: On German shipboard weather stations staffed with trained meteorologists, comparisons have been made between air temperatures measured by (screened and naturally ventilated) resistance thermometers situated at the top of the fore mast (height from 18 to 22 meters) and simultaneous readings of sling psychrometers at the height of the bridge (from 6 to 9 meters). In order to exclude differences due to thermal stratification only the cases near indifferent equilibrium were selected, i.e., the absolute value of the difference between the potential air temperature at the top of the mast and the temperature of the sea surface was always smaller than or equal to O.4°C. If the difference in potential air temperature "mast minus bridge" was negative it was regarded as representing the heating effect
30
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
of the ship s superstructure on the temperature reading on the bridge. The mean value for this difference depended in some way on the particular situation on the ship concerned. A fairly reliable average was estimated to be -0.03°C (number of cases: 558). Owing to varying insolation a diurnal variation of about ± O.13°C was indicated. In addition, the obvious influence of the (relative) wind speed on the potential air temperature difference "mast minus bridge" was present, as may be inferred from Table II. The warming effect of the ship's superstructure on the temperature reading on the bridge evidently decreased with increasing ventilation. With very high wind speed the measurement of the air temperature at the top of the mast, being obtained with natural ventilation, was even higher than the reading on the bridge. That can, perhaps, be ascribed to the influence of sea spray, which may be responsible for the apparent lowering of the air temperature measured at the height of the bridge. TABLE II INFLUENCE OF THE SHIP'S SUPERSTRUCTURE ON THE MEASUREMENT OF AIR TEMPERATURE
Relative wind speed (knots) 0-9.5 10-19.5 20-29.5 >30
Mean difference (oC)a
Number of cases
-0.09 -0.03 -0.00 +0.09
112 249 166 31
a Between the potential air temperature measured on the top of the mast and that read on the bridge (mast minus bridge) for indifferent thermal stratification and different values of relative wind speed.
Air temperatures on shipboard may be measured to an accuracy of about ± 0.3°C if serious errors are avoided. Beside the traditional psychrometrica1 determination of atmospheric humidity, the direct electrical measurement of dew point temperature by means of hygroscopic material was introduced on shipboard during the past few years and it seems to provide a promising method which, however, is also limited to special ships. 2.3.1.4 Temperature of the Sea Surface. There are two principal methods of obtaining this information: (a) Taking a sample from the sea surface by means of a bucket and measuring its temperature with a thermometer.
2.3
REVIEW OF INSTRUMENTS AND METHODS
31
(b) Reading the temperature of the sea water that enters the condenser intake of the ship with a fluid thermometer. Although no attempt has ever been made to standardize the bucket, the thermometer, or the technique, procedure (a) is to be regarded as the standard method, particularly if judged from the scientific point of view, since it is the surface temperature of the sea which is mainly of interest for meteorological purposes. Certainly, it is not possible to obtain the real skin temperature of the sea surface since the sample taken by the bucket will contain water from lower parts, too. This question was investigated by Ball (1954), who found a mean difference between the actual surface temperature and the bucket temperature of - O.25°C. Measurements with this bucket will therefore yield fairly satisfactory values for the sea-surface temperature if they are quoted to the nearest O.5°C. (Further remarks on the thermal stratification in water near the sea surface are made in Section 5.1.2.) Of course, we must take care when constructing and handling a bucket to eliminate or at least minimize all the errors that may affect the water sample within the bucket by heat exchange with its surroundings, including cooling by evaporation. These requirements have been fulfilled quite satisfactorily; e.g., the rubber bucket with an inserted thermometer as described by Goedecke (1951) showed a maximum variation in water temperature of ± O.2°C during the first minute after taking the sample under conditions such that the air-sea temperature difference ranged from + 5°C to - 5°C and the wind speed went up to 8 meters/sec (Roll, 1951b). From the practical viewpoint, however, it must be stated that the bucket method is difficult to apply on large and fast ships and also on small ships in stormy weather. This is the reason that method (b) has been gaining in importance and has now reached a state where it may be considered as the second standard procedure. Its chief disadvantages, however, are that, first, it is not the temperature of the sea surface which is determined but the temperature at a depth of somewhere between 5 and 12 meters, depending on the size of the ship concerned; and, second, the measured value is liable to varying errors due to the heating caused by the ship. Some information about these errors can be derived from comparative measurements using both the bucket and the intake method. This subject has been given close attention by various maritime services (e.g., Kirk and Gordon, 1952). A summary of the discussion was published by the World Meteorological Organization (1954) but no definite conclusion could be drawn as to which of the two methods, (a) or (b), deserved preference. Additional material is presented in the
32
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
following discussion. Figure 6(a) shows a frequency distribution of 5689 differences between simultaneously measured water temperatures obtained by bucket (B) and at the intake (I) at 4.5 meters' depth in the engine room. The mean difference B-1 is -O.18°C, i.e., the average intake temperature is nearly O.2°C higher than the bucket temperature. In 62 per cent of all cases the absolute difference was smaller than or equal to O.3°C; in 6 per cent of all cases the absolute difference exceeded I.O°C. More detailed information on the different effects could be gained by investigating the annual and diurnal variations of the differences B-1 and by discussing the influences of wind force and thermal stratification on them. In addition, water temperatures
o
-I
20 1\
1\ 1\ I }"
I
I
I
I
I
I I I
~b
I
,
I I
* I
I I ,
~ :>
I
u u
o
'0 10
, I I
:
15
'"uc::
I
15
I I
,
iI
I
1
I
,
I I
10
I
I
,
I
I
I
I
\ ,~
II \
5
5
}" \ \
\ \
\
\
-I
0 Temperature difference (OC)
FIG. 6. Results of simultaneous measurements of sea surface temperatures: (a) frequency of temperature differences between bucket and intake method; (b) frequency of temperature differences between bucket and tank method.
2.3
REVIEW OF INSTRUMENTS AND METHODS
33
were measured at the depth of the condenser intake but outside the ship. According to these studies the mean value of the differences B-1 of -O.18°C roughly corresponds to the mean increase of the intake temperature caused by the heating originating from the ship. This value will, of course, depend on the ship concerned and vary according to circumstances. With high insolation and calm weather this temperature increase may even reach O.9°C. On the other hand, investigations carried out by Arnot (1955) and Benditskii (1958) have shown that the heating effect seems to be less serious under different conditions. In addition, results of a comparison reported by Kirk and Gordon (1952) indicated that the transfer of heat from the engine room to the intake pipe is smaller while the ship is under way than the value obtained while the ship is on station. Furthermore, the influence of thermal stratification in water results in compensating approximately the above-mentioned increase of the intake temperature owing to the heating by the ship in summer, since then the sea surface is warmer (in favorable cases up to 1.6°C) than the water below. In winter, with small but reverse stratification in water, both effects are working in the same sense, thus enlarging the absolute amount of B - [. Summarizing this information and that from other sources, and bearing in mind also that the effect of thermal stratification in water will be reduced by the movement of the ship, we may say that the intake method may be liable to varying errors due to the heating of the ship, whereas the fact that the temperature is not measured at the sea surface but at a certain depth of 5-10 meters is significant only if there exists a substantial thermal stratification in water, i.e., in areas or at times with light winds and high insolation. Realizing that these two standard methods are, on the whole, of only limited benefit, the maritime services are searching for better procedures. Methods which try to avoid the limitations mentioned above are the following: . (c) The intake method with distant reading. Here it is assumed that the distant-reading thermometer can certainly be installed more easily than the direct-reading thermometer at a site where the heating effect of the ship is small. Benditskii (1958), for example, found that 96 per cent of all differences between temperatures obtained by bucket and by telemetering equipment at the intake did not exceed ± O.5°C. (d) The skin method. Here the temperature of a copper block attached to the bare metal of the ship's hull inside the ship below the water line, and protected against radiative and conductive heating
34
2
METEOROLOGICAL OBSER VAnONS AND MEASUREMENTS
from within the ship, is measured electrically. This method takes advantage of the relatively great heat conductivity of iron and steel. (e) The tank method. Here the temperature of the water in a small tank below the water line, and connected with the sea water outside the ship by several holes, is measured with resistance thermometers. Results of comparative measurements between bucket and sea water tank are given in Fig. 6(b). This figure shows the frequency distribution of 1158 differences between simultaneously measured water temperatures obtained by bucket (B) and in the tank (T) at 2 meters' depth by distant reading. The mean difference B - T is + 0.04"C. In 80 per cent of all the cases the absolute difference was smaller than or equal to 0.3°e; only in 0.7 per cent of all the cases did the absolute difference exceed l.aae. This result is remarkably better than that reached by the similar comparison made with method (b). (f) The infrared radiation thermometer for measuring the seasurface temperature. This instrument is designed specifically to convert the long-wave radiation from the sea surface into a measure of temperature. Up to now some success has been attained with an airborne model which has proved very useful in getting a rapid survey of the geographical distribution of sea-surface temperature. More recently satisfactory results seem to have been obtained also on shipboard (U.S. Weather Bureau, 1961). The ART (airborne radiation thermometer) senses the temperature of a surface layer about 5 x 10-4 em thick. This implies that the results gained will deviate to a certain degree from those furnished by methods (a)-(e), which give the temperature of a deeper layer. Moreover, the measurement is affected by the amount of water vapor present in the air below the instrument. The accuracy of this method seems to be lower than that of the conventional methods (Richardson and Wilkens, 1958). The improved methods (c)-(e) are practicable but they require certain installations on shipboard which are rather expensive. Therefore it seems unlikely that these methods will be introduced into general use on merchant vessels at present. But they may and should be used on special ships in order to serve the accuracy and economy of meteorological measurements at sea. With a view to the fact that a simple, inexpensive, and fully effective device for measuring sea surface temperature on merchant vessels is still lacking, the efforts to modify and improve the bucket method are worthwhile and deserve attention. Finally it should be mentioned that, with a stationary vessel, there may exist an appreciable increase in sea temperature in the neighborhood of the ship corresponding to insolation and wind drift. Amot
2.3
REVIEW OF INSTRUMENTS AND METHODS
35
(1955) found a difference in sea temperature of about O.3°C between localities close to the ship's side and those farther distant. The accuracy obtained when the sea surface temperature is measured with methods (a)-(e) may be estimated at O.2°C provided that conditions are not too unfavorable and serious errors are avoided. 2.3.1.5 Visibility. Although visibility forms one of the most important weather elements in marine navigation the methods of observing it at sea are comparatively poor. The absence of suitable objects in most cases makes it impossible to estimate visibility as accurately as it can be done at land stations and, therefore, only a IO-figure code is used for determination. Some help can be obtained when landmarks or other ships are sighted, but naturally only if the distances are measured in other ways (e.g., on the chart or by radar). On the high seas, however, the appearance of the horizon, as observed from different levels, is the only basis for estimating visibility. The values obtained in this way are, of course, doubtful, particularly if the visibility is low. Visibility meters of the transmissometer type can be used only if they have been adapted to the relatively short base line or light path available on shipboard. Unfortunately, the smallness of the air sample, the effect of the ship's smoke, and the radiative and convective heating of the air near the ship are severe handicaps which may prevent the measurement from being representative. Hence a visibility meter which functions by measuring the light emitted by a pulsed-light system and back-scattered from the atmosphere may be more suited to shipboard use. In this case no base line is necessary, the back-scatter measurement being made to the side of the ship which results in the sampling of a sufficiently typical atmosphere. 2.3.1.6 Cloud Characteristics. Visual methods prevail when cloud characteristics are observed at sea. The complete absence of disturbing objects-even very near the horizon-is certainly a remarkable advantage over cloud observations on land. Therefore, type and amount of cloud can be observed at sea rather easily, supposing that the observers have the necessary training. Estimating the height of cloud base is, however, as difficult as on land and, bearing in mind that most maritime observers are volunteers, we should not expect too high an accuracy with these estimated values.
36
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
The ordinary method of measuring the cloud height by means of a searchlight is only of very limited value as the base line available on a ship is relatively short. Preference should, therefore, be given to devices that do not require a base line, e.g., a pulsed-light cloud searchlight, which measures electronically the time required for the reflection from the cloud base of a pulse emitted vertically from the ship. The amount and cost of equipment necessary for such measurements, however, restrict the application more or less to special ships, e.g., research vessels and ocean weather ships. 2.3.1. 7 Precipitation. In spite of the importance of getting exact information on the oceanic distribution of the amount of precipitation, this meteorological element has been treated like a stepchild of maritime observing technique. The reasons for this regrettable fact are the particular difficulties connected with rainfall measurements at sea. The ideal solution would require a rain gauge well protected against spray, splashing, and evaporation and installed on a small float in such a way that its orifice is at the sea surface. Then there would be reason to hope that the amount of precipitation arriving at the sea surface could be measured quite accurately. Unfortunately, this method cannot be generally applied at sea, except on very rare occasions (e.g., from stationary ships if the sea is sufficiently quiet). Installing a recording and automatically reporting rain gauge on an anchored buoy may be considered as a good approximation to the ideal solution, but no information on such equipment in use is available at present. Therefore, employing a ship as a base for the rain gauge cannot be avoided and, consequently, the following influences inherent to this procedure must be taken into account: (1) The disturbing effects of the ship and of the rain gauge on the air flow. (2) The effect of the motion of the gauge caused by the ship's movement. (3) The effect of sea spray. Besides, the analysis of rainfall amounts obtained on shipboard is complicated if the measuring is done on a moving vessel. Several investigations were executed in order to study the influences mentioned above, to test the different types of rain gauges, and to find a site on shipboard where the effect of those disturbances is a minimum. Ocean station vessels and lightships provide good opportunities for such studies especially if suitable reference stations exist on land
2.3
REVIEW OF INSTRUMENTS AND METHODS
37
nearby for comparison purposes. Skaar (1955), Verploegh (1957), Spinnangr (1958), and Roll (1958a) published results of relevant investigations which may be summarized as follows (World Meteorological Organization, 1962): The best exposure is to site the shipborne rain gauge (or at least its collector) as high as possible, preferably at a height of 16 meters or more. Then both the disturbing effect of the ship on the air flow and the percentage amount of sea water in the catch (resulting from sea spray) are reduced to a minimum. The influences of roll and pitch are not easy to estimate since their effect depends upon three additional factors as well, namely the mounting of the gauge (rigid or in gimbals), the slant of the rain, and the heeling of the ship. A detailed-mostly theoretical-discussion, however, shows that, first, the rigid mounting should be preferred to the installation on gimbals and, second, that on the whole this effect will cause a total error of less than - 12 per cent in the majority of cases, which is acceptable for the time being, particularly when compared with the errors caused by other influences. The ideal type of rain gauge for use on shipboard has not yet been found. In particular, it is not yet clear what benefit can be obtained from solid or wire mesh wind shields if the gauge is installed high up on a ship. A fixed collector sited high up on the mast and connected with a receiver on deck by a plastic pipe seems to come very near to the best solution if the problem of cleaning salt deposits from the apparatus can be solved. Here special attention must be devoted to fixing the collector in such a manner that its orifice is horizontal when the ship is lying in still water. Furthermore, a telemetering rain gauge installed on a buoy or the use of radar in estimating precipitation amounts at sea may be developed into useful techniques in the future. Until better apparatus is available, the marine rain gauge (Roll, 1959) may be considered as a useful preliminary instrument. The accuracy achieved with such rainfall measurements on shipboard is hard to determine and rather uncertain. Comparisons between monthly precipitation values obtained with marine rain gauges on lightships and on small flat islands nearby (Roll, 1958a) have resulted in a mean percentage rainfall deficit of - 10 per cent for the lightships, the standard deviation of the precipitation differences being 32 per cent.
38
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
2.3.1.8 Ocean Waves. Although ocean waves are not an atmospheric but an oceanic phenomenon, they depend closely on atmospheric influences and, besides, are very important for the security and economy of marine navigation. These facts may be the reason that the observation of ocean waves forms part of the marine meteorological observing procedure at present. Within this scheme mean values of wave direction, height, and period are reported separately for sea and swell waves. The bulk of these observations is obtained not by using instruments but by visual observing methods. With a view to the fact that the chief characteristic of the appearance of the sea surface is its irregularity, little benefit-from the scientific standpoint-may be expected from mean values of wave height and period obtained by visual estimation or observation. Information that is really useful can only be provided by ocean wave recorders which up to now have been more or less confined to special ships, e.g., research vessels or ocean weather ships. The methods of measuring and recording ocean waves are manifold and cannot be treated here. A summary of information and further references were given by Roll (1957). A more detailed and more up-to-date description can be found in the Special Publication on Oceanographic Instrumentation (U.S. Navy, Hydrographic Office, 1960). 2.3.1.9 Radiation. During the past few years radiation measurements have also been included in the observational program at sea. In 1956 radiation measuring equipment was installed aboard the four British weather ships as a contribution to the program of the International Geophysical Year. * Total radiation on a horizontal surface is recorded by a MollGorczynski thermopile solarimeter mounted on a gimballed compass. The site of the instrument must be suitably chosen so that it is least subject to obstruction. Net flux of radiation is measured by means of two ventilated fluxplate radiometers which are mounted on aluminum alloy booms projecting about 4.5 meters outboard on both sides of the ship in the vicinity of the bridge structure. In order to avoid the disturbing influences originating from the ship each radiometer is screened so that only the upper and lower half hemispheres away from the ship
* The details given in the following were taken from a personal communication for which the author is indebted to Cdr. C. E. N. Frankcom, Marine Superintendent, Meteorological Office, London.
2.3
REVIEW OF INSTRUMENTS AND METHODS
39
are used for measuring, giving a pair record on the recording potentiometer. To ensure strict similarity both radiometers are ventilated by one blower. The instruments are stabilized (by a simple undamped pendulum system) for roll but not for pitch. In practical operation some difficulties have arisen from corrosion, which caused electrical faults. Unfavorable weather conditions, such as rain, heavy spray, and high winds of Beaufort 7 and more impeded radiation measurements on shipboard. Further information can be found in the Special Publication on Oceanographic Instrumentation (U.S. Navy, Hydrographic Office, 1960). 2.3.2 Aerological Measurements 2.3.2.1 Historical Review. Until radio techniques permitted one to have meteorological sondes broadcast their measurements to the ground station, aerological work at sea was distinguished from similar measurements on land by certain characteristics related to the necessity of getting the instrument back after it had come down again. In this respect reference could be made to .the tandem balloon technique introduced by Hergesell (1905). In this procedure two balloons were linked together by an electrically controlled hook which released one of the balloons at a predetermined level. The second balloon-not being able to lift the instrument-carried it down gently and acted as a signal in order to facilitate its rescue. This method was used particularly for getting information from the upper troposphere, and possibly from the stratosphere. It required favorable wind conditions, continuous pursuit of the balloon with a theodolite, and a sufficiently powerful vessel, skilfully operated, if a successful sounding were to be achieved. All of these requirements have seldom been present; we have, therefore, only a few such measurements. Also the captive balloon and kite techniques were adapted for use on shipboard, the chief difficulty being in the handling of this apparatus in the disturbed flow around the ship. With the captive balloon technique it was possible to take advantage of the ship's ability to steam downwind at suitable speed, thus keeping the balloon always in a relative calm and simultaneously securing values of the upper wind. The latter method was successfully employed on the Lake of Constance for many years (Kleinschmidt and Huss, 1935; Huss, 1961). With kite ascents there was no such possibility of overcoming the wind turbulence in the neighborhood of the ship. Therefore, in the logs of research voyages, many notes on accidents are to be found, reporting kite and instrument lost. Nevertheless, kites had to be used,
40
2
METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS
since they provided the only possibility of obtaining meteorological information from the lower troposphere up to 3000 meters as to air temperature, pressure, and humidity, as well as wind direction and speed. From 1900 to the early thirties this awkward technique was employed more or less regularly and successfully on many marine expeditions, thus serving as a good example of what can be accomplished in maritime meteorology with skill and tenacity. A detailed description was given by Reger (Kuhlbrodt and Reger, 1933). Turning now to pilot balloon ascents we also have to report on a special development for use on shipboard. The "mirror theodolite" was constructed by Wegener and Kuhlbrodt (1922a, b) and consists of a combination of a theodolite in gimbals and a sextant, thus enabling the observer to measure the elevation from the true horizon. This sounds easier than it has been in practice. Tracking a pilot balloon from a rolling and pitching vessel, which is subject to irregular variations of course, and where unfavorable clouds, parts of the ship's superstructure, and sometimes its own smoke try to interfere, may be indeed a "terrific job," and good luck is indispensable if a high and reliable sounding is to be accomplished. Of course, the ascent rate of the balloon had to be assumed to be constant if the height could not be determined by other means (range finder or radiosonde). A comprehensive account of the pilot balloon technique on shipboard can be found in the report of Kuhlbrodt and Reger (1933) on the ascents carried out during the German Atlantic Expedition 1925-27 on the research vessel Meteor. 2.3.2.2 Modern Equipment. Against this historical background we should see the new electronic methods which were developed and tested in the mid-thirties and which now have reached a remarkable degree of reliability. Only then will we realize what decisive progress has been achieved with regard to the extent, accuracy, and regularity of the soundings, as well as to the simplification of operation on shipboard. For measuring and reporting temperature, humidity, and pressure up to heights of 30 km, radiosondes are carried aloftgenerally twice daily-by means of a free flying balloon. A radar target is suspended from the balloon to allow it to be tracked and, consequently, to enable the upper winds to be measured by means of air search radar or fire control radar, which supply values of azimuth, elevation, and slant range. The latest outfits may even include Doppler radar, a device that directly senses the balloon's speed radial to the radar antenna and relative to the ship. A detailed description of the modern instruments for upper air observations can be found in the
2.3
REVIEW OF INSTRUMENTS AND METHODS
41
"Handbook of Meteorological Instruments," Part II, published by the Meteorological Office, London, in 1961. As far as possible the technique is the same as adopted at land stations, using the same apparatus but with certain modifications, such as gyro-stabilization, in order to conform with the necessities aboard a ship. Since most air search radar sets cannot scan above an elevation of 60° to 70°, it may become necessary during an upper wind sounding to direct the motion of the ship accordingly. Steaming downwind is, furthermore, required with strong winds in order to keep the balloon within radar range. One of the main scientific advantages of these new electronic techniques is the fact that the former "fine weather selection" of pilot balloon ascents, which was caused by the unavoidable influence of the weather, in particular of the cloud amount, on their practicability and maximum height, has now been eliminated. This is an indispensable supposition for every synoptic utilization or statistical evaluation of such measurements. Unfortunately the costs involved in the use of electronic equipment are rather high and confine the method more or less to special ships, e.g., ocean station vessels and research ships. For this reason the aerological network at sea is by no means satisfactory, particularly in the southern hemisphere. Therefore, great efforts are being made to intensify aerological observation on shipboard with the particular aim of executing regular measurements on suitable merchant vessels on the different sea routes. While remarkable success has been achieved in carrying out radiosonde observations on board merchant ships, considerable difficulties have been met with regard to radio wind measurements on shipboard in view of the expensive and complicated equipment needed for them. High priority has been given to the development of a simple, low-cost device which will yield satisfactory radio wind data on board merchant vessels. During recent years meteorological rockets have come into use also on research vessels in order to extend the measuring height up to about 100 km. The main meteorological quantities which can be measured by means of rockets are atmospheric pressure, air temperature and density, ozone content, solar radiation, and wind. In general the instruments used differ greatly from those applied to the balloon technique and are not yet out of the experimental stage. The measuring and reporting is mostly done during the descent of the instruments, which are released from the rocket at its maximum height and carried down by a parachute.
3. Composition and Properties of the Marine Atmosphere 3.1
GENERAL CONSIDERATIONS
Although the purpose of this monograph is to describe the physics of the marine atmosphere we shall now endeavor to summarize some facts which belong to the field of atmospheric chemistry, rather than physical processes. This will not mean a substantial deviation from our original way of presentation, but it should be regarded more as an effort to consider the characteristic properties of the "material" in question before starting with the intended interpretation of its kinetics and dynamics. Our atmosphere consists of the well-known mixture of nitrogen (76-78 per cent by volume), oxygen (20-21 per cent), argon (0.9 per cent), and some other rare gases (in very small percentages), and, additionally, of matter that-although small in volume and weightplays an important role in many meteorological processes. In the first place, of course, water vapor must be mentioned; it exists as a very variable component (up to 4 per cent), present in all three phases (gaseous, liquid, and solid matter) and, therefore, of particular interest. Furthermore, there are ozone, carbon dioxide, and other gaseous substances whose participation in atmospheric processes is not yet completely understood. It is quite obvious that, moreover, reference must be made to atmospheric nuclei which are partly of natural origin and partly produced by human activities. Numerous studies have been devoted to clarifying the nature and origin of the latter colloid constituents of the atmosphere and, in particular, to discovering their significance with regard to atmospheric processes such as the mechanism of cloud formation and precipitation. If these particles bear electrical charges they are called ions and are, if sufficiently small and mobile, of importance for atmospheric electricity. 42
3.2
ATMOSPHERIC NUCLEI ABOVE THE OCEANS
43
Also organic matter may be present and playa certain part in the interchange among ocean, atmosphere, and continent. Finally, radioactive substances originating from natural and artificial sources may be mentioned, although they seem to be more important as tracer substances for the study of atmospheric motion than as agents in such processes. Bearing in mind that we are only concerned with the marine atmosphere we shall attempt to present in the following a condensed review of those results regarding atmospheric nuclei, trace substances, atmospheric electricity, and radioactivity that were obtained by measurements in the marine atmosphere and that are or may become closely related to phenomena and processes in it. 3.2
ATMOSPHERIC NUCLEI ABOVE THE OCEANS
When speaking of the atmosphere as a colloid system wherein solid or liquid matter is suspended or dissolved we may refer to it as an aerosol. Today, we are accustomed to call the particulate substances themselves aerosols, thus deviating from the original notation. The two main classes of aerosol are the condensation nuclei and the freezing nuclei. Condensation nuclei are necessary for the formation of cloud droplets from water vapor in saturated or slightly supersaturated air. Freezing nuclei are assumed to take an active part in the process of ice nucleation in supercooled clouds by inducing supercooled cloud droplets to freeze and so provide the ice crystals necessary for the production of precipitation. Considering the nature of the condensation nuclei, a subdivision may be made between particles that are insoluble in water and those that consist of droplets of solutions. For the process of condensation water droplets are the most important. The significance ofthe insoluble particles depends upon whether they are wettable or not. In the latter case larger supersaturations are needed for condensation than are required for water droplets. Thus such nuclei are of less importance. Owing to coagulation various intermediate or mixed types exist (Junge, 1951). The natural aerosol is characterized by a wide range of particle sizes from about 10- 7 to 10-3 cm in radius and also by variations of nuclei concentrations which cover more than six orders of magnitude (from about 0 to 4 X 166 cmr"). Therefore, it is necessary and also useful to subdivide the whole nuclei spectrum into different parts which are distinguished by certain common features with reference to their nature, origin, and importance for meteorological processes.
TABLE III SUBDIVISION OF THE ATMOSPHERIC NUCLEI SPECTRUM WITH REGARD TO SIZE, ORIGIN, AND METEOROLOGICAL IMPORTANCE OF NUCLEl u
Nomenclature
I
.~
.c .. o ... 0 .c .... .~
~
....
I
Large nuclei
AITKEN nuclei
Giant nuclei
Cloud physics
Atmospheric optics
cD@
"" ....
!i~"
~
.....
electricity
I
Small ions
Large ions
Air chemistry Condensation and sublimation of vapors
:E""
s
:~ ...
S 0
.o ....... ~
'"
""
Particles which contain main aerosol mass
Mechanical disruption and disper-sal of matter
Formation of dust and sea spray
Z
Coagulation
Radius of particles (cm) 110-8 a
After Junge (1952) and Mason (1957a).
10- 7
10- 6
10- 5
10-<
10- 3
10- 2
3.2
ATMOSPHERIC NUCLEI ABOVE THE OCEANS
45
Such a subdivision was attempted by Junge (1952) and discussed by Mason (1957a); it is reproduced in a slightly amended version as Table III. This diagram, which is largely self-explanatory, will serve as a guide for our discussion of the properties of atmospheric nuclei at sea. 3.2.1 Aitken Nuclei Using the information provided by Table III we may start our review with a compilation of the facts known so far on Aitken nuclei at sea, a species which got its name from the inventor of the apparatus that enables us to count their number. Our particular interest lies in their concentration, size, nature, and origin; on their geographical and temporal variation; and also on their correlation with, or importance for, meteorological phenomena. 3.2.1.1 Concentration. Although a vast number of determinations of the atmospheric nucleus content have been made with various descendants of the Aitken counter, most of them refer to the continents, and there are only comparatively few values available which may be taken as more or less representative of oceanic conditions. In 1938 Landsberg published a monograph on "Atmospheric Condensation Nuclei" presenting therein a comprehensive compilation of all Aitken nuclei countings on land and at sea which were known at that date. This detailed tabulation need not be repeated here, but a summary of the older data was combined with the results of more recent measurements (Table IV). We realize that, compared with the vastness of the oceanic regions, the number of concentration measurements (about 900), and also their sporadic distribution, are far from satisfactory. Nevertheless, at least the average values of nucleus content are fairly consistent with one another. They are considerably lower than those found on the continents, where in big cities, for example, averages of 147,000 and maximum values of 4,000,000 may be reached. A frequency distribution computed from the nucleus concentrations collected from 221 oceanic localities during various cruises of the U.S. Research Vessel Carnegie (Landsberg, 1938) shows that concentrations of less than 400 cm-3 comprise 68 per cent of all observations. When treating the Atlantic observations of Hess (1948, 1951), Parkinson (1952), Wigand (1930), and Landsberg (1934) in the same way we find, however, a wider distribution than that given above, with only 30 per cent concentrated in the range below 400 cm f and a cumulative frequency of 71 per cent covering all concentrations below 800 cm".
TABLE IV AVERAGE CONCENTRATIONS OF AITKEN NUCLEI OVER THE OCEANS
Region of 0 bservation
Aitken nuclei counter, Aitken-Liideling nuclei counter, small and large Scholz nuclei counter
Up to 1934
33 Oceanic localities and coastal stations
Height of 0 bs. above sea level (meters)
Apparatus used
Year
Number of nuclei per cubic centimeter
No. of obs.
--
600
Author Average
Maximum
940
39800 (abs.); 4680 (mean)
527
1490·
4440·
659
1780·
4480C
956
3100 a
4150·
1019
2000·
14000c
Minimum 2 (abs.) 840 (mean)
Compiled by Landsberg (I 938)
Atlantic Ocean New York-Le HaVre}
Aitken pocket dust counter
1948
6
39{
Le Havre-New York New York-Le HaVre}
Aitken pocket dust counter
1951
6
40{
Le Havre-New York
78}
Hess (1948)
113 182}
Hess (I951)
188
New York-Rio de Janeiro
1951
Aitken pocket dust counter
9
30
676
1267
264
Ocean station Item: 6I'20'N,13'20'W; 59' N, 19'W
1951
Aitken pocket dust
8
27
703
2460
77
Mace Head (Ireland) in maritime air
1958-59
Photoelectric nucleus counter (Pollack and O'Connor)
54" 36' 48 1
1160'1 690' 8901
-
-
1948
Improved Aitken
67
290
690
70
Ohta (1951)
-
lIS
1040
2200
480
Ohta (1951)
Lower region of trade wind flow
-
--
500
140
Blanchard and Spencer (1957)
Parkinson (I952)
Moore (1952)
counter
Pacific Ocean 39' N, 153 0 E
-
O'Connor et al, (1961)
counter
Japan Sea, 43.3' N, 141' E Near Hawaii
Improved Aitken
1948
counter
Schultz and Casella
1954
counter;
Vonncgut contincounter
UDUS
a In mid-ocean.
• Near Cobh.
r
English Channel.
d
Wind south.
e
Wind southwest.
fWind west.
3.2
ATMOSPHERIC NUCLEI ABOVE THE OCEANS
47
The scatter of the single observations is remarkable in marine areas and there may be some doubt as to whether the relatively high values, which appear mostly in coastal regions, are actually representative of maritime conditions and not influenced by industrial contamination. There is some evidence that such continental effects on nucleus concentration at sea are far reaching. Hess (1948, 1951) found the following distinct differences between the mean concentrations of Aitken nuclei in the western and the eastern parts of the North Atlantic Ocean: Year
1948 1948 1951 1951
Western part Eastern part (nuclei per cm-)
575 813 1512 1229
478 504 462 887
Similar results have been reported by Ohta (1951) for the Pacific Ocean (see Table IV). The authors attribute the higher concentration in the western parts of the oceans to continental influences which affect the air masses traveling in general from west to east. No systematic diurnal variation in the number of Aitken nuclei was found over the ocean, according to either local or Greenwich time (Torreson et al., 1946). 3.2.1.2 Size. Unfortunately the Aitken counter only supplies information on the number of the nuclei but does not reveal anything about their size, nature, and origin. Measurements with the optical microscope are not possible since the size of the largest Aitken nuclei (Table IV) corresponds to the limit of optical resolving power. Therefore, the size range of nuclei detected in an Aitken counter is not well established. Even if an electron microscope is available the investigation will be very difficult, partly owing to the small size of the particles and partly because they may evaporate in the high vacuum or be affected by the electron bombardment. Electron micrographs suggest that the radii of Aitken nuclei fall chiefly into the range of 10- 7 to 10- 5 em as indicated in Table Ill, the maximum concentration being between 10-6 and 10-5 ern. These results were confirmed by measurement of the diffusion coefficient of such particles (O'Connor et al., 1961) as well as by determination of the ionic mobility of charged Aitken nuclei (Junge, 1955; Sagalyn, 1958).
48
3
COMPOSITION AND PROPERTIES
3.2.1.3 Nature and Origin. With regard to the nature and origin of the Aitken nuclei, the following conclusion may be drawn indirectly: The fact that their mean number is much smaller on the oceans than on the continents, as well as their peculiar geographical distribution on the oceans characterized by greater concentration in the western parts, does not suggest that sea spray is the main source for Aitken nuclei. We are much more inclined to presume that they originate on land. Some support for this opinion is received from the work of Moore (1952) and that of Ohta (1951), who stated that no significant correlation was found between the concentration of Aitken nuclei and either wind speed or wave height on the high sea. [In coastal surf regions it may be different as was shown, for example, by Zenker (1953)]. Otherwise the nonexistence of a correlation between concentration of Aitken nuclei and wind speed could only be explained by assuming that any increased production of Aitken nuclei in strong winds is largely counterbalanced by their increased upward transport to higher levels. Up to now no confirmation has been found for the latter assumption. 3.2.1.4 Relations to Meteorological Phenomena. On the other hand, the close association between the concentration of Aitken nuclei and the intensity of vertical mixing, which is well established on land, also exists in oceanic areas as can be seen in Table V where the nucleus counts of Moore (1952) are arranged according to cloud type. As expected, the smallest nucleus contents-on the average as well as in the extremes-are connected with convective clouds, whereas stratus is typical for high concentrations. In the bottom two lines of the table more evidence is given for the effect, mentioned above, that with winds from oceanic areas the concentrations are generally lower than with wind blowing from continental sections. Such land influence is still noticeable at distances of several hundred miles. Another relation between the concentration of Aitken nuclei and meteorological phenomena was reported by Ohta (1951): A sudden increase of nucleus content appeared in the Pacific together with the passing of a discontinuity line in air documenting itself by a rather sluggish rise of water vapor pressure. . So far there has not come to our knowledge any meteorological phenomenon at sea in which Aitken nuclei seem to play an active role. In particular, the majority of them do not act as condensation nuclei under normal conditions, as may be inferred from Table III. Other causes were responsible for simultaneous variations both of Aitken nuclei and of meteorological elements.
3.2
49
ATMOSPHERIC NUCLEI ABOVE THE OCEANS TABLE V
CONCENTRATIONS OF AITKEN NUCLEI AND CLOUD TVPE a
Cloud type
Total number of observations Average concentrationHighest concentration Lowest concentration Average concentration with wind from purely oceanic areas" Average concentration with wind from areas where land is (at least) some 200 miles away"
Stratocumulus or stratocumulus and cumulus
Cumulus or cumulonimbus
7
II
9
1280 2460 290 715(3)
625 1490 132 386(6)
354 740 77 260(6)
1680(4)
917(5)
544(3)
Stratus
After Moore (1952). Numbers in parentheses give number of observations for each type of area. c Concentrations given per cubic centimeter. a
b
Numerous attempts to ascertain correlations between nucleus concentrations and meteorological elements (e.g., wind force, visibility, humidity) were made, with more or less success, in coastal regions. With a view to the scope of this monograph we shall, however, abstain from discussing such investigations. Summarizing the results available on Aitken nuclei at sea, we may say that some sporadic concentration values and some indication of their nonmaritime origin and limited importance in meteorological processes form the sole information that seems to be reliable at present. 3.2.2 Large and Giant Nuclei We are now going to discuss the nuclei found at sea with radii greater than 10-5 em. According to Table III we may assume that a considerable, if not predominant, portion of these particles originates at the surface of the sea where wind action causes the disintegration of sea water, which becomes visible in the formation of "white caps," foam, and spray. It is, therefore, understandable that the chief interest of investigators was devoted to hygroscopic sea-salt nuclei arising
50
3
COMPOSITION AND PROPER TIES
from spray by evaporation and, therefore, consisting of concentrated sea water or of crystalline salt masses. 3.2.2.1 Methods of Measuring. Since in the size range mentioned above the use of the optical microscope is possible-although difficult for the smallest of these particles-there is some hope that we will have at our disposal relatively simple techniques for size determination. Methods of sampling and measuring sea-salt particles have been developed and described by several authors and it is not possible to give a detailed account of this subject here. Only the chief principles applied will be outlined. For sampling the following are employed: (a) Relatively large collectors in air jets of high velocity, thermal, or electrostatic precipitation. (b) Narrow collectors (glass slides, metal rods, or even spider webs) at lower air speeds. The application of the different methods is practicable for measuring sizes or for chemical analyses, the first purpose being the only one of interest here. In this respect, the following should be mentioned: (1) The spot test techniques where physicochemical reactions on (a) a glass slide covered with gelatine or (b) a filter, which act as collectors of particles, result in precipitation, i.e., produce an enlarged spot around each particle depending on its size and permitting microscopic examination. [For further information see Metnieks (1958).] (2) The "isopiestic" (equal pressure) method used by Woodcock and Gifford (1949), Woodcock (1952), Moore and Mason (1954), and others. A brief description of the measuring principle follows. The collectors used are mostly narrow glass slides of various sizes (corresponding to the sizes of the nuclei to be collected) coated with a hydrophobic film which causes water drops to become hemispheric on the slides. After the exposure of these collectors to the impact of the nuclei in the air flow on a wind vane under controlled conditions (air speed, duration) they are examined under the microscope in an atmosphere of known temperature and water vapor pressure. The radii of the nuclei vary with the relative humidity of the air surrounding them. With the relative humidity at a low value, the nuclei are crystalline. By measurement of the equilibrium radii of the hemispheric droplets it is possible to determine the weight of the chloride in the individual nuclei. By titration of larger numbers of dissolved nuclei which were obtained simultaneously with the slide exposures, it was proved by
3.2
ATMOSPHERIC NUCLEI ABOVE THE OCEANS
51
Woodcock and Gifford (1949) that (a) the nuclei deposited on the slides in marine air were really composed of concentrated sea water and that (b) the chlorinity of atmospheric nuclei determined by the isopiestic method was in fair agreement with the chlorinity gained by titration of deposited salts. The nature of the hygroscopic sea-salt particles implies that the "nuclear mass" or "weight of sea-salt in particle" is now used as the primary characteristic figure m, given in grams, for the nuclei instead of the radius. The radius of the corresponding sea-salt nucleus of spherical shape can be computed; its value will, of course, depend upon the relative humidity of the surrounding air, thus being comparable with others only if related to the same humidity or if representing the radius of a spherical particle of equivalent dry salt mass. When evaluating the size distribution we have to correct the counts for deposition error, which arises from the fact that some of the nuclei are deflected by the air flow around the slides and hence fail to impinge on them. This error is particularly large with very small nuclei. With regard to possible errors caused by coalescence or shattering of nuclei upon impact, Woodcock and Gifford (1949) were able to show that these were not significant, even at very high air speed. 3.2.2.2 Size Distribution. The sea-salt nuclei produced at the sea surface are raised to higher levels by turbulence and convection until this vertical transport is hindered or limited at the top of an inversion layer. In the following we shall try to present some information on the size distributions existing in different layers and regions of the marine atmosphere. As an example of the results gained with the isopiestic method, a size distribution of sea-salt nuclei measured by plane over the sea near Hawaii is reproduced from a paper of Woodcock (1953) and is summarized in Fig. 7. This diagram comprises the nuclear mass range from 10-13 to 10- 8 gm and the corresponding particle radii vary between 10-4 and 5 x 10- 3 ern. Consequently, it represents chiefly the size distribution of giant nuclei which will be discussed later on. In trying to get information on large nuclei, we meet difficulties at first because very little has been published on their number and size at sea. The reason for this deficiency is obviously their smallness (radii between 10-5 and 10-4 cm ; see Table III) which is a severe handicap when the optical methods heretofore described are used. A few data are cited in a review by Mason (1957a). They are reproduced in the following although I found it somewhat difficult to verify them-by
52
3
COMPOSITION AND PROPERTIES
WEIGHT OF SEA 10
10-'2
SALT IN PARTICLES.
10- 11
grams
10- 9
10-'0 AL T. rn
518
SEA SALT 10-'2 Q - c rn - 3 IIA 7.5
1070
1550
23 002
2740
3000
I-
:r
(!)
z
w
;: o 10-' w
-2000
>-------+----"..---...p.;~------+---1
1 ~:::;, ~\ _CLOUD
1000
I<X
+~ +
o
o
00
z
,
'0
"
TC
TOP
10-'
LOCAL CU +---BASES 20
25
Z <X
;: 10-2 f--:>...,__---+------+-~c_-~__+IT_-----+-----____::::J 0:
W
I<X W
0:
2740
(!)
...
'E 10-3>-------+--"----+--------+__+---"--~rt_-----__1 u
<3 z
W
--' <.> I-
~ 1O-4f-------+------->,+-------+-+----+1,--~--___1 c,
I-
--'
<X
<X W
24
51 PARTICLE
110 23.7 RADIUS AT 99% RH 110-4 crn )
51.1
FIG. 7. Size distribution of sea-salt nuclei at different altitudes over the sea near Hawaii. (From Woodcock, 1953.)
3.2
ATMOSPHERIC NUCLEI ABOVE THE OCEANS
53
comparison with the original papers-as, beyond any doubt, values for large nuclei. Woodcock and Gifford (1949): 12 nuclei per em" at 15 meters' height near Cape Cod, Massachusetts. Woodcock (1953): 4 nuclei per cm'' at 500 meters over Hawaii. Moore and Mason (1954): up to 12 nuclei per cm'' with 2 x 10-14 < m < 10-11 gm. Since Woodcock collected mostly particles of m > 10-13 gm and Moore and Mason extended their range from 2 x 10-14 to 10- 11 gm, these values should be used with caution as far as large nuclei (mass range from about 10-16 to 10-13 gm) are concerned. Some useful information on size and chlorinity (though not on concentration) of sea-salt nuclei in sea fog and marine aerosol, with radii ranging from about 10-5 to 10-3 em and with 10-16 < m < 10-11 gm, may be taken from a paper by Kuroiwa (1957) describing measurements with the electron microscope and showing the maximum frequency of occurrence of water-soluble nuclei between 10-14 and 10-13 gm in sea fog and of nuclei around 10-14 gm in marine aerosol. With regard to giant nuclei, results have been achieved that are more complete and more satisfactory than those for large particles. First let us have another look at Woodcock's distribution curves reproduced in Fig. 7. From this diagram we gather that the different mass ranges of sea-salt nuclei were present in the following concentrations:
m m m m
> 10-13 gm
10-12
> gm > 8 x 10-10 gm > 10-8 gm
about 4/cm 3 about l/cm3 1/liter about l/meter3
all values referring to a height of 518 meters which was somewhat below the bases of local cumulus clouds. In addition to Woodcock's results a few values taken from other authors will be mentioned briefly. Lodge (1955) measured size distributions of sea-salt particles at Puerto Rico. Some of his results will be dealt with in the next paragraph. Furthermore Fournier D'Albe (1955), Rau (1956a), and Metnieks (1958) contributed concentrations for different size ranges measured in coastal regions. At Karachi Fournier D'Albe (1955) found an average concentration of the particles with m > 10- 9 gm of 8 per meters in winter against 700 per meters in summer when the southwest monsoon establishes a typically maritime regime. Metnieks (1958) took measurements on the west coast of Ireland several times per day and made a tentative statement concerning the
54
3
COMPOSITION AND PROPERTIES
daily variations on sunny days with light winds, i.e., with small production and concentration of sea-salt particles. Under such conditions he experienced a definite minimum concentration for all particle sizes in the early afternoon. A relationship between sea-salt concentration and tide could not be verified, possibly because the production of minute salt crystals during the receding of the tide and the drying of the foreshore escaped detection. 3.2.2.3 Variation with Altitude. From Fig. 7 we learn that the number and weight of the sea-salt nuclei decreased rapidly with height, whereby the character of the particle size distributions seemed to be fairly independent of altitude. This decrease, which again confirms the marine origin of those nuclei, is illustrated by Table VI which we computed from the distribution curves in Fig. 7, using also the values for the total weight of sea salt, present at different heights, indicated therein. We realize that with height the number of the larger particles decreased faster than that of the smaller ones, which may be a combined effect of sedimentation and turbulence. The rate of decrease grew with altitude as can be taken from the different concentration ratios. The most striking feature is the extraordinary decrease at from 1550 to 2740 meters which occurred in the relatively salt-free layer above the cloud tops and above the temperature inversion TABLE VI DECREASE OF CONCENTRATION N
OF SEA-SALT NUCLEI WITH ALTITUDE
OVER SEA NEAR HAWAUu
Ratio of concentrations" Sea- salt particles with mass (gm)
N51S!NI070
N1070!N1550
>10- 1 2 >10- 11 >10- 10 >10- 9
1.4 1.2 2.0 4.7
2.0 4.4 14.5
124 397
Total amount of sea-salt
1.5
3.3
115
U
b
Computed from Fig. 7. Subscripts give heights in meters.
3.2
ATMOSPHERIC NUCLEI ABOVE THE OCEANS
55
(see Fig. 7). In view of these results it is not surprising that the vertical distribution of sea-salt nuclei also showed a marked dependence on thermal stability (Woodcock and Gifford, 1949), the rate of decline being great in thermally stable air, whereas little change with altitude was observed in well-mixed air flowing over warmer water. All these influences may contribute to the fact that the rate of decrease with height of the sea-salt particle concentration was found different by other authors and at other places; a decrease smaller than Woodcock's value, and approximately the same for all particle sizes, was observed by Lodge (1955), who measured the size distributions of sea-salt nuclei up to 3000 meters altitude over Puerto Rico under typical maritime conditions. He even found in four of his five flights that over the sea an increase in chloride particle concentration occurred between 30 and 150 meters altitude when the wind force was low and, therefore, the supply of sea salt from the ocean surface negligible. 3.2.2.4 Correlation with Wind Speed. Contrary to the behavior of the Aitken nuclei, sea-salt particles show a distinct correlation with wind speed which is not surprising for nuclei produced at the sea surface by wind action. As can be inferred from Fig. 8 increasing winds were associated with a rather consistent pattern of increase both in numbers and sizes of particles near the cloud base over the sea in the Hawaii area. Attention should be drawn to the curve for a wind force of 12 Beaufort, which was obtained during a tropical storm near Florida. It is highly impressive to see that the most energetic performance of the marine atmosphere is able to raise the number of largest giant sea-salt nuclei with m > 10- 8 gm from 1 per meters at 4 Beaufort to about 2 x 104 per meter". The remarkable increase with wind speed is particularly distinct if we consider the total amount of sea salt in the air as presented in Fig. 9. Adequate results for the relations between concentration of seasalt nuclei and wind speed were obtained by Moore (1952) on the ocean weather station Item for m > 10-11 gm up to wind speeds of 15 meters/sec. He also found a clear correlation between concentration of nuclei of m > 5 x 10- 9 gm and wave height, which showed a linear increase of the former with growing waves. Metnieks (1958), however, reported a somewhat different relation between concentration and wind speed characterized by a higher rate of increase with wind speeds from 5.1 to 6.7 meters/sec than with lower ones. An effort to explain this dependence of the concentration of seaspray particles on altitude and wind speed was made by Junge (1957a).
56
3
COMPOSITION AND PROPERTIES
Particle radius at 99 % rh (10- 4 em) 5.1
11.0
23.7 Wind force I
51.1 Number of sompling doys I
3
4
7
2
4 11 ~--~-..::----t---5f----+5----,j
1:
12
Ol
I
"w:;: 1 2 10- ~--"""'-t"""~
"0
a
.S:!
"0
.!:
§ 10-2 t - - - - - - t " £ ... 2a Q)
0, 10-3
t------t----),
r
'E o
o
5. 10- 4 ~---+----t--\---t\ ~
U
...
+= a ~ 10-5 t - - - - - - j - - - - + - - - ' \ - + - - \ a (j) a Q)
(f)
10-6 ~---t----+-----I\
10-11
10-10
10-9
H--\--~ 10-6
10-8
Weight of sea salt particles (grams) FIG. 8. Effect of varying wind force upon size distribution of sea-salt nuclei near cloud base over sea in Hawaii area. (From Woodcock, 1953.)
After having stated that neither gravity nor condensation would be able to establish an equilibrium between the upward transport of nuclei and their elimination by the condensation process at cloud level, Junge showed theoretically that the observations about sea-salt particles can be well explained by the nonsteady-state solution. This conclusion, however, still needs confirmation by combined measurements of turbulence and particle concentration.
3.2
ATMOSPHERIC NUCLEI ABOVE THE OCEANS I
57
2 3 4 5 6 7 8 9 10 II 12 /
/
//.
'510- 10
'0
"'E ~
/.
en
/
/
/
•
/
/
+
+/
/
/
/
/
/
/
/
/
/
/
/
/
t
/
/
/
/
/
/: ". t )
E g,IO-11
/1 *+
/'
.S
/>
/:j:
~
5l
en
/
I
/
/
/
1 /
/
/
t /
'. / / Y
2 3 4 5 6 7 8 9 10 II 12 Wind force
FIG. 9. Variation in total amount of air-borne sea-salt with increasing wind force. (From Woodcock, 1953.)
3.2.2.5 Discontinuity in the Size Distribution of Moore and Mason. Let us now devote a few words to a peculiar result obtained by Moore and Mason (1954) which has a bearing on the production of sea-salt nuclei at the sea surface. From measurements on the ocean station Item both authors derived the size distributions of giant nuclei reproduced in Fig. 10. At wind speeds higher than 7 meters/sec (twenty-five cases out of thirty) a marked discontinuity occurred for a certain nuclear mass me. The relevant distribution is called "type I" [Fig. lO(a)] and shows, for m < me, similarity to Woodcock's curves (1953) [Fig. lOeb)], whereas a rapid decrease is observed for m > me. The value of the critical mass me varied from 10-11 gm to greater than 10- 8 gm, accompanied by an increase in the concentration of the largest nuclei, as the wind speed increased from 6 to more than 15 meters/sec. A similar distribution was found by Fournier D'Albe (1951) when measuring sea-salt nuclei over the Bay of Monaco in winds of 9 meters/sec [Fig. 10(c)]. Although there will be a certain reluctance to accept such discontinuities as real-owing to experience which has shown that such extraordinary findings have sometimes been revealed afterward as being caused by instrumentational or other shortcomings-v-I feel
3
58
COMPOSITION AND PROPERTIES
102 r - - - - - - - - - - - - - - - - - - - - - - ,
10
'"E I
(J
10-12 10-11 10-10 10-9 Nuclear mass (grams)
FIG. 10. Discontinuity in the size distribution of sea-salt nuclei over sea. (From Moore and Mason, 1954.) (a) Moore and Mason, type I nuclei, ocean; (b) Woodcock, Florida, tropical storm; (c) D'Albe, Bay of Monaco, wind 9 meters/sec.; (d) Moore and Mason, type II nuclei, ocean.
that the interpretation given by Moore and Mason deserves attention. They explain the presence of a discontinuity or a marked change of slope in the type I distribution in terms of a loss of the larger nuclei by sedimentation, saying that "in strong winds, the part of the curve to the right of the discontinuity probably represents a state of dynamic equilibrium between the rates of production and loss of the larger nuclei." It is expected that this part of the curve should then have a steeper slope with medium winds-owing to increased sedimentation -than with strong winds. This does occur. At wind speeds less than 7 meters/sec, i.e., when no white caps were observed (five cases out of thirty), a distinctly different distribution curve (type II) was found which showed no discontinuity [Fig. lO(d)] between the particle sizes 10-13 and 10- 8 gm. Moore and Mason suggested that, although marine salt particles were identified among the type II nuclei, hygroscopic particles of continental origin may have been present in great numbers, causing the type II nuclei numbers to be somewhat higher than those of type I. With regard to this point
3.2
ATMOSPHERIC NUCLEI ABOVE THE OCEANS
59
further confirmation by additional measurements seems to be necessary. 3.2.2.6 Mechanism and Rate of Production of Sea-Salt Nuclei. The mechanism and rate of production of sea-salt nuclei was investigated by Moore and Mason (1954), Mason (1957b), and Rau (1956b), particularly with a view to contributing to the old, but still unsettled, controversy as to whether or not salt particles produced by the foaming of the sea surface form the main source of the condensation nuclei involved in cloud formation. As the results presented above show, sea-salt particles of m > 10-13 (giant nuclei) were found only in concentrations of about 10/cm 3 in the marine atmosphere and it is quite obvious that they are not numerous enough to constitute a major source of cloud-forming nuclei, although they may be essential for initiating an efficient coalescence process such as Ludlam (1951) indicated was required for the production of showers. On the other hand, the possible assumption that there might exist much larger concentrations of salt particles, too small to be detected by the methods employed for sampling and measuring sea-salt nuclei, and that, consequently, such small particles might be found in an Aitken counter, does not fit in with the results given for Aitken nuclei in Section 3.2.1. In order to clarify the problem of production, one should refer to the following results: Moore and Mason (1954) investigated the rate of production of sea-salt nuclei with m > 2 x 10- 13 gm by breaking waves in a windwave tunnel and obtained a value of 40 cm-2sec-1 for the strongest winds which corresponded to a speed of 16 meters/sec at a height of 10 meters. This result is in good agreement with an estimate made by the same authors from their measured size distributions of large and giant nuclei over the ocean. For nuclei with m > 2 x 10- 14 gm a production rate of about 86 cm-2sec~1 was obtained. For a better insight into the mechanism of sea-salt nuclei production further investigation is necessary. If the wind over the sea is strong enough to create whitecaps, air is captured by the collapsing wavecrests and rises to the sea surface in the form of tiny bubbles. Moreover, all forms of precipitation particles are effective bubble producers when striking the sea surface, as was shown by Blanchard and Woodcock in 1957. When bursting at the surface these bubbles certainly cause a transport of sea water particles into the air which needs to be investigated in detail. Woodcock et al. (1953), Kientzler et al. (1954), Knelman et al, (1954), and also Moore and Mason (1954) studied, partly with the aid
60
3
COMPOSITION AND PROPERTIES
of high-speed motion pictures, the different phases of a bubble bursting at the surface of sea water, and they arrived at the following results: There are two phases when a bursting bubble has an opportunity to eject water particles into the air (Fig. 11): (1) The hemispheric cap of a bubble rising from below breaks the surface where it is thinnest, causing a disruption of the film, probably into many fragments which, however, have not yet been photographed. (2) After the bursting of the cap, a narrow unstable jet evolves from the bottom of the collapsing bubble and breaks up to form from one to five droplets which are ejected upward to heights that are great compared with the size of the bubble. The droplets are about 10-15 per cent of the corresponding bubble size (diameter between 3 x 10-2 and 4.3 x 10-1 em), They carry an appreciable electric charge which may be significant for electrification processes in the marine atmosphere (Blanchard, 1955) (see Sections 3.4.2.1 and 3.4.5.2). According to Mason (1957b) only the droplets produced by very small bubbles during phase (2) may become giant nuclei and so contribute to the supply of potential condensation particles. The droplets resulting from the bursting of bubbles larger than 5 x 10-2 cm in diameter will fall back quickly into the sea. Blanchard and Woodcock (1957), who investigated phase (2) of bubble bursting in greater detail showed that the great majority of the bubbles caused by breaking waves are < 2 x 10-2 cm. They concluded that most of the sea-salt nuclei are produced via the jet mechanism [phase (2)] and, assuming that only one of the droplets ejected from each bursting bubble remains air borne, they estimated the relevant production rate at 34 cm- 2sec-1, which corresponds to about 3 cm-2sec-1 if it is accepted that 10 per cent of the sea surface is active in nuclei production by white caps. In a later paper Woodcock and Spencer (1961) pointed out that enormous numbers of giant hygroscopic particles consisting mostly of sea salt are present in the steam clouds arising when molten lava encounters sea water. Since the rate of production of these nuclei is estimated to be from one to six million times greater than that produced from the sea surface on the average, they suggest that such an occurrence, although rather rare and confined to a very limited area, might even contribute a weight of sea-salt nuclei per unit of time that is equal to a considerable fraction of the total average production of all oceans. Mason (1957b) tried to get an idea of the number of nuclei produced by a bursting bubble in phase (1), which had so far escaped
FIG. 11. Ten consecutive stages of the bursting of an air bubble at a water surface. (From Kientzler et al., 1954.)
62
3
COMPOSITION AND PROPERTIES
detection by cinematography. Observations were made in an expansion chamber of air bubbles, ranging in diameter from 2.5 x 1O~2 to 2.15 x 10-1 cm, bursting in sea water. They led to an overall estimate of 300 ± 80 nuclei per bubble. Electron micrographs proved that the diameters of these particles were mostly between 2 x 10-5 and 5 x 10-5 em and that the smallest ones (10-5 em) contained about 10-15 gm of salt. Summing up all these results, Mason (1957b) came to the following conclusions: (a) Extrapolation of the measured distribution curves in Fig. 10 down to nuclear masses of 10-15 gm gave as an estimate for the total concentration of sea-salt nuclei with m > 10-15 gm 100/cm 3 (b) With (a) the share of sea-salt nuclei in the total nucleus concentration measured by Aitken counter (see Section 3.2.1.1) would be no more than about 20 per cent. Therefore, no strong reaction of the total nucleus concentration is to be expected with wind speed increasing (as observed). (c) Supposing that the concentration of salt particles in the lower layers of the atmosphere is more or less proportional to their rate of production at the sea surface, we arrive, according to (a), at an estimated total production rate of sea-salt nuclei with m > 10-15 gm of about 1000 cm-2sec- 1 since a production rate of about 100 cm- 2sec-1 was necessary to account for a concentration of 1O/cm3 with m > 2 x 10- 14 gm. (d) The result (c) would need a rate of bubble formation of about 3 cm-2sec-1 which seems to be reasonable and is also in agreement with the abovementioned estimate of Blanchard and Woodcock (1957) of the frequency of air bubbles produced by breaking waves. However, no consideration was given to other bubble-producing mechanisms such as the impact of raindrops or the melting of snowflakes. The figures in (a) and (c) estimated by Mason for both the total concentration and the total production rate of sea-salt nuclei account only for about 20 per cent of the quantities of condensation nuclei both needed for the formation of precipitating clouds and lost from the atmosphere by precipitation. This may also be gathered from a very rough evaluation (Mason, 1957b) starting from figures on the annual global rainfall and arriving at an estimate of the necessary production rate of condensation nuclei. This implies that about 80 per cent of
3.2
ATMOSPHERIC NUCLEI ABOVE THE OCEANS
63
the condensation nuclei must be supplied from the continents partly by combustion products and partly by dust particles from the earth's surface. Mason's estimate received some support from electron microscope measurements of nuclei found in cloud and fog droplets near the coast of Japan by Kuroiwa (1953) and Yamamoto and Ohtake (1953), which showed that nuclei produced by combustion amounted to 40 per cent of all droplets whereas both sea-salt and soil particles reached only 20 per cent of the total. A similar investigation by Isono (1957), carried out with residues of cloud droplets at the summit of a mountain, resulted in 30 per cent of the nuclei being mainly composed of sea salt. Mason's results as regards the number of sea-salt nuclei produced by bursting air bubbles were critically viewed by Rau (1956b), who was not able to confirm the production rate of 300 ± 80 nuclei per bubble, estimated by Mason, but found the process of bursting bubbles to be mostly ineffective for producing nuclei. According to his investigation the process of spraying is much more effective and may even account for concentrations of nuclei with m > 10- 15 gm of about 106jcm3 . Such a figure would, of course, considerably modify the outcome of the deliberations described above on the role that sea-salt nuclei play in condensation. There is some doubt, however, whether the level of efficiency of spraying achieved in the laboratory will also be reached in nature. Furthermore, reference should be made to an effect which was studied by Facy (1951) and later by Twomey and McMaster (1955). These authors examined the behavior of salt droplets when the environment humidity was lowered sufficiently (to around 70 per cent relative humidity for droplets of 10- 4 to 10- 3 em radius) for crystallization to take place, and they found that at least several hundred minute salt crystals with a mass range of from 10- 18 to 10- 14 gm were produced during the crystallization of each of the larger salt particles. These small salt crystals are effective condensation nuclei at moderate supersaturation. The process of crystallization should, therefore, also be taken into account when the nature and the origin of the condensation nuclei in the marine atmosphere are considered. Finally, it is worth mentioning that, beside the hygroscopic particles from the sea surface which are well known to be active nuclei for the condensation of water vapor to the droplet state, particles with icenucleating properties also are released from the ocean to the atmosphere, as preliminary tests of Brier and Kline (1959) have indicated. In air samples drawn in a laboratory from near the surface of agitated
64
3
COMPOSITION AND PROPERTIES
sea water they found an increase in concentration of ice nuclei of from about 0.5 to 300 per liter if the temperature was lowered from -15° to - 30°C. The nature of these ice nuclei is, however, not yet quite clear. According to Georgii and Metnieks (1958), who studied the activity of sea-salt particles in the process of ice nucleation of supercooled clouds on the west coast of Ireland during the summer of 1958, the concentration of freezing nuclei active above - 30°C showed no relationship to that of the sea-salt particles. There was even some indication that the most active freezing nuclei were particles of continental origin. Battan and Riley (1960), however, concluded from observations made on Mount Bigelow in southeastern Arizona that their data could be most readily reconciled with the hypothesis that the oceans are an important source of ice-crystal nuclei. After discussing the production of sea-salt nuclei at the ocean surface one might be tempted to trace their further life history, which is determined by transporting and distributing forces, by the processes of condensation, coagulation, and precipitation, and which would certainly show many interesting, sometimes even fascinating, features and problems. Such a review would necessarily have to include the continents, since we know from a paper of Junge and Gustafson (1957) that even large sea-salt particles may travel considerable distances in the atmosphere over the continents without being removed by precipitation. These considerations would, however, go far beyond the range of this monograph. 3.3
CHEMISTRY OF THE MARINE ATMOSPHERE
In the preceding section we dealt with the physical aspects of atmospheric nuclei. We studied their concentration and size, we tried to reveal their interrelation with meteorological elements and phenomena, and, finally, we even endeavored to clarify their nature and origin, as far as this was possible with purely physical and statistical methods. Looking back we realize that, although important and helpful information was gained, neither did we get to the "root of things" -namely, to the fundamental principles which govern those colloid processes and which we ought to know if we aspire to a thorough and full understanding of the phenomena-nor did we acquire sufficient knowledge on the real nature and origin of the substances involved. In this situation effective help and elucidating information can only be expected from atmospheric chemistry, a relatively new branch of meteorology which, however, is developing quickly and has already achieved promising results.
3.3
CHEMISTRY OF THE MARINE ATMOSPHERE
65
Basically, trace substances in the atmosphere can be present as solid or liquid particles, or as gases. It is, therefore, essential that, when dealing with air chemistry, we clearly distinguish between particulate matter and gaseous substances, both of which should be measured simultaneously but separately. Only then will we be able to describe completely and, perhaps, understand the natural process in question. Following these lines we shall deal separately with the composition of particles and gas traces in the marine atmosphere and then we will add some remarks on the carbon dioxide content of marine air, which deserves special attention. 3.3.1 Composition of Particles Relevant measurements were made by Junge in Florida (1956) and in Hawaii (1957b), and by Lodge et al. (1960) in the North Pacific on the ocean station November. The air samples were taken with particular care in order to avoid contamination resulting from human activities on shipboard or at the coast. Thus the results of the analyses can be considered as fairly representative of maritime conditions. While Lodge and his colleagues did not give separate values for the different types of atmospheric nuclei, Junge, by using a two-stage cascade impactor which separated the two radius ranges from 8 x 10-6 to 8 X 10-5 em and from 8 x 10-5 to 8 X 10- 4 em, was able to differentiate almost exactly between large and giant nuclei (see Table III). The analyses were confined to that matter which was soluble in distilled water. The amount of insoluble matter, which may become considerable at some continental locations, could not be measured. The places and periods of observation and the components analyzed are shown in the tabulation. Observer
Place
Date
Junge
Homestead, Florida
July 19-August 3, 1954
Junge
Hilo Harbour, Hawaii
October-November, 1954
Lodge, et
at. Ocean station
November 30° N, 140 W Ocean station November 30° N, 140 W
July 27-August 13, 1957
Components NH!, N03", Cl", S04", Nat NH!, NOi, ci-, S04" Chloride, sulfate
0
Lodge et
at.
0
July 31-August 28, 1958
Chloride, sulfate, nitrate, organic material
66
3
COMPOSITION AND PROPERTIES
Although the number of observations is comparatively small and also unevenly distributed, the results are of importance since very little is known about the composition of aerosols at sea. The results published by Junge are summarized in Table VII. From the concentrations measured in Florida, only the values with sea breeze were included. The figures give the average concentrations of the various components in micrograms (10- 6 gm) per meter" of air. The figures in parentheses are the average limits of detection. Their meaning is as follows: When a component did not show up in the analysis, it can only be said that it was not present above the limit of detection, which depends on the component and on the size of the sample in question. When the averages were computed, this limit of detection was taken in those cases in which the relevant component was too small to be determined by the analysis. Thus maximum values were obtained. The difference between the average value and the average limit of detection is the minimum value. Should both figures be equal, nothing was found above the limit of detection. Lodge and his colleagues published their findings in the form of a cumulative frequency distribution of analyzed components which is reproduced in Fig. 12. All results refer to sea level. The following information can be taken from Table VII and Fig. 12: NH4 was confined almost completely to large particles. That its amount was small, particularly in Hawaii, clearly indicates its continen tal origin. N03 was concentrated predominantly in giant particles. Its amount decreased with increasing maritime influence (Florida -+ Hawaii). This would point to a continental origin. On the other hand, Junge found N03 concentrations even lower than those measured in Hawaii in the giant particles of purely continental air masses on the east coast of the U.S.A., the nitrate also being concentrated in giant particles here. In this region the highest concentrations belonged to maritime air masses, while cities and industrial areas did not contribute substantially to the N03 amount. Junge finally arrived at the tentative conclusion that N03 might be formed by the oxidation of N02 to N03 when sea-salt nuclei mix with continental air masses, thus confining the source of N03 to coastal areas. This result requires further investigation. On some days the samples from Florida were also examined with regard to N02. No trace was found above the limit of detection. Referring to similar results at other continental places, Junge states rather definitely that no N02 is present in natural aerosols.
TABLE VII COMPOSITION OF MARITIME AEROSOLa, Place, kind, and number of data
Florida Average value Average limit of detection Number of values Hawaii Average value Average limit of detection Number of values a b
b
NH1
NO;
Cl-
Large Giant particles particles
Large Giant particles particles
Large Giant particles particles
SO~-
0.057 <0.034 0.034 0.034
0.033 0.033
0.33 0.033
0.041 0.038
2.35 0.038
7
7
7
7
7
0.026 0.022
0.064 0.022
0.093 0.038
4.96 0.038
7
0.026 < 0.021 0.021 0.021 14
14
14
After Junge (1956). Average concentration in micrograms per cubic meter.
14
10
10
Na+
Large Giant particles particles
<0.32 0.32 7 <0.31 0.31 10
Large particles
Giant particles
0.37 0.32
0.074 0.044
1.26 0.044
7
7
7
0.79 0.31 10
68
3 7.0
COMPOSITION AND PROPERTIES
0
o
5.0
~
Chloride Sulfate Nitrate ( 1958 only)
3.0 2.0
r<)
E
<, Cl
:l
C 1.0
o .~ 0.7
"E
fl 0.5 c:
o
U
0.3 0.2 O.I
L...JL---l---l:J!!::.-...L.-....I-....I-...L.-.l...-.l.-..L.---1..---.JL---L.....J
I 2
5
10 20 30405060 70 80 90 95 9899
Per cent of samples with less than stated concentration FIG. 12. Composition of maritime aerosol; cumulative frequency distribution of concentrations of chloride, sulfate, and nitrate. (From Lodge et al., 1960.)
The CI content of the large particles was very small and, therefore, the sea salt was almost completely confined to the giant particles. On the whole the CI content surpassed the amount of nitrate generally by about one order of magnitude, in accord with the findings of Lodge and his colleagues. At Hawaii the CI concentration in both the large and the giant particles was higher than in Florida owing to the more pronounced maritime conditions there. These greater CI values permit the enhancement of our knowledge of the size distribution of seasalt nuclei which, as was shown in Section 3.2.2.2, is comparatively poor with regard to large particles. From his Hawaiian values Junge was able to draw the conclusion that the average CI concentration of the large particles was 2.23 per cent of that of the giant nuclei, if only those values were used where the CI concentration of the large particles was above the limit of detection. The total average amounted to ~ 1.56 per cent. Thus, according to Junge, only about 1 per cent of the total mass of sea salt produced by the sea surface can be found in the large particles (with radii ~ 8 x 10- 5 ern). This important
3.3
CHEMISTRY OF THE MARINE ATMOSPHERE
69
contribution of air chemistry toward revealing the nature and origin of atmospheric nuclei at sea has only been proved true for the trade-wind zone, but Junge believes that it may also be valid for other oceanic regions. Thus a discrepancy seems to result between these findings and those of Mason (l957b) who-stated that (see Section 3.2.2.6) it is by the bursting of a bubble at the sea surface-apart from the giant nuclei generated in phase (2)-that large particles are produced during phase (1). Considering, however, that these large particles consist of surface film material it may well be that their Cl content is small compared with that of the giant nuclei originating from a layer slightly deeper. This subject will be touched upon below. On the whole, the result reported by Junge confirms the statement of Mason (l957b) that by far the greatest part of the condensation nuclei distributed over land and sea is not of maritime origin but must be supplied from the continents. Perhaps it is worth mentioning that Junge also made measurements on the slopes of the volcano Mauna Kea (Hawaii) at an altitude of 2900 meters, which is well above the inversion layer. To avoid contamination from lower levels the air samples were only taken during the night. No Cl above the limit of detection was found there, neither with large nor with giant particles, whereas NH4 clearly predominated. This indicates that the condensation process within the orographic clouds had removed all sea-salt nuclei and that the particles in the subsiding air mass above the inversion were not of maritime origin. No detectable amounts of S04 were obtained with large particles. For giant nuclei, the values of Junge show a distinctly lower S04 concentration than that of CI, and an increase in S04 with enhanced maritime influence (Florida --+ Hawaii). The observed S04 content for Hawaii agrees satisfactorily with the value calculated from the CI concentration in accord with the composition of sea water. Contrary to Junge's findings Lodge and his colleagues report the surprising result that on the ocean station November sulfate levels were generally higher than those of chloride as shown in Fig. 12. Up to now no satisfactory explanation has been given for this discrepancy. With regard to the Na concentration, Junge found that the CljNa ratio in maritime air, as determined from the chloride and sodium values measured in Florida, equaled, within the limits of accuracy, that of sea water. This result may be of meteorological importance if compared with CljNa ratios measured in air or rain water at other places. Organic material was verified by Lodge et al. to a mean level of about 1.6 fLgjmeter 3 • This amount could be produced if a monolayer
70
3
COMPOSITION AND PROPERTIES
of organic matter were present on the sea surface and engaged in the formation of the aerosol. In connection herewith there should be mentioned Wilson's (1959) and Oddie's (1960) papers on the nature of the very thin upper surface layer of the sea. In trying to explain why organic nitrogen occurred in New Zealand snows, Wilson suggested that the surface film of the ocean might be enriched in potassium, ammonium, organic material, and organic nitrogen, in a way that we will not discuss here. These materials could be carried into the air by bursting bubbles in whitecaps (as described in Section 3.2.2.6) thus contributing to the maritime aerosol and, consequently, to the composition of rain water and snow falling on countries influenced by maritime air masses. Wilson was able to establish a relationship, expressed by KINa ratio and nitrogen concentration, between ocean foam and snow water which is strong evidence in favor of their common origin. This result was confirmed by Oddie, who differentiated between "coarse spray," produced during phase (2) of the bursting of an air bubble in sea water (see Section 3.2.2.6) and, therefore, originating slightly below the surface film, and, on the other hand, "fine spray," which is formed during phase (1) from the top film of bubbles bursting at the sea surface and which will consist, therefore, of particles from an extremely thin surface layer. He could show that the "fine spray" contained a much higher proportion of potassium (Na/K ratio about 6) than that of sea water (Na/K ratio = 28), whereas the "coarse spray" had a Na/K ratio of 24, which is close to the latter.
3.3.2 Gaseous Traces The sources of information are the same as mentioned at the beginning of Section 3.3.1, as those investigations comprise results of simultaneous measurements of particulate matter and gases. Junge (1956, 1957b) determined the concentrations of the gaseous equivalents of the following aerosol components: NH3, nitrogen oxides, chlorine components, and S02. Lodge et al. (1960) studied N02, CO, S02, and ozone. The results published by Junge are summarized in Table VIII. Owing to some difficulties arising during the analysis, all values must be regarded as minima. Comparing Tables VII and VIII we realize that for NH3, nitrogen oxides, and S02 the gas concentrations are considerably higher-mostly about 10 times or more-than the corresponding values for particulate matter. Only for Cl are the concentrations of the same order of magnitude.
3.3
CHEMISTRY OF THE MARINE ATMOSPHERE
71
TABLE VIII AVERAGE GAS CONCENTRATIONS MEASURED IN MARITIME Place, kind, and number of data
NHa
Nitrogen oxides
Florida Average value Average limit of detection Number of values
5.7 0.3 7
2.25 0.3 7
Hawaii Average value Average limit of detection Number of values
2.45 0.3 14
3.90 0.3 14
a b
AIRa,b
Chlorine component
S02
2.23 0.25 7
3.35 0.3 7
1.92
1.10 0.3 14
0.3 14
After Junge (1956, 1957b). Concentrations given in micrograms per cubic meter.
The differences in gas concentrations between Florida and Hawaii are not uniform. While there is not much difference in CI, the concentrations of NH3 and S02 in Hawaii are about half as high as those observed in Florida. On the other hand, nitrogen oxides measured in Hawaii surpass the Florida values. As regards the results given by Lodge et al. it should be mentioned that the natural levels of all gases measured, except ozone and S02, were found to be below the limit of detection. The measured concentrations of S02 fall into the range of Junge's values. The daily fluctuations of these concentrations were small for NH3, nitrogen oxides, and S02; they showed no correlation with weather phenomena. The variations of CI were stronger and seemed to coincide with those of the giant particles. One interesting feature was the fact that the NH3 concentration near sea level was higher than the amount measured on the volcano Mauna Kea at 2900 meters and also higher than the equilibrium concentration calculated from the pH values and the NH3 content of sea water. To remove this discrepancy we are again forced to assume the existence of a thin film of organic decomposition products on the sea surface, which releases NH3 into the air as well as, to some degree, into the sea. From the pronounced preponderance of the gases over the aerosols we may draw the important conclusion that, in maritime regions, air
72
3
COMPOSITION AND PROPERTIES
chemistry is largely governed by the gaseous substances. Up to now there has been no confirmation that the relevant results reached in Hawaii and Florida hold true also for other maritime and continental areas. If convincing evidence should be given for this, however, the gas traces could then be considered as the primary sources of the corresponding substances in the particles, with the exception of the CI and S04 components produced by sea spray. Presenting the possible implications of this fact for meteorology and atmospheric chemistry would, however, exceed the limits of this monograph. 3.3.3 Carbon Dioxide Content 3.3.3.1 Meteorological Significance. Here it is difficult to make a distinction between maritime and continental aspects since most of the investigations, particularly the older ones, deal with the carbon dioxide content on a global scale, summarizing all available data. It is only recently that more detailed information on geographical distribution and regional aspects has been brought out. Since however, the most inherently interesting problem, namely that of the secular change of CO 2 concentration, requires global consideration with particular emphasis on those regions, such as the oceans, where the disturbing influences of industry and vegetation are small, involving also the CO 2 exchange between ocean and atmosphere, we feel that a more general treatment will serve the maritime purpose best. Although the CO 2 content of the atmosphere is comparatively small [about 0.03 per cent or 300 ppm (parts per million) by volume], it has an important influence on world climate, as the outgoing infrared radiation from the earth's surface is partially absorbed in the lower atmosphere by CO 2 and water vapor, thus causing an increase in air temperature. This so-called "greenhouse effect" may be of particular importance with regard to the observed long-range climatic changes. For this reason attention has been given to possible long-term variations of atmospheric CO 2 content. Such investigations were favored considerably by the fact that control of the CO 2 content has been tried by measurement since the early 19th century. An examination of these numerous data, such as that done by Fonselius et al. (1956) (Fig. 13), shows a considerable scatter which may be attributed partly to the rather crude and heterogeneous techniques of analysis used in former years and partly to geographical, local, or seasonal effects. 3.3.3.2 Callendar Effect. Those values to which sufficient reliability could be attributed were used by Callendar (1958) to discuss again
550
CO2
ppm
i
500
450
Iillt~VTl
DUE."ST
400
"'~".
:s.
350
300
1800
1810
18Z0
1830
1840
1850
1860
1870
1880
1890
1900
1910
19Z0
1930
1940
19:50
FIG. 13. Mean values of carbon dioxide measurements from 1800 to 1956. (From Fonselius et al., 1956.)
1960 --+ ,eor,
74
3
COMPOSITION AND PROPERTIES
the possibility, already investigated by him in 1938, of whether there has been a trend for the C02 content of the atmosphere to rise since 1900 which may be ascribed to industrial combustion of fossil fuel. His diagram, which is reproduced in Fig. 14, contains, in addition to the observations, a curve representing the CO2 increase in the whole atmosphere due to fossil fuel consumption (computed with 1 ppm CO 2 equal to 8 x 109 tons), supposing that no losses to other CO 2 reservoirs occurred. This "fuel line," which conforms rather well to the observed values, shows an increase of C02 content of 12 per cent between 1900 and 1956. 1880
1920
1900
1940
1960
320
320 E
E a.
a. a. 300
300 a.
N
o
---~----------th
U
19 century bose value of 290 ppm
280
1870
1890
1910
1930
ON U
280
1950
Year
FIG. 14. Amount of carbon dioxide in the free air of the North Atlantic region. (From Callendar, 1958.)
Unfortunately, in natural science good agreement is more often a cause for suspicion than for satisfaction. That is exactly the case here. At first sight, the result seems to offer a rather satisfactory explanation of the observed increase of atmospheric C02 content. Upon closer consideration, however, it gives rise to a number of difficult problems concerning both the reliability of the CO 2 measurements and their relation to the "fuel line." These questions can be touched upon only briefly in the following: (a) The values used by Callendar are confined to the North Atlantic region and can probably not be considered representative for the whole atmosphere. Buch (1948) has already shown that there are considerable differences in CO 2 content between air masses of different origin, extreme arctic air having the least CO 2 content and continental and tropical air the most.
3.3 CHEMISTRY OF THE MARINE ATMOSPHERE
75
These findings were confirmed more recently by the Scandinavian C02 measurements, which were gained by a network of sampling stations (Fonselius et al., 1956). These data indicated that the variations of carbon dioxide content with the origin of the corresponding air masses were such that CO 2 could possibly be used as an additional diagnostic element in synoptic meteorology. Even differences of 10 per cent occurred across a well-developed front. Therefore, averaging single measurements in limited areas appears to be a most questionable procedure if representative values for the whole atmosphere are desired. A recent statistical analysis of observational data on atmospheric CO 2 concentration published by Bray (1959), who used a variety of comparative techniques, indicated, however, an increase in measured C02 for most comparisons during the past 100 years, thus confirming the relevant assumption of Callendar. (b) The complete neglect of the exchange with other CO 2 reservoirs (ocean, biosphere, soil) seems to be a doubtful simplification, particularly as regards the oceans, whose C02 capacity is about 60 times greater than that of the atmosphere. Reference should be made here to the laboratory measurements of Hanya and Ishiwatari (1961), as well as in particular to the field observations published by Buch (1948) and Callendar (1958), who reported C02 fluxes from atmosphere to sea in polar air in high northern and southern latitudes, and to the recent measurements of Takahashi (1961), who found that in the Atlantic Ocean the sea water is absorbing C02 from the atmosphere north of the equator and south of 40° S, whereas the ocean is releasing CO 2 into the atmosphere between the equator and 40° S. (These results were obtained during summer in the southern hemisphere.) A paper of Dingle (1954) also may be mentioned in this respect. He computed an approximate distribution of carbon dioxide exchange rates between the atmosphere and the North Atlantic Ocean assuming a constant CO 2 content in air. The partition of the C02 released by artificial fuel combustion between atmosphere and ocean will largely depend on the rate at which the excess amount of CO 2 in the atmosphere is transferred to the ocean and also on what part of the ocean is engaged in the CO 2 exchange. This will be discussed later on. 3.3.3.3 Result of IG Y Measurements. In order to overcome the difficulties mentioned under (a) in the preceding section a coordinated effort was made during the International Geophysical Year and the following International Geophysical Cooperation in 1959. Regular
76
3
COMPOSITION AND PROPERTIES
carbon dioxide determinations were performed in parts of the world far from industrial regions and also far from densely vegetated areas in order to avoid local effects from contamination and assimilation. The recording stations were located on arctic ice floes, in Hawaii, California, and Antarctica. They were supplemented by aircraft flights and ships' cruises in the North and South Pacific Oceans, as may be seen in Fig. 15 which was taken from a preliminary report by Keeling (1960). ICE FLOE STATIONS
SOUTH POLE (3000m)
FIG. 15. Stations, as well as ship and aircraft tracks, for sampling atmospheric carbon dioxide during the International Geophysical Year and its extension. (From Keeling, 1960.)
The results given therein are very interesting and informative. They are summarized in Figs. 16 and 17. A distinct and regular seasonal variation in C02 concentration dominated in the northern hemisphere showing an increase in the annual range from south to north. Contrary to these findings, there was no indication of any annual cycle
3.3
CHEMISTRY OF THE MARINE ATMOSPHERE
77
in the data from the southern hemisphere. Keeling attributed the seasonal variation to influences coming from the activity of land plants. Some evidence for this was found by comparing the changes in isotopic composition of CO 2 with those in concentration. This interpretation was supported by the fact that the maximum C02 concentration appeared in spring at the beginning of the growing season whereas the minimum concentration was close to the end of it, thus pointing to a hemispherical effect of assimilation. The difference
315
• MAUNA LOA IIAIRCRAFT (HIGHER AIR TEMPERATURE) • AIRCRAFT (LOWER AIR TEMPERATURE) o ICE FLOE STATIONS
A
C02 CONC
(ppm)
/f),\ /f), \
~//
t/II,
1
ne
I
/tl it/
•
FIG. 16. Variation in the concentration of atmospheric carbon dioxide in the Northern Hemisphere. (From Keeling, 1960.)
f), OOWNWIND CRUISE • SOUTH POLE
ns
o LITTLE AMERICA
C02 CONC
( ppm) 310
9101112123
/951
/958 MONTH AND YEAR
FIG. 17. Variation in the concentration of atmospheric carbon dioxide in the Southern Hemisphere. (From Keeling, 1960.)
78
3
COMPOSITION AND PROPERTIES
between the northern and southern hemispheres in the coverage of land masses by vegetation may account for the fact that no seasonal variation occurred in the southern half of the globe. The seasonal variation obtained by Keeling refers to regions predominantly maritime and differs considerably from relevant results gained in continental areas, as may be gathered, for example, from the investigations of Palmquist (1892-1893), Fonselius et al. (1956), and Bischof (1960). In northern Europe the annual cycle of CO 2 concentration is changing from year to year, the average curve for 195559 showing two maximum and two minimum values. This, however, refers only to the near-surface layer of the atmosphere. In the upper air, i.e., at heights between 1000 and 3000 meters, agreement was found between the maritime data given by Keeling (1960) and the C02 measurements made over Scandinavia (Bischof, 1962). In investigating the trend from year to year by means of the Pacific values, Keeling found that the averages showed a rising tendency, which over the North Pacific appeared to be between 0.5 and 1.2 ppm per year, while at the South Pole a rate of about 1.3 ppm per year was observed. This value agrees rather well with the annual increase that could be expected at present if the "fuel line" (Fig. 14) would hold. But considering that the seasonal variation obtained in the northern hemisphere is several times larger than the rate of annual increase, Keeling concluded with caution that the influences producing the large seasonal variation might also have caused a rising annual trend in spite of a reducing oceanic effect. On the whole we may say that the new data from undisturbed sea areas show a certain tendency to confirm the CO 2 values used by Callendar for the foundation of his hypothesis. Additional information is furnished by similar investigations in the Atlantic Ocean. From measurements during a ship's cruise between 35° Nand 60° S in 1957-58, and from samples taken in the northern North Atlantic Ocean between Newfoundland and Greenland in 1959, Takahashi (1961) deduced an average atmospheric C02 concentration of 316.3 ppm with a standard deviation of 3 ppm. The individual analyses ranged from 306 to 324 ppm. No significant difference in the CO 2 content existed between the oceanic air masses over the North Atlantic and the South Atlantic. The CO 2 concentration was found to be slightly higher ('" 320 ppm) in the lower latitudes than in the higher ones. This trend could be correlated with the C02 exchange between ocean and atmosphere. In general the partial pressure of CO 2 in the surface layer of the sea was high in warm water and lower in cold water, the differences being caused not only by the
3.3
CHEMISTRY OF THE MARINE ATMOSPHERE
79
varying water temperature but also by changes in the pH and by biological activities. As was already mentioned in Section 3.3.3.2 the partial pressure of C02 in the sea exceeded that in the air between the equator and 40° S in the summer months of the southern hemisphere, resulting in a CO 2 transfer from the ocean to the atmosphere in these regions, which explains the increase of the atmospheric CO 2 content observed in the lower latitudes. Combining his results with other data (Keeling, 1960, among others), Takahashi (1961) estimated the total amount of atmospheric C02 to be 0.477 gm cm-2 or 2.41 x 1018 gm. 3.3.3.4 Suess Effect. A new and independent method of determining the amount of CO 2 brought into the atmosphere by the combustion of fossil fuel was applied by Suess (1953), who measured the content of radiocarbon (0 4 ) of annual tree rings from the middle of the 19th century and compared it with the 0 4 content of the youngest annual rings in trees recently felled. Since the C02 originating from combustion of fossil fuel is free of 04, the 20th century wood will show a lower specific activity than the samples from 100 years ago, which contain only assimilated C02 from the former "natural" C02 reservoir of the atmosphere characterized by an equilibrium between production and decay of 0 4 • In this way it is possible that, by comparison of the measured C14 activities of the two samples after they have been corrected for the C14 decay by normalizing to equal age, the amount of atmospheric C02 originating from the combustion of fossil fuel may be determined. The values for man-made CO 2 increase in the atmosphere gained by measuring the depression in 0 4 (Suess effect) of annual tree rings up to 1956 range between 0 and 4 per cent of the total CO 2 content (Revelle and Suess, 1957; Arnold and Anderson, 1957). The average is about 2 per cent, or even 1 per cent if estimated globally, which is considerably lower than the estimate of 12 per cent taken from Callendar's fuel line (Fig. 14). 3.3.3.5 Exchange of C02 between Ocean and Atmosphere. Now there arises the difficult question of whether or not the two contradictory results concerning the atmospheric CO 2 originating from fossil fuel combustion are compatible. In order to solve the problem of this discrepancy it is essential to consider the exchange between the different CO 2 reservoirs in nature, particularly between ocean and atmosphere, as has already been indicated under (b) in Section 3.3.3.2. This subject has attracted much interest during recent years and, although no final result has been reached so far and further investigation is indispensable, a short review of the major aspects and results would appear to be useful.
80
3
COMPOSITION AND PROPERTIES
While the dissemination of CO 2 within the atmosphere and the ocean is chiefly governed by turbulent mixing, the transport of that substance across the air-sea interface is a diffusion process which essentially depends on the tension or partial pressure of CO 2, both in air and in sea water. In the case of equilibrium, these two partial pressures are proportional to each other. Carbon dioxide dissolved in the ocean is present in the following four forms: U ndissociated CO 2 and H 2COa 2 Dissociated HCO; and C0 aThe total CO 2 content is composed of the concentrations of all the forms mentioned above. The portion of physically dissolved C02 is very small, however. On the average, 99.4 per cent of the total C02 concentration in sea water consists of ionic components, the amount of the molecular species being only 0.6 per cent. The partial pressure of C02 in the sea is determined by the molecular components CO 2 and H 2COa alone. It varies considerably both with the sea temperature and with the total CO 2 content as was experimentally demonstrated by Kanwisher (1960). He found that a 10 per cent increase in partial pressure was produced by a 0.6 per cent increase in the total CO 2 content. A theoretical analysis of the physical and chemical processes responsible for the exchange of carbon dioxide between air and sea was given by Bolin and Eriksson (1959) and Bolin (1960). By referring to the fact that the concentrations of HCO; and C02a- and, consequently, the total C02 content are controlled by that of un dissociated C02 and H2COa, as well as by the hydrogen ion concentration, and by assuming that the alkalinity, i.e., the concentration of the cations which balance the charges of HCO; and C02a-, remains constant, they showed that any increase of atmospheric CO 2 will generate a proportional increase in the concentrations of CO 2 and H2COa molecules and also change the pH value in the sea, thereby decreasing the dissociation and enlarging the portion present in the molecular species. The effect of this variation in the pH value is that a 12.5 per cent change in the atmospheric C02 would only require a I per cent change in the total C02 content in the sea in order to maintain equilibrium. (Here, the influence of temperature was not considered.) So, with respect to C02, the buffering capacity of the sea is comparatively low. The effect of this peculiar mechanism on the C02 exchange between ocean and atmosphere was first indicated in a paper by Revelle and Suess (1957), who attempted to explain the Suess effect and arrived at the conclusion that the average life time of a
3.3
CHEMISTRY OF THE MARINE ATMOSPHERE
81
C02 molecule in the atmosphere, before it is transferred to the sea, is of the order of 10 years. The amount of CO 2 released into the atmosphere by fossil fuel combustion up until 1956 was estimated from this value to be about 3.9 per cent of the total atmospheric C02 content, which means that most of the carbon dioxide originating from that artificial source must have been absorbed by the oceans. Similar values were derived by Arnold and Anderson (1957). These studies are, however,not entirely satisfactory because a well-mixed reservoir was used as a model of the sea, and this does not comply with our knowledge of the vertical structure of the oceans (Bolin and Eriksson, 1959; Kanwisher, 1960). A better approximation to reality was attempted by Craig (1957), and later by Bolin and Eriksson (1959), who introduced a two-layer model of the ocean that consisted of an upper mixed layer and the deep sea. The first one, located above the thermocline, has direct contact with the atmosphere and comprises about [hI of the total sea. It contains only slightly more C02 than there is in the atmosphere. Bolin and Eriksson, by applying their findings on the mechanism of the CO 2 exchange to the two-layer ocean model, arrived at the following results (which are quite insensitive to variations of the vertical division of the ocean): The net increase of atmospheric C02 which is due to fossil fuel combustion depends very little on the rate of exchange between the atmosphere and the upper mixed layer. This is caused by the fact that the upper mixed layer of the ocean, owing to its small buffering capacity, needs to absorb only a relatively small amount of CO 2 in order to regain equilibrium. Of more importance for the net increase of CO 2 in the atmosphere is the rate of turnover of the deep sea. If the residence time of deep sea water is assumed to range from 200 to 1000 years, the net increase of atmospheric CO 2 varies from 8 to 11.5 per cent. These values are in fair agreement with Callendar's empirical results. There remains the question of how the ratio 0 4/02 is affected by this mechanism of CO 2 exchange. Since a comparatively large increase of CO 2 content in air by inactive CO 2 is connected with a small one in water, the consequence will be that the 0 4/02 ratio of the sea is considerably higher than that of the atmosphere, resulting in a transfer of C14 from the sea to the atmosphere which will tend to decrease the Suess 'effect. Assuming that the residence time for C02 in the atmosphere is 5 years, Bolin and Eriksson (1959) obtained 4-6 per cent for the Suess effect (in 1954) if the rate of turnover in the deep sea ranges between 200 and 1000 years. These values are somewhat larger than the empirical ones, particularly if a long residence time in the
82
3
COMPOSITION AND PROPERTIES
deep sea is assumed. The remaining discrepancy requires further investigation. In the light of this knowledge, the increase of atmospheric C02 of about 12 per cent since 1900, as reported by Callendar (1958), and ascribed by him to the combustion of fossil fuel, may be compatible with a Suess effect of only a few per cent. Bolin and Eriksson (1959) consequently arrived at the conclusion that most of the C02 increase since 1900 must still be in the atmosphere. A precise assessment of the long-term development seems difficult, however. It is not only the consideration of the long-term processes in the deep sea that introduces problematic factors but also that the C02 exchange with the biosphere is not very well known and may playa more important role in the changes of atmospheric C02 concentration than has hitherto been assumed. Bolin and Eriksson (1959) tried to take these uncertainties into account in estimating the changes of atmospheric C02 during the remainder of the 20th century. They obtained + 25 per cent for the most likely value of the net increase of atmospheric C02 in the year 2000, the maximum possible being + 40 per cent. These computations were based on United Nations estimates of CO 2 added to the atmosphere by consumption of fossil fuel (Revelle and Suess, 1957). Certainly, the regular measurements of CO 2 content which are now under way in areas far away from industrial activity will prove in due course whether the computations mentioned above reliably describe the "large-scale geophysical experiment that human beings are now carrying out" by "returning to the atmosphere and oceans the concentrated organic carbon stored in sedimentary rocks over hundreds of millions of years" (Revelle and Suess). 3.3.3.6 Temperature Variations in the Atmosphere Caused by Changes in C02 Concentration. After the main problems connected with the carbon dioxide content in the marine atmosphere have been dealt with, there remains one last question that is meteorologically important. What will be the effect of the increase in atmospheric CO 2 concentration on the temperature of the air? Calculations of the temperature change caused by variations in atmospheric C02 content were attempted several times. The results were all different, which is not surprising if the defectiveness of the basic data and of the computing method is considered. Arrhenius (1896), for example, arrived at a temperature increase of 6°C if the C02 amount were doubled, whereas Callendar (1938) obtained an increase of only 2°C. More recent calculations were made by Plass (1956, 1961),
3.3
CHEMISTRY OF THE MARINE ATMOSPHERE
83
who computed the upward and downward radiation flux in the region of the 15-fL C02 band for intervals of 1 km taken from the surface of the earth to an altitude of 75 km and for three different CO 2 concentrations. No other changes than those in CO 2 content were assumed. He found a rise of the surface temperature of 3.6°C if the C02 amount were doubled and a decrease of 3.8°C if the CO 2 concentration were halved. These values refer to clear-sky conditions. The presence of clouds would tend to decrease the figures given above. The problem of the influence of CO 2 variations on the atmospheric heat balance was re-investigated by Kaplan (1960, 1961), who calculated net fluxes of radiation in the 15-fL C02 band at the level of 100 mb and at the bottom (1000 mb) of the atmosphere under various conditions, including differing cloud heights. Here the error due to the truncation of the atmosphere at 100 mb was found to be very small. The detailed structure of the relevant infrared bands and its dependence on the thermal state of the atmosphere were taken into account. The temperature of the ground was assumed to be equal to the temperature of the adjacent air. The calculated radiation fluxes appeared to be more sensitive to the thermal structure of the atmosphere than to variations of the C02 concentration. For average cloudiness conditions Kaplan found that halving the C02 content would result in a surface temperature decrease of 1.8°C which would be further diminished if the influence of water vapor, which was neglected, were taken into account. Considering that Plass used his clear-sky estimate of 3.8°C, which corresponded to the halving of the CO 2 content, for his discussion on climatic change induced by CO 2 variation, Kaplan arrived at the conclusion that the value given by Plass is too high by a factor of 2 or even 3. According to Kaplan a variation of 10 per cent in atmospheric CO 2 concentration would cause a change of only 0.25°C in the surface temperature. Suitable comparative values of air temperature at the surface have been published recently by Callendar (1961). He investigated the secular change of air temperature for different regions of the earth and, for example, obtained an increase of about 0.4°C for the northern temperate zones when comparing the averages for the 30-year periods 1891-1920 and 1921-1950. According to Plass (1956) this would require a corresponding increase of atmospheric C02 of 7 per cent, which compares rather well with the C02 observations that, in the European region, show an increase of approximately 6 per cent over the period in question (Fig. 14). However, in view of the difficulties inherent in the atmospheric C02 problem too much stress
84
3
COMPOSITION AND PROPERTIES
should not be laid on this agreement. In addition, Callendar (1961) presented some evidence that, in the tropical latitudes and in the southern temperate zones, the temperature increase over the time period mentioned was considerably smaller than in the northern hemisphere. This result might be attributed to a large, but still rather uncertain, time lag in the transport of excess C02 from its main production area, the middle-northern latitudes, across the equator into the mostly maritime southern hemisphere. Hence the recent climatic trends over the earth do not seem to be incompatible with the C02 hypothesis. 3.4
ELECTRICITY AND RADIOACTIVITY IN THE MARINE ATMOSPHERE
3.4.1 Electric Quantities Concerned A treatment of the composition of the marine atmosphere would not be complete if attention were not given to the phenomena of atmospheric electricity connected thereto. Because of the fundamentally electric nature of all matter, a number of thermodynamic processes occurring over the oceans are accompanied or influenced by electric phenomena, which is particularly the case with the formation of clouds and precipitation as well as with the development of thunderstorms. Apart from its importance for meteorological processes at sea, the electricity in marine air is also of general interest since the corresponding measurements will reflect conditions which are not disturbed by atmospheric pollution and, therefore, may be considered as natural. The chief characteristics of atmospheric electricity are the following: (a) The existence of an electric field between the two conductors earth and ionosphere, which together may be regarded as a spherical condenser. (b) The presence of charged particles, called ions, in the space between the two conductors. During fine weather the electric field is represented by an electric potential V which increases with height z. The field strength E= -dVjdz
(3.1)
is negative, or the potential gradient dVjdz is positive under such conditions; their absolute values decrease with altitude. The ions can be subdivided into small and large ions according to their nature, size, and mobility, as has already been indicated in Table III.
3.4
ELECTRICITY AND RADIOACTIVITY
85
A small ion comprises a group of molecules clustered around a single ionized molecule and kept together by the charge. If the charge gets lost, the congregation of molecules dissolves and no trace of it remains. The small ions have mobilities of between I and 2 em/sec per volt/centimeter. Large ions, however, are from about one to two orders of magnitude greater than small ions. As may be seen in Table III they are of about the same size and kind as the Aitken nuclei. Their radii range from 10- 7 to 10-5 ern. If their charges are removed they continue to exist as uncharged nuclei. Their mobilities are, of course, much smaller than those of the small ions. They vary between 3 x 10- 4 and 8 x 10- 3 em/sec per volt/centimeter (Chalmers, 1957). The direction of the electric field in fine weather causes a flow of positive particles toward the earth, to which, therefore, a negative charge must be ascribed. Since neither a neutralization of the earth by such advection of positive particles nor a diminution of the described air-earth current is observed, sources of supply must exist somewhere. Such ionizing agents may be found in cosmic rays and in radioactive matter present in atmosphere and earth. However, the mechanism which maintains the negative charge of the earth in spite of the advection of positive particles during fair weather has presented a formidable problem for the science of atmospheric electricity. There is some evidence (Gish, 1951) indicating that the supply current which seems necessary to compensate for the loss of negative charge by the earth may be connected with thunderstorm activity. If it could be proved beyond any doubt that the supply current is generated in thunderstorms, important progress would have been achieved, i.e., the fair-weather aspects of atmospheric electricity and the electric phenomena in disturbed weather, which have not been related so far, would be combined into a unified presentation of atmospheric electricity. The electric quantities and the problems outlined above will now be considered with a view to their maritime aspects. Measurements of electric quantities in the marine atmosphere are difficult, chiefly because of the disturbance originating from the ship and its movement. Consequently, reliable values are not very numerous. The main sources of information are the data collected during the cruises of the research vessel Carnegie in 1915-21 and 1928-29 (Mauchly, 1926; Torreson et al., 1946). More recently, measurements were gained by Ruttenberg and Holzer (1955) during Operation Capricorn, a five months' geophysical marine expedition to the central Pacific undertaken on the research vessel Horizon. Coastal conditions were studied by Miihleisen (1959, 1962).
86
3
COMPOSITION AND PROPERTIES
3.4.2 Ions in the Marine Atmosphere Some very general information on ions has already been given in the preceding introductory section. These data will now be supplemented by special information available on ions in the marine atmosphere. 3.4.2.1 Production and Destruction of Ions. At first we shall deal with small ions. According to Wait and Parkinson (1951), cosmic radiation can be considered as the chief ionizer in the marine atmosphere. Radioactive matter may be assumed to be negligible as an ionizing agent over the oceans, since its amount was found to reach only 1-2 per cent of the average continental value (see Section 3.4.6). Measurements of cosmic rays, in terms of ion pairs per centimeterper second, were made during the cruises of the Carnegie in the Atlantic and Pacific Oceans (Torreson et al., 1946). The result was that on the average 1.4 ion pairs per centimeters per second were produced in the atmosphere near the sea surface. There is an indication that the values were slightly larger in high latitudes, especially of the northern hemisphere, as shown by the following data: High northern latitudes: 1.4 or 1.5 ion pairs per centimeter" per second. Low latitudes: from 1.1 to 1.4 ion pairs per centimeter- per second. Southern latitudes: 1.2 ion pairs per centimeter'' per second. For the Pacific Ocean 75 per cent of the data fell within the comparatively narrow range of from 1.1 to 1.6 ion pairs per centimeterper second. Comparing these figures with corresponding values obtained on land (Wait and Parkinson, 1951) we may conclude that over the oceans the production of small ions originating from cosmic rays is about the same as on land. The formation of small ions is balanced by processes of small ion destruction which comprise recombination between small ions of opposite sign, neutralization by combination with large ions, or conversion into large ions by fusion with neutral condensation nuclei. (For detailed information consult Wait and Parkinson, 1951). Although recombination is assumed to be the most important destruction process for small ions in marine air, their interaction with condensation nuclei may cause a considerable deficit (44 per cent) in small ion concentration, as was shown by Torreson et al. (1946). This explanation also serves to outline how large ions may be formed or neutralized. For further details reference is made to Wait and Parkinson (1951). Another possible mechanism of ion production at sea was investigated by Blanchard (1958), who determined the
3.4
ELECTRICITY AND RADIOACTIVITY
87
electric charge and radius of drops that were ejected from a bursting bubble at the sea surface [see Section 3.2.2.6, description of phase (2)]. Such processes can be caused by whitecaps, rain drops, or snow crystals. Drops of from 2 x 10- 4 to 2 X 10- 3 em in radius were found to carry mostly positive charges which contributed to the atmospheric space charge. Similar results were reported by Miihleisen (1959, 1962), whose observations indicated a positive space charge not only above the surf zone but also above the open sea. Since the size of the positive particles observed by Blanchard (1958) is very large and, consequently, their mobility will be very low, it is suggested by the author that, in opposition to fair weather potential gradient and gravity, turbulent and convective forces might carry these positive charges into clouds and even to higher regions, thus providing a supply current of the same order of magnitude as the air-earth current during fair weather. Apart from the very large ions studied by Blanchard it would be promising to investigate the possible charge transport by the minute particles originating from the top film of bubbles bursting at the sea surface [see Section 3.2.2.6, description of phase (1)]. In the marine atmosphere the mean life of a small ion has been estimated at about 5 or 6 minutes; that of a large ion will generally be between 15 and 20 minutes (Wait and Parkinson, 1951).
3.4.2.2 Concentration of Ions. Measurements of either positive or negative small ion content of the marine atmosphere were made, by simultaneously counting Aitken nuclei, during cruise VII of the Carnegie in 1928-29 (Torreson et al., 1946). The mean values were 1776, 522, and 422 per centimeters, respectively, for the nuclei, the positive ions, and the negative ions. The number of the small ions was reduced considerably (by about 44 per cent) by recombinations with each other and by combination with condensation nuclei. After these effects had been allowed for, the corresponding number of large ions of each sign was estimated at about 200 per centimeters which agrees well with later measurements in maritime air on the west coast of Ireland (O'Connor et al., 1961). The fact that the number of positive small ions is greater than that of the negative ones may be ascribed to the repelling effect of the negative charge of the earth ("electrode effect"). When comparing the marine-ion content with values obtained on land we find that, in spite of the much lower production rate at sea, the small-ion concentration is nearly the same in the two regions. On the other hand, the large ions are much more numerous over the
88
3
COMPOSITION AND PROPERTIES
continents than over the oceans. Thus the rate of destruction for small ions is lower at sea than on land, which explains their relatively high number in the marine atmosphere. Sagalyn (1958) published an interesting study on large-ion concentration (and also on other electric quantities); the data presented therein were obtained during a series of aircraft flights over the North Atlantic Ocean. She found the average large-ion content of each sign to be about 300 per centimeter- which corresponds to a total condensation nuclei concentration of 1000 per centimeter", These two values refer to the lower layer of the atmosphere that is in exchange with the sea. The large ion content is in satisfactory agreement with the result of cruise VII of the Carnegie. An interesting feature of the result reported by Sagalyn is how quickly the concentration and physical properties of the pollution particles originating from land were modified by coagulation as the air mass concerned left the American continent and moved out over the Atlantic Ocean. After 2 days the average nucleus concentration at a given level in the exchange layer had decreased to about onefourth of the value observed over land at the same altitude while the mean radius of the particles had increased proportionally. 3.4.2.3 Ionic Mobility. The ratio of the velocity of an ion to the field strength is called the mobility of the ion. Average values for small and large ions were given in Section 3.4.1. Mobilities of small ions in marine air were determined by Torreson et al. (1946) from the simultaneous measurements of ion content and conductivity during fair weather aboard the Carnegie. Although there was a comparatively large scatter for instrumental reasons it could be shown that the mean values may be considered as fairly reliable. For cruise VII the values k ; = 1.30 cm/sec per volt/centimeter
k.:
=
1.39 em/sec per volt/centimeter
were found for the average mobilities of the positive and negative small ions, respectively. Although laboratory experiments indicate that at normal temperature and pressure the mobility of the negative small ion generally is greater than that of the positive one, results may be different under natural conditions owing to the effect of various gaseous compounds and water vapor. So far no measurements have been available on the mobilities of large ions at sea.
3.4
ELECTRICITY AND RADIOACTIVITY
89
3.4.3 Electrical Conductivity 3.4.3.1 Definition. The electrical conductivity due to ionic transport may be defined by (3.2) where e = the electronic charge kc = the ionic mobility tu = the concentration of ions of each type All ions are supposed to carry a single electronic charge. The conductivities attributable to positive and negative ions are ~+ and A_, respectively. The sum A+ + L = A is called the total conductivity or simply conductivity. 3.4.3.2 Local and Temporal Variations. The conductivity values measured on board the Carnegie showed a considerable variation, but a simple dependence of conductivity on position or latitude could not be found. However, evidence was given that there existed a "land effect," characterized by large fluctuations and a clear trend toward . lower values when the ship approached the coast. In Honolulu harbor the average conductivity amounted only to about one-third or one-fourth of the value observed at sea before arrival. The explanation for this apparent paradox is easily given: Owing to pollution there will be a considerable increase of nucleus concentration over land leading to an increased transformation of small ions into large ions of low mobility. Thus electrical conductivity is substantially reduced. For purely marine air over the oceans the tabulation shows the mean values of the total conductivity that were found during the different cruises of the Carnegie (Torreson et al., 1956). A conclusive explanation for the variation observed could not be given. Mean epoch
Mean of total conductivity (10-14Q- 1 meters- 1)
1916.2 1920.8 1929.1
2.4 3.0 2.2
There was indication of a small diurnal variation in both positive and negative conductivity if data from days with least disturbance were selected. The variation of negative conductivity, which was
3
90
COMPOSITION AND PROPERTIES
nearly opposite to that of the positive, showed a mmimum in the morning and a maximum just after local noon. The amplitudes amounted to only 4 or 5 per cent of the mean. Sagalyn (1958), however, observed no regular daily variation when measuring electrical conductivity by aircraft over the North Atlantic. 3.4.3.3 Ratio of Polar Conductivities. The ratio >"+/1'-- of positive to negative conductivity was studied in detail by Torreson et al. (1946). They found a linear increase of the conductivity ratio with increasing values of potential gradient in fair weather. The corresponding data are presented in Table IX. The result is a clear demonstration of the "electrode effect" which was mentioned in connection with differences in concentration between positive and negative ions near the sea surface (Section 3.4.2.2). With increasing potential gradient the repelling force of the negative charge of the earth on the negative ions is augmented, resulting in a decrease especially of the negative conductivity. (Occasionally it is the potential gradient that is influenced by conductivity. With ground fog occurring in warm air over cold water the positive and the negative ions are retained at the upper and lower boundaries of the fog, respectively, resulting in an increase of potential gradient.) TABLE IX MEAN
VALVES
OF
THE
POTENTIAL
GRADIENT.
CORRESPONDING
MEAN
VALVES
OF
POSITIVE AND NEGATIVE CONDUCTIVITY AND THEIR RATIOSa.b
Potential gradient (volts/meter)
102 121 140 158 181 219 269 355 a b
Positive conductivity
Negative conductivity ,\-
,\+
(10- 4 sec'! esu)
(10- 4 sec- 1 esu)
1.20 1.14 1.04 1.12 1.06 0.92 0.52 0.51
1.14 1.06 0.96 0.99 0.89 0.77 0.41 0.35
After Torreson et al. (1946). Data obtained in the Pacific Ocean.
Ratio '\+1'\-
1.05 1.07 1.09 1.14 1.19 1.19 1.28 1.47
Number of observations 18 20 22 27 25 24 10 6
3.4
ELECTRICITY AND RADIOACTIVITY
91
If the linear relation between potential gradient and conductivity ratio were extrapolated back to a potential gradient equal to zero, the conductivity ratio A+/L would be about 0.9. This value would correspond to the case in which the polar ions are equal in number and any difference in conductivity may be attributed to differences in mobility (which is greater for the negative ions as mentioned above). Such conditions should be expected especially in higher levels. In agreement herewith Sagalyn (1958), investigating electrical conductivity over the North Atlantic by aircraft in altitudes from 150 to 4600 meters, found A+/L values varying between 0.77 and 1.18, the average being 0.95. Apart from a greater scatter in higher levels no regular variation of A+/L with height was observed.
3.4.3.4 Vertical Distribution. During the cruises of the Carnegie there was no possibility of studying the variation of electrical conductivity with altitude. However, the measurements of Sagalyn (1958), carried out on aircraft, provided remarkable data on spatial distribution and time variations of electrical conductivity and related quantities over the sea. In particular the results showed that the electrical structure of the marine atmosphere is not as simple as it was previously assumed and that strong relations exist between electrical and meteorological properties and processes. The study was chiefly concerned with air masses which had left the American continent some 40-50 hours before and, by exchange with the sea, had acquired a homogeneous bottom layer extending to about 1500 meters above sea level. In the exchange layer the mean total conductivity was found to be rather uniform, its value only varying between 2.3 and 2.4 x 10- 14 Q-l meter -! with altitudes from 150 to 900 meters. If the exchange layer extended to higher levels a slight increase of conductivity was observed (to about 3.8 x 10- 14 Q--l meter") which changed into a strong and continuous rise when the top of the exchange layer was passed. This vertical increase is caused by manifold influences, such as increase of cosmic radiation, decrease of atmospheric density, and others which will not be discussed here. 3.4.3.5 Columnar and Total Resistance. For some purposes it is convenient to use the electric resistance (rather than the electric conductance) computed for a vertical column of air of 1 ern- cross section. This quantity is obtained by integrating the reciprocal of A from the surface up to the ionosphere if possible. For the marine atmosphere Sagalyn (1958) determined such values using measured
92
3
COMPOSITION AND PROPERTIES
conductivity data up to 4600 meters and computed values above this level, assuming small-ion balance and a negligible pollution content. The columnar resistance r obtained in this way varied during two diurnal series between 1.26 x 1017 and 1.32 x 1017 Q meter-. The average change over a period of 24 hours amounted to about 15 per cent and did not show any regularity. The value obtained is in satisfactory agreement with corresponding computations over land. Thus it may probably be concluded that the columnar resistance is not subject to substantial variation. Considering the values of r mentioned above as representative for the whole earth and neglecting the relatively small portion of the earth's surface where thunderstorms are in action at a given instant, we arrive at an estimate of the total effective resistance R of 200 Q (Gish, 1951). Most of this resistance originates at the lower levels, with the lowest 2 km contributing 50 per cent.
3.4.4. Electric Field in Fine Weather 3.4.4.1 Mean Value, Spatial Variation. During fair weather the electric field of the marine atmosphere is characterized by a positive vertical potential gradient which varies from place to place and from time to time. A primary orientation may be obtained from the tabulation which gives average values for oceanic conditions as computed from the material gathered during the cruises of the Carnegie (Torreson et al., 1946) and of the Horizon (Ruttenberg and Holzer, 1955). Ship
Cruise
Carnegie
IV, V, VI
Carnegie
VII
Horizon
Date
Location
1915-21, All oceans all months 1928-29, North Atlantic, Pacific all months 1952-53, Pacific October-February
Average values (V/meter) 116
132 108
Considering the uncertainties found in the determination of the potential-gradient reduction factors, one cannot draw any conclusions about possible secular changes from the differences observed. The Carnegie measurements indicated a tendency of the potentialgradient value to be about 15-20 per cent smaller in the equatorial
3.4
ELECTRICITY AND RADIOACTIVITY
93
zone than at higher latitudes. As there are no changes in air conductivity with latitude this variation of the near-surface gradient can probably be accounted for by a corresponding increase in the columnar resistance from polar to equatorial regions. The latter is mainly caused by the fact that, owing to the geomagnetic field, the intensity and, therefore, the ionizing effect of cosmic radiation above about 6 km is substantially greater at higher latitudes than at lower ones. Since the potential in the high atmosphere is assumed to be the same everywhere on the earth, the conditions described must result in a diminution of the near-surface potential gradient at low latitudes (Gish, 1951; Israel, 1960). As regards the variation of potential gradient with altitude it is well known from balloon flights and other investigations that the potential gradient decreases with height, which is attributable mainly to the vertical increase of the electrical conductivity. Results of relevant measurements at sea have not become known so far. Special conditions obtain within the first few meters above the sea. Here the "electrode effect," which was mentioned in Sections 3.4.2.2 and 3.4.3.3, and the production of positively charged particles at the sea surface cause an accumulation of positive space charge and, in connection therewith, a pronounced decrease with altitude of the potential gradient. Measurements above the Lake of Constance, reported by Miihleisen (1962), showed that near the water surface the electric field strength was twice as large as at a height of 10 meters. There is little doubt that similar conditions also prevail near the sea surface. This fact and the disturbance caused by the ship render it difficult to achieve representative and comparable measurements of the potential gradient at sea, thus explaining why the values obtained by Miihleisen (1962) for maritime air in coastal waters under fair weather conditions are distinctly higher (around 250 Vjmeter) than those found during the Carnegie cruises. 3.4.4.2 Temporal Variations. The most striking discovery resulting from the Carnegie measurements was the existence of a universal diurnal variation of the potential gradient at sea, first noted by Mauchly (1923). In Fig. 18 there is given an illustration of this result, which was confirmed (with regard to phase and amplitude, but not the absolute values) by the later Carnegie measurements during 1928-29 and also by those made by Ruttenberg and Holzer (1955) on the Horizon during 1952-53. It should be noted that the hourly mean values refer to GMT. The gradient was smallest at about 0400 GMT whereas the maximum was observed around 1900 GMT.
94
3
COMPOSITION AND PROPERTIES
The daily range amounted to 35 per cent of the mean. No diurnal variation was obtained when the same data were arranged as to the hours of the local day. The single period with a world-wide maximum was clearly observed only in undisturbed areas, such as on the oceans. On the continents the diurnal cycle is subject to local effects and, consequently, varies considerably from one place to another. IF
3 160- CRUISES lll,ll,lZl- CRUISE lZlI-----
--. _......- .. _----
FEB-MAR-APRIL
......
GMT
I~
----
2.1
~..=---"'-'"=__.::::-~-~~~
/ ' ----~~~. .4'! /
=~~~~ :~i --~-~--1
..,
;/'
NOV.-DEe-JAN
",------- ....---"
/.'
, ./ - MEAN 120
,,
'-
----- ...-
20-------,..---""'==-=--==----=--"""----
......
IOOi=d..""",-"""",=--,--,---L---,----,----...l-.l.-.l.-.l.-.L-L-L-L-'---.JL--l---L----LJ
FIG, 18. Mean diurnal variation of potential gradient for three month periods from observations made on board the Carnegie, 1915-21 and 1928-29. (From Torreson et al., 1946.)
The universal diurnal change in the potential gradient has been correlated with the variation in the total number of thunderstorms over the whole earth (Whipple, 1929; Krumm, 1962). The implications of this correlation will be dealt with in Section 3.4.5.2. There is also an annual variation of the potential gradient exhibited by the character and amplitude of the universal diurnal variation as well as by the daily averages, which show a maximum in the
3.4
ELECTRICITY AND RADIOACTIVITY
95
months from February to April and a minimum in the months from May to July as may be seen from the values given in the tabulation. DAILY
AVERAGES
OF
FAIR-WEATHER
GRADIENT OBTAINED FROM
POTENTIAL
DATA COLLECTED ON
CRUISES OF THE CARNEGIE
Calendar Months
Daily average (Vjmeter) - Years
1915-21
1928-29
132
139 117 119
2-4 5-7 8-10
102 113
120
11-1
140
Ruttenberg and Holzer (1955) pointed to the noise-like fluctuations which were continuously present in the records of both potential gradient and conductivity and which were very probably related to atmospheric turbulence. This phenomenon was particularly investigated by Mlihleisen (1962), who, in maritime air over coastal waters, found considerable, simultaneous fluctuations of both potential gradient and space charge with periods varying between 2 and 12 minutes. The amplitudes of variation were of the same order of magnitude as the potential gradients themselves. According to Muhleisen (1962) these findings might be ascribed to the influence of turbulent flow on a charge-forming mechanism at the sea surface, which may be provided by the electrode effect or by bubbles of air bursting at the sea surface (Blanchard, 1958), or by the charging of atmospheric nuclei through the process of evaporation. These questions need clarification by further study. 3.4.5 Electric Currents 3.4.5.1 Air-Sea Current. According to the definitions given in Sections 3.4.1 and 3.4.3.1 the electric current density i may be expressed by the following relation:
i = (A+
+ A-)E
(3.3)
Under fair weather conditions or, more precisely, in fair weather areas, E is negative and the current will be an electric convective current from the air to the sea. Using for A and E the mean data
96
3
COMPOSITION AND PROPERTIES
found during the Carnegie cruises and given in Sections 3.4.3.2 and 3.4.4.1 and, adding also the relevant results obtained during the cruise of the Horizon as published by Ruttenberg and Holzer (1955), we arrive at the following average values for the density i of the air-sea convection current: Carnegie 1915-21: 3.1 x 10-12 A/meter2 Carnegie 1928-29: 2.9 x 10-12 Ajrneter'' Horizon 1952-53: 3.4 x 10-12 A/meter2 We gather from these figures that there is no clear indication of any secular change in the air-sea current density during the 37-year period concerned. Looking through the daily series of the Carnegie measurements, however, we recognize that the air-sea current density may vary over a considerable range both with time and with locality. As substantial variations in air conductivity A over the sea were not observed we may expect that the variations of the air-sea current density i will chiefly be caused by those of the potential gradient. It is for this reason, for example, that the diurnal variation of air-sea current density shows an obvious similarity to that of potential gradient for the same periods, the daily range in mean curves for several days being from 0.7 to 1.7 x 10-12 A/meter2, whereas the extremes on individual days may be as low as 1.7 x 10-12 and as high as 5.0 x 10-12 A/meter2 • The (small) annual cycle of the air-sea current density, too, corresponds in character and relative magnitude to that of the potential gradient. Regarding local variations, it must be mentioned that an increase with latitude, similar to that observed with potential gradient, is indicated. All these variations refer to "least-disturbed" periods. When, however, the air-sea current density is affected by the presence of a disturbing element in the lower atmosphere (e.g., mist, fog, haze), the amount of the air-sea current density may be reduced considerably. The Carnegie results concerning the diurnal variation of the airsea current density are in satisfactory agreement with the later measurements made on the Horizon (Ruttenberg and Holzer, 1955), apart from a slight, and nearly constant, deviation appearing also in the average values. The Horizon values, however, show that a persistent local diurnal effect may be possible, producing a small increase in the air-sea conduction current density during the daylight hours. The character of this effect could not be revealed.
3.4
ELECTRICITY AND RADIOACTIVITY
97
By multiplying the average value of the air-sea convection current density by the area of the earth, but neglecting the comparatively small regions « 1 per cent) with thunderstorm activity at a given instant, Gish (1951) obtained an estimate for the total electric conduction current I from the air to the earth of about 1800 A, which is subject to a probable error of 10 per cent. This total electric current shows temporal variations similar to those observed with the air-sea current density i, 3.4.5.2. Supply Current. It is quite obvious that there must exist a counterpart to the air-earth current just described by which positive charge is transferred upward from the earth to the ionosphere in some way. The inherent problem was roughly outlined in the introductory Section 3.4.1. For further information reference is made to the detailed and thorough discussion published by Gish (1951). Here, only a presentation of the marine aspects of the problem in question can be undertaken. There are two of principal importance: (a) The correlation between the universal diurnal variation in the fair-weather potential gradient and the total number of thunderstorms over the earth. (b) The positive charge transfer to the atmosphere from bursting bubbles at the sea surface suggested by Blanchard (1958). Evidence for (a) is presented in Fig. 19 in which the diurnal variation of the fair-weather potential gradient at sea is depicted together with computations of the total number of thunderstorms over the earth for two-hour intervals. For the latter quantity, the values recently published by Krumm (1962) were used, in addition to the data calculated by Whipple in 1929. The newer values were based on the charts representing the world distribution of thunderstorm days published by the World Meteorological Organization in 1956. The courses of the two thunderstorm curves are rather similar, apart from the fact that, on the average, the older values are about 10 per cent less than the new ones and that the second maximum around 1900 GMT is not so pronounced in the new calculation as it was before. With regard to the oceans, the computation of Krumm (1962), however, provides a distinct improvement as the diurnal variation of thunderstorms was also taken into account for maritime areas as far as possible, whereas Whipple did not consider any diurnal variation over the oceans. Comparing the thunderstorm activity with the fair-weather potential gradient we may state that there is a rather satisfactory agreement
98
3
COMPOSITION AND PROPERTIES
not only as regards the times of the extremes but also in such details, for example, as the subsidiary maximum around 0800 GMT which corresponds to the peak of the thunderstorm frequency in Asia and Australia.
o
GMT 2
4
6
8
10
12
14
120
p'.d
% 110
•.'
16
18
20
22
24 120
~.-l:J'
110 %
Carnegie (all oceans)
t---------~C!'------------"'n__i
100
90
(Arctic ocean)
801----------------------180
0/0
120
120
110
110
100 t--------,...==-------,lL-----=
100
90
90
80
80
o
2
4
6
8
10
12
14
16
18
20
22
24
GMT
FIG. 19. Diurnal variation (per cent of the mean) of potential gradient over the oceans (above) and of world thunderstorm number (below). Average total of thunderstorms per day: Whipple (I 929), 1520; Krumm (I962), 1670. Each thunderstorm is assumed to cover a mean area of about 1256 krn"; note that the observations on the Maud refer to the northern winter only.
Correlation (a), which is supported by a similar relation between the air-earth current and storm frequency, may be interpreted by assuming a supply current by which negative charge is transferred to the earth in periods and areas of storm and which equals the total airearth current I in magnitude and in the character of its annual and diurnal variations. Here, the problem of clarifying the mechanism of such a current arises, i.e., the separation and transport of electrical charge during a thunderstorm. The discussion of this question would, however, extend beyond the limits of this monograph. Hence
3.4
ELECTRICITY AND RADIOACTIVITY
99
we only mention that, according to Gish (1951) and Miihleisen (1957), the problem of the supply current has not been adequately settled up to now, and we will confine ourselves to quoting some global estimates. The only processes by which charge can reach the earth are the following (Chalmers, 1957): Conduction through the air, point discharge, precipitation, and lightning. Since the earth is a conductor, the electric balance need not be established for certain regions but must apply to the whole globe. Thus we need a global budget containing figures for the different components of charge transfer given above. With a view to the fact that measurements only exist for certain places, and cannot be assumed to be representative for others where conditions are different, it is extremely difficult to make a reliable global estimate. Among others, Israel (1953) attempted to give such a total budget of electric currents in the atmosphere, as is shown in the tabulation. Process
Electric current density (Arrneter")
Fine weather conduction +3 X 10- 12 -3.33 X 10-12 Point discharge Precipitation + 1 X 10- 12 Lightning -0.67 X 10- 12
Some of the figures given are only rough estimates. They were adjusted in part in order to arrive at a balance. Therefore, the mechanism (b), which is not explicitly covered by Israel's budget, should be taken into consideration. As described in Section 3.4.2.1, positive particles are ejected from bursting bubbles produced at the sea surface by wave action, snow, hail, and raindrops, and carried into higher levels by turbulent and convective motions. This effect may be connected with thunderstorm activity or may occur independently. In either case it would not contribute to the universal diurnal variation of the supply current, but it would form part of the more or less constant additive term. Blanchard (1958) estimated the upward flow of positive charges caused by such forces at about 3.3 x 10-12 A/meter 2 , which is nearly equal to the airsea convection current density during fair weather. It is not assumed by Blanchard that this figure should be considered as a representative estimate for the whole ocean. However, considering the fact that about
100
3
COMPOSITION AND PROPERTIES
70 per cent of the earth's surface is covered by the seas, and that whitecaps begin to appear with a wind force of 3 Beaufort and increase rapidly in number and size with growing wind speed, the effect investigated by Blanchard may constitute a significant share in the total balance of electric charges on the earth, the oceans not being a complete charge sink but acting also as a charge generator or separator with an appreciable output. Further evidence must be awaited before a final conclusion can be reached.
3.4.6 Radioactivity in the Marine Atmosphere Within the boundaries of the topic of this monograph, only the natural radioactivity is of interest. Although the available information is far from being complete, it appears to be sufficiently established that the radioactive content of purely marine air reaches only from 1 to 2 per cent of the average continental value. For instance, the mean radon content over the oceans was measured to from about 1 to 2 X 10-18 Ci cm-3 (Mauchly, 1924) while the average radon content of the near-surface layer over the continents amounted to from 100 to 120 X 10-18 Ci em:", if the higher values observed on the mountains were omitted (Israel, 1951). Later measurements (Skorka, 1958) confirmed this conclusion. They resulted in a mean radon concentration of 2 x 10-18 Ci cm-3 for air samples taken at great distance from land masses. Thus it was concluded (Israel, 1951) that the atmospheric radon content is of purely continental origin. These gaseous emanations and similar ones which are emitted from the rocks and the soils into the air were assumed to be transported over the oceans through turbulent motions of large scale. More recently this assumption has been questioned: Some empirical findings suggest a vertical radon transport in the ocean which seems to originate from the sediments of the ocean floor and which might result in an appropriate exhalation of radon from the sea to the air (Israel, 1958), if the exchange at the sea surface is governed by an eddy transfer coefficient that is 200 times as large as the molecular coefficient of diffusivity. Further evidence on this subject is needed.
4. Flow Characteristics of the Marine Atmosphere 4.1
GENERAL CHARACTER OF THE SEA SURFACE AS LOWER BOUNDARY OF AN AIR FLOW
In the marine atmosphere the lower boundary is formed by the sea surface, which is distinguished from the relevant conditions prevailing over land by peculiar properties. On the continents, shape and size of the elements of surface roughness are clearly defined and comparatively easy to determine. Generally, their nature and locality are fixed and neither vary with time nor depend strongly on the wind. Their aerodynamics are relatively well defined and known. Contrary to the conditions found over land the surface roughness encountered at sea is composed of a great variety of ocean waves, i.e., moving elevations which are different in size, shape, and velocity as well as subject to continuous and irregular changes. The dimensions, the spatial distribution, and the temporal variation of the ocean waves, are governed by statistical laws wherein the character and speed of the air flow play a decisive role. Besides, orbital motion and drift current are present in the sea and it is quite obvious that these water movements will react on the air flow. With increasing wind speed, finally, the formation of foam and sea spray, which implies a disintegration of the sea surface, affects large areas and extends to a certain height, thus creating a transition zone between air and sea. Bearing all this in mind, we can hardly speak of the sea surface being simply the lower boundary of the air flow as if it were a solid wall. More important, we must realize that there is an extremely variable and, therefore, ill-defined and hardly accessible boundary zone where the coupling between atmosphere and ocean occurs in a very complicated manner. These dynamic properties of the sea surface considerably increase the difficulties inherent in any investigation concerned with the mechanism of the air-sea boundary layer. This is the reason that so very little is known, for instance, about the pattern of the air flow around moving water waves. With a view to this severe handicap it is only of little comfort that the difficulties mentioned above are more 101
102
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
or less the same in all oceanic regions, thus enabling us to draw general conclusions from studies executed in a certain area. On the other hand, we should not overlook that the marine atmosphere also offers remarkable advantages for experimental studies as compared with the conditions over the continents. The local differences, which are most dominant over land, are nearly absent on the oceans, these being much more uniform as the lower boundary of the air flow, and as sources or sinks for heat and moisture, than the continents are.* Further, since the diurnal and annual variations are much smaller than those on land, there is also a pronounced temporal homogeneity at sea. Thus a number of basic problems, particularly those belonging to the physics of the atmosphere, should be easier to solve over the sea than on land, where the variety of parameters and the complexity of influences render things more difficult. It is for this reason that, in many respects, the oceans can be considered as an ideal field for meteorological investigation provided that it is possible to overcome the experimental difficulties by developing adequate instruments and methods. These general features of the sea surface, which at this stage could be outlined only very roughly, will serve us as a guide and will be refined as far as necessary in the course of our discussion on dynamic processes in marine air. We are now going to describe the nature of the air flow over the sea. Before investigating the behavior of the wind in detail we shall try to collect some additional information on the essentials of the sea surface which are, or may be, related to wind structure. 4.2 GEOMETRY OF THE SEA SURFACE The more or less periodic disturbances of the sea surface originate from atmospheric, seismic, and astronomic causes and comprise a period range from about 10- 2 to 105 seconds (Munk, 1951). The energy is concentrated in the ordinary gravity waves (periods 1-30 seconds) and in the ordinary tides (periods about 12 and 24 hours). As far as the relation to wind structure is concerned, the surface oscillations with periods up to 30 seconds seem to be most relevant. Within this range capillary waves and gravity waves are present. As mentioned above, the frictional coupling between wind and sea is a very intricate problem. Therefore we shall split up the discussion, dealing at first with the larger waves and passing afterwards to wavelets and ripples. * As shown by Brocks [ (1963), see Supplement to references] there is a high correlation (+0.9 to + 1.0) between simultaneous measurements of air temperature as weIl as between such of humidity or wind speed executed within a sea area of at least 50 km.
4.2
GEOMETRY OF THE SEA SURFACE
103
4.2.1 Gravity Waves Best known to all those who are occupied with the sea in some way or other are the waves that are generated by the wind and mainly governed by the force of gravity. Within the period range indicated above, their height (vertical difference between trough and following crest) lies mostly (94 per cent) between 0 and 5 meters with the maximum frequency at from 1 to 2 meters, but during hurricane force winds it may even reach 20 meters. If the waves are growing or being maintained by the local wind they are termed sea, whereas waves that are no longer under the action of the generating wind are called swell. The dimensions of the sea were found to depend on the properties of the generating wind field as given by its characteristics: wind direction and velocity, duration, fetch (length of wind field measured in the direction of the wind), and displacement. The transformation of sea into swell and the propagation of the latter depending upon atmospheric and oceanic factors are much more complicated and not yet completely understood. Sea and swell occur singly or in manifold combination in which they can sometimes be separated only with difficulty. The most obvious feature of the gravity waves is their irregularity, which is particularly pronounced with sea waves but less so with swell. Thus statistics must play a significant role in ocean wave research. A typical record of sea waves, presenting the variation of elevation with time, is reproduced in Fig. 20. Information on the three-dimensional pattern of ocean waves can be drawn from stereophotogrammetric wave measurements (Fig. 21), Although gravity waves are of considerable importance for shipping, naval architecture, and coastal engineering, wartime needs proved to be a still better stimulant for relevant studies. Initiated by the requirements of landing operations during World War II, knowledge of ocean gravity waves has shown an amazing increase during the past twenty years not only as regards the measurement and mathematical representation of the complicated wave pattern but also with respect to the forecasting of the seaway for practical purposes. To somebody who is familiar with the present state of wave theory and, in particular, with its shortcomings the statement given above may appear to be an exaggeration, however, the fact that much remains to be done should not prevent us from appreciating what has been attained so far. One of the main results of wave measuring is that the elevations of the sea surface taken from a wave record are grouped around their mean according to a Gaussian distribution, their standard deviation
104
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
being proportional to the wave energy per square unit. This fact implies several statistical consequences as regards the distribution of wave heights in the irregular sea and the relations between their mean values. Moreover, the wave records proved that a continuous energy
5
u
15
10
:ll
20
Time (sec)--
N§
-; 500 g
u
c
"
B
~
o-
~ 300 ~
o
~
~
200
0.
(f)
02
0.3
04
U5
U6
Wave
50
: 35 i 2.8: 24 i 2.0 4.0 3.0 26 22
O~
U8
09
10
frequency (sec")
1.8
1.6
1.4
1.2
1.0
Wave period (sec)
FIG. 20. Wave record (A) (two parts of 30 sec each out of a total record of 20 min.) and wave spectrum (B). Time: May 28, 1960, 1353 GMT. Site: Lighthouse "Mellum Plate," German Bight. Wind: NW, force 3. Mean wave height: 22.0 em. Significant wave height: 34.1 em. Mean wave period: 2.2 sec.
spectrum is present, depending both on wave frequency and wave direction. Theory succeeded in explaining these findings and in combining them into a (linear) mathematical model. According to it the irregular seaway may be interpreted as a superposition of an
4.2
GEOMETRY OF THE SEA SURFACE
105
"infinite" number of harmonic wave components with infinitesimal heights, different frequencies, different directions, and random phases (Pierson, 1955). Nonlinear effects, such as energy transfer between different wave components, instability of wave crests (whitecaps), and turbulent dissipation, were not taken into account at this stage. There has been much discussion on the mathematical form of the wave spectrum which describes the distribution of wave energy density depending on wave frequency and direction. However, no final solution has emerged up to now. A remarkable attempt to supply
,, 1~; '~/~--
400
meters
FIG. 21. Ocean waves measured photogrammetrically (from Schumacher, 1952.) Position: 47.5" N. 26.8° W. Time: April 3, 1939, 1700 GMT. Isolines of wave height in meters. The greatest height difference in the map amounts to 16.5 meters.
106
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
the necessary information was made by the swap project (Chase et al., 1957), in which stereophotographs of ocean waves were evaluated in terms of the two-dimensional wave spectrum. More such data are needed. Unfortunately the evaluation is very laborious. The mathematical representation of the seaway outlined above has the disadvantage that no relation is established between the wave pattern and the turbulent wind structure above the sea. The sole atmospheric parameters used therein are the characteristic quantities of the generating wind field which are not related to turbulent fluctuations. Since it is quite obvious that the ocean waves are generated by the action of the turbulent wind stresses on the sea surface, an improvement of the theory is needed. Promising attempts in this direction have been made by several authors: At first Phillips (1957) initiated a theory on the generation of waves upon a surface of inviscid water by a random distribution of traveling normal pressure fluctuations associated with the onset of a turbulent wind but assumed independent of the waves. Contrary to Eckart (1953), who used a similar stochastic model but arrived at wave heights too small by one or two orders of magnitude, Phillips found that this linearized model might well be adequate if a resonance mechanism is considered. Each component of the moving pressure fluctuations can generate free surface waves traveling at the same speed, their heights being about ten times as large as Eckart's. Furthermore, some details of initial wave structure, as observed by Roll (195Ia) and Van Dorn (1953), can well be explained by the theory of Phillips. The resonance mechanism displays optimum efficiency when the wave speed is more or less equal to the component of the wind speed in the direction of wave propagation, which implies that directional energy maxima occur for a particular wave frequency at angles such that the condition of resonance is fulfilled. Later studies by Phillips (1958) dealt with the structure of windgenerated waves when the duration and fetch of the wind are large, and nonlinear interactions between the different components of the wave spectrum become important. According to his findings there is developed a statistical equilibrium range, i.e., a state of saturation in which the high frequency components of the wave spectrum are determined by stability conditions at the wave crests. Owing to the breaking of the waves, any local excess of wave energy is lost to turbulence in the water. Then the spectrum is of the form (4.1 )
4.2
GEOMETRY OF THE SEA SURFACE
107
where w is the wave frequency, g the acceleration of gravity, and CI. a dimensionless constant equal to 7.4 x 10-3 • A different approach to the problem in question was published by Miles (1957), who investigated the generation of surface waves by a parallel shear flow in the air and found that the rate of energy transfer to a wave of speed C is proportional to the curvature of the vertical wind profile U(z) at that altitude z where U == C. Finally a rather comprehensive and complete treatment which was given by Hasselmann (1960) should be mentioned. He established and integrated (for special cases) the energy balance equation of windgenerated surface waves, taking into account the generation and growth of the waves by turbulent fluctuations of atmospheric pressure and by sheltering due to waves, as well as the nonlinear effects comprising the interaction between different components of the wave spectrum, the instability of wave crests, and the turbulent dissipation of wave energy in the sea. For detailed information the original papers should be consulted. A review of the state reached up to 1958 was published by Charnock (1958b) while Ursell's (1956) as well as Phillips' (1962) surveys were written with particular attention to the problem of wave generation by wind. Most of the theories need confirmation by more precise and more complete observational data than that hitherto available. 4.2.2. Wavelets and Ripples Apart from the spectacular ocean waves which attract the attention of anybody traveling across the seas there are nearly always present wavelets and ripples, which are much smaller in size and, consequently, in general not considered as important. Figure 22, which corresponds to a wind speed of 10.8 meters per second, gives an idea of the complicated structure of the sea surface where the big waves are superimposed upon by small ones of different sizes down to waves of a few centimeters in length. Evidence is growing that these tiny ripples represent the drag of the wind on the sea much more than the big waves do. In the size range considered, only small masses take part in the oscillations but strong curvatures of the sea surface occur. Thus the influence of gravity is reduced in favor of that of surface tension. The conditions are described by the following relationship between the wave length L and the wave speed C which is valid for periodic surface waves in deep water:
C
=
[(gLj27T)
+ (27TyjpwL)]1I2
(4.2)
108
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
where
g = acceleration of gravity (em sec-2) y = constant of capillarity (gm sec- 2) pw = density of sea water (gm crrr") This relationship is illustrated by Fig. 23. With decreasing wave length L, wave speed C will also decrease down to the minimum value of 23.1 em/sec corresponding to the equilibrium between gravity and
FIG. 22. Structure of the sea surface at a wind speed of 10.8 meters/sec (measured at a height of 19 meters).
capillarity and occurring with a wave length of 1.72 cm. For wavelengths smaller than 1.72 em the effect of gravity is surpassed by that of capillarity and the wave speed increases with decreasing wave length. The periods covered by Fig. 23 are ~ 0.36 sec. In this range determinations of wave spectrum were only made in the laboratory (Lille1eht and Hanratty, 1961). In the field, however, Burling (1955) investigated waves having a period interval of from about 0.5 to 2 sec. His measurements were made on a water reservoir of uniform depth (16 meters) at fetches varying from 300 to 1350 meters. Fourier spectrum analyses of wave records made when wind and waves were more or less in equilibrium are presented in Fig. 24. This diagram also contains the spectral function of the wave energy
4.2
GEOMETRY OF THE SEA SURFACE
109
density as derived by Phillips (1958). It can be seen that, for frequencies w above 5 radians per second (or for periods T below 1.3 sec), the data are well represented by the spectralfunction [Eq. (4.1)]. Below the frequency of 5 radians per second, the spectra reflect the influence 70.-----------------,
60
u
50
'"
j
"0
40
~
5}
?; c
:;: III
t
~Minimum
wave speed,
?; 23.1 em/sec ~ Limiting wavelength, 1.72 em
20
~I:6,.1
10
.
Gravity waves
~ o
5
10 15 Wavelength (em)
20
FIG. 23. Relationship between wavelength and wave speed under the action of gravity and capillarity (y = 75.3 gm sec:").
of fetch, which is understandable considering the very limited area available. Some results on the shape of water waves in the capillary-gravity transition region have been reported by Schooley (1958b). Highspeed motion pictures of capillary waves in a small wind-wave tunnel showed that the profiles of pure capillary waves peak downward contrary to gravity waves which have peaked crests and flat troughs (Fig. 25). The steepness, i.e., the fraction of wave height H through wave length L, whose maximum is 0.14 for gravity waves, was found to be 0.5 for capillary waves. Examples were given of the relationship between capillary and gravity waves in the sea-surface wave pattern. They showed capillary waves having the same speed as the gravity waves and riding just in front of the crests of the latter. 4.2.3. Sea-Surface Slopes When discussing the significance of ripples for the air-sea energy transfer, one must make reference to the measurements of sea-surface
110
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
10 >-
.~
-e c-,
i ~ ~
b c
.2 U
1
10-1
~
0-
10-'2
4
6
8
10
12
Frequency w (radians per second)
2
1.5
1.2
I
r
0.9
0.8
07
06
05
Period T (sec)
FIG. 24. Wave spectra, measured by Burling (1955) compared with the spectral function of wave energy derived by Phillips (1958). (From Phillips, 1958.)
FIG. 25. Profiles of water waves in the capillary-gravity transition region characterized by peaked troughs and rounded crests. The smallest subdivision of the scale is in centimeters. Wind direction from left to right. Wind speed at 35 em height: 8 meters/sec.
4.2
GEOMETRY OF THE SEA SURFACE
111
slope executed by, among others, Cox and Munk (1954), Farmer (1956), and Schooley (1954; 1958a,b; 196Ia,b). Cox and Munk took aerial photographs of the sun's glitter on the sea surface, relating the density of the reflected images of the sun to the statistics of wave slopes. This ingenious method of measuring the fine structure of the wind-affected ocean surface gave the following results: The slope distributions were found to be nearly Gaussian, which means that the zero slopes were the most frequent ones, and which also supports the existence of a continuous wave spectrum. The upwind-downwind slopes showed a skewness resulting in the most probable tilt being not zero but a few degrees pointing downwind, i.e., the downwind side of a wave is generally steeper than the upwind side. The ratio between upwind-downwind and crosswind components in the mean square slope gave some evidence for the directionality of ocean waves by indicating a directional beam width of about 130°, i.e., the relatively short waves observed traveled at up to 65° from each side of the wind direction. The mean square slope, without regard to direction, increased linearly with wind speed up to a value of tan- 16° for a wind speed of 14 meters per second. The further variation of mean square slope with wind speed is, however, not known. Certainly the wave slopes cannot increase indefinitely. Besides, the waves investigated by Cox and Munk obviously comprised sea waves as well as swell. The slope measurements of Farmer (1956) were obtained in a way different from that of Cox and Munk as the sea-surface slope was determined from the difference in sea-surface elevation measured on two vertical wires passing through the water surface and spaced at a fixed distance of about 10 em apart. Thus average values of slope over this distance were obtained, whereas the results of Cox and Munk may be considered as referring to the true slope at a certain point on the sea surface. The slope measuring equipment of Farmer was not installed on a fixed platform (as was the case with others: but on a floating wave pole. This arrangement certainly did not keep the sensing elements completely rigid in space, but it allowed him to get slope measurements in deep water. In spite of these differences in method the results obtained by Farmer do not reveal substantial deviations from those of Cox and Munk. Probability distributions of wave slopes under the conditions of a very short fetch were studied by Schooley (1958a) in a small windwave tunnel. As the fetch considered was only about 37 em the results he obtained refer to the transition region between capillary and gravity
112
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
waves. Compared with the slopes previously obtained by Schooley (1954) with fetches of more than 300 meters, which agreed more or less with the result of Cox and Munk, the upwind-downwind component of mean square slope for the very short fetch was found to be higher for wind speeds above 5 meters/sec (Fig. 26). At a wind velocity of 8 meters/sec the mean square slope for short fetch was 70 per cent greater than the corresponding value for long fetch. This result was confirmed by the laboratory measurements of Cox (1958). o
"0
.~
:u~
008
.
c
:; 0.06 co
2
Meters per second 4 6 8 10
12
x Schooley (I954) o Cox end Munk (I954) • Schooley (I958)
:: 004
i5 g" c
0.02
o
'"
:;
o
4
8 12 16 20 Wind velocity (knots)
24
28
FIG. 26. Mean square slope of the sea surface as a function of the wind velocity for short and long fetch. (From Schooley, 1958a.)
Additionally, for winds in the range 2.4 to 3.2 meters/sec, Cox reported extremely low values of upwind-downwind mean square slope for fetches below I meter and a rapid increase of slope in the fetch range of 1 to 2 meters. This interesting observation of a relation between wind speed and the minimum fetch at which waves begin to grow was associated by Phillips (in a comment on Cox's paper) with the transition of the air boundary layer from laminar to turbulent flow. Relevant observations were made during field experiments by Roll (1951a). Shape and properties of the wave slope distribution curves of Schooley were similar to those shown by Cox and Munk. There was, however, an interesting feature not reported by these authors: the deviations from the Gaussian distribution (skewness and peakedness) seemed to depend on wind speed. A region of maximum nonGaussian shape appeared to exist around 8 meters/sec. Schooley indicated that, in the wind speed region concerned, water droplets are starting to be drawn into the air near the water surface, and suggested the possibility that this phenomenon might tend to make the slope distributions rather more Gaussian for wind speeds higher than 8 meters/sec. Thus some evidence is offered for a "critical wind
4.2
113
GEOMETRY OF THE SEA SURFACE
speed for air-sea boundary processes," the problem of which will be dealt with later on (see Section 4.3.5.5.). When the structure of the sea surface is to be described and understood completely it is not sufficient to consider only the distribution of surface slopes. Much more additional knowledge is needed on the sizes of the facets which compose the sea surface. Relevant information has been provided by Schooley (l96la), who investigated wave profiles obtained photographically in a short-fetch water-wind tunnel. He determined the length of the facet in a certain slope with regard to previously given values of flatness tolerance (Fig. 27). Defining the dimensionless quantity of the "roughness factor" as flatness tolerance
/
/Facet length for flatness tolerance (a)
FIG. 27. Structure of the sea surface. Flatness tolerance used to determine facet length. (From Schooley, 196Ia.)
divided by facet length, Schooley arrived at a relationship among roughness factor, sea surface slope, and wind speed as exhibited in Fig. 28. It is interesting to note that, for small surface slopes between + lO° and - 10°, the roughness factor was greatest with high wind speeds whereas the reverse occurred outside this range, i.e., for slopes above ± 10°. The minimum roughness was greater, and the farther from the zero slope, the higher the wind speed was. The mean 0; ~ .~
.go Qju
0.8
-2 ~
~ s:
g 0.6
....
0
"'~
"" e:E
0.4
~~
:;;o E." 0.2 > 0 <{~
oL-..--'-~---L--,--.L.............L----,--=::"-..L-"'------.!-----,--L--,-...l.-.L.....J
-50 -40
-30
-20
-10
0
10
20
30
40
50
Slope (degrees)
FIG. 28. Empirical relationship among roughness factor, sea surface slope, and wind speed. {From Schooley, 1961a.)
114
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
"roughness factor" for all facets in the upwind-downwind direction was an ascending function of the wind velocity, amounting to about 0.095 at 10 knots and reaching 0.135 at 20 knots (Schooley, 1961b). For a given wind velocity the roughness factors associated with positive (downwind) slopes appeared to be greater than those appertaining to the corresponding negative (upwind) slopes. This would imply that, in general, the structure of the sea surface is rougher at the downwind slopes of the waves than at the upwind ones, a result which is in conformity with the visual impression and which might become important for the understanding of the aerodynamics of the sea surface.
4.2.4. Slicks 0/1 the Sea Surface Slicks are streaks or patches of "smooth" sea surface surrounded by regions where the appearance of the sea surface is rippled or "rough." Herein the terms "smooth" and "rough" shall only describe the visual impression one gets when looking at the sea. They do not refer to the aerodynamics of the sea surface. A typical picture of slicks is reproduced in Fig. 29. Upon closer examination it may be
FIG. 29. Slicks on the sea surface observed in the North Atlantic. Wind speed 5 knots.
4.2
GEOMETRY OF THE SEA SURFACE
115
seen that the ripples and wavelets are reduced in the slick thus giving it a smooth, sometimes glassy appearance. This is the reason that the slick reflects the sky better than the surrounding rough area. Slicks are common in coastal waters, bays, and lakes, and they are most prominent when only a light breeze is present. Information on their geographical distribution is contained in a paper of Dietz and La Fond (1950). It is quite obvious that the phenomena observed point to the existence of a surface film which reduces the surface tension of the sea surface. Such a film may originate from artificial contamination or, perhaps more frequently, consist of organic matter occurring naturally on biologically productive waters. Some proof for the validity of this assumption was given by Dietz and La Fond (1950). We know from experience (Cox and Munk, 1954) that the effect of a surface film can be perceptible in two ways: (1) It may prevent the formation of capillary waves by the wind and (2) it may increase the damping of short waves. The significance of these two effects was investigated by Dorrestein (1951), who elaborated a complete linearized theory of the decay of surface waves by friction with a surface film present, taking into account the wave-induced periodic extensions and contractions of the film which involve variations in surface tension. He obtained the result that "the conspicuous prohibitive action of an oil film on small waves manifests itself not so much by the increased damping, but rather by the prevention of the formation of short waves by the wind." According to Ewing (1950) the increase of the dissipation rate of wave energy caused by a surface film more than doubles the minimum wind velocity necessary for the generation of waves. Thus it seems evident that slicks reflect the ripple-preventing and ripple-damping action of a surface film. Normally, the surface film will tend to spread until it is one molecule thick. If, however, horizontal convergence exists either in the sea surface or in the wind stress, the degree of compaction of the film molecules and, therefore, its ability to prevent or to damp ripples will vary locally, thus giving rise to slicks. There are four different types of slicks differentiated by their structural characteristics and their way of generation. (1) Wind streaks. Most natural bodies of water show a streaky appearance under the influence of wind with a speed of more than 3.5 meters per second. These streaks of smooth water are parallel to the wind (Fig. 30) and show a considerable permanence. Obviously
116
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
they are not the result of any wind pattern. The following explanations have been advanced: (a) A system of convective rolls is developed in the water owing to the action of the wind (Fig. 31). Above the lines of descent between adjacent rolls there is a zone where the convective movement of the water results in the concentration of the surface film and the objects
FIG. 30. Wind streaks on the water surface. Low tide, North Sea coast of Holland (From van Straaten, 1950.)
inherent (seaweed, foam, oil) (Langmuir, 1938). Woodcock (1941) interpreted the phenomenon as principally owing to thermal instability in the upper layer of the water, the surface being cooled by the action of the wind (evaporation). In 1944 Woodcock published some evidence that these vortices were asymmetrical, the larger vortex of each pair rotating clockwise in the northern hemisphere, the smaller counterclockwise (facing downwind). This asymmetry was attributed to the effect of the Coriolis force. In shallow water the distance between the streaks is usually two to four times the water depth (van Straaten, 1950).
4.2
GEOMETRY OF THE SEA SURFACE
117
(b) A pressure is exerted by capillary waves on the contaminated area, tending to compress this region along its sides. Stommel (1952) suggested this mechanism since motion pictures showed that the wind streaks were quickly reoriented (in I to 2 minutes) if the wind direction changed abruptly. This observation and several other
A
FIG. 31. System of convective rolls in water due to wind action. A, view from above; B, side view.
facts seemed to indicate that the mechanism which is responsible for the generation of the streaks was confined to a relatively shallow portion of the sea surface layer. While observations have confirmed the existence of convective rolls as described in (a), evidence is still lacking for the mechanism proposed in (b). (2) Periodic Bands. In coastal waters, but occasionally also in the open sea, a peculiar banded appearance of the sea surface can be observed when the wind is slight (Fig. 32). This effect is due to a systematic variation in the pattern of small waves on the sea surface. The smooth streaks are from 10 to 50 meters broad and sometimes many kilometers long. They are separated from one another by rippled zones about 300 meters wide (Ewing, 1950). In deep water these slicks usually lie transverse to the wind direction whereas in shallow water they tend to follow the bottom contours. They move in a path perpendicular to their long axes at speeds between 10 and 40 em/sec. Woodcock and Wyman (1947), who first tried to explain the phenomenon, interpreted the bands in terms of atmospheric roll vortices. Although the hypothesis of roll vortices was consistent with some of the characteristics observed in the bands, the necessary condition of thermal instability was usually not fulfilled in the atmospheric boundary layer.
118
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
Another possibility of explanation already indicated by Woodcock and Wyman was studied later by Ewing (1950) and La Fond (1959), who succeeded in relating the band form of sea surface slicks to internal waves in a shallow thermocline. The horizontal components of orbital motion associated with such waves produce periodic convergence and divergence zones at the sea surface which alternately
FIG.
32. Periodic bands on the sea surface. (After Woodcock and Wyman, 1947.)
compress and extend the surface film in a manner sufficient to cause perceptible differences in ripple waves. Evidence for this relation between band slicks and internal waves is given in Fig. 33. The usual position of sea-surface slicks was found where the surface water was converging and sinking. When the internal wave was progressive the band slicks were propagated with the same speed as the internal wave. Although the development of internal waves in a shallow thermocline has not yet been fully understood, there is some evidence that they are oriented with their long axes nearly at a right angle to the wind. In shallow water they may be related to bottom topography. As already mentioned these features can also be observed with sea-surface slicks. (3) Intermittent Rippling. This phenomenon was first described by Findeisen (1935) and later investigated more in detail by van Straaten (1950). It can be observed in tidal flats at low tide and consists in the
Time~
1210
Q;
.2!
0. CI> o
1220
1230
1240 II
~
1250
1320
1310
1300
1330
II II
II
~! ~ ~ ~8~~ ~~~:~~~ ' ~::s:=~ ~------560~ ~~~ ~ ~ ~540_ ~!: 154~f0~A~ I I
I I
"'-1i
540
I
Time~
1230
1240
1250
1300
1310
1320
1330
1340
1350
1400
CI> CI>
a.
CI>
o
FIG. 33. Slicks and internal waves in the thermocline. The heavy bars at the surface represent the position of sea surface slicks. Since the internal waves are moving from right to left, the slicks are found over the descending slopes. (From La Fond, 1959.)
120
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
alternation of patches of smooth water and rippled inters paces (Fig. 34). It is confined to very shallow water (average depth not more than 1.5 em). There is a very peculiar flow pattern: the elliptical patches of smooth water, with their long axes perpendicular to the wind, are arranged in trains parallel to wind direction and move downstream with the water, which is driven chiefly by the wind.
FIG. 34. Intermittent rippling. Trains of elliptical patches of smooth water are traveling toward the observer. Tidal flat on the Dutch coast. (From van Straaten, 1950.)
Findeisen (1935) attempted to interpret the phenomenon by assuming an alternate occurrence of laminar and turbulent boundary layers in air, which appears to be rather a forced and unsatisfactory explanation. Van Straaten (1950) suggested the existence of an invisible surface film which is torn up rhythmically if the wind speed exceeds a certain value. Thus, rents develop between the smooth patches, and on these areas, which have practically clean surfaces, ripples instantly appear. Since the film material is compressed within the smooth patches, only larger waves would be able to pass through them but, on the other hand, these larger waves cannot develop on very shallow water.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
121
Therefore, the phenomenon described can only become conspicuous when the water is very shallow. Van Straaten supported his hypothesis by some field observations; an explanation for the characteristic train pattern of the smooth patches could not be given, however. (4) Nonperiodic slicks. Besides the three periodic forms of slicks mentioned before there exist those resulting from non periodic causes that can compress the surface film and thus produce calm streaks. Mechanical means such as the splitting up and compressing of the film by a boat sailing through it, or such as convergent flow (connected with the discharge of a river into the sea, for example) provide frequent occasions for the observation of nonperiodic slicks. Further references on this phenomenon were given by Ewing (1950).
4.3
THE WIND FIELD IN THE FIRST FEW METERS OVER THE SEA SURFACE
After having dealt with the dynamic pecularities the sea surface shows as the lower boundary of an air flow, we proceed to a description and discussion of the wind field immediately above and around the moving ocean waves. The first few meters of the marine atmosphere are of considerable importance since it is here that the frictional coupling between atmosphere and ocean actually takes place. The air flow is influenced by the contact between the air and the sea. The loss of horizontal momentum at the sea surface causes a turbulent downward flux of horizontal momentum, while at the sea-air interface itself a momentum transfer occurs which determines the character of the flow in the boundary layer both in the atmosphere and in the ocean. So we have to deal with a complicated mechanism of transfer and feedback effects which is not yet fully understood. On the other hand, the surface layer of the atmosphere permits some simplifications which facilitate the discussion remarkably. The air density may be considered as constant with height. Since the direction of the mean flow does not vary noticeably with elevation, the entire problem can be treated as a two-dimensional flow. In addition, many investigators have assumed the turbulent shearing stress to be independent of height, although this assumption is questioned by others (Stewart, 1961; Schmitz, 1962b). 4.3.1 Observational Problems Unfortunately, the sea surface does not reveal its aerodynamics very easily. When considering only the requirements for a complete solution without regard to the possibilities available for measurement,
122
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
we must demand that the wind field around the moving ocean waves, with all its characteristic detail, should be fully measured and recorded as a function of time. Up to now this has not been achieved.* In nearly all the observational programs known so far the investigators had to confine themselves to measurements of mean horizontal flow made at several heights on bases which were more or less fixed relative to the moving waves. Several difficulties are connected with procedures of this kind. We may leave aside such factors as the distortion of the wind field by the carrier of the instruments (ship, boat, float, etc.) and also the disturbing effect of the motion of the anemometers because we can assume that these operational handicaps could be overcome by suitable measures. There remain, however, certain difficulties that cannot be avoided. The first one is instrumentational: rotating cup anemometers are inaccurate in fluctuating wind because of the inertia of the rotating parts. Such errors may become significant in the immediate neighborhood of the sea surface where the wind fluctuations are likely to be associated with the moving waves. Owing to the inertia effect the profile of mean wind speed measured in this way will tend to correspond more to the flow conditions above crests than to those above troughs (Neumann, 1951; Roll, 1952a). Other difficulties are related to the determination of the heights above sea level and of the wind speeds relative to wave and water motion. As far as the heights above sea level are concerned the handicap arises from the fact that a certain time interval between, say, land 10 minutes is needed for the determination of the mean wind speed. Since this time interval is large compared with the periods of the waves, a variable number of waves will pass the position of the anemometer during the measurement. There are two possibilities of fixing the height of the mean wind speed obtained in this way: (a) The measurement is made at a point stationary with regard to the ground. The pertinent height is the average distance from the wavy sea surface, i.e., more or less the height above the mean sea level. This arrangement can be realized by placing the anemometer on a fixed construction or on a floating base that does not participate substantially in the wave motion. (Such a float must either be large compared with the length of the waves or anchored in deep water not stirred by the surface waves.) No measurements in the troughs of the waves are taken in this case. * Recently, Schooley (1963) described measurements of the wind field around moving waves in a short-fetch wind-water tunnel by means of neutrally buoyant soap bubbles.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
123
(b) The measurement is made at a point that has the same distance from the wavy sea surface at any instant, i.e., the site of the anemometer oscillates with regard to the ground, corresponding to the oscillation of the sea surface. This arrangement can be realized by using, as the carrier for the anemometer, a float that is small compared with the length of the waves and, therefore, is able to follow the oscillations of the sea surface closely. In this case the instruments may dip into the trough region. No differences in wind speed between the procedures (a) and (b) will occur if the wind speed increases everywhere linearly with altitude. However, with logarithmic vertical distributions, or those following a power law, differences between (a) and (b) must be anticipated, particularly if the wind speed increase with height above wave crests differs from that above troughs. Naturally, the influences of height determination will only be significant in the immediate vicinity of the waves. Unfortunately this is the very height range where the vertical wind profile is of particular interest and importance. In order to get an idea of the difference between procedure (a) and (b), comparisons should be made. No definite results of relevant field studies are known at present. Thus, it seems necessary to make use of the laboratory measurement of Motzfeld (1937), who investigated the air flow over solid wave profiles of different shapes (round-crested and sharp-crested waves). Obviously there are significant differences between these wind channel investigations and the air flow over moving water waves. In the absence of more suitable comparisons these data are perhaps better than nothing.* When using Motzfeld's wind profile data above round-crested waves we arrive at the result (Roll, 1949) that the mean wind speed values gained with procedure (b) are about 5 per cent smaller than those determined for the same height following procedure (a). The sign of the deviation is understandable since Motzfeld's results showed a very strong increase of wind speed above the wave crests, whereas the vertical wind gradient found by him above the troughs was much smaller (Fig. 35). The differences between the procedures (a) and (b) seem to disappear at a height that equals three times the wave height. The question of whether procedure (a) or (b) will lead to a correct representation of the mean wind profile above the sea surface still remains unsettled and deserves further study. * Wind-water tunnel measurements of the wind field above wind-generated water waves, which have recently been published by Schooley (1963), seem to confirm Motzfelds findings.
14
20406080%
20406080% I i '
i
I
12
10
E ~
8
E
0>
I
Q)
6
4
FIG. 35. Wind profiles over a wavy solid surface after wind tunnel measurements of Motzfeld (1937). Wave height 3 em, wavelength 30 em. The wind velocities are given in per cent of their full value in free air.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
125
As regards the mean wind speed measured above the sea there is difficulty in determining how one should account for the motion of the waves and for that of the water surface. In this respect we have to distinguish between waves and currents raised by the present wind, and those pertaining to other wind or tide effects. As to the former phenomena, they should be measured and taken into account when we consider the momentum transfer at the site where the measurement was executed. If other waves and currents are present, the intricate task emerges of finding out to what degree these waves and currents play a significant role in the momentum transfer at the sea surface at the place considered. It is quite certain that, on the whole, purely kinematic corrections are not sufficient. If, for example, the mean wind profile is measured over a tidal current, it seems easy to record this current also and to correct the wind profile accordingly, which would thus refer to a nonflowing sea surface (Roll, 1948a). In this simple procedure the influence that a surface current exerts on the overlying air is neglected (Reiter, 1955) apart from the fact that it also rules out a possible wind-induced surface current. In spite of the observational difficulties described above, the vertical distribution of mean horizontal wind speed in the first few meters above the sea has been measured in a fair number of cases. In Table X a review of these investigations, comprising data on localities, techniques, and height ranges, is attempted. 4.3.2 Theoretical Difficulties In addition to the obstacles that complicate the measuring of the wind field in the layer next to the sea surface, the theoretical interpretation of the problem, too, includes several points that are still unsettled. First, reference must be made to the mechanism of turbulence. Following Prandtl (1932), the momentum of the air flow is mostly considered as the conservative quantity which is preserved during the turbulent exchange. Against this concept certain arguments were raised (Schmitz, 1962b) stating that the transfer of momentum may be affected by turbulent pressure fluctuations. As was shown by Taylor (1915), it is only the vorticity of the turbulent elements that is independent of these fluctuations. The vertical velocity profile in the marine boundary layer of the atmosphere was interpreted by Schmitz (1962b) in the light of Taylor's vorticity transfer hypothesis. The latter author also took into account the acceleration of the average flow and the thermal stability, and applied a particular concept of the air flow immediately at the sea surface, suggesting that not
TABLE X REVIEW OF WIND PROFILE MEASUREMENTS ABOVE THE SEA SURFACE
Year of Publication
1920 1922 1928 1936 1939 1940 1942
Author
Locality
Ulanov Roll
1950
Roll
1952
Sheppard
Maximum height (meters)
Logarithmic profile verified under adiabatic conditions
Remarks
Boat and ship Destroyer
4 4
6 21.3
Buoy Pole of a fish trap
4 2
2.2 -5
-
Kink at 0.7 meter Only two levels
Boat and ship
5
12
-
Kink at 1 meter
Raft
5
2.1
-
Kink at 0.6 meter
Raft
6
6.1
-
White Sea North Sea, tidal flats North Sea, tidal flats
Raft Fixed mast
Departure from log owing to thermal stratification
5 6
3 2
Yes
Fixed mast
4
23
-
Lough Neagh, Ireland
Fixed platform
6
8
-
Baltic Sea Wiist Johnson (cited by Deacon, 1953) Black Sea Shoulejkin Buzzards Bay, Montgomery U.S.A. North Atlantic Schroder et a/. (cited by Roll, 1948a) Lake Sacrow, Bruch Baltic Sea Lake Corpus Owen and Halstead Christi, Texas
1942 1948a
Procedure
Number of heights with wind speed observed
-
Kink at 1 meter
Yes
Departure from log owing to thermal stratification Kink at 1.5 meters
1954 1955
Das and Dhar Charnock
1955
Hay
1956
Hunt
1956
Deacon et al.
1957
Goptarev
1958
Fleagle et al.
1958a
Ogata et al.
1958
Takahashi
1958
Wagner
1959b
Bracks
1960 1961
Portman Izotova, Ogneva, and Smirnova Bruce et al. Deacon
1961 1962a,b
Bay of Bengal Reservoir, England North Sea 800 meters east of British coast Lake Hefner, U.S.A.
Boat Fixed mast
4
Floating platform
3 8
Yes
5
8
Yes
Boat
4
16
Yes
Port Phillip Bay, Small ship Australia, Bass Strait Oil drilling Caspian Sea platform East Sound, Raft U.S.A. Ship North Pacific O.W.S. Tango Kagoshima Bay, Both small fishing boat Japan and pole fixed to the sea floor Gulf of Mexico Oil drilling platform
5
13
Yes
11
50
Yes
Baltic Sea, Buoy German Bight Lake Michigan Buoy Lake Ladoga Mast (at the shore of a small, flat island) Ship Lake Erie Port Phillip Bay, Small ship Bass Strait
-
8
4.4
Yes
4
11.1
Yes
5
4
Yes
3
13
-
5
16
Yes
4 4
4 6.1
Yes Yes
6 2
13.4 13
Yes
-
Kink at 2 meters
Departure from log owing to thermal stratification
Only two levels considered
Only two levels
128
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
only the instantaneous velocities of adjacent air and water particles, but also their average speeds, differ, so that a gliding of the mean air current over the sea surface is assumed (see below). Since the analytical form (although not the physical meaning of the constants) of the wind profile obtained by Schmitz (1962b) equals the formula derived on the basis of Prandtl's hypothesis, we abstain from giving a detailed description of the theory advanced by Schmitz, but follow the conventional concept based on the turbulent momentum transfer hypothesis (see Section 4.3.3.2). In doing so we again meet difficulties which will be discussed here. Experience has shown that there is no substantial variation of the mean wind direction in the first 20-30 meters above the sea surface. Hence, we can assume the mean air flow to be two-dimensional, although turbulent motions perpendicular to the plane of flow may occur. We put the x axis in the direction of the mean wind and the z axis in the vertical. The relevant components, U and w, of the turbulent wind can be composed of their mean values, it and iV, and the turbulent departures from the mean flow, u' and w'.
= u+ u' w = W + w' U
Here
a is defined
(4.3)
as the average Hilt
u(x, z, t) = (lj2M)
J u(x, z, t) dt
(4.4)
t-Ilt
taken at a particular point x, z and at a certain time t over a suitable time interval M. The same procedure applies to w. The shear stress TxZ, which is exerted by turbulence at a certain level z on the flow below that height, is equal to the horizontal momentum transported downward through a horizontal unit area. Thus we obtain TXZ =
where p is the similar to Eq. the unit area along with it.
-p
av
(4.5)
air density and the subscript av indicates a time average (4.4). In Eq. (4.5) - p W is the mass that passes through per unit time while U is the horizontal velocity carried By introducing Eq. (4.3) into Eq. (4.5) we arrive at Txzjp
= -
[uw
+ UW' + wu' + av]
(4.6)
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
129
Normally it is assumed that both wand w' vanish so that only the last term is left in Eq. (4.6). This is particularly true for the flow of fluids through pipes or along an even plane. Now, the question of whether these assumptions are also valid for the marine boundary layer of the atmosphere arises. In most of the studies devoted to this problem tv and w' have both been taken as zero, but there are also other opinions. Raethjen (1961), for instance, suggested that turbulent elements from the free atmosphere might penetrate from above into the layer next to the ground. These turbulent quanta are certainly larger than those originating in the surface layer and might cause that w # 0 or w' # O. In such cases the computation of the turbulent shear stress is affected considerably, as was discussed in detail by Raethjen (1961). A third conceptual difficulty is connected with the .boundary conditions at the sea surface. From observations of mean values of wind and ocean currents and also from theoretical studies we know that there is a considerable difference, amounting to about 45°, between the direction of the wind at about 10 meters above sea level and the direction of the wind-induced surface current. Since in the lowermost part of the atmospheric boundary layer the direction of the air flow does not change noticeably with elevation, the problem of how the mean motions of air and water particles adjacent to the sea surface are related to one another arises. There is no doubt that the two flow vectors are equal in the case of a laminar boundary layer. With turbulent motion however, it is generally accepted that the instantaneous flow vectors are different on both sides of the sea surface. The problem is whether equality may be assumed for the mean motions. In many studies this is done, i.e., it is supposed that the vector of the mean air flow immediately at the boundary is equal to the vector of the mean surface current. In other words, it is taken for granted that, on the average, the air adheres to the water surface. In view of the directional differences observed with wind and ocean currents such an assumption, however, seems questionable. In order to remove this difficulty, Schmitz (1962a) put forward a theory that a continuous transfer of mechanical energy from the air to the water is introduced as a boundary condition. Taking into account that the flow components normal to the instantaneous sea surface must be equal in air and water at any moment (kinematic boundary condition) and that, at the instantaneous sea surface, the stress vector of the air acting on the water must balance the stress of the water acting on the air (dynamic boundary condition), Schmitz found the transfer condition satisfied if the difference vector between
130
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
the surface flows in air and water is perpendicular to the wind stress vector at the surface at any moment and, consequently, for the temporal and spatial mean. Hence, the equality of the vectors of mean flow on both sides of the sea surface is not a necessary (but a sufficient) condition for the continuous transfer of mechanical energy, which can also be fulfilled if the mean values of flow in air and water immediately at the sea surface differ from each other, i.e., if the air glides over the water. According to Schmitz (l962a), because of the continuity of energy transfer at the sea surface, any excess of work due to the average fields of motion must be compensated by an opposite excess of work done by the fluctuant fields of motion. The implications of the theory of Schmitz are rather far reaching but they cannot be discussed here in more detail. Only one important feature should be mentioned: If the mean directions of wind and current are different, there is no possibility that the vectors of wind and stress have the same direction and, in addition, the work done by the average wind field is completely transferred to the mean current without partial transformation into turbulent motion. Much more, the mean vectors of wind and stress can only have an almost equal direction if an appreciable amount of work performed by the average wind stress at the sea surface is converted into turbulent and wave energy. This result provides a new insight into the frictional coupling between atmosphere and ocean. 4.3.3 Vertical Profiles of Mean Wind Speed under Indifferent Thermal Stratification Having given consideration to the difficulties inherent in measuring and theoretically interpreting the wind field in the first few meters above the sea surface, we now pass to a more detailed discussion of the vertical wind profile in the marine boundary layer. Having in mind the particular influence exerted on those profiles by thermal stratification and in order to simplify matters as far as possible we have split up the treatment: A preliminary section (Section 4.3.3) is devoted to the wind profile under neutral conditions, while the effect of thermal stability will be dealt with in the section immediately following it (Section 4.3.4). 4.3.3.1 Simplifying Conditions. When considering the results of wind profile measurements above the sea surface obtained with adiabatic stratification one must account for the following effects: (a) The height of the internal boundary depending on the fetch. (b) The question of equilibrium between the air flow and the state of the sea.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
131
Effect (a) is important if the maritime wind profiles are taken in coastal regions, as is commonly done. Then it may happen that the air flow, originating from land and having its character adjusted to the land surface as lower boundary, arrives at the observation point after having passed only such a short distance over water that the turbulent bottom layer which is influenced by the sea surface, and which starts to develop after the air has left the coast line, does not yet reach the top of the height range to be considered. The upper parts of the wind profile which are above the internal boundary separating land- and sea-influenced flow will consequently reflect land characteristics. The resulting discontinuity will then complicate the interpretation of the wind profiles. Some evidence of this effect of fetch was given by Takahashi (1958), who also showed that the height of the sea-influenced flow increased rapidly with time (or with fetch) under unstable conditions, but slowly in stable cases. In the following, such disturbing influences will not be taken into consideration. With regard to (b) it must be stated that the situation is the simplest if there is an equilibrium between wind and waves which, naturally, can exist only in the absence of substantial changes in wind speed and direction. In addition, the character of the sea surface must be representative for the momentum exchange air-sea, i.e., disturbing influences due to varying depth (refraction of the waves) or due to the presence of a coast (reflection of waves) must be avoided. As shown by Portman (1960), considerable differences occur between wind profiles measured under equilibrium conditions and those under transient ones, the latter being very difficult to interpret. Therefore, we shall abstain from discussing the wind profile in the transient state. 4.3.3.2 Hydrodynamic Analogy. If the discussion is chiefly devoted to a wind profile that corresponds to equilibrium conditions between wind and waves and is subject neither to effects of fetch nor to influences of thermal stability, the interpretation of the results can make use of the controlled experiments on turbulent flow which have been done in hydraulic and -aerodynamic laboratories. The experiments which lend themselves most readily to this application are those on the flow of fluids through pipes. As the mean velocity at a point varies only with the distance from the axis of the pipe, the flow is similar to a horizontally uniform wind, where the mean speed depends only on the distance from the ground. This aerodynamic analogy has proved very useful for the interpretation of field measurements provided that the inherent limitations were recognized. Now,
132
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
a few words must be said about the relevant definitions and relationships established for the turbulent flow in pipes. Subsequent to Eq. (4.6) and within the limits indicated therein, the basic relation for the momentum transport through a unit area in a horizontal plane for a two-dimensional flow is:
au
= A-
az
T
where x, z
=
u, w
=
ii,
w=
u', w' = T
=
Km = p
=
A =
au
= pKM -
az =
- «pw)'u' >av
'" -
p (w'u'
>av
(4.7)
rectangular coordinates with x axis along direction of the mean wind, z vertical component wind velocities along x, z component mean wind velocities along x, z departures from the mean flow internal shear stress or vertical transport of horizontal momentum (dyn cm <) eddy viscosity (em- sec") air density (gm cm P) "Austausch" coefficient [gm crrr! sec-I]. A is equal to eddy viscosity KM times air density p.
The bar or subscript av denotes the average over a period of time at a fixed point, whereas the prime indicates instantaneous departures from that average. Obviously Eq. (4.7) represents two different relations which have been combined here for convenience. Its left side merely serves as defining equation for the turbulent Austausch coefficient A in imitation of the corresponding equation for the molecular momentum transfer, the molecular viscosity I-t being replaced by the turbulent transfer coefficient A. Thus the viscous stress, as compared with the turbulent stress, has been neglected in Eq. (4.7). In general, this simplification is justified, except in a very shallow layer next to the ground, with a thickness of the order of I mm, where the turbulent stresses are reduced owing to the kinematic constraint of the boundary. The right side of Eq. (4.7) is the familiar formulation of Reynolds' turbulent shear stress which is based on the supposition that the vertical flow component is negligibly small when averaged over a period of sufficient duration. The exclusion of the air density p from the averaging, as indicated in Eq. (4.7), does not substantially alter the eddy stress since the effect of the density fluctuations is evident in those of u and w.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
133
Thus the left side of Eq. (4.7) is of integral nature, describing the transfer process as a whole. On the right side of Eq. (4.7), however, there are taken into account the turbulent fluctuations themselves and it can, therefore, be referred to as a differential treatment of the problem. We shall first use the integral part of Eq. (4.7); the eddy correlation term will be considered later. In due course Eq. (4.7) will be extended in order to apply to the . three-dimensional flow (Section 4.4.1) and to the turbulent transfer of sensible heat and moisture (Section 5.2.2). Now the problem of how to find a suitable interpretation of the turbulent transfer coefficient A arises. In an effort to relate this quantity to more concrete parameters of the turbulent flow, Prandtl (1932) pointed to the fact that the dimension of the eddy viscosity KM equals the product of length and velocity. For the characteristic length he introduced the mixing length I, which has a certain analogy to the mean free path used in the kinetic theory of gases. It represents the distance which a fluid particle will travel, normal to the flow at the mean velocity of its original layer, until it is again mixed with its new surroundings. The characteristic velocity is considered to be equal to the difference between the velocity of the specified fluid particle and that of its new surroundings, and for which, as a first approximation, Prandtl assumed I( ou/oz). Detailed consideration of the mechanism of turbulence (see, for example, Lettau, 1939) revealed that this velocity difference is equal to the mean fluctuation iii of the horizontal flow component and proportional to the mean fluctuation w' of the vertical flow component, which are both of the same order of magnitude. With these notations the Austausch coefficient takes the form A = pKM = pI2(oujoz)
(4.8)
According to Eq. (4.7) we now obtain for the turbulent shearing stress T = p12( oujOZ)2 (4.9) which we can write in the form (Tjp)1I2 = I(oujoz) = u;
(4.10)
thus introducing the friction velocity u,.. Experiments in hydraulic laboratories as well as theoretical investigations have shown that, in the absence of thermal stratification, the mixing length is a linear function of the distance from the boundary.
134
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
For the flow along a rough wall I = k(z
+
zo)
(4.11)
is valid where k is the universal von Karman constant, which has been determined to be very close to 0.4. The so-called roughness length or dynamic roughness zo is measured in centimeters and depends upon the shape and distribution of the roughness elements. Owing to Zo, a finite value of the mixing length exists immediately at the rough boundary. Under stationary conditions, Prandtl assumed the shearing stress T to be constant with height and, therefore, equal to the wind stress TO on the ground. In the first few meters of the atmosphere the same is valid for the air density p. Then Eqs. (4.10) and (4.11) can be combined to (4.12) oil/oz = u../[k(z + zo)] and integrated. The result is the well-known logarithmic wind profile over a rough boundary il = (u../k) In [(z + zo)/zo] (4.13) where the wind speed equals zero at z = o. It should be mentioned that, according to Bjorgum (1952) and Monin and Obukhov (1954), the logarithmic wind profile can also be derived theoretically with only the help of considerations of similarity and dimension. Combining Eq. (4.12) with Eq. (4.8) and (4.11) we obtain A = pk(z + zo)u.. and KM = k(z + zo)u..
(4.14)
for the Austausch coefficient A and for the eddy viscosity KM in the fully turbulent flow over a rough boundary under neutral conditions. A somewhat different formula is valid for the flow over an aerodynamically smooth surface that is distinguished by the fact that the roughness elements are small compared with the thickness of the laminar boundary layer next to the surface. In the laminar layer the vertical momentum transfer is wholly due to the molecular viscosity 11- resulting in a linear velocity profile up to a height of about z = 5v/u*, where the kinematic viscosity v of the air is defined by v = 11-/p (for numerical values see List of Physical Constants). Transitional conditions prevail betweeen the altitudes Sv]«, and 30 v[u; while fully turbulent flow is dominant above z = 30 v/u*. Here the wind profile takes the form (von Karman, 1934) il = (u.. jk) In [(const. u*z)!v]
(4.15)
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
135
In earlier publications (for example, Nikuradse, 1932), the constant had been fixed at about 9.0. According to Clauser (1956) a more appropriate value of the constant is 7.5 (with k = 0.41). 4.3.3.3 Discussion of Measured Wind Profiles. The interpretation of the measured vertical profiles of mean wind speed above the sea surface is almost exclusively based on the relationship given in Eq. (4.13), i.e., the results are presented in a semilogarithmic graph with i1 as abscissa and In z as ordinate. If the measured profile fits into a straight line; evidence is given that Eq. (4.13) is true. Values for u; and Zo can be easily derived from the slope of this straight line (u*) as well as from its intercept on the In z axis (In zo) (Fig. 36). In r
'" o
...J
'-------------Wind speed
u
FIG. 36. Schematic representation of the mean wind profile in a semi logarithmic system under different thermal conditions.
An examination of the results obtained by the investigations reviewed in Table X reveals that the vertical profile of mean wind speed over the sea surface is close to logarithmic if thermal stratification is absent. An example is given in Fig. 37. Some of the older measurements showed a kink in the profiles somewhere between 0.6 and 1.5 meters, thus establishing a marked departure from the logarithmic form. However, there is good reason to assume that the effects mentioned in Section 4.3.3.1 under (a) and (b) and, perhaps, errors owing to instruments and exposure were not completely excluded. Although agreement could be attained with regard to the form of the vertical wind profile at sea, considerable differences exist as far as the parameters friction velocity u; and dynamic roughness Zo are concerned. Agreement can be stated, to some extent, only for a negative result which will be described first.
136
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
Since the relationships between the dynamic roughness and the average height and form of the roughness elements are well established for the flow along a solid wall (Prandtl, 1932; Motzfeld, 1937; Lettau, 1939), it seems quite obvious that similar interrelations also should be sought in the case of the wind flow along the sea surface. However, the relevant examination of the observational data did not show any evidence for such a connection. In particular, no relation could be found so far between dynamic roughness and wave height, Wind group
o
e
b
d
200 Q;
>
.!!!
0; 100 f-----r-¥--"t-----1--'+------"f------1--'f-----+-+--
"0;0 c o
Cl>
E
50
Cl>
>
o .0 o
s:
20
0'
Cl>
I
10 f-------+-1,-----,f---+----/t---+---+-----i~----+--
200
400
600
Wind speed (em/sec) FIG. 37. Wind profiles over a water surface under near-adiabatic conditions. (After Roll, 1948a). The profiles are grouped according to wind speed.
even if a wide range of wave heights was considered. This result once more emphasizes the peculiar character of the sea surface as lower boundary of an air flow. Perhaps more success would be obtained if the "roughness factor" defined by Schooley (1961b) (Section 4.2.3) were used as representative of the sea surface characteristics. In this connection it should be mentioned that Miyazaki (1951a, b) theoretically attempted to relate the dynamic roughness of the sea surface to ocean wave elements by assuming that eddies are generated in the air-sea boundary layer and that the width of the eddy-generating
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
137
layer and the largest eddy diameter are determined-for large Reynolds numbers-by the height and the length of the waves, respectively. This concept appears to be based, however, on a rather theoretical idea of the airflow around moving water waves which by no means has been clarified up to now. Besides, mean values of wave height and length cannot be considered as truly representative characteristics of the irregular wave pattern. No verification of Miyazaki's formula has become known so far, apart from recent measurements of Vinogradova (1960) that seem to point to a relation between the dynamic roughness of the sea surface and the mean steepness of the surface waves. While the results concerning a possible relation between dynamic roughness and waves are rather uniform, although only in the negation, the statements are conflicting with regard to the variation of the dynamic roughness depending on the characteristics of the air flow. At first it must be decided which quantity of the air flow shall be taken as representative. The velocity of the wind, although it is often used as an independent variable, does not seem to be a suitable one since it varies with the altitude. It is more satisfactory to take the friction velocity u, as the quantity representative of the air flow. This was done by several authors. Their results may be summarized in two antagonistic statements as follows: (a) Roll (1948a) found that his wind profile measurements led to the relation (4.16) Zo = v!(2.lu*) This equation is in conformity with von Karman's formula [Eq. (4.15)] for the turbulent flow along a hydrodynamically smooth boundary, thus suggesting the conclusion that the air flow over the sea surface seems to obey the law of the hydrodynamically smooth flow, the pertinent dynamic roughness being about four times as high as for a smooth boundary. This is in good agreement with the results of Motzfeld (1937) who, in his wind-tunnel investigations, found that for round-crested (solid) waves Zo was a function of the maximum angle am of the wave profile, so that zn
= (v!3u*)
x
10 3.17(tan Gtm l u . >
(4.17)
It should be mentioned further that Rossby (1936) arrived at a similar
conclusion when considering the lower parts of the wind profile measurements of Wiist (1920) and Shoulejkin (1928). More recently Takahashi (1958) deduced, from his own wind profile data, that the
138
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
concept of the hydrodynamically smooth character of the sea surface holds true. (b) In contradiction to (a), Charnock (1955), discussing his own wind profile measurements and those of some other authors and after stating that the dynamic roughness Zo was comparatively independent of fetch or stability but largely determined by U*, suggested the relation Zo = u~/(ag), (4.18) the approximate value of the dimensionless constant a being 81.1. Equation (4.18) implies an increase of Zo with growing u; and, therefore, differs distinctly from Eqs. (4.16) and (4.17) which show a decrease. Charnock's relation was-at least qualitatively-confirmed by the wind profile measurements of Hay (1955) and Deacon et al. (1956), which also indicated an increase of zn with increasing u., The suitable value of the constant a was about 13 for the former measurements and 20 for the latter. In the range of friction velocities below 10 ern/sec Charnock's formula received some support from relevant results reported by Roll (1948a) and Bruce et al. (1961) and, to a minor degree, from the wind profiles measured by Portman (1960), who obtained extremely small values of the dynamic roughness Zo which, however, seem to be affected by the rather strong unstable stratification that existed there. The relationship advanced by Charnock cannot be interpreted in terms of a hydrodynamically smooth or rough flow. Much more, it may be regarded as an empirical result of the endeavors to find a suitable representation of the air flow over a water surface. A task which remains to be done is to interpret this empirical result in the light of our (as yet rather incomplete) knowledge of the characteristic processes near and in the sea surface. An illustration of the situation, particularly of the discrepancies between (a) and (b), is given in Fig. 38 where only wind profile measurements that are nearly logarithmic and that have been published in a suitable form are used. When looking at this diagram one may have the impression that-a certain scatter of the observations admitted-the data of Roll (1948a) are more or less covered by Charnock's curve, too. Apart from this argument we may further state that Charnock's concept (b) appears to be more realistic and, therefore, more adequate than (a) since it is very difficult to imagine that the roughness elements of the wavy and choppy sea surface should be small as compared with the thickness of the laminar atmospheric boundary layer (order of magnitude '" 0.1 em), which would be implied in the case of a hydrodynamically smooth flow.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
139
Unfortunately, this perplexing situation appears by no means clarified when we refer to more recent profile measurements, e.g, to those which were most carefully executed by Brocks (1959b, 1962). He used a specially constructed buoy as carrier for the instruments. The profiles proved to be closely logarithmic under adiabatic conditions but the variation of the dynamic roughness seemed to be insignificant over a wind speed range of from 2 to 14 meters/sec, i.e., over a range of the X
# ~:
10- 1
\\0,
",0'\
\ 10- 2
,\
,,;
1ROII
"Q.', /'; u
c,"-
\\0,
\\
\~,o
E
<;,<;'\
,(\0 (,'(\0
10- 3
"<, ,
0'_
(19480)
-
....... ........ Mo~--'-~_ -
Zfeld ( 19 - -
3 '1)
0
" V> V>
'"
c s:
C'
::>
e u
10- 4
o Bruce
E 0
er of. (1961)
c;
>-
0
10- 5
•• Ie Portman (1960) 10- 6
• • •
10-7
30 10 20 Friction velocity
40
50
u. (em/sec)
FIG. 38. Dynamic roughness =0 as a function of friction velocity 11*. Results of wind profile measurements over the sea surface and wind tunnel investigations.
140
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
friction velocity u.. from 12 to 50 cm/sec. The mean value of Zo amounted to about 0.004 em for the open North Sea whereas 0.025 em was obtained for the enclosed waters of-the western Baltic Sea. Thus we must state that this problem has not yet been satisfactorily settled but needs further study. More adequate and more exact measurements of the wind distributions over the sea are necessary, which is no easy task in view of the fact that, in order to provide sufficiently exact values, precision anemometry is required under difficult circumstances. In additions- theoretical efforts should be made to contribute to the solution of the problem of why the sea surface, owing to its characteristic properties, behaves neither as a rough nor as a smooth boundary, and how the complicated mechanism of surface friction works. Promising steps in this direction were made by Schmitz (1961; 1962a, b). It is realized quite well that-apart from wind profile measurements-there are other sources of information (measurement of the wind-induced tilt of the sea surface, for example) on such parameters as dynamic roughness and friction velocity. However, in order not to confuse the already complicated situation we have restricted the discussion in this section, devoted to the wind profile over sea waves, to the information gained from profile measurements. The other aspects will be dealt with later on (see Section 4.3.5).
4.3.4 Effect of Thermal Stratification on the Wind Profile over the Sea 4.3.4.1. Introductory Remarks. Hitherto, the treatment of the wind profile has been confined to adiabatic conditions. The turbulent processes involved in creating the peculiar vertical wind distribution reflected the nature of the lower boundary and of the flow itself, the turbulent energy being supplied by the kinetic energy of the flow. We are used to calling this turbulent motion dynamic or isotropic turbulence. The latter designation refers to the fact, already mentioned above, that the velocity fluctuations are of the same order of magnitude for all the components of the turbulent flow. No component is specially distinguished when compared with the others. Their turbulent fluctuations are equally suppressed in the vicinity of the ground. If, however, the thermal stratification is not indifferent but stable or unstable, conditions are modified, since buoyant forces, which influence the vertical flow components alone, are brought into play. This is the case of nonisotropic turbulence and we are now going to discuss its bearing on the wind profile over the sea surface.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
141
In doing so we make use of the relevant knowledge of wind profiles over land. As is to be expected, the effect of thermal stratification is, roughly speaking, that under unstable thermal conditions the turbulent exchange in the vertical is intensified and the vertical wind speed gradient decreases more rapidly with height than in the adiabatic case. The reverse is true for thermal stability. The corresponding types of the wind profile are schematically indicated in Fig. 36. In a semilogarithmic system the nOJladiabatic wind profiles no longer follow straight lines but are bent into curves. Under unstable conditions their curvatures are convex to the u axis; in stable cases they are concave. This effect of thermal stratification diminishes with increasing dynamic turbulence, i.e., with growing wind speed. The influence of stability also decreases when the surface is approached. Very close to the ground the logarithmic law is found to be valid, the roughness parameter Zo having the character of a boundary condition. Although these expectations have been verified sufficiently for wind profiles over land, similar evidence is rather scarce for maritime profiles. As the effect is small, especially in the first few meters from the surface, the requirements, with regard to both instruments and exposure, are not easily fulfilled. This observational handicap, as well as the fact that the influence of thermal stratification must diminish with decreasing altitude or increasing wind speed, may explain why several authors [Roll, 1950; Hay, 1955; Goptarev, 1957 (for wind speeds above 15 meters/sec); Portman, 1960] also have reported nearly logarithmic wind speed distributions under nonadiabatic conditions. Wind profiles over the sea surface which showed the expected effect of stability were published by Bruch (1940), Deacon et al. (1956), and Fleagle et al. (1958). An example is shown in Fig. 39. 15,--------,-----,--------, 10
8 ~
~ 6
.§.
4
~A,.,..4
~4
.»
08 0.9 Relative wind velocity
FIG. 39. Profiles of relative wind speed over the sea surface under different thermal conditions. (From Deacon et al., 1956.) 0, unstable, Ri = - 0.07. x, adiabatic, Ri = +0.01. ~, stable, Ri = +0.18. The Richardson numbers refer to the levels 13 and 4 meters.
142
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
4.3.4.2 Profile Coefficients for Momentum. Since at sea, particularly in the first few meters above the surface, deviations from the adiabatic wind profile are relatively small, some benefit can be expected from approximations of the nonadiabatic wind distributions by means of logarithmic profiles. The vertical gradient of the mean wind speed may then be written in the form OU ruJia (4.19) az z + zo where the quantity
r
U
a
is defined by 1
au aIn(z + zo)
ru = - ---a
ii«
(4.20)
in analogy to Montgomery's (1940) evaporation coefficient. The expression I'U a is called profile coefficient (Brocks, 1956; Deacon and Webb, 1962) or profile contour number (Fleagle et al., 1958), a; being the mean wind speed at the height z = a. As shown by a comparison with Eq. (4.12), the form of Eq. (4.19) corresponds to a logarithmic profile where the product ruaUa has the same function as u,,jk in the adiabatic case. The difficulty now is that, unlike u", I'U a is not independent of the height variable z as might be inferred from Eq. (4.20). Consequently, Eq. (4.19) is valid-strictly speaking-only for z = a and approximately in the neighborhood of this height. In particular, it is neither possible to compute friction velocity and dynamic roughness from Eq. (4.19), nor is it admissable to integrate this equation over a substantial height interval as was pointed out by Brogmus (1958). It is only to adiabatic stratification that the following relations apply (4.21)
r., = (ln~
;0 ZO)-l
(4.22)
which permit the evaluation of u, and Zo if rU a and Ua are known. The difficulties mentioned above restrict the applicability of the profile coefficient in practice, as I'»; can only be computed from measured wind profile data if Eq. (4.19) is integrated. Therefore, the relevant results of different authors are only comparable under adiabatic conditions. Nevertheless, some benefit seems to have been obtained from the concept of the profile coefficient I'U a ' particularly when the observational material that has to be considered is large. Although
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
143
the former values of the profile factor r ua, as given by Brocks (1955) for different stabilities or Richardson numbers (see Section 4.3.4.3), disagreed with those of Fleagle et .al. (1958), even in the adiabatic case, later results obtained by Brocks (1959a) appear to be more in harmony with them. This question will be dealt with in greater detail in Section 5.2.5. 4.3.4.3 The Richardson Number. When attempting to account for the stability effect on the wind profile quantitatively we have to consider the contribution of the vertical heat flux H to the production of turbulent kinetic energy as compared with the share supplied by the shear stress. While the latter is Touloz per unit volume and per second, the additional energy provided by buoyancy forces may be written (gH)/cpTo
where g = acceleration of gravity Cp = specific heat at constant pressure To = mean absolute air temperature of the bottom layer The dimensionless ratio of these two expressions is introduced as the flux form of the Richardson number Rf=
-gH cpToT( ou! oz)
(4.23)
(The negative sign is taken in order to have negative Richardson numbers for positive heat flux values H, i.e., for unstable stratification.) Its relation to the more familiar gradient form of the Richardson number
.
Ri
g(oe!oz) To( ou! OZ)2
=----
(4.24)
where B = mean potential air temperature can be established by means of the proportionality of the fluxes T and H to the corresponding vertical gradients ouloz and oBloz according to Eqs. (4.7) and (5.1). We then obtain Rf = (KH!KM)Ri
(4.25)
where KH is the eddy conductivity. Rf equals Ri if the eddy transfer coefficient for heat (KH) is the same as for momentum (KM). The dimensionless Richardson number serves as an estimate for the energy transfer in a turbulent flow under nonadiabatic conditions. It indicates the energy supplied or consumed by thermal stratification
144
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
as compared with the energy furnished by eddy stresses. It is positive for inversional or stable stratification where the turbulent stresses have to work against gravity. Negative Ri numbers correspond to superadiabatic or unstable cases, whereas Ri equals zero under adiabatic conditions. Ri increases numerically with the height z. 4.3.4.4 The Diabatic Wind Profile in General. It seems reasonable that we should look for a solution where Eq. (4.12), which determines the vertical wind speed gradient under adiabatic conditions, is generalized by adding, on the right side, the dimensionless factor S, which represents the influence of stability and is a function of the flux Richardson number Rf: 8u, ~ SeRf) (4.26) 8z k(z + zo) k] S can then be considered as the generalized von Karman constant k" . For the adiabatic case Rf = the stability function S must equal unity. Applying Eq. (4.23) we eliminate 8a/8z in Eq. (4.26) and subsequently arrive at
°
gkH(z
S=
+ zo)
(4.27)
pCpTou~ Rf
Following Monin and Obukhov (1954) we introduce the quantity pCpTou~
L=----
(4.28)
gkH
which has the dimension of a length and may be called "stability length." Attention should be paid to the inverse relations between the heat flux H and the stability length L: Stable stratification: H < 0, L > Adiabatic stratification: H = 0, L --> ± 00 Unstable stratification: H > 0, L < 0. With Eq. (4.28), Eq. (4.27) takes the form
°
S =
z
+ L
Zo 1
-
Rf
k
k*M
(4.29)
We may consider (z + zo)/L as a dimensionless buoyancy parameter, which is particularly useful when the profiles of both wind speed and air temperature are to be expressed in a dimensionless form. The
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
145
basic assumption of the similarity theory advanced by Monin and Obukhov (1954) is that the deviations S from neutral stability in these two vertical distributions are universal functions of (z + zo)/L. Then, according to Eq. (4.29), the height dependence of Rfis entirely determined by L. For near-neutral conditions, S approaches unity and KH does not deviate much from KM. Thus, in that stability region, the three buoyancy parameters Rf, Ri and (z + zo)/L are nearly equal to each other. The same is valid for k'M and k. The parameter (z + zo)/L serves to clarify the differences in the vertical. Since S must tend to unity if L --+ ± 00, it is obvious that purely dynamic turbulence without appreciable thermal effects will predominate at heights (z + zo) with (z + zo) ~ ILl. Thus Eq. (4.26) approximates to the neutral expression as (z + zo) decreases and a certain fraction of ILl, probably a small one, may be interpreted as the height of the bottom layer with dynamic turbulence prevailing. According to Eq. (4.28), L increases as H approaches zero and/or with growing wind speed. Additional properties of L will be discussed in Sections 5.2.6.1 and 5.2.6.2. Combination of Eq. (4.7), (4.26), and (4.29) leads to a useful relationship between the eddy viscosity KM or the Austausch coefficient A = pKM and the flux Richardson number: KM = ku*LRf
A
=
(4.30)
pku*LRf
4.3.4.5 Approximative Solutions Proposed for the Diabatic Wind Profile. The attempts to determine the still unknown stability func-
tion Sin Eq. (4.26) can be divided into two classes: (a) Those which assume similar profiles for wind speed and temperature. (b) Those which do not presuppose that similarity. Case (a) implies that the stability function for wind speed (Su) differs from that for potential air temperature (So) only by the constant factor y so that Su = v So. Thus, according to Eqs. (4.26) and (5.26) (see Section 5.2.6.1), the ratio of the vertical gradients oil/8z and olJ/oz equals that of the corresponding turbulent fluxes multiplied by y: (4.31) oiljoz : o0j8z = yT : - Hjcp Consequently we have KH = yKM
and
Rf= yRi
(4.32)
146
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
Along this line the following formulae were suggested:
ou
-
oz
U".
= ----
k(z
+ %0)
(1
+
0"1
.
Rt)1/2
(4.33)
by Rossby and Montgomery (1935)
sa oz
1
u;
=----
k(z
(4.34)
._---
+ zo) (1- cr2Ri)I/2
by Holzman (1943)
ea
oz = k(z
,
( Z + Zo) + zo) 1 + rx~
U".
(4.35)
by Monin and Obukhov (1954) Here aI, a2, and o: are constants to be fixed empirically. By applying Eqs. (4.29) and (4.32) and assuming y = 1 (as done by Monin and Obukhov) the last formula can be transformed into ea u; 1 (4.36) oz k(z + zo) 1 - o: Ri For near-neutral conditions [i.e., at very small values of Ri ~ (z + zo)/L] the higher order terms of Ri and (z + zo)/L, respectively, can be neglected and the three formulae given above are reduced to the same approximative equation
ea
-
oz
U".
.
= - - - - (1 + const. Rt) k(z
+ zo)
(4.37)
which requires the constants to be connected by the relation 0"1
=
0"2
(4.38)
= 2rx
Integration can be easily performed for the near-adiabatic case + zo)/L ~ 1] by using Eq. (4.35). It yields the well-known "log + linear" profile [(z
_
U
=
u, (
k
Z + Zo
In - Zo -
rxZ)
+L
(4.39)
which contains the adiabatic case for L --)- 00 and describes the effect of stability by an additional term linear in z. Similar "log + linear" laws have been derived by various authors (see the instructive review given by Charnock, 1958a). It is easy to verify that the nonadiabatic modification of the adiabatic formula [Eq. (4.13)] is given in the right sense as indicated in Fig. 36.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
147
Monin and Obukhov (1954) evaluated the constant o: at 0.60 ± 10 per cent by using wind profile data over land without simultaneous flux measurements. This value is, however, not consistent with Eq. (4.38) as al was determined to be about 9. It was also criticized by Taylor (1960a), who found that Monin and Obukhov (1954) had applied (Eq. (4.39) over too wide a range of (z + zo)/L, i.e., of thermal stability. In a later paper Taylor (1960b) could show that o: varies systematically with stability, and ranges between about 3 and 6 for the stability region - 0.03 < (z + zo)/L < 0 for which Eq. (4.39) does apply. Thus an average value of 4.5 results, which would be consistent with al = 9 and Eq. (4.38). Deacon (1962a), from unpublished data of vertical wind speed and temperature differences measured by Calder over a very level desert surface, derived values of 3.4 and 3.0 for the product rf.y. Since, for near-neutral conditions, any departure of y from unity has not yet been established with certainty, the product rf.y also provides a sound estimate for a: Summarizing, we can say that the "log + linear" wind profile is adequate only for a very narrow stability range which, on the lapse side, seems to be limited by I(z + zo)/LI = 0.03 and which corresponds more or less with the region where mechanical turbulence dominates, i.e., with the conditions of forced convection (see Section 5.2.6.2). In that region the constant y seems to assume values around unity (Taylor, 1960a). Bearing in mind that Eq. (4.39) was derived for near-adiabatic stratification, i.e., for small values of Ri, we cannot expect that this approach will prove useful also under conditions of great instability or stability. Therefore, let us now turn to a discussion of case (b), which is not based on the assumption of similarity as was (a). Consequently, = KHIKM = Rf[Ri is no longer constant but appears as an additional variable. With increasing instability (z/L < - 0.03) the flow enters a region where, in addition to dynamic turbulence, buoyancy forces begin to playa dominant role. If the instability is sufficiently great, the heat flux and buoyancy term is decisive whereas u ; becomes negligible. This is the region of free convection (see Section 5.2.6.2). Ellison (1957) suggested that, with high instability, y = KH/KM might approach a constant value which would again imply similarity between wind and temperature profiles. On this basis Taylor (1960a, b) tested the height dependence (Z/L)-l/3 y
148
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
which is well established for temperature profiles (see Section 5.2.6.2), also against three sets of wind profile observations in free convection, and he found a rather satisfactory agreement for zjl: < - 0.03. The corresponding y values (for two sets of observations) were 1.35 and 1.67. In the case of extreme stability (z/L}> 1) the existence of a limiting Richardson number Rfis assumed. When this Rfvalue is approached, KM no longer increases Wrth height but remains more or less constant, i.e., according to Eq. (4.30), proportional to u.L, Here the elements of turbulence do not explicitly depend on the distance from the ground. They are only of local character. Striving for a solution that would incorporate near-neutral conditions as well as strong instability and stability Ellison (1957) put forward a theory predicting that y = KH/KM would vary strongly with the flux Richardson number Rf, particularly under stable conditions. The variable quantity y tends to zero when Rf approaches a critical value Rferit. which thus appears as the maximum value of Rf for the maintenance of turbulence. The relationship proposed by Ellison reads
oa oz
u..
=
(
Rf A-(z + zo) 1 - Rferit.
)-114
(4.40)
The constant Rfen«. was estimated to be about 0.15. Panofsky et al. (1960) found Eq. (4.40) well confirmed by various wind profile data for unstable conditions if Rf/Rferit. was replaced by 18 Ri, a modification which is caused by the fact that the flux Richardson number Rf cannot be obtained from profile data alone, and which implies y = 18 Rferit. '" 2.7. Under near-adiabatic circumstances this result is consistent with the approximative relation Eq. (4.37), in particular with regard to the factor of Ri which should be 40t '" 4 x 4.5 = 18. If we combine Ellison's formula, Eq. (4.40), with Eq. (4.29), we obtain the following equation for the stability factor 5
1 z + Zo 54 - - - - - 53 = 1 Rferit. L
(4.41)
which serves as a useful link between the wind profile and the heat flux provided that Rfen«. is known. If the wind profile is given, the heat flux can be computed. Conversely, the wind profile can be determined if roughness length Zo, friction velocity u; and heat flux H are known.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
149
With Eqs. (4.40), (4.29), and (4.28) we further arrive at a relation for the eddy viscosity KM (Panofsky et al., 1960) U~ (Oil KM = - - = U~ -
oil/oz
OZ
1 PCpTo Rfcrit.
gH +-
)1/3k
4 /3( Z
+
ZO)4/3
(4.42)
Here, u:( oilj8z) represents the production rate of mechanical turbulent energy (per unit mass" whereas gHjpcpTo gives the rate at which energy is created by buoyancy. The relation between the contributions of dynamical turbulence and convective forces to the vertical momentum transport is determined by IjRfcrit. Panofsky (1961) interpreted Eq. (4.42) in the light of Heisenberg's expression
where € is the rate of energy dissipation and I the eddy size. He suggested that, in the atmosphere, z takes over the function of I, i.e., the eddy scale is identified with the height above the ground. However, according to Panofsky this relation is unlikely to be valid with stable stratification where the turbulent elements seem to be independent of the distance from the ground, as was already mentioned. Further evidence on this case is needed. So far no investigation has become known in which, beside the determination of wind speed profiles, simultaneous measurements of wind stress and heat flux were carried out at sea so that the solutions of the diabatic wind profile, which in part are well established over land, could be examined with regard to their applicability to wind profiles over the sea surface. There is, however, the approach suggested by Deacon (1962a), who, by using Eqs. (4.28) and (4.31), transformed the second term «zujkl: of Eq. (4.39) into rxyzg(08joz)jTo(oiljoz). Hence, the wind stress T = PU.2 and the heat flux H are replaced by the vertical gradients of wind speed and potential air temperature. Consequently, if no fluxes are measured, profile data only permit the evaluation of the product rxy. Deacon (1962a) applied this amended form of Eq. (4.39) to the wind and temperature profile observations carried out over water by Fleagle et al. (1958). The differences between the wind speed measurements ill, il2 at the two levels Zl, Z2 were considered in terms of the wind velocity ile taken at a small height. In addition, the ratio of the gradients (oBjoz)j(oiljoz) was replaced by the ratio of the differences !:1Bj!:1il observed between two convenient heights. The relation derived
150
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
from Eq. (4.39) then reads ii2 - iiI
U"
Z2
- - - = -In - + ue ku; Zl
g
tiJj
IXy - - - ( Z 2 -
ueTo flu
zr)
(4.43)
u..lue is a constant, which, according to Eq. (4.39), implies that the stability term is considered negligible at that small height and that Zo is constant, too. The latter supposition, however, is somewhat questionable when applied to observations over the sea surface. With u,,/Ue taken as constant the first term on the right-hand side of Eq. (4.43) is constant, too. Thus IXy can be evaluated from observed values of Ul, U2, ue, flu, and flO in the near-neutral range. Deacon arrived at an average of IXy = 3.7 which agrees satisfactorily with the values obtained over land and suggests that the concepts developed for an air flow over a rigid boundary may also apply to conditions over a water surface.
It was assumed that
4.3.4.6 Other Wind Profile Formulae. In addition to the formulae given in the preceding section there must be mentioned two further approaches to the diabatic wind profile wherein the influence of stability is taken into account in a way somewhat different from Eq. (4.26), namely, so that the dimensionless factor S does not appear as an explicit function of the Richardson number. The power formula advanced by Deacon (1949, 1953) has been used with particular success. It reads
(Z
ZO)l-fJ
OU u" + OZ = k(z + zo) ~-
(4.44)
The exponent f3 is termed the "Deacon number." It is defined by the equation f3 = _ oln( oujoz) = _ _Z(_0_2u_j_oz_2) (4.45) oln Z (oujoz) Apart from a slight dependence on the height z, the Deacon number f3 is a function of the Richardson number, assuming values greater than unity under unstable conditions and less than unity for stable stratification. In the adiabatic case (f3 = 1) the power formula passes into the logarithmic profile. An analytical expression for the relation between f3 and stability was published by Panofsky et al. (1960). A disadvantage is that the dynamic roughness Zo, which normally is considered as a boundary condition, varies with stability. A similar power law was introduced by Laikhtman (1944).
4.3
151
WIND FIELD IMMEDIATELY OVER SEA SURFACE
A direct approach to the marine wind profile was published by Goptarev (1960). Using the observation that, under unstable thermal conditions, the fluctuations of the horizontal flow component decrease exponentially with height, and applying the concept that this decrease is connected in some way with the intensification of the vertical exchange motion, Goptarev derived the following relation for the height dependence of the mixing length in a stratified atmosphere I = k(z + zo)e-a 0 stable). In the last case the mixing length I increases with z near the surface until a maximum is reached at z + zo = t]«. Above that height the mixing length decreases. The integration of Eq. (4.47) is done by developing the e function into a series. It yields the wind profile in the form _
u
U"
= -
k
(
Z
+
Zo
In - - - + az + Zo
a2(z
+
ZO)2 -
2· 2!
z5)
)
+ ...
(4.48)
The first two terms of this solution correspond to Eq. (4.39) if a is assumed to equal «[L (which would be in accord with Eq. (4.28), at least as far as the sign is concerned). Provided that the higher terms are used, Eq. (4.48) is, however, reported to be valid also for strong deviations from adiabatic conditions, which is not the case with Eq. (4.39). Goptarev interpreted his equation by making use of his profile measurements on an oil drilling platform (Goptarev, 1957). From his results the following is paraphrased here: The dynamic roughness Zo cannot be considered as a direct characteristic of the geometry of the sea surface but as an aerodynamic quantity reflecting the interaction between wind and waves. According to Goptarev this is made evident in particular by his finding that the dynamic roughness Zo decreases with increasing wave height and with decreasing wind speed relative to that of the waves, i.e., with improved flow conditions around the moving waves. With a view to the difficulty inherent in fixing really representative wave
152
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
data these results should, however, be regarded with reserve. Furthermore, the dynamic roughness Zo was found to be greater with unstable thermal stratification than with indifferent or stable temperature distributions, a result which agrees with the observation that, at the same wind speed, the sea is rougher in cold air masses than with warm air over cold water. 4.3.5 The Wind Stress at the Sea Surface 4.3.5.1 Definitions and Designations. When discussing the vertical wind profile in the first few meters above the sea surface we have dealt so far only with the dependence of the dynamic roughness on other factors, e.g., wave height, wind speed, friction velocity. Nothing has been said up to now about the second important parameter of the air flow over the sea: the friction velocity u., According to Eq. (4.10) the friction velocity is closely connected with the vertical flux of the horizontal momentum or the turbulent shear stress T which was defined by Eq. (4.7) and which, as already mentioned, is generally considered as constant with height in the first few meters of the atmospheric boundary layer. Thus we can write T
=
TO =
pu..2
(4.49)
where TO is the tangential stress exerted by the wind on the sea surface = air density). This quantity is of considerable importance as it plays an essential part in all processes of momentum transfer across the air-sea boundary, including generation of ocean surface waves and drift currents by wind action, wind setup, and storm tides. Finally the entire ocean circulation, as well as the momentum balance of atmospheric circulation, is substantially affected by the shearing force of the wind acting on the sea surface. It is customary to express the surface drag TO of the wind at the sea surface in terms of the mean wind speed Uz at a certain height z
(p
(4.50) the factor of proportionality C z being a dimensionless constant, termed "resistance coefficient" or "drag," "shear-stress" or "friction coefficient," and depending on the height z. Usually z = 10 meters is taken as reference level. The problem of determining the surface stress TO is now reduced to ascertaining reliable values of ClO. The drag coefficient C10 can be easily related to the parameters of the vertical wind profile. By combining Eqs. (4.49) and (4.50) we get ClO
=
(U../UlO)2
(4.51)
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
153
Further, if adiabatic conditions prevail the following relation can be derived from Eq. (4.13) 10
+ ZO)2
ClO = k 2 j ( In-~
(4.52)
In the absence of thermal stratification ClO is, therefore, entirely determined by the dynamic roughness zoo With temperature distributions other than neutral ClO has to be computed from Eq. (4.39), which implies an additional dependence on IX/L.
4.3.5.2
Methods of Measuring. Estimates of the drag coefficient
ClO have been based largely on indirect evidence. The following
effects of the wind stress at the sea surface have been used. In air: (1) Vertical wind profile immediately above the sea surface (wind profile method). (2) Departure from the geostrophic wind in the atmospheric boundary layer (geostrophic departure method). (3) Simultaneous fluctuations of the horizontal and vertical components of the air flow from the mean over the recording period using Eq. (4.7) {eddy correlation method). In water: (4) Stationary tilt of the surface of enclosed bodies of water due to wind action (sea surface tilt method). At the sea surface: (5) Contraction of an insoluble monolayer on the water surface by the action of the wind (surface film method). The wind profile method (1) has already been described in Sections 4.3.3 and 4.3.4. Measurements of wind speed at two heights would, at least in an algebraic sense, be sufficient under adiabatic conditions in order to determine u; and/or zn, whereas such values would be necessary at three heights if stable or unstable stratification were present. Should values be available at more than three heights, additional information on the accuracy of the parameters can be obtained. The difficulty inherent in this method was clearly shown by Priestley (l959a), who compared wind stress values derived from wind profiles (over land) with simultaneous measurements of surface stress. Even the close fitting of the measured values to the profile curve did not assure sufficient accuracy in the results inferred therefrom. Evidence was given that values of surface wind stress of acceptable accuracy can only be gained from wind profile measurements "when Zo is
154
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
assigned in advance." This, of course, may be possible over land but offers nearly insurmountable difficulties at sea, where the dynamic roughness is not a constant but an aerodynamic quantity reflecting the interaction between wind and waves. Thus, values of the wind stress on the sea surface derived from wind profile data must be regarded with caution. Similar and further objections against the wind profile method were raised by Schmitz (1961). Since it is particularly difficult to obtain reliable wind profile data on shipboard, Gerstmann (1961) suggested the calculation of u; from measurements of the wind speed taken at one height and combined with values of the air-sea temperature difference. This procedure certainly requires some theoretical background. The computation is done by applying Eqs. (4.39) and (5.32) for the wind and the temperature profiles, respectively, under nonadiabatic conditions, and by using Charnock's relation [Eq. (4.18)] for the roughness parameter, zoo This method may be useful when shipboard observations are applied to the computation of vertical energy fluxes at sea. The weak side of this procedure, however, is that unestablished theoretical concepts have to be used. The geostrophic departure method (2) covers a region beyond the first few meters above the sea surface to which this Section is devoted and will, therefore, be dealt with in a later section. (See Section 4.4.1.1.) The eddy correlation method (3) offers severe difficulties when applied at sea, as the motion of the vessel will falsify the recorded fluctuations of the wind components. This handicap can only be overcome if the carrier of the recording instruments is fixed or completely stabilized. The stabilization might be achieved with the least expenditure if the sensing elements are mounted on a buoy. Apart from preliminary values obtained by McIlroy (1955), and Vinogradova (1959), on fixed near-shore constructions and by Deacon (1960) on a small vessel, no results of eddy flux measurements over the sea have become known so far. * The sea surface tilt method (4) is applicable if an enclosed body of water is available and the wind has blown for a sufficiently long period as to assure steady state conditions. Using Ekman's (1923) assumption that the surface stress then just balances the hydrostatic forces due to the tilt of the surface, the wind slope i can be expressed by the equation i =
TO
+ TB
~~
gpu;d
(4.53)
* Recently Brocks and Hasse (1963) reported the first results of eddy flux measurements executed by means of a gyro-stabilized mast installed on a buoy.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
155
Herein T B denotes the frictional shear stress of the bottom return current on the bed of the lake, g the acceleration of gravity, pw the water density, and d the mean depth of the water. From Eq. (4.53) the surface stress TO can only be derived if the bottom stress is known. Theoretical considerations have shown that TB = To/2 is valid in the special case of laminar flow in water (Van Dorn, 1953) and that the values for TB generally lie between 0 and To/2 if turbulent flow is assumed (Hellstrom, 1941). Measurements of the bottom stress have indicated that, in most cases, TB is quite small compared with TO, e.g., Francis (1953) found TB '" 0.015 TO, and Van Dorn (1953) found T B ~ 0.1 TO. Consequently the bottom stress may be neglected in Eq. (4.53) and the surface wind stress TO is given by TO
= gPwdi
(4.54)
from which, for the drag coefficient ClO, we have the following: ClO =
Pwgdi pil 120
(4.55)
The tilt method has been applied both in laboratory and in field measurements. Examples of the former procedure were published, for instance by Francis (1951) and Keulegan (1951), whereas results of field investigations were reported by Neumann (1948), Van Dorn (1953), Hellstrom (1953), Keulegan (1953), Darbyshire and Darbyshire (1955), and others. The possibilities of achieving the necessary accuracy are somewhat different in laboratory and field investigations. Since the magnitude of the tilt of the sea surface is only of the order of 10- 7 at low wind speeds, the setup must be measured to at least 10-4, 1O~2, or I em for consideration of distances of 10 meters, I km, or 100 km, respectively. From these requirements it could be inferred that using rather large natural bodies of water would offer certain advantages as compared with laboratory tests, where the short distances available demand a hardly realizable exactness of the setup measurements, notwithstanding the fact that in the laboratory it is comparatively easy to establish controlled conditions and to secure the best possible precision in measuring. Even supposing that the required accuracy of 1 em could be fulfilled with water-level indicators in large lakes and seas, the determination of the effective mean depth would raise new difficulties, particularly if the density stratification is such that the wind effects of drift and slope are confined to the upper layer. In addition, tidal and seiche movements, as well as horizontal differences
156
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
in water density, may disturb the slope measurements, apart from the fact that a steady state of equilibrium between wind and setup will be guaranteed only rarely. Finally, near-shore effects due to waves can seriously affect determinations of wind setup if these, as is customary, are derived from water level records taken near the shore (Stewart, 1962). A workable compromise can be attained by investigating the wind effects on ponds which are small enough for an adequate control but large enough for the setup measurements to be done with sufficient accuracy. Therefore, the investigation carried out by Van Dorn (1953) on an artificial pond of about 240 meters length, in which an accuracy in the setup measurement of 5 x 10- 7 could be reached, deserves special attention. The surface film method (5) is a new approach which was practiced by Vines (1959) and seems to provide reliable stress values at very low wind speeds where the other methods are difficult to apply. Surface-active material was introduced into the water in the absence of wind. The resulting monolayer was retracted under the action of a wind until the surface stress exerted by the wind was exactly counterbalanced by the opposing film-pressure gradient. Simultaneous measurements of surface pressure (at the end of the tunnel) and of the extent of the film resulted in proving a linear relationship between these two, the surface-pressure gradient being a measure of the wind stress. 4.3.5.3 Resulting Drag Coefficients. A comprehensive and very useful compilation of the wind stress coefficients ClO determined by the different methods (1) to (4) was given by Wilson (1960). A total of forty-seven investigations are quoted therein. After having coordinated the different results, Wilson arrived at the conclusion that, for strong winds (.» 10 meters/sec, mean about 20 meters/sec), the mean value of ClO is 2.37 X 10- 3 with a standard deviation of 0.56 x 10-3 • For light winds « 10 meters/sec, mean about 5 meters/ sec) the scatter of ClO is particularly wide, the average value being 1.49 x 10-3 with a standard deviation of 0.83 x 10-3 • Greater accuracy is certainly needed for this wind speed range in order to establish reliable values of the drag coefficient. According to Wilson (1960) CI O increases between light and strong winds from about 1.5 to 2.4 x 10-3 , probably in a nonlinear manner, and there is some reason to assume that for very high wind velocities some value in the neighborhood of 2.4 x 10- 3 will be approached asymptotically (Francis, 1959), as is depicted in Fig. 40. The linear relation between drag
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
157
coefficient and wind speed proposed by Sheppard (1958) obviously does not fit the data in that region. When summarizing, Wilson gave equal weight to all the results listed by him. Consequently, his truly "democratic" resume does not show the peculiarities inherent in the data supplied by the five methods. 0003.--------------.:,....-----~
..........
o
<S
~ .;:
xx~~~---~--~--o-
x
s?9 . ' ~ ~;..<.
0002
Q;
V .. .. x x xF
8
.... c )( x
~
~
0001
····
i
0.000
/:
o
5 10
Meters per second
10
15
20
30
Knots
20
40
25 50
30
60
FIG. 40. Shear-stress coefficient CIa for wind action at the sea surface depending on the wind velocity fho. (From Francis, 1959.) Origins of presented data: Straight solid line, F, Francis (1951) (Wind tunnel experiments); 0, Hellstrom (1953); D, Charnock et al., (1956); x, Deacon et al., (1956). Straight dotted line, S, Relation suggested by Sheppard (1958), CIa = (0.80 + 0.114 iilo) x 10- 3 (iho in meters per second).
In order to provide some information on this question, Table XI has been compiled, mainly on the base of the data presented by Wilson (1960). Only experimental results were used therein; mere discussions or reviews of data were omitted, but some other results not considered by Wilson were added. On the whole, fifty-one sets of data have been employed. As can be inferred from Table XI, the field measurements of wind setup are the only ones where a decrease in the drag coefficient C10 with increasing wind speed was repeatedly observed, resulting even in a slight decrease of the mean C10 value. In addition, there should be noticed the exceptionally wide scatter (1.0-6.2 x 10-3) in the drag coefficients obtained by field measurements of wind set up with light winds. As was pointed out by Deacon and Webb (1962), horizontal differences in water density associated with horizontal temperature gradients may affect the surface slope appreciably, in particular with light winds, thus rendering the application of the tilt method difficult under such circumstances. Consequently, we should regard the ClO values for light winds as supplied by the tilt method with reserve and we should not put too much weight on them.
158
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
Readers will remember that similar caution was recommended above with regard to the drag coefficients derived from wind profile data at sea. This is certainly true, as was strongly emphasized by Neumann (1956, 1958) in a controversy with Deacon (1957) on the diverging results obtained with light winds for the wind stress on the sea surface. On the other hand, it must not be overlooked that, apart from the field measurements of the sea surface slope, the other mean TABLE XI WIND STRESS AT THE SEA SURFACE. DRAG COEFFICIENTS CIO DERIVED BY DIFFERENT METHODS
Wind Profile Laboratory Measurements CIO
Year
Author
Hamada et al. 1953 Sibul 1955 Hayami and 1959 Kunishi Average
Field Measurements
x 103
CIO X
Light winds
Strong winds
Author
Year
0.5 1.1 1.2
1.5
Shoulejkin Rossbyand Montgomery Bruch Roll Roll Hay Deacon et al. Hunt Goptarev Farrer Fleagle et al, Takahashi Brocks (Baltic) Hunt Portman Bruce, et al. Brocks (North Sea) Deacon (Port Phillip) Deacon (open sea)
1928 1935
0.9 0.8
1940 1948a 1955 1955 1956 1956 1957 1958 1958 1958 1959b 1959 1960 1961 1962
1.9 1.1 1.2 1.6 1.0
0.9
1.5
2.1 1.7
Eddy Correlation CIO
Year
Light winds
McIlroy 1955 Vinogradova 1959 1960 Deacon
1.45 1.46
Author
Average
1.46
x 103 Strong winds
I
'l 2.3
I
Average
103
Light Strong winds winds
1.1 1.2 1.5
0.4 0.4 1.1
2.2 2.5 2.6 2.4 3.3 1.8 1.9 1.5
2.9 1.1
1962a, b 0.95
0.95
1962a, b 1.2
1.2
1.1
2.0
TABLE XI (Continued) Geostrophic Departure
Tilt of Water Surface
ClO
X
Year
Light winds
Strong winds
Francis Keulegan Johnson and Rice
1951 1951 1952
0.6
2.5 2.6 2.5
Average
-
0.8
ClO
103
Author
1.1
ClO x 103
Field Measurements
Laboratory Measurements
2.5
Author Colding Ekman Palmen and Laurila Hellstrom Schalkwijk Hela Neumann Saville Van Dorn Reid and Clayton Keulegan Hellstrom Darbyshire and Darbyshire Clayton Pollak Average
Year
103
X
Light Strong winds winds
1876 1905 1938
-
2.6 2.5 2.4
1941 1947 1948 1948 1952 1953 1953
2.1
1.5
1953 1953 1955 1956 1960
-
2.6 1.8 2.0 2.5 2.9 4.0
4.2 -
1.0 1.9 2.3 2.1
Author Rossby and Montgomery Rossby Sutcliffe Durst Sheppard et al. Sheppard and Omar Charnock et al.
1935
1.3
-
:::l trl
1936 1936 1950 1952 1952
-
o
0.4 0.4 2.0
2.9
-
s:trl
1.1
-
~ trl
1956
1.5
-
1.1
2.4
-
2.0
2.4
~
r-
~
o
~
o
ra
~
l:I>
~
Surface Film
l:I>
ClO x 103 Author
Year
Light winds
1959
0.9
2.1 2.7
~
Light winds
-
2.9
w
Year
Average
2.5 1.8
6.2
Strong winds
~
Vines
Strong winds
-
~o
trl
....
VI
1.0
160
4
FLOW CHARACTERISICS OF MARINE ATMOSPHERE
ClO values, which were obtained by different methods, are in satisfactory agreement, particularly for light winds (see Table XI). Moreover, this agreement also embraces the drag values derived by Van Dorn (1953) from measurements of surface slope on an artificial pond which can be referred to as obtained with sufficient accuracy (5 x 10- 7) and under well controlled conditions. Bearing all this in mind, we are more or less induced to attach a lower reliability value to the drag coefficients ClO obtained with light winds by field measurements of sea surface tilt than to the other ones. Nevertheless, final evidence obtained by more accurate measurements is indispensable. In this connection, it is of considerable interest that the results of the most recent wind profile measurements (Brocks, 1959b, 1962; Deacon, 1962a, b) indicated a nearly constant drag coefficient (of from about 1.1 to 1.5 x 10- 3) in the wind speed range up to 13 meters/sec, provided that only neutral conditions were considered (Fig. 41). 0002 0
C,O
0.001
0000
0
2
0
+
0
9
+ x
+
0
+ x
10 4 6 8 Wind speed iJ 10 (meters/sec)
+ x
X
12
14
FIG. 41. Drag coefficient ClO for neutral stability, derived from recent wind profile measurements. 0, Brocks (1962), Baltic Sea; x , Deacon (I962a, b), enclosed waters of Port Phillip; +, Deacon (I962a, b), open sea. The straight line represents the relation suggested by Deacon: ClO = (1.10 + 0.04 U10) x 10- 3 (iho in meters per second).
For comparison it should be mentioned that the stress of the wind on the ice of the Polar Sea was determined by Sverdrup (1957), who applied the geostrophic departure method to pilot balloon ascents made when the Norwegian research vessel Maud in 1922-24 was drifting with the ice to the north of northeastern Siberia. He found an average drag coefficient of C7 = 6.9 X 10- 3 , which was reduced to 5.2 x 10- 3 under adiabatic conditions. Thus the drag exerted by the wind on the ice is essentially greater than the wind stress acting on the sea surface. Still larger values have been observed in hurricanes. Myers (1959), who studied the surface friction in a 1949 hurricane by means of a wind analysis at Lake Okeechobee, Florida, obtained drag coefficients of 2.2 x 10- 2 and 2.0 x 10- 2 for over-water friction tangential and normal to the wind.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
161
4.3.5.4 Effect of Atmospheric Stability and Fetch. In Table XI nothing is said about such influences on the drag coefficient as atmospheric stability. Generally it can be assumed that the values given therein refer more or less to neutral conditions. In more recent studies (e.g., Brocks, 1962; Deacon, 1962a, b) particular stress was laid on evaluating the drag coefficient from measurements made with adiabatic stratification. Some indication as to the significance of thermal stability on the wind stress was given by J. and M. Darbyshire (1955). They showed that atmospheric stability has a very marked effect on the tilt of the water surface due to the wind. In measuring the surface slope of a lake under different thermal conditions they obtained stress coefficients that, for a given wind speed, were twice as great in unstable cases as in stable ones. Unfortunately, wind speed and air temperature were not measured over the lake but at an airport a few miles away, a fact that renders the outcome somewhat questionable. The Darbyshires' result is in conformity with the findings of Goptarev (1960), already mentioned in Section 4.3.4.6, and with the well-known observation that, for a certain wind speed measured at the top of a ship's mast, the wind action on the sea surface, as made visible by the generation of foam, spray, and waves, appears to be more intense with cold air over warm water than with warm air over cold water (Roll, 1952b, 1953-1954; Fleagle, 1956a; Brooks and Brooks, 1958). J. and M. Darbyshire also found that the stress coefficient increased with the length of the water which was under the action of the wind. When the fetch varied from 12 to 29 km the drag coefficient increased from 1.6 to 2.5 x 10- 3 , i.e., by about 50 per cent. A similar result was indicated in the wind channel studies by Hayami and Kunishi (1959) and also in the field investigations on the wind profile carried out by Deacon (1962a, b). For relatively enclosed waters (fetches between 20 and 50 km) the latter obtained a mean drag coefficient of 0.95 x 10- 3 whereas 1.2 x 10-3 was found for the open sea (compare Fig. 41). Unfortunately, this evidence is by no means definite, because the results of Brocks (1962) (Table XI) show the opposite effect, i.e., the drag coefficients for the landlocked waters of the western Baltic Sea were greater than those for the large fetches over the open North Sea. It is possible that the opensea results of Deacon were biased by experimental errors owing to the rather great motion of the ship in the heavy southern ocean swell. As far as setup measurements are concerned (Darbyshire and Darbyshire, 1955; Hayami and Kunishi, 1959), quite important uncertainties
162
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
result from wave action and, in particular, from the effect of momentum transport by waves to the lake margin. As was pointed out by Stewart (1962), setup measurements, especially those performed near the shore, can be seriously affected by that phenomenon. Thus, the marked rise of the drag coefficient with fetch observed by J. and M. Darbyshire can, at least in part, be caused by the momentum transport related to the longer waves present with greater fetches (Deacon, 1962b). 4.3.5.5 Critical Wind Speed. If it is assumed that the drag coefficient ClO increases with growing wind speed, the question of whether this increase occurs gradually over a more or less extended wind speed range, or abruptly at a certain wind speed, appears. Some data were assembled by Munk (1947) with the aim of proving the existence of a critical wind speed for air-sea boundary processes at about 7 meters/sec characterized, for example, by a discontinuity in wind stress. The sharp increase of C lO at this critical wind speed is said to accompany a change of the sea surface from an aerodynamically smooth character to an aerodynamically rough one. According to Munk the critical wind speed for air-sea boundary processes corresponds to the well-known (though never verified) KelvinHelmholtz instability criterion, which states that, under the conditions of frictionless potential flow, a water surface will become unstable, i.e., will be roughened by wavelets, if the wind speed exceeds 6.71 meters/sec. Although the connection between the critical wind speed for air-sea boundary processes and the Kelvin-Helmholtz instability has fascinating aspects, the concept proposed by M unk (1947) has not been generally accepted (apart from some favorable results presented by Mandelbaum, 1956) since no convincing evidence for a discontinuity in air-sea boundary processes, particularly in wind stress, at about 7 meters/sec could be found. Later on Takahashi (1958) took up this subject in a somewhat different manner by establishing empirically critical friction velocities u.. for the first formation of wind waves (3.7 em/sec) and for the generation of whitecaps (17 em/sec). Since the wind speed varies with height it is certainly more suitable to give critical friction velocities than critical wind speeds. The values mentioned above need confirmation, however. 4.3.5.6 Tangential Drag and Form Drag. In order to further the understanding of the complex nature of the wind stress on the sea surface, investigations need to be carried out with the aim of separating the different components of this quantity, viz., the tangential
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
163
friction drag and the form drag attributed to the waves. Attempts in this direction were made by Keulegan (1951), Van Dorn (1953), and Munk (1955). In his laboratory studies Keulegan discovered that waves could be virtually eliminated by adding a detergent to the water. This provided a way of measuring the setup produced by a given wind separately with waves present or absent. The same technique was applied by Van Dorn (1953) in his wind stress measurements on an artificial pond. In Fig. 42 the setup S observed by him is reproduced
0.4
E
0.3
.:0 (f)
0.2
0.1
4
6
8
10
12
ii,o (rneters /sec)
FIG. 42. Wind setup S observed at different wind speeds UlO for a clean water surface (B) and for a water surface covered with a soap slick (A). (From van Dorn, 1953.) Each point is a 20-minutetime average for both wind speed and setup. The wind speed is given in a quadratic scale.
as a function of the square of the wind speed. The data referring to a natural surface clearly diverge, at wind speeds iilO above 5.6 meters/ sec (curve B), from those that were obtained when the surface was covered with soap (curve A), which follow a straight line through the origin. The simplest interpretation is to attribute curve A to the tangential skin friction and to assign the incremental stress between the curves A and B to the form drag caused by the waves. Accordingly, Van Dorn (1953) obtained the following expression for the total wind stress (4.56) Here, the first term represents the tangential friction drag (curve A) with drag coefficient CIO = 1.1 X 10-3 . The second term corresponds to the form drag which becomes effective only if the wind
164
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
speed U10 surpasses the so-called formula velocity U10, which was empirically determined to be 5.6 meters/sec at a height of 10 meters. The density of the water is pw. The value of the second dimensionless constant C1~ was fixed at 2.25 x 10- 6 • ' It should be mentioned that no obvious physical changes in the appearance of the water surface could be noted at the wind speed U10 = 5.6 meters/sec and that the formula velocity has nothing to do with Munk's "critical wind speed" (see Section 4.3.5.5). There is some indication (Van Dorn, 1953) that the wind stress, occurring at the wind speed U1O, is associated with a specific value of the surface current, independent of the scale of the experiment. According to Van Dorn the relation given in Eq. (4.56), at a first approximation, appears to be independent of fetch and, therefore, independent of the size of the waves. From this result and his own laboratory measurements Francis (1954) drew the tentative conclusion that the form drag is principally caused by the small, slowly moving ripples and wavelets. This suggestion seems to be widely accepted now, although a complete proof of the ripple theory of drag is still lacking. Some light was thrown on this complicated problem by a theoretical study published by Munk (1955). If h(x, y, t) designates the elevation of the sea surface and p(x, y, t) the pressure at this surface, the components of the stress due to normal pressure are p(ohJox),
p(ohJoy),
-p
Their mean values represent the components of the form drag. Following the sheltering hypothesis introduced by Jeffreys (1925), Munk assumed the existence of sheltered regions with eddies to the leeward of the wave crests, which implies a phase lag between wave profile and pressure distribution. The pressure exerted on surface waves progressing in the x direction with the phase velocity C is then given by p
=
± sp(u - C)2( ohJ ox)
(4.57)
where s is the "sheltering coefficient" which, by wind tunnel experiments on solid wave profiles, was found to be of the order of a few per cent. Munk extended the application of Eq. (4.57) to a spectrum of waves and, in particular, evaluated the mean square slope of the sea surface and the components of the form drag for the fully developed sea under the assumption that the Neumann (1953) spectrum is valid. He obtained a linear relationship between wind speed and
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
165
mean square slope in conformity with the measurements of sun glitter (Cox and Munk, 1954) (see Section 4.2.3). Another remarkable result of the computation is the large contribution to slope and form drag made by the young or high-frequency waves, as is depicted in Fig. 43. This representation shows that the form drag is more closely related to the slope statistics than to the elevation statistics. Consequently, the low-frequency waves which mainly contribute to the mean square elevation seem to be of little significance for the aerodynamics of the sea surface, a conclusion which confirms the findings of Francis (1954) mentioned above.
o
05
1.0
2.0
1.5
Wave age
FIG. 43. Contributions to the mean-square elevation, mean-square slope, and form drag by waves of different wave age (= wave velocity/wind velocity). (From Munk, 1955.)
In connection herewith it was stated by Munk that the form drag is much less affected by limitations in fetch and duration than the wave height, since the high-frequency waves which determine the form drag reach their final state much more rapidly than the lowfrequency waves dominating the wave amplitude. This does not harmonize with the variation of the drag coefficient with fetch observed by J. and M. Darbyshire (1955). On the basis of the results described above, Munk (1955) advanced an interpretation of Van Dorn's wind setup data which is somewhat different from Eq. (4.56). He suggested the following relation for the composite wind stress: -2 (4.58) TO = PC10U + PC101/(gv)-1/3-U 3 10
10
where g is the acceleration of gravity and v the kinematic viscosity of the fluid. The factor (gv)-1/3 was introduced for dimensional reasons; it is related to the minimum wind speed needed to maintain waves
166
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
against viscosity. The dimensionless constant Cl'~ equals 0.68 x 10-6 . In Munk's approach, the form drag is represented by a cubic law, contrary to the relation given in Eq. (4.56) suggested by Van Dorn (1953). The cubic dependence results from the fact that the mean square slope of the sea surface increases linearly with the wind speed iho. This would imply a total drag coefficient that increases linearly with wind speed beginning with ClO = 1.1 X 10-3 , which is not inconsistent with Fig. 40 and Table XI. Comparison with the data of Van Dorn (1953) shows that Eq. (4.56) gives a somewhat better fit than the cubic law [Eq. (4.58)], particularly with high winds, The presentation of the wave drag problem would be incomplete if no reference were made to a new treatment of the energy and momentum transfer from the air to the waves recently published by Stewart (1961). From an inspection of empirical wave data, Stewart drew the conclusion that an appreciable part of the total momentum transfer is originally executed by the wave drag, although some of the momentum put into waves is lost afterwards to the drift current owing to dissipation. The transfer model he suggests is the following: The effective height at which the air loses momentum is not the surface but a height at which the wind speed i1 is at least equal to the phase velocity C of the waves. This concept corresponds to the theory of wave generation advanced by Miles (1957) (see Section 4.2.1). It is required that the energy pass unattenuated through the bottom layer with i1 < C. Motions of this kind must be rather highly organized, i.e., of wavelike character, and can no longer be described as turbulent, although the momentum will be carried down to the sea surface by the Reynolds stress, as in fully turbulent flow. The consequence is that, in the layer immediately above the sea surface, the turbulent stress is no longer constant with height, as is usually assumed, but increases with height up to the level where i1 = C, and above which the stress is carried by turbulence only. According to Stewart further consequences of this concept may possibly involve not only the conventional method of analyzing vertical wind profiles but also the vertical transport of sensible and latent heat above the sea surface, as the organized and wavelike motions transferring momentum will presumably contribute only little to these processes. The approach presented by Stewart (1961) certainly needs verification by suitable measurements. Complete clarification of the mechanism of momentum transport near the sea surface would be attained if the covariance
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
167
4.3.5.7 Stress Due to Rainfall and Sea Spray. As may be noticed in Fig. 42, the setup was increased in the vicinity of the wind speed UIO = 12 meters/sec during a period of heavy rain. An estimate of Van Dorn (1953) indicated that a raindrop initially traveling with the wind and falling from a height of 10 meters through a layer of linearly decreasing wind retains about 85 per cent of its initial horizontal velocity when it arrives at the ground. Thus it appears possible that heavy rainfall can considerably augment the stress on the sea surface. Munk (1955) expressed the opinion that sea spray, picked up by the wind and accelerated before returning to the sea surface, might represent yet another appreciable mechanism for transfer of momentum from wind to water. 4.3.6. Gustiness Near the Sea Surface As already indicated in Section 4.3.5.2, very little information is available with respect to wind fluctuations in the first few meters above the sea surface. Only two investigations are known to the author wherein some results on this subject are given. Hay (1955) published gustiness measurements made by using two Sheppard pattern bidirectional vanes at heights of 1 and 2 meters above the sea. From traces over periods of 5 minutes he obtained values of the lateral gustiness gy and the vertical gustiness gz, the former representing the ratio, with respect to the mean wind speed, of the mean extreme eddy velocity in the horizontal at right angles to the mean wind direction, while the latter is defined similarly for the vertical component. The mean values of gy and gz at 1 and 2 meters, and the corresponding standard deviations as found by Hay, are given in Table XII. We take it from these figures that the lateral gustiness was more than twice as great as the vertical one. This TABLE XII LATERAL AND VERTICAL GUSTINESS OVER THE SEA SURFACE a
Mean values and standard deviations for Height (meters)
2 a
Lateral gustiness gy
Vertical gustiness
0.486 ± 0.017
0.203 ± 0.004
0.440 ± 0.020
0.199 ± 0.003
After Hay (1955).
s,
168
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
effect may possibly be attributed to the site of the measurements, which was about 800 meters east off a coastal cliff rising to a height of 60-90 meters and liable to create large-scale eddies. The scatter of the mean fluctuation values was quite noticeable, particularly with the lateral gustiness. No systematic variation of gy or gz either with wind speed or stability or surface roughness was observed in the considered (limited) range of these factors. As Table XII shows, there seems to exist a definite decrease in the lateral gustiness gy with height increasing from 1 to 2 meters, whereas the vertical gustiness remains practically unchanged. The method used for measuring did not, however, yield any information on the periods of the fluctuations and on the turbulent energy associated with these periods. More comprehensive results, particularly with regard to the dependence of gustiness on the time interval considered, on wind speed, atmospheric stability, and height were reported by Goptarev (1957). The observational material consists of wind speed records gained on a marine oil drilling platform at heights between 5.7 and 50.6 meters. Only the fluctuations of the horizontal wind velocity were investigated. The gustiness is characterized by the ratio (4.59) where Umax designates the maximum wind speed of a gust occurring within a fixed time interval t (1, 10, 20, 40, 60, 120, 200, 300, or 600 seconds) and U600 the average velocity computed for the time interval of 10 minutes = 600 seconds that covers the interval t. Average values of gt for different time intervals and heights are given in Table XIII. TABLE XIII HORIZONTAL GUSTINESS OVER THE SEA SURFACEa,b
Height above the sea surface (meters) Time interval (seconds) 600 300 200 60 10 1 a b
5.7
15.0
27.3
50.6
1.370 1.326 1.300 1.257 1.168 1.060
1.278 1.258 1.233 1.183 1.110 1.024
1.238 1.215 1.203 1.155 1.104 1.022
1.220 1.193 1.182 1.151 1.078 1.022
After Goptarev (1957). Average values of gustiness coefficient gt for different time intervals and heights.
4.3
WIND FIELD IMMEDIATELY OVER SEA SURFACE
169
From this compilation it can be taken that the average gustiness values gt decrease at all levels with decreasing time interval t. This result could have been expected as the chance of experiencing a high wind-speed maximum will be greater the longer the time interval in question. Further, we observe a decrease of the average gustiness gt with increasing height for all time intervals, but it is most pronounced for the longer ones. This general trend seems to support the view that the fluctuations recorded belong to flow disturbances originating from the sea surface. The maximum gustiness coefficients reached 1.6-1.7 and did not show any marked variation with time interval and height. As regards the dependence of the fluctuations on the wind speed, Goptarev found that the gustiness coefficients at first decreased with growing wind speed up to 10-12 meters/sec. Above that value a slight tendency to increase was perceptible, particularly at higher levels, which resulted in the gustiness coefficient, at the wind speed of 34 meters/sec, being enlarged, as compared with its value at IS meters/sec, by the factor 1.034, at the height of 50.6 meters. The corresponding multipliers for the lower levels of 27.3, 15.0, and 5.7 meters were 1.015, 1.007, and 1.004, respectively. While the first decrease of the gustiness with growing wind speed below 10-12 meters/sec can be attributed to the intensified turbulent exchange which tends to smooth the horizontal flow, the later slight but distinct increase with higher winds points to a lessening of dynamic turbulent exchange caused by a strong horizontal current. Of course, this explanation can only be considered as a tentative one. Some support for the interpretation presented above may perhaps be received from the fact that the intensification of thermal exchange leads to a decrease of the gustiness coefficient, too, as can be seen in Table XIV. The gustiness coefficients for unstable stratification are always smaller than those obtained under stable conditions. This difference will, however, decrease and finally disappear the more the wind speed exceeds IS meters/sec and dynamic turbulence dominates. In addition to the average values for the gustiness coefficient gt, Goptarev also studied the frequency of occurrence of single gusts. The frequency distributions obtained for the actual gustiness coefficients were rather closely Gaussian, particularly those for the short time intervals of I and 10 seconds. Thus the gustiness coefficients obey a random distribution. A more detailed investigation has been carried out regarding the gustiness coefficient gl (time interval t = I second) at a wind speed U600 = 34 meters/sec. The
170
4 FLOW CHARACTERISTICS OF MARINE ATMOSPHERE TABLE XIV
EFFECT OF THERMAL STRATIFICATION ON HORIZONTAL GUSTINESS OVER THE SEA SURFACE"
Average gustiness coefficient gt for different time intervals t (seconds) Height above the sea surface (meters)
g600
Stable
Unstable
1.40 1.29 1.25 1.24
1.32 1.27 1.24 1.21
5.7 15.0 27.3 50.6 a
g300
Stable 1.35 1.26 1.22 1.20
g200
Unstable
Stable
Unstable
1.29 1.25 1.22 1.19
1.34 1.25 1.22 1.19
1.27 1.23 1.21 1.17
After Goptarev (1957).
TABLE XV FREQUENCY DISTRIBUTION OF THE GUSTINESS COEFFICIENT OVER THE SEA SURFACE"·b,e
Gustiness coefficient gl
0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-1.6 1.6-1.7
Height above the sea surface (meters) 5.7
15.0
27.3
50.6
0.007 .02 0.22 1.81 8.01 20.33 29.50 24.55 11.83 3.18 0.50 0.04 0.002
0.000 0.002 0.06 1.09 8.14 26.22 36.42 21.78 5.62 0.62 0.03 0.006 0.000
0.000 0.001 0.04 0.96 8.05 27.20 37.80 20.82 4.68 0.42 0.01 0.000 0.000
0.000 0.005 0.12 1.42 8.22 23.04 33.17 23.79 8.54 1.54 0.14 0.006 0.000
After Goptarev (1957). Related to a time interval of 1 second. c Average wind speed over 600 sec: 11600 = 34 meters/sec.
a b
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
171
corresponding distributions at four levels are reproduced in Table XV, from which we learn that the maximum frequencies lie between 1.0 and 1.1 and that a gust of 1.6 times U600 within one second at a height of 5.7 meters has a frequency of occurrence of only 0.002 per cent and, therefore, may be expected only once within 14 hours if a steady wind blows for a period of this length. At a wind speed of 34 meters/sec the mean acceleration was determined to be 3-4 meters/sec»; its maximum value was estimated at more than 10 meters/sec",
4.4
THE WIND STRUCTURE IN THE MARITIME FRICTION LAYER
The basic assumptions underlying the separate treatment of the first several meters above the sea surface presented in Section 4.3 were the following: the turbulent shearing stress was taken as constant with height and the airflow was considered as two-dimensional. If we now want to extend our approach to the whole friction layer above the sea, i.e., throughout the entire height range where the loss in horizontal momentum by bottom friction is compensated by a geostrophic motion, we have to drop these suppositions, and take into account the variation of T with height and the effects of the rotation of the earth which produce the well-known Ekman spiral, sufficiently established in the friction layer on land. Now, the important question of the special shape of the Ekman spiral above the sea arises. Besides the vertical variation of the mean wind vector throughout the maritime friction layer, the vertical distributions of the turbulent wind stress and of the Austausch coefficient, or eddy viscosity, dependent on atmospheric stability, are as much of interest as the nature of the turbulent velocity fluctuations themselves. Thus there lie ahead quite a number of problems which require detailed and particular investigation.
4.4.1 Methods of Study All the methods of measuring are based upon the following equations of the turbulent exchange of horizontal momentum along the vertical (related to a unit area in a horizontal plane): TXZ
= A xz(8u(oz) = - «pw)'u')av
Tyz =
A y z ( ov!oz)
=
-
p(W'u')av
(4.60)
«pw)'v' )av ~ - p <w'v' )av
(4.61)
~ -
172
4 FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
These equations form the necessary completion of Eq. (4.7) for a three-dimensional flow wherein the effect of viscosity, as compared with the exchange motions of larger scale, has again been neglected. The significance of the symbols used is as follows: x, y, z = rectangular coordinates with the x axis along the direction of the mean wind at the sea surface, z vertical u, v, w = component wind velocities along x, y, z ii, V, W = component mean wind velocities along x, y, z u', v', w' = turbulent departures from the mean flow according to Eqs. (4.3) and (4.4) p = air density TXZ(TyZ) = internal shearing stress in z direction for x - (y -) momentum or turbulent transport of x - (y - ) momentum in z direction Axz(A yz) = Austausch coefficient in z direction for x - (y -) momentum (equal to eddy viscosity Kxz(K yz) times air density p). Equations (4.60) and (4.61) imply the assumption that the vertical flux of momentum always descends the gradient of mean horizontal momentum. If, owing to buoyancy forces, significant fluxes should occur more or less independent of this gradient, occasionally even opposed to it, it is thought that such a deviation from the classical concept of turbulent exchange will be confined to regions and periods of very light winds. From Eq. (4.60) and (4.61) we can draw the conclusion that, in order to arrive at a complete description of the turbulent exchange process, we must measure the vertical gradient of the mean wind vector and the vertical distribution of the turbulent shearing stress. The former is generally deduced from a series of double theodolite observations of pilot balloons ascending at a low rate. The latter can be achieved in two different ways: (a) By vertical integration over the ageostrophic flow components (geostrophic departure method). (b) By direct measurement of the correlated turbulent departures from the mean flow (eddy correlation method). 4.4.1.1 Geostrophic Departure Method. If we neglect the effect of fluctuations in air density as well as the shear stress components Tyy
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
173
(which represent the turbulent transports of x and y momentum in x and y direction) and the corresponding horizontal gradients, the following relations can be derived from the equations of motion in the absence of local and advective components of the acceleration of mean motion. pf(v -
v g)
pfeil - Ug)
= =
(4.62)
OTxZ/ OZ
(4.63)
OTyz/OZ
Here, f is the Coriolis parameter (2w sin cp) and Ug, Vg are the component geostrophic wind velocities along x, y. Since it is generally accepted as reasonably obvious that the surface stress is exerted in the direction of the surface wind, the components of the shearing stress at the sea surface (z = 0) are TXZ
=
TO
and
Tyz
(4.64)
= 0
and Eqs. (4.62) and (4.63) can be written as follows:
I pf(v Z
Txz
=
TO -
(4.65)
Vg)dz
o
Z
TyZ
=
I pfeil -
(4.66)
Ug) dz
o
The surface drag TO can be evaluated from Eq. (4.65) in two different ways: (i) If the situation is such that the departure from the geostrophic wind is negligible above a height h, then this level may be taken as the upper limit of integration in Eqs. (4.65) and (4.66). In this case Txz,
TyZ'
OTxZ/OZ
and
OTyZ/OZ
will be equal to zero for z·~ h in Eqs. (4.62), (4.63), (4.65), and (4.66), and the surface drag TO will be given by h
TO
=
I pf(v o
as depicted in Fig. 44.
Vg)dz
(4.67)
174
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
This is the "classical" boundary layer conception. It was first applied to the maritime friction layer by Sutcliffe (1936), who used kite ascents on the Atlantic Ocean carried out by Kuhlbrodt and Reger (1933). Later workers, such as Sheppard et al. (1952), however, did not meet suitable conditions for the application of this procedure as their wind profiles, measured in the Westerlies, did not show the classical friction layer above the sea surface. More recently. Lettau (1950, 1957) pointed out how such cases can be managed. This will be described later on. (ii) The second way of evaluating the surface drag from Eq. (4.65) is applicable when there exists a height z "'" Zx at which oa/oz = 0 and, consequently, the shear stress Txz vanishes. Then we obtain from Eq. (4.65)
Jpf(v -
ZX TO
=
vg)dz
(4.68)
o
z
z -------
h
Vg
Constont with height
Vg
Vorying with height
FIG. 44. Determination of surface wind stress 'TO from geostrophic departure if the classical boundary layer conception is valid (Txz = OTxzjOZ = 0 for Z ;> h). v = Measured profile of mean wind component normal to the surface-wind direction; Vg = vertical variation of corresponding component of geostrophic wind. The shaded area is proportional to the surface drag TO.
The situation is illustrated in Fig. 45. It should be noted that here the surface drag is computed from the integral of the geostrophic departure normal to the surface wind up to the level z = Zx and that at and above this height v is not necessarily equal to Vg as in (i). Thus the approach (ii) differs distinctly from the classical procedure. It is particularly suitable for use in the trade wind region as, owing to
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
175
the opposing directions of pressure and thermal gradients, there is commonly a maximum in the profile of ii at a height of a few hundred meters. Additionally, the Trades constitute a relatively steady airflow and the path acceleration is quite small there. Relevant application of this method was reported by Sheppard and Omar (1952) as well as by Charnock et al. (1956). It is an advantage of method (ii) that the resulting value for TO is not greatly sensitive to the variation of Vg with height, which is difficult to ascertain. After the surface drag TO has been determined from Eq. (4.67) or Eq. (4.68), the turbulent stresses Txz and Tyz at other levels can be calculated from Eqs. (4.65) and (4.66). If, moreover, there exists a level z = Zy at which ov/oz = 0 and, consequently, Tyz = 0, then
I pl( o Zy
Ug) dz = 0
(4.69)
o
may serve as a useful constraint during the calculation. z
z
/
/ /v t
v
g
FIG. 45. Determination of surface wind stress from geostrophic departure if there exists a level z = Zx at which oujOz = 0 and, consequently, Txz = O. ii, v = measured profiles of mean wind component in the direction of the surface wind and normal to it; Vg = vertical variation of the geostrophic wind component normal to the surface wind direction. The shaded area is proportional to the surface drag TO.
Values of the Austausch coefficients A xz , A y z or the eddy viscosities Kee, K y z can finally be derived from Eqs. (4.60) and (4.61). The geostrophic departure method offers the advantage of furnishing average values of shear stress and eddy viscosity that comprise
176
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
the entire momentum transport over all periods of turbulent fluctuation. On the other hand, it suffers from the following two handicaps: (i) The necessity of excluding the influence of acceleration. Since, apart from turbulence, steady motion was assumed, the geostrophic departure method is only applicable to wind measurements averaged over a period which is long enough to allow the components of acceleration to be neglected. In general this will preclude the computation of the momentum balance for shorter periods, such as one day. In addition, the locality chosen for study must not have any marked topographical features (such as those of coasts and mountains) which could tend to interfere with steady flow. The open sea would be a site well suited to this approach. (ii) The difficulty of providing sufficiently accurate data regarding the geostrophic wind both at the surface and at upper levels. The most serious difficulty in applying the method is the practical one of estimating the geostrophic wind. Even on land where a relatively dense network of pressure-observing stations is available, the geostrophic wind may hardly be derived from the pressure distribution with an accuracy greater than 5-10 per cent. The possibility of getting sufficiently accurate values is obviously much smaller at sea than on land, as in general there exists no adequate network of pressureobserving stations and even if there are islands suitably situated the pressure readings may be disturbed by topographic effects. Sea stations are still less qualified. On the other hand, the requirements with regard to the accuracy of the pressure values must be higher at sea than on land, owing to the fact that the bottom friction and its effects on the flow are smaller there. The difficulties are augmented in the baroclinic case. Then the atmospheric density distribution has a horizontal gradient and, consequently, the geostrophic wind varies with altitude. In the absence of suitable measurements, which will generally be the case, a rough estimate of the vertical profile of the geostrophic wind in such a baroclinic atmosphere at sea can only be attained with the help of climatological data concerning the horizontal gradients of both air and sea temperature, a method that is subject to considerable uncertainty. In view of this unsatisfactory situation, some authors dropped the direct determination of the geostrophic wind from the pressure field but tried to derive this quantity from the measured wind profile, assuming that in the higher levels the wind may, on an average, be taken as approximating to the geostrophic wind. This procedure was applied, for example, by Sutcliffe (1936), but Sheppard et al. (1952)
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
177
found it impossible to insert the corresponding component Vg of the geostrophic wind into their measured profile curves of v by inspection. Lettau (1957), however, subjected some of the wind profiles measured by Sheppard et al. (1952) to a new analysis, assuming that the Austausch coefficient is a scalar quantity, thus deviating from Eqs. (4.60) and (4.61) which ascribe to it a tensor structure. This constraint, which still has to be verified generally, served to fix values for the geostrophic wind and its vertical variation from the measured wind profiles with an accuracy considerably greater than attainable otherwise. 4.4.1.2 Eddy Correlation Method. This method is based on the right-hand portions of the basic Eqs. (4.60) and (4.61), which were not used by the geostrophic departure method discussed above. Two procedures have become known so far which enable us to obtain correlated values of the turbulent departures from the mean flow: (i) Series of pilot balloon ascents. Pilot balloons, which have been inflated in order to give them a low rate of ascent of about 1.5 to 2.5 meters/sec, are released at regular intervals of 10, 15, or 20 minutes and tracked by two or three theodolites installed on fixed sea stations, e.g., lighthouses or small, flat islands, a few kilometers apart. Synchronized readings are taken every 15 or 20 seconds. The balloons are followed for 10 minutes or so, until they have reached a height of from about 1000 to 1500 meters, after which they are abandoned. In order to secure the best possible accuracy the angles of bearing and elevation should be read at least to 0.01°. Then the displacement of the balloon, both in the horizontal and in the vertical, can be considered correct to about ± 1 meter and the accuracy of the corresponding component velocities of the balloon can be estimated at ± 5 em/sec. The evaluation of the readings of one ascent yields the actual velocity components of the balloon as measured along its trajectory. While the horizontal components can be taken as representatives for the components u, v of the air flow averaged over the different height intervals, the corresponding vertical components w of the wind are obtained by subtracting the mean vertical velocity of the balloon throughout the entire ascent, under study from the measured vertical velocities of the balloon during the different time or height intervals. When applying this procedure we assume, first, that the rate of ascent of the balloon relative to the air remains constant throughout every ascent and, second, that the air flow has no vertical component when averaged over a complete sounding. Thus, any vertical motion of the air lasting longer than one ascent (10-15 minutes) will escape detection.
178
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
Apart from the difficulty of determining correct values for the vertical component of the air flow, there are other peculiarities inherent in this method which should be examined. This method does not supply any continuous records of the instantaneous components of motion at fixed levels and at a fixed locality, as can be done near the surface, and the detailed structure of the vertical wind profile, as can be determined from photogrammetric measurements of the successive positions of a smoke trail left by a vertically rising missile (Tolefson and Henry, 1961), is not obtained. The pilot balloon technique rather furnishes samples of certain air flow data taken more or less at random every 15 or 20 minutes. Here, each wind value corresponds to an average taken over a time interval of 15 or 20 seconds and along an inclined path covering a height difference of from 25 to 50 meters. Thus, a considerable portion of the small-scale wind variation is filtered out. In addition, the measurements are taken visually and, therefore, confined to areas free of clouds; this will affect particularly the determination of the vertical flow component. It goes without saying that observational material of that kind is far from being ideal. Before the required turbulent departures u', v', w' from the mean flow can be computed, the components of the mean motion ii, '8, w have to be fixed. In most cases it will not be possible to gain a sound estimate of the real mean flow and so we have to confine ourselves to the departures from the observed mean flow, their products being regarded as contributions to the complete products related to the real mean flow. In this connection, the length of time available for averaging plays an important role as it determines the range of fluctuation periods, i.e., the section of the spectrum of turbulence that will become effective in the turbulent departures. In general, the pilot balloon technique will give information about fluctuations ranging from several minutes up to several days (medium scale turbulence), provided that the measurements comprise several weeks. Therefore, the momentum transport obtained by this method does not cover the entire spectrum of turbulent exchange but only a certain part of it which depends on the density of soundings as regards time and on the length of the observational period. The turbulent shearing stresses TXZ and Tyz as well as the corresponding values of the eddy viscosity can be computed from the turbulent departures and from the vertical gradients of the mean horizontal wind components with the aid of Eqs. (4.60) and (4.61). The pilot balloon technique was applied by Sheppard et al. (1952), Charnock et al. (1956), and Roll (l958b).
4.4 WIND STRUCTURE IN MARITIME FRICTION LAYER
179
(ii) Acceleration measurements in an airplane. One disadvantage of the pilot balloon method, namely the restriction of the measurements to cloud-free areas, can be avoided if an airplane is used for turbulence studies at sea, since such a carrier of instruments can be directed to measure within the clouds. When flying through turbulent air, the airplane experiences changes in the angle of attack and in the speed of the apparent air flow in rapid succession, resulting in irregular motions of the plane. For the determination of these effects there are installed in the airplane a pressure anemometer, a vertical accelerometer, a gyroscope, and a drift sight, which yield simultaneous records of the total air speed, vertical acceleration, and the attitude of the plane during short horizontal flights inserted into vertical soundings. After the airplanelift theory has been applied and after the characteristics of the particular type of aircraft have been accounted for, these records allow us to measure the vertical gradient of mean horizontal wind oil/oz as well as to evaluate the simultaneous fluctuations of the horizontal and vertical wind components u' and w'. Here, u designates the component in the direction of the upper wind. Shearing stress Txz and eddy viscosity K x z are computed according to Eq. (4.60). The phugoid oscillations of the airplane, a pendulumlike motion arising whenever a perturbation disturbs the balance between the lift of the airplane and the force of gravity, can be eliminated by computation, unfortunately at the cost of reducing to zero any contribution of wind fluctuations of larger sizes. Thus, also, the airplaneacceleration technique covers only a part of the turbulence spectrum and here particularly the short-period fluctuations are effective. The method described above was developed and applied over the North Atlantic Ocean by Bunker (1955, 1957, 1960). One-fifth-second averages of the observations were used to obtain a time series of the turbulent components. Most of the horizontal runs lasted 2 minutes. Since the speed of the airplane was about 110 knots (= 57 meters/ sec), the area swept out by the plane within 1/5 second amounted to about 360 meters-, which defined the lower limit of the horizontal dimensions of the gusts investigated. The upper limit was set by the procedure applied when eliminating the phugoid motion. This was done by subtracting values averaged over a quarter period (7 seconds) of the phugoid oscillation from the instantaneous values. Consequently, the contributions from the gusts greater than 350 meters in radius were lost. Thus the effective range of gusts measured was from 20 to 350 meters.
180
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
4.4.2 Variation of the Mean Wind with Altitude 4.4.2.1 Profile of Mean Wind Speed. In order to provide preliminary information on the wind field in the maritime friction layer, we shall first consider the vertical profile of the mean wind speed. Relevant results of Sheppard et al. (1952) are shown in Fig. 46, together with similar results obtained by the author. All these observations were taken during the regime of westerly winds. The remarkable fact is that there is no constancy of wind speed with increasing ~ 54
.. .57
...~~
800
:~·63
700
l64
600
'" " E Q;
'
,
19X
r
,r
•• 66
.' 11' ...
67
26X , ,, 26X
200
,,
671'
500
250
I
"
,
= 400
'" Q;
Q;
30X I
"0
150
,
31 ~
/ 33 X
';:
\
,x'"
f
50
............. x
100
33-;:....x Mean wind speed
4 0
100
If
200
" =
,
32 X
300
E
9
10
II
12
13
5 14
6
7
0
15
Mean wind speed (meters/ sec)
FIG. 46. Profiles of mean wind speed in the maritime friction layer with atmospheric pressure gradient parallel to horizontal temperature gradient (westerly winds). 0 - - 0 , measured by Sheppard et al, (1952) at Scilly Isles. Number of ascents 56 below dashed horizontal line. x- - x (inset), measured by the author in the German Bight in 1949; • . . . . •, in 1954. The figures at the different levels indicate the numbers of ascents forming means.
altitude above a certain height such as is implied by the classical boundary layer concept. Sometimes the vertical gradient of wind speed even shows little tendency to decrease noticeably with height above the bottom layer. The explanation of this behavior can be found in the vertical variation of the geostrophic wind occurring in a baroclinic atmosphere
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
181
that is characterized by a horizontal temperature gradient. The equations for the geostrophic motion are (Haurwitz, 1941). OUg
oz OVg
Ug
er
g
er
=-----
T OZ
Vg
et
IT oy g
er
--=--+-OZ
T OZ
IT ox
(4.70) (4.71)
where, in addition to the designations already frequently used, T represents the absolute temperature of the air, g the acceleration of gravity, and I the Coriolis parameter 2w sin rp (w = angular velocity of the earth's rotation, rp = latitude). As the first terms at the right sides of Eqs. (4.70) and (4.71) are small as compared with the second, they can be neglected and, thus, the vertical variation of the geostrophic wind is at a first approximation, constant with height and determined by the horizontal gradient of the air temperature. From this it follows that the geostrophic wind will increase with height when the lower pressure coincides with the lower temperature, as is normally the case in the Westerlies. The contrary will be observed, i.e., the geostrophic wind will decrease with altitude, when the higher pressure is on the side of the lower temperature. The latter case is typical for the trade wind zones, as already mentioned in the foregoing paragraph, but it may also occur with easterly winds in the middle latitudes (Fig. 47). When, finally, the surface pressure gradient is normal to the temperature gradient, which would generally correspond to meridional flow, the geostrophic wind will veer or back with increasing altitude according to whether it is blowing toward lower or higher temperature. To give the reader an idea about the order of magnitude of the thermal wind effect on the height variation of the geostrophic wind, Table XVI has been computed. Taking an x, y system with the axes pointing east and north, respectively, and assuming, for the sake of simplicity, that the air temperature gradient is directed toward the north (oT/ox = 0), we obtain from Table XVI values for the variation of the zonal component of the geostrophic wind with height that roughly agree with the observed mean profiles of westerly winds presented in Figs. 46 and 47. Closer agreement could certainly be reached if actual values of the horizontal temperature distribution were available. In general, from the mean wind speed profiles the conclusion may be drawn that the frictional boundary layer over the sea is clearly perceptible only in the lowest 100-300 meters and that at
182
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
1200
1000 ~
~ 0;
800
.~
600
.5
400
200 75
a
2
e··
3
567
4
Mean wind speed (meters/sec)
FIG. 47. Profiles of mean wind speed in the maritime friction layer with atmospheric pressure gradient opposed to horizontal temperature gradient (easterly winds). 0--0, measured by Charnock et at (1956) in the Trades (Anegada 1953); number of ascents 387. Measured by the author in the German Bight 1954: e ... . e, mean values over 4 days, number of ascents are given; x - - x, mean values for one day, number of ascents, 20.
TABLE XVI VERTICAL
VARIATION
OF
THE
GEOSTROPHIC
WIND IN THE BAROCLINIC ATMOSPHERE a
Horizontal gradient of air temperature, -
oTjoyb
Vertical gradient of geostrophic wind, (OUgjoz)e
CC/IOO km)
(meters sec" krrr")
0.5 0.75 1.00 1.25 1.50
1.51 2.27 3.03 3.79 4.54 5.30 6.06
1.75
2.00
a Computed for 50° latitude and 17°C air temperature. b Or oTjox, as the case may be. e Or (8vgf8z), as the case may be.
4.4 WIND STRUCTURE IN MARITIME FRICTION LAYER
183
higher levels the thermal wind seems to govern the vertical variation of wind speed. The thickness of the frictional boundary layer at sea was investigated in some detail by Roulleau (1952). He applied Eqs. (4.70) and (4.71) to upper wind measurements made in different parts of the Atlantic Ocean, assuming-in conformity with the explanations given above-that the geostrophic wind will be attained when the vertical variation of the wind speed is linear. The height h of the frictional boundary layer as determined in this way amounted to 300 meters for a latitude of 50°, increasing to 650 meters at 10° latitude, thus giving some indication of an inverse proportionality between h and sin q;. 4.4.2.2 Influence of Stability on the Profile of Mean Wind Speed. It is to be expected that thermal stratification will modify the vertical profile of mean wind speed in the frictional layer at sea, as we have already seen with regard to the first few meters over the sea surface. Preliminary investigations in this direction were made by Regula (1939), who measured the vertical variation of wind speed at up to 300-500 meters by means of double-theodolite pilot balloon soundings made on shipboard under different thermal conditions. It is not necessary to emphasize that the relatively short base line available on shipboard, and also the motion of the ship, strongly impeded the measurements and limited their accuracy. Nevertheless, the results of the rather small number of soundings are so striking with regard to the influence of thermal stability that they have been reproduced in Fig. 48. The difference between stable and unstable conditions is very distinct. Of particular interest is the fact that, with cold air above warm water, the flow next to the surface sometimes seems to be even swifter than that at the height of 50 meters, contrary to the general idea of surface friction. This phenomenon can occasionally be observed at sea in a cold air mass when a shower of rain or sleet is viewed from a direction perpendicular to that of the wind and the falling precipitation reveals the wind profile as indicated in Fig. 49. More complete information about the effect of thermal stratification on the wind profile is given later in this volume when the vertical variation of the wind vector is discussed. From statistics published by Jones (1953) it can be taken that the decrease of the wind speed in cold air over warm water is a relatively frequent observation. He compared wind speed values measured at the surface and at 300 and 600 meters in about 800 cases, using the reports of the five ocean weather ships "B," "C," "D," "E," and "H" stationed in the North Atlantic. (See Fig. 2.) Station "H,"
184
4 FLOW CHARACTERISTICS OF MARINE ATMOSPHERE 500.------------------, ~ 400
'" 300
W
~
~ 200
.ijj
100
I
o '---~,........-JIC-~:__-__:_:_--~--.."J 15 20 25 600 500
~ Q;
5
:;:
c
400 300
!'!' 200
'"
I
100
o'--__
~~---J'__:'::__"""''''""=--__=--_='.
15
25
20
Wind speed (meters/sec)
FIG. 48. Influence of the thermal stratification on the vertical variation of wind speed in the maritime friction layer. (After Regula, 1939.) W, warm air over colder water; C, cold air over warmer water.
located at 36° N, 70° W, was discontinued later on. A summary of his results is presented in Tables XVII, XVIII, and XIX. Table XVII clearly shows the remarkable fact that in 43 per cent of the cases a decrease in wind speed was observed between the surface and 300 meters and that this behavior was even more frequent (47 per cent) between the levels of 300 and 600 meters. The possibility of ascribing this result to observational errors is not great, since Sheppard et al. (1952), in their comparatively small sample of measurements with westerly flow at Scilly Isles, also found that nearly 25 per cent of them TABLE XVII FREQUENCY (PER CENT) OF WIND SPEED INCREASE (DECREASE) WITH ALTITUDE OVER THE SEAa
Wind speed difference (knots) Wind levels (meters) 600-300 300-surface a
Decrease
Increase
<-10
-9 toO
1 to 10
> 10
1 3
46 40
48 46
5 11
Rearranged after Jones (1953).
Number of cases 797 793
~
~
~
z
I:j
rn
>-l
~o
>-l
~
tTl
Z s::
~
>-l
~
tTl
FIG.
49. Vertical variation of wind speed in cold air over the sea as made visible by precipitation. Wind direction from right to left.
'Tl
~
o>-l
z15 r-
~
..... 00 VI
.-
00
01
.j:::.
"TI t""
o
~
TABLE XVIII FREQUENCY (PER CENT) OF WIND SPEED INCREASE (DECREASE) FROM THE SURFACE TO 600 METERS OVER THE SEA AS RELATED TO THERMAL STRATIFlCATIONa Air-sea temperature difference CF) Wind speed
> + 2
+1 to-2
Decreasing Unchanged Increasing
0 3 97
20 6 74
Number of cases a
Rearranged after Jones (1953).
67
176
258
45 7 48 166
:I:
~ ;I> o ..., tIl
-3 to -7 -8 to -12 -13 to -17 36 6 58
o
40 7 53 77
< -17
Number of cases
Per cent
32 8 60
247 47 490
32 6 62
40
784
100
~
VJ ...,
oVJ
o "TI
a::;I>
::c
Z tIl
;I> ...,
S VJ
"tl
:I: tIl
::c rn
4.4
187
WIND STRUCTURE IN MARITIME FRICTION LAYER TABLE XIX
FREQUENCY (PER CENT) OF WIND SPEED INCREASE (DECREASE) FROM THE SURFACE TO
600
METERS OVER THE SEA AS RELATED TO WIND DIRECTION a
Wind quadrant Wind speed
North
Decreasing Unchanged Increasing
45 8 47
36 11 53
23 4 73
28 66
247 47 490
201
53
263
267
784
Number of cases a
East
South
West
6
Number of cases
Rearranged after Jones (1953).
showed the wind speed at 300 meters as smaller than or equal to the surface wind. Thus the result should be taken as truly representing the real situation. It may, in part be attributed to the effect of thermal stratification as can be inferred from Table XVIII where the percentage of wind speed decreasing or remaining constant with height is only 3 per cent under stable conditions but attains more than 50 per cent with growing thermal instability. Table XIX, finally, gives us some hints as to the possible participation of thermal wind effects. Since the ocean stations considered are located in the northern and western parts of the North Atlantic, meteorological situations characterized by opposing surface pressure and air temperature gradients will be relatively frequent there. Such influences may, perhaps account for the conspicuously high percentage of wind speed decreasing with height that was observed with winds from northerly and easterly directions. The dependence of the vertical wind profile on the temperature gradient at sea was also studied by Gordon (l950a), who calculated mean values for the ratio of the wind speed at 15 meters to that at 600 meters for a number of soundings made on the ocean weather ship stations "I" (60° N, 20° W) and "J" (53° 50' N, 18°40' W) in the North Atlantic. The result is given in Fig. 50. We see that the ratio U15!U600 slowly increases from minimum values under inversion conditions to a primary maximum of 0.70 which occurs at the isothermal case. A secondary minimum is observed with a lapse rate of about - O.4°CjlOO meters. For higher lapse rates the ratio U15!ii600 resumes the increase. No explanation is offered for the strange behavior
188
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
between 0 and - 0.4°CjI00 meters. The over-all mean of U15/U600 calculated from 710 values taken at random was 0.71. The ratio showed a slight tendency to decrease with increasing wind speed (at 600 meters).
8
l~
.s" 070
°
~
-e
""~
0.65
-e c
~
060
055 -10
-0.5
o
0.5
Temperature gradient (OC/IOOmetersl
FIG. 50. Wind speed ratio fhs/iiaoo as a function of temperature gradient (measured between 15 and 600 meters) over the North Atlantic Ocean. (After Gordon, 1950a.) Figures indicate number of cases.
4.4.2.3 Vertical Variation of Mean Wind Direction. Proceeding from the classical concept of the frictional boundary layer we must expect that, in the northern hemisphere, the wind will veer with height until the direction of frictionless wind is reached. As far as the veer is concerned, the expectations, on the average, are fulfilled, which can be inferred from Fig. 51 where the results obtained by Charnock et al. (1956) in the northeast Trades are combined with similar data referring to the westerlies. We can make the general statement that although, it is true, the mean wind direction veers with altitude, in other respects its vertical variation, in part, deviates substantially from the attributes of the profile for a barotropic friction layer. Apart from this, there also exist considerable differences between observations at different localities. While in the Trades the veering averages nearly 20° at 1000 meters, and a mean value of 15° may be reached with westerly
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
189
winds off the German North Sea coast, west winds under really oceanic conditions seem to be characterized by very small values of veer which seldom surpass a few degrees, as is shown by the results obtained at the Scilly Isles and in the German Bight during a heavy gale. The latter profiles of wind direction apparently come nearest to the barotropic boundary layer conception. 1400
1200
1000
E800 " ~ :2"
s:
'"\ '"\.
r '1-
/
~
~
600
f,t
400
~J
200
0
0
5
10
15
20
25
Veer of wind direction (degrees)
FIG. 51. Veer of mean wind direction with height relative to the surface wind as measured in different maritime regions. D- -0, Scilly Isles, January 1951, averaged over 2 days with westerly winds. Number of cases 58 at the lower levels decreasing to 6 at the top (Sheppard et al., 1952).0--0, Anegada, West Indies, 1953, averaged over fifteen days with northeast trade wind. Number of cases about 400 to 280 (Charnock et al., 1956). x .... x, German Bight, 1954, averaged over 4 days with westerly winds. Number of cases 69 (below) decreasing to 41 (above). German Bight, 1954. averaged over one day with a westerly gale. Number of cases 19 (below) decreasing to 5.
*--*,
Naturally, the thermal wind will come into play if the geostrophic wind blows toward lower or higher temperatures. In the former case, the geostrophic wind will veer with altitude, whereas it will back in the latter. It is relatively easy to give qualitative examples for this behavior but quantitative evidence is much more difficult owing to the uncertainty about the horizontal temperature gradients at sea. Nevertheless, some illustration to this phenomenon will be given here.
190
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
In Fig. 52 two average wind direction profiles are presented that were obtained in the German Bight under opposite conditions. Curve A refers to a southeasterly flow transporting very warm air over colder water, resulting in an air-sea temperature difference of + 5.5°C. In this case the geostrophic wind should veer with altitude. That it did do so can actually be concluded from the very pronounced veer of wind direction with height as exhibited by curve A. 1000
'" ~
600
400
:'
800
,
,x
,,I
600
r
x \ x,
,
200
0
1000
1
800
] l
,,
~
... ,
8
400
'x,
"
- ' , --x ___
---
200 <x /
-100
-75 Mean
-50
-25
I
0
25
50
75
0
wind direction relative to surface wind (degrees)
FIG. 52. Vertical variation of mean wind direction at sea with geostrophic wind blowing toward lower (A) and higher (B) air temperature (Northern Hemisphere).
A Temperature difference, air-sea Surface wind direction (at 40 meters height) Geostrophic wind direction (at the surface) Number of ascents
B
+ 5.5°C 1500
13T 20
Contrary to case A, curve B represents conditions occurring when a northeasterly flow passes over warmer water. Here the wind strongly backs with altitude above a bottom layer of about 100 meters, a fact that might obviously be interpreted as caused by the backing of the geostrophic wind blowing toward higher temperature. Unfortunately, nothing is known of the temperature distribution at the altitudes concerned.
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
191
If we go into greater detail, we are confronted with the remarkable experience that there is an almost symmetrical spread of the variation in wind direction on either side of the frequency maximum for heights up to 500 meters or more, if single flights are considered. Evidence for this fact was given by Westwater (1943), Sheppard et al. (1952), and Roll (1958b). Frequency distributions for the variation of wind direction at different levels in westerly winds are presented in Fig. 53. Frequency of occurrence (%)
I
900
~ 600
+-
+
I
3
7
12
T
25
54+,4+2
I
4I
T
t-
57
+t-++ 14
48
-
I
T T-
49
::l
t- 12 +2 +- + - 66 '0u
63 ~
10
46
+- + + + 67 ~~ +t-+-25 60:t-+-++-- 69 ~E + +- +29- 46+ +- + + 69 39
+ +28
T
500 r-
"400 ;;'
46 1 15
T-. T 26
700-+++
5. ~
5
2
+
800 ~
I 27
+ + t:39 47+ +-
f-
I
60
I
300 f-
9
3
7
•
2
I
+ +- • +28 f-41 + +- + + 3
200 l100 f2
t-
6
+-
I 10
16
I
+- +- +31 I
+-27
-20 -15 -10 -5
5
14
7
14
0
5
10
10
3
.L, I
15 20
3
69 51 25
Vertical variation of wind direction (degrees) Backing
I
Veerrng
FIG. 53. Frequency distribution of the variation of wind direction with height over the sea. Summary of pilot balloon ascents carried out in the German Bight on 4 days with westerly winds in 1954. Each frequency number refers to the layer and to the direction range indicated by the limits of the relevant square. Positive direction means veer relative to the direction at the lower level of the two levels concerned.
The frequency maxima are always on the positive side and the mean values range between +0.5° (900/800 meters) and +2.6° (200/100 meters). On the average the wind veered with altitude, as mentioned before; but there is an appreciable fraction of cases (from 26 to 45 per cent) in which the wind direction at the higher level was backed on the lower one. A similar figure was given by Sheppard et al. (1952), who, when measuring the wind structure at Scilly Isles in winter time, found that over 30 per cent of the flights showed the wind at 300 meters backed on the surface wind. These findings support the interpretation that medium-scale eddy motions of a couple of kilometers in horizontal extent and in time intervals of several minutes may substantially participate in the momentum exchange at sea.
192
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
In Fig. 53 the relative minimum of the spread of the variation in wind direction observed in the layer between 400 and 500 meters is of particular interest. One has the impression that, in the cases considered, the layer in question acted as the upper limit of the eddying motion originating from the sea surface, whereas the increase in directional variability above that layer was caused by the mediumscale eddy motion mentioned above. The influence of thermal stability on the variation of wind direction with height was investigated by Gordon (1952a), who derived mean values for the angles of deviation between the winds at 15 meters and 600 meters over the North Atlantic Ocean as a function of the temperature gradient, using soundings made at the ocean weather ship stations "I" and "J." His results are given in Fig. 54. They agree with what we should expect. The upper wind is veered on the surface wind, the angle of deviation becoming smaller with decreasing thermal stability. The decrease appears to level off for lapse rates greater than the dry adiabatic. The over-all mean of the angles of deviation, calculated from 699 values, amounts to 10.5°.
64 co
.g o
15
s
"
-e
'0
g, 10
-0.5
o
05
Temperature gradient (oG/IOO meters)
FIG. 54. Mean angle of deviation between the winds at 15 meters and 600 meters as a function of thermal stability over the North Atlantic Ocean. (After Gordon, 1952a.) Figures indicate number of cases.
4.4.2.4 Vertical Variation of Mean Wind Components. Having dealt separately with the speed and direction of the wind, we will now attempt to summarize all information that is available at present on the mean wind components ii, ii, w with respect to their vertical variation over the sea. Regarding the horizontal components ii, ii of the mean wind vector, there are two possible ways of depicting the results: Either one could give separate graphs of these two components against altitude, or the vertical variation of the horizontal
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
193
flow components could be presented in a polar vector diagram (Ekman spiral). The first form of presentation was used by Charnock et al. (1956), for instance, when they summarized the results of their wind profile measurements in the Northeast Trades (Fig. 55). The data for all ~
-05
V (meters/sec)
-1.0 -219 -286 -306
-;; 1000
-328
;;
36 20 -378
;;
-341
E
"
500
o :
-385
. 4
1000
500
5 ~ jj
(meters/sec)
FIG. 55. Vertical profiles of mean horizontal wind components in the Northeast Trades, Anegada 1953. (After Charnock et al., 1956.) Average values over 15 working days. Number of ascents is given at each level above 600 meters.
fifteen working days were averaged, the number of ascents being so large (from 466 to 279) that the slight inhomogeneity of data at the upper levels, owing to the fact that some balloons were lost prematurely in clouds or for other reasons, obviously does not diminish the reliability of the upper portions of the profiles to an essential degree. Two characteristic peculiarities can be perceived in the curves for ii and e: (a) The maximum of ii at a height z = Zx = 350 meters, which enables us to compute the surface wind stress according to Eq. (4.68). (b) The constancy of v above z = Zy = 900 meters, which allows us to apply the constraint expressed by Eq. (4.69) when calculating the vertical distribution of the turbulent stresses TXZ and TyZ. In view of the smoothness of the profiles depicted in Fig. 55 it should be mentioned that the daily mean profiles show a greater scatter but, on the other hand, a maximum in ii that is much more strongly defined than for the period-mean profile although it is variable in height. The second form of representation, i.e., the polar vector diagram of the wind speeds at the different heights, implies certain difficulties, as the geostrophic wind in most cases is not constant with height. In
194
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
order to obtain a diagram in the form of an Ekman spiral in these cases, Lettau (1957) proposed plotting the vectors of deviation between observed and geostrophic wind. On the basis of the principles described in Section 4.4.1.1, Lettau succeeded in computing representative wind profiles up to 500 meters altitude for stable and unstable thermal conditions, using suitable measurements of Sheppard et al. (1952) at Scilly Isles. These results are reproduced in Fig. 56. 100
9.5'
~
7
-6
-5
-4
-3 U-Ug
-
-2
20
50
100
150
I
200 300
-I
500
I
-----
(meters/sec)
FIG. 56. Vector differences of observed minus geostrophic wind as a function of height in the maritime friction layer near Scilly Isles. (Derived by Lettau, 1957, from pilot balloon ascents of Sheppard et al., 1952.)
Temp. difference Direction of Ii - Ug axis air-sea A. Advection of warm air B. Advection of cold air
They show that the vertical vanation of the mean horizontal wind components can also be represented by an Ekman spiral in the maritime friction layer if the influence of the vertical variation of the geostrophic wind is eliminated. The differences between the spirals for stable and unstable stratification are clearly perceptible and agree with expectation, the angle between surface and geostrophic wind direction being greater (13.9°) for warm air over cold water than for the inverse case (9.5°). Further, these friction-generated deviations are considerably smaller than the corresponding values over land. For instance, for a
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
195
warm continental air mass Lettau (1950, 1957), on the basis of wind profile measurements carried out near Leipzig by Mildner (1932) determined this angle to be 26.1 The mean vertical flow component w obtained by the procedure described in Section 4.4.1.2 is subject to uncertainties since it is assumed that the velocity of the balloon relative to the air is constant during each ascent and that the mean vertical motion of the air over a complete sounding is zero. For this reason the relevant results must principally be regarded with a certain reserve. Charnock et al. (1956), when applying this method to soundings made on an island in the Trades, were additionally hampered by the presence of this island which, although small and flat, gave rise to a particular pattern of convective clouds during daytime. They investigated the island effect in detail by comparing plan trajectories of balloons released at different points, among them a boat stationed about 1.3 km off the shore to windward, and arrived at the conclusion that the technique adopted made it possible for them to provide fairly representative values of the mean vertical motion as a function of altitude and horizontal position, although greater accuracy would be required to fix reliable absolute values. The height profile of the mean vertical flow component as averaged over all the ascents by Charnock et al. (1956) is reproduced in Fig. 57, which shows that the magnitude of the mean vertical wind component generally oscillated between ± 20 ern/sec and that, on an average, there was an ascending motion below 325 meters and a descending one above that height. Naturally these values are confined to cloudless areas. The initial increase of the upward mean velocity at from 25 to 75 meters' height reflects the influence of the sea surface. Contrary to this result for the Trades are the figures for the mean vertical flow component w that were obtained with on-shore winds in the German Bight by means of the same procedure. They are also plotted in Fig. 57. Here a downward motion was observed in the layer below 300 meters or so and an ascending flow above that height. The order of magnitude of lV is about ± 5 ern/sec and, thus, distinctly lower than in the Trades. The value next to the sea surface might, perhaps, have been falsified (in the negative sense) by eddies, developing to the leeward of the lighthouse (of about 30 meters' height) where the balloons were started. Apart from this handicap the values might be considered representative for maritime conditions in the temperate zones. It is interesting to note also that Charnock et al. (1956), in soundings started from the off-shore boat, observed mainly a downward mean 0
•
196
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
motion throughout the early part of the balloon trajectory, which was wholly over water, a result which agrees with the findings from the German Bight. 1400
1200
. Q;
Q;
.s <:
'"
;;
1000
800
600
I
400
200
-10
-5
20
Mean vertical component of wind velocity (em/sec)
FIG. 57. Vertical profiles of mean vertical component iii of wind velocity. 0--0, Anegada, 1953, northeast trade wind region, number of ascents 387 (Charnock et al., 1956). x - - - - - x, German Bight, 1954, winds from west to northeast, number of cases from 613 (below) to 296 (above).
Some information on the actual vertical wind components w above the sea, in addition to the mean values iii described above, can be found in Figs. 58 and 59. They represent frequency distributions of vertical wind velocities up to 1000 meters as evaluated from doubletheodolite observations with westerly and northeasterly winds in the German Bight. The extreme absolute vertical velocities were 200 em/sec with westerly winds and 100 em/sec with northeasterly ones. With west winds, the largest variability of vertical motion occurred in the layer below about 100 meters, whereas with east winds, the larger scatter was confined to the upper layer above 200 meters. 4.4.3 Turbulent Wind Fluctuations So far we have only dealt with the mean components ii, V, W of the air flow above the sea, occasionally adding some information on the
4.4
197
WIND STRUCTURE IN MARITIME FRICTION LAYER
actual velocities u, v, w. Now we shall attempt to study the turbulent fluctuations u' u a v' v
w'
w
w
of the wind components as well as the corresponding variances
900
I 2 2
800 700
~
~
~
600
'"
.'; I
t
400 0
o
0
o -160
0
I
I 2
I
6 4 4 4 4
"
7
1 4 3 8
15 16. '04 3
1 2
, 2
2
I 2 2 4 8 1613 18 16 6 4 2
I 3
I
o
I
3
s s
I 6 8 1219 17 II 104 2 4 I 4 13 II 2218 8
s
s
I
,
5 3 2
I
I
,,
I
I 2 4 6 II 15 1614 106 4 3 2
I 3 4
I
I 3 4 8 12 1621
I
o
-40
,
I
177
1
210 260 293
1
,
40
I
I 00
0
I
I
- 0
I
o
I 6 6 10 1012 10 7 5 4 4 3 4 2
-80
135
I
0
I 0
5 8 1619 '6 7 8 5 2 , 2
I 4
135
I
7 5 5 2 2 0 I 0
I
-120
, ,
I
4 4 3 3 2
1 I
I
100 - 200
000
s
,
300 200
7 1817
4 5 II 15 1013
, ,
.E 500
s
1 I 4 6
I
422
o
o
I
I 00 I
120
80
Downwards
343
0
o
0
0 00
160
o 403 493 200
Upwards
-Vertical
component of wind velocity (em/sec)
FIG. 58. Frequency distributions of vertical component w of wind velocity at different altitudes with westerly winds [German Bight, 1954 (Roll, 1958b)]. 1000 2
,
900 ~
I
800 I
~ 700 E 600
2
s:
.~ 500
t
I
717 1 I 12 ,
I
, 2 4 8
I
, 2
I
I 2 4 I
400
3 13
I 2 .3
I
,
2 2
300
2 9
3 1231 7
I 5 8
100
o
~"
-120
-80
Downwards
-40
3 2
I
I
5 2 3
4. 3 3
s is
I
I
158
,
159 174
I
,
178
,, ,
180 179
I
I
0
4
I
180
00
125
o
16
s
'"'"E ~
z
168
73' 178 3
I 2 2 1228
-160
I
2'5 8 2 2
I 2 6 12 18 2< 18
200
-200
8El~~
,, ,
310 7 I
,';;f"8'22I',"
161
I
I
40
120 120
80
160
200
Upwards
- - Vertical component of wind velocity tern/sec)
FIG. 59. Frequency distributions of vertical component w of wind velocity at different altitudes with northeasterly winds [German Bight, 1954 (Roll, 1958b)].
198
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
and covariances
in order to produce some data on the characteristics of the turbulent motions, their intensities, and the corresponding turbulent Reynolds stresses in the maritime atmosphere. 4.4.3.1 Effect ofTime of Averaging. As observations of air motions are limited with regard to both time interval and period, real averages ii, ii, W of the flow components which include all possible fluctuations and which are characterized by
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
199
material used therein comprises results of pilot balloon ascents made at hourly or half-hourly time intervals over periods of from 5 to 6 hours. Although the analysis is rather crude, a relatively clear result has come out: there is generally an increase of turbulence with height; 200
24/6/1949 3.2 meterS/55
150 100 50
o v; 200
;;;
~
150
.c
100
~
50
t
o
'"
200
/
.X·
~ UlO ==3.1 meters/sec
--=-- . •
4/7/1949
/
.~
..,.,V
...
.
1..7'
10
V
20
30
uto: 7,2 meters/sec
7/7/1949 illo = 1.9 meters/sec
It /.
.
3/7/1949
•
u1o =5.7 meter s/ sftc /
100
o
If
/( "(
.
~
28/6/1949
150
50
...
27/6/19491 3.5 meters/sec
UIO:
t
UIO:
40
0
10
20
../.' .-. .,. 30
-"
40
- - - - Root-mean-squore deviation velocity (°/0)
FIG. 60. Vertical variation of the turbulent fluctuation of the scalar wind speed (in per cent of the mean speed at the corresponding height) over the sea (German Bight, 1949).
in addition, three cases are distinguished by a more or less strong decrease with height in the lowest 50 meters. A similar increase of the variance of scalar wind speed with height was reported by Sheppard et al. (1952). This result is, on the whole, contradictory to the concept which assumes that the frictional boundary-layer turbulence originates from the sea surface. Rather it must be assumed that eddies of large horizontal extent were mainly investigated by the method concerned. Passing to the discussion of the variances of the horizontal wind components, let us cast a short glance at the results reported by Charnock et al. (1956) for the Northeast Trades which are presented in Fig. 61 together with the values Bunker (1955) obtained at the same time and at the same locality by means of airplane measurements.
200
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
For the sake of clearness the root-mean-square deviation velocities
are given instead of the variances. It should be noted that Bunker's values are not horizontal components related to the surface wind direction but refer to the scalar wind speed at the height concerned. The most striking feature of Fig. 61 is the difference in the order of magnitude of the horizontal wind fluctuations with respect to the
, ,,
1400
~
1200
1000
'" Q;
Q;
800
E
:c
.2' 600
'"
:I:
400
200
1400
x
\ \
\
t
\
1200 \
\
,
X
\
,,
m 'x-,,
t
t
(u'
2
C
,,
'\\
800 \
\
\
xI
600
:
I X
I I
.~
I I
,
400
X
, I I
~ ~
\
( '2)'/2 v cv
,
~
¢ 00
1000
200
I., 50
150
200
250
Root - mecn - square deviation velocity (em
350
0
Isec)
FIG. 61. Root-mean-square deviations of the horizontal wind components as a function of altitude, Northeast Trades, Anegada, 1953. 0--0, 1/2 turbulent fluctuation of the wind component v (normal to the surface wind av direction); 0- -0, turbulent fluctuation of the horizontal wind speed at the height concerned.
Averaging period
I
II III
0.5 to about 3 minutes 6 to 12 hours
27 days
Duration of fluctuations
Author
Method
1 second to a few minutes 1 minute to 4 hours 1 minute to several days
Bunker (1955)
Airplane
Charnock et al. (1956) Pilot balloon Charnocket al. (956) Pilot balloon
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
201
averaging period. The vertical variation is small for the short-time fluctuations (I) but more pronounced for medium-scale turbulence (II and III). In this fluctuation range
1400
1200
•
1200
1000
1000
•
~
'" W
.s s:
'" iU
800
800
600
600
400
400
I
200
200 (w'
a10
15
2
):V
Z
20
30
35
a
Root - mean - square deviation velocity (em/sec)
FIG. 62. Root-mean-square deviation of the vertical wind component as a function of altitude, Northeast Trades, Anegada, 1953. • , I; 0 - 0 , II; x - - - - x, III. For explanation, see Fig. 61.
202
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
to the technique applied. [In spite of this limitation the vertical fluctuations derived for large-scale motions (III) are, however, somewhat bigger than those for the smaller-scale motions (II).] More unexpected is the fact that also the short-time fluctuations of the vertical wind component investigated by the airplane measurements are of the same order of magnitude and more or less show the same vertical distribution as the turbulent motions studied by pilot balloon flights. The restriction of the pilot balloon ascents to clear air conditions obviously was of less importance than expected. As regards the vertical variation of <W'2 )av1 / 2 we observe an initial increase with height up to from 100 to 200 meters, which certainly reflects the limiting influence of the sea surface on the intensity of vertical turbulent motion. The decrease later on may be caused by the thermal stability growing with altitude. The final increase might perhaps be ascribed to convective effects, possibly enhanced by the heated island, since the airplane values, which were collected a few miles off the windward shore, do not show this increase but rather a marked decrease above 1000 meters. Bunker (1955, 1960) also measured root-mean-square vertical velocities <W'2 )av 1l 2 under various weather conditions over the western North Atlantic Ocean. Frequency distributions of the results obtained at different altitudes are given in Fig. 63. They point to a maximum of the turbulent vertical velocity at about from 300 to 500 meters which is followed by a decrease toward higher levels. The absolute maximum value observed was 179 ern/sec.
4.4.3.4 Effect of Thermal Stability on Turbulent Vertical Motion. As indicated above, the turbulent fluctuation of the vertical wind component is strongly affected by thermal stratification. Examples of this effect were published by Bunker (1955, 1957) and Fig. 64 has been drawn from his measurements. It shows both stabilizing and unstabilizing thermal processes. In an unstable air mass over land a maximum <w'2)av1l2 of 191 ern/sec is reached at a height of 300 meters. When such air flows over colder water, the vertical fluctuations are reduced to 46 ern/sec at the same height even after a fetch of only 25 nautical miles. On the other hand, the turbulent vertical fluctuations are increased from 45 to 120 ern/sec when cold air flows over the warm water of the Gulf Stream. Thermal influence on turbulent wind fluctuations is also indicated in a study published by Bunker (1957) wherein turbulence measurements, executed in a young cyclone over the ocean, are given. Particularly strong turbulence was observed in the transition zone
4.4
203
WIND STRUCTURE IN MARITIME FRICTION LAYER Frequency of occurrence (%)
No. of
2200 r--'---'-~-'----'--~~---r--,obs 2000 1800
100
++++++++ + + + +
100
+ + + + 50 25 25 ~ 1400 40+30+20+10+ 1600
E
1200
s:
1000
I
o
+ + + + +
+
+ +
+
+
+
4
10
33+33\3+ + + + + + + + t + + + + + 800 28+3\22+ + II + + 6 + + 21 29 29 4 13 4 600 + + + + + + + + 21 16 5 10 32 16 400 + + + + + + + + 8 22 28 8 12 10 10 2 WO 0
5 0
+ + + + + + + + 36 27 13 10 4
20
4
I
18 24 19
40
99
40 60 80 100120 140 160 180 (em/see)
(W'2)~2
Root- mean -squore deviation velocity
FIG. 63. Frequency distribution of the root-mean-square deviation of the vertical wind component computed for different height ranges. Summary of observations carried out under various conditions over the western North Atlantic Ocean. (After Bunker, 1955, 1960.) Each frequency number refers to the layer and to the speed range indicated by the limits of the relevant square.
2000
2000
1600
x, \
\
1600 \
\
~
0;
\
Q; 1200
.s s:
0'
00; I
I
800
I
\
x
B
A
I
~,
\
,,
,,
X
,
,,
x
800
'x __
- ........ !"arm wcter
\
400
1200
\
Land
Cald\
water~~
-,
--
............x
,
400
.~ (W '2(2 X OV Root-mean-square deviation velocity (em/sec)
FIG. 64. Root-mean-square deviations of the vertical wind component influenced by thermal stability. (After Bunker, 1955.) A
0-0 X ----
x
B
Beverly, Mass. Portland, Me. January 29,1954 December 7, 1953 25 nautical miles off-shore 100 nautical miles off-shore
204
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
between the cool anticyclonic circulation to the southeast of the depression and the jet of warm air constituting the warm sector of the cyclone. After the passage of the cold front characterized by rough air but not by violent turbulence (root-mean-square vertical velocities were estimated at 150 ± 50 em/sec at 300 meters), the cold air behind the front was found to be exceedingly stable with only slight turbulence, a phenomenon explained by a downward heat flux in spite of a cold air flow over warmer water. We shall come back to this question when we deal with turbulent heat transport (see Section 5.3.4). 4.4.3.5 Partition of Turbulent Energy. Of particular interest is the distribution of the turbulent energy among the three components of wind velocity. As can be concluded from Figs. 61 and 62 the turbulent horizontal wind velocities in the Northeast Trades were of nearly equal order of magnitude but, generally, there was no equipartition of eddying energy if the horizontal wind components were compared with the vertical ones. The relation strongly depends on the averaging period. In Table XX the quantitative facts are summarized TABLE
xx
VERTICAL VARIATION OF THE RATIO BETWEEN HORIZONTAL AND VERTICAL FLUCTUATION INTENSITIES
<W'2 >av/av AS A FUNCTION OF AVERAGING PERIOD AND OF ALTITUDEa.b Airplane measurements Bunker (1955)
Pilot balloon ascents, Charnock et al. (1956)
Averaging period:
0.5 to 3 minutes
Duration of fluctuations concerned:
I sec to a few minutes I minute to 4 hours
6 to 12 hours
27 days I minute to several days
Altitudes 0- 100 100- 200 200- 400 400- 600 600-1000 1000-1500
1.61 2.63 3.29 1.99 1.89 2.94
0.13 0.18 0.16 0.14 0.056 0.045
0.013 0.013 0.0079 0.0065 0.0040 0.0047
Northeast Trades, Anegada, West Indies. The fact that, in Bunker's values, u' is defined as deviation from the mean horizontal component of the measured air speed in the altitude considered, whereas in the study of Charnock et al. u' denotes the turbulent fluctuation of the horizontal wind component at a certain height with respect to the direction of the surface wind, is not thought to be of importance in this comparison. c Height range (meters). a b
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
205
as a function of averaging period and altitude. (For this comparison the size range of gusts measured by the airplane method has been transformed into corresponding time fluctuations for which wind speeds between 2 and 16 meters/sec have been assumed.) Table XX clearly shows that the average ratio between vertical and horizontal fluctuation intensities ranges from 1.6 to 3.3 for the short-time fluctuations investigated by the airplane measurements and that this ratio is at least one order of magnitude higher than that for the medium-scale fluctuations studied by pilot balloon ascents averaged over periods of several hours. The latter are about one order of magnitude higher than the fluctuation ratios derived for an averaging period of 27 days. It is interesting to note that this dependence of the ratio <W'2 )av/
i.e., the momentum transports across the respective wind velocity component by motions of the scale being analyzed. Relevant values have been published only for the maritime friction layer in the Northeast Trades (Charnock et al, 1956). In this Section we shall confine ourselves to dealing with
206
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
i.e., for an averaging period of 27 days, the horizontal momentum flux av is positive, i.e., westerly momentum is transported toward the north, its absolute value being from 20 to 50 times as large as that for the turbulent motions of smaller scale. Naturally, all these statistical results cover only the range of turbulent fluctuations detected by the pilot balloon method, i.e., the motions from about a minute up to several days. 1400
1400
,/
x
1200
\
\
~
;;; 800
<;
.s
0'
·w
\
X \
1000
s:
1200
I
\
\
1000 \
x,
" ,, -,
'x, ,
... ...
600
800
...
'x
600
\
I
I
\
,,X \
400
,
/
200
,I
a
x_-------x
-10
r
I
a
10
30 20 Covariance (u'v'lav(cm'/sec')
40
, X
,
/
400
200
50
0,
10'
FIG. 65. Covariance av as a function of altitude in the Northeast Trades. (After Charnock et al., 1956.)
Averaging period 0-0 x ---- x
4.4.4
6 to 12 hours 27 days
Duration of fluctuations concerned 1 minute to 4 hours 1 minute to several days
Vertical Transfer of Horizontal Momentum According to Eqs. (4.60) and (4.61), the turbulent vertical flux of horizontal momentum is given by TXZ, Tyz. Relevant values at different heights over the sea can be obtained by means of either the geostrophic departure method [Eqs. (4.65) and (4.66)] or the eddy correlation method. The two procedures were applied by Charnock et
4.4
207
WIND STRUCTURE IN MARITIME FRICTION LAYER
al. (1956) to soundings taken in the northeast trade wind region, the eddy correlation method being based on motions of periods between 1 minute and 4 hours. Furthermore, the first method was used by Lettau (1957), who re-analyzed ascents made in the Westerlies by the three authors mentioned above. The comparative results -separately for the two flux components-are summarized in Fig. 66. Herein the values published by Lettau have been adapted to our x, y system, with x along the direction .of the mean surface wind (at 20 meters). 1400,--------,--------------,
1200
1200
1000
1000
~
800
.g.
600
~ I
W
,--------,------,1400
800 <xz
2 ] ~
600 -~ I
400
400
200
200
o L-_-'--_--'-_---'-_---'---"<>-_>-----'-------L2=
-0.6
-04
-0.2
04
0.6
08
1.0 -OA
-02
0
02
Vertical shearing stress ldyn/cm 2 )
FIG. 66. Vertical flux "xz, "yz of the horizontal momentum components as a function of altitude.
Geostrophic departure method Geostrophic departure method
Northeast Trades Anegada, 1953
L'l- - ! l
Geostrophic departure method
Westerlies, Scilly Isles, 1951
----
Eddy correlation method
Northeast Trades Anegada, 1953
0-0
x ----x
Westerlies, Scilly Isles, 1951
Surface wind speed 6.1 meters/sec Advection of warm air, surface wind speed 8.1 meters/sec Advection of cold air, surface wind speed 5.6 meters/sec Surface wind speed 6.0 meters/sec.
(Charnocketal., 1956) (Lettau, 1957)
(Lettau, 1957)
(Charnock, et al., 1956)
208
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
As regards TXZ, the argreement achieved is rather satisfactory. In the Trades, the variation of TXZ with altitude below 350 meters is found similar to that of the Westerlies. Below that height the turbulent transport of x momentum is directed downward. Above it an upward flux is observed in the Trades, whereas in the Westerlies the transport seems to be nearly zero. The importance of thermal stratification in the Westerlies can, however, not be separated from that of the wind speed, i.e., the difference in surface wind stress between the two relevant curves may be ascribed to wind speed rather than to thermal stability, which should cause opposite behavior (as was shown in Section 4.3.5.4). It is of particular interest that, above 100 meters, the TXZ values obtained for the Trades by the geostrophic departure method are in fair agreement, both in magnitude and in the form of their vertical variation, with those derived from the fluctuation analysis. While the former values reflect the total transfer of momentum due to all scales of motion, the latter refer to averaging periods of about one day or half a day and, therefore, cover only the fluctuations between 1 minute and 4 hours. This agreement implies that a large fraction of the vertical flux of x momentum in the height range from 100 to 1300 meters can be attributed to medium-scale turbulence. At lower levels, however, the two curves diverge because the fluctuation analysis of pilot balloon ascents does not include motions of a sufficiently small scale characterizing the flow next to the surface. Similar results have been obtained for the vertical momentum flux TyZ' After an error in the signs contained in the original paper of Charnock et al. (1956) was corrected*, rather a good agreement was reached in the vertical variation of Tyz (Fig. 66). The values of Tyz are mostly negative, i.e., there is an upward transport of y momentum from the surface up to 350 meters in the case of cold air advection in the Westerlies and up to 900 meters in the trade wind region. Again satisfactory agreement is found between the geostrophic departure and the eddy correlation methods above the height of 100 meters when they are applied to the trade wind flow. 4.4.5 Eddy Viscosities in the Marine Friction Layer In a turbulent flow the Austausch coefficient A or the corresponding eddy viscosity K = A/p are important quantities characterizing the vertical exchange motion. They can be obtained from Eqs. (4.60) and (4.61) if the turbulent shearing stresses Txz, Tyz and the corresponding vertical gradients ou/oz, ov/oz of mean motion are known.
* The author is indebted to Mr. J. R.
D. Francis for relevant personal communication.
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
209
As the eddy viscosity strongly depends on the vertical gradient of mean wind speed, fairly reliable values can only be expected if representative wind profiles are at hand and if the relevant gradients are of sufficient accuracy. In addition to the difficulty in measuring, there is a certain delicacy of concept, as mentioned in Section 4.4.1.1. While Charnock et al. (1956) ascribed different eddy viscosities Kee, K yz or Austausch coefficients A xz, A yz to the turbulent vertical exchange of x and y momentum, Lettau (1957) postulated that the Austausch coefficient is a scalar quantity which likewise characterizes the exchange of the two flow components. The validity of the latter assumption still awaits proof. At the present state of knowledge we do not think it feasible to argue either for or against one of these two concepts, but it is our intention to present the results reached so far. This is done in Fig. 67. For the computation of the eddy viscosities there were used only values supplied by the geostrophic departure method since the accuracy of the relevant results furnished by the eddy correlation method did not appear to be satisfactory. 1400,------------------,
1200
300
ausraoscn
coefficient (gm ern" sec")
FIG. 67. Vertical distribution of the Austausch coefficient over the sea determined by means of the geostrophic departure method. 0 - 0 , A x z, Northeast Trades, Anegada 1953 (Charnock et al., 1956); x - - - x, A yz, Northeast Trades, Anegada 1953 (Charnock et al., 1956); e - e , A, Westerlies, Scilly Isles, 1951 (Lettau, 1957) (advection of warm air); + - - +, A, Westerlies, Scilly Isles, 1951 (Lettau, 1957) (advection of cold air).
210
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
Starting with the similarities we observe the same vertical distribution of the Austausch coefficients in the Trades and in the Westerlies, namely an initial increase with altitude up to a certain level (about 100-300 meters in the Trades, 100 meters in the Westerlies) above which a decrease takes place. This result contains a qualitative confirmation of the well-known bottom layer concept of Rossby and Montgomery (1935), which implies a linear increase of the Austausch coefficient in the lowermost part (12 per cent) of the entire friction layer. The increase above the 700 meter level in the Trades may reflect the action of the clouds in promoting vertical momentum transfer. Beside these similarities there exists a strong difference with regard to the absolute values of the Austausch coefficient given by the authors mentioned above, the trade wind values being one order of magnitude larger than those obtained in the Westerlies, although there was not much difference in the strength of the flow as can be seen in the legend of Fig. 66. It should, however, be borne in mind that the Austausch coefficients obtained in the trade wind region are based on an average consisting of soundings made every 10 minutes and extended over the entire working period of 27 days, which contained 15 days of observations. In contrast to this comparatively long averaging period, Lettau used some series of ascents executed at different time intervals ranging from 10 to 65 minutes. The corresponding averaging periods did not amount to more than about 1 hour and 3 hours respectively (which, in addition, may make it difficult to ascertain that accelerations of motion were completely absent). Taking these conditions into account we arrive at the conclusion that the turbulent motions contributing to the Austausch coefficients computed for the Trades covered a much larger range than those investigated in the Westerlies (by Lettau). These differences in scale may help to explain the discrepancies observed. Apart from the Austausch coefficients given in Fig. 67 there are available only very sporadic data from over the sea. A broad survey of the values taken from mean wind profiles and from airplane investigations is supplied in Fig. 68. The maximum value of 1500 gm crrr ! sec:" was reached during a heavy storm.
4.4.6 Turbulent Energy Dissipation in the Maritime Friction Layer Based on a relevant study by Lettau (1957) we are now going to discuss the energy transformation occurring in the maritime friction layer. The work done by frictional force is given by (OTxzjOZ)u + (OTyz/OZ)v [ergs cm-3 sec:"] (4.72)
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
211
whereas the loss of energy that mean motion suffers from turbulence is described by Txz(OUjoz)
+ Tyz(OVjoz) [ergs cm-3 sec"]
(4.73)
Both quantities together result in the vertical divergence
+ TyZV) [ergs cm-3 seer"]
(OjOZ)(TxzU
(4.74)
of the vertical eddy flux of mean-motion energy TXZU
+ TyZV [ergs cm-2 sec:"]
(4.75)
1600 0
1400
0
1200
.,
~ 1000 0
0
s:
~'" 800
1 600 400
Ii 200
=
·· · . ·...
0
0
"'0
o
200
400
600
800
1000
1200
1400
1600
FIG. 68. Austausch coefficient at different altitudes over the sea. e, derived from mean wind profiles (Sheppard, 1954); 0, computed from eddy correlation measurements made by airplane (Bunker, 1955).
Lettau computed the energy transformation quantities [Eqs. (4.72) and (4.73)] as a function of height using wind profile measurements made by Sheppard et al. (1952) near the Scilly Isles. Vertical integration of Eq. (4.72) from z = 0 to z = 500 meters yielded the total work of frictional force within a vertical air column of 500 meters height. Lettau (1957) obtained the following results: Scilly wind profile (I): 1.06 x 103 ergs em -2 sec"! (advection of warm air) Scilly wind profile (II): 0.17 x 103 ergs cm-2 sec? (advection of cold air)
212
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
The fact that the total work of the frictional force was more than six times as great for profile (I) as for profile (II) can be attributed partly to the higher wind speed [808 em/sec for (I) as compared with 562 em/sec for (II)] and partly to the higher stability [(I): inversion; (II): superadiabatic]. After defining the "kinematic" energy dissipation e by e = [Txz(OUjoz) + Tyz(OVjoz)]jp [em- seer"]
(4.76)
Lettau, in order to describe the turbulent energy transfer by characteristic time and length figures, introduced the following parameters: 6.t = (u 2 + v2 )j2e
(4.77)
D = 21T(K3je)1I4
(4.78)
a = 21T(vSje)1/4
(4.79)
where K = turbulent viscosity (scalar) v = kinematic viscosity The time interval during which the existmg mean energy of motion lCu 2 + v2) is completely renewed is 6.t. In other words: If the energy influx from the horizontal pressure gradient and the inertial force to the mean flow were stopped at the time ft, the entire original amount of energy }(u 2 + v 2 ) would be consumed by turbulent motion at the time t: + 6.t. The figures D and d represent the upper and the lower limits of the part of the turbulence spectrum that is characterized by a continuous transfer of turbulent energy from greater to smaller turbulent elements ("energy cascade"). For elements greater than D energy is taken from the mean flow whereas turbulent energy is transformed into heat if elements smaller than d are considered. Values for these characteristic figures 6.t, D, and d were computed by Lettau (1957) on the basis of the wind profile measurements mentioned above. They are summarized-as a function of altitude-in Table XXI, which may be considered representative for the Westerlies. According to these findings there is an increase with altitude for all characteristic figures, which is particularly pronounced for 6.t. The order of magnitude is 100 meters for D and 1 em for d. When the air is colder than the sea, the range of turbulent elements taking part in the "energy cascade" extends to D values noticeably higher than under stable conditions, particularly at heights above 100 meters.
4.4
213
WIND STRUCTURE IN MARITIME FRICTION LAYER TABLE XXI
FIGURES CHARACTERIZING TURBULENT ENERGY DISSIPATION IN THE MARITIME FRICTION LAYERa
SciIly wind profile (I); advection of warm air Height (meters) 400 300 200 100 50 20 a
D.t (hours)
D (meters)
d (mm)
180 90 47 19 5 1
80 80 80 75 50 7
14 12 10 9 11
4
SciIly wind profile (II); advection of cold air Height (meters) 360 270 180 90 45 18
D.t (hours)
D (meters)
d (mm)
280 270 53
155 175 130 100 65 40
22 22 14 10 8 6
11
4 2
Computed by Lettau (1957) from wind profile measurements near SciIly Isles.
4.4.7 Surface Wind and Geostrophic Wind 4.4.7.1 General Remarks. When studying the properties of the maritime friction layer we found that the geostrophic wind was of doubtful benefit since it can hardly be determined with the necessary accuracy. Owing to this difficulty some authors even avoided computing the geostrophic wind from the field of atmospheric pressure but tried to derive its value from vertical profile measurements of the wind. Although this is certainly true as regards investigations of the surface friction there may be situations at sea when information on the direction and strength of the air flow can only be obtained from atmospheric pressure. Since ships' observations are unevenly distributed or often completely lacking, as they are occasionally in regions of severe storms or always in areas not traversed by the main shipping lanes, we are compelled to use the pressure field, which is derived from discrete observations by inter- and extrapolation, if we are in need of wind values for such purposes as the study or the forecasting of ocean waves, drift currents, wind setup, and storm surges. It is for this practical reason that many attempts have been made to relate the geostrophic wind or, in the case of strongly curved isobars, the cyclostrophic or gradient wind to the wind acting on the sea surface. In the absence of local and advective accelerations of motion the deviation of the wind vector at the sea surface from the geostrophic
214
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
wind, according to Eqs. (4.62) and (4.63), depends on the Coriolis force, i.e., on the latitude, and on the frictional forces which are composed of the surface friction and the turbulent exchange in the entire friction layer and which can be considered as a function of surface roughness, wind speed, and thermal stability. Owing to the complexity of the subject the approach has mostly been descriptive and theoretical analyses have only been brought out in recent years. It must be emphasized that the problem in question is quite different from the subject treated in Section 4.4.2, which is concerned with the mean vertical variation of the wind above the sea. We are now going to relate the surface wind to the surface pressure distribution without using additional empirical information on the vertical wind profile. This distinction has not always been made in the literature, as sometimes the wind observed at a height of, say, 1000 meters was simply taken as representative of the geostrophic wind.
4.4.7.2 Empirical Results. The latitudinal influence on the relation between surface wind and geostrophic wind was investigated by Gordon (1952b), who calculated mean values for the angle of inclination between the surface wind and the isobars as well as mean values for the ratio between the vector surface wind velocity and the vector geostrophic wind speed. Averages were computed along 10degree belts of latitude for all oceanic regions around the globe, resulting in an empirical relation between the mean surface flow and the mean geostrophic wind as a function of latitude, presented in Fig. 69. 55 45
'"
35
r r
45
'"
4z\
-c
.~ 25
<;
..J
55
""50"-
15
5
o
.~ 25
<;
..J
-, 79
10
35
-c
20
o
30
40
15
/'
\
V
1/
r--. .............
5
<,
I'-...
Rotlo 0.90 0.80 070 0.60 0.50 040
b
FIG. 69. Mean vector surface wind and mean vector geostrophic wind over the oceans as a function of latitude. (After Gordon, 1952b.) (a) Mean angle of inclination of mean vector wind to mean isobars. (Figures indicate numbers of independent 10° squares upon which the mean is based.) (b) Ratio of mean vector surface wind speed to calculated mean vector geostrophic wind velocity.
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
215
At low latitudes the mean angle between surface wind and geostrophic wind is large ( '" 35°) because the Coriolis force is small and the air converges from both hemispheres toward the equatorial low pressure belt. With increasing latitude there is a continuous decrease of this angle of deviation down to about 13° at a latitude of 55°. The ratio between mean vector surface wind speed and mean vector geostrophic wind velocity increases from low latitudes to a maximum of nearly 0.90 at around 30° of latitude. This maximum was attributed by Gordon to the constancy of the trade winds and to the equilibrium between wind and waves reached there, whereby the frictional drag is reduced. However, according to theoretical studies carried out by Lettau (1959) (see Section 4.4.7.3), this result cannot be explained in terms of the roughness parameter (whose influence seems to be rather small) but should be considered as an effect of thermal stability. Further empirical data, or suitable analyses of the available data, will help to decide which of the two concepts is right. At middle latitudes Gordon obtained values between 0.70 and 0.60. For the North Sea Jeffreys (1920), using 566 observations, calculated the angle between the surface wind and the corresponding isobar and arrived at a mean veer of 16.5°, which is in satisfactory agreement with Gordon's results. The spread about the mean value was rather large, however. Reynolds (1956), in his analysis of winds over the northern Irish Sea exceeding 20 meters/sec, obtained an average veer of the geostrophic wind against the surface wind between 2° and 26°, the standard deviation being 21°. The surface wind was of approximately half the speed of the geostrophic wind and 6/10 of the gradient wind speed. Also, the correlation here was rather low (about + 0.55), which means that the scatter was comparatively large. No improvement was attained when the surface wind was compared with the gradient wind instead of with the geostrophic wind. Information on the influence of thermal stability on the ratio between the velocities of surface wind and geostrophic wind can be found in various publications (U.S. Navy, Hydrographic Office, 1951; Revillon, 1953; Johnson, 1955). The values for iisurrace/Ug are assumed to increase steadily from 0.55 to 0.80 when the air-sea temperature difference varies from + 4°C to - 8°C. The effect of thermal stability is said to be most pronounced at low wind speed (less than 7.5 meters/ sec) whereas turbulent friction is liable to become more important at higher velocities.
216
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
4.4.7.3 Theoretical Approaches. Since the empirical results are rather sporadic, variable, and incomplete, an extensive analysis using theoretical methods as far as possible is highly desirable and deserves particular attention. A rather comprehensive treatment of the subject was presented by Drogajcev (1954) who, on the bases both of theory and of measurement, investigated the ratio between surface and geostrophic wind speeds as a function of latitude, geostrophic wind speed, and vertical gradient of air temperature in the friction layer. His findings are given in a number of tables from which Fig. 70 has been drawn. It will be noticed that in Drogajcev's diagrams the influence of the thermal gradient appears to be greater with high (geostrophic) wind velocities 1.0
0
5
10
15
20
25
30 - 1.10
0.9
- 100 -085
---- - - - - - - -
-e e
.j
- 055 -0.20 015 050
o
:c c,
~., 0
-1.10
'"
.2
-1.00
-e c: .j
-085
., o
---- - - - - - -
.;?
~
-055 -0.20 0.15 0.50
'0
.s '§
'" .,
Q;
E 0
2<, u a,
C
.~
-o 0
C;. ~
.,
" -0 c. E
2! <;
..,.,
.,<>
-1.10
(/l
-1.00
.,
o +:
>
-0.85
----- -- - - - - -
-055 -0.20
5
10
15
20
25
30
8~o
Geostrophic wind speed speed (meters/sec)
FIG. 70. Ratio of mean surface wind speed to geostrophic wind speed as a function of geostrophic wind speed for different thermal stabilities and for the latitudes 20, 40, and 60 degrees. Solid curves: after Drogajcev (1954) for air temperature gradients indicated. Dashed curves: after Lettau (1959) for Ri = 0 (at z = 1 meter).
4.4
WIND STRUCTURE IN MARITIME FRICTION LAYER
217
than with low ones, which is contradictory to the opinion mentioned above. In addition, it is remarkable that, for a given latitude and stability, the speed ratio Usurface/Ug decreases with increasing (geostrophic) wind speed. At first glance one is inclined to expect that a stronger flow will be connected with an intensification of the dynamic turbulence and thus reduce the difference between surface and geostrophic wind speeds. However, this simple interpretation may be biased by empirical findings where it is difficult to separate the different influences. In this situation it is welcome that a more recent analysis (Lettau, 1959) deals with the same subject and offers itself for comparison. In analogy to Eq. (4.51) Lettau introduced the so-called geostrophic drag coefficient C g defined by C g = (u".fUgO)2
(4.80)
where the subscript 0 shall indicate that UgO refers to the pressure distribution at the surface. If Cga applies to adiabatic conditions it can be combined with the adiabatic wind profile (4.13) and thus yields the following expression for the ratio surface wind: geostrophic wind U C 1/ 2 Z + Z _ = ~ln 0 (4.81) UgO k zo For determining C~~2 Lettau proposed an empirical relationship between C~~2 and the "surface Rossby number" Roo defined by Roo = Ugo/zo/ (4.82)
(zo = dynamic roughness, f = Coriolis parameter). The empirical relation in question is similar to well-established laws in fluid mechanics. In atmospheric physics its form and, particularly, the numerical constants must be regarded as tentative and subject to further revision depending on more and improved observations. Likewise it was tentatively assumed by Lettau that CgjCga universally depends on the Richardson number (at z = 1 meter), the relevant empirical relationship being based on measurements over the great plains near O'Neill, Nebraska. Thus he obtained the ratio "surface wind to geostrophic wind" as a function of the following five variables: z = height of anemometer Zo = dynamic roughness UgO = geostrophic wind speed at the sea surface cp = latitude Ri = Richardson number.
218
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
At sea neither zo nor rp has great effect on the ratio Usurface!Ugo, the factors of chief importance being UgO and Ri. For computing values of the speed ratio between surface wind and geostrophic wind for various latitudes and geostrophic wind speeds, we assumed adiabatic conditions, fixed the anemometer height at 10 meters, and chose the roughness parameter zo = 0.03 em, which might be considered representative for the sea surface. The results are inserted in Fig. 70 and show a course completely parallel to the data of Drogajcev. However, a discrepancy appears to exist as regards the thermal stability because Lettau's curves, which refer to adiabatic conditions, seem to correspond to a vertical temperature gradient of about - 0.4 0C; 100 meters if considered according to Drogajcev's stability figures. This need not be a real difference as the two stability measures are not strictly comparable. The Richardson numbers were taken at the height of I meter whereas the temperature gradients given by Drogajcev refer to the entire friction layer. Although the results of the two authors seem to agree fairly well we should point to the uncertainties inherent in several of the empirical relationships used by them. The fact that these empirical data were almost exclusively collected on the continents should be kept in mind, too. Thus, we may say that more empirical evidence, particularly from the sea, is needed to verify the above results beyond any doubt. * If the isobars are strongly curved it may become essential to use the cyclostrophic or gradient wind instead of the geostrophic wind. A practical graph for the conversion of geostrophic wind speed Ug into gradient wind speed Ugr was published by Silvester (1955) (Fig. 71). As regards the difficulties inherent in determining the pressure gradient near the centers of cyclones and anticyclones, as well as in hyperbolic regions, a method proposed by Drogajcev (1956) may be of value. A further refinement of the computing procedure was introduced by Bijvoet (1957, 1960) who, in addition to Coriolis force, friction, stability, and curvature of isobars, also took into account the isallobaric gradient, thus including the case of nonstationary pressure distribution. In connection herewith there arises the difficulty of determining the temporal variation of atmospheric pressure with sufficient accuracy. The pressure tendency over 3 hours, as it is given in synoptic weather reports from land stations and stationary ships, appears to be an insufficient approximation in many cases, particularly in the vicinity of fronts and trough axes. Only if the pressure * A new theoretical approach has been published by Blackadar [(1962), see supplement to references].
4.5
219
TIME VARIATIONS OF AIR FLOW
tendency field is known very precisely, as, for instance, from barograms from a sufficient number of stations, is it justifiable to allow for the movement of the pressure systems. f.J¢ ~
1.0 08 06 0.4 0.3 0.2
oI
008 006 0.04 0.03 u
0.02
~
/
/'
/
V
~
v
,y
a.
","
~ 0.0 I ;:; 0008 <3 0006 0004 0.00 3
10~ I----
--- -- ------
~
¢
I--
----- - --___ --- -95"&.1-- -
"' .... ", //:.--:. ..- ~ l;:? ~~~... :;:
.i"
0002
~
0
'-'90ol~
--- --
-
91'5%
2 99'2_150% I 30% I 20% I -I 05%
" /
100
20 c
30 e
40 e
50 "
60 0
Latitude
FIG. 71. Gradient wind speed U g r as a percentage of geostrophic wind speed Ug. (From Silvester, 1955). The anticyclonic case is shown by broken lines, the cyclonic case by full lines.
4.5
TIME VARIATIONS OF AIR FLOW ABOVE THE SEA SURFACE
Aside from the turbulent wind fluctuations which form an essential part of the air flow itself and have been dealt with in the foregoing sections, there occur temporal variations of air motion which are caused by external influences. These variations may be periodic or aperiodic. The diurnal and the annual cycles are natural periods and are due to the oscillating influence of the sun, being particularly marked in regions distinguished by quasi-stationary flow conditions. In other zones they may be veiled by various influences and only made visible by an extensive statistical analysis. Nonperiodic wind variations are connected with moving cyclones and anticyclones or are caused by the different ranges of turbulent motion. 4.5.1 Diurnal Wind Variation Contrary to the behavior of other meteorological elements, such as air temperature, for example, whose daily variation is mainly caused
220
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
by a periodic change occurring at the surface, there is no such influence acting on the wind since the boundary condition is always and everywhere the same, namely, the wind speed is equal to zero or equal to the surface current velocity in the sea. Thus there is no substantial influx of momentum across the lower boundary if the effect that a strong ocean current might exert on the overlying calm air is left out as practically unimportant. A diurnal variation of the wind, if it does exist at all, must, therefore, originate from other causes. On land the temporal oscillation of turbulence, particularly of its variation with altitude, has been made responsible for the wellknown daily variation of the wind vector which, near the surface, is characterized by a maximum shortly after local noon and a wide minimum at night. At sea the problem was difficult to solve since the regular daily variation of the wind seemed to be too small to be detected by means of conventional routine observations. It was not until the continuous wind records taken on board the German research vessel Meteor in the Atlantic Ocean in 1925-27 had been analyzed by Kuh1brodt (Kuhlbrodt and Reger, 1938) that clear evidence was obtained on this subject. The material was worked up separately for different wind regions, e.g., the Trades, the West African Monsoon, the subtropical, and the higher latitudes. The resulting diurnal variation of the scalar wind velocity is shown in Fig. 72. In the trade wind zone we observe a very regular daily oscillation characterized by two maxima (at 0900 and 2300 hours) and two minima (at 0400 and 1500 hours). It is possible to relate this finding to the well-known diurnal double wave of atmospheric pressure which has its maxima at about 1000 and 2200 hours, its minima at 0400 and 1600 hours, local time, and which is particularly marked in the tropics. This regular oscillation of the atmospheric pressure is connected with a periodic motion of the air. There is an additional easterly wind component along the corresponding meridian when the atmospheric pressure wave has its maxima, i.e., at 1000 and 2200 hours, and, vice versa, an additional westerly wind component at the time of the pressure minima (0400 and 1600 hours). With rising pressure additional meridional wind components appear, blowing from the north in the northern hemisphere and from the south in the southern hemisphere. With falling pressure the contrary occurs. The entire system is displayed schematically in Fig. 73. A comparison between these theoretical results and the vector diagram of diurnal wind variation in the Southeast Trades (Fig. 74) shows that there is
4.5
221
TIME VARIATIONS OF AIR FLOW Daily Daily mean range (meters/sec)
Local time (hours)
12
4
0 0.2
24
16
NE and SE
0
7.95
0.46
0
7.5
0.69
1i
~
! c 0
'" E 0
"0
1! E
e c
.~
0 's
'"
0
-02 4
0
16
12
8
24
20
Local time (hours)
FIG. 72. Diurnal variation of scalar wind speed in different regions of the Atlantic Ocean. (After Kuhlbrodt and Reger, 1938.)
Local time
4
0
12
8
16
24
20
Diurnal double wave of atmospheric pressure (proceeding from E to Wl
Additiona I meridional wind components
H
L
Additional zona I wind components (bath hemispheres)
0
N hemisphere
5
hemisphere
0
H
L
0
0
0
0
0
0
0
0
0
0
0
4
8
12
16
20
24
Local time
FIG. 73. Diurnal double wave of atmospheric pressure and corresponding wind components according to theory. (After Kuhlbrodt and Reger, 1938.)
222
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
rather a satisfactory agreement between them (except at 0100 and 0700 hours). The additional easterly wind component reaches its maxima at about 0900-1000 and 2200-2300 hours, whereas the additional westerly wind component does the same at 0400-0500 and 1600 hours.
o !
0.1 [
15 I
0.2 I
03 !
FIG. 74. Mean diurnal wind variation in the Southeast Trades of the Atlantic Ocean Diagram of additional wind vectors. Mean wind vector: 126°, 6.83 meters/sec. Mean daily oscillation of vector wind direction: 5°. Mean daily oscillation of vector wind speed: 0.47 meter/sec. Average over 74 days = 1776 hourly observations. Figures denote hours in local time. (After Kuhlbrodt and Reger, 1938.)
The daily variation of scalar wind speed in the regime of the West African Monsoon (Fig. 72) mainly reflects the characteristics of the diurnal double wave observed in the trade region. A specific feature, however, is the swift increase in speed between 1400 and 1600 hours and, although not perceptible in Fig. 72, the considerable daily variation of wind direction which ranges between 19 and 24 degrees and thus is four to five times greater than in the zone of the trade winds. These observations point to continental influences in spite of the fact that the measurements obtained in coastal areas were excluded from the analysis. In the tropics the same semidiurnal tidal oscillation of the wind predominates up to about 9 km, as was demonstrated by Fletcher (1959) who discussed upper-wind data collected at Guam and Bermuda. A different and much stronger diurnal oscillation, however, was found in a layer, several kilometers thick, just above the tropopause. Here an outflow from the tropics occurs near 1800 hours while
4.5
TIME VARIATIONS OF AIR FLOW
223
a corresponding inflow takes place around 0600 hours. This phenomenon was ascribed by Fletcher to the afternoon heating and to the resulting expansion of the air. In nontropical regions the diurnal double wave in the daily variation of scalar wind speed is almost not to be found (Fig. 72). There is a clear indication of a marked wind speed maximum around midnight, the secondary maxima at 0600 and 1400 hours being of minor importance. This type of daily wind variation can be considered representative for oceanic areas outside the tropics. So far no data on the diurnal wind variation at upper levels above the sea outside the tropics have become known to the author, apart from a few values of the mean wind speed ratio U30/U600 measured on British ships in the North Atlantic west of the Bay of Biscay between 1937 and 1944 and published by Gordon (l950b). They are presented in Table XXII. With the exception of the statement that the two wind speeds considered show equal values at local noon, caused perhaps by turbulent effects, only little information can be gathered from these data as, unfortunately, no absolute values were given. TABLE XXII DIURNAL VARIATION OF WIND SPEED RATIO
ii 3 0 / U60 0
DURING DAYLIGHT HOURSa,b
Local time 0700--0800 0900-1000 1100-1200 1300-1400 1500-1600 1700-1900
0.92 0.99 1.01 0.97 0.82 0.82
After Gordon (1950b). North Atlantic Ocean, 40-50° N, 10-20° W (1937-1944). a b
4.5.2 Annual Wind Variation There may be some argument on whether mentioning the annual cycle of the wind in a monograph devoted to the physics of the marine atmosphere is a matter of necessity or rather an act of politeness to maritime climatology. As regards the quantities concerned, e.g., monthly averages of wind direction and speed, monthly frequencies
224
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
of certain groups of wind direction and wind force, particularly of storms and gales, it is quite clear that they are obtained by means of statistical methods which summarize a large variety of different physical processes. By this procedure the physical relations can be more or less concealed, the result being more of a geographical and climatological significance than of a physical one. Moreover, on the continents, as well as at sea, the annual period of the wind shows various specific features depending on the locality concerned, as can be inferred from the climatic atlases of the oceans and also from Fig. 75. lImIllY:IlIW"llDlIXXXIXlI Name and t.ctrtude
of Station
I------=:::.:-......""""==----p.-.:~-_l
Thorshavn,
Fa roe 151 ands
62° N
3. I
Ponla Delgado, 2.7 1---------'''-<-----------;'7'''''''----1 Azores Is.
38° N
O.5r=====""'-",--======o<>-i
33° N
I .6
Funchal, Made; ra
I =--=...=~::::::,,'==~:::::=::::::"'o;;:----J Las Palmas, Canary Is.
28° N
2.3
1.2.l:::
5.1
2.91---------"'.,---------~ Cape Verde Is.
6.8
2.7b;------/-------;::-------''''''"'-<::!, Noran no
77
St. Helena 31 k-------------;~------1l632 meters)
16° S
7.2
I----+--"'=------------''''''-:---------j Slalen Is
54° S
5.9
!f-.fL---""""'.::::---~,..,a:::.------"~ Laurie Is.
61
Santiago,
15° N
Fernando
4° S
I
0
S
I meter / sec
IlImISl:;Z::IlIlZIl'llIIIXXXIXTI
FIG. 75. Annual variation of mean wind speed at island stations in the Atlantic Ocean. (After Brose, 1936.)
In spite of the fact that the points mentioned above do not advocate the treatment of the annual wind variation in this monograph, we shall attempt to outline a few universal aspects of this subject
4.5
TIME VARIATIONS OF AIR FLOW
225
because it is felt that the annual cycle has the same fundamental physical importance as the daily variation. Of course, we have to abstain from going into detail. Some useful information along these lines can already be obtained from the comprehensive global treatment of the annual wind speed variation given by Brose (1936), although, as regards the oceans, he was completely dependent on the relatively few island stations. An extract from the results published by Brose is presented in Fig. 75, which exhibits the annual variation of mean wind speed at nine island stations located roughly along a meridional cross section through the Atlantic Ocean from north to south. An inspection of the curves shows that the annual variation of wind speed depends on the natural cycle of the sun and the corresponding variations of global circulation. Starting in the north we see that a single wave with its maximum in winter seems to be characteristic for the annual oscillation of mean wind speed in the Westerlies. It must be mentioned that this annual course mainly reflects the varying frequencies of light and strong winds whereas the share of moderate winds remains more or less unchanged throughout the year. This type of annual variation is, although strongly weakened, even perceptible as far south as at 33° N (Madeira). Farther to the south a summer maximum appears (Las Palmas), since this region is embodied into the trade wind flow in summer while in winter it belongs rather to the subtropical high pressure belt. The actual trade wind region is characterized by a wind speed maximum in late winter or spring and a minimum in late summer or fall. Thus we observe an inverse oscillation in the Trades of the two hemispheres (Santiago, Fernando Noronha). The southern Westerlies show the usual winter maximum of wind speed (Staten Island) whereas the subantarctic region (Laurie Island) is distinguished by a pronounced double wave with equal maxima in spring and fall. Summarizing, we may say: On the oceans the annual variation of wind speed generally shows a single oscillation with a winter maximum and a minimum in summer. This type is particularly dominant in the central parts of the oceanic wind regions. Various deviations from this general scheme occur in the boundary zones between two adjacent wind regions because of their annual shifting. In addition to these planetary influences the continents act as powerful agents on maritime wind systems, creating special annual wind variations of monsoon character. These local or regional features would, however, require detailed consideration and will not be discussed here. They belong to the domain of climatology.
226
4
FLOW CHARACTERISTICS OF MARINE ATMOSPHERE
The same oceanic type of annual wind variation is also found at upper levels.
4.5.3 Aperiodic Wind Variation Nonperiodic wind variations occur, at a particular locality, in connection with such meteorological processes as generation and propagation of cyclones and anticyclones, passages of fronts and troughs, arrival of new air masses, or, generally, with changes of the weather. They are many times larger than the periodic variations. The average value of the aperiodic daily variation of wind speed, according to Kuhlbrodt and Reger (1938), amounted to from about 4 meters/sec in the tropical Atlantic Ocean, to 7 meters/sec in its southern subtropical latitudes, and to 9 meters/sec in the southern Westerlies. The smallest value in the tropics corresponded to the periodic oscillation of wind speed, i.e., to 0.5-1 meter/sec, whereas the maximum reached 10 meters/sec. In the southern Westerlies the greatest wind speed change within one day even amounted to 25 meters/sec. The ratio between the average aperiodic wind speed oscillation and the mean wind velocity was 0.8 in the equatorial zone, 0.6 in the trade wind region, and 0.9 in the temperate latitudes. The general aperiodic wind variation-without any reference to time interval-is mostly characterized by the quantity of "constancy" which is defined as the ratio of mean vector wind speed to mean scalar wind speed times 100. The highest constancy values were, of course, observed in the trade wind regions. Kuhlbrodt and Reger (1938) reported 95 per cent for the Northeast Trades and 94 per cent for the Southeast Trades in the Atlantic Ocean. The West African Monsoon showed a somewhat smaller constancy (85-89 per cent) whereas considerably lower values of constancy occurred in the region of westerly winds. For instance, Markgraf and Bintig (1954) obtained constancy data ranging between 3 and 77 per cent (average minimum 12 per cent, average maximum 46 per cent) for a number of squares in the northwest European waters, the minima falling mostly into the transition seasons of spring and autumn. For further details reference must be made to the relevant marine climatic atlases. The aperiodic wind variations caused by turbulent motions are described in Sections 4.3.6 and 4.4.3.
5. Thermodynamic Processes in the Marine Atmosphere This chapter is devoted to a description of those characteristics of the marine atmosphere that are manifest in temperature and humidity. In other words, we shall deal with atmospheric phenomena of small and medium scale, occurring at sea and essentially controlled by the fact that temperature and moisture content are influenced by the sea surface. The general features of the sea surface as the lower boundary of an air flow have already been outlined in Section 4.1. Although that section was mainly written as an introduction to the treatment of the flow characteristics, it covers most of the aspects that are important for thermodynamic processes. 5.1
THE TEMPERATURE OF THE SEA SURFACE
Before we discussed the flow characteristics of the marine atmosphere in Chapter 4 we gave a short introduction to the geometry of the sea surface, having in mind the close interrelation between the relevant properties of the sea surface and the wind structure above it. Taking a similar approach, we now begin the treatment of the thermodynamics above the sea with a short representation of the corresponding properties of the sea surface. Here we can restrict the discussion to temperature because other quantities, e.g., salinity and carbon dioxide, either are of minor importance for atmospheric processes or have already been dealt with in connection with atmospheric chemistry (Chapter 3). We need not emphasize that we do not intend to give a detailed description of the geographical distribution of seasurface temperature. This is done in various climatic atlases and cannot be the subject of a physical approach. It is only the basic and general features of the sea temperature that we are concerned with. At first sight there is little that seems worthwhile, or necessary to mention in this respect, since the oceans, owing to their large heat capacity and to processes of mixing, are said to be distinguished by a 227
228
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
remarkable temporal and spatial homogeneity of temperature. Thus their behavior is very different from that of the continents. At closer examination, however, there emerge peculiarities that may well be of importance for the exchange of heat and water vapor through the sea surface and for the thermal and moisture conditions in the marine atmosphere. These particular features will now be dealt with in some detail. 5.1.1 Factors Affecting the Sea-Surface Temperature The temperature of the sea surface depends on a number of physical factors that in part can be attributed to processes in the sea itself and that, on the other hand, are due to influences from outside or to interaction between the sea and other media. As to the sea-borne factors, there are the advective heat transport by ocean currents, including the vertical displacement by upwelling or downwelling, the effects of convective stirring and of turbulent mixing (caused by waves, permanent and tidal currents), and the heat released by chemical processes in the water. The influences from outside are the heat transfer by precipitation, particularly the loss of heat by the melting of solid precipitation, the gain or loss of heat by fresh water influx (only significant in coastal areas), and, finally, the heat flow through the bottom of the sea. The interaction effects comprise, in the first place, the radiation budget, which consists of the total incoming radiation from the sun and the sky and the effective back radiation from the sea surface, as well as the radiation reflected by it. They further include the exchange of sensible heat between sea and atmosphere and the loss or gain of latent heat by evaporation or condensation of water at the sea surface. As may be inferred from the specification given above the entire problem of clarifying the mechanism that determines the sea temperature is a very complicated one, which at present is far from being completely solved in a quantitative manner. A discussion and an outline of computational procedures for evaluating the different factors has been given by Laevastu (1960),* whereas Kraus and Rooth (1961) have published a quantitative treatment of the temperature and of the heat flux in the ocean surface layers for a steady state model as well as a brief discussion of some cases of transient development (seasonal influences, weather disturbances, diurnal changes). For our purpose such a general and quantitative approach is not necessary. We shall rather limit ourselves to presenting some information on the spatial and temporal variations of sea-surface temperature, including some indication of possible causes.
* And
Sturm [(1963), see supplement to references].
5.1
THE TEMPERATURE OF THE SEA SURFACE
229
5.1.2 Vertical Distribution of Water Temperature Near the Sea Surface The physical factors that mainly contribute to the temperature distribution near the sea surface are the effects of interaction, as described in Section 5.1.1, and the convective stirring, as well as the turbulent mixing, in the sea. Thus we can restrict our discussion accordingly. The short-wave radiation from the sun and the sky is absorbed throughout a layer of several meters of water. According to measurements carried out by Boguslavskii (1956) with a specially constructed underwater pyranometer, the temperature increase owing to solar radiation absorption, as compared with the over-all temperature change, reaches the following percentage values at the depths indicated: 1 meter: 90 per cent 5 meters: 50 per cent 10 meters: 25 per cent 25 meters: 11 per cent Contrary to the substantial downward penetration of short-wave radiation, the effects of long-wave emission as well as of evaporation and condensation are confined to a very thin surface film. If, in addition, the air temperature is lower than that of the sea surface, a flux of sensible heat passes from the sea to the atmosphere, thus augmenting the cooling of the sea surface caused by long-wave emission and evaporation. The consequence is that an unstable stratification in water may appear, which creates and maintains convective motion in the surface layer. There arises the question of how these different processes develop under natural conditions and what the resulting temperature distribution is like. 5.1.2.1 Quiet Sea Surface. In the following we shall attempt to summarize some experimental data in order to demonstrate the thermal stratification in the uppermost layer of the sea. Unfortunately, the disturbing influence arising from the wind-generated surface waves renders measurements of that kind rather difficult if "conventional" thermometric methods are applied. They can only be carried out when the sea surface is sufficiently quiet and therefore represent the thermal stratification in the absence of turbulent mixing. Thus their conclusiveness is restricted. Relevant investigations were performed by Merz (1920), Bruch (1940), Woodcock and Stommel (1947), and Roll (1952c). Owing to
230
5
THERMODYNAMIC PROCESSES OF MARINE ATMOSPHERE
the difficulties mentioned above, all these measurements were confined to relatively small bodies of water such as ponds and lakes. On the ocean, measurements of similar kind were attempted by Houghton (1956), who investigated the vertical temperature distribution in the topmost three meters of the sea from an ocean weather ship, using a series of eight thermocouples mounted in a 12 ft brass tube. Since these observations supplied only values from about 20 em to 3 meters depth they are not truly representative of the conditons at the very surface, which, however, are the most significant for the exchange processes between ocean and atmosphere. In this respect the results of the former studies are more informative. Merz (1920), who measured the thermal stratification in water by means of a special pan thermometer (with a bulb greatly elongated and inclined to the plane of the scale), obtained examples of a strong warming of the uppermost water layer as well as of a cooling by
evaporation. With the water surface covered by seaweed the daily
temperature variation amounted to more than l2.5°C at the surface and decreased to 0.8°C at a depth of 10 em. It is quite clear that the radiation effect is concentrated on the uppermost layer by the seaweed, and, at the same time, the wind action is impeded. On the other hand Merz observed a surface temperature that was 0.9°C lower than that at the 10 em depth when, after a cloudless night and with the air temperature considerably below that of the water, he measured the temperature profile on an early morning in a complete calm. Similar results were reported by Woodcock and Stommel (1947), who, applying the same method as Merz, studied the temperature profile at night, on both sides of a freshwater pond which was warmer by about 1O-l4°C than the overlying air (Fig. 76). Apart from the effect of long-wave emission, the cold surface layer of the water can, in these cases, be ascribed partly to the transfer of sensible heat to the air and partly to the effect of evaporation. The temperature decrease at the surface, mainly as the consequence of evaporation, is perceptible when the air temperature is equal to or even higher than that of the water. Corresponding results were given by Bruch (1940) and Roll (1952c), who executed measurements by thermocouple elements and pan thermometers, respectively. In seventeen or twenty-three cases with air temperature higher than that of the sea Bruch observed a lowering of the sea-surface temperature as compared with the deeper water layers. Three cases showed isothermic stratification and in only three other cases did the sea surface have the highest temperature value of those taken in the water. Some of the measured profiles are reproduced in Fig. 76. The cooling effect of
5.1
231
THE TEMPERATURE OF THE SEA SURFACE
evaporation at the water surface amounted to from about 0.2 to O.4°e at wind speeds between 3 and 4 meters/sec. Thus a thin film of heavier water existed over a lighter one. Obviously this instability was maintained by surface tension whereas heat conduction led to a thermal balance in deeper layers. 8
E
2J.5~
--
A
-:-:-~~
__ IliL.~
~
4
2
~
Water surface
o
_
~.,
-2· ~
6
8
.
.
o - _.::-..
8
~
6
u
-r-
41.5
44.0~
17.9~
•
-2 -4
-4
o _ 6 L-_--'--'--_----' 26 26.5
L -_ _-'---_ _---'--------.J -
22.5
27
Temperature
50~.
23
6
{Oel
8.9~
8
8
]
6
'" .0;
4
I
2
:c
_.-c
6
4
.
2
~ .. ~
Water surface
o --------------------------, -2 s:
-4
-4
"'
-6
-6
0.
0
-8
2
4
6
10
8 Temperature
FIG.
12
14
16
(Oel
76. Temperatures near the water surface: Time
Wind speed (meters/sec)
Weather
Author
Aug., 15301605 hr Aug., 15401605 hr
3.4
No clouds
4.5
Overcast
Roll (1952c) Roll (1952c)
0.4
No clouds, pond steaming
A.
Air warmer than water
B.
Air temperature nearly equal to water ternperature Air cooler than water Oct., 21152245 hr
C.
0
. -2
Woodcock and Stommel (1947)
Black blocks indicate limits of temperature fluctuation over a period of 1 minute. Heights above 8 em are given by figures (not true to scale).
232
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
These results of field measurements were confirmed by laboratory studies under strictly controlled conditions (Haussler, 1955-1956). Here it could be shown that the cooling of the water surface is actually due to evaporation. It does not take place in the presence of an oil film, which prevents evaporation but does not impede the transfer of heat. In Fig. 76 some information is also given on the temperature fluctuations which exhibit a distinct dependence on thermal stability. Roll (1952c), attempting to determine the turbulent conductivity of heat from readings of temperature fluctuation, found values that, near the water surface, were close to the corresponding molecular constants, which indicates that in the cases considered the heat exchange between air and water was mainly executed by molecular heat conduction. 5.1.2.2 Agitated Sea Surface. Owing to restrictions of the experimental methods available all the results mentioned so far refer to a relatively quiet water surface. In view of the fact that the sea is generally stirred by turbulent mixing, great importance must be attached to measurements that are not affected by such a handicap. Reference is therefore made to a study published by Ewing and McAlister (1960), who used a radiation thermometer with spectral sensitivity in the 6-20 I-' band, a region in which the absorption in water is so high that 98 per cent of the outgoing infrared radiation originates in the uppermost water layer that has a thickness of 10- 2 em. The radiation temperature of the sea surface was measured from the pier of Scripps Institution, La Jolla, California, at a point 200 meters offshore, and in water 7 meters deep, and showed a departure of more than -0.6°C from the temperature obtained by conventional methods at a certain depth (about 15 ern), although wind and humidity were not conducive to vigorous evaporation. As this result does not seem to provide any essentially new information we should like to point to the remarkable fact that Ewing and McAlister (1960) were also able to study the effect of turbulent mixing due to breaking waves. In coincidence with the breaking of a wave, a momentary warm signal was recorded, showing the effect of mixing between the cool surface skin and the deeper and warmer water layers. It was followed by a longer-lasting cold signal that obviously coincided with the duration of the blanket of foam left behind the breaking wave. About 12 seconds later the cool surface layer was reestablished. From these findings evidence can be drawn that the cool thermal boundary is also present, at least intermittently, on the open sea where
5.1
THE TEMPERATURE OF THE SEA SURFACE
233
whitecaps and turbulent mixing occur owing to wave action. These results were confirmed and refined by laboratory studies which proved that the negative temperature departure at the water surface also occurred, although at a reduced scale, when strong vertical currents in water were produced by a suitable stirring device. Bearing in mind the different effects of short-wave radiation, longwave emission, and evaporation, which were already mentioned at the beginning of this section, Ewing and McAlister (1960) arrived at the conclusion that the heat flux in the superficial layer of the sea must be upward on the average and that, consequently, the radiation temperature of the ocean is usually lower than the "sea-surface temperature" measured by conventional methods. A similar result was reached by Roll (1948b), who, extrapolating vertical temperature profile measurements obtained above the sea down to the sea surface, was led to attribute lower temperature values to the latter than were measured simultaneously in water at some centimeters depth. Furthermore, it was concluded by Ewing and McAlister (1960) that the transfer of sensible heat at the ocean surface is controlled chiefly by molecular conduction rather than by convection or turbulent exchange and that the surface layer is characterized by strong thermal gradients. It seems, however, questionable whether this conclusion is valid generally, i.e., also during gales and with the complete disintegration of the sea surface as is observed during hurricane force winds. In laboratory experiments Ewing and McAlister (1960) finally studied the temperature fluctuations in the transition zone between the boundary layer and the deeper region where convection and turbulent exchange are fully developed. The thermal unsteadiness in that layer had time constants of less than 1 second and was much more pronounced when the heat flux was upward than when it was downward.
5.1.3 Horizontal Variation of Sea-Surface Temperature Not long ago it was generally assumed that the sea-surface temperature, with the exception of certain boundary zones, is a rather homogeneous and conservative element distinguished by slow and steady horizontal variation. Nowadays, more numerous measurements, particularly rapid surveys of sea-surface temperature distribution by air-borne radiation thermometer and other means, have resulted in furnishing a synoptic picture of that distribution which reveals considerable variations. In the future, radiation measurements carried out by meteorological
234
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
satellites will probably help to complete this synoptic survey provided that the handicap arising from the atmospheric extinction and emission can be overcome (Wilckens, 1962). In the first place, reference must be made to the sea-surface temperature charts published by the U.S. Navy Oceanographic Office which cover the greater part of the North Atlantic Ocean and are based on means for one-degree squares computed from all available synoptic ship reports, including surface data from oceanographic observations, and air-borne radiation thermometer measurements. Since the lateral displacement of currents is slow, a rather adequate reproduction of the general temperature pattern may be obtained by summarizing the data for a lO-day period, which is also required in order that sufficient data coverage may be achieved. Thus, lO-day composite charts of sea-surface temperature are drawn every 5 days on an overlapping basis. A section of such a chart is reproduced in Fig. 77. It shows a very complex pattern of sea-surface temperature characterized by numerous warm and cold tongues and cells which move and alter, as can be found by inspection of consecutive charts (see for example, Gibson, 1962). In addition, Perlroth and Simpson (1962) observed that the position of the water tongues, as well as the orientation of their axes, when compared for a specific month over a number of years, remained remarkably uniform, although the meteorological conditions presumably varied. In order to explain the persistence of the water tongues, Perlroth and Simpson assumed that the horizontal transport between them was negligible. But it seems questionable whether the details depicted in areas of poor data coverage are really representative. For the eastern North Pacific Ocean similar charts are published by the Biological Laboratory, San Diego, California. Certainly these structural features of sea-surface temperature will have an effect upon processes in the marine atmosphere. Such influences have already been known for some time although the necessary rapid and detailed survey of the sea temperature field has been made possible only in recent years. According to Fisher (1958) there is distinct, although not conclusive, evidence that hurricanes tend to form near relatively warm ocean areas, that their tracks usually develop along the region of the warmest water, and that they are apt to weaken when moving over pronouncedly colder water. Also, for local weather forecasting a detailed picture of the actual temperature distribution at the sea surface might be of some benefit, as was pointed out by Lumb (1961) who presented examples of sea-surface isotherm charts for five-day periods covering the waters around the British
5.1
THE TEMPERATURE OF THE SEA SURFACE
235
FIG. 77. Section of the mean sea-surface temperature chart, September 11-20, 1960 (U.S. Navy Oceanographic Office). Isotherms CF) based on means for 1° squares computed from all available synoptic ship reports, from surface readings of oceanographic observations, and from air-borne radiation thermometer measurements when available.
236
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
Isles and showing remarkable local peculiarities as well as substantial and varying deviations from the normal distribution. Owing to the procedure of determination (averages over one-degree squares) the information supplied by the above-mentioned sea-surface temperature charts is confined to the coarser features of the horizontal temperature distribution. In particular, there fail to appear the considerable local differences which frequently occur in areas of pronounced convergence, or in boundary zones, and which can reach 6°C within 3 nautical miles (Kriigler, 1952) or even 8.5°C within 100 meters (Holler, personal communication). The horizontal fine structure of the sea temperature field can only be clarified by special investigation, such as by means of the air-borne radiation thermometer, for example. Relevant results were reported by Malkus (1957) for the Caribbean Sea. Both "warm spots" and "cold spots" were found, the sizes of which ranged from at least 4 to 20 km. in extent along the direction of the wind. The differences observed in the seasurface temperature amounted to 0.1-0.3°C on days with active cumulus convection, the horizontal gradients depending on the wind speed. With light winds the temperature change often was found within 50 meters (at one occasion even within 3-6 meters) in the horizontal, whereas with strong winds the edges were more diffuse, the temperature change occupying about 1 km. The duration of these thermal anomalies is not definitely known. There is some indication that they may persist at nearly the same locality for at least 3-4 hours. Malkus (1957) discovered a close relation between the thermal pattern of the sea surface and the cumulus clouds. These were only associated with warm spots and developed at their downwind boundaries. In the absence of temperature anomalies no oceanic cloud groups were found. On the other hand, sometimes there existed warm spots which were not associated with cumulus clouds, but their temperature anomaly did not exceed about half the amplitude of those related to clouds on a given day. The results reported by Malkus (1957) were obtained in the waters around Jamaica but evidence is available that the thermal patchiness of the sea surface can also be met in other oceanic regions. 5.1.4
Temporal Variation of Sea-Surface Temperature
When actual data of sea-surface temperature are lacking it is a frequent practice in synoptic meteorology to consider temporal averages over many years as sufficiently representative for the actual
5.1
THE TEMPERATURE OF THE SEA SURFACE
237
distribution. From this procedure it might be derived that-apart from the annual oscillation-temporal variations of sea-surface temperature are of minor importance. This may perhaps apply to its diurnal variation but it does not hold true for changes of longer duration which play a significant part in the interaction between ocean and atmosphere. The factors affecting the temperature of the sea surface, as enumerated in Section 5.1.1, change with time owing to various circumstances. Consequently, a temporal variation of sea-surface temperature will take place. In particular the sea temperature will increase when the gain of heat preponderates over its loss and vice versa. Constant or extreme values will occur when gain and loss of heat at the sea surface come to a balance. These temperature changes at the sea surface can be periodic or nonperiodic according to the particular nature of the influences concerned. The periods of importance are the diurnal and annual cycles of solar radiation. To a minor degree, also the quasi-periods associated with the meandering of ocean currents and with ocean waves may become effective. 5.1.4.1 Diurnal Variation. The diurnal variation of the seasurface temperature chiefly depends on the daily changes of radiation income, of heat exchange at the sea surface, and of turbulent mixing in the uppermost layer of the sea. It has been investigated several times, partly on the basis of material assembled during marine expeditions, partly on that of regular observations executed on ocean station vessels. The results thus attained are fairly uniform. Meinardus (1923), summarizing the relevant results of the expeditions of the German research vessel Gauss (1901-1903) and of the British research ship Challenger (1872-76) (Wegemann, 1920), came to the conclusion that the mean diurnal range of sea-surface temperature in the lower latitudes is about from 0.3 to 0.4°C with the extremes occurring at from 0230 to 0300 and at from 1430 to 1500 hr local time. With increasing latitude he observed a decrease of the diurnal range, this being 0.26°C at from 45 to 55° Sand 0.15°C at from 55 to 66° S. A somewhat smaller diurnal range was obtained by Kuhlbrodt (Kuhlbrodt and Reger, 1938), who evaluated the observational material of the German Meteor expedition in 1925-27, treating separately the two trade wind regions, the West African Monsoon, and the southern high pressure belt of the Atlantic Ocean, and
238
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
eliminating the influence of change in ship's position. The result differed only slightly and, thus, an average curve could be drawn for the tropical and subtropical regions. It is reproduced in Fig. 78. The daily minimum is at 0400 hr while the sea-surface temperature reaches its daily maximum at 1500 hr. The mean daily range amounts to 0.26°C. Near the equator there was found a somewhat higher daily range (0.34°C). The time interval with increasing sea-surface temperature covers about 11 hours, whereas 13 hours of the day are characterized by a temperature decline. From 10 A.M. to 8 P.M., i.e., during 10 hours, the sea-surface temperature is higher than the daily average whereas it is lower during 14 hours. Thus the variation does not strictly correspond to a symmetrical sine curve but it may be satisfactorily represented by the first and the second harmonics of the Fourier series. u a,
.. c
o
E
01
01
-01
-01
E
e c o
..:;
C o
0
4
8
12
16
20
24
Locol lime (hours)
FIG. 78. Diurnal variation of sea-surface temperature in tropical and subtropical regions of the Atlantic Ocean (After Kuhlbrodt and Reger, 1938).
More recently the diurnal variation of sea-surface temperature was studied by means of observations made once every 3 hours on ocean station vessels. Among others Koizumi (1956a) published some relevant results for the Pacific ocean stations Extra (39° N, 153° E) and Tango (29° N, 135° E). On the annual average the diurnal range was found to be 0.28°C (Extra) and 0.45°C (Tango), the extremes appearing at 0500 and 1400 hr. Koizumi (1956a) also investigated the seasonal change in the diurnal range of sea-surface temperature. The diurnal range was smallest (0.14°C at Extra and 0.30°C at Tango) in winter, increasing to a summer maximum in July or August (0.54°C at Extra and 0.6rC at Tango). Evidence was also found that in summer the daily maximum occurred later (1500 hr) than in winter (around 1300 hr). This seasonal variation is due to the concurrence of several effects, e.g., incoming radiation, cloud amount, and wind-generated turbulent mixing in the surface layer of the sea. The difference in the diurnal
5.1
THE TEMPERATURE OF THE SEA SURFACE
239
range observed between the two stations Extra and Tango may be ascribed mainly to the latitudinal difference. The effects of cloudiness and wind velocity, which were already held responsible for the seasonal change of the diurnal variation of sea-surface temperature; come out more clearly than in the over-all averages if the observations are classified accordingly. Suitable values for the tropics were given by Schott (Krummel, 1907; Sverdrup et al., 1946). They are reproduced in Table XXIII and, although the numerical values are not beyond doubt, they clearly show that the reduction of the incoming radiation by increasing cloudiness, as well as a stronger turbulent mixing due to wind-generated surface waves, tends to diminish the diurnal range of sea surface temperature. Statistical evidence for the decreasing amplitude of the diurnal temperature variation at the sea surface with growing wind force was furnished by Bintig (1950). A quantitative treatment of these processes was first attempted by Stommel and Woodcock (1951), who related the diurnal temperature change of the surface layer in the Gulf of Mexico in 1942 to the computed net flux of heat at the surface and to the wind force. This analysis, however, remained unsatisfactory owing to lack of information on evaporation and on eddy conductivity in water. Later on Mosby (1958) succeeded in computing the decrease of the diurnal range with increasing turbulent mixing and even in giving a theoretical explanation of a further effect, also reported by Schott, namely that with a fresh breeze the daily maximum of sea-surface temperature occurs earlier than with calm air. TABLE XXIII DIURNAL RANGE OF SEA-SURFACE TEMPERATURE IN THE TROPICS IN RELATION TO CLOUDINESS AND WIND SPEEDa
Wind speed
Moderate to (SkY overcast fresh breeze Sky clear Calm or very ( Sky overcast light breeze Sky clear
a
Diurnal range CC)
Cloudiness
Average
Maximum
Minimum
0.39 0.71 0.93
0.6
0.0 0.3 0.6 1.2
1.59
After Schott from Sverdrup et al., 1946.
1.1 1.4 1.9
240
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
Further theoretical calculations of the daily variation of sea-surface temperature were published by Dobroklonsky (1944) and, more recently, by Kolesnikov (1958), who took into account the diurnal change of air temperature at a certain height, the incoming solar radiation, the albedo of the sea surface, and the characteristics of the turbulent exchange in sea and air. In water the coefficient of turbulent heat exchange was considered as constant, i.e., the calculations refer to the upper mixed layer above the thermocline. The boundary conditions at the sea surface were equality of temperature in air and water and complete balance of heat. The resulting daily variation of the sea temperature in the surface layer was apparently in sufficient agreement with the observations. A further theoretical approach will be discussed in Section 5.4.1.2 in connection with the diurnal variation of air temperature. 5.1.4.2 Annual Variation. In principle the annual variation of the sea-surface temperature originates from the seasonal changes of all the factors enumerated in Section 5.1.1, although experience shows that in most maritime regions the yearly oscillation of solar radiation is the dominating factor. The other influences produce mainly additional modifications with regard to amplitude, phase, and sometimes the shape of the basic curve. Such additional effects were studied by Neumann (1960), for example, who, by comparing long-term mean values with the corresponding zonal averages, showed that the mean sea temperature variation is correlated with the average intensity change of the wind field. Increased atmospheric circulation leads to a drop of the sea temperature and vice versa. The wind speed fluctuations are evidently responsible for the effects of divergence of the surface water and of upwelling. Thus the annual variation gets an essential dependence on the locality. Therefore its study has so far been more a matter of climatological evaluation than of physical investigation. In general the annual temperature range is large in shallow coastal waters but small in the central parts of oceanic current systems. Here is an example: The annual range of sea-surface temperature amounts to about 15°C in the Baltic Sea, 12°C in the southern North Sea, 8°C in the northern North Sea, and 4°C in the northeastern North Atlantic (Bullig and Bintig, 1954). In the middle latitudes of the North Atlantic, as well as in the northeast Trade wind zone, is found an annual sea temperature range between 4 and 6°C, whereas its value drops to from 1 to 2°C in the equatorial region (Bullig, 1954). In polar seas the annual temperature range amounts to from 2 to 3°C (Stepanov,
5.1
THE TEMPERATURE OF THE SEA SURFACE
241
1961). A strong increase of the annual range is observed in and near cold water regions, this phenomenon being most pronounced in the western polar parts of the oceans. In the middle and higher latitudes of the northern hemisphere the maximum mostly occurs in August. In the northeast Trades it may be shifted to September or even to October. Near the equator the maximum passes over to April, thus linking up with the regime of the southern hemisphere where the maximum is mainly in February. The annual minimum of the sea-surface temperature is found chiefly in February or March (northern hemisphere) and in August or September (southern hemisphere). Monsoonal effects cause deviations both in amplitude and phase, particularly in the northern Indian Ocean, where a main maximum is observed in Mayor June, shortly before the southwesterly summer monsoon sets in, whilst a secondary maximum of minor importance occurs at the end of the summer monsoon in October or November. The minimum falls into the month of January. A compilation of the annual course of sea-surface temperature depending on latitude and oceanic region was recently published by Stepanov (1961) (Fig. 79). Sverdrup et al. (1946) presented an over-all picture showing the latitudinal variation of the mean annual range (taken from February to August) of sea-surface temperature in the Atlantic, Indian, and Pacific Oceans which broadly agrees with the results of Stepanov (1961). The general features are: a minimum between 0 and 5° Nand two maxima at from 30 to 40° Nand 30 to 40° S, respectively, followed by a decrease toward higher latitudes. The northern maximum was considerably higher (8-1O°C) than that of the southern hemisphere (5-6°C). When compared with the corresponding ranges in the radiation income, fairly good correlation was achieved only in the southern hemisphere. The large annual sea-surface temperature range in the northern hemisphere must be attributed to continental influences which, suitable wind systems provided, reduce particularly the winter temperatures of the sea surface. Owing to the annual displacement of the intertropical convergence zone semiannual variations of sea-surface temperature take place near the equator. An attempt to explain the annual variation of sea-surface temperature was made by Wyrtki (1957), for example, who calculated the heat and water balance on the basis of monthly averages of the relevant climatological factors in different regions of southeast Asian waters. Using values of total effective radiation at the sea surface and of the
242
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
energy consumed for evaporation, but neglecting the exchange of sensible heat between ocean and atmosphere (because of its relative smallness and its difficult determination), he arrived at estimates for the heat that is available for the heating and cooling of the sea and of the atmosphere, as well as for advective processes. In most of the °C
:]
~~.-=~=~-5°N
30
25~15°N
°C
30
~l'o"'xooO')(~ 5°
25
~---x""x_x~_x-x~15° x/x
/
400
15
15
10
30
/
',\
/",
400N
"-
-------,/ ------- - .... .
25~
10
20
5
15
o 'x
-2
20~'"'' , ,
I
/700
II III IV V VI VIIVIIIIX X IX XII I
A
15°5
_~300.400S "'---...
-
, /
... --'"
....' ............. ~
...
I0 I II III IV V VI VIIVIII IX X XI XII I
B
79. Annual variation of sea-surface temperature for different latitudes. (After Stepanov, 1961.) (A) All oceans: 0 - - 0 , northern hemisphere; x--x, southern hemisphere. (B) Atlantic Ocean, - - (35°W (N) and 20 0 W (S); Indian Ocean, ........ (85°E); Pacific Ocean ------ (l60 0W, 1000W (at 40 0S)). FIG.
regions considered, an inspection of the annual curves showed a strong correlation, at least qualitatively, between the available heat and the increase or decrease of sea-surface temperature: Some information on a theoretical approach to the annual variation of sea-surface temperature is given in Section 5.4.1.4. 5.1.4.3 Other Periods. Sea-surface temperature oscillations with periods of 25 to 45 days were reported by Koizumi (l956b) for the ocean weather station Extra (39° N, 153° E). He related these oscillations to the meandering of ocean currents. The temperature pulsations in the sea-surface layer that are caused by wave motion, i.e., that occur with the same period as the ocean waves, seem to have a range of from 0.06 to 0.08°e (Kontoboitseva, 1958).
5.1
lHE TEMPERATURE OF THE SEA SURFACE
243
5.1.4.4 Nonperiodic Variations. Irregular alteration of sea-surface temperature is caused by aperiodic changes of the factors enumerated in Section 5.1.1. It is quite clear that the considerable number of influences, as well as the large variety of possible combinations, render a quantitative treatment very difficult. Therefore we shall restrict ourselves to briefly describing the changes observed without attempting to discuss the actual or possible causes in full detail. The time scale of the temporal variations observed with the seasurface temperature is extremely wide. There are slow changes which comprise several decades whereas the turbulent fluctuations may occur within fractions of a second. Starting with slow variations, we must call attention to such long term trends as the cooling observed in the northern North Atlantic Ocean from 1890 to the early 1920's and the subsequent warming until the early 1940's which were associated with a strengthening and a weakening of the Icelandic low, respectively (Bjerknes, 1960, 1962). The coupling between oceanic and atmospheric motion is mainly explained by the "vorticity rule," which says that with increasing vorticity of the Icelandic cyclonic vortex, cold water is pumped upward from the deeper layers by the wind-induced and diverging Ekman drift current at the sea surface (Neumann, 1960; Bjerknes, 1960). Conversely, the ocean surface is warmed with decreasing cyclonic vorticity. With such long-term variations the response of the ocean to the atmospheric change appears to be delayed by a couple of years. A similar warming of from 0.6 to 0.9°C was observed from 1922 to 1938 in the tropical Atlantic Ocean (Bullig, 1954; Roden, 1962). Bjerknes (1960) also reported examples for shorter sea-surface temperature fluctuations lasting only from 2 to 5 years and occurring simultaneously in various parts of the North Atlantic Ocean. In this case the ocean surface was cooled or warmed with increasing and decreasing west wind, respectively. The physical process involved is probably of complex nature because several wind-induced effects (transfer of sensible and latent heat from the ocean to the atmosphere, vertical mixing in the ocean, increased Ekman drift from the north) may be made responsible. Sea-surface temperature anomalies of that kind are likely to react on the atmosphere. In the central North Atlantic Riehl (1956) found, for example, a good correlation between the deviations of 5-year averages from the "normal" mean of the seasurface temperature and the frequencies, as well as the places of recurvature, offully developed hurricanes. Going down the time scale, we must now refer to monthly anomalies of sea-surface temperature which show the deviation of the monthly average, determined for a certain area and for a given year, from the
244
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
corresponding "normal" monthly average evaluated over many years. By this procedure the periodic annual variation is eliminated. Such anomalies were computed, for example, by Bullig (1954) for various squares on the sea route from Europe to South America for the period from 1906 to 1939. An example is given in Fig. 80. On the average each of those monthly anomalies is based on 44 single measurements taken at night hours, the standard error being 0.08°e. Figure 80 reveals pronounced variations of sea-surface temperature anomaly which often exceed l°e and may even reach 2°e within a few months. Moreover, the four anomaly curves which correspond to four areas in the eastern North Atlantic Ocean between 37 and 18°N show a remarkable parallelism, even with respect to features of minor importance. This fact favors the concept that in an extensive oceanic region such anomalies of seasurface temperature may be generated simultaneously. Some hints as to the possible causes were given by Bullig (1954), who found the anomaly of sea-surface temperature inversely proportional to cloudiness and wind velocity, the latter effect being twice as strong as the former. Thus the ocean surface seems to be cooled by an increasing trade wind. Objections raised by Bjerknes (1962), who pointed to the possibility that this result might be locally influenced by upwelling water from the African coast, were removed by the fact that similar findings were obtained for the mid-ocean trade wind zone, too. So the inverse relation between wind speed and sea-surface temperature anomaly has been definitely established for the Trades even in those regions where the surface current has a component away from the equator. More recently Roden (1962) subjected the time series of sea temperature, cloudiness, and wind anomalies given by Bullig (1954) to a statistical analysis for the frequency range between zero and six cycles per year. He did not find any periodicities. The inverse relation between sea temperature and wind anomalies was confirmed for the northeast Trades and-for the east wind anomalies-near the equator and off the coast of Brazil. A direct relation seems to exist between sea temperature and north wind anomalies along the Brazilian coast. No significant relation was found between sea temperature and cloudiness or radiation anomalies, a result which was also confirmed by Roden and Groves (1960) when they analyzed two 18-year records of sea-surface temperature, cloudiness, and sea level atmospheric pressure taken in the North Pacific Ocean. Summing up we may say that the monthly anomalies of sea temperature in the trade region can be traced back to the processes of heat transfer, evaporation, turbulent mixing, and advection.
Year 1901
36.5· N
. 135· W
. 00
I I \I
1908
1909
19/0
r . t\ n ~..
I
1911
1912
" \ Nt.
19/3
,1\ I
19"
1922
"I
j
II \ \
1\ 'I
U
I
I
)\II
1I 1
II
V
v
"
I
., \f/ \",
I''=0',
I 1
i1 iI
\
fJI
I
U
31.S·N IS.0·W
25.0· N 17.S·W
19.0·N 22.S·W -0.5'1
"I
',11.1' \.
(\
I
1\ f
1922
1923
'\7'\/
/92'
Year
1925
\,'
1926
1921
lll28
/929
/930
193/
1932
/933
19,.
I
V
1935
1936
1931
1938
1939
FIG. 80. Monthly anomalies of sea-surface temperature in four areas of the North Atlantic Ocean from 1906 to 1939. (From Bullig, 1954.)
246
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
No detailed reference can be given to the large number of publications (see, e.g., Namias, 1959; Rodewald, 1952-1960) that were devoted to the phenomenology and to the physics of monthly or yearly sea-surface temperature anomalies. Apart from the mechanism of their formation, which is by no means clear, the oceanic feedback to the atmosphere and, in particular, the duration of a trend and its eventual reversal are still rather obscure. Some evidence seems to indicate that oceanic feedback contributes to the persistence of positive or negative anomalies of the sea-surface temperature (Bjerknes 1962). A complete treatment must, however, include a careful examination of external influences coming from the sun. Passing to the irregular changes of sea-surface temperature that take place within weeks or several days we might expect that ample information of that kind should have been derived from the continuous observations made on board the ocean station vessels. Unfortunately, no relevant publication has come to the attention of the author so far, apart from a study published by Hay (1956b), who compiled 5-day means of sea-surface temperature at two ocean stations in the eastern North Atlantic and related them to corresponding air temperature and wind data. Autocorrelations of daily sea-surface temperature values were positive for time lags of from 1 to 2 days but negative after from 3 to 6 days. The change of sea temperature showed little relation to surface advection of sea water. Wind direction had little effect either. The aperiodic variation of sea-surface temperature, observed within one day, reflects the influence of local weather phenomena. It was studied by Kuhlbrodt (Kuhlbrodt and Reger, 1938), who found an average of 0.8°C in the tropics. The maxima lay between 1 and 3°C while the minima amounted to from 0.2 to 0.3°C, thus corresponding to the periodic diurnal variation. In the southern latitudes of westerly wind an increase of the mean aperiodic change within one day up to 2°C was observed. Diurnal and interdiurnal changes in sea-surface temperature at the ocean stations in the North Atlantic were investigated by Pagava et al. (1958) with a particular view to their relation to atmospheric processes affecting Europe. Variations of water temperature caused by the passage of typhoons were reported by Uda (1954), who attributed these changes to turbulent mixing and horizontal transport of water masses. A marked rise of sea temperature usually took place during the approach of a typhoon, while after the passage of the typhoon center a decrease was generally observed. Naturally, the kind of the temperature variation is influenced by the particular oceanographic situation. In the north-
5.2
THE TEMPERATURE AND MOISTURE FIELD
247
western Gulf of Mexico, for instance, Pike (1961) found a sea-surface temperature drop of about 1.3°C during the passage of a hurricane; this was followed by an equal rise. Irregular changes of sea-surface temperature which may be ascribed to turbulent motion in water comprised average durations of from 0.8 to 1 second and showed a mean range of from 0.024 to 0.036°C (Kontoboitseva, 1958). 5.2 THE TEMPERATURE AND MOISTURE FIELD IN THE FIRST FEW METERS ABOVE THE SEA SURFACE 5.2.1 General Considerations The boundary layer next to the sea surface is of crucial importance not only for the air-sea transfer of momentum, as described in Section 4.3, but also for the exchange of heat and water vapor between ocean and atmosphere, since it is here that the basic processes occur which ultimately influence the general circulation. For instance, the amount of latent heat that is released in the equatorial convergence zone and transported aloft to the Westerlies depends initially on the energy accumulated by small-scale exchange in the air-sea boundary layer of the Trades. In general, it is assumed that the transfer is effected in the first instance by purely molecular diffusion taking place in a very thin air film with prevailing laminar motion, which covers substantial parts of the sea surface. Over it there is a transitional layer where laminar and turbulent flow are more or less equivalent and very soon a level is reached above which turbulent motion dominates. At sea the laminar layer is scarcely accessible for measuring and, therefore, the question arises whether or not we are entitled to extrapolate from measurements taken in the turbulent region downward into the layer immediately at the sea surface, which defies direct control. In order to overcome this difficulty we might point to the empirical fact that, if fast changing conditions are left aside, the rate with which heat and moisture are accumulated in the first few meters above the sea surface is very small as compared with the vertical fluxes of these quantities passing through this layer. Consequently, the assumption that the turbulent fluxes of heat and moisture are nearly constant with height cannot be very far from reality. This constancy of turbulent heat and moisture fluxes forms the backbone of all relevant discussions on the surface layer conditions, as did the constancy of wind stress in the foregoing treatment of the momentum transfer between ocean and atmosphere.
248
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
Apart from the fundamental significance of the boundary layer near the sea surface there are also practical reasons that demand such studies. As the bulk of meteorological information at sea is obtained on merchant ships, the relevant observations are mostly taken within the first several meters above the sea and at the interface itself. Hence we should aim at developing a method that will enable us to make use of the routine observations supplied by the ships for the treatment of the exchange processes in question. If we should succeed in deriving such a method, the wealth of meteorological information collected by the seamen of all nations could instantly be utilized for the consideration of the problem of air-sea exchange on a global scale. At the same time we should strive for a steady improvement as regards the accuracy of these routine observations made at sea. 5.2.2 Some Basic Formulae 5.2.2.1 Eddy Flux of Heat and Moisture. In analogy to Eqs. (4.7), (4.60), and (4.61) for the vertical momentum transfer, the vertical unit-area eddy fluxes of heat and moisture content can be described by the following relations: H= -CPPKH(::) = -cp«pW)'(}')av '" -cpP<W'(}')av
E=
-pKE(:~) =
-«pW)'q')av '" -p<W'q')av
(5.1)
(5.2)
The significance of the symbols, apart from those frequently used before, is as follows: H = vertical eddy flux of sensible heat [erg cm-2 sec"] E = vertical eddy flux of water vapor [gm cm-2 sec-I]
cp = specific heat at constant pressure (for numerical value see List of Physical Constants, p. 250) KH = eddy conductivity or eddy transfer coefficient for heat [cm'' sec"] KE = eddy diffusivity or eddy transfer coefficient for water vapor [cm'' sec"] () = potential air temperature q = specific humidity of the air The bar again denotes the average over a period of time at a fixed point and the prime indicates instantaneous departures from that average.
5.2
THE TEMPERATURE AND MOISTURE FIELD
249
The signs in Eqs. (5.1) and (5.2) are such that an upward transfer of heat or water vapor is positive. In Eqs. (5.1) and (5.2) the effects of molecular heat conduction and diffusion have been neglected as compared with those of turbulent exchange motion. It should be indicated here that in the immediate neighborhood of the sea surface such neglect may turn out to be an inappropriate procedure. We shall come back to this subject later on (see Section 5.2.7). Further it must be mentioned that the vertical gradient of the mean potential temperature 8 in Eq. (5.1) is only an approximation. The appropriate quantity should be: (oTjoz) + y where T is the mean air temperature and y the dry-adiabatic lapse rate. In the height ranges considered the difference between the two terms is negligible, however. Since Hand E are considered as constant with altitude at nearwater levels, H represents the gain or loss of sensible heat of the sea surface whereas E is equal to the amount of water lost or gained by the sea surface owing to processes of evaporation or condensation. As has been discussed before, the vertical gradient of potential temperature is of particular significance for all turbulent exchange motions, the intensity of turbulence being: Diminished for (08j oz) > 0 Not affected for (08j oz) = 0 Increased for (08joz) < 0
(stable stratification) (neutral stratification) (unstable stratification)
In the treatment given above, the turbulent exchanges of sensible heat and of moisture between ocean and atmosphere have been considered as two different processes. Seeing that in the atmosphere water vapor is but another kind of heat energy, it is also possible to combine these two approaches into one. This was suggested by Montgomery (1948), who derived a relation for the vertical eddy flux of total heat (sensible and latent heat) containing the equivalent air temperature and describing the turbulent motion by the eddy diffusivity. Keeping in mind the fact that, in laminar flow, the molecular constants of conconductivity and of diffusivity (of water vapor in air) are distinct physical quantities (cf. List of Physical Constants) we shall, nevertheless, adhere to the customary procedure and present the transfer of sensible heat and of moisture in parallel but separate treatments. 5.2.2.2 Eddy Transfer Coefficients. Similarly to the procedure applied in dealing with the turbulent transfer of momentum, which resulted in Eqs. (4.14) and (4.30) for the eddy viscosity KM, our efforts should now be directed toward finding a suitable interpretation of the
LIST OF PHYSICAL CONSTANTS RELATED TO EXCHANGE PROCESSES a
Temperature
("C)
-20 -10 0 +10 +20 +30 +40 Definitions: T
Dynamic viscosity of air, P-
Thermal conductivity of air, k
(gm ern"! sec<) (calcm-lsec-lC-l)(ergcm-lsec-1C-l) 1.615 1.667 1.718 1.768 1.818 1.866 1.914
x x x x x x x
10- 4 10- 4 10- 4 10- 4 10- 4 10- 4 10- 4
= p-(ou[oz) =
5.45 5.63 5.80 5.97 6.14 6.30 6.46 pv(ou[oz);
X X X X X X X
10-· 10-· 10-· 10-· 10-· 10-· 10-· H
= -
2.28 2.36 2.43 2.50 2.57 2.64 2.70 k(oT[oz)
X X X X X X X
103 103 103 103 103 103 103
= -
Air density, p, at 1000 mb
(gm crrr") 1.3769 1.3246 1.2761 1.2310 1.1890 1.1498 1.1131
cppve(oT[oz);
X X X X X X X
10-3 10-3 10- 3 10- 3 10-3 10- 3 10- 3 E = -
Nondimensional ratios (at O°C): Prandti number v[ve = cpp-[k = 0.711 ± 0.003;
Kinematic vis- Thermometric Diffusivity of cosity of air, conductivity of water vapor in air, air, D, v = ",[p, at 1000 mb at 1000 mb Ve = k[cpp, at 1000 mb (cm'' sec-l) (em- sec'<) (em- sec-I) 0.1173 0.1259 0.1346 0.1437 0.1529 0.1623 0.1720
0.165 0.177 0.189 0.202 0.215 0.228 0.242
0.197 0.211 0.226 0.241 0.257 0.273 0.289
pD(oq[oz)
vlD = 0.596 ± 0.008; velD
=
0.84 ±
Summary of constants used in computing the values presented above: Absolute temperature of the ice point: (273.16 ± O.Ol)"C. 1 atmosphere = (1013.246 ± 0.004) mb. Density, at O°C and 1 atmosphere, of dry air containing an average amount of C02: (1.2930 ± 0.0001) 10-3 gm cm- 3 • Universal gas constant R = (8.3144 ± Q.0004) 107 erg °C-l mole-:'. Mean molecular weight of dry air: ma = 28.982 ± 0.003. Molecular weight of water: mw = 18.01600 ± 0.00004. mw[ma = 0.6216 ± 0.0001. Isobaric specific heat of dry air at O°C: Cp = (1.004 ± 0.001) 107 erg grrr! °C-l. Poisson constant for dry air: R[(macp) = 0.286. 1 calwc = (4.1855 ± 0.0004) 107 erg. a
From Montgomery (1947).
om.
5.2
THE TEMPERATURE AND MOISTURE FIELD
251
eddy transfer coefficients KH and KE which depend on the characteristics of turbulent motion and, in particular, vary with altitude. Unfortunately, such an approach has not yet been achieved. However, there are available results of simultaneous but independent measurements, carried out over level grassland, of eddy fluxes (by means of the eddy correlation method) and of vertical gradients of wind speed, potential temperature, and specific humidity of the air which enable us to compute values for KM, KH, and KE by means of Eqs. (4.7), (5.1), and (5.2). The findings, as summarized recently by Deacon and Webb (1962), are as follows: (1) There is some evidence that the difference between KM and KE is quite small. Consequently, no serious error should arise if the equality of KE with KM is assumed. (2) Substantial differences were, however, found between KM and KH. They depend on stability, increase with altitude, and show a considerable scatter. Under stable conditions, KH is smaller than KM, while it generally exceeds that quantity in unstable cases. For strongly unstable stratification KH was once determined to be about 200 per cent higher than KM even at the comparatively small altitude of 1.5 meters above the ground (Swinbank, 1955). Thus it does not appear advisable to substitute KM for KH in general. This result is quite understandable. If one realizes that the momentum exchange is influenced by pressure forces on eddies whereas the heat exchange is affected by buoyancy processes, there is little reason for the expectation that KM and KH should exactly equal each other. The summary quoted above does not consider observational evidence obtained over the sea surface, which might lead to a somewhat deviating interpretation. As was reported by Charnock and Ellison (1959), temperature and humidity fluctuations recorded at 134 meters in maritime air, under both stable and unstable conditions, were highly correlated if these fluctuations were interpreted in terms of the Taylor diagram (see Section 5.3.4.2). Thus Charnock and Ellison were led to believe that the processes transferring heat and water vapor and, consequently, also the eddy transfer coefficients KH and KE were identical under the conditions encountered. 5.2.2.3 Bulk Aerodynamic Method. By limiting our discussion to those cases in which KM can be put in for KE or KH (particular caution is necessary in the latter case), we are able to combine Eq. (4.7) with Eqs. (5.1) and (5.2) to obtain: H/T = -c p (c8/oz)/(ou/oz) [ern/sec] (5.3) E/T = -(oij/oz)/(ou/oz) [sec/em] (5.4)
252
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
After approximating the differentials by the corresponding differences and considering Eqs. (4.49) and (4.50), which read
we obtain H = cppCa(80
-
8a)ua
E = pCa(ijo - ija)ua
(5.5) (5.6)
Here, the subscripts 0 and a refer to the two observing levels. The lower height 0 corresponds to the sea surface; 80 and ijo are derived from the sea-surface temperature, whereas iio is assumed to be zero. If a = 10 meters is taken for the upper level, the formulae and values given in Section 4.3.5.3 for the drag coefficient ClO can be applied. The approach so described is called the bulk aerodynamic method. It has been widely used, particularly for the computation of the geographical features of the energy exchange ocean-atmosphere on the basis of climatological values derived from ships' observations (e.g., Jacobs, 1951; Sverdrup, 1951), the coefficients being partly derived from annual energy budget considerations (see Section 5.2.3.4). The bulk aerodynamic method could also successfully be employed for estimating actual values of evaporation over given periods provided that the coefficient Ca was determined empirically according to the particular circumstances under consideration. The standard error of such evaluation amounted to less than 10, 5, or 3.5 per cent for daily, weekly, or monthly values, respectively (Webb, 1960).
5.2.2.4 Bowen Ratio. The resemblance of Eq. (5.5.) to Eq. (5.6) suggests the formation of the ratio H /E. Full dimensional correspondence is attained if E is replaced by the heat HE that is required for the evaporation or obtained by the condensation of the water quantity E (per centimeter- and second). This is (5.7) where LT designates the latent heat of vaporization or condensation which depends on the temperature. If, furthermore, the mean specific humidity ij is converted into the mean vapor pressure e according to ij '" 0.62 Ie/p
(5.8)
(with p = atmospheric pressure), and if the mean air temperature T is taken instead of the mean potential air temperature 8, which does
5.2
THE TEMPERATURE AND MOISTURE FIELD
253
not imply any appreciable error at low levels, we obtain for the said ratio H Cp P To-Ta B - -= - - - - - (5.9) HE LT 0.621 eo - ea which by introduction of the values Cp = 0.240 [cal °C-I grrr"] LT = 585 [cal gm"] p = 1000 [mb]
takes the form
H To -Ta B = = 0.66--HE eo - ea
(5.10)
This is the so-called Bowen ratio, which was derived in a different manner by Bowen (1926) and has been frequently used in energy considerations concerned with the sea surface. It describes the air-sea heat exchange by giving the ratio between the amounts of heat which the sea surface releases to the atmosphere (or receives from it) as sensible heat and that which it loses by evaporation (or receives by condensation). Average values for the Bowen ratio were published by Sverdrup (1951). They amount to about 0.10 in the lower latitudes up to 30° and increase with latitude to about 0.45 at 70° N and to 0.23 at 70° S, respectively. The difference between the values for the two hemispheres is ascribed to the influence of the large continents on the northern hemisphere from which cold air flows out over the oceans in winter. This dependence on the thermal stability is confirmed by statistical values which were taken from a compilation of meteorological surface data obtained on the British ocean weather ships in the North Atlantic Ocean (Gordon, 1952c). The Bowen ratio has been computed from corresponding averages of temperature and water vapor differences, air minus sea, for wind forces of four and eight Beaufort, the results being given in Fig. 81. Apart from the dependence on stability, a slight increase of the (absolute value of the) Bowen ratio with wind force is observed. 5.2.2.5 Deficiencies. Although Eqs. (5.5), (5.6), and (5.10) look rather reasonable and are handy for practical application, we should keep in mind the considerable deficiencies inherent in them. In part these are due to the assumed equality of the eddy transfer coefficients (KM = KH = KE), which is particularly questionable as regards KH.
254
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
Further, it must be considered as rather an inappropriate simplification to suppose that the fully turbulent transfer extends right down to the sea surface, without regarding the peculiar conditions (e.g., the laminar boundary layer and the interaction of wind and waves) which are neither fully known nor understood at present. In addition, the radiative heat exchange, as well as the effect of sea spray upon evaporation, is completely neglected. As was pointed out by Sverdrup (l943b), radiative conduction may become significant when the turbulent transfer is small, i.e., under stable conditions with light winds, while, according to Montgomery (1940), evaporation will be affected by sea spray at higher wind velocities.
o o c
Q)
Ol-----------l:l-----I 0
~
o co
-6
-4
-2
o
2
Temperature difference, air -sea tOC) FIG. 81. Bowen ratio as a function of the air-sea temperature difference. 0, Wind force 4 Beaufort; X, Wind force 8 Beaufort. (Computed from average air-sea temperature and water vapor differences published by Gordon, 1952c.)
Hence it appears that further study is necessary. The relevant theoretical attempts aiming at the clarification of these problems will be discussed after some consideration has been given to observational results. 5.2.3 Observational Problems As can be taken from Eqs. (5.1) and (5.2), the complete investigation of heat and moisture exchange requires simultaneous measurements of the vertical gradients of mean air temperature and humidity as well as of the turbulent fluxes of sensible and latent heat. Only then shall we be able to arrive at sound estimates of the crucial transfer
5.2
THE TEMPERATURE AND MOISTURE FIELD
255
coefficients KH and KE. The difficulties of such measurements are considerable, however, and have prevented, up to now, the achievement of such a complete record.
5.2.3.1 Profile Measurements. The problems connected with windprofile measurements at sea have already been treated at some length in Section 4.3.1. Profile measurements of temperature and humidity are more or less subject to the same handicaps. In addition to the difficulties enumerated in Section 4.3.1, which comprise the disturbances arising from the influence of the ship on the air flow, from the ship's movements, and from the uncertainty connected with the fixing of an adequate datum plane for height, there appear the effects of radiative and convective heating originating from the ship or from other carriers of instruments. The situation is even worsened by the fact that, in general, the vertical gradients observed at sea are rather small. Since the diurnal variations of sea-surface and air temperature are but slight, large gradients can only appear if an air mass crosses a pronounced oceanic convergence zone which separates waters of very different properties or passes over a coast. However, in these special cases also, the air mass will undergo a rapid modification owing to heat and moisture exchange, which tends to diminish the vertical gradients rather quickly. 5.2.3.2 Optical Refraction Measurements. In view of these difficulties, attention should be given to gradient measuring methods that differ from the conventional thermometric procedure, which is characterized by the taking of simultaneous readings or records of air temperature and humidity at single levels above the sea surface. It is evident that the accuracy of the vertical gradients so determined will depend on the accuracy of the single values and on the height differences between them. If, for instance, the air temperature is accurate to ± 0.1°C and the height difference amounts to 5 meters, the accuracy of the temperature gradient will be about ± 4 x 1O-2°C/ meter. A time average of 100 such single values would have an accuracy of about ± 4 x 1O-3°C/meter. This accuracy could be improved by one order of magnitude if optical refraction measurements over adequate distances were employed for the determination of temperature and humidity gradients in air, as was shown by Brocks (1940, 1954). With the aid of different rays he was able to obtain space averages of the refractive index and
256
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
of the vertical gradients of temperature and humidity in the maritime boundary layer as a function of height. With rays of 15 km length an accuracy of ± 5 x 1O-4°Cjmeter could be achieved for the vertical temperature gradient. Thus, this method provides considerable advantages as compared with the conventional procedure. Similar suggestions were made by Fleagle (1950). 5.2.3.3 Eddy Correlation Technique. As regards the flux determinations, the eddy correlation technique which is based on the right sides of Eqs. (5.1) and (5.2) can be considered as the basic method. It demands instruments of sufficiently rapid response. When applied at sea the method implies the necessity of providing a platform for the recording instruments which is fixed or completely stabilized. Owing to the difficulties inherent in such devices the relevant measurements are still in a preparatory or initial stage. As to the turbulent fluctuations in water vapor pressure, good results seem to have been obtained with the microwave refractometer (see Section 5.2.8). 5.2.3.4 Determination of Evaporation. The general idea that the vertical flux of water vapor must equal the loss or gain of water at the sea surface offers further possibilities of measuring this quantity. They comprise direct measurements and indirect assessments on the basis of energy considerations. Direct measurements of evaporation have occasionally been attempted at sea by determining either the loss of water in a suitable bowl or the increase of its salinity. The difficulty is that measurements by means of evaporation pans on shipboard do not supply any values of the actual evaporation from the sea surface since the physical conditions for evaporation are different in each case. Hence, such measurements have to be reduced accordingly, which is a somewhat doubtful procedure. The reduction factor as proposed by WUst (1936, 1954) amounts to 0.55 and is only applicable to average values. To a certain degree these difficulties can be avoided if evaporation is measured by means of a pan floating at the sea surface (Shoulejkin, 1928; Takahashi, 1958). Naturally this can only be achieved when the sea is sufficiently quiet or if the pan is protected against inundation by the waves. Even then the conditions are not strictly natural as the air flow is disturbed by the rim of the pan (Deardorff, 1961a) and because the absorption of radiation, as well as the turbulence, within the pan differs from the situation in the water outside. The latter influences mainly cause temperature differences between the water in the pan and the surrounding sea, which, however, can be substantially
5.2
THE TEMPERATURE AND MOISTURE FIELD
257
reduced by a suitably constructed apparatus (Brockamp and Wenner, 1960). The budget methods are essentially climatological ones and are mentioned here only briefly for the sake of completeness. They rest upon estimations of the energy balance and of the water balance. The first procedure, originating from Schmidt (1915), is based on the estimation of the energy budget of the sea surface. Only the main factors of all those that affect the temperature of the sea surface (see Section 5.1.1) are taken into account. On the assumption that the average temperature of the ocean remains nearly constant from one year to another, the average annual energy the oceans gain by shortwave radiation from the sun and the sky must be equal to the energy losses caused by long-wave radiation, by evaporation, and by heat conduction to the atmosphere. The annual radiation surplus is estimated from radiation measurements and climatological values of sea temperature and cloudiness. If further suitable values of the Bowen ratio (see Section 5.2.2.4) are available, the average evaporation can be assessed for 'different regions, for latitude ranges for example, as the residual of the energy budget. These values are only of climatological significance and cannot be employed in connection with actual humidity profiles. For further reference see Sverdrup (1951). Of course it is also possible to make use of this method for actual values provided that suitable measurements have been taken. The method based on the estimation of the water balance can be applied to the ocean and to the atmosphere as well. When used for the sea, the method requires assessment of all the other factors affecting the amount of water in a certain oceanic region besides evaporation. Thus the applicability of this method strongly depends on the degree of accuracy to which the rates of inflow and outflow of water are known. Even if the region in question can be considered as fairly secluded, there remain the uncertainties inherent in the determination of the amount of precipitation at sea. When applying the water balance method to the atmosphere we deduce the evaporation from the total (local plus advective) variation of humidity along a resultant air trajectory, plus rainfall. If longer periods are considered, the local changes can be neglected. This method is applicable to maritime regions where there exists a suitable network of radiosonde stations (Moller, 1951 a; Franceschini, 1962; Palmen, 1963). Only broad-scale results are obtained. When climatological data are employed, the horizontal advection of water vapor must be carefully assessed. As was demonstrated by Tucker (1962), the divergence of water vapor owing to the mean monthly flow differs completely from the divergence of
258
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
water vapor caused by eddy transports where the eddies are smaller in scale than the mean monthly flow pattern. With continental air flowing out over the sea, a steady state in the air-sea boundary layer may be assumed at short distances from the shore, thus making it possible that the water balance method can be applied to actual cases, too. Relevant values for hydrostatically stable air were reported by Craig and Montgomery (1949). 5.2.4 Measured Profiles of Temperature and Humidity 5.2.4.1 Review of Existing Measurements. For a survey of the available observations, a summary of air temperature and humidity profile measurements above the sea has been compiled. (Table XXIV). This list, which does not claim to be complete, contains roughly the same number of studies as were enumerated in Table X, referring to wind profile investigations. The years of publication clearly show that, since 1940, this problem has attracted the particular attention of research workers and that such efforts have even been intensified in the past decade. The procedures applied exhibit a fairly large variety. In recent years more emphasis seems to have been laid on the necessity of avoiding any disturbing influences caused by the carrier of the instruments than was done in former years, when ships were used rather frequently in spite of the considerable disturbances arising from them. Several investigations included in the list were extended up to heights of a few hundred meters, thus reaching beyond the layer nearest the sea surface, which is going to be discussed here. As the techniques applied in those studies often do not allow the first few meters to be investigated in the necessary detail, we will now disregard these contributions and postpone their discussion until Section
5.3.
Not included in Table XXIV are the great number of aero logical ascents made at sea by airplanes, kites, balloons, etc., for synoptic and special research purposes, such as cloud investigations. They will be dealt with in the course of our discussion in due place. 5.2.4.2 Air Temperature Profiles. Some typical profiles of air temperature under lapse and inversion conditions are presented in Fig. 82. These (as yet unpublished) data were obtained with resistance thermometers installed on a fixed mast that had been erected in shallow tidal waters. As it is normally done, the difference between the potential air temperature and the sea-surface temperature was plotted against the logarithm of height. The curvatures of the profiles
5.2
THE TEMPERATURE AND MOISTURE FIELD
259
are similar to those observed with wind profiles under different thermal stabilities as depicted in Fig. 39. Under unstable conditions the profiles are concave toward the height axis while they are convex in stable cases. For near-neutral stratification the height dependence in the half-logarithmic coordinate system seems to be largely linear, i.e., the vertical profile can be considered as a logarithmic one. 16
16
10
10
7 ~
5
~
3
'"
7
5
1.8
~
3
~
2
:g, ;;
I
0.5
05
o Potential air temperature minus sea surface temperature
FIG. 82. Mean profiles of the difference between potential air temperature and seasurface temperature, measured over a tidal flat off the German North Sea coast in 1949.
Under unstable conditions as much as about 80 per cent of the temperature decrease throughout the layer considered (0-16.5 meters) takes place in the lowest half meter. This percentage varies inversely with the wind speed. With stable stratification, the part of the profile which covers the lowest half meter seems to be somewhat smaller (~70 per cent). The concentration of the vertical temperature change upon a very shallow layer above the sea surface would be even more evident if measurements from those levels very close to the sea surface were available (compare Fig. 76, for example). 5.2.4.3 Humidity Profiles. Specimen profiles of the water vapor pressure above the sea are displayed in Fig. 83. They were measured by Takahashi (1958) and Brocks (unpublished data).* Again the difference between the vapor pressure at the relevant heights and that at the sea surface was plotted against a logarithmic height scale. For the determination of the surface value it is usually assumed that the air that is in direct contact with the sea is almost saturated. Thus the *The author is obliged to Professor Brocks, of Hamburg, for having supplied these data.
TABLE XXIV REVIEW OF TEMPERATURE AND HUMIDITY PROFILE MEASUREMENTS ABOVE THE SEA SURFACE
Temperature Year of pub!.
Author
Locality
1914 1927 1928 1937 1939
Rykachov Johnson Shoulejkin Wiist Roll
1939 1940
Schroder, et Bruch
1940 1941 1942
Montgomery Church Owen and Halstead
1946 1946 1947
Craig Sverdrup Emmons
Baltic Sea Mediterranean Sea Black Sea Baltic Sea North Sea
at.
North Atlantic Lake Sacrow Baltic Sea North Atlantic San Juan Archipelago Lake Corpus Christi, Texas Massachusetts Bay North Pacific North Atlantic
Procedure
Humidity
Number of Max. Number of Max. levels with height levels with height temp. observ. (meters) hum. observ. (meters)
Light vessel Ship Boat Schooner and boat Ship and captive balloon Ship and boat Raft Raft Ship Raft Raft
3 3 6 7 10,14
Ship and airplane Ship Ship and airplane
13
8
-
5 5 6 4
3 20-30
6 22 2.2 9 150,200 20 1.4 1.4 38 4(10)
-
305 26-32 460
3
6
6 7
2.2 9
8
20
6 4 6
38 4(10) 6.1
13
305 26-32 460
3 20-30
1948b 1950c
Roll Gordon
1951 1952
Gerhardt Darlington
1952
Durst and Gordon
1954 1956
Das and Dhar Deacon, et at.
1956 1958 1958
Hunt Fleagle, et at. Shellard
1958
Takahashi
1959a
Brocks
1959 1961
Goptarev Evans, et at.
1961 1962 1962a, b
Bruce, et at. Schumacher Deacon
North Sea, tidal flats North Atlantic OWS"}" Gulf of Mexico Arctic Waters North Atlantic North Atlantic Bay of Bengal Port Phillip Bay, Australia, Bass Strait Lake Hefner East Sound North Atlantic OWS "I" Kagoshima Bay North Sea and Baltic Sea Caspian Sea Tropical North Atlantic Lake Erie South Atlantic Port Phillip Bay, Bass Strait
Fixed mast Ship and tethered balloon Oil drilling platform Ship Ship British ocean weather ships Ship Ship and captive balloon Boat Raft Buoy Boat, partly fixed pole Buoy Oil drilling platform Raft Ship Boat and ship Small ship
6 5-8
2 18-24
6 5-8
2 18-24
5 6 3(4) 5
13.4 9 24(22) 15
5 6 3(4) 5
13.4 9 24(22) 15
3 Various
19.1 60
3 Various
19.1 60
4 4 5
16 3.2 2.9
4 5
3.2 2.9
5
4
5
4
5
16
5
16
10 5
50 2
10 5
50 2
6 4 2
12.2 8 13
6 4
12.2 8
262
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
maximum vapor pressure corresponding to the sea-surface temperature was taken as representative of the vapor pressure at the sea surface. As the salinity of the sea water slightly decreases the vapor tension, its effect had to be taken into account according to Eq. (5.11) (Sverdrup et al., 1946). 20
- 10
- II
- 12
13
-9
- 7 -4
8
-I
\
10
..:g,
2
I
Wind speed (meters/sec) - - at 4 meters-----+-
\
2.8
2.6
1\
'\
3.0
~empe,"lure
difference air - se
\<-10
c5
O.2
NO'lof cbs.
-13
-IO~
----r-° C <-5
\ 1\
64 -II
Difference of
\ \
0.5<
1\
~O.5:S
121 ~6
-9
wcter vapor
\ 1\~78 \
-8
-7
-6
\
so.s
II
~
1o
3.9
t8
Br o cks
\
\, \ \
[\
N'\
1\ 84 -10
\24
-~-05 ~~ I
\
1\
-12
\
~
TrahaS!i
34
2.8
\
20
0.2
\ 1\
0.0 -02
~
0.0
~
-0.2 05
02
2f
-5 -3
pressure against saturated value at the
-2 se~
-I
surface (mb)
FIG. 83. Mean profiles of water vapor pressure above the sea surface. Brocks (unpublished values): Mean profiles (from 0.8 to 13.5 meters) measured over 15 minutes under adiabatic conditions in the Baltic, 1958. Takahashi (1958): Mean profiles (from 0.25 to 4 meters) for different conditions of stability calculated from measurements at Kagoshima Bay, 1953-1956.
esled = 1 - O.000537S
(5.11)
where es is the vapor pressure over sea water and e« the vapor pressure over distilled water of the same temperature. The salinity of the sea water, in parts per thousand, is given by S. In the open ocean, eS/ed is approximately 98 per cent. As can be seen in Fig. 83, the vertical gradient of vapor pressure was always negative, i.e., the humidity decreased with altitude. Hence, the sea surface acted as a source of moisture for the overlying atmosphere. Such behavior is normally encountered over large regions of the oceans. At times, however, particularly over cold water areas, the opposite may happen. The humidity increases with height and at
5.2
THE TEMPERATURE AND MOISTURE FIELD
263
the sea-surface condensation takes place instead of the usual evaporation. Examples of such a vertical increase of the vapor pressure in the bottom layer were given by Goptarev (1959). It occurred with stable stratification and was confined to the lowest 5-10 meters, above which the humidity remained more or less constant. The effect of thermal stability is to be seen very clearly in Fig. 83. Under stable conditions the curvature of the humidity profiles is convex toward the height axes whereas it is concave in unstable cases. For near-adiabatic stratification a linear relationship is indicated. 5.2.4.4 Vertical Gradients as Related to Differences between Air and Sea. With a view to global application, it would appear profitable to attempt to relate the gradient measurements over the sea to the routine observations normally executed on ships cooperating voluntarily, i.e., the temperature and humidity differences between the height of the bridge and the sea surface. If such a relation were found, the large number of ships' observations could be interpreted in terms of the temperature gradient of the air, which would be of great value for studies of air-sea heat transfer, evaporation, radio wave propagation, and other relevant problems. A corresponding diagram was prepared by, among others, Deacon et al. (1956). It is reproduced in Fig. 84 and shows the potential air temperature difference between the levels 12.6 and 4 meters in relation to the air-sea temperature difference. Although the scatter of the data is rather large, a curve could be drawn which represents the observations fairly well. It will be noticed that this curve crosses the origin rather exactly, thus indicating that for neutral stratification the potential temperature difference between air and sea is zero, too. This is not necessarily so, as was shown for example, by Roll (1948b), who, from temperature profiles in the lowest 2 meters, was led to ascribe to the sea surface a cooler skin temperature than was measured by conventional methods. According to Section 5.1.2 this cool skin can be attributed to evaporation. If such an effect were present in the data given in Fig. 84, the mean curve would intersect the horizontal axis at some point between 0 and - 1°F. A relevant graph was also given by Deacon et al. (1956). Perhaps the existence or nonexistence of such a displacement, i.e., of a cool skin, depends on whether the sea surface is clean or covered with a very thin layer of some material impeding evaporation (see Sections 5.1.2 and 5.2.7.6). On the stable side of Fig. 84 the relationship is nearly linear but under unstable conditions the temperature gradient between 12.6 and 4 meters is rather small and hardly shows any distinct dependence
264
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
on the air-sea temperature difference. This is particularly true with light winds where the potential temperature gradient is approximately zero. Thus the evidence indicates that, with unstable stratification, the layer of strong temperature gradients is comparatively shallow, probably comprising only a few meters, whereas the stratification above that shallow bottom layer approaches the adiabatic state. Wind speed and height range are essential factors in this respect as the height of the bottom layer increases with wind velocity. t v; ~
...E
20
/x/xx/ :x /xxx
15
0
N
x
1.0
05
o
0
• MX""
/X x
x x ,~XX)(
XX
xx
x
-lit.. {~
o
Xi~~A x : ~
~
~
x
-0.5 -6
4
-2
o
2
4
6
8
10
Temperature difference, air-sea (OF)
FIG. 84. Potential temperature difference between 12.6 and 4 meters height in relation to the air-sea temperature difference for different wind speed ranges. (From Deacon et al., 1956.) x, U10 > 5.5. 0, U10 = 4.5 to 5.5; and 6, UlO = 2.5 to 4.5 meters/sec. The curve represents the conditions for U10 > 5.5 meters/sec.
The existence of a shallow bottom layer with superadiabatic temperature gradients under unstable conditions was confirmed and specified by Brocks (1956), who determined the thermal stratification near the sea surface by means of optical refractive index measurements. His results are given in Table XXV. They show that the height of the superadiabatic bottom layer grows with increasing instability. Of course, this effect also contributes to the relationship presented in Fig. 84. Further evidence on this subject was given by Brocks (1963). 5.2.5 Profile Coefficients As was indicated in the foregoing section; it appears desirable that the vertical gradient of the potential air temperature and the vertical
5.2
THE TEMPERATURE AND MOISTURE FIELD
265
gradient of the humidity be expressed in terms of temperature and humidity differences where the upper level is at some meters above the sea and the lower one is at the sea surface. Apart from the practical applicability of such a procedure there is the advantage that small quantities like the gradients at some distance from the sea surface are replaced by larger ones that can be measured more easily. The relevant relationships which before have only been dealt with phenomenally will now be investigated more thoroughly. TABLE XXV SUPERADIABATIC BOTTOM LAYER ABOVE THE SEA SURFACEa,b
Temperature difference between the height of 5 meters and the sea surface, Ts - T. CC)
Thickness of the bottom layer with superadiabatic temperature gradient (meters)
-0.5 -1.0 -1.5 -2.0 -2.5 -3.0
6 11
a b
15 19 (21) (23)
Mean wind speed 6 meters/sec at 5 meters height. After Brocks, 1956.
rOa
=
(5.11)
8a
1
(5.12)
The latter quantity is equal to Montgomery's (1940) evaporation coefficient. The subscripts 8a and q« attached to the I"s are to indicate that these coefficients refer to the mean potential air temperature iJ
266
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
and to the mean specific humidity ij, respectively, and that they are only valid at the reference height z = a where these quantities were measured. Since the height functions of Band ij are thus approximated by logarithmic curves at the level z = a, in general it is not possible to extrapolate or integrate these curves unless the height functions of Band ij are logarithmic themselves, i.e., if adiabatic conditions prevail. According to the definitions given above, the vertical gradients of the mean potential air temperature and the mean specific humidity take the form 8B r oa(Ba - Bo) (5.13) 8z z + Zo 8ij r q,,(ija - ijo) (5.14) 8z z + Zo which is already in accord with the desired relation. By means of the r factors, the vertical profiles are replaced, at the level z = a, by logarithmic height functions, the quantities I' oa(Ba - Bo) and I'qa (ija - ijo) having a meaning similar to u.lk in the adiabatic wind profile, Eq. (4.12). However, unlike u.lk, they depend on the variable z and hence cannot be considered constant when Eqs. (5.13) and (5.14) are integrated over z. That is why the application of the profile coefficients I' Oa and I'qa to nonadiabatic conditions demands some caution. A detailed description will be given in Section 5.2.5.3. 5.2.5.2 Adiabatic Conditions. First we will limit our discussion to the case where the eddy transfer coefficients may be considered as equal: KM = KH = KE
If, in addition, adiabatic stratification is assumed for the present we may write, according to Eq. (4.14), KM
=
KH
=
KE
=
k(z
+ zo)u.
(5.15)
and if, further, Eqs. (4.21) and (5.14) are taken into account (the latter adapted to the adiabatic case), Eq. (5.2) for the vertical eddy flux of water vapor E is transformed into Ead
= pk2 r Uar qaCijo - ija)iia
(5.16)
One can evaluate rUa from Eq. (4.21) or Eq. (4.22), which also apply for r qa, which may be derived, for example, from Eq. (5.33) in Section 5.2.6.1, with adiabatic conditions presumed. For the eddy transfer of momentum a similar relation is obtained from Eq. (4.21).
5.2
THE TEMPERATURE AND MOISTURE FIELD
267
It reads Tad
= p(kf uYiia2
(5.17)
This equation is in conformity with Eq. (4.50) as, according to Eqs. (4.21) and (4.51), (kf u J2equals Ca under adiabatic conditions. Equation (5.16) is Montgomery's (1940) formula for the rate of evaporation, which is evident if (kf ua) is replaced by (C a )1I2. According to the derivation given here, the application of Montgomery's relation is restricted to neutral stratification. The eddy flux of heat is not considered at this point because it is zero under adiabatic conditions. 5.2.5.3 Nonadiabatic Conditions. This case can be handled quite clearly if we introduce generalized von Karman coefficients k* in place of the von Karman constant k. As regards the exchange of momentum we must replace Eq. (4.12), which is valid under adiabatic conditions, by Eq. (4.26), which may be written
au OZ
U.
kM*(Z
+ zo)
(5.18)
k u" = kjS(Rf) being the generalized von Karman coefficient for the momentum exchange. Combining Eq. (5.18) with Eq. (4.7) we arrive at the following general formula for the eddy viscosity KM = kM*U.(Z
+ zo)
(5.19)
which is analogous to the adiabatic expression [Eq. (4.14)] and passes into this relation for SeRf) = 1. Similar equations can be derived for the eddy transfer coefficients KH and KE for which different generalized von Karman coefficients k u" and ke" may be assumed. Thus the equality of the eddy transfer coefficients that was supposed in the preceding section now has been dropped. When we apply Eqs. (5.13), (5.14), and (5.19) to Eqs. (5.1) and (5.2) we obtain H = CppkH*f ea«(jO - (ja)U. (5.20) E = pkE*fqa(ijo - ija)U. (5.21) The equations can be modified if we subject the vertical eddy transfer of momentum T to the same procedure. Combination of Eqs. (4.19) and (5.18) results in T = p(kM*f ua)2iia2 (5.22) or
U* = kM*fuau a
268
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
a formula which could serve as a basis for the discussion of the influence of stability on the wind stress (see Section 4.3.5.4). With this relation, Eqs. (5.20) and (5.21) finally take the form
H = CPpkM*kH*rUaroa(Bo - Ba)ila E = pkM*kE*rUarqaCiio - ija)ila
(5.23) (5.24)
It must be emphasized that the profile coefficients in the nonadiabatic transfer formulae [Eqs. (5.20)-(5.24)] are different from those appearing in the adiabatic flux equations [Eqs. (5.16) and (5.17)]. For adiabatic stratification (L --+ ± 00) the relations of Eqs. (5.22) and (5.24), .however, are transformed into those of Eqs. (5.17) and (5.16), respectively. The formulation employed in the above relations is rather general and its applicability to practice depends entirely on whether suitable values for the k*'s and P's are available. Unfortunately, our knowledge is still very defective in that respect. However, if we confine ourselves to near-neutral conditions, i.e., to very small values of Rf ~ Ri ~ (z + zo)/L, a more serviceable solution is reached. Then we can combine Eq. (4.30) with Eqs. (4.29), (4.26), and (4.35) in order to obtain the following approximate form of the eddy viscosity
ku/z + zo) 1 + IX(Z + zo)/L
(5.25)
KM=------
Under the supposition of equal transfer coefficients for momentum, heat, and moisture, the generalized von Karman coefficients ku", k u", and k E * in Eqs. (5.22)-(5.24) can then be substituted for by k/[l + IX(Z + zo)/L]. Likewise the "generalized" profile coefficients r have to be replaced by the "adiabatic" profile coefficients from Eqs. (5.16) and (4.22) respectively, multiplied by the factor
z + Zo) In z + zo/ ( In z + Zo + ( 1 + IX L Zo zn
z)
IX-
L
The resulting values for Hand E are equal to those given in Section 5.2.7.1 and will be described later.
5.2.5.4 Observational Results. Numerical values for the profile coefficients are mostly derived from Eqs. (4.19), (5.13), and (5.14) by means of data on wind speed, potential air temperature, and specific humidity measured at different levels. This procedure involves an integration over a certain height range which is, strictly speaking, not
5.2
THE TEMPERATURE AND MOISTURE FIELD
269
permissible unless under adiabatic conditions. Hence only the profile coefficients rU a and rq a in Eqs. (5.16) and (5.17) can be correctly evaluated in this manner. Of course they will depend on the reference level chosen. . On the other hand, it is customary to apply Eqs. (4.19), (5.13), and (5.14) also if the thermal stratification deviates from the neutral case. In addition to their depending on the reference height, the profile coefficients obtained in this way will be influenced by the character of turbulent motion, i.e., they will vary with stability and wind speed. Following a suggestion of Fleagle et al. (1958) we had better term them "apparent profile coefficients." Relevant results have been reported, for instance, by Brocks (1955, 1956), who computed profile coefficients by using the humidity profile measurements of Wiist (1937), Montgomery (1940), and Sverdrup (1946), and also on the basis of wind profile data of Roll (1953-1954). His values are summarized in Table XXVI. In spite of the considerable uncertainties inherent in those computations the agreement between the ru's and re's is not as bad as it could be. Nevertheless, it does not seem feasible to draw very far-reaching conclusions from such not very representative material. However, the dependence of the profile coefficients both on stability and-to a minor degree-on wind velocity appears to be sufficiently established. The variation with wind speed is confirmed by some I'u. values given by Deacon and Webb (1962) (which increase from 0.090 at U6 = 2 meters/sec to 0.123 at U6 = 14 meters/sec) and-although only qualitatively-by a few r q values reported by Das and Dhar (1954). In addition, the laboratory experiments executed by Okuda and Hayami (1959) must be quoted here. They determined the evaporation from a wavy water surface in a wind-water channel of about 20 meters length by measuring profiles of both wind speed and vapor pressure up to about 30 em height under nearly stationary conditions. Since these profiles proved to be nearly logarithmic, the profile coefficients r q could be correctly evaluated from Eq. (5.14). When adapted to a height of 8 meters they showed a rather slow increase from about 0.09 at Us = 2 meters/sec to about 0.11 at Us = 15 meters/sec. For still greater wind speeds a sudden rise of r a, to 0.20 or more was observed, which might be attributed to the effect of spray. Profile coefficients for wind speed, air temperature and water vapor density were also published by Fleagle et al. (1958). In Fig. 85 their results have been plotted against the Richardson number. They show a distinct increase of the profile coefficient with the Richardson number, thus being in qualitative agreement with Brocks (1955, 1956).
270
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
TABLE XXVI PROFILE COEFFICIENTS
rei AND r
IN RELATION TO WIND SPEED AND AIR-SEA TEMPERATURE DIFFERENCEa,b
U4
Profile coefficients from humidity profilesWind speed at 6 meters (meters/sec)
-3
-2
-1
0
+1
2 4 6 8 10
(0.02) (0.03) (0.07) (0.11) (0.12)
0,03 0.05 0.08 0.12 0.15
0.05 0.08 0.10 0.13 0.15
0.06 0.11 0.13 0.14 0.15
(0.07) (0.14) (0.14) (0.14) (0.16)
Profile coefficients from wind profiles"
2 4 6 8 10 12
-4
-2
-1
0
+1
0,03 0.06 0.07 0.08 0.09 (0.11)
0.03 0.06 0.07 0.08 0.10 (0.11)
0.05 0.07 0,07 0.09 0.10 (0.12)
0.08 0.10 0.10 0.11 0.11 (0.12)
0.12 0.12 0.12 0.12 0.12 (0.13)
Reference level, a = 4 meters. Doubtful values in parentheses. After Brocks (1955, 1956). c Column headings are temperature difference, air (at 6 meters) - sea, in deg. C. d Column headings are temperature difference, air (at 16.5 meters) - sea, in deg. C.
a
b
This behavior appears to be particularly pronounced with I' 8. and rea which, within the limits of observation, are almost identical. Contrary to Brocks, a significant secondary dependence of the profile coefficients on wind speed could not be detected in the speed range encountered (3-9 meters/sec). On the whole, the values of Fleagle et al. (1958) are lower than the results reported by Brocks (1955, 1956); they do, however, closely agree with the profile coefficients that can be deduced from the measurements of Takahashi (1958). Summarizing, we may say that the profile coefficients are useful
5.2
THE TEMPERATURE AND MOISTURE FIELD
271
tools for describing the vertical profiles of atmospheric quantities near the sea surface, on the condition that they are employed with regard to their inherent limitations. Their numerical values, however, need confirmation and completion. "' Q; Oi 0.16 E
co
2
0.14
C
012
'"u
'" u 0
'"
•
~ ~ ~
ib.
00
C
004
0
II
0
0.02 f-
er
o 00
•
Ii
o
-
~o· 0
XXX
x
xx
x x x
.••
x 'Ix o 0 x
0.08 006
a. a.
0
010
'2a. ~
•
• 0
•
0
__-'------' 0.04 005
L---"~--'--~---"---~--'--~L------'-~--'-
-0.02 -0.01
000 001
0.02
0.03
Richardson number Ri at 80 cm
FIG. 85. Profile coefficients for wind speed, air temperature, and water vapor density (at 8 meters) against Richardson number (at 80 cm). (From Fleagle, et al., 1958.) x, Wind speed; 0, air ternperatureg, water vapor density.
5.2.6 Further Theoretical Approaches to Temperature and Humidity Profiles The intention underlying the bulk aerodynamic method and the application of profile coefficients was to provide simple procedures for computing the vertical eddy fluxes based on measurements at a certain height above the sea and on the surface data. Consequently, these efforts were mainly directed toward practical application and had to bear the unavoidable shortcomings of such undertakings. Now we are going to tackle the subject in a more theoretical way without caring too much about observational possibilities. 5.2.6.1 Diabatic Temperature and Humidity Profiles. A fairly general approach to the problem in question starts from the following equations for the vertical gradients of the mean potential air temperature B and the mean specific humidity ij, which are similar to the relevant relations for the vertical distribution of wind speed [Eqs. (4.26)].
8B 8z
0* --SeCRf) Z
+
ZQ
(5.26)
272
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
oij
q*
- = --Sq(Rj)
oz
z + Zo
(5.27)
The quantities 8* and q* correspond to u*/k in Eq. (4.26) and are defined as follows 1 H (5.28) 8* = - - ku; cpp
q*
=
1
E
--ku; p
(5.29)
The dimensionless factors SIJ and Sq represent the influence of the thermal stability and are functions of the flux Richardson number Rf Their indices 8 and q indicate that,in the general case, the stability function describing the transfer of heat is assumed to be different from the functions affecting the turbulent transport of momentum and humidity. Under adiabatic conditions the stability functions must be equal to unity. Considering that observational evidence is still insufficient for a complete determination of the stability functions we have to be content with approximative solutions. In this respect the similarity principle advanced by Monin and Obukhov (1954) has proved rather useful. With the particular form in which this principle was applied by these two authors it is assumed that the stability factors S are functions of (z + zo)/L and are equal for the profiles of wind speed, temperature, and humidity. Consequently y = 1 is accepted, and, according to Eqs. (4.31) and (4.32), this implies the equality of the eddy transfer coefficients and of the Richardson numbers Rf = Ri. With these simplifications, Eqs. (5.26) and (5.27) take the form
00
oz oij
oz
8*
z +
q*
Zo
S(Z + Zo)
(5.30)
s(Z + Zo)
(5.31)
z + zo
L
L
If we further follow Monin and Obukhov (1954) and restrict our considerations to small values of (z + zo)/L, i.e., to the near-adiabatic case, S may be approximately expressed by the linear term [1 + ex (z + zo)/L,] similarly to Eq. (4.35). After integrating Eqs. (5.30) and
5.2
THE TEMPERATURE AND MOISTURE FIELD
(5.31) we obtain the well-known "log air temperature and humidity _
{)z -
110 =
()*
(
In
ijz - ijo = q, ( In
z
+ linear" profiles for potential
az) L + -az)
+ zo + -
(5.32)
+
(5.33)
Zo
z
273
zn
zn
L
The sea-surface values are attained for z = O. The adiabatic case is represented by (). = 0 and L ~ 00. With regard to the value of the constant a, reference is first made to the discussion given in Section 4.3.4.5. As stated there, Taylor (1960b) found that a ranges systematically with stability, assuming values between 3 and 6 for -0.03 < (z + zo)/L < O. In addition, we should mention that an analysis of wind, temperature, and humidity profiles, combined with simultaneous measurements of evaporation (Pasquill, 1949), was carried out by Brogmus (1959), resulting in a = 3.67. Deacon and Webb (1962) fitted together temperature profiles at the boundary between the layers of forced and free convection (see Section 5.2.6.2) and arrived at a = 4.5. On the whole it can be stated that the "log + linear" profile has been confirmed also for temperature and humidity. Its limit of application, on the lapse side, appears to be around I(z + zo)/LI = 0.03, i.e., it applies to the zone of "forced convection," which will be described in the next section. In view of the assumed equality of the S functions for momentum, heat, and moisture exchange, the corresponding transfer coefficients must be calculated from Eq. (4.30), which, by application of Eqs. (4.29) and (4.35), can be transformed into Eq. (5.25). All these statements refer to conditions over land because no relevant results have been reported from the sea. Although it is most likely that in this respect there are no substantial differences between land and sea, conclusive confirmation, based on reliable simultaneous determination of gradients and fluxes over the sea, is still lacking and would be very welcome. So far there are available only some preliminary results which were derived from simultaneous measurements of wind speed, temperature, and humidity profiles above the sea, as well as of evaporation, carried out by Takahashi (1958). Assuming equality of the stability functions S for wind speed and humidity (which implies KM = KE), Roll (1963) calculated corresponding values of Sand Ri from the differences in wind speed, air temperature, and humidity observed
274
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
between the levels of 50 and 200 em, using Eqs. (5.27), (4.26), and (4.24). For the computation, twenty-six measured values of evaporation were selected out of the material published by Takahashi. These data are distinguished by a good temporal coordination with the corresponding 196 profiles. The measured evaporation values were reduced by the factor 0.54, following Deardorff (196Ia) (see Section 5.2.7.2). Unfortunately, there is no information on the heat flux H and hence the stability length L and the flux Richardson number RI cannot be taken as independent variables. Consequently, we are forced to assume y = I. The results so obtained are represented in Fig. 86 and can be compared with the stability functions S suggested by Monin and Obukhov (1954) [Eq. (4.36)] and by Ellison (1957) [Eq. (4.40)]. While the former relationship is reproduced for two values of the constant o: (0.6 and 4.5), the latter function is given in the form applied by Panofsky et al. (1960) with Rlerit = y/18 which, in our case, implies Rlerit = 1/18. I .5 rrr-,------,-----,---,------,------,----,-------,-------,
c
5? o c
"
J:>
a (j,
05
'---~0--_-;c:0'::o.2---c0~A;:-----;:0:'-::.6;------;;0'::o.8---.:"c1.0;;---1:'-2;----' ::. I~
- 1.6
Richardson number Ri
FIG. 86. Stability function S versus Richardson number Ri (reference height 125 em). Circles: Mean values computed from Takahashi's (1958) measurements of wind speed, air temperature, and humidity profiles as well as of evaporation; standard deviation indicated by vertical stretches. Figures: Number of averaged evaporation data used. Curves: Theoretical relationships of Monin and Obukhov (1954) and of Ellison (1957) with constants indicated.
5.2
THE TEMPERATURE AND MOISTURE FIELD
275
If the whole Ri range is considered, the interpolation formula proposed by Ellison (with the constant Rfcrit according to Panofsky et al.) seems to represent the empirical S values best. In view of the rather crude method of investigation, in particular with regard to the determination of evaporation, the result should be considered as a preliminary one. Further study is necessary.
5.2.6.2 Convective Layers. Under lapse conditions, the vertical exchange of momentum, sensible heat, and moisture is effected partly by purely dynamic turbulence and partly by buoyant forces. When both agents are effective, the wind, and in particular the wind shear, must exercise a certain control on the size and structure of buoyant elements besides its direct contribution to vertical exchange. We then speak of forced convection, thus indicating the dominating influence of wind shear on the thermal effects. When, however, the purely dynamic turbulence is negligible as compared with buoyant forces, the resulting exchange motion is termed free convection. It would be of great interest to get some further information on the characteristics of these two regimes of transfer. In particular, their dependence on the height above sea level is of importance. Assuming buoyant motions with local similarity and negligible effect of wind shear, Priestley (1954) derived the following relations for the profile of mean potential air temperature 88/8z ~ Z-4/3 and 8 ~ Z-1I3 (5.34)
respectively, which was verified observationally by Webb (1958) and by Taylor (1960a) up to a height z that is approximately equal to the absolute value ILl of Monin and Obukhov's stability length. A relation similar to Eq. (5.34) had already been suggested years ago by Prandtl (1932). In this height region the dimensionless heat flux H (5.35) H* = pcp(g/O)1I2(80/8Z)3/2 Z2
is constant with a value of about 0.9. Priestley (1955) further showed that the lower boundary of the regime characterized by the temperature profile Eq. (5.34) and by H* ~ 0.9 is at z ~ 0.03 ILl which corresponds approximately to Ri ~ - 0.03. Below that level, forced convection, i.e., mechanical turbulence, is dominant and the dimensionless heat flux H* is a function of the Richardson number given by H* = k21Ril-1I2 (5.36)
276
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
which implies that H* decreases with altitude. Here the height functions of wind speed, air temperature, and humidity are, with sufficient accuracy, represented by the "log + linear" relationships, Eqs. (4.39), (5.32), and (5.33). Above the upper boundary of the layer with H* '" 0.9, the gradient of potential air temperature 80/8z vanishes and the profile (5.34) no longer holds true. From z '" ILl upward, a homogeneous region with neutral or slightly subadiabatic stratification extends to a considerable height. This is the layer of essentially free convection where buoyancy is the governing factor. This motion will be treated in greater detail in Section 5.3.2.1. As was pointed out by Webb (1962) the vanishing of 80/8z at the height z '" ILl [which according to Eq. (4.28) drops when u, decreases] indicates that in the intermediate height region 0.03 < z/[L[ < 1, the wind shear is not completely negligible. In fact, the presence of some mechanical turbulence seems to be even more necessary for the diffusion of heat from the rising buoyant elements into the environment. Thus the temperature profile (5.34) must be connected with the existence of a certain wind shear. Consequently, the name "composite convection" appears to be appropriate for the intermediate height region,0.03 < z/ILI < 1, as was suggested by Webb (1962), who also advanced a theoretical approach on the basis of the consideration outlined above. After the foregoing remarks it seems rather obvious that the comparatively shallow maritime bottom layer with superadiabatic temperature gradients, about which some preliminary information was supplied in Table XXV (Section 5.2.4.4), might be identified with the regions of forced and composite convection up to a height of about z '" IL[. In order to illustrate the functional dependence of the stability length L on Hand U*, some numerical values, according to Eq. (4.28), have been graphed in Fig. 87. From this diagram it can be taken that the thickness of the bottom layer comprising forced and composite convection grows with decreasing heat flux and increasing wind shear, contrary to its apparent growth with increased instability as indicated in Table XXV. Thus the existence of the superadiabatic bottom layer is more a consequence of wind shear than of unstable stratification. The merging across the transition level,z '" 0.03[L[, between the layers of forced and composite convection, i.e., between a "log + linear" temperature profile and the height dependence [Eq. (5.34)], was studied by Webb (1960), who suggested taking a two-sided linear smoothing factor, thus ensuring continuity of the first, second, and third derivatives of O(z) at z = 0.03[LI.
5.2
TIlE TEMPERATURE AND MOISTURE FIELD
277
60 , - - - - - - - - - - - - - - - - - - - - - - - - = 0 , - - - - - - - - - ,
50
r'u
~
2
3
4
5
6
7
8
9
FIG. 87. Stability length ILl as a function of vertical eddy flux of sensible heat Hand friction velocity u* [computed after Eq. (4.28)].
5.2.6.3 Inversion Conditions. Since, on the greater part of the oceans, the sea surface is warmer than the overlying air, lapse conditions predominate at sea and so the profile data obtained during stable stratification are rather scarce. The same impression can be obtained by examining Figs. 82 and 83. Although the profiles presented therein were measured in coastal regions, where with warm continental air flowing over cold water, particularly in spring and early summer, stable conditions are more frequently encountered than on the open sea, the share of stable stratification is small. So, with regard to temperature and humidity profiles, little of importance can be added to the corresponding explanations given in Section 4.3.3 for the wind profile. There is, however, one interesting and important feature that seems worth mentioning: Fleagle (1956b), when applying the optical refraction method to the measurement of the vertical temperature gradient above a cold water surface, discovered an anomaly with regard to this gradient at a height of about 10 em, which obviously must be interpreted as a real feature of the temperature distribution under stable conditions. The rather high accuracy of refractive measurement revealed at that height a cooling which is too small to be detectable by ordinary thermometry. The winds were slight (1-5 knots) and the air (at 3-4 meters above the surface) was 4-8°C warmer than the sea. These are exactly the conditions under which the effect of radiative exchange might become significant.
278
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
Accordingly, Fleagle attributed this cooling to the interaction of convective and radiative processes. If warm air is flowing over a cold sea surface, heat is transferred to the sea by turbulent and molecular exchange. The resulting temperature profile shows a gradient which is very steep close to the surface, but decreases monotonically with increasing height. Radiation tends to modify this profile in such a way that the equilibrium between convective and radiative processes is attained at each height. If the rate of radiative temperature change is computed from the measured temperature distribution on the basis of the emissivity distribution discussed later in Section 5.3.5.4, a radiative warming at a rate of about lOoCjhr is found for the sea surface whereas at about 10 em height the result is a cooling of 6°Cjhr. Above 30 em height the radiative cooling rate remains constant and equals 3°Cjhr. Thus it seems sufficiently established that the anomaly reported by Fleagle (1956b) is due to radiative cooling. This effect may become important in the formation of fog (see Section 5.3.5). 5.2.7 Heat Flux and Evaporation 5.2.7.1 General Relations. It was the purpose of the bulk formulae (Section 5.2.2.3) and of the profile coefficients (Section 5.2.5) to relate the fluxes of sensible heat H and moisture E with the differences in temperature and humidity measured between a single height (e.g., at the ship's bridge) and the sea surface. The shortcomings of such an approach have already been mentioned. They are mainly caused by a complete neglect of the transfer characteristics that are found close to the sea surface, although the models used included those layers. There are two possible ways to overcome these difficulties:
(a) We might avoid the inclusion of the layers next to the sea surface by confining the analysis to levels well above that region. (b) We might apply suitable flow models, taking into account the peculiarities dominating at the sea surface. Dealing first with (a), and limiting our consideration to the nearneutral case, we can well employ Eqs. (5.28)-(5.33) and (4.39), fixing two levels Z2 and zi with Z2 > Zl and assuming that, for L -+ co and 8* = 0, adiabatic conditions are present. We then obtain: (adiabatic stratification) (5.37) Had = 0 2 pk (iiI - t]2)(tl2 - Ul) (5.38) Ead = {In [(Z2 + ZO)/(Zl + zo)]}2
5.2
THE TEMPERATURE AND MOISTURE FIELD
(near-adiabatic stratification) c p pk 2(01 - 02)(il2 - ill)
H=--------------E =
{In [Z2 + ZO)/(Zl + zo)] + «(I.(L)(Z2 - Zl)}2 pk2(ijI - ii2)( U2 - U1) {In [(Z2 + ZO)/(Zl + zo)] + «(I./L)(Z2 - Zl)}2
279
(5.39) (5.40)
After having examined these equations one might argue that the aim described in (a) has not been reached because the relations still contain the roughness parameter Zo which is closely connected with the aerodynamic properties of the sea surface. In order to counter this argument we could say that, in the light of the results given in Section 4.3.3.3, Zo cannot be considered as an actual roughness length, but merely as an empirical factor characterizing the air flow above the sea surface, which is neither rough nor smooth. Thus no possible later interpretation of zo is anticipated. Besides, since Zo is small as compared with Zl and Z2, it can be neglected in most cases. With the help of Eq. (4.39), Eqs. (5.39) and (5.40) can finally be transformed into (5.41) (5.42) in which they apply to adiabatic conditions, too, and are particularly suitable if the wind stress is known. As the equations of Monin and Obukhov (1954), which were used above, are only applicable in the region of forced convection, i.e., for Z ~ 0.03[LI, care should be taken that the levels Zl and Z2 of the measurements concerned fall within that height range. Equation (5.40) is not very appropriate for practical application, because the stability length L is not directly accessible to measurement. It will be noticed that the quotient of Eq. (5.40) over Eq. (5.38) E { In [(Z2 + ZO)/(Zl + zo)] }2 (5.43) = F2 = E ad In [(Z2 + ZO)/(Zl + zo)] + «(I./L)(Z2 - Zl)
-
serves as a link between adiabatic and nonadiabatic moisture transfer. For ease of application the conversion factor F can be written in the form (Brogmus, 1959): g(02 - 01) F = 1 - (I.---(Z2 - Zl) (5.44) TO(U2 - U1)2
280
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
Comparison with Eq. (4.24) shows that the structure of the factor of is similar to that of the Richardson number. Thus this factor can be considered as a stability parameter. From comparison with Eqs. (4.36) and (4.26) we further infer that the whole conversion factor F approximates to the reciprocal of the stability function S. Turning now to (b), we may remember that for the flow over the sea surface the following two models have been suggested: The flow may be assumed as aerodynamically smooth or rough (see Section 4.3.3.2). Since at present there is not available any convincing evidence as to which of the two models is true, or whether there is still another model that might be applied, we shall abstain from going into detail but merely present the resulting formulae. This is done in Sections 5.2.7.2 and 5.2.7.3. (X
5.2.7.2 Aerodynamically Smooth Flow. Following Montgomery (1940), we can characterize the aerodynamically smooth boundary by a very thin layer of laminar flow (of the order of 1 mm thick) immediately over the sea surface wherein the transfer of momentum, sensible heat, and moisture is effected by the molecular coefficients of viscosity (v) conductivity (ve), and diffusivity (D). Numerical values are given in the List of Physical Constants (p. 250). Sverdrup's (1937) conception of this laminar layer was that it must be considered as a statistical quantity representative of the average conditions which comprise a large number of processes where air parcels come into contact with the sea surface and remain so for a certain time, exchanging heat and vapor content by molecular conduction and diffusion. As the derivations are similar for heat and moisture transfer we may restrict our consideration to the latter. Montgomery (1940), after taking into account molecular and turbulent transfer (under neutral conditions) and fitting together the two regimes at the top of the laminar boundary layer, arrived at the following expression for the evaporation from an aerodynamically smooth sea surface:
E=
pk(qo - qa)u* (>"vk/D)
+ In [(ku*a)/ D]
(5.45)
Here a is the level where qa is measured and>" is a dimensionless constant defined by >.. = uJ)/v (5.46) (8 = thickness of the laminar boundary layer). It will be noticed that Eq. (5.45) is equivalent to Eq. (5.21), thus providing an interpretation of kE* rqa • There are, however, considerable discrepancies as
5.2
THE TEMPERATURE AND MOISTURE FIELD
281
regards the numerical value for A, which ranges between 7.8 (Montgomery, 1940) and 27.5 (Sverdrup, 1937), the value for an aerodynamically smooth surface being A = 11.5 according to von Karman (1934). This is not surprising since the assumption of a laminar boundary layer, as well as its thickness and its dependence on wind speed, is completely hypothetical and can only be verified by indirect evidence. An attempt in this direction has recently been made by Deardorff (1961a), who first compared the evaporation rate of an artificial square pond of smooth water with a side length of 1.2 meters, where the evaporation was assumed to be unaffected by the 5 mm rim of this pond, with that from a small pan situated upon it. After having determined the average ratio of these two values to be 0.54, which clearly shows that the evaporation from the pan is increased by the turbulence caused by the upwind portion of its rim, Deardorff measured the evaporation from the same pan located upon a larger water surface, 'thus deducing values for the constant A in Eq. (5.45) pertaining to a smooth water surface. The result was that A appeared not to be constant but ranged between 4 and 6 for low wind speeds and amounted to about 7 for higher ones. Wind tunnel investigations under strictly controlled conditions will be needed before these results may be interpreted in terms of the theoretical model.
5.2.7.3 Aerodynamically Rough Flow. For heat and moisture transfer in the case of an aerodynamically rough flow, a rather large number of different models have been proposed. Sverdrup, in his 1951 review, describes five different approaches. In four of them a true diffusion layer next to the sea surface is assumed while above that laminar layer different concepts of the transition zone between the laminar flow and the fully turbulent one are applied (Sverdrup, 1937; Montgomery, 1940; Norris, 1948; Bunker et al., 1949). In one model (Sverdrup, 1946), the existence of a laminar boundary layer is denied. The results reached by these five methods diverged widely (the discrepancy in prediction being more than four to one) and, since empirical evidence was not sufficient, it was impossible to decide which assumption might be acceptable. Since then some progress has been made. In the first place, it now seems widely agreed that, at the sea surface, there must exist a significant difference between the exchange of momentum and that of other properties such as sensible and latent heat. As was pointed out by Swinbank (1960), molecular viscosity does not playa decisive part, if any, in the momentum exchange, since this
282
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
is brought about by pressure forces acting on the roughness elements. However, this model cannot be applied to the transfer of heat and moisture at the sea surface because, in this case, there is no equivalent to the pressure exerted on the waves. Similar conclusions are reached if we consider the model suggested by Stewart (1961) (see Section 4.3.5.6) in which the momentum is supposed to be transferred to the waves not by turbulence but by an organized and wave-like motion in the layer close to the surface. According to Stewart, also, these motions will presumably contribute only little to the transport of sensible and latent heat. Thus we are led to believe that the final exchange of heat and moisture between air and sea can only be effected by molecular processes. (Some observational evidence for this conclusion has already been mentioned in Section 5.1.2.1). Consequently, the proper representation of evaporation and heat transfer must include the molecular coefficients of conductivity (ve) and diffusivity (D). A suitable approach has been described by Sheppard (1958). It has the advantages of both simplicity and freedom from unknown constants. Sheppard used the basic equations [Eqs. (5.1) and (5.2)] in the following modified form: (5.47) H = - Cpp(ve +.KH)(88j8z) (5.48) E = -p(D + KE)(8ijj8z) Thus there is no longer assumed a distinct layer of exclusively molecular transfer; molecular and turbulent exchanges are rather supposed to exist simultaneously. Since the K's increase linearly with height, Ve and D, respectively, preponderate close to the surface. Sheppard took (5.49) thus neglecting Zo on the argument that the aerodynamic roughness is of more importance for the momentum transfer than for the exchange of sensible and latent heat as was explained above. Integration yields cppk(80 - 8a)u* (5.50) H=------In [eve + ku*a)jve] pk(ijo - ija)u* (5.51) E= In [(D + ku*a)/ D] where the subscripts 0 and a refer to the heights z = 0 and z = a. The equations are confined to near-adiabatic conditions or to the first layer above the sea, where dynamic turbulence dominates.
5.2
THE TEMPERATURE AND MOISTURE FIELD
283
5.2.7.4 Comparison with Observations. We now dispose of quite a number of relations for the determination of heat flux and evaporation at sea. Everything considered, their number may amount to eight for each of the two quantities. However, some of these formulae are related to each other since we may also interpret the equations for H and E derived in Section 5.2.7 in terms of profile coefficients I' 8 and r q by making use of the corresponding equations [Eqs. (5.16), (5.20), (5.21), (5.23), and (5.24)] given in Section 5.2.5, thus furnishing theoretical formulae for the T''s. However, we shall not proceed in this direction. We feel we had better investigate the question of which of the equations given in Section 5.2.7. describes reality best. For such an examination simultaneous profile and flux measurements are required. There is still a serious lack of suitable and reliable measurements taken at sea. In the case of humidity, the only study providing humidity profiles, as well as evaporation measurements, was published by Takahashi (1958). It has already been used in Section 5.2.6.1. No corresponding temperature profile and heat flux measurements have become known up to now. In the case of heat exchange, an additional difficulty arises from the fact that the transfer of radiant heat was not considered in the above deliberations; hence the formulae for H do not include its effect which, however, may become noticeable if the turbulent transfer is small, as with high stability and light winds. In our attempt to use Takahashi's profile and evaporation measurements for the purpose of comparing theory with observation, we undertook an examination of Sheppard's equation [Eq. (5.51)], which does not involve any adjustable constant. Out of Takahashi's series we selected those data where the time periods corresponding to the evaporation values were sufficiently covered by profile measurements. Bearing in mind the deviations from the log profile at the higher levels-caused by internal boundaries owing to short fetches or by thermal stratification-we confined the computation to the lowest 50 em, i.e., the friction velocity u, was evaluated from the wind speed measurements at 25 and 50 em and the air-sea humidity difference referred to the level of 50 em. Air density p and molecular diffusivity D were computed for the intermediate level of 25 cm. The results for-fifty-five cases of comparison are given in Fig. 88A. First there will be noticed the considerable scatter which clearly indicates the deficiencies inherent in such a manipulation. On the average the observed evaporation values seem to be higher than the theoretical ones, a fact that is quite understandable if the work of Deardorff (196Ia) (see Section 5.2.7.2) is taken into account. When
284
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
comparing the evaporation from a pan with that from a small artificial pond, for which the disturbance caused by the rim is assumed to be negligible, he obtained a correction factor of 0.54, i.e., the evaporation from the pan was increased considerably by an eddying motion originating from the rim of the pan. Similar effects must be expected with Takahashi's evaporation measurements because they, too, were obtained by means of a pan mounted on a small wooden float and moored at nearly the central point of a floating square frame with 2 meters side length. Applying the pan-correcting factor determined by Deardorff (1961a), to Takahashi's evaporation values, we obtain the results given in Fig. 88B. Here the agreement between observed and computed evaporation is more satisfactory than in Fig. 88A, although the scatter is still substantial. Apart from this fact, we may say that Takahashi's evaporation measurements appear to be represented by Sheppard's formula [Eq. (5.51)] with appreciable reliability. It should be mentioned that Takahashi (1958) himself compared his evaporation measurements with Eqs. (5.16), (5.38), and (5.45), but he did not establish sufficient agreement. In order to give an idea of the magnitude of the evaporation rate at sea, Fig. 89 has been computed on the basis of Eq. (5.51). 2
2
s:
o o o
o 00
0
0
00
o o
o
~
B
A
0
o
o
o o
x
x
x
2 EObserved (mm/6hr)
0
x x
x
x x x
"0
~
E o
'x xxx \ x x
~
;/x x x:
o
0
o
x
x
x
E E
I
x
2
0 Eobserved (reduced) (mm/6 hr)
FIG. 88. Comparison between evaporation values computed after Eq. (5.51) (Sheppard 1958) and those observed by Takahashi (1958). (A) Observed values as given by Takahashi. (B) Observed values of Takahashi reduced by 0.54 according to Deardorff (1961 a).
5.2.7.5 Effect of Sea Spray. So far we have said next to nothing about the effect that sea spray might exert on evaporation, apart from the remark that this influence must be present at higher wind
5.2
THE TEMPERATURE AND MOISTURE FIELD
285
velocities. It is indeed very difficult to get any quantitative information on this subject because field measurements of evaporation taken at the sea surface can only be made with slight winds where there is no appreciable sea spray and, on the other hand, the problem seems hardly approachable by means of theoretical studies. 25
20
s:
15
""
N
E
~ 10
'"
FIG. 89. Evaporation rate in millimeters per 24 hours as a function of wind speed and water vapor differences computed after Sheppard's formula (5.51). eo - eso = Water vapor difference between the sea surface and 50 em height. Uso - u 2S = Wind speed difference between the levels 50 and 25 em. Tv = 290°K. Diffusivity D = 0.250 cm 2 sec-I.
Montgomery (1940) remarked that sea spray must release water vapor and thus cause an increase of I'q in the layer between the sea surface and the level of measurement. With moderate instability, he estimated this increase at about 40 per cent for a wind speed of 4 meters/sec and at about 100 per cent for 6.5 meters/sec. These figures appear to be rather high in view of the moderate wind velocities concerned (compare Table I). As they were determined in such a way that observational deviations from the theoretical values were more or less interpreted as an effect of sea spray, they can only be considered as a very rough approximation. In accord with the difficult nature of the subject in question, quantitative information can best be expected from laboratory studies. Relevant investigations have been carried out by Okuda and Hayami (1959). They used a wind-water channel of about 20 meters in length and, among other quantities, they observed the sprayed water drops by means of a suitable filter paper exposed vertically to the spray for
286
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
about 5 to 10 seconds. The diameter of the sprayed drops observed was less than 1.5 mm but the lower limit of the drop diameter could not be determined. The vertical distribution of horizontal transport by sprayed water drops is exhibited in Fig. 90. From this diagram it can be taken that, above a height of 10 em, sea spray is negligible with wind velocities below 10 meters/sec. (Unfortunately the exact height of the corresponding wind speed measurements is not given but it must have been approximately 30 cm.) In the wind speed range of 12-13 meters/sec the water transport by spray at 10 em height increases rapidly. A strong decrease is found with height, the water transport by spray at 30 em being only about 10 per cent of its value observed at 10 em height. In conformity with these findings Okuda and Hayami (1959) ascertained that the influence of sea spray on the profile coefficient I'a, was substantial only for a wind speed U8 above, say, 15 meters/sec.
FIG. 90. Vertical distribution of horizontal water mass transport by sprayed drops. (From Okuda and Hayami, 1959.)
This result complies well with the descriptive terms of the Beaufort wind force numbers (Table I) wherein appreciable effects of spray and foam are assigned to wind forces above 7, i.e., to wind speeds of about 15 meters/sec and more. The laboratory measurements did not show any noticeable effect of (mechanically generated) swell waves on spray and on evaporation. Whether or not the results of these wind flume experiments can be applied to field conditions remains an open question, though.
5.2.7.6 Influence ofa Monomolecular Film. Some substances, such as cetyl alcohol, spread spontaneously on water to produce a surface film only one molecule thick. The special structure of such a monolayer is of importance for the transport of water through it, i.e., for
5.2
THE TEMPERATURE AND MOISTURE FIELD
287
evaporation. For instance, cetyl alcohol is a waxy material having a terminal alcohol group attached to a saturated paraffin chain of 16 carbon atoms. The transport of water through a compressed and, therefore, oriented monolayer is not an ordinary diffusion process which involves a small energy barrier but is to be considered as a process in which the water molecule must pass along a molecular pathway between paraffin chains, thus requiring a substantially higher amount of energy (La Mer, 1962). Consequently, a compressed monolayer results in a retardation of evaporation. The resistance to evaporation increases with the length of the chain and with the reciprocal of the absolute temperature. The retarding effect is much smaller if the surface film consists of multilayers of molecules oriented at random. In recent years the effect of a monomolecular film in suppressing evaporation has received increased attention in view of the practical problem of conserving water in lakes and reservoirs (see, e.g., La Mer, 1962). Although in maritime areas this viewpoint is not of as much interest as in arid zones, the subject will be briefly touched upon here because we have seen (d. Sections 3.3.1, 3.3.2, and 4.2.4) that surface films consisting of organic matter or originating from artificial contaminat\on can be found on the sea surface too. Field measurements indicating the reduction of evaporation by natural surface films have been reported by Deardorff (1961b). He compared the evaporation rates of two pans floating at the sea surface. One of these two pans was filled with subsurface sea water while special care was taken in filling the second so that any surface film which might have been present would have been retained. The pans were exposed to light winds and the evaporation rate was determined from the increase of salinity observed. The results of six sets of measurements showed a distinct reduction of evaporation, of the order of 20 per cent, which was obviously caused by natural surface films. Deardorff (1961b) believes that the amount of reduction found in these measurements was even somewhat smaller than that actually occurring, owing to the following circumstances: At the natural water surface the differences of evaporation between clean areas and film-covered areas are liable to be larger than those indicated by the two pans, because the surface roughness is greater under natural conditions than within the corresponding pan. In addition, the surface film, if captured by the relevant pan, may not cover the entire surface area but cling to the interior walls of that pan, thus reducing the effect of the film on the evaporation observed.
288
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
When these results are applied to practice, the areal extent and the frequency of occurrence of natural surface films must be estimated if their effect on evaporation is to be taken into account. This, however, is by no means an easy task. For artificial films it has been shown by Grundy (1962) that a monolayer is carried across the water surface by the wind, its rate of movement being about 400 meters/hr with wind speeds between 4 and 20 knots. Besides, the film may be damaged by waves. For these reasons it is difficult to estimate the portion of the surface covered by a monolayer as well as to maintain an artificial film at full pressure over the whole of a reservoir surface. Field investigations on reservoirs covered by artificial films resulted in evaporation reductions which ranged between 40 and 60 per cent (Grundy, 1962). In Section 5.1'.2.1 it was mentioned that, according to laboratory studies, such a surface film reduces or even prevents evaporation but does not substantially impede the exchange of heat. This would account for the fact that the cool skin which is attributed to evaporation is not always observed at the sea surface. Laboratory investigations (Mysels, 1959) further revealed interesting details of the transfer processes that occur at a quiescent water surface covered by a monolayer. The technique adopted was quite simple because the color change of a filter paper, impregnated with cobaltous chloride and held just above the water surface for a few minutes, gave a good, although only qualitative, indication of the marked effect a monolayer exerts on the pattern of thermal convection and evaporation. Since a monolayer offers hysteretic resistance against extension and contraction, convective motions rising to or sinking from the surface of the water are impeded and can only develop over greater distances and with larger forces present. Thus the convective heat transport from deeper layers to the surface is necessarily affected and localized. However, when the surface is clean the convection pattern is unlike that described above, the local differences being much smaller. 5.2.8 Temperature and Humidity Fluctuations near the Sea Surface As was already indicated in Section 5.2.3.3, at present very little can be said about turbulent fluctuations of temperature and water vapor in the first few meters above the sea surface. The only information as yet available originates from Staley (1960), who recorded from 2- to 30-second-period fluctuations of water vapor in a stable atmosphere over a lake surface by means of a microwave refractometer (Magee and Crain, 1958) and a bead thermistor. The index of
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
289
refraction for microwaves being particularly sensitive to fluctuations in water vapor pressure, the combination of a refractometer (which is not in itself an absolute instrument) with a bead thermistor, having equal response time constants of about t second, allowed the magnitude of the water vapor fluctuations to be derived. Staley has obtained simultaneous records of refractive index and air temperature taken at different heights up to 13.8 meters over a cool lake surface, which showed coincident peaks of high water vapor content and of low temperature. Thus these records are consistent with the measurements of temperature and humidity fluctuations performed at a much greater height (134 meters) in maritime air by Charnock and Ellison (1959) (see Section 5.2.2.2). Since simultaneous wave records led to the supposition that the fluctuations in air temperature and moisture are closely related to the wave motion, it seemed possible to consider these eddies as air parcels forced up from the wave crests. Applying this model, and using the vertical profiles of temperature and vapor pressure for environment and rising parcels measured by himself, Staley (1960) arrived at some estimates of the mixing length for water vapor. They amounted to about 190 em at 4.6 meters height and increased to 765 ern at 13.8 meters. Unfortunately, no wind profiles were measured simultaneously and thus the conclusion must be considered preliminary. The study, however, clearly shows the advantages and possibilities of that new technique. 5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE IN THE MARINE ATMOSPHERE
5.3.1 General Outline It is certainly true that the meteorological phenomena occurring in the immediate neighborhood of the sea surface hold a key position among all the physical processes in the marine atmosphere that we have defined as being controlled by the sea surface as lower boundary. Hence it is quite understandable that the air-sea boundary layer problems have called for a thorough treatment in this monograph, as has been given them in Sections 4.3 and 5.2. Nevertheless there are thermodynamic processes in the marine atmosphere that reach considerably higher than a few meters above the sea surface but, in spite of this, may be claimed to be typically maritime. We are referring here to such processes as convection, condensation, and air mass transformation which involve thicker layers, as well as larger areas
290
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
and bigger air parcels, than we considered when treating the layer next to the sea surface. Consequently, if the latter phenomena can be characterized as small-scale interactions between air and sea, the subject of this section may be termed processes of medium scale. The subdivision which lends itself most readily to this description is the separate representation of lapse and inversion conditions. At sea, the significance of stability is particularly pronounced, both as a characteristic feature and as a directing agent, even at higher altitudes. Thus, it seems justified to take stability as an index of classification. In addition, it would be rewarding and also of rather great interest to treat this subject from the viewpoint of temporal dependence, i.e., to separate the steady state phenomena from the transient processes. But considering "the fact that, even in the trade wind region, truly stationary operation can be secured only rarely, and that, owing to horizontal differences in sea-surface temperature and to dynamic features of the wind field, most of the atmospheric motions at sea involve advective and dynamic transformation of air masses, the principle mentioned above cannot be applied in a strict sense. The particular difficulties inherent in the theoretical treatment of transient processes should also be regarded. Having all this in mind, we decided to subdivide the topic into "general" facts and "transformation" processes. Hence, we will first attempt to describe the general features of the atmospheric motions under different stratifications. In this description the weights cannot be distributed evenly between the two components since, as to the frequency of occurrence, horizontal and vertical extension, and importance, much more can be said about processes under lapse conditions than about those occurring in air masses warmer than the sea. Thereafter, in a separate section, the aspects of air mass modification will be dealt with, i.e., special attention will then be given to the transformation processes. 5.3.2 Lapse Conditions Even a short glance at the climatic charts representing the air-sea temperature difference will reveal the fact that, on the greater portion of the oceans by far, and also during the greater part of the year, the sea surface is warmer than the air above it. The reverse is only found in certain, mostly coastal, regions where upwelling occurs or cold currents dominate. During the early summer months those comparatively small areas show, it is true, a temporary tendency to extend, but on the whole the picture is not changed. Even if we take
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
291
into account that, to a certain degree, the observed preponderance of the situation "water warmer than air" might be biased by the method normally applied to the measuring of the sea-surface temperature which does not furnish values of the actual (probably lower) skin temperature, we can state that, in general, lapse conditions dominate at sea. Thus the study of this case deserves, and has received, particular attention. With lapse conditions prevailing at sea the fluxes of sensible and latent heat pass from the ocean to the atmosphere, thereby initiating the powerful mechanisms of mass exchange and mesoscale convection which may affect considerable portions of the atmosphere. As we are mainly interested in the processes influencing or transforming the maritime atmosphere by energy exchange with the sea, we shall now add a supplement to our description of this energy transfer, which, in the preceding sections, was entirely confined to the layer next to the sea, by discussing how the energy absorbed at the sea surface is transported upwards and how it gives rise to convective motion, cloud formation, and kindred phenomena. The procedure adopted in our discussion is first to describe the main observational facts and afterwards attempt to summarize the existing concept of the mechanism of the processes concerned. 5.3.2.1 The Structure of the Homogeneous Layer. From the treatment given in Section 5.2.6.2, we know that, under lapse conditions, there is, next to the sea surface, a superadiabatic layer extending to about z = ILl. Within this bottom layer "forced convection" or dynamic turbulence dominates up to z = 0.03jLI, whereas wind shear effects are of minor importance in comparison with buoyant forces in the intermediate layer, 0.03 ILl < z < ILl, the layer of "composite convection." It has already been indicated that the vertical gradient of the potential temperature vanishes at the top of the superadiabatic bottom layer. Various measurements executed by means of captive balloons (Roll, 1939, 1950; Deacon et al., 1956) and by airplanes (Craig, 1946, 1947; Bunker et al., 1949; Malkus, 1958) have given evidence of the existence of such a layer which begins above the superadiabatic bottom layer and, within the accuracy of the observations, is roughly characterized by an adiabatic temperature gradient and by vertical constancy of the specific humidity. In this height region, the air thus seems to be completely mixed or homogeneous. An example is given in Fig. 91. This sounding was made in the Caribbean Sea and represents the conditions in the trade-wind zone. There is some indication
292
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
that the homogeneous layer can also be found in other regions, and so it seems to form an essential feature of the vertical temperature and moisture structure under lapse conditions. As most of the knowledge originates from investigations in the Trades, we shall base our description on the findings obtained in that region. In particular, the results of two expeditions performed by scientists of the Woods Hole Oceanographic Institution will be mentioned. These two expeditions are distinguished by the fact that, although both were carried out in springtime, they encountered rather 9
10
II
12
15gm/kg
13 14
1000
1000
--x 900
(
~
900
~x,
x x'
800
Transitional ...~ x.... __ layer
x,f x...
Mixing ratio
x.: k
700
'~~ •
-;;
:E
'xI 600
"x,>
Q;
Q;
.5
700
x)
600
800
500
E 500 :: s:
'"
\x
'"
q;
,)
I
400
300
200
Homogeneous layer
.'"
Q;
0q; I
400
<
\
lx x', , .x
<
I'
300
200
<,
)
100
o 26 27 28 29°C II 12 13 14 15gm/k~ FIG. 91. Potential air temperature and mixing ratio as a function of height showing the "homogeneous layer" and the "transitional layer," Caribbean Sea, April 2, 1946, 1200-1216 hr. (After Bunker et a/., 1949.) Surface wind: 050°, 9 knots. Surface water temperature indicated by arrow.
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
293
different flow conditions. In 1946 the circulation was strong and characterized by vigorous cumulus convection, while the soundings of the later (1953) expedition showed the typical features of weak trade flow regarding the location and season. This time the ordinary trade cumulus convection was only poorly developed although several intense disturbances with large cumulo-nimbus clouds passed through. Some characteristic data on the homogeneous layer have been assembled in Table XXVII. From this summary we gather that, on the average, the homogeneous layer extended to about 550 meters and that its height was distinctly greater in cloudy areas than in clear regions. So it was in cloudy areas that the top of the homogeneous layer came nearest to the lifting condensation level while, on the whole, the height of the homogeneous layer amounted to about 80 per cent of the level of condensation which apparently forms the upper limit of the mixed layer. The temperature gradient was slightly less than dry-adiabatic, thus indicating a downward flux of sensible heat, whereas the lapse rate of the mixing ratio was small. Consequently, a substantial increase of the relative humidity resulted between the bottom and the top of the homogeneous layer. The most significant difference between the two investigations lies in the vertical moisture distribution which in 1953 showed a lapse rate exceeding that of 1946 by an average factor of 3.5. One has the impression that in 1953 the vertical humidity flux was impeded, perhaps by weak dynamic turbulence, which led to moisture accumulation near the sea surface and to reduced evaporation. The upper part of the homogeneous layer is usually somewhat more stable than the lower one and has also a slightly increased moisture lapse rate. The results of a more recent study published by Bunker (1962), however, indicate that an increase of the mixing ratio and, consequently, positive moisture gradients may occur at the upper levels of the homogeneous layer at times. The existence of mixing ratio inversions at a height of about 250 meters was verified during a period of weak trade flow connected with steep negative moisture gradients at lower altitudes. The source of the moist air above 250 meters is unknown. It may perhaps originate from cloud drops settling down into the mixed layer and evaporating there or from the spreading of rising moist air at the stable layer which tops the mixed layer of the Trades. The thickness of the homogeneous layer shows variations of 20 per cent in space and as much as 100 per cent in time. Extreme diurnal variations may amount to about 300-700 meters (Malkus, 1958).
TABLE XXVII CHARACTERISTIC FIGURES OF THE HOMOGENEOUS LAYER OVER THE CARIBBEAN SEAa
Trade wind regime
Lifting Relative humidity Mixing ratio condensation Bottom Top Height level minus Bottom Top height of hom. layer (gm/kg) (gm/kg) (meters) (meters) (%) (%)
Strong (April, 1946) Clear Cloudy Average
549 620 575
186
Weak (March-April 1953) Clear Cloudy Average
496 588 537
204
a
From Malkus (1958).
71 71 71
89 91 90
15.0 15.1 15.05
14
76 81
120
78
85 94 89
15.3 15.6 15.44
87 150
Lapse rate of Mixing ratio
Temperature
(100 meters):'!
CC/100 meters) deg meters/sec
X
14.7
6.4 4.9 5.8
14.4 14.2 14.3
-18.3 -24.0 -20.4
X
14.6 14.8
Wind
X X
X X
10- 5 10- 5 10- 5
-0.90 -0.85 -0.88
10- 5 10- 5 10- 5
-0.90 -0.90 -0.90
87 96 90
131
74 106
8.9 9.5 9.1
5.3 6.1 5.7
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
295
5.3.2.2 Cellular Convection. Occasionally the homogeneous layer above the sea seems to be distinguished by a rather regular form of mesoscale convective motion, which is very similar to the classical experiments of Benard (1900), who observed a regime of polygonal convection cells set up in a thin layer of liquid heated from below if a certain critical temperature gradient was reached. When the liquid was subjected to shear, longitudinal roll vortices similar to those sketched in Fig. 31 developed with their axes parallel to the direction of shear. According to the summary of the theory of convection cells given by Stommel (1947a), the critical temperature gradient 8Tj8z at which the steady state regime changes from one of molecular conduction to one of cellular convection is determined by Rayleigh's relation 8~
-
where
8z
vcv > Rerit - -
gKd4
(5.52)
gKd4 8~
R=-vcv 8z
is the so-called Rayleigh number and Vc = the thermometric conductivity [ern- sec:"] v = the kinematic viscosity [ern- sec-I] K = the coefficient of thermal expansion [OC-l] g = the acceleration of gravity [em sec-2 ] d = the depth of the liquid [ern] The critical Rayleigh number depends on the character of the boundaries but is independent of the geometry of the cells. On the other hand, the geometry of the cells does not depend on the physical parameters. A summary of the data concerned is given in Table XXVIII. The quantity b designates the side of a square cell, the width of a strip cell, or the side of a hexagonal cell, respectively. It should be noticed that in Rayleigh's theory the coefficients of conductivity and viscosity were considered as constant. ' In liquid layers the circulation is directed upward in the center of the cells and downward at their boundaries. The reverse is true for gaseous layers. Up to now no theoretical explanation of this difference has been given. It is only in recent years that a particular form of cellular convection has become known and investigated. We refer to the toroid convection cells for which theoretical evidence was found by Zierep (1958) and for which experimental evidence was given by Tippelskirch (1959). Contrary to Benard's cellular convection, which is
296
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE TABLE XXVIII THEORETICAL FIGURES FOR CONVECTION CELLS a
Cell shape Character of boundaries Square Two free One free, one rigid Two rigid a
R c rlt
b[d
4.00 3.28 2.8
Strip 2.83 2.34 2.00
Hexagon 1.89 1.56 1.34
657.5 1100.7 1707.8
After Stommel (l947a).
initiated by a heat source uniformly distributed over a plane, the toroid convection originates from a point source of heat. The resulting convective motion consists of concentric annular cells around the point of instability. Below the critical temperature gradient (according to Rayleigh's formula) this pattern depends on the horizontal temperature differences; above that value it is transformed into the normal Benard form of cellular convection. The significance of this new convective motion for practical application is not yet fully understood. Turning to marine applications, we should endeavor to find out whether the convective motions described above can also be observed in the marine atmosphere. In general, meteorologists are not in such a privileged situation as are hydrologists, who have occasionally been favored in their efforts toward observing convection cells in water by pure chance, e.g., by a melting ice cover (Woodcock and Riley, 1947) or wet snow squash (H. G. Neumann, 1958) on ponds which thus readily revealed convective structures. In the marine atmosphere, however, ingenious observational techniques had to be applied before any relevant results could be obtained. Woodcock (1940), for instance, interpreted the flight tactics of herring gulls off the New England coast of the United States in terms of convective motion. With cold air over warmer water the birds usually soared in circles when the wind speed ranged from 0 to about 7 meters/sec. This soaring routine seemed to indicate that cellular convection cells were present under such circumstances. For wind speeds between 7 and 13 meters/sec linear soaring prevailed, i.e., the birds soared straight to windward, gaining altitude rapidly. This technique argues in favor of longitudinal roll vortices, the up-moving currents at the striplike cell boundaries being used by the birds. At still greater wind speeds and, in general, for air warmer than water, no continuous
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
297
free soaring could be observed. Thus the regular mesoscale convection pattern apparently does not exist either with high winds or with stable stratification. An interesting additional observation was that the birds did not appear at great distances from the coast until fall, when cold continental air begins to flow out over the warmer sea. In order to get more quantitative results, Woodcock and Wyman (1947) subsequently undertook special investigations, using chemical smoke released from ships and airplanes. The lateral and vertical displacements of the smoke plumes were considerable, so that one portion of the smoke plume changed its direction with respect to another by as much as 47°, although the surface wind direction fluctuated by no more than 5°. All thesedisplacements could easily be reconciled with the concept of convection cells although some difficulty arose from the fact that the orientation of the smoke plume relative to the convection cells was not exactly known but had to be deduced from the observations. The side length of these cells was of the order of 500 meters; the average height was estimated at about 300 meters and seemed to coincide with the height of the homogeneous layer. Thus the ratio between side length and height of the cells appears to be in rough conformity with the theoretical values of Table XXVIII. The vertical motion reached speeds of about 1 meter jsec. In addition to the medium-scale motions caused by cellular convection, small scale turbulence was present and made visible by the diffuse expansion of the smoke plumes. Cellular convection is, however, not confined to the subcloud layer. Quite recently cellular cloud patterns over the Atlantic and Pacific Oceans were revealed by photographs from the Tiros meteorological satellites. Krueger and Fritz (1961) related pictures taken by Tiros I to conventional meteorological observations and found that the cellular cloud formations reported by the satellite occurred in regions where there was a homogeneous layer of about 1500 meters thickness with little variation in wind speed and direction. Superimposed over this convective layer was another one of greater stability which impeded the convection. Although the pictures showed many similarities between the observed cloud organization and the classical Benard convection, there were, however, many important physical differences. Since the diameter of the cells ranged between 20 and 50 nautical miles, the ratio of diameter to depth was about ten times as large as those given in Table XXVIII. It should be noticed that the physical parameters on which Table XXVIII is based are of molecular scale. According to Rayleigh's theory, it is true, the geometry of the cells
298
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
does not depend upon the physical parameters. But in this derivation there are not taken into account several features that are essential in turbulent atmospheric motions, for example, the fact that the horizontal eddy transfer coefficients are large when compared with the vertical ones if a comparatively shallow homogeneous layer is topped by a well-defined inversion and a statically stable layer. Priestley (1962) suggested that such conditions would occur mainly over the oceans, in particular with shallow polar outbreaks, and might be responsible for the geometrical distortion of the convection cells as observed by Tiros 1. Thus, the theory needs some relevant refinement before it is properly applicable to atmospheric convective motions at sea. In addition to the differences in scale there were differences in structure. Contrary to the simple circulation observed in Benard cells, the Tiros I pictures indicated several scales of motions, the cell walls often being made up of individual cloud elements. On the other hand, it is not entirely unreasonable to assume that the theoretical approach, by which Langwell (1951) attempted to provide an explanation of the "clear areas" within the trade wind cloud layer (see Section 5.3.2.4), might serve as a successful model for the cellular cloud pattern observed from Tiros 1. Langwell derived the characteristics of a two-dimensional convection cell within the cloud layer, the particular problem being to investigate whether cool moist pockets under an inversion, in a conditionally stable atmosphere, could initiate cellular, convective circulation. Applying the equations of motion, continuity, and the first law of thermodynamics, Langwell found, in theory, that large, slow-moving cells with diameters of about 10-20 km were possible and could persist for from I to 2 hours, thus constituting a semipermanent feature of atmospheric motion.
5.3.2.3. The Transitional Layer in the Trade Flow. As can be seen in Fig. 91 the trade wind homogeneous layer is topped by another layer wherein the moisture lapse rate is one order of magnitude greater than in the mixed layer below. The temperature profile, however, is much more stable than in the homogeneous layer while, owing to rapid drying, the virtual temperature lapse rate is usually rather steep and similar to that of the cloud layer above. For the latter reason the layer described is termed "transitional layer" since it forms a zone of transition between the homogeneous layer below it and the cloud layer above it. In general it is a rather narrow stratum just below or above the height of the cumulus base. Some figures characteristic of the transitional layer have been summarized in Table XXIX.
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
299
Examination of the data found with a strong trade regime in 1946 reveals that in clear zones the transition layer was always present and had a mean depth of about 200 meters, the lapse rate of the mixing ratio being 22.5 times that rate in the homogeneous layer below. The lapse rates of temperature and virtual temperature amounted to 47 per cent and 70 per cent of the dry-adiabatic gradient, respectively. In cloudy regions there was no transitional layer in about 55 per cent of the cases. However, in about 44 per cent of this portion a layer of either somewhat more stable temperature lapse rate or somewhat steeper moisture gradient intervened between the top of the homogeneous layer and the main body of the cloud layer, thus leading-in combination with 'the 45 per cent of the cases where a transition layer was clearly recognizable-to an average depth of about 140 meters. With a weak trade wind regime (1953), the transition layer as found in clear areas was shallower (125 meters) and distinguished by a markedly greater moisture and virtual temperature lapse rate than in the case of a strong trade flow. In cloudy zones the transitional layer was almost completely missing. Summarizing, we may say that the transition layer seems to be sharply defined in clear spaces whereas in cloudy areas it is either missing or spreads out over the lower 400 meters or so of the cloud layer. Thus we may regard the transition layer as the manifestation of the compensatory subsidence in the clear areas. 5.3.2.4 The Characteristics of the Trade Wind Cloud Layer. The cloud layer extends from the condensation level up to the base of the trade inversion. This definition is valid for both clear and cloudy regions, without any regard to the actual vertical extension of the clouds which, in a considerable part, do not reach the trade inversion. For quantitative information Table XXX has been compiled from data published by Malkus (1958). From this tabulation we may infer that-contrary to the results obtained for the homogeneous and transition layers where pronounced differences existed between clear and cloudy areas as well as between strong and weak trade flow-the conditions within the cloud layer appeared to be rather uniform and that, in particular, no strong deviations were observed between the two measuring periods or between clear and cloudy zones. Bearing in mind the distinct differences of cumulus convection noticed between 1946 and 1953 we might thus be led to assume that the formation of oceanic cumulus clouds is controlled largely by processes in the subcloud layer.
300
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE TABLE
XXIX
CHARACTERISTIC FIGURES OF THE TRANSITIONAL LAYER OVER THE CARIBBEAN SEAa
Lapse rate of Trade wind regime
Depth (meters)
Relative humidity
co
Strong (April, 1946) Clear Cloudy Average
197 138b 177.
Weak (MarchApril, 1953) Clear Cloudy Average
125 Missing Missing
81 88 84
80 Missing Missing
Mixing ratio
Temperature
Virtual temperature (oC/100 meters)
(100 metersrt
eC/lOO meters)
-14.4 x 10-4 - 5'.0 x 10-4 -12.6 x 10-4
-0.47 -0.79 -0.57
-0.70 -0.995 -0.80
-24.5 x 10-4
-0.51 Missing Missing
-0.88
From Malkus (1958). Effectively or totally missing in five cases out of nine. Average given for eight cases out of nine. a b
TABLE
XXX
CHARACTERISTIC FIGURES OF THE CLOUD LAYER OVER THE CARIBBEAN SEA a
Lapse rate of
Trade wind regime
Strong (April, 1946) Clear Cloudy Average Weak (MarchApril, 1953) Clear Cloudy Average a
Depth (meters)
Relative humidity
co
76 79 1328
77
77
1343
From Malkus (1958).
81 79
Height of Mixing ratio Temperature Virtual trade wind (100 metersr! (oC/100 temperature inversion (meters) meters) (oC/100 meters)
-2.4 x 10-4 - 5.2 x 10- 4 -3.5 x 10-4
-0.63 -0.61 -0.62
-0.69 -0.71 -0.70
2080
- 3.1 X 10- 4 -4.6 x 10-4 -3.6 x 10- 4
-0.63 -0.52 -0.58
-0.69 -0.60 -0.65
1932
5.3
301
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
The picture is somewhat changed if we examine the moisture structure of the cloud layer in greater detail. An upward decrease of moisture that is somewhat faster in cloudy regions than in the clear can be noticed in Table XXX. For further investigation of this subject the lapse rates of the mixing ratio were computed separately for each third of the cloud layer (Table XXXI). Marked differences appear there. They occur not only between clear and cloudy areas but also between strong and weak trade flow. In particular, it should be noted that in most cases the in-cloud lapse rates are considerably in excess of the moist-adiabatic rate. TABLE XXXI MOISTURE STRUCTURE OF THE CLOUD LAYERa
Trade wind regime
Lapse rate of mixing ratio? (100 meters)-l in the cloud layer Lower third
Middle third
Upper third
Strong (April, 1946) Clear Cloudy Average
-2.9 x 10- 4 -8.8 x 10- 4 -5.6 x 10- 4
-0.5 -4.8 -2.5
X
10-4 10- 4 10- 4
+0.8 -0.3 +0.2
X
Weak (MarchApril, 1953) Clear Cloudy Average
-3.5 x 10- 4 -4.7 x 10- 4 -3.6 x 10- 4
-2.3 -5.1 -3.6
X
10- 4 10- 4 10- 4
-5.8 -5.9 -5.8
X
a b
X X
X X
X X
X X
10-4 10-4 10- 4
10- 4 10- 4 10- 4
From Malkus (1958). Saturated adiabatic lapse rate of mixing ratio --2.4 x 10- 4 •
These observational findings can be interpreted as follows: The strong trade wind regime of 1946 was distinguished by a large upward moisture gradient (nearly four times the moist-adiabatic one) in the lower third of the cloud layer in cloudy areas. It was nearly halved in the middle third and almost vanished in the upper third. An explanation of the rapid moisture decrease in the lower third was provided by cloud photographs' which showed that medium- and large-sized clouds were mostly surrounded by great numbers of small cloudlets, only a few hundred meters in diameter and thickness and confined to the lower cloud layer. Observations further suggested that the big clouds were formed from an aggregation of these cloudlets.
302
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
In contrast to this situation the average upward moisture gradient in the cloud layer during the weak trade wind regime of 1953 was rather uniform in the vertical and actually increased by a substantial amount from the middle to the upper third of the layer. In cloudy areas there was even observed a continuous increase from the bottom to the top of the cloud layer. Cloud photographs reveal that cumulus formation was poor in general but that a certain fraction of the cumuli penetrated the upper cloud layer and spread out below the trade inversion, thus providing a nearly constant vertical distribution of moisture throughout the entire upper part of the cloud layer (in cloudy areas as well as in clear ones). To a minor degree the same phenomenon could be also observed during the period of strong trade flow. But here a pronounced difference was found between cloudy and clear areas. In cloudy regions the upward moisture decrease became very small near the trade inversion but did not vanish since moisture was permanently supplied from below by cloud activity. In clear zones this supply was lacking, injections from cloudy areas being the only source of moisture at upper levels. The cloud form that can be considered as typical for the trade wind region is the "oceanic trade cumulus," which may be characterized by the following specifications (Malkus, 1958): Horizontal extension = 100 meters-2 km Vertical thickness = 300 meters-3 km Updraft = 0.5-5 meters/sec Since generally the vertical development of these clouds is limited by the trade inversion they often have a "blocklike" appearance. Oceanic trade cumuli commonly appear in irregular groups or clusters of about 10-50 km across and separated by somewhat wider clear areas. Apparently this structure does not alter from day to night. Other types of cumulus clouds can also be found at times, e.g. : "Cumulus humilis" or "fracto cumulus" if the moist layer is shallow and subsidence prevails; "Chimney clouds" if the trade inversion is weak, thus allowing the penetration of the cloud tops through it; "Cumulus congestus" if the cloud tops reach a considerable height, roughly more than 3-4 km, and the resulting cumulus massif presents a mountainous appearance; "Cumulonimbus" if synoptic-scale convergence leads to condensation processes extending far above the freezing level and occasionally reaching the height of the tropopause.
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
303
Showers of different intensity and duration according to the cloud form may fall from nearly all types of cumulus clouds, except fracto cumulus. Some disturbance was caused by the observational evidence, frequently obtained, that cloudy areas were colder than clear zones nearby, in spite of the fact that cloudy regions are considered equivalent to convergence and to ascending motion due to buoyancy. This paradox proved to be a sampling effect. The growing and decaying clouds could not be treated separately. Intensive and detailed investigation (Malkus, 1958; Bunker, 1959) showed that a cloudy region contains only a small fraction (5 per cent) of actively buoyant, rapidly rising updrafts, a similarly small portion (5 per cent) of strongly sinking downdrafts, about 40 per cent of decaying, inactive, and slowly subsiding cloud matter, and around 50 per cent clear spaces between clouds. From this, the following space averages result: Draft + 5 ern/sec Mixing ratio anomaly (vs. clear) = + 1.5 gm/kg Virtual temperature anomaly (vs. clear) = - 0.14°C which show a negative anomaly of virtual temperature although the few active clouds of the group were virtually 2.0°C warmer than their nearby surroundings. Thus, previously divergent statements could be reconciled. The influence of wind shear on cumulus development was studied by Malkus (1952a, 1958). In one of her studies (1952a) it is shown how the slopes of cumulus clouds are related to external wind shear. In particular, the slant of the clouds is considered representative of the interaction between convective elements and the surrounding air. In the latter study the effect of wind shear on cumulus formation was investigated by combining the double theodolite pilot balloon runs made in 1953 by Charnock et al. (1956) near Anegada in the Caribbean Sea together with the aircraft temperature and moisture soundings obtained during the 1953 expedition of the Woods Hole Oceanographic Institution in an observing area that was, for the most part, within 20 miles of Anegada. Some relevant figures have been assembled in Table XXXII, from which we may infer that cumulus development seems to be related to the height of the maximum wind and, in particular, to the wind shear in the lowest 100 meters of the cloud layer. On days with good convection the wind maximum was usually near or well above the cloud base so that the lower part of the cloud layer was only subject to small wind shear. On poor convection days, however, the wind maximum was found considerably below the cloud
304
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
base, resulting in a strong negative wind shear in the lower cloud layer. This evidence might lead us to believe that cumulus development is probably impeded by strong wind shear. TABLE XXXII INFLUENCE OF WIND SHEAR ON CUMULUS DEVELOPMENTa
Mean wind speed
Mean wind shear
Height of maximum wind
(meter secr-)
(meter sec" km")
(meters)
Good convection days Poor convection days Overall average
a
5.8 3.8 4.8
3.1 3.4 3.2
699 524 611
Wind shear in the lowest 100 meters of the cloud layer (meter sec'< krrr') 1.5 4.7 3.1
From Malkus (1958).
5.3.2.5 The Mechanism of the Trade Wind Moist Layer. The trade wind moist layer comprises the four layers described in the foregoing paragraphs, namely the superadiabatic bottom layer, the homogeneous layer, the transitional layer (these three combined forming the subcloud layer), and the cloud layer. Thus the moist layer extends from the surface of the sea, where it gains its moisture by evaporation, up to the trade inversion. The schematic diagram given in Fig. 92 illustrates the situation and also indicates the function that the trade wind moist layer has to perform. This function may be roughly outlined as follows: From the sea surface, sensible and latent heat is transferred to the overlying air by the processes of heat flux and evaporation which, initially, are of molecular scale. Dynamic turbulence and thermal buoyant forces provide for vertical (and horizontal) spreading while the air is transported to the intertropical convergence zone by the trade flow. Thus larger and larger scales of motion come into play. Below the condensation level, i.e., within the subcloud layer, unsaturated convective turbulence dominates. Above that height some of the turbulent eddies condense to small cloudlets which grow and join to form larger trade cumuli. These clouds, by expansion and by interaction with their environment, try to distribute the moisture
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
305
over the entire cloud layer. If the updraft is sufficiently strong, they may occasionally be able to penetrate into the dry air above the trade inversion, thus gradually raising and weakening this upper boundary of the moist layer. Finally, in the downstream parts of the trade flow Dry, stobie, sinking air
>000
o
~-
-
--
117'' ' ' '- -----
2000
Claud layer
1500
1500
~
Q;
0;
5
:;:
s:
a>
~
a>
1000
(
r----~"~~. -r-~~~;~~;'~ICumulus base
500
-
-
----
-
layer
1000
iU
I
500
Evaporation
_1_ ~p~a'::io~a~ ~y~
[
_
Sea surface Cloudy area
o
Clear area
FIG. 92. The trade wind moist layer over the Caribbean Sea (schematic vertical cross section).
near the equatorial convergence zone, the inversion disappears and the trade cumuli grow into enormous cumulonimbus clouds carrying latent heat up to the tropopause, from where the released heat is transferred aloft to the middle latitudes, thus contributing to the maintenance of the general circulation. This crude and sketchy description already shows that the trade wind moist layer forms an important link in the chain of the atmospheric
306
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
energy transport and supply. The question of what consequences would occur arises, e.g., in the trade flow, in the equatorial convergence zone, or even in the Westerlies, if the amount of moisture supplied by evaporation to the trade wind moist layer were, by some cause, substantially reduced. How can we explain the altogether different trade flow conditions experienced over the Caribbean Sea in the spring of 1946 and in the spring of 1953? Shall we attribute these variations in cumulus development to fluctuations in the subcloud layer or to fluctuations in the cloud layer? It is quite clear that a thorough knowledge of the mechanism effective in the trade wind moist layer would bring us nearer to the solution of the problems indicated above. In this monograph, which is only concerned with the marine atmosphere, we do not intend, though, to embark on questions of the general circulation. The latter represents a global problem, and hence it can only be treated globally. We shall rather limit our consideration to describing the mechanism of cumulus generation in the trade wind moist layer without, however, dealing in detail with the physics of the condensation process, which is a general problem and not a specifically maritime one. For further information on the subjects not treated here see, for example, Riehl (1954) and Malkus (1958). Within the scope of this monograph the following question is of major importance. What is the function of the homogeneous layer as regards the formation of the trade cumuli in the cloud layer above it? Does the homogeneous layer furnish the "roots" of the cumuli? The observational evidence is not easily understood. When gathering some information on turbulence in the trade wind moist layer from accelerometer records of the vertical motions of the airplane employed for their investigation, Bunker et al. (1949) experienced no significant differences in turbulence in the homogeneous layer when the plane was flying under the clouds and in clear areas. This comes out very distinctly in Fig. 93. Similarly, the fluctuations of water vapor, which were rather strong in the mixed layer, did not show any pronounced differences between cloudy and clear areas. Moreover, the fluctuations of temperature and moisture as observed in the homogeneous layer tended to be out of phase while in convective layers coincidence of phase is prevalent. Further evidence can finally be taken from Fig. 94, which exhibits the maximum accelerations observed at different heights of the moist layer in clear areas as well as in cloudy ones. The clear air curve, which Bunker et al. (1949) chiefly ascribed to dynamic turbulence originating from surface friction, has a maximum of 0.2 g at about 300 meters and decreases
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
307
continually to a value of 0.025 g at 2000 meters. The vertical motions attributed to cloud development start at about 600 meters, i.e., at the top of the homogeneous layer. They are supposed to be clearly separated from this layer. Clouds
Clear areas
10.IOq
Homogeneous layer
055 0
5 10 15 20 3040 50 60 5 10 15 20 25 TIme (seconds)
FIG. 93. Accelerometer records taken in the homogeneous layer and in the cloud layer (From Bunker et al., 1949.) Unreduced tracings. Zero acceleration line coincides with height at which the run was made. Double-headed arrow indicates displacement equivalent to 0.10 g.
From these findings, Bunker et at. (1949) concluded that the convection which is effective in the cloud layer is obviously not related to any recognizable increase of vertical turbulence in the homogeneous layer below it. The convective motions in the cloud layer neither originate in thermals of the mixed layer nor do they extend an appreciable distance down into that layer. This agrees with the observational fact, mentioned in Section 5.3.2.1, that stability is increased in the upper part of the mixed layer which would damp out any convective motion generated at lower levels before the cloud base is reached. Consequently, organized thermal-convective circulations, e.g., cellular convection, in the homogeneous layer can be excluded as a possible cause for cumulus generation in the cloud layer. Occasional turbulent eddies hitting the condensation level at random can only be responsible for the formation of small cloudlets
308
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
but they do not explain the existence of cloud groups. Furthermore, we may leave aside such causes of updraft as differential heating due to islands, flow over barriers, and synoptic-scale convergence, bebecause these phenomena are irrelevant to the formation of the normal trade cumuli.
OJ.
2000 1900 1800 1700 1600
. ..
1500 1400 1300
'"
~
!
s:
'"
Q; I
1200 1100 1000 900 800 700 600
• In clouds
500
x In clear
400 300 200 100 0
0.1
0.2
0.3
0.4
05
Accolorat;ans 19)
FIG. 94. Maximum accelerations measured at different heights in clear air and in clouds in the trade wind moist layer. (From Bunker et al., 1949.)
Bearing in mind that the height of the homogeneous layer was found distinctly greater in cloudy areas than in clear regions, we should rather seek the origin of the trade cumuli in gradual variations of the thickness of the mixed layer. A corresponding mechanism has been suggested by Langwell (1953), who studied the oscillations of the boundary between the homogeneous layer and the stable-and sometimes even isothermalstratum above it. Unstable gravitational waves were found physically plausible. If a depth of 600 meters was assumed for the mixed layer, the upper limit of unstable wavelengths was calculated to be 2 km. Thus these oscillations would permit the air in the lower mixed layer
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
309
to reach saturation in limited areas provided that the oscillating interface is then located at or above the lifting condensation level. In this way, moisture and latent heat could be transferred from the mixed layer to the cloud layer whereby trade cumuli are formed over the ocean. The calculated cloud diameter seems rather low, however, particularly if one considers that oceanic trade cumuli commonly appear in groups about 10-50 km in diameter and are separated by somewhat larger clear areas. Therefore the processes which are at work below clouds should permit rather large numbers of moist air parcels to reach the condensation level in particular localities simultaneously. When searching for inhomogeneities on a 10-50 km scale, Malkus (1957) encountered sea-surface temperature anomalies which seemed to be closely related to the pattern of cumulus clouds. Some details of the "warm spots" and "cold spots" of the sea surface have been given in Section 5.1.3 and need not be repeated here. We can confine ourselves to describing their effects on the air structure. A remarkable example of an association of cumulus clouds and turbid water has been reported by Isaacs (1962) from the Gulf of Bengal. He observed a circular mass of cumulus clouds, about 60 miles in diameter and reaching, in the center, up to about 7.5 km in altitude, which was situated directly above an equally circular region of turbid water originating from the river Ganges. The phenomenon was attributed to the turbid water being excessively heated by its high solar absorption, thus giving rise to evaporation and convection. Observations from the Trades also showed that oceanic cloud groups were always associated with warm spots and frequently developed at their downwind boundary. In general they were slightly displaced downwind relative to warm spots, thus being very similar to clouds generated over an island or a hill. Therefore, Malkus (1957) was able to apply the island model of differential heating as a first approximation to the horizontally convergent circulation across a warm spot at the sea surface and to the accompanying updrafts above it. Naturally, in the case of the warm spots concerned, the magnitude and scale of circulation superimposed upon the mean wind flow will be strongly reduced as compared with those over an island. A quantitative relation between the observed temperature excess at the sea surface and the main features of the heat-produced circulation across a warm spot could be derived in this way. The relations ascertained in this way were tested satisfactorily for three islands of different sizes in the Atlantic trade wind zone.
310
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
When this model was applied to an oceanic warm spot of 0.2°C in amplitude and of 10 km horizontal extent downwind the following circulation resulted: The average horizontal wind difference at the surface amounted to 0.7 meters/sec, and if the trade wind speed is 6.7 meters/sec the circulation reverses at the height of 1350 meters. The air takes about 25 minutes to cross the warm spot and the updraft at the cloud base (650 meters) is 4.3 em/sec. Thus a streamline starting at that height at the upwind edge is estimated to have risen about 65 meters at the downwind boundary. Ma1kus (1957) further showed that if the inflow air has the typical moisture distribution of a clear area (see Tables XXVII and XXIX and if, in order to satisfy continuity, the amount of air and water vapor entering per second at the upwind side equals the outflow per second through the top of the subcloud layer and through the downwind boundary, then the moisture distribution at the latter place is consistent with that gained in cloudy zones. On the whole, a remarkable upward moisture transport seems to be effected by motions of the scale considered which thus contribute substantially to the upward pumping of water vapor from the sea surface through the homogeneous layer into the cloud layer of the Trades. Small-scale turbulence alone would require rather high values of the Austausch coefficient (see Bunker et al., 1949) if it were held responsible for that moisture transport. Therefore this is no sufficient explanation of the moisture distributions found in the trade wind moist layer. Eddy turbulent transport is of importance mainly as a brake upon convection and in describing the exchange between the clouds and their surroundings. A complete discussion of this subject would, however, necessitate an examination of the circulation occurring both in the cloudy and in the clear areas. This was attempted by Malkus (1958), who advanced a physical model describing the processes at work in the trade wind moist layer. In this paper there were chiefly discussed the following two alternative concepts: (1) Individual cloud groups are stationary or very slowly moving downwind; thus the trade flow passes through them, undergoing rise and subsidence. (2) No relative motion occurs between individual cloud groups and the trade flow while new cloud groups generate and vanish in the latter at random. There was not sufficient observational evidence to be found and
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
311
so it was impossible to decide which model would come nearest to reality. Of course, the real situation may lie between the two extremes. If we adhere to the "warm spot" scheme described above, the cloud group as a whole would remain in nearly the same location for at least 3 to 4 hours, despite a wind speed of 5-7 meters/sec. Individual clouds will form after the air flow has crossed the upwind boundary and will dissipate some 30 minutes later, shortly after passing the temperature step down, several kilometers downwind. Summarizing, we may say that trade wind cumuli and cumulus groups are thermally direct circulation systems, driven by buoyancy obtained from release of latent heat. It is their function to distribute the moisture supplied by evaporation over the entire cloud layer. Cloud groups seem to be associated with weakly convergent flows superimposed upon the mean trade wind and set up by inhomogeneities of the sea-surface temperature on a 10-30 km scale. The discussion given so far has dealt chiefly with the temperature and wind conditions which may lead to convection and condensation. A related question is whether there is a subcloud humidity structure which could be made responsible for certain features of the trade flow, such as the sequence of orographic showers, for example Woodcock (1960) reported that thirty-four showers passed over one rain gauge station on Hawaii while 105 km of air passed in the same period. This could be explained if the humidity structure of the air mass in question varied appropriately with an average wavelength of 3 km. According to Bunker (1962) observations of the mixing ratio were made simultaneously at three levels in the subcloud layer of the trade wind east of the Bahama island of Eleuthera with the particular aim of investigating whether there are similar-sized moist and dry parcels of about 2 km in diameter in the mixed layer. Spectral analysis of the humidity records showed that roughly 75 per cent of the variance of the mixing ratio was contributed by wavelengths longer than 3.75 km, and 22 per cent by the wavelengths between 3.75 and 1 km. Although the concentration lay in longer wavelengths, the moisture variations corresponding to wavelengths between 3.75 and 1 km were of such a magnitude [mean standard deviation 0.14 grn/kg (maximum 0.42 gm/kg) ; mean temperature difference generated by the condensation of the excess water vapor 0.23°C (maximum 0.67° C); that many of these variations appeared to be capable of producing shower cells if the air was forced up a mountain slope. Of course, there may be other effective mechanisms, such as gravitational waves, flow instabilities, and random turbulent gusts. Hence, final evidence as to
312
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
the cause of the sequence of orographic showers in the Trades is sti11lacking.
5.3.2.6 Models of Cumulus Formation and Maintenance. In the foregoing paragraphs the subject of cloud formation was treated in a rather summary manner. The properties of the trade wind moist layer were described, and an attempt was made to arrive at a physical interpretation of the processes inherent. Almost nothing has been said either on the nature of the cumulus clouds themselves or on the forces acting in them. This point is going to be tackled in the following. We are now interested in the formation and structure of the convective elements themselves. A detailed and complete treatment of cloud dynamics must, however, not be expected. It would lie outside the scope of this monograph which is only concerned with the maritime aspects of atmospheric processes. Regarding the general and basic fact of cloud dynamics, as well as of cloud physics, reference is made to the representations given by Moller (1951b), Austin (1951), Malkus (1952b), Riehl (1954), and Ludlam and Mason (1957). Hence, we can content ourselves with briefly reviewing the principal features of cloud formation. In the simplest approach there is assumed a buoyant air parcel which does not mix with its surroundings. In addition, no compensating motions are supposed to occur in the environment. This noninteracting, buoyant parcel first rises dry-adiabatically, then, after passing the condensation level, it is saturated and, provided that the surroundings are cooler, it follows the moist-adiabatic lapse rate until its path intersects the sounding representing the environment. The buoyancy acceleration B is then given by Tv - Tv' B = g (5.53) Tv' where Tv is the virtual absolute temperature within the parcel and Tv' is the corresponding temperature of the surroundings (g = acceleration of gravity). This well-known parcel model meets with severe difficulties. First, the acceleration provided by it is much more powerful than is usually observed. Secondly, the lapse rate inside the clouds is not moist-adiabatic, as required by the model, but considerably steeper (compare Section 5.3.2.4). Furthermore, the tops of trade wind cumuli are generally much below the level which the cloud air could reach if it rose moist-adiabatically from the cloud base (Stommel, 1947b). Finally, the liquid water content in cumulus clouds without precipitation is considerably smaller (about one-fifth) than
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
313
that predicted by the parcel method, which agrees with the fact that the existence of "holes" or regions of apparent zero liquid water content has been verified inside cumuli (Squires, 1958). The latter observation indicates that the mixing in of dry air is a normal feature of these clouds. The deficiencies of the parcel model must be ascribed to the disregard of the following effects: (1) The mass continuity. (2) The interaction between the buoyant parcel and its surroundings. The continuity of mass can be secured if both the upward and the downward motions are taken into account within a limited area (slice model; Bjerknes, 1938). In the absence of divergence or convergence, the upward and downward mass transport across a reference level must be equal. Small areas of strong updrafts will thus be accompanied by weak downdraft in large areas, for instance, by a compensatory sinking of the environment which causes a substantial reduction of the excessive buoyancy given by the parcel method. The interaction between the rising parcel and its environment can be accounted for in different ways. The entrainment model advanced by Stommel (1947b, 1951) rests on the hypothesis that the clouds entrain air from their surroundings as a jet of rising air embedded in relatively quiescent environment does. The major reduction of vertical momentum as compared with that of the noninteracting parcel arises from buoyancy decrease by dilution. Steady state is assumed as well as complete horizontal mixing within the cloud. The entrainment model has been of value mainly in relating observations of buoyancy, updraft, and mixing, as well as in describing the influences of environmental properties on the structure of the cloud. In spite of this there remain the following difficulties in our understanding of cloud dynamics: (1) The downward force due to the weight of the condensed water is neglected. (2) The frictional and turbulent drag forces exerted by the environment on an element of rising air are not taken into consideration. (3) The steady state model says little about the mechanism of entrainment and nothing about the early or late phases of the life cycle of a cloud. The time dependence, missing in the entrainment model, is introduced with the bubble model (Scorer and Ludlam, 1953), which may
314
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
be considered as the next logical step forward from the entrainment model. Time-lapse cloud films, as well as a comparison of these with experiments on bubbles in water, suggest the interpretation of a convective element as a bubble of rising air (also called "thermal") with a characteristic diameter ranging between 100 meters and 2 km. The outer face of such a bubble is eroded by the relative descent of the outside air, thus generating a "wake" in which the surrounding air is mixed with the air of the bubble itself. Above the condensation level the bubble loses cloud material to its en.vironment, and the "wake," behind the rising bubble, is formed of a mixture of cloud and environment. (Fig. 95.) It should be emphasized that, in contrast to the entrain.ment model, no dilution of the bubble cap is assumed.
,
~,
, ,, I
I
~I
,,
, ,,,
~
, ,,, I
I
FIG. 95. Bubble model of cumulus formation. Velocity field around a rising bubble. Left side: Dry ascent; velocity upward at the edges of the wake; upward displacement of the environment. Right side: Condensation in the bubble; sinking motion at the edges of the wake caused by chilling due to evaporation; downward displacement of the environment. (From Scorer and Ludlam, 1953.)
The reduction of vertical momentum is merely caused by the form drag which implies the erosion of the bubble. By this process the bubble is wasted at last, leaving the turbulent mixed wake which causes the environmental air above the original cloud mass to be enriched with
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
315
moisture and which facilitates further convective motion by diminishing the erosion of the subsequent bubble. Consequently, this bubble may penetrate farther than the first one. Successive rising bubbles result in the gradual upward extension of cloud mass. Hence the cumulus cloud can be interpreted as an aggregation of buoyant bubbles of saturated air and their wakes. A cloud penetrating to great heights is generally built up by the successive release of single bubbles. If the vertical wind distribution is subject to shear, the higher winds above the original cloud carry the wake, produced by preceding bubbles, downstream relative to the parent cloud mass. Consequently, the following bubbles, whose development is favored by an environment enriched with moisture, will also tend to appear farther downwind. Thus, the growth of a cumulus is greatest on its downshear side. With strong wind shear present, successive bubbles may even be unable to interact, with the result that the formation of cloud towers would be impeded. The bubble theory was supplemented by Squires (1960), who attributed particular stress to downdrafts of dry air originating at the top of the cloud and assisted by evaporative cooling. It is suggested that these downdrafts penetrate the cloud to a significant depth, thus providing a negative feedback mechanism of vertical mixing which limits the liquid water content of the cloud. Considered qualitatively, the bubble concept conforms well to observation. For instance, time lapse movies of overwater trade cumuli taken by Harrington (1958) indicated that the rise of cloud tops was not continuous, but in steps, which supports the bubble model. Similar conclusions can be drawn from the cross sections through trade-cumulus clouds executed by means of a slow-flying aircraft (Malkus, 1954). The measured draft structures of two cumuli have been summarized in Fig. 96 (A and B). The vertical velocities indicated therein were obtained by integration of the records of an accelerometer in a manner similar to that described by Bunker (1955) (see Section 4.4.1.2). The aggregation of several small neighboring updrafts or bubbles into a large cloud is clearly visible particularly in the lower altitudes. The upper portions of the two clouds, or the towers, belonged to widely differing phases of their life cycles. Cloud A was still in a very active phase with substantial updrafts dominating. On the contrary, cloud B represented a more mature stage characterized by strong downdrafts at its top. Further support for the bubble model was provided by a comparison of cumulus observations and simultaneous soundings made
HEIGHT (KM ABOVE SEA LEVEL)
2.0
A
1.8
1.6
2.0
!2MPS
1.8
WIND (MPS)
1.6
24
1.4
14 1.2
38
1.2
4.9 1.0
1.0
2.0
HEIGHT(KM ABOVE SEA LEVEL)
WIND (MPS) 1.6
1.6
2.0
B
2 MPS
1.8
5:3 ~
1.6
----.;::------=;;:;<W~~+_-----'''''"'''''~---':::-.-----=_-__i
1.4
1.4
i{ (-:-
6.2 1.2
1.2
6.6 1.0
0.6
6.9 0.6
6.7 6.4
0.6
0.6 -200-
-DISTANCE ,METERS---.
FIG. 96. Draft structure of two trade cumuli in different phases of development, combined from airplane records and cloud photographs. (From Malkus, 1954.) Curves represent vertical draft velocities (running averages over 150 meters distance) at relevant altitudes, their origin being thin horizontal lines at each level. Winds obtained by double drift of aircraft are shown at the extreme left. Calculated slopes of clouds are given by heavy curved lines.
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
317
over the North Atlantic (Ludlam and Scorer, 1953). With large clouds, the tops were nearly always found very close to the equilibrium level of the parcel theory. These results suggest that with large clouds the bubbles seem to be rather well protected against dilution when rising through the cloud mass, and that dilution and evaporation are only effective after the bubbles have emerged at the top. Although nothing is said on how the bubble motion is initially created by buoyancy, the bubble concept contains considerable advantages as compared with the other approaches mentioned above, because it attempts to describe the mechanism of entrainment, i.e., the interaction of cloud elements with one another as well as with their environment. 5.3.2.7 Quantitative Treatment of the Bubble Model. A quantitative approach to the bubble model was attempted by Malkus and Scorer (1955), who described the rise of a single, isolated, and saturated bubble by the following differential equation: dwjdt + Kw 2 = B (5.54)
where w = ascent velocity of the bubble K = drag coefficient B = buoyancy acceleration given by Eq. (5.53) minus a correction for suspended hydro meteors According to Eq. (5.54), the acceleration of the bubble cap equals the resultant of the forces (per unit mass) acting upon it, i.e., the buoyancy minus the drag. If these two are balanced, the acceleration of the bubble becomes zero and its limiting velocity WL is given by WL =
(BjK)1I2
(5.55)
The drag coefficient K can be related to the radius R of the curvature of the rounded bubble cap by K = 9j4R
(5.56)
if it is supposed that bubbles in the atmosphere can be treated in a manner analogous to air bubbles in a liquid. Further, it is assumed that the radius of curvature of the bubble cap decreases with the time t in the following manner: (5.57) R = EB( -t) (t is taken negative during the bubble's lifetime, R being zero for t = 0). Since Eq. (5.57) describes the erosion of the ascending bubble, E is called the erosion parameter. After combining Eqs. (5.54),
318
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
(5.56), and (5.57) we arrive at an expression for the erosion parameter E which only depends on the time, on the bubble's ascent velocity, its acceleration, and its buoyancy. In other words: The remarkable result is obtained that the life cycle of the isolated bubble, once it is formed, does not, in the first approximation, depend on environmental parameters except lapse rate. Observations of a number of relatively isolated cumulus bubbles, ranging in diameter from 100 meters to about 1 km, were taken both in the trade wind region and in the middle latitudes. They confirmed the theoretical findings within the limits of measurement. The erosion parameter E was found to be about 50 ± 10 seconds, The same laws seem to apply when a composite bubble is formed at cloud base by amalgamation of several small bubbles into a large one. The theoretical approach is, however, different if several cloud bubbles are present and interact with one another and with their environment. In this case the life cycle of individual bubbles must depend on such environmental factors as wind shear and dryness. The life of each bubble may be divided into two sections: first, there is the "protected range," i.e., the section where the bubble rises within the cloud from its level of origin to its emergence at the cloud top. During this period the bubble is protected from the cooling effects of evaporation by the surrounding inactive cloud mass. When the bubble penetrates the inactive cloud top the "unprotected range" starts where the bubble is in contact with clear air and hence is subject to evaporation and erosion. Malkus and Scorer (1955) found that the maximum bubble radius at its emergence from the cloud approximately equals the unprotected height range, whereas the total range covered by each bubble, according to Ludlam and Scorer (1953), corresponds to the width of the cloud body from which the bubble has emerged. Later on, Saunders (1961) succeeded in relating the diameter of bubbles emerging at the tops or at the flanks of cumulus clouds to the heights penetrated by them. A linear relationship was found between the upper limit of that diameter and the relevant height with a coefficient of proportionality of 0.40. Thus the ascent of a bubble is always accompanied by a corresponding increase of its lateral dimensions, which results from the entrainment of the wakes and residues of former bubbles lying in its path. 5.3.2.8 Origin of Bubbles at Sea. Now the question arises of where the main source of bubbles or thermals is to be sought at sea. In principal, bubbles may generate at the sea surface and enter the cloud layer through the cloud base as well as form entirely within
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
319
the cloud layer. Theoretical examples for the evolution of a convective element near the ground were given by Malkus and Witt (1959). As the initial organization of convection is a basically nonlinear process, such an approach could only be accomplished with the help of electronic computers. The calculation showed that, within a few minutes, the initial perturbation acquires a mushroom-like shape surrounded by a vortex ring circulation at its edges. Two phases of development can be distinguished: First, there is an "organization phase" characterized by the formation of the bubble cap and of the vortex ring and exhibiting only slight upward motion. The second phase comprises the actual ascent of the bubble. These numerical calculations were confirmed by laboratory experiments (Woodward, 1960). Conclusive observational evidence obtained at sea seems to be lacking as yet. Bearing in mind that Bunker et al. (1949) were not able to verify thermals, i.e., bubbles, in the mixed layer which could be regarded as "roots" of the cumuli, we might be led to assume that at sea the bubbles chiefly generate within the cloud layer, usually at any level up to that where the environmental lapse rate becomes more stable than moist-adiabatic (Scorer and Ludlam, 1953). In a later paper, Bunker (1959) concluded from observational studies that the air within the buoyant elements originated in the vicinity of the 100-200 meter level, i.e. within the mixed layer. Its transport to the cloud level could be performed by a lifting motion due to mesoscale convergence, possibly induced by inhomogeneities of sea-surface temperature (compare Section 5.3.2.5). In addition, other effects, e.g., turbulent motion, buoyant acceleration, and pressure variations, could be involved. In this respect it may be worth mentioning that, although no significant increase in the vertical turbulence was found under trade wind cumuli, a distinct increase of the horizontal turbulent component did occur (Bunker, 1955). Further work on this point will be necessary. 5.3.2.9 Structure of Oceanic Cumulonimbus Clouds. In Section 5.3.2.4 it has been mentioned that cumulonimbi are found at sea in synoptic-scale convergence zones, e.g., cold fronts, troughs, easterly waves, and in the region of the intertropical convergence. After the success with which the bubble model has been applied to oceanic cumuli in the Trades it seems worthwhile to focus our attention upon the cumulonimbi and to investigate whether this approach is also suitable for the considerably larger cloud masses of this kind. An example of such a study was given by Malkus and Ronne (1954), who reported observations taken by means of time lapse
320
5
THERMODYNAMlC PROCESSES IN MARlNE ATMOSPHERE
photography during the passage of a strong polar trough near the West Indian island of Anegada. Some extremely large oceanic cumulonimbus clouds extended upwards of 12 km into a region of strong vertical wind shear. The interpretation of the measurements was done in terms of the bubble model. The main results were that the same erosion parameter E as obtained for trade wind cumuli was found to be valid for the penetrative towers and that a certain minimum cloud dimension was required for the development of such vigorous convection. In conformity with the statement of Ludlam and Scorer (1953) on the correspondence between the total range of a bubble and the width of the parent cloud body we may assume that a large aggregation of cloud mass is necessary to protect the innermost core from dilution so that it is able to retain sufficient buoyancy up to altitudes of 12 km. A cloud mass with a diameter of about 9 km produced undiluted bubbles, 2 km in diameter, which emerged every 20 minutes from the cloud top, rising at a velocity of about 11 meters/sec. The conditions for penetrative cumulonimbus development have been investigated more recently by Malkus (1960), who based her study on the improved bubble model advanced by Levine (1959). The characteristics of this model are the following: An isolated bubblelike element is furnished with an internal circulation similar to that of a vortex ring, it is continually turning inside out during its ascent and, at each cycle, it exchanges a constant portion of its mass with the environment. From this short description it can already be taken that the model of Levine incorporates some essential features of the entrainment model into a new bubble model which, in its original form, involved no dilution of the bubble cap at all. The corresponding differential equation is similar to Eq. (5.54), except for the drag term which has to be adapted to the mass exchange mechanism described above, with the result that it is split up into a "form drag" and a "mixing drag." The important result of the computation was that a relationship was established between the entrainment rate and the diameter of the convective element. For bubbles of 500 meters across (trade cumulus size) entrainment rates of the order 0.5-1.0 x 10-5 ern"! were found, whereas for elements of 5 km across (thunderstorm size) the entrainment rate was one order of magnitude smaller, namely 0.05-0.1 x 10- 5 cm". In this connection it should be pointed out that the dilution of clouds is insignificant with entrainment rates ~ 0.1 x 10- 5 crrr ! under saturated conditions; ~ 0.05 X 10- 5 cm- l under fairly dry conditions. Herewith, we have gained a better understanding of the idea of the "protective cores." Confirmation is obtained for the necessity of a critical dimension that the cloud must
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
321
have for a penetrative tower of a given height to develop. Explanation is also provided for some surprising observations, for example, that, except for the lower layers, a temperature lapse rate steepening beyond the moist-adiabatic one was by no means found indicative of a higher readiness for the development of penetrative towers or thunderstorms, or that spectacular cumulonimbi generated in spite of a relatively dry atmosphere above 3 km. It can be concluded that the problem of penetrative cumulonimbus is essentially reduced to that of element size. Malkus (1960) applied the improved bubble model of Levine to hurricane cumulonimbus towers which, by radar measurements, were found to have reached altitudes of about 18 km. The aim was to examine the theoretical relation between size and maximum height of each convective element, which appears as a single tower when emerging from the top of the cloud mass. As can be inferred from Fig. 97, the agreement is rather satisfactory. The measured data lie 15
-:
Hurncane Daisy
14
Aug 27, 1958
13
,-
12
~
II
~ s:
10
E
9
;<
8
:c
E o
::;;
," ,, ,,, ,,
X
,,
I
,//
6
4
x
x
7
5
"
.- """ ."",,,,
x~/ , x
,
,
"
,
- - Theory (Sal) - - - - Theory (R H. 0 70% for ~
>
4km)
x Measured
Diameter (km)
FIG. 97. Relation between diameter and maximum height of active cumulonimbus towers. Comparison between theory and photogrammetric measurements from aircraft nose camera films. (From Malkus, 1960.)
mostly between the two theoretical curves calculated for saturated environment and for a relative humidity of 70 per cent above 4 km. It can be noticed that reducing the humidity of the cloud environment is much less effective with larger bubble diameters than with smaller ones. Further evidence, not reproduced here, shows that reduction in
322
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
environment humidity is most effective at low levels and the less inhibitory the higher it starts. It is almost certain that the larger elements penetrate the tropopause although their buoyancy is negative. This penetration, which seems to be affected only little by the static stability of the lower stratosphere mainly varies with the ascent velocity at the tropopause. For every kilometer of penetration into the stratosphere, an ascent velocity of 20 meters/sec is required at that level. Since the model provides for a maximum updraft of 2.5 times the ascent rate of the element and since, according to reconnaissance reports, updrafts of 50 meters/sec seem to occur in the eye walls of hurricanes, an ascent velocity of 20 meters/sec at the tropopause level can be accepted as sufficiently authentic. Thus, in contrast to the earlier bubble theories, but in agreement with observation, the improved bubble concept of Levine permits an element to overshoot its level of zero buoyancy. 5.3.2.10 Cumulus Organization at Sea. One of the most interesting aspects of maritime cloud distribution is the degree of organization on so many different scales. We have already mentioned the fact that oceanic cumuli are normally to be found in groups of from 10 to 50 km in diameter and separated by somewhat wider clear areas. Attempts were made to connect this rather irregular form of organization with the thermal patchiness of the sea surface (Section 5.3.2.5). We further referred to cellular cloud patterns as revealed by pictures taken by meteorological satellites (Section 5.3.2.2). From aircraft investigations there was obtained the information that the individual cumuli frequently line up into rows which may extend for several hundreds of kilometers. It seems necessary and useful that these different modes of cloud regime should be correlated with the atmospheric flow pattern. Although the larger scales of cloud regime can better be examined by means of suitable satellite pictures, relevant studies on the smaller scales of organization have been carried out during aircraft flights over the tropical Pacific Ocean (Riehl et al., 1959; Malkus et al., 1961a). These aircraft investigations proved that the orientation of the cumulus rows is mostly parallel to the low-level flow. Occasionally, however, another mode of organization, called the "normal" mode, was found which produced cloud lines at a substantial angle to the wind. Preliminary results reported by Malkus and Ronne (1960) showed that the "parallel" mode is related to convective disturbances of
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
323
synoptic scale but it seems to be weak or absent (replaced by random cumuli) in the inversion-dominated regions of the upstream and poleward portions of the Trades. Figure 98 gives a schematic representation of the cloud organization in the neighborhood of a wave trough in the Easterlies. The windinduced orientation is clearly visible. The spacing between the cloud rows amounted to about 4 km at greater distances from the trough line and increased to 25 km as the wave trough was approached. Just west of the disturbance, spaces of 30 km were found. Similar experiences were reported by Bunker (1959), who, in the Atlantic Ocean, observed lines of cumulus clouds that were lying roughly parallel to and under a line of cirrus clouds. It is suggested that the two phenomena were related or possessed a common origin. Further, a lowlevel disturbance was found with lines of cumuli which clearly resulted from the convergence of two wind systems. ~IOOkm-
i?
()
If ()
t;:;l
o 0 r.
o.
g/ f}IO If (/'/0
Clear
AI
~
II
r)
CJ f:-/
,1
o
0
V () () '6 Trough
FIG. 98. Schematic distribution of cumuliform clouds near a wave trough in the North Pacific Ocean at 10° N, 170° E. (From Malkus and Ronne, 1960.) Orientation of cloud rows, spacing between them, and distances between the amplified cloud groups (denoted schematically in the figure as a single large cloud) were measured by timelapse photography from an aircraft. Individual clouds are not drawn according to scale.
According to Riehl et al. (1959), there was some indication that the "normal" mode, which occurred only rarely, was influenced by wind shear. The clouds were found to line up with the shear vector between the trade wind layer and the flow above. Later studies (Malkus et al., 1961a) allowed the authors to give a more detailed description of the factors favoring each mode of organization. They summarized their findings as follows:
324
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
A. Parallel mode Factors favoring 1. Airflow over warmer ocean 2. Strong low-level wind 3. No wind turning with height 4. Unstable cloud layer 5. Synoptic-scale convergence Factors inhibiting 1. Airflow over colder ocean 2. Weak low-level wind 3. Rotation of wind at low levels 4. Inversion domination-e-stable and/or dry cloud layer 5. Synoptic-scale divergence 6. Very pronounced normal mode (?) B. Normal mode Factors favoring 1. Cloud layer penetrating into upper shear 2. Abnormally low shear superimposed on trade cumulus layer 3. Disturbance (convergence) 4. Strong shear confined to narrow vertical layer Factors preventing: Uniform wind throughout troposphere. With parallel mode dominating, the spacing of the cloud rows appears to be directly related to the depth of the moist layer, i.e., the distance between the rows increases when a disturbance is approached (see Fig. 98). The spacing of the normal mode was 75-95 km in all cases studied so far. The frequency of occurrence of cloud organization seems to be highly variable, at least in the area concerned, i.e., the tropical Pacific. For instance, during the flight investigated by Riehl et al. (1959) organization was absent for 9 per cent, weak for 30 per cent, moderate for 33 per cent, and strong for 28 per cent of the time while, for the flight studied by Malkus et al. (1961a), the corresponding figures were: absent 32 per cent, weak 40 per cent, moderate 28 per cent, and strong 0 per cent. Thus, cloud organization was present for 91 per cent and 68 per cent of the time, respectively. A thorough investigation of the cloud pattern in a hurricane (Daisy, 1958) was made by Malkus et al. (1961b). It revealed a remarkable persistence of the cumulonimbus rows and of the cirrus shield which, for more than two days, held nearly the same position with regard to the center of the hurricane. Apart from this persistence, a
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
325
slow and gradual development toward a symmetrical structure around the center was observed. Studies of this kind will certainly be activated and also facilitated by photographs from meteorological satellites. Some preliminary results in this line were described in Section 5.3.2.2. Further observations were given by Fritz (1961) who, in the relatively dry and cold central parts of a mature cyclone over the North Atlantic, found very narrow streets of cumuliform clouds several hundred miles in length and lying closely parallel to the contour lines of the 500 mb chart. Up to now the results have been more or less restricted to describing . the phenomena and to suggesting some qualitative critera for the occurrence of each rhode. Theoretical models appear to be lacking so far.
5.3.3 Inversion Conditions The importance of atmospheric processes in air warmer than water is generally inferior to that attached to phenomena connected with lapse conditions, since at sea the latter occur much more often than inversional cases. Relevant evidence can, for example, be obtained from frequency distributions of the air-sea temperature difference as measured at North Atlantic weather ship stations, In Fig. 99 such distributions are exhibited for the ocean stations "C," "D," and "I" whose positions are indicated in Fig. 1. As can be derived from Fig. 99, the percentage of occurrence of inversion conditions (air warmer than water) during the period in question was: "C" = 37.7 per cent "D" = 25.3 per cent "I" = 9.7 per cent These figures are similar to those given by other authors (see, for example, Brocks, 1956) and clearly show that, in general, inversion conditions are not very frequently found at sea and that, in particular, their frequency of occurrence seems to depend on the locality concerned and its meteorological and oceanographic implications. For instance, a station like "C" situated at the southern outskirts of the cool mixed waters in the northwestern part of the Atlantic Ocean (Rodewald, 1952) is liable to experience warm air flows relative to the sea more often than station "I," which lies in the northwestern branches of the eastern part of the warm North Atlantic drift current. Apart from the differences in occurrence between inversion and lapse conditions, there are dynamic reasons that one should attach more importance to lapse situations. In the latter cases dynamic
326
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
turbulence and convection operate in one and the same sense and therefore ensure a quick, intensive stirring of the air mass in question. The joint effect of these two powerful mechanisms is that a quasistationary state is approached comparatively soon, thus justifying the general treatment of this case as given in Section 5.3.2. 18
18
~
16
16
~
14
14
§
12
12
'0
10
10
"g o
/
4
2
a
_x_x_x-x.....
x"
x-x" xvx_!-~\x D \ x" x
x_x.. . x-rx
x-x-x-x ;...<._:::.....-"'~-'-------'--------'-------'------.L -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2
x,\. \ 4
8 6 4
'.:::
2 X-x
6
8
0 10
Temperature difference air-sea (OF)
FIG. 99. Frequency distributions of the air-sea temperature difference observed at the North Atlantic weather ship stations "C," "D," and ''I'' during 1960. e-e, "C" (52.8° N, 35.5° W); x-x, "D" (44° N, 41° W); 0-0, "I" (59° N, 19° W.)
Under inversion conditions, however, the air mass transformation starting from the sea surface is mainly performed by thermally reduced dynamic turbulence and by radiative cooling, both of these being rather slow-working processes. As shown by Craig (1949), the layer of air that was appreciably affected by the cooler water reached a thickness of only about 100 meters after having flowed about 50 miles over the sea. According to Panofsky (1947) most of the cooling is due to eddy conduction, the share of radiative cooling being estimated at only about 20 per cent of the total cooling rate. In addition, a distinct dependence on time and/or fetch was observed. Besides, the relatively small influence exerted by a cold sea surface on the overlying air is indicated by the fact that the maritime regions, where upwelling occurs and, hence, the air temperature is warmer than that of the sea surface, are also characterized by a small rainfall figure which is mostly due to the small amount of evaporation observed there. Apart from these observations, no general features can be ascribed to inversion conditions, so we will discontinue the discussion of this subject here and come back to it when dealing with transformation processes (Section 5.3.4).
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
327
5.3.4 Modification of Air Masses by the Sea Surface 5.3.4.1 Factors Involved. The problem to be treated in this section results mostly from the fact that the marine atmosphere is not a secluded system but that air masses from the continents cross the coast and flow out over the sea. Hereby the lower boundary of the atmosphere is suddenly and markedly changed, which gives rise to fundamental transformation processes starting from the sea surface and affecting the temperature, moisture, and flow characteristics of the air. To a minor degree a similar modification occurs at sea in areas where there is a substantial horizontal gradient of sea-surface temperature. It is evident that these .transforrnations essentially depend on the air-sea temperature difference. If the air is colder than the underlying sea surface, the flow of heat-in addition to the upward flux of moisture-goes from the sea to the atmosphere and the energy thus gained by the air is rather quickly distributed over substantial portions of the atmosphere by the powerful mechanism of mesoscale convection, in addition to that of eddy diffusion depending on wind speed. Confirmation of a strong association between the fluxes of heat and water vapor going from the sea to the atmosphere with the airsea temperature difference under lapse conditions was given, for example, by Craddock (1951). If, however, the air is warmer than the sea, the turbulent mixing lacks the convective enhancement of the preceding case, but rather is reduced by thermal stability, since the turbulent stresses have to work against gravity. In this situation the maritime influence which emanates from the sea surface spreads out more slowly and is mostly confined to the lower layers of the atmosphere. Apart from the importance of the air-sea temperature difference, the initial stratification that the air possesses when crossing the coast or moving across a bunching of sea-surface isotherms is an additional factor that influences the modification of the air mass. If the sea-surface temperature varies along the path of the air mass, these changes have also to be taken into consideration. Attention must further be given to the fact that not only the temperature of the air flow is modified by the sea but that the sea-surface temperature, also, may be influenced by the contact with the air, as was indicated in Section 5.1. Thus, air mass modification over the sea actually is a process of interaction between atmosphere and ocean, which renders the complete treatment rather difficult. Finally, it must be mentioned that, besides the convective, turbulent, and molecular exchange between air and sea, radiative processes
328
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
also can contribute to the transformation of the air mass in question. This factor is supposed to be particularly significant if the turbulent exchange is small, i.e., with light winds and stable or inversional stratification. 5.3.4.2 Methods of Study. For an observational investigation of air mass modification over the sea, soundings that give the vertical distribution of temperature and moisture in the lower layers of the atmosphere are needed at a sufficiently large number of localities along the trajectory of the air mass concerned. If wind speed and direction vary with altitude it must be taken into account that the air strata at different levels have different over-water trajectories. Appropriate meteorological information can best be obtained by means of suitably equipped aircraft. Since an airplane can neither furnish data from the first few meters above the sea level nor from the surface of the sea itself, additional observations from ships, boats, or buoys are necessary. Only a very small number of data for which measurements were taken at different points of the trajectory have become known so far (see, e.g., Craig, 1946; Emmons, 1947). In most cases, one has to be satisfied with soundings made only at the origin and at the end of the trajectory considered (see, e.g., Craddock, 1951). Some studies are even restricted to considering the surface values only (see, e.g., Farkas and Hutchings, 1953). A valuable tool in the study of such airplane soundings, particularly with inversional cases, has been provided by a characteristic diagram which was introduced by Taylor (1917), discussed in detail by Montgomery (1950), and used by Craig (1946), Emmons (1947), and others. The Taylor diagram, as it is mostly called, shows the temperature along the ordinate and vapor pressure along the abscissa. For discussion of low-level soundings, potential temperature and potential water vapor are taken (Fig. 100). These potential values are referred to sea-level pressure in order to allow direct comparison with the temperature and water vapor at the sea surface. In addition, the saturation curves, representing the maximum vapor pressure over water, sea water (with salinity of about 35 per mille), and ice, are entered in the diagram. Naturally, these curves are only valid at the sea surface. As was shown by Taylor (1917) the diagram fulfils the property of mixtures almost exactly, i.e., if two samples of air of a certain temperature and vapor pressure are represented in the diagram by two corresponding points, any adiabatic mixture of the two samples
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
329
is given by a point which lies on the straight line connecting the two original points. The value of the Taylor diagram lies in the fact that we can apply it to the modification of air masses by assuming that the air layer next to the sea surface possesses the temperature of that surface and is saturated. Consequently, every continental air mass flowing out over the sea will come into contact with the layer next to the sea surface and will get mixed with it. The resulting mixture will then be represented in the Taylor diagram by a straight line between the two points indicating the initial state of the air mass and the sea surface. 40 35 30 G a,
e:> 25 "0 20 Q; a. E
15
!:!
10
2! C
Cl>
"0 a..
5 0 _5
ySaturat;on curve
,,'
for ice
FIG. 100. Taylor diagram applied to air mass modification over the sea. A, Air mass, originally stable, flowing over a cold sea surface; B, homogeneous air mass flowing over a warmer sea surface. T. = sea/surface temperature.
Two (assumed) examples of that kind are exhibited in Fig. 100. Case (A) shows an air mass, originally stable, which flows over a cold sea surface of 15°C temperature, whose cooling influence is clearly recognizable up to point (4). In case (B) an originally homogeneous air mass of constant potential temperature and potential vapor pressure [note the cluster of points at (B)] passes over a warmer sea surface of 30°C resulting in a superadiabatic layer reaching from the sea surface up to point (3). In reality, the points (3) and (4) would correspond to certain altitudes, thus indicating the vertical range of influence of the sea surface. In this way the Taylor diagram serves as a useful aid for investigating air mass modification by the sea surface. It may even be used for extrapolating the value of the sea-surface temperature, in case this was not measured.
330
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
Besides, the slope of the characteristic curve of a sounding is qualitatively significant as an indicator for transfer processes, if radiation is neglected. For example, the flux of sensible heat goes up, is zero, or goes down if the lapse rate of the potential temperature is positive, zero, or negative. Thus the deviation of the slope of the sounding in the Taylor diagram from the horizontal isotherms of potential temperature indicates the direction of the transport of sensible heat. Similar criteria can be given for the eddy fluxes of aqueous vapor and of sensible and latent heat combined, as well as for the hydrostatic equilibrium (Montgomery, 1950). If the observational evidence at sea, particularly in the upper air, is poor, some benefit can be obtained from indirect aerology, which, however, implies the application of a theoretical model. Relevant experience and theoretical knowledge are then needed for describing the conditions in the upper air and their changes, whereas the actual values are mostly the result of surface observations. Naturally, such methods can be very useful when forecasting has to be done on a routine basis, since, for such purposes, the necessary aerological information at sea will generally be incomplete. 5.3.4.3 Some Observational Facts. Before discussing the theoretical background of air mass transformation, let us cast a glance at the results of some relevant measurements. Craig (1946) and Emmons (1947) were the first and-as far as I can see-the only ones who tackled this difficult task systematically by making series of airplane soundings up to 300-500 meters along the trajectories of flowing air masses. Since this investigation was carried out above coastal waters east of the U.S.A. in summer and fall, and since it was chiefly concerned with air masses crossing the coast and moving out over the sea, the great majority of the soundings gathered provided information on the cooling of a warm air mass by a colder water surface. A typical sample of this kind has been taken from Craig (1946) (Fig. 101). The first sounding was made over land and shows nearly homogeneous air up to at least 300 meters. Note the cluster of points representing the measured stratification in the Taylor diagram. After traveling 4 miles over water, the air is cooled and moistened up to a height of 46 meters, the largest gradient being confined to the lowest 6 meters. The Taylor diagram displays the characteristic modification curve as a straight line starting from the cluster of points and intersecting the saturation curve for salt water at the sea-surface temperature. The third sounding was made at a distance of 19 miles (measured
feet
!
1000
\
~
[)£W
PT
50 0
."""
'1
TEMP
;
38
,
40
feel 100 0
42
i'
44
46
~
50 0
100m
'\ ~
!
500
K I
I
I
72
i
,
56F
7
-\
5C
48 ,
50
i
52
'
54
~
56
\
62F
13
I~mb
60F
1\
58F
\
56F
19
~
\
i
20C \
7 72F
\
TEMP
70F
'\
68F 66F
f\
8
9
10
:1 ~
64F
\
C
-,
60 62 64 iii ,
15C
l\-
60F
12
r-,
58F \
./
"
56F
68
70
72
I lit 20e
tqrnb
r-,
<,
I2i
\
\
66 ;
13
1\
62F
58
12
6"
\
J.cy
ii'
~C
'1
i\
66F
f\
I~C
r-:::: f-t..J L-,
\
68F
Ii
~
10
9
"\
70F
0
1 0 36 38 40 42 44 46 iii iii
~
72 F
\
f&..
~
74F
'\
I~
Q£W PT
70
h_ ~
abc
i
5C fee t 100 0
20e
..
,rs;;: '-
0
68
"i
.
TEMP
0
~
60F 58F
\
~
OEW PT
1314mb
62F
1'\
66
12
64F
'\
64
"
10
9
66F
"\
50 52 ~4 56 58 60 62 iii , , i' IOC 15C
48
i
5C
•
70F
i\
36
'.
6'-
[1
5 0
7 72F
74F
FIG. 101. Modification of a warm continental air mass flowing out over a colder sea, Massachusetts Bay, October 18, 1944. Vertical distributions of air temperature and dew point as well as Taylor diagrams. Sea-surface temperature indicated by arrows. (From Craig, 1946.) Location
Time
At 1000 ft Wind
A. 42°10' N, 70°50' W B. 42°13' N, 70°40' W C. 4Z017'N, 70°25' W
Trajectory
.,
230°, 18 mph
Over land
., .,
230°,18 mph
4 mi, coast 19 mi, coast
0,1435-1447 hr; 1449-1454 hr 0,1505-1515 hr; 1520-1526 hr 0,1553-1603 hr; 1605-1610 hr
230°,20 mph
1
4'
hr, from hr, from
332
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
at 300 meters' height) from the coast. The cooling and moistening now goes up to about 100 meters. The Taylor diagram does not show a straight line but a bended curve indicating that besides the turbulent mixing an additional effect must have been present, which was ascribed by Craig to the vertical shear of the horizontal wind. This sample illustrates the three factors that are of primary importance to air mass modification, namely: (1) convective mixing, (2) turbulent mixing, and (3) vertical wind shear. Craig (1949) summarized his findings about the cooling of an air mass by the colder sea surface in an instructive diagram which is reproduced in part as Fig. 102. In these modification cross sections we have the distance from land as the abscissa and the height as the ordinate. The numbers plotted therein represent the "proportional change" in per cent of the difference between the initial values of potential temperature and specific humidity and the corresponding values pertaining to the sea surface. These figures are entered at the distances from the shore where the soundings were made. Temperature excess and wind speed are also given. In addition, there is indicated the amount of their influence on the height up to which the air is affected noticeably during its overwater travel, although the relative significance of these two factors is not quite clear, perhaps owing to the fact that the observational material is not always consistent. In general, we can draw the conclusion that the bottom layer of a perceptible modification increases rather rapidly within the first few miles from shore, while later on the growth is much slower. The height of this modified layer appears to be of the order of magnitude of 60 meters after the first 25 miles' travel over the sea. According to Emmons (1947), the modification will extend to about 180 meters after a trajectory of 300 miles if the initial temperature difference between the air and the water is of the order of 5-1 O°C and the surface wind speed is smaller than about 15 mph. However, with strong winds, both at the surface and aloft, and a temperature excess of less than 2.5°C in the air, the modified layer may reach levels higher than 180 meters. The inverse case, namely the heating of cool air by the sea surface does not readily lend itself to such airplane studies. The powerful transfer mechanism of convection gives rise to a rapid mixing which will result in a homogeneous stratification throughout nearly the entire height range considered. As may be seen in Fig. 103, which was also taken from Craig (1946), the layer with strongly superadiabatic lapse rate was confined to the lowest 6 or 17 meters, respectively and, consequently, escaped investigation by the airplane. The greatest height
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
333
6T=6.5°F U IOOO = 15mi hr- I
2
I I
500
..... Q)
Q)
c: c:
o
300 200
2
00
3
4
10
~
T,/~
4
_--I~-T ~
8-
3Q.°{g__ 12
I 1
_---S.--l 1 10°;'
6
3 100
5
I 1
400
16
20
6 - - -IE>
22
25
24
28
6T=7.5°F U10 0 0=22 mi hr- I
T T ~~ __ ~-
6T=9.9°F U ,ooo=23mi hr- '
300 200
6T=12.4°F U 10 0 o =35 mi hr- I
100
16
20
24
shore in miles FIG. 102. Modification of warm air masses by a colder sea surface. Vertical cross sections showing the "proportional change" of both potential air temperature and specific humidity as a function of elevation and distance from the shore. (From Craig, 1949.) t1T = Difference between the initial air temperature and the sea/surface temperature; UIOOO = wind speed at 1000 ft.
found for the superadiabatic bottom layer was slightly over 30 meters, as reported by Craig (1946). The heating of a cold air mass flowing over warm water does, however, not occur exclusively from below. Bunker (1960), who measured turbulent transports of sensible and latent heat (i.e., of water vapor) from an airplane within southward flowing air masses
\
1 -I
melers
feel 1000
DEW PT
~
TEMP.
~
1 1
•
R38
40
I
42
44
46
48
5C
1000
52
......... ......... V I~
1#
?(
I
56
58
7
8
i
60F
15C II
10
9
12
13
14
58F
DEW PT.
I'\.-TEMP.
56F
T
"
"
~
54F
~ ~~
,......
....
~
IA
15mb
~ l#
~
[
-
B
.,
\.
100
~
~
36
B I\..
r
0 34
15~
~
54
~
200
500
~
50 10C
-.r
meters r. r.
l,....-o' .........
14
13
~
I~
feel
12
A
l\
100
36
II
r.
~
o
10
·tIIII.....
54F
1"'\
-
500
9
56F
1
200
8 58F
te·• 38
40
42
44
46
48
5C
50
52
~
54
, 56
58
60F
11
I
10C
15C
FIG. 103. Heating of cold air by a warmer sea surface. Vertical distributions of air temperature and dew point as well as Taylor diagrams, Massachusetts Bay, September 25, 1944. (From Craig, 1946). Location
Time
.,
At 1000 ft Wind
A. 4r31' N, 70°36' W
0,0956-1006 hr; 1011-1016 hr
50°,10 mph
B. 4r08' N, 70°16' W
0,1052-1102 hr; 1105-1110 hr
.,
50°,9 mph
Trajectory
> 100
mi, 10 from Maine Nova Scotia > 150 mi, > 15 from Maine Nova Scotia
hr, or hr, or
5.3
335
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
over the western North Atlantic Ocean, could show that-apart from the upward heat flux originating from the sea surface-the higher levels above, say, from 400 to 500 meters received heat by diffusion from the subsidence-inversion air aloft. In the middle latitudes this downward heat flux was small as compared with that coming from the sea surface. However, in the tropical zone the warming from above surpassed the heat flux from the ocean. Corresponding figures are given in Table XXXIII. At some longer distance from the shore, and in the tropics, the latent heat flux was found to be one order of magnitude greater than the upward flux of sensible heat. T ABLE XXXIII REGIONAL AVERAGES OF SENSIBLE-~ND LATENT-HEAT FLUXES MEASURED IN AIR FLOWING SOUTHWARD OVER THE WESTERN NORTH ATLANTIC OCEANa
Region Latitude
Longitude
43°-39° N 37°-3r N 20°-19° N 12°_ 9° N
71 0 - 6 8 ° W 70°-65° W 66°-64° W 60°-57° W
a
Upward sensible- Downward sensibleheat flux at or heat flux in the stable below 60 meters layer above 400500 meters (meal em- 2 see- 1 ) (meal cm-" sec- 1 ) 2.30 2.00 0.17 0.10
0.39 0.08 0.46 0.32
Latent-heat flux (values observed in the eloud layer exeluded) (meal em- 2 see- 1) 1.08 8.38 1.54 1.17
From Bunker (1960).
In order to be able to generalize these observational findings and thus to obtain as much benefit from them as possible we must frame them into a suitable theoretical model. Therefore we are now going to treat the problem of air mass transformation from the theoretical standpoint.
5.3.4.4 General Theoretical Formulation of the Problem. If radiative processes are disregarded, the transformation of a continental air mass crossing the coast and flowing out over the sea can be considered as a problem of turbulent heat and moisture exchange. Consequently, the relevant differential equations can be applied to the processes in question. Let us assume that the x axis is placed in the direction of the wind and that x means the horizontal distance from shore (where x = 0)
336
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
while z is measured vertically upward from the sea surface (where z = 0). The time t is counted from the moment when the air crosses the coast (where t = 0). In this two-dimensional system the potential air temperature 8, the specific humidity ij, and the downwind and vertical components i'l and if; of the wind speed are functions of x, z, and t. They have to satisfy the equation of turbulent diffusion which, for a general mass property s, reads ds os os os 0 ( OS) (5.58) dt = + i'lox + if; OZ = OZ K OZ
at
Here, dldt indicates the individual differentiation with respect to a moving air parcel whereas (%t), (%x), and (%z) mean temporal and local differential quotients, respectively, taken at a certain point (x, z) and at a certain time t. K is a general coefficient of turbulent transfer. Equation (5.58) states that the individual change in s experienced by a unit volume of moving air must be balanced by the change that is due to the vertical eddy transfer of s if the effect of horizontal diffusion may be neglected. In our particular case the differential of the property s must be replaced by the change in total heat content: pCp
dT
(isobaric motion assumed)
or by the change in total water vapor content: p
dij
Considering that the variation of actual air temperature T is very closely represented by the variation of the potential air temperature 8 we arrive at the following equations for the modification of an air mass:
=
~(pKHOB)
(5.59)
=
~(pKE oij)
(5.60)
oz
OZ
oz
OZ
where KH = eddy conductivity KE = eddy diffusivity A certain difficulty arises from the fact that part of the water vapor evaporating from the sea surface condenses to clouds, thereby releasing latent heat. Thus, the observed changes in heat content and water
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
337
vapor content cannot be related directly to the fluxes of sensible heat and of water vapor originating from the sea surface and computed according to the theory of turbulent transfer. For a complete treatment, the condensation effects need to be taken into account. Equations (5.59) and (5.60) provide a rather general formulation of the problem of air mass modification and are, therefore, difficult to solve. For practical application simplifying assumptions must be made. First we may neglect the vertical velocity component w because it is small and its determination is a somewhat delicate operation. We should, however, bear in mind that, in regions of horizontal convergence and divergence (Klein, 1946), the neglect of vertical motion may falsify the result of our computation, thus demanding an improvement of the approach in that respect. Further, we may disregard vertical variations of the air density p which seems permissible in the height region considered. Two ways of investigation are now possible: (a) We may consider the transient state and evaluate the temperature and humidity variations of an individual air parcel. In this case we only use the left parts and the right parts of Eqs. (5.59) and (5.60) and obtain {} and il depending on 1 and z. (b) We may assume that the steady state is reached at each point of the trajectory. With
O{}/Ol
=
Oij/Ol
=
0
Eqs. (5.59) and (5.60) reduce to the balance equations between advection and diffusion (5.61)
aoil = ~ (KE Oil) ox oz oz
(5.62)
which refer to a certain point and time and which yield {} and q as functions of the fetch x and of the height z. The further computation depends essentially on what assumptions are made with regard to the vertical distributions of ii, KH, and KE, as well as on the initial stratification of the air mass for 1 = x = 0, and on the boundary conditions for z = O. Hence, a certain transformation model must be adopted to assure further progress.
338
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
5.3.4.5 Transient State Models. In this discussion we will now turn to case (a) described in the foregoing section, i.e., to the transformation of an individual air parcel depending on time and height. The eddy transfer coefficients for heat and moisture are taken as constant. Equations (5.59) and (5.60) are then reduced to d8/dt = KH(028/oz2) (5.63) dqldt = KE(02ij/oZ2) (5.64)
Following Haurwitz (1941), we assume a linear height relationship as initial stratification over land (t = 0) 8 = 80 + jz (5.65) while at sea the boundary condition for z = 0 is 8 = 81
(5.66)
i.e., the sea-surface temperature is constant. The transition from the regime on land to conditions at sea is supposed to be a sudden one. Only the thermal effect exerted on the atmosphere by the sea surface as lower boundary is taken into account while the reverse effect, i.e., the eventual change of the sea temperature caused by the contact with the air, is not considered. The solution obtained by integration of Eq. (5.63) has the form
8 = 80 + jz + (81
-
80) [1 _ P (
Z)]
2(KHt)l/2
(5.67)
P signifies the probability integral
f g
peg) = 7Tl/2 ~
exp( -
7)2)
d7)
(5.68)
o
which is also called the error function and has been comprehensively tabulated (Peirce, 1929). The result [Eq. (5.67)] can be applied to the heating (81 > 80) as well as to the cooling (81 < 80) from below. The effect is best illustrated by introducing the "height of mean change" Zm, which represents the height at which the potential temperature, after a given time t m , has changed by (81 - 80)/2, i.e., by one half of the total possible change. From Eq. (5.67) and the relevant tables of P the "height of mean change" is determined to be Zm = 0.954 (KHt m)l/2 [em] (5.69) Corresponding values of Zm and t m are shown in Fig. 104.
5.3
339
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
Equation (5.67) was first applied to the transformation of an arctic air mass over warmer water by Schwerdtfeger (1932). However, the observational material then available was far too scanty to allow a full representation of the atmospheric process. The opposite problem of a warm air mass flowing over colder water was studied on the basis of Eq. (5.67) by Taylor (1915), who found good agreement with temperature soundings made in warm continental air over the Grand Banks of Newfoundland, resulting in values for the eddy conductivity of between 1 x 103 and 3 x 103 em? sec:". 3000,------,------,-----;r------,-----,
2500
2
X
10'
20 1m (days)
FIG. 104. Air mass modification by the sea surface. Height of mean change Zm with corresponding time 1m for different eddy conductivities KH. (After Haurwitz, 1941.)
A relationship similar to Eq. (5.67) can be derived for the modification of the vertical moisture distribution. Nevertheless Hanzawa and Takeda (1950), when studying the transport of moisture from the evaporating sea surface into a polar continental air mass, did not solve Eq. (5.64) analytically but applied a numerical method of solution. The initial stratification was determined by aero logical soundings on the Japanese island of Hokkaido whereas the transformed air mass was investigated at an ocean station (39 N, 153 E) east of Japan. Assuming a constant value of the eddy diffusivity (KE = 106 cm 2 sec1, which seems to be extraordinarily high), Hanzawa and Takeda 0
0
340
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
found satisfactory agreement between the measured vertical distributions of the mixing ratio and those computed numerically according to Eq. (5.64). Near the sea surface they observed an increase of the mixing ratio of from 2 to 4 gm/kg within about 32 hours. 5.3.4.6 Steady State Models. The theoretical basis of this discussion is provided by Eqs. (5.61) and (5.62). The approaches to be described in this section have the common feature that the models used therein have empirical components to a varying degree. This implies that the methods developed cannot be adopted generally but only in the particular case for which they were introduced. Jaw (1937) was probably among the first to apply Eq. (5.62) to air mass modification. He studied the change of the vertical distribution of specific humidity q in the northeast trade wind where the steady state seems to be well assured. Assuming an initial profile of ij for x = 0 and a function describing the horizontal variation of q along the sea surface (z = 0) he arrived at a formula giving q as a function of x and z which fairly well represented the observed humidity change up to the trade inversion if the eddy diffusivity was taken as constant and equal to 75 x 103 em- sec:". The empirical part of the model proposed by Burke (1945), who investigated the transformation of polar continental air to polar maritime air, is rather substantial. He subdivided the entire height range considered into the following three regions: (1) A boundary layer close to the sea surface, approximately 15 meters thick, and characterized by a strongly superadiabatic lapse rate, as well as by a pronounced decrease of specific humidity. Through this region the fluxes of heat and water vapor are upward and associated with the respective vertical gradients in accord with Eqs. (5.1) and (5.2). (2) A mixed region adjacent to the boundary layer and having nearly constant potential temperature as well as specific humidity. The relevant distributions are given by the Band q values accepted at the top of the lower boundary layer. The upper limit of the mixed region is the level at which the pertinent dry-adiabat intersects the initial sounding. (3) A saturated adiabatic region adjacent to the mixed layer and reaching to that level at which the final saturation-adiabat intersects the initial sounding. This subdivision certainly is somewhat schematic but it harmonizes quite well with several features observed at sea under lapse conditions
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
341
(cf. Section 5.3.2), although, in some respects (regarding the humidity distribution, for example) certain differences exist, as was also pointed out by Klein (1946). Burke (1945) based his computations on the steady state equations (5.61) and (5.62). The vertical wind profile was assumed to be constant, i.e., ih5/Ug = 0.7. Identifying the coefficients of eddy conductivity and diffusivity with that of eddy viscosity and approximating the latter value by Eqs. (4.7) and (4.50) with C15 = 2.6 X 10- 3 , Burke (1945) arrived at a formula predicting the surface air temperature at any point of the trajectory in terms of four variables, namely: (1) initial surface air temperature; (2) initial lapse rate; (3) distance of overwater trajectory; and (4) sea-surface temperature. For ease of practical application, Burke calculated several diagrams that cannot be reproduced here. Reference is made to the original paper. When fixing a suitable average for the sea-surface temperature, Burke suggested putting more weight on the final value of the latter than on the initial one. Comparative studies led to the conclusion that the weight given to the final value should be greater for larger distances from the coast ( >650 km) and for light winds than for short fetches and strong wind velocities. An examination of sixty-eight forecasts shows that the method proposed by Burke worked quite satisfactorily. For 91 per cent of the cases considered the difference between the forecast and the observed change of the surface air temperature lay between ± 2°C, the average error being + 0.4°C. The maximum change that was forecast amounted to + 30°C and the length of the over-water trajectory varied between 240 km and 2590 km. A further study on polar air mass modification over a warm sea surface was published by Frost (1949). It is also a steady state approach based on Eq. (5.61). The vertical distributions of a and KH(KE) were approximated by conjugate power laws in z:
a = aa(z/a)m KH = KE = (aa/a m) mzo2mz1-m
(5.70) (5.71)
where aa = mean wind speed at z = a . Zo = dynamic roughness of the sea surface m = a nondimensional constant that is a function of thermal stability With regard to the initial thermal stratification and to the thermal boundary conditions at sea the following assumptions were made.
342
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
Adiabatic stratification over land:
8 = 80
for x = 0
(5.72)
Sea-surface temperature varying linearly with x: forz = 0;
(5.73)
The potential temperature above the sea as a function of x and z was obtained in the following form:
8 = 80 + (81
-
80)!
+bX[(1 + ~m++/g)!_
(2m + 1) e- g g[m/(2m+ll] ] (m + 1)r[m/(2m + 1)]
(5.74)
where
f e00
g
g g-[(m+l)!(2m+ll]
dg
!=-------r[m/(2m + 1)] and
(I' = gamma function) Z2m+l
g=------
(2m + 1)2mz02mx
(5.75)
(5.76)
The special case of constant sea-surface temperature is contained in Eq. (5.74) if b = 0 is assumed. For practical application numerical values of the functions employed in Eq. (5.74) were given by Frost (1949). A comparison of ten calculated air temperatures with the observed ones resulted in deviations of ± 1.5°C at the most. The average error was O.O°C. The corresponding travel distances of the air masses ranged between 355 and 550 km. Hence, this method, too, seems to provide good results. Frost also studied the vertical transport of water vapor along the trajectory of a polar air mass. In the case of constant mixing ratios over land (x = 0) and at the sea surface (z = 0) the moisture distribution depending on x and z was obtained in a form identical with the first two terms on the right side of Eq. (5.74) if the potential air temperature is replaced by the mixing ratio. Frost finally derived formulae for the moisture change over the sea, which applied to those cases where the initial humidity distribution over land decreases either linearly with the height or as a power of the height. For the results, the original paper should be consulted.
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
343
The investigations discussed so far were concerned with the modification of cold air masses over a warmer sea surface. These studies need to be supplemented by investigations of the opposite case, namely, the transformation of a warm air mass flowing out over a colder ocean. The relevant observational facts have already been discussed in Section 5.3.4.3. An attempt to generalize these measurements by introducing a theoretical model was made by Craig (1949), whose findings will now be briefly reviewed. Using his measurements of the modification of the humidity profile depending on the travel distance x, Craig first deduced values of the eddy diffusivity as a function of height by means of a numerical integration of Eq. (5.62). The -result led him to conclude that, with stable stratification, the eddy diffusivity, from a value of zero at the sea surface, increases linearly with height in the lowest few meters up to a level h yet to be determined, and that, above that shallow bottom layer, the eddy diffusivity is essentially independent of height. The further treatment is based on the empirical fact that the temperature and the specific humidity in the modified air were changed in the same proportion of the total change possible at each height (cf. Section 5.3.4.3). If 80 and qo designate the initial stratification for x = 0 (characterized by constant potential air temperature and humidity) and 81 , iiI the (constant) temperature and humidity values corresponding to the sea surface (z = 0), a combined quantity p, called the "proportional change" may be introduced by
80 - 8 ijo - q p = -- = -80 - 81 ijo - ij1
(5.77)
where
80 > 81 ijo < ij1
Craig converted Eq. (5.61) or Eq. (5.62) into a relation for the proportional change p and solved it. The result, which will not be given here in detail, consists of two terms that correspond to the first three terms in Eq. (5.67) and an additional term which can mainly be explained by consideration of the shallow bottom layer with increasing eddy diffusivity and which, therefore, provides a distinct improvement as compared with Eq. (5.67). The quality of the result so obtained can best be assessed by making a comparison between the measured profiles of the proportional change p (which have already been given in Fig. 102) and the computed
344
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
distributions. This has been done in Fig. 105. The parameters h, KE(Z ~ h), and a have also been entered there. The height of the bottom layer, with KE linearly increasing, is rather small, ranging between 1.4 and 2.5 meters. From Fig. 105 we may draw the conclusion that the model suggested by Craig will render good service in representing the changes of temperature and humidity that take place in a warm air mass moving out over a colder sea. Certainly this satisfactory result has only been secured for the relatively short air trajectories up to 30 miles which were investigated in the study described above. Only here does the basic assumption of the model, which attributes the modification essentially to the turbulent heat and moisture exchange, seem to be sufficiently established. It may well be that at greater distances from the shore the effects of radiation, of wind shear, and of the variation in sea-surface temperature will be of some additional significance. The measurements made by Emmons (1947) offer distinct hints in that direction. 5.3.4.7 Eddy Transfer Coefficients. In Section 4.4.5 some information was given on the numerical values of the eddy viscosity KM or the Austausch coefficient A = pKM in the marine friction layer. Since whether the transfer coefficients for momentum, heat, and moisture may be assumed as equal is still a question that has not been entirely settled, it seems worthwhile to attempt to assemble also the available information on eddy conductivity KH and eddy diffusivity KE, in particular as regards their dependence on altitude. In spite of the importance of those transfer coefficients for the quantitative treatment of atmospheric exchange processes, it must be stated that no theoretical approach attempting to interpret these highly variable factors by characteristic quantities of the turbulent and convective motion has become known up to now, as was already mentioned in Section 5.2.2.2. Hence, we have to be satisfied with empirical data derived from suitable measurements which, however, have the disadvantage of being only applicable to the particular situation for which they were determined. As the transformation of air masses over the sea is chiefly an exchange problem, possibilities for the calculation of eddy conductivity and eddy diffusivity are provided by Eqs.(5.59)-(5.62) under the supposition that the necessary gradients of 8 and q are sufficiently known. Naturally, the assumption, occasionally made before, that the transfer coefficients are independent of height is no longer permissible. Keeping in mind the possibility that the transport of heat may not
5.3
500 400
345
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
"
KE
u.
(meters)
(cm 2 sec")
(mi hr ")
2.5
2.2 x 10'
10
x = 3mi
° Measured -Madel
300 200
.je0
100 0 500
40
0%
20
x' 2 Y2mi Measured Madel
° 400 300
;; ~ c
100
c
0
.s 0>
2.1
1.9 x 10'
10
17
1.5 x la'
10
1.4
1.9 x 103
15
200
.!1 400
w
300
40 X
° -
9~
=2
0%
20
mi
Measured
Model
200
° °
100 0 400 300
40
~
20
0%
x: 2 mi
° -
Measured Model
200 100 0
40
.s-:° 20
0% Proportional
change
FIG. 105. Modification of warm air by a colder sea surface. Comparison between observed profiles of the "proportional change" and computed ones at different distances x from the shore. (From Craig, 1949.) The measured values are averages based on the soundings presented in Fig. 102. The parameters used for the computation are given at the right side. KE = Constant value of eddy diffusivity applied for z ;;. h; h = height of the bottom layer with KE increasing linearly; Uk = wind speed at z = h.
346
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
only be performed by turbulent motion but also by radiative processes, Eqs. (5.59) and (5.61), which represent the modification of the vertical temperature distribution, are not suitable for the determination of turbulent transfer coefficients. Hence, there remain Eqs. (5.60) and (5.62) from which numerical values for the eddy diffusivity at different levels may be derived. Results reported by Lettau (1944) and Craig (1949) may be considered relevant if sporadic data, which, in part, where already quoted above, are disregarded. The eddy transfer coefficients for humidity KE presented by Lettau refer to a vigorous outbreak of arctic air characterized by very strong instability and powerful convection. The values for KE were obtained from estimates of the water-vapor flux E and the pertaining vertical gradients of the absolute humidity, in accord with Eq. (5.2), and an attempt was made to allow for the precipitation that had occurred. The values of KE published by Lettau are given in Fig. 106. They are extraordinarily high, which can be explained by the strong instability. After an initial increase up to 750 meters, their vertical variation shows a decrease with height. In general, but not in detail, this result is in conformity with the vertical variation of the eddy viscosity, as depicted in Figs. 67 and 68. 5000
t>.-J. 'lI... c
''II.
2000 1000 ~
<;
500
I
Q; E
,---x
200
"---
100
_____
1
")l,
x-----x____ x B
--,.
""
I--"
-x,
)" A
50
'\
20 10
<)
I
'x I ,x
! 2
. . ,,,1'
/
x
x'
5
10
20
50
100
200
500
1000 x 10'
Eddy oiffusivity (em 2 sec-I)
FIG. 106. Vertical distribution of eddy diffusivity KE under stable and unstable conditions as derived from measurements of air mass modification. A, Craig (1949), strong stability; B, Craig (1949), light stability; C, Lettau (1944), very strong instability.
5.3
347
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
Contrary to Lettau, the KE values reported by Craig (1949) refer to stable conditions-as was already indicated in Section 5.3.4.6. They were determined by numerical integration of Eq. (5.62). A summary of these data is included in Fig. 106. There is one group (B), characterized by a small temperature excess and a considerable wind speed, for which KE increases upward as far as 75 meters, reaching values of about 35 x 103 ern- sec>, and then rapidly decreases with height. The shape of this profile corresponds more or less to the vertical variation of KE found under adiabatic or unstable conditions. The other values were obtained with more pronounced stability than had been present with the first group. Here the layer with increasing eddy diffusivity seems to be- confined to the lowest meters, while little variation was observed at higher levels. The KE values are quite small, mostly between 1 x 103 and 3 x 103 ern- sec-I, thus comparing well with earlier results obtained by Taylor (1915) in the same maritime region under similar conditions. In addition to the eddy transfer coefficients quoted above, which were particularly considered as depending on altitude and stability, reference is made to relevant values published by Woskresenski and Matwejew (1960) and characterizing the conditions in and near clouds. These data were derived from the turbulence-affected motions of an airplane in, above, and below stratiform clouds over ice-free parts of the Arctic Sea in summer. Hence, these values refer to the eddy viscosity. As the method applied was not given in full detail we restrict ourselves to summarizing some results in Table XXXIV. From TABLE XXXIV EDDY VISCOSITIES OBSERVED OVER ARCTIC WATERS IN SUMMER: FREQUENCY OF OCCURRENCE IN PER CENT a Range (10 3 cm'' sec <): Site of measurement
Above the clouds Within the clouds Below the clouds a
100
1.3 1.0
100200
1.3
200300
9.0
400500
500600
600700
700800
More than 800
15.9
36.4
15.9
13.6
9.1
9.1
44
19.2
33.2
14.1
15.4
2.6
3.9
78
12.6
25.2
18.5
23.3
11.7
7.7
103
300400
From Woskresenski and Matwejew (1960).
Number of runs
348
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
this review it can be inferred that the eddy transfer coefficients mainly ranged from about 200 x 103 to more than 800 x 103 em- sec:", the maximum frequency of occurrence being at 400-500 x 103 emsec:". In single cases more than 1000 x 103 em- seer! were found. The average values observed in stratocumulus and cumulus clouds were greater than those referring to stratus clouds. No direct information as to the height of the measurements was given, but other hints indicated that the measuring was chiefly done in the lowest 100 meters of the marine atmosphere. Hence these results supplement the summary provided by Figs. 67, 68, and 106.
5.3.4.8 Energy Considerations. In the foregoing sections the transformation of air masses flowing over the sea was treated with a view to a possible model by which the atmospheric processes may be fairly represented and taken into account quantitatively. Herein the air mass modification was exclusively considered as a problem of turbulent heat and moisture exchange. The vertical distributions of temperature and humidity, as well as their variation, were the main objects of investigation. The final aim was to provide useful methods for forecasting the expected changes. This statement of the problem merely deals with one side of the whole question. Full clarification is only attained if there is furnished some information on the energy gained or lost by the air flow during its passage over the sea, and on other possible influences besides turbulent transports. The necessary basis for such studies is a thorough survey of the aerological data along the trajectory ofthe air mass concerned or over the corresponding sea area. The relevant investigations are not very numerous owing to the lack of suitable data. Although the method simply determines the change in an air mass, following its flow by means of at least two aerological soundings at different times, the practical realization is rather difficult. Once the initial character of an air mass has been fixed by a suitable ascent, it is a mere matter of luck that later on its track passes near an upper-air sounding station at the appropriate time so that its modification may be accurately measured. Furthermore, there is some complication in connection with vertical wind shear which may cause the air mass to follow different trajectories at different levels. All told, some fifty cases appear to have been analyzed in such a manner by different authors, the results of which will now be summarized. Energy considerations are most easily and lucidly handled in terms of specific enthalpy, i.e., the total content of sensible heat that an
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
349
air column of unit mass possesses. Isobaric motion assumed, the enthalpy is given by the height integral over cpT and expressed in units of calories per centimeter". Thus, the heat transferred during isobaric processes can be measured by changes in enthalpy. It is also convenient to include the latent heat in this procedure, in which case the equivalent temperature has to be integrated over the height and the result may be referred to as the "moist enthalpy." The questions of interest to which an answer is needed are: (1) The order of magnitude of the change in "moist enthalpy" for different cases of air mass transformation. (2) The portion of the change in "moist enthalpy" that is due to the variation in latent heat. . (3) The efficacy of other influences (dynamic heating, radiation).
Among the synoptic situations concerned, the outbreak of co ld arctic air and its subsequent heating over warmer water has attracted the strong attention of the meteorologists, as very pronounced effects can be expected with such a powerful operation. Relevant studies were published by Lettau (1944), Craddock (1951), Collmann (1951), and Manabe (1957), among others. With regard to the first question posed above, the following values were reported for the change of the "moist enthalpy" per day: Lettau (1944) studied two vigorous outbreaks of arctic air which occurred in November-December. They started between eastern Greenland and Spitsbergen and proceeded in a southeasterly direction over the northern waters. Soundings were made both over the icecovered arctic area and at stations in northern Europe. The moist enthalpy (computed for the layer 0-5 km) increased by 2060 cal cm-2 day'". Craddock (1951) investigated twenty-eight cases of polar air masses starting at Reykjavik (Iceland) and passing near British upper-air stations during the winter months between November and April. The increase rate of the moist enthalpy (computed for the convective layer) amounted to 1130 cal cm-2 day! for typical arctic air masses and reached 1900 cal cm-2 day! in extreme cases. Collmann (1951), when studying polar maritime air flowing in January from the Denmark Strait in a southeasterly direction to Portugal, obtained an increase in moist enthalpy (computed for 0-5 km) of 1190 cal cm-2 day-I. Manabe (1957) published a detailed study on the modification of cold air over the Japan Sea in winter from which we can draw the information that the moist enthalpy (integrated from the surface up
350
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
to 500 mb) increased by about 1460 cal cm- 2 day ". Here, the effects of radiation and precipitation were taken into account. The results of the different authors agree fairly well. Summarizing, we may state that, with outbreaks of cold air, the atmosphere gains heat from the ocean at a rate of from about 1100 to 2100 cal cm-2 day ". These figures are very instructive. To have a standard of comparison, we can transform the values given above into the dimensions of calories per centimeter- per minute which we normally use for the solar constant. We then obtain 0.76 and 1.46 cal cm ? min :", respectively. Considering that the solar constant is 2 cal cm-2 min ? and that, during the summer of the middle latitudes, the heat flux coming from the sun, with a clear sky and under the most favorable conditions of atmospheric turbidity, hardly reaches 1.5 cal cm-2 mirr! near the surface around noon, we realize that the heat transferred continuously from a warm sea to the colder atmosphere during day and night hours represents a very powerful mechanism of air mass modification. Thus, in middle latitudes, a cold air mass can be transformed far more rapidly by contact with a warm sea than by solar radiation. It is tempting to investigate what temperature change in the sea would correspond to that observed in the air. Since the specific heat of the water is 1 cal gm- 1 °C-l, a temperature decrease of only 1°C, occurring in a surface layer 20 meters thick within 1 day, would already be sufficient to provide 2000 cal/day to the atmosphere. Thus, the temperature change in the ocean is small compared with the considerable modifications occurring in the atmosphere. The reason for this difference is the fact that the specific heat of the water is about 4000 times greater than that of the air if both are related to unit volume. Figures for the change rate of moist enthalpy that apply to conditions other than those produced by an outbreak of polar air were given by Collmann (1951). He could show that the transformation of warm air starting near the Azores Islands and flowing into western Europe was characterized by a decrease in moist enthalpy of from - 22 to - 87 cal cm- 2 day:". Herewith, the computation had to be confined to the levels below the inversion, as only this layer is subject to modification. These values are in conformity with the case reproduced from Craig (1946) in Fig. 101, to which a decrease in moist enthalpy by about - 100 cal cm- 2 day"! can be ascribed. In this connection, a study published by Franceschini (1954), who investigated the modifications in tropical air crossing the Gulf of Mexico toward the United States, may be mentioned. In general,
5.3
351
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
the changes found could be explained qualitatively by considering the distribution of the sea-surface temperature and the effects of horizontal mass divergence. With regard to question (2), the share that latent heat contributes to the total change of moist enthalpy can be derived from some of the papers mentioned above. The results are given in the tabulation. Date
Investigator
1944 1951
Lettau Craddock
1957
Manabe
Calories per centimeterper day 720 265 (average) 335 (extreme) 450
Per cent 35 23 18 31
Thus, a substantial portion of the increase in moist enthalpy can be explained-even in the relatively high latitudes concerned-by the transfer of latent heat caused by evaporation. Naturally that share is much larger in tropical regions (cf. Table XXXIII). Finally, with regard to question (3), the possible contribution to the change in enthalpy that may originate from causes other than turbulent exchange was investigated by Craddock (1951) and Manabe (1957). According to Craddock other factors leading to a gain of heat by a cold air mass flowing over a warm sea are of no importance except for a small contribution due to radiative effects (which will be dealt with below). In particular, it was stated that the evidence in the cases discussed was against any significant effect of dynamic heating. Violent convection was observed over the sea and there was no sign of a decrease of humidity at the upper levels of the troposphere. Consequently, the only cause for a dynamic warming, namely subsidence, was irrelevant. With regard to the radiative effects, the evidence available is comparatively poor, which results from the fact that the corresponding values were not measured but have to be computed, depending on the water vapor content and the cloud structure in the air mass during its passage. These quantities are highly variable and not sufficiently known. Craddock (1951) estimated the radiative fluxes by means of the Kew radiation chart. He arrived at the result that, within the temperature range considered, the air up to 500 mb lost heat by radiation at a mean rate of less than 7 cal cm-2 hour:".
352
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
Manabe (1957) used other aids (Yamamoto, 1952; Yamamoto and Onishi, 1952) for the computation of the long-wave radiation and of the incoming solar radiation. The latter being insignificant as compared with the former, the result was a net cooling of the lower half of the troposphere (up to 500 mb) during the period of a typical cold air outbreak, although the lowest layers received heat by radiation due to the large air-sea temperature difference (from -10 to -16°C). The total cooling rate of the air amounted to - 93 cal cm-2 day-l which, with even distribution over the hours of the day assumed, is somewhat lower than the value obtained by Craddock. Manabe (1957) also attempted an estimation of the amount of heat released by condensation. This undertaking will always be severely hampered by the fact that the exact amount of rainfall at sea is not known, although in the case considered this deficiency was in part diminished by the small quantity of precipitation at sea and its concentration on the coastal regions of the Japanese islands. Manabe arrived at a precipitation value of 1.3 mmjday, which corresponds to a heating effect of 77 cal cm-2 day! ( = 5.3 per cent of the total change of moist enthalpy). This estimate is included in the increase rate of moist enthalpy given above. 5.3.5 Physics of Sea Fog 5.3.5.1 Delineation of the Problem. In the foregoing section we discussed the modification of air masses flowing over the sea without paying attention to the possibility that, in the course of that transformation, the air layer next to the sea surface might become saturated, thus giving rise to the formation of sea fog. In order to make up for this omission, we will now pass to a detailed treatment of this important subject. Generally speaking, the generation of sea fog is a process transforming water from the gaseous into the liquid phase and occurring within the atmospheric bottom layer next to the sea surface. One prerequisite for such an operation is that there are sufficient atmospheric nuclei which may act as centers of condensation. Following the deliberations given in Section 3.2, we shall assume that in the lower atmosphere above the sea surface there is an abundance of suitable condensation nuclei. The second requirement to be fulfilled is the state of saturation. Since the amount of gaseous water the air is able to hold depends on its temperature and, in particular, is diminished with decreasing air temperature, saturation can be achieved either by a loss of heat or by a gain in moisture.
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
353
The cooling of the air may be accomplished by molecular and turbulent heat conduction or by radiative processes or by a combination of these two effects. The cooling by adiabatic expansion, which plays such an important role in cloud formation, is not significant in the case of fog development since the pressure variations near the ground are too slow. An influx of moisture into the atmospheric boundary layer above the sea can be provided either by the evaporation from the sea surface and the subsequent upward transport of humidity or by evaporating precipitation coming from above. In addition to the possibilities of fog generation enumerated above, there must be mentioned the cases where the fog does not develop within the atmospheric boundary layer at sea but originates at other places and is transported there by horizontal or vertical motion. In this respect, reference should be made to fogs which are generated over land or ice fields and afterwards drift over the sea, as well as to lowering stratus clouds. Hence, there is quite a variety of processes that may lead to the formation of sea fog. Therefore, we shall now have to study the different causes and their interrelations in order to arrive at a formulation of the types of fog occurring at sea and, if possible, at a quantitative estimate of the factors participating in the formation and dissipation of marine fog. It should be noted that some conceptions widely found in literature have not always been formulated with sufficient precision. For instance, it is often assumed (see, e.g., Pincock and Turner, 1956) that, with warm, moist air flowing over cold water, advection fog will be generated because the warm humid air is chilled to its dew point through contact with the cold sea surface so that condensation and fog formation may occur. In reality, an air mass whose dew point is higher than the temperature of the cold sea surface loses heat as well as water vapor to the sea by the processes of molecular and turbulent conduction and diffusion. Hence, the cold sea surface exerts a cooling and drying influence on the air (see Fig. 107). Besides heat, moisture also is transported downward to the sea surface where it condenses. As these two exchange mechanisms are more or less of equal efficiency both air temperature and dew point will decrease and the saturation point is not reached unless other factors, e.g., radiative cooling, appear in addition to turbulent exchange. Emmons and Montgomery (1947) were the first to call attention to this important point. The common interpretation of the opposite case, namely the formation of steam fog observed if very cold air comes into contact with
354
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
warm water, can likewise be considered with some criticism. This type of fog is generally ascribed to the alleged fact that the atmosphere receives more water vapor from the strongly evaporating sea surface than it is capable of carrying. This explanation does not take into account that, besides water vapor, heat also is transferred from the sea to the atmosphere so that saturation does not necessarily result. feet 1500
met~rs
I
~
I DEW
~
17
I~ ~
1
I
400 PT.
1000
~200
;\0
c .\
:.
C •
d·
500
il
\
100
I 11 P
rot' 0
@"" 58
60
62
~ ~~ ~
64
,
66
68
..-.
70
.-. "A
74
62°F
1/
.\.
/.
j
68°F
64°F
78
r
70°F
66°F
:I
76
250' --<
72°F
\
. -•
~.~.
74°F
60°F 72
2324mb
,~
76°F
\
~
• ...e-
78°F
\
P ;l
22
80°F
C; \
.1 c 1\
21
82°F
~
•P
300
20
84°F
\)
(
19
86°F TEMP.
t
~I
18
V
//
.>/
?V rJ
80F
FIG. 107. Cooling and drying influence of a cold sea surface on warm and moist air. Vertical distributions of air temperature and dew point as well as Taylor diagram. (From Emmons, 1947.) At 40°49' N, 71°10' W, June 16, 1945. 0, Ascent 1807-1822 hr; ., ascent 1825-1837 hr. Modification by the sea extends to about 250 ft. Sea-surface temperature indicated by arrow.
Although molecular diffusion is slightly more effective than molecular conduction (see List of Physical Constants, p. 250) and, consequently, the atmosphere receives relatively more moisture than heat by these processes, it is obvious that, apart from molecular and turbulent transfer, other influences must have a share in producing saturation. 5.3.5.2 Aerological and Statistical Information on Ocean Fogs. The measurements made in marine fogs are rather few, which is small wonder as the phenomenon to be investigated is not to be found
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
355
very frequently. Another difficulty is caused by the fact that a thorough study of the problem can only be achieved by means of aerological observations in the first 1000 meters above the sea surface for which special equipment (e.g., airplanes or tethered balloons operated from shipboard) is needed. The necessity that a rare phenomenon and a suitably equipped expedition must coincide provides an explanation for the lack of sufficient empirical information on the physics of ocean fog. Naturally such measurements can be accomplished with the greatest chance of success if marine regions with high frequency of fog are selected, e.g., the cold water areas in the northwestern parts of the North Atlantic and North Pacific Oceans, as well as in the Arctic and Antarctic Seas. Relevant data from the North Atlantic can be found in a paper published by Emmons (1947). An example is displayed in Fig. 108. Here, the air, when traveling over progressively colder water, was cooled and moistened from below so that saturation was reached in the lowest layer up to about 100 meters. Thick fog was observed from the sea surface up to 60 meters. The fog layer had an undulating top which is consistent with the variation with time or space observed in the psychrometric measurements at the altitudes concerned. Fog studies over the northwestern part of the North Pacific Ocean were carried out by some Japanese scientists (see, e.g., Ogata and Tamura, 1955; Ogata et at. 1958c; Arakiseki, 1955). In these papers there are reported several characteristic features of sea fog mostly derived from surface and aerological observations taken at the ocean stations Extra (39° N, 153° E) and Tango (29° N, 135° E) in combination with surface synoptic charts, as well as isotherm charts of the sea-surface temperature compiled for the relevant ten-day periods. Some results of a statistical nature will be quoted, although, in part, they may be of only local significance. At Extra, 83 per cent of the sea fogs observed had a duration of less than 12 hours while 59 per cent lasted less than 6 hours. The upper limit of the fog layer was below or equal to 400 meters in 86 per cent of 50 cases. Sea fog occurred most frequently with southerly winds and with wind forces of from three to five on the Beaufort scale. The air temperature changes accompanied by the formation and dissipation of fog were very slight as compared with analogous processes over land. They amounted to +0.3°C and -0.2°C, respectively. It is of particular interest that the sea fog observed at Extra showed a block structure, i.e., there was no uniform distribution of fog, but masses of fog, with radii, of between 7 and 44 km, were drifting with the wind. The air-sea temperature difference during
feet
1000
meters
II
300 DEW PT.
1\
1\\ 1\
'\
\
1-200
I~
DESCENT
500
TEMP.
j",ooB 1-100
-
\
I ~l
l,sf
I
~
I
\
\
\
05 4 56 58 60 62 64 66 68 70 72 74F feet
2000
\
metiers
1\ '
DEW\ I PT.
\
IlL 1-500
TEMP.
\
I
\
~
I
1500
1\
\ .MII) •
\ I
'{I
~ to-.. 1000 9""00
I
\
:
,
\ \ \ I
I
200
\ I
100
\ \ I
50 0
\
ASCENT
~
I I
r--,
fl
j
!
\
1\
\
\
I
.,.V ~ 0 54 56 58 60 62 64 66 68 70 72 74F FIG. 108. Fog formation through turbulent exchange between a warm air mass and a cold sea surface. Vertical distributions of air temperature and dew point. (From Emmons, 1947.) At 40°32' N, 70°58' W, June 19, 1945. 0, Descent 1853-1859 hr; ., ascent 1859-1915 hr. Modification by water of varying temperature extends to about 600 ft. Upper limit of fog layer at about 200 ft. Sea-surface temperature indicated by arrow.
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
357
sea-fog periods showed a wide scatter between + 2°C and - 1°C, the average being about +0.2°e. With steam fog, however, the sea was about 9°C warmer than the air if the wind speed ranged between 2 and 4 meters/sec. This temperature excess was diminished to 6°C with the wind speed increasing to 11 meters/sec. Typical weather situations accompanied by sea fog at Extra were specified and their frequencies evaluated. But there is no room here for any detailed discussion on this subject. A similar empirical investigation was carried out by Bintig and Markgraf (1957) for the waters of the German North Sea coast. Statistical values were provided, and the synoptic situations connected with fog were subdivided into characteristic types, as well. The discussion was hampered by the fact that aerological data over the sea were not available but had to be substituted for by soundings made at land stations nearby. For this reason, and in view of the local, mainly off-shore significance of the results obtained, no further comment on them is given. As regards the arctic regions, some very useful information can be taken from a paper published by Vorontsov (1959). Soundings were carried out by means of moored balloons from icebreakers, etc., and additional data were obtained during meteorological flights over the Arctic Sea. Out of a total of 278, 36 ascents (= 13 per cent) were made during fog periods whereas 211 soundings (= 76 per cent) showed an inversion. From the 36 cases with fog, 13 (= 36 per cent) were characterized by a surface inversion while with 23 (= 64 per cent), there was an elevated inversion starting at heights up to 800 meters. A more detailed representation of the vertical structure of the atmosphere occurring with fog conditions is provided by Table XXXV. In about 95 per cent of the cases the air was warmer than the sea surface, the average air-sea temperature difference being + 1.1"C. Thus most of the data may be ascribed to the advection of warm air over colder water. The thickness of the inversion amounted to about 350 meters on the average. In the inversion layer the relative humidity decreased rather rapidly while the specific humidity rose slowly, thus giving evidence of a moisture flux directed downward similar to the heat transport. In the fog layer, the values of the specific and relative humidities varied only little, the latter being nearly 100 per cent. Judging from the vertical distribution of the relative and specific humidities, in elevated inversions the upper boundary of the fog must sometimes be somewhat higher than the lower limit of the inversion and perhaps coincide
TABLE XXXV AEROLOGICAL CHARACTERISTICS OF FOG OVER THE ARCTIC SEAG
Lower height of inversion (meters) Range
Thickness of inversion (meters)
Frequency of inversion No. of cases
Mean
%
Air temperature Ce) Surface
Limit of inversion
Specific humidity (gm/kg) Surface
--
Lower Upper 0 10-100 100-300 300-500 500-800
G
0 80 195 430 730
430 370 460 320 160
From Vorontsov (1959).
13 6 11 3 3
36 17
31 8 8
1.4 0.8 -0.1 -1.3 -0.2
1.4 -0.1 -1.3 -3.7 -3.1
5.2 5.1 2.9 0.0 -1.9
Limit of inversion
Relative humidity
(%)
Surface Limit of inversion
Lower Upper 3.8 3.4 3.3 3.7 3.5
3.8 3.5 3.3 3.5 3.1
5.1 3.9 3.7
-
3.1
Wind speed (meters/ sec)
Lower Upper 95 89 95 100 99
95 98 96 100 98
87 70 70 61 78
2.8 5.0 4.2 4.5
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
359
with the beginning of the sharp decrease of the relative humidity. When fogs were connected with elevated inversions the wind speed was distinctly higher than in fogs occurring with surface inversions, thus indicating that the increase of turbulent exchange resulted in a destruction of the surface inversion. Regarding the fog formation over ice fields conditions were particularly favorable if the ice concentrations was 7/10 to 9/10. Compact ice coverage as well as ice concentrations of 2/10 to 5/l0 were found to be less favorable. As the information given above deals mostly with advection fog, some additional remarks on steam fog or arctic sea smoke will be added here.* This kind of fog occurs if very cold air flows over warm water, as may happen on seas adjoining land with intense continental characteristics. Steam fog is distinguished by a strongly turbulent appearance which sometimes is referred to as spiraling steam columns rising from the sea surface. Kyriazopoulos and Livadas (1961), who examined five cases of steam fog occurring in coastal waters of Greece in autumn and winter after the passage of cold fronts, reported air-sea temperature differences of between - 13.0 and - 21.9°C and corresponding water vapor differences of between 6.9 and 15.7 mb. The intensity of fog formation seemed to increase with greater air-sea water vapor differences. The wind speed varied between 2 and 15.5 meters/sec with a prevalence of the greater speeds. The visible condensation only reached up to a few meters but, at some places, scattered columns of fog rose to 20-30 meters. Thus steam fog is normally confined to a shallow surface layer and its density is highly variable and, in general, small. This is due to the strong vertical mixing produced by the warm sea surface. By turbulent motion, the moisture evaporating from the sea is distributed over an appreciable height region. Rubin (1958), however, reported that over antarctic waters there occurred steam fog which was so dense that it reduced the visibility to as low as 100 meters. Aerological evidence revealed that a strong inversion was present near the sea surface which prevented thorough vertical mixing and caused the steam to accumulate in the surface layer. Such conditions can be expected if a shallow layer of very cold continental air flowing out over the warm sea is topped by warm air and if the mechanical turbulence is not strong enough to destroy the inversion. Steam fog may appear even in low latitudes, particularly in winter with outbreaks of cold air along the east or south coasts of the * A thorough study on steam fog was recently published by Saunders [(1964), see supplement to references].
360
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
continents where they are skirted by warm ocean currents [see, e.g., Stevenson (1962) who described a steam fog at Galveston, Texas]. An extreme case was observed 100 miles east of Cape Hatteras where the temperature of the air dropped to 25°C below that of the se a surface (Loewe, 1957). 5.3.5.3 Some Micrometeorological Observations in Ocean Fogs. Apart from the aerological and statistical discussion given in the preceding section, it is certainly of importance to obtain some knowledge of the micro meteorological conditions prevailing next to the sea surface, since, when dealing with fog, this is the zone that deserves the greatest interest. Unfortunately the results available are rather incomplete so far. Some relevant information can be taken from a study published by Wiener et al. (1961) who, although mainly interested in the propagation of audible sound over the sea, undertook a series of profile measurements of wind speed and air temperature in ocean fog up to a level of about 10 meters. In addition, they determined such properties of ocean fog as droplet size, liquid water content, and horizontal visibility. The temperature profiles showed near-neutral stratification and followed a logarithmic law. The shape of the wind speed profiles was, however, not exactly logarithmic, but had a curvature that corresponded to stable stratification. The significance of these results is minimized by the fact that the profiles were not measured over the water but at a location on the shore that was directly exposed to the winds prevailing with fog. The measurements of droplet size and liquid water content of fog led to the result that the most frequent droplet size in the droplet spectrum was appreciably smaller than the droplet size carrying the largest percentage of the total liquid water content. For instance, the most frequent droplet diameter was around 10-3 em, with a liquid water content of 0.0042 gm/rneter", whereas the maximum water content was attached to droplet diameters of about 2 x 10-3 em, The values of the liquid water content ranged between 0.0024 and 0.18 gm/meter", Estimates of horizontal visibility were obtained by observation of a row of marker buoys with black targets. Based on the concept that the visibility range must be a function both of liquid water content and of droplet size, these estimates were correlated to the liquid water content divided by the droplet size that carried the largest percentage of liquid water content. The results have been reproduced in
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
361
Fig. 109. Although the scatter of the measured values is relatively large, owing mostly to the deficiencies inherent in estimations of visibility, the correlation could be reasonably well represented by a straight line, which indicates that horizontal visibility decreases if the liquid water content increases more than the droplet diameter carrying the largest percentage of it. 10,000
,
5000
-,
-, .c -u; s "0 C
2000
•
•
I~
f'f'
.
1000
.,
~
1;
I
500
"-
.• -, • ".,
200
6 5 X 10·'
8
10"
2
3
4 5 6
8
10·'
2
3
4 5 6
gm -m"/cm-'
8
10"
Liquid water content/droplet size carrying the largest percentage of LWC
FIG. 109. Horizontal visibility correlated to the liquid water content (LWC) divided by the droplet size carrying the largest percentage of LWC. (From Wiener et al., 1961.)
5.3.5.4 Theory of Ocean Fog Formation. According to the formulation of the problem outlined in Section 5.3.5.1, the task set to theory is to give a combined quantitative treatment of the turbulent, convective, and radiative effects that may lead to the formation of sea fog. The combination of these processes is of particular importance, since usually, as was pointed out by Emmons and Montgomery (1947), the turbulent exchange alone is not sufficient for generating fog, but a net radiation from the air is required to achieve saturation and condensation. The relevant radiative processes were considered by Fleagle (1953), who computed the rate of temperature change at different heights due to radiation on the base of Schwarzschild's equation, assuming the following temperature profile in the transition layer near the ground: T - To = (Ta - To) (1 - e-l'Z) (5.78)
362
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
where Ta is the temperature of the upper unmodified air and To that of the surface. Here 'Y is a constant with the dimension of centimetervt. The blackbody emissivity of the surface was taken into account, as well as the net flux of radiation between parts of different air temperature within the boundary layer. The computation, in which the effect of radiation absorbed and emitted by carbon dioxide was neglected, led to the following result (see Fig. 110): Above a cold blackbody surface, the effect of radiation is to be seen in the warming of the layer next to the surface, since this does not emit as much as it receives from the warmer upper parts. The contrary occurs at the higher levels where the air is cooled, as there is a radiative outflow on account of the temperature being higher up .there than below. The two height regions of inverse radiative temperature change are separated by a level of zero change.
Height
10
··· ····
T
··, · ·.·
/' ,/,/ ,-'"
-4
-2
4
0
5
T-To
"
10
FIG. 110. Left: Vertical distribution of the rate of radiative temperature change computed for the temperature profile (5.78), using for y (A) 9.0 x 10-3 cm- I and (B) 1.6 x 10- 3 crrr'. Right: Vertical distribution of air temperature computed from (5.78) using y = 9.0 X 10- 3 cm- I and T a - To = 10° C. TD = Distribution of dew point. If curve A (left) is applied the shaded area represents the 15-minute radiative temperature change, and the dotted curve below 70 ern shows the fictitious temperature distribution. (From Fleagle, 1953.)
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
363
Fleagle (1953) estimated the height of this boundary between the regions of radiative warming and cooling at about 70 em. In the case of a warm surface, the effect of radiation is the opposite, i.e., the layer next to the surface is cooled, whereas the upper part is warmed. When applying these results to the formation of fog, Fleagle (1953) concluded that fog is preferably generated in the region of radiative cooling, i.e., it forms above a critical height if the surface is cold and below a critical height if the surface is warm. This result was criticized by Rodhe (1962), who pointed to the fact that the eddy exchange tends to minimize or compensate for the radiative effects and showed that even a change of the temperature profile much smaller than that obtained by Fleagle in the treatment described above would give rise to a turbulent heat exchange sufficient for balancing the radiative effect. Thus, the cooling which leads to fog formation must result from a combined action of both radiative exchange and eddy transfer. Preliminary ideas along this line already have been published by Douglas (1930). A comprehensive study on the subject was given by Rodhe (1962). He first concentrated on finding characteristic elements that remain constant in closed eddies that move upward and downward, irrespective of whether these eddies contain saturated vapor or not. After investigating the thermodynamics of saturated and unsaturated air, the results of which cannot be reproduced here in detail, and assuming that the inertia of the liquid drops is so small that they are transferred by eddies in the same way as vapor, he arrived at the result that the potential wet-bulb temperature B' and the mixing ratio m of the total water content of the air can be considered as such conservative quantities. Here, m is the sum of the saturation mixing ratio me of water vapor and of the mixing ratio m» of liquid water content. With unsaturated air, m.; is negative. Passing to the eddy exchange of heat and moisture, Rodhe (1962) related the vertical eddy transfer of total heat content, which consists of the vertical eddy flux H of sensible heat plus that of latent heat HE, to the vertical gradient of the potential wet-bulb temperature B'. Similarly, the vertical eddy flux E of water vapor and liquid drops is proportional to the vertical gradient of the mixing ratio m of the total water content. Assuming equality of the eddy transfer coefficients for heat and water content, and replacing the potential wet-bulb temperature B' by the wet-bulb temperature T, which is permissible near the surface, as well as neglecting some factors of minor importance, Rodhe arrived at the following relation between the wet-bulb temperature
364
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
and the total water content in a boundary layer adjacent to the ground surface:
_ E [c
~
dT' - H + HE
P
+ T'~ (Lm~)]
(5.79)
T'
dT'
Here, L is the latent heat of vaporization and m~ designates the saturation mixing ratio of water vapor at the wet-bulb temperature. Integration of Eq. (5.79) furnishes the distribution of water content in relation to the temperature and dependent on the boundary conditions. The solutions can best be discussed by means of a diagram in which abscissa and ordinate represent the wet-bulb temperature T' and the mixing ratio m of the total water content, respectively (Fig. 111). The curve A corresponds to saturation; consequently, the ~
E !! c: c:'"0
12 II
10
o
9
'" '0
8
V
~
0
2
6
'0 Ii:
5
!2 ~
'" c .;;<
/'
7 Fog
B,.- /'
4
3 ,-;/
2
./'
/'
"",,;/
/'
/'
/'
»:
/-
Unsaturated air
i 0 -15
-10
-5
o
5
10
15
Wet - bul b temperoture T' (OCI
FIG. 111. T, m diagram with saturation curve (A) and integral curve (B) of Eq. (5.79) for constant Ej(H + HE). (From Rodhe, 1962.)
area to the right of A represents unsaturated air while to the left there is the area of air with liquid drops suspended, i.e., of fog. The area enclosed by the integral curve of Eq. (5.79) and the saturation curve or, more exactly, the area to the left of the saturation curve and to the right of the integral curve, is a measure of the liquid water content available for fog formation. Under nonradiative, steady conditions the quotient Ej(H + HE), which is closely related to the Bowen ratio (see Section 5.2.2.4),
5.3
THERMODYNAMIC PROCESSES OF MEDIUM SCALE
365
may be considered as constant. A corresponding integral curve is labeled B (Fig. Ill). The inclination of the curve to the abscissa essentially depends on the quotient E/(H + HE), as may be determined from Eq. (5.79). The curve shows that, under such circumstances, a comparatively large temperature difference between the base and the top of the fog layer is required if an appreciable amount of liquid water is to be formed. Hence, extreme vertical temperature differences are conditional for fog formation due to turbulent exchange alone. This result does not agree with the conditions prevailing in maritime fogs (see, e.g., Nurminen, 1957). Conditions, however, change if the assumption of constant E/(H + HE) is abandoned, i.e., if processes other than turbulent exchange contribute to E/(H + HE). Supposing that no drops fall out by coalescence and no precipitation occurs, E may be considered as completely determined by eddy exchange. Hence, the possible variation of E/(H + HE) is essentially due to H + HE. Now, radiative effects come into play. The starting process of radiation fog formation is the blackbody radiative cooling of the ground which causes a heat loss by molecular and turbulent convection in the layer adjacent to the surface. With adequate moisture present, fog is generated in the inversion layer. If the density of the fog is increased sufficiently, the blackbody emissivity of the water droplets becomes effective and will result in the upper part of the fog layer taking over the role of the radiating ground. The consequence is that, in order to balance the radiative heat loss at the top of the fog, the downward eddy flux of heat must be greater above the fog layer than in it. Under steady state conditions, this is connected with a vertical gradient of the wet-bulb temperature that is greater above the upper limit of the fog layer than below it. As the eddy flux of the total water content is not influenced by these conditions, but remains constant with height, the radiation will effect a change in the curvature of the characteristic curve in the T', m diagram. Under nonradiative conditions only turbulent exchange is effective, and the integral curve of Eq. (5.79) is as shown by B in Fig. 111, i.e., concave to the m axis. However, with the radiative effects described above, the characteristic curve is convex to the m axis. This change is essential since it provides a reasonable content of liquid water at a temperature difference across the fog layer that is much smaller than was required for the formation of pure advection fog which is only caused by turbulent exchange. After investigating the effects exerted by radiation on the formation of fog, let us now pass to discussing the "mixed" cases where
366
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
radiative and turbulent exchange effects are combined. Following Rodhe (1962), we might best do so by schematically comparing four diametrically different cases. The two cases presented at the top of Fig. 112 show a radiative heat loss near the top of the fog layer (at C) which is compensated by a corresponding eddy heat flux. With warm air above a cold sea surface (left-hand side), the major part of eddy heat transfer occurs above the fog and is directed downward.
rt 3I'f; Warm air Cold surface
~::~',::,
Net.
R
Cold air Warm surface
T'mAmLL C~A c B
-
D
Y
H
..
mc
B
D
;,
. T
FIG. 112. Schematic graphs (vertical distributions of T' and m; characteristic T', m diagrams) describing the effects of radiative heat loss and gain on fog. Upper part: net radiative heat loss R (at C); lower part: net radiative heat gain R (at C), Left: Warm air flowing over a cold surface. Right: Cold air flowing over a warm surface. A, Nonsaturated air above the fog; B, top of fog layer; C, zone of radiative heat loss or gain; D, surface. (From Rodhe, 1962.)
With cold air above a warm sea surface, however, the eddy heat flux is confined to the fog layer and is directed upward whereas, above the fog, the gradient of the wet-bulb temperature and,consequently, the upward eddy transport of heat are reduced to zero. Thus we can say that, in this region, the eddy flux of total heat content is completely replaced by the net radiative transfer. In both cases a discontinuity of the characteristic curve in the T', rn diagram occurs near the top of the fog layer causing an appreciable amount of liquid water to be obtained at not too great a temperature difference. The reason for this result is that, owing to radiative effects, the sink of eddy heat flux is located at a level different from that of the eddy transfer of total water content. There should be mentioned the fact that the eddy transfer of total water content is not affected by the fog. Consequently, with cold air flowing over warm water there must be evaporation at the sea
5.4
TIME VARIATIONS
367
surface in spite of the presence of fog, whereas condensation must occur at the sea surface in the case of warm air above cold water. If we assume that a net gain of radiative heat is established near the top of the fog layer, the lower part of Fig. 112 holds true. From the picture it is clear that under such conditions no amount of liquid water will become available for the maintenance of fog. There will rather be a tendency for fog dissipation.
5.4.
TIME VARIATIONS OF AIR TEMPERATURE AND HUMIDITY
As has been shown in the foregoing sections of this Chapter, the temperature and the humidity at a certain oceanic locality are determined by the combined action of radiative, convective, turbulent, and advective processes. Owing to various circumstances, these influences change with time. Consequently, temporal variations of air temperature and humidity also will occur at such a station, in particular, air temperature or humidity will increase when there is more heat or moisture absorbed than emitted and vice versa. Constant or extreme values can be expected when the gain is balanced by the loss. Owing to the nature of the influences concerned, the temporal variations of air temperature and humidity can be periodic or nonperiodic. Periodic changes must ultimately originate from the diurnal and annual cycles of insolation, whereas aperiodic variations are caused by a broad spectrum of atmospheric phenomena which extends from climatic changes down to turbulent fluctuations. 5.4.1 Diurnal Variation 5.4.1.1 Results of Special Measurements of Air Temperature. The daily variations of air temperature and humidity are studied on the basis of averages referring to particular hours of observation. If the locality is not a fixed station, i.e., if the measurements are taken on a moving ship, allowance must be made for the change of position. This is mostly done by applying the correction of Lamont, i.e., by equalizing the two midnight values of one day and distributing the difference linearly to the observational hours of that day. This simple procedure does not work satisfactorily unless the ship's speed is kept steady. If, however, sailing and drifting periods change in irregular sequence, as they often do with research vessels, special care must be taken to eliminate the disturbing effect of the ship's motion.
368
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
First we are going to gather information on the diurnal variation of air temperature. As the convective and radiative heating originating from the environment of the thermometer may cause a misleading increase in the air temperature readings taken on shipboardan increase which is most pronounced around noon-it does not seem easy to get reliable data for evaluating the diurnal variation. In particular, we should be doubtful as to the reliability of older investigations which resulted in a diurnal temperature range at sea of from 1 to 1.5°C or more. This subject was carefully studied by Kuhlbrodt (Kuhlbrodt and Reger, 1938) who secured comparative records of air temperature at an exposure on the wheelhouse and on the top of the mast during the expedition of the German research vessel Meteor in the South Atlantic in 1925-27. The latter measurements were checked by means of a ventilated psychrometer. After closely scrutinizing the material, Kuhlbrodt obtained the results summarized in Fig. 113. They show a diurnal range of air 0.3,---,----,-----,--,---,----, G
!!.c c
'"E
0.2
>-
c -e
0.1
'"
=
~
0
\
\
\
x,
x, !
!
!
12
16
20
X_X-X'j 24
Local time (hours)
FIG. 113. Diurnal variation of mean air temperature in tropical and extratropical regions of the Atlantic Ocean. (After Kuhlbrodt and Reger, 1938.) Ti, from thermograph records taken in a screen on the wheel house; T2, from resistance thermometer records taken on the top of the mast. Difference of daily averages (Tl - T2) = 0.09° C.
temperature that amounts to 0.45°C if the temperature was measured in a screen on the wheelhouse. On the other hand, the diurnal range was reduced to O.28°C if the distant reading thermometer installed at the top of the mast was used. This result is of considerable interest when compared with the diurnal range of the mean temperature of the sea surface. Bearing in mind that the latter was determined by Kuhlbrodt to be O.26°C for nearly the same maritime regions (see
5.4
TIME VARIATIONS
369
Section 5.1.4.1) one could, similarly to Kuhlbrodt, be inclined to conclude that the diurnal variation of air temperature above the sea is primarily controlled by the processes of convection and turbulence and thus chiefly depends on the diurnal course of the sea-surface temperature. This would imply that direct absorption and emission of radiation by the air does not play more than an insignificant role in producing the diurnal variation of mean air temperature above the sea surface. There are, however, other facts not to be overlooked before a final conclusion can be drawn. First it must be pointed out that in the measurements of Kuhlbrodt the average air temperature wasat all hours and in all oceanic regions-well below (-o.rq the mean temperature of the sea surface. Hence, the average convective heat flux was directed upward from the sea to the air and the determinative influence of the sea, which was stated by Kuhlbrodt, is explained well enough if we assume that the measured values of the sea temperature were really representative for the sea surface. Certainly the case "air colder than water" applies to the majority of the thermal conditions occurring at sea. Nevertheless it would be interesting to know how the diurnal courses of temperature in the air and at the sea surface are related in the admittedly rare cases when the air is warmer than the sea. Up to now no pertinent information has been available. But even if we restrict our discussion to the case "air colder than water," there are still some arguments left advocating the significance of radiative processes for the diurnal variation of air temperature at sea. For instance, evidence was given by Wegener (1911), Braak (1914), and Roll (1939) that the diurnal range of air temperature in the boundary layer above the sea increases with altitude contrary to its behavior on land. [A more recent result, reported by Harris et al. (1962) and stating that the amplitude of the diurnal temperature wave over the Azores decreases with height (from 1.12°C at the surface to 0.14°C at 700 mb) need not contradict the former findings because the lower part of the soundings made on the Azores may not be strictly maritime, but could be influenced by the island of Terceira.) In addition, Roll (1939) furnished observations showing that at sea the daily temperature maximum occurred earlier at higher levels than at lower ones. The phase difference between the height of 150 meters and the lowermost layer amounted to about 1 hour. The observed changes with height of amplitude and phase agree well with the interpretation of the diurnal temperature variation in the planetary boundary layer as given by Schmidt (1920), who assumed
370
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
the phenomenon to be composed of a convective and a radiative component. Above the sea surface, these two partial waves act in the opposite sense, resulting in a diurnal temperature variation that was found to be considerably smaller than that on land. From a comparison of Figs. 78 and 113 we can further derive that the daily temperature maximum occurs considerably earlier in the atmospheric boundary layer (at about 1200 hr) than at the sea surface (at 1500 hr), and that, consequently, during a certain period of time, a decrease of air temperature is accompanied by an increase of sea temperature. All these facts can only be explained if some importance is also attached to radiative processes in the lower atmosphere above the sea. 5.4.1.2 Some Findings on the Basis of Routine Observations of Air Temperature. Besides the laborious study carried out by Kuhlbrodt (Kuh1brodt and Reger, 1938), other investigations on the same subject have been performed more recently. They are based, in part, on observations made on merchant vessels (Bintig, 1950), and, in part, use was made of the temperature measurements obtained on ocean weather ships in the North Pacific Ocean (Koizumi, 1956a, c), as well as in the North Atlantic Ocean (Rosenthal and Gleeson, 1958). Since all these studies deal with routine observations, it is understandable that their results differ from the findings obtained by Kuhlbrodt during a special expedition, particularly as regards the diurnal range of air temperature which, in the more recent publications, is considerably higher than the value of 0.28°C found by Kuhlbrodt and which, hence, must be considered as questionable. Nevertheless, the comprehensive new material allows us to study the influences of latitude, season, wind, cloudiness, and air pressure on the diurnal temperature variation, considerations which could not be discussed in detail when only Kuhlbrodt's older results were available. The latitudinal and seasonal changes in the range of the diurnal variation of air temperature are clearly indicated in Table XXXVI, which was compiled by Rosenthal and Gleeson (1958). The diurnal temperature range is smallest in winter, greatest in summer, and increases with decreasing latitude. Thus these changes reflect the influence of insolation. The same authors also presented evidence for the seasonal change of the time of the daily temperature maximum. In summer it occurs later than in winter. The time lag between the temperature maximum and the true solar noon ranges from 2t to 4 hours in early
TABLE PERIODIC DIURNAL RANGE OF AIR TEMPERATURE
Stations
M,A I, B
C, J D E,H
a
Average latitude 64.0 oN 57.9 52.65 44.0 35.85
From Rosenthal and Gleeson (1958).
XXXVI
(OC) AVERAGED OVER NORTH ATLANTIC WEATHER SHIPS' STATIONS OF SIMILAR LATITUDEa
January February 0.22 0.31 0.33 0.61 0.75
March April
May June
July August
0.47 0.53 0.64 0.83 1.06
0.61 0.81 0.72 1.06 1.36
0.61 0.69 0.75 1.22 1.47
September October 0.36 0.42 0.42 0.89 1.03
November December 0.17 0.22 0.33 0.50 0.72
372
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
summer, whereas it varies from 0 to 2 hours in winter, which is also a radiation effect. In order to study the temperature minimum, Rosenthal and Gleeson (1958) formed bimonthly averages of the zone time of sunrise minus the time of minimum temperature for all the weather ships' stations in the North Atlantic Ocean and obtained about 2t hours in winter and only t hour in summer for that difference. As an explanation of the temperature minimum occurring considerably before sunrise, as it does in winter, the authors offered the conclusion that there must exist a heat source which is capable of exceeding the radiative heat loss of the air during those night hours. It seems quite obvious that this heat is mostly supplied by convective and turbulent transports from the sea surface, whose temperature excess over the lower atmosphere is much greater in winter than in summer. Similar results were published by Koizumi (1956a) for two weather ships' stations in the North Pacific Ocean. The effects of wind speed and cloudiness on the diurnal range of air temperature were studied by several investigators, particularly by Bintig (1950), who found some indication of a decrease of the diurnal temperature range with increasing cloud amount, as well as with growing wind velocity. With zero wind force, it was about 2.6°C. It dropped to 0.9°C if the wind force rose to 8 Beaufort. This wind effect may be qualitatively interpreted in two ways: First, we can state that the higher wind speed is associated with stronger mechanical turbulence, thus causing the heat gained from the sea to spread over a layer of air which, in this case, is thicker than with lower wind velocities, and, consequently, resulting in a decrease of the diurnal temperature variation. On the other hand, the vertical spreading of water vapor by turbulence can be taken into consideration, as was suggested by Rosenthal and Gleeson (1958). With low wind speed, the moisture is mostly concentrated in the lowest atmospheric layer. A relatively high amount of incoming radiation reaches this layer, and is absorbed there, thus giving rise to strong radiative heating and, in connection with an intense outgoing radiation during the night, to a considerable diurnal variation of air temperature. With high wind speed, however, water vapor is distributed over a thicker layer of air and, so, in the bottom layer, we observe a reduction of the radiation effect, as well as of the diurnal temperature variation. Comparing these findings with the results described in Section 5.1.4.1 on the diurnal variation of the sea surface temperature, we
5.4
TIME VARIATIONS
373
can say that, on the whole, there are distinct parallels between these two phenomena. It may be expected that the relation between the diurnal temperature course in the air and that at the sea surface is particularly close when the sea is warmer than the air. So far, no relevant study has been published dealing with that influence of thermal stratification. One difference, which was pointed out by Koizumi (1956a, c) should be mentioned. He obtained diurnal variations of mean air temperature which showed a somewhat more complicated shape than those of the sea-surface temperature, namely, a characteristic swelling occurred at around 0900 hr local time, becoming comparable with, or even surpassing, the primary maximum in the early afternoon. The explanation offered by Koizumi was that the diurnal oscillation of atmospheric pressure might be considered as one of the possible causes of the effect observed. If the variation of the atmospheric pressure progresses adiabatically, the air temperature will rise when the pressure increases and vice versa. Quantitative estimation showed that in most cases the curve of mean air temperature was favorably corrected if the effect of atmospheric pressure variation was taken into account. Naturally, this effect, which in general is much smaller than 0.2°C, deserves attention only at sea where the diurnal range of air temperature is very small. 5.4.1.3 Evaluation of Humidity Records. In conclusion, a few remarks will be added on the diurnal variation of humidity, although the information available is very scanty, owing to the particular difficulties inherent in humidity observations at sea. Perhaps the best study on this subject is still that given by Reger (Kuhlbrodt and Reger, 1938), who discussed the humidity records obtained during the South Atlantic expedition of the German research vessel Meteor in 1925-27. Since these records were taken in a screen fixed just above the wheelhouse, the results must be considered with reserve, though. The diurnal variations of relative and absolute humidity, as computed by Reger by subjecting the records to harmonic analysis, are given in Fig. 114. The two graphs refer to the equatorial zone and to the trade regions, respectively. In both diagrams the diurnal variation of the relative humidity is represented by a single wave with a minimum at 1300 or 1400 hr and a maximum around 0400 hr. In general, this course is inverse to the diurnal variation of air temperature. Of particular interest is the diurnal variation of the absolute humidity which was obtained from the relative humidity by means of
374
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
the corresponding temperature data. Here, a distinct double wave appears in the equatorial zone. Its extreme values coincide completely with those of the diurnal double wave of the atmospheric pressure. %
o
-- --- --'\.
-I
-2
A
"-t'......
..-/
I
/ " , V
"
,,
Relot,ve humidity
o
4
--- --- --, <, o
B
<,
8
,, ,
.>
/'
humidify
-,
r-,
..../, /
"-
,
-01
,
\
/'
\
20
V-
V ,I
I
I I
,
/
/
,
.......
,,
o
4
8
-
,
/
,
/
gm/m 3
,.
02 0.1
<,
00
I
humidity
I
16
.....
//
e.-- Relchve -2
-
/
,/
I-- t--
00
l,f"
12 16 Locol time (hours)
Absolute humidity-,.'
0.1
k7' <,
<, ....--~bsolute
" V
20
- 01
-02 24
Local lime (hours)
FIG. 114. Diurnal variation of mean relative and absolute humidity in the equatorial zone (50 N-5° S) (A) and in the trade regions (B) of the Atlantic Ocean. [From Reger (Kuhlbrodt and Reger, 1938).]
Although conclusive evidence cannot be given, it seems reasonable to assume that the diurnal variation of the absolute humidity is controlled by the diurnal variation of evaporation which, for its part, shows a similar double period (Sverdrup, 1943a), and which possibly depends on the diurnal variation of wind velocity. In tropical regions the latter quantity, too, displays a diurnal double wave (cf. Fig. 72) which is closely related to the well-known diurnal double wave of atmospheric pressure. But there is, as yet, no explanation of the fact that the double oscillation found in the equatorial zone (Fig. 114 A) is not present in the diurnal variation of the absolute humidity derived for the trade regions (Fig. 114 B). 5.4.1.4 Theoretical Approach. Some pertinent information can be drawn from a theory recently published by Bernard (1962), who attempted to give a rational treatment of the diurnal (or annual) temperature variation in the "atmosphere-continent" boundary layer and in the "atmosphere-ocean" boundary layer. On the condition that insolation and global radiation vary with time according
5.4
TIME VARIATIONS
375
to a cosine function, the two equations of heat transport in the atmosphere and in the ocean were integrated. Herewith, there were taken into account all the determining physical factors, except advective influences in atmosphere and ocean, and, in particular, the energy balance equation was regarded as a boundary condition at the sea surface, z = O. The eddy conductivities KH in air and water were supposed to be constant. As a solution, we get the absolute temperature of the air T, as a function of the height z and the time t, in the following form: T(z, t) = To + jz + ao exp[ - (7Tf.&KH)1I2Z] (5.80) cos
[2;t _ (.&;J
1I2
Z -
0
0]
where To = mean temperature of the sea surface over a complete period -& j = vertical gradient of air temperature ao = amplitude of temperature variation at the sea surface (z = 0) -& = period of oscillation of the insolation (day, year) KH = eddy conductivity in air 80 = phase lag of the temperature variation at the sea surface (z = 0) For z = 0, Eq. (5.80) represents the periodic variation of the seasurface temperature generated by the oscillation of insolation. We see, further, that the temperature variation has the same period as the generating oscillation of the insolation but it differs in amplitude and phase from the latter. The damping of the amplitude and the lag in phase depend on the physical factors contributing to the transport and to the transformation of radiative energy in atmosphere and ocean, as well as to the related turbulent and convective transfer processes. As regards the thermal regime in the ocean, two different models were used. The first was an isothermal model, i.e., an extremely well-mixed water mass was assumed as upper layer of the ocean. As a second approximation a more realistic model was studied, characterized by a finite, but constant, value of eddy conductivity in water, and attention was paid to the fact that the variable transparency of the ocean water with regard to the solar radiation requires the introduction of an extinction coefficient which was taken as constant with depth. Finally, it should be mentioned that, by superposition of harmonic oscillations, the theory could be adapted to the more general case
376
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
where insolation and total radiation vary with time according to an arbitrary periodic function. The solution given by Bernard for the maritime model cannot be reproduced and discussed here in full detail. It can only be mentioned that the damping of the thermal amplitude ao at the sea surface is controlled by the eddy viscosities in air and water, by evaporation, by the effective back radiation, and by the transparency of the ocean water. In particular, the decrease in amplitude is the stronger the lower the values are which are accepted as the extinction coefficient. The phase lag 00 at the sea surface depends on the same factors. In the case of extreme transparency of the ocean water, the phase lag can approach its maximum value TT/2 which corresponds to 3 months or to 6 hours for the annual and diurnal variations, respectively. In reality, neither the extinction coefficient nor the eddy conductivity are constant in the ocean as was assumed by Bernard. Rather, it is known that the extinction coefficient decreases with decreasing wavelength of radiation and that the eddy conductivity in water decreases with increasing depth and varies seasonally. Hence, the theory presented by Bernard (1962) offers further possibilities for refinement. Bernard applied his theory to several practical problems and obtained, among others, the result that the damping of the diurnal range of sea-surface temperature is always considerably greater than that of its annual variation. Further, he found that the diurnal range of sea-surface temperature must be confined to only a few tenths of a degree centigrade. Both these theoretical results agree well with observational experience. Up to now no results of comparisons between theoretical and measured values of the diurnal variation of air temperature above the sea have become available. 5.4.2 Annual Variation 5.4.2.1 Air Temperature. As regards the yearly oscillation of the mean air temperature above the sea surface, advantage can be taken of the rather close relation between the temperature in the air and that at the sea surface which was already apparent during the discussion of the diurnal variation. That this connection also exists in the yearly course may be taken from the example given in Fig. 115 which shows the annual variation of both air and sea temperature in an area where the maritime regime is undisputed. The two curves run more or less parallel with exception of the early summer months where the heating in the atmosphere seems to be somewhat more
5.4
377
TIME VARIATIONS
intensive than in the ocean, which suggests the direct absorption of radiative energy in the atmosphere during that period. In both cases, the maxima and minima occur in August and March, respectively, whereas the annual range reaches 6.7°C in the atmosphere and 5.8°C in the sea. Thus, it is, by about 15 per cent, higher in air than in water. °C 18 r-.----.----.--r--r--.------,--,,----,------.--,--,
17 16
15 14
13
II
x ' IO[--X--X'
9 I
!
,
II
III
I
x/
IV
I
I
I
V
I
I
I
I
1
VI
VII VIII
IX
X
XI
XII
I
FIG. 115. Annual variation of mean temperature of the air and at the sea surface in the area 48-49° Nand 24-26° W of the North Atlantic Ocean. (After Markgraf and Bintig, 1956.)
The example given above seems to be applicable also to other oceanic regions so that the relevant results summarized for the seasurface temperature in Section 5.1.4.2 can be used in order to provide a global review of the annual course of the air temperature at sea. This is all the more useful as a new compilation, similar to that provided by Stepanov (1961) for the sea surface temperature (see Fig. 79), obviously does not exist for the air temperature so far. From the U.S. Navy Marine Climatic Atlas of the World some information can be drawn about the annual range of air temperature. There appears to be a maximum of about from 6 to 10°C around the latitudes from 30 to 40° and a decline toward the equator, where the annual range is from 1 to 2°C. Strong deviations, however, occur in the middle latitudes of the western parts of the oceans where influences from the continents and from cold water regions cause an increase of the annual temperature range up to 1O-20°C. Concerning the phase of the annual variation of air temperature, an informative review was given by Prescott and Collins (1951), who published world maps showing the lag, in days, of air and sea temperature behind solar radiation. In general, the phase of sea temperature was 10 days later than that of the corresponding air
378
5
THERMODYNAMIC PROCESSES IN MARlNE ATMOSPHERE
temperature. The greatest lags occurred in the tropical latitudes of the eastern parts of the Atlantic and Pacific Oceans where they reached 100 days for the air temperature and 110 days for the sea-surface temperature. 5.4.2.2 Humidity and Evaporation. Even less is known about the annual variation of the humidity of the air, which is understandable since reliable measurements of atmospheric humidity on a large scale were not started earlier than at the end of World War II. So far, there are available only very few studies which are concerned with the annual course of the humidity at sea. Brown (1952), who compared observations made at the ocean weather station "J" with others obtained on merchant vessels in the same region, found close agreement between these two groups. [See curves (a) and (b) in Fig. 116.] The correlation coefficient between these two sets of average monthly vapor pressures is 0.973. The annual variation of mean vapor pressure showed a maximum in August and almost equally high values in July and September. In addition, both series give a secondary maximum in March followed by a secondary minimum in April which was attributed by the author to the much greater frequency of northwesterly winds, as compared with southwesterly winds, in April than in March in that area. The annual variation of the mean water vapor pressure was closely related to that of the mean saturation vapor pressure computed from the mean sea-surface temperature, the correlation coefficient being 0.97. Another statistical study on humidity at sea was published by Markgraf (1961), who presented some results for the Mediterranean Sea. The annual curve of mean water vapor pressure has its maximum in August, too, but no indication was found of a secondary maximum in March [Fig. 116(c) and (d)]. The annual range is remarkably large and reaches, or even exceeds, the values characteristic of the Indian monsoon region. An interesting finding of that study is that, contrary to the conditions on land and at coastal stations, the maxima of the relative humidity occur in summer, whereas the minima fall in the winter months. This result reveals a general oceanic feature and may be related to the well-known summer maximum of the frequency of sea fog in middle and high latitudes. Markgraf (1961) first attributed the summer maximum of the relative humidity found in the Mediterranean to an increase of evaporation. This interpretation must be questioned, and it certainly cannot be applied in general. Unfortunately, there are no continuous measurements of evaporation at sea
5.4
379
TIME VARIATIONS
which allow us to calculate its annual variation. Therefore, we are dependent upon values that were computed, on the basis of a theoretical formula, by means of marine meteorological data covering a full year. This was done by Hanzawa (1950) for two ocean weather stations in the North Pacific Ocean and, although the formula used by him may meet some criticism, it seems to be rather certain that we can put confidence in the relative proportions of these values. They show, however, a minimum of evaporation in summer and a mb
30 r--.-------r---.-.--..---.-,---,-----r-----,r--.----,
29
t
28
I
I
27 26
I I
25
x
I
24
I I I I I
23
22
I I
.....
.....x
\
\
\
\
\ \
\ \
x \ \
\
\
\
\ \
I
21
k\
I
I
20 19
d I
18
I x I
17 16
I
I
x
\
\
I
\ \ \
\
\\
I
I I I
15
\
\
x
\
\
I I
I
II
\
x
III
IV
V
VI
VII VIII IX
X
XI
XII
I
FIG. 116. Annual variation of mean water vapor pressure (in millibars) at sea, (a) North Atlantic, 50-58° Nand 12-24° W, merchant ships (Brown, 1952). (b) North Atlantic, 52-56° Nand 14-22° W, weather ships (Brown, 1952). (c) Mediterranean, 36-37° Nand 0-3° W, merchant ships (Markgraf, 1961). (d) Mediterranean, 33-34° N and 32-34° E, merchant ships (Markgraf, 1961).
380
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
maximum in winter. This summer minimum can be related to the Bai-u (rainy season) phenomenon of that region. In a later paper, Markgraf (1962) explained the summer maximum of the relative humidity at sea by pointing to the differences between the annual variations of the vertical temperature and water vapor gradients in the lowest layer above the sea. According to Brown (1952), the difference between the saturation vapor pressure computed from the monthly averages of the sea-surface temperature and the corresponding mean vapor pressure of the air is fairly constant throughout the whole year. Contrary to that, the mean sea-air temperature difference is considerably larger in winter than in summer, as may be inferred from Fig. 115. The combination of these two facts with the annual variation of air temperature results in the conclusion that in summer the relative humidity is greater than in winter. 5.4.2.3 Comparison with Theory. Attempts to derive theoretical formulae for the annual variation of air temperature, humidity, or evaporation have only become known with reference to the first quantity (Kurbatkin, 1957; Bernard, 1962). A short discussion of the theory of Bernard, which applies to the diurnal variation of air temperature as well, was already given in Section 5.4.1.4. Here, it must be added that the theoretical values for the lag in phase between temperature and solar radiation can be compared with a statistical study by Prescott and Collins (1951) who examined the annual course of air and sea surface temperatures by harmonic analysis and, in particular, computed the differences between the phase angles of the first harmonics of both air and sea temperature and solar radiation. World maps were presented showing the phase lag of these temperatures behind solar radiation. The annual variation of air temperature on the oceans is distinguished by a much greater phase lag than that on the continents. Inland basins have the smallest lags, about 20 days, whereas up to 100 days are found on the oceans, which clearly shows the great effect of heat storage in water. The maximum values for the phase lag of the sea-surface temperature reach 110 days and thus, surpass the highest possible value that is supplied by theory for an extremely transparent ocean (according to Section 5.4.1.4: 3 months). This difference may, however, be attributed to the effect of marine currents which was not taken into account by the theory of Bernard (1962). 5.4.3 Nonperiodic Variations In view of the fact that the nonperiodic variations of air temperature and humidity comprise an extremely large time scale as far as
5.4
TIME VARIATIONS
381
their duration is concerned, it seems suitable that we apply the same procedure as for the sea-surface temperature (Section 5.1.4.4), namely, that we take the time as principle of order when attempting to compose a concise review on these phenomena. Following this scheme we should start with the discussion of long lasting processes and then proceed to phenomena of shorter duration. Unfortunately the observational material for such a discussion is very incomplete. There exist quite a number of investigations that aim at clarifying the properties and causes of temperature variations of medium and long duration-mostly by means of "anomalies," i.e., deviations from the "normal" values-but they deal, almost exclusively, with the temperature of the sea surface and not with the air temperature above the sea. The reason for this apparent "tradition" may be that the measurements of sea-surface temperature as made on shipboard-in particular those from former timesappear to be more reliable and, owing to their relatively small scatter, also more suitable for such investigations than the corresponding observations of air temperature. In meteorological studies devoted to the interrelations between ocean and atmosphere, the adoption of the sea-surface temperature offers the additional advantage that an element has been selected which represents important oceanic as well as atmospheric features (see, e.g., Bjerknes, 1962). Thus, the scope of this section is very limited. Owing to lack of material, only the aperiodic diurnal range and the interdiurnal variability of the air temperature at sea can be discussed. 5.4.3.1 Aperiodic Diurnal Range of Air Temperature. The aperiodic diurnal range of the air temperature is defined as the difference between the maximum and the minimum temperatures for a given day. Averages can be formed over a month, a year, or any other period. Contrary to the periodic diurnal temperature range, which represents a "quasiabstract" result obtained by averaging over many observations, the aperiodic diurnal temperature range measures the temperature change which actually occurred at a .given day. It contains the periodic component but, in addition, it reflects the influences of the atmospheric circulation, of moving cyclones and anticyclones, and of flowing air masses. As was shown by Rosenthal (1960b), the percentage of days having an aperiodic diurnal temperature range greater than or equal to the periodic one amounts to at least 90 per cent at the North Atlantic weather stations from November to April. The statistics of this quantity describe what can happen really with the air temperature within one day at a certain station.
382
5
THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE
Among the first who supplied some information on this quantity was Kuhlbrodt (Kuhlbrodt and Reger, 1938), who gave relevant statistics of the temperature observations made in the South Atlantic Ocean during the expedition of the Meteor in 1925-27. Summarizing his results, we can say that in the tropical Atlantic Ocean the aperiodic diurnal range of the air temperature had an average of 1.6°C. The maxima ranged between 2.8° and 6°C. The minima lay between 0.3° and 0.6°C, thus approaching the periodic diurnal range of the air temperature. In the middle latitudes of the South Atlantic the average aperiodic diurnal range increased to 2.l°C. Recently, rather comprehensive statistics on the quantity in question were published by Rosenthal (1960b) on the basis of the temperature observations of nine ocean weather stations in the North Atlantic Ocean over a period of about 5 years. In Table XXXVII we reproduce bimonthly averages and maximum values for the winter and summer months. They clearly show that, contrary to the periodic diurnal range of air temperature (cf. Table XXXVI), the aperiodic diurnal range attained its greatest values in winter and had a minimum in summer. The same is true for the dispersion of the frequency distribution, as may be concluded from the maxima given in Table XXXVII. We can easily explain this result by referring to the increase of the atmospheric circulation over the North Atlantic during the winter. Only station "E" is an exception: here almost no seasonal variation occurs, which, according to Rosenthal (1960b) is probably an effect of the location of this station with respect to the North Atlantic subtropical anticyclone. Further, it should be noted that there is a distinct oceanographic influence which we tried to make evident, as far as possible, by arranging the entries in Table XXXVII according to the positions of the stations. Those localities that are situated near zones of discontinuity in the ocean, such as stations "B", "D," "H," and, to a minor degree, "C" which lie in the boundary region between warm and cold currents, are distinguished by a relatively large aperiodic diurnal temperature range. Lower aperiodic changes are observed at the stations lying in the central part of oceanic current systems, which is the case with the stations in the eastern North Atlantic Ocean.
5.4.3.2 Interdiurnal Variability of Air Temperature. The difference between two consecutive mean daily air temperatures is called the interdiurnal variability of air temperature. Average values of this quantity can be formed over a particular month, over a year, or over any other suitable time period.
TABLE XXXVII APERIODIC DIURNAL RANGE OF AIR TEMPERATURE (OC) AT THE NORTH ATLANTIC OCEAN WEATHER STATIONSa,b
Station B (56.5° N, 51.0° W) Mean Max
Jan/Feb.
3.3 9.5
July/Aug.
1.9 3.9
I
Station A (62.0° N, 33.0° W) Mean Max C (52.8° N, 35S W) Mean Max
H (36.7° N, 69.6° W) Mean Max
3.9 10.6
2.3 5.0
Jan/Feb.
2.7 7.8
3.2 8.3
b
July/Aug.
2.4 6.7
1.3 3.3
1.8 4.4
I (59.3° N,c 16.4° W) Mean Max
2.4 7.8
1.3 3.9
J (52S N, 20.0° W) Mean Max
2.2 7.2
1.6 3.9
1.7 3.9
D (44.0° N, 41.0° W) Mean Max
4.3 11.7
2.7 6.7
E (35.0° N, 48.0° W) Mean Max
2.2 5.6
2.2 5.6
Bimonthly averages and maximum values for winter and summer months. After Rosenthal (1960b). c Average position.
a
I
Jan/Feb.
July/Aug.
Station M (66.0° N, 2.0° E) Mean Max
TABLE XXXVIII INTERDIURNAL VARIABILITY OF AIR TEMPERATURE CC) AT THE NORTH ATLANTIC OCEAN WEATHER
Station B (56.5° N, 51.0° W) Mean Max
Jan.
2.6 9.2
July
0.6 3.1
I
Station A (62° N, 33° W) Mean Max C (52.8° N, 35SW) Mean Max
H (36.7° N, 69.6° W) Mean Max
2.7 9.7
0.4 2.5
b
1.5
6.4
1.9 8.6
July
Station
Jan.
July
0.6 3.1
'M (66° N, ZO E) Mean Max
1.2 5.3
0.6 3.1
0.6 4.2
1(59.3° N,c 16.4° W) Mean Max
1.3 6.9
0.4 1.9
J (52S N, 20.0° W) Mean Max
1.3 5.8
0.4 3.1
D (44.0° N, 41.0° W) Mean Max
2.8 10.3
0.9 4.2
E (35° N, 48° W) Mean Max
0.9 4.2
0.4 10.3 !
Monthly averages and maximum values for January and July. After Rosenthal (1960a). C Average position.
a
Jan.
STATIONSa,b
5.4
TIME VARIATIONS
385
Ample information on the interdiurnal variability of air temperature was furnished by Rosenthal (1960a). From his statistics of the observations made on North Atlantic Ocean weather ships over 4 years, some results were selected and are presented in Table XXXVIII. The mean values of the interdiurnal variability are distinctly smaller than the average aperiodic diurnal range, as comparison with Table XXXVII reveals. In other respects, e.g., regarding their seasonal variation or their dependence on oceanographic facts, they show behavior very similar to that of the aperiodic diurnal range. The interdiurnal variability of temperature is largest in winter when advective changes are most frequent and most intense. In summer, there is a clear decline originating from the decreasing strength of the atmospheric circulation. The frequency distributions of the interdiurnal variability spread nearly as wide as do those of the aperiodic diurnal range, which can be inferred from a comparison of the maximum values in the two tables. The seasonal change is also very pronounced. Again, station "E" is an exception, showing a higher maximum in July than in January. Inspection of the frequency distributions for the other months reveals that the dispersion changed rather irregularly from month to month, the highest maximum occurring in September. This leads to the assumption that perhaps the passage of hurricanes might be made responsible for that exceptional result. The primary modes of the frequency distributions of the interdiurnal variability tend to persist throughout the year in the interval between 0.3 and 0.8°C. Hence the distributions have a positive skewness which decreases from winter to summer. Finally, we again point to the fact that the stations "B," "D," "H" (and to a smaller degree also "C") experienced considerably larger interdiurnal variability than the other stations, which is certainly caused by their particular position with respect to the oceanic and atmospheric circulation systems and to the continents. The stations "H" and "D" are situated almost at the northern edge of the Gulf Stream, "B" lies at the eastern edge of the Labrador Current, while, near "C", cold water masses from the north meet the warm North Atlantic Current. In addition, these four stations are quite close to the average position of the Polar Front in the atmosphere. Further, we have to take into account that these stations are not very far away from the continents and that, in winter, cold offshore winds may alternate with warm onshore winds. Summarizing all these facts, we can say that local influences contribute to producing large variations of air temperature at the four ocean stations in question.
6. Concluding Remarks In this monograph, an attempt has been made to summarize our present knowledge of the physics of the marine atmosphere, the discussion being restricted to processes of small and medium scale. Having in mind that the interaction between ocean and atmosphere is the governing factor, we started by discussing the exchange of momentum, energy, and matter at the air-sea interface and further extended the studies to atmospheric processes of larger scale, such as wind structure, convection, air mass modification, and so forth. Naturally, such a procedure provides but a first step-although a necessary one-directed toward a complete delineation of the physics of the marine atmosphere, which must include, or at least aim at embracing, a physical and quantitative treatment of the maritime components of the general atmospheric circulation. A full understanding of the interaction of ocean and atmosphere can only be approached if the exchange of momentum, energy, and matter between these two vast energy reservoirs is discussed with a view to its bearing on the pattern of atmospheric circulation, its instabilities and fluctuations. Herewith, the budgets and dynamics have to be investigated with reference to the average conditions over long periods and large regions, as well as to processes of shorter duration and smaller extensions, e.g., to individual synoptic-scale systems, such as traveling frontal cyclones and anticyclones, easterly waves, equatorial vortices, shear lines, and polar troughs. It is by such studies that light may be thrown upon the sources and sinks of energy and the ways of its transport, and further, they demonstrate which processes and scales of motion are significant. However, owing to the reasons mentioned in the introduction, such discussions could not be included in this monograph. After its completion, the author was much comforted by the fact that, in the meantime, a relevant treatment of the large-scale, airsea interactions had been published by Malkus (1962), who has presented a comprehensive and lucid delineation of "how the whole ocean-atmosphere system works." Herein, the-global climatology of exchange is described, as well as consideration given to its fluctuations 386
6
CONCLUDING REMARKS
387
in some more restricted portions of the system, with particular stress on the air-sea interaction processes in tropical and equatorial zones. More recently, a detailed study of daily heat exchange between oceans and atmosphere has been published by Laevastu (1963), who computed the components of the heat budget of the sea by 5° squares for eight given days over the North Pacific Ocean. Thus, for further information on large-scale interactions, the papers quoted above should be consulted. Apart from the restrictions resulting from the limited scope of this monograph, there are others which are mostly caused by the lack of suitable information. Shortcomings of this kind were indicated in the monograph at many places. So we can draw the conclusion that the acquisition of more and better data is the main requirement that must be fulfilled in order that our knowledge in this field may be enlarged. A similar statement has recently been made by Benton et al. (1963), who, after reviewing the existing information on the interaction between the atmosphere and the oceans, and after examining the major problems connected therewith, advanced a program of research, development, and operation wherein special stress was laid on completing and improving the empirical data. The need for more and better measurements is particularly manifest and urgent with regard to radiation, precipitation, and evaporation, as well as to the turbulent vertical fluxes of momentum and of sensible and latent heat. Although radiation forms an energy transport across the air-sea interface which is of primary importance, climatological radiation data taken close to the sea surface are almost entirely lacking* and so we have to rest content with computations based on empirical formulae into which there have been introduced climatological data and sporadic observations (e.g., Sauberer and Dirmhirn, 1955; Albrecht, 1960, 1961). Similarly, we have got next to * While reading the proofs I was pleased to learn that results of radiation measurements
made at sea had been published since this monograph was written. In particular, I would like to refer to the determination of the radiative heat budget at the ocean-atmosphere interface measured during 1960 and 1961 at the North Pacific weather station "Papa" (Ashburn, 1963), as well as to studies on the influence of cloudiness on the incoming solar radiation at the sea surface. Whereas Pike (1962) combined observations of daily insolation and mean total cloudiness made at sea west of Central America and arrived at a relation which differs from Kimball's (1928) formula, Lumb (1964), using measurements at the North Atlantic weather stations "J" and "A" (Fig. 2), established an empirical relationship between hourly short-wave radiation and the mean of the sines of the solar altitude at the beginning and at the end of the hour for different categories of clouds. Finally, Clarke (1963) presented observations of the long-wave radiative flux in the downstream trade wind region by means of an airborne radiometer and used them to construct a vertical heat budget for the subcloud layer.
388
6
CONCLUDING REMARKS
no direct quantitative information on such significant components of the atmospheric energy and water budget as the space and time distribution of precipitation over the oceans and the evaporation and condensation occurring at the sea surface. The direct measurement of eddy fluxes in the boundary layers above and beneath the sea surface is still in its early stages, although suitable methods are being developed at present. Finally, there must be mentioned the material exchange at the sea surface-besides that of water in vapor and liquid formwhich so far has received only little attention. It comprises the transfer of gases (carbon dioxide, oxygen, nitrogen compounds, etc.), of solids (e.g., salts), of radioactive substances (carbon-s, tritium, oxygen-" deuterium, etc.), and of particles carrying electrical charges. These short remarks already have shown that most of these substances either play an important role in such atmospheric processes as evaporation, condensation, and precipitation or provide helpful information about mixing processes of different scales in the atmosphere. The rate of material exchange seems to depend essentially on the microstructure of the air-sea interface, which, however, is not fully understood at present. Most of these deficiencies have been touched upon in this monograph. So I hope that the two objects connected with such a compilalation may perhaps have been achieved, namely, to assemble some possibly useful information but to show, nevertheless, where the limits of our present knowledge are, thus stimulating further research. I am however, afraid that the amount of information given is inferior to the amount of stimulation. The physics of the marine atmosphere is still at its beginning. Much work lies ahead of us before we will secure a really illuminating insight into the mechanism by which the atmosphere and the oceans are coupled, and discover the "law to which air and sea are obedient" as was prophetically stated by Maury more than 100 years ago. In spite of that only moderately optimistic outlook, it is my opinion that the efforts toward an improved understanding of the physics of the marine atmosphere will continue to be both fascinating and rewarding.
References Albrecht, F. (1960). Jahreskarten des Warrne- und Wasserhaushaltes der Ozeane, Ber, Deut. Wetterdienstes 9, No. 66. Albrecht, F. (1961). Der jahrliche Gang der Komponenten des Warrne- und Wasserhaushaltes der Ozeane. Ber, Deut. Wetterdienstes 11, No. 79. Arnot, A. (1955). Measurements of sea surface temperature for meteorological purposes. Results of observations from Ocean Weather Station M. Meteorol. Ann. 4, No.1. Arakiseki, T. (1955). On the sea fog over the Okhotsk Sea. J. Meteorol. Res. Tokyo 7, 71-76. Arnold, J. R., and Anderson, E. C. (1957). The distribution of carbon-14 in nature. Tellus 9, 28-32. Arrhenius, S. (1896). On the influence of carbonic acid in the air upon the temperature of the ground. Phil. Mag. [5]41,237-276. Ashburn, E. V. (1963). The radiative heat budget at the ocean-atmosphere interface. Deep-Sea Res. 10, 597-606. Austin, J. M. (1951). Cumulus convection and entrainment. Compendium Meteorol. pp.694-701. Ball, F. K. (1954). Sea surface temperatures. Australian J. Phys. 7, 649-652. Battan, L. J., and Riley, J. J. (1960). Ice-crystal nuclei and maritime air. J. Meteorol. 17, 675-676. Bell, J. (1951). Mean-wind-velocity instruments for use on naval craft. Proc. Inst, Elec. Engrs. (London) Pt. B 98,448-452. Bell, J., and Langham, E. M. (1952). Mean-wind-velocity instruments for use on naval craft. Muirhead Tech. 7, 3-5. Benard, H. (1900). Les tourbillons cellulaires dans une nappe liquide. Rev. Gen. Sci. Pures Appl.ll, 1261-1271, 1309-1328. Benditskii, N. D. (1958). Measurement of the temperature of the upper layer of water in an open sea. Meteorol. i Gidrol. 6, 53-54 (in Russian). Benton, G. S., Fleagle, R. G., Leipper, D. F., Montgomery, R. B., Rakestraw, N., Richardson, W. S., Riehl, H., and Snodgrass, J. (1963). Interaction between the atmosphere and the oceans. Bull. Am. Meteorol. Soc. 44,4-17. Berget, A. (1931). Lecons d'oceanographie physique, (2 m • partie) l'ocean et I'atmosphere. Ann. Inst. Oceanog, Monaco 9, 1-396. Bernard, E. A. (1962). Theorie des oscillations annuelles et diurnes de la temperature a la surface des Continents et des Oceans. Arch. Meteorol. Geophys. Bioklimatol. A12, 502-543. Bigelow, H. B. (1931). "Oceanography; Its Scope, Problems and Economic Importance." Houghton, Mifflin, Boston, Massachusetts and New York. Bijvoet, H. C. (1957). A new overlay for the determination of the surface wind over sea from surface weather charts. Koninkl. Ned. Meteor. Inst, Mededel. Verhandel. No. 71. Bijvoet, H. C. (1960). On the relation between the pressure field and the surface wind at sea. Meteorol. Abhandl. 9,19-25. Bintig, P. (1950). Der Einfluss des Windes auf die Wassertemperatur des Ozeans und ihr Zusammenwirken mit der Lufttemperatur. Ann. Meteorol. 3, 193-201, 333-340. 389
390
REFERENCES
Bintig, P., and Markgraf, H. (1957). Nebel in der Deutschen Bucht. Deut. Wetterdienst, Seewetteramt (Hamburg), Einzelveroff. No. 14. Bischof, W. (1960). Periodical variations of the atmospheric C02-content in Scandinavia. Tellus 12, 216-226. Bischof, W. (1962). Variations in concentration of carbon dioxide in the free atmosphere. Tellus 14, 87-90. Bjerknes, J. (1938). Saturated ascent of air through a dry-adiabatically descending environment. Quart. J. Roy. Meteorol. Soc. 64, 325-330. Bjerknes, J. (1960). Ocean temperatures and atmospheric circulation. WMO Bull. 9, 151-157. Bjerknes, J. (1962). Synoptic survey of the interaction of sea and atmosphere in the North Atlantic. Geofys. Publikasjoner 24, 115-145. Bjorgum, O. (1952). Note on the derivation of the logarithmic velocity profile. Quart. J. Roy. Meteorol. Soc. 78, 89-90. Blanchard, D. C. (1955). Electrified droplets from the bursting of bubbles at an air-sea water interface. Nature 175, 334-336. Blanchard, D. C. (1958). Electrically charged drops from bubbles in sea water and their meteorological significance. J. Meteorol. 15,383-396. Blanchard, D. C., and Spencer, A. T. (1957). Condensation nuclei in the vicinity of the island of Hawaii. Tellus 9,525-527. Blanchard, D. c., and Woodcock, A. H. (1957). Bubble formation and modification in the sea and its meteorological significance. Tellus 9, 145-158. Boguslavskii, S. G. (1956). Solar radiation absorption in the sea and its direct effect on sea temperatures. Tr. Morsk. Gidrofiz. Inst., Akad. Nauk. SSSR. Sb. Statei 8, 80-97 (in Russian). Bolin, B. (1960). On the exchange of carbon dioxide between the atmosphere and the sea. Tellus 12, 274-281. Bolin, B., and Eriksson, E. (1959). Changes in the carbon dioxide content of the atmosphere and sea due to fossil fuel combustion. In "The Atmosphere and the Sea in Motion," Rossby Memorial Vol. pp, 130-142. Oxford Univ. Press, London and New York. Bowen, I. S. (1926). The ratio of heat losses by conduction and by evaporation from any water surface. Phys. Rev. 27, 779-787. Braak, C. (1914). Die tagliche Temperaturschwankung der Luft in verschiedenen Hohen tiber dem tropischen Meer. Beitr. Phys. Frei. Atmosphiire 6,141-152. Bray, J. R. (1959). An analysis of the possible recent change in atmospheric carbon dioxide concentration. Tellus 11, 220-230. Brier, G. W., and Kline, D. B. (1959). Ocean water as a source of ice nuclei. Science 130, 717-718. Brockamp, B., and Wenner, H. (1960). Eine neue Verdunstungsapparatur fur Binnengewasser. IUGG, Intern. Assoc. Sci. Hydrology Pub I. No. 53, 386-391. Brocks, K. (1940). Eine Methode zur Beobachtung des vertikalen Dichte- und Temperaturgefalles in den bodenfernen Atrnospharenschichten. Meteorol. Z. 57, 19-26. Brocks, K. (1954). Eine raumlich integrierende optische Methode fur die Messung vertikaler Temperatur- und Wasserdampfgradienten in der untersten Atmosphare, Arch. Meteorol. Geophys. Bioklimatol. A6, 370-402. Brocks, K. (1955). Wasserdampfschichtung tiber dem Meer und Rauhigkeit der Meeresoberfiache, Arch. Meteorol. Geophys. Bioklimatol. A8, 354-383. Brocks, K. (1956). Atmospharische Temperaturschichtung und Austauschprobleme tiber dem Meer. Ber, Deut. Wetterdienstes 22, .10-15.
REFERENCES
391
Brocks, K. (1959a). Ein neues Gerat filr storungsfreie meteorologische Messungen au dem Meere. Arch. Meteorol. Geophys. Bioklimatol. All, 227-239. Brocks, K. (1959b). Measurements of wind profiles over the sea and the drag at the sea surface. Am. Assoc. Advan. Sci., Intern. Oceanog. Congr., New York, 1959, Preprints, pp. 742-743. Brocks, K. (1962).'" Results of wind profile measurements above the sea. Proc. Symp, Math. Hydrodyn, Methods of Phys. Oceanog., Hamburg, 1961, pp. 409-410. Brogmus, W. (1958). Zur Definition und Berechnung der Widerstands- und Verdunstungskoeffizienten bei nicht-adiabatischer Schichtung. Ann. Meteorol. 8, 225233. Brogmus, W. (1959). Zur Theorie der Verdunstung der natiirlichen Erdoberflache. Deut. Wetterdienst, Seewetteramt (Hamburg), Einzelverbff. No.2!. Brooks, C. F., and Brooks, E. S. (1958). The accuracy of windspeed estimates at sea. Trans. Am. Geophys. Union 39, 52-57. Brose, K. (1936). Der jahrliche Gang der Windgeschwindigkeit auf der Erde. Reichsamt Wetterdienst, Wiss. Abhand. I, No.4. Brown, P. R. (1952). Humidity over the sea. Ann. Meteorol. 5, 293-297. Bruce, J. P., Anderson, D. V., and Rodgers, G. K. (1961). Temperature, humidity and wind profiles over the Great Lakes. Great Lakes Res. Div., Univ, of Michigan, Publ. No. 7,65-70. Bruch, H. (1940). Die vertikale Verteilung von Windgeschwindigkeit und Temperatur in den untersten Metern iiber der Wasseroberflache, Veroffentl. Inst. Meereskunde Univ. Berlin, N.F.A., 38. Buch, K. (1948). Der Kohlendioxydgehalt der Luft als Indikator der meteorologischen Luftqualitat. Geophysica (Helsinki) 3, 63-79. Bullig, H. J. (1954). Atlas der Monatswerte von Wassertemperatur, Wind und Bewolkung auf dem Seeweg Europa-Siidamerika. Deut. Wetterdienst, Seewetteramt (Hamburg), Einzelveroff. No.5. Bullig, H. J., and Bintig, P. (1954). Klimatologie der nordwesteuropaischen Gewasser, Deut. Wetterdienst, Seewetteramt (Hamburg), Einzelveroff. No.4, Part I. Bunker, A. F. (1955). Turbulence and shearing stresses measured over the North Atlantic by an airplane-acceleration technique. J. Meteorol. 12,445-455. Bunker, A. F. (1957). Turbulence measurements in a young cyclone over the ocean. Bull. Am. Meteorol. Soc. 38,13-16. Bunker, A. F. (1959). Marine meteorology; cloud and environment velocities, temperatures, humidities and water contents associated with a shear zone in the trade winds. Woods Hole Oceanog. Inst. Ref. No. 59-42, Tech. Rept. 44. Bunker, A. F. (1960). Heat and water vapor fluxes in air flowing southward over the western North Atlantic Ocean. J. Meteorol. 17, 52-63. Bunker, A. F. (1962). Water vapor distribution in the sub-cloud trade wind air. Woods Hole Oceanog. Inst. Ref. No. 62-2, Tech. Rept. 47. (unpublished manuscript). Bunker, A. F., Haurwitz, B., Malkus, J. S., and Stommel, H. (1949). Vertical distribution of temperature and humidity over the Caribbean Sea. Papers Phys. Oceanog. Meteorol. 9, No. I. Burke, C. J. (1945). Transformation of polar continental air to polar maritime air. J. Meteorol. 2, 94-112. Burling, R. W. (1955). Surface waves on enclosed bodies of water. Proc. 5th Conf. Coastal Eng. Grenoble, 1954, I-II. Byers, H. R. (1959). "General Meteorology." 3rd ed. McGraw-Hili, New York. ... For later papers see the Supplement p. 412.
392
REFERENCES
Callendar, G. S. (1938). The artificial production of carbon dioxide and its influence on temperature. Quart. J. Roy. Meteorol. Soc. 64, 223-237. Callendar, G. S. (1958). On the amount of carbon dioxide in the atmosphere. Tel/us 10, 243-248. Callendar, G. S. (1961). Temperature fluctuations and trends over the earth. Quart. J. Roy. Meteorol. Soc. 87,1-12. Chalmers, J. A. (1957). "Atmospheric Electricity." Pergamon Press, New York. Charnock, H. (1955). Wind stress on a water surface. Quart. J. Roy. Meteorol. Soc. 81, 639-640. Charnock, H. (1958a). Meteorology. Sci. Progr. 46, No. 183,470-487. Charnock, H. (1958b). Physical oceanography. Sci. Progr. 46, No. 183,487-501. Charnock, H., and Ellison, T. H., (1959). Fluctuations of temperature and humidity at 134 m over the sea. Deut, Hydrograph, Z.12, 171-180. Charnock, H., Francis, J. D. R., and Sheppard, P. A. (1956). An investigation of wind structure in theTrades, Anegada, 1953. Phil. Trans. Roy. Soc. London A249, 179-234. Chase, J., Cote, L. J., Marks, W., Mehr, E., Pierson, W. J., Ronne, F. C., Stephenson,G., Vetter, R. C., and Walden, R. G. (1957). The directional spectrum of a wind generated sea as determined from data obtained by the Stereo-Wave Observation Project. New York Univ., Coli. Eng., Res. Div., Tech. Rept. for Office of Navel Res. Contr. No. 285(03). Church, P. E. (1941). The summer-time vertical humidity gradient over the cold water of the San Juan Archipelago. Trans. Am. Geophys. Union 22, 484-489. Clarke, D. B. (1963). Radiation measurements with an airborne radiometer over the ocean east of Trinidad. J. Geophys. Res. 68, 235-244. Clauser, F. H. (1956). The turbulent boundary layer. Advan, Appl. Mech. 4, 2-51. Clayton, W. H. (1956). Measurement of wind set-up on an open coast. Ph. D. Dissertation, Agr, Mech. Coli. Texas, College Station, Texas. Colding, A. (1876). Results of certain investigations of the current in the sea caused by the force of the wind. Kgl. Danske Videnskab. Selskabs Skrifter, Naturvidenskab, Math. A/del.ll, 3. Collmann, W. (1951). Beispiele zur Frage der Luftmassentransformation. Ann. Meteorol. 4,444-464. Corwin, E. F., Appleby, I. c., and Allison, L. J. (1959). The floating automatic weather stations of the United States Navy. Weatherwise 12, No.5, 192-199. Cox, C. S. (1958). Measurements of slopes of high frequency wind waves. J. Marine Res. 16, 199-225. Cox, C., and Munk, W. (1954). Statistics of the sea surface derived from sun glitter. J. Marine Res. 13, 198-227. Craddock, J. M. (1951). The warming of arctic air masses over the eastern North Atlantic. Quart. J. Roy. Meteorol. Soc. 77, 355-364. Craig, H. (1957). The natural distribution ofradiocarbon and the exchange time of carbon dioxide between atmosphere and sea. Tel/us 9,1-17. Craig, R. A. (1946). Measurements of temperature and humidity in the lowest 1000 feet of the atmosphere over Massachusetts Bay. Papers Phys. Oceanog. Meteorol. 10, No.1. Craig, R. A. (1947). Observation of vertical temperature and humidity distributions in the convective layer above the sea surface. Ann. N. Y. Acad. Sci. 48, 783-788. Craig, R. A. (1949). Vertical eddy transfer of heat and water vapor in stable air. J. Meteorol. 6,123-133. Craig, R. A., and Montgomery, R. B. (1949). Evaporation (measured) from ocean into hydrostatically stable air. J. Meteorol. 6,426-427.
REFERENCES
393
Darbyshire, J., and Darbyshire, M. (1955). Determination of wind stress on the surface of Longh Neagh by measurement of tilt. Quart. J. Roy. Meteorol. Soc. 81, 333-339. Darlington, C. R. (1952). The variation of humidity with height over the ocean. Gt. Brit., Meteorol. Res. Comm. M.R.P. 725. Das, P. K., and Dhar, N. C. (1954). Meteorological and oceanographic observations on I.N.S. "Investigator" (March-April 1952). Indian J. Meteorol. Geophys. 5, 16--28. Deacon, E. L. (1949). Vertical diffusion in the lowest layers of the atmosphere. Quart. J. Roy. Meteorol. Soc. 75, 89-103. Deacon, E. L. (1953). Vertical profiles of mean wind in the surface layers of the atmosphere. Geophys. Mem. (London) No. 91. Deacon. E. L. (1957). The stress of light winds on the sea. Bull. Am. Meteorol. Soc. 38, 540--542. Deacon, E. L. (1960). Eddy flux measurements over the sea. IUGG, Gen. Assembly, Toronto 1957, Proces verbaux No.7, 212-213. Deacon, E. L. (l962a). Aerodynamic roughness of the sea. J. Geophys. Res. 67, 31673172. Deacon, E. L. (l962b). The drag of the wind on the sea. Proc. Symp. Math. Hydrodyn, Methods of Phys. Oceanog; Hamburg, 1961, pp. 385-398. Deacon, E. L., Sheppard, P. A., and Webb, E. K. (1956). Wind profiles over the sea and the drag at the sea surface. Australian J. Phys. 9, 511-541. Deacon, E. L., and Webb, E. K. (1962). Small-scale interactions. In "The Sea: Ideas and Observations." (M. N. Hill, ed.), Vol. I, pp. 43-87. Wiley (Interscience), New York. Deardorff, J. W. (1961a). Local evaporation from a smooth water surface. J. Geophys. Res. 66,529-534. Deardorff, J. W. (1961b). Evaporation reduction by natural surface films. J. Geophys. Res. 66,3613-3614. Deardorff, J. W. (1962). An experimental ocean buoy for air-sea transfer studies. Univ. of Washington, Dept. Meteorol. Climatol., Occasional Rept. No. 13. Dietrich, G. (1950). ()ber systematische Fehler in den beobachteten Wasser- und Lufttemperaturen auf dem Meere und tiber ihre Auswirkung auf die Bestimmung des Warmeumsatzes zwischen Ozean und Atmosphare. Deut. Hydrograph. Z. 3, 314-324. Dietz, R. S., and La Fond, E. C. (1950). Natural slicks on the ocean. J. Marine Res. 9, 69-76. Dingle, A. N. (1954). The carbon dioxide exchange between the North Atlantic Ocean and the atmosphere. Tel/us 6, 342-350. Dobroklonsky, S. V. (1944). On the diurnal variation of temperature in the surface layer of the sea and on heat currents at the sea-air interface. Dokl. Akad. Nauk. SSSR [N.S.] 45, No.9 (in Russian). Donn, W. L. (1951). "Meteorology with Marine Applications." 2nd ed. McGraw-Hill, New York. Dorrestein, R. (1951). General linearized theory of the effect of surface films on water ripples. Koninkl. Ned. Akad. Wetenschap. Proc., 854,260--272, 350-356. Douglas, C. K. M. (1930). Cold fogs over the sea. Meteorol. Mag. 65, 133-135. Drogajcev, D. A. (1954). Wind profile over the sea. Tr. Inst. Okeanol. Akad. Nauk SSSR 9, 23-53 (in Russian). Drogajcev, D. A. (1956). Construction of the geostrophic wind field over the sea. Meteorol. i Gidrol. 2, 41-44 (in Russian). Durst, C. (1950). On surface friction and turbulence in the ocean. Monthly Notices Roy. Astron. Soc., Geophys. Suppl. 5, 369-373.
394
REFERENCES
Durst, C. S., and Gordon, A. H. (1952). Some observations of vertical temperature and humidity gradients made from ocean weather ships. Gt. Brit., Meteorol. Res. Comm. M.R.P.714. Eckart, C. (1953). The generation of wind waves on a water surface. J. Appl, Phys. 24, 1485-1494. Ekman, V. W. (1905). On the influence of the earth's rotation on ocean currents. Arkiv Matematik Astron. Fysik 2, No. 11. Ekman, V. W. (1923). Uber Horizontalzirkulation bei winderzeugten Meeresstromungen. Arkiv Matematik Astron. Fysik 17, No. 26. Ellison, T. H. (1957). Turbulent transport of heat and momentum from an infinite rough plane. J. Fluid Mech. 2, 456-466. Emmons, G. (1947). Vertical distributions of temperature and humidity over the ocean between Nantucket and New Jersey. Papers Phys. Oceanog. Meteorol. 10, No.3. Emmons, G., and Montgomery, R. B. (1947). Note on the physics of fog formation. J. Meteorol. 4,206. Evans, F., Dickson, G. N., and Kove, N. A. G. (1961). Vertical series of sea and air temperature close to the surface, taken aboard the yacht Petula in the tropical Atlantic. Quart. J. Roy. Meteorol. Soc. 87, 588-591. Ewing, G. (1950). Slicks, surface films and internal waves. J. Marine Res. 9,161-187. Ewing, G., and McAlister, E. D. (1960). On the thermal boundary layer of the ocean. Science 131,1374-1376. Facy, L. (1951). Embruns et noyaux de condensation. J. Sci. Meteorol. 3, 62-68. Farkas, E., and Hutchings, J. S. (1953). Modifications undergone by surface air currents in passing from Macquarie Island to Southern New Zealand. New Zealand, Meteorol. Serv., Tech. Note No. 104 (not published). Farmer, H. G. (1956). Some recent observations of sea surface elevation and slope. Woods Hole Inst. Tech. Rept., Ref. No. 56-37 (unpublished). Farrer, L. A. (1958). Wind tides on Lake Okeechobee. Proc. 6th Coast. Eng. Conf, Gainsville, Florida 1957, Council Wave Res., Berkeley, Calif., pp. 134-146. Findeisen, W. (1935). Uber Beobachtungen auffalliger Wellenbildung auf dunner Wasserschicht im Neuwerker Watt. Ann. Hydrograph. Maritim. Meteorol. (Berlin) 63, 186-189. Fisher, E. L. (1958). Hurricanes and the sea-surface temperature field. J. Meteorol. 15, 328-333. Fleagle, R. G. (1950). The optical measurement of lapse rate. Bull. Am. Meteorol. Soc. 31,51-55. Fleagle, R. G. (1953). A theory of fog formation.J. Marine Res. 12, 43-50. Fleagle, R. G. (1956a). Note on the effect of air-sea temperature difference on wave generation. Trans. Am. Geophys. Union 37, 275-277. Fleagle, R. G. (1956b). The temperature distribution near a cold surface. J. Meteorol. 13, 160-165. Fleagle, R. G., Deardorff, J. W., and Badgley, F. I. (1958). Vertical distribution of wind speed, temperature and humidity above a water surface. J. Marine Res. 17, 141-157. Fletcher, R. D. (1959). Diurnal variations of winds aloft over Guam and Bermuda. Proc. Pacific Sci. Congr., 9th 13, 304-308. Fonselius, S., Koroleff, F., and Warrne, K. E. (1956). Carbon dioxide variations in the atmosphere. Tellus 8,176-183. FournierD'Albe, E. M. (1951). Surles embruns marins. Bull. Inst, Oceanog. No. 995,1-7. Fournier D'Albe, E. M. (1955). Giant hygroscopic nuclei in the atmosphere and their role in the foundation of rain and hail. Arch. Meteorol. Geophys. Biok/imatol. A8, 216-228.
REFERENCES
395
Franceschini, G. A. (1954). Modifications in tropical air crossing the Gulf of Mexico toward the United States. A. & M. College of Texas, Dept. of Oceanog., Contract AF 19 (604)-169-Sci. Rept. No.3, A. & M. Project 44-Ref. 54-34 T. Franceschini, G. A. (1962). Gross air-sea interactions. A. & M. College of Texas, Dept. of Ocean Meteorol., A. & M. Project 286-Ref. 62-14 A, 10-15. Francis, J. R. D. (1951). The aerodynamic drag of a free water surface. Proc. Roy. Soc. (London) A206, 387-406. Francis, J. R. D. (1953). A note on the velocity distribution and bottom stress in a winddriven water current system. J. Marine Res. 12,93-98. Francis, J. R. D. (1954). Wind stress on a water surface. Quart. J. Roy. Meteorol. Soc. 80,438-443. Francis, J. R. D. (1959). Wind action on a water surface. Proc. Inst. Civil Engrs. (London), 12,197-216. Fritz, S. (1961). Satellite cloud pictures of a cyclone over the North Atlantic Ocean. Quart. J. Roy. Meteorol. Sac. 87, 314-321. Frost, R. (1949). A note on polar air-mass modification. Proc. Roy. Soc. (London), AI98,27-38. Georgii, H. W., and Metnieks, A. L. (1958). An investigation into the properties of atmospheric freezing nuclei and sea-salt nuclei under maritime conditions at the west coast of Ireland. Geofis. Pura Appl. 41,159-176. Gerhardt, J. R. (1951). Temperature and moisture soundings over the Gulf of Mexico for March, 1949. Trans. Am. Geophys. Union 32,15-25. Gerstmann, W. (1961). Beitrag zur Bestimmung der Schubspannungsgeschwindigkeit tiber dem Meer aus Schiffsbeobachtungen. Z. Meteorol. 15, 147-150. Gibson, B. W. (1962). The nature of the sea surface as deduced from composite temperature analysis. Deut. HydrographZ.15, 72-77. Gish, O. H. (1951). Universal aspects of atmospheric electricity. Compendium Meteorol. pp. 101-119. Goedecke, K. (1951). Die Marine-Piitz mit Wasserthermometer. Ann. Meteorol. 4,479. Goptarev, N. P. (1957). Some results of wind profile measurements on marine oil drilling platforms. Tr. Gos. Okeanogr. Inst. 36, 128-202 (in Russian). Goptarev, N. P. (1959). Vertical distribution of humidity in the bottom layer above the sea as observed on oil drilling platforms in the Caspian Sea. Tr. Gos. Okeanogr. Inst. 46,32-40 (in Russian). Goptarev, N. P. (1960). On the influence of dynamic and thermal factors on the wind speed above the sea and on the motion at the sea surface. Tr. Gos. Okeanogr. Inst. 51, 5-23 (in Russian). Gordon, A. H. (I 950a). The ratio between observed velocities of the wind at 50 feet and 2000 feet over the North Atlantic Ocean. Quart. J. Roy. Meteorol. Soc. 76, 344-348. Gordon, A. H. (l950b). Variation of wind with height at low levels over the sea. Meteorol. Mag. 79, 295-297. Gordon, A. H. (I 950c). Temperature and humidity lapse rate near the surface. Meteorol. Mag. 79, 141-143. Gordon, A. H. (I 952a). Angle of deviation between the winds at 50 ft and 2000 ft over the North Atlantic Ocean. Meteorol. Mag. 81, 59. Gordon, A. H. (I 952b). The relation between the mean vector surface wind and the mean vector pressure gradient over the oceans. Geofis. Pura Appl. 21, 49-51. Gordon, A. H. (l952c). Relation of atmospheric humidity at low levels over the sea to wind force and the difference in temperature between air and sea. Meteorol. Mag. 81, 289-295.
396
REFERENCES
Graham Millar, F., and Macphail, H. W. (1951). Observing the apparent wind on shipboard. Marine Observer 21, No. 152, 126-130. Groen, P. (1960). Ice islands and drifting pole stations. Zee 81, No.4, 164-171. Grundy, F. (1962). Some problems of maintaining a monomolecular film on reservoirs affected by winds. In "Retardation of Evaporation by Monolayers" (V. K. La Mer, ed.), pp. 213-218. Academic Press, New York. Hamada, T., Mitsuyasu, H., and Hose, N. (1953). An experimental study of wind effect upon water surface. Rept. Transportation Tech. Res. Inst. 8, 22 pp. Hanya, T., and Ishiwatari, R. (1961). Carbon dioxide exchange between air and sea water (I). J. Oceanog. Soc. Japan 17,28-32. Hanzawa, M. (1950). On the annual variation of evaporation from the sea surface in the North Pacific Ocean. Oceanog. Mag. (Tokyo) 2,77-82. Hanzawa, M., and Takeda, N. (1950). Preliminary report on the transformation of the Siberian Pc airmass travelling over sea in winter. Oceanog. Mag. (Tokyo) 2, 69-75. Harrington, E. L. (1958). Observations on the appearance and growth of tropical cumuli. J. Meteorol. 15, 127-130. Harris, M. F., Finger, F. G., and Teweles, S. (1962). Diurnal variation of wind, pressure, and temperature in the troposphere and stratosphere over the Azores. J. Atmosph. Sci. 19, 136-149. Hasselmann, K. (1960). Grundgleichungen der Seegangsvoraussage. Schiffstechnik 7, (39), 191-195. Haurwitz, B. (1941). "Dynamic Meteorology." McGraw-Hili, New York. Haussler, W. (1955-1956). Uber Temperaturprofile beiderseits einer verdunstenden Wasserflache, Wiss. Z. Tech. Hochschule Dresden 5, 435-450. Hay, J. S. (1955). Some observations of air flow over the sea. Quart. J. Roy. Meteorol. Soc. 81, 307-319. Hay, R. F. M. (1956a). A comparison between observations from Ocean Weather Station J and contemporaneous British selected ships for the locality. Marine Observer 26,No.173,154-159. Hay, R. F. M. (1956b). Some aspects of variations of air and sea temperature in short periods at ocean weather stations I and J of significance to the synoptic climatologist. Gt. Brit. Meteorol. Res. Comm. M.R.P. 949. Hayami, S., and Kunishi, H. (1959). A wind flume study on the generation of waves. Am. Assoc. Advan. Sci., Intern. Oceanog. Congr., New York, 1959, Preprints, pp. 753-755. Hela, I. (1948). On the stress of the wind on the water surface. Geophysica (Helsinki) 3, 146-161. Hellstrom, B. (1941). Wind effect on lakes and rivers. Ing. Vetenskaps. Akad. Handl. No. 158. Hellstrom, B. (1953). Wind effect on Ringkobing Fjord. Trans. Am. Geophys. Union 34, 194-200. Hergesell, H. (1905). Ballon-Aufstiege tiber dem freien Meere zur Erforschung der Temperatur- und Feuchtigkeitsverhaltnisse sowie der Luftstromungen bis zu sehr grossen Hohen der Atmosphare, Beitr. Phys. Frei. Atmosphiire 1, 200-204. Hergesell, H. (1906-1907). Die Erforschung der freien Atmosphare tiber dem Polarmeer. Beitr. Phys. Frei. Atmosphdre 2, 96-98. Hess, V. F. (1948). On the concentration of condensation nuclei in the air over the North Atlantic. Terrestial Magnetism Atmospheric Elec. 53, 395-403. Hess, V. F. (1951). Further determinations of the concentration of condensation nuclei in the air over the North Atlantic. J. Geophys. Res. 56, 553-556.
REFERENCES
397
Hilleary, D. T., and Christensen, F. E. (1957). "Instrumentation of National Hurricane Research Project Aircraft." U.S. Weather Bureau, National Hurricane Research Project Report, No. 11. Hohne, W. (1960). Eine Windmessanlage fur Schiffswetterstationen. Z. Meteorol. 14, 225-233. Hohne, W. (1963). Die Schiffswetterstation SWS 2. Z. Meteorol. 16, 325-334. Holzman, B. (1943). The influence of stability on evaporation. Ann. N. Y. Acad. Sci. 44, 13-18. Houghton, D. M. (1956). The measurement and interpretation of near-surface seatemperature profiles. Quart. J. Roy. Meteorol. Soc. 82, 515-517. Hunt, I. A. (1956). Effects du vent sur les nappes liquides. Houille Blanche 11, 575-607; 781-812. Hunt, I. A. (1959). Winds, wind set-ups and seiches on Lake Erie. U.S. Lake Survey, Corps of Eng., U.S. Army, 59 pp. Huss, E. (1961). Technik von Fesselaufstiegen auf See. In "Handbuch der Aerologie" (W. Hesse, ed.), pp. 228-249. Akad. Verlagsges. Geest & Portig. Leipzig. Isaacs, J. D. (1962). Note on an association of cumulus clouds and turbid water. J. Geophys. Res. 67,2076. Isono, K. (1957). On sea-salt nuclei in the atmosphere. Geofis, Pura Appl. 36,156--164. Israel, H. (1951). Radioactivity of the atmosphere. Compendium Meteorol., pp. 155161. Israel, H. (1953). Bemerkungen zum Energie-Umsatz im Gewitter. Geofis. Pura Appl. 24,95-103. Israel, H. (1958). Die natiirliche Radioaktivitat in Boden, Wasser und Luft. Beitr. Phys. der Atmosphiire 30,177-188. Israel, H. (1960). Meteorologische Vorgange im Spiegel der Luftelektrizitat, Ann. Geofis. (Rome) 13, 327-367. Izotova, A. F., Ogneva,T. A., and Smirnova, N. P. (1961). The wind profile over the Lake of Ladoga in the layer adjoining the water surface. Dok!. Akad. Nauk. SSSR 136,587-590 (in Russian). Jacobs, W. C. (1951). Large-scale aspects of energy transformation over the oceans. Compendium Meteorol., pp. 1057-1070. Jaw, J. (1937). Zur Thermodynamik der Passatgrundstrornung. Veroffentl, Meteorol. Inst. Univ. Berlin 2 (6). Jeffreys, H. (1920). On the relation between wind and distribution of pressure. Proc. Roy. Soc. (London) A96, 233-249. Jeffreys, H. (1925). On the formation of water waves by wind. Proc. Roy. Soc. (London) AI07,189-206. Johnson, J. W., and Rice, E. K. (1952). A laboratory investigation of wind-generated waves. Trans. Am. Geophys. Union 33,845-854. Johnson, N. K. (1927). Some meteorological observations made at sea. Quart. J. Roy. Meteorol. Soc. 53, 59-63. Johnson, P. W. (1955). The ratio of the sea-surface wind to the gradient wind. Proc. 1st Conf. on Ships and Waves, Hoboken, New Jersey, 1954, p. 104-110. Jones, D. R. (1953). Note on observed wind shear at low levels over the ocean. Bull. Am. Meteorol. Soc. 34, 393-396. Junge, C. E. (1951). Nuclei of atmospheric condensation. Compendium Meteorol. pp. 182-191. Junge, C. E. (1952). Die Konstitution des atmospharischen Aerosols. Ann. Meteorol.5, Suppl.
398
REFERENCES
Junge, C. E. (1955). The size distribution and aging of natural aerosols as determined from electrical and optical data on the atmosphere. J. Meteorol. 12, 13-25. Junge; C. E. (1956). Recent investigations in air chemistry. Tel/us 8,126-139. Junge, C. E. (1957a). The vertical distribution of aerosols over the ocean. Artificial Stimulation Rain, Proc. Coni Phys. Cloud Precipitation Particles, 1st, Woods Hole, 1955 pp. 89-96. Junge, C. E. (1957b). Chemical analysis of aerosol particles and of gas traces on the island of Hawaii. Tel/us 9,528-537. Junge, C. E., and Gustafson, P. E. (1957). On the distribution of sea salt over the United States and its removal by precipitation. Tel/us 9, 164-173. Kanwisher, J. (1960). pC02 in sea water and its effect on the movement of C02 in nature. Tel/us 12, 209-215. Kaplan, L. D. (1960, 1961). The influence of carbon dioxide variations on the atmospheric heat balance. Tel/us 12, 204-208; 13,301-302. Karman, T. von (1934). Turbulence and skin friction.J. Aeron. Sci. 1, 1-20. Keeling, C. D. (1960). The concentrations and isotopic abundances of carbon dioxide in the atmosphere. Tel/us 12,200-203. Keulegan, G. (1951). Wind tides in small closed channels. Natl. Bur. Std. (U.S.) Res. Paper 2207, Keulegan, G. (1953). Hydrodynamic effects of gales on Lake Erie. J. Res. Natl. Bur. Std. 50, 99-110. Kientzler, C. F., Arons, A. B., Blanchard, D. C., and Woodcock, A. H. (1954). Photographic investigation of the projection of droplets by bubbles bursting at a water surface. Tel/us 6, 1-7. Kimball, H. H. (1928). Amount of solar radiation that reaches the surface of the earth on the land and on the sea, and methods by which it is measured. Monthly Weather Rev. 56, 393-398. Kirk, T. H., and Gordon, A. H. (1952). Comparison of intake and bucket methods for measuring sea temperature. Marine Observer 22, No. 155, 33-39. Klein, W. H. (1946). Modification of polar air over water. J. Meteorol. 3, 100-101. Kleinschmidt, E., and Huss, E. (1935). Fesselaufstieg vom Schiff aus. In "Handbuch der meteorologischen Instrumente und ihrer Auswertung," pp. 520-538. Springer, Berlin. Knelman, F., Dombrowski, N., and Newitt, D. M. (1954). Mechanism of the bursting bubbles. Nature 173, 261. Koizurni, M. (1956a). Researches on the variations of oceanographic conditions in the region of the ocean weather station Extra in the North Pacific Ocean (IV). Papers Meteorol. Geophys. (Tokyo) 7,144-154. Koizumi, M. (1956b). Researches on the variations of oceanographic conditions in the region of the ocean weather station Extra in the North Pacific Ocean (V). Papers Meteorol. Geophys. (Tokyo) 7,155-160. Koizumi, M. (1956c). Researches on the variations of oceanographic conditions in the region of the ocean weather station Extra in the North Pacific Ocean (VI). Papers Meteorol. Geophys. (Tokyo) 7, 322-326. Kolesnikov, A. G. (1958). On the calculation of daily variations of sea temperature. Proc. Pacific Sci. Congr. Pacific Sci. Assoc., 9th, Bangkok, Thailand 195716,201-203. Kontoboitseva, N. V. (1958). Measurement of temperature pulsation in the surface layer ofthe sea. Izv. Akad. Nauk SSSR, Ser. Geofiz: 1,47-50 (in Russian). Kraus, E. B., and Rooth, C. (1961). Temperature and steady state vertical heat flux in the ocean surface layers. Tel/us 13,231-238.
REFERENCES
399
Krueger, A. F., and Fritz, S. (1961). Cellular cloud patterns revealed by TlROS I. Tellus 13,1-7. Kriigler, F. (1952). Uber extrem starke ortliche Schwankungen der Wasseroberflachentemperatur in Eisnahe am Rande des Ostgronlandstromes, Ann. Meteorol. 5,185188. Krummel, O. (1907). "Handbuch der Ozeanographie," Vol. 1, 526 pp. Engelhorn, Stuttgart. Krumm, H. C. (1962). Der weltzeitliche Tagesgang der Gewitterhaufigkeit. Z. Geophys. 28,85-104. Kuhlbrodt, E., and Reger, J. (1933). Die aerologischen Methoden und das aerologische Beobachtungsmaterial. Wiss. Ergebnisse Deut. Atlantische Expedition "Meteor" 1925-27, 15. Kuhlbrodt, E., and Reger, J. (1938). Die meteorologischen Beobachtungen; Methoden, Beobachtungsmaterial und Ergebnisse. Wiss. Ergebnisse Deut, Atlantische Expedition "Meteor" 1925-27, 14. Kurbatkin, G. P. (1957). The theoretical determination of the annual variation of the air temperature at sea level. Izv. Akad. Nauk SSSR, Ser. Geofiz. 2, 228-243 (in Russian). Kuroiwa, D. (1953). Electron microscope study of atmospheric condensation nuclei. In "Studies on Fog," Hokkaido Univ., Inst. of Low Temp. Sci., pp. 349-382. Sapporo, Japan. Kuroiwa, D. (1957). Studies on physical and chemical properties of sea-fog nuclei and maritime aerosols by means of electron microscope. Teion Kaguka A16, 79-117. Kyriazopoulos, B. D., and Livadas, G. C. (1961). Steam fog in Greek seas. Meteorologika, Publ. Meteorol. Inst. Thessaloniki, No.7. Laevastu, T. (1960). Factors affecting the temperature of the surface layer of the sea. Soc. Sci. Fennica, Commentationes Phys. Math. 25,1. Laevastu, T. (1963). Energy exchange in the North Pacific; its relations to weather and its oceanographic consequences, Parts I-III. Ocean Div., Hawaii Inst. of Geophysics, Univ. of Hawaii, Interim Rept. No.1, 2, 3. La Fond, E. C. (1959). Sea-surface features and internal waves in the sea. Indian J. Meteorol. Geophys. 10,415-419. Laikhtman, D. L. (1944). Windprofil und Austausch in der bodennahen Schicht der Atmosphare, Nachr. Akad. Wiss. USSR. Ser. Geograph. u. Geophys. 8, No.1. Quoted from "Sammelband zur Statistischen Theorie der Turbulenz." H. Goering, ed. Akademie Verlag, Berlin (1958). La Mer, V. K. (ed.) (1962). "Retardation of Evaporation by Monolayers." Academic Press, New York. Lamont, J. v. (1868). Monatliche und jahrliche Resultate der an der koniglichen Sternwarte bei Miinchen in dem lO-jahrigen Zeitraume 1857-1866 angestellten meteorol. Beobachtungen. Ann. d. Miinchener Sternwarte, Suppl. 6, 216 pp. Landsberg, H. (1934). Zahlungen von Kondensationskernen auf dem Taunusobservatorium und auf dem Nordatlantischen Ozean, Bioklim, Beibl. Meteorol. Z. 1, 125-128. Landsberg, H. (1938). Atmospheric condensation nuclei. Ergeb. Kosmischen Physik 3, 155-252. Langmaack, W. (1938). Tabellen zur Berichtigung der auf See gemessenen mittleren Windgeschwindigkeit. Ann. Hydrograph. Maritimen Meteorol. 66, 357. Langmuir, I. (1938). Surface motion of water induced by wind. Science 87, No. 2250, 119-123. Langwell, P. A. (1951). Forced convection cell circulation in clear air. Trans. Am. Geophys. Union 32, 7-14.
400
REFERENCES
Langwell, P. A. (1953). A mechanism for convection over the ocean. J. Meteorol. 10, 187-190. Larsson, P. (1959). Studies of micrometeorology of Fletcher's Island. Geophys. Res. Directorate Res. Notes No. 29, 26-31. Lettau, H. (1939). "Atmospharische Turbulenz. Akad. Verlagsges., Leipzig. Lettau, H. (1944). Die thermodynamische Beeinflussung arktischer Luftmassen tiber warmen Meeresflachen als Problem der meteorologischen Stromungs- u. Turbulenzlehre. Schr. Deut, Luftfahrtforschung 8, (3), 85-115. Lettau, H. (1949). Isotropic and non-isotropic turbulence in the atmospheric surface layer. Geophys. Res. Papers (U.S.) No. 1. Lettau, H. (1950). A re-examination of the "Leipzig Wind Profile" considering some relations between wind and turbulence in the frictional layer. Te/lus 2, 125-129. Lettau, H. (1957). Windprofil, innere Reibung und Energieumsatz in den unteren 500 m tiber dem Meer. Beitr. Phys. der Atmosphiire 30,78-96. Lettau, H. (1959). WInd profile, surface stress and geostrophic drag coefficients in the atmospheric surface layer. Advan. Geophys. 6,241-257. Levine, J. (1959). Spherical vortex theory of bubble-like motion in cumulus clouds. J. Meteorol. 16,653-662. Lilleleht, L. U., and Hanratty, T. J. (1961). Measurement of interfacial structure for co-current air-water flow. J. Fluid Mech. 11,65-81. Lodge, J. P. Jr. (1955). A study of sea-salt particles over Puerto Rico. J. Meteorol. 12, 493-499. Lodge, J. P. Jr., MacDonald, A. J. Jr., and Vihman, E. (1960). A study of the composition of marine atmospheres. Te/lus 12, 184-187. Loewe, F. (1957). Arctic sea smoke in low latitudes. Australian Meteorol. Mag. No. 16, 45. Ludlam, F. H. (1951). The production of showers by the coalescence of cloud droplets. Quart.J. Roy. Meteorol. Soc. 77,402-417. Ludlam, F. H., and Mason, B. J. (1957). The physics of clouds In "Handbuch der Physik" (S. Flugge, ed.), Vol. 48, pp. 479-504. Springer, Berlin. Ludlam, F. H., and Scorer, R. S. (1953). Convection in the atmosphere. Quart. J. Roy. Meteorol. Soc. 79, 317-341. Lumb, F. E. (1961). Seasonal variation of the sea-surface temperature in coastal waters of the British Isles. Meteorol. Office, London, Sci. Paper No.6. Lumb, F.E. (1964). The influence of cloud on hourly amounts of total solar radiation at the sea surface. Quart. J. Roy. Meteorol. Soc. 90, 43-56. Magee, J. B., and Crain, C. M. (1958). A recording microwave hygrometer. Rev. Sci. Instr. 29,51. Malkus, J. S. (1952a). The slopes of cumulus clouds in relation to external wind shear. Quart. J. Roy. Meteorol. Soc. 78,530-542. Malkus, J. S. (1952b). Recent advances in the study of convective clouds and their interaction with the environment. Tellus4, 71-87. Malkus, J. S. (1954). Some results of a trade-cumulus cloud investigation. J. Meteorol. 11,220-237. Malkus, J. S. (1957). Trade cumulus cloud groups: Some observations suggesting a mechanism of their origin. Te/lus 9,33-44. Malkus, J. S. (1958). On the structure of the trade wind moist layer. Papers Phys. Oceanog. Meteorol. 13, No.2. Malkus, J. S. (1960). Recent development in studies of penetrative convection and an application to hurricane cumulonimbus towers. In "Cumulus Dynamics," Proc. 1st
REFERENCES
401
Conf. on Cumulus Convection, Portsmouth, New Hampshire pp. 65-84. Pergamon Press, New York. Malkus, J. S. (1962). Large-scale interactions. In "The Sea: Ideas and Observations" (M. N. Hill, ed.), Vol. 1, pp. 88-294. Wiley (Interscience), New York. Malkus, J. S., Riehl, H., Ronne, C., and Gray, W. S. (1961a). Cloud structure and distributions over the tropical Pacific. Part II. Woods Hole Oceanog. Inst, Ref. No. 61-24. (Unpublished). Malkus, J. S., and Ronne, C. (1954). On the structure of some cumulonimbus clouds which penetrated the high tropical troposphere. Tellus 6, 351-366. Malkus, J. S., and Ronne, C. (1960). Cloud distributions over the tropical oceans in relation to large-scale flow patterns. Am. Geophys. Union Geophys. Monogr. No.5, 45-60. Malkus, J. S., Ronne, c., and Chaffee, M. (1961b). Cloud patterns in hurricane Daisy, 1958. Tel/us 13, 8-30. Malkus, J. S., and Scorer, R. S. (1955). The erosion of cumulus towers. J. Meteoro/. 12, 43-57. Malkus, J. S., and Witt, G. (1959). The evolution of a convective element: a numerical calculation. In "The Atmosphere and the Sea in Motion," Rossby Memorial Vol. pp. 425-439. Oxford Univ. Press, London and New York. Manabe, S. (1957). On the modification of air-mass over the Japan Sea when the outburst of cold air predominates. J. Meteorol. Soc. Japan [2]35,311-326. Mandelbaum, H. (1956). Evidence for a critical wind velocity for air-sea boundary processes. Trans. Am. Geophys. Union 37,685-690. Markgraf, H. (1961). Jahresgange des Dampfdruckes und der relativen Feuchte in verschiedenen Gebieten des Mittelmeers. Geofis. Pura Appl. 49, 244-248. Markgraf, H. (1962). Zum Jahresgang der relativen Feuchte iiber dem Mittelmeer. Geofis. Pura App/. 52, 229-230. Markgraf, H., and Bintig, P. (1954). Klimatologie der Nordwesteuropaischen Gewasser, Teil 2 Deut. Wetterdienst, Seewetteramt, Einzelveriiff. No.4. Markgraf, H., and Bintig, P. (1956). Klimatologie der Nordwesteuropaischen Gewasser, Teil 3 Deut. Wetterdienst, Seewetteramt, Einzelveroff. No. 10. Mason, B. J. (1957a). The nuclei of atmospheric condensation. Geofis. Pura Appl, 36, 9-20. Mason, B. J. (1957b). The oceans, a source of cloud-forming nuclei. Geofis. Pura Appl, 36,148-155. Mauchly, S. J. (1923). Diurnal variation of the potential gradient of atmospheric electricity. Terrestial Magnetism Atmospheric Elec, 28, 61-81. Mauchly, S. J. (1924). The radium-emanation content of sea air from observations aboard the Carnegie, 1915-1921. Terrestia/ Magnetism Atmospheric Elec. 29,187194. Mauchly, S. J. (1926). Studies in atmospheric electricity based on observations made on the Carnegie, 1915-1921. Carnegie Inst. Wash. Publ. No. 175(5),385-424. Maury, M. F. (1858). "The Physical Geography of the Sea and its Meteorology," Harper & Brothers, New York. McIlroy, I. C. (1955). The atmospheric fine structure recorder. Australia, Commonwealth Sci. Ind. Res. Organization, Div. Meteorol. Phys. Tech. Paper No.3. Meinardus, W. (1923). Meteorol. Ergebnisse der Deutschen Siidpolar-Expedition 19011903. (v. Drygalski, ed.) Vol III. Meteorologie I, 1, Merz, A. (1920). Die Oberflachentemperatur der Gewasser, Veroffentl. Inst. Meereskunde Univ. Berlin 5.
402
REFERENCES
Meteorological Office, London. (1961). "Handbook of Meteorological Instruments," Part II: Instruments for Upper Air Observations. Metnieks, A. L. (1958). The size spectrum of large and giant sea-salt nuclei under maritime conditions. Geophys. Bull. (Dublin Inst. Advan. Studies, School of Cosmic Phys.) No. 15. Mildner, P. (1932). Uber Reibung in einer speziellen Luftmasse. Beitr. Phys, Frei. Atmosphdre 19, 151-158. Miles, J. W. (1957). On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185-204. Miyazaki, M. (1951a). On the relation among wind speed, tangential stress, and roughness parameters of the sea surface. Oceanog. Mag. (Tokyo) 3, 17-21. Miyazaki, M. (1951 b). Averaged wind-stress relation on the sea surface. Oceanog. Mag. (Tokyo) 3, 75-77. Moller, F. (1951a). Die Verdunstung als geophysikalisches Problem. Naturw. Rundschau 4, 45-50. . Moller, F. (1951b). Thermodynamics of clouds. Compendium Meteorol., pp. 199206. Monin, A. S. and Obukhov, A. M. (1954). Fundamentale Gesetzmassigkeiten der turbulenten Vermischung in der bodennahen Schicht der Atrnosphare. In "Sammelband zur statistischen Theorie der Turbulenz," (H. Goering, ed.) pp. 199-226; Akadernie Verlag, Berlin (1958). Trans. Inst . Geophys. Akad. Nauk . SSSR No. 24,151. Montgomery, R. B. (1936). On the momentum transfer at the sea surface, Part II. Papers Phys. Oceanog. Meteorol. 4, No.3, 21-22. Montgomery, R. B. (1940). Observations of vertical humidity distribution above the ocean surface and their relation to evaporation. Papers Phys. Oceanog. Meteorol. 7, No.4. Montgomery, R. B. (1947). Viscosity and thermal conductivity of air and diffusivity of water vapor in air. J. Meteorol. 4,193-196. Montgomery, R. B. (1948). Vertical eddy flux of heat in the atmosphere. J. Meteorol. 5,265-274. Montgomery, R. B. (1950). The Taylor diagram (temperature against vapor pressure) for air mixtures. Arch. Meteorol. Geophys. Bioklimatol. A2, 163-183. Moore, D. J. (1952). Measurements of condensation nuclei over the North Atlantic. Quart. J. Roy. Meteorol. Soc. 78, 596-602. Moore, D. J., and Mason, B. J. (1954). The concentration, size distribution and production rate of large salt nuclei over the oceans. Quart. J. Roy. Meteorol. Soc. 80, 583-590. Mosby, H. (1958). Variation diurne de la temperature de surface. Centre BeIge d'Oceanogr. et de Rech. Sous-Mar., Journees des 24 et 25 Fevrier 1958, pp. 165-173. Motzfeld, H. (1937). Die turbulente Stromung an welligen Wanden, Z. Angew. Math. Mech. 17, 193-212. Muhleisen, R. (1957). Atmospharische Elektrizitat, In "Handbuch der Physik," (S. Fliigge, ed.), Vol. 48, II, pp. 541-607. Springer, Berlin. Mirhleisen, R. (1959, 1962). Die luftelektrischen Verhaltnisse im Kiistenaerosol I, II. Arch. Meteorol. Geophys. Bioklimatol. All, 93-108; A12, 435-446. Munk, W. H. (1947). A critical wind speed for air sea boundary processes. J. Marine Res. 6,203-218. Munk, W. H. (1951). Origin and generation of waves. Proc. 1st Conf. on Coastal Eng. Long Beach, California, 1950, Council on Wave Res., The Eng. Foundationpp. 1-4. Munk, W. H. (1955). Wind stress on water: an hypothesis. Quart. J. Roy. Meteorol. Soc. 81,32Q-332.
REFERENCES
403
Myers, V. A. (1959). Surface friction in a hurricane. Monthly Weather Rev. 87, 307-311. Mysels, K. J. (1959). Direct observation of evaporation from quiescent water. Science 129,96-97. Namias, J. (1959). Recent seasonal interactions between North Pacific waters and the overlying atmospheric circulation. J. Geophys, Res. 64, 631-646. National Bureau of Standards. (1956). An ocean-based automatic weather station. J. Franklin Inst. 261, 654-656. Neumann, G. (1948). Uber den Tangentialdruck des Windes und die Rauhigkeit der Meeresoberflache. Z. Meteorol. 2,193-203. Neumann, G. (1951). Gibt es eine "kritische Windgeschwindigkeit" fur die Grenzflache Wasser-Luft? Deut. Hydrograph. Z. 4, 6-13. Neumann, G. (1953). On ocean wave spectra and a new method of forecasting windgenerated sea. U.S. Army, Beach Erosion Bd. Tech. Mem. No. 43. Neumann, G. (1956). Wind stress on water surfaces. Bull. Am. Meteorol. Soc. 37, 2Il-217. Neumann, G. (1958). Notes on the stress of light winds on the sea. Bull. Am. Meteorol. Soc. 40,146-148. Neumann, G. (1960). Some meteorologically important relationships between the ocean and atmosphere. Trans. N. Y. Acad. Sci. [2]22,615-633. Neumann, H. G. (1958). Zellmuster auf der Oberflache eines Teichs. Beitr. Phys. Atmosphiire 30, 215-222. Nikuradse, J. (1932). Gesetzmassigkeiten der turbulenten Stromung in glatten Rohren. VDI-Forschungsh. 356, 36 pp. Norris, R. (1948). Evaporation from extensive surfaces of water roughened by waves. Quart.J. Roy. Meteorol. Soc. 74,1-12. Nurminen, A. (1957). Variations in the difference between the dew point of the air and the water temperature before sea fog. Ilmat. Keskuslaitoksen Toimituksia No. 42. O'Connor, T. c., Sharkey, W. P., and Flanagan, V. P. (1961). Observations on the Aitken nuclei in Atlantic air. Quart. J. Roy. Meteorol. Soc. 87, 105-108. Oddie, B. C. V. (1960). The variation in composition of sea-salt nuclei with mode of formation. Quart. J. Roy. Meteorol. Soc. 86, 549-551. Ogata, T., Kanazawa, M., and Kitamura. N. (l958a). On the meteorological conditions near the sea surface at "Tango." Part 1. Kishocho Kenkyu Jiho, J. Meteorol. Res. Tokyo, 10,164-172. Ogata, T., Kanazawa, M., and Kitamura, N. (l958b). On the meteorological conditions near the sea surface at "Tango." Part 3. Kishocho Kenkyu Jiho, J. Meteorol. Res. Tokyo, 10, 911-916. Ogata, T., Kanazawa, M., and Yoshida, F. (1958c). The sea fog over the open sea, Part 2. Kishocho Kenkyu Jiho, J. Meteorol. Res. Tokyo, 10, 253-259. Ogata, T., and Tamura, Y. (1955). The sea fog over the open sea, Part 1. Kishocho Kenkyu Jiho, J. Meteorol. Res. Tokyo, 7, 633-642. Ohta, S. (1951). On the contents of condensation nuclei and uncharged nuclei on the Pacific Ocean and the Japan Sea. Bull. Am. Meteorol. Soc. 32, 30-31. Okuda, S., and Hayami, S. (1959). Experiments on evaporation from wavy water. Records Oceanog. Works Japan [NS] 5, 6-13. Otto, L. (1961). The influence of tidal currents on wind estimates. Konikl. Ned. Meteorol. Inst. Wetenschap. Rappt. 61-1, De Bilt. Owen, J. c., and Halstead, M. H. (1942). The measurement of wind- and moisturegradients over a reservoir. Trans. Am. Geophys. Union 23,255-257. Pagava, S. T., Aristov, N. A., Bliumina, L. I., Zakharova, N. M., and Sevalkina, N. A. (1958). Influence of the North Atlantic on the development of synoptic processes.
404
REFERENCES
(N.V. Sagatovskii, ed.) Tsentral'nyi Inst. Prognozov, Moscow, Gidrometizdat, 71 pp, (in Russian). Palmeri, E. (\963). Computation of the evaporation over the Baltic Sea from the flux of water vapor in the atmosphere. IUGG Int. Assoc. Sci. Hydrol. Congr. Berkeley, 1963, Comm. for Evapor., Publ. No. 62, 244-252. Palmen, E. H., and Laurila, E. (\938). Uber die Einwirkung eines Sturmes auf den hydrograph. Zustand im nordlichen Ostseegebiet. Soc. Sci. Fennica, Commentationes Phys. Math. 10,1-53. Palmqvist, A. (\892-1893). Undersokningar ofvar atmosferens Kolsyrehalt. Svens. Vetenskap Handlingar 18,1-39. Panofsky, H. A. (1947). Radiative cooling in the lowest layer of an atmosphere warmer than the ground. J. Meteorol. 4, 35-37. Panofsky, H. A. (\961). An alternative derivation of the diabatic wind profile. Quart. J. Roy. Meteorol. Soc. 87,109-110. Panofsky, H. A., Blackadar, A. K., and McVehil, G. E. (1960). The diabatic wind profile. Quart. J. Roy. Metearol. Soc. 86, 390-398. Parkinson, W. C. (1952). Note on the concentration of condensation nuclei over the western Atlantic. J. Geophys. Res. 57, 314-315. Pasquill, F. (1949). Eddy diffusion of water vapor and heat near the ground. Proc. Roy. Soc. (London), AI98, 116-140. Peirce, B. O. (1929). "A Short Table of Integrals," 3rd ed., 156 pp. Ginn and Co., Boston. Perl roth, J., and Simpson, L. (1962). Persistance of sea-surface temperature pattern. Undersea Technol. 3 (4),16-22. Petersen, P. (1927). Zur Bestimmung der Windstarke auf See. Ann. Hydrograph, (Berlin), 55,69-72,394. Phillips, O. M. (1957). On the generation of waves by a turbulent wind. J. Fluid. Mech. 2, 417-445. Phillips, O. M. (1958). The equilibrium range in the spectrum of wind-generated waves. J. Fluid Mech. 4, 426-434. Phillips, O. M. (1962). Recent developments in the theory of wave generation by wind. J. Geophys. Res. 67, 3135-3141. Pierson; W. J. (1955). Wind generated gravity waves. Advan. Geophys. 2, 93-178. Pike, A. C. (1961). The oceanic heat budget as affected by Hurricane Audrey (1957). Colorado State Univ., Atmosph. Sci. Tech. Paper No. 24. Pike, A. C. (\ 962). Estimating the effect of cloudiness on incoming solar radiation. Colorado State Univ., Atmosph. Sci. Tech. Paper No. 31. Pincock, G. L., and Turner, J. A. (1956). Advection fog along the British Columbia coast and over the North Pacific Ocean during late summer and early autumn. Proc. Pacific Sci. Congr. Pacific Sci. Assoc., 8th, Quezon City, 1953, 2A, 955-962. Plass, G. N. (1956, 1961). The carbon dioxide theory of climatic change. Tellus 8, 140154; 13,296-300. Polar Record (l959a). Soviet drifting stations in the Arctic Ocean, 1958-59. Polar Record 9, No. 63, 570. Polar Record. (1959b). Soviet automatic radiobuoys and meteorological stations. Polar Record 9, No. 63, 577-578. Pollak, M. J. (1960). Wind set-up and shear-stress coefficient in Chesapeake Bay. J. Geophys. Res. 65,3383-3389. Portman, D. J. (1960). An improved technique for measuring wind and temperature profiles over water and some results obtained for light winds. Great Lakes Res. Div., Univ. of Michigan, Publ. No.4, 77-84.
REFERENCES
405
Prandtl, L. (1932). Meteorologische Anwendungen der Stromungslehre, Beitr. Phys. Erei. Atmosphiire 19,188-202. Prescott, J. A., and Collins, J. A. (1951). The lag of temperature behind solar radiation. Quart.J. Roy. Meteorol. Soc. 77,121-126. Priestley, C. H. B. (1954). Convection from a large horizontal surface. Australian J. Phys.7,176-201. Priestley, C. H. B. (1955). Free and forced convection in the atmosphere near the ground. Quart. J. Roy. Meteorol. Soc. 81,139-143. Priestley, C. H. B. (l959a). Estimation of surface stress and heat flux from profile data. Quart. J. Roy. Meteorol. Soc. 85,415--418. Priestley, C. H. B. (1959b). "Turbulent Transfer in the Lower Atmosphere." Univ. of Chicago Press, Chicago, Illinois. Priestley, C. H. B. (1962). The width-height ratio of large convection cells. Tel/us 14, 123-124. Raethjen, P. (1961). Uber die Anwendung der technischen Turbulenzlehre auf die Reibungsschicht der Atrnosphare. Geofis. Pura Appl. 49, 225-243. Rau, W. (l956a). Bestimmung der Grosse und der Haufigkeit der Chloridteilchen im maritimem Aerosol. Meteorol. Rundschau. 9, 210-214. Rau, W. (l956b). Experimentelle Untersuchungen tiber die Erzeugung von Salzteilchen aus den Meeren. Geofis. Pura Appl. 33, 113-120. Regula, H. (1939). Geschwindigkeitsverteilung in Warm- und Kaltluftstrornungen tiber See. Ann. Hydrograph, Maritimen Meteorol. 67, 310-315. Reid, R. 0., and Clayton, W. H. (1953). Transfer processes operating at the ocean boundaries. Technical Report Texas A. and M. Research Foundation (unpublished). Reiter, E. R. (1955). Der mitftihrende Einfluss einer Flussoberflache auf die dariiberliegenden Luftschichten. Arch. Meteorol. Geophys. Bioklimatol. A8, 384-396. Revelle, R., and Suess, H. E. (1957). Carbon dioxide exchange between atmosphere and ocean and the question of an increase of atmospheric C02 during the past decades. Tel/us 9, 18-27. Revillon, P. (1953). Vent du gradient et vent reel sur mer. Meteorologic, Juillet-Sept., 171-186. Reynolds, G. (1956). A wind analysis for the northern Irish Sea. Quart. J. Roy. Meteorol. Soc. 82,469--480. Richardson, W. S., and Wilkens, C. H. (1958). An airborne radiation thermometer. Deep-Sea Res. 5, 62-71. Rider, N. E. (1954). Eddy diffusion of momentum, water vapor and heat near the ground. Phil. Trans. Roy. Soc. London A246, 481-501. Riehl, H. (1954). "Tropical Meteorology." McGraw-Hill, New York. Riehl, H. (1956). Sea surface temperature anomalies and hurricanes. Bull. Am. Meteorol. Soc. 37,413--417. Riehl, H., Gray, W. S., Malkus, J. S., and Ronne, C. (1959). Cloud structure and distributions over the tropical Pacific. Part I. Woods Hole Oceanog. Inst. Ref. No. 58-62. (Unpublished). Roden, G. I. (1962). On sea-surface temperature, cloudiness and wind variations in the tropical Atlantic. J. Atmospheric Sci. 19, 66-80. Roden, G. I., and Groves, G. W. (1960). On the statistical prediction of ocean temperatures. J. Geophys. Res. 65,249-263. Rodewald, M. (1952-1960). Beitrage zur Klimaschwankung im Meere. Contribution No. 1-12. Deut. Hydrograph, Z. 5,131-140; 6,170-185; 9,137--412; 182-186, 187188,290-297;10,147-151, 151-157;11,78-82;12,204-210;13,142-143.
406
REFERENCES
Rodhe, B. (1962). The effect of turbulence on fog formation. Tellus 14, 49-86. Roll, H. U. (1939). Zur Frage des taglichen Temperaturganges und des Warmeaustausches in den unteren Luftschichten iiber dem Meere. Arch. Seewarte u. Mar. Obs. 59, No.9. Roll, H. U. (1948a). Wassernahes Windprofil und Wellen auf dem Wattenmeer. Ann. Meteorol.l,139-151. Roll, H. U. (1948b). Uber die vertikale Temperaturverteilung in der wassernahen Luftschicht. Ann. Meteorol. 1,353-360. Roll, H. U. (1949). Vergleichende Betrachtung und Kritik von Windprofilmessungen auf See. Ann. Meteorol. 2, 71-78. Roll, H. U. (1950). Gedanken iiber den Zusammenhang der vertikalen Profile von Windgeschwindigkeit u. Temperatur in der wassernahen Luftschicht. Ann. Meteorol. 3,1-9. Roll, H. U. (1951a). Neue Messungen zur Entstehung von Wasserwellen durch Wind. Ann. Meteorol. 4, 269-286. Roll, H. U. (1951b). Zur Genauigkeit der Wassertemperaturmessung mit dem Wasserschopftherrnometer (Marine-Piitz). Ann. Meteorol. 4, 480-482. Roll, H. U. (1952a). Gibt es eine "kritische Windgeschwindigkeit" fur Prozesse an der Grenzflache Wasser-Luft? Geofis. Pura Appl. 21,3-19. Roll, H. U. (1952b). Ober Grossenunterschiede der Meereswellen bei Warm- und Kaltluft. Deut. Hydrograph Z. 5,111-114. Roll, H. U. (1952c). Temperaturmessungen nahe der Wasseroberflache. Deut. Hydrograph. Z. 5, 141-143. Roll, H. U. (1953-1954). Beaufort-Aquivalente auf See bei verschiedenen thermischen Schichtungen etc. Ann. Meteorol. 6, 193-201. Roll, H. U. (1955). Discussion on airflow over the sea. Quart. J. Roy. Meteorol. Soc. 81, 631-632. Roll, H. U. (1957). Oberflachenwellen des Meeres. In "Handbuch der Physik" (S. Fliigge, ed.), Vol. 48, pp. 671-733. Springer, Berlin. Roll, H. U. (1958a). Zur Niederschlagsmessung auf See: Ergebnisse von Vergleichsmessungen auf Feuerschiffen und benachbarten Inseln. Deut. Wetterdienst, See wetteramt (Hamburg), Einzelveroff. No. 16. Roll, H. U. (1958b). Der Austauschkoeffizient tiber dem Meere. Beitr, Phys. der Atmosphiire30,149-169. Roll, H. U. (1959). Regenmessung auf See. Der Seewart 20, 91-98. Roll, H. U. (1963). On the application of turbulence theory to the determination of marine evaporation. Geofis. Pura Appl. 56, 150-158. Rosenthal, S. L. (1960a). The interdiurnal variability of surface-air temperature over the North Atlantic Ocean. J. Meteorol. 17, 1-7. Rosenthal, S. L. (1960b). The aperiodic diurnal range of temperature over the North Atlantic Ocean. J. Meteorol. 17,78-83. Rosenthal, S. L., and Gleeson, T. A. (1958). An investigation of the variability of surface-air temperature over the North Atlantic Ocean. Florida State Univ., Dep. Meteorol. Rept. Contr. No. CWB-9272. Rossby, C. G. (1936). On the momentum transfer at the sea surface. Part I. Papers Phys. Oceanog. Meteorol. 4, No.3, 3-20. Rossby, C. G., and Montgomery, R. B. (1935). The layer of frictional influence in wind and ocean currents. Papers Phys. Oceanog. Meteorol. 3, No.3. Roulleau, J. (1952). L'altitude de la base de I'atmosphere libre au-dessus de l'ocean, J. Sci. Meteorol. 4,135-142.
REFERENCES
407
Rubin, M. J. (1958). An occurrence of steam fog in Antarctic waters. Weather 13, 235-238. Ruttenberg, S., and Holzer, R. E. (1955). Atmospheric electrical measurements in the Pacific Ocean. Geophys. Res. Directorate Geophys. Res. Paper No. 42, 101-108 (Wentworth Conf.). Rykachov, M. M. (1914). Meteorologische Beobachtungen in verschiedenen Schichten auf dem schwimmenden Leuchtturm Luserort, Meteorol. Z. 31, 328-339. Sagalyn, R. C. (1958). The production and removal of small ions and charged nuclei over the Atlantic Ocean. "Recent Advances in Atmospheric Electricity" (L. G. Smith, ed.) pp. 21-41. Pergamon Press, New York. Sanuki, M., and Kimura, S. (1954). Experiments on a marine combination wind vane on anemometer in pitching or rolling motion. Papers Meteorol. Geophys. (Tokyo) 5, 35-40. Sanuki, M., and Kimura, S. (1955). Experiments on a cup-anemometer in pitching and rolling motion. Papers Meteorol. Geophys. (Tokyo) 5, 233-235. Sauberer, F., and Dirmhirn, I. (1955). Uber den Strahlungshaushalt der Ozeane auf der NordhalbkugeI. Arch. Meteorol. Geophys. Bioklimatol. B6, 113-127. Saunders, P. M. (1961).* An observational study of cumulus. J. Meteorol. 18,451-467. Saville, T., Jr. (1952). Wind set-up and waves in shallow water. U.S. Army, Beach Erosion Bd. Tech. Mem. No. 27. Schalkwijk, W. F. (1947). A contribution to the study of storm surges on the Dutch coast. Koninkl. Ned. Meteorol. Inst. 125, III pp. Schmidt, W. (1915). Strahlung und Verdunstung an freien Wasserflachen Ann. Hydrograph. (Berlin) 43,111-124; 169-178. Schmidt, W. (1920). Uber den taglichen Temperaturgang in den unteren Luftschichten. Meteorol. Z. 37,49-59. Schmitz, H. P. (1961). Kritische Betrachtungen zu gebrauchlichen Methoden der Ermittlung des Windschubs auf dem Meere. Deut. Hydrograph Z. 14, 169-193. Schmitz, H. P. (1962a). A relation between the vectors of stress, wind, and current at water surfaces and between the shearing stress and velocities at solid boundaries. Deut. Hydrograph Z. 15,23-36. Schmitz, H. P. (1962b). Uber die Interpretation bodennaher vertikaler Geschwindigkeitsprofile in Ozean und Atmosphare und die Windschubspannung auf Wasseroberflachen, Deut. HydrographZ.1S, 45-72. Schooley, A. H. (1954). A simple optical method for measuring the statistical distribution of water surface slopes. J. Opt. Soc. Am. 44, 37-40. Schooley, A. H. (1958a). Probability distributions of water-wave slopes under conditions of short fetch. Trans. Am. Geophys. Union 39, 405-408. Schooley, A. H. (1958b). Profiles of wind-created water-waves in the capillary-gravity transition region. Trans. Am. Geophys. Union 39,531. Schooley, A. H. (1961a). Relationship between surface slope, average facet size, and facet flatness tolerance of a wind-disturbed water surface. J. Geophys. Res. 66, 157-162. Schooley, A. H. (1961b). Mean roughness factor as a function of wind velocity. J. Geophys. Res. 66, 2863-2866. Schooley, A. H. (1963). Simple tools for measuring wind fields above wind-generated water waves. J. Geophys. Res. 68, 5497-5504. Schroder, B., Roll, H. D., and Seifert, G. (1939). Bericht tiber die meteorologischen Arbeiten wahrend der Internationalen Golfstrom-Untersuchung 1938 auf Dampfer "Altair." Abhandl. Preuss. Akad. Wiss. Phys. Math. Kl. No.5, Anlage 1. * For later papers see the Supplement, p. 412.
408
REFERENCES
Schumacher, A. (1952). Results of exact wave measurements (by stereophotogrammetry) with special reference to more recent theoretical investigations. Natl. Bur. Std. (U.S.) Circ. 521, 69-78. Schumacher, A. (1962). Verdunstungsmessungen. Wiss Ergebnisse. Deut. Atlant, Exped. "Meteor" 1925-27,7 (2), Part B. Schwerdtfeger, W. (1932). Temperaturverhaltnisse in einem Polarluftausbruch. Erfahr, Deut. Flugwetter. 3, 35-42. Scorer, R. S., and Ludlam, F. H. (1953). Bubble theory of penetrative convection. Quart.J. Roy. Meteorol. Soc. 79, 94-103. Seilkopf, H. (1955-1956). Bemerkungen tiber die Wirkung des "Plankton-Faktors" des Schaumens des Meerwassers auf die Bestimmung der Geschwindigkeits-Aquivalente der Windschatzungen auf See. Ann. Meteorol. 7,404-409. Shellard, H. C. (1958). Some measurements of temperature and humidity profiles near the sea surface. Marine Observer 28, 198-204. Sheppard, P. A. (1952). Current research at Imperial College, London, on the effects of turbulent flow-eddy fluxes. Geophys. Res. Papers (U.S.) No. 19, 345-354. Sheppard, P. A. (1954). The vertical transfer of momentum in the general circulation. Arch. Meteorol, Geophys. Bioklimatol. A7, 114-124. Sheppard, P. A. (1958). Transfer across the earth's surface and through the air above. Quart; J. Roy. Meteorol. Soc. 84, 205-224. Sheppard, P. A., Charnock, H., and Francis, J. R. D. (1952). Observations of the westerlies over the sea. Quart.J. Roy. Meteorol. Soc. 78,563-582. Sheppard, P. A., and Omar, M. H. (1952). The wind stress over the ocean from observations in the Trades. Quart.J. Roy. Meteorol. Soc. 78, 583-589. Shoulejkin, W. (1928). The evaporation of sea water and the thermal intercourse between the sea and atmosphere. Gerlands Beitr, Geophys. 20, 99-122. Shoulejkin, W. (1953). "Fizika moria" (Physics of the Sea). Akad. Nauk, SSSR, Moscow. Sibul, O. J. (1955). Water surface roughness and wind shear stress in a laboratory windwave channel. U.S. Army, Beach Erosion Bd., Tech. Mem. No. 74. Silvester, R. (1955). Method of obtaining the gradient wind from the geostrophic wind. Meteorol. Mag. 84, 348-350. Skaar, J. (1955). On the measurement of precipitation at sea. Geofys. Publikasjoner, Nordske Videnskaps. Akad. Oslo 19, No.6. Skorka, S. (1958). Messungen der Luftradioaktivitat wahrend einer Seereise nach Australien. Atomkernenergie 3,182-186. Spinnangr, F. (1958). Some remarks on precipitation measurements at sea. Meteorol. Ann. 4, No.7. Squires, P. (1958). The spatial variation of liquid water and droplet concentration in cumuli. Tel/us 10, 372-380. Squires, P. (1960). Mixing processes in convective clouds. In "Cumulus Dynamics," Proc. 1st Conf. on Cumulus Convection, Portsmouth, New Hampshire, pp. 44-49. Pergamon Press, New York. Staley, R. C. (1960). Some observations of water vapor fluctuations in a stable atmosphere over a lake surface. Arch. Meteorol. Geophys. Bioklimatol. AIl, 458-464. Stepanov, V. P. (1961). The annual course of water temperature at the surface of the world ocean. Okeanologiya 3,399-406 (in Russian). Stevenson, R. E. (1962).* A steam fog at Galveston, Texas. Weatherwise 15,188-191,213. Stewart, R. W. (1961). The wave drag of wind over water. J. Fluid Mech. 10, 189-194. *For later papers see the Supplement, p. 412.
REFERENCES
409
Stewart, R. W. (1962). Wind stress on water. Proc. Symp. Math. Hydrodyn. Methods of Phys. Oceanog., Hamburg, 1961, pp. 399-408. Stommel, H. (I 947a). A summary of the theory of convection cells. Ann. N. Y. Acad. Sci. 48, 715-726. Stommel, H. (l947b). Entrainment of air into a cumulus cloud. J. Meteorol. 4, 91-94. Stommel, H. (1951). Entrainment of air into a cumulus cloud. II. J. Meteorol. 8,127-129. Stommel, H. (1952). Streaks on natural water surfaces. Geophys. Res. Papers (U.S.) No. 19, 145-154. Stommel, H., and Woodcock, A. H. (1951). Diurnal heating of the surface of the Gulf of Mexico in the spring of 1942. Trans. Am. Geophys. Union 32,565-571. Straaten, L. M. J. U. van (1950). Periodic patterns of rippled and smooth areas on water surfaces, induced by wind action. Koninkl. Ned. Akad. Wetenschap. Proc. 53, No.8, 1217-1227. Suess, H. E. (1953). Natural radiocarbon and the rate of exchange of carbon dioxide between the atmosphere and the sea. Proc. Conf. on Nuclear Processes in Geologic Settings, Williams Bay, Wise. 1953. Natl. Res. Council. Publ. pp. 52-56. Sutcliffe, R. C. (1936). Surface resistance in atmospheric flow. Quart. J. Roy. Meteorol. Soc. 62, 3-12. Sverdrup, H. U. (1937). On the evaporation from the oceans. J. Marine Res. 1, 3-14. Sverdrup, H. U. (1943a). "Oceanography for Meteorologists." Prentice-Hall, New York. Sverdrup, H. U. (l943b). On the ratio between heat conduction from the sea surface and heat used for evaporation. Ann. N. Y. A cad. Sci. 44, 81-88. Sverdrup, H. U. (1946). The humidity gradient over the sea surface. J. Meteorol. 3, 1-8. Sverdrup, H. U. (1951). Evaporation from the oceans. Compendium Meteorol., pp. 10711081. Sverdrup, H. U. (1957). The stress of the wind on the ice of the Polar Sea. Norske Polarinst. Skrifter No. 111. Sverdrup, H. U., Johnson, M. W., and Fleming, R. H. (1946). "The Oceans." PrenticeHall, New York. Swinbank, W. C. (1955). An experimental study of eddy transports in the lower atmosphere.,Australia, Commonwealth Sci. Ind. Res. Organization Div. Meteorol. Phys. Tech. Paper No. 2. Swinbank, W. C. (1960). Evaporation from the oceans. In "Studies in Weather Analysis and Forecasting" (S. Pettersen, ed.), Contr. AF 19 (604)-2179 Weather Forecasting Res. Center, Dept. Meteorol., Chicago. Part B, 1-16. Takahashi, Tadao (1958). Micro-meteorological observations and studies over the sea. Mem. Fac. Fisheries Kagoshima Univ. 6, 1-46. Takahashi, Taro (1961). Carbon dioxide in the atmosphere and in the Atlantic Ocean water. J. Geophys. Res. 66,477-494. Taylor, G. I. (1915). On eddy motion in the atmosphere. Phil. Trans. Roy. Soc. London A215,1-26. Taylor, G. I. (1917). The formation of fog and mist. Quart. J. Roy. Meteorol. Soc. 43, 241-268. Taylor, R. I. (I 960a). Similarity theory in the relation between fluxes and gradients in the lower atmosphere. Quart. J. Roy. Meteorol. Soc. 86, 67-78. Taylor, R. I. (I 960b). The form of wind profile in the layer of atmosphere near the ground. Izv. Akad. Nauk. SSSR, Ser. Geofiz. No. 12, 1821. Tippelskirch, H. v. (1959). Weitere Konvektionsversuche: Der Nachweis der Ringzellen und ihrer Verallgemeinerung. Beitr. Phys. der Atmosphdre 32, 2-22.
410
REFERENCES
Tolefson, H. B., and Henry, R. M. (1961). A method of obtaining detailed wind shear measurements for application to dynamic response problems of missile systems. J.Geophys.Res.66,2849-2862. Torreson, O. W., Gish, O. H., Parkinson, W. c., and Wait, G. R. (1946). Ocean atmospheric-electric results. Carnegie Inst. Wash. Publ. No. 568. Tucker, G. B. (1962). Convergence of horizontal flux of water vapor in the general circulation of the atmosphere. J. Geophys. Res. 67, 3129-3133. Twomey, S., and McMaster, K. N. (1955). The production of condensation nuclei by crystallizing salt particles. Tellus 7, 458-461. Uda, M. (1954). On the variation of water temperature due to the passage of typhoon. IUGG Assoc. Phys. Oceanog. Congr, Rome, 1954, Proc. Verb., Bergen, pp. 297-298. Ulanov, H. (1942). The change of the velocity of wind with height above the sea. Bull. Am. Meteorol. Soc. 23, 81. Ursell, F. (1956). Wave generation by wind. In "Surveys in Mechanics." (G. K. Batchelor and R. M. Davies, eds.), pp. 216-249. Cambridge Univ. Press, London and New York. U.S. Navy, Hydrographic Office (1951). Techniques for forecasting wind waves and swell. U.S. Navy Hydrographic Office, Publ. No. 604. U.S. Navy, Hydrographic Office (1960). Oceanographic Instrumentation, 2nd ed., U.S. Navy Hydrogr. Office, Washington, D.C., SP-41. U.S. Weather Bureau (1959). Marine automatic weather station, 1959 test program. Marine Weather Log 3, 225-226. U.S. Weather Bureau (1961). Infrared radiation thermometer. Marine Weather Log 5, 118-119. Van Dorn, W. G. (1953). Wind stress on an artificial pond. J. Marine Res. 12,249-276. Verploegh, G. (1956). The equivalent velocities of the Beaufort estimates of the wind force at sea. Koninkl. Ned. Meteor. Inst, Mededel. Verhandel. No. 66. Verploegh, G. (1957). Rainfall measurements aboard the Netherlands Ocean Weather Ships Cirrus and Cumulus. Koninkl. Ned. Meteorol. Inst. Wetenschap. Rappt. 57-003 (IV-014); see also Appendix (1958). Vines, R. G. (1959). Wind stress on a water surface: measurements at low wind speeds with the aid of surface films. Quart. J. Roy. Meteorol. Soc. 85,159-162. Vinogradova, O. P. (1959). The tangential stress of the wind on a disturbed sea surface. Izv. Akad. Nauk. SSSR, Ser. Geofiz, No. 11, 1646-1655 (in Russian). Vinogradova, O. P. (1960). The intensity of turbulent exchange and the roughness parameter of the sea surface. Trudy Morsk, Gidrofiz, Inst. Moscow 20, 44-50 (in Russian). Vorontsov, P. A. (1959). Aerological characteristics of sea fog. Arkt, i. Antarkt. Inst . Leningrad, Trudy 228, 38-54 (in Russian). Wagner, N. K. (1958). An analysis of some over-water wind profile measurements. Trans. Am. Geophys. Union 39, 845-852. Wait, G. R. and Parkinson, W. C. (1951). Ions in the atmosphere. Compendium Meteorol. pp.120-127. Walden, H. (1952). Temperaturbeobachtungen auf den Segelschiffen "Passat" und "Pamir" und Folgerungen fur die Berechnung des Warmehaushaltes Ozean-Atmosphare. Ann. Meteorol. 5, 303-312. Walden, H. (1953-1954). Zur Feuchtigkeitsmessung in alteren Thermometerhiitten auf Schiffen. Ann. Meteorol. 6,124-125. Webb, E. K. (1958). Vanishing potential temperature gradients in strong convection. Quart.J. Roy. Meteorol. Soc. 84,118-125.
REFERENCES
411
Webb, E. K. (1960). An investigation of the evaporation from Lake Eucumbene. Australia, Commonwealth Sci. Ind. Res. Organization Div. Meteorol. Phys, Tech. Paper No. 10. Webb, E. K. (1962). Thermal convection with wind shear. Nature 193, 840-842. Wegemann, G. (1920). Der tagliche Gang der Temperatur des Meeres etc. Wiss. Meeresuntersuchungen (Kiel) [N.S.] 19, No.2. Wegener, A., and Kuhlbrodt, E. (1922a). Der Spiegeltheodolit fur Pilot- und freie Registrierballonaufstiege auf See. Ann. Hydrograph Maritimen Meteorol. 22, 241244. Wegener, A., and Kuhlbrodt, E. (1922b). Pilotballonaufstiege auf einer Fahrt nach Mexiko. Arch. Deut, Seewarte (Hamburg) No. 40 (4). Wegener, K. (1911). Uber den Anteil der direkten Strahlung an der Temperaturperiode der Luft in niedrigen und mittleren Hohen der Troposphare. Gottingische gelehrte Anzeigen, pp. 382-408. Westwater, F. L. (1943). Wind structure over the sea. Quart. J. Roy. Meteorol. Soc. 69, 207-213. Whipple, F. J. W. (1929). On the association of the diurnal variation of electric potential gradient in fine weather with the distribution of thunderstorms over the globe. Quart. J. Roy. Meteorol. Soc. 55,1-17. Whipple, F. J. W., and Scrase, F. J. (1936). Point discharge in the electric field of the earth. Geophys, Mem, (London) 68,1-20. Wiener, F. M., Ball, J. H., and Gogos, C. M. (1961). Some micrometeorological measurements in ocean fog. J. Geophys. Res. 66, 3974-3978. Wigand, A. (1930). Zahlungen der Kondensationskerne auf dem Nordatlantik. Ann. Hydrograph. (Berlin) 58, 212-216. WiIckens, F. (1962). Anwendbarkeit von Satellitenmessungen in der Ozeanographie. Deut. Hydrograph Z. 15,93-102. Wilson, A. T. (1959). Surface of the ocean as a source of air-borne nitrogenous material and other plant nutrients. Nature 184, 99-101. Wilson, B. W. (1960). Note on surface wind stress over water at low and high wind speeds.J. Geophys.Res.65,3377-3382. Woodcock, A. H. (1940). Convection and soaring over the open ocean. J. Marine Res. 3, 248-253. Woodcock, A. H. (1941). Surface cooling and streaming in shallow fresh and salt waters. J. Marine Res. 4,153-161. Woodcock, A. H. (1944). A theory of surface water motion deduced from the windinduced motion of the Physalia. J. Marine Res. 5, 196-205. Woodcock, A. H. (1952). Atmospheric salt particles and raindrops. J. Meteorol. 9, 200-212. Woodcock, A. H. (1953). Salt nuclei in marine air as a function of altitude and wind force. J. Meteorol. 10,362-371. Woodcock, A. H. (1960). The origin of trade wind orographic shower rains. Tellus 12, 315-326. Woodcock, A. H., and Gifford, M. (1949). Sampling atmospheric sea-salt nuclei over the ocean.J. Marine Res. 8,177-197. Woodcock, A. H., Kientzler, C. F., Arons, A. B., and Blanchard, D. C. (1953). Giant condensation nuclei from bursting bubbles. Nature 172,1144-1145. Woodcock, A. H., and Riley, G. A. (1947). Patterns in pond ice. J. Meteorol. 4,100-101. Woodcock, A. H., and Spencer, A. T. (1961). Lava-sea-air contact areas as sources of sea-salt particles in the atmosphere. J. Geophys, Res. 66, 2873-2887.
412
REFERENCES
Woodcock, A. H., and Stommel, H. (1947). Temperatures observed near the surface of a fresh-water pond at night. J. Meteorol. 4, 102-103. Woodcock, A. H., and Wyman, J. (1947). Convective motion in air over the sea. Ann. N. Y. Acad. Sci. 48,749-776. Woodward, B. (1960). Penetrative convection in the sub-cloud regime. In "Cumulus Dynamics," Proc 1st. Conf. on Cumulus Convection, Portsmouth, New Hampshire, pp. 28-38. Pergamon Press, New York. World Meteorological Organization (1954). Methods of observation at sea. Part I. Seasurface temperature. WMO Tech. Note No.2, WMO-No. 26. TP. 8. World Meteorological Organization (1956). World distribution of thunderstorm days, part 1 and 2. WMO Publ. No. 21, TP. 6 and 21. World Meteorological Organization (1959). International Meteoro!. Vocabulary, Provisional Edition, WMO Secretariat, Geneva. World Meteorological Organization (1961). Commission for Maritime Meteoro!., Abridged Final Rep. 3rd Session, Utrecht 1960. WMO Pub!. No. 101 RP.41. World Meteorological Organization (1962). Precipitation measurements at sea. Review of the present state of the problem. WMO Tech. Note No. 47, WMO-No. 124. TP. 55. Woskresenski, A. J., and Matwejew, L. T. (1960). Liquid water content and turbulence in stratiform clouds over the Arctic. Meteorol. Gidrol. No. 11, 14-19 (in Russian). Wust, G. (1920). Die Verdunstung auf dem Meere. Veroffentl, Inst. Meereskunde Univ. Berlin, [N.F.]6. Wust, G. (1936). Oberflachensalzgehalt, Verdunstung und Niederschlag auf dem Weltmeer. Liinderkundl. Forschung; Festschrift Norbert Krebs, pp. 347-359. Wust, G. (1937). Ternperatur- und Dampfdruckgefalle in den untersten Metern tiber der Meeresoberflache. Meteorol. Z. 54,4-9. Wust, G. (1954). Gesetzrnassige Wechselbeziehungen zwischen Ozean und Atmosphare in der zonalen Verteilung von Oberflachensalzgehalt, Verdunstung und Niederschlag. Arch. Meteorol. Geophys. Bioklimatol. A7, 305-328. Wyrtki, K. (1957). Precipitation, evaporation and energy exchange at the surface of the southeast Asian waters. Marine Res. Indonesia No.3, 7-40. Yamamoto, G. (1952). On a radiation chart. Sci. Rept. Tohoku Univ. Ser. V, Geophys. 4, 9-23. Yamamoto, G., and Ohtake, T. (1953). Electron microscope study of cloud and fog nuclei. Sci. Rept. Tohoku Univ. Ser. V, Geophys. 5,141-159. Yamamoto, G., and Onishi, G. (1952). Absorption of solar radiation by water vapor in the atmosphere. J. Meteorol. 9, 415-421. Zenker, H. (1953). Brandung und Kondensationskerne an der Ostseektiste. Angew. Meteorol. 1, 372-375. Zierep, J. (1958). Eine rotationsymmetrische Zellularkonvektionsstromung. Beitr. Phys . der Atmosphiire 30, 215-222. Supplement Blackadar, A. K. (1962). The vertical distribution of wind and turbulent exchange in a neutral atmosphere. J. Geophys. Res. 67, 3095-3102. Brocks, K. (1963). Probleme der mariti men Grenzschicht der Atmosphare, Ber. Deut. Wetterdienstes 91, 34-46. Brocks, K., and Hasse, L. (1963). Fluctuation measurements made at sea with a gyroscopic stabilised floating mast. Intern. Assoc. Meteorol. Atmos. Phys. Proc. IUGG Gen. Assembly, Berkeley, 1963, Publ. IAMAP No. 13, 117.
REFERENCES
413
Saunders, P. M. (1964). Sea smoke and steam fog. Quart. J. Roy. Meteorol. Soc. 90, 156-165. Saur, J. F. T. (1963). A study of the quality of sea water temperatures reported in logs of ships' weather observations. J. Appl. Meteorol. 2, 417-425. Stevenson, R. E. (1964). The influence of a ship on the surrounding air and water temperatures. J. Appl, Meteorol. 3, 115-118. Sturm, M. (1963). Uber Methoden zur empirischen Berechnung der Hauptkomponenten des Warmehaushaltes der Meeresoberflache aus mittleren hydrometeorologischen Daten. Beitr. Meereskunde 9, 36-66. Thornthwaite, C. W., Superior, W. J., and Field, R. T. (1962). Evaluation of an ocean tower for the study of climatic fluxes. C. W. Thornthwaite Assoc. Publ. in Climat. (Centerton, N.J.) 15, No.3.
Textbooks for Mariners Published Since 1950 France J. A. P. Rouch: "Meteorologic et physique du globe" Vol. I: Meteorologic nautique, 2nd ed. Soc. d'Edit. Geogr, Maritimes et Coloniales, Paris, 1950. R. Clausse and A. Viaut: "La Mer et le Vent; Meteorologic nautique. "Blondl la Rougerie, Paris, 1963. Germany W. Stein: "Wetter- und Meereskunde fur Seefahrer," 5th ed. Springer, Berlin, 1963. M. Rodewald: "Die Faxfibel" (Was der Seefahrer von Wetterkarten wissen muss), Dr. Ing. R. Hell, Kie1, 1963. Netherlands J. A. van Duijnen Montijn, H. A. Pastoor, and G. Verploegh: "Maritieme Meteorologie en Oceanografie." C. de Boer Jr. Hilversum, 1958. Poland B. Gladysz: "Meteorologia dla zeglugi morskiej" (Meteorology for sea navigation). Wydawnictwo Morskie, Gdynia, 1957. Spain S. Hernandez-Yzal: "Tratado de Meteorologia nautica". Ediciones Carriga, Barcelona, 1960.
U.K. C. R. Burgess: "Meteorology for Seamen." Brown, Son & Ferguson, Glasgow, 1950. Meteorological Office: "Meteorology for Mariners," with a Section on Oceanography. H.M. Stat. Office, London, 1956. U.S.A. W. L. Donn: "Meteorology with Marine Applications," 2nd ed. McGraw-Hill, New York,1951. U.S.S.R. N. A. Belinski: "Morskie gidrometeorologicheskie informatsii i prognozy" (Maritime hydro meteorological information and forecasting), 2nd ed. Gidrometeorol. Izd, Leningrad, 1956. 414
Author Index Numbers in italics refer to pages on which the complete references are listed
A Albrecht, F., 387, 389 Allison, L. J., 17, 19, 392 Arnot, A., 33, 34, 389 Anderson, D. Y., 127, 138, 158,261,391 Anderson, E. c., 79, 81, 389 Appleby.T, C., 17, 19,392 Arakiseki, T., 355,389 Aristov, N. A., 246, 403 Arnold, J. R., 79, 81, 389 Arons, A. B., 59, 61, 398, 411 Arrhenius, S., 389 Ashburn, E. Y., 387, 389 Austin, J. M., 312, 389
B Badgley, F. 1.,127,141,142,143,149, 158, 261,269,270,271,394 Ball, F. K., 31, 389 Ball, J. H., 360, 361, 411 Battan, L. J., 64, 389 Bell, J., 27, 389 Benard, H., 295, 389 Benditskii, N. D., 33, 389 Benton, G. S., 387, 389 Berget, A., 2, 389 Bernard, E. A., 374, 376, 380,389 Bigelow, H. B., 2, 389 Bijvoet, H. C., 218, 389 Bintig, P., 226, 239, 240, 357, 370, 372, 377,390,391,401 Bischof, W., 78, 390 Bjerknes, J., 243, 244, 246, 313, 381, 390 Bjorgum, 0., 134, 390 Blackadar, A. K., 148, 149, 150,218,274, 404, 412 Blanchard, D. C., 46, 59, 60, 61, 62, 86, 87, 95, 97, 99, 390, 398, 411 Bliumina, L. 1., 264, 403 Boguslavskii, S. G., 229, 390
Bolin, B., 80, 81, 82, 390 Bowen, 1. S., 253, 390 Braak, C., 369, 390 Bray, J. R., 75, 390 Brier, G. W., 63, 390 Brockamp, B., 257, 390 Brocks, K., 18, 19,26, 102, 127, 139, 142, 143,154,158, 160, 161, 255, 261,264, 265,269,270,325,390,391,412 Brogmus, W., 142, 273, 279, 391 Brooks, C. F., 23, 161,391 Brooks, E. S., 23, 161,391 Brose, K., 224, 225,391 Brown, P. R., 7, 378, 379, 380, 391 Bruce, J. P., 127, 138, 158,261,391 Bruch, H., 126, 141, 158, 229, 230, 260, 391 Buch, K., 74, 75, 391 Bullig, H. J., 240, 243, 244, 245, 391 Bunker, A. F., 179, 199, 200, 201, 202, 203,204,211,281,291,292,293,303, 306,307,310,311,315,319,333,335, 391 Burke, C. J., 340, 341,391 Burling, R. W., 108, 110,391 Byers, H. R., 2, 391 C Callendar, G. S., 72, 74, 75, 82, 83, 84, 392 Chaffee, M., 324, 401 Chalmers, J. A., 85, 99, 392 Charnock, H., 107, 127, 138, 146, 157, 159, 174, 175, 176, 177, 178, 180, 182, 184, 188, 189, 191, 193, 194, 195, 196, 198, 199, 200, 201, 204, 205, 206, 207, 208, 209,211,251,289,303,392,408 Chase, J., 106,392 Christensen, F. E., 12,397 Church, P. E., 260, 392 Clarke, D. B., 387, 392 415
416
AUTHOR INDEX
Clauser, F. H., 135, 392 Clayton, W. H., 159, 392, 405 Colding, A., 159,392 Collins, J. A., 377, 380, 405 Collmann, W., 349, 350, 392 Corwin, E. F., 17, 19,392 Cote, L. J., 106,392 Cox, C., 111, 115, 165,392 Cox, C. S., 112, 392 Craddock,J. ~.,327, 328, 349, 351,392 Craig, H., 81, 392 Craig, R. A., 258, 260, 291, 326, 328, 330, 331, 332, 333, 334, 343, 345, 34~ 34~ 350,392 Crain, C. ~., 288, 400
D Darbyshire, J., 155,159,161,165,393 Darbyshire, ~., 155, 159, 161, 165,393 Darlington, C. R., 261, 393 Das, P. K., 127,261,269,393 Deacon, E. L., 26, 126, 127, 138, 141, 142, 147, 149, 150, 154, 157, 158, 160, 161, 162,251,261,263,264,269,273,291, 393 Deardorff, J. W., 19, 127, 141, 142, 143, 149, 158, 256, 261, 269, 270,271,274, 281,283,284,287,393,394 Dhar, N. C., 127,261,269,393 Dickson, C. N., 261, 394 Dietrich, G., 7, 393 Dietz, R. S., 115,393 Dingle, A. N., 75, 393 Dirmhirn, I., 387, 407 Dobroklonsky, S. V., 240, 393 Dombrowski, N., 59, 398 Donn, W. L., 3, 393 Dorrestein, R., 115,393 Douglas, C. K. ~., 363, 393 Drogajcev, D. A., 216, 218, 393 Durst, C., 159,393 Durst, C. S., 261, 394 E Eckart, c., 106, 394 Ekman, V. W., 154, 159,394 Ellison, T. H., 147, 148,251,274,289,392, 394
Emmons, G., 260, 328, 330, 332, 344, 353, 354, 355, 356, 394 Eriksson, E., 80, 81, 82, 390 Evans, F., 261, 394 Ewing, G., 115, 117, 118, 121,232,233, 394 F
Facy, L., 63, 394 Farkas, E., 328, 394 Farmer, H. G., 111,394 Farrer, L. A., 158,394 Field, R. T., 412 Findeisen, W., 118, 120,394 Finger, F. G., 369, 396 Fisher, E. L., 234, 394 Flanagan, V. P., 46, 47, 87, 403 Fleagle. R. G., 127, 141, 142, 143, 149, 158, 161,256,261, 269, 270, 271, 277, 278, 361, 362, 363, 387, 389, 394 Fleming, R. H., 239, 241, 262, 409 Fletcher, R. D., 222, 394 Fonselius, S., 72, 73, 75, 78, 394 Fournier D'Albe, E. ~., 53, 57, 394 Franceschini, G. A., 257, 395 Francis, J. R. D., 155, 156, 157, 159, 164, 165, 174, 175, 176, 177, 178, 180, 182, 184, 188, 189, 191, 193, 194, 195, 196, 198, 199, 200, 201, 204, 205, 206, 207, 208,209,211,303,392,395,408 Fritz, S., 297, 325,395, 399 Frost, R., 341, 342,395 G
Georgii, H. W., 64, 395 Gerhardt, J. R., 261, 395 Gerstmann, W., 154, 395 Gibson, B. W., 234, 395 Gifford, ~., 50, 51, 53, 55,411 Gish, O. H., 47, 85, 86, 87, 88, 89, 90, 92, 93, 94, 97, 99, 395, 410 Gleeson, T. A., 370, 371, 372, 406 Goedecke, K., 31, 395 Gogos, C. ~., 360, 361, 411 Goptarev, N. P., 127, 141, 151, 158, 161, 168,170,261,263,395 Gordon, A. H., 31, 33, 187, 188, 192,214, 223,253,254,261,394,395,398 Graham ~iIIar, F., 23, 396
417
AUTHOR INDEX Gray, Wo S., 322, 323, 324, 401, 405 Groen, P., 22, 396 Groves, Go Wo, 244, 405 Grundy, F., 288, 396 Gustafson, Po E., 64, 398
H Haussler, Wo, 232, 396 Halstead, Mo n., 126, 260, 403 Hamada, To, 158,396 Hanratty, T. J., 108,400 Hanya, To, 75, 396 Hanzawa, Mo, 339, 379, 396 Harrington, E. L., 315, 396 Harris, M. r., 369, 396 Hasse, L., 154,412 Hasselmann, x., 107, 396 Haurwitz, a., 181,281,291,292,306,307, 310,319,338, 339, 396 Hay, J. S., 127, 138, 141, 158, 167,396 Hay, R. F. Mo, 7, 246, 396 Hayami, So, 158, 161, 269, 285, 286, 396, 403 Hela, 10' 159, 396 Hellstrom, n., 155, 157, 159,396 Henry, n. Mo, 178,409 Hergesell, n., 39, 396 Hess, v, r., 45, 46, 47, 396 Hilleary, D. To, 12,397 Hahne, W., 22, 27, 397 Holzer, n. E., 85, 92, 93, 95, 96, 407 Holzman, a., 146, 397 Hose, N., 158,396 Houghton, Do M., 230, 397 Hunt, I. Ao, 127, 158,261,397 Huss, Eo, 39, 397, 398 Hutchings, r. So, 328, 394 I
Isaacs, r, D., 309, 397 Ishiwatari, R., 75,396 Isono, x., 63, 397 Israel, B., 93, 99, 100,397 Izotova, A. F., 127, 397 J Jacobs, Wo Co, 252, 397 Jaw, J., 340, 397
Jeffreys, rr., 164,215,397 Johnson, J. Wo, 159,397 Johnson, Mo Wo, 239, 241, 262, 409 Johnson, No K., 260, 397 Johnson, P. Wo, 215, 397 Jones, Do n., 183, 184, 186, 187, 397 Junge, C. E. 43,44,45,47, 55,64, 65, 67, 70,71,397,398 K
Kanazawa, M., 26, 127, 403 Kanwisher, r., 80, 81, 398 Kaplan, L. Do, 83, 398 Karman, To von, 134,281,398 Keeling, C. D., 76, 77, 78, 79, 398 Keulegan, G., 155, 159, 163,398 Kientzler, Co r., 59, 61, 398, 411 Kimball, n. n., 387, 398 Kimura, So, 26, 407 Kirk, To n., 31, 33, 398 Kitamura, No, 26, 127,403 Klein, W. n., 337, 341, 398 Kleinschmidt, E., 39, 398 Kline, D. B., 63, 390 Knelman, s., 59, 398 Koizumi, M., 238, 242, 370, 372, 373, 398 Kolesnikov, »: Go, 240, 398 Kontoboitseva, N. V., 242, 247, 398 Koroleff, r., 72, 73, 75, 78, 394 Kove, No Ao Go, 261, 394 Kraus, E. B., 228, 398 Krueger, s, r., 297, 399 Krugler, r., 236, 399 Krummel, 0., 239, 399 Krumm, H. Co, 94, 97, 98, 399 Kuhlbrodt, Eo, 40,170,220,221,222,226, 237, 238, 246, 368, 370, 373, 374, 382, 399,411 Kunishi, B., 158, 161,396 Kurbatkin, Go Po, 380, 399 Kuroiwa, Do, 53, 63, 399 Kyriazopoulos, n. Do, 359, 399 L
La Fond, E. Co, 115, 118, 119,393,399 La Mer, v, K., 287, 399 Laevastu, To, 228, 387, 399 Laikhtman, D. L., 150,399 Lamont, J. VO, 399
418
AUTHOR INDEX
Landsberg, H., 45, 46, 399 Langham, E. M., 27, 389 Langmaack, W., 26, 399 Langmuir, 1., 116,399 Langwell, P. A., 298, 308, 399, 400 Larsson, P., 22, 400 Laurila, E., 159,404 Leipper, D. F., 387, 389 Lettau, H., 133, 136, 174, 177, 194, 195, 207, 209, 210, 211, 212, 213, 215, 216, 217,346,349,351,400 Levine, J., 320, 400 Lilleleht, L. D., 108, 400 Livadas, G. c., 359, 399 Lodge, J. P., Jr., 53, 55, 65, 68, 69, 70, 71, 400 Loewe, F., 360, 400 Ludlam, F. H., 59, 312, 313, 314, 317, 318, 319,320,400,408 Lumb, F. E., 234, 387, 400 M
McAlister, E. D., 232, 233, 394 MacDonald, A. J., Jr., 65, 68, 69, 70, 71, 400 Mcllroy, 1. C., 154, 158, 401 McMaster, K. N., 63, 410 Macphail, H. W., 23, 396 McVehil, G. E., 148, 149, 150,274,404 Magee, J. B., 288, 400 Malkus, J. S., 236, 281, 291, 292, 293, 294, 299, 300, 301, 302, 303, 304, 306, 307, 309, 310, 312, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 386, 400, 401, 405 Manabe, S., 349, 351, 352, 401 Mandelbaum, H., 162, 401 Markgraf, H., 226,357,377,378,379,380, 390, 401 Marks, W., 106, 392 Mason, B. J., 44,45,50, 51,53,57, 58, 59, 60,62, 69, 312, 400, 401, 402 Matwejew, L. T., 347, 412 Mauchly, S. J., 85, 93, 100,401 Maury, M. F., 2, 401 Mehr, E., 106,392 Meinardus, W., 237, 401 Merz, A., 229, 230, 401 Metnieks, A. 1., 64, 395
Metnieks, A. L.,.50, 53, 55, 402 Mildner, P., 195, 402 Miles, J. W., 107, 166,402 Mitsuyasu, H., 158,396 Miyazaki, M., 136, 402 Moller, F., 257, 402 Monin, A. S., 134, 144, 145, 146, 147,272, 274, 279, 402 Montgomery, R. B., 126, 142, 146, 158, 159, 210, 249, 250, 254, 258, 260, 265, 267, 269, 280, 281, 285, 328, 330, 353, 361,387,389,392,394,402,406 Moore, D. J., 46, 48, 49,50,53,55,57,58, 59, 402 Mosby, H., 239, 402 Motzfeld, H., 123, 124, 136, 137,402 Muhleisen, R., 85, 87, 93, 95, 99, 402 Munk, W., Ill, 115, 165,392 Munk, W. H., 102, 162, 163, 164, 165, 167, 402 Myers, V. A., 160, 403 Mysels, K. J., 288, 403 N
Namias, J., 246, 403 Neumann, G., 122, 155, 158, 159, 164,240, 243, 403 Neumann, H. G., 296, 403 Newitt, D. M., 59, 398 Nikuradse, J., 135, 403 Norris, R., 281, 403 Nurminen, A., 365, 403
o Obukhov, A. M., 134, 144, 145, 146, 147, 272, 274, 279, 402 O'Connor, T. c., 46, 47, 87, 403 Oddie, B. C. V., 70, 403 Ogata, T., 26, 127, 355, 403 Ogneva, T. A., 127, 397 Ohta, S., 46, 47, 48, 403 Ohtake, T., 63, 412 Okuda, S., 269, 285, 286, 403 Omar, M. H., 159, 175,408 Onishi, G., 352, 412 Otto, L., 23, 403 Owen, J. c., 126,260,403
419
ADTBORINDEX p
Pagava, S. T., 246, 403 Palrnen, E., 257, 404 Palmeri, E. B., 159,404 Palmqvist, A., 78, 404 Panofsky, H. A., 148, 149, 150, 274, 326, 404 Parkinson, W. c., 45, 46, 47, 85, 86, 87, 88, 89, 90, 92, 94, 404, 410 Pasquill, F., 273, 404 Peirce, B. 0.,338,404 Perlroth, J., 234, 404 Petersen, P., 23, 404 Phillips, O. M., 106, 107, 109, 110, 404 Pierson, W. J., 105, 106,392 404 Pike, A. C., 247, 387, 404 Pincock, G. L., 353, 404 Plass, G. N., 82, 83, 404 Pollak, M. J., 159, 404 Portman, D. J., 127, 131, 138, 141, 158, 404 Prandtl, L., 125, 133, 136, 275, 405 Prescott, J. A., 377, 380,405 Priestley, C. B. B., 153,275,298,405 R
Raethjen, P., 129, 405 Rakestraw, N., 387,389 Rau, W., 53, 59, 63, 405 Reger, J., 40,174,220,221,222,226,237, 238,246,368,370,373,374,382,399 Regula, B., 183, 184,405 Reid, R. 0., 159, 405 Reiter, E. R., 125, 405 Revelle, R., 79, 80, 82, 405 Revillon, P., 215, 405 Reynolds, G., 215, 405 Rice, E. K., 159,397 Richardson, W. S., 34, 387, 389, 405 Rider, N. E., 405 Riehl, B., 243,306,312,322,323,324,387, 389, 401, 405 Riley, G. A., 296, 411 Riley, J. J., 64, 389 Roden, G. 1., 243, 244, 405 Rodewald, M., 246, 325, 405 Rodgers, G. K., 127, 138, 158,261,391 Rodhe, B., 363, 364, 366,406 Ronne, F. C., 106, 392
Roll, B. D., 23,31,37,38,106,112,122, 123, 125, 126, 136, 137, 138, 141, 158, 161, 178, 191, 197,229,230,231, 232, 233, 260, 261, 263, 269, 273, 291, 369, 406, 407 Ronne, C., 319, 322, 323, 324, 401, 405 Rooth, C., 228, 398 Rosenthal, S. L., 370, 371, 372, 381, 382, 383, 384, 385, 406 Rossby, C. G., 137, 146, 158, 159,210,406 Roulleau, J., 183,406 Rubin, M. J., 359, 407 Ruttenberg, S., 85, 92, 93, 95, 96, 407 Rykachov, M. M., 260, 407 S
Sagalyn, R. c., 47,88,90,91,407 Sanuki, M., 26, 407 Sauberer, F., 387, 407 Saunders, P. M., 318, 359, 407, 412 Saur, J. F. T., 412 Saville, T., Jr., 159, 407 Schalkwijk, W. F., 159, 407 Schmidt, W., 257, 369, 407 Schmitz, B. P., 121, 125, 128, 129, 130, 140, 154,407 Schooley, A. H., 109, 111, 112, 113, 114, 122, 123, 136, 407 Schroder, B., 126, 260, 407 Schumacher, A., 105,261,408 Schwerdtfeger, W., 339, 408 Scorer, R. S., 313, 314, 317, 318, 319, 320, 400, 401, 408 Scrase, F. J., 411 Seifert, G., 126, 260, 407 Seilkopf, H., 23, 408 Sevalkina, N. A., 246, 403 Sharkey, W. P., 46, 47, 87, 403 Shellard, H. c., 408 Sheppard, P. A., 26, 126, 127, 138, 141, 157, 158, 159, 174, 175, 176, 177, 178, 180, 182, 184, 188, 189, 191, 193, 194, 195, 196, 198, 199, 200, 201, 204, 205, 206,207,208,209,211,261,263, 264, 282,284,291,303,392,393,408 Shoulejkin, W., 2, 19, 126, 137, 158, 256, 260,408 Sibul, O. J., 158, 408 Silvester, R., 218, 219, 408 Simpson, L., 234,404
420
AUTRORINDEX
Skaar, J., 37, 408 Skorka, So, 100,408 Smirnova, N. P., 127,397 Snodgrass, J., 387, 389 Spencer, A. T., 46, 60, 390 411 Spinnangr, F., 37, 408 Squires, P., 313, 315, 408 Staley, R. Co, 288, 289, 408 Stepanov, V. P., 240, 241, 242, 377, 408 Stephenson, Go, 106,392 Stevenson, R. E., 360, 408, 412 Stewart,R. W., 121, 156, 162, 166,282,408 Stommel, R., 117,229,230,231,239,281, 291, 292, 295, 296, 306, 307, 310, 312, 313,319, 409, 411 Straaten,L. M.J. U.van, 116, 11~, 120,409 Sturm, M., 228, 412 Suess, R. E., 79, 80, 82, 405, 409 Superior, W. r., 412 Sutcliffe, R. Co, 159, 174, 176,409 Sverdrup, R. U., 2,160,239,241,252,253, 254,257,260,262,269,280,281,374,409 Swinbank, W. C., 251, 281, 409
T Takahashi, Tadao, 131, 137, 158, 162,256, 259,261,262,270,273,274,283,284,409 Takahashi, Taro, 75, 78, 79, 409 Takeda, N., 339, 396 Tamura, Y., 355, 403 Taylor, G. I., 125, 328, 339, 347, 409 Taylor, R. I., 147, 273, 275, 409 Teweles, S., 369, 396 Thornthwaite, E. W., 412 Tippelskirch, R. v., 295, 409 Tolefson, R. B., 178,409 Torreson, O. W., 47, 85, 86, 87, 88, 89, 90, 92,94,410 Tucker, G. Bo, 257, 410 Turner, J. A., 353, 404 Twomey, S., 63, 410 U
Uda, M., 246, 410 Ulanov, R., 126, 410 Ursell, F., 107,410 V
Van Dorn, W. G., 106, 155, 156, 159, 160, 163, 164, 166, 167,410
Verploegh, G., 23, 25, 37, 410 Vetter, R. C., 106, 392 Vihman, E., 65, 68, 69, 70, 71, 400 Vines, R. G., 156, 159,410 Vinogradova, O. P., 137, 154, 158, 410 Vorontsov, P. A., 357, 358, 410
w Warme, K. E., 72, 73, 75, 78, 394 Wagner, N. K., 127, 410 Wait, G. n., 47, 85, 86, 87, 88, 89, 90, 92, 94,410 Wait, R. G., 86, 87, 410 Walden, R., 28, 410 Walden, R. G., 106, 392 Webb, E. K., 26, 127, 138, 141, 142, 157, 158, 251, 252, 261, 263, 264, 269, 273, 275, 276, 291, 393, 410 Wegernann, Go, 237, 411 Wegener, A., 40, 411 Wegener, K., 369, 411 Wenner, R., 257, 390 Westwater, F. L., 191, 411 Whipple, F. J. W., 94, 97, 98, 411 Wiener, F. M., 360, 361, 411 Wigand, A., 45, 411 Wilckens, F., 234, 411 Wilkens, C. R., 34, 405 Wilson, A. T., 70, 411 Wilson, B. W., 156, 157,411 Witt, G., 319, 401 Woodcock, A. R., 50, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 116, 117, 118, 229, 230,231,239,296,297,317,390,398, 409,411 Woodward, B., 319, 412 Woskresenski, A. J., 347, 412 Wiist, G., 126, 137, 256, 260, 269, 412 Wyman, J., 117, 118,297,411 Wyrtki, K., 241, 412
y Yamamoto, G., 63, 352, 412 Yoshida, F., 355, 403
Z Zakharova, N. M., 246, 403 Zenker, R., 48, 412 Zierep, J., 295, 412
Subject Index
A Acceleration measurements in an airplane, 179, 199-205, 210-211 Aerosol, 43 Air-borne meteorological reconnaissance, 11-12 Air mass modification at sea, 327-352 eddy transfer coefficients, 344-348 energy considerations, 348-352 factors involved, 327-328 methods of study, 328-330 observational facts, 330-335 radiative effects, 351-352 steady state models, 340-344 theoretical formulation of the problem, 335-337 transient state models, 338-340 Air temperature, measurement of, 28-30 Aitken nuclei, 45-49 concentration, 45-47 nature and origin, 48 relations to meteorological phenomena, 48-49 size, 47 Atmospheric electricity, 84-100 electrical conductivity, 89-92 electric currents, 95-100 electric field in fair weather, 92-95 electric quantities concerned, 84-85 ions in the marine atmosphere, 86-88 Atmospheric humidity, measurement of, 28-30 Atmospheric nuclei, 43-64 Atmospheric nuclei spectrum, 44 Atmospheric pressure, measurement of, 27-28 Atmospheric radioactivity, 100 Austausch coefficient, 132-134, 171-172, 175, 177, 208-211, 344
immediately over the sea surface, 132-134 in the maritime friction layer, 171-172, 175,177,208-211,344 Auxiliary ships, 8 B
Bowen ratio, 252-254 Bubble bursting at the sea surface, 60-62 Bubble model, see Cumulus formation Bulk aerodynamic method, 251-252
c CapiIIary waves, 107-109, 115, 117 Captive balloon technique, 39 Carbon dioxide content, 72-84 Callendar effect, 72-75 exchange ocean-atmosphere, 79-82 meteorological significance, 72 result of lOY measurements, 75-79 Suess effect, 79 temperature variations caused, 82-84 Chemistry of the marine atmosphere, 64-84 carbon dioxide content, 72-84 composition of particles, 65-70 gaseous traces, 70-72 Cloud characteristics, observation of, 35-36 Commission for Maritime Meteorology, 8 Composition and properties of the marine atmosphere, 42-100 chemistry, 64-84 electricity and radioactivity, 84-100 general, 42-43 nuclei, 43-64 Condensation nuclei, 43 421
422
SUBJECT INDEX
Convection, 147,275-276,291,295-298 cellular, 295-298 composite, 276, 291 forced, 147, 275-276, 291 free, 147, 275-276 Convective layers above the sea surface, 275-276 Convective rolls, 116-117,295-298 in air, 295-298 in water, 116-11 7 Crystallization of salt particles, 63 Cumulus formation and maintenance, 312-322 bubble model, 313-318 entrainment model, 313 origin of bubbles at sea, 318-319 parcel model, 312-313 slice model, 313 structure of oceanic cumulonimbus clouds, 319-322 Cumulus organization at sea, 322-325 Cyclostrophic wind, see Gradient wind
in: heat exchange near the sea surface, 248,251,266-268 Eddy correlation, 153-154, 177-179, 256 Eddy diffusivity, 248-249, 251, 266-268, 336-341, 344-347 in: air mass modification, 336-341, 344-347 in: moisture flux near the sea surface, 248-249, 251, 266-268 Eddy flux of heat and moisture, 248-249, 363-367 basic formulae, 248-249 formation of sea fog, 363-367 Eddy size, 149 Eddy stress, see Wind stress Eddy transfer coefficient for heat, see Eddy conductivity for matter, see Eddy diffusivity for momentum, see Eddy viscosity Eddy viscosity, 132-135, 143-150, 172, 175, 178-179, 208-209, 249, 251, 266-268, 344, 347-348 in: air mass modification, 344, 347-348 in: heat and moisture flux near the sea D surface, 249, 251, 266-268 in the maritime friction layer, 172, 175, Deacon number, 150 178-179,208-209 Dissipation of turbulent energy, 149, near the sea surface, 132-135, 143-150 210-213 Ekman spiral, 171, 193-194 Drag coefficient at the sea surface, 152-166 Electrical conductivity, 89-92 effect of atmospheric stability on the, columnar and total resistance, 91-92 161 local and temporal variations, 89-90 effect of fetch on the, 161-162 ratio of polar conductivities, 90-91 methods of measuring, 153-156 vertical distribution, 91 resulting values, 156-161 Electric currents, 85, 87, 95-100 Drag of the wind at the sea surface, air-sea current, 95-97 152-166 supply current, 85, 87, 97-100 Drifting stations, 19-22 Electric field in fair weather, 84, 92-95 in air, 19 mean value, spatial variation, 92-93 in water, 19-20 time variations, 93-95 on sea ice, 20, 22 Electric potential, vertical gradient of, 84, Dynamic roughness of the sea surface, 92-95 134-153 Electrode effect, 87, 90, 93, 95 Enthalpy, 348-352 E moist, 349-352 specific, 348 Eddy conductivity, 143-150, 248, 251, Evaporation at the sea surface, 256-258, 278-288 266-268, 336-341, 344 comparison with observations, 283-284 in: air mass modification, 336-341, 344 determination, 256-258 in: diabatic wind profile, 143-150
423
SUBJECT INDEX effect of sea spray, 284-286 general relations, 278-280 influence of a monomolecular film, 286-288 with aerodynamically rough flow, 281-282 with aerodynamically smooth flow, 280-281
F Fetch, 103, 130-131 Fixed stations, 12-19 Floating automatic weather stations, 16-19 Freezing nuclei, 43, 63-64 Friction coefficient, see Drag coefficient Friction velocity, 133-153,266-268, 272, 279-280, 282-283 G
Gas concentrations in maritime air, see Chemistry of the marine atmosphere gaseous traces Geostrophic departure, 153-154, 172-177, 207-208 Geostrophic wind, 153, 172-177, 180-183, 189-190, 193-194, 213-219 ageostrophic flow components, 153, 172-177 baroclinic atmosphere, 180-183 compared with surface wind, 213-219 Ekman spiral, 193-194 Gradient wind, 218-219 Gravity waves, 103-107 Gustiness near the sea surface, 167-171 gustiness coefficient, 168-171 lateral and vertical gustiness, 167-168
H Heat flux, vertical turbulent, 143-150, 278-288 comparison with observations, 283 general relations, 278-280 influence on the wind profile, 143-150 with aerodynamically rough flow, 281-282 with aerodynamically smooth flow, 280-281
Humidity, see Temperature and humidity Hurricane monitoring buoy, 20-21 I
Ice islands, 22 Intermittent rippling, 118-121 Internal waves in a shallow thermocline, 118-119 Ions in the marine atmosphere, 84-88 concentration, 87-88 mobility, 88 production and destruction, 86-87 Isopiestic method, 50-51 Isotropic turbulence, 140 K
Kite ascents, 39-40 L
Laminar boundary layer at the sea surface, 134, 280-281 Lamont, correction of, 367 Large and giant nuclei, 49-64 correlation with wind speed, 55-57 mechanism and rate of production, 59-64 methods of measuring, 50-51 size distribution, 51-54 variation with altitude, 54-55 Lightships, 13 M
Marine automatic meteorological observing station, 16-17 Marine rain gauge, 36-37 Maritime aerosol, composition of, see Chemistry of the marine atmosphere, Composition of particles Merchant ships, 8-9 Meteorological buoys, 18-21 Meteorological observations and measurements at sea, 6-41 aerological measurements, 39-41 basic problems, 6-7 instruments and methods, 22-41
424
SUBJECT INDEX
operational questions, 8-22 surface observations, 22-39 Meteorological rockets, 12,41 Microwave refractometer, 288-289 Mirror theodolite, 40 Mixing length, 133-134, 151 Mobile stations, 8-12 Moisture flux, see Evaporation Molecular conductivity of air, 250, 280-282, 295 thermal, 250 thermometric, 250, 280--282, 295 Molecular diffusivity of water vapor in air, 250, 280-283 Molecular viscosity of air, 132, 134, 250, 280--282,295 dynamic, 132, 250 kinematic, 134, 250, 280-282, 295 N
Nonisotropic turbulence, 140
o Ocean waves, 38, 102-121 gravity waves, 103-107 observation of, 38 sea-surface slopes, 109, 111-114 slicks on the sea surface, 114-121 theory on generation of, 106--107 wavelets and ripples, 107-110 Ocean weather stations, 13-16 Optical refraction measurements, 255-256, 277 P
Parachute weather buoy, 19-20 Periodic bands at the sea surface, 117-118 Phugoid oscillations of an airplane, 179 Physical constants related to exchange processes, 250 Pilot balloon ascents, 40, 172, 177-178, 191, 194-196, 199-202, 204 Prandtl number, 250 Precipitation, determination of, 36--37 Profile coefficient, 142-143, 264-271 apparent, 269
effect of spray, 269 for heat and humidity, 264-271 for momentum, 142-143 observational results, 268-271 Profile contour number, see Profile coefficient R
Radar wind measurements on shipboard, 40-41 Radiation measurements at sea, 38-39, 387 Radiative processes, 228-229, 277-278, 351-352, 361-363, 365-367 in: air mass modification at sea, 351-352 in: fog formation at sea, 361-363, 365-367 in the air layer next to the sea surface, 277-278 in the water layer next to the sea surface, 228-229 Radiosonde ascents at sea, 40-41 Resistance cofficient at the sea surface, see Drag coefficient Richardson number, 143-150, 269, 271-275 Ripples at the sea surface, 107-110, 115 Roughness length, 134-153
s Satellites, meteorological, 12 Sea, 103 Sea fog, physics of, 352-367 advection fog, 353, 359 aerological and statistical information, 354-360 arctic sea smoke, 353-354, 359-360 delineation of the problem, 352-354 micrometeorological observations, 360-361 over ice fields, 359 steam fog, 353-354, 359-360 theory of ocean fog formation, 361-367 Sea-salt nuclei, see Large and giant nuclei Sea spray, effect on evaporation, 284-286 Sea surface, 101-121 general character as lower boundary of an air flow, 101-102
425
SUBJECT INDEX geometry of the, 102-121 mean square slope, 111-114 roughness factor, 113-114, 136 slicks, 114-121 Sea-surface film, 69-71,115-116,118-121, 153,156,286-288 chemical effects, 69-71 effect on evaporation, 286-288 effect on surface waves, 115-116, 118-121 method for measuring wind stress, 153, 156 Sea-surface slope, 109-114 facet length, 113 flatness tolerance, 113 Sea-surface temperature, 227-247 annual variation, 240-242 aperiodic diurnal variation, 246 diurnal variation, 237-240 factors affecting the, 228 horizontal variation, 233-236 monthly anomalies, 243-246 nonperiodic variations, 243-247 temporal variation, 236-247 variations caused by the passage of typhoons, 246-247 vertical distribution near the sea surface, 229-233 Sea-surface temperature, determination of, 30-35 bucket method, 30-31 infrared radiation thermometer, 34 intake method, 31-33 skin method, 33-34 tank method, 34 Sea-surface temperature charts, 234-236 Seaway, 103-107 Selected ships, 8 Shear-stress coefficient, see Drag coefficient Shipboard weather station, 29-30 Slicks at the sea surface, 114-121 Special ships, 9-11 Stability factor, see Stability function Stability function, 144-150, 271-275 in: temperature and humidity profiles, 271-275 in: wind profile, 144-150 Stability length, 144-150, 272-279
Superadiabatic bottom layer above the sea surface, 264-265, 276 Supplementary ships, 8 Swell, 103
T Tandem balloon technique, 39 Taylor diagram, 328-334 Temperature and humidity fluctuations near the sea surface, 288-289 Temperature and humidity profiles above the sea surface, 145, 255, 258-278 air temperature profile, 145, 258-261 convective layers, 275-277 diabatic temperature and humidity profiles, 271-275 humidity profile, 259-263 inversion conditions, 277-278 profile measurements, 255, 258-263 theoretical approaches to, 271-275 vertical gradients and differences in air-sea, 263-264 Temperature and humidity, time variations of,367-385 annual variation, 376-380 aperiodic diurnal range of air temperature, 381-383 diurnal variation, 367-376 interdiurnal variability of air temperature, 382, 384-385 nonperiodic variations, 380-385 Temperature and moisture field in the first few meters above the sea surface, 247-289 Thermal wind, 181-183, 189-190 Thermodynamic processes in the marine atmosphere, 227-385 medium scale, 289-367 small scale, 247-289 Tilt of the sea surface, 153-156, 161-166 Trade flow, structure of, 291-312 cellular convection, 295-298 cloud forms, 302 cloud layer, 299-304 homogeneous layer, 291-294 influence of wind shear on cumulus development, 303-304 mechanism of moist layer, 304-312 transitional layer, 298-299 Transobuoy, 19
426
SUBJECT INDEX
Transosonde, 19 Trawlers, 8-9 Turbulent departures from the mean flow, 128,132,172,178-179,196-206 Turbulent energy, 143, 204-205, 210-213 dissipation, 210-213 in connection with Richardson number, 143 partition, 204-205 Turbulent shear stress, see Wind stress Turbulent wind fluctuations, see Turbulent departures from the mean flow
v Visibility, 35, 360-361 determination, 35 related to droplet size and liquid water content, 360-361 Von Karman coefficient, generalized, 267-268
w Wave record, 104 Wave spectrum, 104-107, 110 Wavelets, 107-109 Weather buoys, 18-21 Wind,22-27 estimating the wind visually, 23-25 measuring the wind on board ship, 26-27 observation of wind speed and direction, 22-27 Wind field immediately over the sea surface, 121-171 Wind force, 22-25 Beaufort numbers, 23-25
Wind speed equivalents, 23-25 Wind profile, 123-124, 126-127, 130-152 adiabatic, 130-140 diabatic, 140-152 measurements, 126-127, 135-140 over a rough surface, 134 over a smooth surface, 134-135 over a solid wavy surface, 123-124 Wind setup, see Tilt of the sea surface Wind speed, 22-27, 112-113, 162 critical, 112-113, 162 methods of measuring and estimating, 22-27 Wind streaks at the sea surface, 115-117 Wind stress, 132-135, 143, 149, 152-167 Wind stress at the sea surface, 152-167, 172-177 critical wind speed, 162 due to rainfall and spray, 167 methods of measuring, 153-156, 172-177 tangential and form drag, 162-166 Wind structure in the maritime friction layer, 171-219 eddy correlation method, 177-179 eddy viscosities, 208-210 geostrophic departure method, 172-177 methods of study, 171-179 surface wind and geostrophic wind, 213-219 turbulent energy dissipation, 210-213 turbulent wind fluctuations, 196-206 vertical transfer of horizontal momentum, 206-208 vertical variation of mean wind, 180-196 Wind, time variations of, 219-226 annual, 223-226 aperiodic, 226 diurnal,219-223
