Ladoga and Onego - Great European Lakes: Observations and Modeling

Ladoga and Onego - Great European Lakes Observations and Modelling

Leonid Rukhovets and Nikolai Filatov (Editors)

Ladoga and Onego - Great European Lakes Observations and Modelling

~ Springer

Published in association with

Praxis Publishing Chichester, UK

Editors Professor Leonid Rukhovets Institute for Economics and Mathematics at St. Petersburg Russian Academy of Sciences St Petersburg Russia

Professor Nikolai Filatov Institute of Northern Water Problems Karelian Research Centre Russian Academy of Sciences Petrozavodsk Russia

SPRINGER-PRAXIS BOOKS IN ENVIRONMENTAL SCIENCES SUBJECT ADVISORY EDITOR: John Mason, M.B.E., B.Sc., M.Sc., Ph.D.

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Contents

List of contributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

IX

Preface

Xl

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv 1 The Great European lakes: state of the art. . . . . . . . . . . . . . . . . . . . . . . .. 1 1.1 Physiographic features and history of the formation of the lakes and their catchments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1 1.2 History of research of the lakes. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9 1.3 Characteristics of temperature and currents 14 1.3.1 The thermal regime and limnic zones 14 1.3.2 Currents and circulations 23 1.4 The cycle of substances in Lake Ladoga and the dynamics of its warer~osy~em 31 1.4.1 Lake ecosystem phosphorus supply. . . . . . . . . . . . . . . . . . . . . 31 1.4.2 Phytoplankton in the Lake Ladoga ecosystem 33 1.4.3 Bacterioplankton, water fungi and destruction processes 39 1.4.4 Zooplankton..................................... 41 1.4.5 The role of the zoobenthos in the ecosystem 42 1.4.6 Dissolved organic matter 44 1.4.7 The role of seston and bottom sediments in the lake phosphorus cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.5 The cycle of substances in Lake Onego and its water ecosystem 47 1.5.1 Phosphorus supply to the Lake Onego ecosystem 48 1.5.2 Biological communities in the Lake Onego eutrophication state 51

vi

Contents

1.6

1.5.3 Relation between the primary production and the destruction of organic matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59 1.5.4 Peculiarities of Lake Onego eutrophication . . . . . . . . . . . . .. 60 The main tendencies in the evolution of large, deep, stratified lakes. . .. 61

2 Hydrothermodynamics of large stratified lakes 2.1 Ensemble of thermo- and hydrodynamical processes and phenomena in lakes 2.2 Lake models: state of the art. Problem formulation for the simulation of lake hydrothermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.2.1 Introduction.................................... 2.2.2 Equations of geophysical hydrodynamics. . . . . . . . . . . . . . .. 2.3 A climatic circulation model for large stratified lakes . . . . . . . . . . . .. 2.3.1 General comments 2.3.2 Mathematical formulation. . . . . . . . . . . . . . . . . . . . . . . . . .. 2.3.3 Realization of the model. . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.3.4 Generalized formulations of the mathematical model . . . . . .. 2.3.5 About the discrete model . . . . . . . . . . . . . . . . . . . . . . . . . .. 3

67 67 69 69 70 73 73 76 80 80 83

Climatic circulation and the thermal regime of the lakes . . . . . . . . . . . . . .. 85 3.1 The climatic circulation in Lakes Ladoga and Onego from observational data and estimates. . . . . . . . . . . . . . . . . . . . . . . . . . .. 85 3.2 On the problem of simulating climatic circulation . . . . . . . . . . . . . . .. 87 3.3 Setting of external forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91 3.4 Simulation of the Lake Ladoga climatic circulation. . . . . . . . . . . . . .. 97 3.4.1 Computational procedure. . . . . . . . . . . . . . . . . . . . . . . . . .. 97 3.4.2 Description and analysis of thermal regime calculation results.. 99 3.4.3 Description and analysis of current calculation results. . . . .. 112 3.5 Simulation of the Lake Onego climatic circulation . . . . . . . . . . . . .. 122 3.5.1 Computational procedure. . . . . . . . . . . . . . . . . . . . . . . . .. 122 3.5.2 The results of thermal regime modelling. . . . . . . . . . . . . . .. 122 3.5.3 The results of currents simulations. . . . . . . . . . . . . . . . . . .. 129

4 Estimation of the lakes' thermohydrodynamic changes under the impact of regional climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.1 Climate change over the lakes' catchments. . . . . . . . . . . . . . . . . . .. 4.1.1 Climatic features and their variability . . . . . . . . . . . . . . . .. 4.1.2 Probable climate changes over the lakes' catchments. . . . . .. 4.1.3 Estimates of potential changes in the thermal regime of the lakes by 2050. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.2 Modelling the thermohydrodynamics of the lakes under different climatic conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.2.1 Modelling thermohydrodynamics: statement of the problem and numerical experiments. . . . . . . . . . . . . . . . . . . . . . . .. 4.2.2 Analysis of the results of simulations. . . . . . . . . . . . . . . . ..

134 134 134 138 143 150 150 155

5

6

7

Contents

vii

Three-dimensional ecosystem model of a large stratified lake . . . . . . . . . . . 5.1 Modelling the functioning of the lake ecosystems: state of the art 5.2 Aquatic ecosystem mathematical model 5.3 Discrete models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Discretization of the solution domain 5.3.2 Reconstruction of transport, turbulent diffusion and the sedimentation of substances in the model . . . . . . . . . . . . . . . 5.3.3 Reconstruction of the transformation of substances. . . . . . . . 5.3.4 Total variation of the concentration of substances in additional division cells 5.3.5 Discrete analogue of the total substances content variation law in lake waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.6 Changes in the discrete model with coarsening of the domain decomposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163 163 165 168 169

Ecosystem models of Lakes Ladoga and Onego . . . . . . . . . . . . . . . . . . . 6.1 The history of the ecosystem modelling of Lakes Ladoga and Onego. 6.2 Complex of Lake Ladoga ecosystem models . . . . . . . . . . . . . . . . . . 6.3 Ecosystem model for Lake Onego, based on the turnover of biogens nitrogen and phosphorus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Ecological formulation of the model 6.3.2 Mathematical formulation of the model 6.3.3 The discrete model 6.3.4 Reproduction of Lake Onego annual ecosystem functioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Lake Ladoga phytoplankton succession ecosystem model . . . . . . . . . 6.4.1 Formulation of the model 6.4.2 The discrete model 6.4.3 Model verification, computation experiments 6.4.4 Reproduction of phytoplankton succession

171 173 173 173 175

. 179 . 179 . 182 . 186 186 188 192 . 197 . 206 208 212 217 219

Estimating potential changes in Lakes Ladoga and Onego under human and climatic impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Modelling changes in the Lake Ladoga ecosystem under different scenarios of climate change and anthropogenic loading . . . . . . . . . . . . 7.1.1 Modelling changes in the ecosystem under different scenarios of climate change 7.1.2 Modelling changes in the ecosystem under different scenarios of climate change and changes in the level of anthropogenic loading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Modelling changes in the Lake Onego ecosystem under different scenarios of climate change and anthropogenic loading . . . . . . . . . . . .

227 228 228

232 238

viii

Contents

8 Lake Ladoga and Lake Onego models of fish communities . . . . . . . . . . .. 8.1 Introduction......................................... 8.2 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8.3 The models study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9 Natural resources of Lakes Ladoga and Onego and sustainable development of the region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9.1 Water supply and management in the catchments. Legal and regulatory aspects of water use. . . . . . . . . . . . . . . . . . . . . . . . . . .. 9.2 Assimilation potential of lake ecosystems and sustainable development of the region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9.2.1 Introduction................................... 9.2.2 Assimilation potential of the natural environment. . . . . . . .. 9.2.3 Quantification of the assimilation potential of the ecosystems of Lakes Ladoga and Onego . . . . . . . . . . . . . .. 9.2.4 Economic quantification of assimilation potential. . . . . . . .. 9.2.5 Mathematical economic model . . . . . . . . . . . . . . . . . . . . .. 9.2.6 Computational experiments. . . . . . . . . . . . . . . . . . . . . . . .. 9.2.7 Conclusions....................................

247 247 249 354 261 261 268 268 271 271 273 274 276 280

Afterword. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 281 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 283 Index

The colour plate section appears between pages 144 and 145.

299

List of contributors

G. P. Astrakhantsev N. N. Filatov A. V. Litvinenko V. V. Menshutkin T. R. Minina L. E. Nazarova N. A. Petrova V. N. Poloskov L. A. Rukhovets A. V. Sabilina Ju. A. Salo A. Yu. Terzhevik T. M. Timakova

Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, S1. Petersburg Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, S1. Petersburg Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, S1. Petersburg Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Institute of Limnology, Russian Academy of Sciences, S1. Petersburg Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, S1. Petersburg Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, S1. Petersburg Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk

Preface

Problems of environment pollution and depletion of natural resources have become global. One such problem is the shortage of potable water in many parts of the world. Although Russia is one of the world's richest countries in terms of water resources, some problems with public potable water supply do exist here too. The region of the Great European Lakes is very rich in surface and ground waters, and the water factor does not limit economic development of northwest Russia. The Great European Lakes - Ladoga and Onego - attract the continuously increasing attention of both researchers and end-users. The importance of the Great European Lakes proper, to drinking purposes, recreation, transport, and energy, together with the use of bioresources and the impacts of the pulp-and-paper industry and the discharge of waste from cities and towns located on the shores and in the catchment areas, will require the working out of scientifically substantiated recommendations for the rational use and the protection of the resources. A serious problem for the Great Lakes of Europe, as for the other very large lakes of the world, is anthropogenic eutrophication. The necessity of minimizing the impact of anthropogenic eutrophication and water pollution, which have reached a global scale and jeopardize the quality of already limited freshwater resources, has triggered quite a number and variety of studies in limnology, mathematical modelling, and economics, with view to the conservation, restoration, and efficient use of the resources of large stratified lakes. The authors undertook to develop a set of mathematical models that help to rework available knowledge about hydrophysical, chemical and biological processes in large stratified lakes into adequate reconstructions of circulation, temperature regime and function of the ecosystems. This set of models is meant to be a tool for handling the tasks of managing water use and conservation of the natural resources of large stratified lakes, the prime consideration being water quality. This monograph is based on the authors' work in the development of mathematical models of the hydrothermodynamics of deep stratified lakes and ecosystem

xii

Preface

models, as well as in the application of the models to reproducing circulation, temperature regime and function of the lake ecosystems. An equally important component of the book is the description of the results of long-term limnological studies of Lakes Ladoga and Onego implemented by researchers from the Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences, and Institute of Limnology, RAS, and development of mathematical models in the Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, including the authors of this monograph. This book Ladoga and Onego - Great European Lakes: Observations and Modelling addresses the contemporary state of the largest lakes of Europe and their catchment under anthropogenic and climate changes, with special emphasis placed on feedforward and feedback interactions between aquatic ecosystems, watershed hydrology and the economy of the region. To investigate the responsiveness of both environments to the respective counter-impacts, as well as to regional and global climate change, data analysis of multi-year field observation numerical modelling are exploited. This book is a first attempt to apply a quantitative approach to the assessment of changes occurring at present and anticipated in the future to dynamic relationships between the anthropogenic impacts, climate change and water ecosystems of both of the largest lakes of Europe. Thus, the book is primarily a synthesis of multifaceted interdisciplinary studies conducted by a team of experts working in a wide spectrum of natural and human sciences. Indeed, it is a synthesis of limnology, mathematics, hydrobiology, hydrochemistry, thermohydrodynamics , aquatic ecology, and economics. The book consists of nine chapters. Chapter 1 addresses a wide range of issues related to the geographical position, origin and palaeogeological background of Lakes Ladoga and Onego catchments. The knowledge of the physical geography of the catchments is essential for understanding the fundamental features of the lacustrine environments. Discussed here are the most reliable and recently updated data on the hydrodynamics of the lakes. The dynamics of human impact on the lakes and their catchments is analysed. Special attention is paid to investigations of material cycles in Lakes Ladoga and Onego and dynamics of the ecosystems. The chapter contains detailed information on the chemistry and biology of the lakes. The last paragraph of the chapter is devoted to the main tendencies in the evolution of great deep lakes Ladoga and Onego. Chapter 2 discusses the range of water movements in the lakes, circulation patterns and currents, as they are influenced by atmospheric forcing. The approaches to choosing the hydro thermodynamic model are explained. The state of the art of the lake models is reported. Geophysical hydrodynamics equations and their applications for description and simulation of lake hydrothermal dynamics are presented. The main objective of modelling the dynamic hydrothermal regime in our monograph is to offer ecological models with information on abiotic environment factors, first of all hydrophysical processes, which to a large extent control the functioning of aquatic ecosystems. Chapter 3 is devoted to the reproduction of climatic circulations in lakes. The problem statement is given, and the issues of setting the external parameters

Preface

xiii

are discussed. The central issue in the chapter is the results of modelling water dynamics in the lakes. Chapter 4 is dedicated to data analysis of long-term observations of the hydrometeorological regime in the catchment. Estimates of regional climate changes are made, climatic data are put together and analysed to reveal tendencies in climate change in the lakes' catchment. Climatic fluctuations in the region evidence ongoing warming. Possible climate scenarios are estimated using global climate models (ECHAM-4) and IPCC scenarios for Lake Ladoga and Onego basins. Based on these analyses, numerical simulations were performed in order to explore the options of future alterations to the regional climate against the background of global climate change scenarios. In the second part of the chapter, the hydro thermodynamic model for large stratified lakes is applied to estimate potential changes in the lakes' temperature regime and currents until the year 2050. Chapter 5 formulates the 3D mathematical model of the aquatic ecosystem of an abstract waterbody, represented as a system of nonlinear differential equations in partial derivatives. The chapter postulates requirements to the structure of the descriptors of the processes of biochemical transformation of matter in lake ecosystems. If these requirements are satisfied, long-term (many-year) calculations can be performed by the models. The ecosystem model for Onego is an adaptation of the model produced for Ladoga (Astrakhantsev et al., 2003). The biotic part of the model is based on the model developed by Menshutkin and Vorobyova (1987). The model of Lake Ladoga ecosystem is the phytoplankton succession model the most advanced one of all the ecosystems models developed for Ladoga. Chapter 6 focuses on the development of ecosystem models. The history of Ladoga and Onego ecosystem modelling is briefly described in this chapter. Also, the models of the lakes' ecosystems developed by the authors in recent years and representing, in fact, an integrated complex, are reviewed. Major attention in this chapter is paid to two models, that is, the Lake Onego ecosystem model, based on the nitrogen and phosphorus cycles, and the latest one developed by the authors: the model of phytoplankton succession in Lake Ladoga. The coupled thermohydrodynamic and ecosystem models for Lakes Ladoga and Onego have been developed to study the contemporary situation, to understand the main mechanisms of the ecosystem transformation, and to learn what may happen in future under the varying anthropogenic impact and climate change. Models are developed that enable simulation of hydrodynamics, phytoplankton, zooplankton communities, distribution and transformation of dissolved oxygen, distribution and transformation of substances/pollutants, evolution of the lakes' ecosystems, and reliable quantitative estimation of eutrophication in Lakes Ladoga and Onego. Descriptions of the models are followed by examples of their application for the present day and for hind- and forecasting. Chapter 7 analyses the dynamics of the lakes' water ecosystems under climate change (warming and cooling) and anthropogenic impacts relying on observed and modelled data. The advanced mathematical model of phytoplankton succession including nine species of phytoplankton was developed. Special attention here is given to the feedforward and feedback interactions in these lakes and the

xiv

Preface

catchment under various scenarios of regional climate change and anthropogenic nutrient loading. The results of analysis of observed data and numerical experiments are presented. Chapter 8 tells about the state of the art in modelling fish populations and their variability. In fish community models, active migration plays a dominant role in fish movements from one region to another within Lakes Ladoga and Onego. The main idea of constructing fish community models consists in separate description of trophic, population, and fishery processes that take place in the fish community. This study deals with the succession of the fish community species composition under eutrophication. Chapter 9 is devoted to the analysis of water supply problems, economy of the regions of the Great European Lakes, and their sustainable development. It describes modern systems of water management for the large lakes of the Russian Federation. The environment assimilation potential (EAP) is the ability of an environment to restore itself with regard to matter and energy loading as the result of economic activities. The authors suggest that economic estimates of EAP are obtained using the iterative procedure based on the 'trial and error method'. We combined ecosystem models with economic and mathematical models of the enterprises that use water resources in the catchment areas of the lakes. The main goal of economic estimation of EAP is definition of the fees for discharges of nutrients and pollutants to ensure conservation of the resources and aquatic ecosystems of the largest lakes of Europe. The book offers useful answers and tools for decision-makers. In the Afterword the authors show that the important feature of this book devoted to the study of the Great European Lakes is a combination of traditional limnological research with numerical modelling. A satisfactory correspondence between the results of numerical modelling and observational data collected in Lakes Ladoga and Onego, especially well-reproduced successive stages of the lake ecosystem transformation, allows us to conclude that the main patterns of ecosystem functioning are reliably described by numerical models. This means that it is possible to use the models developed as a powerful tool in decision-making on the management of water use of the great lakes, and also for cognitive purposes. This book was written by the team of authors under the editing professors L. A. Rukhovets and N. N. Filatov. G. P. Astrakhantsev took part in Chapters 2 to 7; N. N. Filatovin the Preface, the Afterword, Chapters 3,4 and 9 and sections 1.1,1.6, 2.1, 6.1 and 7.2; A. V. Litvinenko in section 9.1; V. V. Menshutkin in Chapters 6 and 8; T. R. Minina in Chapters 6 and 7; L. E. Nazarova in section 4.1; N. A. Petrova in Chapters 6 and 7 and sections 1.4 and 1.6; V. N. Poloskov in Chapters 3, 4, 6 and 7; L. A. Rukhovets in the Preface, the Afterword, Chapters 2 to 7 and 9 and sections 1.1 and 1.6; A. V. Sabilina in section 1.5; Ju. A. Salo in section 4.1; A. Yu. Terzhevik in Chapter 4 and sections 1.3, 2.1, 3.1 and 6.3; T. M. Timakova in sections 1.5 and 1.6.

Acknowledgements

This book is based on the results of the cooperations of the authors during the teamwork at the Institute of Limnology, Russian Academy of Science and those under realization of joint projects of the Russian Fund for Basic Research (RFBR) by the teamwork of the Institute for Economics and Mathematics at S1. Petersburg, Russian Academy of Sciences, and Northern Water Problems Institute, Karelian Research Centre, Russian Academy of Sciences. We involved some research results obtained by the Northern Water Problems Institute (NWPI), Karelian Research Centre, Russian Academy of Sciences, and the Institute of Limnology, Russian Academy of Sciences, and some published data of the Hydrometeorological Service. The authors of the book thank the projects of Basic Research supported by the Department of Earth Sciences of the Russian Academy of Sciences. The authors of the book thank their colleagues from NWPI, Drs N. Kalinkina, N. Belkina, P. Lozovik, M. Sjarki , T. Tekanova and Dr G. Raspletina from the Institute of Limnology, for kindly provided data analysis and useful recommendations and Dr R. Zdorovennov from NWPI for help. The authors also express their gratitude to Dr V. Podsechin for very important help, Mrs M. Bogdanova for preparing and redrawing figures for the present book. Special thanks go to academician S. Inge-Vechtomov and academician O. Vasiliev and Dr T. Florinskaja for support of our work. The authors extend their sincere gratitude to Dr T. Podsechina and O. Kislova for the translation of the book. The authors thank Mr I. Georgievsky for fine pictures of Lakes Ladoga and Onego.

1 The Great European Lakes: state of the art

1.1 PHYSIOGRAPIDC FEATURES AND IDSTORY OF THE FORMATION OF THE LAKES AND THEIR CATCHMENTS Lake Ladozhskoe and Lake Onezhskoe (Ladoga and Onego respectively) are the greatest lakes in Europe. Another geographical object in Northern Russia has a similar name: the Onega River. At first the definition for the Great European Lakes (GEL) like Ladoga and Onego by analogy with the Great American Lakes (GAL) was used in a book written by Gusakov and Petrova, In front of the Great Lakes (1987). The authors called these European lakes 'Great', because of their size, their dimensions are larger than those of any other lake in Europe (Fig. 1.1, Table 1.1). From the point of view of geophysical hydrodynamics the Large Lakes of Europe (Ladoga and Onego) are the largest because the baroclinic Rossby radius of deformation is too small RR < L if compared with the lakes' horizontal dimensions. RR = Cdfwhere C, is the phase speed andfis the Coriolis parameter. In these lakes, the baroclinic Rossby radius of deformation RR during summer stratification is several kilometres, i.e, smaller by several orders than the lakes' horizontal dimension (RR < L); epilimnion thickness (hI) is much smaller than hypolimnion thickness (h2), hI < h2. That is why the effect of the Earth's rotation on water hydrodynamics is so essential. The Burger number Si, is defined as the ratio of the internal (baroclinic) Rossby radius deformation, RR' to a length scale, L, that characterizes the basin dimension. In the large lakes of Europe and North America this parameter in summer time is about 0.03-0.05 and in other large European lakes - Vennern, Geneva, Saimaa, Constance and others - this parameter is about 0.2-0.6. GEL as GAL represents system of a unified lake. Lake Ladoga is connected with Lake Onego via River Svir, which is 224 km in length, with Lake Saimaa via River Vuoksa (Burnaya) and Lake Ilmen via River Volkhov (Fig. 1.I(b)). Lake system is linked with the Gulf of Finland in the Baltic Sea via River Neva. The surface area of Lake Ladoga is 17 891 km 2 and volume is 902 krrr', it ranks among the top fifteen world's freshwater lakes and is comparable with surface area

2

The Great European Lakes: state of the art

[Ch. I

... ......"""-.-

,.

. . . ----.-..J---

~r lIt.

I. ~ ·

I'

- -- - ...

r'

. .. "':-

Russi

- - .... . . ;. ... r~

Germ n

r'

- -- """

-'

. ' • .,..... ..J'

•......, --~...

.., '....

•

r- J

.... ~.

,-

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(a)

Fig. 1.1. Largest lakes on European map (a) and catchment of Lake Ladoga (b).

of Lake Ontario (Figs. 1.2 and 1.3; Table 1.1). Lake Onego's surface area is 9600 km 2 and its volume is 292 krrr' (Chernyaeva, 1966).1 The water renewal time is 11 years for Lake Ladoga and 14 years for Lake Onego and indicates that the lake ecosystems are rather conservative. The catchment of the Great European Lakes is 258 000 km 2 and extends through northwestern European Russia and the eastern part of Finland, including the large lakes Onego, lImen and Saimaa (see Fig . 1.1). Lakes Ladoga and Onego are 1 Other dimensions of the lakes are published in a paper by M. A. Naumenko in Lake Ladoga. At/as , St. Petersburg, Nauka, 2002.

Sec. 1.1]

Physiographic features and history of the formation of the lakes

3

(b) Fig. l.l(h).

an important link in the Caspian-Baltic-White Sea waterway system. Ladoga and Onego are also a key section in the drainage basin of the Baltic Sea, which at present is receiving very deep interest from the research, monitoring and protection communities. Both systems of Great Lakes in North America and Northern Europe have certain common features due to a similar genesis and the similar geological evolution of their hollows and catchments. They both were generated between contrasting crystalline shields (the Canadian in North America and the Fennoscandian (Baltic) in Europe) and plates: North American and Russian respectively, composed of Palaeozoic rocks. In the area of crystalline shields the ancient Earth rocks - granites

4

The Great European Lakes: state of the art

[Ch. I

Table 1.1. Physiographic parameters of the largest European Lakes. Lake

Ladoga Onego Vennem Pskovsko-Chudskoe (Peipsi) Yettem Saimaa

Square, km 2

Above sea level m

Maximum depth, m

Average depth, m

Volume, km 3

18000 9840 5648 3558

4 33 44 30

230 120 106 15

51 30 27 7

910.0 295.0 152.5 24.9

1856 1800

89 76

128 58

40 20

74.2 36.0

:ero I

:i ~~

,>;,1 © .I

""'1

91 Q,~

a) ~~,t

= l :co J

"J. -.__ .~-:::_~_. ~-~--~ ..__.-/ ! ;: 3 z '5 E:

,....-----------------, '

Fig. 1.2. Volume in km? (a) and area in km2 (b) of the large lakes of Europe: I, Ladoga; 2, Onego ; 3, Vennem; 4, Pskovsko-Chudskoe (peipsi); 5, Yettem; 6, Saimaa.

and gneisses - are found at the surface with an age up to 2 billion years. The regions of neighbouring plates are presented mainly by limesstone, dolomites and sandstones with an age of less than 570 million years. The northern parts of the basins and catchments of Lakes Ladoga and Onego, as well as Lakes Superior and Huron, were formed on crystalline shields in places of ancient tectonic cracks, and the southern parts of these lakes, as basins of Lakes Michigan , Erie and Ontario were formed in

Sec. 1.1]

Physiographic features and history of the formation of the lakes

5

La

On

Fig. 1.3. Bathymetry of Lakes Ladoga and Onego.

sediments during the last glacial period. The last Ice Age of the Quaternary period, at a maximum approximately 25-10 thousand years ago , was the most important factor affecting the basins and catchments of both lake systems. At their maximum stage glaciers completely covered the northern parts of North America and Europe, including the regions occupied by the modern Great American and European Lakes. The highest degree of glacial erosion took place in the boundary shield regions , where vast systems of near-glacial lakes were formed (Kvasov, 1975; Gusakov and Petrova, 1987; The History of Ladoga and Onego ... , 1990). The history of the development of Lakes Ladoga and Onego is linked with the initial stage of the formation of the Baltic Sea - the Baltic system of near-glacial lakes. The territories of Lakes Ladoga and Onego were covered with ice at that time (Kvasov, 1975). About 11.8 thousand years ago with regression of the ice the Baltic glacial lake was formed, which occupied the major part of the modern Baltic Sea basin. At that time the near-glacial lakes system was generated. The main waterbody of this system was the Southern Baltic glacial lake, which existed approximately 12-13 thousand years ago. This lake water level was higher than the ocean level and saline water did not penetrate into it. At that time Lake Ladoga was a bay of the Baltic Lake, connected with it via a narrow strait in the northern part of the Karelian

6

The Great European Lakes: state of the art

[Ch.l

Isthmus. About the same time the southern and the eastern part of pre-Onego Lake basin were released from ice. As a result the Vytegorskoye and Vodlinskoye nearglacial lakes were formed. Later these lakes were connected, forming the Southern Onego glacial lake, which was not then a connected system with Lake Ladoga with outflow towards the basin of the White Sea. Only after glacier regression, did the River Svir carry its waters to Ladoga Bay of the Baltic glacial lake. Nearly 10 thousand years ago the Baltic Sea water level dropped by more than 20 m and equalled the ocean level. Oceanic waters penetrated into the Baltic Sea and created a waterbody, which was named the Ioldy Sea. The consequence of declination of the Baltic glacial lake level was that Lake Ladoga was no longer a bay and for the first time became a separate waterbody. The river appeared where the strait was, which carried its waters from Lake Ladoga to the Ioldy Sea. Since the Lake Ladoga level was at that time considerably higher that the Ioldy Sea level, brackish sea waters did not penetrate into the lake, where water remained fresh. During the same years which saw regression and melting of the ice, the formation of Lake Onego continued, of which the northern part was much larger than it is nowadays. After complete release from glacial cover about 4.5 thousand years ago, the northern shores of the lake underwent an isostatic rise, which has continued at a low rate up to the present day, and Lake Onego acquired something close to its modern shape. During the isostatic rise of Scandinavia the level of the ancient Baltic waterbody started to grow again and a freshwater body was formed out of the brackish water of the Ioldy Sea, named Lake Antsylovoye. At its maximum the water level of this lake exceeded the threshold magnitude for Lake Ladoga inflow and, as a result, in the northern part a shallow strait was formed. Lake Ladoga became a bay, this time of Lake Anstylovoye. About 8.4 thousand years ago Lake Antsylovoye formed a new threshold flow mark in the region of the modern Danish straits and, under the influence of erosion processes, the flow threshold mark decreased and the level of Lake Antsylovoye declined by 12m. Sea waters later penetrated into the ancient Baltic waterbody and for some time the Littorinovoye Sea existed there but, even at the stage of its maximal development, the level of Lake Ladoga was always higher, which prevented the spreading of saline sea waters. During the whole formation period Lakes Ladoga and Onego remained freshwater bodies. Thawing glacial waters brought to forming lakes a large amount of coarse and fine mineral particles and dissolved substances, including biogens that were stocked earlier in the glacier. These waters, comprising the basis of income water balance, were relatively rich in biogens; the lakes ecosystem productivity was low for several reasons: first, incoming glacial waters had low transparency and light was one of the limiting factors for phytoplankton development, and, second, low temperatures and a short vegetation period, typical for the late post-glacial period, influenced biota development (Davidova and Subetto, 2000). Thus, at the end of the Pleistocene, preLadoga and pre-Onego were oligotrophic cold water bodies. Lake ecosystems were formed under the influence of gradual climate warming. The beginning of the Boreal period and climate warming resulted in further development of forest vegetation on the lakes' catchments and was characterized by deposition in the deep lakes of

Sec. 1.1]

Physiographic features and history of the formation of the lakes

7

homogeneous clays with high biogenic concentrations. The climate warming and high humidity over the territory led to growth on the catchments of mixed conifer and broadleaved forests with an admixture of oak, lime, elm, and maple, which provided the growth of the organic component in bottom sediments (Davidova and Subetto, 2000) and higher accumulation rates of sludge. Approximately 4-5 thousand years ago the formation of the modern Baltic Sea was practically complete. By this time Lake Onego had reached its modern shape, while the Lake Ladoga basin continued to transform. About 5 thousand years ago (Saarnisto et al., 1995) on the edge of atlantic and sub-boreal periods, the isostatic rise in the near-Ladoga region modified the hydrographic network, redirecting flows and turning the flow of the Saimaa lake system through River Vuoksi to Lake Ladoga, which increased by approximately one-third the income component of the lake water balance. The northern coast of Lake Ladoga experienced considerable isostatic rise and, as a result, the outflow from the lake to the northern part of the Karelian Isthmus nearly stopped. The lake level started to rise, and that affected mostly the southern coastal part. The highest lake water level was reached about 2 thousand years ago. When the lake water level reached the height of the watershed dividing the Mga River, inflowing to Lake Ladoga, from the Tosna River, inflowing to Gulf of Finland, Lake Ladoga waters washed away the narrow isthmus of the watershed and the Neva River was formed. After the generation of the new threshold flow value, the level of Lake Ladoga started to decline. The northern flow had stopped completely and the relatively short, 74 km long, Neva River became the only outflow from Lake Ladoga to the Baltic Sea. Its average discharge equalled 2500 m 3/s, and it has not changed in fact since that time. The final formation of the Neva River and the whole system of Great European Lakes took place less than 2 thousand years ago. By this time the level of Lake Ladoga had attained its modern magnitude (about 4-5 m above sea level). At the same time erosion processes were intensified on the catchment, which created favourable conditions for natural but fairly gradual lake ecosystem eutrophication processes. The peculiarities of the Ladoga and Onego lake basin and catchment generation and evolution had created such specific features of the coastline as its high embayment in the north and its regular smoothness in the southern, southeastern and southwestern parts. A high degree of similarity is observed in the northern parts of the lakes' coasts - a large amount of narrow long coves, bays and fiords, elongated from north to south or from northwest to southeast, and the existence of skerries. Lakes Ladoga and Onego in general are very similar to the Great American Lakes in their origin, coast types, and bottom relief and in the contrast between the northern and the southern parts of their basins. Lake Onego is the upper one in the system of Great European Lakes. Comparing the two largest lake systems of the North American and European continents, it could be mentioned that they are relatively young by origin and reached their modern shapes only a few thousand years ago. The ecosystem dynamics of the Great Lakes in Europe and America have a lot in common, but there also exist some individual features specific to each.

8 The Great European Lakes: state of the art

[Ch.l

(a)

(b)

(c)

Fig. 1.4. Satellite images of the lakes in winter. Ladoga: (a) satellite 'Resource 01'; Onego (b) cold year, 04 FEB 2005, and (c) warm year 05 FEB 2007, satellite 'Terra'.

Sec. 1.2]

History of research of the lakes

9

Summing up, it is possible to point out that, regardless of the initial similarity in the limnological characteristics of GAL and GEL, the contemporary evolution of these lake ecosystems over recent centuries has proceeded differently. Moreover, even within each lake system the processes of eutrophication and toxic contamination differ quite distinctively. These differences are promoted by specificity in limnogenesis, in morphometry, in thermohydrodynamic processes and in catchment changes, as well as in legislation, practical water resources management and investments in nature preservation. Current and future tendencies in climate change are allegedly bound to drive the evolutionary paths of the lake systems even further apart. Though Lakes Ladoga and Onego are located more towards the north than American lakes, climatic peculiarities of their catchments are to a certain degree similar. Air masses of a different origin collide there and unstable climatic conditions develop with frequent changes of weather conditions. Air masses, coming from the Atlantic Ocean over the catchments of Lakes Ladoga and Onego, bring intensive snowfalls and thaws in winter, and in summer rainy and windy weather. The intrusion of arctic air masses causes abrupt cooling, sometimes below -40°C. The invasion of continental air masses from the east and southeast leads to dry and hot weather in summer and to clear and frosty weather in winter over the lakes' catchments. The Great American Lakes never freeze completely, while Lakes Ladoga and Onego are completely covered with ice during cold winters; in warm winters the ice covers only part of lakes (Fig. 1.4). Ice cover thickness on Lake Ladoga and Lake Onego may reach 1m and even more in some years. On Lake Ladoga during the winter period quasi-steady polynyas exist, dividing the ice cover of the coastal area (fast ice) from that of the central part of the lake. In years when the lake is not completely covered with ice, the ice mass in the central part drifts, depending on prevailing wind direction. This ice mass is usually fractured (Tikhomirov, 1982). Ice cover destruction usually takes place in May, but in a cold spring floating ice may be observed in June. The same origin of the Great American and Great European Lakes basins and the geological peculiarities of their catchment are revealed in their similarity of morphometric features and thermal regime formation. Lakes Ladoga and Onego belong to the so-called dimictic lake type (Ryanzhin, 1994). 1.2 HISTORY OF RESEARCH OF THE LAKES Lakes Ladoga and Onego have been studied during the last hundred years, both before the pronounced influence of human activities and during the period of catastrophic ecosystem change under increased anthropogenic pressure in 1970s and 1980s. Taking into consideration the common features of the abovementioned lakes, we will show in this work that mathematical models developed and tested for Lakes Ladoga and Onego, contain formulations of the problems and algorithms suitable for the ecosystem modelling of other large lakes located in temperate latitudes. Lakes Ladoga and Onego, located between 59°54' Nand 62°55' N are among the northernmost of the world's great lakes. The tremendous catchment area of Lake

10 The Great European Lakes: state of the art

[Ch.l

Ladoga, located in different landscapes, determines the wide diversity of natural and anthropogenic factors affecting the lake ecosystem dynamics. The considerable size of the lake and the slow water exchange (the ratio of the lake volume to annual inflow, that is the conventional water exchange coefficient, equals 0.08) are the reasons for ecosystem conservativity. The complicated morphometry of the lake basin and its large proportions account for heterogeneity of hydrophysical, hydrochemical and hydrobiological processes in different parts of the waterbody. The variability of limnetic parameters, typical for deep, large lakes, is especially intensified under the heavy and essentially always non-uniform anthropogenic impact. The studies of this waterbody are typical, since all changes that take place in Lake Ladoga are reflected in the water quality of the Neva river, and thus in the water supply of St. Petersburg, and influence the water quality of the Neva Bay of the Gulf of Finland. The initial studies of Lake Ladoga date back to the end of the nineteenth and the beginning of the twentieth centuries (Andreev, 1875; Molchanov, 1945). The significant results of that period are generalized in the monograph written by I. V. Molchanov (1945). Knowledge of the ice regime helped in the building and maintaining of a temporary road (the so-called 'road of life') over the ice cover across the southern part of Lake Ladoga during the Second World War. This road provided a connection with Leningrad city during the blockade period. It helped to maintain a temporary road on the ice which was used to evacuate refugees and to organize the delivery of supplies to Leningrad city. The bibliography of Lake Ladoga studies includes several hundreds of titles (Bibliography . . . , 1997). Comprehensive investigations of the limnological processes in Lake Ladoga were conducted by the specialists of the Laboratory of Limnology of the USSR Academy of Sciences (now the Institute of Limnology of the Russian Academy of Sciences) in 1956-1963. The results of these studies were published in eight monographs from 1961 to 1968 (Hydrological Regime ... , 1966). In this period of time, precise spatial and seasonal characteristics of the main hydrochemical and hydrobiological processes, which appeared as a result of increasing anthropogenic loading, were obtained. Until the mid-1960s industrial activities in the catchment had very little influence on the state of the ecosystem and the water quality in Lake Ladoga. The lake preserved its status as an oligotrophic waterbody, as it had at the beginning of the century. Insignificant bacterial pollution was registered only in the vicinity of the wastewater outlets of the paper mill establishments. Noticeable changes in the lake ecosystem were related to increasing phosphorus loading in the waterbody, mainly from the wastewaters of the Volkhov aluminium plant and agricultural activities. The increase of phosphorus loading led to the development of the process of anthropogenic eutrophication. The first step in studying this process, which nowadays has the central role in the evolution of the ecosystem of Lake Ladoga, is related to the period 1975-1980. The research was carried out by the Limnological Institute of the Russian Academy of Science and the results were published in the monograph of Petrova (1982). The main features of the anthropogenic eutrophication were described and the reasons for its existence were

Sec. 1.2]

History of research of the lakes

11

established. The next step in this research, dating from 1981 to 1990, made it possible to formulate a series of theoretical concepts, necessary for understanding and forecasting the tendencies of waterbody development (Lake Ladoga. Atlas, 2002). Estimates were made of the principal difference of anthropogenic eutrophication in large deep lakes compared with its natural evolution, of the effect of morphological homogeneity in the lake basin on the formation of limnological processes, and of the dangerous consequence of eutrophication - the decrease of oxygen content in water. An important result of these studies was the comparison of alteration scales in the ecosystem under the influence of anthropogenic activities with the natural diversity, and the selection of an optimal number of parameters - ecological criteria - which can be used during analysis, modelling and forecasting of the state of the lake. The beginning of the development of a mathematical ecosystem model dates to this period In all studies attention was mainly paid to the interaction of phosphorus with the carbon cycle in the lake ecosystem, which defines production-destruction relations, and as a result the rate of its destabilization (Modern states . . . , 1987; Lake Ladoga ... , 1992). It was pointed out that anthropogenic eutrophication is a phenomenon comparable to the scale of natural processes. Furthermore a number of approaches for the estimation of the degree of pollution and the potential for such pollution in different parts of the waterbody was developed. The starting point was the analysis of the lake processes which determined the development of significant consequences of anthropogenic impact. Unfortunately the studies carried out in the 1990s were less regular and were limited mainly to the summer periods. Let us mention the international research on the lake which was conducted in these years (Viljanen and Drabkova, 2000). The monitoring of the main lake processes was carried on and the results could be found in the proceedings of three international Lake Ladoga symposiums and in the collective monographs (Lake Ladoga, 2000; Lake Ladoga. Atlas, 2002; Rumyantsev and Drabkova, 2006). In these years a number of substantial studies, started earlier, were fulfilled: the conclusions of the long-term analyses of the generation of lake organic substances pool were drawn (Kulish, 1996), and the phosphorus fluxes at the water-bottom interface were estimated (Ignatieva, 1997). There were studies of the role of humic complexes in lake organic substances during the accumulation process, conservation and recirculation in the lake phosphorus cycle. This analysis made it possible to understand the mechanism of lake ecosystem stability and the reasons for its transformation during long-term anthropogenic pressure (Korkishko et al., 2002). During the period 19962005 the phosphorus loading on Lake Ladoga noticeably decreased. Its mean value during this period did not exceed 4000 tons of phosphorus per year. Such low levels of phosphorus loading on the lake had not been registered in more than 20 years, from 1975 until 1995. The following publications devoted to the analysis of the process of anthropogenic eutrophication from the 1960s until 2005: Petrova et al. (2005) and Rumyantsev and Drabkova (2006). Generalizations of the data obtained over several decades are presented in Lake Ladoga. Atlas (2002). Geographical descriptions of Lake Onego, performed by travellers and researchers were rare and incomplete before the nineteenth century. In ancient times Lake Onego was called Anizskoye (from Finnish Aiininen jdrvi; iiiini means

12 The Great European Lakes: state of the art

[Ch.1

voice, sound) and later Onego. Academician Ozeretskovky, who visited Lake Onego in 1785, first published a review about the lake at the end of the eighteenth century (1792). In the nineteenth century several expeditions were organized there to study water level, thermal regime and sediments; a general geographic description of the lake was prepared by Bergshtresser, Stabrovsky, Keppen, Andreev and Drizhenko, Sovetov (see in Molchanov (1946) and in Lake Onego. Atlas (2009)). From the 1870s, water level recording and collecting observation data was organized at meteorological stations on Lake Onego and its catchment. Beginning from the end of the nineteenth century Russian Geographical Society initiated systematic investigations on Lake Onego. The first water-temperature data recordings on the lake were obtained in 1903 by N. A. Pushkarev. In 1914 the expedition under the leadership of S. A. Sovetov measured water temperature and transparency at 15 deepwater stations from a steamboat, and took sediment samples to fulfil mechanical, chemical and biological analyses. During the period 1924-1933 the complex Onezhskaya expedition of the State Hydrological Institute under the guidance of S. A. Sovetov conducted studies on the lake; the results were generalized in monograph by Molchanov (1946). Since 1933, after the construction of Belomorsko-Baltyisk Canal, the lake has been connected with the White Sea and joined the united system, linking the White, the Baltic and the Caspian seas. In 1953 on the River Svir, connecting Lake Ladoga and Lake Onego, an Upper Svir (Verhnesvirskaya) hydropower station was constructed, since then the lake water regime was regulated and the Upper Svir reservoir was formed. In 1964 the complex Onezhskaya expedition was organized to study the lake pollution problems and their influence on water quality and biological productivity (Ecosystem of Lake Onego ... , 1990). The expedition combined the Limnological Institute of the USSR Academy of Sciences, the Department of Water Problems of the Karelian Branch of the USSR Academy of Sciences, SevNIORH and the Petrozavodsk hydrometeorological observatory of UGMS. The studies were organized according to a special programme in the areas of the highest pollution. In 1970-1971 real-time measurements were conducted on a hydrophysical polygon in Bolshoye Onego Bay with different biotopes. Investigations were carried out by specialists of the Department of Water Problems of the Karelian Branch of the USSR Academy of Sciences, the Institute of Zoology of the USSR AS, and the Computing Centre of the USSR AS (Limnological Investigations ... , 1982). In 1981-1985 the Department of Water Problems of the Karelian Branch of the USSR AS performed complex studies of the lake all over the waterbody including measurements at 200 stations in connection with possible redistribution of water resources on the European territory of the USSR starting from the White Sea, via the lake system of Arkhangelsk and Vologodsky regions, through Lakes Ladoga and Onego to the south of the USSR (Ecosystem of Lake Onego ... , 1990). But the diversion of river flow from the north to the south with abstraction of the waters of Lakes Ladoga and Onego was not realized. At the end of the 1980s and the beginning of the 1990s the Limnological Institute of the USSR AS and the Department of Water Problems of the Karelian Branch of the USSR AS conducted a unique hydrophysical experiment 'Onego-89' using three

Sec. 1.2]

History of research of the lakes

13

research vessels, autonomous buoy stations, an airborne laboratory and three satellites. The aim of this experiment was the development of operational methods for checking water quality parameters (Lake Onego ... , 1999; Filatov, 1991). In the volume and spread of its observations it could be compared with the International Field Year of Great Lakes (IFYGL) on the Great American Lakes (Mortimer, 1974). In 1991 the Department of Water Problems was reorganized into the Northern Water Problems Institute of the Karelian Research Centre of the RAS. Since 1992 NWPI Karelian RC RAS has started regular observations on Lake Onego in accordance with a programme of complex monitoring (Ecosystem of Lake Onego ... , 1990). Since 1991 the Hydrometeorological Service of the RF has started to diminish the observation network and meteorological stations, so, the measurements of hydrophysical parameters of Lake Onego using research vessels and an airborne laboratory were stopped. At the present time, monitoring on the lake and its catchment are performed by the NWPI and the Karelian Hydrometeocentre of Roshydromet. All information about the origin of the lake and its hydrophysical, hydrobiological and hydrochemical processes, collected during the last 50 years, are generalized in Lake Onego. Atlas (2009). Appreciating the results for Lakes Ladoga and Onego of all researches mentioned above, it is worth mentioning that as a rule obtaining generalized conceptions about the processes in ecosystems and its quantitative estimates were conducted without using mathematical models of waterbody ecosystems. The application of mathematical models for quantitative estimates of phosphorus fluxes and of the input of different hydrobiotic complexes in the regulation of matter and energy exchange in the ecosystem, of matter fluxes in the water/atmosphere and water/ bottom interfaces and for forecasting calculations appears to be not only useful but necessary. The main reasons for that were on the one hand the absence of relative mathematical models and on the other hand the lack of cooperation between specialists in ecological modelling and so-called naturalists (limnologists, biologists, ecologists, hydrologists etc.). The first mathematical model of the Lake Ladoga ecosystem, developed by V.V. Menshutkin and O.N. Vorobjova (1987) for the study of Lake Ladoga ecosystem response to the increase of phosphorus loading, is exclusion. Regarding the research into the hydrothermal regime of Lakes Ladoga and Onego, its development and its model applications, it started quite a long time ago (Okhlopkova, 1966; Tikhomirov, 1982; Akopyan et al., 1984; Astrakhantsev et al., 1987; Beletsky et al., 1994; Podsetchin et al., 1995). Reviews of studies devoted to the problem of modelling lake dynamics can be found in Filatov's books (1983, 1991) and in Kondratyev and Filatov (1999). Lake Ladoga and Lake Onego research results based on mathematical model applications carried out during the last two decades by the authors are presented in this monograph. It is worth mentioning that this monograph presents the development of conceptions expressed in the previous monograph, where were reflected mainly the studies of Lake Ladoga (Astrakhantsev et al., 2003). For the first time the results of Lake Onego studies applying mathematical modelling are presented in this monograph.

14 The Great European Lakes: state of the art

[Ch.1

A brief description of the evolution of Lakes Ladoga and Onego ecosystems in the process of anthropogenic eutrophication and of observation data is presented below. The focus is on the main processes causing ecosystem destabilization and the new trophic state of the lake. Wide national and international experience within scientific programmes concerning the problem of lake ecosystem anthropogenic eutrophication shows that many processes in these lakes are similar to those which took place, or have been observed at the present time, in other lakes of the temperate zone. Furthermore, according to all their characteristics, Lakes Ladoga and Onego provide classical examples of large stratified lakes in the temperate zone. 1.3 CHARACTERISTICS OF TEMPERATURE AND CURRENTS 1.3.1 The thermal regime and limnic zones The complicated morphometry of Lake Ladoga basin determines the spatial heterogeneity of processes in the Lakes Ladoga and Onego waterbodies. So, the difference in depths within the waterbody leads to significant inhomogeneity in the heating and cooling of water masses. According to the Hutchinson classification (Hutchinson, 1975), Lakes Ladoga and Onego belong to the dimictic type of lake, where the complete mixture of the waterbody takes place twice a year - in spring and in autumn. The thermal cycle is divided into two periods: heating (hydrological spring and summer) and cooling (autumn and winter). Long spring and winter seasons strongly affect variations of limnetic processes. Due to specific freshwater density distribution, spring and autumn thermal heterogeneity initiates the formation of a unique phenomenon: the so-called 'thermal bar' (Tikhomirov, 1982). The early studies of the thermal bar in Lake Ladoga and Lake Onego by Tikhomirov (1963) along with Rodgers (1971) publications on the Great American Lakes are the classical studies on this subject. The thermal bar is a zone of intensive lake water mixing; the resulting effect is that water temperature in this zone reaches the temperature of maximal density +4°C all through the waterbody. This frontal zone, extending along the coastal line, divides the lake into two regions: the warmer coastal and the deep, colder central one. In the frontal zone, from both warm and cold directions, appear steady vertical downwelling movements (Fig. 1.5). In the bottom layer water starts moving aside from the thermal bar: in the coastal zone to the shore, in the central zone towards the open parts of the lake. Besides vertical downwelling water movements, density flows along the thermal bar front are formed. Circulation density flow in the coastal region is of a cyclone type (oriented anti-clockwise); in the central part it is of anticyclone type. This flow pattern along the thermal bar additionally supports its sustainable state. Due to cyclonic coastal flow, tributary waters are spread far away from the mouth, not mixing with the lake waters of the central region. This phenomenon is especially significant for Lake Ladoga: the chemical compound of the Volkhov river water flowing into the southeastern part of the lake differs considerably and it spreads along the eastern coast far away to the north. The Volkhov waters are formed within the Lake Ilmen

Characteristics of temperature and currents

Sec. 1.3]

':IV

15

I

'j)

.....

-, r'

"I-

l...... . . W~

M'

~-

~5

\

, u

\

r." ... i

....,

-

)

-....,

j .u

Fig. 1.5. Mean perennial location of the spring thermal bar in Lake Ladoga (Lake Ladoga. Atlas, 2002).

catchment where sedimentary rocks prevail. Those waters are the main source of biogenic elements in Lake Ladoga, phosphorus in particular. As the lake waters warm up, the thermal bar moves towards the deeper regions (Naumenko, 1994; Zilitinkevich et al., 1992). When water temperature exceeds +4 °C (exactly 3.98°C) all through the waterbody the thermal bar completely disappears . The thermal bar horizontal mixing speed in Lake Ladoga at the end of May is nearly 150m S-I, sometimes reaching 600m S-1 (Tikhomirov, 1982). The disappearance of the thermal bar occurs usually at the end of June - beginning of July, within 50-60m depth, and defines the end of the spring period of the lake hydrological cycle. In the late 1980s-early 1990s, the theoretical, laboratory, and field studies of the thermal bar phenomenon in Lake Ladoga were continued. First, a theoretical model taking into account the horizontal heat transport from the warm to the cold zone was proposed (Zilitinkevich and Terzhevik, 1989), which was further developed in (Zilitinkevich et al., 1992).

16 The Great European Lakes: state of the art

[Ch.1

In the years 1991-1992, the joint Soviet-Swedish field study of the thermal bar in Lake Ladoga was initiated to validate the theoretical parameterizations received. The surveys along two cross-sections with different bottom slopes perpendicular to the southern and western shores were performed in the spring 1991 and 1992 two and three times, respectively, to collect data on the vertical distribution of water temperature and currents. The results of the 1991 (Malm et al., 1993) and 1992 (Malm et al., 1994) field campaigns can be summarized as follows. The measured current velocity distributions were found to be strongly dependent on wind conditions. The density-induced currents seemed to be of secondary importance compared to the observed currents, even during calm conditions. Estimates of the heat content change along crosssections revealed the presence of horizontal heat transport from the nearshore warm zones to the thermal bar. The estimates of the thermal bar propagation rates based on observational data were compared with those received from the theoretical models. The model accounting for the horizontal heat transfer (Zilitinkevich et al., 1992) was found to better predict the propagation rate compared to earlier models (e.g. Elliot and Elliot (1970), and similar). The depth-integrated advective flux calculated from the temperature distribution observed and the along-section velocity component computed with a one-dimensional k-c model was found to be 100 times smaller than that estimated from heat content change calculations. The analysis of the satellite images (Kondratyev et al., 1988) clearly demonstrated the presence of the warm-water vortex trails on the cold side of a thermal bar, which should accelerate the front propagation. The mechanism of these intrusions is not clear yet, but Zilitinkevich has suggested that such a phenomenon can occur due to baroclinic instability of the currents on the warm side of the thermal bar. As surface water warming proceeds, the horizontal thermal heterogeneity near the coasts becomes the vertical thermal stratification. Along with disappearance of the thermal bar the vertical stratification is formed in the deep regions, marking the beginning of the hydrological summer. The isotherm +4°C in every vertical cross-section defines the lower boundary of the heated layer, dividing it from the waterbody thickness, forming the cold water dome in the deep water part of the lake. By the moment of dense water dome formation the difference in the surface water temperature over the lake exceeds the maximal annual value and the cyclone circulation its utmost development. The drift flows start to lie over the cyclone circulation. The surface temperature over the whole lake gradually becomes even, under the influence of convective-wave mixing. The water dome and the limiting layer of rapid temperature decrease, the so-called thermocline or depth of metalimnion, drops down. The upper layer of the lake becomes isothermal, forming a sustained epilimnion (the upper quasi-homogeneous layer). The water temperature in the lake exceeds its maximal value. The thicknesses of epi- and hypolimnion gradually increase and in the deep layers (hypolimnion) the water temperatures remain nearly +4°C. According to Tikhomirov (1982) classification Lakes Ladoga and Onego belong to the classification: hypothermal lakes - those lakes where, during the period of summer warming, the main water mass forms the hypolimnion.

Sec. 1.3]

Characteristics of temperature and currents

17

By the beginning of the hydrological autumn the dense water dome is observed at depths of more than 100m. Starting with water cooling in the coastal regions, the autumn horizontal thermal heterogeneity becomes settled. This phase is characterized by the coming into existence of the thermal bar, intensive water cooling in shallow coastal waters, ice cover formation and the long-term preservation (until December-January) of a water temperature of nearly +4°C in the deep parts of the lake. Complete ice cover of the lake occurs during cold winters only. Over the deepest regions ice cover is observed for short periods of time: 10-15 days. The deep part of the lake is not covered with ice during warm winters (Fig. 1.4(a)). Ice cover disappears in AprilMay (Tikhomirov, 1982). Water masses the thermal heterogeneity of water masses is responsible for the variation in most limnological features within the waterbody. Of greatest significance during the period of the hydrological spring is the horizontal thermal heterogeneity. The existence of the frontal thermal bar zone defines the accumulation of the initial water masses, the lake tributary waters, preserving their specific chemical, physical and other features. That is to say, the biogenic elements of the epilimnion mainly participate in the consumption cycle during the summer period - regeneration related to biological processes. That is why only here is recorded the reduction of dissolved mineral phosphorus and nitrogen concentrations, whereas in the hypolimnion its storage is preserved at the winter-spring level. Equally all changes of hydrophysical and hydrochemical indicators caused by the photosynthetic activities of phytoplankton (high values of pH, reduction of transparency, the increase of water oxygen concentration) are revealed in the epilimnion. The hypolimnion mainly is the zone of the development of destruction processes - the tropholytic area of the lake. The main process leading to essential changes of limnetic parameters in the hypolimnion is the decrease of oxygen concentration in water. The mixing of the whole water column during the periods of spring and autumn homothermy provides the equalizing of hydrophysical and hydrochemical parameters. As a result of long-term Lake Ladoga studies the lake was divided into four limnetic zones (Lake Ladoga ... , 1992) each of which plays a special role in ecosystem functioning and in general has its value from the point of water supply (Fig. 1.6). In Lake Ladoga the coastal zone I, where the depths are the shallowest and less than 15m, is subjected to the maximum influence of its catchment processes including anthropogenic impact. It is here that tributary waters, industrial and agricultural wastewaters, surface runoff, drainage waters of land reclamation systems and so on enter the lake. At the same time only in the coastal zone are located industrial and municipal water intakes, recreational areas and the most of the spawning-grounds. In spring and autumn months the thermal bar front prevents free water exchange with the deep central part of the waterbody. The flood waters of tributaries enriched with biogenic elements and allochthonous organic matter are retained in the near-shore zone for a long time. In summer time in the well-heated coastal zone the composition of water organisms is diverse and their production

18 The Great European Lakes: state of the art

[Ch.l

Fig. 1.6. Limnetic zones of Lake Ladoga.

rate is high. During the summer stratification period the coastal zone, due to its shallowness, generally is well mixed. The declinal zone II, with depths in the range 15-52 m, is typically characterized by the existence of the stable thermal bar front which is clearly pronounced during the spring period. As the thermal bar passes through downwelling water movements, the suspended solids of autochthonous and allochthonous origin penetrate to the near-bottom layers. At the same time, in the larger part of the declinal zone, formation of autochthonous organic matter takes place due to the high productivity of spring phytoplankton and the spreading into this area of coastal water masses enriched with allochthonous organic matter. Thus the tremendous amount of organic matter, both of allochthonous and autochthonous origin is accumulated in the near-bottom layers of the declinal zone. During the summer stratification period the hypolimnion has a relatively small thickness, being the peripheral part of the lake hypolimnion. Consequently, in the minimal hypolimnial volume the considerable share of organic matter annually incoming to the lake, spring phytoplankton production and flood organic matter is gathered . The declinal zone is the place of the

Sec. 1.3]

Characteristics of temperature and currents

19

primary accumulation and mineralization of organic matter in the hypolimnion. This is the place where the considerable consumption of dissolved oxygen initially occurs during destruction processes and, as a consequence, the near-bottom oxygen deficit might develop. Two other areas, the profundal zone III (52-89 m) and the ultraprofundal zone IV (more than 89m) are the most conservative parts of the lake. All limnetic processes are slowed down in these two zones, the largest by their volumes and the least heated. This is the accumulating and generating area of organic matter in the water column and in the silts on the bottom. Thus the two shallower zones are the areas of primary accumulation and the deep water zones are the regions where the accumulated substances are transformed, entrained in the inner waterbody cycles or conserved. The thermal regime and currents in Lake Onego were studied in detail by Tikhomirov (1982), Okhlopkova (1972), Boyarinov et al. (1994), and Filatov (1991). To derive average perennial characteristics of the Lake Onego thermal regime, the observation data of the Karelian Republic Centre on hydrometeorology and monitoring of the environment for the period 1958-1989, both from research vessels and an airborne laboratory were used. Observations performed by the Northern Water Problems Institute from 1992 to 2007 were used as well. The measurements were made during a navigation period on a fixed stations grid at offshore verticals with a temporal resolution of 10-30 days. The unique survey of currents and water temperatures was conducted during experiment 'Onego'; later these data were used for numerical computations of currents in Lake Onego on the basis of mathematical models (Filatov, 1991; Beletsky et al., 1994). For calibration and verification of models described in this monograph, both 'Onego' experimental data and averaged data on the thermal regime, is included in the Lake Onezhskoe Atlas (T. V. Efremova; see Lake Onego. Atlas, 2009). To calculate the mean perennial variations of water temperatures at different layers the continuous-in-time approximation parametric function was used, making it possible to obtain daily mean water temperature values at standard depths in different parts of Lake Onego. On the basis of modelled curves, the monthly maps/ diagrams of water temperature distribution from 1 June till 1 November, at different depths, were produced and limnetic zones were contoured (Fig. 1.7). Data analysis of the lake thermal regime has showed that seasonal variations of water temperature are influenced by peculiarities of the lake basin, its dimensions, coast line unevenness and, mainly, by depth. That is why seasonal changes of water temperature in different parts of the lake are clearly distinguished. Ice destruction in Lake Onego usually happens at the beginning of May, and its complete disappearance is observed in average on 18 May. With ice destruction and ice melting, the amount of heat penetrating into the water column increases essentially. In May the thermal bar formation starts; it divides the lake into two regions: the coastal stratified region and the deepwater homogeneous one. The 4°C isotherm on 1 June contours the lake and it is located at 20-25 m depth. The thermal bar phenomenon results in heat redistribution and water masses mixing in Lake Onego for rather a long period of time. According to mean perennial data it disappears in

20

The Great European Lakes: state of the art

(I

[Ch. I

N

6' <.0>

...

m

m

....

\"

Fig. 1.7. Mean perennial location of the spring thermal bar front in Lake Onego (Lake Onego. Atlas, 2009).

the third decade of June, and a direct thermal stratification is established, when the summer heating period starts. During summer heating the lake becomes steadily stratified in the vertical direction with an upper warm homogeneous layer (the epilimnion), a layer with a high temperature gradient (the thermocline) and a bottom cold layer (the hypolimnion). The transition layer with high vertical temperature gradients prevents penetration of heat flux from the upper layer towards the bottom. After thermal bar front destruction, in the deep central part of the lake the temperature growth rate in June in the near-surface layer (0-5 m) increases by 3.5-4 times and equals approximately 0.35-0AO°C day" , At a depth of 20m it is close to its spring value of O.l oC day:", and at a depth of more than 40 m it is less than 0.03°C day", Starting from 1 July the minimum temperature in the nearsurface layer is observed in the deep central part of the lake, and the maximum temperature in coves and bays. At this time the seasonal thermocline layer in the deepwater area is at a depth of 5-IOm. The dome of cold water is formed over the deepwater part at a depth of more than 50 m, where water temperature is less

Sec. 1.3]

Characteristics of temperature and currents

21

than 4°C. From the beginning of July the gradual smoothing of temperature over the whole of the lake and a reduction of horizontal inhomogeneity is observed. According to average perennial data, at this time the transition of water temperature in the surface layer over 10°C takes place all over the lake; the so-called 'biological summer' begins. The biological summer is a period when surface water temperature steadily exceeds 10°C. On the basis of available data on surface-water temperature the 'biological summer' begins earlier in the shallow Zaonezhsky Bay, in early June. The delay period for biological summer in the deep central part of the lake is on average 30 days. The end of July-beginning of August is characterized by the greatest warming of the surface 5 m water layer. Mean surface water temperature reaches its maximum value; its distribution over the waterbody becomes rather homogeneous; the seasonal thermocline deepens to the depth of 15-25 m, depending on the lake region. In the first decade of August the autumn cooling starts, i.e, in the lake heat balance, losses prevail over heat income. In the near-surface layer the temperature inversion is formed, and that creates gravitational instability, destruction of stratification and formation of the surface quasi-homogeneous layer. The deepening rate of the mixed layer from August to October increases from 0.3 to 3.0mday-l. The thickness of the quasi-homogeneous layer with a temperature of 13°C equals 10m on 1 September. By 1 October this value increases to 20m, and water temperature decreases to 9.5°C. Maximum water temperature is registered at a depth of 0.1 m at the beginning of July-beginning of August, at a depth of 10m at the beginning of September, at a depth of 20m in the middle of September, at a depth of 50m in the first half of October; at a depth of 80m the maximum temperature, 6.6°C, is registered after 20 October. So the time delay of maximum temperature between the bottom layers and the surface layer in Lake Onego reaches 3 months. In the second half of October homothermy is established in the lake with a temperature of 6-8°C. The lake water cooling at this time happens gradually: the decrease of temperature throughout the water column occurs at a rate of about 0.1°C day ": On 1 November in the central part of the lake, homothermy with a temperature higher than 6°C is observed. In the coastal regions with depths up to 20 m, water temperature is, as a rule, below 5°C. In shallow near-coast areas, water cools at this time to 4°C, the temperature of maximum density. The 4°C isotherm slowly moves with water cooling to deepwater areas, leaving behind the regions with inverse temperature stratification, where water temperature is less than 4°C. The 4°C isotherm disappears on 22-25 of November. By 1 December in the surface layer of coastal regions the water temperature is 1.9-2.2°C; in the central part it is higher than 3°C. The ice appears on the lake on average between the second decade of November and the middle of December after a steady decrease of water temperature below 0.2°C and cooling of the surface layer down to freezing point. In some years, autumn ice phenomena are observed as early as the second half of October (1945, 1946, 1959, and 1968). Sometimes, for example in 1960-1961, complete ice cover is not formed, and wide polynyas to the south of the island of Mayachny and in Bolshoye Onego are observed (Fig. 1.4(c)). The maximum thickness of white ice at the end of the ice

22

The Great European Lakes: state of the art

[Ch. I

cover period exceeded one metre (104cm) near the village of Longasy in the third decade of April, 1956. The initial ice erosion stage on the lake is observed in the first decade of May (in the southern part of the lake, in the third decade of April), and at the latest by the middle of May; and ice destruction starts in narrow bays and skerries. Mean dates of ice clearance correspond to the second decade of May; in skerries and in the southern part of the lake it is the third decade of May. For the whole observation period, starting from 1884 and up to the present time, the tendency of the ice cover period to reduce has been registered at certain observation stations and all over the lake. For the ice-free period a positive trend has been observed (the coefficient of the linear trend is about 7 days per 100 years). Schematic zoning of depths in Lake Onego was carried out using statistical approach, suggested by Gusakov and Terzhevik (1992) for limnetic zoning of Lake Ladoga. According to this method, boundaries between limnetic zones are marked along isobaths with values of mean lake depth (15) and depths: (15 - So) and (15 + So), where So is the mean square-root deviation of the depth field. The

Fig. 1.8. Limnetic zones of Lake Onego (Lake Onego. At/as, 2009).

Sec. 1.3]

Characteristics of temperature and currents

23

statistical calculations for Lake Onego zoning were based on the grid (with a resolution of approximately one kilometre) built by S. F . Rudnev. As a result, the following values of statistical parameters were obtained: 15 = 30m and So = 20m. Thus, Lake Onego was divided into four depth zones: coastal, declinal (or slope), profundal (or deepwater) and ultraprofundal, morphometric feaures of which represent the most essential morphological peculiarities of the lake basin (Fig. 1.8).

1.3.2 Currents and circulations While the first long-term measurements of currents in Lakes Ladoga were made in the 1940s by specialists from Finland, the systematic study of thermal structure and circulation in Lakes Ladoga and Onego began only in the late 1950s (Tikhomirov, 1982). Shipborne observations of currents were realized by Okhlopkova (1966, 1972). The first moorings with current-meters were deployed in the middle of the 1960s, in Lakes Ladoga and Onego, and the results of numerous observations of currents and temperature variability were summarized by Boyarinov et ai. (1994) and Filatov (1983). The first maps of water mass circulations of Lakes Ladoga and Onego were presented by Okhlopkova (1972) Fig. 1.9.

Fig. 1.9. Geostrophic currents in the summer period: Lake Ladoga (a) and Onego (b) (Okhlopkova, 1966, 1972)

24

The Great European Lakes: state of the art

[Ch.l

Complex hydrological and meteorological data were collected in Lakes Ladoga and Onego during the last two decades and created a database for physical analysis and modelling experiments (Filatov, 1991; Beletsky et ai., 1994). Synoptic ship surveys were conducted during the periods of spring and autumn thermal bar formation and the full stratification period too. Long-term currents and temperature data were recorded using a network of buoys (ABS). The primary emphasis is given to the temporal and spatial variability of currents and temperature, numerical modelling of hydrophysical fields and model verification. The data on water temperature obtained during the 'Onego' experiment (Filatov et ai., 1990) have the best temporal and space resolution, compared with data collected on other large

II

..,

13

-(f-' /

it

I "

Fig. 1.10(a). Long-term observations of currents in Lake Ladoga averaged for all periods of observations 1969-1975. On the scheme is shown the number of ABS, the distributions of directions (a), the speed of currents (b) and the vector of the currents in ems"! (from Kondratyev and Filatov, 1999)

Sec. 1.3]

Characteristics of temperature and currents

25

lakes of the world. The synchronic ship surveys for Lake Onego were conducted during the period of one day and were repeated three times by three research vessels of the NWPI and the Institute of Limnology of RAS (Beletsky et ai., 1994). At the same time data were recorded using a network of buoy stations with currents and temperature measurements on several horizons (in the epi-, meta- and hypolimnion) together with remote sensing infrated airborne and satellite observations. These data were used for calibration, parameterization and 3D verification diagnostic and prognostic models for the Great European Lakes (Filatov, 1991; Beletsky et ai., 1994). The long-term multi-year observations of currents and water temperature on Lakes Ladoga and Onego were made at the end of the 1960s and in the early 1970s

[r

(b) Fig. 1.10(b). Water circulations in Lake Onego calculated from multi-year observations of currents averaged for the period 1969-1990 on 5-7m horizons . On the scheme is shown regions of the lake (1,2,3) and the number of observations (a), the distributions of directions (b) and the vector of the currents in cm S-1 (c) (Boyarinov and Rudnev, 1990).

26

The Great European Lakes: state of the art

[Ch.l

and the 1980s. The maximum length of the time series was up to 5 months with the time-step ranging from 10 to 30 minutes. These data allowed us to study the variability of currents and water temperature with characteristic timescales from several hours to 15 days. The data were averaged for all periods of observations (May-November) and showed that there exists a tendency to anticlockwise circulation in Lake Ladoga (Fig. 1.10(a)) and Lake Onego; but in Lake Onego integral circulation is more complicated them in Llake Ladoga due to complicated morphometry (Fig. 1.1O(b)). This kind of circulation in large lakes is characterized by the so-called 'climate' of currents. The spectra of currents for all points of measurement on anchored stations were calculated using the tensor analysis technique (Filatov, 1991). The frequencytemporal spectrum (linear-invariant) and bi-spectral of currents in Lake Ladoga illustrates the non-stationary character of the current variability (Kondratyev and Filatov, 1999). Analysis of currents showed spectrum transformations from nearshore to offshore regions and from depth of measurements. In Lakes Ladoga and Onego (Fig. 1.11), the spectral constituents with frequencies of 0.02 rad h- I (correspond to a timescale of about 2 weeks), 0.06-0.12 rad h- I (2-4 days), 0.24 rad h- I (1 day) and close to the inertial frequency corresponding to the latitude 61 N is 0.45 rad h- I (13.5 h) stand out more clearly. There are several peaks corresponding to the frequencies which are lower than the local inertial oscillations (period of about 13.5h). In the offshore regions, lowfrequency oscillations with periods from days to weeks are usually caused by largescale synoptic wind variations. In the coastal zone some low-frequency waves should also be taken into consideration; for example, it may be the manifestation of internal Kelvin waves and topographic waves which can be generated by wind and can persist long after the decrease of the initial wind impulse, causing the characteristic increase of the current velocity (Filatov et al., 2009). There is a pronounced peak in the 0

--

I

I}

Fig. 1.11. Spectrum of currents (I I-linear-invariant of tensor), (a) in the offshore zone of Lake Ladoga at metalimnion (1), at epilimnion (2), and at depths of 30 (3), 50 (4) and 70 (5) m and (b) spectrum of currents in the near-shore zone at horizons 10m (1) and 20m (2).

Sec. 1.3]

Characteristics of temperature and currents

27

current spectrum which corresponds to the frequency of the Poincare waves with local inertial oscillations (Fig. 1.11). This peak may be caused by the inertial oscillation of currents provoked by spatially inhomogeneous winds and also by the internal Poincare waves which dominate in large lakes at distances exceeding the internal Rossby radius of deformation (about 3-5 km from a shore). Maxima of energy of Poincare waves observed at the metalimnion (Fig. 1.II(a)). In Lakes Ladoga and Onego the lifetime of these motions does not exceed the duration of two or three inertial periods. The data of observations reveal large-scale current and temperature variability in both lakes with several energy peaks reflecting the lake's response to the atmospheric forcing and the lake's own system movements. This is the so-called 'weather' of hydrodynamical processes which follows atmospheric weather changes. The wind-induced coastal upwelling is among the main components of the mentioned hydrological weather in a lake. In response to the wind, coastal upwelling continually changes its strength and location, which can be most easily traced in the surface-temperature field. For numerical calculations of currents in Lakes Ladoga and Onego, over the thermal bar and full stratification period, a 3D nonlinear diagnostic model was used (Akopyan et al., 1984; Filatov, 1991; Beletsky et al., 1994); it had previously been used for ocean dynamics studies (Sarkisyan, 1977; Demin and Sarkisyan, 1977). The 3D diagnostic and prognostic circulation models for the description of meso- and macro-scale processes of Lakes Ladoga and Onego have a resolution in the horizontal plane of approximately 2-4 km; they were created by (Beletsky et al., 1994). Lake-wide circulation patterns typical for spring and summer conditions in two of the largest European lakes have been shown to depend heavily on the two important hydrodynamical processes: the thermal bar and wind-induced upwellings. Calculations showed that in spring when the thermal bar exists the circulation pattern is fairly regular. Lake-wide cyclonic circulation induced generally by the density gradients (geostrophic currents) occupies a narrow zone between the shore and the front of the thermal bar. Wind observations from meteorological stations around the lake reveal that at the early stages of the thermal bar a local atmospheric cyclone appears due to the sharp temperature gradients between the lake and the land surface. This cyclonic vorticity of the wind serves as an additional source of cyclonic circulation in the lake. In a closed waterbody with complex bottom relief, however, wind fluctuations cause topographic vortices, eddies, or circulations, or topographic Rossby waves (Csanady, 1977). Topographic waves have been considered for waterbodies with ideal shape. Allender and Saylor (1979) have described the generation of topographic waves in a lake of simple elliptic shape with a parabolic bottom. Calculations of topographic waves for several phases show that topographic motions normally have 'double-gyre' circulation. In Lake Ladoga, as an effect of the wind, there appeared signs of the development of motions with a tendency towards anticlockwise rotation. The main gyres fall apart and relatively small eddies with a horizontal size of the order of several kilometres are formed (Kondratyev et al., 1989; Kondratyev and Filatov, 1999). The difference in the bottom and shore slope between the western and the eastern parts of

28

The Great European Lakes: state of the art

[Ch.l

the lake caused a disagreement in the frequency of topographic waves and baroclinic Kelvin waves. Hence, topographic waves by the eastern shore left Kelvin waves 'behind'. In this case spectra of the currents show two energy maxima corresponding to the mentioned waves in the low-frequency scale. The data reveal large-scale current and temperature variability in both lakes with several energy peaks (Fig. 1.11), reflecting the lakes' response to the atmospheric forcing and their strong variability with a hydrological 'weather' scale. Bear in mind Mortimer's (1979) remarks about the 'underwater' weather, which follows atmospheric weather changes. The wind-induced coastal upwellings are among the main components of the abovementioned hydrological weather in Lakes Ladoga and Onego. In response to the wind, coastal upwellings continually change their strength and locations, which can be most easily traced in the surface-temperature field. In the case of especially strong winds, the area occupied by the cold upwelled water, can reach up to 30% of Lake Onego's surface (Filatov, 1991). In the evolution cycle of coastal upwelling, three main phases can be discerned: generation, steady-state and relaxation (Beletsky et al., 1994). Usually after a few hours of moderate wind forcing a double-gyre circulation becomes dominant in a large lake. The prominent features of double-gyre circulation are narrow coastal currents in the direction of the wind and a broad countercurrent in the deeper part of the lake (Bennet, 1974). With wind-induced upwelling, in the case of string winds the thermocline can reach the lake surface. This fact is vital for the lake ecosystem because of the enhancement of water exchange between the epilimnion and the hypolimnion and, as a consequence, the ventilation of the hypolimnion and the increased supply of nutrients to the epilimnion. After the cessation of the wind, upwelling relaxation begins. Following Csanady (1977), two types of relaxation event were identified (Beletsky et al., 1994). Type-l relaxation is characterized by simultaneous anticlockwise propagation of cold and warm temperature fronts and by the relevant coastal jet reversals around the lake. In contrast to Type-l , only one front moves in the case of the Type-2 relaxation. Mortimer (1963) was the first to discover such warm front propagation along the southern coast of Lake Michigan; later, another case of Type-2 relaxation was described for Lake Ontario (Simons and Schertzer, 1987). Near the eastern shore of Lake Onego the coastal jet structure is clearly seen; intense currents are also observed along the thermal front zone. The observations showed that the upwelling front moved along the eastern coast to the north, in the direction which coincided with the direction of Kelvin wave propagation. Diagnostic and prognostic model calculations have demonstrated that Type-2 relaxation leads to the enhancing of cyclonic circulation in Lake Onego (Fig. 1.12). The evolution of wind-induced upwellings has been described in Lake Onego with a focus on thermal front dynamics and circulation pattern changes (Beletsky et al., 1994). The effect of rivers on the formation of large-scale circulation in the summer period is negligible. Coastal streams observed in lakes are divided into jets and plumes. The former are jets which do not possess neutral buoyancy in relation to the

Sec. 1.3]

Characteristics of temperature and currents

29

Fig. 1.12. Results of prognostic calculations of (a) water temperature and (b) currents in Lake Onego (Beletsky et al., 1994).

lake water, but do have momentum; the latter are jets with positive buoyancy but zero momentum (Csanady, 1977). Jets and plumes can also be recorded by space imagery data. Jets in lakes may fall under the effect of being trapped by the shore. These circulations spread several kilometres into the lake with an anticlockwise direction of motion under the slight action of eddy diffusion, which is demonstrated by the appearance of the 'plume' in the space image. During the most intensive upwellings the dilution of sewage in this area is accompanied by the movement of sewage from the hypolimnion to the surface (Kondratyev and Filatov, 1999). Coastal upwelling in lakes was studied experimentally on Lake Onego by Bojarinov et al. (1994), on Lakes Ladoga and Onego by Filatov (1991), and on the Great American Lakes by Csanady (1977), Simons (1975, 1976), and Simons and Schertzer (1987). The basis for the study of upwelling in the lakes was mainly the data of long-term observations at moored buoy stations. Several types of upwelling were singled out: Ekman near-shore upwelling, flotation , and offshore upwelling in the centre of anticlockwise circulations with a dome kind of water-temperature structure. Remote sensing techniques with IR sensors have been used to study features of upwelling in Lakes Ladoga and Onego (Filatov et al., 1990). The average period of upwelling relaxation is less than the synoptic period . Therefore, simultaneous manifestations of upwelling by the western and eastern shores are quite rare. For Lake Ladoga, however, such cases have been recorded in the data of long-term remote sensing IR observations from the airborne laboratory of the Hydrometeorological Service for 1968-1992. The space remote sensing combined with ship-based observations and the results of modelling at upwellings in different lake zones allowed adjustment of the integral water circulation schemes obtained earlier to various hydrometeorological conditions. In hydrological spring and autumn periods

30 The Great European Lakes: state of the art

[Ch. I

during the presence of the thermal bar, Ekman near-shore upwellings do not appear in the lake (Fig. 1.13). Water circulations, however, are quite changeable, even when winds remain steady. Continuing water circulation is important for the formation of circulation under specific conditions, though sufficiently prolonged winds (up to 0.5 of the synoptic period) in certain directions quickly change water circulation. For the formation of Ekman near-shore upwellings these are northern and southern point winds. The period of upwelling relaxation is about two times shorter than the period of upwelling formation. Our estimates suggest that the speed of water rising and sinking was 10-2 and 5 x 10-2 cm/s respectively. Indirectly, the persistence of cyclonic circulation at the early stages of the thermal bar may be confirmed by analysis of the surface-temperature pattern. For this purpose we used remote sensing observations of Lakes Ladoga and Onego derived from an airborne laboratory, AN-28, and satellites equipped with infrared radiometers. As the observation indicate (Filatov et al., 1990; Filatov, 1991), wind-induced upwellings are practically absent until the stratified zone occupies less than approximately 40% of the surface area. Presumably cyclonic circulation can be persistent at that time in both lakes, even in the presence of strong winds (Fig. 1.13). Progressive warming of the lake during the summer leads to the advance of the thermal bar front into the deep part of Lake Ladoga and to the increased spatial extent of the stratified zone. Thermal gradients between the land and water become weaker and the local atmospheric cyclone vanishes; this makes lake-wide cyclonic (a

(b

.,

~

\~ v\~I

t

r

Fig. 1.13. Diagnostic scheme of integral circulations in Lake Ladoga (a) and Lake Onego (b) , locations of Ekman's near-shore upwelling zones (I-IV) for early spring with thermal bar (a), summer with thermal bar (b and c), period of full stratifications (d and e) and autumn (f) under the special directions of wind (2).

Sec. 1.3]

The cycle of substances in Lake Ladoga

31

circulation more and more responsive to wind fluctuations. In this period windinduced upwellings arise in the various parts of the lake. Wind-induced upwellings are also frequent during the full stratification period. Though cyclonic circulation remains typical, especially for the deep central and northern basins, local anticyclonic circulation connected with upwellings in the southern shallow part of the lake are frequently generated. Data of long-term observations (1965-1992) in Lake Onego were used to describe more than 50 cases in different zones of the lake. They sometimes are recorded simultaneously. The observations and modelling results show that no Ekman's upwelling occurs in the lake in the spring and autumn thermal bar period, and there is usually no total anticlockwise water circulation in the period of complete thermal stratification. At a climatic scale of the average of currents in the largest lakes of Europe the cyclonic circulation of waters dominates. In the winter phase when these lakes covered completely or partially by ice the circulation of waters is a very weak (less than 2cm s"), But on the Great American Lakes (Beletsky et al., 1999; Beletsky and Schwab, 2008a, b) the intensity of circulation of cyclonic character is higher in the winter phase than in the summer stratification period due to the joint effect of wind and bottom relief, and also density. This is a basic difference in the singularities of the hydrodynamics between the Great European and the Great American Lakes. 1.4 THE CYCLE OF SUBSTANCES IN LAKE LADOGA AND THE DYNAMICS OF ITS WATER ECOSYSTEM 1.4.1 Lake ecosystem phosphorus supply During the last 40 years Lake Ladoga has undergone the process of anthropogenic eutrophication. The rapid increase of phosphorus content in the lake water played the initial role in the evolution of its ecosystem. Natural surface waters of the temperate zone in the northern hemisphere are poor in phosphorus as a result of specific hydrochemical processes in conditions of higher humidity. From the three main components which are necessary for the construction of living substance by autotrophic organisms (the primary production) - phosphorus, nitrogen and carbon - the lake ecosystem is strictly limited only by phosphorus. Its transmission into the lake is exceptionally correlated with the discharge of tributaries (surface, underground runoff) and precipitation. A deficit of nitrogen and carbon in water is compensated by supply of these elements from the atmosphere as a result of gas exchange (carbon) and algal fixation. The ecological status of Lake Ladoga remained oligotrophic in the middle of the twentieth century and the low phosphorus water content was the limiting factor for the development of vital processes. Phosphorus income in the lake

Until the beginning of the 1960s river runoff phosphorus income in Lake Ladoga was 1790 t Pyear"! and, in total, including precipitation and industrial wastewaters,

32

The Great European Lakes: state of the art

[Ch. I

Fig. 1.14. Total phosphorus loading into Lake Ladoga for 1961-2006.

2430tPyeac l . The dynamics of phosphorus loading into the lake during the research period is shown in Fig. 1.14 (Lake Ladoga ... , 1992, Table 17, pp.78-79; Lake Ladoga .. . , 2002; Petro va et al., 2005; Rumyantsev and Drabkova, 2006; Raspletina, 1992). The main source of phosphorus supply was the Volkhov River, which drained waters, enriched by phosphorus easily dissolved from the sedimentary rocks of the lImen Lake catchment. The rapid changes in the lake phosphorus supply in the mid-1960s appeared to be related to the Volkhov River water composition. Sewage superphosphates waters from the Volkhov aluminium plant enriched with phosphorus compounds were discharged into the Volkhov River. The mean annual concentration of total phosphorus in the Volkhov River waters increased from 48l!gPI- 1 in 1959-1960 to 230 l!gPI- 1 in 1976-1979. Simultaneously, as a result of human activity in the catchment, total phosphorus concentration doubled in two other large tributaries of Lake Ladoga, the Svir River and the Burnaya River (Vuoksa). In numerous other small rivers of the Lake Ladoga catchment observed total phosphorus concentrations were 1.5-4 times higher. In general, the annual supply of phosphorus in the lake was 7100tP year"! during 1975-1983, and in 1982 it reached 8110t. Phosphorus loading decreased after 1983 and made up 6100tPyear- 1 for the period 1984-1990. The year 1991 appeared to be abnormal for that period as phosphorus income reached the value of 8200t P year:" . A much more noticeable decline of phosphorus loading to 3580tPyear- 1 on average was registered in 1996-2005 (Lake Ladoga ... , 2002; Petrova et al., 2005; Rumyantsev and Drabkova, 2006; Raspletina, 2006, personal communication) .

Sec. 1.4]

33

The cycle of substances in Lake Ladoga

Table. 1.2. Phosphorus concentrations in the waters of Lake Ladoga (averaged for the period of open waters) (J.lg Ptota11-1) (Raspletina, 1992; Raspletina and Susareva, 2002, p.77; Raspletina, 2006, personal communication). Limnic

zone I Coastal zone II Declinal zone III Profunda1 zone IV Ultraprofunda1 zone A111ake

1976- 1981- 1984- 1987- 1990- 1994- 1999 2000 2000- 2004 2005 2006 2003 1980 1983 1986 1989 1993 1998 46 27 28 24

37 27 22 22

32 24 21 22

31 23 20 20

43 21 19 19

23 17 16 17

26 27 22 16

24 21 21 21

20 18 16 16

20 16 12 12

18 17 13 12

17 15 13 12

26

23

22

21

20

17

22

21

17

13

13

13

Phosphorus concentrations over the waterbody increased rapidly as a result of mixing the contaminated waters of the Volkhov River into the dense circulation system with currents oriented from the south to the north along the eastern coast. The distribution of phosphorus concentrations conserved the general tendency of maximum values in Volkhov Bay and minimum values in the northern deep regions. Table 1.2 shows the distribution of total phosphorus concentrations within different lake regions (see Fig. 1.6) during the observed period of time, the gradual decline of its variability over the waterbody and some general decline of phosphorus content in the water column as a result of sedimentation (Lake Ladoga . . . , 1992; Lake Ladoga ... , 2002; Petrova et al., 2005; Rumyantsev and Drabkova, 2006; Raspletina, 2006, personal communication). The increase of phosphorus concentration in Lake Ladoga, the element that always limited the lake productivity level, accelerated the beginning of the next phase of anthropogenic eutrophication - primary production growth.

1.4.2 Phytoplankton in the Lake Ladoga ecosystem In large lakes, where pelagic prevails over littoral, such as in Lake Ladoga, the algal plankton community - phytoplankton - is the basic allochthonous organic matter producer. The succession of mass phytoplankton species composition in Lake Ladoga took place in two stages. Until the end of the 1960s the lake phytoplankton was typical for large, deep, cold-water, oligotrophic waterbodies. Diatomic algae prevailed there all through the year, forming quantity and biomass maxima during the spring. Four typical species were observed, all four of which were diatomic. In quantity dominants rarely exceeded 1 million cells per litre. Total species composition was diverse - 380 species and types. Besides diatomic algae, green and blue-green algae were observed, especially in summer. The increase in phosphorus concentration led to a rapid intensification of algal development and expansion of its mass representatives. The total species composition had changed a little, but the quantity of dominants reached millions and tens of millions cells per litre. By 1976

34 The Great European Lakes: state of the art

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22 dominant types were registered; 7 diatomic, 11 blue-green, 3 green and 1 yellowgreen algae were among them. In an annual cycle of phytoplankton development up to the 1960s in the coastal and declinal zones (zone I and zone II) three maxima were observed - the maximal in spring and the other two, lesser in magnitude, in summer and autumn. In the deep part of the lake, as a result of slow spring warming, only the summer-autumn maximum formed. The dates of seasonal succession of the most developed forms during the period of lake eutrophication remained the same. It derives from the fact that in large, deep lakes the dates are determined in general by the warming and cooling regimes of water masses in various parts of the waterbody. Spring plankton in the coastal and declinal zones, the development of which is observed when water temperature is below +8°C, remained almost entirely diatomic. In summer diatomic plankton were to a considerable extent replaced by representatives of the other groups, mainly by blue-green algae. In summer and autumn algal development in the coastal and declinal zones reached a magnitude comparable with the spring level. In deep zones only the summer maximum remained, but algal quantity at this period reached the values typical for shallower areas. Detailed analysis of the changes that took place in widely spread groups of algae during 1970-1990 makes it possible to draw a conclusion about the sequence and the regularity of phytoplankton succession. In the first considerable outbreak of algal development in 1970, when the quantity exceeded normal inter-annual variations, the dominant role was played by the most widespread species of the oligotrophic period: Aulacosira islandica in spring, Fragilaria crotonensis, Tribonema affine, Aphazimenon flosaquae and Woronichinia naegeliana in summer. Beginning in 1972 the dominant succession became obvious, marked by the mass development of Microcystis representatives in summer, and then, in late spring of 1975, Diatoma elongatum var. elongatum. New widely spread species belonged to algae that are common in eutrophic lakes. Among species that determined later the type of phytoplankton succession in the process of anthropogenic eutrophication of the lake, the typical inhabitants of an oligotrophic waterbody were: diatomic, Aulacosira islandica, Asterionella formosa, and Fragilaria crotonensis; yellow-green, Tribonema affine; and blue-green, Afazimenonflosaquae and Woronichinia naegeliana. To algae, the mass development of which usually occurs in eutrophic lakes, belonged: diatomic, Diatoma elongatum var. elongatum; and a number of blue-green algae from the genera Oscillatoria and Microcystis. The most typical representatives of bluegreens were Oscillatoria tenuis and Microcystis aeruginosa. Until 1980 the role of species typical for eutrophic waterbodies grew among both mass and episodically appearing algae. Phytoplankton reached the maximum diversity in 1981-1985. Low water temperatures limited the enrichment of spring dominant phytoplankton groups by new species. In the thermally active area of the coastal and declinal zones the most cold water species in Lake Ladoga, Aulacosira islandica, remained dominant. Its quantity varied from year to year but the tendency of growth was preserved. In early spring when the temperature is below +6°C Aulacosira was the only dominant and phytoplankton was almost monocultural. The traditional species plankton of the oligotrophic period in late spring and early

Sec. 1.4]

The cycle of substances in Lake Ladoga

35

summer, Asterionellaformosa, was displaced from summer to the late spring phase. Diatoma elongatum var. elongatum, the representative of eutrophic lakes, replenished the dominant group in the late spring stage. These diatom algae developed most intensively in 1980-1985. In the deep profundal and ultraprofundal zones of Lake Ladoga, spring phytoplankton growth starts only at the end of June; in July, Aulacosira vegetation lasts less than a month and complexes Asterionella or Asterionella-Diatoma appear during epilimnion formation, i.e. at the beginning of the hydrological summer. The dominance of Diatoma over Asterionella was also observed there until 1985. In summer blue-green algae typical of the eutrophication process (Oscillatoria in July and Microcystis in August) by 1985 almost completely replenished the former summer diatom complexes (Asterionella and Fragilaria). But, depending on weather conditions, their growth level fluctuated considerably. Starting from 1986-1987 a new stage of phytoplankton succession has begun. The species typical for eutrophic lakes were replenished by the former dominants of the oligotrophic period more distinguishably. The amount of Asterionella increased once more in spring. Afanizomenon flosaquae, the typical representative of Lake Ladoga plankton, became dominant in summer. The secondary succession of mass form became especially obvious in 1989, when Woronichinia naegeliana appeared and Tribonema affine growth rate increased rapidly. By 1994 Fragilaria crotonensis became dominant. The composition of Lake Ladoga phytoplankton dominant groups was restored and became the same as it was during the oligotrophic ecosystem stage in 1956-1963. Interpretation of the succession of widely spread phytoplankton species in the lake eutrophication process may be found in particularities of algae ecology. The special role of each plankton species is determined to a great extent by its productivity: an ability to reproduce in favourable conditions. At the same time, the need of different species for phosphorus, as the energy supply for their productivity and the development of the rate at which they consume phosphorus are constrained by the range of its concentrations. The determination of functional characteristics for particular species in Lake Ladoga was conducted experimentally by the autography method using carbon 14C and phosphorus p 33 isotopes (Gutelmacher and Petrova, 1982). Experimentally obtained values of carbon assimilation coefficients (CAC) and of phosphorus (F AC) per cell biomass unit characterize correspondingly individual productive abilities and the need for phosphorus of algal species. To a large degree these characteristics depend on species cell dimensions: the metabolism of small organisms is more active. Nevertheless they reflect evolutional features of species ecology. The least need in phosphorus supply (PAC) and the poorest productivity (CAC) are common for oligotrophic stage species, in conditions of restricted supply of biogenic elements supply. High values for these indicators are typical for mass algae of eutrophic waterbodies (Table 1.3). It is obvious that it is not that essential for species to belong to the same type: the need for phosphorus of the diatom Diatoma elongatum and yellow-green Tribonema affine is nearly equal. At the same time the consumption of these two species is higher than that of blue-green Afanizomenon and Woronichinia of the oligotrophic period, and is much less than that of blue-green algae typical of the eutrophic stage. The

36

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Table 1.3. Main ecological parameters of dominant species of plankton in Lake Ladoga. Species

Volume CAC of cell, 3 J.lm

FAC

CACI FAC

Water temperature in period of species growth, TOC

Aulacosira islandica Asterionella formosa Diatoma elongatum Fragilaria crotonensis Tribonema affine Oscillatoria tenuis Aphanizomenon flosaquae Microcystis aeruginosa Woronichinia naegeliana

4000

1.6

0.03

53

0.1-8

1010

2.7

0.05

54

5-20

80

640

17.3

1.09

16

6-20

70

1360

2.6

0.04

65

8-20

60

529 85 137

18.9 48.2 5.1

1.06 2.40 0.28

18 20 18

8-20 10-20 10-20

40 100 20

113

28.3

2.07

14

15-20

90

118

4.8

0.32

15

10-20

20

Reduction of production under wind > 10 mis, in % 60

ratio of CAC/FAC is an important characteristic and reflects the cell production per unit of phosphorus consumption. Observation data attest that species of the oligotrophic type, being content with lower phosphorus concentrations, use it twice as effectively as eutrophic type species. At the first stage of anthropogenic eutrophication the rapid increase of phosphorus supply is favourable for every waterbody species. Thus highly productive forms develop faster, driving less productive species aside. For algae consuming phosphorus in considerable quantities (Microcys tis, Oscillatoria) very high phosphorus concentrations are necessary for their mass development. During the maximum spreading period of their quantity the rate of phosphorus turnover reduces to several hours. That explains their appearance as the dominant group no earlier than the phosphorus concentration reaching 20-25 ug Ptotall-l. As the intensification of biological processes proceeds during eutrophication, the inner phosphorus cycle becomes more active at the expense not only of phytoplankton but also of bacterial consumption. Phosphates, composing nearly half of total phosphorus content in lake water, could be regarded as phosphorus available for algae consumption. Knowing the habitats and the dates of the expansion of particular seasonal algae complexes over the lake, mean and upper limit rates of their phosphorus consumption, the rate of phosphorus turnover in various parts of the lake can be estimated. Calculations, based on 1982 observation materials, have shown that the turnover time of biologically active phosphorus in the lake is about 2.5 days. In retrospective calculation for the oligotrophic period let us

Sec. 1.4]

The cycle of substances in Lake Ladoga

37

conclude that, despite the low phosphorus concentration in the water, its turnover was by one order of magnitude slower - 25 days. Hence, along with the development of the eutrophication process the phosphorus deficit appears for phosphorusdependent algae once again, but this time because of its intensive consumption by hydrobionts. Thus, after a period of eutrophic stage species prevalence, the inhabitants of oligotrophic lakes gain the advantage once more, since they consume phosphorus more conservatively and they are better adjusted to lower phosphorus concentrations. Alignment of vegetation period with low water temperatures and resistance to unfavourable weather conditions, especially to intensive wind mixing, are additional conditions of species competitiveness in large cold lakes such as Lake Ladoga. Spring diatoms Aulacosira and summer-autumn blue-greens Aphanizomenon and Woronichinia have these advantages in Lake Ladoga. In the earliest models of the Lake Ladoga ecosystem (Menshutkin and Vorobyeva, 1987; Leonov et al., 1991; Leonov et al., 1995; Astrakhantsev et al., 1992) phytoplankton was represented as a homogeneous biomass. Naturally this description is rather generalized and does not consider considerable differences of productive features and ecological peculiarities of mass species. These features determine the direction of succession among species and the final productivity of the algal community. The first step towards more detailed description of phytoplankton in Lake Ladoga ecosystem models was the division of phytoplankton into three ecological groups. Mass spring, cold water algae, mainly Aulacosira Islandica, formed the first group. Summer and summer-autumn diatoms and blue-greens, typical for the oligotrophic stage were included in the second group. The third group consisted of blue-greens, the new dominants whose ecological demands were formed in shallow eutrophic well heated lakes, rich in biogenic elements. Low rates of phosphorus (FAC) and carbon assimilation (CAC) and a considerable increase of production per unit of consumed phosphorus (CAC/ FAC) are typical for the first group. The second group species are better adjusted to high temperatures, but have a relation between phosphorus and carbon assimilation rates that is similar to that of the first group; they are both inhabitants of oligotrophic waterbodies. The species in the third group, typical for eutrophic lakes, became dominant in summer and autumn at the first stage of Lake Ladoga eutrophication. They need a high phosphorus concentration for mass development and their productivity is high. They produce less organic matter per unit of phosphorus consumed than oligotrophic stage species. Such a division of phytoplankton into three groups enables us to reproduce in the model the dynamics of the general production process during anthropogenic eutrophication of the lake. At the next stage of model development, in order to obtain a more realistic version of mass algae species succession, the main mechanism of phytoplankton community transformation, a more detailed description of algae was achieved by including, as an unknown variable, each seasonally dominant species.

38 The Great European Lakes: state of the art

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The total balance of organic matter from phytoplankton production (autochthonous) in Lake Ladoga at the beginning of eutrophication process was about half of its income from the catchment (allochthonous). Inter-annual variations due to different weather conditions were essential (on average, threefold). Under the influence of increased phosphorus supply, phytoplankton production by 1978 had risen by more than one order of magnitude. The value of phytoplankton primary production and mass species composition changed in two stages. During periods of eutrophic stage species prevalence, phytoplankton production for the vegetation period was on average 49 gCm- 2 (production load) and 353-2357 thousand tons C from the lake surface (1977-1985). The amount of autochthonous organic matter produced by phytoplankton became equal to the allochthonous organic matter that came from the catchment. When the prevailing role of traditional dominants in the phytoplankton community was restored (1986-1990) the production load also increased in some degree because of the more important role of the deep zones, on average, up to 76gCm-2 • The production for the vegetation period from the lake, 681-1636 thousand tons C, slightly decreased. The amount of autochthonous organic matter was approximately 1.5 times greater than the annual income of allochthonous organic matter. The increased rate of organic substance accumulation in the lake ecosystem was an important signal of the changes in the trophic status of the waterbody. According to measurements taken in 1996-1998 mainly during the summer period, the daily primary production of phytoplankton was approximately 200-400 g C m ? day"! (Lake Ladoga, 2000; Timakova and Tekanova, 2004, Tekanova and Timakova, 2007), that is close to the values observed in 1977, 1981, 1982 and 1988. In these years the total production for the vegetation period was within the limits 45-65 g C m-2 , and the amount of organic substances produced by phytoplankton was in the range from 800 to 1125 thousand tons of carbon from the lake surface.

Cryptophyte algae From the middle of 1980s the share of cryptophyte algae in Lake Ladoga phytoplankton has grown. These organisms attracted researchers' attention during studies of anthropogenic eutrophication mainly after more sophisticated optical research methods came into existence. In this connection the single-cell flagella species group was isolated, mostly from the pyrophyte algae, into the independent division of cryptophytes. Cryptophytes appear periodically in considerable amounts in all freshwater bodies of all trophic states (Stewart and Wetzel, 1986). Usually their mass development takes place between maxima of seasonal dominants, coinciding with peaks of bacterial destruction, which is probably linked with their mixotrophic nutrition type (utilization of the phosphorus supply along with phosphates, compounds of low molecular fractions of organic matter). Unfortunately, the absence of data on the functional characteristics of the species (individual values of phosphorus assimilation rates from different sources, their carbon assimilation rate and also the carbon forms available for this group) does not allow us yet to define

Sec. 1.4]

The cycle of substances in Lake Ladoga

39

their input in primary production, and, possibly, destruction, of organic matter in model simulations. 1.4.3 Bacterioplankton, water fungi and destruction processes Bacterioplankton is the main biological community that carries out organic matter mineralization process (destruction) and recurrence of biogenic elements in the lake's turnover. Lake Ladoga in the 1960swas an oligotrophic waterbody with a low level of bacterioplankton development homogeneously distributed over the waterbody. Higher bacterial quantities were registered only in the northwestern part of the lake near to the Priozersk paper pulp mill. The level of bacterioplankton development by the 1980s had tripled in the southern coastal part of the lake and doubled in its deep regions. In 1977-1987 mean annual bacterial total amounts increased from 400 to 800 thousand cells ml"! in the epilimnion and from 200 to 400 thousand cells ml"! in the hypolimnion. Bacterial amounts reach two maxima in a yearly cycle: a spring maximum, a little higher, in May, and a summer maximum in August. The spring maximum is mainly related to the inflow of floodwaters enriched with organic matter from the catchment and summer one to the period of maximum phytoplankton development. The greatest bacterial development in the hypolimnion is registered from July to October without distinct maxima. Inter-annual fluctuations of bacterial amount occur in the epilimnion and they gradually grew in the period 1970-1990. Mean bacterial production, derived from experimentally determined carbon heterotrophic assimilation, during 1981-1987 for the whole Lake Ladoga in spring was 143.9-292.6 thousand tons C; in summer it was 48.1-765.8 thousand tons C; and in autumn 41.1-1704.8 thousand tons C. The deep regions have the major role in producing bacterial organic matter in the lake. Bacterial production of the deep areas, especially in summer, exceeded phytoplankton primary production. In balanced lake ecosystems, bacterial production usually is 3-5 times lower than phytoplankton primary production. It seems that, during the period of anthropogenic eutrophication in Lake Ladoga, the abovementioned ratio is one of the essential indicators of destabilization of the lake ecosystem Aleksandrova, 1973. Organic matter destruction by bacterioplankton in Lake Ladoga in 1981-1987 was 24-94% of its total biochemical transformation (70% in general). Microorganisms mineralized 1.5-3.7 times more organic matter than was produced by phytoplankton. The total bacterial destruction during the period of open water in the lake volume made up 855.5-3375.2 thousand tons C, including 315.8-945.7 thousand tons C in spring, 151.3-2376.5 thousand tons C in summer, and 131.61535.2 thousand tons C in autumn. The autumn of 1985 was especially rich in phytoplankton (5502 thousand tons C). Unfortunately destruction for the whole vegetation period was not estimated because of the lack of spring observations, but in the summer and autumn period its value was 7074 thousand tons C. The value of bacterial destruction during the vegetation period in the lake water volume after 1981 exceeded the total amount of annual phytoplankton primary production and allochthonous organic matter from the catchment. Thus the

40

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heterotrophic component of the lake energy budget exceeded autotrophic component, and that was an essential point in ecosystem reconstruction. According to 1990s data (Lake Ladoga ... , 2002), the amount of bacterial destruction was 45-92% of the total biochemical transformation of organic matter (on average 68%); in other words it did not decrease, compared with the previous decade, though the phosphorus load into the lake declined. Fungi

Beginning from 1978 a new group of organic matter destructors, water fungi, was registered in Lake Ladoga (Qureshi and Dudka, 1974; Pourroit and Meybeck, 1995). Initially mass development of micoflora was observed in the southern area of the lake after the spring maximum of diatomic algae. Later, in summer 1986, fungi appeared continually in all lake zones and their maximum quantity equalled 32 500 diaspore per litre in the profundal zone. Experimental studies of comparative bacterial and fungi input in heterotrophic carbon assimilation revealed that in March, in the northern deep part of the lake, fungi assimilated 0.02-0.29 ug C 1-1 day"! and bacteria - 0.06-0.27 ug C 1-1 day", In August these values were 0.04-0.21 ug C 1-1 day"! and 0.01-0.81 ug C 1-1 day"! respectively. Carbon assimilation by fungi prevailed in the bottom water layers and coastal shallow areas; assimilation by bacteria prevailed in tghe summer epilimnion. The intensive water fungi development in Lake Ladoga and other large lakes was registered only during only the period of anthropogenic eutrophication. Fungi are capable of deep transformation of the most conservative components of dissolved organic matter. Regeneration and phosphorus consumption by bacteria

The process of organic matter destruction is accompanied by phosphorus regeneration. Using personal experimental data T. N. Maslevtseva (Lake Ladoga ... , 1992) estimated phosphorus regeneration in the process of destruction by heterotrophic organisms in Lake Ladoga at 1725 thousand tons a year. The rate of phosphorus consumption by bacteria in Lake Ladoga, according to experimental records in 1987-1989, varied over a wide range. It changed from 0.4 JlgPl- 1 min"! in June (water temperature 24.4°C) to 0.001 JlgPl- 1 min"! in September (water temperature 10.2°C). The rate of phosphorus consumption by bacteria is probably related to their amount, to the water temperature and to the supply of biologically available mineral phosphorus. The spatial distribution of phosphorus consumption rates by bacteria was usually in proportion to the change of these parameters. The rate of phosphorus consumption by bacteria in the dark was one order of magnitude less than during daylight. Such rates in May in the coastal and declinal zones were 0.003-0.050 ug P 1-1 min-I, and 0.010-0.040 ug P 1-1 min"! in profundal zones. The value varied in June in two shallow zones from 0.001 to 0.100JlgPl- 1 min"! and in profundal zone it was 0.0004-0.013 JlgPl- 1 min-I. The rate constants changed within the range 0.006-0.140min- 1 • The maximum intensive phosphorus

Sec. 1.4]

The cycle of substances in Lake Ladoga

41

turnover was registered more often in July: the turnover period was 2-9 min. In most cases it was the same in May and in July: 20-100min. 1.4.4

Zooplankton

Zooplankton diversity in Lake Ladoga usually consists of lake species common in northernwestern Russia and widespread in the temperate zone of the northern hemisphere. By now, more than 370 zooplankton species are registered in Lake Ladoga. The main groups are rotifers (Rotatoria), protista (Protozoa), cladocerans (Cladocera), and copepods (Copepoda). The general plankton composition, as a mass species group, has not changed since the first half of the twentieth century. But essential changes have taken place in the quantitative composition of particular species and systematic groups, typical in the process of anthropogenic eutrophication. By 1976 the role of rotifers, both in quantity and in biomass, increased by 2.5 times; for cladocerans that was by 2 times. The ratio of copepods in plankton decreased from 24% to 20% in quantity and from 45% to 40% in biomass. Zooplankton distribution over the lake is defined by a number of factors and the most important among them is the depth and water mass dynamics determined by peculiarities of the thermal regime. Zooplankton quantity in early summer is related to the development of rotifers, in August to cladocerans, and in September to copepods. The maximum values of zooplankters quantity and biomass in the coastal zone exceeded 600 thousand specimens m" and 13 gm-2 , and in the profundal zone 400 thousand specimens m -3 and 17 g m -2. The role of zooplankton in the functioning of an ecosystem depends on the differences in zooplankter nutrition. According to nutrition type, zooplankton organisms are divided into two groups: those that consume phytoplankton filtrators and detritus particles with bacteria living on them, and those that are predators. Some species at different age stages switch to another type of nutrition: young individuals are filtrators and adults are predators. Filtrators have a greater degree of influence on biological and biochemical ecological cycles, compared with predators, due to huge amounts of filtrated water in the process of nutrition. The features, characterizing the role of zooplankton in ecosystem processes, are the rate of nutrition (food allowance) and the volume of filtrated water, which is related to the quantity of nutrition consumed and to its concentration. The limiting factor is nutrient electivity which is more frequently related to the dimensions of zooplankters and their nutrient objects. Particles of the scale fraction of 20-40 urn are those most available to zooplankters (Gutelmacher, 1988). Comparing filtrators' nutritional composition with the primary production of the lakes allows us to estimate the ratio of primary production in the food chain of a waterbody. The value of the primary production consumed by zooplankton is in reverse proportion to the primary production of the waterbody. It is nearly 40% in oligotrophic lakes and decreases to 4-8% in eutrophic lakes or in those undergoing the eutrophication stage. According to publications, zooplankton in Lake Ladoga during 1977-1988 in various limnic zones consumed from 3.9% to 22% of the primary production (Gutelmacher, 1988).

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Knowing the productivity of Lake Ladoga zooplankton makes it possible to estimate calculations based on 1977-1981 data (Smirnova, 1988). The mean value of filtrators' production during the vegetation period in the coastal zone was 75-80gCm-2 , and in the profundal zone was 120-192gCm-2 • At the same time primary production of predators decreased noticeably: in the coastal zone from 47 gCm- 2 to 19g Cm-2 , and in the profundal zone from 48 g Cm-2 to 12 g Cm v'. The reduction of the predators' contribution to plankton reconstruction is typical during the process of anthropogenic eutrophication. The phosphorus excretion rate by crustacean plankton in spring was 108 J,.lgPm-2 day" (coastal zone) and 204 J,.lgPm-2 day"! (profundal zone). The role of summer zooplankton in the phosphorus cycle was considerably larger: from 2022J,.lgPm- 2 (ultraprofundal zone) to 5000 J,.lgPm-2 day"! (declinal zone). Crustacean phosphorus excretion in autumn was nearly the same as in spring, but in deep zones (8301538J,.lgPm-2day-l) was much higher than in shallow ones (107-217J,.lgPm- 2 day"), Calculations accomplished in July 1987 were based on the same method (Smirnova, 1988) and the value for a day's phosphorus excretion by zooplankton (filtrators and predators) was obtained varying from 0.3 to 315 J,.lgPm-2 day" The author estimated the phosphorus quantity being returned to the lake cycle from zooplankton during the vegetation period as 2.9 thousand tons.

1.4.5 The role of the zoobenthos in the ecosystem The zoobenthos is the animals living on the bottom of the waterbody: protista (protozoa), worms, sponges, molluscs, crustaceans and the larvae of insects. The zoobenthos is divided currently into the meiobenthos and the macrobenthos. The lake meiobenthos is composed of small organisms with a body size 0.3-4.0mm and weights up to 1-2 mg. Among them exist permanently meiobenthic (nematodes, ostracods, garpacticids, bottom Cyclopes, tartigrades and so on) and also the bottom stages of zooplankters, for example, planktonic Cyclopes. Nematodes and inferior crustaceans play an important role in the Lake Ladoga meiobenthos, larvae of Hironomids and Oligochaetes are the most important among the electively meiobenthic. The size of the lake macrobenthos varies from a few millimetres to centimetres. The major systematic groups are Oligochaetes, Hironomids, Hammarids and Molluscs. Oligochaetes prevail in Lake Ladoga at depths of more than a hundred metres. At lower depths various fauna of Oligochaetes, Hammarids, Hironomids and Molluscs could be found with Hammarids prevailing by biomass. Benthic animals live on the surface or in the upper layer of the lake sediments. Prey and predators can be found among them. Prey zoobenthos feeds mainly on detritus or fine silt particles of bottom sediments. The shallow areas of the waterbody are rich in benthic fauna that could be explained by the variety of bottom types, better heating of the water column, the abundance of phytoplankton that die off yielding then a detritus rich in organic substance. The poverty of benthic communities in the central deep areas of large lakes is characterized by monotonous bottoms and two other important factors. Detritus, which is formed in the

Sec. 1.4]

The cycle of substances in Lake Ladoga

43

epilimnion as a result of phytoplankton die-off, to a large extent is mineralized by bacterioplankton and zooplankton during the lake summer stratification. It reaches the hypolimnion and the bottom impoverished in organic matter, which is vital for benthic animals. Besides, the larvae of insects (Hironomids) cannot survive in the deep and have moved off the shore regions of the lake bottom, as favourable conditions are required for the imago. That is why Oligochaetes predominate at depths of more than 100m. The most intensive development of meiobenthos organisms in Lake Ladoga is registered in the coastal zone, especially within the littoral zone: up to 600 thousand specimens m ? and a biomass of7.5 gm-2 • There is less intensive development in the profundal zone: up to 200 thousand specimens m ? and a biomass of 6.5 gm- 2 (Kurashov, 2002). Maximum values of quantity and macrobenthos biomass are in the declinal zone: about 700 thousand specimens m ? and biomass of 23 gm- 2 , while in the profundal and ultraprofundal zones they did not exceed 850 specimens m ? and a biomass of 2.2gm-2 • The functional characteristics of meiobenthos and macrobenthos in Lake Ladoga were compared by Kurashov (1994, 2002) in order to estimate the role of each community in the lake ecosystem. The calculations show that, in energy equivalent for the whole lake, benthos produces during June-September 33.49 kJ m-2 , including for macrobenthos 22.31 kJm- 2 and meiobenthos 11.18kJm-2 (1 gC corresponds to 39.49 kJ/m2) . The benthic community consumes 223.93 kJ m ? (macrobenthos 124.18kJm-2 , meiobenthos 99.7kJm-2) . During respiration 88.99kJm-2 is dissipated (45.83 kJm- 2 by macrobenthos and 43.16 kJm- 2 by meiobenthos). The highest mean value of the ratio between the meiobenthos and macrobenthos productions is registered in the coastal zone: 109.8%; the lowest is registered in the ultraprofundal: 13.2%. The relation of the respiration consumptions of the two benthic communities, describing their participation in the transformation of organic matter and energy in these zones is, respectively, 177% and 32% (1 gC is equivalent to 39.22kJ). On average for the whole lake meiobenthos production is 50%, and its respiration value is 94%, of macrobenthos production. Again, averaged over the lake, benthos production was 1.6% of the primary production and 2.4% of bacterial destruction. It follows that the meiobenthos consumes 4.7% of phytoplankton production and 6.9% of bacterioplankton production and the macrobenthos 5.9% and 8.6% respectively. In the lake phosphorus turnover zoobenthos plays a visible role (Kurashov, 1994). Since released mineral phosphorus is one of the final products of the water animal's metabolism, the release rate can be estimated using the energy exchange rate (Gutelmacher, 1988). Thus, the value of phosphorus excretion for benthic organisms is estimated indirectly by estimating energy expenditures on respiration. Mean values of phosphorus excretion by zoobenthos of Lake Ladoga during one season (May-October, 180 days) were equal to 366 tons for the coastal zone, 299.2 tons for the declinal zone, 52.8 tons for for the profundal zone, 11 tons for the ultraprofundal zone and 719 tons for the whole waterbody (Kurashov, 1994). Special attention should be paid to data obtained by E. A. Kurashov about essential changes in species composition and the values of meiobenthic community biomass in the profundal and ultraprofundal zones, started in 1998 and clearly seen

44

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in 1999-2000 (Lake Ladoga ... , 2002). The author noted the appearance in Lake Ladoga bottom deep water areas of mass diapaused copepodites concentrations of planktonic Cyclops, typical for large lakes only, when they undergo long-term and heavy anthropogenic impact, as in Lake Constance (Bodensee). Such radical meiobenthos structure change in deepwater areas is a new manifestation of the anthropogenic eutrophication, in this instance in one of the most conservative biotopes of the lake ecosystem. 1.4.6

Dissolved organic matter

A pool of dissolved organic matter is a buffer system, which is able to accumulate different compounds and return them under various conditions in the lake turnover. Hence, dissolved organic matter is an important element, sustaining the lake ecosystem stability. In lakes with low productivity the income of allochthonous organic matter often prevails, especially when inflowing waters have a high humic content. Although it was accepted for a long time that only 1-10% of allochthonous organic matter can be used and decomposed by bacteria, there are numerous evidences of its participation and even dominance in biological carbon cycles in humic lakes. Bacterial utilization of allochthonous organic carbon, according to the opinion of a number of authors, should be considered separately as a mobilization of energy from an external source, by analogy with photosynthesis (Jones, 1992; Jansson et al., 2003). Bacterial energy mobilization dominates not only in coloured lakes but also in lakes with high water transparency (Karlsson et al., 2002). The content of organic matter in lake water is usually estimated by the concentration of the 'total organic carbon' (TOC). For a long time it was constant in Lake Ladoga, about 7536 thousand tons of C in the lake volume from 1956-1963 until 1981. The average concentration fluctuated over seasons in 1976-1979 within 8.1-13.7mgCl- 1 in shallow areas and within 8.2-10.4mgCl- 1 in deep areas; but the mean magnitude for the lake remained constant (8.3 mg C 1-1). The first rapid decline in these values was recorded in summer 1981, when TOC concentration in two deep zones was equal to 4.4mgCl- l . This determined the general reduction of organic carbon in the lake to 5811 thousand tons. That was the year, when organic matter destruction dominated in the Lake Ladoga ecosystem; it was associated not only with bacterial activity but also with the showing up of mass water fungi, especially in the winter period. In 1983-1984 the kinetic curves of biochemical oxygen consumption changed radically; that also testified that the species composition of organisms - destructors of organic matter - had changed. According to the experimental data ofT. M. Tregubova and T. P. Kulish the transformation degree of lake organic matter increased (Lake Ladoga . . . , 1992). In succeeding years both seasonal variations of TOC in all lake areas and changes of the total carbon store became constant. In 1983-1985 total storage of TOC in the lake grew considerably, that could be explained by maximum summer phytoplankton activity in deep water areas and was equal to 8263-8626 thousand tons. The next, more extended, period

Sec. 1.4]

The cycle of substances in Lake Ladoga

45

of low organic carbon content in lake waters was formed by 1988 and continued until 2000. This period was characterized by minimum low limits of TOC seasonal variations in all areas (4.9-18.8mgCI- 1 in shallow parts and 3.4-11.8mgCI- 1 in deep areas), and the storage in the lake volume was equal 5266-7536 thousand tons. In 2001-2003 the maximum upper limits of TOC concentrations in the lake (8.530.4mgCI- 1 in shallow areas and 7.3-30.0mgCI- 1 in deep areas) promoted the maximum storage of organic matter generation in the lake ecosystem, equal to 9080 thousand tons in 2003. In the years 2004-2007 the TOC amount decreased in the lake from 7627 thousand tons C to 5993 thousand tons in 2006 and to 6447 thousand tons C in 2007. Such high inter-annual variations of organic matter accumulation rates, non-inherent in large lakes, indicated severe ecosystem destabilization. Conservative fraction of dissolved organic matter - water humic substance

Lake Ladoga studies have shown that more than 80% of total organic carbon is bound to a conservative fraction of DOC - water humic substance (Korkishko et al., 2002). It was shown that nowadays water humic substance is more actively entrained into the organic carbon cycle compared to the period before the anthropogenic eutrophication. Water humic substance is a unified, highly molecular complex, including besides carbon, a large amount of the biogenic elements contained in lake waters. According to experimental studies the humic substance coming to Lake Ladoga with inflow waters is in a maximum recovered form and the level of its oxidation does not exceed 3-10%. But in deep parts of the lake the oxidation level of humic substance can reach 70-75% and that points to its oxidation in lakes. The transformation process is accompanied by changes in the element composition of humic substance, particularly as the result of a decrease in the phosphorus content per carbon unit (in atomic equivalent, by 2-5 times). Experimental data make it possible to conclude that, although high molecular humic complex, inflowing with tributaries is subjected to a biochemical oxidation less than 10%, this process is accompanied by the disruption of chemical links and further generation of humic substance with lower molecular mass and low-level molecular compounds. A part of the biogenic elements is converted into the low-level molecular fraction of humic substance. Later this fraction can be subjected to biocatalytic oxidation by lake organisms, possessing peroxidized and catalysed activity, and that facilitates the return of biogenic matter, including phosphorus, to the lake turnover. As was mentioned earlier, intensive phytoplankton development in the process of anthropogenic eutrophication led to an increase in the consumption rate by this community by only an order of magnitude as compared with the lake oligotrophic stage. More phosphorus is needed by destructors, especially bacterioplankton. The internal phosphorus deficit in biologically available form stimulates the emergence of organisms' communities capable of the biocatalytic decomposition of the molecular fractions of low-level humic complexes, at the same time drawing into lake turnover a part of the conservative organic matter. Lifetime phytoplankton excretions also possess biocatalytic activity, and the higher the primary production level, the greater their role in the lake processes. As a result, the pool of biologically available

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phosphorus grows, sustaining further development of autochthonous organic matter production and allochthonous matter destruction. The studies conducted in 1995-1999 have shown that the relative content of humic substance high-level molecular fraction in Lake Ladoga was sufficiently stable, at 85-95% of TOC level. By 2003 the amplitude of spatial-temporal variations increased by 36-97%. Up to 64% of dissolved organic matter as low-level molecular fraction was transferred into the lake turnover during different seasons in the coastal zone; in profundal zone, up to 51%; in the ultraprofundalzone, up to 27%. This proves the existence of at least two- to three-fold acceleration of carbon and, hence, of phosphorus cycles in the lake processes, and explains the absence of the expected phytoplankton productivity reduction under conditions of permissible phosphorus loading (petrova et al., 2005). According to standard station measurements of a longitudinal section of Lake Ladoga in 2003-2007, the of low-level molecular fraction of organic matter in the lake volume was: in spring (May-beginning of June), about 2 thousand tons C; and in summer (July-August), 3.2-4.5 thousand tons C. Probably because of its entrainment; the total amount of dissolved organic matter in the lake at that time varied from 5993 to 9080 thousand tons C. Changes in the ratio between carbon and phosphorus in the high-level molecular fraction of humic substance during its transformation in the lake enable us to estimate the quantity of phosphorus transferred to the low molecular fraction, i.e., to biologically available forms. It should be, during the period 2003-2007, in spring for the whole lake, 2-6 thousand tons of phosphorus; in summer, 6-9 thousand tons; in autumn, 2.5-8 thousand tons; while the general storage of total phosphorus in Lake Ladoga was estimated at 12 thousand tons in 2003 and at 10 thousand tons in 2007.

1.4.7 The role of seston and bottom sediments in the lake phosphorus cycle Generation of seston

Generation of seston (suspended matter) in water column of Lake Ladoga, sedimentation and transformation rates were studied in 1987-1988 in two small bays. The materials collected during these experiments showed the dynamics of seston and its components, particularly phosphorus, during sedimentation to the bottom layers. The concentration of total phosphorus in suspended solids increased from 6 to 32JlgPI- I , and, in the hypolimnion, from 6 to 59 JlgPI- I . Very high concentrations were recorded at the beginning of October - up to 119 JlgPI- I . The accumulation rate of phosphorus in seston was, in the epilimnion, 6.2-12 JlgPm- 2 day", and in the hypolimnion, 13-17JlgPm-2 day", The average seston sedimentation rate was 1-6.6mg (m- 2 day") in the epilimnion and 3.7-20 mg m ? day"! in the hypolimnion. In the epilimnion seston has a high content of labile organic matter; in the hypolimnion it is already transformed considerably, containing mainly mineralized phosphorus compounds.

Sec. 1.4]

The cycle of substances in Lake Onego and its water ecosystem 47

Transport of substances through the water - bottom interface

The diffusive flux exists practically all the time, but it becomes the main transport mechanism only in anaerobic conditions during the stagnation period (Ignatyeva, 1997). In aerobic conditions convective transfer plays the main role in the transport of phosphorus from the bottom sediments to the water. In modern conditions Lake Ladoga sediments are formed mainly by suspended solids of autochthonous origin. The role of allochthonous substances is essential only in the coastal zone. The modern sedimentation rate for the larger part of the lake is small: from 0.06 mm year" in the southern sandy shallow part to 0.5-0.6 mm year" in the area of maximum depth in the profundal and ultraprofundal zones. Income ofphosphorus

The income of phosphorus to the bottom sediments takes place basically as a component of organic compounds. The weight ratio C :P in the organic matter of the upper layer of bottom sediments is 40 : 90. The average phosphorus accumulation rate in bottom sediments in different lake zones is: in the coastal areas, 0.46 mg P day"; in the declinal zone, 0.59; in the profundal zone, 0.39; in the ultraprofundal zone, 0.70mgPday-l. The annual income of phosphorus to the bottom sediments in the different zones is 620, 1140, 830 and 760 tons year-I, respectively, in total 3350 tons over the whole lake. The declinal zone is the place of initial accumulation and mineralization of organic substances in the hypolimnion. The average proportion of buried phosphorus for the whole lake from its influx to the bottom is 74% or 2475 tons annually. The declinal zone and the shallower parts of the profundal zone are the main regions where mineral layers in bottom sediments are formed. They are not only accumulating phosphorus but also become the barrier in the path of vertical diffusion of phosphorus. The phosphorus sedimentation is 56% of the external phosphorus load, and dumping is 41%. Calculation of the phosphorus flux from bottom sediments showed that its mean value for the lake is 0.13mgPm-2 day-lor 0.05gPm-2year- l, 875 tons of phosphorus is released annually from the bottom sediments of Lake Ladoga (coastal zone, 155, declinal, 285, profundal, 215, ultraprofundal, 220 tons year-I). The calculated value of phosphorus released from bottom sediments is 26% of its sedimentation and 15% of the external phosphorus load. Part of the released phosphorus is transported to the trophogenic layer and can be used for phytoplankton primary production; the remaining phosphorus, staying in the hypolimnion, can be utilized by microorganisms (Ignatyeva, 1997).

1.5 THE CYCLE OF SUBSTANCES IN LAKE ONEGO AND ITS WATER ECOSYSTEM The distribution and the rate of anthropogenic eutrophication differ in Lakes Ladoga and Onego. In Lake Onego, with its more complicated morphometry and

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water current structure, the distribution of the phosphorus which is brought into the lake by tributaries and which comes directly from industrial and community wastewaters is not involved in the lake-wide cycle as in Lake Ladoga. Water enrichment with phosphorus up to the levels triggering the enhancement of eutrophication takes place, as a rule, in the bays, which is where the tributaries and waste waters are received. 1.5.1

The phosphorus supply to the Lake Onego ecosystem

River inflow is the main source of phosphorus income both for Lake Onego and Lake Ladoga. The prevailing role belongs to three main tributaries - the Shuya River, the Vodla River and the Suna River, that bring altogether about 90% of the biogenic influx from the catchment area; the input of other rivers, inflowing from the southeast to the lake is less essential (Lozovik et ai., 2006; Lozovik and Raspletina, 1999; Pirozhkova 1990). The phosphorus loading that came via the main tributaries varied insignificantly from 1980 till the middle of 1990 and depended mainly on the dryness of the year (Fig. 1.15). A considerable decline in phosphorus content in the main tributaries was observed during the second half of the 1990s, due to the economic crisis in the country, when the usage of mineral fertilizers in agriculture and, as a result, biogenic matter washout reduced significantly. After the year 2000 the total phosphorus transport via the tributaries equalled 441 tons. Industrial and communal waters of enterprises located in the coastal area in this case are of less importance. Their share of Ptotal is 174 tons annually.

p

tons

1100

1000 900

800 700

600 500

400

960

965970

9751980 -1985 '1990 '1995 2000 2005 2010

Fig. 1.15. Total phosphorus loading (tons per year) to Lake Onego for 1963-2006.

Sec. 1.5]

The cycle of substances in Lake Onego and its water ecosystem 49

Phosphorus contained in industrial sewage waters distinctively influences water composition in the lake's large bays. It is determined by phosphorus load value and the intensity of water exchange in the bays and the lake pelagial part of the lake. Povenetsky Bay receives a small amount of phosphorus from Medvezhyegorsk city wastewaters compared with the other bays. Phosphorus concentration in the bay waters has not varied much in recent decades and equals on average 10.1 JlgPI- I. Wastewater phosphorus there is partially buried in silts, and its content in the coastal zone slightly increases (Belkina, 2003; Belkina et al., 2006). The process of anthropogenic eutrophication is apparently not revealed here. The wastewaters of Petrozavodsk city, communal ones mainly, treated biologically, enrich the bay waters and the contiguous lake areas with phosphorus. A sharp increase in phosphorus loading in Petrozavodsk Bay began in the 1980s as a result of the intensification of agriculture and forestry and of population growth in the lake catchment. By the middle of the 1990s the total anthropogenic phosphorus, Ptotah impact was on average 2.7 gm-2 and the natural phosphorus (via tributaries) was 1.2 g m ? annually. The total phosphorus income to Petrozavodsk Bay from the catchment itself was at that time 333 tons year": The situation has changed drastically since the late 1990s: P total income via tributaries was 111 tons year-I, and from sewage waters was 103.6 tons year"! and 214.6 tons year"! annually in total (Sabylina, 2007). Nowadays the total phosphorus income from the lake catchment and with Petrozavodsk city wastewaters is estimated to equal 223.8 tons year" for Petrozavodsk Bay, which permits us to consider Petrozavodsk Bay to be the main phosphorus supplier to the central lake areas. Mean annual Ptotal concentration in Petrozavodsk Bay waters equalled 25 JlgPI- I in the 1980s; it declined to 17 JlgPI- I in 1990s and was recorded to be 20 JlgPI- I in 2000-2007. Intensive water exchange between Petrozavodsk Bay and the central lake areas is determined both by the basin structure, with its gradual decline towards the deep regions, and also by the tributaries efficient water volume, 3.09 krrr' year" (Filatov et al., 2006). The water exchange period equals 14-20 days during the summer period, rehabilitating the bay water quality, and, in particular, reducing the phosphorus concentration in the water. Wastewaters flowing into Kondopoga Bay in the water, specified as organomineral, contain a large amount of suspended matter. According to the degree of phosphorus supply coming in with the sewage waters, the bay water composition differs crucially from that of other lake regions. The incoming over several decades the amount of phosphorus coming into the bay varied in accordance with the production volumes of, and environmental measures taken by, the local paper-mill. Phosphorus carry-over grew considerably at the beginning of the 1980s, and rather rapidly after the launch of the first turn of biological refining station at the Kondopoga paper-mill plant, and at that point the phosphorus load due to tributary inflow was exceeded. The total amount of phosphorus, Ptotah in the river inflow through the Kondopoga channel was relatively permanent and equalled 28 tons year": Phosphorus concentration reached values of 15-40 JlgPI- I in Kondopoga Bay. In the late 1990s the phosphorus flux from the municipal treatment plant was 2.5 times the income from tributaries. P total carry-over into the bay via river inflow

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and from wastewaters reached 120 tons in 2004 (Sabylina, 2007). Phosphorus loading (0.5 g m ? year-I) on Kondopoga Bay exceeded the level permitted for an oligotrophic waterbody (Vollenweider, 1975). Kondopoga Bay has a long coastline (its length is 30 km) and its water exchange period equals 1.93 years. Water exchange with the lake water masses is hindered and much more sewage water is located there than in Petrozavodsk Bay. Total phosphorus income via river inflow and precipitation in Lake Onego in the first half of the 1990s is estimated at 1005tons year-I, but by 2001-2002 it decreased to 676 tons year-I. Phosphorus outflow via the Svir River at that time was 298 and 230 tons year" respectively. Nearly 70% of the annual phosphorus income (70% in the 1960s and 66% in 2001-2002) remains in the lake. Phosphorus in Lake Onego bottom sediments

Phosphorus enters Lake Onego bottom sediments mainly with the suspended particles fraction ( < 0.01 mm). The accumulating ability of Lake Onega bottom sediments towards phosphorus and the phosphorus accumulation rate in bottom sediments vary on a large scale depending on sediment type, on the morphological peculiarities of the lake basin, on the hydrodynamic conditions and on the degree of anthropogenic impact. Studies conducted by Semenovich (1973), Vasileva et. al., 1999) and Belkina (2003) on Lake Onego exposed regularities in the spatial distribution of phosphorus in bottom sediments and its tendency to be transformed under anthropogenic impact. During four decades of intensive catchment exploration, and of industrial and municipal development in the lake coastal regions, phosphorus concentrations increased in sediments over almost all of the lake bottom. Nowadays the total phosphorus amount in the surface layer solid phase (O-5cm) in bottom sediments is above the natural concentration level (from 0.05% up to 0.7%) and it increases with water bodydepth and the degree of sediment dispersiveness. The highest concentrations are measured in industrial sediments in Kondopoga and Petrozavodsk Bays. Regardless of granulometric bottom sediment feature, phosphorus exists mainly in a form of non-organic compounds, except for the Kondopoga Bay bottom sediments which contain suspended solids from papermill plant sewage waters. Before the dispersive wastewater facility and the biological refining station were put into operation, the major part of the solid discharge sedimented in the upper part of the bay. Nowadays intensive phosphorus accumulation is registered in the regions more than 10km distant, from the plant. During the last 20 years the phosphorus amount (in the 0-5 em layer) in the bay bottom sediments increased by 1.5-2 times. Reducing conditions (Eh up to 60 mV) point to the development of anaerobic processes in the sediment strata and the formation of secondary waterbody pollution conditions by phosphorus. Particle size distribution (high ferric phosphate ratio) and high phosphorus concentrations in porous waters (up to 1000JlgPI- I) in the upper bottom sediment layers prove that there is also an intensive development of eutrophication processes in this bay (Belkina, 2003). A noticeable phosphorus content increase in silts is observed in Bolshoe Onego bay, which appears to be a kind of settling area and sedimentation zone for

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51

suspended matter coming from Kondopoga Bay. River and terrigenous discharge is negligible here. During last 15 years Ptotal concentration doubled in general. The labile phosphorus ratio is 60-70% from Ptotal. Total phosphorus concentration in the bottom sediments of the central lake region on average tripled during the last two decades and that of labile phosphorus increased by more than an order of magnitude. The bottom sediments in Petrozavodsk Bay are formed as a result of the lake, the river and municipal sewage waters mixing. The River Shuya waters, which contain in suspended matter plenty of persistent organic matter of humic origin, essentially influence the formation of bottom sediments in the northwestern part of the bay. Suspended matter of anthropogenic origin accumulates along the western coast of the lake. The phosphorus level in bottom sediments, compared with 1980s data increased by 1.5 times. Maximal concentrations are registered near municipal wastewater outlets. A part of Povenets Bay called Large Bay has the lowest anthropogenic and river impact, unlike Petrozavodsk and Kondopoga Bays. Data obtained in the 1970s shows that the phosphorus content in silts increased to some extent there. The peculiarity of bottom sediments in Lake Onego is their high accumulative capacity towards phosphorus. In the central waterbody regions on average nearly 80% of the phosphorus income is buried in the bottom sediments. Similar values for the bottom accumulation capacity (about 70%) are obtained for Lake Ladoga and the Great American Lakes Erie and Ontario, which reflects characteristic features of large, deep, cold-water bodies (Chapra and Sonzogni, 1979; Raspletina, 1992; Bostrom et al., 1982; Manning, 1987; Sandman et al., 1999, Ignatyeva, 2002). Reconstructive conditions, developed in the sediments of polluted bays, provide immobilization and the return of phosphorus back into the water column (Belkina, 2003). Internal phosphorus loading estimation by the balance method has shown that phosphorus removal from bottom sediments in polluted bays is 3-60 times higher than from bottom sediments in the lake central regions - l Dmg PmFday"! and 0.03 mg Prn f day", Industrial silts in Kondopoga and Petrozavodsk Bays are characterized by poor retaining capacity. The phosphorus-retaining coefficient of polluted silts is estimated to be in the range of 20-60%.

1.5.2

Biological communities in the Lake Onego eutrophication state

Phytoplankton The first display of changes in the phytoplankton community along with phosphorus impact increasing is the growth of quantity characteristics and, then, the change in species type. Lake Onego phytoplankton is represented by a diverse flora (780 taxonomic units), common for large, deep, cold oligotrophic lakes of the temperate zone. As in the pelagic so in the littoral zone plankton diatoms (50%), green (26%), yellow-green (10%) and blue-green (8%) algae are presented diversely. The dominant

52 The Great European Lakes: state of the art

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complex is represented by species common for Lake Onego: the diatoms Aulacoseira islandica, Aulacoseira subarctica, Aulacoseira alpigena, Asterionella formosa, Tabellariafenestrata; the blue-green algae Coelosphaerium kuetzingianum f. kuetzingianum, Oscillatoria limosa, Oscillatoria planctonica; and the yellow-green algae Dinobryon divergens (Vislyanskaya, 1998, 1999; Chekrizeva, 2008). For Lake Onego phytoplankton, as for other deep temperate zone waterbodies, a seasonal dynamic of one or two peaks of the main characteristics is typical, with the maximum occurring during the vegetation period of diatomaceous algae. In the process of lake eutrophication and pollution as a result of wastewater discharges, phytoplankton, in general, did not undergo considerable structural changes. So, as a result of dominance all through the year of diatoms (60%), it still preserves its floristic diversity and the systematic inter-relations between algae departments typical for oligotrophic waterbodies. In spring plankton the dominant role belongs to recent-years dominants from the diatomaceous algae group. Along with summer heating of the water column, a more diverse complex is developed with summer diatom forms prevailing with a considerable amount of yellow-green, green and blue-green algae. The representation of species that are common, not only for higher trophic level waterbodies, but also as indicators of organic pollution, noticeably increase. For deep lake areas (central region, Povenets and large Onego bays) comparison of modern data (2004-2006) with those published earlier (Vislyanskaya, 1999; Petrova, 1969, 1971, 1973, 1990), testifies that there is insignificant change in phytoplankton development level. A distinct increase in the quantity characteristics of phytoplankton communities occurred in the northwestern areas - Kondopoga and Petrozavodsk Bays. Phytoplankton amount in Petrozavodsk Bay grew during the increase of phosphorus loading on the aquatic ecosystem, especially during the development of spring algae complexes, up to 1.7-3.0 million cells 1-1 and its biomass value reached 5-9gm- 3 • Much deeper changes in the phytoplankton community were observed in Kondopoga Bay and were related to the changes in the quality of wastewater composition. Until the 1960s the phytoplankton community structure was similar to that of the open regions of the lake. Local surges in green chlorococcales blue-green development were registered that designated the existence of organic pollution. The situation began to change rapidly in the 1970s after the launch of the paper-mill sewage waters purifying station and the consequential enlargement of phosphorus income into the bay. In the early 1980s it became obvious that the dominant group, consuming relatively small amounts of phosphorus, was enlarged by eutrophic waterbody species, highly productive, but demanding for their development high phosphorus concentrations in the water. By 1989 algae quantity increased by 5 times (1226 thousands cells 1-1), and its biomass doubled comparing with 1982. Since the end of the 1990s, along with enhancement of the number of species typical of shallow eutrophic lakes, the former dominants of the oligotrophic period started to develop intensively again. These species have the advantage over eutrophic ones that they are satisfied with lower phosphorus concentrations in the water mass.

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The composition of bay phytoplankton dominants at this new level was identical to that observed during oligotrophic period in the late 1960s and 1970s. At the same time the phytoplankton development level remained high enough (1200 thousand cells 1-1). Similar features of phytoplankton development level in Petrozavodsk and Kondopoga Bays can be marked out: considerable phytoplankton quantity and biomass growth in spring, as a result of intensive Aulacoseira islandica subsp. helvetica, the oligotrophic period dominant, significant blue-green and green chlorococcales algae, along with diatoms development when the summer phytocoenosis structure is relatively stable; and summer and autumn phytoplankton prevailing in the annual cycle (Vislyanskaya, 1999). Primary phytoplankton production

Determination of primary production in Lake Onego was the focus of a number of studies (Romanenko, 1966; Sorokin and Fyodorov, 1969; Petrova, 1973; Rossolimo, 1977; Trifonova et al., 1982; Umnova, 1982; Vislyanskaya, 1999). Since 1989 monitoring has been based on these studies and it covers nearly all the waterbody. By primary production magnitude Lake Onego can be classified as a typical oligotrophic waterbody, excepting Kondopoga and Petrozavodsk Bays, where the ecological state is characterized by mesotrophic features. During 17 years period from 1989 to 2006, primary production values over the major part of the lake (central and southern areas, Petrozavodsk Bay, Small Onego, Povenets and Zaonezsky Bays, and Unitskaya Bay) did not change essentially, and were less than 100mgCm-2 day": In the frontal zone where the eutrophicated bays meet the open pelagic areas, and where during the periods of dynamic activity of water masses contamination penetrates (Bolshoe Onego and the northwestern part of the open area), phytoplankton production values are slightly increased up to 150mgCm-2 day" (Table. 1.4). Table 1.4. Phytoplankton production in different Lake Onego regions in summer period, mg Crrr'
1989-1996

1999-2006

Mean 1989-2006

Southern Onego Central Onego Bolshoe Onego Bay northwestern lake, open part central part Petrozavodsk Bay outer part top part Kondopoga Bay central part outer part

91.9 ± 24.4 104.5± 26.2 133.1 ± 9.6 140.6± 1.0 225.7± 58.4 161.7 ± 60.1 390.5± 90.2 286.1 ± 33.9 233.9± 27.3

86.0±24.5 89.7 ± 15.2 168.9 ± 35.4 90.2 174.2± 54.8 115.2 ± 18.3 440.9 ±98.0 288.0± 35.7 196.7 ±41.9

88.3 ± 15.5 96.3 ± 10.5 146.6 ± 14.5 123.8 ± 16.8 199.8 ± 38.3 122.3 ± 21.7 412.9 ±62.7 286.7 ±24.2 217.4±23.3

1989-1996 according to Timakova 1999; 1999-2006 according to Tekanova and Timakova, 2007.

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High reproduction activity of plankton algae is observed in two northwestern bays and its maximal concentrations are 585mgCm-2day-l and 1037mgCm-2 day" in Petrozavodsk and Kondopoga bays respectively. Increased primary production magnitudes in these areas are of a systematic nature. The surface photosynthesis intensity there by 3-10 times exceeds similar characteristics in the open lake regions, and total primary production by 1.5-3.0 times. Accelerated algae photosynthesis activity has taken place in the central part of Kondopoga Bay since the end of the 1980s. In the frontal zone of Kondopoga Bay with the Bolshoe Onego region the tendency towards increasing primary production during the 19781979 period (Umnova, 1982) is also clearly revealed. According to 'high productive' and 'low productive' years, obtained on the basis of 1978-1979 and 1989-1993 research periods, calculated for vegetation seasons, primary production values increased by 1.3-2 times. Its growth is mostly noticeable in 'low productive' years. As was mentioned above, this lake region plays the role of accumulation zone for pollution (including phosphorus) discharged from the bay. Phosphorus concentrations in the water are not registered, but its content in silts has already tripled, though it has not exceeded the oligotrophic state level. Primary production is 1,5 times lower in Petrozavodsk Bay than in Kondopoga Bay, due to intensive water exchange and phosphorus income to the open lake areas; but in the boundary Petrozavodsk Onego region it is sometimes higher than in the bay itself. The seasonal fluctuation in the lake pelagic areas is characterized by two maxima in extremely warm years only. As a rule, there is one maximum in July and early August; primary production development in the bays is registered twice a year, in spring and in summer. In the annual cycle of primary production spring photosynthesis dominates and its ratio is up to 70% of total seasonal production. Interannual production variability, obtained for the vegetation period, is not high - 2 and 1.5 times more in the bays and in the pelagic lake regions respectively. A year's primary production in Kondopoga and Petrozavodsk Bays reaches 11.7-18.7 thousand tons (14.6 thousand tons on average) of organic carbon, and for the whole lake including these bays it reaches 150.6-207.4 thousand tons (172.1 thousand tons on average). Thus the proportion of primary production in the bays, where eutrophication is developing, compared with the whole lake is approximately 9%. Phytoplankton production input into the organic matter pool of the waterbody is not high. Daily primary production in total waterbody organic matter supply is evaluated as 0.08-0.35%, and in its labile fraction as 0.38-04.85%. It is less than in most waterbodies (Mineeva et al., 2004). During the 180 days vegetation period its input magnitude increases to 12-54%. Bacterioplankton

Bacteriocoenoses on the lake are characterized by the high variability of its features. Their quantity and functional characteristics are the first to reflect all spatial and temporal transformations in the ecosystem. In the deep lake areas the

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The cycle of substances in Lake Onego and its water ecosystem

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bacterial regime has not undergone noticeable alterations during recent decades. Central Onego, the northern bays, and Povenets Bay still nowadays are characterized by minimal bacterial density. Its total amount during the summer period is 0.79 millions ml", and in spring 0.59 millions ml", its biomass is 0.26gm-3 and 0.20 g m" respectively. The annual bacterial quantity relation in the coastal areas is slightly different: 1.51 millions ml"! (0.5 gm- 3 for biomass) in summer and 1.96 millions ml"! (O.64gm- 3 for biomass) in spring. The upper maximum heated water layer is the most enriched with bacterioplankton Considerable changes occurred in the northwestern bays under the influence of eutrophication and industrial water contamination. Until the 1970s the process of eutrophication in Petrozavodsk Bay was more accelerated than in Kondopoga Bay, where the phytoplankton development level and its composition were similar to those of the lake. The bacterial component in Kondopoga Bay eutrophication was essential, as allochthonous organic matter, being involved in the biotic cycle, prevailed over autochthonous. After the launch of the paper-mill refining plant, beginning in the 1980s the situation began to change. After an increase of 3-6 times in the amount of total phosphorus, Ptotah discharge into the bay with sewage waters, the period of rapid growth in the quantity of phytoplankton characteristics started, and at that point the accelerated eutrophication of Kondopoga Bay, compared with Petrozavodsk Bay, began. Autotrophic development became more significant. Bacterioplankton quantity stabilized after dissipative emission of wastewaters was set in operation. In recent decades the tendency of the amount of bacteria to increase is revealed in the deep central part of the bay. Bacterial plankton mass growth is traced also in Bolshoe Onego, especially while contamination discharges from Kondopoga Bay. Slightly increased bacterial amount in this region has stabilized in comparison during the last decades. Bacterial quantity has featured in Petrozavodsk Bay in the last 15 years due to intensive water exchange at the 0.9-1.8 millionsrnl"! level. Eutrophication processes can be definitely described by such parameters as dark assimilation of CO 2 , bacterial production, and intensity of destruction processes. Carbon dioxide dark assimilation in the lake central region since 1989 has been characterized by permanent values equal to 0.002-0.9mgCI- 1 day", 0.09mg CI- 1 day " in average. In Bolshoe Onego during the last 16 years there has been a tendency towards dark assimilation CO 2 growth, but as a result of its high variability it has not been proved statistically. During the vegetation period, on average for the lake, 1.0-18gCm-2 of carbon dioxide is consumed by bacterioplankton, that is 6-16% of the C-C02 assimilated by phytoplankton. Calculated mean annual bacterial production magnitudes, on the basis of carbon dioxide dark assimilation, reach during the vegetation period 23.9 gCm- 2 in the central part of the lake, 21.9 gCm- 2 in Petrozavodsk Bay and 17.0 - 135.5 g Cm v'. In various years the proportion between bacterial and primary productions is different: mean annual magnitudes indicate that only in Petrozavodsk Bay and the open part of Kondopoga Bay does primary production exceed bacterial production by two times. In deep regions bacterial production values are higher and it shows that a large amount of allochthonous organic matter is involved in the biotic cycle, and proves the

56 The Great European Lakes: state of the art

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ecosystem is functioning heterotrophically. The major part of bacterial production, about 60-70%, is synthesized during the three summer months. The inter-annual fluctuation of its values is in the range 2.1-2.6gCm-2 • Zooplankton Lake Ladoga zooplankton, in general, has similar features to zooplankton in other large waterbodies of the temperate zone. Noticeable sustained changes in zooplankton structure, its density and biomass, and its ratio in organic matter formation and transformation are observed in the lake areas under strong anthropogenic impact with strong eutrophication features. The list of zooplankton includes 212 revealed taxons, among them 113 rotifers, 99 crustaceans (Cladocera, 67; Calanoida, 5; Cyclopoida, 24; Harpacticoida, 3). The species composition in the lake is quite homogeneous and is more diverse in the bays only. The dominant complex is represented by a few species (10-12 of them). Permanent representatives of the zooplankton are five species with an occurrence frequency exceeding 80%: Eudiaptomus gracilis Sars, Thermocyclops oithonoides Sars, Mesocyclops leuckarti Claus, Bosmina lacustris Sars, and Kellicottia longispina (Kellicott). The average value of zooplankton biomass during the vegetation period is 0.1-0.33 gm- 3 (its density is 4.0-46 thousand individuals m"), Maximal values are permanently common for Petrozavodsk and Kondopoga Bays (O.3-0.6gm- 3 and 1.2gm-3 and 200 thousand individuals m" respectively); minimal values are found in Bolshoe Onego Bay (0.05-0.07 g mr'), Fluctuation in zooplankton development is of a distinct seasonal type and its maximum species diversity is observed in July. Seasonal fluctuations in amplitude (max-min) defines the stability of a community and it reaches high magnitudes in the most highly eutrophicated bay areas (15-30 times), that of the other regions. Structural changes in the bays are reflected in the proportion of the main community groups and in the increasing role of the small size fraction (Kulikova et al., 1999, 2007). The dominant plankton group (up to 80% of biomass) in the not-yeteutrophicated regions of the lake over the whole vegetation season appears to be the Copepoda; the ratio of Cladocera and Rotifera increases. In Bolshoe Onego, Petrozavodsk and Kondopoga Bays the proportion of mean biomass values for the vegetation season among these groups was 1 : 3.9 : 7.6. Quantitative features and zooplankton structural stability is observed only in the central lake areas. The number, biomass and composition of small summer crustaceans has not changed there since the 1960s. The same picture remains since that time for species composition of and the proportions of the main groups in the dominant complex (Smirnova, 1972). The summer months of July and August are the most productive (7-54.5 kcal m"), The maximal productive level is typical for Kondopoga and Petrozavodsk bays - 9.5-26.0kcalm-2 • Production values for the open areas of the lake do not exceed 8.8-21.6kcalm-2 • Substance and energy flux value through the plankton community, estimated by the nutrient quantity of prey bionts consumed, in the open regions of the lake is 45-151 kcal m ? or 23-76gm-2 of organic matter. It is noticeably higher (1.5-2

Sec. 1.5]

The cycle of substances in Lake Onego and its water ecosystem 57

times) in eutrophicated areas and it is maximal (up to 540kcalm-2 or 270gm-2 of organic matter) in highly eutrophicated Kondopoga Bay regions. Along with the region trophicity in the total zooplankton ratio the predatory plankton ratio decreases to 7-11 %. In conclusion it is worth mentioning that, in the most eutrophicated lake areas (the upper part of Kondopoga Bay) where zooplankton experience specific conditions, the small size fraction ratio increases in the community, and filterer numbers grow due to the declining number of predators, which is as the result of the increasing abundance of bacterioplankton and small-size algae (such as chlorococcales and pyrophytes). At that same time the trophic structure alteration is also reflected in the main energetic characteristics: the total production of the community and its life maintenance supplies increase.

Afacrozoobenthos Average values of macrozoobenthos abundance in the lake nowadays in general have reached 4.53 ± 0.85 thousand individuals m" and 6.66 ± 1.08gm-2 • Nearly 60% of its amount and 40% of its biomass consists of oligochaetes. Relict crustaceans form 42% of its biomass and a little more than 17% of the quantity of animals. Over vast areas of the profundal zone the benthic population is notable for its species monotony and is represented by an incomplete invertebrates complex. It consists of oligochaetes and some bivalve molluscs. Their total quantity and biomass reaches 90-97% of the whole community amount. The composition of the bottom coenoses, their dominant complex and the proportions of the main bionts groups in this region have remained relatively permanent for decades. At the same time, as a result of undergoing the influence of water masses enriched with biogenic elements for a long time, in the process of waterbody internal circulation from eutrophicated bays, sustained growth in the quantity of macrobenthos has taken place. During the last 10-15 years biomass growth has tripled - from 1.2 up to 3.5gm-2 • In the southern part of the lake available macrozoobenthal quantity and biomass fluctuations were not sufficient to reveal statistically reliable trends of its quantitative development. Nowadays, in fact, does not differ from the benthal groups of the central region either in by structure, composition and dominant species, or in quantitative characteristics. The long-term human impact on benthal coenoses in Petrozavodsk and Kondopoga Bays, has led to the disturbance for initially balanced intra- and interspecies relations, to an increasing role for eurybiontic species, and to considerable reconstructions in communities. These bays stand out for their high quantitative macrobenthos development, which in abundance is several times higher, in some cases by an order of magnitude, than in the lake open areas. The main tendency observed during more than 40 years of Kondopoga Bay studies is a gradual enlargement of the bottom area involved in these changes. The level of benthos quantitative development (average value for the bay), comparing it with the initial observation period in 1964, increased by nearly 40 times - and biomass by 16 times. Since then and until the present time, steady

58 The Great European Lakes: state of the art

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quantitative characteristics growth has occurred in benthal biocoenoses. In the upper, and most eutrophicated and contaminated, part of the bay, an area of nearly 3 km 2 is deprived of macrobenthal organisms. A provisional community inhabits the area. It includes the most adaptive species of Oligochaetes, nematode worms and sporadic inhabitants from other lake regions, such as Chaoborus crystallinus. Benthal groups on the remaining area are characterized by extremely high values of quantity and biomass (up to 41 thousand individuals m ? and 58 gm-2) , determined by the mass development of Oligochaetes (tubificid worms), bloodworms and Procladius genus larvae. In general in this zone benthos the Oligochaete-Chironomidae complex dominates with a considerable prevailence of worms in quantity and, to a lesser extent, in biomass. Epibiotic Amphipodas are not present. Biocoenosis growth, especially apparent for two groups, Oligochaetes and the small cretacean M. affinis, occurs equally in the deep central part of the bay and in its outer part. Communities amount and biomass value can here reach 9 thousand individuals m ? and 9.5-15 gm- 2 which is, by an order of magnitude or more, higher than the similar characteristics of the 1980s. Kondopoga Bay bottom biocoenoses in general can be characterized at the present time by high quantity, typical of mesotropic and eutrophic waterbodies (6 thousand individuals m ? and 10.5 gm- 2) . Petrozavodsk Bay benthos still in the mid-1970s differed a little from the lake central region (Nikolaev, 1980). Observed mean values of benthos quantity and biomass in Petrozavodsk Bay nowadays are one thousand individuals m ? and 9 gm- 2 • An active hydrodynamic regime, suspended matter sedimentation of rivers Shuya, Neglinka and Lososinka, the influence of industrial, domestic and urban runoff and the drainage Petrozavodsk city sewage waters determine the diversity in the distribution and composition of bottom biocoenoses in Petrozavodsk Bay. The basis of the bottom macrofauna consists mainly of three animal groups - small Oligochaete worms, Chironomidae larvae and relict crustaceans. Oligochaetes mostly prevail near the urban coast, Amphipodas are concentrated in the central part of the bay. The degraded biocoenoses zones are registered in the vicinity of municipal wastewater outlets. These biocoenoses are presented entirely by worms of tolerant forms (Tubificidae) and dipterans (Chironomus larvae) sometimes with considerable values of abundance and biomass - 33 thousand individuals m ? and 21.0gm-2 • Mean values of benthos quantity and biomass in the bay at the present time equal 7.3 thousand individuals m ? and 9.0gm-2 • In the deep part of the bay, where organic matter concentrations during the last 20 years have increased by 1.5 times, for nitrogen (N) and phosphorus (P) it tripled (Belkina et al., Belkina, 2003). Macrobenthos quantity nowadays exceeds in quantity by 6 times and nearly by an order of magnitude, respectively, the similar characteristics of the late 1960s. The values of bottom community production in eutrophicated bays 5-6 times exceeds the similar characteristics of the lake central part. The ratio between communities production and total metabolism losses (P/R), which usually expresses the functional state of the biocoenosis, was in the range 0.37-0.57, achieving

Sec. 1.5]

The cycle of substances in Lake Onego and its water ecosystem 59

maximum magnitudes in the most eutrophicated regions. In other words, up to 60% of assimilated nutrient energy in communities is consumed in achieving production. Benthos participation in organic matter and biogenic elements transformation reflects the main biocoenosis features. The macrozoobenthal ratio in total organic matter destruction is estimated as 1.5-10% in silts of the profundal lake zone. Nevertheless, taking into account the spacious areas of this zone, benthal organisms there are a powerful regulator of benthal bottom sediments. The reaction of the lake benthal communities to industrial impact in general is of a regular nature and a differs little from similar processes in other lakes undergoing an anthropogenic influence of the same type (Popchenko, 1999; Slepukhina and Alekseeva, 1982). In the profundal zone of the central region and Bolshoe Onego, at depths greater than 50 metres, the changes are less distinct and are typified by slightly increased benthal groups' quantitative characteristics. In the coastal zone the processes are more accelerated and there is a wider diversity of anthropogenic disturbance. In general, with some degree of caution, it is possible to confirm some stabilization in the lake bottom community state, but essentially at the level of magnitudes prevailing in the 1970s. When external conditions change, for example anthropogenic impact increases, the structure and community functions inevitably will change and the system will evolve into a different state with different quantitative and qualitative features. 1.5.3 Relation between the primary production and the destruction of organic matter As is known, destructive processes in a waterbody to a large extent depend on the supply of allochthonous organic matter. Organic matter entering Lake Onego with allochthonous inflow is quite sufficient for the development of destructive processes. In river inflow, conservative, hardly mineralized fractions prevail, and with sewage waters from paper-mills (Kondopoga Bay) there arrives a considerable amount of biochemically unstable organic matter. The role of bacterial biosynthesis in waters enriched with organic matter (3-6% of primary production) is insignificant (Timakova and Tekanova, 1999), as too are the roles of macrophytes and periphyton. The general organic matter destruction, determined experimentally by the generally accepted oxygenic method, takes place in summer time in the whole lake water column. The epilimnion is the most active layer, despite its minor size compared with the whole water column, where the main newly synthesized organic matter mass is concentrated. The metalimnion is an area of active mineralization too. At depths down to 30m, epilimnion and hypolimnion thickness is comparable and wind-driven mixing often influences the process development; but already at depths of about 50 m the relatively steady hypolimnion exceeds the epilimnion by 2, at depths down to 70m by 6, and at depths of over 70m by 9 times, respectively. The hypolimnion volume typically has low temperatures throughout the year in the range of 4.0-6.0°C. Photosynthetic processes do not occur there. At the same time, due to the enormous water mass volume, especially in deep regions, an amount

60

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of organic matter comparable with that of the epilimnion, and even exceeding it in quantity, is mineralized in this area. Destruction intensity in the hypolimnion of the open regions of the lake is in the range of 0.02 ± 0.002 mg C m" day": When the depths are less than 30m in the epilimnion zone twice as much organic matter is destructed per square metre as in the hypolimnion; and when depths are less than 50 m organic matter destruction values are comparable. But in the deeper regions of the lake organic matter mineralization in the hypolimnion zone is much higher. Integral destruction per square metre in the hypolimnion depending on its thickness is 0.3-1.7gCm-2day-1. Destruction and production values (including extracellular) in the upper lake central region are comparable, that is, all organic matter (excluding allochthonous) that is newly formed as the result of photosynthesis is destructed within the euphotic zone. Integral values (per square metre) comparison, shows that destruction exceeds production by 10-12 times. Similar magnitudes (13 times) were obtained by Sorokin and Fyodorov (1969) that confirmed experimentally the data being calculated of the possible nutrient requirements in the water column of the lake bacterial population. For Lake Ladoga, noticeably exceeding Lake Onego in primary production volume, the destruction excess is 4 times. In Kondopoga and Petrozavodsk Bays, where the allochthonous component in organic matter is high, the distribution of destruction values in the bays' water columns differs from that of the pelagic areas and does not depend on the temperature profile. The excess of destruction over production there is more than 8 times. The small primary production input into the total organic matter store for Lake Onego and the excess of destruction over production gives evidence of the implication of a considerable amount of organic matter of allochthonous origin in the cycle and reflects a heterotrophic type of ecosystem functioning. 1.5.4 Peculiarities of Lake Onego eutrophication Generally Lakes Ladoga and Onego have had a regular historical development; the mechanisms of the acceleration factors of the processes going on in waterbodies are fully presented in section 1.4. But along with all these general mechanisms there are specific peculiarities for each lake, defining the process developing rate, for which each waterbody has its own history. Lake Onego, in spite of having mean dimensions that put it among the great lakes of the world, and having anthropogenic loading over most of its area, still preserves an oligotrophic state due to its morphometric features and its thermal regime. The first signs of anthropogenic eutrophication development in Lake Onego appeared in the middle of the 1970s - the period of intensive catchment reclamation, industrial development and population growth along the coast line. These circumstances led to phosphorus loading on the waterbody. The principal source of phosphorus at that time was river inflow, which exceeded in significance any phosphorus from industrial and municipal discharges. An essential point, determining the scenario of eutrophication development in the lake, was the combined

Sec. 1.6]

The main tendencies in the evolution of large lakes

61

influence of two main sources of the phosphorus intake (the river and industrial/ domestic discharges) in bays isolated from the open lake water mass. That, on the one hand, resulted from an increase in phosphorus loading on the bays' ecosystems and, on the other hand, localized this process, did not allow it to spread rapidly over the whole waterbody. For Kondopoga Bay an important factor was its bottom elevation in its outer part - a kind of natural border, separating it from Bolshoe Onego Bay and preventing the outflow of eutrophication matter into the lake open regions. Inflows of transformed bay waters enriched with phosphorus occur during periods of high dynamic activity in the water mass and development of outflows from the bay. This is usually observed at a time when the long-term winds are from the north east. The morphometric peculiarities of Petrozavodsk Bay (the basin declines towards the outer part and it has a high river inflow) promote the outflow of bay waters into the central lake region. An essential issue in the Lake Onego eutrophication process is the involvment in the biotic cycle of a considerable amount of organic matter as a component of the allochthonous inflow into the waterbody. It is a powerful potential source of phosphorus mineral forms, which are released as a result of mineralization, and it forms the basis for the development of heterotrophic processes. At the same time bacterial production values being higher than phytoplankton values and the substantial excess of destruction over primary production is quite representative. To an even greater extent, bacterioplankton along with phytoplankton determine the specific nutrient conditions for secondary biotic chains and, via trophic relations, influence their formation. This allows us to assume that anthropogenic eutrophication, especially in the bays of Lake Onego, is inclined to a heterotrophic way of development which was mostly evident before the 1980s. After wastewater refining stations were put into operation in Petrozavodsk and Kondopoga Bays, phosphorus loading on ecosystems grew noticeably and the consequence was the acceleration of primary production processes. 1.6 THE MAIN TENDENCIES IN THE EVOLUTION OF LARGE, DEEP STRATIFIED LAKES The principal way in which large, deep hypothermic lakes are different is that the exchange between the water mass and its bottom sediments is not as great as in shallow epithermal lakes where it is one of the significant factors. Lake basin morphometry plays a large part in defining the balance of production/destruction processes. The major factor influencing organic matter sedimentation and transformation rates in deep stratified lakes is the degree to which the tropholytic area exceeds the trophogenic area; this determines the dominance of organic matter mineralization in the ecosystem. These features, playing an important role in anthropogenic eutrophication and contamination, require large stratified lakes being considered as a particular type of waterbody. Most of the world's lakes, including the large lakes, are in the temperate zone of the northern hemisphere. The humid type of limnetic genesis, when organic matter

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of allochthonous origin prevails over the autochthonous component and effects physicochemical matter exchange in lakes (Abrosov, 1982), is common for this geographical area. Lakes Ladoga and Onego are among such lakes. Autochthonous primary production in the natural ecosystem of the lakes of this zone is not large, as it is limited by light, temperature conditions and low phosphorus concentrations in the natural waters. In allochthonous organic matter the major part of the phosphorus is concentrated in humic complexes and is limited for biota organisms' consumption. Bacterial production and organic matter destruction are limited to a greater extent by phosphorus concentrations. For bacteria the need for this element is significantly nearly one order of magnitude higher than for algae (Currie and Kalff, 1984; Jansson et al., 2003; Johnsson, 1995). When phytoplankton productivity increases during eutrophication of the large lakes, other factors start to limit algal growth in natural eutrophic waterbodies. In lake plankton, diatoms play the foremost role, so their spring mass development can be indicated by the decline of silicon concentrations in the water. Silicon concentration in Lakes Ladoga and Huron decreased by nearly two times during the last 15 years; in Lake Michigan in the last 40 years it was around 75% (Schelske, 1976). A silicon concentration of 0.05 mg 1-1 is considered to be the threshold magnitude for the development of diatoms. At the time of development of diatom mass in Lake Ladoga's coastal zone, the silicon supply in the water decreased to 0.06 mg Si 1-1 as phytoplankton production magnitude was over 300 ug C 1-1 day ", Apparently silicon can be the limiting factor for spring diatomaceous plankton. Enrichment in phosphorus in the process of anthropogenic eutrophication in lakes can also change the proportion between phosphorus and nitrogen favourable for algae, which is considered to be N: P = 7 : 1. However, in large lakes, a decline in N : P value compared with the optimum magnitude is rarely registered. It is worth mentioning that during anthropogenic eutrophication the reduction in nitrogen concentrations in lake water should activate the growth of blue-green algae. This type of algae has been proved to possess the capacity for nitrogen fixation; hence this factor will not lead to a dedline in phytoplankton production in general. The spatial heterogeneity of hydrophysical processes in the complicated morphometric basins of the large lakes, which determine the different rates of heating in the areas with various depths, in the end defines the general primary production of the waterbody, not only in natural evolution but also in the process of anthropogenic eutrophication. Existing heterogeneity of the basin morphometric features leads to the fact that, for the large lakes, diversity between natural development and ecosystem transformation under human impact is of great importance. An estimation of the lake trophic status as an evolution stage is based on a comparison of biogenic loading and primary production values. The idea of trophic status with definition of 'oligotrophic' and 'eutrophic' stages in waterbody evolution has recently been supplemented by a 'dystrophic' stage for lakes with a high allochthonous component of dissolved organic matter in their water (Theinemann, 1928). The ranking of lakes according to the amount and the origin of dissolved organic carbon (DOC) made it possible to distinguish the 'allochthonous' type, when organic matter comes from the catchment and the 'self-nourishing' type, when the

The main tendencies in the evolution of large lakes

63

pool is formed as a result of processes internal to the lake (Rodhe, 1969). Rodhe's formalized the conception of ranking the lakes according to their DOC source and amount along two axes: from oligotrophic to eutrophic and from oligotrophic to dystrophic. In the 1970s these classifications were forgotten, as a close relationship between phosphorus loading and autochthonous primary production was revealed. The correlation was urgently needed for solving the principal issue of that time: anthropogenic eutrophication of the lakes connected just with phosphorus overloading. Research conducted within national and international programmes on different lake types in connection with increased anthropogenic impact provided the development of modern limnology. The role of dissolved organic carbon in ecosystem processes was studied more precisely (Wetzel, 1983; Currie and Kalff, 1984; Salonen et al., 1992; Williamson et al., 1999; Jonsson et al., 2001; Jansson et al., 2003). Specific attention was paid to the problem of difference in the ways the autochthonous and the allochthonous components are transformed in the dissolved organic carbon pool of the lake ecosystem, and to the competition among organisms - producers and destructors - for concentrations of biologically available phosphorus and carbon. In the process of anthropogenic eutrophication in large stratified lakes the most important fact is that the concentration of biogenic elements in water grows rapidly due to external loading. Oligotrophic status is preserved in deep waters and so is slow heterogeneous heating and cooling over the waterbody. A complicated thermal and dense water mass structure is preserved. The differences in water heating rates over various depths determine the existence of relatively permanent lake zones which alter thermal regime and their role in ecosystem processes. The duration of the spring season in large lakes of the temperate zone is the same in conditions of anthropogenic eutrophication and it results in the formation of substantial autochthonous primary production in spring within coastal and declinal zones. The principal role of spring diatomaceous plankton in oligotrothic waterbodies along with high summer productivity, characteristic for natural eutrophic waterbodies, has an essential meaning for the evolution of the lake ecosystem. Creating a high total productivity of the waterbody, autochthonous spring and summer plankton organic matter is involved in the lake cycle in two different ways. Spring phytoplankton develops in a zone restricted by the thermal bar and, dying off, concentrates there in the nearbottom water layers. Spring autochthonous matter is almost uninvolved in the lake trophic chain and in fact its entire amount presents a fund for bacterial the development of destruction processes and biocatalyst oxygenation. The same happens with the allochthonous organic matter from flood waters. In the hydrological summer after vertical thermal stratification forms, the region of accumulation of spring phytoplankton and of flood-water organic matter becomes the periphery of the lake hypolimnion. The thickness of the hypolimnion in these regions is minimal, as also is the concentration of dissolved oxygen. The oxygen discharge from destruction processes is maximal. There, within the declinal zone, can develop the first features of the oxygen regime destabilization. Summer phytoplankton production of the deep zones plays a completely different role in the ecosystem processes of large lakes. It is formed in the epilimnion

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and right here is partly involved in the trophic chain of the lake as a result of zooplankton consumption of living and died-off algae. Other organic matter also undergoes bacterial destruction within the epilimnion. The major part of summer production is formed within spatial in area profundal and ultraprofundal zones and it is especially noticeable during anthropogenic eutrophication. Incompletely mineralized summer plankton organic matter with the beginning of autumn vertical circulation appears to be part of the general lake cycle. This organic matter does not participate directly, within one annual cycle, in the deterioration of the oxygen regime in the near-bottom layers of the hypolimnion deep zones. That is why in deep lakes hypolimnial oxygen deficit can be not exposed for a long time, in spite of the existence of considerable biogenic loading on the waterbody. The hypolimnion of large stratified lakes is the area of the largest-scale processes of organic matter mineralization over the whole annual cycle, in particular of the low-molecular fraction of humus complexes. At present the lake ecosystem is going over to the use of an unlimited phosphorus supply of humus complexes of allochthonous organic matter, after long period of high phosphorus loading. This transition is probably the same irreversible evolution stage of deep, stratified, lakes of the humid zone as the use of the phosphorus supply of the bottom sediments in the ecosystems of shallow lakes. In the anthropogenic eutrophication process the lake biota secondary producers as well as phytoplankton depend on morphological and hydrophysical ecosystem processes peculiar to oligotrophic lakes. Zooplankton communities in the coastal and declinal zones and in the deep-water parts the summer epilimnion are the most diverse and productive. The productivity and the species variability of benthic complexes is limited by depth and remoteness from the coast. The reconstruction of biota components is revealed first in the shallow zones. Any changes in composition and in amount of the deep region biological communities testify to considerable changes in the balance of the ecological system. Studies of the spatial and temporal heterogeneity of hydrophysical features determined by the lake morphometry are the basis for the transformation analysis of large lake ecosystems under the impact of anthropogenic factors and for the division into regions where the negative consequences are exposed, or will be exposed to the greatest extent. The anthropogenic eutrophication of the large lakes affects ecosystems in general, as the process of natural evolution. Morphometrical heterogeneity dictates the inflow of biogenic elements that is first exposed in the coastal zone. The increase in primary production and productivity as a whole takes place in the coastal and declinal zones, water oxygen reduction takes place in the declinal zone and the buffer system of dissolved organic carbon destabilization appears in the profundal and ultraprofundal zones. It should be admitted that the existence of any, even slight, changes in any ecosystem chain in conservative, deep areas of large lakes should be considered as an indication of notable disturbances in the balance of the lake processes. Thus, the aim of field surveys and studies based on mathematical modelling of the processes in large stratified lakes should be the reproduction of the temporal and spatial diversity of ecosystem functioning and their combined influence on its evolution.

Sec. 1.6]

The main tendencies in the evolution of large lakes

65

The essential role of phosphorus in the regulation of rates of transformation in an ecosystem and the dependence on its concentration in lake water of all biotic and biological processes on water catchment justifies, in the authors' opinion, the development of ecosystem models describing the phosphorus cycle in a waterbody.

2 Hydrothermodynamics of large stratified lakes

2.1 ENSEMBLE OF THERMO- AND HYDRODYNAMICAL PROCESSES AND PHENOMENA IN LAKES The main task of our study in modelling the thermohydrodynamics of Lakes Ladoga and Onego is to describe the thermal structure, the currents, and the ice regime dynamics under conditions of the regional climate warming/cooling, and to provide the ecosystem model with information on abiotic factors under inter-annual and seasonal variability. The hydrophysical conditions in such great stratified lakes as Ladoga and Onego, with substantial length and depth scales - hundreds of kilometres and metres, respectively - and complicated bottom topography, are considerably diverse, especially in the vegetation period. This is determined by the presence of well-developed stratification in the vertical as well as in the horizontal plane. In Lake Ladoga, variations of water temperature in both directions may reach 15°C (Tikhomirov, 1982). A wide spectrum of hydrodynamic phenomena affecting the evolution of great stratified lakes is shown in Fig. 2.1. To simplify the case, the hydrodynamics are simulated on a large-scale level. In the first instance, it is important to realistically reproduce the main features of the large-scale circulation and the main hydrodynamic phenomena, such as the thermal bar, ice cover formation and disappearance, and dynamics of the upper mixed layer and thermocline, by numerical models. The large-scale circulation in great stratified lakes, by analogy with oceans, can be determined as a statistical ensemble of movements which can be individually described (Monin, 1982). Taking into account the computational capacities and resources, we consider the large-scale circulation in great stratified lakes as water movements, the size of which is comparable to or larger than the mesh width in the discrete models used. With lake horizontal and vertical scales of 105 and 102m, respectively, the mesh width possible for use in a model with 30 vertical layers is expected to be 103 m. Thus, the individual description can be provided for large-scale phenomena only. As a timescale, it is natural to choose the typical time of their evolution, which in our case was equal to

68

[Ch.2

Hydrothermodynamics of large stratified lakes

1 ye L

ge sc r ~

cI ul

OD S .

DYJf,!S

1 mo h

1

lin.

1 Se-t .

S urfa (;~

nl

ai/es. O-!:

I~

turbu r~me

Fig. 2.1. Temporal-spatial scales of hydrodynamic phenomena in the great lakes.

the synoptical period, i.e, several days. The most significant factors that define the development of lake hydrodynamics are wind stress and irregularity of the density field. The thermal effects can be important on climatic and seasonal timescales (Schwab and Beletsky, 2003) but for timescales shorter than seasonal, wind stress curl and topographic effects are the major driving forces of gyres, and the contributions from internal waves are minor . To evaluate the effect of anthropogenic load and regional climate on the lake ecosystem for a period of 10-15 years, it is reasonable to assume that lake circulation corresponds to long-term average external forcing, i.e. wind, total heat flux to the lake surface, river inflow/outflow, precipitation, and evaporation. The circulation corresponding to average forcing is considered as climatic.

Sec. 2.2]

Lake models

69

A coupled simulation of the lake hydrodynamics and ecosystem evolution by 3D models has been performed for the Great American Lakes (Chen et al., 2002, Schwab and Beletsky, 2003), for Lake Baikal (Tsvetova, 2003), and the Great European Lakes (Menshutkin and Vorobyeva, 1987; Rukhovets et al., 2006a). In the present book, the authors describe the results of simulations of hydrodynamics and chemical-biological processes on the climatic and seasonal scales in Lakes Ladoga and Onego, performed by coupled models. 2.2 LAKE MODELS: STATE OF THE ART. PROBLEM FORMULATION FOR THE SIMULATION OF LAKE HYDROTHERMODYNAMICS 2.2.1 Introduction Modelling of currents and thermal regime in waterbodies implies, explicitly or implicitly, that researchers state the problem before themselves to reproduce events of particular spatial and temporal scales. Selection of scales depends on the purposes of study, on what are, at the time of the investigations, the achieved levels in the given knowledge area in describing the study problem and, finally, on what options researchers have (Imberger, 1994; Wust et al., 2000). Let us try to answer these questions, but very briefly. The main objective of hydrothermodynamic regime modelling of waterbodies in our monograph, as mentioned above, is to provide ecological models with information about the abiotic environmental factors, primarily hydrophysical processes, that control to high degree the functioning of aquatic ecosystems. For large stratified lakes with considerable horizontal dimensions (hundreds of kilometres) and depth (hundreds of metres), complex morphometry and a high variability of hydrophysical conditions, especially during the vegetation period, is typical. This is defined by the existence during this period of both vertical and horizontal temperature stratifications. For example, in Lake Ladoga the amplitude of horizontal temperature changes reaches 15°C between the shallow part in the south and the deep-water zone in the northwestern part of the lake (Tikhomirov, 1982). When summer stratification is well developed the amplitude of vertical change fluctuations also can reach 15°C (Tikhomirov, 1982). In Lake Onego the amplitude of temperature variations is also considerable: in the horizontal direction not less than 6°C, and in the vertical not less than 10°C (Lake Onego . . . , 1999). This dictates the necessity to use three-dimensional models for simu1ations. In this work mathematical modelling tools will be used to reconstruct the largescale circulation of Lakes Ladoga and Onego. The classification scheme of movements in the World Ocean suggested by A. S. Monin, defines large-scale circulation as a statistical ensemble of movements of such formations that can be described individually. This point of view has led in numerical modelling to a relation between 'large-scale' circulations and the computing power used to build this model. Byanalogy with this approach, and taking into consideration the computing resources available to the authors, by the term large-scale circulation of a large stratified lake we

70

Hydrothermodynamics of large stratified lakes

[Ch.2

shall understand the dynamics of such forms whose dimensions are comparable with spatial grid resolution in discrete models. For example, when lake horizontal length is of the order of 105 m and depth is of the order of 102 m, the horizontal grid resolution possible to use is about 103 m and the vertical resolution is about 30 layers. By this the individual description can be given only to global elements of lake dynamics. While modelling the large-scale circulation of large stratified lakes, it is logical to choose for the temporal scale the time of the global lake dynamic elements scale. It is reasonable to use in this case a synoptic interval equal to 5-7 days. For reproduction of annual ecosystem functioning on the basis of mathematical modelling for forecasting 10-15 years' reaction to anthropogenic loading changes, it is natural to consider that the lake circulation corresponds to some mean climatic conditions of external forces on the waterbody. Wind, heat flux through the water surface, tributary inflow and discharge, precipitation and evaporation describe this forcing. The lake circulation that can be defined by mean annual monthly values of external impact on the waterbody we will call climatic circulation. The lake internal circulations' classification is presented by Filatov (1983). According to this classification, the climatic circulation consists of the general waterbody circulation, covering the major part of the lake water volume, repeating from one year to another cyclonic and anticyclonic flows and local currents in the near-shore regions, i.e, formations comparable in size with the lake dimensions and in time of existence with the synoptic scale. 2.2.2

Equations of geophysical hydrodynamics

For describing the large-scale circulation and thermal regime of large stratified lakes located beyond the equatorial zone in the northern hemisphere, three-dimensional mathematical models described in the Cartesian coordinate system of ocean geophysical hydrothermodynamics are used. The Cartesian coordinate system can be used in this case because, as a rule, the length of freshwater lakes allows us to neglect the Earth's curvature and to consider the undisturbed water surface as flat (Oganesyan and Sivashinsky, 1983). Similarly as for the ocean the following hypotheses are valid: the Boussinesque assumption, the hydrostatic hypothesis, simplification of Coriolis terms, and the equation of entropy transport written approximately, in the form of a heat transfer equation in moving media. The dimensions of Lakes Ladoga and Onego enable us to use a constant Coriolis parameter. A nonlinear empirical relation is used as the freshwater state equation. To write down model equations the following notation is introduced. Let the plane x 0 y of the Cartesian coordinate system coincide with the undisturbed liquid surface and axis z is directed upward. Let us denote by So a two-dimensional domain corresponding to the undisturbed waterbody surface. A three-dimensional domain occupied by the waterbody will be denoted as n, the vertical lateral boundary of the waterbody as SI, the waterbody bottom-surface z = -H(x,y) as S2. Let denote an = So U SI U S2 as a boundary of n. Designate n as an external normal vector to an.

Lake models

Sec. 2.2]

71

In the case where there are islands in the waterbody domain, n is multiconnected. To simplify the situation, i.e. to consider single-connected domains only, it is possible to use a 'submerged' islands approach. This method was justified by Rukhovets (1990). From now on domain n is considered to be single-connected. Let us consider that H(x,y) ~ H o > 0, where H o is a given value. Let us write down model equations (Marchuk and Sarkisyan, 1980; Marchuk et al., 1987)

au au au au 1 ap a (au) -+u-+v-+w--lv=---+k zat ax ay Bz Pw ax Bz Bz

a ( k -au) +a ( kau) +ax x ax ay Y ay

(2.1)

et et et et at + u ax + v ay + w az =

ap az = -pg,

(2.3)

au all aw_ ax + ay + Bz - o,

(2.4)

a (aT) az liz az

a (aT) lIx ax

+ ax

p = p(T,P).

v

a (

+ ay

lIy

aT) ay ,

(2.5) (2.6)

Here = (u(x, y, z, t), v(x, y, z, t), w(x, y, z, t)), is the water velocity vector; I is the Coriolis parameter; P(x,y,z, t) is the pressure; T(x,y,z, t) is the water temperature; p is freshwater density; Pw is the average freshwater density; g is gravity acceleration; kx(x, y, z, t), ky(x,y, z, t), kz(x,y, z, t) is the coefficient of turbulent viscosity; and vx(x,y, z, t), vy(x,y, z, t), vz(x,y, z, t) is the coefficient of turbulent diffusion. The system of equations (2.1)-(2.5) provided that density p is given by (2.6), includes five unknown functions: projections of velocity vector, u, v, w, hydrodynamic pressure P and temperature T. When applying boundary conditions it should be kept in mind that for many large lakes the river inflow and outflow have to be taken into account because of their role in lake water balance, thermal regime and water quality generation. It is also important to include precipitation and evaporation, which is simpler to do by varying river inflow and outflow. A free waterbody surface is given by a function ~(x,y, t), i.e. the equation z = ~(x,y, t). Since the main objective of hydrothermodynamic modelling is to reproduce a large-scale climatic circulation, for large deep lakes it is possible to consider that ~(x,y, t) is small compared to waterbody depth and that surface boundary conditions can be applied on undisturbed water surface at z = 0 (Kamenkovich, 1973; Pedlosky, 1986). This is true both for kinematic and dynamic boundary conditions. On the surface of lakes such as Lakes Ladoga and Onego the horizontal atmospheric

72

Hydrothermodynamics of large stratified lakes

[Ch.2

pressure gradient is neglected and it is assumed that P(x,y, z, t) in equations (2.1)-(2.3) is a deviation of the hydrostatic pressure from atmospheric pressure. Let us write down the boundary conditions at a surface z = 0:

k z

au _

Tx

k,

Bz - Pw '

av =

(2.7)

Ty •

Bz

Pw

Here T x , Tv are wind stresses. For w on the surface at z = 0 the boundary condition is applied

w=

8~

Bt '

Q

Q

= 0,1.

(2.8)

When Q = 0, this is the 'rigid lid' boundary condition (Kamenkovich, 1973; Pedlosky, 1986); when Q = 1, this is a linear approximation of the condition

w = 8~ + U 8~ + v 8~ 8t Bx 8y at the free surface. On a waterbody bottom at z = -H(x,y) for u, v, w the slip boundary conditions are prescribed (2.9)

u = v = w = 0, or TH x

8u 8N

Pw

w= where T!f,

H

8v 8N 8H 8x

T --L Pw

(2.10)

8H 8y

(2.11)

-U--V-,

Tf bottom friction stresses, and 8cp _

8cp

8cp

+ k y ay

aN = k x ax cos(n, x)

cos(n, y)

8cp

+ k, az cos(n, z)

is a derivative along the co-normal. On the vertical lateral boundary of the waterbody the following boundary conditions are used: on the solid part of the boundaries (2.12)

u = v = 0, at the inflow and outflow rivers sites

u= ur ,

v=

Vr

(2.13)

where u-, Vr are given functions of space coordinates and time. For temperature boundary conditions the following are used: at z = 0

8TI

Vz -

Bz

So

1 =-v-Q, cpPw

(2.14)

A climatic circulation model for large stratified lakes

Sec. 2.3

73

where Q is the heat flux through the surface of waterbody, or (2.15)

Tis = T s,

where T, is a surface temperature; at bottom and solid lateral boundaries the thermal isolation conditions are prescribed

aT =

aN

0

'

et et aN =. V x ax cos(n, x)

et

+ "» ay

et cos(n,y) + V z az cos(n, z).

(2.16)

At the sites of inflowing rivers the following condition is used

;~- vnCT- Tr) =

0,

(2.17)

where v" is the projection of velocity vector on the outer normal to the 'live' river transect, and T, is the given water temperature in the river. At the sites of outflow rivers the condition (2.16) is applied. Besides boundary conditions the initial conditions at t = 0 should be given u(x,y,z, 0) = uo(x,y,z),

v(x,y,z,O) = vo(x,y,z),

T(x,y,z,O) = To(x,y,z)

(2.18)

There now exist enough examples of this type of mathematical model application to solve prognostic problems of ocean dynamics. One of the first was a model by Bryan (1969, 1975). Nowadays the three-dimensional ocean model developed at Princeton (USA) in 1977 (Blumberg and Mellor, 1987) is one the most widespread numerical circulation models. This model has been updated from time to time. One of the latest revisions was done in 1996 (Mellor, 1996). It is also used to model large stratified lakes.

2.3 A CLIMATIC CIRCULATION MODEL FOR LARGE STRATIFIED LAKES 2.3.1

General comments

A large number of studies are devoted to mathematical modelling of the dynamics and thermal regime of the greatest lakes of the world. Mathematical modelling results of the Great American Lakes are presented in Bennet (1974, 1978), Simons (1973, 1974, 1975, 1976), Lick (1976); of Lake Sevan in Satkisyan (1977); of Lake Issyk-Kul in Arkhipov (1986); of Lake Ladoga in Okhlopkova (1966), Akopyan et al. (1984), Astrakhantsev and Rukhovets (1988), Astrakhantsev et al. (1987, 1998) and others. The review of works devoted to lake modelling can be found in monograph of Filatov (1983, 1991). At the present time, for the hydrodynamic modelling of large stratified lakes three-dimensional oceanic models are used that have proved to be reliable. One of them is the already-mentioned model of Blumberg and Mellor (1987) and its modifications. So this model, based on the primitive equations (2.1)-(2.6), is used for the hydrothermodynamic regime study of the Great American Lakes (Beletsky et al., 1999; Beletsky and Schwab, 2008a, b; Chen et al., 2002; Beletsky et al., 2006).

74

Hydrothermodynamics of large stratified lakes

[Ch.2

For reproducing large stratified lakes climatic circulation the authors use a slightly modified mathematical model of the ocean climatic circulation (Marchuk and Sarkisyan 1980; Marchuk et al., 1987). The latest model is a simplification of the model described in section 2.2.2. The climatic circulation model used by the authors (Astrakhantsev and Rukhovets, 1993; Astrakhantsev et al., 1998, 2003) has a number of differences compared with the ocean climatic circulation model (Marchuk and Satkisyan, 1980; Marchuk et al., 1987). This model takes into consideration factors that are not so essential for the ocean, such as river tributaries inflow and outflow, precipitation and evaporation. As the equation of state a nonlinear equation is used, i.e, water density anomaly in fresh water plays a substantial role in the formation of waterbody circulation (the fields of velocity flows and fields of temperature) when its temperature equals 4°C. Furthermore, in the equation for density evolution (Marchuk and Sarkisyan, 1980; Marchuk et al., 1987) the terms describing the horizontal turbulent diffusion of density are absent. The analysis of temporal-spatial scales shows that in equations of heat distribution for large lakes, terms describing horizontal turbulent diffusion are as significant as terms describing vertical heat turbulent diffusion. Let us estimate, as is usually done (Sarkisyan, 1977; Filatov, 1983; and others), the comparative value of terms

aza (Vz aT) az

and

a ( aT) ax Vx ax '

in the equation of heat distribution, using characteristic values of variables in these terms for Lake Ladoga. To perform such estimates let introduce the following notation for the characteristic scales of the corresponding variables and functions: L - characteristic linear scale in horizontal direction, H - characteristic linear scale in vertical direction, v~ - characteristic scale for the coefficient of horizontal heat turbulent diffusion, v~ - characteristic scale for the coefficient of vertical heat turbulent diffusion,

TO - characteristic scale for water temperature. Introducing nondimensional values

x=x/L, y=x/L, z=z/H,

Vx =

V

vx/v~, z = vz/v~,

follows:

T=

T/To; let us transform the terms we are interested in as V~

L2TO

a(_ aT) ax .

ax

V

x

Thus the comparative estimates of the considered terms is reduced to a comparison of values v~/H2 and v~/L2: characteristic scales of variables and functions for Lake Ladoga we have taken from the publications of Filatov (1983) V~

v~

L

H

5 ·10-3ms-1

102ms- 1

105m

102m

A climatic circulation model for large stratified lakes

Sec. 2.3

75

Calculations give o

2= 5.10-7 H2

'

For Lake Onego similar estimates are of the same order of magnitude, despite the fact that Lake Onego is smaller than Lake Ladoga. Hence, for these lakes it is not reasonable to neglect terms describing horizontal diffusion of heat, since they do not differ considerably from the retained terms. For this reason, in the model of lake climatic circulation, equation (2.5) is used without modifications. In the model of large-scale climatic circulation of the ocean (Marchuk and Sarkisyan, 1980; Marchuk et al., 1987), in equations of motion nonlinear terms and terms describing horizontal turbulent impulse exchange are neglected. Such simplification of the motion equations for large stratified lakes can be justified, as was mentioned above, after comparative analysis of different motion equation terms for the dimensional-temporal scales of the waterbodies examined. Taking into account the evolution of large-scale dynamics elements over time, it is impossible to make this analysis universal. So, for example, in Lake Ladoga in summer during the period of developed stratification the difference between bottom and surface temperatures exceeds 15°C, and in autumn vertical homothermy is observed. The specific surface flow velocity in ice-free Lake Ladoga is about 10- 1 m, and under ice the velocity is less by an order of magnitude. The same considerations are true for the differences in other hydrothermodynamic characteristics for various parts of the lake. According to Filatov (1983), the coefficient of vertical turbulent viscosity in the upper layer is about 5 . 10-3 m2 s", as near the bottom its magnitude is around 5 . 10-5 m2 s:'. To justify excluding nonlinear terms and terms describing horizontal turbulent viscosity let us determine an order of Rossby and Ekman numbers (Sarkisyan, 1977)

where uo is the characteristic horizontal velocity, 1is the Coriolis parameter, Land H are characteristic values of horizontal and vertical linear scales, and k~, k~ are characteristic values of coefficients of horizontal and vertical turbulent viscosity, accordingly. For Lake Ladoga and Lake Onego, with the water surface free of ice, beyond coastal and the near-bottom boundary layers it is possible to consider as characteristic scales the following:

uo =

10-1ms-1 ,

Then we will get that

L= 105m,

1= 10-4 S-

1

,

H= 10m,

76

Hydrothermodynamics of large stratified lakes

[Ch.2

This simple analysis shows, that neglected nonlinear terms in the motion equation and terms describing horizontal turbulent viscosity are small, compared with other terms of these equations. Besides, it follows from this statement that in the near-surface layer the known geostrophic relations (the balance between pressure gradient and Coriolis force (see, for example, Sarkisyan, 1977)) are not suitable even for rough estimations. As already mentioned, the magnitude 105 s, used as the characteristic timescale, equals the synoptic scale. Taking this value into account in the relative analysis of terms in the motion equation, we will find that the order of coefficients with derivatives in time is 10- 1, and that is why there is no reason to neglect them. For the near-bottom layer, during the period of developed stratification, dimension analysis shows that the Rossby number and the horizontal Ekman number are of the same order, around 10-3 • Thus the relative roles of nonlinear terms and terms describing horizontal turbulent viscosity change, but, as mentioned above, they are still small compared with the retained terms of the equations. A special treatment is needed for the coastal and near-bottom boundary layers. But the possibility of their reproduction in the frame of the general threedimensional computational model of the waterbody depends on the resolution of the grid used. According to estimates and velocity field observation data, the nearcoastal boundary layer in Lake Ladoga does not exceed several kilometres (not more than 10 km), and the near-bottom layer does not exceed several metres (Filatov, 1983, 1991). The rectangular grid used in the discrete model permits a grid size of about 2.5 km in the horizontal dimension. It is obvious that this does not allow correct reproduction of the coastal boundary layer. Insofar as grid steps along the vertical axis in the deep part have an order of tens of metres, then in fact the same situation takes place in the near-bottom boundary layer. It is worth mentioning that at the present time the authors use for computations a grid with 0.6-km resolution in the horizontal direction and larger number of steps in the vertical direction than in Astrakhantsev et al. (1998, 2003). This approach has improved modelling results. These aspects will be discussed more precisely when the modelling results are described. The remarks and plausible reasoning mentioned above make it possible to conclude that model selection for the reproduction of the climatic circulation of a large stratified lake is sufficientlyjustified. Further, when discussing the computation experiments we will once more return to the problem of model adequacy. 2.3.2 Mathematical formulation The equations of motion and continuity, where the deviation of pressure from atmospheric is replaced by the relation from the hydrostatic equation (2.3) in the following way:

A climatic circulation model for large stratified lakes

Sec. 2.3

77

look like (2.19) (2.20) (2.21)

It should be emphasized that compared with equations (2.1) and (2.2) momentum terms and terms describing horizontal turbulent exchange have been neglected here. The Coriolis parameter I, is considered constant for the sake of simplicity. As equation of state one of the empirical relations such as

p = p(T), is accepted, where the dependency between density and pressure is not taken into consideration. For Lake Ladoga with depths not exceeding 230 m it is justified. For Lake Baikal in the model developed by Tsvetova (2003) the dependency between density and pressure is taken into account. As for the considered model, the following equation of state is used (Simons, 1973)

p(T) = Pw[1 - 6.8 . 10-6(T - 4)2],

[T] = DC.

(2.22)

The heat transfer equation in the climatic circulation model for lakes coincides with equation (2.5):

et a ( x aT) a ( y aT) a ( aT) at + u et ax + v et ay + W et az = ax V ax + ay v ay + az Vz az

(2.23)

Coefficients vx , vy, Vz in (2.23) and k z in (2.19)-(2.20) are considered to be the functions of variables x, y, z and t. For projection of the velocity vector the boundary conditions are the following:

k,

au I Bz

So

T

x

k,

Pw

wl so =

Q

av I Bz

So

T

y

(2.24)

Pw

a~

at'

(2.25)

where T x , T» are the horizontal components of the wind stress; on the bottom when z = -H(x,y)

k, P

I

= k;

U

+ V2,

C::I=k;

en- - Ven wi So = - U -, ax ay

2+V

(2.26) (2.27)

78

Hydrothermodynamics of large stratified lakes

where

V=

r,

[Ch.2

r,

(U, V) is the vector of average depth velocities U=

~

u(x,y,z, t)dz,

V=

~

v(x,y,z, t)dz,

at the vertical lateral surface (2.28) where v" is the projection of the velocity vector onto the external normal to the lateral surface and VQ

0 in solid boundary points (no-flux boundary condition), = { prescribed values in inflow and outflow river sites.

The boundary conditions for T (x, y, z, t) here are determined in the same way as for equation (2.5); these are conditions (2.14), (2.16) and (2.17). For further convenience we will repeat them: on the waterbody surface at z = 0

aT I

aN

= _1_

cpPw

So

Q

(2.29)

'

on all solid boundary and in sites of outflowing rivers

aTI aN

(2.30)

=0, SOUl

at locations of outflowing rivers

[~~- vnCT- Tn)] Iso =

(2.31)

O.

2.3.3 Realization of the model In this section we will discuss some aspects of the mathematical model important for the development of the discrete model (Astrakhantsev and Rukhovets, 1993). First of all it should be mentioned that equations

v

wl so=

div = 0,

a~ Q

at'

wl S2 =

-u

en en ax - v By '

are equivalent to equations divv= 0,

en- - Ven wi S2 = - U -, ax ay

(2.32)

In fact, averaging (integrating) the continuity equation along the z axis in a range from -H(x,y) to 0, we will get the equality

r .- r r -H

a dlvvdz=-a X

-H

a udz+-

aY

-H

vdz+wl so -

(aH )I "»:X + ven aY- +w S2,

A climatic circulation model for large stratified lakes

Sec. 2.3

79

from which this equality follows. It is worth noting here, that instead of using the boundary condition (2.25), equation (2.32) eliminates the need to comply with two boundary conditions for w (at the surface (2.25) and at the bottom (2.27)). Such a necessity arises from determining w from the continuity equation, as is common in geophysical hydrodynamic models. Using equations (2.32) along with equations (2.19), (2.20) and boundary conditions (2.24), (2.26) and (2.28) makes it possible at every time-step, assuming that function T(x,y, z, t) is known, to formulate the closed mathematical problem for defining U, V and e. Actually, let us average equations (2.19), (2.20) and boundary conditions (2.28) by z within limits from -H(x,y) to 0, applying boundary conditions (2.24) and (2.26). Then for determining U, V and ~ we will get the following system of equations 8_

at

fV

+ g W = _ h jUV+~_-L( f8PdZdz',

ax

H

Hpw

Hpw

J-H z ax

(2.33) Q

8(, + 8(HU)

at

+ 8(HV) =

ax

ay

0

and boundary condition 1 V1aso = Va == H

r-H

(2.34)

vnl S1 dz.

Boundary conditions (2.26) at the waterbody bottom, used for receiving the system (2.33), (2.34), represent the well known simplest parameterization of waterbottom friction (Stommel, 1963). Such parameterization in the linearized representation was used in Marchuk and Sarkisyan (1980). Boundary conditions (2.26), naturally, are quite a rough parameterization. In computer experiments to reproduce the climatic circulation of Lake Ladoga (Astrakhantsev and Rukhovets, 1988) parameterization by local velocities was used, for example, at the bottom, the following boundary conditions were imposed

Kz

;U!

=

J/ +

Kz

t!

=

+ v2 .

(2.35)

We will point out, that equations (2.19), (2.20) seemingly do not require the definition of boundary conditions (2.28) at the vertical lateral boundary because (2.19) and (2.20) do not contain derivatives of functions u and v with respect to variables x and y. Nevertheless, the condition (2.28) is necessary if we want heat and mass conservation laws to be met. The selection of the boundary condition (2.31) at inflowing rivers is related to the fact that in the discrete model is easier to impose boundary conditions of the second and third type (natural boundary conditions) and also because, when condition (2.31) is used, it is possible to reproduce accurately in the discrete model the law of heat variation. If we keep in mind the real values of vx , vy, vz , then it easy

80

Hydrothermodynamics of large stratified lakes

[Ch.2

to understand that boundary condition (2.31) can be interpreted as an approximation by a penalty method of the conventional boundary condition imposed at inflowing rivers

Tlsin 2.3.4

=

r;

Generalized formulations of the mathematical model

To build a discrete (numerical) model approximating the original mathematical model the authors turned to the generalized formulation of the initial model in the form of integral equations equivalent to the original equations. This approach is rather traditional. It dates back to works by Courant et al. (1940) and Ladizhenskaya (1970). For the equations of geophysical hydrodynamics this approach was used in the works ofPenenko (1981), Astrakhantsev and Rukhovets (1986) and others. This approach is also used when discrete models are built using the finite element method. Heat distribution equation

Multiplying equation (2.23) by an arbitrary differentiable function (x,y, z, t) and integrating the obtained equality over the domain n, after the integration by parts of higher derivatives and taking into account boundary conditions (2.29)-(2.31), the following integral identity is obtained

et

J8icI>dO fl

= -

J( fl

Vx

et a

et a

et a
ax ax + vy ay ay + Vz az az

dO

-J(u aT + v aT + w aT) cI> dO + --i- J Q dS ax ay Bz cpPw n

So

+ Lin vo(T- Tr)cI>dS,

(2.36)

dO = dxdydz.

Law of heat variation in a waterbody

Assuming that in this identity == 1 and integrating by parts the convective terms, we will get the equality a J Tdn=J TdivVdn-J v"TdS+J Vo(T-Tr)dS+--i-J QdS. at n n an Sin cpPw So By virtue of boundary conditions after the multiplication by c;Pw this equality will take the form:

J

: c;Pw Tdn = t n

J Q dS - c;Pw J voTdS - c;Pw J voT dS - QC;Pw J ~~t TdS. So

r

SOUl

Sin

So

(2.37) It is generally agreed to call this equality the law of heat variation.

A climatic circulation model for large stratified lakes

Sec. 2.3

81

Momentum equations Momentum equations (2.19), (2.20) correspond with the following integral identities:

J lv

J at o

au dO -

J

J Pw dS Bz Bz - gJo aa~x dO + k2 J uJU2 + V2

dO = -

0

0

k, au

a dO +

T

x



So



S2

Jax cI> dO, J k, avBz awBz dO + J Pw W dS

x cos(n, z) dS -

J avat w + J luw dO

o

dO = -

0

af

fl

T

0

(2.38)

y

So

-gJo =~WdO+k2J Y x cos(n, z) dS -

J fl

S2

VJU2+ V2w

af ay "I]!dO,

(2.39)

where , Ware arbitrary differentiable functions. The derivation of these identities is similar to that of the heat distribution equation. Law of mechanical energy variation Let the deviation of a pressure from atmospheric be represented in the form:

gpw(~ - z) + g

p =

f

p'dz' == -gpw z

+ P',

p' = p - Pw·

It should be noted also that in equalities (2.38) and (2.39) functions can be rewritten as follows

af = ~ ax ax

(.!-fp' dZ)' Pw

af = ~ ay ay

z

cr- dZ). Pw

Substituting into the identities (2.38) and (2.39) as and

u =

u =

Pw U ,

af/ax and aflay

z

w

Pw v

After the identical rearrangements, integrating by parts, and taking into consideration continuity equation and boundary conditions for w, the following relation is derived

ata Pw

J u2 + v2 0 --

2

J -oj

+

(TxU

So

So

dO = -Pw

J fl

+ TyV) dS - k2pw

p,a~ dS -

at

J

SinUSout

k,

[(00)2 az + (av)2] az

dO -

J' fl

J (uU + vV)JU2 + V2 dS S2

P'vndS.

gp wdO

82

Hydrothermodynamics of large stratified lakes

[Ch.2

r

Let us replace pI in this equality with the formula

r' in the integral, containing

ata

[J

a~/at.

= gpwf.

+g

(2.40)

p' dz'

We come to

2

u + v2 n Pw - 2 - dO+a

J gPw"2~2] dS So

J (TxU + TyV) dS - k2pwJ (uU + vV) JU2 + V2 dS - J r'v; dS. +

So

SO

(2.41)

Sin US out

This mathematical relationship describes variations of the mechanical energy of horizontal movements. Further, we will call this relation a law of mechanical energy variation (conservation). This law is one of the characteristics of our model of climatic circulation in a stratified lake. Let compare this law with the other one for the model formulated in section 2.2.2. We will write it down without going into the details of its derivation,

+ v2 ~2] ata [Jn Pw -u 2 - dO + a J So gpw "2 dS 2

= -

In

-J

n

+

pw{ k x

[

(=:Y (=:Y] +

+ ky

[

(=;Y (=;Y] +

gplwdn+J (UTx+VTy)dS+J

J.

~U~~

So

Pw ( : u; + : ; vr ) dS -

+ k, [

(~:Y + (=:Y] }dO

Pw u;;v; vndS Sin U S out

J.

~U~t

r's; dS - a

J Po u ~

2 ;

v2

~; dS. (2.42)

Skipping the details due to differences in boundary conditions at the bottom of the waterbody in compared models, we compare only the terms describing dissipation: at characteristic scales of horizontal velocity uo = 10- 1 m s", linear horizontal dimension of the waterbody L = 105 m, and average depth of the waterbody 50m, we will find that the dissipative terms absent from (2.41) are by at least two order of magnitude smaller than the present dissipative term. Laws of heat and mechanical energy variation (2.37) and (2.41) for the model of climatic circulation practically coincide with the analogous relations for the 'full' model described in section 2.2.2, despite the fact that the equations of climatic

A climatic circulation model for large stratified lakes

83

circulation were obtained by simplification of the 'full' model equations. The similarity of these laws is one of the confirmations of the physical adequacy of the model of climatic circulation in a waterbody to represent reality. 2.3.5 About the discrete model For the computer realization of a climatic circulation model of a large stratified lake a discrete model was developed by the authors and an algorithm for computation was suggested (Astrakhantsev and Rukhovets, 1986, 1993; Astrakhantsev et al., 1998, 2003). The first finite-difference models of large-scale ocean dynamics originate in the publications of Sarkisyan (1977), Bryan (1969) and Marchuk and Sarkisyan (1980). As has already been mentioned, by the present time a lot of computational algorithms have been developed for the realization of three-dimensional mathematical ocean circulation models. Here only the work previous to the authors' discrete model will be mentioned. This is the study ofPenenko (1981), where discrete models for the approximation of hydrothermodynamic models of the atmosphere are constructed by the method of sum approximation. The same method was used for the construction of the Lake Baikal discrete model (Tsvetova, 1977). The first discrete model for the reproduction of the climatic circulation of large stratified lakes was constructed by the authors using the method of sum approximation of the integral identities (2.36), (2.38), (2.39), representing generalized formulations of mathematical model equations (Astrakhantsev and Rukhovets, 1986). On the basis of this model the annual climatic circulation of Lake Ladoga was reproduced (Astrakhantsev et al., 1987; Astrakhantsev and Rukhovets, 1988). Later Astrakhantsevand Rukhovets (1993) developed a discrete model; its computer realization was completed only in 1999 (Astrakhantsev et al., 1998). This model is used at present in the authors' studies of Lake Ladoga and Lake Onego dynamic modelling (Astrakhantsev et al., 2003; Rukhovets et al., 2006c). The creation of discrete models usually starts with decomposition of the mathematical model into separate blocks such as, for example, equations of motion, heat transfer equations and others. The capacity of sufficiently powerful computers allows us to solve the problems only on grids for which, strictly speaking, it is not always possible to confirm that discrete models at full scale adequately reproduce the 'behaviour' of mathematical models. That is why it is especially important to require from discrete models the correct reproduction of the main qualitative and quantitative properties of the models. As has been mentioned by many authors during the development of discrete models, it is desirable to obtain the following objectives: - implementation of the main relationships between the blocks of the discrete model and the blocks of the mathematical model; - implementation for the discrete model of the laws of conservation (variation) discrete analogues of mathematical model conservation laws which should be implemented precisely, for example, with round-off error precision, not with approximation error precision.

84

Hydrothermodynamics of large stratified lakes

[Ch.2

These statements are especially important in the development of long-term computational models. The sum approximation method used by the authors first allowed us to develop schemes for three-dimensional approximation on a minimal seven-point pattern; secondly the approach selected by the authors allowed us to reproduce in discrete form the main properties of the initial mathematical model, such as heat transfer, mass conservation, mechanical energy changes of horizontal motion and others. For the Navier-Stokes equations difference schemes with the feature of convective terms neutrality were constructed by Ladizhenskaya (1970). The authors used this approach for the construction of the heat transfer equations scheme. Further details concerning the discrete model developed by the authors and the methods of its construction can be found in (Astrakhantsev et al., 2003).

3 Climatic circulation and the thermal regime of the lakes

3.1 THE CLIMATIC CIRCULATION IN LAKES LADOGA AND ONEGO FROM OBSERVATIONAL DATA AND ESTIMATES The definition of 'climatic circulation' for large stratified lakes has already been given in the previous chapters. Let us briefly discuss the climatic circulations of Lake Ladoga and Lake Onego characteristics on the basis of observations and empirical calculations (Hydrological Regime . . . , 1966; Tikhomirov, 1968, 1982; Demin and Ibraev, 1989; Filatov, 1983, 1991; Lake Onego, 1999). The lake water mass dynamics depends on various factors. Firstly, there is the influence of atmosphere - roughness, friction resistance on the water surface, heat exchange through the water surface (cooling or heating), moisture exchange (precipitation and evaporation). The nature of the dynamic and thermal processes is also defined by the morphometry of a lake and the river runoff (tributaries inflow and outflow). Atmosphere-water interactions, heat flux, tributary inflow and outflow generate density stratification and, as a result of water temperature distributions, create water currents. Lakes Ladoga and Onego are both dimictic. In autumn and spring vertical homogeneity is observed in the lakes. In spring, after ice melting, the upper layer heating starts. As the maximal density of fresh water is observed, when the water temperature is nearly 4°C, convective mixing arises as a result of heating. Gradually it reaches the bottom, as in winter, both in Lake Ladoga and Lake Onego, water temperature is lower than the temperature of the maximum density (in winters with fractured ice cover, the water temperature near the bottom in Ladoga goes down to 2°C (Tikhomirov, 1963)). Water column mixing takes place for the second time during autumn cooling. Lake Ladoga

When the water temperature in spring exceeds 4°C, vertical stratification starts to develop in the lake. At that time heating increases hydrostatic stability. Wind-mixing

86

Climatic circulation in Lakes Ladoga and Onego

[Ch.3

results in the formation of an upper mixed layer (epilimnion) and a thermocline (metalimnion) below it. It is worth noting that twice a year, as already noted, the mixed layer reaches the bottom. In the ocean, unlike in lakes, the salinity stratification prevents the penetration of the mixed layer to great depths. Vertical stratification reaches its maximum development by the end of summer. A massive dome of cold water with a temperature of about 4 DC is formed in the bottom layers (hypolimnion). Autumn cooling destroys stratification. Inverse stable stratification is built up in winter. The temperature gradients during this period are small, the amplitude of temperature fluctuations is within the interval 0-4 The thermal bar is an important phenomenon in the lake and is related with horizontal stratification (Tikhomirov, 1963). In spring, after ice melting, the heat flux to the waterbody can be considered with reasonable accuracy to be homogeneous over the whole surface. That is why shallow coastal waters are heated more strongly than the deep part of the lake. Due to temperature stratification in the 4 C isotherm area, are intensive downwelling flux of 'dense' water is formed (Tikhomirov, 1963, Zilitinkevich and Terzhvik, 1989; Zilitinkevich et al., 1992). The frontal zone generated by this flux is called a thermal bar, as already mentioned in Chapter 1. In the heating process the 4 DC isotherm moves farther from the coast to the deep part of the lake until the water temperature exceeds 4 C. According to observations (Tikhomirov, 1963, 1982) the speed of thermal bar movement in Lake Ladoga is on average 0.15kmday-l, sometimes reaching 0.6kmday-l. The thermal bar substantially influences the flow field. Its front divides the lake into two parts almost without horizontal exchange between them. The thermal bar exists in Lake Ladoga for 2.0-2.5 months (from the end of April till the middle of July). It is worth mentioning that the thermal bar plays an important role in the transfer of substances coming into the lake via tributaries and surface runoff. Thus all incoming substances are concentrated in the coastal zone while the thermal bar is in existence. A brief description of water-temperature variability in Lake Ladoga given here and in Chapter 1 shows that it is significant in both the vertical and horizontal directions. That is why the application of one- and even two-dimensional models to reproduce the temporal dynamics temperature field is rather problematic. The problem of water-temperature field reconstruction and its evolution, as mentioned by a number of researchers, is in fact the only large-scale dynamics issue that can be reliably verified since water temperature is measured almost regularly. It is also true when considering large lakes. Lake Ladoga according to Tikhomirov (1982) 'is a classical water object, where fully and clearly thermal structures are revealed'. A vast experimental database has made it possible to compare modelling results and observations, both qualitatively and quantitatively. It is worth mentioning that reproduction of annual thermal dynamics for Lake Ladoga using a numerical model was performed for the first time by Astrakhantsev et al. (1987) and Astrakhantsevand Rukhovets (1988). Large-scale circulations in Lake Ladoga have not been studied as well as the thermal regime, in spite of long-term research. The results of experimental studies, summarized in the book Hydrological Regime and Water Balance of Lake Ladoga (Malinina, 1966) give an impression of the large-scale circulation in spring, summer DC.

D

D

Sec. 3.2]

On the problem of simulating climatic circulation

87

and autumn (partly) periods. Late autumn and especially winter circulation in Lake Ladoga, as in many other large lakes, is not well known. An intensive cyclonic circulation during the open water period is observed in Lake Ladoga, as in other large stratified lakes in the northern hemisphere (Okhlopkova, 1966; Filatov, 1983, 1991). A deep understanding of the large-scale circulation in Lake Ladoga was achieved using mathematical modelling. Computations of currents were reported in the following publications: Okhlopkova (1966) and Filatov (1983, 1991). In the pioneer work of Okhlopkova (1966) density currents were calculated by a dynamic method using the data of thermal observations during spring, summer and autumn. The results of current simulations presented by Filatov (1981, 1991). In these publications, full three-dimensional models of geophysical hydrodynamics in diagnostic version were used to compute flow fields in Lake Ladoga. Lake Onego

As has been mentioned, Lake Onego is smaller than Lake Ladoga and located to the northwest of Lake Ladoga. Nevertheless the general characteristics of temperature field evolution are similar to those of Lake Ladoga. Later in this chapter were present annual climatic circulation calculation results for Lakes Ladoga and Onego obtained with the computer models formulated in mathematical terms in section 2.3. This chapter content is based on the authors' works (Astrakhantsev et al., 1998, 2003; Lake Onego, 1999; Rukhovets et al., 2006d).

3.2 ON THE PROBLEM OF SIMULATING CLIMATIC CIRCULATION To reproduce the climatic circulation the numerical periodic solution of the mathematical model (2.19)-(2.31) with a period equal to one year should be found. It is natural to assume that all external forcing periodic functions of time with a period equal to one year, i.e. cp(x,y, z, t + 1 year) = cp(x,y, z, t). In order to build the periodic solution, as is usually done, the initial conditions for v and T should be given: vlt=o = Vo = (uo(x,y,z), vo(x,y,z), wo(x,y,z)), 11t=o = To(x,y,z),

(3.1)

and then the initial boundary value problem (2.19)-(2.31), (3.1) has to be solved until we get a periodical solution. To get the periodical solution of the problem (2.19)-(2.31) let us introduce denotations: Vp = (up, vp, wp), Tp . In this case it is essential to estimate the physical time needed by the system to obtain a periodical regime. It is natural, that T ---+ Tp , ---+ p at t ---+ 00, that is why a 'transition time' here means a time interval after which the differences between T and Tp , vand vp are already small.

v v

88

Climatic circulation in Lakes Ladoga and Onego

[Ch.3

It is understandable that to estimate this time interval is not simple. Let us confine ourselves to an elementary estimate of the time interval to get the periodical solution of the mean water temperature value of the waterbody:

Tn(t) =

me~(o)

In

T(x,y, z, t) dO

(3.2)

According to the heat transfer mechanisms in the waterbody (2.37) for difference 8 == T - Tp we will get an equation

~J 8ds=-J dt 0

vQ8ds.

SOUl

When the right-hand side of this equation is replaced by qr80, where qr == VQ mes(Sout) - a discharge of outlet river and

8n(t) =

me~(o) In 8 dO.

As a result the following ordinary differential equation is obtained: d qr -80=---80·

dt

mes(!1)'

its solution has the following form:

80(t) = 80(0) e-q,t/mes(O). These simple discussions show, that the time interval for getting the periodical regime for the value To, with reasonable accuracy is defined by the lake waterexchange period. If we will take into consideration that Lake Ladoga's volume equals approximately 908 krrr', and the annual discharge of the Neva River is 74 krrr', then the water-exchange period for Lake Ladoga is about 12 years. The waterexchange period in Lake Onego is the same - approximately 12 years. Thus, the physical time for the computation period should be not less than 12 years. Two obvious remarks should be made here. First, it follows from the above elementary reasoning that the right choice of initial conditions accelerates transition to the periodical regime; second, the magnitude of mes(!1)/qr may, in fact, differ considerably from the period of water exchange in the lake. This problem will be discussed below more precisely in connection with the problem of admixture diffusion. If a waterbody is closed, the periodical regime for To is always true, as (T - Tp)o = const. For a closed waterbody, Tp(x,y, z, t) in the problem (2.19)-(2.31) is defined with accuracy up to constant. To get an estimate of the nonlinear initial boundary problem solution (2.19)(2.31), (3.1), convergence to the periodical problem (2.19)-(2.31) solution is demanding. For the complete ocean dynamic linear model solution, stabilization rates are obtained, which are equivalent, due to linearity, to the transition rate to the periodical regime (Marchuk and Sarkisyan, 1980). For the nonlinear model (2.19)(2.31) we will confine ourselves to simple considerations to help us in estimating the time needed to adjust the temperature field to a given periodical in time velocity field

On the problem of simulating climatic circulation

Sec. 3.2]

89

at periodical boundary conditions for the heat diffusion equation. As an example we will discuss the problem for 8 = T - Tp • a8

7ft =

&8 a8 k x ax2 - u ax' 8lx=o

u > 0,

= 0,

0 ~ x ~ Lx,kx = const,

= a81 x x=L x

8

(3.3)

0,

81t=0 = To(x),

(3.4)

where To(x) is a given function. The transition time for the solution of the problem (3.3)-(3.4) to a period is a time of the problem solution convergence to zero. The problem (3.3)-(3.4) can be described as heat diffusion in a channel, where the initial temperature distribution is given, and liquid (water) moves along the channel axis with a speed u = const. Here we assume that density variations do not affect the dynamics of the fluid. Let solve the problem (3.3)-(3.4) explicitly. By introducing a substitution 8(x, t) = e(u/2kx)xTJ(x, t), we will get for TJ(x, t) the problem 8T] a2 TJ 8t = k x 8x 2 TJlx=o = 0;

(k x

-

u2 4kx'TJ

(3.5)

=~ + ~ 'TJ) 1_ = 0 x-Lx

TJI t=O = e-(u/2kx)XTo(x).

(3.6)

Using the Fourier method we can find that

where

Vn

are the roots of the equation 2k x tgv=--v. uLx

Since, usually ul.; » 2k x , then it is simple to find first several roots: VI ~ 7f, vz ~ 27f. Coefficients TJn are Fourier coefficients of the function e-(u/2kx)xTo(x). It is obvious, that

II e-(u/2kx)x8(x , t) II L2(O,Lx)

=

x)t x)x 11'.11(x / ' t) II L2(O,Lx) < - e-(,} /4k II e-(u/2k T,o(x)II L2(O,Lx)

From this we can get an estimate Lx 11 81Ii2(o,Lx ) = 0 8 2(x , t) dx :::;

J

118 e(u/2kx )xIIL 2(o ,L x ) 118 e-(u/2kx )xIIL x (o,L x )

< e-(,}/4kx)tll e-(u/2kx)xT, (x) II x max Ie(u/2kx)xI 11811 0 L2(O,Lx) O:5x:5L L2(O,Lx) x x)t+(u/2kx)Lx ~ e-(,} /4k 11 81I L2(o,Lx ) II To(x) II L2(o,Lx ) ·

90

Climatic circulation in Lakes Ladoga and Onego

[Ch.3

1181IL2(O,Lx)' we will get < e(u/2kx)Lx-(zil/4kx )t llT, (x) I . 0 L2(O,Lx )

By dividing both parts of this inequality with

(3.7) 11 8 11L2(O,Lx ) The estimate (3.7) at t < 2Lx /u at first glance, permits 1181IL2(O,Lx) not to diminish, but this is not correct because of the following energy estimate 2 ~ dt 118L2(O,L < 0 x) -

•

It can be easily obtained, multiplying (3.3) in scalar form by 28 and integrating by parts:

:t

I e IlL =

-

J:2 2k (=~) x

2 dx

-

ue (L x , t) < o. 2

It is worth noting that estimate (3.7) at t < 2L x /u makes it possible for 1181IL2(O,Lx) to diminish slowly. And it should be stressed also, that at t < 2Lx /u for 1181IL2(O,Lx) is guaranteed the diminishing along the exponent (3.7). The results of this example can be interpreted in the following way. The value Lx/u for a channel is equal to mes(!1)/q, where mes(!1) is the water volume in the channel, and q is the discharge though the cross-section of the channel, so that the value mes(!1)/q is the time for water exchange in the channel. Thus, there are some reasons to assume that with reasonable accuracy the transition time of the temperature field to velocity field in Lake Ladoga differs not more than several times from the water-exchange period in water body. The transition-time problem of velocity field to the given periodic temperature field will be dealt with again. The stream function equation in the model with upper surface boundary condition (2.25) at Q = 0, i.e. 'rigid lid' condition, will be used. Introducing stream function W with the formulae 18w

U = H By '

18w

V= - H

ax '

(3.8)

out of (2.33), (2.34) the following boundary value problem for determination of of w will be derived:

(3.9)

o < s < L, where L is the length of 8So.

(3.10)

Setting of external forcing

Sec. 3.3]

The equation (3.9) will be simplified by replacing IVwl/H = VU2 Vs = (Us, Vs) and

IVsl, where

Us=

~S)J U(x,y,t)dxdy, 0 So

Vs=

mes

(1

8

+ 8y

- [8 = -k2l Vsl -

(1

8
(1

8

+ 8y

l(S)! V(x,y,t)dxdy. 0 So

(1

w is

the solution of the initial

(fH 8x

8
8 -8
8
with

mes

Then for the difference where w- wp == , where boundary value problem in the domain So 8 [8 8
+ V2

91

(f

8 8
]

(3.11) (3.12)

laso = 0,

where o =

(w - wp)lt=o.

Multiplying (3.11) in scalar form by and rearranging the relation obtained using the integration by parts method, we will get

8J

-8

-1 IVI 2 dO = -k21 Vsl

t soH

J

21 IV I2 dO,

soH

dO = dxdy,

from which follows

~ J -.!.8t So H

J

V'cI> 12 dn < k IVsI -.!.- 1V'cI> 12 dn. max H(x,y) So H 2

1

(x,y)ESo

As a result the estimate is derived

~

JsoH

1\7<1>1 2 dO

< e-(k2!Vsl/maxH)t J ~ 1\7<1>01 2 dO. soH

(3.13)

Taking into consideration that for Lake Ladoga IVsl could be equal to 5 x 10-2 m, max H = 200 m, then flow field transition time to temperature field is of 106 secondorder magnitude. These arguments can serve as a guide during computational experiments. It is worth noting that according to derived estimates the flow field adaptation is faster by at least two orders of magnitude faster than water temperature field.

3.3 SETTING OF EXTERNAL FORCING It has already been mentioned above, that for climatic circulation reproduction information about all external forcing on the waterbody, such as heat flux, wind, water discharges in rivers and so on, averaged temporally and spatially, is necessary. Nowadays, for setting information about potential external forcing the possibility

92

Climatic circulation in Lakes Ladoga and Onego

[Ch.3

exists to use data obtained with regional models of atmosphere circulation, such as HIRLAM the model, developed by a consortium of organizations of Northern European countries (Gustafsson, 1993). But for the development of climatic circulation external forcing could be prescribed, using long-term observation data. As external forcing data average long-term mean monthly values of all required characteristics were considered to be related to the middle of every month. The values in arbitrary time moment were defined with the linear interpolation method. The main sources of information were study results found in the publications of specialists of the Institute of Limnology, Russian Academy of Science, and of the Northern Water Problems Institute of Karelian Research Centre, Russian Academy of Science, and in other publications. River inflow and runoff

Discharges of five inflowing rivers were taken into consideration for Lake Ladoga modelling: Vuoksa, Syas, Svir, Volkhov, and Neva. The total inflow of the four main tributaries, Vuoksa, Syas, Svir, and Volkhov, equals 59 km'' year"! (Hydrological Regime . . . , 1966). The inflow of other rivers unaccounted for in our case, equals 8 km'' year-I. Precipitation (precipitation minus evaporation) and subsurface inflow give approximately the same amount - 7 km'' year"! of water inflow. The annual outflow equals 74 krrr' year-I. As the conservation water mass law should be fulfilled in the model at Q = 0 in (2.25) inflow should be equal to outflow, i.e, the following condition should be satisfied

J

o; ds =

0,

SinUSout

being the consequence of continuity equation (2.21) and boundary conditions (2.25), (2.27), (2.25). The water inflow from unaccounted-for rivers, precipitation and subsurface inflow (15km3year- l ) is distributed between the four main tributaries (Vuoksa, Sjas, Svir, Volkhov) proportionally to the annual runoff. Monthly mean discharges of these rivers, adopted from publication (Hydrological Regime ... , 1966), are magnified correspondingly. Monthly mean discharges of the Neva River are equal to monthly total inflow values and comprise in all, as has already been mentioned, 74km3 year " (Table 3.1). Monthly mean water temperatures in tributaries were given by mean long-term data from publication (Lake Ladoga. Atlas, 2002). It is worth mentioning that the water temperature in the outflowing River Neva is computed in the model. In model simulations for Lake Onego, the fivemain rivers ofits catchment: Shuya, Suna, Vodla, Vytegra and Svir were included. The total inflow of four tributaries (Shuya, Suna, Vodla, and Vytegra) equals 8.3 krrr' year ": The inflow of unaccountedfor rivers and subsurface flow comprise 8.5 km'' year ": Precipitation (precipitation minus evaporation) gives approximately 1.8 km' year-I. The annual outflow equals 18.6km3 year " (Lake Onego .. . , 1999). These figures characterize the lake water balance in the model.

Setting of external forcing

Sec. 3.3]

93

Table 3.1. Mean annual discharges of Lake Ladoga main tributaries (m 3 S-I). Month

I

II

III

IV

V

VI

VII

VIII

IX

X

XI

XII

River Svir Volkhov Vuoksa Syas Neva

573 573 668 955 1146 1003 764 860 860 860 668 621 438 361 335 1127 1712 1221 817 550 447 516 567 507 770 770 770 770 770 724 679 724 770 770 770 770 19 47 47 28 25 57 52 76 57 38 33 66 1819 1732 1806 2877 3647 3014 2317 2186 2124 2222 2062 1945

Table 3.2. Mean annual discharges of the main Lake Onego tributaries (m 3 S-I). Month I

II

III

IV

V

Shuya 125.2 102.0 93.9 191.0 544.5 Suna 58.5 45.3 36.6 42.4 130.1 Vodla 120.5 80.8 59.8 236.5 827.8 Vytegra 12.0 11.4 8.3 31.5 78.8 Svir 316.2 239.4 198.6 501.4 1581.2

VI

VII

VIII

IX

X

XI

XII

323.6 147.0 395.0 46.0 911.5

180.3 149.1 151.1 180.5 218.9 170.5 102.9 75.9 66.9 76.3 87.0 76.3 256.6 236.5 258.8 323.6 294.5 182.5 44.6 39.0 38.4 31.5 28.3 20.5 584.4 500.5 515.2 611.8 628.8 449.8

As in the model the water mass conservation law should be fulfilled, i.e. inflow equals outflow. The water inflow of unaccounted-for rivers, precipitation and subsurface inflow (15km3year-1) is distributed between four main tributaries (Shuya, Suna, Vodla and Vytegra) proportionally to the annual runoff. The monthly mean discharges of these rivers adopted from publication (Lake Onego ... , 1999), correspondingly magnified are presented in Table 3.2. The monthly mean discharges of the River Svir have an annual total equal to 18.6km3 and the monthly inflow equals the outflow (Table 3.2). Data on monthly mean tributaries' water temperature for every month were obtained from observation records.

Thermal flux Reliable determination of heat flux through the water surface is one of the complicated problems in the realization of the model. Two approaches to this problem can be outlined. One of them, the general approach, is related to the application of the waterbody surface heat balance equation. The heat balance for the waterbody surface can be written as follows (Oceanology, 1978)

Q = (1 - A)F1 + Fi - H - ZEE - B(T), where Q is the heat flux through water body surface, Fi and FL are downward fluxes of short-wave solar radiation and long-wave atmospheric radiation respectively, A is the lake surface albedo, Hand E are vertical turbulent fluxes of heat and moisture, ZEis specific evaporation heat, B(T) is the long-wave lake radiation flux (the flux of

94

Climatic circulation in Lakes Ladoga and Onego

[Ch.3

a black body having the temperature of the waterbody surface, Tlz=c). Application of the heat balance equation is complicated by the fact that additional information about the near-surface air layer - solar radiation, cloudiness, air temperature and humidity - are required. This information should be defined with high confidence, otherwise large errors in heat flux estimations are possible. It follows from the fact that terms in the right-hand side are of similar magnitude whereas the resulting value Q is small compared to them. Nevertheless, it is worth mentioning that wide experience was gained in the use of this approach in ocean circulation modelling. The heat balance equation was also used in lake studies (Rumyantsev et al., 1986; Rukhovets, 1990). The other approach is based on using direct measurements of waterbody heat storage. Heat storage changes in the waterbody according to (2.37) are defined by equality

:t In c;Pw

=J

So

Tdn

Qds-c;Pwi

v"Tds-c;Pwi

SOUl

v"Trds-ac;pwi

So

Sin

~~TdS. t

(3.14)

The main term in the right-hand side is the first integral describing the income (or outcome) of heat through the surface. The other terms in the right-hand side (3.14) are negligibly small, compared to the first one, although they are important for the generation of the thermal regime (see section 3.2). Neglecting the last three terms (3.14) one can get

I

So

J

QdS = dd c;PwT dn. t n

Then for the average value of the heat flux over lake surface we will get the expression Qs =

1

mes(S) 0

lQdS Id -d J mes So

=

(S) 0

t n

v T dn. cpPw

(3.15)

This average value was used in simulations of all lake surface points. Naturally, prescribing the heat flux in such a way does not match with the real heat exchange through the surface in different areas of the waterbody. However, as was stressed by Tikhomirov (1982), in large stratified lakes heat flux is unidirectional over the entire year at all surface points. It will be shown below that this method of heat flux determination gives satisfactory results despite the obvious 'roughness' of the approach. From the physical point of view using the average water temperature as initial information (the average water temperature equals the lake heat storage divided by the volume) makes reproduction of the temporal-spatial water field structure to a certain degree a diagnostic one. The application of this method is linked to the fact that Tikhomirov (1963, 1982) estimated the monthly specific heat storage of water masses in 1957-1962 for Lake Ladoga and 1956-1967 for Lake Onego. Annual specific heat storage curves are built

Setting of external forcing

Sec. 3.3]

95

on the basis of observation data. The heat flux in the discrete model was calculated as the difference time derivative of Qs(t).

Wind Specification of average multi-annual monthly mean wind stresses requires knowledge of the wind speed and direction distribution functions. Wind speed and direction recurrence tables from hydro-meteostations (HMS) at Medvezhyegorsk, Kondopoga, Klimenitsy, Petrozavodsk, Vasilisin, Terbovskaya, and Voznesenye were used as a basis for estimations in the case of Lake Onego. Using these tables, monthly mean values of wind stresses Tx

=klPa --

Pw

I_I

W x W,

Tv

klPa Pw

I_I

= - - wy W,

are calculated with the following formulae Tx

klPa" = - L.J Pij 1-1 Wi cos 'Pj,

T»

k1Pa" = - L.J Pit Wi

2

Pw

Pw

.. I,l .. I,l

1-12 sm . 'Pj,

where Iwl cos 'P = wx , Iwl sin e = wy , Pij are probabilities (frequencies) that wind direction falls within the interval 'Pj - (7f/8) ~ 'P ~ 'Pj + (7f/8), and wind speed lies within the interval IWil - 8 ~ Iwi ~ IWil + 8; 8 is the gradation step of wind speed. The reference on climate in the territory of the USSR for wind (1966) contains average multi-annual wind speed and direction distribution data for HMS Vasilisin. Wind observations time series at the other Lake Onego stations do not contain correlated speed and directions data. Data analysis has shown that wind-forcing on Lake Onego varies significantly in different areas as a result of the complicated lake coastal line. Figure 3.1 illustrates mean annual wind direction distributions in Povenets Bay (north part of Lake Onego) and in the Lake Onego offshore zone. In order to simplify the task, the lake surface area was divided into three zones: northeastern, northwestern and southern (Fig. 3.2). Wind loadings within these three lake zones were calculated using regression analysis of data from the abovementioned meteostations. In addition, variation of the wind speed over the coastal zone was taken into consideration. Thus wind speed and direction were imposed independently for three lake zones, and wind speed in the coastal zone was corrected with the corresponding reduction coefficients. By the time that ice cover disappears from Lakes Ladoga and Onego, the water temperature is considerably lower than the temperature of the surrounding land. In spite of intensive heating of the coastal area, the relatively cold water masses of the larger lake volume part determine the existence of a so-called 'cold dome' over the lake, which plays the role of a local anticyclone. Clear skies and calm weather are

96

[Ch.3

Climatic circulation in Lakes Ladoga and Onego

NW

N

E

I·

•E

sw

s

sw·

s

s

SE

A Fig. 3.1. Mean annual wind direction distribution in Povenets Bay (A) and in the offshore zone (Bolshoe Onego) Lake Onego (B) according to observations.

Fig. 3.2. Division of the lake surface for the purpose of wind-stress estimations.

Sec. 3.4]

Simulation of the Lake Ladoga climatic circulation

97

typical in this part of the waterbody. This fact has been confirmed by multiple observations. The wind regime over the lake while the 'cold dome' is in existence, in absence of strong cyclones, is characterized by heterogeneous movement speed of air masses and a tendency for them to decline in the offshore direction (Terzhevik, 1981). This observation was taken into consideration by the authors. Wind stresses for every month of the year were calculated on the basis of these data. Wind stresses for Lake Ladoga were estimated in a similar manner. 3.4 SIMULATION OF THE LAKE LADOGA CLIMATIC CIRCULATION 3.4.1 Computational procedure The Lake Ladoga climatic circulation, as already mentioned, was initially reproduced on a coarse-resolution grid; the number of nodes at the waterbody surface did not exceed 300 and there were 16 layers in the vertical direction (Astrakhantsev et al., 1987; Astrakhantsev and Rukhovets, 1988). The climatic circulation calculation results used in this work are based on a horizontal grid with equidistant steps hx = hy = 2.5 km by 30 vertical layers. With the dimensions of Lake Ladoga along the longest axes being approximately 200 km in length and 150 km in width, the number of computational nodes at the lake water surface equalled 3000 (Astrakhantsev et al., 2003). In the discrete model the surface area and volume of Lake Ladoga are equal to widely recognized values (18 000 km2 and 908 krrr'), derived on the basis of surveys and calculations (Lake Ladoga . . . , 1992). To obtain the periodic solution, calculations were performed for the period of nearly 25 years of physical time. The discrete model equations were integrated with time-steps of 5 days at the beginning of calculations and up to 1 day after 20 years of physical time. At each time-step in the solution of the difference heat distribution equation the discrete analogue of the heat variation law in a waterbody (2.37) was used to control the calculations. Initial conditions

To construct the periodic solution of the problem (2.19)-(2.31) the initial conditions (3.1) should be prescribed. And, as follows from the considerations in section 3.2, a successful selection of the initial conditions may significantly reduce computational time. As the initial values for temperature To(x,y, z) in Lake Ladoga the data of temperature surveys conducted by Filatov and researchers of the Institute of Limnology in the first decade of August 1981 on a 10 x 10km grid at five levels, were used. The survey results were interpolated (or extrapolated) on the discrete model grid. As the initial conditions for the flow fields uo(x,y,z), vo(x,y,z), wo(x,y,z) the solution of the stationary diagnostic problem was used. This problem is derived from (2.19)-(2.31) under the condition that the temperature field is known and all external forcing is steady. The solution of the steady diagnostic problem was obtained by the stabilization method.

98

Climatic circulation in Lakes Ladoga and Onego

[Ch.3

lee cover modelling

The method of modelling the formation of ice cover used in our calculations is more correctly termed imitation. Heat flux, without ice cover, was given a constant value all over the waterbody according to formula (3.15); in the case of ice cover, the heat flux was redistributed over that part of the waterbody that was free of ice in such a way, that the integral heat flux through the whole surface was the same. Starting from the moment when the waterbody was completely covered with ice, the heat flux 'was extracted' evenly from the whole lake surface until the start of the ice-free period. The ice formation process was imitated in the way discussed below. As the water temperature T ij k in the lake surface grid node was less than a certain value "IT > 0 (the parameter of ice formation) all flat grid cells on So having the given node vertex are declared to be covered with ice and the heat flux in these cells was assumed to be equal zero. Therewith, the following changes were introduced in the problem solution algorithm. In the surface nodes covered with ice, instead of the boundary conditions (2.24) the friction boundary conditions for water-ice friction were given k,

%'

= -kAUVP

yJ

M; ,

= -k

U2+

V

(3.16)

Such an imitation of the ice formation process in numerical experiments, as is described below, gave satisfactory results. Turbulence modelling

In turbulence modelling, for the prescription of turbulent viscosity and turbulent temperature conductivity coefficients, biparametric turbulence models are frequently used nowadays (Marchuk and Sarkisyan, 1980; Mellor, 1996; Mellor and Yamada, 1982). For vertical turbulent viscosity modelling the authors used a relatively simple and traditional approach. The vertical turbulent viscosity coefficient was given by the Obukhov formula (Marchuk and Sarkisyan, 1980), which is the consequence of the turbulence energy balance equation in quasi-stationary approximation, as a result of ignorance of turbulence energy diffusion. Since in the lake circulation modelling we consider events with a not less than synoptic timescale, the application of the Obukhov formula (Marchuk and Sarkisyan, 1980) should be justified. Let us introduce the Obukhov formula (Marchuk and Sarkisyan, 1980, p.221):

+ ~ (8 P) + 1-£0, (8BzU) + (8v)2 Bz Pw Bz 2

(3.17)

where h is a parameter that could be interpreted as the quasi-homogeneous layer, and J.to is the molecular turbulent diffusivity. This formula has already been used in lake circulation modelling. Marchuk and Sarkisyan (1980) have pointed out that the application of formula (3.17) in ocean dynamics models gives in practice the same results as application of the turbulent energy balance equation, or biparametric model, where, along with the turbulent energy balance equation, the turbulent energy dissipation equation is used (Marchuk and Sarkisyan, 1980).

Sec. 3.4]

Simulation of the Lake Ladoga climatic circulation

99

To prescribe the vertical turbulent temperature conductivity coefficient Vz the link between k, and Vz : Vz = ok-, where a = const, was used. Coefficients of horizontal turbulent temperature conductivity V x and v y were given constant and equal values in all numerical experiments. Their specific values were selected in such a way as to provide better correspondence of the horizontal stratification of the temperature field to observation data. 3.4.2 Description and analysis of thermal regime calculation results The results of the periodic solution of (2.19)-(2.31), reproducing Lake Ladoga's large-scale climatic circulation, are presented in this and the next section. We will consider the constructed solution in detail, giving, when it is possible, a comparison with the observation data. Annual variations in waterbody heat storage for calculated periodic solution and on the basis of Tikhomirov data (1968, p. 208) are presented in Fig. 3.3. There is a noticeable difference between curves (a) and (b) (curve (a), modelling results; curve (b), annual dynamics of mean perennial waterbody heat storage according to Tikhomirov data (1968, p.208)). The information about waterbody heat storage in the winter period is less reliable, since it is based on measurements at few points. As in the constructed solution, heat flux calculated on the basis of the heat storage

..

:-

•

l

x-

•

t

1\ I'

20

IJ

(

0

--

to

Jo

L·/

'

f

,',

/

I

"

/1,

-~

\' \

I~

\

1I

b

'I

.( ..~

'\

\....... \<

""'....<

."" .... ........ c~

Fig. 3.3. Annual variations of waterbody specific heat storage (in kcal cm- 2) for Lake Ladoga: (a) modelling, (b) data from observations.

100

Oimatic circulation in Lakes Ladoga and Onego

[Ch.3

curve (b) was used; the distinctions between curves (1) and (2) are very likely due to the existence of rivers. Without the influence of the inflow from rivers, the temperature field would be determined in the model (2.19)-(2.31) with accuracy to the constant. The major role in the formation of the vetical structure of the temperature field in lakes belongs to buoyancy effects (Zilitinkevich et al., 1992) related to the fresh water density anomaly at the temperature of 4°C, and, hence, is determined by the fresh water equation of state in the form (2.22). In correspondence with this fact, the formation of the vertical structure of the temperature field at the initial stage of spring heating (when water temperature in the surface layer is within the limits O°C to 4°C) and at initial stage of autumn cooling (when water temperature in the lake is above 4°C) is mainly controlled by the convection regime or convective mixing. Thus, in the initial period of autumn cooling, at the waterbody surface a colder and, hence, denser layer than below is generated. Hydrodynamic instability develops in the following way. In the discrete model evolved, the convective mixing process is imitated using the convective adjustment method, which finalizes every timeintegration step of the heat distribution equation. Convective adjustment is applied in the nodes where hydrodynamic instability is found. For this purpose the temperature is modified with a simple iteration algorithm in each temperature field vertical column. Thereat water temperature is changed in such a way that waterbody heat storage remains the same. Although the adjustment algorithm is relatively well known, we will give it in the form it is used in this work. Namely, if pz = (Piik - Pi,i,k-l)/hk-l > 0, Piik = p(Tijk), i.e, if density declines with depth, then in nodes (Xi,Yi, Zk) and (Xi,Yi, Zk-l) values T iik and Ti,i,k-l should be replaced by the value, T i,i,k-l/2, calculated with formula T i,i,k-l/2

x

==

[Tijk~ ( ~

[~( ~

[K"f3,/-- 1

[K"f3,/-- 1

8i+0i,J+f3,k+7)

8i+0i,J+f3,k+7)

+ T i,j,k-1 ~ (

~ ~

+ (

[K"f3,/-- 1

~

[K"f3,/-- 1

8i+0i,J+f3,k-1+7)]

8i+0i,J+f3,k-1+7)] -1.

Along with convection, the vertical structure of the temperature field is formed under wind mixing conditions during the open water period. The description of the temporal evolution of the waterbody temperature field, according to modelling results, will be presented according to Tikhomitov's division of the year into the hydrological periods: spring, summer, autumn and winter. In Table 3.3 the main characteristics of the Lake Ladoga thermal regime on the basis of perennial observations and modelling results are presented. In Figs 3.4-3.11 the lake surface water temperature is shown and in Figs 3.12-3.14 the temperature in a vertical transect along the axes connecting Valaam Island and Volkhov Bay. For the open water period (from May 15 to October 15), along with surface water temperature calculations, in Figs 3.4-3.11 measurements averaged over nearly a hundred-year period, from the database developed at the Institute of Limnology RAS (Naumenko, 1994; Lake Ladoga. Atlas, 2002), are presented.

Simulation of the Lake Ladoga climatic circulation

Sec. 3.4]

101

Table 3.3. Some characteristics of the Lake Ladoga thermal regime on the basis of modelled and observed data (Tikhomirov, 1963, 1982; Filatov, 1983). Phenomenon

Climatic circulation

Mean perennial data

Establishment of full ice cover

February 10, 94% February 14, 95% February 23, 97% March 16, 100%

February 10

Disappearance of ice cover

May 16

May 25

Appearance of 4°C isotherm (spring thermal bar)

April 27

May 1

Disappearance of 4°C isotherm (spring thermal bar)

July 9

July 15

The smallest epilimnion thickness and time of its occurrence

July 21-26

20m

Appearance of 4°C isotherm (autumn thermal bar)

October 24

October 1

Disappearance of 4°C isotherm (autumn thermal bar)

December 14

December 15

Beginning of ice cover establishment

{

{

October 29, 1% November 3,3% November 12 (December 21), 5%

December 30

Spring heating period

The beginning of the spring heating period coincides with the moment of time when the resulting heat flux through the waterbody surface becomes non-negative. According to perennial data, this happens at the beginning of March. This moment takes place on March 18 in the model. The lake at that time is completely covered with ice. In reality, the lake was completely covered with ice during the 1960s-1990s only one winter out of three. Complete ice cover was not formed on the lake during the last two decades. Waterbody heat storage changes drastically depending on whether ice cover is complete or partial. The destruction of ice cover begins on April 11 and by May 7 its area has reduced by half. The lake is completely free of ice by May 17 (Fig. 3.15), according to modelling data. In accordance with Tikhomirov (1982), ice cover in Lake Ladoga disappears in the first half of May (Table 3.3). About the same time the thermal bar starts to develop. These phenomena happen in similar periods of time. The calculation results testify that in the deepwater lake area water the temperature is actually

102

[Ch.3

Climatic circulation in Lakes Ladoga and Onego

a

b

Fig.3.4. Surface water temperature (modelling): (a) 15 January, (b) 15 April.

b Fig. 3.5 . Surface water temperature 15 May: (a) results of modelling, (b) average data of

observations (Naumenko et al. in Lake Ladoga. Atlas, 2002).

Simulation of the Lake Ladoga climatic circulation

Sec. 3.4]

103

a Fig. 3.6. Surface water temperature 15 June: (a) results of modelling, (b) average data of

observations (Naumenko et al. in Lake Ladoga. Atlas , 2002).

b Fig. 3.7. Surface water temperature 15 July: (a) results of modelling, (b) average data of

observations (Naumenko et al. in Lake Ladoga. Atlas, 2002).

104 Climatic circulation in Lakes Ladoga and Onego

.

[Ch.3

.

a

b

Fig. 3.8. Surface temperature 15 August: (a) results of modelling, (b) average data of observations (Naumenko et al. in Lake Ladoga. Atlas, 2002).

a

b

Fig.3.9. Surface water temperature 15 September: (a) results of modelling, (b) average data of observations (Naumenko et al. in Lake Ladoga. Atlas , 2002).

Simulation of the Lake Ladoga climatic circulation

Sec. 3.4]

105

Fig. 3.10. Surface water temperature 15 October: (a) results of modelling , (b) average data of observations (Naumenko et al. in Lake Ladoga . Atlas , 2002).

-hi

V'"~ ~

<.-

(>

{

"

.,

J,

li

.~

.L

~

,L

~

.'

a Fig. 3.11. Surface water temperature: (a) 15 November, (b) 15 December. Results of modelling.

106

[Ch.3

Climatic circulation in Lakes Ladoga and Onego

I [~

' 4

IS

-, -f '-

~-

,~

-

I) ~ - I ~-

.-

';

~·I

a

.

... -

J).

1

'!

t

1

1.

- - il'

:1

...,

b --

~-..T

1~ -="'"

~--

Ii

Y..

yo , _L;--=',

-~-

---

c

..., 9

-

1 ~

-

~

- - Q.!. - 1

-

r-

d Fig. 3.12. Temperature of water on section along Lake Ladoga (modelling) 15 January (a), 15 February (b), 15 March (c), 15 April (d).

constant and equals approximately 2°C. In the shallow lake zone, between the coast and thermal bar, the thermocline starts to develop (Figs 3.5 and Fig. 3.13 (a, b)). The disappearance of the thermal bar marks the end of the spring heating period. According to Tikhomirov (1963) this happens on average in the middle of July. The simulated thermal bar, identified by the isotherm 4°C at the water surface, disappears on July 10 (Fig. 3.7).

Simulation of the Lake Ladoga climatic circulation

Sec. 3.4]

1

~; I I

II

\..j

J.

--"'\,1

'L

\

.-"-' - ' . - ' -

......

r

..."-:l

107

.I~ .:..--

a

..... ...

b

.

....

"

I I I

~~/

- - 1-

.,

I

i

II I _

I,

(

'-'

c _ _....L..------- ~-

II-~- I I " 1

,

,...)

--.J "

- .----;--===:....~=-=-- ...!I ~

- -, - -.

----1

L

,r

d Fig. 3.13. Water temperature on section along Lake Ladoga (modelling) 15 May (a), 15 June (b), 15 July (c), 15 August (d).

Summer heating period

The summer heating period starts with the beginning of steady temperature stratification (in the model and in reality) about the middle of July and ends at the moment when heat flux through the water surface reaches zero; heat storage reaches its maximum value. In the model this moment relates to September 2. The thermocline reaches its greatest development (peak) at July 15 (Fig. 3.13(b)). By this moment the upper quasi-homogeneous layer (UQL) with a depth of IO-12m

108 Climatic circulation in Lakes Ladoga and Onego

-.

[Ch.3

- - ::....-=.-==r.

1--

,....' -

----'

a '---1 I , I_ ~" -

.........'

.,

- - .. I'"

b

!

"I

I

~

'\

1

....,

..._....

"-

-.

1

__

-.............-'

~

C

[

-

,~

.-'

'\

I

I.,

~

;.l {-

.:."-

~ - ~'

-

]

.~

d Fig. 3.14. Temperature of water on section along Lake Ladoga (modelling): 15 September (a), 15 October (b), 15 November (c), 15 December (d).

is formed (Fig. 3.14(a)) and it exists until September 4-9. Water temperature at depths from 12 to 30m declines by 6-rc. The lower thermocline boundary, if it is considered to coincide with the 6°C isotherm (in vertical waterbody sections), is observed in the deep part of the lake at depths from 7 to 12m, but in the shallow part, where the depth is less than 50m, at depths of 25-30 meters (Fig. 3.13(d)). The lower boundary, by the end of September, submerges to deeper than 50 m.

Simulation of the Lake Ladoga climatic circulation

Sec. 3.4]

...

%

100

109

I

I

80

I

I I

60

I

I

I

·0

I

'" I

20

,I

I

I

I

I

I

I

I

I

,

1 - J II

i

2{l - F ~

I

I

1(l - A ~ r

i

ii

i

30 - M y

i

I

I

I

I

i

I

I

I

i

- J I 7 -SttJ) 27 -0<: 1 1 6- 0& (:

-F~

Fig. 3.15. Annual dynamics of Lake Ladoga ice area (modelling).

By August IS the temperature difference on the lake surface is 9°e (Fig. 3.8). Water masses with temperatures of 10-12°e are observed in the northern part of the lake, but, near the Neva River outlet, the surface water temperature is nearly 17-18°e. This is the moment when the surface water temperature reaches its maximum. Further, at September 15, the temperature difference at the water surface decreases to 4-5°e (Fig. 3.9). Autumn cooling period

The autumn cooling period starts from the moment when the integral heat flux through the water surface becomes negative. According to Fig. 3.3, it happens in the first decade of September, approximately on September 4. Epilimnion thickness starts to increase and by September 15 it reaches 60m and the epilimnion temperature changes in the range 6-12 °e (Fig. 3.14(a)). Water temperature is about 5-6°e at depths greater than 100m. According to observation data (Tikhomirov, 1982) at the beginning of October in 30-40m the near-surface-layer water temperature is 8-lO oe, and 4-6°e is observed below 60m. The autumn thermal bar, whose existence is defined by the 4°e isotherm on the lake water surface, is formed on October 24. On Fig. 3.14(c) it is not yet seen. The thermal bar appears near the southern coast at depths of 2-7 m. (Fig. 3.14.(a)). In shallow areas, between the thermal bar and the coast, ice formation starts after October 27 (Fig. 3.15). At that time water temperature in the deep lake zone is 4-6°e (Fig. 3.14(b)). The area of ice cover by November 30 is 27% of the lake area (Fig. 3.15). According to observations (Tikhomirov, 1968) the thermal bar initiation

110

Oimatic circulation in Lakes Ladoga and Onego

[Ch.3

takes place over depths of7-10m at the end of October, and the water temperature observed at that time in the deep lake zone is 5-6°C. The thermal bar, according to calculations, moves towards the deep lake parts and by November 15 it disappears; in Fig. 3.11(b) the 4°C isotherm is absent. In the deep lake areas, vertical homothermal conditions are formed and the water temperature there is nearly 3°C (Fig. 3.14(d)). Winter cooling period

The beginning of the winter cooling period is usually associated with the moment when the temperature of water masses reaches the point of its maximum density. According to calculations, it starts from December 17. In November-December the model calculation results point out a decline in ice cover area (Fig. 3.15), and observation data confirm these simulation results. By the middle of February, 95% of the lake area is covered with ice (Fig. 3.15). By the end of the winter cooling period, the isotherm is close to horizontal. Water temperature in the hypolimnion is in the range 1.5-2.2°C. The winter thermocline is most clearly represented in Fig. 3.12(c,d). The lake heat storage at that time is minimal and its alteration is insignificant. Ice formation proceeds not only in the near-surface water layers but also in the whole water column. Gradual deepening of the isotherm T = 2°C is clearly seen in Fig. 3.12. In what way does heat transfer occur from the deep waterbody areas to the surface? There are two mechanisms: turbulent diffusion and advection. Taking into account that the magnitude of vertical turbulent diffusion coefficient 5 2 liz in the deep areas is close to 10- m s-1, and that the vertical velocity in the hypolimnion is of the same order, 10-5 m2 s-1, it is impossible to derive any kind of definite conclusion about the prevailing mechanisms. Rukhovets (1990) is devoted to the estimation of the significance of these mechanisms for developed periodical solution (Astrakhantsev et al., 1987; Astrakhantsev and Rukhovets, 1988). Integrating equation (2.23) over the domain On, below the plain Z = Zn, accounting for boundary conditions, it is simple to derive the relation (3.18) Thus, heat transfer variation in the deep area takes place due to diffusion and transport. In order to calculate the discrete analogue of integrals in the left side of (3.18), we will sum for all nodes (Xi,Yi,Zk) E On both the terms in the difference equations describing diffusion and advection. The first sum gives the value of the amount of heat variation (with accuracy to dimensional cofactor cpPw) in the deep lake part due to diffusion, and the second sum, that due to advection. Computation has shown that in the deep lake area at depths greater than 15m, heat exchange through the surface Z = Zn is determined mainly by advection, the second sum exceeds the first by an order of magnitude. Of all others, advection is the mechanism of near-bottom layer cooling. Water temperature in the near-bottom layer, calculated on the basis of new and old model versions, corresponds to observation data in those years when the lake was completely covered with ice (Tikhomirov, 1982). This

Sec. 3.4]

Simulation of the Lake Ladoga climatic circulation

111

fact indirectly confirms the verity, or at least compliance, of water temperature and flow fields. According to calculations, in a 7 m thick layer of the epilimnion, turbulent heat diffusion is the main contributor to heat exchange. Quality estimation of thermal regime reproduction

Verification of the discrete model is the most important issue in the estimation of its capabilities. In the description of the constructed periodic solution in this chapter we compared calculated results and averaged data, where information on the mean perennial thermal regime of the lake was available. A comparison shows that the qualitative character of the dynamics of surface temperature fields and its distribution over waterbody in calculations are in good agreement with the averaged observation data (Naumenko et al., 2000). So, the processes of spring heating (Figs 3.5-3.8) and autumn cooling (Figs 3.9-3.11) take place synchronously with averaged observation data. In particular, the 4°C isotherms in Figs 3.5(a), 3.6(a) and 3.5(b), 3.7(b) are close, during the spring heating period, testifying that the calculated thermal bar movement coincides with data obtained by Naumenko and others (see Lake Ladoga. Atlas, 2002). A comparison of calculations at other time moments shows (Figs 3.9-3.12) that, though they differ from averaged measurement data more noticeably, these differences do not exceed 3°C. At the same time, the directions of maximum temperature changes at the water surface are similar. Calculated horizontal temperature stratification, until the middle of July, corresponds with the data, and from the middle of August till the middle of September it is different from the observed one. Surface-water temperature variation in simulations is reproduced correctly and it is typical for November: surface-water temperature is higher in the deep water part of the lake than in the shallow southern part. The comparison made enables us to conclude that the lake surface thermal regime in the constructed climatic circulation during the vegetation period is reproduced in the model realistically, both qualitatively and quantitatively. It should be pointed out that the adequacy of the reconstruction of the surface-layer temperature is important, since it is in this photic layer that primary phytoplankton production takes place, which is the main producer in the trophic lake chain. At the same time temperature, along with luminance and the supply of biogens, is the main regulator of phytoplankton development. The calculation results can be examined by comparing the modelled water temperature in the Neva River outlet with observation data (Fig. 3.16). The general characteristic of constructed temperature fields is as follows: the climatic Lake Ladoga temperature regime is reproduced qualitatively and, to large extent, quantitatively, adequately to available information. The starting dates of hydrological periods, thermal bar formation and destruction, and thermocline formation in the model correlate well enough with average dates obtained on the basis of Tikhomirov's data (1982). The simulated temporal temperature field evolution is quite realistic, and in solution all the main large-scale structures and processes of Lake Ladoga thermal regime are revealed.

112

[Ch.3

Climatic circulation in Lakes Ladoga and Onego

1-

1 2

I

I

. '1

,./" ,I

,,'

~"I

/ .z->:..... (11.(11 .

..

"

·x

\\

~(I ' .

Fig. 3.16. Water temperature in the outlet of River Neva: (1) mean perennial of observation data; (2) modelling.

3.4.3 Description and analysis of currents calculation results As is known, in all large lakes of the northern hemisphere during the major part of the year, water mass movement assembly takes place against the background of cyclic water mass turnover. The principal scheme of integrated Lake Ladoga circulation for different seasons during the open water period is presented in a monograph by Filatov (1991). This principal scheme is proved, to a considerable extent, by the streamline function calculation in the work of Rukhovets, (1990), also being published in Menshutkin (1997). In spite of the fact that level lines of the streamline function have a relatively complicated structure, for nearly all time moments it is possible to select not more than two main circulation cells: whether one, cyclonic, or two, one cyclonic, the other anticyclonic. Brief characteristic of the constructed all-year-round Lake Ladoga circulation

During the period when the lake is not covered with ice, it is possible to identify the following general characteristic of the velocity speed field. The idea of the general (integrated) lake circulation is given in Figs 3.17 and 3.18, averaged over the depth flow velocities during the open-water period . The characteristic values of the averaged velocities within the depth during this period are 0.02-0.04m S-I . Under ice cover, depth-averaged velocities do not exceed 0.01 m S-I .

Simulation of the Lake Ladoga climatic circulation

Sec. 3.4]

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The upper near-surface layer of the waterbody moves mainly due to wind effect. Velocity values at the surface are within the range O.OS-o.lSms- l , in NovemberDecember surface velocities are maximal: 0.3 m S-I. The damping of wind influence with depth can be obtained using the friction depth value estimate he = .jkJi, where k, is the vertical turbulent viscosity coefficient, I is the Coriolis parameter. As calculations show, at the surface on average k, ~ S · 10- 3 (m2 S-I), I ~ 10- 4 (Ijs) , and then he ~ 7m. This estimate correlates with calculations: the main variability of the flow field during summer period is concentrated in the surface layer (Fig. 3.19). Computational results clearly reveal the Eckman turn of velocities relative to the wind direction at the surface. At the depth z = -7.5 m counter-currents with respect to surface currents are observed (Fig. 3.20(a,b)). Realignment of currents at depths

114

[Ch.3

Climatic circulation in Lakes Ladoga and Onego ~

I

...

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greater than 7.5 m is negligible. Thus, the currents at depths z = -15.5, z = -42.5 actually do not differ (Fig. 3.20(c,d)). In general current shift is observed near layer boundaries . It is plausible to suggest that this is a sequence of current intensification along the bottom slopes. The noticeable distinctions between currents at the depth z = -15.5 m and those at the depth z = -7.5 m are observed in November-December only, when wind effect penetrates to a considerable depth (Fig. 3.21). When the waterbody is completely covered with ice, near-surface currents are of the order of 10- 2 m s-l . Some increase of velocities up to 0.02-0 .03m S-1 is observed with depth. This is an effect of density stratification (the baroclinic effect). As was

Sec. 3.4]

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Simulation of the Lake Ladoga climatic circulation

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mentioned above, advection is the main mechanism of heat transfer in the lake during this period. Let us describe the characteristics of vertical water mass movements. Calculated values of w vary in general within the range 10- 6 to 10- 4 m S-I . At these values of the vertical velocity, the liquid travel time from the surface to a depth of about 50m (the average depth of Lake Ladoga) is of the same order as liquid particle transport in the horizontal direction through the whole waterbody with the mean speed of

116

[Ch.3

Climatic circulation in Lakes Ladoga and Onego

a

b

Fig. 3.21. Surface currents in Lake Ladoga on November 15 at depth (m): (a) 705m, (b) 1505m.

10- 1 m s". This trivial reasoning shows the role of vertical movements in waterbody dynamics. It should be mentioned that direct measurements of vertical velocities are not available. That is why modelling results could be useful in the refinement of the flow field picture in Lake Ladoga. Analysis of the vertical velocity field demonstrates that the whole year could be divided into seasons when the vertical flow field structure changes slightly with depth and in time. That is why, in illustrations (Fig . 3.22) of upwelling and downwelling zones of water masses, the presentation of these zones is restricte to the depth z = -5.5m. In all figures downwelling zones are attenuated towards the windward shore , as confirmed by observations, which is caused by water surge. But this simple explanation is not universally applicable. Spring circulation has a wide downwelling zone in the western and southwestern parts of the lake . In the central area of the lake, upwelling and downwelling has a local character. Along with thermal bar movements towards the centre of the lake, local zones are combined, forming clearly divided zones of upwelling and downwelling. Summer circulation is characterized by a wide downwelling zone in the south and southeastern parts of the lake. An upwelling zone exists nearly permanently in the northwest. Autumn circulation is associated with the destruction of distinct upwelling and downwelling zones. At the same time the downwelling zone is shifted into southeastern and eastern parts of the lake . Thus within a year there is clear replacement of the 'winter' field picture with 'summer' one . Results, partially presented in Fig. 3.22, show that during May-July and November-March there is a lateral vertical transect: on one side upwelling prevails and on the other, downwelling . Actually, it turns out that during these two periods water masses are rotated around lateral axes, around one in May-July and around another in November-March, but in May-July in one

Simulation of the Lake Ladoga climatic circulation

Sec. 3.4]

a

b

c

d

117

Fig. 3.22. Zones of upwelling and downwelling (shaded) at 5.5m depth: (a) 15 May, (b) 15 June, (c) 1 August, (d) 15 November.

direction and in November-March in other. Such water mass movements, being rather slow, are a factor in the mixing of hydrodynamically neutral admixtures presented in lake waters. Notes on the reproduction of the thermal bar phenomenon in calculations

As was mentioned in section 1.3, 'location and movement' along the lake surface of isotherm 4°C in calculations is adequate for mean perennial data . The thermal bar,

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as a frontal interface, should be drawn along an approximately vertical surface, the general for which is the 4°C isotherm. In reality, the width of the thermal bar is 100-200 m, and currents in the vicinity of the thermal bar are directed from the surface towards the bottom. Horizontal grid steps are such that adequate reproduction of the thermal bar is problematic. Flow field analysis shows that the thermal bar has smearing boundaries. The existence of the thermal bar can be confirmed by the flow field structure in vertical transect, perpendicular to the frontal interface (Fig. 3.23). One more confirmation of thermal bar reproduction in calculations is the fact that between the coastline and the thermal bar front is a hydrostatically stable state of water mass, and a horizontal stratification with vertical homothermy exists in the forefront ZOne. The influence of bottom friction parameterization changes

The mathematical model of climatic circulation (2.19)-(2.31) used by the authors differs from other three-dimensional models mainly in that, first, the reduced momentum equations (2.19)-(2.20) are used and, second, bottom friction is parameterized with depth-averaged velocities (2.26). The justification of the simplification of equations (2.1), (2.2) was discussed in section 2.3, but concerning boundary conditions (2.26) in the same section 2.3 it is only noted (Astrakhantsev and Rukhovets, 1990; Astrakhantsev et al., 2003) that the other parameterization of friction at the water-bottom interface (2.35) was used as well. What is the reason for the replacement of boundary condition (2.26) with (2.35)? The answer is that in some cases the boundary condition (2.26) is not physical. For example, in a waterbody of the constant depth H = const, without stratification, with spatially constant wind the model equations will give that U = 0, V = 0, i.e. that depth-averaged velocities equal zero. Then the boundary condition means the absence of bottom friction. The application of boundary condition (2.35) leads to the necessity to use for momentum equations explicit/implicit schemes. As a result the restriction On the

Simulation of the Lake Ladoga climatic circulation

Sec. 3.4]

119

time-step appears. To understand the character of time-step limitations we will consider a one-dimensional model. At the interval -H ~ Z ~ 0 let us consider a onedimensional initial-boundary-value problem

au

&u

at = k z az2'

2

aul -a = Z z=-H

k z = const,

ulz=o = 0,

'YUlz=-H'

ult=o = cp(z).

At the interval -H ~ Z ~ 0 an equidistant grid with a step h, h = H/N, will be built, where N is an integer. Let consider for this problem the following explicit/implicit difference scheme in grid nodes Zi = -(N - i)h, i = 0, I, ... ,N,

Uo - Uo

k -

U·-u· T

= kzuzz,

-----v;;- = hz

Uz -

'Y

It uo, i = 1,2, ... ,N -1,

UN = O.

Here U z and U z are 'upward' and 'backward' differences, respectively. Let rewrite these equations in the following way

(ui-htkzuzz) = Ui,

i=I,2, ... ,N-I, UN=O.

Square both equalities and sum them, taking the first one with the factor l, We will get N-l

~ (Ui -

k)2 = ~ uT + (1 - 2ht'f) ;.

1(

N-l

htkzuzzi + 2: Uo - 2ht ; Uz

272.

Rearranging the left-hand side of the equality, using the formula of summation by parts, N-l

-

N-l

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~l

we will get

=

N-l

N-l

i=l

i=l

k

L uT + ML J2;U;z + 2ht ;

UOU z + 2ht

N-l

L J2;uz i=l

120

Oimatic circulation in Lakes Ladoga and Onego

[Ch.3

This implies that

IIul1

2

N-l

=

U?:.

LuT + ; i=l

provided that

11 -

2h t

~ I < 1.

Hence, for stability of the explicit/implicit scheme the requirement for the time-step is h, ~ h/,,!. So, by analogy with the modelled situation, suppose y = k2lul. Then at h = 10m, k2 = 2.6.10- 3 and lui ~ m s"! we will get that h, ~ 50 min. Therefore, in the modelled example the time-step restriction was acceptable. Numerical experiments with the model (Astrakhantsev et al., 1987; Rukhovets 1990), using boundary condition (2.35) have shown that the periodic solution with this condition differs negligibly from the one with boundary condition (2.26). What is the reason for such a small difference between solutions? The arguments formulated below have more the character of plausible reasoning and are not a proof, but, as we suppose, are sufficiently sound. First of all, we will recall once more that in the lake there actually exists an all-year-round general cyclonic circulation which is why the depth-averaged velocity is basically different from zero. Further, due to the fact that the major variability of flow field is concentrated in the near-surface layer and at depths greater than 10m, depthwise flow field modification takes place only in separate parts of the lake; depth-averaged velocities in direction and magnitude are close to boundary velocity values. The annual large-scale climatic circulation of Lake Ladoga, constructed using the computer model, complies with existing views about the actual circulation in the lake. This relates to the character of the integral circulation, to the distribution of horizontal velocities with depth, to the magnitude and distribution of vertical velocity, to the reproduction of the thermal bar, though very schematic, and, finally, to the temporal evolution of the flow field. It should be mentioned that the existing concept about the actual circulation in Lake Ladoga is based mainly on modelling results described in the monographs of Filatov (1983, 1991). These results, obtained with diagnostic models, in general correspond with our results; but there are some differences in velocity magnitudes and in current schemes also. Unfortunately, there is not enough data for an extended comparison. Refinement ofgrid cells steps in computational experiment

In the process of waterbody hydrothermodynamic computer model development two problems can be distinguished: testing the correctness of the program runs (code) and determination of the adequacy of calculation results to observation data. The degree of adequacy depends on the accuracy of the discrete model approximation of the original mathematical problem. Approximation accuracy, in turn, tangibly depends on the computational grid resolution. In this regard, one of the adequacy

Sec. 3.4]

Simulation of the Lake Ladoga climatic circulation

121

control methods is calculations on refined grids. In this reasoning it is actually assumed that the mathematical model credibly describes the modelled physical phenomenon or process. It is worth mentioning that the climatic circulation being described in this work (Astrakhantsev et al., 2003) much better reproduces the annual evolution of the waterbody temperature field compared with the circulation built in earlier publications (Astrakhantsev et al., 1987; Rukhovets, 1990; Menshutkin, 1997) on coarser grids. Let us illustrate as grid refinement influences the quality of calculations. Fig. 3.24 presents isotherms for the same June data for climatic circulation, built on refined grids with horizontal steps hx = hy = 2.5 km, 1.25 km and 0.625 km respectively. Modelling results can be compared with the data for the same date data (Fig. 3.6(b)) from the Limnology Institute of RAS (Naumenko et al., 2000). A comparison demonstrates that, with grid refinement, isotherms T = 3°C, 4°C and 5°C correlate better with isotherms from observations. On the other hand, intercomparison shows that the grid with steps hx = hy = 2.5 km is reasonably acceptable and further refinement is not required. In conclusion we would like to note the indirect confirmation of the reliability of Lake Ladoga climatic circulation reconstruction and the computational results where calculated flow and temperature fields are used. For example, the authors verified the calculations of conservative substance spreading, conducted to estimate the consequences of the release of polluted matter in Syas PPM to the River Sjas and Lake Ladoga at the end of December 1998. Using an admixture as tracer (Astrakhantsev et al., 2003), the authors analysed the character of the circulation in the southeastern part of the lake in the winter period . It turned out that calculations indicated transport from Volkhov Bay to Petrokrepost Bay. The existence of

~.

~---'.'

c. :

J~

c Fig. 3.24. Surface water temperature for June 15 calculated on different grids (in m): (a) 2470 x 2470, (b) 1235 x 1235, (c) 617.5 x 617.5.

122

Oimatic circulation in Lakes Ladoga and Onego

[Ch.3

such currents was, as a matter of fact, registered in the study of Kruchkov and Terzhevik (1982). Thus, field observations (Kruchkov and Terzhevik, 1982) confirm the reliability of computational results. It is relevant to mention that cyclonic circulation, existing in the lake for most of the year, generates an almost constant water flux from Volkhov Bay towards the north along the eastern lake coast.

3.5 SIMULATION OF THE LAKE ONEGO CLIMATIC CIRCULATION 3.5.1

Computational procedure

Lake Onego climatic circulation was first constructed in 2003 (Rukhovets and Filatov, 2003). In this publication the calculation results of Rukhovets et al. (2006d) are also used. It should be noted that for Lake Onego calculations the same hydrothermodynamic discrete model was used as for Lake Ladoga (Astrakhantsev et al., 2003). Calculations were performed on a grid that was equidistant in horizontal directions with steps hx = hy = 2.5 km at 27 vertical layers. The number of computational nodes at the lake surface was approximately 1500. In the Lake Onego discrete model the surface area and lake volume had the measurements: lake surface area 9850 km 2 , and lake volume 280 krrr' (Lake Ladoga, 2000). The prescription of initial conditions, in the process of ice cover modelling and turbulence, were similar to that of Lake Ladoga. Since the Lake Onego geometric dimensions are of the same order as those of Lake Ladoga, the same empirical parameters were used in calculations as for Lake Ladoga. Due to the similarity of the hydrothermodynamic processes in Lakes Ladoga and Onego, the authors made the Lake Onego modelling description more concise.

3.5.2 The results of thermal regime modelling In this section and in the following subsections calculation results of the periodic solution (2.19)-(2.31) reproducing large-scale climatic circulation in Lake Onego are discussed. In Fig. 3.25 the annual fluctuation of Lake Onego specific heat storage, based on modelling results, is compared with the curve built using observation data by Tikhomirov (1982). Their close coincidence indicates that the calculated annual dynamics of waterbody-specific heat storage repeats the real behaviour of annual specific heat storage in the lake. This is one fact to confirm the credibility of the calculation. The description of the evolution of the waterbody temperature field is performed in accordance with Tikhomirov's (1982) subdivision of the year into hydrological periods: spring, summer, autumn and winter. In Table 3.4 the main characteristics of the Lake Onego thermal regime based on mean perennial data and modelling results are presented.

Sec. 3.5]

Simulation of the Lake Onego climatic circulation

,.

/

/

f\

123

\

1!'h1

Fig. 3.25. The annual fluctuations of Lake Onego specific heat storage (in kcal cm- 2) : solid line, data of observations; dotted line (modelling). Table 3.4. Some characteristics of the Lake Onego temperature regime within a year, according to observed and modelled data. Observed phenomenon

Observations

Modelling results

Disappearance of ice cover Appearance on the surface of the 4°C isotherm End of hydrological spring Upper mixed layer thickness in late summer Appearance on the surface of the 4°C isotherm Disappearance on the surface of the 4°C isotherm Formation of complete ice cover

May 18 May 10-25

May 25 May 18

June 20-25 20-25m

June 13 25-50m

End of October to beginning of November Middle of December

Middle of November December 12

January 18

January 28

Spring heating period

This period is divided into two phases. The first one starts when the resulting water mass heat flux value rises above zero and then stays positive. In the model this moment corresponds with the beginning of April (Fig. 3.25), when the lake is completely covered with ice (Fig. 3.26). Starting from April 20, ice cover destruction begins; by May 18 the area of ice cover halves; and, by the middle of the last decade of May, ice cover completely

124 Climatic circulation in Lakes Ladoga and Onego

O'--

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--'-_--'-_ _L-

I....,

...L..

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--'----"-'--_---J

Fig. 3.26. Annual dynamics of the ice area of Lake Onego (in %) .

u

.-------.----T""T"--_:_

L•

12U

IIIlJ

Fig. 3.27. Lake Onego surface water temperature: (A) 21 May, (B) 15 July. Dotted line in (A) shows the position of the cross-section.

Sec. 3.5]

Simulation of the Lake Onego climatic circulation

125

disappears (Fig. 3.26). During the first phase, an inverse temperature stratification with horizontal isothermy turns into stratification with vertical isothermy (Fig. 3.28(a)-(d)), which is typical for lakes completely covered with ice during winter (Tikhomirov, 1982). Surface-water temperature on May 21 is 1.4-5.3°C (Fig. 3.27(A)); near-bottom water temperature in the deep water part is nearly 2.25°C (Fig. 3.28(c)). The second phase of the spring heating period starts with the beginning of thermal bar formation at the end of May. According to observations, the thermal bar front forms, depending on winter type, between May 10 and 25 (Tikhomirov, 1982). The appearance of the 4°C isotherm on the lake surface manifests development of the thermal bar (Fig. 3.27(a); Table 3.4). The movement of this isotherm towards the deeper parts of the lake can be observed in Fig. 3.28(e)-(f). The modelled thermal bar has smeared boundaries and that can be explained by the large grid-cell size compared with the near-surface thermal bar width in the direction perpendicular to its front. Modelling results demonstrate that in the deep part of the lake water temperature is constant and is in the range 2.5-3°C (see Lake Ladoga, 2000, Fig. 1.9). According to observations, the water temperature at the surface of the shallow water areas in Bolshoye, Onego and Povenetsky Bays reaches 14°C (Lake Ladoga, 2000, Fig. 1.9, Fig. 1.10). Calculation results correlate with this data (Fig. 3.27(b)). By the end of the second phase in the shallow water areas between the coastline and the thermal bar, located over 50m depths, a thermocline starts to develop (Fig. 3.28(e), (f)), which corresponds to the observation data (Tikhomirov, 1982, p.67). The spring heating period ends between June 10 and 15, when the thermal bar disappears and a dome of water with a temperature f"'.J4°C starts to develop (Lake Ladoga, 1992; Filatov, 1999). In the model this takes place at nearly the same dates as in the observed data (Fig. 3.28(g)). Summer heating period

According to observations the summer heating period starts with establishment of the stable temperature stratification on June 15 and ends approximately on August 15 when heat influx through the lake surface becomes a heat loss. The dense water dome top, formed at 4°C, sinks by the middle of June from a depth of 7-10m to about 40-50m in the western part of the lake and to 20m depth in the eastern part by the end of June (Fig. 3.28(f), (g)). In accordance with the model results the temperature over deepwater parts is 6-9°C lower than over the shallow near-coastal zone (6-7°C lower according to observations (Lake Ladoga, 2000, Fig. 1.10)). The thermocline is a few metres thick at this time, with a temperature decrease of 2.5--4°C (Fig. 3.28(g)). Autumn cooling period

The first phase of autumn cooling starts, according to observations, after August 15 with the establishment of the steady negative mean daily heat balance of Lake

126

[Ch.3

Climatic circulation in Lakes Ladoga and Onego

HZ=X5J ..

..

b

..

n

n

;S C?J II

ICI

I

It'

•

Fig. 3.28. Water temperature distribution on a section across the lake: (a) 01.04, (b) 01.05, (c) 21.05, (d) 31.05, (e) 10.06, (f) 15.06, (g) 20.06, (h) 14.08, (i) 13.09, (j) 03.10, (k) 02.11, (I) 07.12.

Sec. 3.5]

Simulation of the Lake Onego climatic circulation

h

Fig. 3.28. (Continued).

127

128

Oimatic circulation in Lakes Ladoga and Onego

[Ch.3

Onego. Epilimnion thickness, based on modelling results, in the deepwater part of the lake increases to 20-25m by the middle of August (see Lake Onego ... , 1999, p. 76) the value 20-25 m is given), by the end of August the final destruction of the thermocline takes place (Fig. 3.28(j)) and vertical homothermy starts to develop (Fig. 3.28(k)-(m)). In the middle of November the model results show the generation of the autumn thermal bar (Lake Onego ... , 1999, p. 87) - at the end of October to the beginning of November) that defines the end of the first and beginning of the second phase of autumn cooling. In accordance with observed data (Tikhomirov, 1982), the autumn thermal bar formation is related to the end of October, beginning of November. The thermal bar appears near the southeastern shore and in shallow parts of the skerries region. At the same time between the thermal bar and the coastline ice formation starts that corresponds to observation data. The thermal bar moves to the open lake and disappears in the first half of December. The inverse stratification is formed in the shallow area (Fig. 3.28). The homogeneous water-temperature distribution within the water column is observed in the deepwater part where these values are close to 4°C. By the middle of December the autumn cooling period ends; that corresponds with observations (Tikhomirov, 1982). The ice-covered area at this time is 36% of the lake surface area. Winter cooling period

The beginning of the winter cooling period is related to the moment when water masses reach the maximum density temperature. According to modelled data it starts on December, 12 (Table 3.4). Lake cooling through the open surface enhances inverse temperature stratification. In the third decade of December the slowdown of ice edge movement is marked during redistribution of heat between covered and icefree parts of the lake. At the end of December to the beginning of January the ice generation rate is maximal (Fig. 3.16): on December 28 50% of the lake area is covered with ice, and on January 4 it is already 95% (Fig. 3.26). After January 5 ice formation decelerates sharply and the lake is completely covered with ice by of January 28 (Table 3.4). In accordance with observations the lake is completely covered with ice on January 18 (Tikhomirov, 1982). By the end of January with inverse temperature stratification the thermocline is formed at a depth of about 15m, which slowly declines to 30 m depth by the beginning of hydrological spring. The location of isotherms 0.5-2°C is close to horizontal. Water temperature near the bottom is approximately 2-2.5°C (Fig. 3.28(a)). The end of the winter cooling period is the moment when heat influx steadily prevails over heat loss; according to observations it happens on April 1. The specific heat storage is minimal in the lake at this moment. Fig. 3.25 demonstrates a good agreement of modelling results and observations, both in dates and values. The change of heat flux direction is really close in time to April 1. Let us characterize in general the quality of Lake Onego thermal regime modelling. As can be seen from Table 3.4, the occurrence dates of some phenomena in the model virtually coincide with observations. The main differences appear in late spring and continue to the end of summer. Among them are the earlier beginning of

Simulation of the Lake Onego climatic circulation

Sec. 3.5]

129

hydrological summer, overestimated thickness of the upper mixed layer in late summer, and higher values of water temperatures in the hypolimnion. The reproduction of frontal zones is the important characteristic of the hydro dynamic model from the ecosystem modelling point of view. So, the dynamics of the 4°C isotherm at the lake surface can be used to estimate the generation and forma tion of the thermal bar. The presence of the thermal bar has to be confirmed by intensive waters submerging near the 'vertical' surface, for which the 4°C isotherm at the surface is a guiding line. But to reproduce distinctly the thermal bar in Lake Onego with a grid step of 2.5 km in the horizontal direction does not succeed. Nevertheless, the dynamics of the movements of the 4°C isotherm along the lake surface and along the lateral transect during hydrological spring corresponds with observed data (Tikhomirov, 1982). The structure of the temperature field is generally reproduced adequately in calculations. In computations the winter temperature regime and the formation and melting of ice are also reconstructed. The dates of ice cover establishment and disappearance in the model correspond with mean perennial values (Table 3.4). 3.5.3 The results of currents simulations It should be noted that the more complex bottom morphometry and coastline

configuration in Lake Onego compared with Lake Ladoga affected the quality of currents reproduction. This is probably linked to the fact that the boundary layers in Lake Onego occupy a relatively larger part of the waterbody than in Lake Ladoga. However, the results of currents simulations show that the constructed circulation in Lake Onego corresponds with limnologists' ideas (Tikhomirov, 1982; Filatov, 1983, 1991; Lake Onego ... , 1999). The general characteristic of the Lake Onego a)

.,

••

~ .~

'M

0_.

-_ -.... - - - - -

~

I

I, I

:J

..

-

..

b)

"

--...

.....

~

.

o - - - - -

I

-

I f

. -

-

... ... Fig. 3.29. Distribut ion of current speed (in ern S-I) with depth at points (a) and (b) shown on Fig. 3.2 for (1) 10 June, (2) 14 August, (3) 3 October, (4) 2 November .

130

Climatic circulation in Lakes Ladoga and Onego 2D

60

100 ,..,

A

[Ch.3 2Q

60

WO

kl

B

Fig. 3.30. Currents at depth 6m (1 em corresponds to 0.25ms- I ) : (A) 10 June, (B) 3 October.

reconstructed circulation is as follows. The highest variability of currents during the open water period is attenuated to the near-surface layer. In Fig. 3.29 graphs are presented showing variations of the velocity module with depth at two points in Lake Onego, located in different parts of the waterbody with different depths (the location of these points is shown in Fig. 3.30). The major velocity module variability during the open water period occurs at depths of less than 7 m. In Fig. 3.30 current velocities at a depth of 6 m are depicted. The intensification of currents in the autumn period is revealed in the figures. During the ice-covered period a drastic reduction of current velocities takes place. Meanwhile current velocities under the ice do not exceed I em S-I and, at inflowing river sites, values of only several em S-I are observed.

Conclusion For the first time the annual climatic circulation of Lake Onego is reproduced . The analysis of computational results and their comparison with observed data has demonstrated that the model adequately reproduces the main elements of Lake Onego's large-scale circulation: summer and winter stratification, sufficiently clearly delineated thermocline in summer; spring and autumn isothermy; ice formation and

Sec. 3.5]

Simulation of the Lake Onego climatic circulation

131

destruction processes; reliable dynamics of the 4°C isotherm along the waterbody surface. The adequacy of the correspondence between the annual transformations of the constructed hydrophysical fields and the real ones observed in the lake permits the use of computational results in models of admixture transport and in ecosystem models.

4 Estimation of the lakes' thermohydrodynamic changes under the impact of regional climate change

Global climate change is accepted by the larger part of the scientific world. The issue most hotly discussed is the causes of global warming and, in particular, the role of the human component. At the same time many scientists point out the inhomogeneity of the influence of global warming in various regions of the planet. Thus by the end of the last century the mean annual temperature of the atmospheric surface layer had increased by by 0.6°C, while on Russian territory it had increased by 0.9°C (Melesko et al., 2004). An attempt to reveal the tendencies of modern climate changes on the Large European Lakes catchment for the period until 2050 and to estimate their impact on the thermohydrodynamic regimes of Lake Ladoga and Lake Onego is undertaken in this chapter. 4.1 4.1.1

CLIMATE CHANGE OVER THE LAKES' CATCHMENTS Climatic features and their variability

A number of publications have been devoted to the results of studies ofclimate change regularities over the Large European Lakes, perennial and inter-annual water temperature and level fluctuations, and river runoff. Among them are the works of Molchanov (1946), Shnitnikov (1966), Malinina (1966), Adamenko (1987), Doganovsky and Mjakisheva (2000), Golytsin et al. (2002), Filatov et al. (2002, 2004), Filatov (1997), Rumyantsev et al. (1997), Kondratyev (2007), and Nazarova (2008). Observation data indicate that, beginning in the twentieth century, definite global climatic system changes have occurred which have become more obvious during the last 20 years. To estimate the flexibility of climate and water balance elements (WBE), the lakes' water level fluctuations as an integral characteristic of climate changes,

134

Estimation of the lakes' thermohydrodynamic changes

[Ch.4

long-term observation data of air temperature, precipitation, evaporation, river runoff, sunshine duration (SD), ice cover on lakes, water levels on lakes and other parameters during the period 1880-2006 was collected at observation stations of the Federal Agency for Hydrometeorology of the Russian Federation. Beginning in the second half of the twentieth century, the Large European Lakes' ecosystems were under the influence of anthropogenic factors and feasible climatic changes. As a result, it is rather difficult to estimate separately the impact of climatic factors and the impact of anthropogenic factors on lake ecosystems, and especially to predict them. To attain this goal it is necessary, along with analysis of long-term series of observations of hydrometeorologic characteristics, to use estimates of possible climate changes obtained by applying oceanic and atmospheric circulation models, the so-called Coupled General Circulation Models (CGCM) or GSM. Regional changes within the Large European Lakes reflect in general the positive tendencies of air temperature changes at the end of the twentieth and the beginning of the twenty-first century. But observed warming is rather inhomogeneous spatially. Feasible changes in the Lake Ladoga catchment hydrological regime and inflow to the lake depending on climate changes were estimated by Kondratyev, Efimova and others (Lake Ladoga, 2002). The investigations of Trapeznikov (Trapeznikov et al., 2000) are devoted to studies of the formation mechanism of annual and perennial lake water level fluctuation under the influence of air temperature and precipitation using the methods of the theory of periodically correlated stochastic processes. It is shown that the lake water level has noticeable statistical correlations with air temperature and precipitation of the present and two previous years. And the maximal input to the lake level fluctuation is given by the air temperature and precipitation of the previous year. Considerable changes in the lake water level regime could be determined by drifting of the hydrological seasons' time boundaries. To understand the impact of climate changes on the lakes' ecosystems it was essential to estimate parameters that could be applied in a 3D coupled hydrodynamical and ecological model. First of all were river runoff, heat flux through the water surface, and air and lake water temperatures. The climatic regime within the Lake Ladoga and Lake Onego catchments could be characterized as a transitional one, changing from a marine climate to a continental climate. According to Alisov B.P. classification the region is referred to the Atlantic-Boreal region of moderate climatic zone. Prevailing air masses of Atlantic and arctic origin are typical here all through the year. A high degree of flow regulation in the catchment by numerous small lakes and rivers provides formation of specificclimatic conditions. On average, 550-750mm of precipitation is registered here. Winds of southern, southwestern and western directions prevail in the region. Mean annual air temperature varies from O°C in the north to 3°C in the south. The coldest month is January (with average temperatures -12-13°C in the northern part and -9-10°C in the southern part). The year's warmest month is July (-14-15°C in the northern part and 16-17°C in the southern part).

Sec. 4.1] ella T

A

Climate change over the lakes' catchments •

135

"c

3

.:J.

1B4Q

18150

9DD

1800

1920

1940

196D

1980

2000

Fig. 4.1. Derivation of the mean annual air temperature from its normal magnitude in Karelia during 1840-2006.

Over Lake Ladoga and Lake Onego air temperature annual variation became smoother and amplitudes decreased; marine climate features became more apparent. This could be related to the lengthening of the duration of the period that the lakes were without complete ice cover, which, as a result of the enormous water mass, essentially influenced the maximal and minimal air temperatures, enhancing winter minimums and depressing summer maximums, resulting in a decline in annual temperature amplitudes. The value of the mean perennial air temperature averaged over the Karelia region during the period 1961-1990 is used as a climatic norm. Beginning from 1989 a steady rise in mean air temperature (the years 1993 and 1998 are exceptions) in the Karelia region is observed. The normal mean annual air temperature rOse from 1.6 to l.re during the abovementioned period . The curve on Fig. 4.1 shows the mean climatic norm of annual air temperature alteration in Karelia . The relatively smooth temporal rate of its mean perennial values in the nineteenth century can be distinguished and a considerable rise in the normal value with the beginning of industrial period in the last approximately 100 years. The warming period in 1930s replaced by a cooling period in 1960-1970 and succeeded by a rise in air temperature at the end of 1980, continuing up to the present time, was reflected in alterations in the mean perennial air temperature calculated using a 30-year moving average (Table 4.1). Table 4.1. Monthly mean air temperature trends CC per 50 years) during 1951-2000 on the basis of meteorological station data: (1) Petrozavodsk. Lake Onego; (2) Olonets, Lake Ladoga. Point I

1 2

2.0 2.5

II

III

IV

V

VI

VII

VIII

IX

2.3 2.5

3.6 4.7

1.9 2.9

0.6 0.9

0.8 1.4

1.1 1.1

0.0 0.6 -0.6 0.1

X

XI

1.1

-0.6 0.2 1.1 -0.4 -0.4 1.3

0.6

XII

Year

136 Estimation of the lakes' thermohydrodynamic changes

[Ch.4

Fluctuations in lake water levels are integrated indicators both of natural climatic and of anthropogenic factors. Before the beginning of the 1950s when Lake Onego was not regulated, trends in water level changes in Lakes Ladoga and Onego were similar. After Lake Onego became a regulated reservoir in 1953, its water level slightly increased. If the anthropogenic component were be removed from Lake Onego water-level values, water-level fluctuations in the two lakes would be coherent. The positive trend is revealed in totals of annual precipitation time series and that is, firstly, a consequence of the increased duration western transfer within a year of water masses over the lake catchments. The growth of annual precipitation totals in the twentieth century could be mentioned. In general, precipitation enhancement and annual air temperature rise causes an increase in total evaporation in the region, but it does not compensate the growth in the income component of the water balance.The abovementioned results show that climate and total catchment humidity are subjected to significant natural fluctuations overlain with fluctuations caused by anthropogenic factors. Thus the variability of secular and intersecular hydrometeorological fields considerably influence the natural background where water ecosystems develop. The fluctuations in lake water levels and the main statistical characteristics based on modern data up to 2002 are presented in Fig. 4.2 and Table 4.2. Before the 1950s, the tendencies of both lakes were similar, but, beginning in 1953 after Lake Onego was regulated, these changes during the last two climatic cycles in the years 1940-2000 has been such that the mean annual level of Lake Ladoga is below the normal values and that of Lake Onego is above the normal values (Table 4.2). Starting from the 1990s the declining trend in the water level of the lakes appeared. At the same time dispersion of water level fluctuation has been minimal during the last level of climatic cycle in 1970-2000. During the last decade a low inflow phase has been registered for both lakes. But the mean annual water level values for the lakes are a long way from those minimal values observed in the 1940s and 1970s.

E

LI

ri a

l:

o

u

ti )0

-1

Fig 4.2. The main trends in water level fluctuations (em) of the Large European Lakes: Lake Ladoga (1) and Lake Onego (2) (regulated regime since 1953), and Lake Onega (3) (natural regime in 1953-2003).

Climate change over the lakes' catchments

Sec. 4.1]

137

Table 4.2. The main statistical characteristics for the lakes water levels based on 1881-2002 observation data. Lake Ladoga, em a.s.l. (Baltic system)

Statistical value Mean value Median value Maximum Minimum

Lake Onego, above 31.8 m, in cm

479

111

480 620 364

113 165 26

According to observation data a tendency for mean annual precipitation magnitudes on all meteorological stations for the period from October to April is revealed and, beginning from May until September, both enhancement and decline of precipitation values during a month is registered. As well as having an understanding of the fact that climatic characteristics are subject to changes, it is important to determine the causes of these fluctuations. For the region being studied alteration in these characteristics should be examined simultaneously with the North Atlantic Oscillation (NAO) indexes. It is known that indexes characterizing the fluctuation of this parameter in time correlate with variations in climatic parameters over the vast territory of North Eurasia. Further peculiarities of NAO index variability and the parameters characterizing climate variability on the lake catchments, will be considered. Fig. 4.3 presents graphs of the NAO index and the near-surface layer air-temperature fluctuations over Lake Ladoga (Valaam meteorological station data) from 1881 until 2002. It should be mentioned that for Lake Onego the similar graph has the same shape (petrozavodsk meteorological station data) . 1),5

,6

5,5

,2

I-

4,6

a


..E :J

3,5

as

a. E

-<...

.e I},f,

-D.5

!:J

~

:;:!

2 ~

s ~

*

~ ~

Fig. 4.3. NAO index and near-surface layer air temperature fluctuations over Lake Ladoga: solid line shows air temperature values; dotted line shows NAO.

138

[Ch.4

Estimation of the lakes' thermohydrodynamic changes

1= I

0,30 0,2&

T AO

G,

3,1 3,0

0

2,9 ~ (1)

....

G,1B

~

fa

0 G,14 Z G,10

.: !

.~ .r '-J

D,O

~

m

;"-1., ./

~

I

,:

a.

E

....

L •

~

~.

~

D,02 .0,02 18:81

2,3 19 00

920

1940

96 0

198(J

2000

2,2

Fig. 4.4. NAG indexes and surface-layer air-temperature fluctuations over Lake Onego (3D-year moving averages).

Initial data analysis, as well as cross-correlation functions between NAO and the near-surface air temperature over the lakes (petrozavodsk and Valaam meteorological stations) reveal a high degree of compliance (the cross-correlation coefficient is greater than 0.5), as the relation between lake water level fluctuation and NAO index has a low correlation, about 0.3. It is explained by the fact that water levelfluctuations and the duration of ice-free period as well depend not only on the temperature of the atmosphere, but also on complex atmospheric and processes within the waterbody and catchment. It is known that the NAO index better correlates with late winter air temperatures (January-March) than with annual temperatures. As the initial data presented in Fig. 4.3 is difficult to interpret, 30-year moving averages of NAO indexes and air temperature series over the lakes were used. Variations of water temperature and NAO indexes for Lake Onego are presented in Fig. 4.4. The mean correlation coefficient for these characteristics equals 0.53, but in some time intervals coefficients range from 0.16 to 0.76. The ice-free period (the number of days when the lake is free of ice) has low correlation with NAO on Lakes Ladoga (Karetnikov and Naumenko, 2007) and Onego (Filatov et al., 2004). Calculations of the cross-correlation of these values in spectral domain show a low dependence at the temporal scales considered. 4.1.2

Probable climate changes over the lakes' catchments

Numerical modelling results obtained by applying the coupled model of global ocean-atmosphere circulation developed at the Max Planck Institute for Meteorology (Bengtsson, 1997) were used to estimate climate changes over the lakes' catchments. Calculations were based on two scenarios of global climate change developed by the intergovernmental panel of experts on climate change (IPCC) . In the first scenario, G, doubling of carbon dioxide and greenhouse gases in the Earth's

Sec. 4.1]

Climate change over the lakes' catchments

139

atmosphere over the period 2000-2100 is assumed; in the second scenario, GA, the increase in aerosol of techno genic origin concentrations is additionally considered. Lake Ladoga The estimates of future climate changes over the Lake Ladoga catchment (Meleshko et al., 2004) showed that mean annual air temperature growth over the catchment for the period 2000-2049 in relation to the period 1981-1990 will be 3.0°C. The increase in precipitation over the catchment will be 159mmyear- 1 for the period 2000-2049. Essential seasonal redistribution of precipitation is expected, the maximum amount will fall in the autumn-winter period. Along with warming and the increase in precipitation, the magnitude of the runoff layer might be significantly enhanced. According to the results of this study, runoff value enlargement on average during 2000-2049 will be 45% compared with the model testing period. But estimates of precipitation fluctuations have an essential level of uncertainty. In this connection the authors conclude that it is necessary to apply modelling results averaged over the set of global climate models. Observed monthly and annual mean near-surface air temperature, monthly and annual precipitation sums, and near-surface air temperature based on monthly global climatology data for the period 1860-2005 were used to compare modelling results with observations. The most specific feature of regional mean annual temperature variability in the model is the temperature growth trend over the Lake Ladoga catchment for the whole period beginning from the middle of the nineteenth century that is strongly revealed in the twenty-first century. The most noticeable tendency of near-surface air temperature enhancement is received for mean January air temperature, and the minimal linear trend is for July air temperature. It was shown that the mean annual modelled air temperature over the Lake Ladoga catchment which equalled 3.8°C on average for the twentieth century increases in general up to 6.6°C for the first half of the twenty-first century. The tendencies of climate parameter change over the Lake Onego catchment For the estimation of the compliance of observation data and model results for monthly and annual precipitation and air temperature computation, obtained for several meteorological stations, the comparison was made with the nearest model grid nodes. This analysis has shown a close correspondence of monthly mean air temperature; but for monthly precipitation totals the correlation is unsatisfactory. For annual values, calculated in general over each region, the model data correspond properly with the measured air temperature and precipitation. According to the computational results derived from the ECHAM4/0PYC3 model, noticeable climatic and hydrological regime alterations are feasible in the study region. The probable increase in temperature is from 1.6°C to 2.7-3.0°C; the probable increase in the total annual precipitation is from 582mm to 610-635mm; at the same time the total evaporation may increase from 264 to 323-348 mm over the Lake Onego catchment. Taking into account these relations the overall river

140

Estimation of the lakes' thermohydrodynamic changes

[Ch.4

runoff under predicted climatic conditions might decline from 319 mm in modern climate conditions to 280-290 mm by 2050. In both scenarios under predicted climatic conditions the maximal air-temperature enhancement will occur in the winter period (December-February). According to simulation results considerable changes in monthly mean air temperature are possible: beginning from May until October predicted air temperatures might be higher than at the present time. A simple statistical model of the water balance for the Lakes catchments based on 15-year moving averages was developed. Further numerical computation was performed on the basis of the ECHAM4/0PYC3 model and the trends of change in the water balance elements (WBE) for the years 2000-2050 were estimated according to the two scenarios of climate change. Averaged over 15-year intervals, time series were used in the regional water balance model. And further, evapotransporation, total evaporation and, ultimately, water runoff for the period 2000-2050 were obtained, both for the G scenario (doubling of CO 2 concentrations in the Earth's atmosphere during the period 2000-2100) and for the GA scenario (direct effect of atmospheric aerosol is considered). It is necessary to mention that the compliance of these two models allows us to estimate those feasible WBE alterations which are absent from the ECHAM4/0PYC3 model output. These estimates reveal that all WBE in the study region, except river runoff, in predicted climatic conditions according to both scenarios will increase. Summarized evaporation will grow fastest, by 1.2-1.3 times, or will be 60-80 mm higher than during the period 1950-1999. This assessment conforms to modelling results received on the basis of other global circulation models (GCM) presented in the literature. As was shown above, at the present time fluctuations in spring air temperatures over the territory studied mostly have a significant positive trend. In future, in accordance with the G and GA scenarios, more intensive air temperature growth will be typical for winter seasons (December-February). The seasonal distribution of monthly air temperatures might change under future climatic conditions. The most intensive warming is possible in the autumn and winter period, while in spring and summer the increase in air temperature will not be so marked. It should be pointed out that the estimates of monthly precipitation totals under future climatic conditions were incorrect, since the model data give unsatisfactory approximations of calculated and measured precipitation values during the control period, 1960-1999. Estimated changes in climatic parameters over the Lake Onego catchment have been presented in the literature (Filatov et al., 2002; Nazarova, 2008). The general tendency for annual air temperature to increase will continue during the following decade. Annual air temperature will increase from 1.6°C to 2.7-3.0°C by 2050. Annual totals of precipitation over the territory will increase from 580mm to 610635mm during the first half of the twenty-first century. Autumn and winter precipitation values will be higher by 30%. The spring precipitation amount will not change noticeably, and total precipitation values will decrease by 18% with respect to the model testing period. Over the Lake Onego catchment the increase in air temperature might be 0.5-1.7°C by 2050. Growth in the annual normal values of total evaporation might

Sec. 4.1]

Climate change over the lakes' catchments

141

vary from 20mm (scenario GA) to 80mm (scenario G). Changes in the total annual precipitation differ in the two scenarios. According to the G scenario, the annual increase in precipitation might be 40 mm; scenario GA predicts an annual precipitation decline of 10mm. As a result the inflow values to Lake Onego will change insignificantly, within inflow measurements (calculations) limits (Table 4.3 and FigA.5). On the basis of ECHAM modelling results it is possible to suppose that by the end of the twenty-first century the timing of maximal spring flood discharges will shift towards the earlier dates as a result of the foreseen warming. A significant increase in total evaporation during the warm season will lead to a decrease in low-water period discharges of 20% compared to the initial period, and probably insignificant reduction of the total annual runoff from the territory studied (Kondratyev, 2007). Table 4.3. Feasible mean perennial air temperature and water balance elements changes in the Lake Onego catchment. Characteristic

Period

Mean during the period

Air temperature, DC

1951-2000 2001-2050, scenario G 2001-2050, scenario GA

2.3±0.2 4.0±0.3 2.8±0.3

1951-2000 2001-2050, scenario G 2001-2050, scenario GA

744±25 783 ± 17 735± 12

+39 -9

1951-2000 2001-2050, scenario G 2001-2050. scenario GA

434± 13 516±17 453±9

+82 +19

1951-2000 2001-2050, scenario G 2001-2050, scenario GA

346± 14 351 ±7 335±7

+5 -11

Precipitation, mm

Total evaporation, mm

River runoff, mm

Feasible change compared with 1951-2000

+1.7 +0.5

In mill ~aa

.--------------------------------,

~~a

~aa

J~a

.

.

".

. ./:o::..~. ;" -. :\ f. ~:~:.:. » "~'./ ~.-.~~ . r'.. .:: :; :

- ,-

~'-----l

-R

• . . ill ... ....... I"\-/}-' 1 a~ D

1n~D

,a~D

Fig. 4.5. Observation data (until 2001) and modelled time series of total river inflow into Lake Onego (Nazarova, 2008).

142

[Ch.4

Estimation of the lakes' thermohydrodynamic changes

An increase in air temperature causes an increase in water temperature in lakes. To estimate feasible fluctuations of monthly mean water temperature in Lake Onego, the relation between these characteristics and the weighted average of the air temperature over the Lake Onego waterbody was defined. As a result of the analysis conducted it was determined that the mean annual water temperature increment in Lake Onego according to the ECHAM4/0PYC3 model could be from 0.6 to 0.8°C in accordance with various scenarios. Besides the climate warming scenarios the hypothetical reduction of air temperature and atmospheric precipitation (increase and decrease of air temperature by I-2°C while precipitation amount varies within a range of 10-20%) were used for ECHAM-4 model to study the influence of climate change on river inflow to Lake Onego. Modelling results are presented in Fig. 4.6. With air temperature increasing by 1°C, the total inflow to Lake Onego may remain constant along with an annual precipitation growth of 3%; in the case of air temperature increasing by 2°C annual precipitation may increase by approximately 6%. With a decrease in mean annual air temperature of 1°C the river inflow will not change provided the total annual precipitation reduces by approximately 3%; in the case of it cooling by 2°C, river inflow will not change if precipitation decreases by about 7%. Thus it was determined that for the Lake Onego catchment during the second half of the twentieth century, typical annual air temperature, total evaporation, and precipitation increase by 0.9°C, 40-50 mm, and 45 mm respectively. The increase in annual precipitation is compensated by an increase in total evaporation and, as a result, there is no linear trend in the river inflow time series (1951-2000).

o o

+1'C

, 0 e:

.

T

,/

c·

-c

II

/ / ....

320 /: II

~.

';,o',r

»:

-:

/

/'

..-

-: . . . . ~

r

1

1

1 0

nual pr clpllat on I

%

Fig. 4.6. Fluctuations in river inflow into the lake according to different scenarios of climate change (air temperatures Ta warming and cooling scenarios) (Nazarova, 2008).

Sec. 4.1]

Climate change over the lakes' catchments

143

Alteration of the thermal regime in the near-surface layer in the region studied is revealed in the lengthening in the ice-free period on Lake Onego. By the end of the twentieth century the period free of ice increased on average from 217 to 225 days. It was found that the dates of ice-cover formation and destruction on Lake Onego are not only determined by autumn and spring temperatures, but are also dependent on large-scale processes that can be characterized by North Atlantic Oscillation (NAO) indexes. IPCC scenarios and the ECHAM4/0PYC3 model results have shown that by 2050 the increases in annual air temperature, total evaporation and precipitation augmentation could be 0.5-1.7°C, 5-18% and 5% respectively. At the same time the increase in annual river runoff into Lake Onego is negligible (1-4%). 4.1.3 Estimates of potential changes in the thermal regime of the lakes by 2050 On the basis of long-term data analysis and the results of computation using mathematical models as described above, changes in the thermal regimes of Lakes Ladoga and Onego were estimated and made the basis for three-dimensional lake ecosystem model simulations. Lake Ladoga water mass temperature (TWM ) for the period 1956-1967 was established by Tikhomirov (1982). The results are presented in Table 4.4. On the basis of this data a relation between mean monthly TWM and average weighted air temperature (Ta) over the Lake Ladoga waterbody for the same period was established (Fig. 4.7). The values of T a were calculated using the method of inclined areas and the data of the following coastal stations: Sortavala, Olonets, Priozersk, Novaya Ladoga, Petrokrepost and the island station Valaam. In analytical form this relation is described fairly accurately by the fifth-degree polynomial (Fig. 4.7): (a) for the period February-July TWB = 0.336 + 0.057Ta + 0.017T;

- 3.38· 10-s

r: + 1.9· 10-

+ 8.52· 10- sTi

6Ti,

(4.1)

Table 4.4. Mean monthly averaged and extreme Lake Ladoga water mass temperatures (WMT) during 1956-1967 according to Tikhomirov (1982). Month

I

II

III

IV

V

VI

VII

VIII IX

X

XI

XII

Year

Mean WMT

1.6

0.8

0.4

0.5

1.9

3.9

5.8

7.2

7.0

6.2

4.7

2.9

3.6

Minimal WMT

1.2

0.7

0.3

0.4

1.4

3.5

5.0

6.6

6.6

5.8

3.7

3.5

3.4

Maximal WMT

2.4

1.0

0.8

0.8

2.4

4.2

6.1

7.9

7.2

6.8

6.0

4.2

3.9

144

Estimation of the lakes' thermohydrodynamic changes

[Ch.4

(b) for the period August-January TWB

= 4.891 + 0336Ta - 4.57· 1O-5T:

O.012T~ - 4.32· 10-4Ti

+ 1.31· 1O-6T i,

(4.2)

Fig. 4.7. Correlation curve between water mass temperature, TWM , and T a •

r

,T

-c

B r-~~--~~----------------, 1

e

4

•

Fig. 4.8. Observed (Tobs) and calculated (TW M ) mean monthly water temperature of the water mass in Lake Ladoga for the period 1956-1967 .

A view of Lake Ladoga .

Valaam Monastery, Lake Ladoga.

Valaam Island, Lake Ladoga.

A view of the north coast of Lake Onego.

Sec. 4.1]

Climate change over the lakes' catchments

. ' "pI'

145

D .•... 2 -- 3

·12 L...-- - - - - - - - - - - - - - - - - - - - ----' Fig. 4.9. Mean monthly air temperature over Lake Ladoga for the period 1950-1999 (1) and its feasible changes in 2000-2050: (2) scenario G ; (3) scenario GA.

Thus, it is possible to estimate feasible monthly mean water temperature alterations in Lake Ladoga for two global climate change scenarios using regression equations (4.1) and (4.1), applying as the expected values of T a the results of the ECHAM4 model numerical experiments. The analysis of ECHAM4 model data has shown that under future climatic conditions the seasonal air temperature variation over the lake will change, monthly mean air temperature maximum will occur in August, the period from August till January will be warmer, and the period March-June will be slightly cooler than at the present time (Fig. 4.9). Simulation results of TWM values by regression equations (4.1) and (4.2) under predicted climate conditions are presented in Table 4.5 and in Fig. 4.10 for scenario

146

[Ch.4

Estimation of the lakes' thermohydrodynamic changes

TW M ,a C 6 ,.---~~-~~--~-~-----~-~~-,

7 6

4 3 2 1

1

2 3

0'------------------------' C

Fig. 4.10. Mean monthly water mass temperature in Lake Ladoga for the 1950-1999 period (1) and its feasible changes in 2000-2050: (2) scenario G; (3) scenario GA).

G (doubling ofCO 2 concentrations in the Earth's atmosphere during 2000-2100) and scenario GA (direct effect of atmospheric aerosol is considered additionally). Besides the mean perennial water mass temperature of the lake, available ECHAM4 model data allow us to calculate these characteristic values during the 2000-2050 period. Similar simulations are in progress at the present time for Lake Onego . Feasible water mass temperature estimations for Lake Onego in 2000-2050 Mean monthly air temperature norm calculations for the Lake Onego region were performed On the basis of observation data from six coastal and two island meteorological stations during the 1961-1990 period. The inclined areas method (Tissen polygons) was used and its calculation formula looks as follows: (4.3) where TCP,i is the average weighted air temperature over Lake Onego for month i, °C; Tt ,i,"" Ts,i is the mean monthly air temperature at corresponding meteorological station for month i, °C; at, ... , as are weight coefficients, equal to the ratio of inclining to the corresponding meteorological station area to the lake water surface area, at + a2 + ... + as = I. Calculations of feasible changers in air temperature in the Lake Onego region are performed On the ECHAM4/0PYC3 model basis for two scenarios (scenario G supposes doubling ofci2 concentrations in the Earth's atmosphere during 20002100; and scenario GA considers additionally the direct effect of atmospheric aerosol

-3.3 -6.3 -4.9 -2.9 1.3 -7.0 0.0 -7.0 -8.9 -7.9 1.8 -11.2

G: -8.7 -12.3 -10.2 -13.0 0.0 -9.3

scenario -8.6 -14.0 -16.0 -17.0 -5.3 -4.1

Model 2001-2050 period, scenario GA: -4.2 mean value for the period -5.2 -14.4 -9.6 2005 -11.9 -8.0 2010 2027, the coldest -23.3 -18.1 -6.9 -6.2 2043, the warmest -4.0 -11.0 2050

-5.6

-10.9

-11.4

Observation data: mean values in 1961-1990 Model, 2001-2050 period, mean value for the period 2005 2010 2012, the coldest 2035, the warmest 2050

III

II

I

Period

3.0 -0.3 3.2 -5.4 3.8 1.3

1.0 -1.5 -2.5 -0.8 6.5 -0.9

0.4

IV

9.2 9.8 7.8 7.7 15.6 12.4

9.2 10.9 10.8 7.3 9.3 12.7

6.4

V

13.7 16.7 14.6 13.7 18.2 18.3

15.3 18.7 19.4 10.8 17.1 20.8

11.8

VI

Table 4.6. Mean perennial water mass seasonal changes in Lake Onego.

15.5 17.1 18.2 15.7 18.8 18.8

17.6 19.1 20.3 15.3 23.0 19.6

15.8

VII

15.7 16.4 18.0 17.7 18.0 16.7

17.4 18.8 17.5 15.7 18.4 18.7

14.4

VIII

11.9 11.5 11.5 9.6 12.8 14.1

12.2 10.0 7.4 12.6 15.3 12.1

9.5

IX

7.8 2.1 2.5 9.5 3.4 5.5

6.5 2.2 4.4 4.3 7.3 6.0

4.1

X

3.5 -4.6 -5.0 2.5 1.4 -5.2

0.4 -1.2 -5.1 -0.4 1.4 1.8

1.4

XI

-1.0 -12.9 -9.9 -4.5 -4.1 -13.4

-4.8 -9.3 -14.5 -9.8 -2.4 -10.3

-6.6

XII

5.8 2.1 2.7 1.4 6.4 3.5

4.5 3.1 2.2 1.9 7.7 5.0

2.2

Year

f

oJ;::. .......:J

~

I

~

t")

fI.l-..

~

f

~ ....

0

~

~

~

~

n

...::::

~

~

00

148

[Ch.4

Estimation of the lakes' thermohydrodynamic changes

of techno genic origin). The calculation period is assumed to be equal 50 years (20012050). The normal air temperature value for each month was calculated as an average weighted value on the basis of modelled data from model grid nodes A, B, D by the formula Tmod,i

= 0.30TA,i + 0.45TB,i + 0.25TD,i,

(4.4)

where Tmod,i is the modelled average weighted air temperature for month i over the Lake, DC; TA,i, TB,i, TD,i are the mean monthly air temperature for month i in the corresponding grid node, DC. Mean monthly air temperature calculation results for the present climatic conditions (1961-1990) and their feasible changes (2001-2050, scenarios G and GA) are presented in Table 4.6. Besides normal values, the intra-annual air temperature distribution for extremely warm and cold years is presented, calculated using equation (4.4) and model data for each scenario . For calculation of the intra-annual water mass temperature fluctuations in Lake Onego under given climatic conditions Tikhomirov (1982) data and described above (see Table. 4.6), normal values of mean monthly air temperatures for the lake region during the 1961-1990 period were used. The regression equation of mean monthly water mass temperatures in general (TWM) and air temperature over Lake Onego (Ta) is derived for two dependency types (Fig. 4.11) as the following: (a) for February-July period TW M

T

= 0.535 + 0.050Ta + 0.0169T~ + 0.0008T~ -

fl .

0.00002T:,

(4.5)

"c

12 r--~--~--~-~--~-------~

fO

x

/

oS

•

~

2 0

·2

· f~

I -. II · fO

II

IV 2

G

10

14

l . >"c

Fig. 4.11. Relation curve between Lake Onego water mass temperature (TW M ) and air temperature (Ta) for mean perennial conditions

Sec. 4.1]

Climate change over the lakes' catchments

149

(b) for August-January period

= 0.528 + 0497Ta + 0.00179T~ + 0.001 T~ - 0.00001T:,

TW M

(4.6)

Feasible mean monthly Lake Onego water mass temperature changes are calculated by equations (4.5) and (4.6), whereas predicted Ta values, the results of computational experiments on the basis of the ECHAM4 model, were used for the two global climate change scenarios (Table 4.6). Computational results of TWB values (equations 4.1 and 4.2) for predicted climatic conditions are shown in Table 4.7 and in Fig. 4.12. For scenario G (doubling of CO 2 concentration in the Earth's atmosphere during the 2000-2100 period) and scenario GA (where the direct effect of atmospheric aerosol is considered).

w

,
12

1[}

1<>-

B

~I

6

Fig. 4.12. Mean perennial Lake Onego water mass temperature for the 1950-1999 period (I) and its feasible changes in 2000-2050: (2) scenario G; (3) scenario GA) . Table 4.7. Mean monthly water mass temperature in Lake Onego: average for the 2000-2050 period and for two global climate change scenarios . Period scenario

I

1956-1967° 1.3 2000-2050, G 1.8 2000-2050, GA 3.0 a According

II

III

IV

V

VI

VII

VIII IX

X

XI

XII

0.7 0.7 1.0

0.6 0.5 0.5

0.6 0.6 0.7

1.7 2.9 2.5

4.6 7.0 5.3

7.9 9.1 7.3

9.8 9.3 9.6

7.5 8.4 8.9

4.8 5.7 7.2

2.5 3.2 5.0

to Tikhomirov (1982, 232c).

9.3 9.7 9.7

150

Estimation of the lakes' thermohydrodynamic changes

[Ch.4

Conclusions

During climate warming in the region, according to study results, the air temperature and the lake water temperature will increase, the ice-free period will enlarge, the amount of precipitation will grow and that will cause alteration of the lake water levels (Filatov, 1997; Kuusisto, 1992). Such kinds of change in hydrometeorological characteristics will impact water and land ecosystems. Peculiar hydrodynamic changes in the Large European Lakes are possible, as was determined for the Great American Lakes (Beletsky and Schwab, 2008). Along with warming, as a result of the ice cover area on the Great European Lakes diminishing, an intensification and mixing of currents due to the increase in their speed in winter time is possible. As the latest studies have shown (Beletsky et al., 2008), in the Great American Lakes the winter period circulation intensity is higher because they are not covered with ice, except for Lake Erie; the Great European Lakes are completely or partly covered with ice during the winter and water hydrodynamics is not intensive there. The water level might decrease during the warming period. As the regional economies of the Great American Lakes and the Great European Lakes are determined by water resources, usage of the lakes for hydro-energy, water supply, transport, recreation, and mining needs, and also as receivers of waste waters, including the heated waters from nuclear power stations, if the water level decreases considerable damage may be caused. Definate changes will occur not only in the lake water column, but also in the catchments. And these changes will affect the lakes themselves. As the period of snow cover on the catchments declines, soil erosion will increase. For these and a number of other reasons, the eutrophication of waterbodies will be even further enhanced. Changes in climatic and water regimes will determine changes in hydroeconomic systems and economic sector management based on water resources usage (hydro-energy, industrial and domestic water supply, agriculture etc.). 4.2 MODELLING THE THERMOHYDRODYNAMICS OF THE LAKES UNDER DIFFERENT CLIMATIC CONDITIONS 4.2.1 Modelling thennohydrodynamics: statement of the problem and numerical experiments As has already been mentioned, one of the main objectives in modelling the thermohydrodynamic regime of large stratified lakes is to provide ecological models with information about the evolution over time of abiotic factors in the water environment. In this connection it is natural that for estimating possible changes in lake ecosystems as consequences of climate changes within the catchment, it is necessary first of all to estimate probable variations in the thermohydrodynamic regime in lakes. Studies on the analysis of trends and the scenarios of climate change in northwestern Russia are presented in Golytsin et al. (2002); Filatov et al. (2004) and

Modelling the thermohydrodynamics of the lakes

Sec. 4.2]

151

Nazarova (2008). These researches are based on time series data analysis (e.g. Filatov, 1997) and on modelling results (Golytsin et al., 2002) received on the basis of general atmospheric and oceanic circulation models - global climate models (GCM). The dynamics of such parameters as surface air temperature, solar radiation and long-wave radiation, precipitation, transpiration and water level in lakes is analysed in these publications. The results of studies of climate change during the second half of the twentieth century within the Lake Ladoga atchment, including that of Lake Onego, are presented in the early sections of this chapter. Besides that, the estimates of possible changes in surface air temperature, and water and thermal balances in the lake catchments in the first half of the twenty-first century are obtained on the basis of the GCM developed in the Meteorological Max Planck Institute (Germany) and implemented by Dr Kuzmina (Nansen International Environmental and Remote Sensing Centre, S1. Petersburg). The preliminary estimates of possible water mass temperature fluctuations in Lakes Ladoga and Onego at the beginning of the twentyfirst century, under the global climate change scenarios discussed earlier, are from Filatov et al. (2004) and Rukhovets et al. (2006a). For the modelling of the hydrothermal regime of large stratified lakes, in particular for Ladoga and Onego, the most essential external impact on the waterbody is heat flux through the surface and integral water inflow, i.e, water inflow plus precipitation minus evaporation. For their determination the annual heat and water balance components of lake catchments are needed. For defining heat flux and integral water inflow in lakes in the context of feasible future climate changes within the lake catchments it could be conceivable to use prognostic calculations results. So, in the literature (Meleshko et al., 2004; Golytsin et al., 2002) the results of simulations on the GCM basis of feasible climate changes over Russian territory and, in particular, in its northwest, for various scenarios of CO 2 concentration and other greenhouse gas variations in the planet's atmosphere. As the authors' (Rukhovets et al., 2006a) objective was to receive only the estimates of the feasible changes in hydro-thermodynamic regimes of waterbodies, the following approach was chosen. On the basis that climate change calculations on the lake catchment determine fluctuations of thermal flux through the water surface and integral water inflow, the authors in the computation process modified the external impacts on the waterbody, using retrospective data. First, it should be mentioned, that heat flux at the water-atmosphere boundary in the thermohydrodynamic model in the lake under consideration is posed as a temporal derivative of specific heat storage in the lake. This approach is described in detail in section 3.3. The average heat flux value through the waterbody surface, Qs, is determined as the temporal derivative of the specific heat storage, SHS, of the waterbody: d Qs = dt SHS(t),

SHS(t) =

J

l(S ) c;PwT(x, y, z, t) dO. mes 0 n

(4.7)

Application of this method for heat flux determination in Lakes Ladoga and Onego appeared to be possible due to the fact that in Tikhomirov (1968, 1982) the

152

Estimation of the lakes' thermohydrodynamic changes

[Ch.4

specific heat storage values of the lake were calculated for each month during the periods 1957-1962 for Lake Ladoga and 1956-1967 for Lake Onego using observation data. In the discrete model, the computation of heat flux was performed as a finite temporal derivative from the specific heat storage of the waterbody (4.7). For both Lake Ladoga and Lake Onego the average and the fluctuation range of SHS(t) values for the middle of each month are presented in Table 4.8. The data observed and calculated by Tikhomirov (1968, 1982) was the basis for the results obtained and presented in Table 4.8. In the modelling process, the year when for each lake the specific heat storage in the middle of a month equals the average, the maximal and the minimal SHS(t) values shown in Table 4.8 will henceforth be called 'climatic', 'warm' and 'cold' accordingly. The data from Table 4.8 will be called the observation data for climatic, warm and cold years. Circulations, constructed in each lake for heat flux, calculated on the basis of maximum SHS(t) values in the middle of every month, will be considered later on as circulations that could occur in the future as a result of climate change within the lake catchments due to global warming. By defining heat flux in this way three hypothetical circulations instead of one were constructed for each lake. The first one in Lake Ladoga, constructed for the integral mean water inflow (average perennial water inflow is 67 km'' year "; precipitation minus evaporation equals 7 km'' year-I), equals 74 km' year " (Malinina, 1966); the second (for what was probably the highest integral annual water inflow in the twentieth century) equals 112.3 km'' year-I, Table 4.8. Mean specific heat storage values (kcal cmr"), for the middle of a month and the range of their variation in observation data (Tikhomirov, 1968, 1982). Months

Specific heat

storage

1957-1962

I

II

III

IV

V

VI

VII

VIII

IX

X

XI

XII

10.6

5.8

3.4

2.3

4.9

15.2

27

35.2

38.4

35.5

28.9

19.7

1.81

1.81

5.12

13.85 23.78 29.50 27.99 22.58 14.45

2.6

1.5

3.6

13.7

1.24

1.55

3.72

11.78 21.08 25.73 23.78 18.6

7.2

5.1

3.1

6.2

16.3

28.4

3.7

2.4

2.8

7.26

15.5

32.86 36.89 33.91 27.9

Lake Ladoga average value 1956-1967

3.91 2.11

7.53

Lake Onego average value Lake Ladoga minimum value Lake Onega minimum value

8

Lake Ladoga maximum value Lake Onego maximum value

16

5.1

1.55 1.24

7.6

23

33.2

36.6

36.3

40

32.7

38.8

23.8

13.8

10.54 4.03 39.2

28.2

19.84 12.71

Sec. 4.2]

Modelling the thermohydrodynamics of the lakes

153

registered in 1962 (petrova , 1982). And, finally, the third (for abnormally low integral water inflow) equals 47 km' year-I, registered in 1940 (Malinina, 1966). The first of these circulations we will henceforth call warm, the second warm with high water inflow, and the third warm with low water inflow. For Lake Onego the first of these three circulations is related in the model with the average perennial integral water inflow (average perennial water inflow is 16.8 km ' year"; precipitation minus evaporation equals 1.8 km'' year-I), that was 18.6km3year- l ; the second (for abnormally high integral annual water inflow in 1962) equals 26.3 km'' year-I. And, finally the third (for abnormally low integral annual lake water inflow) equals 9.5 km'' year" (Lake Onego, 1999 ). As for Lake Ladoga, these three circulations will be called warm, warm with increased inflow and warm with decreased inflow. Besides warm circulations, one more circulation based on heat flux, determined for minimal SHS(t) values in the middle of every month was constructed for each lake. Integral annual lake water inflow while computing these circulations was made equal to average perennial inflow: 74 krrr' year" for Lake Ladoga and 18.6 krrr' year" for Lake Onego. Each of these circulations will henceforth be called 'cold'. In calculations the circulations were used for reproduction of the lake ecosystems functioning. Experiments with cold circulations were conducted for determination of feasible variations from the results obtained on the basis of climatic and warm circulations. It is related to the fact that during the last decade an intensification of the fluctuation in the perennial hydrodynamic regime has been observed in the lakes. In this way the amplitude of feasible variations was determined. Thus for reproduction of the functioning of the lake ecosystems five hypothetical circulations (climatic, three warm and one cold) were calculated. Construction of three warm and one cold circulations for each lake required obtaining periodical solutions of the problem (2.19)-(2.31). Calculation results of the corresponding climatic circulation at the moment of time when the lake specific heat storage is minimal were used as initial values in the computations. In every case the physical time for obtaining periodical solutions for the lake was not less than 20 years. The year-round tributary discharges (the Vuoksa, Volkhov, Syas and Svir rivers for Lake Ladoga, and the Shuya, Suna, Vodla and Vytegra for Lake Onego) were defined as integral annual water inflow distribution related to average perennial integral water inflow presented in Tables 3.1 and 3.2. Annual outflows of the Neva and the Svir rivers were defined for each month and were equal to integral water inflows to Lake Ladoga and Lake Onego (see section 3.3). All wind shear stresses at the lake surfaces were defined to be the same as for climatic circulation (section 3.3). All external forces were considered to be periodical functions with a l-year period. To justify the chosen approach it should be mentioned that the integral water inflow fluctuations (i.e. water balance fluctuations) used in the construction of the lake circulations enhance the changes forecast on the basis of global model for the middle of the twenty-first century. Thus, according to one of the forecasts, river runoff and precipitation in the Baltic Sea catchment in 2050 will increase in the range 6-9% comparing with

154 Estimation of the lakes' thermohydrodynamic changes

[Ch.4

the period 1981-2000 (Melesko et al., 2004). According to ECHAM4/0PYC3 model simulations performed by Dr S. Kuzmina (Nansen International Environmental and Remote Sensing Centre), by the middle of the twenty-first century integral water inflow to Lake Onego could even decrease a little (see section 4.1.2). In our procedures both for Lake Ladoga and for Lake Onego an increase and decrease of integral water inflow by 1.5 times is considered while constructing warm circulations (with high and low integral inflow), and particular values are obtained from retrospective observation data. It is worth mentioning that specific heat storage values obtained in the computation process for the lakes in the middle of every month, for warm, climatic and cold circulations, in fact coincide with those, used to obtain heat flux values in Table 4.8. This can be clearly seen in Figs. 4.13 and 4.14, which reflect modelling results and data from Table 4.8. This coincidence allows us to compare the calculated average annual water mass temperature fluctuation in lakes with the corresponding feasible estimates obtained on the basis of long-them scenario simulations. In Filatov (2004) and mentioned at the beginning of this chapter, preliminary estimates of feasible changes in the value of mean monthly water temperature in Lake Ladoga for the future period until 2050 are presented. These estimates were obtained for two long-term IPCC scenarios of greenhouse gas and aerosol emission in the atmosphere in the twenty-first century: the first reflects the situation where CO 2 concentration doubles in the twenty-first century (scenario G), the second

-.-

2'Hl

1 •

..

1

2

3

5 6 7

a 11

III

Fig. 4.13. Lake Ladoga specificheat storage (observation data and model results): 1, climate, observations; 2, climate, model; 3, warm, observations; 4, warm, model; 5, warm with high inflow, model; 6, warm with low inflow, model; 7, cold, observations; 8, cold, model.

Modelling the thermohydrodynamics of the lakes

Sec. 4.2]

•

.+

+

•

155

•

•

Fig. 4.14. Lake Onego specific heat storage annual fluctuation for different circulation types: I, climatic (observations); 2, climatic (model results) ; 3, warm (observations); 4, warm (model results); 5, warm with high inflow (model results) ; 6, warm with low inflow (model results) ; 7, cold (observations); 8, cold (model results).

additionally considers aerosol influence (scenario GA) (section 4.1.2). The results of these preliminary estimates show that mean annual lake water mass temperature for one of the scenarios is O.2°C. For warm circulation this augmentation is not less than OSC (according to Table 4.8 here Table 18 in Tikhomirov (1968). Thus, mean annual water mass temperaturese for constructed warm circulations exceed thos for climatic circulation by not less than they are increased by mean annual water mass temperatures, obtained as preliminary estimates for the middle of the twenty-first century (see sections 4.1.2 and 4.1.3) on the basis of Global Climate Models. 4.2.2 Analysis of the results of simulations To evaluate computation results in warm and cold circulation cases we will compare them with the results of climatic circulations for Lake Ladoga and Lake Onego respectively.

Lake Ladoga Fig . 4.13 shows the annual fluctuation in specific heat storage in Lake Ladoga for three warm, one cold and climatic circulations based on computation results and

156 Estimation of the lakes' thermohydrodynamic changes

[Ch.4

observation data. The reference time for this illustration is the beginning of March, as the least mean annual heat storage in Lake Ladoga relates to the middle of March (Tikhomirov, 1968). Differences between lake heat storage values for warm circulations and climatic circulation during the waterbody heating period are in general insignificant, though slight distinctions exist for warm circulation with high inflow. During the lake cooling phase these differences are much more noticeable and they are maximal for warm circulation with high inflow. All through the year, specific heat storage differences among warm circulations are negligible (Fig. 4.13). Fig. 4.15 presents the curves that characterize Lake Ladoga ice-cover changes for all five circulation types. Changes in the ice regime are quite explainable: for warm circulation with high inflow ice-cover duration is minimal, for cold circulation it is maximal. Comparison of surface water temperature in the summer period for various circulations (Fig. 4.16) shows that the largest divergence from climatic circulation is in surface temperature distribution for cold circulation and for warm circulation with high inflow. The differences for warm circulation and warm circulation with low inflow are less significant. Differences in water temperature variations along the vertical transect (Fig. 4.17) for the same circulations could be estimated from the location of 4°C isotherm location. It is also possible to estimate the changes in every circulation case for Lake Ladoga by comparing its thermal regime characteristics (only three circulations were chosen: warm, climatic and cold (Table 4.9). This analysis shows that existing

.. +

...

":I

~

- r.

-

-

-:-.

~

~ ~ ~ ~

;;

::

Fig. 4.15. Lake Ladoga ice cover area as a percentage of lake area (model results): 1, climate; 2, warm; 3, warm, with high inflow; 4, warm with low inflow; 5, cold.

Modelling the thermohydrodynamics of the lakes

Sec. 4.2]

157

... ~I

. •

f

~

• -

~I

• ~ I

..

~

~

~

' :'

•

II=" ·

~

...

a

I:'... f

,,

1

I

•

'.

...

'

~­

I

c

d

Fig.4.16. Lake Ladoga surface temperature on June I for different types of circulation (model results): (a) warm, (b) climatic, (c) cold, (d) warm with high inflow.

distinctions are in compliance with a priori conception about their nature. The dates of observed phenomena for various types of circulation differ insignificantly. The analysis of changes in the regime of currents is not considered here, as visual estimates of these observations are not informative enough and , besides that, changes in the distribution of velocities with depth and general circulation character are inessential. The analysis of the hydro-thermodynamic regime modelling results for Lake Ladoga shows that its main changes are determined by heat flux changes and increased inflow. It allows us to further restrict ourselves to considering only some, not all, circulations.

158

[Ch.4

Estimation of the lakes' thermohydrodynamic changes

0

\

. 50

I

i

l

\

. 100

J\ 1\

I

\ a

1

- !SO

, 'l

I

\ r:' \ I~

· 00

~ I

b 0

-~

.

\

\ ~\L

. 5{)

LJ

· 100

I

\

c .... . 60

. 100

I

I

\.\

...

,-"-"

A,

(~

L,

\

d Fig. 4.17. Water temperature along Lake Ladoga transect on July 1 for different types of circulation (model results): (a) warm, (b) climatic, (c) cold, (d) warm with high inflow.

Modelling the thermohydrodynamics of the lakes

Sec. 4.2]

IIIJ

y-+-

---

;

~

t

159

, Z

l -4 S

III

- 1" t

III ...: .

..-

+

D ~ , I .J l l

D 01

D -Z

I •• 1, 0 1. l

DIJJI

.1 I)1m

L' -,

Fig. 4.18. Lake Onego ice cover area as a percentage of lake area (results of modelling): 1, climate; 2, warm; 3, warm, with high inflow; 4, warm with low inflow, model; 5, cold .

Lake Onego

As has already been mentioned, the annual fluctuation in specific heat storage in Lake Onego (Fig. 4.14), for warm and climatic circulations subsequent to computation results, in fact coincide with the data presented in Table 4.8. With Lake Onego specific heat storage for all three warm circulations being noticeably greater than the specific heat storage for climatic circulation over the whole year than in Lake Ladoga. Lake Onego, in accordance with the specificheat storage changes, is subject to greater influence from climate changes within its catchment than Lake Ladoga. Lake Onego ice-cover regime alterations are presented for all five circulations in Fig. 4.18. The period when the lake is completely covered by ice is longest for a cold year and shortest for warm circulation (Fig. 4.18). Essential surface water temperature changes in Lake Onego compared with climatic circulation take place for warm circulation with high inflow and, especially, for warm circulation (Fig. 4.19). The same situation occurs along the Lake Onego vertical transect and the distinction is more significant for warm circulation (Fig. 4.20). Modelling results compliance with a priori conceptions or ideas about feasible climate changes on the Lake Onego catchment can be seen in Table 4.10. Let us emphasize a number of differences between the warm and the climatic circulations in view of the modelling results: • •

vertical homothermy in spring disappears 10 days earlier; the thermal bar, subsequent to the appearance on the surface of the 4°C isotherm, is formed 20 days earlier;

160 Estimation of the lakes' thermohydrodynamic changes

[eh. 4

Table 4.9. Lake Ladoga thermal regime characteristics obtained using modelling and observation data (Tikhomirov, 1982; Filatov, 1983). Observed phenomenon

Circulation

Mean

perennial date

Warm

Climatic

Cold

Complete ice cover date

February 6 - 94% February II 95% February 19 - 97% March 12 - 100%

February 10 - 94% Febru ary 14 - 95% February 23 - 97% March 16 - 100%

Janu ary 4 - 94% Janu ary 7 - 95% Janu ary 17 - 97% February I - 100%

February 10

Ice-cover disappearance date

May 29

May 16

June 10

May 25

4°C isotherm appearance Apri123 date in spring

Apri127

April 28

May I

4°C isotherm disappearance date in spring

June 29

July 9

July 26

Julyl 5

Smallest epilimnion thickness and its appearance date

July 16-21

July 21- 26

August 5- 10

20 m

4°C isotherm formation November 15 date (autumn thermobar).

October 24

October 12

October 1

4°C isotherm disappearance date (autumn therm obar) Complete icc-cover formation date

January 2

December 14

November 20

December 15

November 28 - 1% December 2 - 3% December 6 (December 24) - 5%

October 29 - 1% October 17 - 1% November 3 - 3% October 25 - 3% November 12 October 30 - 5% (December 21) - 5%

December 30

b

Fig.4.19. Lake Onego surface temperature on Jun e 15 (model results): (a) climatic circulation, (b) warm circulation, (c) warm circulation with high inflow.

Sec. 4.2]

Modelling the thermohydrodynamics of the lakes

161

a

b

- !i)

· 100

c Fig. 4.20. Lake Onego water temperature along the transect on July 15 (model results): (a) climatic circulation, (b) warm circulation , (c) warm circulation with high inflow.

162

Estimation of the lakes' thermohydrodynamic changes

[Ch.4

Table 4.10. Some characteristics of Lake Onego annual temperature regime changes. Observed phenomenon

Model results

Observed date

Climatic circulation

Warm circulation

Ice-cover disappearance date

May 18

May 28

May 16

4°C isotherm appearance date on water surface

May 10-25

May 18

April 29

Last date of hydrological spring

June 20-25

June 13

June 10

Thickness of top mixed layer in late summer

20-25m

25-50m

35--45m

4°C isotherm appearance date on water surface

Late Octoberearly November

November 2

November 17

4°C isotherm disappearance date on the surface

mid-December

December 12

January 8

Complete ice-cover formation date

January 18

January 28

March 4

• • •

by the end of June in the lake vertical transect the 4°C isotherm is located considerably lower; an autumn thermal bar for warm circulation is not revealed in the simulation results; the ice-cover formation rate is maximal in the first half of February; as for climatic circulation this phenomenon is observed at the end of Decemberbeginning of January.

Conclusion

The analysis of Lake Ladoga and Lake Onego thermohydrodynamic regime modelling shows that the main changes are the result of heat fluxes and the changes in total inflow. Henceforth in ecosystems modelling we will restrict ourselves to using only those circulations where the changes are more obvious. The most significant integral estimate of changes in the temperature and currents regime is the changes in lake ecosystems - the changes in phytoplankton productivity and its structure, and, in turn, the changes in the trophic state of the lakes.

5 Three-dimensional ecosystem model of a large stratified lake

5.1 MODELLING THE FUNCTIONING OF THE LAKE ECOSYSTEMS: STATE OF THE ART A traditional way of constructing mathematical models to describe natural processes and abiotic phenomena consists in defining the system of physical laws with differential equations being the base of studied systems. This is applied in full measure to geophysical hydrodynamics mathematical models. For models of biotic systems the picture is different, although differential equations still serve as a descriptive tool. The governing equations of these models are not based on physical laws (concerning the transformation of substances) nor on chemical reaction equations, since transformation mechanisms, considered at the micro level, are not described by physical laws and cannot be described accurately in terms of chemical reactions. These transformations (practically all) are very complicated and most of them are not studied well enough even nowadays (Menshutkin, 1993). Different empirical relations established during the study and data processing provide the background of ecological models and contain in abundance empirical parameters and dependences. In aquatic systems, for example, a lot of ecological relationships derived in the studies ofVinberg (1960), Alimov (1989, 2000) and others are of theoretical and empirical origin as well. In this connection, as mentioned by Menshutkin (1993), any attempts to give Lotka-Volterra equations the same generalization level as continuum mechanics equations are not justified in practice. Lotka-Volterra equations form the base of competition models for joint resources or prey-predator models. Numerous assumptions and hypotheses are required while applying these equations, depriving them of specific biological meaning (Menshutkin, 1993, p. 3). As a rule, aquatic ecosystem mathematical models, if the processes of biochemical transformation are taken into account, are balance relations written down in the form of differential equations. Accordingly, the change rate of hydrobiont

164

Three-dimensional ecosystem model of a large stratified lake

[Ch.5

biomass could be summarized as a balance of biomass growth rate - production, mortality rate, respiration rate, metabolism processes and biomass consumption rates by hydrobionts standing higher in the trophic chain. The mass conservation law is the most fundamental and undeniable base of these equations. Mathematical ecosystem models are formulated sometimes not as differential equations but like discrete analogues - systems of difference equations. However, computer realizations of these models apply the systems of difference equations. It appears that better ways of describing ecological models do not exist at our present level of knowledge. The empirical and theoretical data of modern hydrobiology was built on the foundation of this work (Vinberg, 1960), but not the abstract mathematical relations that appeared in publications of American researchers (Garfinkel, 1962; Patten, 1968; Parker, 1968). This aspect was developed further by introducing biogeochemical cycles of phosphorus and nitrogen into the model (Menshutkin, Umnovand 1970). Progress in lake ecosystem modelling (Jorgensen, 1976, 1983; Di Toro, 1976; Di Toro and Connoly, 1982) for many years was related to anthropogenic eutrophication processes developing in lakes worldwide. A review of studies on freshwater ecosystem modelling can be found in monograph of Straskraba and Gnauck (1989). There exist several examples of coupled 3D hydrodynamical and ecosystem models on the Great American Lakes (Chen et al., 2002; Beletsky and Schwab, 2008b), Baikal (Tsvetova, 2003) and the Largest (Great) European Lakes (Menshutkin and Vorobyeva,1987; Rukhovets et al., 2006a). A good example of a well developed ecosystem model for simulations is the 3D hydrodynamic model ELCOM (Estuary, Lake and Coastal Ocean Model) presented in Blumberg and Mellor (1987). Beletsky and Schwab (2008a) applied a 3D circulation model of Lake Michigan to calculate lake circulation and thermal structure in 1998-2007 on a 2-km grid. The model is based on the Princeton Ocean Model of Blumberg and Mellor (1987). For modelling the ecosystem of large lakes (Kinneret, Biwa, Balaton) it possible to apply a simplified analysis of data as a basis for the decision about model structure. the guideline for selecting model complexity in datapoor cases recommended by Jorgensen (1994) is not to have a more complex model than the dataset can bear. Hakanson and Boulion (2002) developed algorithms for the numerical modelling of rather large lakes. Nowadays interest in lake ecosystems modelling does not lessen (Jorgensen, 1994, 2009; Jorgensen and Bendoricchio, 2002). Publications devoted to this issue are widely presented in the scientific journals Ecological Modelling, Hydrobiologia, Water Resources, Limnology and Oceanography, and The Great Lakes Research. Anthropogenic loading on the large lakes of the world has remained high during recent years; lake ecosystems went through a period of drastic changes and reached the phase of a certain stabilization of internal processes under the new conditions. Attempts to restore the oligotrophic state totally has failed for both European and American lakes, in spite of considerable reductions in biogenic loading. We would like to stress once more that modelling the ecosystem of large lakes requires the application of 3D models owing to the high degree of variability in the hydrophysical conditions of a waterbody related to its large dimensions. These models should reproduce organic matter and biogen transformation processes,

Aquatic ecosystem mathematical model

Sec. 5.1]

165

transport, sedimentation and turbulent diffusion of substances. The fulfilment of the mass conservation law is essential, in cases where sinks and sources are omitted, or of the variation laws in the case of mass exchange at waterbody boundaries. The fulfilment of these laws is guaranteed, on the one hand, by the correlation of ecosystem models with hydrodynamic models for which the water mass conservation law is valid, and, on the other hand, by the conservativity of operators describing organic matter and biogen transformations. This correlation is especially important for discrete models. In large lakes the reaction time of ecosystems to external forcing lasts for many years (for example, in the case of Lake Ladoga and Lake Onego it takes over 10 years); that is why, in order to reproduce ecosystem functioning, calculations should be performed for long periods of physical time. Long-term simulations are not possible if discrete equations difference schemes are not conservative. That is why the techniques of constructing discrete approximations construction for ecosystem mathematical models correlated with discrete circulation models are described in this chapter.

5.2 AQUATIC ECOSYSTEM MATHEMATICAL MODEL In the models (Astrakhantsev and Rukovets, 1994; Astrakhantsev et al., 2003) presented below the waterbody ecosystem state at each moment of time is described by biogens and organic matter concentration fields At, A 2 , ••• , Am. Here as biogens we understand the available forms of phosphorus and nitrogen dissolved in water. In many models carbon and silica are also included as biogens. Organic matter consists of biotic (different forms of hydrobionts) and dead organic matter (detritus, organic matter dissolved in water). Here, as in other models, dissolved oxygen is included as a variable characterizing the ecosystem state. The following processes are taken account of in the mathematical model: transport of substances with currents, turbulent diffusion and sedimentation of substances, and transformation of organic matter and biogens. All these processes are governed by initial-boundary value problems for partial differential equations. Model equations

In the three-dimensional domain !1, occupied by a waterbody, model equations are the following:

a~j + K(v -

vA;,A j) = D(v,A j)

+ B j(A j,A2, ... , Am),

i = 1,2,3, ... .m

(5.1)

Here (5.2)

v=

(u, v, w) is the velocity vector;

rate,

W Ai

> 0;

VA i

= (0, 0, -WA i ) is the substance Ai sedimentation

(5.3)

166

Three-dimensional ecosystem model of a large stratified lake

[Ch.5

Vx , v y, Vz are the coefficients of turbulent diffusion. Expressions K(v - VA i , Ai), D(v,A i) are the transport and diffusion operators. The terms B i(Al,A2, ... ,Am) describe hydro-biochemical transformation of substances Al,A2, ... ,Am. The construction of these terms will be given while describing specific models. Only those requirements that guarantee fulfilment of the conservation laws will be formu1ated here. The natural restrictions are formulated as equalities

m

A~ta1 ==

E miAi = const

(5.4)

i=l

for some n. These equalities should be satisfied for any elementary cell when there is no exchange of substances through cell boundaries (i.e, when transport pro cesses, sedimentation and turbulent diffusion are neglected). As will be shown below, this type of equality holds for the biogens: phosphorus, nitrogen, carbon and silica. The satisfaction of (5.4) poses the following requirements on expressions Bi(Al' A2, .. . ,Am) in (5.1) m

(5.5)

EmiBi(Al,A2' ... ,Am) = 0 i=l

for the same n, as in (5.4). It is assumed further that equalities (5.5) are valid. Boundary conditions

At the waterbody surface So at z = 0 fluxes of substances through the surface are prescribed (5.6)

where QAi is the given substance flux through the surface. Precipitation, for example, can bring phosphorus compounds to the waterbody. At water body bottom and at vertical solid boundaries the following conditions are applied 8A i = 0 8N '

8A i aN

==

Vx

8A i

ax cos(n,x)

+ vy

8A i

ay cos(n,y)

+ Vz

8A i

az cos(n,y).

(5.7)

At inflowing rivers sites Sin: 8A i _ ( () ) 8N - vn Ai - Ai r = 0,

(5.8)

where (Ai)r is the prescribed substance Ai concentration in river water. At effluent river sites Sout the boundary conditions are the following 8A i = 0 8N .

(5.9)

Note. In some models for specific substances the hypothesis that horizontal turbulence diffusion is present can be far from reality; then it is reasonable to assume

Aquatic ecosystem mathematical model

Sec. 5.1]

167

that Vx = v y = O. In this case for the given substance, instead of boundary condition (5.8), the following boundary condition is used (5.10) and as a consequence there is no need to apply boundary conditions at the site of the effluent rivers. For some substances at inflowing river sites, instead of boundary condition (5.10), the following condition is used 8A I = 0, an Sin

8A i 8A i 8A i an == ax cos(u,x) + ay cos(u,y).

(5.11)

This condition is used when reliable information about (Ai)r is not available. Such a boundary condition is not always correct. A variant of the application of condition (5.11) is programmed in discrete models. Substance quality variation laws in the waterbody

v

Let us assume that velocity vector is the solution of the waterbody circulation problem formulated in Chapter 2. Thus, satisfies the continuity equation and nonflux boundary conditions at all solid boundaries. We assume under these conditions that equalities (5.4), (5.5) are satisfied, and then the following laws of variation (conservation) are valid

:t JA~ota1 n

dO =

J Q dS - J So

Sout

v

v"A~ta1 dS

The relations (5.12) are useful to control the computations using discrete models. They are also required when calculations are performed for a long period of time. Note. In the case when for one group of substances the boundary conditions (5.10) (for 1 ~ i ~ ml) is used, and for others the condition (5.11) (ml + 1 ~ i ~ m), in the variation law (5.12) mi

m

i=l

i=ml+l

A~tallSin == LmiAi + L

mi(Ai)r·

About the reproduction of waterbody ecosystem functioning The main task of waterbody ecosystem modelling is its annual regime reproduction under already reproduced climatic circulation conditions. The problem is to build a periodic solution of the system (5.1)-(5.11) under assumptions that all external forcing (prescribed values) are periodic functions with a period equal to one year. To obtain a periodic solution, as in the case of a thermohydrodynamic waterbody

168

Three-dimensional ecosystem model of a large stratified lake

[Ch.5

model, the initial conditions for all unknown variables Ai, i = 1, 2, ... , m, should be given (5.13) The periodic annual regime of ecosystem functioning is obtained as a result of the integration of the system of equations (5.1) with boundary conditions (5.6)(5.11) and initial conditions (5.13) for the period compared to the integration period of the thermohydrodynamic model. Besides the construction of periodic solutions, the problems of forcing on a waterbody which is variable from year to year are considered, as, for example, phosphorus loading. In these types of problems the values of periodic solutions with specifically selected external forcing conditions are used as initial values.

5.3 DISCRETE MODELS Three-dimensional biogens and organic substances fields are calculated within frames of three-dimensional ecological models, and there can be dozens of these fields in advanced models. Realization of these models on computers with sufficiently fine spatial resolution is very time-consuming. That is why it is natural to use for this purpose a coarsening of grids and to try not to distort pre-calculated hydrodynamic information about waterbody circulation (climatic circulation), which is needed to feed ecological models. The problem is that, in order to reproduce the large-scale circulation in a water body with reasonable accuracy, relatively high spatial resolution is required. It is worth recalling that for Lakes Ladoga and Onego the climatic circulations (Astrakhantsev et al., 2003; Rukhovets et al., 2006b) were built on grids with horizontal steps hx = hy = 2.5 km at 30 and 28 vertical layers respectively. To simulate the waterbody ecosystem dynamics it is reasonable to adopt such a solution domain partition into cells that within each one the physical, abiotic conditions can be considered homogeneous or, at least that variations of physical and abiotic parameters within cells are at such a level of magnitude that they do not affect the accuracy of ecosystem modelling. This plausible reasoning was taken into account while dividing the solution domain into cells for ecological model purposes. The authors assumed that for ecological models it is reasonable to use coarser grids. In order to base the selection on computational experiments, simple transfer algorithms from fine grids to coarser ones are suggested in this chapter, retaining such grid properties that provide the possibility of long-term simulations. First of all, the developed algorithms are required to aggregate the thermohydrodynamic information. In this chapter, first in sections 5.3.1-5.3.5, the discrete ecosystem model is built using the same division of solution domain that was used in the thermohydrodynamic model of a waterbody (Astrakhantsev et al., 2003). Then, in section 5.3.6, the automated algorithms for aggregation (coarsening) of grids and for aggregation of hydrodynamic information are suggested. It is important to underline that the coarse discrete model represents the identical system of difference equations as

Discrete models

Sec. 5.3]

169

the original model. The computer realization uses the same algorithms and program codes as in the original model.

5.3.1

Discretization of the solution domain

It is necessary to describe the computational grid and computational domain for the thermohydrodynamic model since this information is used in the ecological model. Grids and grid domain

The main irregular rectangular grid of (Xi, Yj, Zk) is built using planes X = Xi, Y = Yj, = Zk, parallel to coordinates planes. We will assume that plane Zo = 0 coincides with undisturbed lake surface. Let introduce the notation of grid steps:

Z

hi(x) = Xi+1 - Xi,

hj(y) = Yj+1 - Yj,

hk(Z) = zk+1 - Zk·

The minimal union of grid cells IIijk == {x < X < Xi+1,Yj < Y < Yi+1, Zk < Z < Zk+1}, belonging to the domain 0, will be called the grid domain and the same notation will be kept for it. Further below it will be presumed that the original domain is the union of grid cells and an, So, S1, S2 are, in fact, unions of the corresponding flat facets of the grid cells. Let us introduce the notation 8ijk = mes(IIijk n n). For the constructed grid domain the value Hij

==

n a depth in the

node (Xi,Yj, 0) E So will be called

o

L

hk(Z),

ho(z) = 0,

k=-k i j

where kij is the number of the lowest node along the vertical grid line, transmitted through the node (Xi,Yj,ZO). Besides the main grid, staggered grids will be utilized as well. That is, additionally to the nodes with integer indices (Xi,Yj, Zk) the nodes (Xi+1/2,Yj+1/2, Zk+1/2), located in the centres of IIijk, and also the nodes (Xi,Yj, Zk+1/2), lying in the middle of the vertical edges of cells IIijk. Here

Several notations will be introduced for the further discussion. As ibijk we will denote the grid function, prescribed in nodes (Xi, Yj, Zk) E O. If this function is timedependent, then ibijkwill denote its value at the moment of time t, and ibijk its value at the moment of time t + hf, where h, is the time-step. For the function 'P(x, Y, z) the notation 'Pi+1/2,j+1/2,k+1/2 means its value in the node (Xi+1/2' Yj+1/2, Zk+1/2). _ The waterbody surface So is the union of upper cell facets II i,j,-1, belonging to n. Let rr., == aII i,j-1 n So, 8ij == mes(IIij).

170

Three-dimensional ecosystem model of a large stratified lake

[Ch.5

Thus, the domain n is the union of the main grid cells. We will assume that in the nodes (Xi, Yi, Zk) the values of the grid function are given Tiik(T(Xi, Yi, Zk) is the water temperature) at certain moments of time with a time-step h, magnitude of one day. These values are obtained as a periodic solution, describing annual circulation regime of a waterbody. The values of the velocity vector projections Ui+l/2,i+ 1/ 2,k+l/2, Vi+l/2,i+ 1/ 2,k+l/2 are prescribed in the cell nodes IIiik = {Xi ~ X ~ Xi+l,Yi ~ Y ~ Yi+l,Zk ~ Z ~ Zk+l} at the same moments of time. Projections of the velocity vector WiJ,k+l/2 are given in the middle of the vertical edges of cells IIiik. The domain n will be divided additionally into cells, where in ecological models the transformation processes of organic substances and biogens will be reconstructed and the exchange of substances between cells by currents will be defined on the basis of the constructed flow fields (Astrakhantsev et al., 2003; Menshutkin et al., 1998). For these purposes for every node of the main grid (xi,Yi, Zk) E n we will consider a corresponding cell of an additional subdivision of the domain

n:

1/2

II iik = {Xi-l/2

-

< X < Xi+l/2'Yi- 1/2 < Y < Yi+1/2,zk-l/2 < Z < Zk+l/2} n n,

where, as a reminder, Xi+l/2 = (Xi + xj+l)/2, Yi+1/2 = (Yi + Yi+l)/2 and so on. Thus, one more subdivision of the domain n appears: For example, in the vertical transect of the domain n by the plane Y = Yi as shown in Fig. 5.1 the cells of the additional division are shaded, corresponding to four nodes, one internal and three boundary. It should be pointed out that functions Ui+l/2,i+ 1/ 2,k+l/2, Vi+l/2,i+ 1/ 2,k+l/2 are given at the tops of internal cells and 2, the grid function WiJ,k+l/2 is prescribed in the centre of internal cell facets II:jk parallel to the plane XOY.

II:j;,

z x

Fig. 5.1. Cells of the main and additional division of the domain

!1.

Discrete models

Sec. 5.3]

5.3.2

171

Reproduction of transport, turbulent diffusion and the sedimentation of substances in the model

Utilization of hydrodynamic information The new additional division of the domain n allows us to present the continuity equation, which should be met by flow fields, constructed with the discrete model (Astrakhantsev et al., 2003; Menshutkin et al., 1998) as a balance of discharges through facets of cells II:j; in the new subdivision: (qi+l/2,i,k - qi-l/2,i,k) + (qi,i+1/2,k - qi,i-1/2,k) + (qi,i,k+l/2 - qi,i,k-l/2) = 0,

(5.14)

where q are discharges through facets of cells II:j;. It should be noted that introduced values q are discrete analogues of corresponding integrals. For exam~le, qi+l/2,i,k has the meaning of JudS, taken over the right facet of the cell IIij;, orthogonal to the axis OX. In such a way, every cell in new division is related with six numbers, representing hydrodynamic information required for the reproduction of the transport of substances between cells. In practice, the temperature field, which plays an important role in ecosystem models, also belongs to the hydrodynamic information. The temperature field is given in the nodes (Xi,Yi' Zk) E n of the main grid. It is further assumed in ecosystem models that in the cell of the additional subdivision II:j; water temperature is equal to Tiik. Approximation of transport, turbulent diffusion and sedimentation processes To build a discrete model, approximating the initial-boundary value problem (5.1)(5.13), we will use a so-called balance method (Samarsky and Andreev, 1976)Changes in the quantity of substances in the cells of the additional subdivision II:i ; due to transport, turbulent diffusion and sedimentation for the time interval hf, where h, is the integration time-step, are defined as a balance between income and outcome of substances through the cell's facets. Let us define as C any of substances Ai, (i = 1,2, ... ,m). The difference operator reconstructing all the abovementioned variations in the cell will be denoted as LWc, then in II:j; (LWcC)iik

== - ht{qf-tl/2,i,kCi,i,k + qi+l/2,i,k Ci+ 1,i,k - qi-l/2,i,k Ci- 1,i,k - qi-l/2,i,k Ci,i,k} - ht{qti+l/2,kCi,i,k + q~i+l/2,kCi,i+l,k - qti-l/2,kCi,i-l,k - q~i-l/2,kCi,i,k} - h t{qti,k+l/2 Ci,i,k + q~i,k+l/2Ci,i,k+l - qti,k-l/2 Ci,i,k-l - q~i,k-l/2Ci,i,k}

+ ht{qZi,kCi,i,k+l + qZi,k-l/2 Ci,i,k -

+ h t [(Vz \ -

j,k+l/27f i,j,k+l/2

Ci,i,k+l hk(z)

(qZi,k+l/2 - qZi,k-l/2)Ci,i,k}

<»

- Ci,i,k-l] (V- z )i,i,k-l/2 7fi,i,k1/2 Ci,i,khk-1(Z)

) + ht8L(Q k c i,i7fii

(5.15)

172

Three-dimensional ecosystem model of a large stratified lake

[Ch.5

Here qf-tl/2,i,k

== (qi+l/2,i,k +i+l/2,i,k 1)/2.

qi+l/2,i,k

== (qi+l/2,i,k -i+l/2,i,k 1)/2.

qtl/2,i,k' qti±1/2,k' qti,k±1/2 are defined by analogy. Further, to take into account

sedimentation, the following values are introduced w

qi,J,k+l/2 =

1

:4 h 1

~

We

(z) L.J 8i+cx,i+f3,k, k cx,f3=-l

1

7fi,i,k-l/2

== :4 ~()

L 8i+cx,i+f3,k-l, cx,f3=-l

k-l Z

== 4:

~

0

11

1

7fi,j

We

0

== :4 h

k

1

:4 ~() L.J 8i+cx,i+f3,k-l, k-l Z cx,f3=-l

L 8i+cx,i+f3,k, cx,f3=-l

7fi,i,k+l/2

(z)

w

qi,J,k-1/2 =

0

L 8 + ,J+f3 , cx,f3=-l i

0i

8i ,i = mes(IIij

n So),

8k =

{ 1,

0,

k=O, k i= O.

Coefficients Vz are defined here as averages of v z :

+ 8iik(Vz)i+l/2,i+l/2,k+l/2

+ 8i,i-l,k(Vz)i+l/2,i-l/2,k+l/2

+ 8i-l,i-l,k(Vz)i-l/2,i-l/2,k+l/2}'

And the expression for (Vz )i,i,k- l/2 is obtained from the one given by the replacement of k with k - 1 The expressions in curly brackets (5.15) describe in discrete form advection and sedimentation or, more precisely, they approximate terms K(v - Ve , C) in the system of equations (5.1). The applied approximation, taking into consideration the direction of fluid movements between cells, is, in fact, a scheme with directed differences. It can be demonstrated that when this approximation is used for the heat conduction equation, the scheme viscosity appears. The presence of scheme viscosity justifies neglecting terms describing horizontal diffusion of substances, i.e, Vx = v y = o. The application of boundary conditions (5.10), (5.11) at the sites of inflowing rivers requires additional explanation concerning the calculation of binomial terms C x q in curly brackets in (5.15), describing horizontal advection in the cell nodes adjacent to the inflowing river sites. It is, if q = 0, then the binomial term is supposed to be

Discrete models

Sec. 5.3]

173

equal to zero. If q i= 0, then in the case when C corresponds to the node not belonging to 0, there is a need to define the value of C. For boundary condition (5.10) this value is equal to Cr , prescribed substance concentration in river C. This situation first represents the river inflow through the facet with corresponding q, and, second, complies with the first type of boundary condition C = C, at the inflowing river site. In the case of boundary condition (5.11), the value C is supposed to be equal to the value in the node, where at that moment the expression (LWcC)ijk is calculated, i.e, C == Cijk. The other terms in (5.15) approximate vertical advection, vertical turbulent diffusion when boundary conditions (5.6), (5.7) are applied in the near-boundary cells.

5.3.3 Reproduction of the transformation of substances Changes of concentration for each substance Ai(i = 1,2, ... ,m) in a cell of the new 2 division rrJjk during the time period h, is defined with the following formula in the discrete model (5.16)

5.3.4 Total variation of the concentration of substances in additional division cells Equalities (5.2) and (5.3) enable us to write down the general variation of each of 2 the substances AI, A2, A3, ... ,Am contained in the cell rrJjk as an explicit scheme CijkOijk = CijkOijk

+ (LWcC)ijk + (.dC)ijkOijk,

(5.17)

where Cjik and Cjik are concentrations of any of substance Ai, A ,A3, ... ,Am at the moments t + h, and t correspondingly; Oijk - is the volume of l Equations (5.17) are approximations of the system (5.1) and boundary conditions (5.6)-(5.11). It is easy to understand if we divide all the terms in the equation by the value h, x Oijk. It should be noted also that, in this way, the income of biogens through the surface with inflowing river waters, and also the outgoing with effluent rivers, are incorporated in the model. Without going into detail, we will note that further in the models point-source (lumped) loading of biogens is also included.

rrJj;.

5.3.5 Discrete analogue of the total substances content variation law in lake waters The discrete analogue of the variation law (5.12) for substances that obey the relations (5.4), can be obtained by the summation of the equations (5.17) for all nodes (Xi,Yj, Zk) E O. For brevity we will introduce the notation A == A~tal' where A~tal is defined in (5.4) when writing down the discrete analogue of the variation law. Then after the summation of equations (5.17) for nodes belonging

174

Three-dimensional ecosystem model of a large stratified lake

[Ch.5

to 0, we will get

L (Xi,YjJZk)EO

AijkOijk =

L

AijkOijk

(Xi,Yhzk)EO

L

- h,

[qA]i,j,k

(Xi,YjJZk)ESout

(5.18) where kij is the number of the lowest node under the surface node (Xi,Yj, 0) E So. The calculations of the terms, corresponding to the nodes at the river sites Sin and Sout in (5.18), should be done in conformance with following explanations. For node (Xi,Yj,Zk) E Sin: - if the domain So is located to the right of the node (Xi,Yj, 0) in the figure plane, coincident with the plane Z = 0, then

- if the domain So is located to the left of the node (Xi,Yj, 0), then [q(

)ijk == qt+l/2,j,k(· .. )ijk;

- if the domain So is located above then node (Xi,Yj, 0), then [q(

)ijk == qtj-l/2,k(· .. )ijk;

- if the domain So is located below the node (Xi,Yj, 0), then [q(

)ijk == q~j+l/2,k(· .. )ijk·

Discrete models

Sec. 5.3]

175

-if the domain So is located to the right of the node (xi'Yi' 0), then [qA]iik

== qi-l/2,i,k A iik;

- if the domain So is located to the left of the node (xi'Yi' 0), then [qA]iik

== qf-rl/2,i,k A iik;

and so on. It should be noted that every sum in (5.18) is, in a fact, the approximation of integrals from (5.12). At the end of this section we will point out that equalities (5.18) are valid due to the fact that (5.5) and (5.14) are true. The last equality is the continuity equation, providing the fulfilment of the water mass conservation law in the discrete thermohydrodynamic model. By this, the validity of the conservation law in discrete ecosystem models is the consequence of the requirements formulated as equalities (5.5), and conformity of the discrete ecosystem models with discrete thermohydrodynamic models, for which the discrete water mass conservation law holds. 5.3.6

Changes in the discrete model with coarsening of the domain decomposition

Let us describe the construction process of the coarse divisions using the original division as the basis. The coarsening of the division corresponds to an increase in the spatial steps of the main rectangular grid. The unions of the cells belonging to the original grid are the cells of the new coarse grid, which cannot form parallelepipeds near the boundary of the domain O. But this does not complicate the realization algorithms. Let the limits of the original grid node indices be the following: 1 < i < Nx,

1 <j

< Ny,

- K

II:j;,

< k < o.

The coarsening of the grid cells is the union of cells relating to nodes, belonging to the group of the neighbour lines of the original grid, which have to be united. Formally this process can be described as the combination of indices groups into one group and a full renumbering: i = 1,2, [3,4,5],6, 7, [8, 9]" 10, 11, ... .te;

I = 1,2,3,4,5,6, 7,8, ... .F; The indices J and k are defined similarly. How is the cell of the coarsened division defined? This cell is the

II:j; combination of cells II:j;:

II~/; -= i.j.k

UII:~, _}

iE£

iEi

kEf

O[,],f =

L iE£

iEi

kEf

Oiik·

176

Three-dimensional ecosystem model of a large stratified lake

[Ch.5

The construction of the advective terms in model equations, described above, are such that aggregation of the information keeps place automatically. This is related to the fact that a 'flux language' was selected to describe the transport of substances between cells, and hydrodynamic information is presented as a balance of fluxes (discharges) of water through cell facets of the additional division of the domain 0 on cells Let us define for the coarse grid cells II~/;k- discharges through 'facets' of these i.r. cells, i.e. relate each cell II~j,k to a set of numbers q~1/2,],k' qtJ±1/2,k'qt],k±1/2' being the discharges through facets of coarsened cells, parallel to coordinate planes. Their cablc~ation on the blasis of corresponding discharges q~I/2,],k' qtJ±I/2,f' qt],k±I/2 is o VlOUS. For examp e,

q~1/2,],k =

L

(5.19)

Qf±1/2,j,k

where the summation is made over all calculated nodes, for which i E ~ j E], k E k, and such that either i + 1 ¢ ~ or (Xi+l,Yi' Zk) is the node not belonging to O. It is not difficult to understand how other discharges through facets of the coarsened cell are calculated. The discrete model construction for the coarsened division without restrictions on river location is possible, but then binomial calculations in the formula corresponding with (5.15) for the coarsened division can be complicated. That is why we introduce three simple constraints, that all algorithm of substance variation in II:j; as a result of advection, diffusion and sedimentation is described with the same formula (5.15), where i, j, k are replaced with ~], k. These constraints are the following: - each facet of the cell II~<~k can contain the site of no more than one river, - the facet where the rivetlis located, besides the site, is composed from the facets of the original fine division only, forming the solid boundary, - cell II~l;k- is a connected set. i.r. After the replacement of i, j, k with ~], k in the formula (5.15) it should be decided how to define values q~~k±I/2' hf(z), (lIz )l,],k±I/2' 7fl,],k±I/2' 7fl,J. Let us define We

_~

We

ql,],k±I/2 - L..J qi,i,k±I/2'

where the summation is done all over calculation nodes, for which i E ~ j E], k E k, and such that either (k + 1) ¢ k or node (Xi,Yi' zx+1) does not belong to O. In a similar manner, the value q~e~k1/2 is defined using values q~e. k-l/2. l,l, l,l, In order to preserve the form of the formula (5.15) for the coarsened division, set: (Vz )l,],k+l/27f l,],k+l/2 ==

L (V )i,i,k++l/2 i,i,k++l/2, z

7f

iE£

iEi

where k" = max kEk k. The value hf(z) is introduced using the formula: hk(z)

== ! [0l,],k/ 7fl,],f+l/2 + °l,J,k+l/7fl,],f+3/2]

Discrete models

Sec. 5.3]

177

where 7fll~ k+l/2 is the area of the upper facet of the cell II~~2k-: , , ll, 7fi,],k+1/2 =

~

7fi,j,lC++1/2.

iE£ jEj

Finally, 7fl,]

=

L

»o

iE£ jEj

By these means, as a result of the coarsening the discrete model is built, which is defined by the same formulae as in the case of original division. For this discrete model the equality (5.18), where i,j, k are replaced with~], k, is true. It should be pointed out that water temperature in the coarsened cells II~~~ is defined with the formula n,

T~l,l,~k- =

"L...J

Til'kOil'k/O~i.r.~k-·

iEl,jE],kEk

The coarsening algorithm being suggested in this chapter, probably, looks rather cumbersome. But the authors have striven to make its realization relatively simple: the algorithm requires minimal modifications during transition from one grid to another. One more important point should be emphasized. The suggested algorithm possesses a very useful feature: due to the definitions (5.19) the information on water exchange between neighbour cells of the coarse grid is preserved, i.e, it contains information how much water comes from the first cell to the second one and vice versa. In many ecosystem model realizations the water exchange balance between coarse cells is taken into consideration only with the aggregation of hydrodynamic information.

6 Ecosystem models of Lakes Ladoga and Onego

The history of the ecosystems modelling of Lakes Ladoga and Onego is briefly described in this chapter. In addition, a review is presented of models of the Lakes ecosystems, representing, in fact, an integrated complex, that have been developed by the authors during recent years. Attention in this chapter is paid mainly to two models: the Lake Onego ecosystem model, based on the turnover of nitrogen and phosphorus and, the latest one developed by the authors, the model of phytoplankton succession in Lake Ladoga. 6.1 THE IDSTORY OF THE ECOSYSTEM MODELLING OF LAKES LADOGA AND ONEGO In Chapter 1 a brief history of the research on Lake Ladoga and Lake Onego on the basis of mathematical models was introduced. The research history of using mathematical models on these lake ecosystems started nearly twenty years ago. The first three-dimensional model of the Lake Ladoga ecosystem was developed by Menshutkin and Vorobyeva (1987). The main difficulty in developing lake ecosystem mathematical models for particular waterbody consists in adequate selection of hydrobiological dependencies and empirical coefficients. The Lake Ladoga ecosystem model (Menshutkin and Vorobyeva, 1987), unlike many other eutrophication models (e.g. Leonov et al., 1991), was based on observed data, obtained during expeditions (under the direction ofN.A. Petrova) on Lake Ladoga organized by the Institute of Limnology RAS during the 1976-1983 period. These unique data were collected by the authors; that was the way to get a more realistic picture of the processes at first hand. The effectiveness of such an approach was tested in practice for quite a long time while modelling the ecosystem of the small Dalneye Lake on Kamchatka (Krogius et al., 1969). In this monograph only three-dimensional ecosystem models are observed, though it is necessary to point out that several different models were developed for Lake Ladoga. They could be classified as one- and two-box models for simulation

180

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

either of separate ecosystem chain processes in the lake or of the ecosystem dynamics in particular parts of the lake. In this connection it is worth mentioning the zooplankton models for southern and central Lake Ladoga regions (Kazantseva and Smirnova, 1996). The zooplankton community in these models is represented by more than two dozen selected groups of the main zooplankton population. Each division of the population is made according to physiological age and trophic features. Changs in the numbers of each zooplankton group are reproduced in the models, depending on the increase or decrease of individuals in the group due to their growth, propagation, mortality and seasonal vertical migration. As the biotic part of the Menshutkin and Vorobyeva model (1987) has become the foundation for a large complex of Lake Ladoga ecosystem models and the basis for the Lake Onego ecosystem model, a brief description of this model will be reproduced. Lake Ladoga ecosystem model developed by Menshutkin and Vorobyeva (1987) Vertical division of the lake waterbody into two layers was used in this model and a relatively small number of cells - 60 units only. Mean depth in the shallow part of the lake was considered to be constant. A currents system averaged over depth was used in the model and it was assumed to be unalterable all through the year. The water temperature field was defined on the basis of long-term observation data. The model biotic part was represented by summarized phyto- and zooplankton biomasses, distributed among separate cells, representing the waterbody division. The hydrochemical part of the model was based on knowledge about the nitrogen and phosphorus balance in both organic and mineral forms. Ecosystem state was described by six variables: composite phyto- and zooplankton raw biomasses A and Z; concentrations of dissolved-in-water forms of phosphorus, P, available for algae consumption; concentration of dissolved-in-water forms of nitrogen, N; concentration of phosphorus in detritus and bacterioplankton DP; concentration of nitrogen in detritus and bacterioplankton DN. The parameters and coefficients of biochemical transformation of organic matter and biogens were defined by Menshutkin on the basis of observed data during the Ladoga expedition of the Institute of Limnology of the Russian Academy of Science, collected in 1976-1979. The developed model was verified on observation data of the 1981-1983 period. In spite of considerable schematization of the lake hydrodynamic and its geometry and the absence of a winter period block in the model, it quite realistically described the dynamics of the phytoplankton biomass during the vegetation periods of 1981-1983, total phosphorus concentration distribution within the waterbody and the outflow of total phosphorus with the Neva River. Prognostic estimates of annual phytoplankton dynamics at various levels of phosphorus loading on the waterbody were simulated using this model. It was shown that when the loading declines to 4000 t Pyear"! (in 1981-1983 period the loading was on average 7500tPyear- 1) the lake returns to a low mesotrophic state. An important feature of the Menshutkin and Vorobyeva model (1987) is the assumption of mass conservation laws for biogens. This peculiarity, as has already been mentioned, made long-term model computations possible.

Sec. 6.1]

The history of the ecosystem modelling of Lakes Ladoga and Onego

181

The model developed by Leonov, Ostashenko and Lapteva (1991)

This model became the second Lake Ladoga ecosystem model. The biotic part of the model includes phytoplankton and zooplankton, heterotrophic bacteria and protozoa. The hydrochemical part of the model is represented by carbon, nitrogen and phosphorus. Oxygen is also included in a list of model variables. For computational purposes the whole lake (Leonov et al., 1991) is divided into eight parts, as was done in the eutrophication processes study (Petrova, 1982). Each part was divided into epi- and hypolimnion. Transport of matter in the lake is carried out only by means of advection. The currents system, constructed with diagnostic models (Filatov, 1991), was used for this purpose. The model, as the authors affirm, without significant correction of parameter values, was used for waterbody ecosystems research purposes with different chemical/biological properties. This is an undeniable advantage of the model. In this model conservation laws are not satisfied for biogens in equations describing the transformation of chemical and biological compounds.

The third model

The third model for theLake Ladoga ecosystem was developed, in fact, as a coupled model, combining the ecosystem model (Menshutkin and Vorobyova, 1987) and the Lake Ladoga thermohydrodynamic model (Astrakhantsev et al., 1987) into one (Astrakhantsev et al., 1992, 1996). At the initial stage of model construction the authors concept was to use more adequate thermohydrodynamic information which made it possible to improve the quality of the lake ecological model, where a considerable diversity in the hydrophysical conditions of ecosystem functioning is found in different parts of the waterbody. This model is fully presented in the collective monograph, The Neva Bay - Modelling Experience (Menshutkin, 1997).

Modelling of the Lake Onego ecosystem

The first computational experiments to reproduce the Lake Onego ecosystem functioning were conducted within the project framework on water resources redistribution in the European part of the Russian Federation in joint studies of the Department of Water Problems of the Karelian Branch at that time and the Computation Centre of the Academy of Science of the USSR (CC AS USSR). The box model for the dynamics of seven generalized components of the lake ecosystem (beginning with the mineral biogen forms and fish) was developed by the members of CC AS USSR (Lukyanov and Svirezhev, 1984). At the end of 1980 researchers from the Leningrad Institute of Informatics USSR AS to estimate the status of Lake Ladoga applied a balance-empirical coupled model of total nitrogen and total phosphorus mean annual dynamics. The initial identification of parameters and demonstration imitation experiments were performed using field data collected by members of the Department of Water Problems of the Karelian Branch AS USSR.

182

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

But further continuation of the partnership was not achieved and the applied model of the Lake Onego ecosystem was not built. Kolodochka and Chekrizheva (2003) continued the development of the lake ecosystem model. The main scientific objective considered in their work, was the numerical reproduction and theoretical analysis of seasonal productive/destructive characteristics of pelagia 1plankton communities in Lake Onego, and their variability in deep zones. As a result of numerical experiments a diagnosis of the hydrophysical and hydrobiochemical determinacy of the seasonal variability of production/destruction processes in pelagic Lake Onego and computations of nitrogen and phosphorus hydrobiochemical balances for different scenarios of biotic turnover dynamics were performed. 6.2 COMPLEX OF LAKE LADOGA ECOSYSTEM MODELS The third Lake Ladoga ecosystem model (Astrakhantsev et al., 1992, 1996; Menshutkin, 1997) became the basis for the whole complex of Lake Ladoga ecosystem models (Menshutkin et al., 1998; Rukhovets et al., 2003; Astrakhantsev et al., 2003), where changes, starting in the second half of the 1980s, in the Lake Ladoga ecosystem were taken into account. According to the research results (Lake Ladoga ... , 1992), the significance of dissolved organic matter and bacterioplankton in internal waterbody turnover has grown, during the period when the thermocline is most developed, zones with decreased oxygen content appear, and a change in the species composition of dominant phytoplankton groups alteration is also registered. The description of phytoplankton as one homogeneous group as in the previous models did not enable us to increase the accuracy of primary production determination under changing biogen loadings and weather conditions. The process of lake anthropogenic eutrophication demanded for the lake study the development of mathematical ecosystem models in order to clarify the visualization of the process, to estimate the different hydrobionts group input into the inner waterbody regulation of priority substance and energy, to estimate priority substance fluxes at water-bottom and water-atmosphere boundaries, to reproduce the seasonal phytoplankton species succession and so on. These models are constructed as models of phosphorus turnover in a chain of biochemical transformations, since, according to specialist opinion, during recent decades phosphorus has been the main and the only limiting factor in Lake Ladoga ecosystem functioning (Lake Ladoga ... , 1992). So taking into consideration that it is only one limiting biogen, the number of the model parameters necessary for description of the ecosystem state might be decreased. The ecosystem models complex is a tool for solving the abovementioned problems. Lake Ladoga circulation, presented in Chapter 3, was used in all models of this complex. All these models are in fact based on variations of the first one, and variations are the result of the necessity to take into account peculiar ecosystem elements which were not included in consideration in the first model. This approach was also justified because the aim was not to magnify the number of variables used for ecosystem state description. The complex of models, like those

Sec. 6.2]

Complex of Lake Ladoga ecosystem models

183

already mentioned (Menshutkin and Vorobyeva, 1987; Leonov et al., 1991; Astrakhantsev et al., 1992, 1996) are, first of all, the models of the pelagic part of the lake. The role of the near-coastal macrophytes is not taken into consideration. As the pelagic lake significantly prevails over the littoral, this assumption for littoral communities is justified as its part in the formation of lake water quality is probably small. This assumption is to some extent also true concerning the benthos, because the lake depth is great and the coastline is not dissected (with the exception of the northern part). The northern Lake Ladoga skerries region is so peculiar, the water mass is so isolated, that this region should be regarded as a separate water system. According to the investigations of recent years there exists in Lake Ladoga an essential phosphorus flux from bottom sediments (Ignatyeva, 1997), and within the framework of one of the models the influence of the flux (the internal phosphorus loading) on ecosystem development is studied. The scale of phenomena selected is an essential issue while applying the model. The models are supposed to reproduce only those effects and scales of natural phenomena which are observed in practice on the basis of available methods of limnological research being carried out on Lake Ladoga. That is why biotic and abiotic diurnal alterations of ecosystem elements, as well as daily vertical zooplankton migrations, are not considered in the models. The lack of observations of lake ecosystem elements, and their inhomogeneity, made it impossible to reproduce all phenomena related to synoptic alterations and weather conditions (e.g. the influence of storms on phytoplankton development). That was also the reason to use, in the computation process, the lake climatic circulation corresponding to the mean monthly external impacts on the waterbody, averaged within the perennial period. To improve the spatial description of the process, horizontal and vertical grids that are much more detailed than in the previous models are used in the complex of models. The basic model of the complex (Astrakhantsev et al., 2003)

The content of the first of these models, called the basic, includes such hydrobionts as phytoplankton and zooplankton. Phytoplankton is represented in the model by three separate ecological groups that differ among themselves in their various dependencies of productivity on water temperature, phosphorus assimilation rates, size etc. The division of phytoplankton into three groups is an approach to reproducing seasonal species succession, applying the available information about the specifics of the functioning of particular algae groups. The first group contains species prevailing in the spring period (spring diatoms, Aulacosira, Diatoma, Asterionella etc.); the second group consists of summer species, with prevailing dominance of blue-green algae (Microcystis, Oscillatoria); the third group consists of the species of summer and autumn periods (the blue-green inhabitants, Woronichinia, and also Aulacosira, Tribonema and Aphanizomenon). Zooplankton in this model is represented, as in previous models (Menshutkin and Vorobyeva, 1987; Astrakhantsev et al., 1992), as a single entity, characterized by generalized biomass. According to previous studies (Lake Ladoga . . . , 1992), the

184

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

scales of phytoplankton and zooplankton participation in phosphorus turnover are not incomparable: phosphorus consumption by phytoplankton during the vegetation period reaches 230 thousand tons, whereas phosphorus regeneration by zooplankton equals 2.9 thousand tons a year. That is why applying three variables for phytoplankton description and one for zooplankton is justified. The concentration of organic matter in water in two forms only, suspended detritus and dissolved organic matter (DOM), is described by the model variables without defining their degree of lability, which could be explained by the lack of data about the destruction of organic matter by bacteria in Lake Ladoga. It is not appropriate to divide detritus into an easy to decompose and a difficult to decompose fractions. Dissolved oxygen and dissolved-in-water mineral phosphorus are also among the model variables. The process was reproduced applying the basic model on the basis of the data of phosphorus exchange at the water-bottom boundary obtained in the Institute of Limnology of the RAS (Ignatyeva, 1997,2002). Simulation experiments have shown (Astrakhantsev et al., 2003), that the relatively small influence of the internal phosphorus loading on ecosystem functioning is explained by the large phosphorus supply in the lake water and also by the fact that, during the essential part of the vegetation period, clearly expressed water density stratification takes place. It prevents phosphorus transport from the lake bottom to the photic layer where phytoplankton primary production is created. Ecosystem model with three trophic levels (Astrakhamse» et al., 2003)

In the ecosystem basic model, unlike phytoplankton, zooplankton is represented as generalized biomass. In a given model its hierarchic structure is not represented by two trophic levels as is done in other Lake Ladoga ecosystem models, but by three levels actually existing in the waterbody: the first, phytoplankton; the second, filtrators or prey zooplankton; and the third, predatory zooplankton. Fish represent the fourth trophic level. The fish community model developed by Menshutkin is described further as a separate model in Chapter 8. Thus the difference of this model from the basic one is that zooplankton is divided into two groups prey and predatory. Zooplankton is divided into two groups because otherwise clear description of the trophic interaction between zooplankton and phytoplankton, and between fish and zooplankton, is impossible. Besides, such a modelling approach can clarify the behaviour of zooplankton itself. By the present time several models have been developed to describe zooplankton development; the model for Lake Ladoga is among them (Kazantseva and Smirnova, 1996). But many of them do not reproduce the interactions of zooplankton with other ecosystem elements and the habitat. That is why, along with their undeniable advantages, these models do not allow us to comprehend all the interaction dynamics with phytoplankton and other elements in the zooplankton ecosystem. And besides, in the framework of the ecosystem generalized model, one should not outline only one ecosystem element too precisely lest the balance in the description of different ecosystem elements is

Sec. 6.2]

Complex of Lake Ladoga ecosystem models

185

disturbed. At the same time, when the number of variables in the model is so considerable, the calibration procedure and its application for long-term period simulations might be too complicated. Thus, representing zooplankton, according to trophic characteristics, by two groups seems to be reasonable, taking into account the generalization and the precision in the description of other ecosystem elements. Ecosystem model, including the zoobenthos submodel (Astrakhamse» et al., 2003)

All the Lake Ladoga ecosystem models reviewed above describe in fact the pelagic part of the lake. In these models, except for one (Leonov et al., 1991), hydrobionts are represented only by phyto- and zooplankton or as generalized biomass, or as asset of ecological groups. One of the negative sides of the models mentioned above is that phosphorus exchange at the water-bottom boundary was not taken into account. An exception is the basic model, where this procedure is included. In other words, the sedimentation process of detritus and phosphorus being absorbed on suspended matter was considered. Phosphorus settled on the bottom was excluded from turnover. Phosphorus regeneration by bacterioplankton from detritus continued in these model procedures until the detritus reached the bottom of the waterbody. Including the benthos submodel in the model might change, at least partly, the excretion of phosphorus from the waterbody turnover, make it possible to estimate the role ofhydrobionts in phosphorus exchange at the water-bottom boundary. The change can be the result of part of the detritus being consumed by zooplankton and phosphorus beng returned to the turnover with the products of its life-sustaining activity. Thus, adding the benthic part to the model can define phosphorus turnover more precisely and improve the modelling approach to benthic communities. A two-box lake ecosystem model (Menshutkin, 1993), considering the epilimnion and the hypolimnion, included a benthos submodel. A further development that this concept received in the study of Astrakhantsev et al. (2003) was Menshutkin's benthos submodel being coupled with the abovementioned basic model which contained a benthos submodel as well. As the main issue was to reproduce benthos functioning in the waterbody phosphorus turnover, the benthos in the first iteration is described without division but as generalized biomass distributed over the waterbody bottom. The benthos is not divided into species populations in the Neva Bay model either (Menshutkin, 1997). Mathematical models of the secondary producers, benthic animals among them, were developed some time ago (Straskraba and Gnauck, 1989). Benthos modelling appears to be a complicated issue due to the great variability of benthic communities. Nevertheless, benthos submodels exist in many ecosystem models of lakes and reservoirs (patten et al., 1975), but experience in the benthic modelling of lakes in general is considerably less than that in modelling plankton communities. Due to the fact that Lake Ladoga phytobenthos is poorly developed, mainly in the bays and in the narrow littoral zone of the open part of the lake, only zoobenthos is taken into consideration in the model. Lake Ladoga zoobenthos was studied in detail by the scientists of the Institute of Limnology RAS (Slepukhina and Alekseeva, 1982; Kurashov, 1994, 2002; Menshutkin, 1993).

186

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

The amounts of phosphorus mineralization and its return to Lake Ladoga turnover in the process of detritus and bottom sediments consumption by benthic animals (Slepukhina and Alekseeva, 1982; Kurashov, 1994, 2002). The mean value of phosphorus excretion by zoobenthic animals for the whole lake during the season May-October equals 719 t. The total amount of phosphorus from Lake Ladoga sediments, the so-called 'internal phosphorus loading' is equal to 875 t Pyear"! according to calculations done by Ignatyeva (1997). The participation of plankton animals in phosphorus regeneration is much greater. Zooplankton produces 2940 tons of phosphorus per year; phosphorus regeneration by bacterioplankton from organic matter equals 1725 tons of phosphorus per year (Lake Ladoga . . . , 1992). Nevertheless, the role of zoobenthos is noticeable and the zoobenthos contribution in modelling phosphorus turnover in a waterbody ecosystem defines more exactly the description of substance exchange in the lake ecosystem. Zooplankton biomass distribution is necessary information for a fish community model considering spatial fish nutrition distribution, including benthivoric fish. Modelling the results of zoobenthos participation in phosphorus exchange at the water-bottom boundary has shown (Astrakhantsev et al., 2003) that, during the period from May until November, according to the results of the basic model, 2290tP are deposited on the lake bottom including 1166tP in detritus, and 2254tP in the model with zoobenthos, including 1117tP in detritus. Thus, including the zoobenthos submodel into the basic Lake Ladoga ecosystem model had no effective influence on the phosphorus flux towards the lake bottom. Total phosphorus distribution in the lake volume according to modelling results and to observation data are similar. Simulation results have also shown that the role of zoobenthos in phosphorus flux formation from the bottom sediments into the water ('internal loading') is not significant. An important result of the developed model application is the possibility of its being coupled with the Lake Ladoga fish community model (Chapter 8) for determination of the nutrient base of benthivoric fish. 6.3 ECOSYSTEM MODEL FOR LAKE ONEGO, BASED ON THE TURNOVER OF BIOGENS - NITROGEN AND PHOSPHORUS The model discussed in this section is developed in fact by the adaptation of he Lake Ladoga ecosystem model to Lake Onego conditions, described in detail by Menshutkin and others (Menshutkin, 1997; Rukhovets et al., 2006c). 6.3.1 Ecological formulation of the model The detailed review of the state and the dynamics of the Lake Onego ecosystem is given in Chapter 1. Let us briefly characterize the physical and hydrochemical peculiarities of the lake that should be taken account of in its ecosystem modelling.

Sec. 6.3]

Ecosystem model for Lake Onego, based on the turnover of biogens

187

The general hydrochemical characteristics of Lake Onego catchment surface waters, which are formed in over-moisturized conditions, is low mineralization of hydrocarbonate-ealcareous compound, low nitrogen and phosphorus content and high dissolved organic matter content. Lake Onego is one of the less mineralized lakes in the world, where water total mineralization value equals 37 mg 1-1. The water mass oxygen regime is determined mainly by physical factors. The value of the oxygen maximum content equals 13-14mgl- 1 and it coincides with minimum water temperatures. Oxygen supply as a result of the photosynthesis process is small and it does not affect oxygen dynamics over the largest part of the waterbody. Due to the fact that oxygen concentration is one of the main characteristics of the lake status, it is one of the variables describing the ecosystem state in the model. An essential peculiarity of the lake ecosystem for defining the set of ecosystem model variables is the level of relative biogen concentrations in the lake waters. So, the ratio of total nitrogen content in Lake Onego to total phosphorus content, N: P, is not less than 20, which testifies to the absence of a deficit in this element in the lake waters. Silica concentration in the lake waters is in the range 0.3-0.5 mg 1-1, which provides for the biota demands, primarily of all diatom algae, for this element. Thus, the situation with the main biogens that in fact might limit the development of biota in Lake Onego is nearly the same as in Lake Ladoga and the main biogenic limiting element in both lakes appears to be phosphorus. While developing Lake Onego ecosystem model it was natural to consider the principal similarity of the main characteristics of the Lakes Ladoga and Onego ecosystems. The species composition of flora and fauna in Lake Onego has been well studied. Its phytoplankton numbers 430 species and algal forms. In Lake Oneo, as in Lake Ladoga, but not that distinctly, the pelagic part prevails over the littoral. In such types of lakes the main producer of autochthonous organic matter is the plankton algae community. Phytoplankton is the first element of the biota to respond to changes in concentration of biogenic elements in the lake waters. The composition of phytoplankton, the intensity of its dependence on the abiotic factors of the water environment (temperature, lighting, mixing conditions and so on) for its development, and its position in the lake's trophic chain determine the central role of phytoplankton in the Lake Onego ecosystem. The process of anthropogenic eutrophication in large, historically oligotrophic lakes, such as Lake Onego is accelerated by the increase in external biogenic loading on the waterbody as a result of the intensification of human activities in the catchment area. Enhancement of biogenic loading on the waterbody stimulates biota development and first of all producers. Change in the lake ecosystem occurs at incomparably higher rates than during the natural evolution of the lake. It leads to disturbance of the productive/destructive balance of the ecosystem. In large stratified lakes imbalance is enhanced by the fact that morphometrical and hydrophysical parameters of water body remain the same.

188

Ecosystem models of Lakes Ladoga and Onego

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During recent decades, for nearly half a century, Lakes Ladoga and Onego have both undergone considerable anthropogenic impact. The process of eutrophication began earlier in Lake Ladoga than in Lake Onego and developed faster. But changes taking place in the Lake Onego ecosystem nowadays testify that the transformation stages of the lake processes are mostly similar to those observed in Lake Ladoga. At the present time in Lake Onego, eutrophication features are clearly seen in the level of phytoplankton development. The general floristic algae composition remains the same as the ratio of systematic groups in seasonal complexes. Diatomaceous algae dominate in spring, diatoms and blue-green in summer and autumn. In comparison with the data of the 1970s, phytoplankton quantity and biomass in Bolshoye Onego Bay has changed insignificantly, but in Petrozavodsk Bay their values have tripled and in Kondopoga Bay the enhancement has been by an order of magnitude (Filatov, 1999). The modern state of the ecosystem corresponds to the first stage of phytoplankton mass species succession with gradual primary production growth. The spatial differentiation in all lake processes make it difficult to give an integrated estimate of the degree of change in the trophic status, but the threat of anthropogenic eutrophication development is obvious. In spite of the similarity in the main mechanisms of ecosystem functioning in large stratified lakes, in each individual lake the same mechanisms have different priorities (Menshutkin, 1993). For this reason, applying the model developed for Lake Ladoga could not give positive results for Lake Onego. But the abovementioned similarity of many ecosystem characteristic in these lakes made it possible to apply the model developed by the authors to both lakes.

6.3.2 Mathematical formulation of the model The following processes are reproduced in the model: transfer of substances by currents, turbulent diffusion and settling of some substances, organic matter transformation (phytoplankton, zooplankton and detritus), biogens (dissolved in water, mineral forms of phosphorus and nitrogen) and oxygen dissolved in water. The state of the ecosystem is described by three-dimensional concentration fields of the following seven substances: • • •

A - generalized phytoplankton raw mass, measured in mg l"; Z - generalized zooplankton raw mass, measured in mg l"; P - mineral forms of phosphorus dissolved in water (JlgP 1-1);

• •

N - mineral forms of nitrogen dissolved in water (JlgN 1-1); DP - detrital phosphorus (phosphorus contained in detritus), measured in JlgPl- 1 DN - detrital nitrogen (nitrogen contained in detritus), measured in ug N 1-1; OX - oxygen dissolved in water, measured in mg 0 1-1.

• •

Ecosystem model for Lake Onego, based on the turnover of biogens

Sec. 6.3]

189

All processes are described by a system of equations in partial derivatives, representing the system (5.1)-(5.3):

~~ + K(v, A) =

D(v, A) - mpA + Prod - Ep,

(6.1)

~~ + K(v, Z) =

D(v, Z) - mzZ + UCon - ZR,

(6.2)

a~t + K(v -

VDP, DP) = D(v, DP)

a~; + K(v -

VDN, DN) = D(v, DN)

a;; +

K(v -

+ kr Des + k N Des -

s». P) = D(v, P) + kp(prod -

~~ +K(v- vN,N) = a~tX + K(v, OX) =

Rp,

(6.3)

RN,

(6.4)

ZR) + Rp,

(6.5)

D(v,N) +kN(prod - ZR) + RN,

D(v, OX) + hA Prod - hzZR - hDPRp

(6.6) -

hDNRN.

(6.7)

The application of turbulent diffusion equations for transfer description of substances reviewed in the model is sufficiently justified only for dissolved nonorganic phosphorus and dissolved nonorganic nitrogen, and for oxygen dissolved in water. Applying these equations for describing phytoplankton behaviour, and even more for zooplankton behaviour, needs special explanation. As phytoplankton is considered to be hydrodynamically neutral it is justified to assume that it is transferred with currents. Inclusion of a diffusion term in the equation might lead to increased phytoplankton concentrations in the hypolimnion. That is why in equations for phytoplankton (6.1) coefficients vx , vy and Vz are set essentially lower than in equations (6.5)-(6.7). Zooplankton cannot be considered hydrodynamically neutral as it has its own dynamics in water - diurnal vertical migrations. That is why application of the equation (6.2) in this case is to some extent conventional. Nevertheless, applying this equation in previous studies (Astrakhantsev et al., 1992, 1996) allowed a quite precise description of the generalized zooplankton biomass and its distribution in the water column. It is worth mentioning that computational algorithms of model realization allow us to set coefficients vx , vy and Vz in (6.2) to zero. In this model, as in the previous one (Menshutkin and Vorobyeva, 1987), diurnal fluctuations in biotic and abiotic ecosystem parameters are not taken into consideration. In order to achieve this, it is necessary to pose diurnal fluctuations of all internal impacts on the waterbody, but such kinds of data are mostly insufficient. In all the models discussed in this monograph, diurnal variation in waterbody functioning is not taken into consideration. In equations (6.1)-(6.7) along with new parameters, there are those that have already been used in section 5.2. In each equation (6.1)-(6.7) the diffusion operator is followed by the terms describing transformation of substances A, Z, DP, DN, P, N

190

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

and ox. So, in equation (6.1) the term mpA is phytoplankton mortality rate, mp is phytoplankton mortality coefficient; Prod = PIB· A is primary production, understood as the augmentation rate of phytoplankton biomass (Alimov, 1989), PIB is the growth rate coefficient, and Ep is is the grazing rate of phytoplankton by zooplankton. In equation (6.2) term mzZ is the zooplankton mortality rate, m, is the mortality coefficient; U> Con is the zooplankton growth rate. The term ZR is the excretion rate of nitrogen and phosphorus mineral forms by zooplankton in the process of metabolism. This magnitude was calculated in the model of Menshutkin and Vorobyeva (1987), according to Gutelmacher (1982), in proportion to wastes from metabolism. Detritus supplies are refilled from phyto- and zooplankton dying, and from nondigested nutrition, that is reflected in the expression for the term Des: (6.8) where U is the coefficient for nutrition digestion by zooplankton, En is the rate of detritus grazing by zooplankton. The transformation of detritus into dissolved mineral form as the result of bacterioplankton life activity is considered in equations (6.3)-(6.6) with terms Rn and RN representing the transformation rate of phosphorus and nitrogen from detritus to dissolved form. In equation (6.7) term hAProd describes the oxygen flux in water as a result of photosynthesis, and other terms describe oxygen consumption in zooplankton respiration and detritus destruction. It is assumed in the model that the composition of elements of the phyto- and zooplankton biomass is unchangeable and such that C:N:P=40:10:1. It is supposed that 1mg of raw biomass contains 2.5 ug of phosphorus, 25 ug of nitrogen and 100 ug of carbon; then determination conversion coefficients for phosphorus and nitrogen quantity in the phyto- and zooplankton biomass can be added kp = 2.5 ug Prng"! of raw biomass, k N = 25 ug N mg" of raw biomass.

The following measurement units for substances were set in the model: [A]=mgl- 1,

[Z]=mgl- 1,

[DP] = JlgPI- 1,

[P]= JlgPI- 1,

[DN] = JlgNI- 1,

[N]= JlgNI- 1

[OX] = mg l"

While constructing the model it was assumed that in each elementary grid cell in the ecosystem model the balance of phosphorus and nitrogen is valid if transport processes are neglected. These natural requirements are formulated as the equalities (see (5.4)):

+ Z) + DP + P = const, Ntotal == kN(A + Z) + DN + N = const. Ptotal == kp(A

(6.9)

The form of terms in (6.1)-(6.6), describing the transformation of substances, requires the validity of the following equality Ep

+ En

- con = 0,

(6.10)

Sec. 6.3]

Ecosystem model for Lake Onego, based on the turnover of biogens

191

that arises as a necessity of the correctness of equation (5.5) with the respect to the considered model. Fulfilment of (6.10) on the basis of present knowledge about the modelled processes cannot be guaranteed. That is why, to satisfy (6.10), the description of the processes was simplified in the model. The meaning of equality (6.10) is that zooplankton nutrient consumption consists of phytoplankton and detritus. Due to this fact the description seems to be appropriate. It is impossible to satisfy the equation; all its terms are derived independently. That is why, in the model of Menshutkin and Vorobyova (1987), all terms were constructed in such a way that equality (6.10) was valid. The construction of the model (6.1)-(6.6) was carried over from that of Menshutkin and Vorobyeva (1987) and was formulated as a system of partial differential equations. Boundary conditions

Boundary conditions for the system of equations (6.1)-(6.7) are applied in compliance with boundary conditions for system (5.1). At the waterbody surface So as z = 0 fluxes of substances A, Z, DP, DN, P and N are prescribed; these are conditions (5.6). At the waterbody bottom, as z = H(x,y) and there is a solid vertical boundary for all substances except OX, boundary conditions (5.9) are applied. At tributary sites, Sin and at outlet sites, Sour, boundary conditions (5.8) and (5.9) are used respectively. Boundary conditions for the equation (6.7) are applied in the following way. At the waterbody surface z = 0 the condition Vz

aox = &

*

rno(OX - OX)

(6.11)

describes oxygen exchange at the water-atmosphere interface, where rno is the aeration coefficient, OX* is the saturation oxygen concentration in water, [OX] is the dimension of OX in mg OXI- I . The value OX* in grid cells is calculated using the well-known empirical relation (Vavilin, 1983): OX* = 14.61996 - 0.4042T - 0.0842T 2

-

0.009T 3 ,

where T is the water temperature in Celsius degrees. According to Vavilin (1983, p. 133) the re-aeration coefficient rno varies within the range 0.2-1.25 day ", At the waterbody bottom z = -H(x,y), the boundary condition for 16 is given as follows:

aox aN

=kb OX .

(6.12)

This boundary condition is determined by processes of oxygen consumption and release in bottom sediments. The value of coefficient k b is defined in the model on the basis of measurements data provided to the authors by Ignatyeva (1997). At tributary sites the boundary condition for OX can be given in the form (5.8), and (OX)r

==

OX*(Tr),

where T, is the given water temperature at the tributary site.

192

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

For model realization in the case of Vx = v y = 0 at tributary sites for DP, DN, P, N and OX, the boundary condition (5.10) is used, and at outlets no boundary conditions are applied for any substances. For phyto- and zooplankton at tributary sites, two versions of boundary conditions were used, either (5.10), or (5.11). Variation laws

For Ptotal and Ntotal, due to the fact that when (6.10) is true (6.9) is also correct and variation laws (5.12) are valid, we will present only the variation law for dissolved oxygen, since boundary conditions for OX differ from boundary conditions for other substances. For example, the law of variation in the concentration of OX has the following form:

:t JOXdn=J mo(OX*-OX)dS-J kb OX d S -J v,,(OX)r dS - J v"OXdS n

~

~

Sin

+

In

SOUl

[hAProd - hzzr - hDPRp - hDNRN] dO.

(6.13)

Discrete analogues of the variation laws for Ptotal, Ntotal and OX were used in computational experiments to control the simulation results. 6.3.3

The discrete model

The discrete analogue of the formulated mathematical ecosystem model, except for the biotic block, was built in section 5.3. The construction of the biotic block is a particularization of equations (5.16). Biotic block of the model

II:j;

Variations of every substance concentration in the cell during the time-step h, from the moment t to t+h t are written as (see (6.1)-(6.7)): .6.A

== h t( -mpA + Prod -

Ep),

.6.Z == ht(-mzZ + U· Con - ZR), .6.DP

== ht(kpDes -

== h t( -kp(Prod -

.6.N == ht(-kN(Prod -

(6.15) (6.16)

Rp),

.6.DN == ht(kNDes - RN), .6.P

(6.14)

+ Rp), ZN) + R N),

ZR)

.6.0X == ht(hAProd - HzZR - hDPRp - hDNRN).

(6.17) (6.18) (6.19) (6.20)

Sec. 6.3]

Ecosystem model for Lake Onego, based on the turnover of biogens

193

The dependencies of coefficients mp , m, and coefficients, in terms Prod, Con and Des, used in (6.14)-(6.20) on temperature and solar radiation in many cases are formulated as piecewise linear functons (Menshutkin and Vorobyeva, 1987), which in practice approximated curves with saturation. Curves with saturation gained acceptance in the description of the abovementioned relations - Michaelis-Menten equations (Bierman and Dolan, 1981). Further, all piecewise-linear functions are given using the standard template YI, f(X,XI,X2,YI,Y2)

=

YI { Y2,

when x < Y2 - YI

+ X2 -Xl when

Xl,

(X -

Xl),

Xl

~

X

~

X2,

(6.21)

> X2·

X

The definition of primary production, Prod, begins with calculation of the growth coefficient P/B using the following formula (6.22) where dependence of P/B on the following factors is reflected: water temperature T, solar radiation (illuminance level), mineral phosphorus and mineral nitrogen concentrations, and also phytoplankton concentration. The equality (6.22) is based on Liebig's Law of the minimum law (Bierman and Dolan, 1981), according to which controlling is the most limiting factor. Sometimes to determine primary production the minimum operator is replaced with a multiplication operator (Jorgensen, 1976; Di Toro, 1976; Leonov et al., 1991). Each of the coefficients in the right-hand side of (6.22) is defined using functions in the form of (6.21): P/B T = f(T, T min, Tmax, p/B¥n, p/B¥n, P/B Tax), P/Bs = f(S, 0, Smax, 0, P/B ax),

s

P/Bp = f(P, 0, P max, 0, P/Brpax), P/BN = f(N, 0, N max, 0, P/B Nax ), P/BA =f(A,O,Amax, P/B ax, p/Btfn).

(6.23)

s

Specific values of parameters in formula (6.23) are derived on the basis of observations (Petrova, 1982; Modern State . . . , 1987) and multiple investigations (Vinberg, 1960; Gutelmacher, 1988). As is stressed by Menshutkin (1993) the introduction of production rate dependency on temperature requires caution, because the phytoplankton community reacts to water-temperature variations, not by production decline but by changes in species composition: warm-loving species are replaced with cold-loving and vice versa. This note is important for understanding the factors affecting the phytoplankton succession. Later on we will return to this remark. The dependence of production rate on solar radiation takes into account the elevation of the Sun at all times at the latitude of Lake Onego.

194

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

Naturally, the production rate is controlled by biogen concentrations and also by phytoplankton concentration. In (6.23) the following values of parameters are used:

P/B ~x = 2 day ",

s

Smax = 220,

P/B ax = 10 day" ,

P max = 23 ug PI-I,

P/Bpax = 2 day ",

N max = 120 JlgNl- 1,

P/B Nax = 2 day ",

Amax = 0.5 ug 1-1,

p/Btfn = 1.2day-l.

Then the growth of biomass during time-step h, is defined as

htProd = min(ht/B x (A

+ Amin) x PL, P x PL/kp,N x PL/kN ) .

(6.24)

Here the value Amin = 0.05 Jlg- 1 is introduced in order to avoid zero values of A; otherwise the process of primary production growth will never start. It is supposed that phytoplankton generation takes place only in the near-surface layer with a depth of PL', where enough light penetrates. The coefficient PL in (6.24) determines the part of the elementary cell where photosynthesis occurs, i.e. the part of the cell volume above the depth PL': 1,

(PL)ijk =

if IZk - hk-l(Z)/21

< PL'

0, if IZk - hk(Z)/21 < PL' -PL' + IZk + hk(Z)/21 (hk - 1(Z) + hk (z))/2 .

(6.25)

The thickness of the photosynthesis layer PL' is controlled by water transparency, which, in turn, besides the background value, also depends on shadowing effect of phytoplankton and detritus:

PL' = f(A

+ DP/kp, Sesmin, Sesmax, Lmax, Lmin),

(6.26)

where Sesmin = 1 Jlgl- 1, Sesmax = 8 Jlgl- 1, Lmax = 8m, Lmin = 2m. Mortality coefficients mp and m, are defined in the following manner: mp =

f(A, A min , Amax, mpin, mrpax),

Amin = 2 ug 1-1, Amax = 8 ug 1-1, mpin = 0.1 day",

mrpax = 0.98 day "

(6.27)

and (6.28)

Sec. 6.3]

Ecosystem model for Lake Onego, based on the turnover of biogens

195

where

m~ = f(T, T~n' T~ax, mfmin' mfmax), T~n = 2.2°C,

T~ax = 3.9°C,

mfmin = 0.05 day",

mfmax = 0.1 day-I.

(6.29)

Phyto- and zooplankton mortality was assumed to dependent on their own concentration. With increase of concentration the mortality grew up to a certain limit value. For zooplankton in coefficient m, its mortality in summer and autumn months was taken into account due to intensive preying on planktonic crustaceans. The zooplankton biomass growth is defined in the model as follows: (6.30) U . Con = U x TK x (Z + Zmin) xf(PD, Fmin, Fmax, 0, Con max ) where U = 0.75 is the coefficient of nutrient assimilation by zooplankton; TK is a non-dimensional coefficient; TK = f(T:mn' T~ax, TKmin, TKmax),

T:mn =

2°C,

T~ax = 22°C,

TKmin = 0.43,

TKmax = 2.3;

(6.31)

Zmin = 0.05Jlg1-1 has the same meaning as Amin; PD = A

+ h, Prod + Det,

(6.32)

Det = min(DP/kp , DN/kN ) , F min = 0.2 ug 1-1,

F max = 0.8 ug 1-1,

Con max = 0.7 day":

(6.33)

The dependence of phytoplankton growth on nutrient concentration PD was defined as threshold value (0.2mgl- 1) and saturated (0.8mgl- 1) concentration. Below the threshold value the feeding stopped, and above the saturated value filtration for feeding became constant. Variation of zooplankton feeding needs with temperature change is included using the correction factor TK. According to (6.32) detritus is a part of nutrients; Det is the died-off biomass of phyto- and zooplankton. It is worth mentioning that in the model DP and DN are variables determining the amount of organic phosphorus and organic nitrogen in detritus. In this model, as in many others, the invariability of elementary phyto- and zooplankton biomass composition is assumed. The application of this assumption concerning detritus is justified by the aim to reduce the number of parameters for ecosystem description. The determination of detritus concentration using formula (6.33) and of light absorption using formula (6.26) is sufficiently conventional.

196

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

The variation of concentrations DP and DN in the model is defined in accordance with (6.16) and (6.17); phosphorus and nitrogen concentrations in died-off phyto- and zooplankton, and in undigested nutrition, are defined by terms h, k p Des and h, k N Des respectively. Regeneration of mineral phosphorus and nitrogen as a result of bacterioplankton life activity was supposed to depend only on temperature and the existing stock of died-off organic matter: R p = DP xf(T, RN = DN xf(T,

rz: T~ax,Rprn-,Rpax),

rs: T:mx, RWn, R Nax),

where

0.05 day",

R pax = 0.21 day",

RWn = 0.03 day",

R Nax = 0.05 day":

Rpin =

The supply of mineral phosphorus and nitrogen are regulated in the model by their consumption by phytoplankton in (6.18) and (6.19), regeneration processes, and also at the expense of the term Z R, which represents excretion of mineral phosphorus (kpZ R) and mineral nitrogen (k N ZR) as a result of zooplankton life activity (Gutelmacher, 1982). The construction of the term ZR is given in the form (6.34)

where ZRo = 0.25 day ", TKis defined according to (6.31). To finalize the description of the biotic block of the discrete model, let us consider the construction of terms E p and En. The natural assumption, that gazing rate of phytoplankton and detritus is proportional to their concentrations, i.e. E p = E AZ x (A

+ htProd),

En = E nz x Del.

As was mentioned above, obtaining the balance of phosphorus and nitrogen in every elementary cell is necessary to satisfy the equality (6.10). To provide the fulfilment of the condition (6.10), the reasonable assumption is made that E AZ = E nz = E and E = Con/(A

+ h t Prod + Det).

(6.35)

Total variation of substances content in cells IIJj;

Equalities (6.14)-(6.20) enable us to write down equation (5.17) for all substances, included in the model. These equations are approximations of a system of differential equations (6.1)-(6.7) and corresponding boundary conditions.

Sec. 6.3]

Ecosystem model for Lake Onego, based on the turnover of biogens

197

Discrete analogues of the variation laws

For total phosphorus and total nitrogen the discrete analogues of conservation laws (5.12), written for Ptotal and Ntotal are valid. These discrete analogues are derived in an obvious manner from (5.18). For dissolved oxygen the discrete analogue (6.13) is satisfied. 6.3.4 Reproduction of Lake Onego annual ecosystem functioning The lake ecosystem functioning simulations were performed for two versions of biogenic loading. The first version corresponded to an annual loading equal to 1003t P total year"! and 117739 t N total year ": The loading expresses the mean annual loading for the periods 1986-1987 and 1992-1997 (Filatov, 1999, pp. 62-64). According to observation data, tributaries bring in 705 t Ptotal year " , atmospheric precipitation gives 95 tPtotalyear-l and waste waters 203 tPtotalyear-l. For nitrogen it is the following: from tributaries 13167tNtotalyear-l, from atmospheric precipitation 3800tNtotalyear-l and from waste waters 772tNtotalyear-l (Filatov, 1999). The annual distribution of biogenic loading into the lake and its distribution among tributaries is based on biogen outflow data (Shuya River, 201 tPtotalyear-l and 2259 t N total year': Vodla River, 194 t P total year " and 3353 t P total year " t N total year; Suna River, 28 tPtotalyear and 1714t Ntotalyear-l), and data on annual water flow distribution in the lake tributaries. Analysis of the annual distribution data for biogenic loading shows that it strongly correlates with the annual distribution of water inflow, is why additional income ofbiogens into the lake with waste waters and precipitation were distributed in the model according to the revealed relation. The second version corresponded to an annual loading for the period 20012002 and equalled 786 tPtotalyear-l and 15051 tNtotalyear-l (the data was obtained at Northern Water Problems Institute, Karelian Research Centre of the RAS by Basov and Lozovik). A decline in biogen loading is related mainly with decline of phosphorus income from tributaries: in 2001-2002 tributaries carried out 517 t P total year"! and 10 562 t Ntotalyear-l of biogens, though before that period it was 706 tPtotalyear-l and 13167tNtotalyear-1. Biogen carry-over with waste waters also declined, from 203 t P total year"! and 772 t N total year"! to 174 t P total year"! and 689 t N total year-I. Annual distribution data for biogens Ptotal and Ntotal are shown in Table 6.1 (Rukhovets and Filatov, 2003). The reproduction of the annual lake ecosystem functioning for each biogenic loading version consisted of receiving a discrete model periodical solution, approximating the system of equations in partial derivatives described above, and reproducing the processes studied. All external impacts, biogenic income, water inflow and discharge, were set as periodical functions with a period equal to one year. In order to construct the periodical solution, calculations were performed on a period of not less than 15 years. This exceeds the Lake Onego retention period. The retention period determines the lake ecosystem response to external impact. Data on water temperature and current velocity regimes obtained while constructing the full-year

198

[Ch.6

Ecosystem models of Lakes Ladoga and Onego

Table 6.1. Annual distribution of total phosphorus and total nitrogen (in tons) in the water inflow of the Vodla, Shuya, Suna (Kondopoga canal) and Vitegra rivers in 2001-2002 (data from NWPI). 2001 spring IV

V

2002

summer VI

VII

VIII

IX

X

E

winter

autumn XI

XII

I

II

III

River Vodla p

9

18.5 13

N

280

558

320

19.8 15.7

20

276

250 299

230

15

10.3 3.8

3.7 3.7

3.2

135.7

250

107

75

75

74

2794

River Shuya p

12.4 29.2

14

7

5.6

8.2 7.8

7.8

5.0

4.7 4.7

4.7

111.1

N

230

270

130

82

125 100

100

91

91

98

106

1871

448

River Suna P

1.2

1.8

1.2

2.0

2.5

2.6

1.8

2.2

3.4

2.4 2.4

2.4

25.9

N

110

151

110

181

236

102 87

87

83

57

59

64

1327

0.6

0.5 0.4

0.6

17.4

9.5

8.2 8.2

8.2

288

River Vytegra P

1.5

1.7

1.2

2.2

2.6

1.8 2.5

N

32

60

28

31

34

25

1.8

23.9 20

climatic circulation in Lake Onego, which was discussed in Chapter 3, were applied in the computation process. Analysis of modelling results

Modelling results are shown in Figs 6.1-6.14. Raw phytoplankton biomass mean annual dynamics in the Lake Onego epilimnion are presented in Fig. 6.1 for both loading versions. Mean phytoplankton biomass values in spring for the 1989-1993 period according to published figures (Filatov, 1999, Table 5.2, p. 150) for Bolshoye Onego, Petrozavodsk and Kondopoga bays considerably differ and equal 1.3mg 1-1, 7.1 mg l"! and 14.2mgl- 1 respectively. In our computation results for the first loading version, the maximum value of mean concentrations in spring equals 2.1 mg 1-1.

Ecosystem model for Lake Onego, based on the turnover of biogens

Sec. 6.3]

199

It.

12

\

I,

\

o

I I

I'lL"

tit n

11'

M.QI

Z1 ~

I

r ' ~.oo

f

'I

-'

till'"

'IoJ.'"

te ~~

II II JlI II

D .0 O!'lM

I'

I~.o:r

'I I

I

'11111

I

I' II ".., 1"1' arm

'I

I

r

tI 1

111 "1 DiI.IA:I

12.'0 27tJ 21.11 1HZ 11'01

Fig. 6.1. Phytoplankton biomass concentration in the epilimnion of Lake Onego (mg l"). Climatic circulation underloading: 1003 t Pyear" , 17739 t Nyear"! (solid line); 786 t Pyear", 15051 t Nyear" (dotted line).

In summer time during 1989-1993 according to the same data, corresponding data in these bays equal 0.9mg 1-1, 1.22mg I-I and 2.3 mg I-I respectively. In numerical experiments, calculations of the summer phytoplankton biomass mean concentration value in the lake epilimnion give l.4mgl- 1 (Fig. 6.1). There are two maxima in mean phytoplankton biomass annual dynamics (Fig. 6.1), One at the end of June and the second at the beginning of October. Observation data gives the same picture (Filatov, 1999, Table 5.1, p.149), the phytoplankton biomass value in October of 1991 and 1993 in Bolshoye Onego Bay is noticeably higher than in September. Thus, the results of phytoplankton calculations for the first loading version qualitatively and numerically coincides with observation data. Presented in Fig. 6.2, mean raw zooplankton biomass annual dynamics values reach a maximum magnitude later than phytoplankton biomass, as was expected. According to computation results the minimum magnitude of mineral phosphorus concentrations minimum magnitude in epilimnion coincides with phytoplankton biomass spring maximum (Fig. 6.3). Modelled values of mineral phosphorus concentrations fluctuations in this picture are within the range of similar observed characteristic alterations in the region of Central Onego (Filatoved., 1999; pp.149-154). The results of simulations of phyto- and zooplankton raw biomass dynamics, organic phosphorus and organic nitrogen concentrations (in detritus), dissolved-inwater mineral phosphorus and dissolved-in-water mineral nitrogen over the waterbody of the Petrozavodsk Bay are shown in Figs 6.7-6.14. The behaviour of reviewed

200

[Ch.6

Ecosystem models of Lakes Ladoga and Onego

\,

(u

... ...

,

\

1.1

ilII.Dl iIJJ(12

I~OO

21..,

'IJ.04

~

2

II

[>1

O;ttol

Fig. 6.2. Zooplankton biomass concentration in the epilimnion of Lake Onego (mg l"). Climatic circulation underloading: 1003 t Pyear" , 17739 t Nyear"! (solid line); 786 tP year:", 1505 t Nyear" (dotted line).

/

------------

\

'\

II

II

II

II ,I, ", ~.

----------

Fig.6.3. Mineral phosphorus concentration in the epilimnion of Lake Onego (J1g I-I). Climatic circulation under loading: 1003tPyeac', 17739tNyear- 1 (solid line); 786tPyear- l , 15051 t Nyear" (dotted line).

Ecosystem model for Lake Onego, based on the turnover of biogens

Sec. 6.3]

20 I

l 'I

--

\

-----

...

'\

I

Fig. 6.4. Detrital phosphorus concentration in epilimnion of Lake Onego (ug l"). Climatic circulation underloading: 1003 t Pyear", 17739 t Nyear" (solid line); 786 t Pyear" , 15051 t Nyear "! (dotted line).

11il"

I:Q.I -

Dl -

m

i" " I HDl

,"""I

'1

'"

l'

noll 1113 10[0<

'I ~

"

I'

nlll it4D11

'I Ivm

'

I"

I

1oJ!'

[I;'

'I' IJI..)J

r' ZT.I

'I"

'I

Z II

'I U

"

D~

It"l

Fig. 6.5. Mineral nitrogen concentration in epilimnion of Lake Onego (J,lgl-I) . Climatic circul at ion under loading: 1003 t P year:", 17739 t N year"! (solid line); 786 t P year:" , 15051 t Nyear" (dotted line).

202

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

I '

Fig. 6.6. Detrital nitrogen concentration in the epilimnion of Lake Onego (J,lgl-I). Climatic circulation underloading: 1003 t Pyear", 17739 t Nyear"! (solid line); 786 tP year:", 15051 t Nyear"! (dotted line).

S'.-

mg/I \,

,

"

I

'"

I, \.

} 'I "

1 "

'I"

1:ka1 lUll' 1ll.1
'I " J'

I

""0 011:.;] 111

r•.o1I

Fig. 6.7. Phytoplankton biomass concentration in the epilimnion of Petrozavodsk Bay (mg I-I). Climatic circulation under loading: 1003 t Pyear" , 17739 t N year"! (solid line); 786tPyear- l , 15051 t Nyear" (dotted line).

Ecosystem model for Lake Onego, based on the turnover of biogens 203

Sec. 6.3]

mg/I

r

~

\

I

t n oll :l2oJl 312

I ~~

IDL04

~L~

:Il.De

~~

'Il oJT IJ III [);' N

a UJ 27.t]

21.11

Fig. 6.8. Zooplankton concentration in the epilimnion ofPetrozavodsk Bay (mg l" ). Climatic circulation underloading: 1003t Pyear", 17739 t Nyear"! (solid line); 786 tP year:", 15051 t Nyear "! (dotted line).

11

Fig. 6.9. Mineral phosphorus concentration in the epilimnion of Petrozavodsk Bay (~gl-I) . Climatic circulation under loading: 1003t Pyear" , 17739 t N year"! (solid line); 786 t Pyear" , 15051 t Nyear- 1 (dotted line).

204

Ecosystem models of Lakes Ladoga and Onego

, I"

I

/

I I

---

~

I

.- I

I I

I

I I I ,I II

'I

,I z

I

,I

'I

"

[Ch.6

~,

....

II

f

, ,I,

'\

\,

'

.... ., ....

Fig. 6.10. Detrital phosphorus concentration in the epilimnion ofPetrozavodsk Bay (JlgI- 1) . Climatic circulation underloading: 1003 t Pyear" , 17739 t Nyear"! (solid line); 786 tP year:", 15051 t Nyear" (dotted line).

\I ' -,

Fig. 6.11. Mineral nitrogen concentration in the epilimnion of Petrozavodsk Bay (JlgI- 1) . Climatic circulation under loading: 1003 t Pyearr" , 17739 t Nyear"! (solid line); 786 tP year:", 15051 t Nyear- 1 (dotted line).

Ecosystem model for Lake Onego, based on the turnover of biogens 205

Sec. 6.3]

' Ill

Ill'

I I

I

1

I

~'

Fig. 6.12. Detrital nitrogen concentration in the epilimnion of Petrozavodsk Bay (ug l" ). Climatic circulation underloading: 1003 t Pyear" , 17739 t Nyear"! (solid line); 786 t Pyear" , 15051 t Nyear" (dotted line).

mg/I

..

.j

I

I'

I II

l

1-1

a

l

'1-<' I I' ,~

:K'DS

~-

I' I

,.

~JlC.

,

., ,

I' ., 'I ' • ,.

tl IT I)

"'.<so

'.

tlltJ

•I

zr.1J

'i 'I'

ll .lt

I' -'I

'I O;Ui;l

tIS'l IDot

Fig. 6.13. Phytoplankton biomass concentration in the River Shuja mouth of Petrozavodsk Bay (mg 1-1). Climatic circulation underloading: 1003t Pyear" , 17739 t N year"! (solid line); 786tPyear- l , 15051 t Nyear"! (dotted line).

206

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

mg/I u

I'" 12

I

I

'I II

I' I

I /

Fig. 6.14. Zooplankton concentration in the River Shuja mouth ofPetrozavodsk Bay (mg l"). Climatic circulation underloading: 1003 t P year"! , 17739 t N year"! (solid line); 786 t P year:", 15051 t Nyear" (dotted line).

characteristics related to the River Shuya outlet is presented in Figs 6.9-6.14. Computation results, as well as observation data, show that, according to available data, Petrozavodsk Bay is under high ecological pressure, especially in its upper part. Simulation results for the second loading version show that in fact a decline in the concentrations of substances takes place for all points of time (Fig. 6.1-6.14).

Conclusions Computation results show that the model simultaneously reproduces a year-round Lake Onego ecosystem functioning . This model could be applied in water usage management for the Lake Onega catchment. A decline on biogenic loading, especially in the upper parts of Petrozavodsk and Kondopoga bays, could have a favourable influence on water quality in these areas and in the whole lake. 6.4 LAKE LADOGA PHYTOPLANKTON SUCCESSION ECOSYSTEM MODEL

Anthropogenic eutrophication causes changes in lakes similar for the most part to the process of waterbody natural 'ageing'. These changes essentially accelerate a lake ecosystem transformation, disrupting useful lake productivity and reducing water

Sec. 6.4]

Lake Ladoga phytoplankton succession ecosystem model

207

quality. The main mechanism of lake ecosystem transformation, under both natural evolution conditions and anthropogenic influence, is the succession of hydrobiont species composition at all trophic levels, first of all phytoplankton. While developing the phytoplankton succession model, the authors assumed that consideration of the role of phytoplankton in ecosystem functioning is very important to the ability to reproduce in a mathematical model the mechanisms of phytoplankton community transformation during eutrophication process. The succession model will make it possible to clarify phytoplankton species composition dynamics and, as consequence, of total phytoplankton during anthropogenic eutrophication. This will make it possible to analyse and quantitatively estimate the main changes in the ecosystem. Besides, the model will help in general to predict and estimate the possible lake ecosystem transformation in the near future, and to estimate the influence of the dominant phytoplankton groups on the lake water quality. Right at the beginning of the anthropogenic eutrophication study with mathematical modelling methods the problem of the transformation of planktonic communities had attracted the attention of researchers. For example, anthropogenic eutrophication of the Great American Lakes was the main reason for the planktonic community succession model in Saginaw Bay of Lake Huron (Bierman et al., 1981). Five complexes of phytoplankton were considered as community elements in this model. Planktonic community structural transformations were discussed in the literature (Jorgensen, 1992, 1994; Wirtz and Eckhardt, 1996) from different points of view. Theoretical problems of the phytoplankton succession process are presented in (Kesh et al., 1997). The succession process, being a temporal alteration of species and community structures is interpreted as a Lotka-Volterra interaction type ('predator-prey' relation) within the frame of an existing mathematical problem. Succession connected with environmental changes, primarily in nutrition levels, is studied applying the model (Kesh et al., 1997; Armstrong, 1979; Svirezhev and Logofet, 1983). Actually phytoplankton succession could be interpreted as a competition for total resource. The aim of creating the model discussed is to reproduce Lake Ladoga's real algal community succession under changing anthropogenic loading, associated in the model with phosphorus loading. The first succession model for Lake Ladoga (Menshutkin and Vorobyeva, 1989) was developed for the phytoplankton community in Volkhov Bay. In this single-box model phytoplankton is represented in eight separate complexes. Primary production in the model depended on temperature conditions and biogenic supply. Phytoplankton grazing by zooplankton and fish was not considered in the model. While considering biogenic loading into the lake, it was assumed that the mixing process occurred instantly; sedimentation was modelled using non-conservativity coefficient. Despite the considerable schematization of the processes, the authors managed to reproduce the phytoplankton succession due to changes in phosphorus supply and thermal conditions. The model (Menshutkin and Vorobyeva, 1989) was the first approximation for phytoplankton succession reproduction in Lake Ladoga. Here the model of phytoplankton succession from Astrakhantsev et al. (2003) and Rukhovets et al. (2003) is presented.

208

6.4.1

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

Formulation of the model

Ecological structure of the model

In the basic Lake Ladoga ecosystem model (Astrakhantsev et al., 2003), mentioned in section 6.2, the division of phytoplankton into three ecological groups made it possible firstly, more accurately than in previous models, to compute phytoplankton biomass alteration and, secondly, to adequately reproduce seasonal species changes. But consideration of the ecological peculiarities of only three algal groups is not sufficient for succession reconstruction - the regular change of dominating algal species composition in the process of eutrophication (Petrova, 1990). A more detailed description of the plankton community is required. In the succession model, phytoplankton is represented, as in the study of Menshutkin and Vorobyeva (1989), as a set of species populations named after the dominant species. Such kinds of assemblies are called complexes. The whole phytoplankton community in the model is represented as an assembly of nine complexes. As Lake Ladoga studies have shown (Gutelmacher and Petrova, 1982; Petrova, 1990), dominant species production comprises 55-95% of the primary production of a complex. Each algal complex is considered to be ecologically homogeneous, but the complexes have distinctive features. The principal point of the succession model is to reproduce not only the seasonal changes in the dominant algal form, but also their regular changes from year to year, depending on their ecological peculiarities. The direction of this process is given by the natural abiotic conditions in the lake, in this case, disturbances of biogenic loading. It is the phytoplankton succession that controls autochthonous organic substance in the lake, which in turn leads to the transformation of the lake ecosystem. Nine complexes were chosen to describe the plankton community in the Lake Ladoga model. Four of them are diatoms, represented by dominants: Aulacosira islandica (0. Miill.) Sim.; Asterionellaformosa Hass.; Diatoma elongatum (Lyngb.) Ag. var. elongatum; Fragilaria crotonensis Kitt. Yellow-green algae are represented by one complex with dominant Tribonema affine West. Blue-green algae are represented by four complexes: Oscillatoria tenuis Ag.; Aphanisomenon jlos-aquae (L.) Ralfs.; Microcystis aeruginosa Kutz, emend. Elenk. and Woronichinia naegeliana (Und.) Elenk. At the same time Aulacosira islandica, Asterionella formosa and Diatoma elongatum represent complexes, prevailing in spring. Complexes Microcystis aeruginosa, Oscillatoria tenuis and Fragilaria crotonensis are blue-green algae dominating in summer. And complexes of blue-green algae Woronichinia naegeliana, Aphanisomenon jlos-aquae, and also Aulacosira islandica, and Tribonema affine, represent summer/autumn plankton. As was pointed out above, only phosphorus is included in this model as biogen. This is also explained by the desire to reduce the number of parameters in the description of ecosystem. In the model by Menshutkin and Vorobyeva (1989) biogens are presented by phosphorus, nitrogen and silica. Testing of models (Astrakhantsev et al., 2003) has shown that the absence of nitrogen in the model does not noticeably

Sec. 6.4]

Lake Ladoga phytoplankton succession ecosystem model

209

affect the adequacy of the model. Nevertheless, with such a detailed description of the phytoplankton, it would be significant to account for the nitrogen fixation capability of blue-green algae. The excess of mineral phosphorus in water is a condition of nitrogen fixation. While determining the growth rate of blue-green algae (Menshutkin and Vorobyeva, 1989)their ability to fix nitrogen was accounted for when the ratio of mineral nitrogen concentration to mineral phosphorus concentration in water fell below the specific prescribed value, namely, N: P = 7: 1 (Schindler, 1977). But, to date the reduction of this ratio in Lake Ladoga below 8 has never been registered by researchers (see Chapter 1). Nowadays the deficit of biologically available phosphorus intensifies in the lake as a result of intense internal turnover of this element in the lake biota. Besides, the leading role played by phosphorus in the regulation of ecosystem processes allows us to accept the simplification outlined. Concerning silica, along with its consumption by diatoms, a threshold value exists, preventing its production below this level. According to observations (Petrova, 1990; Rumyantsev and Drabkova, 2002), silica concentration in Lake Ladoga was never lower than the threshold value of 60 ug Si 1-1 adopted for all diatom complexes (petrova, 1982, p.254; Lund et al., 1975). For this reason, neglecting silica in the model seems to be acceptable. A more detailed justification of the decision to use only one biogen in the succession model is given in Chapter 1. The arguments outlined in sections 6.2 and 6.3 about the ecological structure of large stratified lake ecosystem models, in particular of Lakes Ladoga and Onego, the notes about the scales of simulated events and processes, and the considerations about the application of differential equations to the description of full-scale ecosystem functioning all relate to the phytoplankton succession model. Besides phytoplankton complexes, the model variables include: zooplankton, detritus, dissolved organic matter, dissolved mineral phosphorus and dissolved oxygen. In all, fourteen parameters are used in the model to describe the ecosystem state. Phytoplankton succession in Lake Ladoga

During the 1962-1991 period and for 15 recent years the phytoplankton succession in Lake Ladoga is described in detail in Chapter 1. As noted there, change in phosphorus loading considerably affects the transformation of the plankton community. This conclusion is supported by long-term studies at the Institute of Limnology, RAS (Petrova, 1982; Modern State ... , 1987; Lake Ladoga ... , 1992; Petrova et al., 2005). In this connection it is worth noting that one of the aims in this mathematical model development is the confirmation in numerical experiments of limnologists' conclusions concerning structural changes in the phytoplankton community. The model mathematical formulation

The state of the ecosystem at any moment of time in the model is defined by threedimensional concentration fields of the following substances.

210

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

Phytoplankton complexes (mg 1-1 of raw biomass): Al - Aulacosira islandica A2 - Asterionella formosa

diatoms,

A3 - Diatoma elongatum A4 - Fragilaria crotonensis

} yellow-green,

A5 - Tribonema affine A6 A7A8 A9 -

Oscillatoria tenuis Aphanisomenon flos-aquae Microcystis aeruginosa W oronichinia naegeliana

} blue-green.

Also represented in the model are: Z - zooplankton (mg 1-1 in raw biomass); P - dissolved-in-water mineral forms of phosphorus (J,.lgPl-1) ; DP - phosphorus in detritus, further called detritus (J,.lgPl-1) ; DOP - dissolved organic matter (J,.lgPl-1) ; OX - dissolved in water oxygen (J,.lgOXl- 1) .

The system of the model equations has the following form:

= D(v, AJ) - mp[AJ]

+ Prod[AJ] -

Ep[AJ],

J = 1,2,3, ... , 9

(6.36)-(6.44)

~~ +K(v,Z) = a~t + K(v P

aa

t

aDOP

+ K(v _

D(v,Z) - mzZ + U x Con - ZR,

vDP,DP) = D(v,DP)

vp , P) = D(v, P)

----at + K(v,DOP)

sox

+ kp

= D(v, DOP)

+ kpDes -

t

~1

RDP - RDOP,

Prod[AJ]

+ Roor -

+ RDP + TRDOP,

TRnop,

(6.45) (6.46) (6.47)

(6.48)

L 9

- a + K(v, OX) = D(v, OX) + hAkp Prod[AJ] J=1 t

(6.49)

Lake Ladoga phytoplankton succession ecosystem model

Sec. 6.4]

211

In this system of equations only one biogen is used - phosphorus. The meaning of most of the notation is similar to the system (6.1)-(6.7). So, the term Des in equation (6.46) is analogous to the term (6.8) from (6.4), namely, 9

Des =

L

mp[AJ] x AJ + m.Z + (1 - U)Con - En.

(6.50)

J=l

Decomposition and transformation of detritus in the form of dissolved mineral phosphorus and dissolved organic matter by means of bacterioplankton activity is accounted for in equations by the terms Rn p , Rn op , characterizing the transformation rate into dissolved mineral and organic phosphorus respectively. Destruction of dissolved organic matter, DOP, is described by the term TR n op . In (6.49) fluctuations in dissolved-in-water oxygen concentration are controlled by oxygen release in the process of photosynthesis and its consumption in the processes of oxygenation. In the present model the same assumption is made about the stability the elementary composition of hydrobionts as is made in section 6.3. The biomass concentration of hydrobionts is measured in milligrams of green mass per litre. Other substances are measured as phosphorus concentrations in JlgPI- l . As in (6.9) it was supposed in the model that, if transport processes are neglected, the true phosphorus balance is in each elementaryh grid cell of the ecosystem model.

Ptotal == kp

(t

AJ + Z )

+ DP + P + DOP =

canst.

(6.51)

To fulfil (6.51) it is necessary that 9

L

Ep[AJ]

+ En

- Con = O.

(6.52)

J=l

Further, as was explained in section 6.3 the fulfilment of equality (6.52) can be satisfied by the selection of the terms constructing this equality. Boundary conditions

At the waterbody surface and the solid boundaries, the boundary conditions for (6.36)-(6.49) are similar to those of (6.1)-(6.7). They are set accordingly as boundary conditions for the system (5.1). At the waterbody surface So, when z = 0 fluxes of substances Al, A2, ... , A9, Z, DP, P, DOP, OX are prescribed; these are conditions (5.6). At the waterbody bottom, when z = -H(x,y) and there is a vertical solid boundary for all substances except OX, boundary conditions (5.9) are applied. For realization of the model we sometimes further assumed that Vx = v y = 0; at tributary sites for substances C = DP, P, DOP, OX the boundary condition (6.53) was imposed

Cisin

=

Cr,

(6.53)

212

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

and, for other substances

aCI an

=0.

(6.54)

Sin

At outlets no boundary conditions were applied for any substances when Vx = v y = o. The boundary condition for the equation (6.49) is the same as in section 6.3. These are conditions (6.11) and (6.12). Variation law of total phosphorus

When equality (6.52) is true, the equality (6.51) is also correct; then for Ptotal the variation law

:t J n

Ptotal dO =

J QPtotaJ dS - Js.: v"Ptotal dS So

-t.. +

Vn [(np + p

+ nOp), + kp

(t

AJ + Z ) ] dS

J (wDP(DP + wpP)cos(n, z) dS

(6.55)

S2

is satisfied. 6.4.2

The discrete model

In general form the discrete model for the realization of the formulated mathematical model is built in section 5.3. An approximation of the terms in equations (6.36)-(6.49), describing transport, turbulent diffusion of substances and sedimentation, is the equality (5.15). An exception is the biotic block of the model. Its construction is detailed in equation (5.16). Biotic block of the model

IIJj;

Variation of the concentration of each substance in the cell during time-step h[, without exchange of substance between cells, is written in the form: l:i.AJ == h t( -mp[AJ] . Prod[AJ] - Ep[AJ]), l:i.Z

J = 1, 2, ... ,9,

== ht(-mzZ + U· Con - ZR),

l:i.DP == ht(kpDes - RDP - RDOP), !::i.P

== h t ( -kp

(t

Prod[AJ] -

(6.56)-(6.64) (6.65) (6.66)

ZR) + RDP + TRDOP) '

(6.67)

Lake Ladoga phytoplankton succession ecosystem model

Sec. 6.4]

213

(6.68)

sox «

(6.69) Dependencies of coefficients and other terms in equations (6.56)-(6.69) on temperature, solar radiation, concentration of substances, included in the model here, as in (6.14)-(6.20), are described by a continuous piecewise linear function of the form (6.21), and also by the discontinuous functions Y~n'

f(x, Xmin, Xmax' Y~n' Y~ax) =

+ Ymax

when x < Xmin,

+ Y;ax Xmax -

Y~n (x Xmin

y;tax, when x

)

Xmin , W

h en

Xmin

< X < XmaX'

> Xmax (6.70)

Phytoplankton

The type of empirical relations used to define the coefficients P/B for phytoplankton will be presented sequentially. Let us start with P/BT : P/BT[AJ] =f(T,Tmin,Tmax,P/BTfAn,P/B~x), J= 1,2, ... ,9,

where parameters are given in Table 6.2. The value of P/Bs for all complexes is the same as in (6.23). Values P/BA [PhJ] are defined in the following manner:

s

P/BA[AJ] = f(AJ, O,AJmax, P/B ax, P/B~n),

where p/Br;m = I.Z day"

s

P/B ax = 10 day"

AJmax = 2.0mgl- 1,

when J= 1,2,3,4,

AJmax = 0.5mgl- 1,

when J = 6,8,

AJmax = 0.6mgl- 1,

when J = 5,7,9.

The value of P/Bp for each complex is defined with the continuous function: P/Bp[AJ] = g(P, Pmin[AJ]" Pmax[AJ], 0, P/Bpax[AJ]),

214

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

Table 6.2. Coefficient for determination of PIBT[AJ] (day:") for the phytoplankton community. Tmin,OC

Tmax,oC

0.1-3 5 6 8 8 10 10 15 10

Al A2 A3 A4 A5 A6 A7 A8 A9

8 25 15 15 15 20 16 20 16

PIB?

PIB~

0.1 0 0 0 0 0 0 0 0

0.6 0 0 0 0 0 0 0 0

PIB~

PIBJ?}~

4 12 12 12 12.5 12 12.5 12 12.5

0 12 12 12 12.5 12 12.5 12 12.5

where

gt», Xmin, x max , Ymin, Ymax) when x < Xmin,

Ymin, Ymin

eYmax-Ymin -

+ In [ 1 + X

1

max - Xmin

(x -

]

Xmin) ,

when

Xmin

< X < X max ,

when x > X max '

Ymax,

(6.71)

It is worth mentioning here that the function (6.71) may be used instead of (6.70). During the model calibration it was found that continuous piece-wise linear approximation of dependency PIBp on mineral phosphorus concentration 'does not work'. As a consequence the more complex 'curve with saturation' was used. It should be pointed out that the coefficients in Tables 6.2 and 6.3 are obtained on the basis of data partially published in other works (Petrova, 1990, 1996; Lake Ladoga ... , 1992). The primary production of phytoplankton complexes is determined as: PIB[AJ] = min(PIBT[AJ], PIBs, PIBp[AJ], PIBA[AJ]), htProd[AJ] = min(htPIB[AJ](AJ + Amin)PL, p. PLlkp ) , A min = 0.05mgl- 1 . (6.72) Table 6.3. Values of coefficients used for the calculation of PIBp[AJ] (day ") for the phytoplankton community. J PIBpax[AJ] Pmax[AJ] Pmin[AJ]

1.6 40 1.5

2

3

4

5

6

7

8

2.7 30 2.6

17.3 50 4

2.6 30 1

18.9 45 3.2

48.2 50 1.4

5.1 50 1

28.3 60 1.4

9 4.8 45 0.95

Lake Ladoga phytoplankton succession ecosystem model

Sec. 6.4]

215

Table. 6.4. Values of coefficients used for the calculation of mp[AJ] for the phytoplankton community. J

0.1 4

2,4

6,7,8,9

3,5

0.1

0.01 0.1

0.05 0.6

1

Here PL is specified by the formula (6.25). The coefficient PL in (6.72) defines the share of the elementary cell where photosynthesis occurs. The thickness of the photosynthesis layer PL' is governed by water transparency, which, in turn, apart from its constant background value, depends also on the shadowing effect of phytoplankton and detritus: (6.73)

PL' = f(WG, Sesmin, Sesmax, Lmax, Lmin), where 9

WG =

L

AJ + DP/kp ,

J=1

Sesmin = 1 mg 1-1,

Sesmax = 8 mg 1-1, Lmax = 8 m,

Lmin = 2 m.

Mortality coefficients for AJ are defined as follow: mp[AJ] = f(AJ, AJmin, AJm ax , mpinmrpax), = 1,2, ... ,9, mpin = 0.05 day ",

mrpax = 0.2 day":

The values of AJrnm and AJm ax are given in Table 6.4. Zooplankton The growth rate in zooplankton biomass in (6.65) is defined similarly as in (6.30) U· Con = U· TK· (Z + Zmin) ·f(PD, Fmin , Fm ax , 0, Conmax), (6.74) Here U is the coefficient for nutrition assimilation by zooplankton, U = 0.75. The non-dimensional coefficient TKis defined with formula (6.31). In (6.74)fis the share of phytoplankton and detritus filtered by zooplankton during a day. Herein

216

Ecosystem models of Lakes Ladoga and Onego 9

PD =

L

~[J]AJ + ~DDP/kp

J=l

[Ch.6

9

+ h, L

~[J]Prod[AJ],

[PD] = mg l",

J=l

Coefficients ~[J] determine the share of 'eatable' part of the specific phytoplankton group; ~D is the same for detritus: ~[1] = ~[2] = ~[3] = ~[4] = ~[6] = ~[8] =

10%,

68%,

~[5] = ~[7] = ~[9] =

62%,

~D =

12%.

Zooplankton mortality coefficients are defined in this model as in section 6.3 by the formulae (6.28) and (6.29). Finalizing the description of zooplankton interaction with phytoplankton and detritus, the construction of terms Ep[AJ] in (6.56)-(6.64) and ED (6.50) and, respectively, (6.66) should be defined. For this purpose the hypothesis is adopted that the zooplankton grazing rate of 'eatable' parts of phytoplankton and detritus is proportional to their concentrations Ep[AJ] = EJ· ED =

~[J](AJ

+ htProd[AJ]),

J = 1,2, ... ,9, (6.75)

EDZ~DDP/kp.

Then according to (6.52), assuming equality of all coefficients El = E2 = ... = E9 = E DZ = E, we will get that Con

E= -------------9

L

(6.76)

~[J](AJ + htProd[AJ]) + ~DDP/kp

J=l

Detritus

Variation of detritus concentration is determined in the biotic block of the model by the equation (6.66). All the terms on the right-hand side of this equation are already defined, except R DP and RD OP , which describe detritus destruction and its transformation either into dissolved mineral phosphorus, or dissolved organic matter (Modern state . . . , 1987): R DP = DPf(T, T~, T~:'x,Rtffp,RD~X), P TDOP R min R max ) T DO R DOP = DPf(T' m i n ' max, DOP, DOP, [RDP] = ug Pday", [RDOP] = ug Pday", D9P = T D!, DP 5°C R min 0 05 d -1 R min min T min = , DP = . ay, DOP = R DP, T mm nuns max DP max max DO P DP -1 R DOP = R DP, T max = T max, T max = 15°C, R DP =0. 21 d ay,

Lake Ladoga phytoplankton succession ecosystem model

Sec. 6.4]

217

The term TRn op in (6.67) and (6.68) describes the regeneration of mineral phosphorus by bacterioplankton from dissolved organic matter. The construction of this term is extremely simple TR Dop = 8· DOP,

8=0.01.

The term ZR in (6.65) in the described model is determined as in section 6.3 in accordance with (6.34). Oxygen

Processes linked to oxygen OX([OX] = mg l"), include its release during photosynthesis and consumption during oxygenation processes. Let us write down the values of parameters, included in (6.69): hA = 40

X

10-3

2.6mg OX/~gP,

hz = hDP = h~op = hI/6p = h».

In this way, all terms in the right-hand sides of equalities (6.56)-(6.69) are defined. Total variation of substance contents in the discrete models for the cell IIJj; is determined by equalities (5.17). The discrete analogue of the variation law for total phosphorus for the described discrete model in accordance with (5.18) has the following form (Astrakhantsev et al., 2003):

L

(Ptotal)iikOiik

(Xi lYjJZk)EO

L

(PtotaDiikOiik

+ h,

(XilYjJZk)EO

- h, - ht

(Xi'Y~ESin [q( (kp

t

L

(QPtoto/)ijOIIij - h,

(XilYjJZk)ESO

L

[q . Ptotal]iik

(Xi lYjJZk)ES out

AJ+kpZ) + (DP+ P+DOP))

J

ijk

L _[QZfkij-I/2(DP)iilkij + QZi,kij-I/2Pii,kij (XilYjJZk)ESO

where -kij is the number of the lowest node under the node (xi'Yi' 0) E So. The rules of binomial [q x C]iik calculations at river sites are described in detail in section 5.3.5.

218

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

6.4.3 Model verification, computation experiments The model verification was based on observation data on Lake Ladoga during 19841990 (Lake Ladoga ... , 1992). The simulated climatic circulations discussed in Chapter 3 were used in the computation procedure. Phosphorus loading on the waterbody in our calculations was 6100tPyear- 1, and equalled the mean value of annual phosphorus incoming in 1984-1990 (Fig. 1.14). Phosphorus loading comes from tributary inflow, precipitation, and waste waters from industrial enterprises, paper mills, livestock farming complexes, municipal waste water treating plants. It is considered that the loading consists of dissolved-in-water mineral phosphorus, detritus and dissolved-in-water organic matter. The lake was divided into four zones in the process of model verification (Fig. 1.6). The aim of the computational experiment was to build a periodical solution at an indicated phosphorus loading. Simulation was performed for a 15-year physical time series until an all-year-round regime of the lake ecosystem functioning was obtained, corresponding to the mean phosphorus loading value during the 1984-1990 period. Computation results were compared with observation data. Coincidence of the simulated and the observed total phosphorus spatial distribution is one of the most important measures of the model adequacy. Simulations of total phosphorus concentration results and its observed mean values for the 1984-1999 period in four lake zones during the open water period are shown in Table 6.5 (Lake Ladoga ... , 1992, Table 19, p.79). Comparison of modelling results and observation data shows that considerable differences occur in summer and autumn in the lake coastal zone only (zone I). The zone volume does not exceed 3% of the total waterbody volume of the lake. Table. 6.5. Average concentration total phosphorus (J.lgPI- 1) in Lake Ladoga under a loading of 6100 t Pyear" (1, data; 2, results of modelling). Spring May-June

Limnic zone

Summer July-August 2

I II III IV

2

31.6 25.4 22.7 21.1

30 24 20 20

Autumn September-October

33 23 21 21

26.2 23.9 23.1 21.7

2 24.4 22.6 22.8 22.5

30 24 21 21

Table 6.6. Carry out of total phosphorus by River Neva (t Pyear") from Lake Ladoga. ~ear

Data Model

1959-1962 40 50

1976-1979 1981 1982 1984 1985 1986 1987 1988 1992-1995 1996-2000 040 300

140 940 170 460 530 840 340 350 480 320 210 180 280 290

620 045

320 520

Lake Ladoga phytoplankton succession ecosystem model

Sec. 6.4]

219

-.- .... - - - "-'I

---

2

Fig. 6.15. Annual dynamics of raw total biomass of phytoplankton (mg l") in the Lake Ladoga epilimnion (results of modelling).

In Table 6.6 observation data about total phosphorus excretion by the Neva River and computation results can be found (Lake Ladoga . . . , 1992; Kondratyev et al., 1997; Lake Ladoga . . . , 2002). Comparison of the data presented in Table 6.6 confirms the model adequacy, at least from the point of view of total phosphorus turnover reconstruction in the waterbody, e.g. the balance of phosphorus income into the waterbody, its settling in bottom sediments and its excretion with river flow. The accuracy, i.e, the difference between observed and simulated data, excluding the 1992-1995 time period, does not exceed 20%; moreover for the most part of the period 1962-1995 the error does not exceed even 10% . The results On phosphorus excretion with the Neva River were obtained in the process of the main computational experiment for succession model verification. That was an experiment On the reproduction of the evolution of the Lake Ladoga ecosystem during the 19622005 period with changing phosphorus loading (Fig. 1.14). In Fig. 6.15 a graph of mean summarized annuaol fluctuations in phytoplankton raw biomass in the epilimnion for selected years of the period considered is presented. Comparison of the data received for different years shows that the model correctly quantitatively reflects phosphorus loading fluctuations in the waterbody. 6.4.4

Reproduction of phytoplankton succession

In this section the results of the 'evolution' computational experiment will be discussed in more detail from the point of view of succession reproduction. It is

220

[Ch.6

Ecosystem models of Lakes Ladoga and Onego

worth mentioning that the phosphorus loading in the computational process was changing according to observation data (Fig. 1.14) and the climatic circulation described in Chapter 3 was applied. It should be mentioned that, during verification of succession modelling results for Lake Ladoga, the lack of phytoplankton observation data was experienced. It resulted from the fact that, during the vegetation period from year to year, no more than one survey was accomplished. Nevertheless, quantitative estimates in particular allow us to obtain reliable comparison results for modelled and observed data. For the whole lake, or for the epilimnion to be more precise, it turned out to be impossible to compare phytoplankton simulation results. But they appeared to be real for the Neva River outlet. The results of diurnal phytoplankton observations over four years - 1981, 1982, 1987 and 1988are presented in the literature (petrova, 1996). For each phytoplankton complex (AJ, J = 1,2, .. . , 9) computational results and observation data of raw biomass annual fluctuations, both of the total phytoplankton and of the different complexes, are available for the Neva River outlet. Provision of data for the various complexes is different. The most data available for total phytoplankton. In Fig. 6.16 the annual dynamics of modelled total phytoplankton raw biomass on a logarithmic scale is compared with observation data. The comparison shows that modelling results differ quite noticeably for measured data; nevertheless, maximum values in general are reproduced with satisfactory accuracy along with timing of these events. With much less accuracy minimum phytoplankton

t r.t

•

1

....

Fig. 6.16. Annual dynamics of raw total biomass of phytoplankton (mg r") at the head of River Neva.

Lake Ladoga phytoplankton succession ecosystem model

Sec. 6.4]

221

Fig. 6.17. Annual dynamics of the raw biomass of Aulacosira islandica (mg l:') at the Neva

River head.

.

+

+

4 "9'

~ .

..

- ... "

...

t

...

..

.

••

....

+ •

Fig. 6.18. Annual dynamics of the raw biomass of Fragilaria crotonensis (mg r") at the Neva

River head.

222

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

Fig. 6.19. Annual dynamics of raw the biomass of Oscillatoria tenuis (mg lv") at the Neva River head.

concentrations are reproduced; but that is not as essential for predicting phytoplankton development under conditions of anthropogenic eutrophication as defining correctly the upper limit of waterbody productivity . The modelling results and observation data for three out of the nine phytoplankton complexes in the Neva River outlet are shown in Figs 6.17-6.19. Analysis of these graphs (for nine complexes these graphs could be found in Rukhovets et al., 2003) shows that the model satisfactorily reconstructs the annual dynamics of the raw biomasses of the phytoplankton complexes. To a greater degree it relates to the reproduction of maximum values and their timing. Returning to the annual phytoplankton dynamics in 19622000, it should be mentioned that, (Fig. 6.15) along with phosphorus loading, the increase in both spring and autumn peaks appeared after 1970. Structural changes in the phytoplankton community are presented in Figs 6.20 and 6.21. The position of the Aulacosira islandica complex within the community did not change, in fact; its productivity has grown only along with the increase in production of the whole community. The relative structure of the diatom complexes did not change; their productivity gradually increased, achieving its maximum in 1982-1983, and started to decline slowly; only after 1991 did the declining trend become more obvious. The slight growth by 2005 is related to phosphorus loading growth in 2004-2005 (Fig. 1.14). The raw biomass dynamics of the Tribonema affine complex after 1970 is such that, jointly with the Aphanisomenon flos-aquae complex they become the dominant complexes among the blue-greens and yellow-greens. Thus, as a whole, the main phytoplankton community structure change affected the blue-green complexes

Sec. 6.4]

Lake Ladoga phytoplankton succession ecosystem model

223

Fig. 6.20. Average annual dynamics of the biomass (mg l") of the diatom complexes of the Lake Ladoga epilimnion (results of modelling).

--_.

.......

Fig. 6.21. Average annu al dynamics of the biomass (mg 1-1) of yellow-green and blue-green complexes of phytoplankton in the Lake Ladoga epilimnion (results of modelling).

224

[Ch.6

Ecosystem models of Lakes Ladoga and Onego

mg/l

4

3) 16.

.1% 1

b) 16.06.1970

o

4

o c) 16.06.19&.2

~)

16. .1991

4

o =) 16.

.2()()()

f) 16.06 .2005

Fig. 6.22. Integral distribution of the total biomass of phytoplankton in the Lake Ladoga epilimnion (results of modelling).

Lake Ladoga phytoplankton succession ecosystem model

Sec. 6.4]

mgl

225

Ilg 1

11 1.

15 1
9 8

.,

~

7

e

J

•

2

1 1

(I .~

:.I

3

(I

(I

a)

b)

Fig. 6.23. Results of modelling the distribution of (a) the total biomass of phytoplankton (mg l") in the epilimnion 01.06.1982; and (b) the chlorophyll a concentration (ug l") in June 1982 (field observations)

.2

0.8

0.0

Fig. 6.24. Dynamics of the annual average biomass of phytoplankton (mgl- I ) in the Lake Ladoga epilimnion for the period 1962-2005.

226

Ecosystem models of Lakes Ladoga and Onego

[Ch.6

during lake eutrophication, as shown in Fig. 6.21. So, according to Fig. 6.21, the role change of Aphanisomenonflos-aquae during the 1962-2005 period was observed. The total raw biomass distribution in the epilimnion for the several years 1962-2005 is shown in Fig. 6.22. The results of a chlorophyll a survey compared with simulated phytoplankton distribution is presented in Fig. 6.23. It is clear that the distributions are similar. Finally, it should be noted that the dynamics of the mean annual values for total phytoplankton biomass (Fig. 6.24.) correlates significantly with annual phosphorus loading dynamics (Fig. 1.14). Conclusion

The main tendencies of phytoplankton succession in the 'evolution' experiment are reproduced. Modelling results confirm the opinion of the limnologists (Petrova et al., 2005; Timakova et al., 1999), who studied eutrophication processes experimentally, in 'field' experiments, that the increase in phosphorus loading in the waterbody is the main factor controlling the succession process. It is interesting to mention that in the 'evolution' experiment it was possible to separate the influence of the interannual variability weather conditions on the eutrophication process from other factors. The succession model adequately reproduces phosphorus turnover in the waterbody ecosystem. With application of the model it is possible to complete information on spatial distribution of substances considered in the model, especially for those periods that lack of this information. As with the Lake Onego ecosystem model, the phytoplankton succession model may be used as a tool within the frame of a decision-support system for water-resource management in the Lake Ladoga basin, for studies of the lake limnic processes and for predicting possible changes in the lake ecosystem under human and climatic impacts.

7 Estimating potential changes in Lakes Ladoga and Onego under human and climatic impact

Interest in studies of the consequences of climate change for different regions in Russia, and in particular for its northwest, has grown considerably since the signing of the Kyoto Protocol by the Russian Federation. This fact emphasizes the importance of studies on estimates of possible changes in large stratified lakes ecosystems - the largest freshwater reservoirs. In the northwestern part of Russia these are Lakes Ladoga and Onego. In studies of anthropogenic eutrophication processes in Lake Ladoga using mathematical modelling methods, the problems of the influence inter-annual variability in weather conditions on the functioning of the lake ecosystem was considered by the authors. In publications (Astrakhantsev et al., 1996; Menshutkin et al., 1998) it has been shown that in 1962-2000 the major factor controlling the lake ecosystem transformation was changes in the phosphorus loading. Inter-annual variability in weather conditions influenced the annual dynamics of phytoplankton biomass insignificantly. In this chapter, the results of further studies are, in fact, the development of previous researches enumerated in the abovementioned publications. The main aim of these studies is to obtain estimates of possible changes in the ecosystems of Lakes Ladoga and Onego under the possible climate changes within their catchments at different anthropogenic loading levels. Year-round functioning of the lake ecosystem is determined by the dynamics of the physical factors of the waterbody - temperature, current velocities, water transparency, mixing conditions, gas exchange at the water-atmosphere interface, and biogenic concentration levels incoming into the lake from different sources: tributary inflow, industrial and municipal sewage waters and bottom sediments. The climatic circulation in Lakes Ladoga and Onego constructed in Chapter 3 was applied to reproduce the ecosystem functioning in Chapter 6. For each lake, four versions of the year-round atmospheric circulation were constructed, in order to estimate changes in the ecosystems of Lakes Ladoga and

228

Estimating potential changes in Lakes Ladoga and Onego

[Ch.7

Onego under feasible climate changes due to global warming within the lake catchments, as was shown in Chapter 4. Thus, for each lake there are five climate circulations: climatic, warm, warm with high river inflow, warm with low river inflow and cold (Chapter 4). In order to estimate possible changes in the lake ecosystems under climate changes over their catchments, year-round ecosystem functioning was simulated for each of the constructed circulations. The ecosystem models of Lakes Ladoga and Onego presented in Chapter 6 were applied.

7.1 MODELLING CHANGES IN THE LAKE LADOGA ECOSYSTEM UNDER DIFFERENT SCENARIOS OF CLIMATE CHANGE AND ANTHROPOGENIC LOADING 7.1.1 Modelling changes in the ecosystem under different scenarios of climate change Description of computational experiments

In developing Lake Ladoga ecosystem models (Menshutkin et al., 1998; Rukhovets et al., 2003; Astrakhantsev et al., 2003), the lake ecosystem functioning data averaged over the 1984-1990 period were used for their verification (Lake Ladoga ... , 1992). Mean phosphorus loading during 1984-1990 equals 6100 t P total year" . For this particular loading value, computational experiments under changing hydrophysical conditions in the waterbody were conducted. For every type of circulation the periodic solution of the discrete model, approximating the phytoplankton succession mathematical model was built (see Chapter 6). The physical time for periodic solution construction was not less than 15 years. Analysis of modelling results

Annual dynamics of the total phytoplankton raw biomass in the epilimnion for all five circulations is shown in Fig. 7.1(a). For three warm circulations corresponding to possible climate change during global warming, phytoplankton biomass changes occur mainly in the autumn. This corresponds with the fact that noticeable changes in the thermal regime are also observed in autumn (Fig. 4.13). The reduction of phytoplankton biomass in the autumn for warm circulation conditions, compared with biomass calculated under climatic circulation conditions (Fig. 7.1(a)), can be explained by the fact that Aulacosira islandica algae develops in water temperature not higher than 8°C (Table 6.2). That is why water temperature exceeding 8°C in autumn might lead to a decline in biomass, as algae is the main contributor to phytoplankton biomass in spring and autumn. In autumn, under the cold circulation condition, this algae provides more input into the total phytoplankton biomass (Fig. 7.1(a)).

Sec. 7.1]

Modelling of Lake Ladoga ecosystem changes 229

-- I

- +- ,

----- .3

-- 4

2

... a mol "!-

--1 _ 4-

..

-- ~

- - ft

+-----t_ ---+-- ..

til 01

3'.I.[J'I M 12

l~oJJ

1[I.tJl

r;e~

)1~

2J..o:z: ISo.Dl'

IJ III

oar~

1L'.lto

71 I

Z 11

12

ltom

~

b

Fig. 7.1. Annual dynamics in Lake Ladoga (a) of the raw biomass of total phytoplankton, (mg l"), and (b) of the raw biomass of zooplankton (mg l"); results of modelling under a phosphorus load of 6100t Ptotal year:" : (1) climatic circulation , (2) warm circulation with increased inflow, (3) cold circulation, (4) warm circulation , (5) warm circulation with decreased inflow (Rukhovets et al., 2006a, Fig. 3).

230 Estimating potential changes in Lakes Ladoga and Onego

[Ch.7

rno'

...

r

"~IY

IZ.""

I

ll1l

., 11 I

a

l

1M If

UoJ:I

IXI'" I Ul . ' 11 • 12 tl(lt

b Fig.7.2. Annual dynamics of the raw biomass of total phytoplankton, (mg l"), in the offshore zone of Lake Ladoga (a) and Volkhov Bay (b); results of modelling under a phosphorus load of 6100t Ptotalyear- 1: (1) climatic circulation , (2) warm circulation with increased inflow, (3) cold circulation.

Modelling of Lake Ladoga ecosystem changes

Sec. 7.1]

231

Conditions of warm circulation are more favourable for zooplankton, whereas, under cold circulation conditions, zooplankton biomass noticeably declines (Fig. 7.1(b)). Thermal regime variations influence zooplankton more effectively than phytoplankton. Examination of phytoplankton development dynamics in different parts of the lake enables us to estimate the spatial variety of conditions, mainly related to thermal regime differences (Fig. 7.2). For example, in the central part of the lake, spring bloom occurs approximately one month later than in the shallow Volkhov Bay. Distinctions in phytoplankton productivity, under steady state annual phosphorus loading obained in computational experiments, are determined by variations in the hydrothermodynamic regime in the lake. These distinctions are less noticeable than those related to changes in phosphorus loading. This fact is reinforced by limnologists on the basis of long-term studies of phytoplankton in Lake Ladoga (petrova, 1982; Lake Ladoga ... , 1992; Modern State ... , 1987) and also in numerical experiments with computer models. Comparison of Figs 7.1 and 6.15 shows that variations in phosphorus loading have a stronger effect than changes in climate conditions. Adequate Ptotal distribution over the waterbody is one of the important characteristics in lake ecosystem functioning. In the process of model verification, this characteristic is first compared with observation data. As the results of warm circulation experiments have shown, abiotic conditions in the lake differ insignificantly for warm circulations; here the spatial Ptotal distribution is considered only for warm, cold and climatic cases. In Table 7.1 Ptotal concentrations are presented, averaged over the lake zones (Fig. 1.6), under a loading of 6100 tPtotal year"! for the three mentioned circulations and compared with observations (Lake Ladoga ... , 1992). The results of calculations for climatic and warm circulations (Table 7.1) differ, in general, not more than 0.5 JlgPI- l . For cold circulation the differences are somewhat greater. Essential differences between computation results and observations are in zone I in summer and autumn only, which probably indicates the insufficient grid resolution in this zone. The non-satisfactory reproduction of the process of thermal Table 7.1. Average concentrations (J.lgI-1) over the lake zones (Fig. 1.6), under a loading of 6100 t P total year"! for three circulations (warm, climatic, cold) compared with observations (Lake Ladoga . . . , 1992) Limnic zone

Spring: May-June

Warm Climatic Cold I

n

m

IV

29.7 24.6 21.6 20.2

30.9 23.8 21.1 19.9

31.7 23.9 20.3 19.2

Summer: July-August

Data Warm Climatic Cold 30 24 20 20

24.3 22.2 22.4 21

24.3 21.9 21.9 20.7

23 20.9 21.7 20.3

Autumn: September-october

Data Warm Climatic Cold 33 23 21 21

23.4 21.4 21.9 21.9

23.1 21 21.5 21.6

22.4 20.2 20.9 21.4

Data 30 24 21 21

232

Estimating potential changes in Lakes Ladoga and Onego

[Ch.7

bar formation and development could also be a reason for that. But it should be mentioned once again that the share of zone I in the lake volume is only 3%. Conclusion

The results of computational experiments show that the influence of abiotic conditions on ecosystem functioning under a fixed phosphorus loading in the lake is not essential. 7.1.2

Modelling changes in the ecosystem under different scenarios of climate change and changes in the level of anthropogenic loading

Not only the influence of climate change was considered in modelling procedure, but also, the influence of phosphorus loading alterations on Lake Ladoga ecosystem functioning. Scenarios in computational experiments

Work by Rukhovets and Filatov (2003) was conducted to predict, on the basis of numerical experiments the development of the Lake Ladoga ecosystem in a shortterm perspective for the period 2001-2005. Computational experiments (Rukhovets and Filatov, 2003) were conducted for conditions of climatic and warm circulations. Warm circulation, as well as climatic circulation, was constructed for mean perennial water inflow conditions in the lake (see Chapter 4). Calculations were made for two scenarios of phosphorus loading changes, selected on the basis of previous studies (Menshutkin and Vorobyeva, 1987; Astrakhantsev et al., 1996). It was shown with the usage of ecosystem models that keeping external loading at a level below 4000 t P total year" preserves the lake in weakly mesotrophic conditions. Phosphorus loading over 7400 t P total year"! leads to a mesotrophic state with a tendency towards transition to a eutrophic one. Phosphorus loading in 1996-2000 was lower than 4000 t P total year-I. In this connection for the first scenario, called optimistic, the phosphorus loading in 2001-2005 was set at the level of 4000 tPtotal year-I, and for the second scenario, called critical, the phosphorus loading changed linearly from 3935 to 7400tPtotalyear-l (Rukhovets and Filatov, 2003). Modelling results in the abovementioned publications have shown that, when the phosphorus loading up to 2005 is kept at the level of 4000tPtotalyear-l, the lake ecosystem state is stabilized. When the phosphorus loading grows up to the level of 7400tPtotalyear-l, the Lake Ladoga ecosystem returns to the state observed at the beginning of the 1980s. It is worth recalling that at the beginning of the 1980s the lake turned into a mesotrophic state from the oligotrophic one that was observed until the beginning of the 1970s (Lake Ladoga ... , 1992). For the selection of phosphorus loading change scenarios the authors here used similar assumptions. The lake ecosystem state at the end of 2000, calculated with the

Modelling of Lake Ladoga ecosystem changes

Sec. 7.1]

233

model for the period of 1961-2000 (Rukhovets et al., 2003; Astrakhantsev et al., 2003), was adopted as the initial scenario. It is worth mentioning that the reconstruction of the transformation of the Lake Ladoga ecosystem in section 6.4 gave results that were close for the year 2000 (see Fig. 6.15 and modelling results in Astrakhantsev et al., 2003, p. 261, Fig. 53). To reproduce ecosystem functioning (Astrakhantsev et al., 2003) the annual Lake Ladoga climatic circulation and data for phosphorus loading on the waterbody in 1961-2005 (Fig. 1.14) from (Lake Ladoga . . . , 1992; Rumyantsev and Drabkova, 2002) were used. The same two versions for phosphorus loading changes were selected. In the first scenario, the phosphorus loading for the period 2010-2015 was set at the level of 4000tPtotalyear-1. Therewith it is supposed that phosphorus loading is within the limits which are favourable for preserving ecosystem stability (Menshutkin and Vorobyeva, 1987; Rukhovets and Filatov, 2003, pp.23-51). The selection of this time interval (15 years) is explained by the fact that during this period, as follows from the numerical experiments in Chapter 6 and in the work of Astrakhantsev et al. (2003), the periodic annual regime of Lake Ladoga ecosystem functioning develops. In the case of the other scenario, phosphorus loading in 2001-2005 grows linearly from 3935 to 7400tPtotalyear-l, and in 2006-2015 it stays at the level of 7400tPtotalyear-1. Actually, simulation results, as we expect, represent the situation in the Lake Ladoga ecosystem which could be observed in the lake by the middle of the twenty-first century. By this means, for numerical experiments a set of scenarios was selected (Table 7.2). For each scenario the type of circulation used in the succession model and a version for change in external phosphorus loading are given. Modelling results analysis

The results of Lake Ladoga ecosystem transformation simulations for the 1961-2000 period under climatic circulation conditions and variable phosphorus loading (Fig. 1.14) are presented in Chapter 6. For better presentation and estimation of possible Table 7.2. Scenarios of numerical experiments for external phosphorus loading (in tons) for 2001-2015. Scenario

Circulation

External phosphorus loading, tons

2001 1 2 3 4

Warm Warm Warm with increased inflow Warm with increased inflow

2002

2003

2004

2005

3935

4805

4000 5675 4000

6545

7400

3935

4805

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. .

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234 Estimating potential changes in Lakes Ladoga and Onego

[Ch.7

changes in ecosystem functioning under varying abiotic factors and phosphorus loading, the realization of scenarios 1-4 are compared in Figs. 7.3-7.6 with modelling results from Chapter 6. Compared with 1962, phosphorus loading (Fig. 1.14) has grown by 3.3 times comparing with 2430 tPtotal year" in 1962 and 81ootPtotalyeacl in 1982. The lake ecosystem reaction was such that maximum values (spring bloom peak) of total phytoplankton raw biomass increased by more than two times (Fig. 7.3): from 1.1mg l"! in 1962 to 2.9mgl in 1982. Phosphorus loading reduction after 1991 has led to a decline in maximum values by 2000 to the values of 2.1 mg l"! (by 30%). Annual dynamics of the total phytoplankton raw biomass for scenario 1 stays at the level of the year 2000 during the whole period 2001-2015 (Fig. 7.3). In the third scenario at the same phosphorus loading level as in scenario 1 by 2015 the reduction of total phytoplankton raw biomass maximum values is observed (approximately by 10%) compared with 2000 and 2015 for the first scenario (Fig. 7.4). The explanation for this phenomenon has already been given. In fact, for warm circulation with high inflow volume, water temperature in the epilimnion during the vegetation period is over 8°C, and, for the largest algae species, Aulacosira islandica, the development is limited by temperature increase above 8°C. As can be seen in Figs 7.5 and 7.6, by 2015 the annual mean value of Aulacosira islandica biomass for the third scenario declines compared with scenario 1.

Fig. 7.3. Annual dynamics of the raw biomass of total phytoplankton (mg l'") in the epilimnion. (1) 1962; (2) 1982; (3) 2000; (4) 2005-2015, scenario 1; (5) 2005, scenario 2; (6) 2010, scenario 2; (7) 2015, scenario 2 (model results).

Modelling of Lake Ladoga ecosystem changes

Sec. 7.1]

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The lake ecosystem response in the case of the second scenario shows that maintenance of phosphorus loading at the level of 7400t P total year"! over a long time leads to these maximum values (spring peak) of total phytoplankton raw biomass (Fig. 7.3) reaching the values that were observed in 1982, when phosphorus loading was the highest for the whole period of 1961-2000 (8100 t P total year:"). The fourth scenario realization shows that the influence of the increased water temperature values leads, as in the case of the third scenario, to some total phytoplankton raw biomass reduction, as compared with the second scenario. This occurs during the period close to the spring peak and, to a greater extent, during the autumn peak (Figs 7.3 and 7.4). During the autumn peak there is, in fact, no difference in maximum values of total phytoplankton raw biomass, for the second scenario, between years 2015 and 1982 (Fig. 7.3), whereas, for the third scenario, this difference is not less than 15% of the autumn peak in 1982 (Fig. 7.4). The changes in the phytoplankton community structure are presented in Figs 7.5 and 7.6. The comparison of Aulacosira islandica mean annual biomass dynamics for the second and fourth scenarios shows that biomass grows faster by the year 2015 in the second than in the fourth scenario. The structure of diatoms does not change, mean annual values of algal biomass increase for the second and fourth scenarios only, and for the first and the third scenarios these values are stabilized. Changes in phosphorus loading have noticeable influence on the phytoplankton community

236 Estimating potential changes in Lakes Ladoga and Onego

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Modelling of Lake Ladoga ecosystem changes

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238

Estimating potential changes in Lakes Ladoga and Onego

[Ch.7

structure; so, mean annual values of Woronichinia naegeliana and Afanizomenon flosaquae biomasses vary considerably among all four scenarios (Figs 7.5 and 7.6). The distinctions related to phosphorus loading changes are much more obvious than those related to to the type of circulation variation for which the numerical experiments were conducted. Conclusion

The results of the modelling of the functions of the Lake Ladoga ecosystem based on different circulation types has shown that the largest changes in the ecosystem were observed in the case of warm circulation with increased inflow. When phosphorus loading is at the level of 4000tPtotalyear-l the lake status can be characterized as weakly mesotrophic. When phosphorus loading increases up to the critical level of 7400 tPtotal year", the greatest differences are observed in the case of warm circulation and by 2015 the lake returns to its 1982 state when phosphorus loading was at its highest level of 8100 t P total year": The level of anthropogenic loading is a decisive factor in determining the state of the large stratified Lake Ladoga ecosystem. Climatic variations, as our estimates show, only enhance or weaken to some degree the role of the anthropogenic factor. With the increased attention being paid to the problem of global climate warming, the effects of climatic variations on the biosphere in general and on its components are of particular interest to those studying large freshwater lake ecosystems as the reservoirs of drinking water. That is why computational experiments aimed at estimating possible changes in lake ecosystems appear to be important. These studies should be continued when more accurate climate change forecasts over the Lake Ladoga catchment are produced and more sophisticated models are available. 7.2 MODELLING CHANGES IN THE LAKE ONEGO ECOSYSTEM UNDER DIFFERENT SCENARIOS OF CLIMATE CHANGE AND ANTHROPOGENIC LOADING The estimates of possible changes in the Lake Onego ecosystem under the influence of possible climate changes over the lake catchment will be accomplished applying a slightly different scheme than for Lake Ladoga. For Lake Onego, as for Lake Ladoga in Chapter 4, four circulations were constructed for the estimation of possible variations in the lake hydrothermodynamic regime resulting from climate changes over its catchment due to global warming. For each of five circulations the authors have reproduced the annual functioning of the Lake Onego. Description of the computational experiments

The first group of numerical experiments was devoted to estimates of possible changes in the Lake Onego ecosystem under assumed climatic circulation. Since the

Sec. 7.2]

Modelling changes in the Lake Onego ecosystem

239

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240

Estimating potential changes in Lakes Ladoga and Onego

[Ch.7

annual variation of specific heat storage of the waterbody for the three warm circulations varies slightly, the calculations were made for warm circulation only with two phosphorus and nitrogen loading combinations: 1003tPtota/year-' and 17739tNtotalyear-', and 786tP totalyear-' and 15051 tNtota/year-'. The results of these experiments, in comparison with the calculations under climatic circulation conditions, are shown in Fig. 7.7(a). It is worth mentioning that under conditions of warm circulation for both loading scenarios, spring phytoplankton biomass maxima are slightly higher than under climatic circulation, and autumn maxima and summer biomass are essentially lower than under warm circulation conditions (Fig. 7.7(a)). This is explained, as for Lake Ladoga, by the fact, that the largest contribution to biomass is made by algae preferring low water-temperature conditions in summer and autumn (for example, Aulacosira islandica). The zooplankton response to water-temperature fluctuations is different: under warm circulation conditions zooplankton biomass is higher for both loadings (Fig. 7.7(b)). In Figs 7.8-7.11 the annual variations of dissolved mineral phosphorus, dissolved mineral nitrogen, detrital phosphorus and detrital nitrogen are presented. These dynamics correspond with phyto- and zooplankton biomass dynamics.

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Sec. 7.2]

Modelling changes in the Lake Onego ecosystem

241

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242

Estimating potential changes in Lakes Ladoga and Onego

[Ch.7

~ ~

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Fig. 7.11. Annual variations of detrital nitrogen in the epilimnion of Lake Onego under climatic circulations and loadings: solid line, 1003 tPtotalyear- 1 and 17739 tNtotai year"! , dotted line, 786tPtota1yeac' and 15051 tNtotalyeac l ; lines with +, calculated under warm circulations with the same loadings.

To study changes in the Lake Onego ecosystem under possible future increase in anthropogenic loading enhancement and variation in climatic conditions over the lake catchment, the second group of numerical experiments was conducted. In these experiments, for each of five constructed Lake Onego circulations under two hypothetical versions of biogenic loading, calculations were made to reproduce the functioning of the lake ecosystem. In the first version, a loading of 1500 t P10101 year"! and 27 000 tNlolalyear-1 was considered; in the second it was 2000 tP lolal year"! and 36000 N lolal year". These loadings are by 1.5 and 2 times higher than observed loadings averaged over the 1992-1997 period. The authors assume that such an increase will inevitably be realized if the Gross Regional Product (GRP) grows drastically while the present character of the economy and policy towards water resources conservation remains as it is. The results of these numerical experiments are presented in Figs 7.12-7.13. The analysis of simulation results shows that biogenic loading growth under all circulation types leads to an increase in spring and autumn maxima in the annual dynamics of mean values of phytoplankton raw biomass. Raw phytoplankton biomass values averaged over the summer period vary to a lesser extent. In this case, warming leads to a reduction in biomass compared with in climatic circulation . It should be pointed out that the results obtained are not unexpected. As earlier, in the reconstruction of Lake Ladoga anthropogenic eutrophication, the statement was proved that the general tendency of the transformation of the Lake Onego ecosystem

Sec. 7.2]

Modelling changes in the Lake Onego ecosystem

243

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244 Estimating potential changes in Lakes Ladoga and Onego m

[Ch.7

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(b) of the total raw biomass of zooplankton, mg l" ; results of modelling under a load of 2000tPtotalyear- 1 and 36000 tNtotalyear-l ; (1) climatic circulation, (2) warm circulation, (3) climatic circulation with increased inflow, (4) warm circulation with decreased inflow, (5) cold circulation.

Sec. 7.2]

Modelling changes in the Lake Onego ecosystem

245

is more dependent on biogenic loading changes than on climatic variations within the limits defined in forecasts or based on our estimates. Conclusion

We would like to recall that alterations in the hydro thermodynamic regime of Lake Onego related to possible climate changes over the lake catchment are more significant than for Lake Ladoga (Figs 4.13 and 4.14). Accordingly, the reaction of phytoplankton and zooplankton to climatic variations in Lake Onego is more critical. The main conclusion, drawn from the numerical experiments, is that anthropogenic influence on the Lake Onego ecosystem is more indicative than possible climate change, at least, until the middle of the twenty-first century.

8 Lake Ladoga and Lake Onego models of fish communities

8.1 INTRODUCTION The hierarchical structure of the ecosystem models in the previous chapters was represented by two trophic layers. In fact in the Lake Ladoga and Lake Onego ecosystems five trophic levels can be distinguished: (1) phytoplankton and bacterioplankton, (2) zooplankton and benthos filtrators, (3) predatory zooplankton, benthos and fish (planktophages and detritophages), (4) predatory fish of the first order, (5) predatory fish of the second order and Ladoga ringed seal. Only fish community models not algorithmically connected with the other models are discussed in this chapter. In these models net zooplankton and net benthos production are used as the feeding base for planktophage and benthophage fish. Fish community models differ considerably from those discussed above. Fish community (ichthyocoenosis) spatial structure is represented by large fisheries (Fig. 8.1) where statistical catching data is available (Lake Ladoga. Atlas, 2002; Lake Onego Bioresources, 2008). If in the above-described models the spatial transfer of hydrobionts was brought about by water flows only, in fish communities' models active fish migration has a dominant role in their movements from one region to another within a waterbody. The other specific difference of the model described below from those discussed in the previous chapters is a large temporal step equal to one year. This approach is determined mainly by the fact that the observed data from the fish community have, as a rule, an annual cycle. Seasonal fish community observations demand special studies, which were not undertaken either in Lake Ladoga or in Lake Onego. On the basis of the above reasoning fish community models were originally formulated not in terms of differential equations, but in the form of finite-difference equations. As in ecological system models, the basis of the model is the organic matter balance, fish biomass. Besides, in addition to fish biomass, a quantity balance of the given fish species is taken into account. This last means that individuals of all species appearing

248

Lake Ladoga and Lake Onego models of fish communities

[Ch.8

Fig. 8.1. Fishery regions defined in Lake Ladoga (A) and Lake Onego (B). Lake Ladoga regions: I, Southern coast; 2, Petrokrepost Bay; 3, Western coast ; 4, Northern part; 5, Northeastern coast; 6, Svir Bay; 7, Volkhov Bay; 8, Central part. Lake Onego regions: I, Povenets Onego; 2, Tolvuysk Onego; 3, Pelemsk Onego and Chelmuzhskaya Bay; 4, Maloe Onego; 5, Velikaya Bay; 6, Bolshoe Onego; 7, Svir Bay; 8, Andomskaya Yama; 9, Sheltozersky region; 10, Central Onego.

as young fish should in the end either die as a result of natural mortality, be eaten by other fish, or be removed from the waterbody in the process of fishing. The fish community inhabiting a lake represents a complicated dynamic system. While the fishery population theory has a century-long history and undeniable achievements, it is impossible to say the same about icthyocoenosis dynamics. The formal combination of fish population models is possible when the diversity of fish species' inhabiting the waterbody is not large. The pelagic fish community model in Lake Dalneye (Kamchatka) can serve as an example of such an approach. Only three fish populations are described in the model: red salmon (sockeye salmon), stoneloach and three-spined stickleback (Krogius et al., 1969). Difficulties of a methodical and a computational character were revealed while icthyocoenosis models were being constructed for Lake Vozhe in Vologda region (Zhakov, 1984) and for Tsimlyansk reservoir (Kazansky , 1981). The number of possible interactions among the various fish-age groups rapidly increases even when starting from five-six populations in the fish community, and these interactions are already impossible to describe with available observation and experimental data. Constructing models, using the Monte Carlo method , with different fish species individuals' description, looks to be a good prospect nowadays, but technical obstacles still restrict the usefulness of the method . The modelling complex increases considerably when the movements of each individual, the spawning

Sec. 8.1]

Model description

249

and feeding migrations and the vertical distribution of fish within water column have to be described. Taking account of fish migration is of considerable importance when constructing models of river and lake/river fish communities (Zhakov and Menshutkin, 1989). Lake Ladoga is inhabited by more then 50 fish species (Lake Ladoga. Atlas, 2002): roach, silver bream, blue bream, bleak, bream, pikeperch, whitefish, vendace, European smelt, burbot and others. Even if you omit from consideration such fish species as lamprey, sturgeon, salmon, trout, eel and goby that are small in number, more than a dozen species that are important in fishery still remain, without which it is impossible to analyse the Lake Ladoga fish community as a component of the ecological system and as an object of economic usage. The species referred to in the described model are: perch (Perea fluviatilis) , roach (Ruti/us ruti/us), pike (Esox lucius), bream (Abramis brama), pope (Gymnoephalus cernua), vendace (Coregonus albula), European cisco (Coregonus albula ladogensis), burbot (Lota Iota), whitefish (Coregonus lavaretus), pikeperch (Stizostedion lucioperca) and European smelt (Osmerus eperlanus). Icthyofauna in Lake Onego is similar in general to that of Lake Ladoga. The absence of European cisco in Lake Onego was taken into consideration in the model. Besides, in the Lake Onego fish community model the salmon (Salmo salar) population is described. Although the salmon inhabits Lake Ladoga, its fishery is significant only in Lake Onego. The outline of Lake Onego's waterbody is more complicated and dismembered than that of Lake Ladoga, which is why the definition of local fish communities in Lake Onego is of large importance. If the initial version of the fish community model for Lake Ladoga was developed without specifying local fish populations (Astrakhantsev et al., 2003), for Lake Onego such a simplification appeared to be unacceptable from the very beginning. The first fish community model for Lake Ladoga was built up by Ladanov and Tikhonov (1985). Each fish population in this model was represented by two components only - juveniles and mature individuals. Such an approach simplified the age structure of populations in the model considerably. That is why in the fish community model for Lake Vozhe (Zhakov, 1984) and for Solina reservoir (Klekowski and Menshutkin, 2001) all age groups were examined, as is assumed in the present model. 8.2 MODEL DESCRIPTION The main idea of constructing a fish community model is in the separate description of trophic, population and fishery processes that take place in fish community. The element in a trophic net icthyocoenosis is the trophic group, where a fish is distinguished by its size (detritophage, small and large planktophage, small and large benthophage, small and large predatory). The element of a population structure is the age-group and, from the fishery point of view, the main feature is the size of the individual related to the type of fishing gear. This division is in a way hypothetical, because in trophic interaction among fish and in the food chain, features of the

250

[Ch.8

Lake Ladoga and Lake Onego models of fish communities

5

3 2

4

Fig. 8.2. Fish community trophic structure. 1, detritophages; 2, small planktophages; 3, large planktophages; 4, small benthophages; 5, large benthophages; 6, small predators; 7, large predators; 8, detritus; 9, zooplankton; 10, benthos.

species play an essential role; but as a first approximation these peculiarities can be neglected and can be combined in one trophic group, for example, of large pike and pikeperch 6-8 years old. The model trophic structure is presented in Fig. 8.2. As was mentioned above, the spatial fish community structure is presented by separating fishery regions. As the model time-step is assumed to be one year, to distinguish within one population spawning, feeding and hibernating migrations appeared to be impossible. Therefore, the definition of fishery regions reflects only the fact of the existence in the community of only those local populations where an exchange of individuals takes place. Unlike the previous icthyocoenosis models (Astrakhantsev et aI., 2003) fish growing rate is considered not to be a constant but to fluctuate and depend on the specific feeding conditions in each trophic group. For each fish species the upper and the lower individual mass limits are mentioned when a specific age is reached. If, according to balance relations , the minimal individual fish mass cannot be reached, the additional fish mortality due to lack of food is introduced. The maximal individual mass, appropriate to fish species and their age, is used for determining the maximal demands for fish food . When describing the reproduction process in the model a definition of effective fecundity is used, which is determined by the quantity of young fish surviving per one spawner. Unlike absolute fecundity (number offish eggs per female) effective fecundity describes integrally a whole set of processes (sex ratio , syngamy effectiveness, fish egg and larva mortality), though it is difficult to give a direct definition. External

Sec. 8.2]

Model description

25I

factors such as water level and temperature during the spawning season, contamination of spawning grounds, capacity of spawning areas and so on considerably influence the effective fecundity (Bobyrev and Kriksunov, 1996). The dependence of accession value on the quantity of surviving juvenile fish, suggested by Beverton and Holt (1957), is adopted in the model. In the construction of fish population models the dependence, suggested by Ricker (1954), is often used, where the maximum survival of juveniles and the effect of the overloading of spawning places is taken into consideration. This dependence is applied only to the salmon community, and in Lake Ladoga and Lake Onego conditions, where the salmon community is depressed, there is no question of spawning places being overloaded. The distribution of all species within trophic groups in the fish community model is presented in Fig. 8.3. In the process of model application it is possible to change the trophic status of each age-group and the minimal and the maximal fish individual mass in a studied waterbody. The block-scheme of the modelling algorithm is shown in Fig. 8.4. For imitation of the interaction between trophic groups the TROPHREL procedure is followed. The biomass values of each trophic group are entered into this procedure (BTRG), as are their total nutrition needs (pPTRG), and also the annual zooplankton production (PLAN), benthos (BENT) and detritus consumption (DET) .

• , ." . I •

I~ '

14• • 5. ,

n

.' ~,'$

.•",.(_

II

.I

Fig. 8.3. Age-group distribution among trophic groups . Trophic group indices are shown in Fig. 8.2. A part of the computer model user interface is presented in the figure. By pushing a button with the trophic group index for specific fish species at a given age it is possible to change the index.

252

[Ch.8

Lake Ladoga and Lake Onego models of fish communities

POPUL

Fig. 8.4. Block-scheme of the fish community modelling algorithm. I, the beginning; 2, initial state of all fish community populations input; 3, annual cycles; 4, fishing regions cycle; 5, actual nutrition base definition; 6, searching through all trophic groups; 7, each trophic group biomass definition; 8, nutrition needs definition; 9, trophic relations coefficientscalculation; 10, mortality coefficients calculation; II , search through all fishing regions populations; 12, search through all age-groups of the population; 13, determination of survived juveniles; 14, determination of fish biomass increase considering trophic conditions; 15, determination of natural and fishery mortality; 16, local fish population transition to the next-year state; 17, selection through population and age; 18, fishing mortality and overall catch determination; 19, community dynamics graphical presentation; 20, determination of average substances fluxes between trophic groups; 21 , the end.

Nutrient needs are composed of the nutrient needs of the age-groups in different populations within the trophic group. These last are defined as the multiplication of the maximal annual growth gains by the appropriate feeding coefficient (KKK). PP(I,J) = KKK(G)

* (WMAX(J, I) -

W(J, I, B»

* NO,J, B),

(8.1)

where W(J, I, B) is the current fish individual mass in the age-group, WMAX(J, I) is the maximal fish individual mass in the age-group, and NO, J, B) is the quantity of J age-group in I population in a region B. The trophic interaction stress is defined as the quotient of nutrient needs and available feeding stock: KTRG(G) = PPPTRG(G)/BTRG(G)

(8.2)

Model description

Sec. 8.2]

253

where KTRG(G) is the trophic interactions stress in G trophic group. In the case when nutrient needs are divided among several trophic groups (e.g. large predatory fish distribute their nutrition among small predatory fish, large benthophages and planktophages), this division occurs in proportion to the biomasses of trophic groups in compliance with the nutrient selectivity coefficient. Mortality coefficients as a result of predatory activities (nutrient consumers) in G trophic group are determined by Ivlev's (1955) modified formula. MTRG(G) = 1 - exp(- E(G) * KTRG(G))

(8.3)

where E(G) is the specific coefficient for each trophic group. The processes taking place at the level of separate fish populations are reflected in the POPUL procedure (Fig. 8.4). The age-groups of each population are related by ageing and breeding. For checking the species peculiarities in each population, a database for the 11 fish species included in the model is created. The base structure is as follows: Lname - fish species name, Amax - maximum age, WMAX(J) - maximum body mass at J age fish, WMIN(J) - minimum body mass at J age fish, FERT(J) - reduced fecundity, TRO(J) - trophic group including J age fish, HOLTl, HOLT2 - reproduction function parameters, SEL(J) - fishery tools selectivity relating to fish of J age, PIC - schematic picture of actual fish age. The model interface program provides for the possibility of correcting all database elements in the process of model development. In the POPUL procedure, effective fecundity for all fish species that reached puberty in each population is calculated. Summation of these fecundities multiplied by the appropriate fish number of a particular age, gives the number of juveniles of a given species in the next year (SS(I)). Age-group transition in the state of the next year is calculated by relation: N(I,J) = N(I,J - 1) * (1 - MSTRG(TRO(I,J - 1)))

(8.4)

Survival of juveniles is determined from the number of juveniles and the spawning places capacity according to the Beverton and Holt formula (1957). N(I, 1) = SS(I)/(HOLTl(l) * SS(I) + HOLT2(1))

(8.5)

It is assumed that fish mortality due to lack of nutrition can appear only in the case when the total food allowance cannot provide the minimal fish body mass corresponding to this fish age.

254

Lake Ladoga and Lake Onego models of fish communities

[Ch.8

Fishery impact on the fish community is imitated by the FISHING procedure. Derived from the given fishery tools selectivity and the fishery intensity related to each population, the fishery mortality in each fish age-group is determined. Summation of total catches in the fishery regions and of all fish species is calculated in this procedure. 8.3 THE MODELS STUDY The first problem in the Lake Ladoga and Lake Onego fish community models study was the definition of the value of the numerical parameters. Fish growth rate, puberty age, fecundity and nutrition type data were obtained from a relatively comprehensive reference literature (e.g. Lakes of Karelia, 1959). However, the reproduction function parameters (HOLT1, HOLT2) remain quite uncertain. The main reliable data on the state of the fish communities studied are statistical data on fish catches during recent years (Kudersky, 1996; Lake Ladoga. Atlas, 2002, Biological Resources of Lake Onego, 2008). The selection of the reproduction function parameters was performed by a random search method (Pervozvansky, 1970). The proximity criteria between the model and the observed phenomenon was annual fishery distribution of all fish species obtained in the model study with reference to fishery statistics. The state of the fish community is assumed to be stationary, and for each fish species catch intensities are constant. The data on the conformity achieved between observed and calculated fish catch values, as a sequence of parameter fitting, are shown in Table 8.1. It would not be reasonable to expect better Table 8.1. Comparison of the actual and the modelled fish catch values in Lake Ladoga and Lake Onego. Lake Ladoga

Species

Perch Roach Pike Bream Pope Whitefish European cisco Burbot Vendace Pikeperch European smelt Salmon

Lake Onego

Actual fishery value (kg ha")

Model results (kg ha ")

Actual fishery value (kg ha")

Model results (kg ha")

0.14 0.2 0.05 0.1 0.02 0.30 0.36 0.03 0.26 0.3 1.52 0.01

0.17 0.21 0.06 0.05 0.02 0.2 0.39 0.09 0.22 0.37 1.32 0.00

0.07 0.04 0.02 0.04 0.03 0.06

0.08 0.05 0.04 0.04 0.02 0.04

0.09 0.38 0.03 1.38 0.01

0.09 0.39 0.05 1.38 0.02

The models study

Sec. 8.3]

255

coincidence between observed and calculated data not only because of the low reliability of the statistical data, but also because of the numerous assumptions made in the process of developing the model. After it has been shown that the developed models reflect the state of the fish communities in Lake Ladoga and Lake Onego it is possible to examine the features of the models. In Figs 8.5 and 8.6, fluctuations of fish mass populations over time are presented. It is important to emphasize the fact that in both cases communities do not reach stationary state, but execute non-damping auto-fluctuations. In the examples mentioned the most significant are the icthyomass fluctuations of the European smelt population, and their amplitude is larger in Lake Ladoga than in Lake Onego. When fishery impact increases these fluctuations are undergone by all community populations. The initial reason for the fluctuations is the existing intense trophic relations. As the reproduction function in the form of Beverton and Holt is used in the model, auto-fluctuation initiation due to overloading of spawning places, as is typical, for example, for the Far East salmon populations, in this case is impossible. In the reviewed examples the auto-fluctuation period equalled 4 years, which coincides with the life-cycle duration of the European smelt. But with other combinations of model parameters, icthyomasses underwent fluctuations with both shorter and longer cycles. In general, the whole frequency spectrum was represented in icthyomass fluctuations of fish populations. It should be pointed out that isolated populations possess a feature of auto-fluctuation only in the case of cannibalism (for example, perch and pike populations). Dombrovsky et ai. (1991) came to a

6 5

3 2

Fig. 8.5. Temporal var iation of fish population icthyomasses in the Lake Onego community under steady-state external forcing . 1, total icthyomass of all populations; 2, European smelt; 3, pikeperch; 4, burbot; 5, vendace; 6, whitefish; 7, perch ; 8, roach ; 9, pike.

256

Lake Ladoga and Lake Onego models of fish communities

[Ch.8

3

2

Fig. 8.6. Temporal variation offish population icthyiomasses in the Lake Ladoga community under steady-state external forcing. 1, total icthyomass of all populatio; 2, European smelt; 3, pikeperch; 4, burbot; 5, vendace; 6, whitefish; 7, perch; 8, roach, 9, pike.

Fig. 8.7. (A) Dependence of the total icthyomass in Lake Onego (1) and total catch (2) on fishery intensity (F ). (B) Dependence of the fish commun ity structure in Lake Onego on fishery intensity (F ). 1, perch; 2, roach ; 3, pike; 4, bream; 5, pope; 6, whitefish; 7, burbot; 8, vendace; 9, pikeperch; 10, Europe an smelt; 11, salmon.

Sec. 8.3]

The models study

257

conclusion, that cyclic and pseudo-stochastic behaviour is an immanent feature of populations and fish communities. This corresponds with our results, though Dombrovsky used a completely different model type. Now we will discuss the impact of fishery on fish community dynamics in Lake Ladoga and Lake Onego (Fig. 8.7). After a complete fishing ban the overall community icthyomass sharply increases and auto-fluctuations disappear. Along with a growth in the impact of harvesting intensity, total fish catch increases and reaches its maximum. The maximum value F for the example discussed is within a range of 0.15-0.20. Regions of maximum fishing, and especially regions of over-fishing, are characterized by auto-fluctuation development and intensification along with a decline in total fish community biomass. An area of irretrievable over-fishing is characterized not by a decline in catch and in total community icthyomass, but by particular populations dropping out of the community. Thus, the first populations to drop out due to intensive harvesting are salmon, bream, and then pope populations. Then comes the turn of whitefish and European smelt populations. European smelt population destruction occurs very rapidly - from dominating in the community to complete disappearance. Vendace follows European smelt in this way. As a result of extremely intensive catching, when the selectivity of fishing tools is the only reason why the juveniles of the lake's fish community survive, the perch, roach and pike populations are the only ones remaining in existence. This is the typical, according to the Zhakov (1984) fish community base. Observed auto-fluctuations in the fish communities of the studied allow us to calculate the correlation coefficients of particular populations icthyomasses (Fig. 8.8). This approach made it possible to define differences between Lake Ladoga and Lake Onego fish icthyocoenoses. Thus, the Lake Ladoga fish community falls into two slightly correlated subsystems. In the first is European smelt, burbot and pike and, in the second, all other populations. At the same time the degree of correlation between perch, roach, pope, vendace and European cisco is extremely strong. In the Lake Onego fish community such a separation into subsystems is not found; the degree of correlation between the ichtyomasses of populations is much weaker than in Lake Ladoga. It is worth mentioning that the correlation structure of the Lake Ladoga fish communities described reflects the state only under a certain set of parameters. Thus, a sufficient change in the nutrient base or in the migration intensity between local populations can markedly change the correlation structure of a fish community. The balance approach applied in the construction of the model allows us to develop the scheme of substance fluxes in the fish community (Fig. 8.9) in a way that it is common in research into water ecological systems (Vinberg, 1983). Unlike in Hakanson and Boulion (2002) model, where trophic group biomasses are the main model variables, in our approach trophic groups are formed on the basis of the generalization of particular species population models. It allows us to consider not only the specification of the species populations comprising a fish community, but also to take into account such common definitions in fishery practice as catching intensity and selectivity, reproduction function and population age structure.

258 Lake Ladoga and Lake Onego models of fish communities

[Ch.8

Fig. 8.8. Correlation coefficients of the temporal variations in population icthyomasses in Lake Ladoga (A) and Lake Onego (B).

Fig. 8.9. Fluxes of substances in the Lake Ladoga fish community . Trophic group icthyomasses in g m- 2 are in the large rectangles. Total sum components of total food allowance, in g m- 2 a-I) are in the small rectangles. Trophic group notation is the same as in Fig. 8.2. The large planktophage trophic group in this case is not represented.

Sec. 8.3]

The models study

R u ..

I'

259

B

h'h... PUf""

" h ;j~ .

I'i k

rd

lh. Fig. 8.10. Age structure of the populations belonging to the fish community of Lake Ladoga. Abscissa axis: age in years; ordinate axis: normalized quantity of age-group. The salmon population disappeared because of over-fishing.

Combining the model population and the balance approaches discussed allows us to observe at each moment of time the age-groups of all populations (Fig. 8.10). Any disturbance in the pyramidal age structure (in our case, in the bream and the pope populations) is evidence of the existence of auto-fluctuations in these fish populations. Finally we will emphasize that, unlike fish population models (Kriksunov and Bobyrev, 2002), there have been few fish community models developed recently. The fish community model for the cooling reservoir of the Ingalina nuclear power station (Verbickas et al., 1993), being a sub-model of a waterbody ecological model, does not consider spatial fish distribution, which is reasonable for a small-sized waterbody. The multi-species fish community utilization model of Wilson et al. (1991) clearly shows that the determination approach in fish community modelling used in the present work is not the only one, and stochastic processes are essential in icthyocoenosis dynamics. Similar conclusions were derived in the work devoted to fish community behaviour modelling in Syamozero (Kriksunov et al., 2005). This study deals with icthyocoenosis species composition succession in a waterbody undergoing eutrophication.

9 Natural resources of Lakes Ladoga and Onego and sustainable development of the region

9.1 WATER SUPPLY AND MANAGEMENT IN THE CATCHMENTS. LEGAL AND REGULATORY ASPECTS OF WATER USE Lakes Ladoga and Onego are the largest freshwater bodies in Europe, exceeding by far all other lakes on this continent in respect of water volume and other parameters (see Table 1.1 and Fig. 1.2). Onego and Ladoga are tremendous reservoirs of high-quality potable water, which is of great value for Northwest Russia both as a basis for its economic development, and as a potential export item in the near future (Runyantsev and Sorokin, 2008). Today Lake Ladoga is the sole source of drinking water supply for one of Russia's largest metropolitan areas, S1. Petersburg, and for a number of other fairly big cities in The Republic of Karelia and several other districts. The significance of water quality in the Neva lake-river system for the environmental situation in the Gulf of Finland and the Baltic Sea should also be kept in mind. Lakes Ladoga and Onego are elements of large water transport routes (Baltic-White Sea and Volga-Baltic), and have high value for fisheries and recreation. Two large hydropower plants (Verkhne-Svirskaya and Nizhne-Svirskaya) operate on the Svir River, which connects Lakes Onego and Ladoga. Since the mid-1950s, Lake Onego has fallen in the zone of the Verkhne-Svirskaya hydropower station backwater, thus being, in fact, an impoundment reservoir (Verkhne-Svirskoye). Economic development in the region of the Great Lakes of Europe is at a very high level, higher than in Russia in general (Kudersky et al., 2000). In addition to the Great European Lakes, the economy makes active use of the water situated in their catchments. Numerous extracting and processing industries operate there, most of them water- and resource-intensive, such as pulp-and-paper mills, oil refineries, chemical plants, wood-processing, non-ferrous metal processing and food industry enterprises, hydropower and heat power plants, building material industries, etc. The region possesses mineral, forest and balneological resources. During Soviet times,

262 Natural resources of Lakes Ladoga and Onego and sustainable development

[Ch.9

agriculture used to be quite well developed. It is now gradually recovering, but the application of fertilizers - sources of nutrient pollution - has been reduced several times (Kuznetsova and Smirnova, 2000). The Lake Ladoga catchment area has a population of 3.5 million people, including 2.7 million urban residents . Population density in the Russian part of the catchment is 12.4 person km- 2 • Agricultural usage covers 11% of the area. Several hydropower plants operate on a number of rivers in the catchment (Rumyantsev and Drabkova, 2006). In 2006, water withdrawal from the lake catchment amounted to ca. 1500000m3, of which about 750000m3 were utilized by S1. Petersburg communal facilities (Alkhimenko et ai., 2007). Intensive economic development results in a substantial human impact on water objects which comprises effluents from industries, communal facilities (point

SUojurvi

5

Fig. 9.1. Main point sources of anthropogenic loading . Specialization of industrial centres: 1, pulp and paper industry ; 2, other branches of industry . Water discharge: 3, effluent after poor treatment; 4, untreated effluent; 5, areas with raised water polIution.

Water supply and management in the catchments

263

sources), fish farming and agriculture, as well as dissolved and suspended impurities from arable land, pastures, fertilized and abandoned land (non-point sources or diffuse loading), which is the main cause of pollution and eutrophication of the waterbodies (Kondratyev, 2007). The greatest hazard for the lake ecosystems among point sources is direct wastewater discharges. Nearly all the major water consumers in the Lake Ladoga catchment are situated in the Onego and Ladoga coastal zone (exceptions are the cities of Suojarvi, Volkhov and Kirishi) (Fig. 9.1). The impact of wastewater on lake ecosystems largely depends on how well it is treated. Most industrial centres have sewage treatment plants (STP). The only community with no STPs is Medvezegorsk, which has for many years discharged wastewater into Lake Onego with no treatment at all (wastewaters were 620000m3 in 2007). However, most STPs cannot purify wastewater sufficiently, and the bulk of wastewater is classified as 'undertreated'. One should note that some changes have taken place in the past few decades on the issue of protecting water from wastewater impact. For example, nature conservation authorities have become more active; Priozersky pulp-and-paper mill on Lake Ladoga, which had harmed the lake ecosystem greatly as it had no treatment facilities, was shut down in the 1980s; treatment facilities at the Volkhovsky aluminium smelter, which used to be the main source of phosphorus compounds for Ladoga, Kondopoga pulp mill plant on Lake Onego and some other enterprises were markedly upgraded. The current structure of the region's water management sector (WMS) can be schematized as shown in (Fig. 9.2). The diagram shows only those functions of the sector that serve to satisfy the demand of the economy for water resources, leaving

Water ecoro 'i

Fig. 9.2. Structural organization of the water economy in the region of the Great Lakes of Europe.

264

Natural resources of Lakes Ladoga and Onego and sustainable development

[Ch.9

aside the functions of water study, accounting and protection, as well as the mitigation of harmful impacts (Litvinenko et al., 1998). The system of water relations that had operated in the USSR could not ensure sustainable use and protection of the resources of the European Great Lakes. For example, there existed no fees for the utilization of water resources, for environment pollution, etc. Today, nature use is controlled by laws and regulations of the Russian Federation and its regions, by legal documents issued by local authorities. The baseline acts in the sphere are Constitution of the Russian Federation, RF Water Code # 167-FZ of 16.05.2006, RF Law 'On Environment Protection' #7-FZ of 10.01.2002, RF Land Code #136-FZ of 25.10.2001, RF Forest Code #200-FZ of 4.12.2006, RF Inland Water Transport Code #24-FZ of 7.03.2001, as well as RF Law 'On Payments for the Use of Water Objects' #71-FZ of 6.05.1998, RF Law 'On Waterworks Safety' #117-FZ of 21.07.1997, RF Law 'On Fisheries and Conservation of Aquatic Biological Resources' #166-FZ of 20.12.2004, RF Government Decree 'On Endorsement of Regulations on Waterside Protection Zones of Water Objects and Their Coastal Buffer Strips' #1404 of 23.11.1996, and some others. Relations concerning water use and protection are regulated also by other documents, such as RF Presidential Decrees, RF State Duma and Government Decrees, resolutions (ordinances) of regional executive authorities, international treaties, conventions, agreements and other international legal acts in which RF is a party (signatory). The main Law of the Russian Federation is the Constitution, adopted on December 12, 1993. According to Article 72 of the RF Constitution, issues of nature use, environment protection and environmental security are under the shared authority of the Russian Federation and the RF regions. Article 76 stipulates that federal acts, and regional laws and regulations pursuant thereto are to be passed on these issues. The main act of the Russian Federation for sustainable use and protection of water resources is the RF Water Code passed by the State Duma on April 12, 2006. It considers all aspects of water relations in the Russian Federation. The principal ones are: -

basic principles of water legislation; relations regulated by water legislation; right of property and other rights to water objects; decisions on water use allocation, water use contract; water use fees; governance of water use and protection; powers of RF federal, regional and local authorities In the sphere of water relations; public water monitoring; public water register; schemes of multipurpose water use and protection; public control and surveillance of water use and protection;

Water supply and management in the catchments

-

265

water use for various purposes; protection of waterbodies and watercourses; waterside protection zones and coastal buffer strips; protected waterbodies and watercourses; liability for violation of water legislation, and a number of others.

The acting Water Code was adopted to substitute the former one (1995) with substantial changes. Some of its clauses now contradict other laws and regulations (e.g., RF Government Decree #1404 'On Endorsement of Regulations on Waterside Protection Zones of Water Objects and Their Coastal Buffer Strips' 23.11.1996), creating a serious consistency problem. Furthermore, the new Water Code is not always good for the protection of lakes. Thus, waterside protection zones for Ladoga and Onego used to be 1 km wide, but are now cut down to 50 m, i.e. 20 times! Waterside protection zones of many other water objects in the catchment also decreased considerably. The Lake Ladoga catchment area is huge - 258 000 km 2 - even greater than Great Britain (244000 km"), The area holds some 50000 lakes, a great number of wetlands, 3500 rivers with a combined length of 45 000 km (Kudersky et al., 2000). The catchment is made up of four secondary catchments (Fig. 1.1): Ladoga (28400 km'); Onego-Svir (83200 km 2 ) ; Saimaa-Vuoksa (66700 km 2 ) ; and Ilmen'Volkhov (80200 km"), The Lake Ladoga catchment is shared by three countries - Russia (80.0%), Finland (19.9%) and Belorussia (0.1%). Seven regions share it within Russia: Leningrad Region (39%), Republic of Karelia (29%), Novgorod Region (17%), Pskov Region (6%), Tver Region (4%), Vologda Region (3%), and Arkhangelsk Region (2%) (Viljanen and Drabkova, 2000) (Fig. 9.3). This situation creates challenges in the regulation of economic activities, including utilization, protection and monitoring of resources. Although conformation to the ED Water Directive, Russia, like Europe, employing the catchment principle as the basis for regulating relations concerning water resources, there still exist many conflicts among different administrative bodies, laws and regulations. Some steps to improve the water management system in the area of the European Great Lakes relying on international experience were taken late in the previous century. The water management policy of large lakes (Water management ... , 2000) was studied within the project 'Development and implementation of an integrated programme for environmental monitoring of Lake Ladoga: protection and sustainable use of aquatic resources' (DIMPLA, TACIS project #40/97). In this project, the approaches practised in Europe in accordance with the Water Directive (Kontio and Hilden, 1998) were employed to analyse the water management of a number of large lakes of North America and Eurasia: American Great Lakes, Constance, Saimaa, Vannern, Pskov-Chudskoye, Baikal, Ladoga. A group of experts produced guidelines on enhancing resource management systems in the Lake Ladoga catchment area. However, the ongoing administrative reform in Russia hindered implementation of the guidelines.

266

Natural resources of Lakes Ladoga and Onego and sustainable development

[Ch.9

Fig.9.3. Administrative divisions of the catchment of Lake Ladoga (Lake Ladoga. Atlas, 2002).

The organizational system of the water management sector in the RF has changed markedly since the late twentieth century. It now has the form shown in (Fig. 9.4). Water fees, which are distributed among federal bodies (20%), regional and municipal bodies (40% each), have been set according to the scheme shown in Fig. 9.4 and to acting laws (Fig. 9.5). Relying on available experience, the Russian Academy of Science Institute of Limnology proposed the draft 'Law on Ladoga ' in order to improve legislation on Lake Ladoga and its catchment (Alkhimenko et al., 2007). In the absence of such law, the effectiveness of the efforts undertaken by federal and regional authorities, legal entities, people and public associations to tackle environmental problems of the European Great Lakes is impeded. There already is an example of a special law on a

Water supply and management in the catchments

na

m n fu c )o Waf

Gove

molll lOl1ng

267

me nt bod ie

Hydrornaleo

!r'" r:I~ -I.

I~~~==1

II 1 -···.. : ~:=======~ 'I

1

! !I

II !r'+" ! '--------------

rt·~l-=1'----------r-r-~1

L-_L·..::::.L

Loc al

ri li ~

_

Fig. 9.4. Organigram of the Ministry of Natural Resources of the Russian Federation and its interactions on water resource management with authorized environment protection bodies. large lake in Russia - the Law on Lake Baikal. Scientists from the Institute of Limnology have by now worked out the concept of the Federal Law 'On Protection of Lake Ladoga' (Alkhimenko et al., 2007). The main idea of the draft Federal Law 'On Protection of Lake Ladoga' is to create favourable conditions for the conservation and improvement of the state of the Lake Ladoga ecological system through legal regulation of the activities of all actors in the social relations that affect this unique natural object in one way or another (Alkhimenko et al., 2007). Adoption of the law and implementation of the measures envisaged therein would make possible

268

Natural resources of Lakes Ladoga and Onego and sustainable development

Em

[Ch.9

harge

within permitted

limit "

Regional budg t 4 1" 'D Fig. 9.5. Scheme of the distribution among sectoral, regional and municipal bodies of the fees payable for negative influence on water objects.

a profound solution of the problems of sustainable use and conservation of the lake resources, and recovery of the lake nutrient status. It would promote economic development in Northwest Russia based on progressive, resource-saving technologies, resulting in the establishment of favourable living conditions in the drainage basin of the Great Lakes of Europe. 9.2 ASSIMILATION POTENTIAL OF LAKE ECOSYSTEMS AND SUSTAINABLE DEVELOPMENT OF THE REGION 9.2.1 Introduction

In Russia, which is one of the world's richest countries in terms of water resources (Russia has the world's second greatest river runoff - 4262m3 year" ; per capita value in the country is 30000m3 year-I , in Europe 4500m 3 year-I , in Asia 5200m3 year:", on the Earth on average 9000m3 year:"), the problem of water supply is topical for a few regions only. Although water resources are abundant, public supply of good potable water is still a serious problem. Hence, the role of the largest lakes cannot be overestimated. The water factor does not limit economic development in Northwest Russia. The greatest problems are the quality of fresh water and the sustainable use and the conservation of aquatic ecosystems.

Sec. 9.2]

Assimilation potential of lake ecosystems and sustainable development 269

The water system Lake Ladoga - Neva River - Neva Bay of the Baltic Sea is of great importance, not only for the northwestern regions, but also for Russia at large. The catchment is one of the most densely populated and developed parts, where nearly 16 million people (over half the population of Northwest Russia) reside, and over 11% of the gross domestic product is produced. Potential uses of the resources of the European Great Lakes have lately been actively discussed. Potential uses of lake freshwater (Rumyantsev and Sorokin, 2008), or prioritized development of water-intensive industries in Russia (Danilov-Danil'ian, 2007), which are, in fact, already widely present in the catchment of the European Great Lakes (pulp-andpaper, metallurgy, mining, etc.), are considered. For the coming several decades, however, these lakes are the only feasible source of potable water supply for most people in the region, and the region's economy should be developing accordingly. This section of the book deals with the application of economic mechanisms for the regulation and conservation of Ladoga and Onego water resources. One should note the high economic significance of water conservation for the whole task of nature conservation in the catchment of Lake Ladoga and the Gulf of Finland. Nature conservation, namely water protection, is very efficient. According to Gusev et al. (2004), one rouble invested in water conservation measures prevents an economic loss of 10 roubles. The authors of the computations argue that one can hardly find another sphere of economic activities with such a high profitability (about 1000%). There is an essential difference in the conservation of water resources between large and deep lakes, such as Lakes Ladoga and Onego, as well as the other great lakes of the world (Baikal, the American Great Lakes, etc.), and other water objects, such as rivers and small lakes: the period of response to external impacts for the former is several tens of years. For Lakes Ladoga and Onego, this period is at least 12 years. Hence, water-use regulation measures may have a long-lasting effect on the lake ecosystem, even after the activity has stopped (e.g., after the termination of pollutant discharges). The economic mechanisms and methods of regulating nature conservation activities are defined in the RF Law 'On Environment Protection' passed in December 2001. This Law, like its previous 1991 edition, is directly related to the country's transition to sustainable development. The Law declares that: One of the principles of economic and other activities of legal entities and individuals, authorities of all levels, where these activities affect the environment, is scientifically grounded combination of environmental, economic and social interests of people, society and the state for sustainable development and a favourable environment. By law, the economic mechanism of environment protection is based on a number of instruments, such as: - state forecasting of socio-economic development based on environmental forecasts; - providing tax and other benefits for those using best technologies, alternative energy sources, and recycled materials, recycling wastes, and taking effective nature conservation measures;

270

Natural resources of Lakes Ladoga and Onego and sustainable development

[Ch.9

- setting limits for the use of natural resources, limits and standards for pollution discharges; - defining and collecting fees for the use of natural resources, for polluting discharges; - supporting conservation-oriented entrepreneurial and innovative activities, including environmental insurance; - recoupment for environmental impact following the established procedure; - licensing of specific environment protection activities, and environmental certification. As regards environment protection, one of the most important instruments of the economic mechanism is payments for discharges of pollutants and nutrients. This instrument is implemented by setting limits and standards for the discharges and fees for discharging pollutants and nutrients into waterbodies. The superiority of this economic instrument over direct regulation has been theoretically proven and recognized by all developed nations. Pollution fees are to stimulate transition to non-waste technologies, and companies can choose the most economically beneficial solutions. Thus, a company may choose to spend money paying for pollution, or invest in the construction of treatment facilities or technological upgrading. One could expect the above qualities of pollution fees to ensure the establishment of an effective system of environment pollution control - all the more so given that Russia today has advanced perhaps even further than other countries in the practical application of this economic instrument, as Academician D. S. L'vov (Russia's Way towards the 21st Century, 1999) maintains. Many regions of the country already have the experience of establishing and collecting such fees. However, some studies (L'vov, 1999; Hofman, 1991) prove that existing pollution fees are one or two orders of magnitude lower than necessary. Current fees do not encourage companies to adopt resource-saving technologies or invest substantially in environment protection. Yet, a sharp rise in the fees may negatively influence economic development. Of the two major functions of the fees - stimu1ation of environment protection activities and accumu1ation of targeted financial resources - only the latter works in Russia today. The former is inactive because of low fee rates, inadequate for the estimated economic losses. There is another, more important reason for the failure of the first function of the fees (Gusev, 1995). The effectiveness of the economic instrument of pollution fees largely depends on how well developed market relations are. Being in a non-competitive environment, or even holding the monopoly in the market, the producer can integrate nature conservation costs into the price of goods and services, so that eventually it is the consumer who pays for pollution. This is the reason why the function of stimu1ating nature conservation measures (construction of treatment facilities, process modifications to reduce wastes, etc.) is not fulfilled. In modern Russia, the markets of the energy, petrochemical, water supply and other heavy pollution industries are highly monopolized, so that the burden of pollution payments can be easily shifted to consumers (Gusev and Guseva, 1996). All the above is obviously true for Northwest Russia, since the industries mentioned above are present in its territory. And one last

Sec. 9.2]

Assimilation potential of lake ecosystems and sustainable development 271

thing concerning pollution fees: the second purpose of the fees accumulation of targeted financial resources for nature conservation measures would work only if the financial resources do not get consolidated in the budgets of respective levels (which are multi-purpose by nature), as happens in Russia today. Scientifically grounded setting of limits and norms for pollutant and nutrient discharges, and assignment of pollution fee rates is a challenging environmentaleconomic task that requires the involvement of mathematical models of ecosystems. A few models have been developed for Lakes Ladoga and Onego (Menshutkin et al., 1998; Rukhovets et al., 2003; Astrakhantsev et al., 2003; Rukhovets et al., 2005, 2006a, 2006c), and two of them are described in Chapters 3 and 6 of this book. These models serve to set the thresholds of anthropogenic loading on a waterbody at which stability of its ecosystem is maintained. In fact, the thresholds identified are the limits for the development of the economy in the lake catchment.

9.2.2 Assimilation potential of the natural environment The problem of conservation of lake water resources is, in fact, the problem of conserving the assimilation potential (AP) of these aquatic ecosystems. The AP of the natural environment is its capacity for self-regeneration with respect to material and energy supply into the natural environment as the result of human activities. The AP of the natural environment is an essential component of the natural wealth of each nation, as well as the whole biosphere (L'vov, 1999). AP is a peculiar kind of natural resource, and can, like any other natural resource, be economically estimated, given that the demand for it exceeds its availability. Economic quantification of AP is a multifaceted task. As with other natural resources, utilization of AP entails the introduction of the rent (Gusev, 1997). Therefore, a key issue is the property right to the resource, i.e. to AP. Since AP is part of the national wealth (at least, the AP of the Ladoga and Onego ecosystems is), it would be logical to make the Russian Federation the owner, and the right of disposal may be transferred to regions (Gusev, 1997). In application to water resources, demand for AP is localized to water objects. To get the economic estimate of a water object's AP one first has to estimate it by ingredients. A reasonable quantifier would be a system of limits (by ingredients) on volumes of pollutant and nutrient discharges, to ensure that the stability of the aquatic ecosystems is maintained. Determination of such limits is a challenging task. Comprehensive information on the water object is needed to this end.

9.2.3 Quantification of the assimilation potential of the ecosystems of Lakes Ladoga and Onego The AP values of the Ladoga and Onego ecosystems are estimated separately for each pollutant or nutrient. Let us remember that the principal control (limiting element)

272

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of the state of the Ladoga and Onego ecosystems is phosphorus. We therefore consider the procedure for the estimation of AP values for phosphorus discharges. The computational experiments reproducing the annual functioning of the Lake Ladoga ecosystem and reported in Chapter 7 demonstrate that in the situation of climatic circulation the lake would remain slightly mesotrophic if external phosphorus loading did not exceed 4000 t P total year": Hence, this value can be taken as the AP estimate for Lake Ladoga on phosphorus discharge. Forecasts of changes in the Ladoga ecosystem (Chapter 7) suggest that the value of 4000 tPtotal year"! can be regarded as the AP estimate on phosphorus discharge under global warming also. Analysis of the results of computational experiments for Lake Onego (Chapter 7) shows that in the situation of mean multi-annual (climatic) circulation the AP estimate for nutrient discharges into the lake may be 800tPtotalyear-l for phosphorus and 15 000 tNtotal year" for nitrogen. The same values also can be used as AP estimates for nutrient discharges into Onego in the situation of potential climate change in the catchment at least until the middle of the twenty-first century. According to the latest research into the Lake Ladoga ecosystem (Rumyantsev and Drabkova, 2006; Petrova et al., 2005), phosphorus loading on Ladoga over quite a long time-period between 1996 and 2003 stayed within 4000tPtotalyear-l Table 9.1. Total phosphorus concentration (J.lgI-1) in the water of Lake Ladoga in 1997-2015, calculated by the succession model based on the loading corresponding to the value of 1996. Spring May-June

Season

Zone no.

Warm Climatic circulation circulation with elevated runoff

Summer July-August Climatic Warm circulation circulation with elevated runoff 1996 17.5 17.7 19.4 19.5

Autumn September-October Climatic Warm circulation circulation with elevated runoff

I II III IV

19.3 19.3 19.9 19.9

17.2 17.5 18.5 18.9

I II III IV

13.2 10.5 9.5 9

10.5 9.2 8.3 7.9

2005 10.8 9.9 9.7 9.3

9.2 8.6 8.5 8.1

10.2 9.4 9.5 9.6

8.7 8.3 8.4 8.3

I II III IV

12.6 9.8 8.7 8.2

10 8.6 7.6 7.2

2015 10.2 9.2 9 8.5

8.7 8.1 7.8 7.4

9.5 8.8 8.8 8.9

8.2 7.7 7.8 7.7

Sec. 9.2]

Assimilation potential of lake ecosystems and sustainable development 273

(Fig. 1.14). Nevertheless, the lake ecosystem shows no tendency for a return to the oligotrophic status it had had before 1962, before anthropogenic eutrophication of the lake began. It therefore appears more appropriate to estimate the AP of the Ladoga ecosystem on phosphorus discharge at 2500tPtotalyear-1. In view of the above, the following computational experiment was carried out. The phytoplankton succession model from Chapter 6 (section 6.4) was employed to make calculations with an external loading of 2445tPtotalyear-l for the period of 1997-2015 until the periodic solution was obtained. The value of 2445 tPtotalyear-l corresponds to the loading recorded in 1996. The condition of the Lake Ladoga ecosystem late in 1996 was taken as the initial state in the calculations. The results of this computational experiment are shown in Table 9.1. Judging by the distribution of mean total phosphorus concentrations among zones of the lake (Fig. 1.14) shown in Table 9.1, total phosphorus concentration in the lake on average will not exceed 10J,.lgPtotall-l by 2015. According to Lake Ladoga . . . (1992, p.77), mean annual total phosphorus content calculated by the Dillon-Riegler-Vollenweider formula using observed data also equals 10 J,.lgPtotall-l. Note that calculations in this experiment were carried out both for climatic circulation and for warm circulation with elevated runoff. This means the value of 2500tPtotalyear-l can also be used as the estimate of the AP of the Ladoga ecosystem for phosphorus discharge even if global warming proceeds. 9.2.4 Economic quantification of assimilation potential As reported above, AP estimates for the ingredients most significantly affecting the state of the ecosystem have already been determined. Economic estimates of AP are found separately for each pollutant and nutrient. They appear as minimal fees for discharging 1 ton of pollutants and nutrients, such that total supply of the substance to the waterbody from the activities of water user companies in the catchment does not exceed quantitative estimates of the AP. This system is based on the assumption that when deciding on the degree of wastewater treatment, the company strives to maximize its profits. In the short term, such motivation for a company appears quite realistic. Indeed, water-use regulations are, as a rule, designed for short-term periods (a year or more). To get economic estimates of AP we shall employ mathematical economic models of the operation of the water-user companies developed earlier (Astrakhantsev et al., 2000; Andreev et al., 2002). The main purpose of such models is to estimate how much of pollutants and nutrients a water user company would discharge into a waterbody at fixed pollution fees and constant standard parameters of water intake and discharge. Note that discharge volumes depend on the company's output, processes in use, available capital and its distribution among key activities and nature conservation (effluent treatment, and investing in nature conservation equipment). The computational experiments aimed not so much at reproduction of the operation of the actual mechanism of pollution payments, but rather at model-based determination of minimal pollution fees, such that total discharges (by ingredients)

274

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do not exceed quantitative estimates of AP. In the experiments, AP quantitative estimates act as discharge limits that must not be exceeded. To model operation of water-user companies one needs information about production volumes, staff numbers, basic production assets, treatment facilities, etc. In reality, getting such information is a problem. It is much easier to get sector profiles and apply the averages to companies within specific sectors of the economy. Contributions of all water-user companies situated along all watercourses in the catchment should be taken into account. To this end, after the volumes of pollutant and nutrient discharges into the watercourse are determined by the mathematical economic model, one has to use one-dimensional models of substance transfer down the watercourse (river), which can be found in some papers (Alimov et al., 2001). This section introduces modifications concerning water-use fees into the model of the operation of a water-user company taken from Astrakhantsev et al. (2000) and Andreev et al. (2002). For the abovementioned reasons of the model dataware, further references to water-user companies should be interpreted as references to sectors.

9.2.5 Mathematical economic model Within this model, we shall consider the water-user company as a production unit made up of mainline production and auxiliary treatment facility. Denote by K the company's basic production assets in value terms. Denote annual material costs of mainline production by M, and annual costs of the auxiliary treatment facility by V. Let the manpower and salaries be constant. Then, the following production function can be used (Kleiner, 1986)

where Y is the output, (3 the dimension factor, k the volume of basic production assets used, and Q production capital elasticity coefficient. Suppose that for the annual production cycle the company has a total amount of assets G, excluding the value of the company's basic production assets. Let the profit of the company follow the relationship 7[=

Y-M- V- W,

(9.1)

where W is payments for pollutant and/or nutrient discharges, W depends on the volume Q of the ingredient discharged and the fee s for discharging 1 ton of the ingredien1: W=Qs.

In the model, the volume of pollutants and/or nutrients discharged with wastewater after treatment during a year is determined by the relationship

Q=

~Df(v),

Sec. 9.2]

Assimilation potential of lake ecosystems and sustainable development 275

where D is the annual volume of wastewater from mainline production yielding an output Y; ~ is the concentration of pollutants or nutrients in the wastewater before treatment;f(v) ~ 1 is the nonlinear monotonically decreasing function of treatment indicating the degree of the effluent pollution with the ingredient. The value of D is determined by the relationship D= Yw,

where w is the water volume per rouble unit of output. Finally, v = VI D is unit costs per cubic metre of wastewater subject to treatment. Using this model one can find what distribution of costs between mainline and auxiliary processes would maximize the company's profit (9.1). The following limits must be observed: k~K,

M+V~G

at a fixed fee for pollutant and nutrient discharge. The results of the solution of the problem on maximizing the profit of a specific company to be further used to get economic estimates of the AP of water ecosystems are the volumes of pollutant and nutrient discharges into the waterbodies at fixed fees for pollutant and nutrient discharge. To get economic estimates of the AP of Lakes Ladoga and Onego for pollutant discharges we suggest an iterative procedure based on application of this mathematical economic model. This procedure involves the following sequence of steps: (1) the decision-making expert (or body) sets the fees for discharge of 1 ton of pollutants and nutrients; (2) the model is applied to each company at fixed fees, and the pro blem of optimizing the company operation is solved to determine the volumes of pollutant and nutrient discharges and, hence, the volumes of supply of each pollutant and nutrient into the lake. Thus, anthropogenic loading on the lake is determined; (3) if the loading of some substances on the waterbody exceeds the AP quantitative estimates, suggesting that demand for AP exceeds its supply, fees for this substance are raised, and the process continues; (4) the rule for termination of the process appears evident. Through this algorithm, minimal pollution fees ensuring that the loading on the waterbody satisfies AP quantitative estimates can be determined. These fees are, in fact, the economic estimate of the lake ecosystem AP. Since the AP is state property, the authority regulating water use will rely on the resultant fees in selling pollution permits to water-user companies. The mechanism of trading pollution rights now mainly operates for emissions. As regards water use in river catchments, application of the mechanism of trading pollution rights here is problematic since the environmental impact of pollutant discharges by different companies varies. With an object like Lake Ladoga, the total supply of some pollutants and nutrients into the lake can be controlled irrespective of the source location, given that the standard for effluent quality is fulfilled. One should note that this standard can be fulfilled by means of

276

Natural resources of Lakes Ladoga and Onego and sustainable development

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wastewater dilution. In this case, application of the mechanism of trading pollution credits is permissible. This approach, where AP is regarded as a specific natural resource, creates a natural rent for the society. However, nature conservation expenditures of wateruser companies in this situation are not limited to the cost of discharge permits, because it is usually not possible to buy discharge permits covering the whole volume of wastes actually produced, and the companies also bear the costs of treating the part of the wastes exceeding the purchased quota of the waterbody AP. Such treatment costs can also be regarded as a public necessity, for they secure that the environment quality is maintained. Therefore, the introduction of the market mechanism of trading pollution permits among water-use companies may result in a redistribution of pollution permits such that total treatment costs are reduced. The operability of the suggested algorithm is further tested through economic estimation of the AP of Lake Ladoga for phosphorus discharge. 9.2.6

Computational experiments

Following the suggested algorithm, finding the economic estimate of AP by means of the above-described mathematical economic model, which is a modification of the model from Astrakhantsev et al. (2000), involves getting information about production volumes, about the production function of the mainline production, and about the major parameters of the treatment facility. In practice, the AP pricing procedure should be performed by stakeholders who have the required information concerning their own company. To model this process, let us presume this information to be known. For instance, available information by sectors can be used. This is the approach the authors have chosen to check the operability of the suggested algorithm using the abovementioned mathematical economic model of operation of water-user companies (Rukhovets et al., 2007). The phosphorus loading on Lake Ladoga was estimated at 3150tPtotalyear-1. This was the value in 2002, according to Raspletina (personal communication). In the first experiment, the assumption was that all phosphorus loading was generated by one big company (or one sector comprising all companies in the catchment). It was presumed also that the company had at its disposal certain assets Gt , excluding the value of capital assets in use, and Gt was current assets. The company distributes these assets between mainline production and treatment so as to maximize its net profit. The company is thus free to choose how much it pays for pollution, and how much it spends on treatment. The solution of this optimization problem at a fixed fee for the discharge of 1 ton of phosphorus yields the total volume of phosphorus discharge into the waterbody. The aim of the computational experiment is to determine what fee for the discharge of 1ton of phosphorus ensures that discharge volumes do not exceed the AP quantitative estimate for phosphorus discharge, i.e, 2500 t year": In reality, the answer to the question is very much dependent on the treatment technology and costs. The data in the experiment were based on 2002 prices taken from Kocharyan and Safronov (2006).

Assimilation potential of lake ecosystems and sustainable development 277

Sec. 9.2]

In the first experiment, the value of G1 was set at 280 billion Rubl. yeac l , and the volume of capital assets in use corresponded to the amount of material costs of mainline production. The calculated relationship between the amount of phosphorus discharged and the fee is plotted in Fig. 9.6. According to the graph, the reduction of phosphorus discharge from the 2002 volume (3150tyeac l ) to a level within the AP (2500tyeac l ) can be achieved by introducing a discharge fee of 5000 Rubl. kg" . The information shown in Figs 9.7-9.10 represents the reasons for such high fees. An important factor is the high cost price of treatment (Kocharyan and Safronov, 2006), whereby treatment costs are much higher than payments for Q . tlyea r ;)

scoo

r-,

2500

........

2000

""'-...

r--

1500 1000 500

o

e

§,....

,....

Fig. 9.6. Relationship between phosphorus discharge volume and the phosphorus discharge fee.

Y. Bill. u I 390

385

r-,

380

3

r-, ........ <,

3 0 36

360

o

0 0

'0

00 00 0

"""" ..-

o

0 ~

0 0 ~

0 0

g

0

a

~

0

a 0

0 0 ~

0 0 ~

0 0 ~

0 0

g

o 0 o 0 ~ ~

sO,

Fig. 9.7. Relationship between output and the phosphorus discharge fee.

I g

278

Natural resources of Lakes Ladoga and Onego and sustainable development

[Ch.9

V, mlll.rubi

12QOC1 '10QOCl

/

V

J

1/

4QOC1

2QOC1

o

/

/ 000 o 0

~

0

0 0

~

0 0

~

0 0 0 000

~

~

0 0

~

0

v

V

0 0

0

000 000

~

~

SO,

ru b ~k.g

~

Fig. 9.8. Relationship between optimal costs of water treatment for a company and the phosphorus discharge fee.

discharging respective amounts of phosphorus, and a company would rather pay a penalty than treat the wastewater at such a high cost price (Fig. 9.8). Results of the modelling are interpreted in terms of the mechanism of pollutant discharge payments. Speaking of the mechanism of trading effluent credits, the factor determining the AP price is the cost price of treatment, which makes treatment costs much higher than the economic estimate of the AP for phosphorus. In this situation, it is more beneficial for a company to buy effluent credits than to treat wastewater at high cost price. The withdrawal of assets from mainline processes to channel them to treatment reduces output (Fig. 9.7) and, hence, the profit (Fig. 9.9). Thus, the company is likely to buy phosphorus discharge credits only if the costs of it are not greater than the costs of treating the respective amount of phosphorus, which are made up of direct investments in treatment facilities and output losses. In terms of the price of the assimilation potential, the right to discharge 1kg of phosphorus should cost at least Rubl. 5000. The assumption in the second experiment was that the phosphorus loading of 4600tPyear- 1 is generated by two companies rather than one. The characteristics of the first company are the same as in the first experiment. The second company is said to have a 02 = 110 billion Rubl. year:" . The treatment technology and cost are presumed to be the same at both companies. The relationship between the amount of phosphorus discharged by the two companies and the phosphorus discharge fee is shown in Fig. 9.10.

Sec. 9.2]

Assimilation potential of lake ecosystems and sustainable development

n,

279

ill.

30000 500 0

.........

..............

20000

r-,

<,

500 0

r-, r--...

0000

'<,

.....,

<,

5000

<,

.......

I)

000

g

g N

0 ~ C')

0

g

-=t"

0 ~

l()

Fig. 9.9. Relationship between the profit of a company and the phosphorus discharge fee.

a,v 5000 500 000

3500 3000 2500

-., r-,

<, ...........

2000 1 0

1000

o

(J

Fig. 9.10. Relationship between the amount of phosphorus discharged by two companies and the phosphorus discharge fee

Because the initial phosphorus discharge volume is higher, a fee of 5000 Rubl, kg-I would only reduce the discharge to 4000 t year" . To reduce discharge volumes to 2500tPyear- 1 (AP quantitative estimate) the fee should be raised to 7000 Rub!. kg". Judging by the results of the computational experiments, it is safe to say that to conserve the Lake Ladoga AP the fees for phosphorus discharge (price of

280

Natural resources of Lakes Ladoga and Onego and sustainable development

[Ch.9

phosphorus discharge credits) into the lake should be quite high. It should be kept in mind, however, that a sharp rise of the fees may have destructive consequences for the region's economy. Therefore, the rise should be gradual. On the other hand, if one analyses the nature conservation expenditures of a water-user company, their high level may cause production volumes to decrease, and the companies would thus be motivated to change the technologies in the mainline process to reduce phosphorus discharges. The rates of fees for phosphorus discharge into Lake Ladoga determined in this chapter can be used as the initial values for trading discharge permits in the market mechanism of redistributing quotas among water-user companies. Note here that when estimating the economic value of AP, it is wiser to aggregate companies by sectors, since building production functions for individual companies may be quite problematic in terms of data input. When considering discharge permit trading, such aggregation appears inexpedient. Similar experiments can be carried out to find economic estimates of the AP of the Lake Onego ecosystem. Anthropogenic eutrophication has also affected Lake Onego, but its pelagic part generally remains oligotrophic. It is only the Petrozavodsk and the Kondopoga Bays that are suffering significant eutrophication and pollution. Conclusions

The results of the studies were applied in the system of integrated water management of the biggest aquatic system of Northwest Russia: Lake Ladoga - Neva RiverNeva Bay and its catchment, including Lake Onego and its catchment, as well as large lakes such as Il'men' and the Finnish Lake Saimaa (Alimov et al., 2001; Rukhovets, 2007). Within this system, not only can one apply the economic mechanism of water resource conservation based on setting the norms and limits of pollutant and nutrient discharge into the region's water objects, but one can also get quantitative and economic estimates of the water ecosystem AP by means of the mathematical models and databases included in the system, and using the AP estimation algorithm suggested in this chapter.

Afterword

The important feature of this book devoted to the study of the Great European Lakes is the combination of traditional limn0 logical research with numerical modelling. Together with a description of the current state and dynamics of limnic processes, preference is given to the mathematical modelling of lake hydrodynamics and ecosystems. In developing lake ecosystem models, a synthesis of experience and knowledge in such fields as geophysical hydrodynamics, limnology, numerical modelling, etc. is required. The basis of these models (developed in the Institute for Economics and Mathematics at St. Petersburg and also in the Northern Water Problems Institute) is not only a considerable body of observational data but mostly the use of knowledge of the interaction of different limnic processes expressed in quantitative relations and qualitative interpretations described in the publications of scientists from the Northern Water Problems Institute (Petrozavodsk) and the Institute of Limnology (St. Petersburg). Another fundamental principle of the models developed is an adequate concept for the biotic module of the Lake Ladoga ecosystem model, that is, the use of a reasonably small number of parameters to reproduce the main features of the functioning of the great stratified lake ecosystem. A satisfactory correspondence between the results of numerical modelling and observational data collected in Lakes Ladoga and Onego, especially the wellreproduced successive stages of the lake ecosystem transformation, allows us to conclude that the main patterns of ecosystem functioning are reliably described by numerical models. This makes it possibile to use the models developed as a powerful tool in decision-making on the management of water use of the great lakes, and also for cognitive purposes. Further development of numerical modelling of the great lakes ecosystems should be directed towards research into possible ecosystem transformation in the future under different climate and anthropogenic impacts. In the frames of approach chosen by authors, some reserves to increase the adequacy of models undoubtedly exist. Those comprise the consideration of processes in the lake littoral zone, the effect of wind action on productivity, a more accurate description of primary production

282

Mterword

and destruction, and well-targeted field studies to collect observational data for a better understanding of the behaviour of the ecosystem. It may happen that further development in the numerical modelling of aquatic ecosystems will be linked to the use of other approaches. For instance, professor V. V. Menshutkin suggests that models based on principles of adaptation and self-organization would probably be more successful in the future. In any case, the development and use of numerical models for the great stratified lakes remains a challenging task.

References

Abrosov, V.N. Zonal Types of Limnogenesis. Leningrad: Nauka Press [in Russian]. Adamenko V.N. 1987. Lakes and Climate. Leningrad: Nauka Press [in Russian]. Akopjan M.A., Gurina A.A., Demin Y.L., Filatov N.N. 1984. Diagnostic model of currents in Lakes Sevan and Ladozhskoe. Izvestia Russian Geographic Society, 1, 28-32. Aleksandrova D.N. 1973. Bacterial plankton and microbial flora of bottom sediments in Lake Onego. Microbiology and Primary Production of Lake Onego. Leningrad, R. 5-83 [in Russian]. Alkhimenko A.P., Kudersky L.A., Rumjantsev V.A., Sobol I.A. 2007. A conception of the Federal law 'About Lake Ladoga protection'. Water Resources Under Global Climate Changes. St. Petersburg: Nauka Press, pp. 192-226. Alimov A.F. 1989. Introduction to the Production of Hydrobiology. Leningrad: Hydrometeoizdat. [in Russian]. Alimov A.F. 2000. Elements of the Theory of Water Ecosystems. St. Petersburg: Nauka Press [in Russian]. Alimov A.F., Frolov, A.K. (Eds). 1996. Ecological State of Water Bodies and Water Courses Pertaining to the Neva River Basin. St. Petersburg: Nauka Press [in Russian]. Alimov A.F., Rukhovets L.A., Stepanov, M.M. (Eds). 2001. Integrated water resources management of Saint-Petersburg and Leningrad Oblast (District). St. Petersburg: St. Petersburg Research Center RAS [in Russian]. Allender J., Saylor J. 1979. Model and observed circulation throughout the annual temperature cycle of lake Michigan. J. Phys. Ocean. 1, 573-583. Andreev A.P. 1875. Ladoga Lake (Ladozhskoe ozero), vol. 2, 1875. St. Petersburg. Andreev V.A., Astrakhantsev G.P., Rukhovets L.A. 2002. Modelling of activities of water supply enterprises under ecological-economical limitation. Economy of the North- West: Problems and Perspectives ofDevelopment. St. Petersburg, Vol. 11, pp. 23-30 [in Russian]. Andronikova, I.N. 1996. Zooplankton characteristics in monitoring of Lake Ladoga. Hydrobiologia, 322, 153-157. Arkhipov B.V. 1986. Analysis of applying a conservative scheme of 3-D equations of baroclinic currents. Moscow Academy of Science [in Russian]. Armstrong R.A. 1979. Prey species replacement along a gradient of nutrient enrichment: A graphical approach. Ecology, 60(1), 76-84.

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Index

aerobic conditions, 47 aerosol, 139 air temperature, 135, 137, 145 airborne laboratory, 13 albedo, 93 algae, 33, 38, 183 allochthonous origin, 18 anaerobic conditions, 47 annual climatic circulation, 83 anthropogenic eutrophication, 10 anthropogenic impacts, 10 anticyclonic circulation, 31 approximation processes, 171 aquatic ecosystem, 52, 165 assimilation potential, 271 autochthonous origin, 18 bacterial destruction, 39 bacterial pollution, 10 bacterioplankton, 39 Baltic glacial lake, 5 baroclinic effect, 114 bays lCondopoga, 5, 49, 188 Petrokrepost, 121 Petrozavodsk, 5, 49 Volhov, 5, 121 biogens, 6, 164 biological communities, 51 biota, 6,64 biotope, 12, 44 blue-green algae, 33, 208

Boreal period, 6 bottom friction, 72, 118 boundary conditions, 71 budget, 40 buoyancy effect, 100 buoyancy flux, 28 carbon dioxide, 138 catchment, 3 chemical composition, 285 chlorophyll, 222, 225 circulation anticyclonic, 31 atmospheric, 134 climatic, 68 cold, 153 cyclonic, 27 large-scale, 67 warm, 153 circulation patterns, 27 classification of water, 63 climate, 67 climate warming, 68 coarse-resolution grid, 97 coastal zone, 47, 64 coefficients of turbulent viscosity, 71 communities, 63, 179, 183 continuity equation, 78 convective mixing, 16, 85 crystalline shield, 5 currents, 23

300

Index

database, 86 decomposition, 45 density stratification, 85 destruction, 9 deterioration, 46 detritus, 165 diagnostic model, 120 diatom, 34 diffusion, 47 dissolved organic matter, 44 dissolved oxygen, 14 diurnal sunshine duration, 135 double-gyre circulation, 27 downwelling, 18, 116 ecological system, 65 ecology, 35 economic mechanisms, 269 economic quantification of assimilation potential, 271 economy, 242 ecosystem, 31 Ekman number, 75 environment protection, 270 equation of state, 73 eutrophication, 31 evaporation, 68 explicit difference scheme, 119 external forcing, 68 fish, 182 fish fauna, 247 floods, 142 forecasting, 10, 264 freezing, 21 frontal zone, 53 fungi, 40 Great American Lakes (GAL), 1 Great European Lakes (GEL), 1 geostrophic circulation, 23 greenhouse gases, 138 gyres, 68 heat heat heat heat heat

balance equation, 93 exchange, 94 flux, 68 storage, 94 variation law, 97

heating, 107 hydrobiont, 163 hydrodynamic models, 69 hydrodynamic phenomena, 67 hydrodynamic processes, 24 hydrodynamics, geophysical hydrostatic hypothesis, 70 hydrostatic equation, 76 ice, 85 ice cover, 98 ice-free period, 98 ichthyocoenosis, 247 impact, 12 implicit difference scheme, 119 Index NAO, 135 indicators, 136 inflow, 13, 137 joint effect, 30 Karelia, 135 Kelvin waves, 27 lakes Baikal, 69 Constance, 1 Geneva, 1 Ilmen, 1 Ladoga, 1 Ladozhskoe, 1 Michigan, 5 Onego, 1 Onezhskoe, 1 Ontario, 5 Pskovsko-Chudskoe (Peipsi), 2 Saimaa, 2 Venn em , 4 Vettern, 4 law of conservation, 83 law of mechanical energy variation, 82 limnic zones, 14 long-term analyses, 11 macrophyte, 59 macrozoobenthos, 57 management, 261 manifestation, 26

Index mathematical model, 13 measurements, 26 melting, 85 metabolism, 164 microphytes, 59 mixing, 60 modelling, 150 model discrete, 111 ecological, 134, economical, 274 ecosystem, 31, 163 three-dimensional, 165 thermohydrodynamical, 69 molecular thermal diffusivity, 38 natural boundary condition, 79 nearshore zone, 16 neutral buoyancy, 28 nitrogen fixation, 209 nonlinear models, 275 non-point sources, 262 North Atlantic Oscillation (NAO), 137 nutrients, 27, 210 oligotrophic state, 164 oscillations, 27 outflow, 6 oxygen concentration, 17 periodic solution, 87 piecewise linear function, 193 phosphorus, 31 photosynthesis, 54 phytoplankton, 33 plankton algae community, 187 pollution, 46 post-glacial uplifts, 9 primary production, 31 primitive equations, 73 productivity, 32 pelagic zone, 52 phosphorus, 10 photosynthesis, 18, 187 phytoplankton, 17 phytoplankton productivity, 46 precipitation, 68, 134 primary production, 13

productivity, 6 pulp and paper mills, 262 quantification, 271 quasi-homogeneous layer, 16, 98 regime hydrodynamic, 58 hydrological, 11 thermal, 122 water level, 137 region Archangelsk, 12 Karelia, 135 Leningrad 0 blast, 283 Vologodsky, 12 regional changes, 134 regression equations, 145 river discharge, 92 river inflow, 92 river run-off, 92 rivers Burnaja, 2 Neva, 2 Onega, 1 Shuya, 48 Suna,48 Svir, 5 Syas, 5 Vodla, 48 Volkhov,2 Vuoksi,2 retention period, 197 Rossby radius of deformation, 1 roughness, 85 trophic chain, 164 runoff, 85 salinity, 86 satellite images, 16 sediments, 7 seasonal characteristics, 10 simplified equations, 89 snow, 149 socio-economic considerations, 263 solar radiation, 93 specific heat storage, 94, 151 spectra of currents, 26 stratification, 86, 135

301

302

Index

substance, 87 succession, 36 surface roughness, 85 suspended matter, 46 sustainable development, 261 supply, 10 total organic carbon (TOC), 44 temperature air, 94 water, 95 thermal bar, 14, 117, 160 thermal flux, 93 thermal gradients, 86 thermal regime, 14, 99 thermal stratification, 86 thermocline, 28 topographic effects, 69 toxic contamination, 7 transparency, 12 trend, 22 trophic chain, 164 trophic level, 31 turbulence, 98 turbulent diffusion, 71 turbulent mixing, 100 turbulent viscosity, 98 turnover, 39 variability climate, 137 currents, 129 flow, 113 seasonal, 181 synoptic-scale, 69 variations annual, 99 climatic, 237 interannual, 34 vertical advection, 110 vertical mixing, 116 vortex, 16

water drinking, 26 waste, 11, 262 water balance, 6, 136 Water Code, 264 water dome, 16 water exchange, 9, 18 water economy, 263 water ecological system, 257 water quality, 10 water level, 5 water movements, 18 water mass temperature, 14, 145 water management, 263 water pollution, 262 water renewal time, 1 water resources, 9, 264 water supply, 11, 261 water temperature, 10, 15, 100 water transparency, 194 waste, 11,262 waterbody, 3, 259 watershed, 3 water-user company, 276 waves internal, 68 Kelvin, 27 Poincare, 27 Rossby,27 topographic, 27 trapped, 29 whitefish, 248 wind, 13,95 wind stress, 95 winter cooling, 110 year cycle, 39

zoobenthos, 57 zooplankton, 41