STREAMFLOW CHARACTERISTICS
DEVELOPMENTS I N WATER SCIENCE, 22 OTHER TITLES IN THIS SERIES
G. BUGLIARELLO AND F. GUNTER
1
COMPUTER SYSTEMS A N D WATER RESOURCES
2
H.L. GOLTERMAN
PHY SI 0 LOG ICA L LIMN 0 LOGY
Y. Y. HAIMES, W.A.HALL AND H.T. FREEDMAN
3
MULTIOBJECTIVE OPTIMIZATION I N WATER RESOURCES SYSTEMS: THE SURROGATE WORTH TRADE-OFF-METHOD
4
J.J. FRIED
GROUNDWATER POLLUTION
5
N. RAJARATNAM
TURBULENT JETS
6
D. STEPHENSON
PIPELINE DESIGN FOR WATER ENGINEERS
7
v. HALEK AND J. SVEC
GROUNDWATER HYDRAULICS
8
J.BALEK
HYDROLOGY AND WATER RESOURCES I N TROPICAL AFRICA
9
T.A. McMAHON AND R.G. MElN
RESERVOIR CAPACITY A N D Y I E L D
10 G. KOVACS SEEPAGE HYDRAULICS
1 1 W.H. GRAF AND C.H. MORTIMER (EDITORS) HYDRODYNAMICS OF LAKES: PROCEEDINGS OF A SYMPOSIUM 12-13 OCTOBER 1978, LAUSANNE, SWITZERLAND
12 W. BACK AND D.A. STEPHENSON (EDITORS) CONTEMPORARY HYDROGEOLOGY: THE GEORGE BURKE MAXEY MEMORIAL VOLUME
1 3 M.A. M A R I ~ OAND J.N. LUTHIN SEEPAGE A N D GROUNDWATER
14 D. STEPHENSON STORMWATER HYDROLOGY AND DRAINAGE
15 D. STEPHENSON PlPLELlNE DESIGN FOR WATER ENGINEERS (completely revised edition of Vol. 6 i n t h e series)
16
w. BACK AND
R . LETOLLE (EDITORS)
SYMPOSIUM ON GEOCHEMISTRY OF GROUNDWATER
17 A.H. EL-SHAARAWI (EDITOR) I N COLLABORATION WITH S.R. ESTERBY TIME SERIES METHODS I N HYDROSCIENCES
18 J.BALEK HYDROLOGY AND WATER RESOURCES I N TROPICAL REGIONS
19 D. STEPHENSON PIPEFLOW ANALYSIS
20 I. ZAVOIANU MORPHOMETRY OF DRAINAGE BASINS
21 M.M.A. SHAHIN HYDROLOGY OF THE N I L E BASIN
STREAMFLOW CHARACTERISTICS H. C. RIGGS 3415 Executive Avenue, Falls Church, VA 22042, U.S.A.
ELSEVIER Amsterdam - Oxford
- New York - Tokyo
1985
ELSEVIER SCIENCE PUBLISHERS B.V. Molenwerf 1 P.O. Box 21 1, 1000 A E Amsterdam, The Netherlands
Distributors for the United States and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 52, Vanderbilt Avenue New York, N Y 10017
ISBN 0-444-42480-6 (v01.22) ISBN 0-444-41669-2 (Series)
0 Elsevier Science Publishers B.V., 1985 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./Science & Technology Division, P.O. Box 330, 1000 AH Amsterdam, The Netherlands. Special regulations for readers in the USA - This publication has been registed with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made i n the USA. A l l other copyright questions, including photocopying outside of the USA, should be referred t o the publisher, Elsevier Science Publishers B.V., unless otherwise specified. Printed in The Netherlands
V
PREFACE
A f l o o d d i s c h a r g e may be thousands of t i m e s
Streamflow i s h i g h l y v a r i a b l e .
g r e a t e r than t h e d i s c h a r g e d u r i n g a drought.
Such flow r e g i m e s can be d e s c r i b e d
by v a r i o u s s t a t i s t i c s c o l l e c t i v e l y r e f e r r e d t o a s s t r e a m f l o w c h a r a c t e r i s t i c s . These c h a r a c t e r i s t i c s p r o v i d e i n f o r m a t i o n n e e d e d i n t h e d e s i g n o f s t r u c t u r e s b u i l t i n o r along stream channels, ing t h e a v a i l a b l e w a t e r supply.
f o r e v a l u a t i n g f l o o d h a z a r d s , and f o r d e f i n -
V a r i o u s m e t h o d s may b e u s e d t o c o m p u t e f l o w
c h a r a c t e r i s t i c s ; t h e a l i p r o p r i a t e ones f o r a p a r t i c u l a r s t r e a m depend on i t s flow regime and on t h e amount and t y p e of d a t a a v a i l a b l e . d e f i n i n g f l o w c h a r a c t e r i s t i c s have been proposed,
Although many methods of
and a r e b e i n g used.
descrip-
t i o n s and e v a l u a t i o n s of t h e s e a r e w i d e l y s c a t t e r e d i n t h e l i t e r a t u r e .
book b r i n g s t o g e t h e r some of t h e m o r e u s e f u l m e t h o d s
-
This
ones t h a t a r e simple,
p r a c t i c a l , a n d r e q u i r e o n l y commonly a v a i l a b l e o r r e a d i l y o b t a i n a b l e d a t a . These methods produce r e s u l t s comparable i n a c c u r a c y w i t h t h o s e from more sop h i s t i c a t e d methods f o r many problems. An a n a l y s t needs more t h a n d e s c r i p t i o n s of methods.
He needs t o understand
the hydrology i n t h e r e g i o n s t u d i e d and t h e p r i n c i p l e s of t h e s t a t i s t i c a l techniques used,
and t o have some f e e l f o r t h e r e l i a b i l i t y of h i s d a t a .
Discussions
of t h e e f f e c t s of c l i m a t e , geology, and topography on t h e s t r e a m f l o w regime,
of
s t a t i s t i c a l p r i n c i p l e s , and o f methods f o r c o l l e c t i n g h y d r o l o g i c d a t a respond t o these n e e d s . The a n a l y s t s h o u l d know how h i s i n t e r p r e t a t i o n s w i l l b e u s e d .
Some o f t h e
p r i n c i p a l a p p l i c a t i o n s of s t r e a m f l o w c h a r a c t e r i s t i c s t o w a t e r - r e l a t e d of e n g i n e e r i n g and management a r e i n c l u d e d f o r t h a t purpose.
problems
Also i n c l u d e d i s
i n f o r m a t i o n on t h e changes t o b e e x p e c t e d i n s t r e a m f l o w c h a r a c t e r i s t i c s because of n a t u r a l o r man-made changes on t h e land. The m a t e r i a l i n t h i s book was s e l e c t e d f o r i t s v a l u e t o p r a c t i c i n g hydrolog i s t s ; t h e b o o k i s i n t e n d e d t o b e b o t h a m a n u a l and a s o u r c e o f r e f e r e n c e s .
Engineers s h o u l d f i n d some p a r t s u s e f u l f o r a p p r a i s i n g t h e r e l i a b i l i t y of hydrol o g i c i n f o r m a t i o n on which t h e i r d e s i g n s w i l l be based.
E n v i r o n m e n t a l i s t s may
f i n d t h e i n t e r p r e t a t i o n s of v a r i o u s s t r e a m f l o w c h a r a c t e r i s t i c s h e l p f u l . T h i s i s n o t a hydrology book i n t h e u s u a l sense.
Some i m p o r t a n t e l e m e n t s of
the h y d r o l o g i c c y c l e a r e n o t covered i n d e t a i l b e c a u s e adequate d a t a on them a r e often d i f f i c u l t t o obtain; here.
t h e s e e l e m e n t s a r e n o t used i n t h e t e c h n i q u e s g i v e n
L i k e w i s e , c e r t a i n well-known
too time-consuming
f o r common use.
t e c h n i q u e s a r e n o t i n c l u d e d because they a r e Ground w a t e r i s i n c l u d e d o n l y t o t h e e x t e n t
VI needed t o p r o p e r l y e v a l u a t e t h e s u r f a c e - w a t e r hydrology.
Water q u a l i t y i s
discussed b r i e f l y . The m a t e r i a l h a s been drawn from many s o u r c e s , t h e p r i n c i p a l ones b e i n g t h e l i t e r a t u r e of government a g e n c i e s and p r o f e s s i o n a l s o c i e t i e s .
I am p a r t i c u l a r l y
i n d e b t e d t o t h e U.S. G e o l o g i c a l S u r v e y w h i c h p r o v i d e d me t h e o p p o r t u n i t y t o p a r t i c i p a t e i n many h y d r o l o g i c i n v e s t i g a t i o n s , a n d f o r u s e of e x a m p l e s a n d e x p l a n a t o r y m a t e r i a l f r o m t h e i r many p u b l i c a t i o n s on h y d r o l o g y .
I also
acknowledge t h e p e r m i s s i o n of Pergamon P r e s s t o i n c l u d e p a r t s of my a r t i c l e s i n c l i m a t i c f a c t o r s o f r u n o f f (Chapter 2 ) and i n snowmelt r u n o f f (Chapter 12).
VII
CONTENTS 1
INlRODUCTION
1
General, 1 Probability and Recurrence Interval, 3 Units, 3 Conversion Factors, 3 References, 4 2
FACTORS AFFECTING STREAMFLOW
5
Introduction, 5 Climatic Factors, 5 Effects of the Precipitation Regime, 5 How Temperature Modifies Runoff, 9 Climatic Differences Along a Stream. 15 Effects of Geology. 16 Effects of Topography, 2 2 References, 23 3
COLLECTION OF HYDROLOGIC DATA Streamflow, 2 5 Stage Measurement, 25 Discharge Measurement , 28 Rating Curve, 3 1 Discharge Computation and the Hydrograph. 3 4 Special Gaging Methods, 34 Indirect Measurements, 3 9 Crest-Stage Gaging Stations, 4 0 Time of Travel, 4 0 Sediment Transport, 4 2 Chemical and Biological Quality, 4 4 Weather Observations, 46 Pr ec ip i tat ion, 4 6 Evaporation From Water Surfaces, 4 7 Temperature, 4 9 Snow Accumulation. 4 9 Basin Characteristics, 5 1 Transmission of Hydrologic Data, 5 2 References, 53
25
VIII 4
STATISTICS
51
Introduction, 57 Frequency Curves, 57 Distributions, 57 Cumulative Distributions, 60 Recurrence Interval, 63 Graphical Fitting, 63 Fitting Theoretical Distributions, 67 Evaluation of Fitting Methods, 71 Interpretation of Frequency Curves, 72 Describing Frequency Characteristics, 73 Statistical Inference, 74 Correlation and Regression, 77 Standard Error, 79 Multiple Correlation and Regression, 80 Serial Correlation, 82 Regression Methods, 8 3 Regression Models, 83 Transformations, 84 Example of Simple Linear Regression, 8 5 Multiple Linear Regression, 89 Graphical Regression, 90 Graphical Multiple Regression, 92 Graphical Vs. Analytical Method, 96 Application of the Regression Method, 97 Characteristics of Ifydrologic Data, 100 Effects of Data Characteristics on Analysis, 101 Out1 iers, 103 References, 104 5
STREAMFLOW CHARACTERISTICS AT A GAGED SlTE
Introduction, 107 Means, 107 Frequency Characteristics, 107 Extending Streamflow Records in Time, 109 Flow-duration Curves, 111 Base-Flow Recession Curves, 112 Theory, 113 Derivation, 114 Assumptions as
to
Recharge, 116
Seasonal Variability, 116
107
IX Water-Qua1 ity Characteristics, 116 References, 118 6
RELATION OF GROUND WATER TO SIREAMFLOW
121
Introduction, 121 Aquifer Recharge, 122 Bydrograph Interpretation, 123 Bank Storage in Surface Reservoirs, 127 The Water Resource, 128 References, 128
7
FLOW CHARACTERISTICS AT UNGAGED SITES
131
Introduction, 131 No Data at Site, 131 Regression Analysis, 131 From Rainfall, 134 Interpolation Along a Channel, 134 Some Data at Site, 135 Mean Flow From Monthly Measurements, 136 Low-Flow Characteristics From Base-Flow Measurements, 139 Flow Characteristics From Channel Size, 139 References, 143 8
FLOOD-FREQUENCY ANALYSES Introduction, 145 Annual Floods, 145 Floods Above a Base, 145 Annual and Partial-Duration Frequency Curves, 145 Fitting Annual Frequency Curves, 146 A Uniform Method, 149 Record Extension, 150 Relation to Basin Characteristics, 151 Reliability of Flood-Frequency Curves, 153 Flood Characteristics a t Ungaged Sites, 155 Regression on Basin Characteristics, 155 Index-Flood Method, 156 From Channel Geometry, 156 From Precipitation, 160 Interpolation Along a Channel, 161 Regulated Streams, 162 References, 163
145
x 9
LOW-FLOW CHARACTERISTICS
+
165
Introduction, 165 Frequency Curves, 165 Interpretation, 167 Reliability, 168 Seasonal Frequency Curves, 169 Regulated Streams, 170 Low-Flow Characteristics at Ungaged Sites, 170 Partial-Record Method, 171 Seepage Runs, 172 Interpolation Along a Channel, 173 References, 175 10
THE CHANGING ENVIRONMENT
177
Introduction. 177 Changes Due to Natural Events, 178 Effects of Man's Activities, 182 Surface Storage, 182 Land-Use Changes, 187 Cloud Seeding, 197 Air Pollution, 197 Quantifying Effects of Changes, 198 Environmental Changes, 198 Diversion and Regulation, 201 References, 201 11
APPLICATIONS OF IIYDROLOGIC DATA Introduction, 207 Reservoir Design, 207 Mass Curve, 207 Use of Simulated Streamflows, 208 Annual Mass-Curve Method, 209
Probability Routing, 210 Evaporation, Sedimentation, and Bank Storage, 212 Draft-Storage at Ungaged Sites. 214 Spillway Design Floods, 215 Storage for Flood Control, 216 Dependable Flow Without Storage, 219 Bridge and Culvert Openings, 220 Forecasting Streamflow. 220 Floods, 221
207
XI Snowmelt Runoff, 222 Seasonal Low Flows, 225 Streamflow Droughts, 228 Seasonal Streamflow Drought, 229 Multiyear Streamflow Drought, 229 Adaptation to Drought, 232 Flood-Prone Area Mapping, 233 Estimation of Environmental Impact, 234 References, 235 12
SOURCES OF DATA AND INFORMATION
239
Introduction, 239 Water-Resources Data, 239 Climatic Data, 240 Maps, 241 Current Conditions and Outlooks, 241 Interpreted Data, 242 General, 242 References, 243 INDEX
245
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1
Chapter 1
INTRODUCTION
1.1 GENWAL S t r e a m f l o w changes c o n t i n u a l l y i n r e s p o n s e t o w e a t h e r and t h e modifying e f f e c t of t h e land.
But t h e c l i m a t e over a d r a i n a g e b a s i n f o l l o w s a p a t t e r n
throughout each y e a r and t h i s r e s u l t s i n a y e a r l y c y c l e i n s t r e a m f l o w .
On t h i s
c y c l e a r e imposed t h e v a r i a t i o n s of flow b e c a u s e of t h e p a r t i c u l a r w e a t h e r i n t h e p r e c e d i n g days o r months.
Both t h e c l i m a t e and t h e l a n d v a r y from s t r e a m t o
s t r e a m and t h u s t h e f l o w s a l s o d i f f e r . H y d r o l o g i s t s e x p l a i n t h e movement o f w a t e r on t h e e a r t h b y t h e h y d r o l o g i c c y c l e , an e x t r e m e l y g e n e r a l i z e d c o n c e p t t h a t b e g i n s w i t h e v a p o r a t i o n of m o i s t u r e from t h e oceans and t r a n s p o r t of t h a t m o i s t u r e i n c l o u d masses o v e r l a n d where i t is precipitated.
The p r e c i p i t a t i o n ,
i f r a i n , may b e d i s p o s e d of by r u n o f f on
t h e l a n d s u r f a c e , i n f i l t r a t i o n i n t o t h e s o i l , and by e v a p o r a t i o n .
The i n f i l -
t r a t e d w a t e r may r e m a i n as s o i l m o i s t u r e t o b e l a t e r e v a p o r a t e d or t r a n s p i r e d by p l a n t s , o r some of i t may move down t o a w a t e r t a b l e from which i t may r e a p p e a r as streamflow.
E v a p o r a t i o n and t r a n s p i r a t i o n t a k e an a d d i t i o n a l t o l l f r o m
s t r e a m f l o w b e f o r e t h a t w a t e r r e t u r n s t o t h e ocean.
Obviously t h e t r a n s f o r m a t i o n
of p r e c i p i t a t i o n i n t o s t r e a m f l o w i n a p a r t i c u l a r b a s i n i s e x t r e m e l y c o m p l i c a t e d because of t h e many v a r i a b l e s of w e a t h e r , geology, and topography.
Although t h e
l a n d p h a s e o f t h e h y d r o l o g i c c y c l e i s w e l l u n d e r s t o o d , t h e i n p u t a n d t h e many r e l e v a n t l a n d c h a r a c t e r i s t i c s c a n n o t b e m e a s u r e d a c c u r a t e l y enough t o d e f i n e streamflow completely d e t e r m i n i s t i c a l l y .
C h a p t e r 2 d e s c r i b e s how v a r i o u s meas-
u r a b l e f a c t o r s a f f e c t t h e flow regime.
General p r i n c i p l e s a r e explained i n
t e x t s on hydrology such a s one by L i n s l e y ,
Kohler,
and Paulhus (1982).
Q u a n t i t a t i v e hydrology i s a r a t h e r r e c e n t s c i e n c e .
Streamflow measurements
were n o t w i d e l y a v a i l a b l e u n t i l a f t e r 1888 when t h e U.S. s y s t e m a t i c gaging.
G e o l o g i c a l Survey began
Subsequent demands f o r i r r i g a t i o n w a t e r ,
hydropower,
flood
c o n t r o l , m u n i c i p a l and i n d u s t r i a l w a t e r s u p p l i e s , and s o i l c o n s e r v a t i o n l e d t o major a c t i v i t y i n hydrologic analysis.
F u l l e r and Hazen h a d s t u d i e d t h e f r e -
quency d i s t r i b u t i o n s of f l o o d s b y 1914 and f l o w - d u r a t i o n
c u r v e s and methods o f
e s t i m a t i n g f l o w s of ungaged s t r e a m s w e r e a v a i l a b l e a t t h a t time.
J a r v i s (1936)
and Hoyt (1936) g i v e b r i e f summaries of developments up t h e t h e mid 1930s.
Many
of t h e developments s i n c e t h e n r e s u l t e d from g r e a t e r u s e of s t a t i s t i c s . The a v a i l a b i l i t y o f d i g i t a l c o m p u t e r s f u r t h e r e x p a n d e d t h e c a p a b i l i t y t o u t i l i z e l a r g e a m o u n t s o f d a t a i n a n a l y s e s t h a t w e r e not p r e v i o u s l y f e a s i b l e . The i m p r o v e d u n d e r s t a n d i n g of g r o u n d - w a t e r movement a l s o h a s c o n t r i b u t e d t o
p r o g r e s s i n s u r f a c e - w a t e r h y d r o l o g y : s u r f a c e and ground w a t e r a r e i n t i m a t e l y r e l a t e d i n most r e g i o n s . Streamflow c h a r a c t e r i s t i c s a r e q u a n t i t a t i v e measures o f v a r i a b i l i t i e s of d a i l y ,
monthly,
t h e magnitudes and
and a n n u a l means and of f l o w extremes.
They
c a n b e computed from s t r e a m f l o w r e c o r d s o r by i n d i r e c t means where no r e c o r d s are available;
t h e s e computed v a l u e s a r e of c o u r s e o n l y e s t i m a t e s of t h e long-
term values. Streamflow c h a r a c t e r i s t i c s a r e used i n a wide v a r i e t y of problems such a s d e f i n i n g a v a i l a b l e f l o w w i t h and w i t h o u t s t o r a g e ; f o r e c a s t i n g f l o o d s , d r o u g h t s , and s n o w m e l t r u n o f f : d e s i g n i n g b r i d g e w a t e r w a y openings: p l a n n i n g p r o t e c t i o n from f l o o d s : and e s t a b l i s h i n g r e g u l a t o r y r e q u i r e m e n t s .
P r o b a b l e changes i n f l o w
c h a r a c t e r i s t i c s r e s u l t i n g e i t h e r from n a t u r a l o r a r t i f i c i a l m o d i f i c a t i o n s of a b a s i n a r e needed t o e v a l u a t e t h e impact of such m o d i f i c a t i o n s . The m a t e r i a l p r e s e n t e d h e r e i s d i r e c t e d t o h y d r o l o g i s t s who a r e f a c e d w i t h p r a c t i c a l p r o b l e m s and t o e n g i n e e r s and p l a n n e r s who u s e h y d r o l o g i c d a t a a n d would p r o f i t from knowing how i t was d e r i v e d and how i t s h o u l d b e i n t e r p r e t e d . T h i s book p r o v i d e s s e l e c t e d t e c h n i q u e s and t h e o t h e r i n f o r m a t i o n needed t o e s t i m a t e s t r e a m f l o w c h a r a c t e r i s t i c s and t o e v a l u a t e t h e i r r e l i a b i l i t y . l i t e r a t u r e on hydrology and h y d r o l o g i c a n a l y s i s i s e x t e n s i v e .
The
Any c o l l e c t i o n o f
t e c h n i q u e s i n a book of r e a s o n a b l e l e n g t h would n o t b e complete.
The t e c h n i q u e s
s e l e c t e d f o r i n c l u s i o n i n t h i s book a r e l i m i t e d t o o n e s t h a t a r e r e a s o n a b l y s i m p l e t o d e f i n e and t h a t r e q u i r e o n l y commonly a v a i l a b l e d a t a .
More complex
methods a r e mentioned and r e f e r e n c e d . Any d e s c r i p t i o n of a h y d r o l o g i c t e c h n i q u e i s i n c o m p l e t e w i t h o u t some means of e v a l u a t i n g t h e r e l i a b i l i t y of t h e r e s u l t .
Such e v a l u a t i o n s should b e based on
an u n d e r s t a n d i n g o f t h e hydrology of t h e b a s i n o r r e g i o n , of s t a t i s t i c a l p r i n c i ples,
and of t h e r e l i a b i l i t y of t h e d a t a used.
The c h a p t e r s on F a c t o r s A f f e c t -
i n g Streamflow, C o l l e c t i o n o f Hydrologic Data.
R e l a t i o n o f Ground W a t e r t o
S u r f a c e Water, and S t a t i s t i c s a r e i n c l u d e d t o p r o v i d e t h a t u n d e r s t a n d i n g . tionally,
Addi-
throughout t h e book e v a l u a t i o n s and l i m i t a t i o n s of t h e v a r i o u s tech-
niques are discussed.
This information should help the reader t o s e l e c t the
most a p p r o p r i a t e t e c h n i q u e f o r t h e p a r t i c u l a r a p p l i c a t i o n a s w e l l a s t o make a ( s u b j e c t i v e ) e s t i m a t e of t h e r e l i a b i l i t y of t h e r e s u l t . Many s t a t i s t i c a l t e c h n i q u e s a p p l i c a b l e t o hydrology can b e a p p l i e d w i t h o u t knowledge of s t a t i s t i c a l theory.
F o r example,
a n a l y s i s and m u l t i p l e r e g r e s s i o n can b e used, of e i t h e r s t a t i s t i c s o r hydrology.
computer programs f o r frequency and o f t e n a r e ,
w i t h o u t knowledge
B u t a n a n a l y s t w i t h no s t a t i s t i c a l b a c k -
g r o u n d may make a s s u m p t i o n s o f w h i c h h e i s n o t a w a r e a n d h e may i n c o r r e c t ' l y interpret h i s results.
The m a t e r i a l i n t h e c h a p t e r on s t a t i s t i c s i s d i r e c t e d t o
t h o s e w i t h l i t t l e t r a i n i n g in t h a t f i e l d ;
i t c o n c e n t r a t e s on t h e o r y (non-mathe-
m a t i c a l ) r a t h e r than on c o m p u t a t i o n a l d e t a i l s .
3 By e m p h a s i z i n g a p p l i e d h y d r o l o g y i n t h i s book,
t h e coverage of p r a c t i c a l
s u b j e c t s i s b r o a d e r and t h e a n a l y s e s a r e d e s c r i b e d i n more d e t a i l t h a n i s u s u a l i n one source.
On t h e o t h e r hand t h e h y d r o l o g i c s u b j e c t s a r e l i m i t e d t o t h o s e
useful i n applying the techniques presented.
Consequently, s e v e r a l s u b j e c t s
commonly i n c l u d e d i n h y d r o l o g y t e x t s d o n o t a p p e a r h e r e . unit-hydrograph
method,
ting. channel hydraulics,
Among them a r e t h e
i n f i l t r a t i o n , c h a r a c t e r i z i n g p r e c i p i t a t i o n , f l o w rouevapotranspiration,
computer modeling, and e s t i m a t i o n
of f l o w c h a r a c t e r i s t i c s from p r e c i p i t a t i o n i n a r i d and s e m i a r i d r e g i o n s . 1.2
PROBABILITY AND RECURRENCE INTERVAL F o r many y e a r s e n g i n e e r s h a v e d e s c r i b e d t h e f r e q u e n c y c h a r a c t e r i s t i c s o f
annual e v e n t s i n t e r m s of r e c u r r e n c e i n t e r v a l ,
t h e r e c i p r o c a l of p r o b a b i l i t y .
F o r e x a m p l e , t h e a n n u a l f l o o d w i t h a p r o b a b i l i t y o f 0.01 o f b e i n g e x c e e d e d i n any one y e a r i s commonly c a l l e d t h e 100-year flood.
E i t h e r way of d e s i g n a t i n g
t h a t f l o o d i s c o r r e c t b u t b e c a u s e laymen o f t e n m i s i n t e r p r e t t h e meaning of a f l o o d o f a g i v e n r e c u r r e n c e i n t e r v a l , t h e U.S.
W a t e r R e s o u r c e s C o u n c i l recom-
mended t h a t t h e p r e f e r r e d d e s c r i p t o r b e p r o b a b i l i t y .
Recurrence i n t e r v a l i s
g e n e r a l l y used i n t h i s book b e c a u s e r e c u r r e n c e i n t e r v a l was used i n most of t h e a n a l y s e s s e l e c t e d a s examples.
No p r e f e r e n c e for r e c u r r e n c e i n t e r v a l should b e
imp1 i e d . 1.3
UNITS Some E n g l i s h - s p e a k i n g n a t i o n s u s e t h e B r i t i s h o r I m p e r i a l s y s t e m of u n i t s
a l t h o u g h i n s u r v e y i n g and i n hydrology t e n t h s and h u n d r e d t h s of f e e t a r e used instead of inches.
I n t e r n a t i o n a l j o u r n a l s r e q u i r e u s e of m e t r i c o r S y s t e m e
I n t e r n a t i o n a l d'Unites tists.
(SI u n i t s ) which have been adopted by n e a r l y a l l s c i e n -
A c o m p l e t e and a b r u p t c h a n g e t o t h e m e t r i c s y s t e m i n h y d r o l o g y i s n o t
f e a s i b l e i n t h e United S t a t e s b e c a u s e many e x i s t i n g l a w s , r e g u l a t i o n s , r e c o r d s , and s t a n d a r d s a r e based on t h e B r i t i s h system.
For d e m o n s t r a t i n g p r i n c i p l e s and
explaining techniques e i t h e r system of u n i t s i s adequate.
The p r o b l e m s and
e x a m p l e s g i v e n i n t h i s book a r e i n t h e u n i t s i n w h i c h t h e y w e r e o r i g i n a l l y reported.
R e s u l t s c a n e a s i l y b e c o n v e r t e d f r o m o n e s y s t e m of u n i t s t o t h e
other. 1.4
CONVERSION FACTORS 1 i n c h = 25.4 m i l l i m e t e r s
1 foot
= 1 2 i n c h e s = 304.8
millimeters
1 m i l e = 5280 f e e t = 1.609 k i l o m e t e r s 1 m i l l i m e t e r = 0.039 i n c h e s 1 m e t e r = 39.37 i n c h e s = 3.281 f e e t
1 k i l o m e t e r = 0.621 m i l e s 1 a c r e = 43.560 s q u a r e f e e t
4 1 s q u a r e m i l e = 640 a c r e s 1 s q u a r e meter
=
10.76 s q u a r e f e e t
1 h e c t a r e = 2.471 a c r e s 1 square kilometer 1 cubic f o o t 1 U.S.
=
=
100 h e c t a r e s
7.4805 U.S.
=
0.386 s q u a r e m i l e s
g a l l o n s = 0.028
cubic meters
g a l l o n = 3.785 l i t e r s
1 acre-foot
=
43,560 c u b i c f e e t = 1233.5 c u b i c m e t e r s
1 c u b i c meter = 35.31 c u b i c f e e t 1 million cubic meters
=
810.7 a c r e - f e e t
1 c f s ( c u b i c f o o t p e r second) = 0.028 cms ( c u b i c m e t e r s p e r second) 1 cfs-day = 0.0864 m i l l i o n c u b i c f e e t = 1.983471 a c r e f e e t = 0.6463 m i l l i o n g a l l o n s
1 cfs-year = 723.97 a c r e f e e t ( f o r 365 d a y s ) 1 c f s per square mile f o r one day = 0.03719 inches d e p t h on t h e d r a i n a g e b a s i n Annual r u n o f f i n i n c h e s = 13.58
times annual mean, i n c f s p e r s q u a r e m i l e
1 pound = 0.4536 kilograms 1 g a l l o n = 8.33 pounds ( w a t e r ) 1 c u b i c f o o t = 62.4 pounds ( w a t e r ) 1 kilogram = 2.205 pounds 1 f o o t p e r second = 0.682 m i l e s p e r hour REFERENCES Eoyt. W.G.. States:
1936, S t u d i e s o f R e l a t i o n s o f R a i n f a l l and Runoff i n t h e U n i t e d U.S. G e o l o g i c a l Survey Water-Supply Paper 772, 301 p.
J a r v i s , C.S., 1936, F l o o d s i n t h e U n i t e d S t a t e s , M a g n i t u d e and F r e q u e n c y : Geological Survey Water-Supply Paper 771, 497 p.
U.S.
L i n s l e y , R.K.,, K o h l e r , M.A., and P a u l h u s , J.L.H., 1982, H y d r o l o g y f o r E n g i n e e r s , Third E d i t i o n : New York. McGraw-Hill, 496 p.
5
Chapter 2
FACTORS AFFECTING STREAMFLOW 2.1 INTRODUCTION The process by which precipitation becomes streamflow is well known in a general way.
But for a specific drainage basin it is not possible to quantify
all the relevant variables and to describe the paths that the water takes a t various times.
Nevertheless some knowledge of the probable processes in a basin
is essential if realistic estimates of streamflow characteristics in that basin are to be obtained.
Climate, geology, and topography are the principal basin
characteristics affecting streamflow.
Unusual streamflow patterns usually can
be explained qualitatively by some feature or combination of features of these. This chapter provides such explanations using examples of flows from various regimes.
More information on hydrologic characteristics throughout the world is
given by L'vovich (1980).
The following section, 2.2, is from Riggs (1980) by
permission of Pergamon Press. 2.2
CLIMATIC FACTORS The climatic factors of precipitation, temperature, sunshine, humidity, and
wind all affect stream runoff to some extent, but only precipitation and temperature account for major differences among runoff regimes in regions of similar geology and topography.
Precipitation, the source of runoff, is disposed of in
several ways, some is evaporated from the surfaces on which i t falls, some infiltrates into the soil, and some moves directly to stream channels.
Of the
water that infiltrates the soil, some will be removed later by evaporation and transpiration and some may reach a ground-water body which maintains stream runoff between storms. Temperature, in conjunction with sunshine and wind, determines the evapotranspiration losses.
In temperate and tropical regions of
low annual precipitation, evapotranspiration losses may nearly equal the precipitation.
At the other extreme, evapotranspiration may be
percent of precipitation in regions of high rainfall.
as
l i t t l e as 10
Below-freezing tempera-
tures affect runoff by delaying runoff from snowfall and by modifying the winter runoff because of ice formation. 2.2.1
E f f e c t s of t h e p r e c i p i t a t i o n r e g i m e
The response of Shetucket River to an intense storm rainfall associated with a West Indian hurricane is shown in Figure 2.1.
The extremely high peak dis-
charge is followed by a high base flow resulting from the recharge of ground water in the drainage basin.
6
’”’
The magnitude of a f l o o d peak i s n o t o n l y a f u n c t i o n of t h e r a i n f a l l magnit u d e and d u r a t i o n ,
2000 i
-
b u t a l s o of t h e a r e a l coverage of t h e s t o r m r e l a t i v e t o t h e
v
T
500
5 1
20
10
SEPT F i g . 2.1.
30 1938
10
20 OCT
Runoff from i n t e n s e r a i n f a l l , S h e t u c k e t R i v e r , C o n n e c t i c u t .
d r a i n a g e b a s i n of t h e stream.
Thus t h e c h a r a c t e r of s t o r m s i n a r e g i o n d e t e r -
mines t h e r e l a t i v e magnitudes of u n u s u a l f l o o d s f o r v a r i o u s d r a i n a g e a r e a s i z e s . In some a r i d and s e m i a r i d r e g i o n s t h u n d e r s t o r m s produce e x c e p t i o n a l f l o o d peak discharges per u n i t area for the smaller drainage areas.
Thunderstorms a l s o
produce r e c o r d f l o o d s from s m a l l b a s i n s i n humid r e g i o n s , b u t t h o s e r e g i o n s a r e a l s o s u b j e c t t o more w i d e s p r e a d s t o r m s which produce t h e m a j o r f l o o d s from l a r g e r basins.
The d i f f e r e n c e i n f l o o d p o t e n t i a l between a s e m i a r i d and a humid
r e g i o n i s shown b y p l o t s o f maximum k n o w n f l o o d - p e a k d i s c h a r g e s ( C r i p p e n a n d Bue, 1977) a g a i n s t d r a i n a g e a r e a f o r s e m i a r i d A r i z o n a a n d f o r h u m i d V i r g i n i a (Fig. 2.2).
The l e s s e r f l o o d p o t e n t i a l f r o m l a r g e b a s i n s i n A r i z o n a i s d u e
p r i n c i p a l l y t o t h e l i m i t e d a r e a l e x t e n t of major storms.
I n b a s i n s where snow does n o t accumulate, and where b a s i n c h a r a c t e r i s t i c s a r e n o t unusual,
t h e s e a s o n a l d i s t r i b u t i o n of r u n o f f c l o s e l y f o l l o w s t h e s e a s o n a l
d i s t r i b u t i o n of p r e c i p i t a t i o n . the r e s u l t i n g runoff
F i g u r e 2.3 compares t h e monthly p r e c i p i t a t i o n t o
f o r S e t i Khola.
Nepal,
i n a r e g i o n of h i g h r a i n f a l l .
T y p i c a l d i s t r i b u t i o n o f r u n o f f i n a c l i m a t e w i t h w e t w i n t e r s a n d d r y summers. a l s o f o l l o w s t h e p r e c i p i t a t i o n c l o s e l y so long a s t e m p e r a t u r e i s g e n e r a l l y above f r e e z i n g ( P i g . 2.4). Seasonal v a r i a b i l i t y of l a r g e s t r e a m s t e n d s t o be l e s s t h a n f o r s m a l l ones because l a r g e ones may have s o u r c e s i n d i f f e r e n t c l i m a t e s so t h a t t h e c u m u l a t i v e
7
5 r
x
X
a
s
VIRGINIA (Humid) ARIZONA (Semiarid)
100 1000 DRAINAGE AREA, IN KM*
10,000
Fig. 2.2 Maximum known floods in a humid and a semiarid area.
1000
1
I
1
,
,
I
I
l
l
, , /\
z
8
v)
=
z
8001
600 PRECIPITATION A T P 0/
;
A
-
I
4001
\
I
_I
g
200
///
O'J
RUNOFF
1,
,
c---
\
F M A-M
J MONTH
A
6
1 - L
I
0 N D
Fig. 2.3. Average monthly precipitation and runoff, Seti Khola, Nepal.
I
O
'
j
I
,
F
M
I A
I M J J MONTH
l A
l S
O
N
'
o
Fig. 2.4. Monthly distribution of precipitation and runoff, Tualatin River, Oregon.
8
effect of inputs at various times and the lag in runoff from headwaters is a reduction in the variability of downstream flow among seasons.
This is illus-
trated by the seasonal distribution of flow in the Amazon River and of the precipitation at two sites in the basin (Fig. 2 . 5 ) .
3
0
~
~ J - A S~ O NA D MONTH
~
~
Fig. 2.5. Seasonal distribution of runoff of Amazon River and of precipitation at two sites in the basin. The seasonal distribution of precipitation also influences the low-flow characteristics of a stream.
Frequent storms throughout the year, and especial-
ly during the late summer, tend to maintain streamflow whereas, in a climate characterized by little or no rain during summer, the late summer streamflows may be small or zero.
The ephemeral stream, one which flows only in direct
response to precipitation, and the intermittent stream, which flows for only part of each year on the average, are typical of regions with dry summers. The above comparisons of seasonal runoff to precipitation have been for average conditions.
Variability of weather from year to year accounts for the
considerable variation in monthly runoff, in flood peaks, and in low flows.
The
annual low flow may result from no precipitation for a considerable period or from small amounts of precipitation on each of many days of an extended period,
no amounts large enough to do more than supplement the soil moisture.
A long
period of no precipitation causes a drought both hydrologically and agriculturally, whereas frequent small rainfalls may not produce runoff yet may maintain adequate soil moisture for plants. Annual precipitation on a river basin varies from year to year.
The re-
sulting runoff is more variable than the precipitation because the percentage of precipitation that becomes runoff decreases with decreasing precipitation. Figure 2.6 shows a long record of annual runoffs for Red River of the North, North Dakota, USA.
The period of low runoff in the 1930’s resulted from several
consecutive years of below normal precipitation. mean runoffs shown in Figure 2.7.
More typical are the annual
The large year-to-year variability in runoff
of Rio Guadalquivir in southern Spain is the result of the highly variable
9
L
$05 4
1916 1920 1924 1928 1932 1936 I t 4 0 1944 1&8 YEAR
Fig. 2.6. Annual runoff of Red River of the North, North Dakota.
g
100'
1910 1920
1930
1940 YEAR
1950 1960
Fig. 2 . 7 . Variability of annual runoffs in a humid region (Sweden) and in semiarid region (Spain). annual precipitation characteristic of a semiarid region.
a
In contrast, the
annual runoffs of Vanern-Gota. Sweden, in a cool humid climate, are much less variable. 2.2.2
How temperature modifies runoff
Temperature influences runoff in two principal ways:
(1) high temperatures
increase evapotranspiration and thus reduce the amount of runoff from precipitation, and ( 2 ) freezing and thawing change the timing of runoff by delaying the response of runoff to precipitation and by modifying the flow of water already in the channel. The amount of moisture returned to the atmosphere by evaporation and by transpiration of plants depends on climate, principally temperature, sunshine, and wind, and on the supply of moisture.
Frequent rains provide a nearly
10
continuous supply of moisture, but infrequent storms leave little moisture for evapotranspiration for long periods.
Thus both potential evapotranspiration and
the difference between potential and actual evapotranspiration depend on the climate. Annual evapotranspiration, or annual water loss, can be quantified as the difference between precipitation on a basin and the resulting runoff.
Figure
2.8 shows water losses plotted against mean annual temperature for basins with
L
MEAN ANNUAL TEMPERATURE, IN " C Fig. 2.8. Annual water loss as a function of temperature, eastern USA (from Williams, 1 9 4 0 ) . mean annual precipitation greater than 500 mm.
Annual water loss is a moderate
percentage of the annual precipitation in a humid region but a very large percentage in regions of low precipitation.
Thus the annual runoff is highly
variable where precipitation is low (Red River of the North and Rio Guadalquivir in Figs. 2.6 and 2.7).
In temperate and tropical arid regions, potential evapo-
transpiration is larger than precipitation except for short periods during and following rainstorms.
Thus there are no perennial streams in such regions.
Temperature and thus evapotranspiration rates change seasonally in most parts of the world.
160
'
Figure 2.9 shows that losses during that summer are larger than
,
J F M A M J J A S O N D MONTHS 1947
Fig 2 . 9 . Seasonal relation of precipitation and runoff showing the large evapotranspiration losses in summer in North Carolina. (January precipitation probably was snow.!
11 a t o t h e r t i m e s of t h e year.
T h e p r e c i p i t a t i o n o n t h e H o mi n y C r e e k b a s i n
probably i s n o t t h e same a s a t A s h e v i l l e b u t t h e monthly t r e n d s s h o u l d be similar.
The d i f f e r e n c e b e t w e e n p r e c i p i t a t i o n and r u n o f f f o r a s i n g l e month i s
o n l y a rough a p p r o x i m a t i o n o f l o s s b e c a u s e o f t h e c a r r y o v e r of w a t e r from one month t o t h e ne xt. Diurnal v a r i a t i o n s i n e v a p o t r a n s p i r a t i o n o f t e n produce d i u r n a l f l u c t u a t i o n s i n t h e f l o w o f s m a l l s t r e a m s wh er e t h e t e m p e r a t u r e d i f f e r e n c e b e t w e e n n i g h t and a sunny day i s l a r g e .
F i g u r e 2.10 shows t h e d i s c h a r g e h y d r o g r a p h d u r i n g s u c h a
JUNE, 1941
F i g . 2.10. D i u r n a l f l u c t u a t i o n s i n s t r e a m f l o w c a u s e d by e v a p o t r a n s p i r a t i o n l o s s e s ( m o d i f i e d from Du n fo r d an d F l e t c h e r , 1 9 4 7 ) . period.
variable
The e f f e c t o f e v a p o t r a n s p i r a t i o n on s t r e a m f l o w i s s o m e t i m e s m a n i f e s t e d
i n t h e d r y i n g up o f a s m a l l s t r e a m d u r i n g summer and i t s s u b s e q u e n t r e s u m p t i o n of f l o w i n t h e a b s e n c e o f r a i n a s t e m p e r a t u r e d e c r e a s e s i n t h e f a l l months.
The
m a g n i t u d e o f e v a p o t r a n s p i r a t i o n may a l s o b e i n d i c a t e d b y a s h a r p i n c r e a s e i n s t r e a m f l o w a f t e r t h e f i r s t h a r d f r o s t o f au tumn k i l l s t h e r i p a r i a n v e g e t a t i o n . The w i t h i n - y e a r d i s t r i b u t i o n o f r u n o f f o f A r c t i c s t r e a m s i s d e t e r m i n e d by temperature, not precipitation, because the winter p r e c i p i t a t i o n remains i n s t o r a g e a s i c e o r sn o w u n t i l s u m m e r .
The mean m o n t h l y r u n o f f s o f a t y p i c a l
A r c t i c s t r e a m , Yan a R i v e r , D z a n h k y , USSR, a r e s h o w n i n F i g u r e 2.11 a l o n g w i t h t h e p r e c i p i t a t i o n and t e m p e r a t u r e a t Verhoyansk.
Imw f l o w s d u r i n g w i n t e r r e s u l t
from f r e e z i n g of n e a r l y a l l w a t e r i n t h e channel; t h e base flow of a stream draining a permafrost regime is negligible. A l e s s e x t r e m e r a n g e i n m o n t h l y f l o w s o f a n o r t h e r n s t r e a m o c c u r s on Yukon River,
Canada a nd A l a s k a , w h e r e t h e f l o w u n d e r i c e c o v e r r e c e d e s t h r o u g h o u t t h e
w i n t e r b u t i s n e v e r l e s s t h a n s e v e r a l hundreds o f c u b i c m e t e r s p e r second. Temperature i s a g a i n t h e major f a c t o r i n s e a s o n a l d i s t r i b u t i o n of fl ow a l t h o u g h t h e maximum p r e c i p i t a t i o n d o e s c o i n c i d e w i t h t h e summer h i g h f l o w .
A s h a r p r i s e in t e m p e r a t u r e f o l l o w i n g a p r o l o n g e d c o l d s p e l l w i l l r e l e a s e t h e h e a v y i c e c o v e r on a r i v e r .
The r e s u l t i n g i c e j a m s may damage s t r u c t u r e s i n and
a l o n g t h e r i v e r and c a u s e o v e r b a n k f l o o d i n g .
N o r t h w a r d f l o w i n g s t r e a m s a r e mo st
12
10,000
--
~
__
-7
YANA RIVER, DZA NG HKY, USSR
. rn
0
I
z ti
U
0
3 z
a
z
5
I
t-
MONTH
F i g . 2.11. S e a s o n a l d i s t r i b u t i o n o f r u n o f f o f a n a r c t i c s t r e a m s h o w i n g t h e e f f e c t of t e m p e r a t u r e . s u s c e p t i b l e t o i c e j a m s because t h e s o u t h e r n h e a d w a t e r s thaw b e f o r e t h e n o r t h e r l y downstream r e a c h e s of t h e channel. Small s t r e a m s i n n o r t h e r n c l i m e s f r e e z e t o t h e b o t t o m d u r i n g t h e w i n t e r .
In
c e r t a i n nonpermafrost reaches, ground w a t e r c o n t i n u e s t o f e e d t h e s t r e a m b u t b e c a u s e t h i s w a t e r c a n n o t f l o w down t h e s t r e a m c h a n n e l i t f l o w s o v e r t h e i c e u n t i l i t freezes.
T h u s , t h e i c e c o v e r on t h e s t r e a m a n d o v e r b a n k i s b u i l t u p
throughout t h e winter.
T h i s i c i n g may e n c o m p a s s r o a d s , b l o c k c u l v e r t s , and
invade b u i l d i n g s along a stream. Temperature e f f e c t s on s t r e a m f l o w where c o m p l e t e i c e c o v e r d o e s n o t o c c u r throughout t h e w i n t e r a r e somewhat d i f f e r e n t t h a n t h o s e above. l a r g e s t r e a m i s shown i n F i g u r e 2.12 (Simons. 1953).
The e f f e c t on a
Extremely c o l d w e a t h e r f o r .
a few d a y s p u t s w a t e r in s t o r a g e a s i c e i n t h e c h a n n e l a n d r e d u c e s t h e f l o w .
13 Recovery of u s u a l flow f o l l o w s an i n c r e a s e i n t e m p e r a t u r e . flow i n e a r l y F e b r u a r y was caused by above-freezing
The b i g i n c r e a s e i n
t e m p e r a t u r e s and r a i n .
PRECIPTTATION. IN MM n
Fig.
2.12.
n
D
E f f e c t of t e m p e r a t u r e on streamflow. Salmon River, Idaho.
I n more s o u t h e r l y c l i m e s ,
and g e n e r a l l y a t h i g h e l e v a t i o n s ,
t h e temperature
d u r i n g w i n t e r may r a n g e f r o m much b e l o w f r e e z i n g a t n i g h t t o a b o v e f r e e z i n g d u r i n g t h e day.
During c l e a r ,
c o l d n i g h t s anchor i c e forms on t h e r o c k s o f t h e
s t r e a m b e d b e c a u s e o f l o s s o f h e a t by r a d i a t i o n t o t h e a t m o s p h e r e . from t h e sun t h e n e x t day warms t h e r o c k s and r e l e a s e s t h e ice. n o t form under s u r f a c e i c e cover.
Radiation
Anchor i c e does
The f o r m a t i o n and s u b s e q u e n t r e l e a s e o f
anchor i c e c a u s e s s u b s t a n t i a l f l u c t u a t i o n s i n w a t e r l e v e l i n t h e s t r e a m (Fig. 2.13) and s m a l l e r f l u c t u a t i o n s i n d i s c h a r g e .
FEBRUARY. 1953
Fig. 2.13. W a t e r l e v e l f l u c t u a t i o n s i n a s m a l l s t r e a m d u e to f o r m a t i o n a n d r e l e a s e of anchor i c e (modified from Moore, 1957).
14 G l a c i e r s and s n o w f i e l d s a r e common i n mountainous r e g i o n s a t h i g h l a t i t u d e s . Runoff from t h e s e f e a t u r e s i s more c l o s e l y r e l a t e d t o t e m p e r a t u r e t h a n t o t h e previous w i n t e r p r e c i p i t a t i o n . t y p i c a l l y h i g h summer r u n o f f . i n Washington
g
State,
USA,
S t r e a m s w i t h g l a c i e r s i n t h e i r h e a d w a t e r s have Hydrographs of a g l a c i a l and a n o n g l a c i a l s t r e a m i n F i g u r e 2.14,
show t h e o p p o s i t e e f f e c t s o f
20 (Glacialin headwaters)
wl c
2 15
-~
MAY
~
JUNE
JULY
AUGUST
1962
F i g . 2.14. H y d r o g r a p h s s h o w i n g t h e o p p o s i t e e f f e c t s o f a d r y J u l y on a g l a c i a l and a n o n g l a c i a l stream. t e m p e r a t u r e on r u n o f f d u r i n g a t y p i c a l l y d r y J u l y .
High t e m p e r a t u r e i n c r e a s e s
t h e l o s s e s from both basins, but i n c r e a s e s g l a c i e r melt i n White River basin. During o t h e r s e a s o n s t h e f l o w s of t h e two s t r e a m s respond s i m i l a r l y t o temperat u r e and p r e c i p i t a t i o n . G l a c i e r s s o m e t i m e s c a u s e unusual f l o o d s by i m p o u n d i n g w a t e r a n d t h e n r e leasing i t abruptly.
From a t l e a s t 1948 t o 1962. Knik G l a c i e r , Alaska, advanced
a c r o s s Knik R i v e r each w i n t e r and t e m p o r a r i l y s t o r e d t h e s p r i n g r u n o f f .
De-
s t r u c t i o n o f t h e g l a c i e r dam e a c h summer b y m e l t i n g a n d e r o s i o n r e l e a s e d t h e s t o r e d w a t e r c a u s i n g a n o u t s t a n d i n g f l o o d on K n i k R i v e r .
F i g u r e 2.15 s h o w s
hydrographs f o r y e a r s w i t h and w i t h o u t t h e g l a c i e r e f f e c t .
Annual r u n o f f s f o r
t h e s e 2 y e a r s a r e v i r t u a l l y t h e same.
I n t e m p e r a t e r e g i o n s p r e c i p i t a t i o n may occur a s snow d u r i n g t h e w i n t e r and b e r e l e a s e d i n s p r i n g o r e a r l y summer, p a r t i c u l a r l y i f t h e s t r e a m s b e a d a t h i g h elevations.
Maximum s t r e a m f l o w s o f t e n o c c u r a s a r e s u l t of s n o w m e l t .
The
amount of r u n o f f from a snowpack depends on t h e w e a t h e r d u r i n g t h e m e l t p e r i o d .
A r a p i d m e l t w i l l produce t h e most r u n o f f .
An e x t e n d e d m e l t p e r i o d c a u s e d by
c o o l t e m p e r a t u r e s p e r m i t s more loss by a b l a t i o n and by i n f i l t r a t i o n . 2.2.3
C l i m a t i c d i f f e r e n c e s along a s t r e a m
Some s t r e a m s d r a i n a r e a s h a v i n g o n e c l i m a t i c r e g i m e i n t h e h e a d w a t e r s a'nd a n o t h e r i n t h e downstream p a r t of t h e b a s i n .
Commonly t h e p r i n c i p a l r u n o f f
is
g e n e r a t e d i n t h e h e a d w a t e r s which h a s t h e h i g h e r p r e c i p i t a t i o n ; t h e n tlx: downstream runoff c h a r a c t e r i s t i c s a r e a c o m p o s i t e .
15
z
2ooM r
i 100
-1
Fig. 2.15. Hydrographs f o r Knik River, Alaska, showing t h e e f f e c t of impoundment and r e l e a s e of w a t e r by a g l a c i e r (1961). and a y e a r w i t h no impoundment ( 1 9 6 3 ) . Two f l o o d p e r i o d s p e r y e a r a r e produced on Merced River, C a l i f o r n i a , one from l o w - e l e v a t i o n r a i n f a l l i n w i n t e r and t h e second from t h e m e l t i n g of t h e snowpack i n t h e S i e r r a Nevada i n l a t e s p r i n g .
F i g u r e 2.16
s h o w s t h e annual f l o o d -
f r e q u e n c y c u r v e s f o r t h e two t y p e s of f l o o d s (Crippen, 1978).
The s n o w m e l t
f l o o d i s t h e l a r g e r i n most y e a r s b u t t h e m a j o r f l o o d s a r e produced by r a i n f a l l . Commonly, a s t r e a m t h a t h e a d s i n t h e h i g h m o u n t a i n s w i l l r e a c h i t s a n n u a l maximum d i s c h a r g e i n i t s u p s t r e a m r e a c h e s from snowmelt w h i l e f u r t h e r downstream t h e annual maximum d i s c h a r g e may be e i t h e r from snowmelt o r from r a i n f a l l or, occasionally.
a c o m b i n a t i o n of
t h e two.
The annual r u n o f f a t a downstream s i t e
on such a s t r e a m may b e l a r g e r o r s m a l l e r t h a n t h e r u n o f f a t some p o i n t upstream
depending on t h e downstream c l i m a t e . Typically,
b u t n o t always.
t a t i o n than t h e l o w e r reaches.
t h e h e a d w a t e r s o f a s t r e a m r e c e i v e more p r e c i p i I f t h e d i s p a r i t y i n p r e c i p i t a t i o n between t h e
upper and l o w e r b a s i n s i s n o t t o o g r e a t , o r i f t h e l o w e r b a s i n i s s m a l l r e l a t i v e t o t h e upper b a s i n . then r u n o f f w i l l i n c r e a s e downstream.
no c o n t r i b u t i o n f r o m t h e l o w e r b a s i n ,
If there i s l i t t l e or
two r e s u l t s c a n occur:
(1) a l a r g e
upstream runoff w i l l be t r a n s m i t t e d through the downstream b a s i n w i t h only r e l a t i v e l y moderate l o s s e s ,
o r (2) upstream r u n o f f may be g r e a t l y ( o r e n t i r e l y )
d i s s i p a t e d by e v a p o t r a n s p i r a t i o n and by i n f i l t r a t i o n through t h e channel bed i n t h e lower basin.
The N i l e R i v e r i s an example of t h e f i r s t .
Many examples of
t h e s e c o n d a r e known i n a r i d r e g i o n s a l t h o u g h t h e f l o w i s u s u a l l y r e d u c e d by manmade d i v e r s i o n s i n a d d i t i o n t o t h e n a t u r a l l o s s e s .
Many s t r e a m s t h a t f l o w
16
50 I--
: : / P E
/ I
20-
i
0 w-
u
+
v , ?n y
5'--
RAINFALL
i
/
2t
2 5 20 50 RECURRENCE INTERVAL IN YEARS
Fig. 2.16. Flood-frequency Cal i f o r n i a .
c u r v e s of snowmelt and r a i n f a l l f l o o d s , Merced R i v e r ,
i n t o a r i d r e g i o n s t e r m i n a t e i n c l o s e d l a k e s ; G r e a t S a l ! L r k e , Dead S e a , Lake Chad, a n d C a s p i a n S e a a r e w e l l known e x a m p l e s . p l a y a s which may b e d r y f o r l o n g p e r i o d s .
Other streams t e r m i n a t e i n
S t i l l o t h e r s t r e a m s , such a s t h e many
wadis d r a i n i n g toward t h e i n t e r i o r of t h e s o u t h e r n Arabian P e n i n s u l a ,
gradually
disappear i n t o the desert.
2.3
EFFECTS OF GEOLOGY Under t h e same c l i m a t i c i n f l u e n c e s , g r e a t l y d i f f e r e n t s t r e a m f l o w r e g i m e s a r e
produced from d r a i n a g e b a s i n s h a v i n g d i f f e r e n t s o i l s and rocks.
The s o i l o r
o t h e r s u r f i c i a l m a t e r i a l d e t e r m i n e s how much and a t what r a t e t h e p r e c i p i t a t i o n w i l l i n f i l t r a t e and t h u s what p r o p o r t i o n w i l l become o v e r l a n d r u n o f f .
Some of
t h e i n f i l t r a t e d w a t e r w i l l b e e v a p o r a t e d a n d t h e r e s t w i l l move t h r o u g h t h e rocks e i t h e r t o a stream channel or, t i o n below any s t r e a m channel.
i n some a r i d r e g i o n s ,
t o a zone of s a t u r a -
The c h a r a c t e r of t h e r o c k s d e t e r m i n e s how t h e
w a t e r moves underground and a t what r a t e s . Rapid s u r f a c e r u n o f f and l i t t l e b a s e f l o w a r e a s s o c i a t e d w i t h low i n f i l t r a tion rates.
Conversely,
a high i n f i l t r a t i o n rate.
t h e s t r e a m f l o w i s much l e s s v a r i a b l e from a b a s i n w i t h The f o l l o w i n g examples d e m o n s t r a t e how geology modi-
f i e s s t r e a m f l o w ; i n most b - ; l n s
geology may be o n l y one of s e v e r a l s i g n i f i c a n t
b a s i n c h a r a c t e r i s t i c s and i t s e f f e c t on s t r e a m f l o w may n o t b e r e a d i l y a p p a r e n t .
17 Regions i n which p r a c t i c a l l y a l l t h e p r e c i p i t a t i o n s o a k s i n t o t h e ground u s u a l l y a r e d r a i n e d by s t r e a m s w i t h l i t t l e v a r i a t i o n i n flow. Nebraska i s such a region.
F i g u r e 2.17
1000,
The Sand H i l l s of
c o m p a r e s t h e m o n t h l y mean f l o w s of
-v
v)
LL
0
z
3
PONCA CREEK
750 -
-
500 -
-
9
LL
" O N D J
F
M
A
M
J
J
A
S
1978 WATER YEAR
Fig. 2.17. Monthly mean f l o w s o f two Nebraska s t r e a m s . S a n d h i l l s Region. Dismal River,
a Sand H i l l s s t r e a m ,
Dismal R i v e r i s i n t h e
w i t h Ponca Creek, which i s not.
A less
e x t r e m e d i f f e r e n c e i s shown between two North C a r o l i n a s t r e a m s , Drowning Creek w h i c h d r a i n s a s a n d y a r e a , and U w h a r r i e R i v e r whose b a s i n i s l e s s p e r m e a b l e (Fig. 2.18).
V a r i a t i o n i n d a i l y f l o w s of two g e o l o g i c a l l y - d i f f e r e n t
streams is
shown i n F i g u r e 6.3 (Chapter 6 ) . The P a h s i m e r o i R i v e r i n I d a h o f l o w s through an a l l u v i a l v a l l e y between h i g h mountains.
Snowmelt r u n o f f from t h e t r i b u t a r i e s s i n k s i n t o t h e ground b e f o r e
reaching the river.
Low-elevation s p r i n g s i n t h i s b a s i n u s u a l l y reach t h e i r
maximum d i s c h a r g e s i n August o r September.
The m o d e r a t i n g e f f e c t of t h e a l l u -
v i a l f i l l i s s o g r e a t t h a t many o f t h e a n n u a l f l o o d p e a k s o n P a h s i m e r o i R i v e r o c c u r i n November or December a l t h o u g h a l l o t h e r gaged s t r e a m s i n t h e v i c i n i t y peak i n s p r i n g o r e a r l y summer. The Yucatan P e n i n s u l a of Mexico i s a f l a t , a r e few s t r e a m channels.
l i m e s t o n e p l a t e a u i n which t h e r e
P r a c t i c a l l y a l l of t h e p r e c i p i t a t i o n i n f i l t r a t e s i n t o
t h e ground and t h e n d r a i n s d i r e c t l y t o t h e ocean.
Some sandy c o a s t a l a r e a s i n
humid p a r t s of t h e w o r l d a l s o a r e w i t h o u t s t r e a m channels. B a s i n s w i t h s i m i l a r i n f i l t r a t i o n c h a r a c t e r i s t i c s may h a v e v e r y d i f f e r e n t o u t f l o w r e g i m e s due t o d i f f e r e n c e s i n t h e r a t e of movement through t h e ground and i n t h e amount of s t o r a g e i n t h e a q u i f e r .
T r o x e l l (1953) showed t h a t a major
18
0
looo --1
1
UWHARRIE R
DROWNING CR
" J F M A M J J A S O N D MONTHS, 1957 F i g . 2.18. M o n t h l y mean f l o w s o f t w o N o r t h C a r o l i n a s t r e a m s s h o w i n g t h e d i f f e r e n c e due t o b a s i n i n f i l t r a t i o n r a t e s .
F i g . 2.19. H y d r o g r a p h f o r M i l l C r e e k , C a l i f o r n i a , s h o w i n g t h a t t h e m a j o r recharge i n 1922 contributed t o the base flow f o r the next t h r e e y e a r s ( a f t e r Troxell, 1953). r e c h a r g e of t h e s m a l l ,
s t e e p b a s i n of M i l l Creek i n s o u t h e r n C a l i f o r n i a c o n t r i -
b u t e d t o t h e b a s e flow f o r s e v e r a l s u c c e e d i n g y e a r s ( F i g u r e 2.19),
an i n d i c a t i o n
of a l a r g e ground w a t e r body t h a t d r a i n e d r e l a t i v e l y s l o w l y t o t h e s t r e a m . McDonald and L a n g b e i n ( 1 9 4 8 ) c o n c l u d e d t h a t t h e g r o u n d w a t e r s t o r a g e i n t h e b a s i n of M e t o l i u s R i v e r , Oregon was about t h r e e t i m e s t h e annual runoff.
Meto-
l i u s R i v e r d r a i n s a b a s a l t b a s i n a n d i t s f l o w i s uncommonly s t e a d y .
On t h e
o t h e r hand t h e f l o w of Drowning Creek ( F i g u r e 2.18) responds r a t h e r p r o m p t l y t o p r e c i p i t a t i o n , i n d i c a t i n g a more l i m i t e d a q u i f e r c a p a c i t y . describes t h e occurrence, origin, ex ample s
.
Meinzer (1949)
and d i s c h a r g e of ground w a t e r and g i v e s many
19 Some b a s i n s t r a n s m i t i n f i l t r a t e d w a t e r t o s t r e a m c h a n n e l s v e r y r a p i d l y through s o l u t i o n c h a n n e l s , porous l a v a , o r c o a r s e a l l u v i a l m a t e r i a l . g r a p h o f J a c k D a n i e l S p r i n g i n F i g u r e 6.2
The hydro-
( C h a p t e r 6) r e s p o n d s r a p i d l y t o
p r e c i p i t a t i o n presumably b e c a u s e t h e w a t e r i s t r a n s m i t t e d through openings i n the limestone.
R e l a t e d o c c u r r e n c e s a r e t h e d i s a p p e a r a n c e and subsequent reap-
pearance of s t r e a m c h a n n e l s i n l i m e s t o n e o r v o l c a n i c t e r r a n e s .
F i g . 2.20.
F i g u r e 2.20
Pop0 Agie River, Wyoming, where i t d i s a p p e a r s i n t o t h e ground.
s h o w s t h e Pop0 A g i e R i v e r i n Wyoming g o i n g u n d e r g r o u n d f r o m w h i c h i t e m e r g e s within a short distance. then reappears.
Rogue R i v e r i n Oregon d i s a p p e a r s i n l a v a t u b e s and
And L o s t R i v e r , i n t h e h e a d w a t e r s o f t h e P o t o m a c R i v e r , g o e s
underground n e a r W a r d e n s v i l l e , W. Va. i n a l i m e s t o n e t e r r a n e . Streams f l o w i n g i n porous m a t e r i a l may l o s e w a t e r through t h e channel bed and banks i n c e r t a i n reaches.
T h u s t h e s u r f a c e f l o w a t a p a r t i c u l a r p o i n t on t h e
channel may be o n l y a p a r t of t h e t o t a l flow p a s t t h a t s e c t i o n .
Gaging s t a t i o n s
a r e u s u a l l y l o c a t e d above o u t c r o p s which f o r c e t h e t o t a l flow t o t h e s u r f a c e . Furthermore,
d i s c h a r g e s of ground w a t e r t o a s t r e a m o f t e n a r e n o t d i s t r i b u t e d
uniformly along the channel.
Large i n c r e a s e s o r d e c r e a s e s i n ground-water
c o n t r i b u t i o n s may occur w i t h i n a s h o r t d i s t a n c e along a r e a c h a s i n d i c a t e d by t h e f l o w p r o f i l e of a s h o r t r e a c h of Spokane R i v e r ( F i g u r e 2.21).
There a r e no
a p p r e c i a b l e s u r f a c e w a t e r c o n t r i b u t i o n s i n t h i s reach. The c o n t r i b u t i o n of ground w a t e r t o a s t r e a m o f t e n i n c r e a s e s w i t h d i s t a n c e downstream a s t h e stream c u t s deeper i n t o t h e aquifer.
This e f f e c t has been
20
ui u
1600
7-1
J
I
+ z 0
0
0
4
8
12
16
20
24
28
MILES DOWNSTREAM
I
Fig. 2.21. E f f e c t of ground w a t e r on t h e f l o w of Spokane R i v e r from P o s t F a l l s , Idaho, t o mouth of L a t a h Creek i n Spokane, Washington, September 1950. observed on some Long I s l a n d , New York. s t r e a m s whose b a s e f l o w s i n c r e a s e c o n s i d e r a b l y a s t h e y approach t h e ocean.
15
1
05
F o r example s e e F i g u r e 2.22.
0
MILES ABOVE MOUTH
F i g . 2.22. B a s e f l o w o f Carman C r e e k , Long I s l a n d , New York, s h o w i n g i n c r e a s e toward mouth, 12/28/78. Basin geology may p e r m i t s u b s t a n t i a l amounts of ground w a t e r t o move a c r o s s t o p o g r a p h i c b o u n d a r i e s , c a u s i n g an unequal d i s t r i b u t i o n of r u n o f f w i t h r e s p e c t t o surface-water drainage areas.
The l a r g e d i f f e r e n c e i n y i e l d p e r s q u a r e m i l e
of two s m a l l s t r e a m s i n a l i m e s t o n e t e r r a n e i n s o u t h e a s t e r n Idaho (Fig. 2.23) i s a t t r i b u t e d t o t h i s cause.
Drainage a r e a s of Cub Creek and Bloomington Creek a r e
a r e 19.4 and 22.1 s q u a r e m i l e s r e s p e c t i v e l y .
Bloomington Creek h a s l a r g e
s p r i n g s i n i t s headwaters.
I n a r i d and s e m i a r i d r e g i o n s w h e r e t h e w a t e r t a b l e i s below s t r e a m c h ~ i n n e l s t h e p e r m e a b i l i t y of t h e s t r e a m bed d e t e r m i n e s t h e r a t e a t which s t r e a m f l o w s e e p s i n t o t h e ground.
T r a n s f e r of w a t e r between t h e s u r f a c e and t h e ground a l s o may
21
20 -
15-
CUB CREEK
10-
-
BLOOMINGTON
1947 WATER YEAR
F i g . 2.23. D i f f e r e n c e in y i e l d f r o m t w o a d j a c e n t I d a h o d r a i n a g e b a s i n s i s a t t r i b u t e d t o movement of ground w a t e r a c r o s s topographic d i v i d e s .
+ 99
30
F i g . 2.24. R e d u c t i o n i n mean f l o w s d u e t o s t r e a m s c r o s s i n g t h e B a l c o n e s F a u l t a r e a , Texas. occur a t geologic f a u l t s .
F i g u r e 2.24 shows m e a n . f l o w s a t g a g e d s i t e s i n t h e
upper b a s i n s of t h e Nueces and F r i o Rivers,
Texas.
The f l o w l o s s e s ,
indicated
by t h e mean f l o w s , occur where t h e s t r e a m s c r o s s t h e Balcones F a u l t area.
22 2.4
EFFECTS OF TOPOGRAPHY
In mountainous b a s i n s ,
l a n d s l o p e s a r e s t e e p , s t r e a m g r a d i e n t s a r e high,
p r e c i p i t a t i o n r e a c h e s t h e c h a n n e l s quickly. peaks i n c r e a s e w i t h channel slope.
and
Pany s t u d i e s have shown t h a t f l o o d
P r e c i p i t a t i o n r e a c h e s t h e c h a n n e l s more
s l o w l y where b a s i n s l o p e s a r e g e n t l e ; c o n s e q u e n t l y s t r e a m s t a k e l o n g e r t o r i s e t o a peak and t h e peaks tend t o b e f l a t t e n e d .
A f l o o d peak may move downstream
two o r t h r e e t i m e s a s f a s t on a h i g h - g i a d i e n t
s t r e a m a s on one of low g r a d i e n t .
And low g r a d i e n t c h a n n e l s tend t o b e i n wide v a l l e y s where l a r g e r i p a r i a n a r e a s a r e inundated by s i g n i f i c a n t f l o o d s ; t h e r e s a l t i n g channel s t o r a g e r e d u c e s t h e peak d i s c h a r g e a l t h o u g h much of t h e o v e r f l o w i s r e t u r n e d t o t h e s t r e a m r a t h e r promptly.
Overflows o f some c h a n n e l s i n v e r y f l a t topography may n e v e r r e t u r n
t o t h e main channel.
This n a t u r a l d i v e r s i o n r e d u c e s b o t h t h e f l o o d peak and t h e
y i e l d downstream. Lakes,
swamps, and marshes a r e common i n b a s i n s o f low r e l i e f .
The n a t u r a l
s t o r a g e i n t h e s e a r e a s g e n e r a l l y r e d u c e s t h e downstream f l o o d peaks.
Evapora-
t i o n from t h e w a t e r s u r f a c e s and e v a p o t r a n s p i r a t i o n from t h e p e r i m e t e r s o f t h e w e t l a n d a r e a s and fro m t h e s h a l l o w ground w a t e r r e d u c e b a s i n r u n o f f s n b s t a n t i a l l y a t times.
The v a r i a b i l i t y i n s t o r a g e due t o w e a t h e r p a t t e r n s r e s u l t s i n
a h i g h v a r i a b i l i t y of annual low f l o w s downstream. f l o w s o f Suwannee River, Georgia,
For example t h e annual low
which d r a i n s t h e 6 5 0 square-mile Okefenokee Swamp i n
range from about 700 c f s t o z e r o a t t h e Georgia-Florida
S t a t e line.
I n extremely f l a t regions where t h e d r a i n a g e d i v i d e s a r e n o t w e l l defined w a t e r may flow i n one o r t h e o t h e r of two d i r e c t i o n s . wetland i s t h e headwater of both streams.
U s n a l l y a s h a l l o w pond o r
An e x a m p l e i s t h e h e a d w a t e r s o f
Curlew Creek and San P o i 1 R i v e r i n e a s t e r n Washington S t a t e . Channels i n f l a t , c o a s t a l a r e a s t e n d t o be i n t e r h o n n e c t e d and t h e i r f l o w s depend on t i d a l a c t i o n and on t h e l o c a t i o n s of s t o r m s and i n f l o w s .
The f l o w i n
a p a r t i c u l a r r e a c h may b e i n one d i r e c t i o n a t o n e t i m e , and i n t h e o p p o s i t e a t another;
b e t w e e n t h o s e t i m e s t h e c h a n n e l may b e f u l l o f w a t e r t h a t i s n o t
moving. Stream p a t t e r n can be c o n s i d e r e d a topographic f e a t u r e . c h a r a c t e r i s t i c s along t h e main channel.
It a f f e c t s the flood
Tributaries entering a channel a t
r e g u l a r i n t e r v a l s o f d i s t a n c e w i l l produce a f l o o d t h a t i n c r e a s e s downstream i f t h e t r i b u t a r y peaks a r e s u b s t a n t i a l and more o r l e s s c o n c u r r e n t w i t h t h e peak on t h e main channel.
J u s t below t h e c o n f l n e n c e of two s t r e a m s of s i m i l a r s i z e and
regime, t h e combined f l o o d peak may approximate t h e sum of t h e two c o n t r i b u t i n g peaks u n l e s s t h e two peaks a r r i v e a t d i f f e r e n t times, i n which c a s e a double peak may r e s u l t .
I n a long channel r e a c h w i t h o u t t r i b u t a r i e s , o r w i t h t r i b u t a r -
i e s t h a t do n o t c o n t r i b u t e a t t h e same t i m e a s t h e headwaters, upstream w i l l be a t t e n u a t e d ; s e e F i g u r e 8.12 (Chapter 8 ) .
a flood generated
23
A common indicator of stream pattern is some index of basin shape but shape is often a poor descriptor of flood potential.
Unless the pattern is extreme,
and the basin hydrology is m o r e or less homogeneous,
the effect of pattern
probably is small and will be masked by other basin characteristics. The effect of stream pattern on mean flow or low flows is either negligible or to small to detect.
A topographic feature that affects streamflow in arid regions is the closed basin f r o m w h i c h no surface f l o w leaves. flows into a terminal lake or a sink.
W a t e r generated in a closed basin
W e l l k n o w n large closed basins are the
Great B a s i n i n w e s t e r n United States, the J o r d a n River b a s i n in the Arabian Peninsula, and t h e Caspian Lake B a s i n in Asia.
Considerable s t r e a m f l o w is
generated in these basins but none of it reaches the oceans. Small closed basins are common in semiarid regions of the world.
The contri-
buting drainage areas of some streams in western United States are less than the areas enclosed b y the topographic boundaries because of closed basins w i t h i n those boundaries. floods.
Some of these small closed basins may overflow during extreme
Basins a r e closed because of l o w precipitation: if the precipitation
were high enough the basin would become a lake and drain to an ocean. REFERENCES Crippen. J.R. 1978, Composite log-type I11 frequency-magnitude curve of annual floods: U.S. Geol. Survey Open- File Report 78-352, 5 p. Crippen, J.R., and Bue. C.D., 1977, M a x i m u m f l o o d f l o w s i n the conterminous United States: U.S. Geol. Survey Water-Supply Paper 1887, 52 p. Dunford. E.G., and Fletcher, P.W.. 1947, Effect of removal of streambank vegetation u p o n w a t e r yield: Am. Geophysical Union, Trans., Vol. 28, No. l, Feb 1947, p. 105-110. L'vovich, M.I.. 1980, World water resources and their future (translation edited 416 p. b y R.L. Nace): Am. Geophysical Union, Washington, D.C.. McDonald, C.C. and Langbein, W.B.. 1948, Trends i n runoff in t h e Northwest: Trans. Am. Geophysical Union, Vol. 29, No. 3, J u n e 1948, p. 387-397. Meinzer, O.E.,
1949, Hydrology:
New York, Dover Publications, 712 p.
Moore, A.M., 1957, Measuring s t r e a m f l o w under ice conditions: Am. SOC. Civil Engineers Proc., Jour. Hydraulics Div., v. 83, HY1, P a p e r 1162, 1 2 p. Riggs, H.C., 1980. Climatic factors of runoff, in Pollution and Water Resources: Columbia University Seminar Series, V. XIII, Part 111, Pergamon Press, p. 7383. Simons, W.D., 1953, Concept and characteristics o f base flow in t h e Columbia River basin: Western Snow Conf. Proc., 21st meeting, Boise, Idaho, p. 57-61. Troxell. H.C., 1953, The influence of ground-water storage on the runoff in the San Bernardino and eastern S a n Gabriel M o u n t a i n s of southern California: Trans. Am. Geophysical Union, Vol. 34, No. 4, p. 552-562. Williams, G.R.. 1940, Natural w a t e r loss in selected drainage basins: Geol. Survey Water-Supply Paper 846, 5 2 p.
U.S.
This Page Intentionally Left Blank
25
Chapter 3
COLLECTION OF HYDROLOGIC DATA 3.1
STREAMFLOW Continuous streamflow records a r e obtained a t a gaging s t a t i o n a t which t h e
stream stage (water-surface o r is recorded continuously.
h e i g h t above some datum) i s e i t h e r r e a d f r e q u e n t l y D i s c h a r g e i s measured,
u s u a l l y by c u r r e n t m e t e r ,
a t v a r i o u s s t a g e s f o r d e f i n i n g t h e stage-discharge r e l a t i o n ( r a t i n g curve) which
i s used t o convert the stage record t o a discharge record.
Only t h e g e n e r a l
p r o c e d u r e s a r e g i v e n h e r e ; f o r more d e t a i l s e e WMO (1980) o r Rantz (1982). 3.1.1
S t a g e measurement
Gaging s t a t i o n s a r e o f s e v e r a l t y p e s .
The s i m p l e s t c o n s i s t s o f a s e r i e s of
s t a f f g a g e s (Fig. 3.1) on w h i c h an o b s e r v e r r e a d s t h e s t a g e o n e or more t i m e s a
Fig. 3.1. day.
S t a f f g a g e s on Rio C i a , B r a z i l .
Recording g a g e s e i t h e r s e n s e t h e w a t e r s u r f a c e i n a s t i l l i n g w e l l hydraul-
i c a l l y c o n n e c t e d t o t h e s t r e a m o r by means o f a gas-purge
( b u b b l e gage) s y s t e m
w h i c h m e a s u r e s t h e p r e s s u r e on an o r o f i c e p e r m a n e n t l y m o u n t e d i n t h e s t r e a m . R e c o r d i n g g a g i n g s t a t i o n s a l s o h a v e s t a f f g a g e s ( F i g . 3.2) f o r v e r i f y i n g t h e s t a g e s b e i n g s e n s e d b y t h e equipment.
A simplified stilling-well
installation
is shown i n F i g u r e 3.3 and a g a g i n g s t a t i o n s t r u c t u r e i n F i g u r e 3.4. A bubble-gage
i n s t a l l a t i o n c o n s i s t s of an i n s t r u m e n t s h e l t e r on a c o n c r e t e
s l a b on t h e r i v e r bank. A t u b e c o n n e c t s t h e i n s t r u m e n t t o t h e o r o f i c e i n t h e stream.
N i t r o g e n gas i s bubbled t h r o u g h t h e o r o f i c e t o a c t u a t e t h e s e n s o r .
26
Fig. 3.2.
Lor-rater staff gage.
Fig. 3.3.
Simplified stilling-well installation.
Recording instruments are either analog or digital.
The latter produces a
punched-tape record for processing by digital computer; the punch interval commonly used is 15 minutes but this can be as short as 5 minutes or an hour.
as
long as
The two types of recorders are shown in Figures 3.5 and 3.6.
A gaging station should be located above a stable section of channel in order
that the relation between stage and discharge be well defined and unchanging
21
Fig. 3.4.
Gaging station.
Fig. 3.5.
Analog water-stage recorder.
with time.
T h e feature of the channel that maintains a more-or-less
stage-discharge relation is called the control.
stable
The control m a y be at a sec-
tion, such as a stable riffle ( F i g . 3.7) o r it m a y be a fairly long reach of the
28
F i g . 3.6.
D i g i t a l water-stage
F i g . 3.7.
Natural section control.
channel i t s e l f .
recorder.
A r t i f i c i a l s e c t i o n c o n t r o l s s u c h a s l o w dams a r e s o m e t i m e s
c o n s t r u c t e d where n a t u r a l channel f e a t u r e s a r e n o t s u i t a b l e . t r o l s a r e expensive,
e s p e c i a l l y f o r l a r g e streams,
A r t i f i c i a l con-
and a r e hard t o m a i n t a i n i n
e r o d i b l e c h a n n e l s c a r r y i n g heavy s e d i m e n t loads. 3.1.2
D i s c h a r g e measurement
D i s c h a r g e m e a s u r e m e n t s o f s t r e a m s a r e u s u a l l y made by currant-meter.
The
p r o c e d u r e c o n s i s t s o f (1) m e a s u r i n g t h e w i d t h , d e p t h , a n d v e l o c i t y o f f l o w i n
29
e a c h of s e v e r a l s u b s e c t i o n s of a s t r e a m c r o s s s e c t i o n , ( 2 ) c o m p u t i n g t h e d i s c h a r g e i n e a c h s u b s e c t i o n a s t h e p r o d u c t of a r e a and mean v e l o c i t y , summing t h e p a r t i a l d i s c h a r g e s t o o b t a i n t h e t o t a l .
and (3)
R e f e r r i n g t o F i g u r e 3.8.
t h e d e p t h a t e a c h of t h e s e l e c t e d v e r t i c a l s i s m e a s u r e d by s o u n d i n g and t h e width of each s u b s e c t i o n i s computed from t h e spacing of t h e v e r t i c a l s .
A t each
v e r t i c a l t h e mean v e l o c i t y i s o b t a i n e d from one or more v e l o c i t y o b s e r v a t i o n s by
Verticals
Meter locations
F i g . 3.8. S t r e a m c r o s s s e c t i o n showing m e t e r l o c a t i o n s f o r a d i s c h a r g e measurement. c u r r e n t meter.
Many s t u d i e s have demonstrated t h a t t h e mean of t h e v e l o c i t i e s
a t 0.2 and 0s of t h e d e p t h f r o h t h e w a t e r s u r f a c e i s v i r t u a l l y t h e mean velocity i n the vertical. mean i n t h e v e r t i c a l .
L i k e w i s e t h e v e l o c i t y a t 0.6 d e p t h v e r y n e a r l y e q u a l s t h e V e l o c i t y o b s e r v a t i o n s a r e u s u a l l y made a t 0.2 and 03 of
t h e depth i n each v e r t i c a l where t h e depth i s adequate. The b a s i c equipment needed f o r a d i s c h a r g e measurement c o n s i s t s of a c u r r e n t meter,
a d e v i c e f o r i n d i c a t i n g t h e r e v o l u t i o n s of t h e meter,
a s t o p watch,
and
some means of measuring d e p t h and w i d t h and of holding t h e m e t e r i n t h e proper l o c a t i o n s for v e l o c i t y observations.
In shallow s t r e a m s , measurements a r e made
by wading; t h e c u r r e n t meter i s mounted on a wading rod which i s used t o measure d e p t h and t o p o s i t i o n t h e m e t e r i n t h e v e r t i c a l .
H o r i z o n t a l c o n t r o l i s main-
t a i n e d by a t a p e or b e a d e d w i r e s t r e t c h e d a c r o s s t h e s t r e a m .
See F i g u r e 3.9.
In use, t h e number of r e v o l u t i o n s of t h e meter r o t o r i s obtained by an e l e c t r i c a l c i r c u i t w h i c h p r o d u c e s c l i c k s i n a n e a r p h o n e or r e g i s t e r s o n a c o u n t i n g device.
Elapsed t i m e i s measured by a stopwatch.
v e l o c i t y through t h e meter r a t i n g t a b l e . measurement.
These d a t a a r e t r a n s l a t e d t o
F i g u r e 3.10 shoks n o t e s of a d i s c h a r g e
30
F i g . 3.9.
Wading equipment and a measurement i n p r o g r e s s .
Deep s t r e a m s a r e m e a s u r e d f r o m a b r i d g e , c a b l e w a y , o r b o a t .
The m e t e r i s
suspended on a c a b l e above a sounding weight which i s used f o r d e p t h measurement and t o h o l d t h e c u r r e n t m e t e r a t t h e c o r r e c t p o s i t i o n i n t h e v e r t i c a l f o r Sounding w e i g h t s used range from 1 5 t o 300 pounds or more
v e l o c i t y observation.
depending on t h e d e p t h and v e l o c i t y of t h e stream. i n F i g u r e s 3.11,
3.12,
and 3.13.
Methods of gaging a r e shown
S e e Buchanan a n d S o m e r s ( 1 9 6 9 ) f o r a m o r e
complete d e s c r i p t i o n of measurement t e c h n i q u e s i n c l u d i n g measurement under i c e cover. The m o v i n g - b o a t velocity-area
method i s s i m i l a r t o t h e above method i n t h a t i t u s e s t h e
approach t o d e t e r m i n i n g d i s c h a r g e b u t i t d i f f e r s i n t h e method of
d a t a c o l l e c t i o n ; t h e de?t:..
r n d v e l o c i t i e s a t e a c h o b s e r v a t i o n p o i n t a r e ob-
tained while the boat is rapidly traversing the cross section.
Thus a measure-
ment of d i s c h a r g e by t h i s method c a n be made on wide s t r e a m s i n a few m i n u t e s a t s i t e s without fixed f a c i l i t i e s .
However,
made and t h e r e s u l t s a v e r a g e d .
The e q u i p m e n t ( F i g . 3.14) c o n s i s t s o f a s o n i c
sounder,
a vane w i t h a n g l e i n d i c a t o r ,
in practice 6 traverses usually are
a component p r o p e l l o r - t y p e
c u r r e n t meter.
and a maneuverable s m a l l boat. The t r a v e r s e o f t h e c r o s s s e c t i o n i s made w i t h o u t s t o p p i n g a n d d a t a a r e collected a t regular intervals.
The b o a t o p e r a t o r m a i n t a i n s c o u r s e by "crab-
b i n g " i n t o t h e d i r e c t i o n of f l o w s u f f i c i e n t l y t o keep on l i n e .
The f o r c e
e x e r t e d on t h e c u r r e n t m e t e r i s t h e c o m b i n a t i o n of two f o r c e s a c t i n g s i m u l t a neously,
one f o r c e d u e t o t h e movement o f t h e b o a t a n d t h e o t h e r f r o m t h e
o t r e a m f l o r normal t o t h e path.
A d d i t i o n a l i n f o r m a t i o n needed i s t h e v e r t i c a l
........................................................... qz"uan ........................................................................ ..............................................
.......
-
. . . .
..."a?3....... I
0Al"q)
...............................................
-
..................................................................... r,rmqiJ py,"s )q,", ................ p'"nu,, p , ~ , ~ n..........................
..........
-
~
.qo i+,p.J"~u
........ . . .................. .... ...... P.3 o,... a , . & ........ ~,~... . . . *y ........................................... 'WJ .......................... -* ?nj.?.... , ~ y l , ~ & ..................... &.zc J., Iu .~ ..... ............................. . . . . . . . . . . . . . "Dll,al "0'3 : N O I I ! p Y O > ~~~
'i~~LUs
yuqpJ"0 p m q
'(0'8
-
n r o ) rmd
'(Oh@) I!*)
...... .... ... ............................................. ............. .................... ........................... pYmJ 9.93 ',.q-q>q,
,.
.......................................
PY.
. 1 . *
CI '(0'5)
pms '(%Z)
>">[,a,.>
p3p,
l"?w,inrwly H 3
..
....
n 8-2
3 W Pilix"b
,
Ib!'B:./4!18.l?:!'s:l:::::::::+c:~! H
32
Fig. 3.11.
Gaging from a bridge (during a flood at left).
F i g . 3.12.
Measuring from a cableway.
the stage-discharge relation w i l l change either gradually or abruptly in response to such factors as aquatic growth, ice formation and release, erosion or deposition by floods, and other natural or man-made changes in the channel.
The
definition and application of rating curves require an understanding of stream hydraulics and considerable experience. Kennedy (1983).
S e e WYO (1980) or R a n t z
(1982). and
33
F i g . 3.13.
J e t b o a t equipped f o r gaging.
I ,Indicator
Sighting d e v i c e \
I
and dial
/"
L
L
I
F i g . 3.14. E q u i p m e n t f o r m e a s u r i n g by t h e m o v i n g - b o a t m e t h o d (From Smoot and Novak, 1969).
A stage-discharge
r e l a t i o n c a n be computed from a s u r v e y of t h e downstream
channel and e s t i m a t e s of channel roughness. backwater method,
The technique,
known a s t h e s t e p -
i s u s e f u l where t i m e does n o t p e r m i t o b t a i n i n g c u r r e n t - m e t e r
d i s c h a r g e measurements throughout t h e range of s t a g e , or where h i g h accuracy i s not required.
The method i s d e s c r i b e d i n many h y d r a u l i c t e x t s and by Davidian
(1984) and was v e r i f i e d for t h i s a p p l i c a t i o n by B a i l e y and Bay (1966).
34
Fig. 3.15
Stage-discharge relation (rating curve).
Streamflow records are sometimes needed on stream reaches affected by variable backwater.
T h e discharge past a section on such a reach is a function of
stage and the slope of the water surface through the reach.
A continuous stage
record at each end o f a reach is required to define the slope. analysis depends on the hydraulic conditions.
The method of
See W M O (1980) or Bantz (1982).
and Kennedy (1983) for rating curve theory and details of applications to various channel and flow conditions. 3.1.4
Discharge computation and the hydrograph
Given a continuous stage record or frequent stage observations, and a stagedischarge relation, the discharge can be computed for any particular time within the period of stage record.
Daily mean discharges are usually computed although
discharges at intervals of an hour or less are used to define the changes during a flood.
An annual s t r e a m f l o w record as published b y U S G S is s h o w n in F i g u r e
3.16. The daily mean discharges of Figure 3.16 the hydrograph shown in Figure 3.17. various events.
are plotted against time to produce
Hydrographs show how a stream responds to
An uncharacteristic pattern of a segment of a hydrograph may
indicate s o m e unnatural f l o w modification o r an error in the record or in t h e analysis on which the discharge record is based. Flood hydrographs are usually defined by discharges at short intervals, such as hourly, and by the peak discharge. 3.1.5
Figure 3.18
is an example.
Special gaging methods
Variable backwater due to operation of a dam or other control on a stream may result, at times, in
SO
little fall in the r a t e r surface through a reach that
35
POTOMAC RIVER BASIN
183
01600000 NORTH BRANCH POTOMAC RIVER AT PINTO, MD LOCATION.--Lat 3 9 " 3 3 ' 5 9 " , long 78'50'25''. Mineral County, W. Va., Hydrologic Unit 02070002, on right bank a r downstream side of Western Maryland Railway bridge at Pinto, 2.8 m i ( 4 . 5 km) downstream from M i l l Run, and a t mile 3 2 . 6 (52.5 km). DRAINAGE AREA:-S96
mi'
(1.544
krn'). WATER-DISCHARGE RECORDS
PERIOD OF RECORD.~-October1 9 3 8 to current year REVISED RECORDS.--WSP 1332:
1943
GAGE.--Water~stagerecorder. Datum of gage is 648.23 ft (197.581 rn) National Geodetic YeTtxCal Datum of 1 9 1 9 . P r i o r to Dec. 10, 1938, "onrecording gage at highway bridge 2 5 0 ft (76 a) downstream at same datum. REMARKS.--Water-dischargerecords good except those for winter periods. uhxch are fair. Some regulation at low flow by Stony River Reservoir, 6 6 m i (106 km) above statxon ( s e e statxon Ol59S200), and since December 1950, by Savage River Reservoir, 25 "11 ( 4 0 ke) above Station ( s e e Station 0 1 5 9 7 5 0 0 ) . AVERAGE DISCHARGE.--41 years, 886 ft'ls
(25.09 m ' l s ) ,
20.19 inlyr (513 mnlyr), unadJusred.
EXTREMES FOR PERIOD OF RECORD.--Maximum discharge, 37,000 ft'ls (1,050 " ' I s ) Oct. 16, 1954. gage height, 23.23 ft (7.081 n); minimum, 31 ft'ls (0.88 m'ls) Dec. 18, 19, 1 9 4 3 , gage height, 1.37 fr (0.418 m), result of freereup. EXTREMES OUTSIDE PERIOD OF RECORD.--Flood of Mar. 29. 1924, reached a stage of about 24 ft (7.3 m), discharge. about 5 5 , 0 0 0 ft3/s (1,560 m'/s). Flood of Mar. 17 1936. reached a stage of about 23.5 ft (7.16 m). from floodmarks, discharge, about 1 0 , 0 0 0 ft'lr ( 1 , 4 2 0 m i l s ) . EXTREMES FOR CURRENT YEAR.--Maximum discharge 1 2 800 ft'ls (362 r n ' l s ) Feb. 26. gage height, 13.28 ft ( 4 . 0 4 8 m ) ; minimum, 126 ft'ls (3.57 m'15) NO". 15. g a i e h;ight, 1.88 ft (0.573 m ) . D I S C H A R G E , I N CUSIC FEE7 PEH SECOND+ lb7ER 7 E b X OCTOBER I978 10 SEPTEUBER 1 9 7 9 UEbN VbLUES
011
OCT
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OEC
JAN
FEB
MbH
APT(
UbY
JUN
JUL
bUG
SEP
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111 170
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2410 3050
1930
318
,200 6140 6330 9570
2160 2010 2220 2650
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1030 899 710 8* 1 169
319 250 2bl 298 1140
217 188 112 161 157
564
483
169
1750 3990 3870 2700
161 165 164
2240 1500 15.0 3720 3050
1340 1230 2050 1990 1610
320 380
10400 7890
2210
3550
147
2550
6610
1170
151 159 181
1590
352 343
1560 1680 1500
631 376 286 2b3 230
152
6350 5480
I k70 1290 1130 981 893
586
36Y
LO
114 171 169 168 172
11
171
1 63 164 167 165 152
1990 2090 17.0 1260
1190
3bO 350 370 390 450
2710 2350 2010 2150
1060
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988 174 600 476 403
233 22* 206 270 260
115 406 911 $15 266
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179 184 183
250 618
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255 231 224 226 213
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209 217 463 1090 678
2330
26 21 28 29 30 31 TOT&L WEbN MAX *IN
CAL
YR I7R VR
554
165 169 235 242 20 1
_--
183
8.09 280 1090 152
5501 171 242 161 1078 1919
TOTAL l07AL
Fig. 3.16.
4BP 509
.'tP
730
3360
850 1900
2310 2100 2210
2180 5390 9280 11100 1550 5220
loso
1530 1310 1200 1010 832 969
52h7 1702 3120 514
51295 1655 3990 139
54139 1955 11100 320
2200 1610 959 1030
390628 414643
UEbN
MEAN
2410
107% 1136
_-_ ___ ---
MAX
*AX
10700 11100
3180
1810
1310 1180 1090
low
1430
1054 1044 931
1630 1160 853
'. Dz o1 e0
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15.
1010 Y36 819 1160 2720
111
631
663 660 895 753
625 1210 3080
1150 1580
TO,
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2200 2040 1830 1530 968 817
746 1530
---
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99270 3202
39624 1321 26511 660
43416 1k01 3090 595
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333
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---
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---
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669
IN 24.38 I N 25.88
Published annual streamflow r e c o r d .
the f a l l cannot be measured c l o s e l y enough ( o r i s a f f e c t e d by wind) for use i n a stage-f a l l - d i s c h a r g e
relation.
Several a l t e r n a t i v e s a r e a v a i l a b l e .
36
Fig. 3.17.
I:
Hydrograph of daily discharges of Figure 3.16.
20,000
I
10,ooo
-
I
z W'
U [r
40
1 m -
cn n
10050 50 21
lqIl Fig. 3.18. (i)
I
t
'I
23
"I
"
,
l
25
27
1
JUNE 1972
Flood hydrograph.
Deflection meter.
The simplest alternative is use of a deflection vane
set at a fixed position below the minimum stage and at a right angle to the current (Fig. 3.19).
The angular deflection of the vane is a function of the
velocity in the cross section, and the stream stage is related to the cross sectional area.
Deflection and stage are measured at the gage site and the
relation with discharge is based on current-meter measurements. The deflection vane is used in small channels having little change in stage. Both downstream and upstream flow can be measured so it is suitable for tidal
37
High tide7
Low tidei
River bottom-
F i g . 3.19
Deflection-meter vanes.
channels.
D i s c h a r g e s c o m p u t e d by t h i s m e t h o d a r e g e n e r a l l y of low a c c u r a c y ,
e s p e c i a l l y t h o s e n e a r zero. ( i i ) A c o u s t i c method.
V e l o c i t y a t some f i x e d l e v e l i n t h e s t r e a m i s ob-
t a i n e d by d e t e r m i n i n g t h e t r a v e l t i m e s of sound i m p u l s e s moving i n b o t h d i r e c t i o n s along a d i a g o n a l p a t h between t r a n s d u c e r s (sound g e n e r a t o r s o r r e c e i v e r s ) mounted n e a r e a c h bank. shown i n F i g u r e 3.20.
The l a y o u t of a n o p e r a t i n g s y s t e m on Columbia River i s The i n s t a l l a t i o n a n d o p e r a t i o n o f t h a t s y s t e m i s deC a l i b r a t i o n i s by c u r r e n t meter.
s c r i b e d b y S m i t h and o t h e r s (1971).
Laenen
and S m i t h ( 1 9 8 2 ) h a v e a s s e m b l e d p u b l i s h e d and u n p u b l i s h e d i n f o r m a t i o n on t h e o p e r a t i o n , a p p l i c a t i o n s , performance, and l i m i t a t i o n s of a c o u s t i c v e l o c i t y measurement s y s t e m s w i t h s p e c i f i c a p p l i c a t i o n s t o measurement of streamflow. ( i i i ) E l e c t r o m a g n e t i c method.
tromagnetic meter.
P o i n t v e l o c i t y can b e measured by a n elec-
Continuous r e c o r d s of v e l o c i t y a t one p o i n t i n a c r o s s
s e c t i o n and of t h e s t a g e can b e t r a n s f o r m e d i n t o a continuous d i s c h a r g e r e c o r d a f t e r c a l i b r a t i o n w i t h c u r r e n t - m e t e r measurements.
The r e l i a b i l i t y of t h e
computed d i s c h a r g e depends on how c l o s e l y t h e v e l o c i t y a t t h e one p o i n t repres e n t s mean v e l o c i t y through t h e range of d i s c h a r g e experienced a s w e l l as on t h e r e l i a b i l i t y of t h e p o i n t v e l o c i t i e s .
Such a n i n s t a l l a t i o n s h o u l d b e o f r e l a -
t i v e l y low c o s t b u t t h e e l e c t r o m a g n e t i c m e t e r i s a l w a y s s u b j e c t t o damage from
38
Fig. 3.20. 1971).
Layout o f an a c o u s t i c v e l o c i t y measuring system (Smith and o t h e r s ,
d e b r i s i f i t i s s u i t a b l y located.
Lack of s t a b i l i t y of t h e m e t e r c a l i b r a t i o n i s
a l s o a problem. Green and Herschy (1978) d e s c r i b e an e l e c t r o m a g n e t i c g a g i i g s t a t i o n based on t h e total-flow
e l e c t r o m a g n e t i c method.
T h i s a p p l i c a t i o n i s s t i l l under develop-
ment. (iv)
D i l u t i o n methods.
D i l u t i o n methods o f measuring s t r e a m d i s c h a r g e a r e
u s e f u l under flow c o n d i t i o n s t h a t e x i s t i n s h a l l o w , Current-meter
e x t r e m e l y rough channels.
measurements a r e g e n e r a l l y q u i c k e r and more r e l i a b l e a t a l l b u t
extremely unfavorable s i t e s . The f i e l d p r o c e d u r e i n v o l v e s i n j e c t i n g a t r a c e r of g i v e n c o n c e n t r a t i o n i n t o a s t r e a m and sampling t h e c o n c e n t r a t i o n downstream where t h e t r a c e r i s c o m p l e t e l y mixed w i t h t h e w a t e r .
The t r a c e r may b e i n j e c t e d a s a s l u g o r a t a c o n s t a n t
rate.
U s e f u l t r a c e r s i n c l u d e s a l t s , r a d i o a c t i v e m a t e r i a l s , and f l u o r e s c e n t
dyes.
The method r e q u i r e s s k i l l e d o p e r a t o r s , c o n s i d e r a b l e t i m e ,
and a c o n s t a n t
discharge. Stream d i s c h a r g e for c o n s t a n t - r a t e Q =
injection is
c1 - c2 c -cb
2 where q i s t h e t r a c e r i n j e c t i o n r a t e and cb,
c1
and C2 a r e c o n c e n t r a t i o n s of t h e
39 stream a t t h e i n j e c t i o n p o i n t , of t h e i n j e c t e d t r a c e r , and of t h e s t r e a m a t t h e downstream c r o s s s e c t i o n r e s p e c t i v e l y .
See White (1978) or K i l p a t r i c k and Cobb
(1984) f o r d e t a i l s . 3.1.6
I n d i r e c t measurements
I t i s o f t e n i m p o s s i b l e t o measure f l o o d d i s c h a r g e s a t p a r t i c u l a r t i m e s because o f l a c k of a c c e s s t o t h e s i t e , s h o r t a g e of manpower, o r i n a d e q u a t e advance n o t i c e of t h e flood.
Engineers have t h e r e f o r e d e v i s e d methods of computing peak
d i s c h a r g e a f t e r t h e passage of t h e f l o o d : t h e common ones a r e slope-area, tracted-opening,
flow-over-dam,
and fl o w -t h r ongh- cul ver t .
con-
These methods a r e
b a s e d on h y d r a u l i c e q u a t i o n s t h a t r e l a t e t h e d i s c h a r g e t o t h e w a t e r - s u r f a c e p r o f i l e , t h e geometry of t h e channel, and t h e channel roughness.
These measure-
ments may be e x p e n s i v e and t h e y a r e l e s s a c c u r a t e t h a n c u r r e n t - m e t e r
measure-
ment s. The s l o p e - a r e a m e t h o d i s t h e m o s t w i d e l y u s e d .
An i d e a l s i t e i s a r e a c h o f
u n i f o r m c h a n n e l on w h i c h t h e f l o o d p e a k p r o f i l e i s d e f i n e d on b o t h b a n k s by high-water
marks.
Surveys o f t h e s e p r o f i l e s and o f channel c r o s s s e c t i o n s ,
and
e s t i m a t e s o f t h e r o u g h n e s s c o e f f i c i e n t i n t h e Manning e q u a t i o n a r e r e q u i r e d . F i e l d e x p e r i e n c e i n s e l e c t i n g roughness c o e f f i c i e n t s i s d e s i r a b l e b u t guidance can be o b t a i n e d from t h e photographs i n t h e r e p o r t by Barnes (1967). I n d i r e c t methods a r e d e s c r i b e d by Barnes and Davidian (1978).
Users g u i d e s
t o t h e v a r i o u s t e c h n i q u e s a r e g i v e n by D a l r y m p l e and Benson (1967). B o d h a i n e (1968).
M a t t h a i (1968).
and Hulsing (1968).
Common t o a l l t h e s e methods i s t h e need t o s e l e c t t h e roughness c o e f f i c i e n t subjectively.
The roughness c o e f f i c i e n t o f a n a t u r a l channel i s a f u n c t i o n of
bed roughness,
bank i r r e g u l a r i t y ,
e f f e c t of v e g e t a t i o n ( i f any), d e p t h o f w a t e r ,
c h a n n e l s l o p e , and o t h e r f a c t o r s .
No o b j e c t i v e way o f c o m b i n i n g a l l t h e s e
e f f e c t s i n t o one c o e f f i c i e n t i s a v a i l a b l e .
F u r t h e r m o r e t h e v e r i f i e d v a l u e of a
roughness c o e f f i c i e n t f o r a p a r t i c u l a r channel r e a c h and f l o o d i s a f f e c t e d by i n a c c u r a c i e s i n measuring o t h e r v a r i a b l e s i n t h e Manning e q u a t i o n ; t h i s r e s u l t s i n some a p p a r e n t i n c o n s i s t e n c i e s among v e r i f i e d r o u g h n e s s c o e f f i c i e n t s . avoid t h i s s u b j e c t i v i t y .
Riggs (1976) developed a s i m p l i f i e d s l o p e - a r e a
To
method
i n w h i c h d i s c h a r g e i s r e l a t e d t o c r o s s - s e c t i o n a l a r e a and t o w a t e r - s u r f a c e slope.
A roughness c o e f f i c i e n t i s n o t used because, i n n a t u r a l channels, roughThe e q u a t i o n i s
n e s s and s l o p e a r e r e l a t e d . l o g Q = 0.366
+
1.33 log A
+
0.05 l o g S
-
0.056 ( l o g S ) *
w h e r e Q i s i n c f s , A i s a v e r a g e c r o s s s e c t i o n a l a r e a i n s q u a r e f e e t , and S i s d i m e n s i o n l e s s s l o p e of t h e w a t e r s u r f a c e through t h e reach. Mud f l o w s or d e b r i s f l o w s i n s m a l l ,
steep-gradient
channels leave physical
e v i d e n c e t h a t may b e m i s i n t e r p r e t e d a s i n d i c a t i n g t h e p a s s a g e o f a f l o o d .
A
40
flood-peak d i s c h a r g e computed f r o m s u c h e v i d e n c e m i g h t b e e x t r e m e l y l a r g e , p o s s i b l y g r e a t e r t h a n t h e p o t e n t i a l f o r t h e b a s i n o r region.
Costa and J a r r e t t
(1981) d e s c r i b e how t o make t h e p r o p e r i n t e r p r e t a t i o n of t h e evidence. 3.1.7
Crest-stage
gaging s t a t i o n s
A c r e s t - s t a g e gaging s t a t i o n p r o v i d e s a r e c o r d of peak s t a g e s and t h e c o r r e s I t s purpose i s t o p r o v i d e d a t a f o r d e f i n i n g t h e
ponding d i s c h a r g e s a t a s i t e . flood-peak
f r e q u e n c y c h a r a c t e r i s t i c s where t h e c o s t o f c o l l e c t i n g a c o n t i n u o u s
s t r e a m f l o w r e c o r d cannot b e j u s t i f i e d .
A crest-stage
gage u s u a l l y c o n s i s t s of a 2-inch
t h e s t r e a m bank.
p i p e mounted v e r t i c a l l y on
The p i p e i s c a p p e d a t b o t h e n d s and c o n t a i n s a wooden s t a f f .
and i n t h e bottom cap, some ground cork.
I n t a k e h o l e s i n t h e bottom cap, and an
a i r h o l e i n t h e top cap, p e r m i t w a t e r t o e n t e r t h e p i p e a s t h e s t r e a m r i s e s . The c o r k f l o a t s on t h e w a t e r and some o f i t s t i c k s t o t h e s t a f f a t t h e c r e s t stage.
The gage i s i n s p e c t e d p e r i o d i c a l l y t o r e c o r d t h e c r e s t s t a g e ,
the staff,
t o clean
and t o r e p l e n i s h t h e cork.
Crest-stage
gages a r e u s u a l l y l o c a t e d where a s t a g e - d i s c h a r g e
computed from channel c h a r a c t e r i s t i c s , a r e a c h s u i t a b l e f o r step-backwater
r e l a t i o n can be
u s u a l l y above a b r i d g e o r c u l v e r t ,
analysis.
F i g u r e 3.21
o r on
shows a c r e s t - s t a g e
gage i n s t a l l a t i o n on a n ephemeral s t r e a m i n South Dakota. Data produced by c r e s t - s t a g e
gaging s t a t i o n s u s u a l l y a r e l i m i t e d t o t h e
maximum s t a g e and d i s c h a r g e e a c h y e a r , a l t h o u g h a d d i t i o n a l p e a k s may b e r e corded. 3.1.8
Time of t r a v e l
Time of t r a v e l i s u s u a l l y c o n s i d e r e d t h e mean t r a v e l t i m e of w a t e r p a r t i c l e s f l o w i n g from one c r o s s s e c t i o n t o a n o t h e r , a t a g i v e n d i s c h a r g e .
I t i s much
l o n g e r t h a n t h e t i m e r e q u i r e d f o r a f l o o d wave t o p a s s t h r o u g h t h e same reach. E s t i m a t e s o f t h e r a t e o f movement o f w a t e r b o r n e p a r t i c l e s i n s t r e a m s a r e needed f o r d e f i n i n g t h e w a s t e - a s s i m i l a t i v e
c a p a c i t i e s of s t r e a m s and t o f o r e c a s t
t h e movement of a s l u g of contaminant such a s might r e s u l t from a n a c c i d e n t a l spill. Various h y d r o l o g i c t r a c e r s such a s s a l t , have been used.
radioisotopes,
and f l u o r e s c e n t d y e s
The d y e Rhodamine WT i s a p o p u l a r t r a c e r .
It is injected
i n s t a n t a n e o u s l y a t a s t r e a m c r o s s s e c t i o n and t h e dye c o n c e n t r a t i o n is m o n i t o r e d a s t h e dye c l o u d p a s s e s each of a s e r i e s of c r o s s s e c t i o n s .
Dye c o n c e n t r a t i o n
i s measured by a f l u o r o m e t e r which i s s e n s i t i v e t o c o n c e n t r a t i o n s a s low a s 0.05 p a r t s per billion.
F i g u r e 3.22
shows t h e measured c o n c e n t r a t i o n a t f o u r p o i p t s
on t h e M i s s i s s i p p i R i v e r r e s u l t i n g f r o m t h e i n j e c t i o n o f d y e a t B a t o n Rouge. The maximum c o n c e n t r a t i o n d e c r e a s e s and t h e l o n g i t u d i n a l d i s p e r s i o n i n c r e a s e s w i t h d i s t a n c e downstream. l e a d i n g edge,
Time o f t r a v e l c a n b e e x p r e s s e d a s t i m e f o r t h e
t h e peak c o n c e n t r a t i o n , o r t h e l a s t d e t e c t a b l e dye t o p a s s a g i v e n
41
Fig. 3.21.
Crest-stage gage installation.
r B A T O N ROUGE
k
Q: 6700 M3/5EC.
I00 KM 147
20
KM
40 60 80 HOURS AFTER DYE RELEASE
202 KM (NEW ORLfANS)
100
I
Fig. 3.22. Distribution of dye concentration with time at midstream sampling points, Mississippi River, Louisiana, September, 1965 (From Wilson, 1968).
42 point.
A l l t h r e e t i m e s may b e n e e d e d f o r some p r o b l e m s .
D e t a i l s of time-of-
t r a v e l m e a s u r e m e n t s a r e g i v e n b y Hubbard a n d o t h e r s (1982).
See a l s o White
(1978) on d i l u t i o n gauging. t r a v e l i s g r e a t l y increased a s stream discharge i s decreased.
Time o f
Buchanan (1964) showed t h a t t r i p l i n g t h e d i s c h a r g e of Swatara Creek, Pa. reduced t h e t r a v e l t i m e about h a l f . r e a c h of S t .
Mary's
River,
T a b l e 3.1 s h o w s t r a v e l t i m e s t h r o u g h a 14.4 m i Indiana f o r a range i n discharge,
a s given by
Eikenberry and Davis (1976). TABLE 3 . l T r a v e l time v e r s u s d i s c h a r g e Discharge
T r a v e l time ( h o u r s )
cfs
% mean
22 120 620 810 1220
4.6 25 130 170 255
3.1.9
l e a d i n g edge
peak
105 33 .o 13.8 12.0 10.8
1 30 40 .O 16.8 14.8 12 .o
Sediment t r a n s p o r t
Sediment-laden
w a t e r i s n o t o n l y u n s u i t a b l e f o r many u s e s w i t h o u t t r e a t m e n t ,
b u t i t a l s o d e p o s i t s s e d i m e n t i n c h a n n e l s , c a n a l s , and r e s e r v o i r s .
Thus, de-
s i g n e r s and o p e r a t o r s of w a t e r p r o j e c t s need i n f o r m a t i o n on t h e amounts and t i m e d i s t r i b u t i o n of sediment t r a n s p o r t e d so a s t o minimize t h e d e t r i m e n t a l e f f e c t s . Sediment i s t r a n s p o r t e d by a s t r e a m a s suspended sediment, which i s c o n t i n u a l l y i n suspension, and a s bed l o a d which moves by r o l l i n g , ing along t h e bottom.
sliding,
or bound-
The a m o u n t o f s e d i m e n t b e i n g t r a n s p o r t e d i s h i g h e s t
d u r i n g a p e r i o d of f l o o d r u n o f f because of t h e e r o s i o n produced by t h e c a u s a t i v e r a i n f a l l and because of t h e h i g h e r v e l o c i t i e s and t u r b u l e n c e i n t h e channels.
A sediment-discharge
measurement,
and a c o n c u r r e n t w a t e r - d i s c h a r g e
ment, p r o d u c e d a t a from w h ich t h e f o l l o w i n g c a n be o b t a i n e d :
measure-
mean s u s p e n d e d
s e d i m e n t c o n c e n t r a t i o n , p a r t i c l e s i z e d i s t r i b u t i o n , s p e c i f i c g r a v i t y of t h e suspended sediment, t e m p e r a t u r e of t h e sediment-water m i x t u r e , w a t e r d i s c h a r g e , and t h e d i s t r i b u t i o n of flow i n t h e s t r e a m c r o s s s e c t i o n .
In a sediment-discharge
measurement water-sediment
selected v e r t i c a l s i n the cross section.
samples a r e c o l l e c t e d a t
The s a m p l e a t e a c h v e r t i c a l i s ob-
t a i n e d a s t h e s a m p l e r (Fig. 3.23) i s lowered t o t h e streambed and r a i s e d t o t h e s u r f a c e a t a uniform r a t e or, a l t e r n a t i v e l y , by c o l l e c t i n g samples a t s e l e c t e d points in the vertical. water-discharge
Laboratory analyses of t h e samples a r e used w i t h t h e
measurement t o p r o d u c e t h e d e s i r e d i n f o r m a t i o n .
g i v e n by Vanoni (1975, p. 317-349)
On s m a l l ,
Details are
and by Guy and Norman (1976)
f l a s h y streams n e a r l y a l l t h e sediment i s transported during t h e
s h o r t p e r i o d s of h i g h d i s c h a r g e .
Because t h e s e f l o o d p e r i o d s a r e r a r e l y known
43
F i g . 3.23.
Sediment sampler.
i n advance, a u t o m a t i c sampling equipment h a s been developed.
T h i s may b e a
s e r i e s of c o n t a i n e r s a t d i f f e r e n t e l e v a t i o n s f o r c a t c h i n g samples a s t h e s t r e a m r i s e s , or a pumping s a m p l e r p r o g r a m m e d t o t a k e s a m p l e s a t s e l e c t e d i n t e r v a l s according t o stream stage. Records o f sediment d i s c h a r g e o v e r a c o n s i d e r a b l e p e r i o d o f t i m e a r e needed t o d e f i n e i t s v a r i a t i o n w i t h s t r e a m f l o w and w i t h seasons, and t o d e f i n e t h e mean annual l o a d of sediment t r a n s p o r t e d .
If a d a i l y r e c o r d i s d e s i r e d , one or more d e p t h - i n t e g r a t e d
samples a r e t a k e n
e a c h d a y a t one v e r t i c a l : t n e s e a r e s u p p l e m e n t e d by p e r i o d i c , m o r e - d e t a i l e d suspended-sediment
measurements.
The d a i l y measured c o n c e n t r a t i o n s a r e p l o t t e d
on a c h a r t of gage h e i g h t a g a i n s t t i m e ( u s u a l l y t h e one from t h e analog r e c o r d e r a t t h e stream-gaging
s t a t i o n ) and t h e graph of s e d i m e n t c o n c e n t r a t i o n i s drawn
between observed p o i n t s u s i n g t h e s t a g e graph a s a guide. t i o n graph and t h e s t r e a m f l o w record, ( P o r t e r f i e l d , 1972).
From t h e concentra-
t h e d a i l y sediment l o a d can be computed
P a r t o f a p u b l i s h e d s e d i m e n t r e c o r d i s shown i n F i g u r e
3.24. The t o t a l suspended sediment l o a d f o r a y e a r c a n be approximated from occas i o n a l s e d i m e n t measurements by u s e of a s e d i m e n t - t r a n s p o r t d u r a t i o n curve.
curve and a flow-
The f o r m e r i s a p l o t o f s e d i m e n t d i s c h a r g e a g a i n s t s t r e a m
d i s c h a r g e ( F i g . 3.25) and t h e l a t t e r s h o w s t h e d i s t r i b u t i o n o f d a i l y s t r e a m d i s c h a r g e s during t h e y e a r (Chapter 5 ) .
The d u r a t i o n c u r v e i s d i v i d e d i n t o
i n t e r v a l s of t i m e and t h e mean d i s c h a r g e f o r e a c h i n t e r v a l i s determined.
This
d i s c h a r g e i s used t o d e f i n e t h e sediment t r a n s p o r t f o r t h a t i n t e r v a l of time. The a n n u a l s e d i m e n t d i s c h a r g e i s t h e sum f o r a l l o f t h e i n t e r v a l s . (1963) and,
f o r a n example,
See C o l b y
Simmons (1976).
The m e a s u r e m e n t s and t h e c o m p u t e d s e d i m e n t l o a d s d e s c r i b e d a b o v e a r e o f suspended sediment.
T o t a l sediment l o a d i n c l u d e s t h e bed l o a d which i s u s u a l l y
44
11477000 SUSPENDED-SEDIMENT
EEL RIVER AT SCOTIA, CA--Continued
OlSCtlAHGE ITONS/OAY), WATER YEAR 0CTlJt)ER 1979 TO SCPTEM~CF? 1980
OCTOBER
NOVEMBER
ME.M MEAN
COiCENTRATlDN IYGILJ
DISCHARGE DAY
ICFSL
I
106
L
100 96 91 93
3 4
5 b
7 8
9 10
11
12 1>
ZY
30 31 TOTAL
-26
I
.25 .50
2
3 3 3 3 3
133 156 169 348 984
26 27 28
1
98 96 99
16 17 18 19
21 22 23 24 25
.29 .27
2 2
123
20
I 1
93 94 94 V6 96
1* 15
.50 .5L -76 .78 .7e
3 3 3
I21
1
2 2 5 20
2400 2540 2e20
85 68 125 234 1740
472U
23000 20600 6580 3700 2540 1930
1150 220
1610
16
75726
---
10
35 16
Fig. 3.24. computed,
SEDIMENT DISCHARGE ITDNSIDAY)
.18 .18
.no
1.0 .9e -36 .e4 .91 4.7 53
MEAN DISCHARGE ICFSJ
MEAN CONCEN-
TRATION
1370 1340 SO50 11200 9270 14000
29000 15700 8960 6130
IMGILl
12100 6010
646 1260 340 I40 10
33509 10400U 116U
3150 2900 2600 2500 2310
4s 24 16
563 237 131
2150 2020 1910
11 LO
7s 6L
ieoo
1730
5
6890 lO8OOU 2140U 5230 2050
1 b50
4 5 4
5220
271 1160
20300
6460
55
b66
7340 z&eoo 19500 25500
910 502 560
196743.1
359090
I2
400 240
34700
--_
52 55 30 22 17
6510
12100 e440
3910 699 240 83 70
6180 5290 4550 3940 3440
30
4630 3660 3040 2610 22eo
26800 19000 12800 9510 7+m0
tCF5l
MEAN CONCENIRATION IMGILL
9 196
624
64000
DISCHAHGE ITONS/UAV)
MEAN DISCHARGE
e
390 160 90
952 3630 122000
DtCEMBER
SCDIMLNT
33
14400
339u
95Y 5370 67800 28000
174
e6e 786 369 234
158 102 7s 101
10
54 62
e
46
6
33 31 39 23
b
e
10
38
in 21 I7 52 293
inso
4540 8290 7980 30300 37600
220
518U
25700 15900 11300
355 215 105
24IU
8680
60
lllU
9660 38300
218
1410 7070
1310
144000
m600
643
6ezou
295 150 94 55
151ou
_--
--_-_
ITON51DAY)
10 14
e
1580 1540 1920 2860
StO 1MEN1 DISCHARGE
536503
I27 320 916 741
---
254350
7160 4740 14500
iseoo
24600 9230 3100
366945
Published sediment record. o r i s e s t i m a t e d a s a p e r c e n t a g e of t h e suspended load.
of bed load g e n e r a l l y a r e n o t r e l i a b l e .
Measurements
See Vanoni (1975).
I f a stseam f l o w s through a r e s e r v o i r most of t h e sediment w i l l b e t r a p p e d i n the reservoir.
The volume of m a t e r i a l d e p o s i t e d and i t s volume-weight
d e t e r m i n e d b y s u r v e y s a t i n t e r v a l s of s e v e r a l y e a r s.
can be
Of c o u r s e t h e r e s e r v o i r
outflow w i l l c o n t a i n some suspended m a t e r i a l ; t h u s t h e t o t a l i n f l o w load w i l l b e somewhat g r e a t e r than t h a t measured i n t h e r e s e r v o i r .
F i e l d measurement tech-
n i q u e s t o d e t e r m i n e t h e volume occupied by s e d i m e n t s d e p o s i t e d i n a r e s e r v o i r a r e d e s c r i b e d i n Vanoni (1975, p. 349-382).
Runoff and sediment y i e l d of ephe-
m e r a l s t r e a m s c a n b e o b t a i n e d f r o m d a t a c o l l e c t e d a t s m a l l r e s e r v o i r s a s des c r i b e d by P e t e r s o n (1962). 3.1.10
Chemical and b i o l o g i c a l q u a l i t y
Whether w a t e r i s c o n s i d e r e d of good or poor q u a l i t y depends on t h e use t o be made of it.
Drinking w a t e r should n o t c o n t a i n b a c t e r i a .
c e r t a i n m i n e r a l s , or d i s s o l v e d gases.
suspended m a t e r i a l s ,
Water f o r i r r i g a t i o n should c o n t a i n o n l y
45
100,000
I
I
I
40,000
10,000
4000
300 L 5000
I
10,000
I
I
20,000
50,000 100,000
DAILY MEAN WATER DISCHARGE, IN CFS
F i g . 3.25. Sediment-transport c u r v e f o r Sacramento R i v e r a t Sacramento. C a l i f o r n i a (From P o r t e r f i e l d , 1980). a l i m i t e d amount o f sodium and o f some o t h e r elements; and suspended sediment i s u n d e s i r a b l e because i t c l o g s t h e p i p e s and d i t c h e s . r e q u i r e w a t e r s o f v e r y s p e c i f i c c h e m i c a l content.
Some i n d u s t r i a l p r o c e s s e s Esthetically,
w a t e r i s con-
s i d e r e d good i f i t i s c l e a r ( h a s l i t t l e or no suspended or f l o a t i n g m a t e r i a l ) , h a s no c o l o r or odor, and s u p p o r t s f i s h and o t h e r b i o t a . Water q u a l i t y c a n be d e s c r i b e d i n two ways,
by i d e n t i f y i n g and q u a n t i f y i n g
the i n o r g a n i c and t h e o r g a n i c m a t e r i a l s i n t h e w a t e r , or by some measures o f t h e e f f e c t s of t h e s e m a t e r i a l s .
F o r example.
t h e c o n c e n t r a t i o n of d i s s o l v e d s o l i d s
is r e l a t e d t o t h e e l e c t r i c a l conductance: t h e t y p e s o f d i s s o l v e d s o l i d s d e t e r mine t h e pH,
a measure of hydrogen-ion
a c t i v i t y ; and t h e c o n c e n t r a t i o n of d i s -
s o l v e d oxygen is an i n d i c a t i o n of t h e b i o c h e m i c a l c o n d i t i o n of t h e water.
These
t h r e e i n d i c a t o r s p l u s t e m p e r a t u r e c a n b e m e a s u r e d i n t h e f i e l d a n d a r e good g e n e r a l measures o f w a t e r q u a l i t y .
But f o r c e r t a i n u s e s one needs t o know t h e
k i n d s a n d c o n c e n t r a t i o n s of t h e v a r i o u s d i s s o l v e d e l e m e n t s in t h e r a t e r . and
46
whether dangerous b a c t e r i a l or c h e m i c a l p o l l u t a n t s a r e p r e s e n t .
This informa-
t i o n i s o b t a i n e d by l a b o r a t o r y a n a l y s e s of samples o f w a t e r from t h e stream. D e t e r m i n a t i o n of w a t e r q u a l i t y i s a d e t a i l e d and s p e c i a l i z e d o p e r a t i o n a s i n d i c a t e d by t h e wide range of p h y s i c a l , chemical, b i o l o g i c a l , and r a d i o c h e m i c a l i n f o r m a t i o n p u b l i s h e d i n t h e a n n u a l w a t e r - d a t a r e p o r t s of t h e USGS f o r t h e
A purpose of t h e s e
N a t i o n a l S t r e a m - Q u a l i t y A c c o u n t i n g (NASQUAN) s t a t i o n s . NASQUAN s t a t i o n s i s t o m o n i t o r changes i n w a t e r q u a l i t y ,
consequently s p e c i f i c
conductance,
concentration a r e re-
pH.
water temperature,
corded continuously.
and dissolved-oxygen
T h i s d e t a i l i s n o t n e c e s s a r y on n a t u r a l ( u n p o l l u t e d )
w a t e r s whose c h a r a c t e r d o e s n o t c h a n g e a p p r e c i a b l y f r o m y e a r t o y e a r .
Hem
(1972. p. 40-50) d e s c r i b e s how e n v i r o n m e n t a l i n f l u e n c e s a f f e c t n a t u r a l w a t e r qua1 i ty. Methods f o r c o l l e c t i n g and a n a l y z i n g w a t e r - q u a l i t y o f t h i s book.
d a t a a r e beyond t h e scope
S e e Hem ( 1 9 7 2 , p. 60-68) f o r g u i d e l i n e s o f s a m p l i n g ; S k o u g s t a d
(1979) f o r d e t e r m i n a t i o n of i n o r g a n i c s u b s t a n c e s : B a r n e t t and M a l l o r y (1971) f o r d e t e r m i n a t i o n o f m i n o r e l e m e n t s ; G o e r l i t z and Brown ( 1 9 7 2 ) f o r m e t h o d s f o r a n a l y s i s o f o r g a n i c s u b s t a n c e s ; Greeson and o t h e r s (1977) for methods f o r coll e c t i o n and a n a l y s i s of a q u a t i c b i o l o g i c a l Thatcher, J a n z e r .
and m i c r o b i o l o g i c a l s a m p l e s ;
and Edwards (1977) f o r methods f o r d e t e r m i n a t i o n of r a d i o a c -
t i v e s u b s t a n c e s i n w a t e r ; and Stevens,
Picke,
and Smoot (1975) f o r measurement
of water temperature.
WEATHER OBSERVATIONS
3.2
The p r i n c i p a l w e a t h e r o b s e r v a t i o n s o f concern t o h y d r o l o g i s t s a r e p r e c i p i t a t i o n , t e m p e r a t u r e . and e v a p o r a t i o n from w a t e r s u r f a c e s . 3.2.1
.
Precipitation
A t most m e t e o r o l o g i c a l s t a t i o n s , t h e p r e c i p i t a t i o n i s caught i n a can and t h e c a t c h measured d a i l y .
The N a t i o n a l Weather S e r v i c e 8-inch nonrecording gage i s
shown i n F i g u r e 3.26.
D e t a i l s o f t h e gage and i n s t r u c t i o n s f o r making observa-
t i o n s a r e g i v e n by t h e N a t i o n a l Weather S e r v i c e (NWS, 1972). t a t i o n i s snow, t h e gage c a t c h may n o t be r e p r e s e n t a t i v e .
When t h e p r e c i p i -
Then a sample of snow
o n t h e g r o u n d i s o b t a i n e d b y i n v e r t i n g t h e c a n and c u t t i n g a v e r t i c a l s a m p l e which i s m e l t e d t o d e t e r m i n e t h e w a t e r c o n t e n t . Recording p r e c i p i t a t i o n gages commonly weigh t h e c a t c h and r e c o r d t h e cumulat i v e c a t c h on a n a n a l o g c h a r t or a s p u n c h e s a t s e l e c t e d i n t e r v a l s on a p a p e r tape. Data from t h e s e gages a r e commonly t a b u l a t e d a t h o u r l y i n t e r v a l s ; c a t c h e s a t s h o r t e r i n t e r v a l s c a n be o b t a i n e d most r e a d i l y from t h e d i g i t a l t a p e , l i m i t e d of c o u r s e by t h e punch i n t e r v a l . The t i p p i n g - b u c k e t r a i n g a g e , commonly u s e d i n h y d r o l o g i c s t u d i e s , i s a c t u a t e d by s m a l l i n c r e m e n t s o f r a i n ( u s u a l l y 0.01 i n c h e s i n U.S.). ments a r e r e c o r d e d on an analog c h a r t .
The i n c r e -
41
F i g . 3.26.
N a t i o n a l Weather S e r v i c e n o n r e c o r d i n g r a i n gage.
I n remote areas, p r e c i p i t a t i o n i s caught i n s t o r a g e gages, 8-inch cans of c o n s i d e r a b l e depth.
The c a n s a r e charged w i t h c a l c i u m c h l o r i d e t o m e l t snow and
t o prevent severe freezing of the catch.
O i l i s sometimes used t o reduce
The c a n i s u s u a l l y e l e v a t e d on a tower and
e v a p o r a t i o n between o b s e r v a t i o n s .
e q u i p p e d w i t h a s h i e l d to r e d u c e w i n d v e l o c i t y ( F i g . 3 . 2 7 ) . serviced a t i r r e g u l a r intervals,
Storage gages a r e
sometimes o n l y 3 o r 4 t i m e s a year.
Generally
o n l y s e a s o n a l o r annual p r e c i p i t a t i o n i s o b t a i n e d . The c a t c h o f a p r e c i p i t a t i o n g a g e d e p e n d s on i t s l o c a t i o n w i t h r e s p e c t t o trees, buildings,
and o t h e r o b s t r u c t i o n s .
A l o c a t i o n i s considered s a t i s f a c t o r y
i f t h e r e a r e no o b s t r u c t i o n s w i t h i n a n i n v e r t e d 45-degree However,
cone above t h e gage.
a gage l o c a t i o n may become u n s u i t a b l e because of t r e e growth o r b u i l d -
ing construction.
Gages on windy,
open a r e a s tend t o c a t c h t o o l i t t l e p r e c i p i -
tation. A l t h o u g h a p r e c i p i t a t i o n g a g e may c o l l e c t s a m p l e s r e p r e s e n t a t i v e o f t h e immediate l o c a l i t y ,
t h e r e c o r d a t t h e s i t e may n o t d e s c r i b e t h e p r e c i p i t a t i o n
p a t t e r n some d i s t a n c e away, e s p e c i a l l y i n mountainous country. N a t u r a l p r e c i p i t a t i o n may be a f f e c t e d by man's a c t i v i t i e s .
Smoke and o t h e r
a i r b o r n e e f f l u e n t s from i n d u s t r i a l a r e a s t e n d t o i n c r e a s e p r e c i p i t a t i o n downwind, and l a r g e urban a r e a s become h o t t e r than undeveloped a r e a s and induce more thunderstorms.
I n addition t o inadvertent modifications.
enhance p r e c i p i t a t i o n i n some regions.
3.2.2
c l o u d s a r e seeded t o
See Chapter .lo.
Evaporation from w a t e r s u r f a c e s
E v a p o r a t i o n i s commonly m e a s u r e d i n a n o p e n pan.
The w i d e l y - u s e d W e a t h e r
B u r e a u C l a s s A p a n i s 4 f t i n d i a m e t e r and 1 0 i n c h e s d e e p ( F i g . 3 . 2 8 ) .
It i s
48
Fig. 3 . 2 1 .
S t o r a g e r a i n gage w i t h s h i e l d .
F i g . 3.28.
Evaporation pan.
f i l l e d t o a d e p t h of 8 inches and t h e d e p t h i s measured d a i l y w i t h a hook gage. Evaporation i s t h e d i f f e r e n c e between r e a d i n g s , during the interval. refilled.
a d j u s t e d f o r any p r e c i p i t a t i o n
When t h e w a t e r l e v e l h a s r e c e d e d a n i n c h ,
t h e pan i s
An e v a p o r a t i o n s t a t i o n i n c l u d e s r a i n a n d t e m p e r a t u r e g a g e s . a n d
sometimes a n anemometer f o r measuring r i n d .
49 The r a t e o f e v a p o r a t i o n f r o m a p a n i s g r e a t e r t h a n t h a t f r o m a l a k e o r r e s e r v o i r because of t h e h e a t t r a n s f e r r e d t h r o u g h t h e pan w a l l s .
Although t h e
"pan c o e f f i c i e n t " t o a d j u s t annual pan e v a p o r a t i o n t o annual l a k e e v a p o r a t i o n i s c o n s i d e r e d t o b e a b o u t 0.7,
f o r s h o r t e r p e r i o d s i t v a r i e s c o n s i d e r a b l y and
cannot b e d e f i n e d re1 iably. O t h e r ways o f m e a s u r i n g w a t e r - s u r f a c e e n e r g y b u d g e t , and m a s s t r a n s f e r .
evaporation include w a t e r budget,
These methods r e q u i r e c o n s i d e r a b l e d a t a
c o l l e c t e d on a r e s e r v o i r f o r a y e a r or more. Water budget i s t h e s i m p l e s t . s t o r a g e a r e measured.
Inflow, outflow,
Water-surface
the o n l y unknown i n t h e water-budget
rainfall,
and change i n
e v a p o r a t i o n c a n be computed because i t i s equation.
R e l i a b i l i t y of t h e r e s u l t de-
p e n d s on t h e m a g n i t u d e of t h e e v a p o r a t i o n r e l a t i v e t o t h e m a g n i t u d e s o f t h e o t h e r e l e m e n t s : a s m a l l d i f f e r e n c e between two l a r g e numbers, some e r r o r ,
each s u b j e c t t o
tends t o be unreliable.
The e n e r g y - b u d g e t e q u a t i o n i n c l u d e s t h e e n e r g y i n p u t s a n d o u t p u t s , a l l o f which,
except evaporation,
c a n b e measured.
Data c o l l e c t i o n and a n a l y s i s a r e
d e s c r i b e d i n a c o m p r e h e n s i v e i n t e r a g e n c y p r o j e c t r e p o r t (U.S. Geol. S u r v e y , 1954). The m a s s - t r a n s f e r
E = Np ( e o
-
equation is
e,)
where E i s e v a p o r a t i o n , N i s t h e mass t r a n s f e r c o e f f i c i e n t .
p i s wind speed, and
eo and ea a r e s a t u r a t i o n vapor p r e s s u r e and a c t u a l vapor p r e s s u r e r e s p e c t i v e l y . M e a s u r e m e n t s o f w i n d s p e e d , and w a t e r and a i r t e m p e r a t u r e a r e r e q u i r e d .
The
c o e f f i c i e n t , N, m u s t b e d e r i v e d f r o m e v a p o r a t i o n m e a s u r e d b y a n o t h e r m e t h o d (See T u r n e r , 1966). 3.2.3
Temperature
D a i l y maximum and minimum a i r t e m p e r a t u r e s a r e o b t a i n e d a t many l o c a t i o n s by t h e N a t i o n a l Weather Service.
D e t a i l s of c o l l e c t i o n a r e g i v e n i n t h e i r Observ-
i n g Handbook No. 2 (NWS, 1 9 7 2 ) . 3.2.4
Snow accumulation
Snow f a l l i s r e p o r t e d a t w e a t h e r s t a t i o n s b u t t h e a c c u m u l a t i o n of snow on t h e ground o r d i n a r i l y is not.
Snow on t h e ground i s p o t e n t i a l r u n o f f which can be
f o r e c a s t i f t h e amount and c h a r a c t e r of t h e snowpack a r e known. t h e snowpack,
Measurement of
c a l l e d snow surveying, c o n s i s t s of measuring t h e d e p t h and w a t e r
c o n t e n t a t snow c o u r s e s ( F i g . 3.29).
A t u b e i s u s e d . t o e x t r a c t c o r e s of snow
f r o m t h e p a c k a t d e s i g n a t e d d i s t a n c e s a l o n g t h e l i n e m a r k i n g t h e snow c o u r s e . D e p t h is r e c o r d e d a t e a c h s a m p l i n g p o i n t and t h e c o r e i s w e i g h e d t o d e t e r m i n e t h e w a t e r c o n t e n t ( F i g . 3.30). D e p t h s and w a t e r c o n t e n t s a r e a v e r a g e d o v e r a l l
F i g . 3.29. Snow s u r v e y o r s a t a marker d e s i g n a t i n g o n e end o f a snow c o u r s e ( U . S . S o i l Conservation S e r v i c e ) .
Snow surveying: I n s e r t i n g t h e tube, reading t h e depth. and weighing F i g . 3.30. the tube w i t h the snow c o r e i n i t (U.S. S o i l Conservation S e r v i c e ) .
51 the sampling points to give the result.
Snow surveys are usually made near the
first of each of the spring months. In mountainous regions travel to a snow course by skis or snowshoes is time consuming;
if by helicopter the travel is expensive.
The number of visits can
be reduced by using a snow pressure pillow which is a flat flexible container filled with anti-freeze.
The pillow indicates the snow-water equivalent by the
pressure of the snow pack on the pillow.
Pressure readings are transmitted by
radio or satellite and transformed to water content by a previous calibration of the pillow (Ballison, 1981).
Soil Conservation Service (1972) describes snow-
surveying procedures in detail.
Use of snow survey results is described in
Chapter 11. 3.3
BASIN CHARACTERISTICS Knowledge of drainage basin characteristics is useful in understanding a
streamflow record and is a requirement in some methods of estimating flow c h a r acteristics at nngaged sites. Size of drainage area is the most common basin characteristic. basin is delineated on topographic maps and its area measured.
The drainage
In arid or
semiarid regions a major drainage basin may encompass an area which has no surface drainage; the contributing drainage area excludes that interior area. Drainage area may not be a good indicator of streamflow if the topographic and the ground-water divides are not coincident.
This disparity cannot be
easily quantified but its recognition will help to understand the measured flows or to estimate flows at ungaged sites. Basin topography influences runoff in several ways
-
steep slopes concentrate
the rainfall quickly and result in high flood discharges; flat slopes result in slow runoff, increased gronnd-water recharge, increased evapotranspiration, and consequently in decreased total runoff.
Basin topography is commonly quantified
by some approximation of the slope of the main channel.
An additional index is
the percentage of lakes and swamps in the basin. Vegetative cover can sometimes be quantified as the percentage of the area forested, or under cultivation.
In a natural basin, the vegetative cover de-
pends on climate and on soil characteristics. Soil characteristics determine the rate of infiltration of rainfall to the soil and thus affect the rate and amount of runoff.
The Soil Conservation
Service (1971) classifies each soil into one of four ranges according to infiltration rate. The geology of a basin affects the rate of runoff',
the losses or gains along
the channels, and especially the low-flow characteristics. Knowledge of the geology as i t affects the water resource may be very useful even though i t is only qualitative.
52 P r e c i p i t a t i o n usually i s considered a basin characteristic. p r e s s e d a s mean annual p r e c i p i t a t i o n ,
t h e 12-hour s t o r m p r e c i p i t a t i o n a t 50-year a p p r o p r i a t e t o a p a r t i c u l a r problem.
I t c a n b e ex-
some measure of s t o r m i n t e n s i t y such a s r e c u r r e n c e i n t e r v a l , or i n o t h e r ways
Likewise,
monthly mean t e m p e r a t u r e s a r e
b a s i n c h a r a c t e r i s t i c s in t h a t t h e y a r e i n d i c a t o r s of p o t e n t i a l e v a p o r a t i o n and t r a n s p i r a t i o n r a t e s and of whether p r e c i p i t a t i o n w i l l be snow and whether i c e w i l l form i n s t r e a m s .
Stream channel geometry,
esthetic character,
stability,
and s u i t a b i l i t y f o r
f i s h a n d w i l d l i f e h a b i t a t a r e useful d e s c r i p t o r s a l t h o u g h q u a n t i f i c a t i o n i s somewhat s u b j e c t i v e . 3.4
TRANSMISSION OF HYDROLOGIC DATA Conventionally, t h e s t a g e d a t a observed o r recorded a t a gaging s t a t i o n i s
o b t a i n e d when t h e hydrographer v i s i t s t h e s t a t i o n , a t monthly or l o n g e r i n t e r vals.
T h i s frequency of c o l l e c t i o n i s adequate i f t h e d a t a a r e t o be used f o r
w a t e r r e s o u r c e s t u d i e s or f o r p r o j e c t design.
But f o r w a t e r management p u r p o s e s
t h e d a t a may be needed immediately, or i n s o - c a l l e d " r e a l time."
B a s i c e l e m e n t s f o r a s a t e l l i t e d a t a - c o l l e c t i o n s y s t e m (From U.S. F i g . 3.31. Geological Survey). V a r i o u s s y s t e m s f o r t r a n s m i t t i n g d a t a d a i l y or m o r e f r e q u e n t l y u t i l i z e phone l i n e s o r r a d i o s .
Xn t h e l a s t few y e a r s automated s a t e l l i t e t e l e m e t r y h a s
become a p r a c t i c a l means of p r o v i d i n g water-data t i o n w i t h i n t h e t i m e frame needed.
u s e r s w i t h h y d r o l o g i c informa-
S a t e l l i t e data-collection
s y s t e m s use e a r t h -
o r b i t i n g s a t e l l i t e s t o r e l a y d a t a from c o l l e c t i o n s i t e s t o r e c e i v i n g s t a t i o n s . The system c o n s i s t s of s e n s o r s ,
small radios called data-collection
platforms.
53 satellites, earth receiving sites, and a data processing and distribution system.
See Shope and P a u l s o n (1981) and F l a n d e r s (1981).
T h e system is illus-
trated in Figure 3.31. REFERENCES Bailey, J.F. and Ray, H.A., 1966, Definition of stage-discharge relation in natural channels by step-backwater analysis: U.S. Geol. Survey Watersupply Paper 1869-A, 24 p. Barnes, H.H., Jr., 1967, Roughness characteristics of natural channels: Geol. Survey Water-Supply Paper 1849, 213 p. Barnes, H.H., Jr. and Davidian. J., 1978, Indirect methods Herschy, ed., New York. John Wiley and Sons.
U.S.
Hydrometry, R.W.
Barnett, P.R. and Mallory, E.C., Jr., 1971, D e t e r m i n a t i o n of m i n o r elements in w a t e r b y e m i s s i o n spectroscopy: U.S. Geol. Survey Techniques of WaterResources Investigations, Book 5, Chapter A2, 31 p. Bodhaine, G.L., 1968, M e a s u r e m e n t of p e a k discharge at culverts b y indirect methods: U.S. Geol. Survey Techniques of Water-Resources Investigations, B o o k 3, Chapter A3. 60 p. Buchanan, T.J., 1964, Time of travel of soluble contaminants in streams: of Sanitary Engineering Division, ASCE, Vol. 90. No. SA3, 12 p.
Jour.
Buchanan, T.J. and Somers, W.P., 1969, Discharge m e a s u r e m e n t s at gaging stations: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapter A8, 6 5 p. Colby. B.R., 1963, P l u v i a l s e d i m e n t s - A s u m m a r y of source, transportation, deposition, and m e a s u r e m e n t of sediment discharge: U.S. Geol. Survey Bull e t i n 1181-A, 4 7 p. 1981, Debris f l o w s i n s m a l l m o u n t a i n stream Costa, J.E. and Jarrett, R.D., channels of Colorado and their hydrologic implications: Bulletin of the Assoc. of Engineering Geologists, Vol. xviii, No. 3, August 1981. Dalrymple, T. and Benson, M.A., 1967, M e a s u r e m e n t of p e a k discharge b y the slope-area method: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapter A2, 12 p. Davidian, J., 1984, C o m p u t a t i o n of water-surface profiles: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapt. Al5. 1976, A technique for estimating t i m e of Eikenberry, S.E. and Davis, L.G., travel of water in Indiana streams: U.S. Geol. Survey Water Resources Investigations 9-76. 3 9 p. Flanders, A.F., 1981, Hydrological data transmission: W o r l d Meteorological Organization, Operational Hydrology Report No. 14, WMO-No. 559, 3 4 p., Geneva, Switzerland. Goerlitz, D.F. and Brown, E., 1972, M e t h o d s for analysis of organic substances in water: U.S. Geol. Survey Techniques of Water-Resources Investigations, B o o k 5, Chapter A3, 40 p. Green, M.J. and Herschy, R.W.. 1978, N e w methods & J Hydrometry, R.W. ed., Chichester, W, John Wiley and Sons.
Herschy,
Greeson, P.E.. Elke, T,A., Irwin. G.A., Lium, B.W., and Slack, K.V., 1977, Methods for collection and analysis of aquatic biological and microbiological samples: U.S. Geol. Survey Techniques o f W a t e r Resources Investigations, B o o k 5, Chapter A4, 3 3 2 p.
54 Guy, H.P. and Norman, V.W.. 1976, Field methods for measurement of fluvial sediment: U.S. Geol. Survey Techniques of Wa t er-Resources Investigations, Book 3. Chapter C2, 5 9 p. Hem. J.D.. 1972. Study and interpretation of the chemical characteristics of natural water: U.S. Geol. Survey Water-Supply Paper 1473, Second Edition, 363 p. Hubbard. E.F.. Kilpatrick, F.A., Martens, L.A.. and Wilson, J.F.. Jr., 1982, Measurement of time of travel and dispersion in streams by dye tracing: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3. Chapt. A9. 44 p. Hulsing. H., 1968, Measurement of peak discharge at dams by indirect methods: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapter A5. 29 p. Kennedy, E.J., 1983. Discharge ratings at gaging stations: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapt. A10. Kilpatrick. F.A. and Cobb. E.D.. 1984. Measurement of discharge using tracers: U . S . Geol. Survey Open-File Rept. 84-136, 73 p. Laenen, A. and Smith, W., 1982. Acoustic systems for the measurement of streamflow: U.S. Geol. Survey Open-File Rept. 82-329, 45 p. Matthai. H.F.. 1968, Measurement of peak discharge a t width contractions by indirect methods: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapter A4. 44 p. NWS,
1972, Substation observations, National Weather Service Observing Handbook No. 2: National Weather Service, Data Aquisition Division, Office of Meteorological Operations, Silver Spring, Md.
Peterson, H.V.. 1962. Hydrology of small watersheds in western States: Geol. Survey Water Supply Paper 1475-1, 137 p.
U.S.
Porterfield, G., 1972. Computation of fluvial-sediment discharge: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3 . Chapter C3. 66 P. Rallison. R.E.. 1981, Automated system for collecting snow and related hydrological data in mountains of western United States: Hydrological Sciences Bulletin, Vol. 26, No. 1, March 1981, p 83-89. Rantz, S.E.. 1982. Measurement and computation of streamflow: U.S. Water-Supply Paper 2175. 631 p.
Geol. Survey
Riggs. H.C., 1976, A simplified slope-area method for estimating flood discharges in natural channels: U.S. Geol. Survey Jour. of Research, 4 (3). p 285-291. Shope. W.G. and Paulson, R.W., 1981, Data collection via satellite for water management: Transportation Engineering Journal, ASCE, Vol. 107, No. TE4, July 1981. p 445-455. Simmons, C.E., 1976. Sediment characteristics of streams in the eastern Piedmont and western Coastal Plain regions of North Carolina: U.S. Geol. Survey Water-Supply Paper 1798-0. p 10-14. Skougstad. M.W.. Ed., 1979, Methods for determination of inorganic substances in water and fluvial sediments: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 5 . Chapter Al. 626 p. Smith, W., Hubbard, L.L.. and Laenen. A., 1971, The acoustic streamflow-measuring system on Columbia River at The Dalles. Oregon: U.S. Geol. Survey OpenFile Report, Portland, Oregon.
55 Smoot, G.F. and Novak, C.E.. 1969, M e a s u r e m e n t of discharge b y the moving-boat method: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapter All, 2 2 p. Soil Conservation Service, 1971, Hydrology, SCS National Engineering Handbook, Section 4: Soil Conservation Service, U.S. Dept. of Agriculture, Washington, D.C. Soil Conservation Service, 1972, Snow survey and water-supply forecasting: SCS National Engineering Handbook., Section 22, Soil Conservation Service. U.S. Dept. of Agriculture, Washington. D.C. Stevens. H.H.. Jr., Ficke, J.F., and Smoot. G.F., 1975. W a t e r temperature influential factors, field measurement. and data presentation: U.S. Geol. 65 Survey Techniques of Water-Resources Investigations, Book 1, Chapter D1, P. Janzer, V.J., and Edwards. K.W.. 1977. Methods for determination Thatcher. L.L., of radioactive substances in water and fluvial sediments: U.S. Geol. Survey 95 p. Techniques of Water-Resources Investigations, Book 5. Chapter AS, Turner, J.F., Jr., 1966, Evaporation study i n a h u m i d region, Lake Michie, North Carolina: U.S. Geol. Survey Prof. Paper 272-6. U.S.
Geological Survey, 1954. W a t e t l o s s investigations Volume 1 - Lake Hefner studies: U.S. Geol. Survey Prof. P a p e r 269.
Ed., 1975, Sedimentation engineering: Vanoni, V.A.. Practice, 745 p.
ASCE Manual of Engineering
White, K.E., 1978, Dilution methods & H y d r o m e t r y by R.W. Pork, John Wiley and Sons.
Herschy, Ed.:
New
Wilson, J.F., Jr.. 1968, Time of travel measurements and other applications of dye tracing: International Assoc. of Scientific Hydrology Publ. NO. 76, Bern. p 252-262. WMO, 1980, Manual on stream gauging: World Meteorological Organization Operational Hydrology Report No. 13. W M O - No. 519. Vol. 2, Geneva. Switzerland.
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51
Chapter 4
STAT1STICS 4.1
INTRODUCTION Some u n d e r s t a n d i n g o f t h e p r i n c i p l e s of s t a t i s t i c s i s needed t o a n a l y z e and
i n t e r p r e t hydrologic d a t a properly.
I n t h i s chapter p r i n c i p l e s a r e described
without use of h i g h e r m a t h e m a t i c s b u t w i t h t h e a s s u m p t i o n t h a t t h e r e a d e r h a s some f a m i l i a r i t y w i t h s t a t i s t i c s terminology, mentary p r o b a b i l i t y . inference,
c o m p u t a t i o n procedures,
and e l e -
Coverage i s l i m i t e d t o f r e q u e n c y c u r v e s , s t a t i s t i c a l
and r e g r e s s i o n and c o r r e l a t i o n .
S t a t i s t i c a l i n t e r p r e t a t i o n s a r e v a l i d o n l y t o t h e e x t e n t t h a t t h e d a t a and the p h y s i c a l c o n d i t i o n s conform t o t h e a s s u m p t i o n s r e q u i r e d by t h e s t a t i s t i c a l method used.
Many s t a t i s t i c a l p r o c e d u r e s r e q u i r e t h e assumption t h a t t h e d a t a
a r e n o r m a l l y d i s t r i b u t e d , b u t t h e t y p e s of d a t a used i n hydrology commonly a r e n o t n o r m a l l y d i s t r i b u t e d , and some have no p r o b a b i l i t y d i s t r i b u t i o n a t a l l .
The
h y d r o l o g i s t must s e l e c t p r o c e d u r e s most n e a r l y s u i t a b l e t o t h e c h a r a c t e r of h i s d a t a and must i n t e r p r e t t h e r e s u l t s a c c o r d i n g l y . This c h a p t e r p r o v i d e s t h e b a s i c s t a t i s t i c a l t o o l s , b o t h a n a l y t i c a l and graphical,
and c o n c l u d e s w i t h a d i s c u s s i o n of t h e c h a r a c t e r i s t i c s of h y d r o l o g i c d a t a .
Applications t o s p e c i f i c problems a r e given i n l a t e r chapters.
Most o f t h e
m a t e r i a l i n t h i s c h a p t e r i s t a k e n from USGS p u b l i c a t i o n s a u t h o r e d by Riggs. 4.2
FREQUFNCY CURVES
4.2.1
Distributions
T h e concept of a p o p u l a t i o n of o b j e c t s having a d i s t r i b u t i o n of s i z e s (or of some o t h e r c h a r a c t e r i s t i c ) i s b a s i c t o t h e s t a t i s t i c a l method.
It i s n o t p o s s i -
b l e t o c o l l e c t enough d a t a t o d e f i n e a f r e q u e n c y d i s t r i b u t i o n e x a c t l y , b u t t h e e x i s t e n c e of a p a r t i c u l a r one can be proven t o t h e d e s i r e d degree of c o n f i d e n c e by r e p e a t i n g an experiment many times. K e n d a l l ( 1 9 5 2 , p. 2 3 ) r e p o r t e d t h e r e s u l t s o f a d i c e - t o s s i n g e x p e r i m e n t i n which 1 2 d i c e w e r e t o s s e d s i m u l t a n e o u s l y and t h e number of s i x e s was r e c o r d e d f o r each t o s s . 4.1.
The d i c e were t o s s e d 4,096 t i m e s w i t h t h e r e s u l t s shown i n Table
A l s o shown a r e t h e r e l a t i v e f r e q u e n c i e s c o m p u t e d f r o m t h e e x p e r i m e n t a l
r e s u l t s and t h e t h e o r e t i c a l r e l a t i v e f r e q u e n c i e s c o m p u t e d f r o m t h e b i n o m i a l distribution.
The c l o s e a g r e e m e n t b e t w e e n t h e t h e o r e t i c a l a n d e x p e r i m e n t a l
frequencies indicates t h a t the binomial d i s t r i b u t i o n i s applicable t o t h i s problem. The b i n o m i a l d i s t r i b u t i o n i s a d i s c r e t e d i s t r i b u t i o n , t h a t i s , i t c a n t a k e v a l u e s o n l y a t s p e c i f i c p o i n t s along a s c a l e .
In t h e d i c e - t o s s i n g experiment,
58
TABLE 4.1 R e s u l t s of d i c e - t o s s i n g
experiment ( A f t e r Kendall,
No. of sixes
Belat ive f requency
Frequency
441 1,145 1.181 796 380 115 24 8 4,096
0 1
2 3 4 5 6
I and over Total
0.109 .280 .288 .194
.093 .028 .006 .002
1.oo
1952)
Theoretical relative frequency
0.112 .269 .296 .197 -08 9 .029
.001
.001 1.oo
i t i s p o s s i b l e t o o b t a i n an i n t e g e r number of s i x e s o n l y ; t h e r e i s no such t h i n g
a s 5.5
o r 3.2 s i x e s .
More commonly,
a v a r i a b l e may t a k e any v a l u e along a s c a l e .
and i t s d i s t r i b u t i o n a r e known a s continuous.
Such a v a r i a b l e
A v a r i a b l e may be c l a s s i f i e d a s
continuous i f i t can t a k e any v a l u e along a s c a l e even though t h e l i m i t a t i o n s of measurement r e s t r i c t t h e o b s e r v a t i o n s t o d i s c r e t e values.
This condition e x i s t s
w i t h most n a t u r a l phenomena.
To a i d i n u n d e r s t a n d i n g a d i s t r i b u t i o n , c o n s i d e r 1,000 t r e e - r i n g ranging in s i z e from 2 t o 240. a histogram,
size,
0
60
i n c r e m e n t s of
o r frequency d i s t r i b u t i o n , i s o b t a i n e d (Fig. 4.1.
120 WIDTH INDEX
F i g . 4.1.
I f t h e s e a r e grouped by s i x - u n i t
180
indices
left).
The
240 WIDTH INDEX
Histogram and p r o b a b i l i t y - d e n s i t y c u r v e of 1000 t r e e - r i n g
indices.
i r r e g u l a r i t y of t h e p r o f i l e of t h i s d i s t r i b u t i o n i s due t o t h e s m a l l ( i n a s t a t i s t i c a l s e n s e ) number of i n d i c e s used i n i t s p r e p a r a t i o n . number used,
The g r e a t e r t h e
t h e smoother would be t h e p r o f i l e of t h e frequency d i s t r i b u t i o n .
I f t h e number of o b s e r v a t i o n s a p p r o a c h e s i n f i n i t y a n d t h e s i z e i n c r e m e n t approaches zero, t h e enveloping l i n e of t h e frequency d i s t r i b u t i o n w i l l approach a smooth curve.
Then i f t h e o r d i n a t e v a l u e s a r e d i v i d e d by a number such t h a t t h e
59
area under the curve becomes one, the resulting curve is a probability density curve. or probability distribution, as shown on the right of Figure 4.1.
The
process just described requires the additional assumption that the variable can take any value within the range, that the variable is continuous, not discrete. A theoretical probability distribution describes the relation between size
(or some other characteristic) and probability.
For this relation to be valid,
the individuals must occur randomly or be drawn randomly.
The size of any
individual drawn should not depend on the size of any one previously drawn. Probability. in the concept of frequency distributions, is defined as relative frequency.
The distribution of the number of sixes obtained from repeated
tosses of 12 dice could be illustrated by plotting the theoretical relative frequencies of Table 4.1.
The relative frequencies of each of the 6-unit incre-
ments in Figure 4.1 could likewise be computed.
In the first of these examples,
a probability is associated with each possible outcome.
In the second, a proba-
bility is associated with each increment of size; here the probability is of obtaining not a specific individual but any individual within the increment of size.
This interpretation is required for continuous distributions because
there is an infinite number of possible values and, thus, no probability of occirrence of a particular individual.
Referring to the right curve of Figure
4.1, probability is related to the continuous distribution in the following way: The area under the curve represents the sum of all probabilities and therefore must equal one. Because every item was used in defining the distribution for which the total area is one, then the probability that any item will fall in the distribution is one and the probability that an item will fall in any segment of the distribution is the ratio of the area of that segment to the total area. The distributions just described, both discrete and continuous. are called relative-frequency distributions, probability distributions, or just distributions.
However, the probability interpretation is valid only if the data used
are random.
For example, the daily mean flow of a stream is closely related to
the flows of previous days, s o the distribution of daily means is not one to which the probability interpretation strictly applies. approximate
a
It is possible also to
distribution which merely describes the sample.
For instance, the
distribution of grain sizes of a sample of a streambed is measured to characterize the material; there is no interest in the probability of obtaining a grain in a particular size range by additional sampling.
Here the sample is not the
individual grain but an aggregate of grains of various sizes. Only a few standard theoretical distributions are widely used.
Sampling
theory and inference are based largely on the normal distribution with which the reader is assumed to be familiar. introduced as appropriate.
Other theoretical distributions will be
60
4.2.2
Cumulative distributions
Suppose w e know the probability density curve (probability distribution) for a variable and are interested in the probability of a random event being greater than some particular value E.
This probability can be obtained by measuring or
computing the proportion of the total area above the base value.
For instance,
the left curve of F i g u r e 4.2 s h o w s an area under the c u r v e to the right of E of
0.1, that is, P = 0.1.
Thus the probability of a r a n d o m event exceeding E is
0.1.
-E
0.I PROBABILITY OF EXCEEDANCE
MAGNITUDE
F i g . 4.2.
Probability density curve (left) and its cumulative form (right).
Another f o r m of the probability curve can be prepared by c u m u l a t i n g the probabilities f r o m one end o f the curve and plotting each of these c u m u l a t e d probabilities against the magnitude of its appropriate event. right-hand curve of Figure 4.2.
The result is the
Cumulative distributions are commonly plotted
to a probability scale such that the theoretical curve is a straight line. a scale can be devised for any two-parameter distribution. plotting paper is widely known and used. hydrologic frequency analyses.
Such
Normal probability
Gumbel plotting paper is used in many
(Although the Gumbel extreme-value distribution
is a three-parameter distribution.
one parameter, the skew, is constant for the
form used and permits the construction of a scale which gives a straight-line plot).
B o t h the n o r m a l and G u m b e l probability plotting papers are available
with either arithmetic or logarithmic ordinate scales. four distributions
-
Thus plotting papers for
normal, log-normal, Gumbel, and log-Gumbel
-
are available.
W h e n the probability density curve is c u m u l a t e d f r o m the right end, the probabilities of exceeding the various magnitudes are obtained.
If cumulated
from the left, probabilities of being less than those magnitudes are obtained. The appropriate cumulative curve, commonly called a frequency curve in hydrology. depends on the desired use.
61 A more detailed examination of the relation between a
curve and its cumulative form (the frequency curve) follows. two normal distributions shown in Figure 4.3.
20
14
26
MAGNITUDE
Fig. 4.3.
32
0.9
We begin with the
Their cumulative forms can be
I 8
probability density
I
0.8 0.7
I 0.5
1
1
1
0.3 0.2
01
PROBABILITY THAT A RANDOMLY-DRAWN INDIVIDUAL WILL EXCEED THE INDICATED MAGNITUDE
Two normal distributions and their cumulative forms.
expressed as straight lines by use of the special abscissa scale which is derived from the characteristics of the normal distribution.
Both distributions
have the same median value, 20. and these medians plot at 0.5 probability on the cumulative graph.
The variability of a distribution is indicated by the slope
of the cumulative distribution; that is, the greater the variability, the greater the slope.
The standard deviation is half the difference between magnitudes
at probabilities of 0.16 and 0.84; (See a table of the cumulative normal distribution). Many frequency distributions are nonsymmetrical. For such distributions, the mean, median. and mode have different values which consequently correspond to different probabilities on the cumulative graph. is classified as skewed.
A nonsymmetrical distribution
Skewness may be shown graphically as right or left; it
may be described mathematically by a number, either positive or negative.
Two
skewed distributions and a symmetrical distribution are shown in Figure 4.4, which also shows the corresponding cumulative distributions (frequency curves). For a normal. or any symmetrical. distribution the mean and median are the same value.
Thus, the value corresponding to the probability of 0.5 on the
Cumulative frequency curve is the mean as well as the median for such distributions.
The relative positions of the mean, median, and mode for skewed
62
I
30 r
10
IS
20
30
MAGNITUDE A - Right s k e w e d B - Normal C - Left skewed
0 0.9
0.80.7
0.5
0.30.2
0.1
PROBABILITY T H A T A RANDOMLY-DRAWN INDIVIDUAL W I L L EXCEED THE I N D I C A T E D M A G N I T U D E
F i g . 4.4. Normal and s k e w e d d i s t r i b u t i o n s a n d t h e i r c u m u l a t i v e f o r m s on a normal-probabil i t y p l o t . d i s t r i b u t i o n s a r e shown i n F i g u r e 4.5. from t h e c u m u l a t i v e p l o t .
Only t h e median v a l u e can be d e t e r m i n e d
The p o s i t i o n of t h e mean w i t h r e s p e c t t o t h e median
R e l a t i v e p o s i t i o n s o f t h e mean, m e d i a n , a n d mode f o r p o s i t i v e or F i g . 4.5. r i g h t - s k e w e d ( l e f t g r a p h ) a n d f o r n e g a t i v e or l e f t - s k e w e d ( r i g h t g r a p h ) distributions.
on t h e c u m u l a t i v e p l o t d e p e n d s on t h e d e g r e e o f s k e w n e s s , skewness,
t h e d i r e c t i o n of
and t h e d i r e c t i o n i n which t h e frequency d i s t r i b u t i o n i s cumulated.
F o r e x a m p l e , 43 p e r c e n t o f t h e s a m p l e s d r a w n f r o m a p a r t i c u l a r r i g h t - s k e w e d d i s t r i b u t i o n w i l l e x c e e d t h e mean and 5 7 p e r c e n t w i l l b e l e s s t h a n t h e mean. Thus,
i f t h e d i s t r i b u t i o n i s c u m u l a t e d f r o m t h e h i g h end.
t h e mean i s t o t h e
r i g h t of t h e m e d i a n ; i f c u m u l a t e d f r o m t h e l o w end. t h e mean i s t o t h e l e f t o f t h e median. 4.6
These r e l a t i o n s a r e r e v e r s e d for left-skewed d i s t r i b u t i o n s .
illustrates the relations.
Figure
The p r o b a b i l i t y s c a l e s o f t h e t w o p l o t s of
63
n
I\
/ A
I
LEFT SKEW
MEDIAN
-
0.5
B
0.5
PROBABILITY OF EXCEEDANCE (A) OR OF BEING LESS THAN (B)
Fig. 4.6. Frequency c u r v e s showing e f f e c t of d i r e c t i o n of skew and d i r e c t i o n of cumulation on p o s i t i o n of t h e mean w i t h r e s p e c t t o t h e median. F i g u r e 4.6
a r e d i f f e r e n t : each i s designed f o r t h e p a r t i c u l a r d i s t r i b u t i o n
plotted. 4.2.3
Recurrence i n t e r v a l
Frequency c u r v e s of h y d r o l o g i c d a t a commonly r e l a t e magnitude t o r e c u r r e n c e i n t e r v a l o r r e t u r n p e r i o d i n s t e a d of t o p r o b a b i l i t y .
Recurrence i n t e r v a l i s t h e
r e c i p r o c a l of p r o b a b i l i t y when t h e p o p u l a t i o n c o n s i s t s o f annual events.
Thus
t h e r e c u r r e n c e i n t e r v a l o f a p a r t i c u l a r v a l u e i s t h e a v e r a g e number o f y e a r s between o c c u r r e n c e s g r e a t e r t h a n (or l e s s t h a n ) t h a t value. 4.2.4
GraDhical f i t t i n e
A f r e q u e n c y c u r v e can be d e f i n e d g r a p h i c a l l y from a l i s t of items. method, interval.
In t h i s
e a c h i n d i v i d u a l i n t h e sample i s a s s i g n e d a p r o b a b i l i t y or r e c u r r e n c e Then magnitudes of t h e i n d i v i d u a l s a r e p l o t t e d a g a i n s t t h e s e proba-
b i l i t i e s or recurrence intervals,
and a l i n e i s drawn t o p r o p e r l y i n t e r p r e t t h e
points. A s s i g n m e n t o f p r o b a b i l i t i e s i s by means o f a p l o t t i n g - p o s i t i o n
formula.
V a r i o u s f o r m u l a s may b e u s e d , e a c h b a s e d on a d i f f e r e n t a s s u m p t i o n a s t o t h e c h a r a c t e r i s t i c s of ting-position
t h e sample.
Langbein (1960) r e l a t e s t h e better-known
f o r m u l a s t o t h e i r u n d e r l y i n g assumptions.
plot-
Benson (1962b) compares
t h e r e s u l t s o f u s i n g v a r i o u s p l o t t i n g p o s i t i o n s on t h e economics o f e n g i n e e r i n g planning.
RI
A widely-used f o r m u l a i s t h e Weibull
= 1 / p = (n+l)/m
where R I i s r e c u r r e n c e i n t e r v a l i n y e a r s ,
p i s p r o b a b i l i t y of an erceedence i n
any one y e a r , n i s t h e number of i t e m s i n t h e sample, and m i s t h e o r d e r number of t h e i n d i v i d u a l i n t h e sample a r r a y (Dalrymple,
1960).
Although Beran (1981,
p 26) j u s t i f i e s use of t h e G r i n g o r t e n formula,
t h e Weibull i s used i n t h i s book
because o f i t s wide use i n t h e United S t a t e s .
The sample d a t a may be a r r a y e d
-
64 arranged in order of magnitude
-
beginning w i t h the largest as No. 1, or w i t h
the smallest as No. 1, according to whether the frequency curve is to describe the probability of exceedence or of being less than.
A distribution curve can
be cumulated from either end, and in the graphical method this effect is accomplished by selecting the direction in which the data are arrayed. The next step is plotting magnitude against recurrence interval (or probability) on a graph. results.
I f arithmetic coordinates are used, an S-curve usually
It is difficult to define such a curve by the few observations; it is
customary, therefore, to use a graph sheet having the abscissa graduated in such a w a y that a particular theoretical frequency curve w i l l plot as a straight
line.
Such g r a p h sheets are available for the normal, log-normal, and G u m b e l
Type I distributions.
It is possible to prepare such a scale for any two-
parameter dis tribut ion. A l t h o u g h sets o f data of the s a m e type m a y not appear to lie on straight lines on a particular plotting paper, the lines of good fit usually are only slightly curved i n one direction.
An additional advantage of the probability
graph appears when a straight line is a reasonable interpretation of the plotted points; then the straight line is a frequency curve of the theoretical type on w h i c h the plotting paper is based.
It should be clearly understood that a
frequency curve is not necessarily normal just because the points are plotted on normal-probability paper (or has a Gumbel distribution because the points are plotted on G u m b e l probability paper); only w h e n the frequency curve is a straight line is this true. T h e m e a n of a n o r m a l distribution corresponds to the 0.5 probability or to the %-year recurrence interval.
But a curved line on normal-probability paper
represents a siewed distribution whose mean is not at 2-year recurrence interval.
T h e effect of a s k e w on the relation of m e a n to recurrence interval is
easily demonstrated by use of the Gumbel Type I distribution which has a fixed positive skew. rence interval.
As used for flood analyses, the mean occurs at 2.33-year
recur-
But if the s a m e G u m b e l distribution is used to represent t h e
frequency of floods less than. the positions of the m e a n and m e d i a n are reversed, and the mean plots at about 1.59 years. 4.5 and 4.6.
This effect is shown by Figures
The discharge corresponding to the 2.33-year
recurrence interval
as obtained from a curved line on Gumbel probability paper is not the mean.
It
can, however, be used as a characteristic discharge as could the 2-year value or any other near the central part of the distribution. The annual discharges for the years 1915-50 inclusive in Table 4.2, can be used to define a frequency curve.
column 2.
T h e curve can be cumulated from the
65 TABLE 4.2 Computation of p l o t t i n g p o s i t i o n s Water year
Discharge
Order number, m; highest a s No. 1
Plotting position (n+l)/m
Order number, m ; lowest a s No. 1
Plotting p o s i t ion (n+l)/m,
1915 16 17 ia 19
264 374 332 346 359
34 11 19 16 13
1.09 3.37 1.95 2.31 2.85
3 26 ia 21 24
11.2 1.43 2.06 1.76 1.54
1920 21 22 23 24
333 483 417 346 320
ia 3 5 17 21
2.06 11.2 7.40 2.18 1.76
19 34 32 20 16
1.95 1.09 1.16 1 .a5 2.31
1925 26 27 28 29
271 214 530 304 271
31 36 2 25 32
1.19 1.03 i a .5 1.48 1.16
6 1 35 12 5
6.16 37.0 1.06 3.09 7.40
1930 31 32 33 34
27 1 304 400 327 415
33 26 9 20 6
1.12 1.43 4.11 1 .a5 6.16
4 11 28 17 31
9.25 3.37 1.32 2.18 1.19
1935 36 37 3a 39
402 362 320 272 244
a 12 22 30 35
4.62 3.09 1.68 1.23 1.06
29 25 15 7 2
1.28 1.48 2.47 5.30 ia .5
1940 41 42 43 44
279 303 3 10 27 5 317
28 27 24 29 23
1.32 1.37 1.54 1.28 1.61
9 10 13 14
4 .ll 3.70 2 .a5 4.62 2.65
1945 46 47 4a 49
350 387 359 449 406
15 10 14 4 7
2.47 3.70 2.65 9.25 5.30
22 27 23 33 30
1.68 1.37 1.61 1.12 1.23
1950
570
1
36
1.03
37 .O
a
h i g h end o r from t h e low end, depending on whether t h e d a t a a r e a r r a y e d from t h e high end or from t h e low end. Arraying 20 or 25 items,
Both a r r a y s a r e g i v e n i n t h e t a b l e . t h a t is.
a r r a n g i n g them i n o r d e r of magnitude, and
a s s i g n i n g o r d e r numbers, can be done r e a d i l y by o b s e r v a t i o n .
For a larger
number of items, v a r i o u s schemes may be used. The p l o t t i n g p o s i t i o n s g i v e n in Table 4.2 a r e p r e l i m i n a r y r e c u r r e n c e v a l s ; p r o b a b i l i t i e s would be t h e i r r e c i p r o c a l s ; n i s t h e number of i t e m s
- 1915 + 1 = 36). a n d m i s t h e o r d e r number.
inter-
(1950
66 Discharge i s p l o t t e d a g a i n s t r e c u r r e n c e i n t e r v a l on a p l o t t i n g p a p e r having e i t h e r a n a r i t h m e t i c or l o g a r i t h m i c o r d i n a t e s c a l e and a n a b s c i s s a s c a l e based
on t h e normal o r some o t h e r 2-parameter p l o t t e d f r o m T a b l e 4.2 d a t a .
distribution.
F i g u r e s 4.7 and 4 8 a r e
S e l e c t i o n of t h e o r d i n a t e s c a l e was a r b i t r a r y ;
b o t h a b s c i s s a s c a l e s a r e based on t h e Gumbel Type I d i s t r i b u t i o n .
The l i n e s
N e i t h e r of t h e s e c u r v e s r e p r e s e n t Gumbel
are graphical interpretations.
d i s t r i b u t i o n s because t h e y a r e n o t s t r a i g h t l i n e s .
v)
500.
Z
I
W'
9
400
0
v,
0
I
I
200
l
l
1.3 1.6 2
1.1
I
I
I
3
5
10
1
1
20 30
J 50
RECURRENCE INTERVAL, IN YEARS
F i g . 4.7. F r e q u e n c y c u r v e b a s e d on d a t a f r o m T a b l e 4.2 a s s u m i n g t h a t d a t a a r e annual maximums.
!K
I
:
l0O0
I
I
I
I
I
I
Z
@z
4
1
1
-
. -1-
300-
200
I
-
0
v, 0
100
I
I
I
t
I
I
I
I
I
F i g . 4.8. F r e q u e n c y c u r v e b a s e d on d a t a f r o m T a b l e 4.2 a s s u m i n g t h a t d a t a a r e annual minimums.
61 4.2.5
Fitting theoretical distributions
T h e first step is to decide w h i c h distribution w o u l d be most appropriate. The ones most commonly used in hydrology are normal, lognormal. and log Pearson Type 3.
(Gumbel and Weibull), ble.
extreme value
Selection depends on the varia-
Previous analyses may be used as a guide.
(i)
T h e n o r m a l distribution h a s o n l y 2 parameters,
N o r m a l distribution.
m e a n and standard deviation.
E s t i m a t e s of these are c o m p u t e d f r o m the dis-
charges of Table 4.2 by
Mean =
6
= ZQIN = 12,486136 = 341
ZQZ
Variance
=
-
tZQ)Z/N
Sz =
-
4,542,500
N-1
-
155,900,196136 =
6055
35
Standard deviation = S = 11.8 Using these, the detailed characteristics of the distribution can be extracted from a table of the cumulative normal distribution, which is available in many statistics texts.
In a table of the cumulative normal distribution, magnitude
is expressed as the mean plus or minus some multiple of the standard deviation. We assume that
a
and S are equal to their respective population parameters p and
Then for selected values of magnitude in terms of p and a we determine the
a.
probabilities f r o m the table at enough points to define the frequency curve. Results using a mean of 341 and a standard deviation of 11.0 are shown in Table
4.3. TABLE 4.3 Frequency characteristics of data from Table 4.2 assuming a normal distribution
xa p - 2.0a p - 1.5~ p - 1.0~ p - .8a
-
.5a .2a
p + p +
.2a .5a
p p
P(X<Xa)
Recurrence Interval of Exceedance
= = = =
191 230 269 285
0.02 01 .16 .21
0.98 .93 .8 4 .I9
1.02 1.08 1.19 1.21
=
308
.31 .42 .50 .58 .69
.69 .58 .50 .42 .31
1.45 1 .I2 2 .oo 2.38 3.22
.I9 .8 4 .93 .98
.21 .16 01 .02
4.16 6.25 14.4 50 .O
= 331 =
p + .8a p + 1.00 p + 1.5~ II + 2.0~
P(X>X,)
341
= 363 = 386 = 409 = 425 = 464 =
503
.
.
68 The same r e s u l t s c o u l d have been o b t a i n e d from a p l o t on normal p r o b a b i l i t y The mean i s p l o t t e d a t 0.5 p r o b a b i l i t y .
paper.
the standard d e v i a t i o n i s plot-
t e d p l u s and minus from t h e mean a t p r o b a b i l i t i e s o f 0.16
and 084, r e s p e c t i v e -
ly, a s t r a i g h t l i n e i s drawn through t h e p l o t t e d p o i n t s , and p r o b a b i l i t i e s a t s e l e c t e d l e v e l s a r e r e a d from t h e l i n e . The lognormal d i s t r i b u t i o n i s a normal d i s t r i b u t i o n of t h e l o g a r i t h m s o f t h e data.
E i t h e r Naperian o r common l o g a r i t h m s can b e used b u t common l o g a r i t h m s
a r e most w i d e l y u s e d i n h y d r o l o g y .
I n terms of the untransformed data the
lognormal d i s t r i b u t i o n h a s a r a n g e from z e r o t o p l u s i n f i n i t y and t h u s i s positively
skewed.
The lognormal d i s t r i b u t i o n i s u s u a l l y t r e a t e d s i m p l y a s a
n o r m a l d i s t r i b u t i o n of l o g a r i t h m s a n d c a n b e f i t t e d t o d a t a a s shown i n t h e above example by s u b s t i t u t i n g l o g Q f o r Q i n T a b l e 4.2. Type I E x t r e m e - v a l u e d i s t r i b u t i o n (Gumbel).
(ii)
d i s t r i b u t i o n having a c o n s t a n t skew of 1.139.
-
u = X
-
J.N /a
This i s a 2-parameter
The p a r a m e t e r s a r e
l/a = S/aN
and
w h e r e u i s t h e mode, l/a i s a s c a l e p a r a m e t e r , standard d e v i a t i o n respectively, i t e m s i n t h e sample.
Values o f
Gumbel (1958, p. 228).
x and S a r e
t h e s a m p l e mean a n d
and TN and aN a r e f u n c t i o n s o f yN and aN f o r N from 8 t o 1,000
N.
t h e number of
a r e t a b u l a t e d by
P a r t o f Gumbel's t a b l e i s g i v e n i n T a b l e 4.4.
TABLE 4.4 Means and s t a n d a r d d e v i a t i o n s of reduced extremes (from Gumbel. 1958)
YN
N
10 12 14 16 18 20 25 30 40 50 60 80 100 200 500 1000
UN
0 -4952
,5035 -5100 .5157 .5202 .52355 .53086 .53622 .54362 .54854 .55208 .55688 .56002 .56715 .57240 .51450
0.9497 .9833 1.0095 1.0316 1.0493 1.06283 1.09145 1.11238 1.14132 1.16066 1.17467 1.19382 1.20649 1.23598 1.25880 1.26851
The mean a n d s t a n d a r d d e v i a t i o n o f t h e s a m p l e a r e c o m p u t e d ,
yN a n d
aNa r e
r e a d f r o m t h e t a b l e , u a n d l/a a r e c o m p u t e d f r o m t h e a b o v e f o r m u l a s . a n d t h e straight line
69
is determined.
On Gumbel probability graph the mean is plotted
at 2.33 years
and the approximate relation y = In RI can be used to locate another point on the straight line. Following is a sample computation for annual floods on Columbia River near Data are from USGS WSP 1080.
The Dalles, Oregon for 1858-1946. Mean flood is 606,200 cfs = Standard deviation, S
=
f
d(ZX2
- *;)IN
-
1 = 175,200.
From Table 4 . 4 for N = 89,
YN
= ,558 and uN = 1.20
then l/a = SluN = 175,200l1.20 = 146,000 and u =
x - 7Nla = 606,200
-
(.558)(146.000)
= 524.100.
The equation of the straight line is
X = u + y/a = 524,700 + 1 4 6 . 0 0 0 ~ . The relation y = In T may be used to define plotting points for large recurrence intervals. y = In T = 2.303 log T.
For T = 50 years, X = 524,700
y = 3.91,
i146,000(3.91)
and = 1,096.000
cfs.
The straight line is defined on the graph of Figure 4.9 by the points X = 606,200 cfs at 2.33 years and 1,096,000
cfs at 50 years.
The plotted points for
the period 1858-1948 are shown to indicate the fit of the computed line. Several analysts have concluded that the above fitting procedure recommended by Gumbel ( 1 9 5 8 ) may produce biased estimates.
See
Lettenmaier and Burges
(1982) and references given in their paper.
(iii) Pearson Type 3 distribution.
The Pearson Type 3 distribution is a
70 flexible distribution in three parameters with a limited range to the left and unlimited range to the right.
Plotting paper is not available for this distri-
bution because s k e w n e s s varies.
This distribution is c o m m o n l y fitted to the
1200
800
r
400
0 1 .01
Fig. 4.9.
1.2
5 10 20 RECURRENCE INTERVAL, IN YEARS 2
50
100
Gumbel frequency curve.
common logarithms of flood magnitudes because this results in a smaller skew. The Pearson T y p e 3 distribution w i t h zero s k e w is identical to the n o r m a l distribution. Fitting a 3-parameter distribution starts w i t h c o m p u t a t i o n of the mean, standard deviation, and coefficient of skew.
The mean and standard deviation
(347 and 77.8) o f the discharges o f T a b l e 4.2 normal distribution.
cs
were c o m p u t e d for fitting t h e
The coefficient of skew is
(36)a(1,738,665.756)
-
3(36)(12,486)(4,542,500) + 2(12,486)'
=
(36)(35)(34)(6055)(77.8)
Cs = 1.04. These data parameters may be used to fit any 3-parameter distribution but the procedure is indirect because the probability density function cannot be integrated directly and thus there is no formula for the cumulative distribution. The relation between magnitude and probability of being larger than (or smaller than) is commonly determined from a table of frequency factors for the chosen distribution.
Frequency factors for the P e a r s o n T y p e 3 distribution, adapted
71 f r o m a m o r e extensive table b y W a t e r Resources Council (1982), are given in Specific points on the fitted distribution are computed by
Table 4.5.
where X
is the variable
probability),
-X
at
a selected
recurrence
interval
(or
is the mean, K is the frequency factor for the same recurrence
interval, and S is the standard deviation. Using the above value of mean. standard deviation, and skew, and T a b l e 4.5, the discharge at 20-year recurrence interval would be
X = 341
+
1.88
(71.8) = 493 c f s
Additional points would be computed as needed to define the curve. T h e log P e a r s o n T y p e 3 distribution is fitted s i m i l a r l y except that the c o m m o n l o g a r i t h m s of the discharges are used i n c o m p u t i n g t h e three parameters. Frequency curve fitting is usually done by digital computer. 4.2.6
Evaluation of fitting methods
Fitting to theoretical distributions has the following advantages: 1.
For the same theoretical distribution. every analyst using a given set of data would get the same answer.
2.
Fitting can be done quickly by use of computer programs.
3.
The curve can be completely described by 2 or 3 parameters and the name of the distribution.
and the following disadvantages:
1.
Selection of the theoretical distribution is arbitrary.
2.
No one theoretical distribution will adequately fit a11 hydrologic data of one type such as flood peaks.
3.
Some data cannot be fitted by a distribution with only 3 parameters.
4.
T h e highest and l o w e s t data points m a y b e given too m u c h weight (the objective i n hydrology is to best define o n e end o f a frequency curve, not to define the best fit throughout the range).
Graphical fitting has the following advantages: 1.
Procedure is simple and can be done quickly.
2.
No assumption as to the type of distribution need be made.
3.
Analyst can use other information in interpreting the plotted points.
4.
Historical data may be readily incorporated.
and these disadvantages: 1.
Even though the same plotting position formula is used, different analysts will draw somewhat different frequency curves.
2.
A graphical curve cannot be described by 2 or 3 parameters.
72 TABLE 4.5 Frequency factors for Pearson Type 3 distributions Recurrence Interval, in Years
CS
100
20
2.0 1.8 1.6 1.4 1.2
3.61 3.50 3.39 3.27 3.15
2.00 1.98 1.96 1.94 1.91
1.30 1.32 1.33 1.34 1.34
1.0
1.88 1.84 1.80 1.75 1.70
1.34 1.34 1.33 1.32 1.30
.38 .41
.6 -4 .2
3.02 2.89 2.76 2.62 2.47
0
2.33
1.64
1.28
-52
0
2.18 2.03 1.88 1.73 1.59
1.59 1.52 1.46 1.39 1.32
1.26 1.23 1.20 1.17 1.13
.55 .57 .59 .60 .62
.8
- -2 - -4 - .6 - .8 -1.0 4.2.7
10
3.33 .20
.24 .28 .31 .35
.44 .47 .50
2
1.43
1.11
-.64
-
-.64
- .94
-.64 -.64
1.05
-
.99 -1.04 -1.09
- .95 -1.02 -1.09 -1.17 -1.24
-.55
-1.13 -1.17 -1.20 -1.23 -1.26
-1.32 -1.39 -1.47 -1.52 -1.59
-.52
-1.28
-1.64
-03
-.SO
.07 .10 .13 .16
-.41
-1.30 -1.32 -1.33 -1.34 -1.34
-1.70 -1.75 -1.80 -1.84 -1.88
-.31 -.28 -.25 -.23 -.20 -.16 -.13 -.lo -.07 -.03
-.63 -.62 -.60 -.59 -.57
-.44 -.41 -.38
.89
Interpretation of frequency curves
A frequency curve based on random homogeneous data is an estimate of the cumulative probability distribution of the population from which the sample was drawn.
The following interpretations of the frequency curve require the assump-
tion that the curve is a good representation of the population distribution. Referring to the graphical curve of Figure 4.7, the recurrence interval of 500 cfs is 16 years.
This means that the annual maximum will exceed 500 cfs at
intervals averaging 16 years in length, or that the probability of the annual maximum exceeding 500 cfs in any one year is 1/16. From Figure 4%
the recurrence interval of 2 5 0 cfs is 13 years.
Thus, the
annual m i n i m u m discharge will be less than 2 5 0 cfs at intervals averaging 13 years in length, and the probability that the minimum discharge in any one year will be less than 250 cfs is 1/13. Many interpretations of frequency curves in hydrology have been stated in terms of the probability "of equaling or exceeding" a selected value.
Most
variables in hydrology, notably streamflow, are continuous - but reported as discrete
-
and the theoretical probability of occurrence of any particular value
in a continuous distribution is zero.
Therefore it seems desirable to delete
"of equaling." The interpretations of frequency curves given above will not answer questions such as the probability of an event o f 10-year recurrence interval being exceeded in a 10-year period.
Intuitively, one might expect that probability to
13
be 0 . 5 , but it is not.
The correct probability can be computed a s follows.
Since the probability of exceeding the 10-year event in 1 year is 0.1, the probability of not exceeding it in 1 year is 0.9.
Then, the probability of not
exceeding it in 10 years is, by the multiplicative law of probabilities ( 0 . 9 ) l o = 0.35 and the probability of one or more events exceeding the 10-year event in 10
years is 0.65.
A more complete interpretation of a frequency curve is given by
Riggs (1961). Although frequency curves are used a s though they were accurate representations of the population distribution, w e know that they may not be.
Benson
(1960) sampled from a known distribution and showed a wide range in shape and position of frequency curves defined by different samples of the same size. Another way of assessing the reliability of a frequency curve is by computing the confidence limits.
Chow (1964, p. 8-31) describes a method.
These compu-
tations indicate that the frequency curve is most reliable in the vicinity of the mean.
4.2.8
Describing frequency characteristics
A mathematically-fitted frequency curve can be described by the name of the
distribution and the mean, standard deviation, and skew.
For use in hydrologic
analyses, or for quantifying a regulatory flow, the discharge at some point on the frequency curve is used; for example the 100-year (0.01 probability) flood and the 10-year low flow are commonly used indices.
The measure of central
tendency commonly used is the median which is the discharge at 2-year recurrence interval or at 0.5 probability. Variability of a distribution is described by its standard deviation, S.
For
comparison of variabilities among frequency curves the dimensionless ratio of standard deviation to the mean is used.
This is called the coefficient of
variation
cv
=
Sli
If logarithms of the data are used to define the frequency curve, the standard deviation of the logarithms is called the index of variation, I,;
unlike S,
I,
is already dimensionless and need not (and should not) be divided by the mean. The mean and standard deviation of graphically-fitted frequency curves are readily obtained from the graph if the frequency curve is a straight line on normal or lognormal probability paper.
But the usual graphically-fitted fre-
quency curve is not a straight line on the plotting paper used; consequently, the mean is not at a known probability or recurrence interval, the standard deviation cannot be accurately determined, and the curvature indicates the
14 existence of skewness.
For such curves it is customary to use the median flow
as the characteristic of central tendency.
Discharges at selected recurrence
intervals also are readily obtained but an index of variability can only be approximated from the graphically-defined curve. 4.3
STATISTICAL INFERENCE
W e have 5 4 years of record on the Rappahannock River of Virginia and might ask two questions about the mean flow. First, what is the mean flow for the period of record?
This is a unique value which can easily be computed.
The
second question, what is the mean flow of the stream?, cannot be answered
W e can only assume that the mean of the 54-year sample is an
definitely.
estimate of the true (population) mean.
In other words, we infer the population
characteristics from those of a sample from that population. Statistical inference is based on the theory of sampling.
From a population
of known characteristics many samples are drawn (either actually or conceptually), and the relation of the sample characteristics to the population characteristics is defined. Sampling theory requires use of the concept of a probability distribution. Assume that the distribution of some random variable is normal with mean, p, and standard deviation, u, a s shown in Figure 4.10.
(The term "random", a s used
here, means that the probability of drawing any one item of the population is the same a s for any other).
Fig. 4.10.
Normal distribution.
Now suppose we take many samples of size N from this distribution, compute the mean of each of these samples, and compute the mean and variance of these sample means.
The distribution of the means of samples of size N is superposed
on the original distribution in Figure 4.11.
It can be shown that the distriba-
tion of the means is centered at p and that the standard deviation of the distribution of means is u / a .
Therefore, the mean of the means of samples of
DISTRIBUTION OF MEANS OF SIZE N
ORIGINAL DISTRIBUTION
F i g . 4.11.
D i s t r i b u t i o n o f means o f s a m p l e s from a n o r m a l d i s t r i b u t i o n .
s i z e N i s a n u n b i a s e d e s t i m a t e o f p.
Furthermore,
Consequently,
u n b i a s e d e s t i m a t e o f p.
e s t i m a t e o f t h e p o p u l a t i o n mean.
t h e mean o f o n e s a m p l e i s an
we i n f e r t h a t t h e s a m p l e mean,
Obviously,
X, i s a n
i f we u s e d o t h e r s a m p l e s we would
o b t a i n d i f f e r e n t e s t i m a t e s o f t h e p o p u l a t i o n mean. From a s i n g l e s a m p l e , we c a n a p p r a i s e t h e r e l i a b i l i t y of t h e e s t i m a t e , t h e p o p u l a t i o n mean.
Consequently,
two-thirds
of t h e v a l u e s s h o u l d f a l l
w i t h i n o n e s t a n d a r d d e v i a t i o n (u/fi) o n e a c h s i d e o f t h e mean. IJ
of
The d i s t r i b u t i o n o f means o f v a l u e s d r a w n f r o m a n o r m a l
d i s t r i b u t i o n i s normal.
n o t know
%,
H o w e v e r , we d o
so we h a v e t o s u b s t i t u t e S f o r i t ( w h e r e S i s t h e s t a n d a r d d e v i a t i o n
computed from t h e sample).
The d i s t r i b u t i o n o f
x
having a s t a n d a r d d e v i a t i o n of
S/fi i s known a s t h e S t u d e n t ’ s t d i s t r i b u t i o n , v a l u e s o f w h i c h a r e t a b u l a t e d i n s t a t i s t i c s t e x t s f o r v a r i o u s s i z e s o f N. S u p p o s e now t h a t we h a v e K s a m p l e s o f s i z e N a n d h a v e d e f i n e d K d i f f e r e n t s a m p l i n g d i s t r i b u t i o n s o f t h e mean o f s i z e N.
For each sampling d i s t r i b u t i o n ,
we c a n d e f i n e a m e a n a n d a r a n g e o f r e l i a b i l i t y , w h e t h e r s u c h a r a n g e i n c l u d e s t h e t r u e m e a n p.
a n d we a r e i n t e r e s t e d i n
Considering the range a s a
we may s t a t e t h a t t h e p r o b a b i l i t y ( P ) t h a t t h e random i n t e r v a l
random i n t e r v a l , i n c l u d e s p i s 1-e.
where e i s t h e l e v e l of s i g n i f i c a n c e .
Mathematically,
for e
= 0.32.
P[x - u/\TN)
<
p
<
C% + u/fi)I
= 1-e
=
0.68.
The i n t e r v a l i n b r a c k e t s i s c a l l e d a c o n f i d e n c e i n t e r v a l and t h e e x t r e m e s a r e c a l l e d confidence limits. i n s t e a d o f S.
Note t h a t t h e a b o v e r e l a t i o n h o l d s o n l y i f w e u s e u
I f we u s e S. t h e n 1-e i s a f u n c t i o n o f t h e s a m p l e s i z e , a n d t h e
appropriate probability statement is
16
P
[x - tS/!6)
<
(x +
<
p
t i s 1.09 f o r 1 0 d e g r e e s o f f r e e d o m , f o r example.
where Student's
t h e confidence i n t e r v a l
i n c r e a s e s a s t h e l e v e l of
The w i d t h o f
s i g n i f i c a n c e decreases.
For
t h e 95 p e r c e n t c o n f i d e n c e l i m i t s (e = 0 . 0 5 ) a r e
example,
(2 -
t S / f i ) l = 1-e = 0.68,
<
2.23S/m)
p
<
(x +
2.23S/fi),
where 2 . 2 3 i s from t h e t t a b l e f o r 10 d e g r e e s o f freedom. The c o n f i d e n c e i n t e r v a l d e s c r i b e d i n t h e p r o b a b i l i t y i n t e r v a l , n o t a s p e c i f i c one.
s t a t e m e n t i s a random
T h e p r o b a b i l i t y s t a t e m e n t ( f o r e = 0.05) m e a n s
t h a t 95 p e r c e n t of a l a r g e number o f i n t e r v a l s s i m i l a r l y o b t a i n e d would i n c l u d e t h e t r u e mean.
T h i s p r o b a b i l i t y s t a t e m e n t cannot be extended t o one s p e c i f i c
i n t e r v a l b e c a u s e a s p e c i f i c i n t e r v a l e i t h e r c o n t a i n s t h e t r u e mean o r i t d o e s n o t and t h e p r o b a b i l i t y i s e i t h e r one or z e r o .
The t r u e mean i s n o t a v a r i a b l e ,
i t i s unique.
But we a r e i n t e r e s t e d interval.
i n making a p r o b a b i l i t y
s t a t e m e n t a b o u t one s p e c i f i c
We may s a y t h a t t h e p r o b a b i l i t y o f our o b t a i n i n g a r a n d o m i n t e r v a l
w h i c h i n c l u d e s t h e t r u e mean i s 0.95,
or t h a t we h a v e 9 5 - p e r c e n t
confidence t h a t
t h e i n t e r v a l o b t a i n e d i n c l u d e s t h e t r u e mean. Using t h e above t h e o r y ,
f r o m a random s a m p l e we c a n c o m p u t e a n e s t i m a t e o f
t h e p o p u l a t i o n mean a n d a m e a s u r e o f i t s r e l i a b i l i t y .
T h i s i s a n e x a m p l e of
s t a t i s t i c a l inference. Returning t o t h e sampling theory,
c o n s i d e r t h e d i s t r i b u t i o n of v a r i a n c e s of
s a m p l e s of s i z e N from a normal d i s t r i b u t i o n .
This d i s t r i b u t i o n i s n o t c e n t e r e d
a r o u n d u z b u t i s t o t h e l e f t o f i t , a s shown by t h e l e f t g r a p h o f F i g u r e 4.12. Therefore S 2
i s known a s a b i a s e d e s t i m a t o r o f u2.
I t c a n b e made u n b i a s e d by
m u l t i p l y i n g i t b y N/(N-1) a s s h o w n i n t h e r i g h t g r a p h o f F i g u r e 4 . 1 2 . s t a n d a r d d e v i a t i o n o f t h e s a m p l i n g d i s t r i b u t i o n o f S 2 (N/N-1)
The
c a n a l s o b e com-
puted. A f u r t h e r use of i n f e r e n c e i s i n t e s t i n g hypotheses. given.
One e x a m p l e w i l l b e
S u p p o s e we s e t up t h e n u l l h y p o t h e s i s , Ho, t h a t t h e mean o f a p o p u l a t i o n
i s zero; that is,
we h y p o t h e s i z e t h a t t h e r e i s n o d i f f e r e n c e s t a t i s t i c a l l y
b e t w e e n t h e mean and z e r o .
This n u l l hypothesis i s w r i t t e n
Ho:p = 0 We draw a s a m p l e f r o m t h i s p o p u l a t i o n and c o m p u t e t h e s t a t i s t i c s o f t h e s a m p l i n g d i s t r i b u t i o n of
t h e mean.
d i s t r i b u t i o n o f means,
We n e e d some e s t i m a t e of
t h e hypothetical sampling
and s o we d e f i n e i t a s n o r m a l w i t h mean z e r o ,
dard d e v i a t i o n e q u a l t o S/fi
a s c o m p u t e d f r o m t h e s a m p l e ( F i g . 4.13).
and s t a n -
I1 Now if
5
(as computed from the sample) lies within one standard deviation
of zero, we would conclude that there is no basis for doubting the hypothesis.
Fig. 4.12.
Distribution of variances of samples.
Fig. 4.13.
Hypothetical sampling distribution of means.
If, on the other hand,
x
were two or three standard deviations away from zero,
w e would conclude that it is unlikely that the mean of the population is zero. F o r this latter condition the probability is s m a l l of obtaining an size from a population having a m e a n of zero.
5
of s u c h
Therefore, w e w o u l d reject the
hypothesis and would state that the result was significant at a certain probability level,
meaning that the results obtained differ significantly from the
hypothesis.
A c o m m o n problem is the test of significance of a regression coefficient. The null hypothesis is again that the true value of the regression coefficient is zero, and t h e test m a y be m a d e in the s a m e w a y as before.
See Test of
Significance under Regression Methods.
4.4
CORRELATION AND REGRESSION
T h e distinctions b e t w e e n correlation and regression must be recognized in order to apply and interpret either of the methods.
These distinctions are very
78 marked a l t h o u g h t h e y may seem of l i t t l e importance because of t h e s i m i l a r i t y of t h e computation procedures.
Dixon and Massey (1957, p. 189) made t h e f o l l o w i n g
d i s t i n c t i o n between t h e two:
"A r e g r e s s i o n p r o b l e m c o n s i d e r s t h e f r e q u e n c y d i s t r i b u t i o n o f one v a r i a b l e when a n o t h e r i s h e l d f i x e d a t e a c h o f s e v e r a l l e v e l s .
A c o r r e l a t i o n problem
c o n s i d e r s t h e j o i n t v a r i a t i o n o f two measurements, n e i t h e r of whi ch i s r e s t r i c t e d by t h e experiment." C o r r e l a t i o n i s a p r o c e s s by which t h e d e g r e e of a s s o c i a t i o n between samples of two v a r i a b l e s i s d e f i n e d . d e f i n i t i o n of t h a t association.
The c o r r e l a t i o n c o e f f i c i e n t i s a m a t h e m a t i c a l
I t i s , of course, p o s s i b l e t o compute a c o r r e -
l a t i o n c o e f f i c i e n t from any two s e t s of data. a s s o c i a t i o n i m p l i e s no c a u s e - a n d - e f f e c t
The m a t h e m a t i c a l d e f i n i t i o n o f
r e l a t i o n n o r even t h a t t h e r e l a t i o n
between t h e two v a r i a b l e s r e s u l t s from a common cause. C o r r e l a t i o n t h e o r y r e q u i r e s t h a t t h e d a t a be drawn randomly from a b i v a r i a t e normal d i s t r i b u t i o n .
However,
McDonald (1957) r e p o r t e d t h a t e x p e r i m e n t a l sam-
p l i n g s t u d i e s show t h e n o n n o r m a l i t y e f f e c t s , u s u a l l y r e g a r d e d a s d i s t u r b i n g by s t a t i s t i c i a n s , t o b e of i n c o n s e q u e n t i a l ma gni t ude g e o p h y s i c a l l y .
A further
r e q u i r e m e n t of c o r r e l a t i o n i s t h a t b o t h v a r i a b l e s X and Y b e w i t h o u t e r r o r due t o measurement.
Nothing can be measured w i t h o u t e r r o r , so t h e above r e q u i r e m e n t
i s one of degree.
The q u e s t i o n of t h e e r r o r a l l o w a b l e i s s u b j e c t t o a r b i t r a r y
d e c i s i o n s , p a r t i c u l a r l y s i n c e t h e t r u e e r r o r of t h e d a t a i s never known. The end p r o d u c t of t h e p r o c e s s o f c o r r e l a t i o n i s t h e c o r r e l a t i o n c o e f f i c i e n t ; i t i s n o t an equation.
The e q u a t i o n s which d e s c r i b e Y a s a f u n c t i o n of X, and X
as a f u n c t i o n o f Y, a r e r e g r e s s i o n e q u a t i o n s , n o t c o r r e l a t i o n equations.
Anoth-
e r way o f s t a t i n g t h e d i s t i n c t i o n b e t w e e n c o r r e l a t i o n and r e g r e s s i o n i s t h a t c o r r e l a t i o n measures t h e d e g r e e o f a s s o c i a t i o n between two v a r i a b l e s ,
whereas
r e g r e s s i o n p r o v i d e s e q u a t i o n s f o r e s t i m a t i n g i n d i v i d u a l v a l u e s of one v a r i a b l e from g i v e n v a l u e s o f t h e o t h e r . R e l i a b i l i t y o f c o r r e l a t i o n r e s u l t s d e p e n d s on t h e n u m b e r o f i t e m s u s e d t o compute t h e c o r r e l a t i o n c o e f f i c i e n t and t h e magnitude of t h e computed c o r r e l a tion coefficient.
Confidence l i m i t s a r e q u i t e wide f o r samples of 30 i t e m s o r
less, unless the c o r r e l a t i o n c o e f f i c i e n t i s verylarge.
For example, a c h a r t
shown by Bennett and F r a n k l i n (1954, p. 275) i n d i c a t e s t h a t a c o r r e l a t i o n coeff i c i e n t of + 0 8 computed from a sample of 20 i t e m s would have a c o n f i d e n c e b e l t e x t e n d i n g f r o m 0.6 t o 0.9 f o r 9 5 - p e r c e n t p r o b a b i l i t y . tainty,
Because of t h i s uncer -
two c o r r e l a t i o n c o e f f i c i e n t s d i f f e r i n g only by a few h u n d r e d t h s cannot
be m e a n i n g f u l l y compared.
There a l s o seems t o be no j u s t i f i c a t i o n f o r r e p o r t i n g
c o r r e l a t i o n c o e f f i c i e n t s t o more t h a n two s i g n i f i c a n t f i g u r e s . I f t h e d a t a can r e a s o n a b l y b e assumed t o be drawn f r om a nor m al b i v a r i a t e distribution,
then b o t h c o r r e l a t i o n and r e g r e s s i o n a n a l y s e s a r e a p p r o p r i a t e .
It
i s under t h i s a s s u m p t i o n t h a t most o f t h e exam pl es i n s t a t i s t i c s t e x t s a r e
I9 analyzed.
However, r e g r e s s i o n i s a l s o a p p r o p r i a t e u n d e r c e r t a i n o t h e r c o n d i -
t i o n s when c o r r e l a t i o n i s n o t .
The o n l y a s s u m p t i o n s r e q u i r e d f o r r e g r e s s i o n
are :
1.
The d e v i a t i o n s of t h e dependent v a r i a b l e about t h e r e g r e s s i o n l i n e ( f o r any f i x e d X ) a r e normally d i s t r i b u t e d ,
and t h e same v a r i a n c e e x i s t s throughout
t h e range of d e f i n i t i o n . 2.
Values of t h e independent v a r i a b l e a r e known w i t h o u t e r r o r .
The dependent
v a r i a b l e i s c o n s i d e r e d a s a n o b s e r v a t i o n on a random v a r i a b l e ,
and t h e
i n d e p e n d e n t v a r i a b l e a s some known c o n s t a n t a s s o c i a t e d w i t h t h i s random variable. 3.
Observed v a l u e s of t h e dependent v a r i a b l e a r e u n c o r r e l a t e d random events.
4.
Each of t h e v a r i a b l e s i s homogeneous; t h a t i s , a l l i n d i v i d u a l v a l u e s o f a v a r i a b l e m e a s u r e t h e same t h i n g .
D a t a a r e c o n s i d e r e d homogeneous i f a n y
s u b g r o u p t o w h i c h c e r t a i n o f t h e s e d a t a may b e l o g i c a l l y a s s i g n e d h a s t h e same e x p e c t e d mean a n d v a r i a n c e a s a n y o t h e r s u b g r o u p o f t h e p o p u l a t i o n . N e i t h e r v a r i a b l e need have a p r o b a b i l i t y d i s t r i b u t i o n i n r e g r e s s i o n (but, of course, Y values corresponding t o a fixed
X a r e assumed t o b e n o r m a l l y
distributed). The end p r o d u c t s o f a r e g r e s s i o n a n a l y s i s a r e two e q u a t i o n s , Y = f(X) and X = f(Y) ( u s u a l l y o n l y one i s computed), b e c a u s e r e g r e s s i o n i s d i r e c t i o n a l . contrast,
In
c o r r e l a t i o n g i v e s one index o f t h e r e l a t i o n between v a r i a b l e s .
The r e g r e s s i o n e q u a t i o n g i v e s t h e average amount of change i n t h e dependent v a r i a b l e c o r r e s p o n d i n g t o a u n i t change i n t h e i ndependent v a r i a b l e . g i v e s more s p e c i f i c i n f o r m a t i o n t h a n c o r r e l a t i o n .
Thus i t
The r e g r e s s i o n c o e f f i c i e n t
c a n be t e s t e d t o d e t e r m i n e whether i t i s s i g n i f i c a n t l y d i f f e r e n t from zero,
and
t h i s t e s t i s i d e n t i c a l t o t h e t e s t of s i g n i f i c a n c e of t h e c o r r e l a t i o n c o e f f i c i e n t ( p r o v i d i n g t h e d a t a a r e drawn from a b i v a r i a t e normal d i s t r i b u t i o n ) . 4.4.1
Standard e r r o r
The r e l i a b i l i t y of a r e g r e s s i o n i s measured by t h e s t a n d a r d e r r o r ,
which i s
t h e s t a n d a r d d e v i a t i o n of t h e d i s t r i b u t i o n (assumed normal) of r e s i d u a l s about the regression line. tion,
( F i g u r e 4.14 shows d i s t r i b u t i o n of r e s i d u a l s . )
t h e s t a n d a r d e r r o r i s t h e same throughout t h e range of X.
By d e f i n i -
This s t a n d a r d
e r r o r w a s c a l l e d t h e s t a n d a r d e r r o r o f e s t i m a t e b y E z e k i e l ( 1 9 5 0 , p. 1 3 1 ) .
It
i s a l s o r e f e r r e d t o a s t h e s t a n d a r d e r r o r o f r e g r e s s i o n and a s t h e s t a n d a r d d e v i a t i o n from r e g r e s s i o n . The s t a n d a r d e r r o r of a p r e d i c t i o n from r e g r e s s i o n i s made up of t h r e e p a r t s : t h e e r r o r o f t h e mean,
error of e s t i m a t e .
t h e e r r o r of t h e s l o p e of t h e l i n e ,
and t h e s t a n d a r d
A l l t h r e e may be expressed i n t e r m s of t h e s t a n d a r d e r r o r of
e s t i m a t e so t h a t t h e s t a n d a r d e r r o r of a p r e d i c t i o n ( S ) i s P
80
J
s =se P
1 (X - % , a I+-+n Z(X - 3 )
s
where Se i s s t a n d a r d e r r o r of e s t i m a t e , n i s number of i t e m s i n t h e sample.
X i s the independent v a r i a b l e .
and
Thus t h e e r r o r o f a p r e d i c t i o n i n c r e a s e s w i t h
d i s t a n c e from t h e mean (Snedecor, 1948, p. 120)
$f
. 0
.*
I X
F i g . 4.14. 4.4.2
Normal d i s t r i b u t i o n of p l o t t e d p o i n t s about t h e r e g r e s s i o n l i n e .
M u l t i p l e C o r r e l a t i o n and r e g r e s s i o n
Most a n a l y s e s r e q u i r e use of m u l t i p l e c o r r e l a t i o n or r e g r e s s i o n .
A multiple
c o r r e l a t i o n i s e v a l u a t e d by p a r t i a l c o r r e l a t i o n c o e f f i c i e n t s and by a n index of t o t a l correlation.
A p a r t i a l c o r r e l a t i o n c o e f f i c i e n t i s a n index of t h e d e g r e e
of a s s o c i a t i o n between one independent v a r i a b l e and t h e dependent v a r i a b l e a f t e r t h e e f f e c t s of t h e o t h e r independent v a r i a b l e s have been removed. I n a multiple regression equation the regression c o e f f i c i e n t s a r e c a l l e d p a r t i a l regression coefficients.
Each shows t h e e f f e c t on Y o f a u n i t change i n
t h e p a r t i c u l a r independent v a r i a b l e ,
t h e e f f e c t s of t h e o t h e r independent v a r i a -
b l e s being held constant. I f t h e independent v a r i a b l e s i n a r e g r e s s i o n a n a l y s i s a r e r e l a t e d t o each o t h e r , t h e p a r t i a l r e g r e s s i o n c o e f f i c i e n t s w i l l be of a d i f f e r e n t magnitude from the simple regression coefficients.
(The independent v a r i a b l e s i n a r e g r e s s i o n
u s u a l l y a r e r e l a t e d t o each o t h e r a s w e l l a s t o the dependent variable.)
See
t h e s e c t i o n on " A p p l i c a t i o n o f t h e R e g r e s s i o n Method" f o r e l a b o r a t i o n o n t h i s s u b j ec t . The a s s u m p t i o n s r e q u i r e d f o r c o r r e l a t i o n a r e i n f r e q u e n t l y met i n e n g i n e e r i n g problems and n o t g e n e r a l l y met i n h y d r o l o g i c problems.
Many of t h e s e problems
t o which t h e c o r r e l a t i o n method d o e s not a p p l y c a n be handled by t h e r e g r e s s i o n method because of t h e l e s s r e s t r i c t i v e assumptions.
Thus t h e r e g r e s s i o n method
81 may be used for such relations as that of concrete strength to time of setting. where neither value is randomly selected and neither variable has a probability distribution.
Obviously the definition o f s u c h a relation is l i m i t e d to the
range of the data selected. Under the above conditions the correlation coefficient does not apply but, Of course, can be computed from the relation
w h e r e r = correlation coefficient, Se = standard error of estimate, and Sy = standard deviation o f the values o f the dependent variable. formula it can be seen that r depends on S
Y'
F r o m the above
which depends on the range of data
selected for problems such as the concrete strength relation to time of setting. Therefore,
if the variables used in a regression are not randomly sampled, the
computed value of r changes with the range of the arbitrarily selected sample and is therefore meaningless.
Empirical verification of this statement is given
b y the d a t a plotted in F i g u r e 4.15.
(These d a t a w e r e selected to demonstrate
DRAINAGE AREA, IN SQUARE MILES
Fig. 4.15. Plot used to show the effect of sample range on computed correlation coefficient. Dashed line is the relation for 14 drainage areas ranging from 40 to 2,000 square miles. this principle; the relation is not hydrologically significant.) points, the relation is computed to be log MAF
= 2. 21
+ 0.59 log D A
Using all the
82
The s t a n d a r d e r r o r i s 0.22
l o g u n i t and t h e computed c o r r e l a t i o n c o e f f i c i e n t i s
MAP i s mean a n n u a l f l o o d a n d DA i s d r a i n a g e a r e a .
0.91.
I f o n l y t h e 14 p o i n t s
f o r d r a i n a g e a r e a s r a n g i n g from 40 t o 2.000 s q u a r e m i l e s a r e used,
the relation
is l o g MAF = 2 . 3 1
+
0.57
l o g DA.
T h i s r e l a t i o n h a s a s t a n d a r d e r r o r o f 0.23
l o g u n i t ( a l m o s t t h e same a s t h e
p r e v i o u s s t a n d a r d e r r o r ) , b u t t h e computed c o r r e l a t i o n c o e f f i c i e n t i s 0.83, much lower t h a n t h a t o b t a i n e d by u s i n g s a m p l e s from a g r e a t e r range.
Obviously such
v a r i a b i l i t y i n t h e c o r r e l a t i o n c o e f f i c i e n t would r e n d e r i t u n s u i t a b l e a s a measure o f t h e d e g r e e of r e l a t i o n f o r t h i s t y p e of a p p l i c a t i o n . R e g r e s s i o n i s emphasized o v e r c o r r e l a t i o n ,
n o t o n l y because c o r r e l a t i o n i s
commonly i n a p p l i c a b l e t o p a r t i c u l a r h y d r o l o g i c d a t a b u t b e c a u s e r e g r e s s i o n p r o v i d e s q u a n t i t a t i v e a n s w e r s t o s p e c i f i c problems.
I n general,
regression is
p r e f e r r e d o v e r c o r r e l a t i o n f o r h y d r o l o g i c problems even when t h e d a t a a r e s u i t a b l e f o r a correlation analysis.
Uses of r e g r e s s i o n a n a l y s i s a r e :
To e s t i m a t e i n d i v i d u a l v a l u e s o f t h e d e p e n d e n t v a r i a b l e c o r r e s p o n d i n g t o
1.
s e l e c t e d v a l u e s of t h e independent v a r i a b l e s .
To d e t e r m i n e t h e amount of change i n t h e dependent v a r i a b l e a s s o c i a t e d w i t h
2.
a u n i t change i n an independent v a r i a b l e . 3.
To d e t e r m i n e whether c e r t a i n v a r i a b l e s (which do n o t have p r o b a b i l i t y d i s t r i b u t i o n s ) a r e r e l a t e d t o a dependent v a r i a b l e . C o r r e l a t i o n i s most u s e f u l i n t h e o r e t i c a l s t u d i e s and i n t i m e - s e r i e s
analy-
sis. 4.4.3
Serial correlation
It h a s been p o i n t e d o u t t h a t f o r a p r o b a b i l i t y d i s t r i b u t i o n t o be v a l i d t h e i n d i v i d u a l s must o c c u r randomly. c h a r g e s form a t i m e s e r i e s , occurrence.
Hydrologic d a t a such a s d a i l y stream d i s -
t h a t is.
a sequence of v a l u e s a r r a n g e d i n o r d e r of
The c h a r a c t e r i s t i c s and a n a l y s i s o f h y d r o l o g i c t i m e s e r i e s h a v e
been d e s c r i b e d by Dandy and M a t a l a s (1964).
A common c h a r a c t e r i s t i c o f a t i m e
s e r i e s i s t h e e x i s t e n c e o f a nonrandom e l e m e n t w h i c h p r o d u c e s a d e p e n d e n c e between o b s e r v a t i o n s k u n i t s a p a r t . tion,
This dependence i s c a l l e d s e r i a l c o r r e l a -
and i t s d e g r e e i s measured by t h e s e r i a l c o r r e l a t i o n c o e f f i c i e n t .
First-order
s e r i a l c o r r e l a t i o n i s t h e dependence between o b s e r v a t i o n s adja-
c e n t i n time: t h e k t h o r d e r i s t h e dependence between o b s e r v a t i o n s k u n i t s apart.
A p l o t of t h e s e r i a l c o r r e l a t i o n c o e f f i c i e n t a g a i n s t o r d e r i s a c o r r e -
logram (Dandy and Matalas.
1964).
To d e t e r m i n e t h e s e r i a l c o r r e l a t i o n , t h e t i m e s e r i e s i s r e l a t e d t o i t s e l f offset k units.
F o r example, t h e t i m e s e r i e s i n t h e f i r s t column below i s
a3 r e l a t e d t o i t s e l f s h i f t e d one o b s e r v a t i o n t o o b t a i n t h e f i r s t - o r d e r
serial
c o r r e l a t i o n coefficient.
-
x1
xl ‘2
x3
. . ‘n-1
‘n
Computational d e t a i l s a r e t h e same a s f o r t h e r e l a t i o n between two v a r i a b l e s and a r e g i v e n i n t h e s e c t i o n 4.5.3.
A t e s t of s i g n i f i c a n c e of a f i r s t - o r d e r
serial
c o r r e l a t i o n c o e f f i c i e n t i s g i v e n by Dawdy and M a t a l a s (1964). REGRESSION METHODS
4.5
The p r e v i o u s s e c t i o n d e s c r i b e d r e g r e s s i o n i n g e n e r a l t e r m s and concluded w i t h some u s e s of r e g r e s s i o n .
T h i s s e c t i o n d e s c r i b e s t h e computation and i n t e r p r e t a -
t i o n of r e g r e s s i o n e q u a t i o n s , b o t h a n a l y t i c a l and g r a p h i c a l , and some c h a r a c t e r i s t i c s of t h e r e g r e s s i o n method.
4.5.1
Regression models
We b e g i n a r e g r e s s i o n p r o b l e m w i t h a d e p e n d e n t v a r i a b l e w h i c h we w a n t t o p r e d i c t from one o r more independent v a r i a b l e s .
The independent v a r i a b l e s a r e
v a l u e s o r c h a r a c t e r i s t i c s which seem t o be p h y s i c a l l y r e l a t e d t o t h e dependent variable.
Next we need a model which d e s c r i b e s t h e way i n which t h e independent
v a r i a b l e s a r e r e l a t e d t o t h e dependent v a r i a b l e . w i t h known p h y s i c a l p r i n c i p l e s ,
The model should be i n accord
b u t i t s e x a c t form may be d i c t a t e d by t h e d a t a
used. Using a dependent v a r i a b l e , Y, and independent v a r i a b l e s , X and Z,
t h e equa-
t i o n s and g r a p h s of some more common r e g r e s s i o n models a r e shown i n F i g u r e 4.16. J o i n t r e l a t i o n s , t h o s e which i n c l u d e a v a r i a b l e whi ch i s t h e p r o d u c t of two o t h e r v a r i a b l e s , h a v e b e e n d i s c u s s e d i n d e t a i l b y E z e k i e l and Fox (1959). The p r o d u c t of two v a r i a b l e s i s c a l l e d an i n t e r a c t i o n term.
Com bi nat i ons of t h e
models shown i n F i g u r e 4.16 can be used t o d e s c r i b e more c o m p l i c a t e d r e l a t i o n s , and t h e e q u a t i o n s c a n b e r e a d i l y e x t e n d e d t o i n c l u d e a d d i t i o n a l i n d e p e n d e n t variables. Having s e l e c t e d a s u i t a b l e model,
t h e c o e f f i c i e n t s i n t h a t model e q u a t i o n a r e
computed from s a m p l e d a t a by t h e method o f l e a s t s q u a r e s a s d e s c r i b e d subsequently. Note t h a t a l t h o u g h t w o o f t h e g r a p h s i n F i g u r e 4.16 a r e c u r v e d , a l l o f t h e model e q u a t i o n s a r e i n l i n e a r form.
This l i n e a r i t y of t h e model e q u a t i o n i s a
84 requirement f o r d i r e c t least-squares solution.
L i n e a r i t y c a n s o m e t i m e s be
a t t a i n e d by t r a n s f o r m i n g t h e v a r i a b l e s .
X
X
Y = o + bX+ CZ
Y =o
X
+ bX +cZ+ dXZ
Y
%”
x Fig. 4.16.
4.5.2
Equations and graphs o f some common r e g r e s s i o n models.
Transformations
There a r e two p r i n c i p a l r e a s o n s f o r t r a n s f o r m i n g d a t a b e f o r e a n a l y s i s :
(1)
t o o b t a i n a l i n e a r r e g r e s s i o n model, and (2) t o a c h i e v e e q u a l v a r i a n c e about t h e r e g r e s s i o n 1i n e throughout t h e range. We h a v e s e e n f r o m F i g u r e 4.16
t h a t t h e e q u a t i o n s f o r c e r t a i n two-variable
r e g r e s s i o n s may b e l i n e a r i z e d w i t h o u t t r a n s f o r m i n g t h e v a r i a b l e s .
The method is
known a s p o l y n o m i a l r e g r e s s i o n i n w h i c h a d d i t i o n a l v a r i a b l e s i n successively h i g h e r powers of t h e independent v a r i a b l e a r e added t o t h e model.
But suppose
we know o r p o s t u l a t e t h a t a r e l a t i o n should be of t h e form
By t a k i n g l o g a r i t h m s o f b o t h s i d e s o f t h e e q u a t i o n t h e r e s u l t i n g l i n e a r equation i s obtained:
l o g Y = log a + b l o g X i n w h i c h l o g a and b a r e c o n s t a n t s w h i c h c a n b e c o m p u t e d b y a l e a s t - s q u a r e s a n a l y s i s u s i n g t h e v a r i a b l e s log Y and l o g X.
Y = abx c a n be transformed t o
Likewise the r e l a t i o n
85
log Y = l o g a + X log b w h e r e l o g a and l o g b a r e t h e c o n s t a n t s a n d l o g Y a n d X a r e t h e v a r i a b l e s . Other t r a n s f o r m a t i o n s a r e sometimes used, b u t t h e l o g a r i t h m i c t r a n s f o r m a t i o n i s by f a r t h e most common. The s e c o n d r e a s o n f o r t r a n s f o r m i n g d a t a , and t h e m o r e i m p o r t a n t one, i s t o a c h i e v e e q u a l v a r i a n c e about t h e r e g r e s s i o n l i n e .
One of t h e a s s u m p t i o n s b a s i c
t o t h e r e g r e s s i o n method i s t h a t t h e d i s t r i b u t i o n o f e r r o r s about t h e r e g r e s s i o n l i n e i s n o r m a l and c o n s t a n t t h r o u g h o u t t h e r a n g e ( F i g . 4-14). t r a n s f o r m a t i o n i s o f t e n used.
For example,
Again a l o g
t h e g r a p h on t h e l e f t of F i g u r e 4.17
shows i n c r e a s i n g s c a t t e r o f p o i n t s w i t h i n c r e a s i n g r a i n f a l l .
B u t when t h e
v a r i a b l e s a r e p l o t t e d on t h e l o g c h a r t ( r i g h t g r a p h ) , t h e s c a t t e r o f p o i n t s i s a l m o s t uniform throughout t h e range.
Thus, i f i t had been d e s i r e d t o c a r r y t h e
a n a l y s i s beyond t h e g r a p h i c a l p r e s e n t a t i o n , s h o u l d have been made.
a transformation of the v a r i a b l e s
( O r d i n a r i l y t h e v a r i a b l e s would be r e v e r s e d on t h e c h a r t
i f a r e g r e s s i o n were t o be made because r u n o f f i s t h e dependent v a r i a b l e . )
2 0 2 4 6 RUNOFF, IN INCHES
0.3
0.5 1 2 3 RUNOFF, IN INCHES
5
F i g . 4.17. D a t a p l o t t e d on n a t u r a l and l o g s c a l e s s h o w i n g t h e a c h i e v e m e n t o f e q u a l v a r i a n c e about t h e r e g r e s s i o n l i n e by use of t h e l o g t r a n s f o r m a t i o n . O t h e r r e a s o n s f o r t r a n s f o r m i n g d a t a a r e d i s c u s s e d by A c t o n (1959, p . 219-
223). 4.5.3
Example o f s i m p l e l i n e a r r e g r e s s i o n
Computation o f a r e g r e s s i o n e q u a t i o n by t h e method of l e a s t s q u a r e s u s i n g t h e model Y = a + bX i s d e m o n s t r a t e d u s i n g t h e d a t a g i v e n i n T a b l e 4.6. a l s o shows c o m p u t a t i o n s of means,
Cross p r o d u c t s ,
and squares.
That t a b l e
The i n d i v i d u a l
c r o s s p r o d u c t s and s q u a r e s need n o t be r e c o r d e d ; t h e sum of c r o s s p r o d u c t s , s q u a r e s , c a n b e c u m u l a t e d on a c a l c u l a t o r .
or
The c o e f f i c i e n t s a and b i n t h e
86 regression equation, and the standard error of estimate are computed as shown below.
ZXY
--ZXZY N
ZX'
-
b =
(ZX)' N
-
(1,801)(1.799) 18 189,291 - (1,801)a 18
192,042 b =
a = Y
-
bX = 99.94
-
=
1.325
(1.325)(100.06)
= -32.6
Then the equation of the least-squares line is
Y = a + bX = -32.6 + 1.32X (ZX)* -N
zx2
Variance of X = S:
=
Variance of Y
=
-
Y
Error Variance = S;.x
18
= 534.76
17
(XY)= N
-
N-1
=
(1,801)a
189,291-
N-1
ZY' = S'
-
197,373
-
-
(1,799) 18
= 1,033.71
17
~ [ S Y* - b ~ S=~ %[1,033.71 N-2 l = 100.8
-(1.325)'(534.76)1 Standard error of estimate of Y = S Y.= Correlation coefficient = r =-
b SX sY
=
=
10.0
(1.325) 23'13 -= 0.95. 32.15
The locus of the regression equation and the data used are plotted in Figure 4.18. (i) Test for significance.
4.18
Although i t is apparent from the plot of Figure
that there is a significant relation between the variables, this is not
always the case.
Sometimes i t is desirable to test for significance.
regression coefficient, b, is the slope of the line. regression is meaningless.
The
If that slope is zero the
We start with the hypothesis that the true value of
b is zero and assume that the distribution of sample regression coefficients is approximately normal with a zero mean and a standard deviation,
s;.x
'==N=189.291-(1.801)1/18 and S,, = 0.105
100.8 =
0.011
%,
computed as
87
TABLE 4.6 Data and computations for example of two-variable regression Percent of Mean Year
Runoff (Y)
Precipitation (X)
1928 9 30
125 61 68
110 13 14
1 2 3 4 35
71 118 144 169 138
91 108 13 0 152 13 4
6 8 9 40
102 91 125 81 84
98 90 119 11 100
1 2 3 4 1945
58 I9 124 62 81
84 85 115 10 91
1199
1801
I
Totals Mean
99.94
XY
X2
Y2
--192,042 189,291
191,313
100.06
ANNUAL PRECIPITATION AT BUMPING LAKE. IN PERCENT OF MEAN ( X )
Fig. 4.18.
Plot of data from Table 4-6 showing computed regression line.
The a s s u m e d d i s t r i b u t i o n o f r e g r e s s i o n c o e f f i c i e n t s i s i n F i g u r e 4.19.
I f we
sample from t h i s normal p o p u l a t i o n , we would e x p e c t about 2 / 3 of t h e s a m p l e s t o f a l l w i t h i n p l u s o r m i n u s o n e s t a n d a r d d e v i a t i o n o f t h e mean,
and a b o u t 95
p e r c e n t of t h e s a m p l e s t o f a l l w i t h i n p l u s o r minus two s t a n d a r d d e v i a t i o n s of t h e mean.
S i n c e we have o n l y one sample, we can s a y t h a t (1) i f i t f a l l s w i t h i n
t w o s t a n d a r d d e v i a t i o n s o f z e r o , we h a v e n o r e a s o n t o b e l i e v e t h a t t h e t r u e v a l u e i s n o t z e r o , and (2) i f i t f a l l s f a r t h e r t h a n two s t a n d a r d d e v i a t i o n s from z e r o , i t i s u n l i k e l y t h a t t h e mean i s zero.
-1
-2
0
The second c o n d i t i o n would l e a d t o
2
1
STANDARD DEVIATIONS
F i g . 4.19.
D i s t r i b u t i o n of r e g r e s s i o n c o e f f i c i e n t s .
r e j e c t i o n o f t h e h y p o t h e s i s a t t h e 95 p e r c e n t p r o b a b i l i t y l e v e l ; t h a t i s , we conclude t h a t t h e r e g r e s s i o n c o e f f i c i e n t i s s i g n i f i c a n t l y d i f f e r e n t from z e r o , o r a s commonly s t a t e d , s i g n i f i c a n t . I n t h e a b o v e e x a m p l e b i s 12.6 (1.325/0.105)
s t a n d a r d d e v i a t i o n s f r o m t h e mean
and t h u s i s h i g h l y s i g n i f i c a n t .
F o r a n o r m a l d i s t r i b u t i o n 95
p e r c e n t of t h e s a m p l e s would l i e w i t h i n 1.96 s t a n d a r d d e v i a t i o n s p l u s and minus of t h e mean.
The a p p l i c a b l e d i s t r i b u t i o n f o r s m a l l s a m p l e s i s t h e t d i s t r i b u -
t i o n i n w h i c h t h e p r o b a b i l i t y a s s o c i a t e d w i t h d i s t a n c e f r o m t h e mean t o a n y g i v e n m u l t i p l e of t h e s t a n d a r d d e v i a t i o n changes w i t h t h e sample s i z e a s measu r e d by t h e d e g r e e s of freedom.
For t h e a b o v e e x a m p l e t h e r e a r e 18-2 = 1 6
d e g r e e s of freedom f o r which t = 2.12 s t a n d a r d d e v i a t i o n s r a t h e r t h a n t h e 1.96 f o r t h e normal d i s t r i b u t i o n ; t h u s t h e r e g r e s s i o n c o e f f i c i e n t i s s i g n i f i c a n t a t t h e 95 p e r c e n t l e v e l i f i t i s more t h a n 2.12 s t a n d a r d d e v i a t i o n s from t h e mean of zero. Most r e g r e s s i o n a n a l y s e s a r e made by d i g i t a l computer.
The o u t p u t i n c l u d e s
t e s t s of s i g n i f i c a n c e of t h e r e g r e s s i o n c o e f f i c i e n t s . ( i i )D e g r e e s o f Freedom.
I n t h e above example t h e d e g r e e s of freedom were
two l e s s than t h e number of items.
One i l l u s t r a t i o n of t h e c o n c e p t of d e g r e e s
of freedom can b e e x p l a i n e d from r e g r e s s i o n .
The p u r p o s e o f r e g r e s s i o n i s t o
p r e d i c t , n o t t o i n d i c a t e what happened i n t h e p a s t .
I f a c u r v e i s drawn t h r o u g h
89 a l l p o i n t s u s e d i n i t s d e f i n i t i o n , no c h e c k on t h e p o s i t i o n o f t h e c u r v e i s provided;
that is,
t h e r e a r e no d e g r e e s of freedom.
two v a r i a b l e s r e q u i r e s two p o i n t s
t3
A l i n e a r r e l a t i o n between
d e f i n e i t ; t h e r e f o r e , t h e number of d e g r e e s
of freedom i s t h e number of i t e m s used i n i t s d e f i n i t i o n minus 2.
The number of
l o s t d e g r e e s of freedom i n any r e g r e s s i o n i s e q u a l t o t h e number of c o e f f i c i e n t s i n t h e r e g r e s s i o n equation.
4.5.4
Multiple l i n e a r regression
The r e l a t i o n of a v a r i a b l e t o two o r more o t h e r v a r i a b l e s can be o b t a i n e d by m u l t i p l e r e g r e s s i o n u s i n g a l i n e a r model.
The l e a s t - s q u a r e s method i s employed;
i t p r o v i d e s t h e e q u a t i o n f o r which t h e sum of s q u a r e s of d e v i a t i o n s of t h e d a t a f r o m t h e v a l u e s g i v e n b y t h e e q u a t i o n i s a minimum.
D e t a i l s of computation
methods a r e g i v e n i n s t a t i s t i c s t e x t s ; t h e r e q u i r e d c o m p u t a t i o n s a r e e x t e n s i v e . Consequently most m u l t i p l e r e g r e s s i o n e q u a t i o n s a r e o b t a i n e d by d i g i t a l computer.
The o u t p u t o f a r e g r e s s i o n program i n c l u d e s t h e c o e f f i c i e n t s i n t h e equa-
tion,
t h e s t a n d a r d e r r o r of e s t i m a t e of t h e dependent v a r i a b l e ,
t e s t s of s i g n i -
f i c a n c e o f t h e c o e f f i c i e n t s , and o p t i o n a l l y t h e r e s i d u a l s f r o m t h e e q u a t i o n . R e s i d u a l s a r e t h e d i f f e r e n c e s b e t w e e n t h e d a t a and t h e c o r r e s p o n d i n g v a l u e s given by t h e equation. Some computer programs w i l l s e l e c t ,
from t h e independent v a r i a b l e s e n t e r e d ,
t h o s e which a r e most h i g h l y r e l a t e d t o t h e dependent v a r i a b l e . i n two ways. variables,
T h i s may be done
The step-backward program f i r s t d e f i n e s t h e e q u a t i o n u s i n g a l l t h e then d e f i n e s o t h e r e q u a t i o n s by s u c c e s s i v e l y d e l e t i n g t h e l e a s t
s i g n i f i c a n t v a r i a b l e i n t h e p r e c e d i n g equation.
A t y p i c a l o u t p u t of t h e s t e p -
backward method u s i n g log-transformed d a t a i s : l o g Q = -0.841 + 1.01 l o g A
-
0.12 l o g L + 0.17 l o g E + 0.38 l o g P + 0.80 l o g I
Q = -0.569 + 1.01 l o g A + 0.12 l o g L + 0.23 l o g E + 1.36 l o g I Q = -0.538 + 1.01 l o g A + 0.25 log E + 1.27 l o g I l o g Q = 0.086 + 1.01 l o g A + 0.10 l o g E log
log
Not a l l t h e v a r i a b l e s i n t h e s e e q u a t i o n s a r e n e c e s s a r i l y s t a t i s t i c a l l y s i g n i f i cant.
Those c o n t a i n i n g n o n s i g n i f i c a n t v a r i a b l e s should n o t be used.
The step-forward program p r o v i d e s one e q u a t i o n c o n t a i n i n g o n l y those independent v a r i a b l e s t h a t a r e s t a t i s t i c a l l y s i g n i f i c a n t a t the prescribed p r o b a b i l i t y level.
In e v a l u a t i n g r e g r e s s i o n e q u a t i o n s w i t h d i f f e r e n t n u m b e r s o f i n d e p e n d e n t v a r i a b l e s . a d i s t i n c t i o n s h o u l d b e made b e t w e e n s t a t i s t i c a l s i g n i f i c a n c e and p r a c t i c a l significance.
An independent v a r i a b l e may be s t a t i s t i c a l l y s i g n i f i-
c a n t a t t h e 95 p e r c e n t o r 99 p e r c e n t l e v e l and y e t h a v e a n e g l i g i b l e e f f e c t on t h e computed v a l u e s o f t h e d ep en d en t v a r i a b l e . such an i ndependent v a r i a b l e o r d i n a r i l y would n o t be i n c l u d e d i n t h e f i n a l equation.
90
Selection of a regression equation from several which differ only in the number of independent variables can be made on basis of the sizes of the standard errors.
A slight reduction in standard error because of including an
additional variable does not necessarily indicate that the equation with the smaller standard error will produce more reliable estimates. Further discussion of multiple regression is given in section 4.58. 4.5.5
Graphical regression
The assumptions required of graphical regression are the same as those required for analytical regression.
The results of a graphical regression can be
expressed mathematically if no restrictions are added to the graphical analysis, and the standard error can be estimated. Graphical regression is less restrictive than analytical regresion in that the model need not be completely specified in advance.
In fact, if an analyti-
cal model cannot be selected on a physical basis, it is conventional to prepare a preliminary graphical regression which will indicate an appropriate model. For example, consider the four data plots of Figure 4.20:
the upper left one
indicates use of the model
Y
=
a + bX
The upper right requires
Y
=
a
+ bX + blXz
where the direction of curvature determines the sign of bl.
The lower left
indicates the need for a transformation unless the divergence can be explained by an additional variable.
The lower right shows no relation between Y and X.
and. if only a two-variable relation is being considered, no further analysis would be made. A relation, however, between Y and X in the fourth plot may be obscured by the effect of another variable Z which has not been included.
This
aspect is discussed under Graphical Multiple Regression. The preparation of simple linear relations between two variables is well known but the regression line is not necessarily the same line as one would draw through the plotted points. and another for X
=
There are two regression lines, o n e for Y
f(Y) (Fig. 4.21).
=
f(X),
The structural line, which balances the
plotted points in both directions, has a slope approximately midway between the two regression lines.
The differences in slope among the three lines depend on
the degree of correlation of the variables. lines have the same slope.
For perfect correlation all three
Regardless of the correlation, both regression lines
pass through the mean; the structural line may or may not pass through the mean.
TO approximate the regression Y
=
f(X),
(1) group the points by small incre-
ments of X, ( 2 ) estimate the mean of each group in the Y direction, and (3) draw
91 a line which averages these means.
The procedure can be understood by referring
to Figure 4.21 and remembering that the distribution of points about the regression line in the Y direction is a s s u m e d to b e the s a m e throughout the range.
Y
I
X
X
Y
... .:
.
'
__
I
*
I
.
.. . .. -
1
X
X
Four possible outcomes of plotting Y against X .
Fig. 4.20.
L
1
1
r
1
I
I
I
1
I
1
I
I
1
I
X
Fig. 4.21.
Plot showing the two regression lines and the structural line.
Obviously that assumption cannot be true for a small number of points, but it is the condition which w e try to approximate.
The regression line of Y = f(X) will
92 have a flatter slope than that of a line drawn to balance the points in both Y and X directions. The standard error of estimate of a graphical regression can be estimated readily.
Remembering (1) that the standard error of estimate is the standard
deviation of plotted points about the regression line, (2) that two-thirds Of the points should be within one standard deviation on each side of the mean of a normal distribution, and (3) that a regression line theoretically passes through the mean value of Y corresponding to any value of X. then two lines, parallel to the regression line and one standard deviation above and below (in the Y direction), should encompass two-thirds of the plotted points.
In practice it is
simpler to draw the lines s o as to exclude one-sixth of the points above and below, and then use the average of these two deviations from the mean as the estimated standard error of estimate. 4.22 for a log relation.
The procedure is illustrated in Figure
The standard error can be described in l o g units but
more commonly is expressed in percent.
This value is readily obtained by using
dividers to lay off one standard error above and below a cycle separation if the relation is plotted on log paper. Figure 4.22.
The percentages are measured as shown in
S
The standard errors in percent can be computed by 100 (10 -1) and
-100 (l-lO-s) where S is the standard error in log units.
For regressions on arithmetic plots, the standard error will be in the same units as Y and can be read from the plot. The reliability of the graphically determined standard error is influenced by two factors having opposite effects.
If the graphical-regression line has a
steeper slope than the least-squares regression 1 ine, the graphical standard error will be larger than the computed standard error.
If w e assume that the
graphical line of relation is the same as the least-squares line, the graphically computed standard error will underestimate the computed standard error when a few plotted points are far from the line but the majority are close.
In any
case the graphically determined standard error is only an approximation but is adequate for many problems. 4.5.6
Graphical multiple regression
There are two general methods of graphical multiple regression.
The method
of deviations is based on a model of the type
Y
= a
+ blXl + b2X2 +
. . . bnXn,
or a similar one allowing for curvilinearity.
This method is probably the
simplest and most useful one available.
The coaxial method of graphical multiple regression formerly used for runoffprecipitation relations, is a more flexible method than the method of deviations in that it allows both for interactions and curvilinearity.
However, these
93 advantages a r e o b t a i n e d a t t h e expense of much a d d i t i o n a l r o r k and a t t h e l o s s of a s i m p l e method of e v a l u a t i n g t h e r e l i a b i l i t y of t h e r e s u l t .
F i g . 4.22.
Linsley, Kohler
Method of e s t i m a t i n g t h e s t a n d a r d e r r o r of a g r a p h i c a l r e g r e s s i o n .
and Paulhus (1949,
p.
650-655)
d e s c r i b e d t h e procedure i n d e t a i l .
The d e s c r i p -
t i o n s of g r a p h i c a l m u l t i p l e r e g r e s s i o n i n t h i s s e c t i o n r e f e r t o t h e method of deviations. The purpose of m u l t i p l e r e g r e s s i o n i s t o d e t e r m i n e how a dependent v a r i a b l e changes w i t h changes i n two o r more independent v a r i a b l e s .
T h i s problem cannot
be s o l v e d by c o n s i d e r i n g one independent v a r i a b l e a t a t i m e i f t h e independent v a r i a b l e s a r e c o r r e l a t e d w i t h each other. analyzing t h e f o l l o w i n g s y n t h e t i c d a t a :
No. 1 2 3 4 5 6
7
Y 500 250 3 00 100 200 200 50
X1 100 150 50 30 100 20 50
x2 25 160 30 110 150 20 7 00
T h i s s t a t e m e n t c a n b e v e r i f i e d by
94 Assume t h a t t h e l o g a r i t h m s o f t h e v a r i a b l e s a r e l i n e a r l y r e l a t e d . f o r p l o t t i n g on l o g paper.
This c a l l s
F i r s t make a g r a p h i c comparison between Y and X1
p l o t t i n g t h e a p p r o p r i a t e d a t a (Fig.
4.23).
by
(In s t a t i s t i c a l work t h e dependent A l s o p l o t Y a g a i n s t X2.
v a r i a b l e i s u s u a l l y p l o t t e d on t h e o r d i n a t e s c a l e . )
These p l o t s i n d i c a t e t h a t Y cannot be e s t i m a t e d r e l i a b l y from e i t h e r parameter. Now d e t e r m i n e t h e r e l a t i o n between Y and b o t h of t h e o t h e r v a r i a b l e s .
The
procedure i s a s f o l l o w s : 1.
On F i g u r e 4 . 2 3 , p l o t l . w r i t e b e s i d e e a c h p o i n t t h e c o r r e s p o n d i n g v a l u e o f
It w i l l b e s e e n t h a t t h e h i g h v a l u e s o f X2 t e n d t o b e on o n e s i d e o f X2. t h e g r o u p a n d t h e low v a l u e s on t h e o t h e r . T h i s i s a n i n d i c a t i o n t h a t X2 v a l u e s a r e r e l a t e d t o Y.
Draw a s t r a i g h t l i n e through t h e p o i n t s i n such a
way t h a t i t r e p r e s e n t s roughly some c o n s t a n t v a l u e of X2.
The l i n e p r o b a b l y
w i l l not balance the p l o t t e d points. 2.
P l o t d e v i a t i o n s ( a l s o c a l l e d r e s i d u a l s ) of Y from t h e s t r a i g h t l i n e of p l o t 1 a g a i n s t X2 a s t h e a b s c i s s a on p l o t 3. p l o t 1 or t r a n s f e r r e d by d i v i d e r s .
The d e v i a t i o n s may b e s c a l e d f r o m
Because t h e y a r e r a t i o s ,
t h e y should be
measured above or below 1.00 on p l o t 3. 3.
Draw a s t r a i g h t l i n e a v e r a g i n g t h e p o i n t s on p l o t 3.
4.
Measure t h e d e v i a t i o n s of t h e p o i n t s f r o m t h e c u r v e o f p l o t 3 and r e p l o t them on p l o t 1.
These d e v i a t i o n s a r e measured from t h e s t r a i g h t l i n e i n
p l o t 1 and d e f i n e t h e r e l a t i o n b e t w e e n Y and X1 removed.
w i t h t h e e f f e c t of X 2
Sometimes t h e s e r e p l o t t e d p o i n t s a r e n o t randomly d i s t r i b u t e d
about t h e l i n e ,
i n w h i c h c a s e t h e l i n e s h o u l d b e r e d r a w n and t h e whole
p r o c e s s r e p e a t e d (not n e c e s s a r y i n t h i s example). b a l a n c e i s a t t a i n e d t h e r e g r e s s i o n i s complete.
When a s a t i s f a c t o r y
The s c a t t e r of t h e a d j u s t e d
p o i n t s a b o u t t h e l i n e o f p l o t 1, i s a m e a s u r e of t h e e r r o r .
The s t a n d a r d
e r r o r of a g r a p h i c a l m u l t i p l e r e g r e s s i o n may b e approximated by u s i n g t h e a d j u s t e Q p o i n t s , a s d e s c r i b e d i n s e c t i o n 4.5.5. r e l a t i o n b e t w e e n Y a n d X1 f o r t h e X2 c r o s s e s t h e 1.0 v a l u e of X 2
l i n e (X2 = 6 6 ) .
The l i n e on p l o t 1 i s t h e
v a l u e a t whi ch t h e l i n e of p l o t 3
The r e l a t i o n o f Y t o X1
f o r any o t h e r
w i l l b e a l i n e p a r a l l e l t o t h e l i n e o f p l o t 1, a t a p o s i t i o n
d e f i n e d by t h e c u r v e of p l o t 3 f o r t h e d e s i r e d v a l u e of X2. The example used gave much b e t t e r r e s u l t s t h a n o r d i n a r i l y would b e expected i n hydrologic analyses.
The d a t a were manufactured (1) t o i l l u s t r a t e t h e proce-
d u r e and ( 2 ) t o p o i n t o u t t h a t a good r e l a t i o n may n o t b e r e c o g n i z e d i f o n l y two v a r i a b l e s a t a time a r e studied. G r a p h i c a l r e g r e s s i o n s i n v o l v i n g more t h a n two independent v a r i a b l e s c a n be made.
The r e s i d u a l s from each l i n e a r e p l o t t e d a g a i n s t t h e n e x t v a r i a b l e u n t i l
a l l v a r i a b l e s a r e used.
Then t h e r e s i d u a l s f r o m t h e l a s t l i n e a r e r e p l o t t e d
95
20
500
100
20
500
500
200
200 Y
100
1M)
50
50
Y
7M)
100
+
c :20
EXPLANATION
v
0
6
W
Item number
$10
a Plotted point
V
5
(150) Corresponding value of X ,
?05
A Plotted point adlusted for X,
0
from dot 3
203 W 0
1on
20
1000
X,
F i g . 4.23.
Example of g r a p h i c a l m u l t i p l e r e g r e s s i o n .
from t h e f i r s t a s d e s c r i b e d i n s t e p 4.
I n p r a c t i c a l work i t i s u s u a l l y d i f f i -
c u l t t o d e f i n e t h e e f f e c t s of more t h a n t h r e e independent v a r i a b l e s , p a r t i c u l a r l y when t h e i n f l u e n c e s o f one or two of t h e v a r i a b l e s a r e s m a l l . L i n e a r r e g r e s s i o n should be used whenever t h e p l o t t e d p o i n t s do n o t d e f i n i t e l y d e f i n e a c u r v e and when no p h y s i c a l r e a s o a i s known f o r e x p e c t i n g t h e r e l a t i o n t o be curved. criteria,
I f a c u r v e or c u r v e s a r e i n d i c a t e d by b o t h o f t h e a b o v e
t h e n c u r v e s should be used.
points f o r definition.
Complicated c u r v e s r e q u i r e f o u r or more
They should b e avoided when o n l y r e l a t i v e l y few p o i n t s
are available t o define the relation. G r a p h i c a l m u l t i p l e r e g r e s s i o n s need n o t be made on l o g a r i t h m i c paper. m e t i c and s e m i l o g p l o t s can be handled a s r e a d i l y .
Arith-
F i g u r e 4.24 r e l a t e s summer
r u n o f f t o s p r i n g w a t e r c o n t e n t of t h e snowpack and t o summer p r e c i p i t a t i o n . g r a p h i c a l procedure i s t h e same a s i n t h e f i r s t example,
The
except t h a t d e v i a t i o n s
a r e measured i n t h e same u n i t s a s t h e dependent v a r i a b l e and t h e d e v i a t i o n s c a l e m u s t h a v e i t s c e n t e r a t z e r o w i t h p o s i t i v e v a l u e s a b o v e and n e g a t i v e v a l u e s below.
Obviously t h e m a t h e m a t i c a l model d e s c r i b i n g t h i s r e l a t i o n i s d i f f e r e n t
from one f o r a g r a p h i c a l r e l a t i o n developed on l o g paper.
96
40t/ I
20 1 6 0 ’
t
/
10 77
1
“O“* E o -z
?jo7
9 41 Prectpitation
0 X
Plotted potnt Point adlustedfor eflect 01 precipitation lrom curve at right
,
0‘ I 1 1 10 20 30 WATER CONTENT OF SNOW ON APRIL 1
0
4 a 12 PRECIPITATION AT THREE CREEK
ON GOAT CREEK SNOW COURSE, IN INCHES
Fig. 4 . 2 4 .
APRIL-JULY, IN INCHES
Example of graphical multiple regression using arithmetic scales.
The plotting paper selected for a particular problem should be that on which the distribution of the dependent variable f o r a fixed value of the independent variable is approximately the same for all values of the independent variable as in Figure 4.14.
This criterion is more important than that of attaining linear-
ity. 4.5.1
Graphical
VS.
analytical method
A graphical method is particularly useful for exploratory work and f o r making preliminary estimates.
The graphical method has the following advantages:
1.
It is rapid.
2.
It helps define the appropriate model.
3.
It points out the need for transformations, if any.
4.
I t brings attention to extremely wild points if they exist in the data.
(See the wild point in Fig. 4.24 which was given no weight in the analysis). Disadvantages of a graphical method are:
1.
Small effects of independent variables cannot be identified.
2.
The number of independent variables is limited to about three because of the
3.
Tests of significance of the effects of individual variables are not avail-
cumulative effect of inaccuracies in plotting and in locating the lines. able. 4.
The resulting relation involving three or more variables is confusing to the user unless expressed mathematically or replotted in another form.
97
An a n a l y t i c a l method h a s t h e f o l l o w i n g advantages:
1. For t h e model used,
i t gives the best estimate
of t h e e q u a t i o n c o n s t a n t s ,
and of t h e s t a n d a r d e r r o r . 2.
I t a l l o w s t e s t i n g of t h e c o e f f i c i e n t s f o r s i g n i f i c a n c e .
3.
R e s u l t s c a n be p r e s e n t e d i n a c l e a r ,
c o n c i s e manner which most h y d r o l o g i s t s
c a n understand. 4.
R e s u l t s a r e unique f o r t h e model and sample used: d i f f e r e n t i n v e s t i g a t o r s would g e t t h e same r e s u l t s .
Disadvantages o f an a n a l y t i c a l method a r e : Computation i s time-consuming u n l e s s t h e a n a l y s t has a c c e s s t o a d i g i t a l
1.
computer and knows how t o e n t e r h i s d a t a . 2.
The e x i s t e n c e o f w i l d p o i n t s o r o f nonhomogeneous d a t a i s n o t r e a d i l y
3.
The s e l e c t e d model may n o t be a p p r o p r i a t e .
4.
No p r o c e d u r e i s a v a i l a b l e f o r g i v i n g a p o i n t l e s s t h a n f u l l weight.
noticed.
I n g e n e r a l a g r a p h i c a l method i s u s e f u l f o r examining t h e d a t a and d e f i n i n g a s u i t a b l e model: f i n a l c o n c l u s i o n s a r e u s u a l l y based on a computed r e l a t i o n . 4.5.8
A p p l i c a t i o n of t h e r e g r e s s i o n method
An a n a l y t i c a l p r o b l e m t o b e s o l v e d by r e g r e s s i o n i n v o l v e s ( 1 ) s e l e c t i o n o f f a c t o r s which a r e expected t o i n f l u e n c e t h e dependent v a r i a b l e , these f a c t o r s quantitatively, t h e r e g r e s s i o n equation,
(3) s e l e c t i n g t h e r e g r e s s i o n model,
( 2 ) describing
(4) computing
t h e s t a n d a r d e r r o r of e s t i m a t e , and t h e s i g n i f i c a n c e of
the regression coefficients,
and ( 5 ) e v a l u a t i n g t h e r e s u l t s .
S e l e c t i o n of t h e a p p r o p r i a t e f a c t o r s should not b e a s t a t i s t i c a l problem, b u t s t a t i s t i c a l c o n c e p t s must e n t e r i n t o t h e p r o c e s s .
I f t h e a n a l y s t m e r e l y wants
t o know t h e r e l a t i o n o f a n n u a l p r e c i p i t a t i o n t o a n n u a l r u n o f f , h e c a n p r o c e e d d i r e c t l y t o s e l e c t i o n o f a model.
But i f h i s p r o b l e m i s t o make t h e b e s t
p o s s i b l e e s t i m a t e of r u n o f f , h e w i l l i n c l u d e o t h e r f a c t o r s , some of which may be r e l a t e d t o each other a s well a s t o runoff.
The p r o b l e m o f d e t e r m i n i n g i f
c e r t a i n f a c t o r s a r e r e l a t e d t o t h e dependent v a r i a b l e r e q u i r e s c a r e f u l s e l e c t i o n of i n d i c e s d e s c r i b i n g t h e s e f a c t o r s q u a n t i t a t i v e l y .
These i n d i c e s should accu-
r a t e l y r e f l e c t t h e e f f e c t s , and no two should d e s c r i b e t h e same thing.
It i s a
c h a r a c t e r i s t i c o f r e g r e s s i o n t h a t i f a f a c t o r i s r e l a t e d t o a dependent v a r i a b l e and t h i s f a c t o r i s e n t e r e d i n t h e r e g r e s s i o n model t w i c e ( a s two d i f f e r e n t v a r i a b l e s ) , t h e e f f e c t on t h e dependent v a r i a b l e w i l l be d i v i d e d e q u a l l y between t h e two.
Thus, i f t h e t o t a l e f f e c t i s s m a l l , t h e r e s u l t o f d i v i d i n g i t i n two
p a r t s may be t o produce n o n s i g n i f i c a n c e i n each of t h e p a r t s . c l o s e l y r e l a t e d v a r i a b l e s may compute a s n o n s i g n i f i c a n t , s e l e c t e d index would show a r e a l e f f e c t .
Likewise, s e v e r a l
whereas one p r o p e r l y
Thus, t h e independent v a r i a b l e s should
be s e l e c t e d w i t h c o n s i d e r a b l e c a r e ; t h e shotgun approach should n o t be used.
98 Another consideration in selection of variables is to avoid having a variable, or a part thereof, on both sides of the equation.
Such a condition may be
A
acceptable for certain problems, but the results must be evaluated carefully.
spurious relation may result, or the relation may be correct but its reliability difficult to assess.
Benson (1965) described ways in which spurious relations
may be built into a regression. T h e user of the regression m e t h o d should understand the effect of related independent variables on the computed regression coefficients. dent variables are entirely unrelated,
If the indepen-
the simple regression coefficients and
the corresponding partial regression coefficients would be the same. such conditions rarely occur in nature.
However,
The multiple regression method provides
a w a y of separating the total effect of the independent variables into the effect of each independent variable and a n unexplained effect.
Consider the
simple regression
Y = a
+
blXl
+
(1)
error,
where Y also is affected by another variable, X2
,
which is related to X1
.
The
regression using X1 and X2 will be
y = a'
+
biXl + b2X2 + error.
where bi # bl. are linear),
(2)
If X1' and X2 are the only variables affecting Y (and the effects then equation 2 completely describes Y, and bi
and b2 are the true
values of the regression coefficients (except for sampling errors).
If X1
and
X2 are positively correlated with each other and with Y, consider the effect on the m a g n i t u d e of bl.
For e a c h value of X l in equation 1. Y w i l l appear to be
more closely related than it actually is because X2 influence on Y is real though unmeasured.
increases with X1
and its
Therefore the regression coefficient
b l is larger than its true value bi. S i m i l a r changes i n b l and b 2
would occur if another factor. related to X 1
and X2 and Y, were included in the regression.
These changes in the magnitudes
of the regression coefficients due to addition or deletion of a variable are characteristic of regression.
They are sometimes interpreted as indicating that
partial regression coefficients have no physical meaning. are not necessarily correct.
Such interpretations
If the variables used in the regression are se-
lected o n physical principles and the effects o f each of t h e variables is appreciable,
then the partial regression coefficients should be in accord with
physical principles.
In fact, it is good practice to compare the sign and the
general m a g n i t u d e of each partial regression coefficient w i t h that expected. Benson (1962a. p. 52-55) made a thorough comparison of this kind.
99
The r e g r e s s i o n c o e f f i c i e n t s of c e r t a i n v a r i a b l e s may change s i g n when a n o t h e r r e l a t e d v a r i a b l e i s a d d e d t o or d e l e t e d f r o m t h e r e g r e s s i o n .
T h i s e f f e c t may
r e s u l t b e c a u s e (1) t h e s u b j e c t v a r i a b l e i s n o t a good i n d e x o f t h e p h y s i c a l feature represented,
(2) t h e e f f e c t of t h e v a r i a b l e i s s m a l l r e l a t i v e t o t h e
sampling e r r o r , ( 3 ) t h e v a r i a b l e i s so h i g h l y c o r r e l a t e d w i t h one o r more o t h e r v a r i a b l e s i n t h e r e g r e s s i o n t h a t i t s r e a l e f f e c t i s o b s c u r e d , or ( 4 ) t h e r a n g e of t h e v a r i a b l e sampled may b e t o o s m a l l t o d e f i n e a s i g n i f i c a n t e f f e c t .
A r e g r e s s i o n e q u a t i o n does n o t imply a cause-and-effect i n d e p e n d e n t v a r i a b l e s and t h e d e p e n d e n t v a r i a b l e . some o t h e r f a c t o r n o t r e a d i l y measured.
Eowever,
r e l a t i o n between t h e
B o t h may b e i n f l u e n c e d by
t h e r e should be some p h y s i c a l
t i e between t h e v a r i a b l e s i f t h e r e s u l t s can be c o n s i d e r e d meaningful. S e l e c t i o n of a r e g r e s s i o n model u s u a l l y b e g i n s w i t h a g r a p h i c a l a n a l y s i s .
A
model w h i c h p l o t s a s a s t r a i g h t l i n e i s commonly u s e d u n l e s s t h e r e i s s t r o n g evidence t o t h e c o n t r a r y . I f t h e sample d a t a e x i s t n e a r a n asymptote or n e a r a maximum o r minimum p o i n t
on t h e c u r v e , a s i m p l e model may b e i n a d e q u a t e t o d e s c r i b e t h e r e l a t i o n and a more s o p h i s t i c a t e d one may n o t be j u s t i f i e d u n l e s s many d a t a a r e a v a i l a b l e .
An
example showing t h e c h a r a c t e r i s t i c s of t h r e e common models when a p p l i e d t o d a t a d e f i n e d n e a r z e r o i s g i v e n i n F i g u r e 4.25.
Physical c o n s i d e r a t i o n s suggest t h a t
n e i t h e r b n o r Q7 s h o u l d b e l e s s t h a n z e r o a n d t h a t t h e l i n e s h o u l d b e c u r v e d . The z e r o l i m i t a t i o n can be o b t a i n e d by u s i n g t h e v a r i a b l e s l o g b and l o g Q7 and t h u s making t h e curve a s y m p t o t i c t o z e r o on b o t h axes. (log
Q7P w i l l
provide t h e necessary curvature.
The a d d i t i o n of a term
The r e g r e s s i o n e q u a t i o n u s i n g
t h e s e t h r e e v a r i a b l e s i s t h e t o p o n e on F i g u r e 4.25.
I t i s n o t a good f i t t o
the data. Next,
assume t h a t i t i s n o t n e c e s s a r y t h a t t h e c u r v e by a s y m p t o t i c t o Q7 = 0 .
Then a s e m i l o g model u s i n g t h e v a r i a b l e s log b. Q7, and Q; would be a p p r o p r i a t e . B u t t h e e q u a t i o n b a s e d on t h i s model r e a c h e s a maximum t o o soon and i s a v e r y poor f i t .
Q;.
As a l a s t r e s o r t assume a s i m p l e model w i t h t h e v a r i a b l e s b, Q7, and
This e q u a t i o n i s a good f i t t o t h e d a t a . The mechanics of computing t h e r e g r e s s i o n equation,
t h e t e s t s o f s i g n i f i c a n c e have been d e s c r i b e d .
the standard error,
One i m p o r t a n t t a s k remains, t h a t
of e v a l u a t i n g t h e r e s u l t s .
First,
s i o n equation developed,
e v e n t h o u g h i t i s a good f i t t o t h e d a t a ,
ne cessarily c o r r e c t i f extrapolated.
and
t h e a n a l y s t should r e c o g n i z e t h a t t h e r e g r e s -
is not
For e x a m p l e , t h e c u r v e c o r r e s p o n d i n g t o
t h e b o t t o m e q u a t i o n o f F i g u r e 4.25 i s a good f i t t o t h e s e v e n p o i n t s b u t i n c r e a s e s d i r e c t l y w i t h Q7
f o r v a l u e s o f Q7
g r e a t e r t h a n 7.
On t h e o t h e r hand,
t h e dashed c u r v e f i t s t h e l o w e r f i v e p o i n t s b u t becomes a s y m p t o t i c t o z e r o a s Q7 increases.
A v a i l a b l e i n f o r m a t i o n does n o t i n d i c a t e which e x t r a p o l a t i o n i s more
n e a r l y correct.
100 The s i g n s of a l l s i g n i f i c a n t r e g r e s s i o n c o e f f i c i e n t s should b e i n accord w i t h The r e g r e s s i o n i s n o t n e c e s s a r i l y i n c o r r e c t i f t h e y a r e
physical principles.
log b =0.30+0.12 Q,-0.06Q;
b=3.44- 1.05Q ,+O .083 0 :
L
I
I
I
I
1
I
I
I
I
I
0
1
2
3
4
5
0
7
8
9
10
0
Fig. 4.25.
Equations and graphs of 3 models based on t h e p l o t t e d d a t a .
n o t ; t h e nonconformity may be due t o i n t e r r e l a t i o n s among t h e independent v a r i a bles.
Such a r e g r e s s i o n may b e u s e f u l f o r e s t i m a t i n g v a l u e s o f t h e d e p e n d e n t
v a r i a b l e s from known v a l u e s o f t h e independent v a r i a b l e s , and t h e r e l i a b i l i t y of the r e s u l t s ,
i f w i t h i n t h e d e f i n e d range of t h e r e g r e s s i o n , can be computed.
The more d i f f i c u l t problem of d e t e r m i n i n g whether a p a r t i c u l a r v a r i a b l e i s r e l a t e d t o t h e dependent v a r i a b l e may n o t have a d e f i n i t e answer.
Even though a
regression coefficient is s t a t i s t i c a l l y significant, there i s a small probabilit y t h a t t h i s r e s u l t o c c u r r e d by chance.
Other samples c o u l d produce c o n f l i c t i n g
results. 4.6
CHARACTERISTICS OF BYDBOLOGIC DATA Streamflow i s a continuous p r o c e s s which v a r i e s w i t h time,
flow d a t a a r e s a i d t o form a time s e r i e s .
and t h u s stream-
A p l o t of s t r e a m f l o w a g a i n s t t i m e
would show a p a t t e r n o f v a r i a t i o n r e c u r r i n g each y e a r : t h a t i s , h i g h f l o w s t e n d t o occur a t p a r t i c u l a r t i m e s of t h e y e a r and low f l o w s a t o t h e r s i n r e s p o n s e t o c l i m a t o l o g i c a l c h a r a c t e r i s t i c s which a l s o v a r y s e a s o n a l l y . Because s t r e a m f l o w s a r e n o t d i s c r e t e v a l u e s ,
we need t o chop t h e hydrograph
i n t o p i e c e s which we w i l l c o n s i d e r a s i n d i v i d u a l streamflows.
The p a r t i c u l a r
p i e c e s we u s e have c e r t a i n c h a r a c t e r i s t i c s which must be c o n s i d e r e d i n a n a l y s i s . The m o s t common p i e c e i s t h e d a i l y mean d i s c h a r g e .
A d a i l y mean d i s c h a r g e i s
101 r e l a t e d t o t h e d i s c h a r g e o f t h e p r e v i o u s day and l i e s w i t h i n a r a n g e w h i c h d e p e n d s on t h e t i m e o f y e a r .
I n s t a t i s t i c a l t e r m s , d a i l y mean d i s c h a r g e i s a
s e r i a l l y c o r r e l a t e d v a r i a b l e , t h a t i s , i t i s nonrandom.
The d a i l y mean d i s -
charges f o r a y e a r a r e a l s o n o t homogeneous; t h e y a r e more l i k e l y t o be l a r g e r a t one t i m e of t h e y e a r t h a n a t another.
Data a r e c o n s i d e r e d homogeneous i f any
subgroup t o which c e r t a i n of t h e s e d a t a may be l o g i c a l l y a s s i g n e d h a s t h e same expected mean and v a r i a n c e as any o t h e r subgroup of t h e population. M o n t h l y mean d i s c h a r g e s f o r d i f f e r e n t c a l e n d a r m o n t h s a r e a l s o s e r i a l l y c o r r e l a t e d and nonhomogeneous. ues.
Annual mean d i s c h a r g e s may b e homogeneous v a l -
They may or may n o t b e s e r i a l l y c o r r e l a t e d , d e p e n d i n g on t h e a m o u n t o f
b a s i n s t o r a g e a t t h e t i m e t h a t t h e h y d r o l o g i c y e a r begins. I n s t e a d o f a s t r e a m f l o w v a r i a b l e made up o f a d j a c e n t s e g m e n t s o f a h y d r o g r a p h , we may c o n s i d e r v a r i a b l e s s u c h a s J u l y mean, a n n u a l p e a k d i s c h a r g e , o r
annual minimum flow.
These v a r i a b l e s a r e made up of one i n d i v i d u a l from each
y e a r and thus a r e independent of t h e y e a r l y c y c l e of streamflow.
They a r e a l s o
independent of each o t h e r ( w i t h t h e p o s s i b l e e x c e p t i o n of annual minimum f l o w s which may i n c l u d e e f f l u e n t from ground-water
r e c h a r g e of a p r e v i o u s year).
P r e c i p i t a t i o n , t e m p e r a t u r e , sediment d i s c h a r g e , evaporation,
water quality, transpiration,
and s o l a r r a d i a t i o n v a r y t h r o u g h o u t t h e y e a r ; i n d i c e s d e s c r i b i n g
them may be nonrandom and nonhomogeneous. O b v i o u s l y t h e d i s t i n c t i o n b e t w e e n random and nonrandom d a t a and between homogeneous and nonhomogeneous d a t a i s n o t always c l e a r .
The a n a l y s t w i l l have
t o d e t e r m i n e whether t h e e f f e c t s of p o s s i b l e moderate nonrandomness o r nonhomog e n e i t y w i l l i n v a l i d a t e t h e c o n c l u s i o n s of h i s p a r t i c u l a r a n a l y s i s .
It i s
i m p o r t a n t t h a t t h e c h a r a c t e r of t h e d a t a be c o n s i d e r e d i n d e s i g n i n g t h e a n a l y s i s and i n i n t e r p r e t i n g t h e r e s u l t s . Another t y p e of v a r i a b l e used e x t e n s i v e l y i n hydrology cannot b e c o n s i d e r e d t o have a p r o b a b i l i t y d i s t r i b u t i o n , o r even t o be drawn from a p o p u l a t i o n as t h o u g h t of i n t h e u s u a l s e n s e .
Basin c h a r a c t e r i s t i c s such as drainage area,
s l o p e , e l e v a t i o n , and v e g e t a l i n d ex a r e i n t h i s c a t e g o r y .
(It i s p o s s i b l e t o
c o n c e i v e of c e r t a i n p h y s i o g r a p h i c p a r a m e t e r s a s random v a r i a b l e s , b u t r a r e l y can t h e a v a i l a b l e sample be c o n s i d e r e d randomly s e l e c t e d or r e p r e s e n t a t i v e . ) Time i s sometimes used a s a v a r i a b l e i n r e g r e s s i o n .
I t h a s no d i s t r i b u t i o n
and i s u s e d o n l y a s a s u b s t i t u t e f o r t h e r e a l f a c t o r or f a c t o r s ( w h i c h a r e unknown or cannot be e x p r e s s e d by i n d i c e s ) a s s o c i a t e d w i t h changes i n a dependent v a r i a b l e .
4.6.1
E f f e c t s o f d a t a c h a r a c t e r i s t i c s on a n a l y s i s
We p r e p a r e a f r e q u e n c y d i s t r i b u t i o n o f d a i l y mean d i s c h a r g e s f r o m s e v e r a l y e a r s o f d a t a ; t h i s i s t h e d u r a t i o n curve.
The i n d i v i d u a l v a l u e s a r e nonrandom
102 and nonhomogeneous. quency curve.
T h e r e f o r e t h e d u r a t i o n c u r v e cannot b e c o n s i d e r e d a f r e -
The p r o b a b i l i t y o f e x c e e d i n g a c e r t a i n v a l u e on a p a r t i c u l a r
f u t u r e d a y d e p e n d s b o t h on t h e p r e c e d i n g v a l u e and on t h e t i m e o f y e a r .
Thus,
t h e d u r a t i o n c u r v e i s m e r e l y t h e d i s t r i b u t i o n of d a i l y means t h a t h a s occurred.
It can be c o n s i d e r e d a n e s t i m a t e of t h e d i s t r i b u t i o n d u r i n g a f u t u r e p e r i o d s e v e r a l y e a r s long. On t h e o t h e r hand,
frequency c u r v e s of annual f l o o d peaks c a n be i n t e r p r e t e d
a s p r o b a b i l i t y c u r v e s because t h e i n d i v i d u a l s a r e u n r e l a t e d and u s u a l l y homogeneous (but s e e s e c t i o n 8.5).
Most l o w - f l o w
frequency curves can be s i m i l a r l y
i n t e r p r e t e d , b u t o c c a s i o n a l l y a s e r i a l l y c o r r e l a t e d s a m p l e w i l l b e f o u n d and c e r t a i n i n d i v i d u a l s may be nonhomogeneous ( s e c t i o n 9.2). The e f f e c t of u s i n g nonhomogeneous d a t a i n a r e g r e s s i o n problem i s shown by F i g u r e 4.26
i n w h i c h i s p l o t t e d 4 y e a r s o f m o n t h l y mean d i s c h a r g e f o r e a c h of
0
x A
0 0
= A 1
-
+ A
Oct Nov Dec Jan Feb March Apr May June July Aug Sept
-
/’ /’
100
F i g . 4.26
<
t 1000 4 30 MONTHLY MEAN DISCHARGE OF SOUTH FORK BOISE RIVER NEAR FEATHERVILLE. IDAHO, IN CUBIC FEET PER SECOND
Spurious r e l a t i o n s from u s e of nonhomogeneous d a t a .
t h e 1 2 c a l e n d a r m o n t h s f o r t w o s t a t i o n s . one i n T u r k e y and o n e i n I d a h o , USA. The r e l a t i o n l o o k s f a i r l y good, b u t t h e r e i s a c t u a l l y no r e l a t i o n b e t w e e n t h e two s t r e a m s f o r a p a r t i c u l a r c a l e n d a r month.
The a p p a r e n t r e l a t i o n u s i n g a l l
c a l e n d a r months a r i s e s because t h e y e a r l y c y c l e of s t r e a m f l o w i n Idaho r e s e m b l e s
103 t h a t i n Turkey.
D i s c h a r g e s i n w i n t e r m o n t h s a r e low and i n s p r i n g s n o w m e l t
months a r e high. L e s s e x t r e m e c o n d i t i o n s a r e shown b y r e l a t i o n s b e t w e e n m o n t h l y mean d i s c h a r g e s from c o n t i g u o u s b a s i n s .
For example,
t h e r e i s no r e l a t i o n between
monthly mean d i s c h a r g e s o f Lake Fork above Moon Lake. a t Provo R i v e r T r a i l , 4.27).
Utah,
and Duchesne River
f o r J a n u a r y ; t h e r e i s a f a i r r e l a t i o n f o r J u n e (Fig.
Utah,
The d a t a f o r a l l c a l e n d a r months a r e o b v i o u s l y nonhomogeneous.
0 MONTHLY MEAN DISCHARGE OF DUCHESNE RIVER, IN CFS
Fig. 4.27. 4.6.2
Discharge r e l a t i o n s f o r i n d i v i d u a l months,
two Utah s t a t i o n s .
Outliers Many f a c t o r s i n f l u e n c e t h e f l o w of a s t r e a m ; some e x e r t g r e a t i n f l u e n c e a t
o n e t i m e and, none a t a n o t h e r ; m o s t e x e r t e f f e c t s w h i c h a r e i n t e r r e l a t e d w i t h e f f e c t s of o t h e r f a c t o r s .
O n l y a few f a c t o r s c a n b e i n c l u d e d i n a r e g r e s s i o n
used t o e s t i m a t e s t r e a m f l o w , mated.
and t h e e f f e c t s of t h e s e f a c t o r s a r e o n l y approxi-
Consequently t h e r e i s a s c a t t e r of p o i n t s about t h e r e g r e s s i o n l i n e and
o c c a s i o n a l l y a w i l d p o i n t occurs. statistics,
Such'wild p o i n t s a r e c a l l e d o u t l i e r s i n
and s t a t i s t i c a l t e s t s a r e a v a i l a b l e f o r u s e i n d e t e r m i n i n g whether
or n o t a p a r t i c u l a r p o i n t should b e r e j e c t e d a s n o t b e l o n g i n g t o t h e group.
It
seems q u e s t i o n a b l e whether o u t l i e r s i n h y d r o l o g i c a n a l y s e s should b e r e j e c t e d on t h e b a s i s of a s t a t i s t i c a l t e s t .
C o n s i d e r t h e w i l d p o i n t i n F i g u r e 4.24.
t h e p r e c i p i t a t i o n had been about 7 i n c h e s i n s t e a d o f 3.4 inches, n o t be wild.
If
t h e p o i n t would
It i s possible t h a t p r e c i p i t a t i o n a t t h e higher elevations i n t h e
J a r b i d g e River b a s i n was much g r e a t e r t h a n a t Three Creek.
I f i t were,
t h e same
t h i n g c o u l d happen a g a i n and more w e i g h t should have been g i v e n t o t h a t p o i n t i n
104 the analysis.
However, if some of the data for that year are found to be
unreliable we could reject the point. Acton (1959) devoted a short chapter to the rejection of unwanted data.
He
says, in part, "But the plain truth is that physical scientists and engineers need not be encouraged to ignore obstinate outlying data
-
rather they need to
be held in check". The term "outlier" a s commonly used in hydrologic frequency analysis does not imply that the observation is in error or that i t is from another population, only that it deviates widely from the others in the sample. REFERENCES Acton, F.S., 1959. Analysis of straight-line data:
New York, John Wiley and
Sons.
Bennett, C.A. and Franklin, N.L., 1954, Statistical methods in chemistry and the chemical industry: New York, John Wiley and Sons. Benson, M.A., 1960, Characteristics of frequency curves based on a theoretical 1000-year record in Dalrymple, T., Flood-frequency analyses: U.S. Geol. Survey Water-Supply Paper 1543-A. Benson, M.A.. 1962a, Factors affecting the occurrence of floods in a humid region of diverse terrain: U.S. Geol. Survey Water-Supply Paper 1580-B, 64 p. Benson, , M.A., 1962b, Plotting positions and economics of engineering planning: Am. SOC. Civil Engineers Proc.. Vol. 8 8 , No. HY6, p. 56-71. Benson, M.A., 1965, Spurious correlation in hydraulics and hydrology: Am. SOC. Civil Engineers Proc., V. 91, No. HY4, p. 35-42. Beran, M.A., 1981, Recent advances in statistical flood estimation techniques in Flood Studies Report - Five Years On: Institution of Civil Engineers, London. Chow, V.T., 1964, Frequency analysis, i n Chow, V;T., Handbook of applied hydrology: New York, McGraw-Hill, p. 8-17. Dalrymple, T., 1960, Flood-frequency analysis: Paper 1543-A, 8 0 p.
U.S.
Geol. Survey Watersupply
Dandy. D.R. and Matalas, N.C., 1964. Analysis of variance, covariance, and time series in Chow, V.T., Handbook of applied hydrology: New York, John Wiley and Sons. Dixon, W.J. and Massey, F.J., 1957, Introduction to statistical analysis: York, McGraw-Hill Book Co. Ezekiel, 1.. 1950, Methods of correlation analysis, second edition: John Wiley and Sons, Inc.
New
New York,
Ezekiel, M. and Fox, K.A., 1959, Methods of correlation and regression analysis: New York, John Wiley and Sons, Inc. Gumbel, E.J., 1958, Statistics of extremes: Press, 375 p.
New York, Columbia University
Kendall, M.G., 1952, The advanced theory of statistics: London, Charles Griffin and Co., Vol. 1, 457 p. Langbein, W.B.. 1960, Plotting positions in frequency analysis, in Dalrymple. T.. Flood-frequency analysis: U.S. Geol. Survey Water-Supply Paper 1543-A, p. 48-51.
105 Lettenmaier, D.P. and Burges, S.J., 1982, Gumbel's extreme value I distribution: A new look: Journal of Hydraulics Division, ASCE. Vol. 108, NO. HY4, April 1982, p. 502-514. Linsley. R.K., Kohler, M.A., and Paulhus, J.L.H.. York, McGraw-Hill Book Co.. Inc. 689 p.
1949, Applied hydrology: New
McDonald, J.E., 1957, A critical evaluation of correlation methods in climatology and hydrology: Arizona Univ. Inst. of Atmospheric Physics Science Report 4, 3 5 p. Riggs, H.C., 1961, Frequency of natural events: Vol. 87, NO. HY1, p. 15-26.
Am. SOC. Civil Engineers Proc.,
Snedecor. G.W., 1948, Statistical methods, 4th edition: Press, 485 p.
Iowa State College
Water Resources Council, 1982, Bull. 17B, Guidelines for determining flood-flow frequency: U.S. Water Resources Council, Washington, D.C.
This Page Intentionally Left Blank
107
Chapter 5
STREAMFLOW CEARACTERISTICS AT A GAGED SITE 5.1
INTRODUCTION The c o n t i n u o u s l y v a r y i n g f l o w of a s t r e a m i s c h a r a c t e r i z e d by t h e mean and
v a r i a b i l i t y of d a i l y , monthly, and a n n u a l flows: by f r e q u e n c y c h a r a c t e r i s t i c s of f l o o d peaks, low f l o w s , and o t h e r e l e m e n t s : and by base-flow r e c e s s i o n curves. 5.2
MEANS
Streamflow r e c o r d s a r e p u b l i s h e d a s d a i l y mean f l o w s from which t h e monthly means a n d t h e a n n u a l mean a r e c o m p u t e d .
The s t r e a m f l o w r e c o r d i n F i g u r e 3.16
(Chapter 3 ) shows d a i l y means, monthly means, and t h e annual mean f o r w a t e r y e a r 1979, and t h e average d i s c h a r g e f o r t h e p e r i o d of r e c o r d .
Average d i s c h a r g e i s
t h e mean d i s c h a r g e computed from a l l c o m p l e t e y e a r s of r e c o r d .
The a v e r a g e of
m o n t h l y mean d i s c h a r g e s f o r a p a r t i c u l a r c a l e n d a r m o n t h i s t h e mean m o n t h l y ( r e a d a s mean o f t h e m o n t h l y ) d i s c h a r g e .
The meau m o n t h l y d i s c h a r g e s f o r a l l
t w e l v e months show t h e flow d i s t r i b u t i o n w i t h i n t h e year.
See F i g u r e 5.1 f o r an
example.
K
4
>; W 2 U
O
N
D
J
F
M
A
M
J
J
A
S
MONTH
F i g . 5.1. 5.3
Mean monthly d i s c h a r g e s , E.F.
J a r b i d g e R i v e r , Idaho.
FREQUENCY CHARACTERISTICS V a r i a b i l i t y of f l o w can b e d e s c r i b e d by t h e c o e f f i c i e n t of v a r i a t i o n or t h e
i n d e x o f v a r i a t i o n , b o t h of w h i c h c a n b e c o m p u t e d r e a d i l y ; s e e S e c t i o n 4.2.8. More commonly f l o w v a r i a b i l i t y i s d e s c r i b e d b y a f r e q u e n c y c u r v e f r o m w h i c h
108 s e l e c t e d p o i n t s a r e used a s d e s c r i p t o r s . data a r e asymmetrically distributed,
Furthermore,
because most h y d r o l o g i c
t h e median f l o w ( a t 0.5 p r o b a b i l i t y o r 2-
y e a r r e c u r r e n c e i n t e r v a l ) i s o f t e n used a s t h e index o f c e n t r a l tendency r a t h e r t h a n t h e mean.
The f r e q u e n c y c u r v e o f a n n u a l mean d i s c h a r g e s o f F i g u r e 5.2
shows t h e p r o b a b i l i t i e s t h a t a n annual mean f l o w w i l l be l e s s t h a n v a r i o u s c u r v e values.
F o r e x a m p l e , t h e p r o b a b i l i t y i s 1 0 p e r c e n t t h a t a f u t u r e a n n u a l mean
flow w i l l b e l e s s t h a n about 450 c f s .
1
3000
z
w-
1000
2a
I
?L! n
500
200 99
90
50
10
1
DEFlClE.NCY PROBABILITY, IN PERCENT
Fig. 5.2.
Frequency c u r v e of annual mean d i s c h a r g e s f o r Red River, Tennessee.
Flood-frequency
c n r v e s and low-flow
frequency c u r v e s a r e u s u a l l y d e f i n e d i n
t e r m s o f r e c u r r e n c e i n t e r v a l ; c h a r a c t e r i s t i c s such as t h e 100-year
f l o o d and t h e
l o - y e a r l o w f l o w a r e common d e s c r i p t o r s t a k e n f r o m t h e s e c u r v e s .
Methods o f
p r e p a r i n g frequency c u r v e s a r e g i v e n i n Chapter 4 and o t h e r examples a r e g i v e n i n C h a p t e r s 8 a n d 9. The r e l i a b i l i t y of a frequency c u r v e depends on t h e number of y e a r s o f d a t a on w h i c h i t i s b a s e d , on t h e v a r i a b i l i t y o f s t r e a m f l o w , and on w h e t h e r o r n o t t h e f l o w r e g i m e was changed d u r i n g or s u b s e q u e n t t o t h e p e r i o d of r ecor d.
A
r e q u i r e m e n t f o r v a l i d i t y of a f r e q u e n c y c u r v e i s t h a t t h e d a t a a r e a l l drawn from t h e same p o p u l a t i o n ;
t h i s i s u s u a l l y met by f l o w s which a r e averaged o v e r
some p e r i o d o f t i m e - s u c h a s m o n t h l y o r a n n u a l means; i t may n o t b e m e t b y f l o o d p e a k s on e p h e m e r a l s t r e a m s o r b y a n n u a l l o w f l o w s i n h u m i d r e g i o n s . f u r t h e r r e q u i r e m e n t i s t h a t t h e d a t a n o t be s e r i a l l y c o r r e l a t e d .
A
Thus an under-
s t a n d i n g of t h e b a s i n h y d ro lo g y i s needed f o r p r o p e r i n t e r p r e t a t i o n of a f r e quency curve. low-flow
The v a r i o u s f a c t o r s t h a t i n f l u e n c e f l o o d - f r e q u e n c y
c u r v e s and
frequency c u r v e s a r e d i s c u s s e d i n t h e c h a p t e r s on t h o s e s u b j e c t s .
109 JBTWDING STREAMFLOW RECORDS I N TIME
5.4
A frequency c u r v e b a s e d on 1 0 or 15 y e a r s of r e c o r d may n o t be v e r y r e l i a b l e . E s t i m a t e s for a d d i t i o n a l y e a r s can b e made by r e g r e s s i o n s on p r e c i p i t a t i o n or on a longer s t r e a m f l o w r e c o r d c o n c u r r e n t w i t h t h e one f o r t h e s i t e t o be e s t i m a t e d .
These e s t i m a t e s a r e t h e n combined w i t h t h e f l o w s of r e c o r d t o d e f i n e a n o t h e r . and p r e s u m a b l y b e t t e r , f r e q u e n c y c u r v e . t r a t e t h e procedure.
D a t a i n T a b l e 5.1 a r e u s e d t o i l l u s -
Assume t h a t annual f l o o d peaks f o r B l a c k w a t e r River a r e
a v a i l a b l e o n l y 1951-60.
The r e g r e s s i o n r e l a t i o n between f l o o d peaks f o r t h e two
streams f o r t h a t period i s log B = 1.035 + 0.676 l o g L and t h e c o r r e l a t i o n c o e f f i c i e n t i s 085.
T h i s r e l a t i o n i s used t o e s t i m a t e
B l a c k w a t e r f l o o d p e a k s f o r 1922-50; t h e e s t i m a t e s a n d t h o s e f o r 1951-60 a r e shown i n Table 5.1.
F i g u r e 5.3
shows f r e q u e n c y c u r v e s f o r B l a c k w a t e r based on
1951-60; on t h e a c t u a l r e c o r d ; and on t h e c o m b i n a t i o n of e s t i m a t e s f o r 1922-50 and a c t u a l f o r 1951-60.
I n t h i s example, t h e f r e q u e n c y curve d e f i n e d p a r t l y by
e s t i m a t e s i s p o o r e r t h a n t h e one b a s e d on o n l y t h e 1 0 y e a r s of record. TABLE 5.1 Annual f l o o d s , i n c f s , on two M i s s o u r i s t r e a m s . Year
Lamine R. Record
1922 3 4 1925 6 7 8 9 1930 1 2 3 4 1935 6
7 8 9 1940
15200 9300 7640 10100 11300 25000 7620 33000 7260 8500 11200 17800 5190 25000 13200 22200 16600 40200 4280
Blackwater R. Record
9280 10800 7060 10000 17400 21800 54000 7990 3200 9680 6900
9810 5300
Year
From Regression
7280 5230 4580 5530 5 960 10200 4570 12300 4420 4920 5930 8110 3520 10200 6620 9410 7730 14100 3090
1941 2 3 4 1945 6 7 8 9 1950 1 2 3 4 1955 6 7 8 9 1960
Lamine R.
Blackwater R.
Record
Record
18600 21400 60000 32500 12200 14500 14300 32500 12400 12200 65500 9750 5360 3830 8260 14000 6740 25 500 9980 28700
3890 13400 27900 32400 12600 11300 12900 15600 9760 13200 23900 7100 5880 3290 5170 3960 3150 8100 3570 16200
From Regression 83 50 9180 18400 12200 6280 7060 6990 12200 6350 6280 19600 5 400 3600 2870 4820 6890 4200 10300 5480 11200
F i e r i n g (1963) h a s shown t h a t u n l e s s t h e c o r r e l a t i o n c o e f f i c i e n t i s g r e a t e r t h a n a b o u t 0.8, u s e o f r e g r e s s i o n e s t i m a t e s w i l l n o t i m p r o v e t h e e s t i m a t e of variance.
The e x a m p l e r e g r e s s i o n h a s a n r o f 0.85; and F i g u r e 5.3 s h o w s t h a t
t h e v a r i a n c e ( s l o p e of t h e l i n e ) i s i m p r o v e d by u s e o f e s t i m a t e s , b u t t h a t t h e
110 mean i s n o t .
Apparently t h e r e l a t i o n between f l o o d peaks of t h e two s t r e a m s
d u r i n g 1951-60 i s c o n s i d e r a b l y d i f f e r e n t t h a n f o r o t h e r p e r i o d s .
In g e n e r a l ,
u s e of r e g r e s s i o n e s t i m a t e s produces a n improved frequency c u r v e o n l y when t h e two v a r i a b l e s a r e v e r y h i g h l y c o r r e l a t e d .
I
100,000,
uU
1922-33 1939-60
/
(r
4V
E Q Y
20,000
-
10,000
-
-
$ Q
3 Z
PLUS 23 ESTIMATES
-
Z Q
5000 _ _ _ .
1.5
-4
2
3 '
5
10
20
30
50
RECURRENCE INTERVAL, IN YEARS
F i g . 5.3. R e s u l t of a t t e m p t t o improve a flood-frequency regression estimates.
c u r v e by u s e of
Streamflow r e c o r d s may be extended i n t i m e f o r purposes o t h e r t h a n frequency curve improvement.
A mean f o r some s p e c i f i c p a s t month o r y e a r may be needed.
T h i s c a n b e o b t a i n e d by s i m p l e r e g r e s s i o n o r by r e g r e s s i o n m o d e l s w i t h b o t h s t r e a m f l o w and p r e c i p i t a t i o n a s independent v a r i a b l e s .
S c h n e i d e r (1961), Riggs
(1964a) and M a r t i n (1964) proposed and e v a l u a t e d s e v e r a l models f o r e s t i m a t i n g monthly mean d i s c h a r g e s f o r months o u t s i d e t h e p e r i o d of r e c o r d from d i s c h a r g e a t a n e a r b y g a g e d s i t e and f r o m t h e m o n t h l y p r e c i p i t a t i o n t o t a l s on t h e t w o sites.
Carroon (1970) extended monthly flow r e c o r d s a t many s i t e s in t h e upper
Colorado R i v e r b a s i n by a g r a p h i c a l method.
The r e l i a b i l i t y of such a r e g r e s -
s i o n e s t i m a t e i s i n d i c a t e d by t h e s t a n d a r d e r r o r . Rainfall-runoff
models which account f o r t h e d e t a i l e d d i s p o s i t i o n of r a i n f a l l
may b e u s e d t o e x t e n d s t r e a m f l o w r e c o r d s .
T h e s e may b e r e g r e s s i o n m o d e l s i n
w h i c h r u n o f f i s r e l a t e d t o s t o r m m a g n i t u d e , s t o r m d u r a t i o n , and a n i n d e x o f a n t e c e d e n t s o i l m o i s t u r e ; o r d i g i t a l computer models which model t h e l a n d phase of t h e h y d r o l o g i c cycle.
Both t y p e s of models r e q u i r e s e v e r a l y e a r s of concur-
r e n t s t r e a m f l o w and h o u r l y p r e c i p i t a t i o n r e c o r d s f o r c a l i b r a t i o n ;
t h e i r output
111
i s continuous d a i l y s t r e a m f l o w , record. (1969).
l i m i t e d i n t i m e by t h e a v a i l a b l e p r e c i p i t a t i o n
R e g r e s s i o n m o d e l s a r e d e s c r i b e d by Moore ( 1 9 6 8 ) and S i t t n e r , e t a 1 There a r e many d i g i t a l computer models f o r producing a c o n t i n u o u s flow
record from p r e c i p i t a t i o n ; most a r e some m o d i f i c a t i o n o f t h e S t a n f o r d Watershed Model (Crawford and L i n s l e y , 1966).
Rainfall-runoff
models produce s y n t h e t i c
s t r e a m f l o w r e c o r d s t h a t a r e a d e q u a t e f o r many p u r p o s e s i f t h e p r e c i p i t a t i o n r e c o r d i s r e p r e s e n t a t i v e o f p r e c i p i t a t i o n on t h e b a s i n .
But t h e s y n t h e t i c
record i s n o t r e l i a b l e enough t o improve f r e q u e n c y c u r v e s of d a i l y extremes.
A
r a i n f a l l - r u n o f f model t h a t s y n t h e s i z e s s t o r m h y d r o g r a p h s f o r t h e p u r p o s e o f extending a f l o o d r e c o r d i s d e s c r i b e d i n s e c t i o n 8.7. 5.5
FLOW-DURATION CURVES The f l o w - d u r a t i o n
c u r v e i s a c u m u l a t i v e f r e q u e n c y c u r v e based on d a i l y d i s -
charges f o r one or many complete y e a r s of record.
The u s u a l g r a p h i c a l method o f
d e f i n i n g a frequency c u r v e by p l o t t i n g each p o i n t i s n o t f e a s i b l e when t h e r e a r e many p o i n t s :
i n t h i s a p p l i c a t i o n t h e r e a r e 365 f o r each year.
Consequently,
the
numbers of d a y s h av in g d i s c h a r g e s w i t h i n ea ch o f 20 o r 30 r a n g e s of d i s c h a r g e a r e determined, u s u a l l y by computer. of t h e t o t a l ,
These numbers a r e c o n v e r t e d t o p e r c e n t a g e s
t h e p e r c e n t a g e s a r e cumulated from t h e upper end (of d i s c h a r g e ) .
and t h e cumulated v a l u e s a r e p l o t t e d a g a i n s t t h e a p p r o p r i a t e d i s c h a r g e s on a l o g normal graph. cumulated
F i g u r e 5.4 i s a n e x a m p l e .
from t h e high-discharge
end,
Because t h e p e r c e n t a g e s of d a y s a r e any p o i n t on t h e d u r a t i o n c u r v e shows
t h e p e r c e n t o f d a y s ( d u r i n g t h e p e r i o d u s e d ) t h a t had d i s c h a r g e s g r e a t e r t h a n t h e i n d i c a t e d value. Although t h e d u r a t i o n c u r v e i s a c u m u l a t i v e frequency curve i t should be i n t e r p r e t e d m e r e l y a s an e x p r e s s i o n o f what happened i n a p a r t i c u l a r t i m e p e r i o d , n o t a s a p r o b a b i l i t y c u r v e because d a i l y d i s c h a r g e s a r e n o t o n l y s e r i a l l y c o r r e l a t e d b u t t h e i r c h a r a c t e r i s t i c s change throughout t h e year.
Consequent-
l y t h e p r o b a b i l i t y of a d a i l y d i s c h a r g e b e i n g g r e a t e r t h a n some s p e c i f i e d v a l u e d i f f e r s f r o m t h a t g i v e n b y t h e d u r a t i o n c u r v e b e c a u s e i t d e p e n d s b o t h on t h e p r e c e d i n g f l o w s and on t h e t i m e of year. The d u r a t i o n c u r v e c a n b e i n t e r p r e t e d a s f o l l o w s :
a d a i l y f l o w may b e
e x p e c t e d t o e q u a l or e x c e e d Q c f s P p e r c e n t o f t h e t o t a l t i m e i n a p e r i o d of y e a r s e q u a l t o t h e p e r i o d used i n d e f i n i n g t h e d u r a t i o n curve.
This i n t e r p r e t a -
t i o n would b e r e a s o n a b l e o n l y i f t h e d u r a t i o n c u r v e is based on t e n s of y e a r s of record.
D u r a t i o n c u r v e s based on one or o n l y a few y e a r s of r e c o r d may d e v i a t e
g r e a t l y from t h e curve based on a long record. D u r a t i o n c u r v e s may be used t o d i s p l a y g r a p h i c a l l y t h e v a r i a b i l i t y of flow, a change due t o s t r e a m r e g u l a t i o n ,
or t h e d e p e n d a b i l i t y of low flows.
d u r a t i o n c u r v e may be used w i t h a s e d i m e n t - r a t i n g sediment load.
An annual
c u r v e t o compute t o t a l annual
D i s c h a r g e s a t 95 p e r c e n t on t h e l o n g - t e r m d u r a t i o n c u r v e a r e
112
Fig. 5.4.
Flow-duration
c u r v e f o r James R i v e r a t Buchanan. V i r g i n i a .
r e l a t e d t o p o i n t s on t h e l o w - f l o w
frequency curve b u t t h e s e r e l a t i o n s change
geographically. 5.6
BASE-FLOW RECESSION CURVES Streamflow v a r i e s n o t o n l y because t h e c a u s a t i v e s t o r m s a r e random i n t h e i r
o c c u r r e n c e , g e o g r a p h i c a l e x t e n t , d u r a t i o n , and i n t e n s i t y b u t a l s o b e c a u s e v a r i o u s p o r t i o n s of t h e p r e c i p i t a t i o n a p p e a r a s measured s t r e a m f l o w a t d i f f e r e n t times.
The l a g between p r e c i p i t a t i o n and r u n o f f depends on t h e p a t h which t h e
w a t e r f o l l o w s from t h e s u r f a c e of t h e ground t o t h e stream.
That p o r t i o n which
f l o w s on t h e s u r f a c e of t h e ground t o t h e s t r e a m channel i s most c l o s e l y r e l a t e d in time t o precipitation.
Another p o r t i o n may t r a v e l through t h e upper l a y e r s
of t h e s o i l and a r r i v e a t t h e s t r e a m c h a n n e l s r a t h e r promptly b u t somewhat l a t e r t h a n s u r f a c e runoff.
The s u r f a c e flow and t h e s h a l l o w s u b s u r f a c e f l o w a r e o f t e n
c o n s i d e r e d t o g e t h e r under t h e t i t l e of d i r e c t r u n o f f , of s t r e a m f l o w d u r i n g f l o o d s . ward i n t o t h e ground-water
which i s t h e major p o r t i o n
A t h i r d p o r t i o n of t h e p r e c i p i t a t i o n s e e p s down-
a q u i f e r t h a t f e e d s t h e stream.
This t h i r d p o r t i o n i s
t h e l a s t t o r e a c h t h e s t r e a m and i s t h e p o r t i o n t h a t m a i n t a i n s s t r e a m f l o w d u r i n g p e r i o d s of no r a i n .
I t i s commonly c a l l e d t h e b a s e flow of t h e stream.
113
The h y d r o g r a p h o f s t r e a m f l o w d u r i n g p e r i o d s when a l l d i s c h a r g e i s d e r i v e d f r o m g r o u n d w a t e r s o u r c e s i s known a s a b a s e - f l o w a v e r a g e s t h e s e r e c e s s i o n s i s t h e base-flow 5.6.1
recession.
A curve which
r e c e s s i o n curve.
Theory
T h e o r e t i c a l e q u a t i o n s f o r f l o w i n an a q u i f e r a r e t h e b a s i s f o r e q u a t i o n s d e s c r i b i n g a s t r e a m f l o w r e c e s s i o n c u r v e ( H a l l , 1968).
These e q u a t i o n s a r e
g e n e r a l l y of t h e form
Qt
= Qo
K-t
w h e r e Q t i s t h e d i s c h a r g e a t a n y i n s t a n t , Qo i s t h e d i s c h a r g e a t some i n i t i a l time, K i s t h e r e c e s s i o n c o n s t a n t , and t i s t h e t i m e i n t e r v a l between Qo and Q,. The p l o t o f l o g Q t a g a i n s t t i s a s t r a i g h t l i n e on s e m i l o g p a p e r .
Rorabaugh
(1964) showed t h a t e q u a t i o n 1 i s n o t c o r r e c t s h o r t l y a f t e r a r echar ge. e q u a t i o n f o r t h e movement of ground w a t e r , h a s many t e r m s ,
adapted from a heat-flow
Eis
equation,
a l l b u t t h e f i r s t of which become v e r y s m a l l a f t e r s u f f i c i e n t
time has elapsed.
A f t e r t h a t c r i t i c a l t i m e , w h i c h may b e w e e k s o r m o n t h s
d e p e n d i n g on t h e a q u i f e r c h a r a c t e r i s t i c s , R o r a b a u g h ' s e q u a t i o n g i v e s r e s u l t s comparable t o e q u a t i o n 1.
The Rorabaugh e q u a t i o n a p p l i e s t o one a q u i f e r t h a t i s
u n i f o r m , i s o t r o p i c , and h o m o g e n e o u s ; h a s a h o r i z o n t a l w a t e r s u r f a c e ; and h a s o t h e r s p e c i f i c boundary r e s t r i c t i o n s . restrictions.
N a t u r a l a q u i f e r s do n o t conform t o t h e s e
In a d d i t i o n , a s t r e a m may be f e d by s e v e r a l a q u i f e r s , each having
d i f f e r e n t d i s c h a r g e c h a r a c t e r i s t i c s and d i f f e r e n t r a t e s and t i m e s of recharge. Furthermore,
t h e a q u i f e r or a q u i f e r s may l o s e w a t e r through e v a p o t r a n s p i r a t i o n ,
and t h e w a t e r d i s c h a r g e d t o t h e s t r e a m i s s u b j e c t t o v a r i a b l e e v a p o t r a n s p i r a t i o n w i t h d r a w a l s d a i l y and s e a s o n a l l y s o t h a t t h e r e c e s s i o n o f s t r e a m f l o w i s n o t n e c e s s a r i l y a t t h e same r a t e a s t h e r e c e s s i o n of a q u i f e r outflow.
Other f a c t o r s
such as changes i n channel s t o r a g e f u r t h e r modify t h e streamflow recession. Consequently,
the theoretical straight-line
semilog recession curve i s not
a p p l i c a b l e t o many s t r e a m f l o w r e c e s s i o n s . Suppose a b a s i n h a s a l a r g e - c a p a c i t y
a r t e s i a n a q u i f e r which r e l e a s e s w a t e r
s l o w l y t o t h e s t r e a m and which i s recharged o n l y i n u n u s u a l l y wet years. pose t h i s b a s i n a l s o h a s a w a t e r - t a b l e
Sup-
a q u i f e r which i s r e c h a r g e d s e a s o n a l l y .
Assume i n i t i a l l y t h a t b o t h a q u i f e r s a r e r e c h a r g e d t o c a p a c i t y a t t h e same t i m e and t h a t t h e i n d i v i d u a l r e c e s s i o n s a r e r e p r e s e n t e d by t h e s o l i d l i n e s beginning a t z e r o days i n F i g u r e 5.5.
Then t h e t o t a l b a s e flow of t h e s t r e a m w i l l be t h e
sum of t h e two r e c e s s i o n curves.
T h i s i s r e p r e s e n t e d by t h e dashed l i n e which
becomes t a n g e n t t o t h e s o l i d l i n e of f l a t t e r s l o p e a s t h e c o n t r i b u t i o n from t h e o t h e r a q u i f e r approaches zero.
A s u b s e q u e n t r e c h a r g e o n l y of t h e w a t e r t a b l e
a q u i f e r a t 60 days w i l l produce a combined r e c e s s i o n c u r v e of d i f f e r e n t s l o p e
114 and shape.
Thus, b a s e flow r e c e s s i o n s of s t r e a m s f e d by more t h a n one a q u i f e r
may t a k e a v a r i e t y of shapes and s l o p e s a t d i f f e r e n t times.
0
120
60
180
240
DAYS
Fig. 5.5. Assumed r e c e s s i o n c u r v e s ( s o l i d l i n e s ) f r o m t w o a q u i f e r s a n d t h e streamflow r e c e s s i o n s (dashed l i n e s ) which a r e t h e sums. 5.6.2
Derivation
Base-flow
r e c e s s i o n c u r v e s a r e commonly d e r i v e d from segments of d i s c h a r g e
hydrographs when t h e r e i s no s u r f a c e r u n o f f
i n t h e channels.
Weather r e c o r d s
should be u t i l i z e d i n j u d g i n g which segments a r e u n a f f e c t e d by p r e c i p i t a t i o n . A f t e r t h e end of a s t o r m s u f f i c i e n t t i m e i s a l l o w e d f o r t h e d i r e c t r u n o f f a n d d r a i n a g e from channel s t o r a g e t o have passed t h e gage.
T h i s t i m e may range from
a few d a y s f o r a s m a l l s t r e a m t o s e v e r a l weeks f o r a l a r g e one.
Ordinarily the
segment s e l e c t e d should be a t l e a s t 10 d a y s long because s h o r t e r segments may n o t be r e p r e s e n t a t i v e .
And a segment should be s t e e p enough so t h a t subsequent
d i s c h a r g e s do n o t f a l l below an e x t e n s i o n o f t h a t segment.
Usually several
y e a r s of h y d r o g r a p h s a r e needed t o i d e n t i f y an a d e q u a t e number of r e c e s s i o n segments. These s e l e c t e d segments c a n b e s y n t h e s i z e d i n t o a f u l l r e c e s s i o n c u r v e on a p i e c e o f t r a c i n g p a p e r h a v i n g d i s c h a r g e and t i m e s c a l e s i d e n t i c a l t o t h o s e o f t h e hydrographs.
A f t e r t h e f i r s t segment i s t r a c e d ,
i z o n t a l l y so t h a t t h e o t h e r s e g m e n t s f a l l alignment.
t h e s h e e t i s s h i f t e d hor-
i n t o a common a n d c o n t i n u o u s
F i g u r e 5.6 shows t h e segments t r a c e d on the s h e e t .
A mean r e c e s s i o n
curve c a n be drawn through these. S t r e a m f l o w may r e c e d e a t d i f f e r e n t r a t e s i n d i f f e r e n t s e a s o n s b e c a u s e o f changes i n e v a p o t r a n s p i r a t i o n .
The g r a p h i c a l s y n t h e s i s d e s c r i b e d a b o v e w i l l
produce s e a s o n a l l y d i f f e r e n t r e c e s s i o n curves o n l y i f t h e y e a r i s d i v i d e d a priori.
A method w i t h o u t t h i s l i m i t a t i o n b e g i n s w i t h s e l e c t i o n ,
from t h e iden-
t i f i e d r e c e s s i o n s , o f s e g m e n t s o f a common l e n g t h , s u c h a s 10 d a y s .
For each
115
200
'
0
I
I
I
I
20
40
60
80
100
DAYS
F i g . 5.6. S e g m e n t s o f h y d r o g r a p h r e c e s s i o n s t r a c e d on a s h e e t t o d e f i n e t h e r e c e s s i o n c u r v e , James R i v e r , V i r g i n i a . segment, t h e d i s c h a r g e s o f t h e b e g i n n i n g day and t h e t e n t h day f o l l o w i n g a r e p l o t t e d a s shown on t h e l e f t g r a p h of F i g u r e 5.7.
The p o i n t s c a n b e i d e n t i f i e d
cn LL
0
z
cn LL
Ir
0
t-
4 cn
w
2
I
W
a
t
2
w 2
4 0
1OoL100 200
1 0 0 500
1000
2000
0
20
DISCHARGE A T BEGINNING DAY, IN CFS
40
60
80
100
DAYS
F i g . 5.7. S y n t h e s i s o f a b a s e - f l o w r e c e s s i o n c u r v e f r o m s e l e c t e d 10-day g r a p h segments, B u f f a l o R i v e r n e a r L o b e l v i l l e , Tennessee.
hydro-
b y month so t h a t mean r e l a t i o n s by s e a s o n s c a n b e d r a w n i f s i g n i f i c a n t d i f f e r e n c e s a r e found ( t h e y were n o t found i n t h e s e d a t a ) .
The mean l i n e of f i g u r e
5.7 was t r a n s f o r m e d t o t h e r e c e s s i o n c u r v e b y b e g i n n i n g a t 1 0 0 0 c f s p l o t t e d a t z e r o days.
T h e n t h e d i s c h a r g e 1 0 d a y s l a t e r i s p l o t t e d a t d a y 10.
Nest, t h e
d a y 1 0 d i s c h a r g e i s u s e d a s b e g i n n i n g d i s c h a r g e t o d e t e r m i n e t h e d i s c h a r g e 10
116 This process i s repeated u n t i l the complete
days l a t e r ( t o be p l o t t e d a t 2 0 ) .
r e c e s s i o n c u r v e ( t h e r i g h t c u r v e of F i g u r e 5.7) 5.6.3
i s defined.
Assumptions a s t o r e c h a r g e
Most s u b s t a n t i a l r i s e s i n s t r e a m f l o w a r e accompanied by an a p p a r e n t i n c r e a s e
i n base f l o w which may be drainage from bank storage rather than from a recharge t o the aquifer.
The a s s u m p t i o n s made a s t o r e c h a r g e , or l a c k o f i t , f r o m a
p a r t i c u l a r s t o r m i n a p a r t i c u l a r season g r e a t l y i n f l u e n c e t h e c h a r a c t e r i s t i c s of t h e d e r i v e d r e c e s s i o n c u r v e and c o n s e q u e n t l y i t s r e l i a b i l i t y and meaning.
The
a p p r o p r i a t e assumption a s t o r e c h a r g e depends on t h e b a s i n and channel characteristics,
t h e magnitude of t h e p r e c i p i t a t i o n ,
t i m e o f year.
antecedent conditions,
and t h e
Knowledge of t h e b a s i n and s t u d y of t h e hydrograph i n c o n j u n c t i o n
w i t h w e a t h e r r e c o r d s s h o u l d l e a d t o a r e a s o n a b l e concept f o r a p a r t i c u l a r s t r e a m site. 5.6.4
Seasonal v a r i a b i l i t y
E v a p o t r a n s p i r a t i o n l o s s e s from t h e a q u i f e r and from t h e channel v a r y g r e a t l y w i t h t i m e o f y e a r and may v a r y w i t h e l e v a t i o n of t h e w a t e r t a b l e and w i t h s t r e a m discharge.
Consequently,
i t h a s been t h e p r a c t i c e t o d e f i n e s e p a r a t e r e c e s s i o n
c u r v e s f o r summer a n d f o r w i n t e r p e r i o d s .
The w i n t e r r e c e s s i o n c u r v e s h o u l d
more c l o s e l y r e p r e s e n t t h e d i s c h a r g e f r o m g r o u n d - w a t e r s o u r c e s b e c a u s e t h e l o s s e s t o t h e atmosphere a r e minor d u r i n g w i n t e r .
Unfortunately,
t h e frequency
o f p r e c i p i t a t i o n d u r i n g w i n t e r and t h e f l u c t u a t i o n s o f t e m p e r a t u r e a b o v e and below f r e e z i n g produce s u c h f l u c t u a t i o n s i n s t r e a m f l o w t h a t i t becomes n e a r l y i m p o s s i b l e t o d i s c r i m i n a t e p e r i o d s o f b a s e f l o w f o r many streams. m o s t r e c e s s i o n c u r v e s a r e d e f i n e d f o r summer c o n d i t i o n s .
Consequently,
Data a v a i l a b l e f o r
B r a n d y w i n e C r e e k a t Chadds F o r d , Pa. p e r m i t t h e d e f i n i t i o n o f c u r v e s f o r b o t h summer and w i n t e r ( s e e F i g u r e 5.8).
Obviously, t h e r e c e s s i o n r a t e does n o t
change a b r u p t l y from one c u r v e t o t h e o t h e r ; t h e r e f o r e t h e s e c u r v e s do n o t a p p l y t o s p r i n g and f a l l c o n d i t i o n s .
Other f a c t o r s t h a t cause v a r i a b l e recession
r a t e s a r e d e s c r i b e d by Riggs (1964b). 5.7
WATER QUALITY CHARACTEBISTICS The g r e a t many c o n s t i t u e n t s and c h a r a c t e r i s t i c s of a n a t u r a l w a t e r r u l e o u t
any s i m p l e d e s c r i p t i o n of t h e q u a l i t y of a water.
But some g e n e r a l i z a t i o n s a r e
u s e f u l a s i n d i c a t o r s of whether a w a t e r i s l i k e l y t o be s u i t a b l e f o r a p a r t i c u l a r purpose.
The s i g n i f i c a n t c h a r a c t e r i s t i c s of w a t e r and i t s i m p u r i t i e s t h a t
a f f e c t q u a l i t y f o r v a r i o u s u s e s a r e d i s c u s s e d by Camp (1963) and by Hem (1972, p. 320-336).
T h e s e c h a r a c t e r i s t i c s i n c l u d e t e m p e r a t u r e and t h e a m o u n t s o f
suspended sediment, d i s s o l v e d s o l i d s , and b i o l o g i c a l m a t e r i a l i n t h e water. Water t e m p e r a t u r e changes s e a s o n a l l y ; i t may even change throughout a day on s m a l l streams.
The v a r i a t i o n o f weekly or monthly mean t e m p e r a t u r e s throughout
117 t h e y e a r p r o v i d e s i n f o r m a t i o n n e e d e d f o r many u s e s .
F i g u r e 5.9
shows t h e
s e a s o n a l c y c l e s o f w a t e r t e m p e r a t u r e i n a n o r t h e r n and a s o u t h e r n S t a t e .
0
60
30
90
120
DAYS
F i g . 5.8. W i n t e r ( u p p e r ) a n d summer ( l o w e r ) b a s e - f l o w Brandywine Creek n e a r Chadds Ford, Pennsylvania.
recession curves f o r
The s e d i m e n t t r a n s p o r t e d by a s t r e a m i s a measure o f w a t e r q u a l i t y , and i t i s t h e b a s i s f o r c o m p u t a t i o n of t h e sediment d e p o s i t i o n t o be expected i n r e s e r voirs,
downstream channels,
or e s t u a r i e s .
Sediment c o n c e n t r a t i o n i s needed i n
t h e d e s i g n and management of w a t e r - t r e a t m e n t
facilities; it
ized by t h e frequency d i s t r i b u t i o n of d a i l y means.
can be c h a r a c t e r -
Where only o c c a s i o n a l s e d i -
ment measurements a r e a v a i l a b l e t h e d i s t r i b u t i o n of d a i l y mean c o n c e n t r a t i o n s c a n b e a p p r o x i m a t e d f r o m a s e d i m e n t - r a t i n g c u r v e ( S e c t i o n 3.1.9) a n d a f l o w d u r a t i o n curve. The mean annual sediment l o a d i s t h e a p p r o p r i a t e c h a r a c t e r i s t i c f o r use in
A
e s t i m a t i n g t h e amount o f s e d i m e n t t h a t w i l l b e d e p o s i t e d i n a r e s e r v o i r .
s h o r t r e c o r d o f annual sediment l o a d may be extended by u s e of a long s t r e a m f l o w r e c o r d and a s e d i m e n t r a t i n g curve. Chemical q u a l i t y of a w a t e r depends on t h e amounts of each of many c o n s t i t u e n t s (Swenson and Baldwin,
1965).
The w a t e r may c o n t a i n m i n e r a l s and o r g a n i c
compounds t h a t a r e u n d e s i r a b l e f o r c e r t a i n uses.
Mineral c o n t e n t also d e t e r -
mines whether t h e w a t e r i s hard or s o f t and a c i d or a l k a l i n e . S p e c i f i c c o n d u c t a n c e i s an i n d i c a t i o n o f t o t a l d i s s o l v e d s o l i d s .
Waters
having s p e c i f i c conductances o f l e s s than a few hundred micromhos p e r c e n t i m e t e r g e n e r a l l y a r e c o n s i d e r e d good.
But t h e c o n c e n t r a t i o n of d i s s o l v e d s o l i d s ,
t h u s t h e conductance, changes w i t h d i s c h a r g e .
and
A more i n f o r m a t i v e c h a r a c t e r i s t i c
t h a n t h e maximum or t h e average conductance would be t h e frequency d i s t r i b u t i o n of d a i l y mean conductances or t h e r e l a t i o n of conductance t o s t r e a m d i s c h a r g e .
*
118
LL v)
W
U
30
J
I
F
I
1
M
A
I M
I J
I
I
I
1
I
J
A
S
O
N
D
MONTHS
Fig. 5.9.
Variation in mean monthly water temperatures.
Various methods of graphically representing the concentrations of the principal dissolved constituents are described by Hem (1972). Such graphs permit ready comparisons among waters. Hardness is indicated by the concentration of calcium carbonate or its equivalent: water with less than 60 mg/l of hardness is considered soft.
The pH is
the characteristic that indicates whether the water is acid or alkaline and to what degree. The biological content of a water is usually the result of pollution and cannot be simply characterized quantitatively, although the dissolved oxygen content is an indicator. Simplistic indicators of chemical quality are useful for preliminary studies and evaluations but more detailed information is usually required in planning a specific use of a water. REFERENCES Camp, T.R, 1963, Water and its impurities: New York, Reinhold Publ. Corp., 355 P. Carroon, L.E., 1970, Correlative estimates of streamflow in the upper Colorado River basin: U.S. Geol. Survey Water-Supply Paper 1875, 145 p. and Linsley, RK., 1966, Digital simulation in hydrology: StanCrawford, N.& ford Watershed Model IV: Dept. of Civil Engineering, Stanford University, Tech. Rept. No. 39, 210 p.
119 Piering, M.B., 1963. Use of correlation to improve e s t i m a t e s of the m e a n and variance: U.S. Geol. Survey Prof. Paper 434-c. Hall, P.R., 1968, Base-flow recessions - a review: Vol. 4. NO. 5, p. 973-983.
W a t e r Resources Research.
Hem. J.D., 1972, Study and interpretation of the c h e m i c a l characteristics of natural water: U.S. Geol. Survey W a t e r S u p p l y Paper, 1473. Second Edition. 3 6 3 p. 1964, Use of precipitation records in the correlation of streamMartin, R.O.R., flow records: International Assoc. of Scientific Hydrology Boll., Vol. IX. NO. 4. p. 24-31. 1968, Synthesizing daily discharge from rainfall records: Journal Moore, D.O.. o f Hydraulics Division, ASCE, Vol. 94, No. HYS, Proc. P a p e r 6119, p. 12831298. 19641. Stream discharge regressions using precipitation: Riggs. H.C., Geol. Survey Prof. P a p e r 501-C, p. 185-187.
U.S.
Riggs. H.C., 1964b, T h e base-flow recession c u r v e a s a n indicator of ground water: International Assoc. of Scientific Hydrology Pnbl. 63. Berkeley. p. 352-363. Rorabaugh, M.I., 1964. Estimating changes in b a n k storage and ground-water contribution to streamflow: International Assoc. of Scientific Hydrology Publ. 63. Berkeley, p. 432-441. Schneider, W.J.. 1961, Precipitation as a variable in the correlation of runoff data: U.S. Geol. Survey Prof. P a p e r 424-B, Article 9. Schauss, C.E., and Monro. J.C., 1969. Continuous hydrograph Sittner. W.T.. synthesis w i t h a n API-type hydrologic model: W a t e r Resources Research, Vol. 5, NO. 8, p. 1007-1022. Swenson, H.A. and Baldwin, H.L., Survey, 2 7 p.
1965. A p r i m e r on w a t e r quality:
U.S.
Geol.
This Page Intentionally Left Blank
121
Chapter 6
RFLATXON OF GROUND WATER M STREAMFLOW 6.1
INTRODUCTION Ground w a t e r and s u r f a c e w a t e r a r e o f t e n s t u d i e d i n d e p e n d e n t l y b u t a p a r t i c -
u l a r p a r t i c l e o f w a t e r may b e c o n s i d e r e d ground w a t e r a t one t i m e and s u r f a c e w a t e r a t a n o t h e r i n i t s t r a n s i t of t h e land.
A p r o p e r i n t e r p r e t a t i o n of stream-
flow c h a r a c t e r i s t i c s r e q u i r e s an u n d e r s t a n d i n g of how ground w a t e r i s r e p l e n i s h ed and d e p l e t e d and how t h e s e changes r e l a t e t o streamflow. Ground w a t e r f i l l s t h e pore s p a c e s and f r a c t u r e s i n t h e e a r t h m a t e r i a l s t o a l e v e l known a s t h e w a t e r t a b l e . c a l l e d an aquifer.
The p o r o u s m a t e r i a l t h a t c o n t a i n s w a t e r i s
I f t h e porous m a t e r i a l e x t e n d s t o t h e ground s u r f a c e ,
SO
t h a t t h e w a t e r t a b l e i s f r e e t o move v e r t i c a l l y i n response t o changes i n volume of w a t e r i n storage, the a q u i f e r i s c a l l e d a water-table
aquifer.
I f t h e upper
p a r t i s c o n f i n e d by a n i m p e r m e a b l e or s e m i p e r m e a b l e r o c k f o r m a t i o n , and t h e ground w a t e r i s under p r e s s u r e ,
the aquifer i s artesian.
Many a q u i f e r s i n humid r e g i o n s d i s c h a r g e a t l e a s t f o r p a r t o f t h e y e a r t o t h e ground s u r f a c e e i t h e r through s p r i n g s or d i r e c t l y t o a s t r e a m channel a s shown i n F i g u r e 6.1.
K i l p a t r i c k (1964) showed t h a t t h e low flow of a s m a l l s t r e a m i n
Georgia was d e r i v e d from d i s c h a r g e s of a w a t e r - t a b l e leakage from an a r t e s i a n a q u i f e r .
a q u i f e r and from upward
A q u i f e r s i n a r i d r e g i o n s may d i s c h a r g e o n l y
by e v a p o t r a n s p i r a t i o n .
Fig. 6.1. V a l l e y c r o s s s e c t i o n showing how a q u i f e r s d i s c h a r g e t o a s t r e a m and t o a spring. The r a t e of movement of ground w a t e r depends on t h e h y d r a u l i c g r a d i e n t and t h e t r a n s m i s s i v i t y of t h e a q u i f e r m a t e r i a l . t h a n 2 o r d e r s o f magnitude.
T r a n s m i s s i v i t y may range o v e r more
Consequently t h e v e l o c i t y of ground w a t e r may range
122 f r o m a f e w f e e t p e r y e a r i n c l a y t o many f e e t p e r d a y t h r o u g h v e r y p o r o u s material.
Soluble rocks, such a s limestone, o f t e n c o n t a i n s o l u t i o n channels
t h r o u g h w h i c h g r o u n d w a t e r moves r a p i d l y .
F i g u r e 6.2 s h o w s h y d r o g r a p h s o f 2
s p r i n g s which i l l u s t r a t e t h e d i f f e r e n t r a t e s o f g r o u n d - w a t e r Daniel Spring d r a i n s a l i m e s t o n e a r e a ;
movement.
Jack
i t s r a p i d response t o r a i n f a l l i n d i c a t e s
t h e p r o b a b l e e x i s t e n c e o f s i n k s and s o l u t i o n c h a n n e l s i n t h e b a s i n .
The more
t y p i c a l hydrograph of I n d i a n Ford S p r i n g r e f l e c t s slow i n f i l t r a t i o n through t h e s o i l and slow movement through t h e a q u i f e r ; i t does n o t f o l l o w t h e hydrograph of t h e nearby stream.
50
500
20
10
5
2
1
x
\I,
200
100
50
20 I
I
OCTOBER 1975
10
SPRING
I
1
OCTOBER 1947
Fig. 6.2. Eydrographs of two s p r i n g s , and of a s t r e a m n e a r one of them, t h e d i f f e r e n c e s i n flow v a r i a b i l i t y .
showing
Spring flow i s l e s s v a r i a b l e i f t h e recharge a r e a i s d i s t a n t from t h e d i s c h a r g e p o i n t and i f t h e a q u i f e r i s n o t s u b j e c t t o e v a p o t r a n s p i r a t i o n . s p r i n g s a r e b e t t e r i n d i c a t o r s of ground-water
Such
d i s c h a r g e t h a n a r e t h e low f l o w s
of streams. AQUIFER RECHARGE
6.2
Ground w a t e r i s r e p l e n i s h e d b y r a i n or m e l t i n g snow w h i c h i n f i l t r a t e s t h e soil.
In t e m p e r a t e , humid c l i m a t e s t h e major r e p l e n i s h m e n t or r e c h a r g e o c c u r s
d u r i n g t h e w i n t e r and s p r i n g months when p r e c i p i t a t i o n i s p l e n t i f u l , evapotransp i r a t i o n i s low,
and s o i l m o i s t u r e i s high.
During t h e growing s e a s o n a l a r g e
p a r t of t h e p r e c i p i t a t i o n i s h e l d i n t h e s o i l u n t i l i t i s r e t u r n e d t o t h e atmosphere by e v a p o t r a n s p i r a t i o n .
Thus t h e c o n t r i b u t i o n of a s u b s t a n t i a l r a i n
123 t o t h e ground w a t e r body r a n g e s from a maximum i n w i n t e r o r e a r l y s p r i n g t o v e r y l i t t l e f o l l o w i n g a l o n g d r y p e r i o d i n summer.
In m o s t a r i d r e g i o n s t h e w a t e r t a b l e i s b e l o w t h e s t r e a m b e d s and t h u s t h e s t r e a m s a r e ephemeral.
Here a s u b s t a n t i a l s t o r m w i l l produce s t r e a m f l o w and
some i n f i l t r a t i o n over t h e b a s i n b u t l i t t l e of t h a t i n f i l t r a t e d w a t e r g e t s below plant roots.
Recharge,
i f any,
o c c u r s a s l e a k a g e through t h e s t r e a m b e d s whose
p e r m e a b i l i t y may be i n c r e a s e d t e m p o r a r i l y by t h e f a s t ,
t u r b u l e n t flows.
Jordan
(1977) r e p o r t e d s u b s t a n t i a l t r a n s m i s s i o n l o s s e s i n s t r e a m s i n w e s t e r n Kansas; most of t h e w a t e r l o s t from t h e s e c h a n n e l s i s a c c r e t i o n t o ground water. The amount o f r e c h a r g e t o a n a q u i f e r f r o m a s t o r m may b e c o m p u t e d f r o m t h e r i s e i n t h e w a t e r t a b l e a s measured i n w e l l s , t h e e s t i m a t e d p o r o s i t y of t h e aquifer material.
and t h e e x t e n t of t h e a q u i f e r .
P o r o s i t y i s t h e p e r c e n t a g e of
void s p a c e r e l a t i v e t o t h e t o t a l volume of t h e mass. 6 .3
HYDROGRAPH INTERPRETATION The s t r e a m f l o w hydrograph c o n t a i n s c o n s i d e r a b l e i n f o r m a t i o n about t h e hydrol-
ogy o f a b a s i n .
Highly-variable
d a i l y d i s c h a r g e s i n d i c a t e r a p i d r u n o f f and
l i t t l e i n f i l t r a t i o n , e s p e c i a l l y i f t h e mimimum f l o w s a r e p a r t i c u l a r l y low.
Very
uniform f l o w s throughout t h e y e a r a r e produced by b a s i n s on which much of t h e p r e c i p i t a t i o n r e a c h e s t h e w a t e r t a b l e on i t s way t o t h e stream. The hydrographs of F i g u r e 6.3 c o n t r a s t t h e r u n o f f p a t t e r n s of d r a i n a g e b a s i n s o n l y 50 m i l e s a p a r t .
R u n o f f s i n i n c h e s a r e a b o u t t h e same b u t t h e a n n u a l
Pig. 6.3. C o n t r a s t i n r u n o f f p a t t e r n s of s t r e a m s d r a i n i n g b a s i n s of d i f f e r e n t p e r m e a b i l i t y (From McGuinness, 1963).
124 v a r i a b i l i t y a s w e l l a s t h e d a i l y v a r i a b i l i t y i s much g r e a t e r on W i l d c a t Creek. According t o YcGuinness (1963) W i l d c a t Creek f l o w s f r om a b a s i n f l o o r e d w i t h clayey till.
The c r e e k r e s p o n d s q u i c k l y t o p r e c i p i t a t i o n a n d t h e n f a l l s o f f
r a p i d l y t o a low b a s e flow.
T i p p e c a n o e R i v e r d r a i n s a b a s i n i n much o f w h i c h
permeable sandy g r a v e l l y g l a c i a l outwash l i e s a t t h e s u r f a c e . a b s o r b s much of t h e p r e c i p i t a t i o n ,
This outwash
p r e v e n t i n g s h a r p f l o o d peaks and r e l e a s i n g
w a t e r s l o w l y t o m a i n t a i n a l a r g e r b a s e flow. The r e l a t i o n o f g r o u n d w a t e r t o s t r e a m f l o w c a n b e i m p l i e d b y s t u d y o f t h e s t r e a m hydrograph.
A t t h e end o f a l o n g p e r i o d o f f a i r w e a t h e r t h e f l o w i n a
s t r e a m u s u a l l y w i l l b e from ground w a t e r ( b u t i t w i l l b e l e s s t h a n t h e d i s c h a r g e from t h e ground-water body because o f e v a p o t r a n s p i r a t i o n ) .
Overland f l o w from a
heavy r a i n w i l l i n c r e a s e t h e f l o w i n t h e s t r e a m channel a s shown i n F i g u r e 6.4.
Fig. 6.4. Streamflow hydrograph showing t h e i n c r e a s e i n b a s e flow (Ground w a t e r d i s c h a r g e ) r e s u l t i n g from a storm. Some o f t h e w a t e r t h a t a r r i v e s r a t h e r q u i c k l y i n t h e c h a n n e l t r a v e l s by a s h a l l o w s u b s u r f a c e course:
i t may be r e g a r d e d a s ground w a t e r a l t h o u g h i t be-
longs i n a d i f f e r e n t c a t e g o r y than w a t e r i n t h e f o r m a t i o n s below t h e w a t e r table.
A n o t h e r p o r t i o n o f t h e r a i n f a l l i n f i l t r a t e s t o t h e g r o u n d w a t e r body,
r a i s i n g t h e w a t e r t a b l e , i n c r e a s i n g t h e head t o w a r d t h e s t r e a m , and t h u s i n c r e a s i n g t h e b a s e f l o w r a t e o v e r t h a t p r i o r t o t h e s t o r m a s shown i n F i g u r e 6.4. The p o r t i o n of s t r e a m f l o w d e r i v e d from ground w a t e r d u r i n g o r c l o s e l y f o l l o w ing a p e r i o d of overland runoff cannot b e e s t i m a t e d c l o s e l y .
However w a t e r -
t a b l e p r o f i l e s n e a r a s t r e a m d u r i n g changes i n s t r e a m s t a g e i n d i c a t e t h e d i r e c t i o n of ground-water
flow a t various times.
A s shown i n F i g u r e 6.5, t h e g r a -
d i e n t of t h e w a t e r t a b l e i s towards t h e s t r e a m when t h e s t r e a m s t a g e i s low. the stage r i s e s , the water-table
As
g r a d i e n t d e c r e a s e s and f i n a l l y r e v e r s e s , a t
which t i m e w a t e r from t h e s t r e a m f l o w s i n t o t h e banks.
A t t h e same t i m e ground
w a t e r t h a t o t h e r w i s e would have gone t o t h e s t r e a m i s b e i n g s t o r e d f u r t h e r inland.
As the stream s t ag e recedes t h e water t a b l e gr adi ent begins i t s r e t u r n
t o normal.
125
W
U
Q
13LAND SURFACE
0
11
-
-
9-
7-
51 I
I
I
I
HORIZONTAL DISTANCE, FEET
Ground w a t e r l e v e l s and flow d i r e c t i o n s d u r i n g t h e r i s i n g and f a l l i n g Fig. 6.5. s t a g e s of a s t r e a m ( A f t e r D a n i e l and o t h e r s , 1970). Two c o n c l u s i o n s can be drawn from t h i s .
F i r s t , t h e ground-water c o n t r i b u t i o n
t o s t r e a m f l o w d u r i n g a f l o o d r u n o f f becomes n e g a t i v e d u r i n g t h e r i s i n g s t a g e and l a t e r i n c r e a s e s above t h e p r e v i o u s b a s e flow a s t h e s t a g e d e c r e a s e s (Fig. 6.6). Second, t h e w a t e r s t o r e d n e a r t h e c h a n n e l d u r i n g t h e r i s e t a k e s some t i m e t o d r a i n away,
thus,
f o r some t i m e a f t e r t h e flood.
t h e s t r e a m f l o w r e c e s s i o n in-
c l u d e s d r a i n a g e b o t h from bank s t o r a g e and channel s t o r a g e i n a d d i t i o n t o aquif e r drainage.
In t h e e x a m p l e o f F i g u r e 6.5, t h e s t r e a m s t a g e w a s n o t h i g h e n o u g h t o i n u n da te the adjacent land surface. t h e i r channels,
When m a j o r f l o o d s i n u n d a t e l a r g e a r e a s along
t h e v e r t i c a l i n f i l t r a t i o n i s l a r g e and t h e r e s u l t a n t s t o r a g e in
t h e f l o o d p l a i n may c o n t r i b u t e t o s t r e a m f l o w f o r a long period.
126
Hydrograph showing ground w a t e r c o n t r i b u t i o n t o a s t r e a m d u r i n g a F i g . 6.6. r i s e i n streamflow. The above i n t e r p r e t a t i o n of t h e s t r e a m f l o w hydrograph d u r i n g and f o l l o w i n g a f l o o d i s h e l p f u l i n i d e n t i f y i n g t h o s e segments of a hydrograph which r e p r e s e n t only b a s e flow.
Such s e g m e n t s a r e u s e d t o d e f i n e b a s e - f l o w r e c e s s i o n c u r v e s
( S e c t i o n 5.6) and t o e s t i m a t e t h e ground-water
y i e l d t o a s t r e a m (Riggs,
1963).
O b v i o u s l y t h e r e c e s s i o n s h o r t l y a f t e r a h y d r o g r a p h r i s e may i n c l u d e d r a i n a g e from bank s t o r a g e b u t whether a r e c h a r g e of t h e p r i n c i p a l a q u i f e d s ) was assoc i a t e d w i t h a r i s e may be l e s s c l e a r .
A hydrograph l i k e t h a t of F i g u r e 6.4 d o e s
n o t always i n d i c a t e t h a t a r e c h a r g e occurred.
In F i g u r e 6.7,
t h e hydrograph f o r
t h e l a t t e r p a r t o f J u l y and t h e f i r s t h a l f o f A u g u s t d e f i n e s t h e s l o p e o f t h e base-flow
r e c e s s i o n curve.
An e x t e n s i o n of t h a t curve through September would
b e v e r y c l o s e t o t h e h y d r o g r a p h f o r m o s t o f t h a t month, i n d i c a t i n g t h a t t h e storm of l a t e August d i d n o t r e c h a r g e t h e a q u i f e r a p p r e c i a b l y .
v)
;f
500
z
JULY
AUG
SEPT
Fig. 6.7. Hydrograph f o r N.F. Obion River, b l e r e c h a r g e from t h e l a t e August storm.
Tennessee,
which i n d i c a t e s n e g l i g i -
The assumption t h a t r e c h a r g e o c c u r r e d from a s t o r m t h a t produced a p p r e c i a b l e d i r e c t r u n o f f c a n b e checked.
C o n s i d e r F i g u r e 6.8
(dashed) i n d i c a t e a p p r e c i a b l e r e c h a r g e i n May and June.
i n which t h e r e c e s s i o n s The volume of r e c h a r g e
i s t h e d i f f e r e n c e i n t h e volumes under t h e two r e c e s s i o n c u r v e s from some common d a t e t o such t i m e a s t h e curves reach n e g l i g i b l e discharges.
The Red R i v e r
127
5000 !
I
I
.
100
I
I
I
MAY
JUNE
I
I
i
JULY
Fig. 6.8. Hydrograph f o r Red River, Tennessee, 1955, which i n d i c a t e recharge from May and June storms.
showing r e c e s s i o n curves
r e c e s s i o n curve would drop from 500 c f s t o 1 c f s i n about 150 days. d i f f e r e n c e can be d e f i n e d g r a p h i c a l l y recession curve i s defined. respect t o the rainfall, i t i s not,
- or
The volume
m a t h e m a t i c a l l y i f t h e equation of t h e
The computed r e c h a r g e s h o u l d b e r e a s o n a b l e w i t h
t h e measured runoff, and t h e e s t i m a t e d evaporation.
If
t h e e s t i m a t e of t h e amount of base flow f o l l o w i n g ( o r preceding) t h e
r i s e i s incorrect.
I n t h e a b s e n c e of r a i n f a l l r e c o r d s one m i g h t a p p r a i s e
w h e t h e r t h e computed r e c h a r g e i s r e a s o n a b l e f o r t h e m a g n i t u d e of t h e r i s e i n streamflow.
Data f o r o t h e r r i s e s would be needed f o r t h i s t e s t :
see references
i n s e c t i o n 11.5.3.
A word o f w a r n i n g : t h e s t o r m h y d r o g r a p h o f a n e p h e m e r a l s t r e a m may l o o k s i m i l a r t o one f o r a s t r e a m w i t h a dependable ground-water c o n t r i b u t i o n .
Study
o f s u c h a h y d r o g r a p h f o r a few months w i l l show t h a t t h e a p p a r e n t i n c r e a s e i n b a s e f l o w f o l l o w i n g a p e a k i s n o t due t o r e c h a r g e o f a g r o u n d - w a t e r body: i t probably r e f l e c t s t h e d r a i n a g e from channel and bank storage. 6.4
BANK STORAGE IN SURFACE RESERVOIRS .The s t o r a g e c a p a c i t i e s of s u r f a c e r e s e r v o i r s a t v a r i o u s l e v e l s a r e defined by
topographic surveys. operations.
The r e s u l t i n g stage-capacity
curves a r e used i n r e s e r v o i r
But when some r e s e r v o i r s a r e f i l l e d f o r t h e f i r s t t i m e t h e y t a k e
c o n s i d e r a b l y more w a t e r t h a n i s i n d i c a t e d b y t h e s t a g e - c a p a c i t y later,
curve.
a r e d u c t i o n i n r e s e r v o i r s t a g e produces more w a t e r than expected.
And These
e f f e c t s a r e d u e t o t h e i n f i l t r a t i o n o f w a t e r i n t o t h e b a n k s of t h e r e s e r v o i r ( p r e s u m a b l y t h e p r o j e c t i n v e s t i g a t i o n a s s u r e d t h a t t h e g e o l o g i c s e t t i n g cont a i n e d nothing t h a t would p e r m i t s t o r e d w a t e r t o bypass t h e dam). Bank s t o r a g e below t h e o p e r a t i n g s t a g e of a r e s e r v o i r i s merely an a d d i t i o n t o dead sto r a g e .
B u t w i t h i n t h e o p e r a t i n g r a n g e bank s t o r a g e i s i n c r e a s e d
128 d u r i n g r i s i n g s t a g e s and i s d e c r e a s e d d u r i n g f a l l i n g s t a g e s .
The magnitude of
bank s t o r a g e changes may b e l a r g e enough t o b e taken i n t o account i n r e s e r v o i r operation.
F o r e x a m p l e , Simons a n d R o r a b a u g h (1971) c o m p u t e d t h e d e a d or i n -
a c t i v e a q u i f e r - s t o r a g e c a p a c i t y o f Hungry H o r s e R e s e r v o i r , Montana a s a b o u t 50.000
cfs-days.
and t h e a c t i v e c a p a c i t y about 100,000 cfs-days.
However,
the
a v a i l a b l e w a t e r f r o m a q u i f e r s t o r a g e d e p e n d s on t h e m a g n i t u d e of t h e s t a g e r e d u c t i o n and on t h e t i m e t h e s t a g e i s h e l d a t t h e l o w e r l e v e l :
complete d r a i n -
age from a bank a q u i f e r may t a k e months. 6.5
THE WATER RESOURCE Although t h e r e a r e many r e a s o n s f o r s t u d y i n g ground w a t e r and s u r f a c e w a t e r
separately,
one should r e c o g n i z e t h a t t h e t o t a l renewable w a t e r r e s o u r c e of a
b a s i n i n t h e flow of t h e s t r e a m a s i t l e a v e s t h e bazin.
The g r o u n d - w a t e r
r e s o u r c e i s i n c l u d e d i n t h e s t r e a m f l o w : any w i t h d r a w a l of ground w a t e r w i l l reduce streamflow.
B u t t h e two r e s o u r c e s a r e i n d e p e n d e n t , o r n e a r l y so, i n
r e g i o n s where t h e w a t e r t a b l e i s below s t r e a m c h a n n e l s and i s n o t a f f e c t e d by i n f i l t r a t i o n from t h e streams. able:
Here o n l y t h e s u r f a c e w a t e r r e s o u r c e i s renew-
t h e ground w a t e r r e s o u r c e i s not.
Within a b a s i n i t i s p o s s i b l e t o p r o v i d e a more dependable s u p p l y by u t i l i z i n g s t o r a g e o f w a t e r i n t h e g r o u n d i f t h e s t o r a g e a q u i f e r i s n o t c l o s e l y conn e c t e d ( i n t i m e ) t o a stream.
Then w i t h d r a w a l s of ground w a t e r w i l l n o t reduce
streamflow d u r i n g t h e low-water period. supplement low s t r e a m f l o w s ;
Conjunctive u s e i s a management t o o l t o
i t does n o t change t h e t o t a l supply.
O t h e r a c t i v i t i e s o f man i n w h i c h g r o u n d w a t e r n e e d s t o b e c o n s i d e r e d a r e channel deepening,
which may provide a b e t t e r c o n n e c t i o n t o an a q u i f e r :
raising
a r i v e r l e v e l b y dams, w h i c h r a i s e s t h e l e v e l of t h e a d j a c e n t w a t e r t a b l e : d i v e r s i o n of s t r e a m f l o w from a l o s i n g stream, ground-water
recharge:
which may reduce t h e downstream
and r o u t i n g o f r e s e r v o i r r e l e a s e s down a channel where
the w a t e r t a b l e i s i n c o n t i n u i t y w i t h the stream.
Moench. S a n e r a n d J e n n i n g s
(1974) f o u n d t h a t r e s u l t s o f r o u t i n g r e s e r v o i r r e l e a s e s w e r e a p p r e c i a b l y i m proved by i n c l u s i o n of a gross s i m p l i f i c a t i o n of t h e ground-water
system.
RPPERENCES D a n i e l , J.F., C a b l e , L.W., and Wolf, R.J., 1 9 7 0 , Ground w a t e r - s u r f a c e w a t e r r e l a t i o n d u r i n g p e r i o d s o f o v e r l a n d f l o w : U.S. Geol. S u r v e y P r o f . P a p e r 700-B, p. 219-223. 1977. Streamflow t r a n s m i s s i o n l o s s e s i n w e s t e r n Kansas: Jordan, P.R., t h e H y d r a u l i c s D i v i s i o n , ASCE, Vol. 1 0 3 , No. HY8, p. 905-919.
Jour. of
K i l p a t r i c k , F.A., 1964, Source of base flow of s t r e a m s : I n t e r n a t i o n a l Assoc. of S c i e n t i f i c Hydrology Publ. No. 63, Berkeley, p. 329-339. McGuinness, C.L., 1 9 6 3 , The r o l e o f g r o u n d w a t e r i n t h e n a t i o n a l w a t e r s i t u a tion: U.S. Geol. Survey Water-Supply 1800, 1121 p.
-
129 Moench, A.P., S a n e r , V.B., and J e n n i n g s , M.E., s t r e a m f l o w by channel loss and base flow: 10, No. 5, p. 963-968.
1974, M o d i f i c a t i o n o f r o u t e d Water Resources Research, Vol.
R i g g s , H.C., 1963, The b a s e - f l o w r e c e s s i o n c u r v e a s a n i n d i c a t o r o f ground water: I n t e r n a t i o n a l Assoc. of S c i e n t i f i c Hydrology P u b l . NO. 63, Berkeley, p. 352-363.
Simons, W.D. and Rorabaugh, M.I., 1971, Hydrology of Hungry Horse R e s e r v o i r , n o r t h w e s t e r n Montana: U.S. Geol. Survey Prof. Paper 682.
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131
Chapter 7
FLOW CHARACTERISTICS AT UNGAGED SITES
7.1
INTRODUCTION Although hydrologic data have b e e n collected at thousands o f sites, those
sites constitute only a small sample of the sites where flow characteristics may be needed.
The information at gaged sites permits the calibration of various
procedures for transferring flow characteristics to ungaged sites or estimating them from rainfall.
Methods are categorized into ones that require drainage-
basin and climatic characteristics obtainable from maps and climatic records, and those that require a s m a l l amount of data to be collected at the site of interest.
I .2
NO DATA AT SITE
I .2.1
Regression analysis
Regional analysis of streamflow characteristics is a widely applicable and fairly simple method.
Using data at gaging stations, a flow characteristic is
related to basin and climatic characteristics, usually by multiple regression. An example is log Q25 = -2.07 + 0.97 log A + 2.11
log P
(1)
where Q25 is the 25-year flood in cfs in the Snohomish River basin, Washington:
A is drainage area in square miles; .and P is m e a n annual precipitation in inches.
The equation is in a linear form, a requirement of the usual regression
method.
It may be transformed to
QZ5 = 0.0085
AoSg1 P2*11
(2)
F o r a stream site in the S n o h o m i s h River b a s i n QZ5 can be e s t i m a t e d f r o m the equation using drainage area measured above the site, and the mean annual rainfall on that drainage area from an isohyetal map.
The reliability of the result
is indicated by the standard error of the regression, 0.14 log units, w h i c h corresponds to +38 and -28 percent. Multiple regression is directly useful as a regionalization tool because the discharge for a given frequency level can be related to basin characteristics, leaving residuals that may be considered as due to chance. averages these residuals.
The regression line
Thus, in one operation, the effects of differing
basin characteristics are preserved and the chance variation is averaged.
132 The r e g r e s s i o n model used s h o u l d a p p r o x i m a t e t h e p h y s i c a l p r o c e s s a s c l o s e l y a s p o s s i b l e and i t must be i n a l i n e a r form.
The l o g - l i n e a r f o r m i s s u i t a b l e
f o r many h y d r o l o g i c r e l a t i o n s b u t i t s h o u l d n o t be a c c e p t e d b l i n d l y .
Graphical
m u l t i p l e r e g r e s s i o n i s a good way t o d e f i n e t h e s u i t a b l e m o d e l ; a g r a p h i c a l s o l u t i o n need n o t b e l i n e a r ,
F i g u r e 7.1
however.
u s i n g t h e d a t a on which eq. 1 was based.
shows t h e g r a p h i c a l s o l u t i o n
This confirms t h a t the r e l a t i o n s with
A and P a r e l o g l i n e a r and t h a t t h e form of eq. 1 i s a p p r o p r i a t e € o r t h e s e data. The e q u a t i o n o f t h e g r a p h i c a l r e l a t i o n o f F i g u r e 7.1- i s v i r t u a l l y t h e s a m e a s e q u a t i o n 1.
100,000
1
-
10
n
Z
0 U
"/
I
Y
m p:
u a
=;
10,000-
LL Y
vm 3 U
? a O
9
1000-
'
Y
-i
0
25
EXPLANATION o Plotted point
0 47
50
100
300
M E A N ANNUAL
i
053
,
IL
1
PRECIPITATION, I N INCHES
'
Point a d j u s t e d I
for P 100' 1
1
1
10
100
i
1 1000
D R A I N A G E AREA, IN SQUARE M I L E S
Fig. 7 . 1
G r a p h i c a l a n a l y s i s of d a t a used t o d e f i n e e q u a t i o n 1.
I f a g r a p h i c a l m u l t i p l e r e g r e s s i o n i s developed on a r i t h m e t i c g r a p h p a p e r , r a t h e r than on l o g paper, and i s found t o be l i n e a r t h e model i s Y = a
+ blXl + b2X2
(3)
and t h e s t a n d a r d e r r o r i s i n u n i t s o f Y. sometimes s t a t e d i n p e r c e n t of mean Y ; from t h e mean.
S t a n d a r d e r r o r u s i n g t h i s model i s
the percentage increases w i t h d i s t a n c e
See s e c t i o n 4.4.1.
I n model e q u a t i o n 3 t h e e f f e c t s of t h e v a r i a b l e s a r e a d d i t i v e whereas i n t h e model used i n e q u a t i o n 1 t h e e f f e c t s a r e m u l t i p l i c a t i v e .
I f a v a r i a b l e can t a k e
a v a l u e of z e r o t h e n t h e l o g - l i n e a r model c a n n o t be used w i t h t h a t v a r i a b l e because z e r o does n o t have a r e a l l o g a r i t h m .
T h i s l i m i t a t i o n can be overcome by
133 adding a small constant, commonly 1 or 0.1, using the variable in regression.
to all values of the variable before
Before doing this the analyst should assure
himself that the addition will not violate the concepts used. The independent variables selecred for use in the regression analysis should be ones that can be readily quantified at ungaged sites and that are postulated to have a particular effect on the dependent variable (the flow characteristic). Selection of independent variables is often made on a statistical basis;
that
is, m a n y variables are used in p r e l i m i n a r y regressions and those that l a c k statistical significance are discarded.
This approach occasionally results in
retention of a variable whose effect on the dependent variable does not conform to hydrologic principles.
Usually the effect of such a variable is trivial.
It
s e e m s better to select in advance those variables w h i c h are expected to h a v e practical significance tical selection.
-
to rely on hydrologic judgment rather than on statis-
However, a variable that is known to affect a flow character-
istic in a particular way may not be statistically significant in a regression if the range of that variable in the s a m p l e is small.
Channel slope as a n
estimator of flood characteristics is an example of a variable that has little range in some regions. Some variables such as basin storage, channel slope, and storm magnitudes are appropriate for estimating flood characteristics but have little effect on mean flow.
Mean flow in humid regions of homogeneous geology is closely related to
drainage area and mean annual precipitation. Not all important variables c a n be quantified f r o m maps. desirable or necessary to use surrogates.
It is s o m e t i m e s
Occasionally the regression coeff i-
cient of a variable selected on a hydrologic basis appears to represent something other than that intended.
For example, consider the relation of 50-year
flood to drainage area and percent of area forested, P50 = 6.03 for California mountain streams.
For this region of large topographic relief
the regression indicates that an increase in percent area forested will produce an increase in 50-year flood, contrary to expectation.
But examination of maps
shows that forest cover increases with elevation, and presumably with precipitation.
Thus forest cover may be a surrogate for precipitation.
Although surro-
gate variables are useful, extrapolation of a regression equation which includes surrogates may produce questionable results.
The applicability of a regression equation to ungaged streams in the region for w h i c h it w a s derived depends on h o w w e l l the data used i n its derivation cover the ranges of variables in the region, and whether the variables used are adequate descriptors of the flow characteristic at all of the streams to which the regression equation might be applied.
134 If more than one regression equation is derived for a single flow characteristic, the equation with the smallest standard error is commonly used.
However,
one with fewer variables or with only those variables that are easy to quantify at an ungaged site may be selected if its standard error is not appreciably greater than the smallest standard error obtained.
There lray be no practical
difference in the results from two equations whose standard errors differ considerably. Only equations in which all the regression constants are statistically significant should be considered.
Computer programs for regression analysis either
produce regression equations which include only those variables whose effects or they show
are statistically significant at the specified level (usually 95%). the statistical significance of each variable in the equation.
Regression on basin characteristics produces best results in humid regions of fairly uniform terrain and gradual areal changes in precipitation.
The method
is not generally useful for estimating low flows because of the large influences of basin geology and evapotranspiration on those flows.
Among the factors that
limit the method are (1) large interchanges of surface and ground water due to geologic conditions, ( 2 ) large ranges in elevation in the basins, and the corresponding large range in basin precipitation, (3) poor definition of precipitation in arid regions, and (4) flow modification due to man's activities. Regression equations and their standard errors are given for many flow characteristics in four regions of the United States by Thomas and Benson (1970). 7.2.2
From rainfall
Techniques for estimating flood-peak characteristics from rainfall are discussed in Chapter 8 . Rainfall ordinarily is not a major indicator of low-flow characteristics. Mean flows of ungaged streams may be approximated from an isohyetal map if
(1) flow records from some basins in the region are available to develop a calibration, (2) the isohyetal map is based on precipitation records (someisohyetal maps are based partly on streamflow records) and (3) the geology of the region is more or less homogeneous.
In regions of high relief and the
consequent high range in precipitation from the upper to the lower part of the basin,
a
runoff-altitude relation can be developed by trial-and-error from gaged
records, even in the absence of precipitation records (Riggs
6
Moore, 1965).
This relation can be used to estimate mean flow from the measured areas in each of several elevation ranges of an ungaged basin; the sum of these partial runoffs is the runoff from the ungaged basin. 7.2.3
Interpolation along a channel
Interpolation of flow characteristics between gaged points on a stream usually produces more reliable results than regression on basin characteristics.
The
13 5 flow characteristics a r e plotted against channel length (Fig. 7.2); points of interest c a n be readily identified on the g r a p h by their relation to a gaged point.
A method of interpolating low flows is given in Chapter 9.
See Chapter
8 for another example of the method applied to floods.
I
200,000 -
1
I
I
I
1
I
I
1
I
I
100.000 50,000 -
10,000 -
5000 2000 1000
Fig. 7.2. 7.3
Flow characteristics along the main stem of James River, Virginia.
SOME DATA AT SITE
F l o w characteristics in s o m e regions are not closely related to variables that can be obtained from maps, the usual variables cannot be quantified reliably, or a s i m p l e regression m o d e l does not explain t h e relation.
In arid and
semarid regions precipitation is highly variable in time and space, extent of s t o r m s is o f t e n limited, and w e a t h e r records are few.
the areal
In basins of
large topographic relief, precipitation in the headwaters may be 4 or 5 times that in the l o w e r reaches; a b a s i n average w o u l d be a poor indicator of flow characteristics.
When topographic and ground-water divides are not coincident
the runoff f r o m a b a s i n m a y be more, or less, than that indicated by basin precipitation.
For example,
the annual runoffs of two adjacent streams in the
h e a d w a t e r s of U m p q u a River, Oregon, are 3 3 and 5 4 inches; the difference is largely due to interbasin movement of ground water.
Some drainage basins in-
clude areas that do not contribute surface runoff or that contribute only occasionally. reliably.
The contributing drainage area for such a basin cannot be defined And the efficiency with which a stream system transmits water depends
136 b o t h on geology and on topography n e i t h e r of which c a n be a d e q u a t e l y e x p r e s s e d by s i m p l e v a r i a b l e s i n some regions.
A consequence of one o r more of t h e s e c o n d i t i o n s i s t h a t mean f l o w or f l o o d p e a k s on some s t r e a m s d e c r e a s e w i t h i n c r e a s i n g d r a i n a g e a r e a .
A regression
model c a n n o t b e d e v i s e d t h a t w i l l a p p l y t o a r e g i o n i n w h i c h some s t r e a m s e x h i b i t t h i s anomalous c h a r a c t e r i s t i c . Flow c h a r a c t e r i s t i c s of s t r e a m s i n t h e s e t t i n g s d e s c r i b e d above u s u a l l y c a n be e s t i m a t e d more r e l i a b l y from some i n f o r m a t i o n a t t h e s i t e t h a n from informat i o n t a k e n f r o m maps or c l i m a t o l o g i c a l r e c o r d s .
D i s c h a r g e m e a s u r e m e n t s and
measurements of channel geometry a r e t h e most u s e f u l s i t e d a t a . 7.3.1
Mean flow from monthly measurements
Where mean f l o w i s n o t c l o s e l y r e l a t e d t o d r a i n a g e a r e a , B i g g s ( 1 9 6 9 ) h a s shown t h a t r e l i a b l e e s t i m a t e s i n some r e g i o n s can be made from monthly d i s c h a r g e measurements f o r a year. F i g u r e 7.3.
The prooedure i s d e m o n s t r a t e d i n t h e r e g i o n shown i n
The p l o t o f F i g u r e 7.4
establishes that drainage area is not a
u s e f u l e s t i m a t o r of mean f l o w i n t h i s region.
49"
--------I---
I
ALBERTA
MONTANA /---
0~
/
...
-
0
46" 113"
F i g . 7.3.
I
20
40
6 0 MILES
t-
109"
P a r t o f M i s s o u r i River b a s i n showing l o c a t i o n s of gaging s t a t i o n s .
lo00
/// I
I
5
1
li
13
F i g . 7.4.
137
R e l a t i o n o f mean flow t o d r a i n a g e a r e a a t gages shown i n F i g u r e 7.3.
B o t h a n e x p l a n a t i o n a n d a v e r i f i c a t i o n o f t h e m e t h o d a r e p r o v i d e d by u s i n g d a t a f r o m two g a g e d s t r e a m s , o n e o f w h i c h , Two M e d i c i n e C r e e k (number 7) i s c o n s i d e r e d ungaged.
C u t Bank C r e e k (number 9 ) i s u s e d a s t h e i n d e x s t a t i o n .
Assume t h a t t h e d i s c h a r g e s of Two Medicine Creek on t h e 1 5 t h of each month a r e e q u i v a l e n t t o what would have been measured on t h o s e days.
The c o n c u r r e n t d a i l y
d i s c h a r g e s and t h e monthly means of Cut Bank Creek would be a v a i l a b l e from t h e record.
T h e s e t h r e e i t e m s o f d a t a a r e l i s t e d i n T a b l e 7.1.
Although t h e
o b j e c t i v e o f t h i s t e c h n i q u e i s t o e s t i m a t e a n n u a l f l o w , t h i s i s o b t a i n e d by e s t i m a t i n g and summing monthly d i s c h a r g e s . The p l o t o f c o n c u r r e n t midmonth d i s c h a r g e s o f t h e two s t r e a m s shows t h a t t h e r e l a t i o n ch an g es a t l e a s t monthly.
i n F i g u r e 7.5
These changes a r e due t o
d i f f e r e n c e s i n t h e t i m i n g o f snowmelt and t o a p a t t e r n of m ont hl y d i v e r s i o n s from Two Medicine Creek,
ranging from z e r o t o o v e r 10,000 a c r e - f e e t ,
r e a s o n a b l y c o n s i s t e n t from y e a r t o year.
which i s
Obviously a l i n e a v e r a g i n g t h e p o i n t s
of F i g u r e 7.5 would n o t be a r e a s o n a b l e b a s i s f o r e s t i m a t i o n . The Riggs method u s e s a d i f f e r e n t r e l a t i o n o f u n i t s l o p e f o r each month, p o s i t i o n d e t e r m i n e d by t h e p l o t t e d point.
its
The dashed l i n e through p o i n t 10 on
F i g u r e 7.5 i s t h e r e l a t i o n used f o r t r a n s f e r r i n g t h e October monthly mean of Cut Bank C r e e k t o g e t t h e Two M e d i c i n e C r e e k e s t i m a t e . necessary:
Graphical t r a n s f e r is not
t h e monthly mean flow of Two Medicine Creek u s u a l l y i s o b t a i n e d by
m u l t i p l y i n g t h e measured monthly mean flow of Cut Bank Creek by t h e r a t i o of t h e midmonth d i s c h a r g e s .
R e s u l t s a r e shown i n T a b l e 7.1 a l o n g w i t h t h e m e a s u r e d
v a l u e s f o r comparison.
Some of t h e monthly e s t i m a t e s a r e c o n s i d e r a b l y i n e r r o r
b u t t h e annual mean i s l e s s t h a n 6 p e r c e n t from t h a t measured.
138 TABLE 7.1
Data and results of computing annual mean flow from monthly measurements
Date
Daily mean discharge. cfs
~~
Two Medicine Creek
Month
~
~~
Monthly mean discharge, cfs
Cut Bank Creek
Cut Bank Creek
Two Medicine Creek Computed Measured
lO/l5/60 11/15 12/15 11 15/61 2/15 3/15 4/15 51 15 6/15 7/15 8/15 9/15
36 26 44 30 65 72 82 332 470 164 74 42
244 56 50 40 50 156 175 978 8 50 82 50 85
10 11 12 1 2 3 4 5 6 7 8 9
32.6 28.5 26 .O 23.9 48.3 67 .O 94.2 47 1 509 148 58.6 40.7
Annual mean, 1961 water year
129
220 61 30 32 37 140 200 1040 920 74 40 82
55.3 58.2 36.1 29.5 82.2 128 23 1 1211 1010 114 22.6
240
254
60.5
1000
300
100
30
20
I
I
I
I
50
100
200
500
CUT BANK CREEK
Fig. 7.5.
Concurrent mid-month discharges, in cfs, from Table 7.1.
The final step in this procedure is to relate annual means for 1961 to means of record for s t r e a m s i n the area, to define a m e a n relation line (Figure 7.6) and to transfer the estimated 1961 mean of 240 through that relation to get an
139 e s t i m a t e of t h e long-term
mean f o r Two Medicine Creek.
The long-term
mean of
430 c f s , a s e s t i m a t e d by t h i s method, compares f a v o r a b l y w i t h 385 c f s based on 31 y e a r s of record. T h i s m e t h o d is a p p l i c a b l e t o s t r e a m s i n r e g i o n s w h e r e f l o w i s p r i n c i p a l l y from snowmelt o r from ground w a t e r , o r where s t o r m s c o v e r l a r g e a r e a s .
1000 I
I
I
lool
1
1
P/
1
10 4
1
10
100
1000
MEAN FLOW, 1961 WATER YEAR
Fig. 7.6. R e l a t i o n of 1961 mean f l o w s t o mean f l o w s of r e c o r d i n c f s . a t gaging s t a t i o n s i n F i g u r e 7.3 ( e x c e p t gage 7). 7.3.2
Low-flow c h a r a c t e r i s t i c s from base-flow
measurements
The p r o c e d u r e i s d e s c r i b e d i n Chapter 9. 7.3.3
Flow c h a r a c t e r i s t i c s from channel s i z e
Channel morphology s t u d i e s have shown c o n s i s t e n t r e l a t i o n s between d i s c h a r g e and t h e c o r r e s p o n d i n g width,
depth,
and v e l o c i t y i n n a t u r a l channels,
partic-
u l a r l y a t or n e a r b a n k f u l l s t a g e ( L e o p o l d , Wolman, a n d M i l l e r , 1 9 6 4 ) .
The
g e o m e t r y o f t h e c h a n n e l o f a n a t u r a l s t r e a m i s t h o u g h t t o b e d e v e l o p e d by discharges near bankfull. geometry,
Thus b a n k f u l l d i s c h a r g e should b e r e l a t e d t o channel
s u b j e c t o f c o u r s e t o v a r i a t i o n s d u e t o t h e t y p e s o f bed and b a n k
m a t e r i a l i n which t h e channel i s formed and t o t h e s e d i m e n t load. Flood c h a r a c t e r i s t i c d i s c h a r g e s a t v a r i o u s r e c u r r e n c e i n t e r v a l s have been shown t o be r e l a t e d t o channel width.
A common r e l a t i o n is
Q=aWn w h e r e Q i s a f l o o d c h a r a c t e r i s t i c , W is c h a n n e l w i d t h , and a and n a r e c o e f f i cients.
140 Channel geometry representative of flood characteristics occurs only in certain stream reaches. A straight, narrow reach is best.
The bed and banks
should be stable but should be of a material that has permitted the channel to develop to a size just adequate to handle the flow regimen.
Most reaches
suitable for slope-area measurements would be suitable for channel-geometry measurements.
Proper selection of the cross section and of the level within the
cross section at which the width is measured is critical to success.
In
meandering channels the most restricted section is just downstream from a bend. The level at which the width is measured is defined by channel features. Two levels are widely used; they identify the active-channel section and the wholechannel section (Fig. 7.7).
The width of the active-channel section is a
within-channel dimension represented by (1) the width of the low-water channel, ( 2 ) the distance between within-channel bars, or ( 3 ) the distance between annual
vegetation lines.
FLOOD
WHOLE-CHANNEL WIDTH ACTIVE-CHANNEL
Fig. 7.7.
Idealized stream cross section showing two width measurements.
The reference level for the whole-channel section is variously defined by breaks in bank slope, by the edg,es of the flood plain or by the lower limits of permanent vegetation. In perennial streams the whole-channel width is the width at bankfull stage.
In ephemeral streams a flood plain may not exist.
Width
measurements are shown in Figures 7 8 and 7.9. To define a calibration, flood characteristics from gaging-station or creststage-gage records are plotted on log paper against the corresponding channel widths measured near the gaged sites a s in Figure 7.10.
Relations of 10-year
flood to width generally differ for perennial and for ephemeral streams because of the differing channel shapes.
And even among perennial streams the channel
shapes differ according to the material in which the channels have developed.
An index of channel shape such a s some function of depth may appreciably improve the calibration if a wide range of shapes are included in the sample. Channel shape is also a function of bed and bank material, and indices of these may be used (Osterkamp, 1977). Channel geometry has also been used for estimating mean streamflow (Hedman,
1970).
A relation between channel size and mean flow presumably exists because
141
Fig. 7.8.
Whole-channel width of a perennial stream is shown by the tape.
Fig. 7 . 9 .
Measuring active-channel width of an ephemeral stream.
of a relation of mean flow to flood Characteristics; such a relation for perennial streams obviously would not hold for ephemeral streams. graphical area of applicability of
a
Thus, the geo-
relation for estimating mean flow from
channel width would be much more limited than one for estimating flood-peak characteristics.
142
20 z d
1000 i
0 0 _1
U
100
:
W
t
10
1
100
1000
WHOLE-CHANNEL WIDTH, IN FEET
F i g . 7.10. R e l a t i o n o f 1 0 - y e a r f l o o d t o c h a n n e l w i d t h f o r s t r e a m s i n Owyhee County, Idaho (From Riggs and Harenberg, 1976). The r e l i a b i l i t y of a f l o o d e s t i m a t e made by t h e channel-geometry
method a t an
ungaged s i t e depends p r i n c i p a l l y on t h e s t a n d a r d e r r o r of t h e c a l i b r a t i o n and on t h e r e l i a b i l i t y of t h e w i d t h measurement a t t h e s i t e .
Wahl (1977) d e s c r i b e d a
t e s t t o d e t e r m i n e t h e r e l i a b i l i t y of measurements o f channel w i d t h ;
seven i n d i -
v i d u a l s i n d e p e n d e n t l y v i s i t e d 22 s i t e s and measured c h a n n e l d i m e n s i o n s f o r 3 d i f f e r e n t r e f e r e n c e l e v e l s i n s e c t i o n s o f t h e i r own choosing.
Wahl a t t r i b u t e d
an a v e r a g e s t a n d a r d e r r o r f o r d i s c h a r g e o f a b o u t 30 p e r c e n t t o d i f f e r e n c e s i n w i d t h measurements alone.
Combining t h a t w i t h an assumed 40 p e r c e n t c a l i b r a t i o n
s t a n d a r d e r r o r ( l o w e r t h a n m o s t ) g i v e s a 50 p e r c e n t s t a n d a r d e r r o r of t h e discharge estimate. E s t i m a t i n g r e l a t i o n s a p p l i c a b l e t o many r e g i o n s of w e s t e r n United S t a t e s have been p u b l i s h e d ,
f o r example s e e Hedman and Osterkamp (1982).
In g e n e r a l t h e s e
r e l a t i o n s a r e f o r r e g i o n s i n which f l o w c h a r a c t e r i s t i c s a r e n o t c l o s e l y r e l a t e d t o d r a i n a g e area.
The channel-geometry method i s a p p l i c a b l e t o most s t r e a m s b u t
i t s u s e i s recommended o n l y w h e r e b a s i n c h a r a c t e r i s t i c s a r e p o o r i n d i c a t o r s . B e t t e r e s t i m a t e s of flood c h a r a c t e r i s t i c s u s u a l l y can be obtained from b a s i n c h a r a c t e r i s t i c s i n humid r e g i o n s .
A d i s a d v a n t a g e of t h e channel-geometry
method
i s t h e need f o r a channel measurement n e a r t h e s i t e where t h e f l o w c h a r a c t e r i s t i c i s needed.
See s e c t i o n 8.10.3
f o r a way of reducing t h e f i e l d work r e q u i r e d
t o apply t h e technique. A p p l i c a t i o n s and l i m i t a t i o n s of t h e channel-geometry p u b l i s h e d r e p o r t s a r e g i v e n by Riggs (1978).
method and r e f e r e n c e s t o
See a l s o Wahl (1984).
143 REFERENCES Hedman, E.R. 1970. Mean annual runoff as related to channel geometry in selected streams in California: U.S. Geol. Survey Water-Supply Paper 1999-E. Bedman, E.R. and Osterkamp, W.R., 1982, Streamflow characteristics related to channel geometry of streams in western United States: U.S. Geol. Survey Water-Supply Paper 2193, 17 p. Leopold, L.B., Wolman, M.G., and Miller, J.P., morphology: San Francisco, W.E. Freeman
1964, Fluvial processes in geoCo., 522 p.
6
Osterkamp, W.R., 1977, Effect of channel sediment on width-discharge relations. with emphasis on streams in Kansas: Kansas Water Resources Board Bull. NO. 21, 25 p. Riggs, EC.. 1969, Mean streamflow from discharge measurements: Bull. of International Assoc. of Scientific Hydrology, Vol. XIV, No. 4, p. 95-110. Riggs, H.C., 1978, Streamflow characteristics from channel size: Journal Of Hydraulics Division, ASCE, Vol. 104, No. E l , January 1978, p. 87-96. Riggs, E.C. and Moore, D.O., 1965, A method of estimating mean runoff from ungaged basins in mountainous regions: U.S. Geol. Survey Prof. Paper 525D, p. 199-202. Thomas. D.M. and Benson, M.A., 1970, Generalization of streamflow characteristics from basin characteristics: U.S. Geol. Survey Water-Supply Paper 1975. 55 p. Wahl, K.L., 1977, Accuracy of channel measurements and the implications o n estimating streamflow characteristics: Jour. Research, U.S. Geol. Survey, Vol. 5, NO. 6, p. 811-814. Wahl, K.L., 1984, Evaluation of the use of channel cross section properties for estimating s treamflow characteristics: U.S. Geol. Survey Water-Supply Paper 2262, p. 53-66.
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145
Chapter 8
FLOOD-FREQUENCY ANALYSES
8.1
INTRODUCTION The p r i n c i p l e s g i v e n i n s e c t i o n s 4. 5 , a n d
I
f o r d e f i n i n g t h e magnitude-
frequency r e l a t i o n s of streamflow c h a r a c t e r i s t i c s . i l l u s t r a t e d by a p p l i c a t i o n s t o f l o o d s .
b o t h gaged and ungaged.
were
But t h e v a l u e of r e l i a b l e f l o o d informa-
t i o n and t h e r a n g e of problems a s s o c i a t e d w i t h g e t t i n g t h a t i n f o r m a t i o n j u s t i f y a more d e t a i l e d d i s c u s s i o n . 8 .2
ANNUAL FLOODS An a n n u a l f l o o d i s t h e h i g h e s t p e a k d i s c h a r g e d u r i n g a y e a r .
Most f l o o d -
f r e q u e n c y a n a l y s e s a r e concerned w i t h e s t i m a t i n g t h e c h a r a c t e r i s t i c s of a n n u a l floods.
I n d i v i d u a l s t h a t make up a p o p u l a t i o n s h o u l d b e i n d e p e n d e n t o f e a c h
o t h e r and s h o u l d o c c u r randomly i f a sample from t h a t p o p u l a t i o n i s t o p r o v i d e a r e a s o n a b l e e s t i m a t e of t h e frequency c h a r a c t e r i s t i c s .
Annual f l o o d s u s u a l l y
m e e t t h e f i r s t r e q u i r e m e n t , b u t s h o r t r e c o r d s o f f l o o d s t e n d t o b e made up of nonrandom e v e n t s b e c a u s e t h e c a u s a t i v e m a j o r s t o r m s a r e n o t randomly d i s t r i b u t e d i n time.
8.3
FLOODS ABOVE A BASE
An o b j e c t i o n t o t h e use o f t h e annual f l o o d s e r i e s i s t h a t t h e second h i g h e s t f l o o d i n some y e a r s i s h i g h e r t h a n t h e a n n u a l f l o o d s f o r o t h e r y e a r s b u t i t i s n o t c o n s i d e r e d ’ i n d e f i n i n g t h e frequency curve.
l l i s o b j e c t i o n can be r e s o l v e d
by u s i n g a l l i n d e p e n d e n t f l o o d s a b o v e a n a r b i t r a r y b a s e d i s c h a r g e d u r i n g t h e p e r i o d of record. partial-flood
These f l o o d s a r e c a l l e d t h e p a r t i a l - d u r a t i o n
series,
o r f l o o d s above t h r e s h o l d .
series, the
The b a s e d i s c h a r g e i s s e l e c t e d
so t h a t s e v e r a l p e a k s w i l l q u a l i f y i n most y e a r s .
Only t h o s e p e a k s t h a t a r e
r e a s o n a b l y independent of each o t h e r s h o u l d b e i n c l u d e d ; i n d e p e n d e w e i s assumed i f t h e p e a k s a r e w i d e l y s e p a r a t e d i n t i m e and by a s u b s t a n t i a l r e c e s s i o n i n discharge.
8.4
ANNUAL AND PARTIAL-DURATION FREQUENCY CURVES F r e q u e n c y c u r v e s b a s e d on t h e a n n u a l s e r i e s a n d on t h e p a r t i a l - d u r a t i o n
s e r i e s a r e s i m i l a r a b o v e a r e c u r r e n c e i n t e r v a l o f a b o u t 10 y e a r s ( F i g . 8.1). The t h e o r e t i c a l r e l a t i o n between t h e two f r e q u e n c y c u r v e s wns d e m o n s t r a t e d b y Langbein (1949).
E m p i r i c a l r e l a t i o n s a p p r o x i m a t e t h e t h e o r e t i c a l one b u t i n d i -
c a t e some g e o g r a p h i c v a r i a t i o n . The f r e q u e n c y c u r v e of
annual f l o o d s i s used f o r d e f i n i n g t h e p r o b a b i l i t i e s
of f l o o d s t h a t a r e exceeded i n f r e q u e n t l y .
F o r p r o b a b i l i t i e s o f l e s s t h a n 0.10
146 ( r e c u r r e n c e i n t e r v a l s g r e a t e r t h a n 1 0 y e a r s ) e i t h e r t h e annual or t h e p a r t i a l d u r a t i o n f r e q u e n c y c u r v e c o u l d b e used b u t a n n u a l f l o o d s a r e more r e a d i l y a v a i l a b l e t h a n f l o o d s above a b a s e so t h e annual c u r v e i s more w i d e l y used.
1.1
2
5
10
50
100
RECURRENCE INTERVAL, IN YEARS
F i g . 8.1. Annual a n d p a r t i a l - d u r a t i o n f l o o d - f r e q u e n c y n e a r St. Regis, Montana. The p a r t i a l - d u r a t i o n
c u r v e s f o r C l a r k Fork
f r e q u e n c y c u r v e i s used f o r e v a l u a t i n g r i s k f o r a p e r i o d
of a few y e a r s or where a l l ex ceed an ces a r e of i n t e r e s t , n o t j u s t t h e l a r g e s t one o f t h e y e a r . FITTING ANNUAL FREQUENCY CURVES
8.5
G r a p h i c a l f r e q u e n c y a n a l y s i s i s d e s c r i b e d i n s e c t i o n 4.
I n t e r p r e t a t i o n of
t h e p l o t t e d p o i n t s by drawing a mean l i n e i s somewhat s u b j e c t i v e , p a r t i c u l a r l y a t the high recurrence i n t erv als .
RI
=
The Weibull p l o t t i n g formula,
(n+l)/m.
commonly used f o r t h e annual s e r i e s a l s o h a s been used f o r t h e p a r t i a l - d u r a t i o n series.
The n u m b e r o f y e a r s o f r e c o r d , n, i s t h e same f o r b o t h s e r i e s .
a n n u a l s e r i e s t h e o r d e r n u m b e r , m. r a n g e s f r o m one t o n. duration series,
In t h e
But i n t h e p a r t i a l -
m w i l l t a k e v a l u e s much g r e a t e r t h a n n ; t h u s t h e f o r m u l a
produces some r e c u r r e n c e i n t e r v a l s l e s s t h a n one which cannot b e i n t e r p r e t e d a s t h e r e c i p r o c a l of p r o b a b i l i t y .
The a b s c i s s a s c a l e f o r a p a r t i a l - d u r a t i o n
fre-
q u e n c y c u r v e s h o u l d b e p r o b a b i l i t y o f e x c e e d a n c e or n u m b e r o f f l o o d s p e r 1 0 0 y e a r s exceeding a g i v e n value. Mathematical f i t t i n g o f flood-frequency c u r v e s e l i m i n a t e s t h e s u b j e c t i v i t y of g r a p h i c a l f i t t i n g a l t h o u g h t h e s e l e c t i o n of a s u i t a b l e d i s t r i b u t i o n r e m a i n s subjective.
The m o s t common t h e o r e t i c a l d i s t r i b u t i o n s now u s e d f o r a n n u a l
147 floods are log Pearson Type 3 , log normal, and the extreme-value (Gumbel).
The
log-normal distribution is the same a s the log Pearson Type 3 with zero skew. Methods of fitting are given in section 4.
Digital computer programs are
commonly used. Mathematical methods of defining flood-frequency characteristics are not suitable without modification if some of the annual floods are unusually small. In Figure 8.2 the one extremely small annual flood introduces so much curvature (negative skew) into the fitted curve that the upward, extrapolation of that curve is unrealistic.
Hydrologically the occurrence of an unusually low annual
flood should be unrelated to the flood potential of the stream, and consequently it should not influence the upper end of the flood distribution.
Such reasoning
is the basis for modifying the purely statistical fitting process.
2
50,000
I
.
I
I
I
I
I
I
I
I
V W-
U IT
4u
10,000 -
v,
Q Y
a
W
a
1000
0 1
Fig. 8.2 Frequency curve for Platte River, Missouri, showing how a low outlier distorts the upper end of the frequency curve. Deletion of the unusually low annual flood or floods before fitting the distribution mathematically is a common practice.
If the lowest peak discharge
in Figure 8.2 had not been used in the curve fitting, the SO-year flood would have been 40 percent greater than that shown.
This is still well below the SO-
year floods obtained by a graphical interpretation or by a Gumbel fit, both of which are confirmed by the subsequent record which includes 2 peaks over 50.000 cfs. The flexibility of the log Pearson Type 3 distribution is sometimes a disadvantage; for the record in Figure 8.2 it gives too much weight to peaks on both ends of the array.
Objective methods for identifying low "outliers" and for
148 e l i m i n a t i n g them from t h e f i t t i n g p r o c e s s a r e given by Water Resources Council (1981). Some annual f l o o d r e c o r d s of s m a l l , ephemeral s t r e a m s i n c l u d e z e r o f l o w s f o r s e v e r a l years.
In o t h e r r e c o r d s t h e annual peaks a r e a v a i l a b l e o n l y f o r t h o s e
y e a r s i n w h i c h t h e p e a k was a b o v e some b a s e ; s u c h a r e c o r d m i g h t b e o b t a i n e d from a c r e s t - s t a g e a n n u a l peaks. Montana.
g a g e w h i c h was n o t low enough t o r e c o r d t h e s t a g e s o f a l l
A r e c o r d c o n t a i n i n g z e r o s i s t h a t of T u s l e r C r e e k t r i b u t a r y ,
f o r 1957-73;
t h e a n n u a l p e a k s a r e 1.71.
45.2, 0.03, 0. 0. 0. 0 . 0 8 , 1.12, 1.00.
4.20.
0, 1.04,
a n d 0.17 m ’ l s .
2.38,
0. 0 . 0.84.
The f r e q u e n c y c u r v e
can be d e f i n e d g r a p h i c a l l y from t h e 8 h i g h e s t d i s c h a r g e s i n 17 y e a r s ; t h e r e s t of t h e a n n u a l p e a k s need n o t b e p l o t t e d ( F i g . 8.3).
DO
I
W
a 0.41 1.5
I
1
,
3
I
I
,/Ill
1
5 10 20 RECURRENCE INTERVAL. IN YEARS
2
Fig. 8.3. Graphically-defined Montana, 1957-73.
f l o o d frequency c u r v e for T u s l e r Creek T r i b u t a r y .
Frequency c u r v e s c a n be d e f i n e d m a t h e m a t i c a l l y from r e c o r d s c o n t a i n i n g some a n n u a l f l o o d s whose m a g n i t u d e s a r e o n l y known t o b e l e s s t h a n some b a s e .
The
frequency curve f o r T u s l e r could b e computed by f i t t i n g t h e l o g Pearson Type 3 d i s t r i b u t i o n t o t h e 8 h i k h e s t d i s c h a r g e s and then a d j u s t i n g t h a t d i s t r i b u t i o n t o a c c o u n t f o r t h e a d d i t i o n a l y e a r s of r e c o r d ( J e n n i n g s a n d Benson. 1 9 6 9 ) .
An
example of t h i s type of computation i s given by Water Resources Council (1981, p. 12-32). F l o o d i n f o r m a t i o n a t a g a g e d s i t e may i n c l u d e s t a g e s o f m a j o r f l o o d s t h a t o c c u r r e d p r i o r t o t h e gaged period.
E s t i m a t e s of d i s c h a r g e s of t h e s e h i s t o r i c
f l o o d s may be i n c o r p o r a t e d i n a g r a p h i c a l frequency a n a l y s i s by a s s i g n i n g approp r i a t e recurrence intervals.
For example.
given a flood-peak
r e c o r d from 1940
t o 1980 and an e s t i m a t e of t h e d i s c h a r g e of t h e 1916 f l o o d which i s known t o be l a r g e r than any subsequent one a t t h e s i t e , a t 65 y e a r s on t h e graph. h i s t o r i e s and w i t h i n - r e c o r d
t h e 1916 e s t i m a t e would b e p l o t t e d
Dalrymple (1960) d e s c r i b e s how o t h e r combinations of f l o o d s can b e analyzed g r a p h i c a l l y .
The g u i d e l i n e s
149 recommended b y the W a t e r Resources Council (1981) for determining flood frequency curves m a t h e m a t i c a l l y include procedures for incorporating historic flood information. 8.6
A UNIFORM METHOD Flood characteristics are used for various purposes a n d b y various people.
Conflicts or inconsistencies may arise if different flood frequency curves are derived from the same data.
Uniform methods of analysis reduce such problems.
Bulletin No. 15, "A uniform technique for determining flood flow frequencies",
issued by the Hydrology Committee of the United States Water Resources
Council in 1967. recommended use of the log-Pearson Type 3 distribution as the base method but allowed for other m e t h o d s of analysis if justification w e r e provided.
Guidelines in subsequent Bulletins in 1976, 1979, and 1 9 8 1 specify
use of the log Pearson Type 3 distribution and provide specific procedures for using historic data, for identifying and adjusting for the effects of high and low "outliers", and for weighting skew coefficients computed from a flood record with generalized mapped skew coefficients (Water Resources Council, 1981). The weighting of the skew coefficient computed f r o m the s a m p l e w i t h an average skew coefficient for the geographic area was recommended because a skew coefficient computed f r o m a s a m p l e of a f e w tens of y e a r s is k n o w n to have a large error.
This procedure is based on the assumption that the skewness varies
geographically.
The adjustments for low and high "outliers" are also intended
to make the sample more representative. The decision to use the log-Pearson Type 3 distribution for flood peaks was based on comparisons of frequency curves fitted by various statistical distributions to the graphically-defined frequency curves.
F l o o d records for many
streams encompassing a wide range of sizes and characteristics were used in the tests. T h e s a m e m e t h o d o f testing also w a s used on floods of streams in Great Britain.
That investigation plus other statistical considerations led to the
conclusion that the Gumbel extreme-value
distribution was appropriate for the
majority of British streams although the conclusion was qualified by "Statistics do not point to a single distribution being certainly the correct o n e and therefore a choice must involve an element of subjectivity."
(National Environ-
ment Research Council (1975, p. 241, 155-160). T h e guidelines o f the W a t e r Resources Council for c o m p u t a t i o n of floodfrequency curves at gaging stations are not widely supported by the profession. Some hydrologists question the validity of a map of generalized skew and consequently its use in modifying the frequency curve at a gaged site.
B u t the
principal objection is that no single nonsubjective statistical method w i l l
150 produce t h e b e s t e s t i m a t e s under a l l c o n d i t i o n s . provided by P a t t i s o n (1977).
Support f o r t h a t o b j e c t i o n i s
commenting on A u s t r a l i a n experience:
"The purpose of t h e p r e v i o u s e d i t i o n s of A u s t r a l i a n R a i n f a l l and Runo f f was t o p r o v i d e an u n o f f i c i a l code of recommended p r a c t i c e i n t h e s e l e c t i o n and a p p l i c a t i o n of methods of d e s i g n f o r v a r i o u s t y p e s of hydrologic problems.
The work was taken by many p r a c t i c i n g e n g i n e e r s ,
and o f t e n by t h e Courts, a s a guide t o s t a n d a r d p r a c t i c e . "
"It i s t h e view of t h e N a t i o n a l Committee on Hydrology t h a t t h e r o l e of A u s t r a l i a n R a i n f a l l and Runoff (1958 e d i t i o n ) a s a code of pract i c e h a s been abused.
There a r e , f o r example.
i n s t a n c e s of t h e hy-
d r o l o g i c d e s i g n of i m p o r t a n t f a c i l i t i e s i n which t h e r e q u i r e m e n t s of good e n g i n e e r i n g p r a c t i c e have been ignored, t o some e x t e n t , when r e l e v a n t assumptions have been drawn u n c r i t i c a l l y from g u i d e l i n e s s e t o u t i n A u s t r a l i a n R a i n f a l l and Runoff.
Also i t i s a p p a r e n t
t h a t some e n g i n e e r i n g and l e g a l b o d i e s view any h y d r o l o g i c d e s i g n procedure which d e p a r t s from t h a t recommended i n A u s t r a l i a n R a i n f a l l and Runoff a s b e i n g unacceptable.
T h i s i s t h e approach t r a d i t i o n a l l y
taken w i t h codes of p r a c t i c e , and tends t o i n h i b i t i n n o v a t i v e d e s i g n based on l o c a l knowledge, customs, and e s t a b l i s h e d c r i t e r i a .
Insis-
t e n c e t h a t h y d r o l o g i c d e s i g n f o r a l l p a r t s of A u s t r a l i a f o l l o w a p a t t e r n u s i n g a methodology p r e s c r i b e d i n a s i n g l e compendium w i l l , in many i n s t a n c e s .
l e a d t o d e s i g n s which a r e t e c h n o l o g i c a l l y i n f e r i o r
and economioally unsound." 8.7
RECORD EXTWSION
Annual f l o o d s o u t s i d e t h e p e r i o d o f r e c o r d may b e e s t i m a t e d f r o m a l o n g e r f l o o d r e c o r d o r from p r e c i p i t a t i o n .
Except f o r s t a t i o n s on t h e same stream, t h e
f i r s t technique i s r a r e l y u s e f u l f o r improving t h e frequency curve; f l o o d peaks a r e so h i g h l y i n f l u e n c e d by a r e a l v a r i a t i o n s i n p r e c i p i t a t i o n and by topography t h a t peaks from nearby s t r e a m s a r e n o t c l o s e l y c o r r e l a t e d . Rainfall-runoff o r volumes,
See s e c t i o n 5.4.
models may be used t o s y n t h e s i z e long r e c o r d s of f l o o d peaks,
from r a i n f a l l .
Continuous-flow
models such a s t h e S t a n f o r d Water-
shed Model (Crawford and L i n s l e y , 1966) o r ones t h a t model o n l y t h e storm r u n o f f (Dawdy and o t h e r s , 1 9 7 2 ) a r e e x a m p l e s .
F o r s m a l l s t r e a m s , r a i n f a l l and d i s -
charge a t 15-minute o r s h o r t e r i n t e r v a l s a r e n e e d e d f o r a d e q u a t e c a l i b r a t i o n . The o n l y o t h e r i n p u t t o t h e model developed i n Dawdy and o t h e r s (1972) is d a i l y pan evaporation.
O r d i n a r i l y 8 t o 1 0 y e a r s of r e c o r d a r e n e e d e d t o d e f i n e a n
adequate c a l i b r a t i o n ; s h o r t e r r e c o r d s u s u a l l y include o n l y s m a l l floods.
Figure
8.4 shows t h e r e s u l t s o f c a l i b r a t i n g on 1 6 f l o o d e v e n t s i n 1936-46 on B e e t r e e Creek,
North Carolina.
a 5.41 s q u a r e - m i l e
basin.
An a d e q u a t e c a l i b r a t i o n
151 u s u a l l y r e q u i r e s t h a t a r a i n gage be i n t h e basin.
I f basin r a i n f a l l i s not
uniform, more t h a n one r a i n gage r i l l be needed.
OBSERVED PEAK DISCHARGE, IN CFS
F i g . 8.4. R e s u l t s of c a l i b r a t i n g a r a i n f a l l - r u n o f f o t h e r s , 1972).
m o d e l ( A f t e r Dandy and
The f l o o d r e c o r d i s extended by a p p l y i n g a long r e c o r d i n g r a i n f a l l r e c o r d t o t h e c a l i b r a t i o n and s e l e c t i n g t h e a n n u a l f l o o d s f r o m t h e s y n t h e s i z e d peaks. Whether t h e f r e q u e n c y c u r v e based on t h e extended r e c o r d i s an improvement o v e r t h e one based on t h e gage r e c o r d depends on t h e q u a l i t y of t h e c a l i b r a t i o n and
on t h e r e p r e s e n t a t i v e n e s s o f t h e long r a i n f a l l r e c o r d a s w e l l as on t h e repres e n t a t i v e n e s s of t h e o r i g i n a l gage reco rd .
I t h a s b e e n o b s e r v e d t h a t some
r a i n f a l l r e c o r d s o f 6 0 or more y e a r s d o n o t c o n t a i n s t o r m s a s l a r g e a s o t h e r s which have been o b t a i n e d i n t h e v i c i n i t y i n much s h o r t e r p e r i o d s .
An a d d i t i o n a l
u n c e r t a i n t y i s i n t r o d u c e d when t h e l o n g r a i n f a l l r e c o r d i s a p p l i e d t o a b a s i n d i s t a n t from where t h e r a i n f a l l was observed. 8.8
RELATION TO BASIN CHARACTERISTICS Flood-frequency
c h a r a c t e r i s t i c s depend on basin and c l i m a t i c c h a r a c t e r i s t i c s .
I f t h e geology and topography of a b a s i n a r e more o r l e s s homogeneous and major storms cover l a r g e a r e a s , then t h e flood-frequency
curve can be r e p r e s e n t e d
a d e q u a t e l y by a log-Pearson Type 3 d i s t r i b u t i o n w i t h a s m a l l skew.
But suppose
t h e b a s i n e n c o m p a s s e s a l a r g e r a n g e i n e l e v a t i o n s o t h a t f l o o d s may r e s u l t e i t h e r from snowmelt or r a i n f a l l as i n t h e Merced River b a s i n ,
California.
The
Merced R i v e r frequency c u r v e (Fig. 8.5) h a s a shape t h a t cannot be approximated by any 3-parameter
distribution.
The r a i n f a l l peaks and t h e snowmelt peaks of
M e r c e d R i v e r a r e s e p a r a t e d by s e v e r a l m o n t h s i n m o s t y e a r s .
Thus d a t a a r e
152 a v a i l a b l e f o r d e f i n i n g s e p a r a t e f r e q u e n c y c u r v e s o f a n n u a l r a i n f a l l a n d of snowmelt peaks.
These c u r v e s , shown i n F i g u r e 2.16 (Chapter 2)
c o u l d have been
f i t t e d t o l o g P e a r s o n Type 3 d i s t r i b u t i o n s and t h e two d i s t r i b u t i o n s c o u l d have been combined on t h e b a s i s of p r o b a b i l i t i e s t o g e t t h e f r e q u e n c y c u r v e of annual floods.
500
The a l t e r n a t i v e i s a g r a p h i c a l f i t t o t h e annual f l o o d s .
I
I
I
I
I
I
I
I
v)
:: z
zu’
200
L3 U
6
3
100
2 cl ?L
$
50
a
30
I
I
I
1
1.01
1.11
2
5
20 5c
RECURRENCE INTERVAL, IN YEARS Fig. 8.5. Frequency c u r v e of annual f l o o d s f o r Merced River, Crippen, 1978 )
.
California (After
More commonly, some o f t h e f l o o d p e a k s f r o m b a s i n s o f l a r g e r e l i e f a r e n o t e n t i r e l y f r o m r a i n f a l l or f r o m s n o w m e l t a n d i t i s n o t f e a s i b l e t o d e v e l o p s e p a r a t e f r e q u e n c y curves.
Nor h a s i t proved f e a s i b l e t o d e f i n e s e p a r a t e f r e -
quency c u r v e s f o r f l o o d s caused by f r o n t a l s t o r m s and by h u r r i c a n e s b e c a u s e t h e r e a r e t o o few of t h e l a t t e r t o d e f i n e a f r e q u e n c y c u r v e a t a s i t e and b e c a u s e t h e c l a s s i f i c a t i o n of some of t h e c a u s a t i v e s t o r m s must b e a r b i t r a r y . Under t h e s e c o n d i t i o n s o n l y a s i n g l e f r e q u e n c y c u r v e can be defined.
Whether a
s i n g l e m a t h e m a t i c a l l y - f i t t e d c u r v e i s r e a s o n a b l e can b e judged from a computer p l o t of t h e c u r v e and of t h e d a t a p o i n t s .
An u n d e r s t a n d i n g o f t h e b a s i n hy-
d r o l o g y and of t h e f l o o d r e c o r d w i l l h e l p i n d e c i d i n g w h e t h e r t h e c u r v e i s t o b e a c c e p t e d o r m o d i f i e d , and i f so, how. The s l o p e s a n d s h a p e s o f f l o o d - f r e q u e n c y c u r v e s may c h a n g e f r o m p o i n t t o p o i n t a l o n g t h e same s t r e a m .
I n r e g i o n s s u c h a s t h e e a s t e r n s l o p e s of t h e
Colorado Rocky Mountains, f l o o d s i n t h e h e a d w a t e r s a r e from snowmelt, t h o s e i n t h e m i d d l e r e a c h e s may b e f r o m r a i n a s w e l l a s s n o w m e l t , a n d t h o s e n e a r t h e Plains, p a r t i c u l a r l y the major floods,
a r e from t h u n d e r s t o r m . r a i n f a l 1 .
I f such
a s t r e a m i s gaged a t s e v e r a l p o i n t s , t h e s t a n d a r d d e v i a t i o n and t h e skew of t h e annual f l o o d s w i l l i n c r e a s e downstream.
153 8.9
RELIABILITY OF FLOOD-FREQUPNCY CURVES The nonrandomness o f w e a t h e r c o n d i t i o n s f a v o r a b l e t o major f l o o d s i n d i c a t e s
t h a t a long f l o o d r e c o r d s h o u l d p r o v i d e t h e b e s t e s t i m a t e of t h e f r e q u e n c y curve.
R e l i a b i l i t y of t h e l a r g e r annual discharges,
i f d e f i n e d by i n d i r e c t
measurement, w i l l a l s o a f f e c t t h e f r e q u e n c y c u r v e r e l i a b i l i t y b u t o n l y moderately unless the discharges a r e g r e a t l y i n error. s a m p l e i s t h e m a j o r unknown.
The l a c k o f r a n d o m n e s s i n t h e
For t h i s reason, s t a t i s t i c a l confidence l i m i t s
about a frequency c u r v e a r e n o t n e c e s s a r i l y dependable i n d i c a t o r s o f t h e r e l i a b i l i t y of a frequency curve, p a r t i c u l a r l y i f t h e r e c o r d i s s h o r t . The upper end of a flood-frequency c u r v e may be e v a l u a t e d by comparing i t t o the maximum f l o o d s of r e c o r d i n t h e region.
I f a f r e q u e n c y c u r v e shows a 100-
y e a r f l o o d i n e x c e s s o f a n y t h i n g e x p e r i e n c e d i n t h e r e g i o n , and t h e f r e q u e n c y curve i s n o t s u p p o r t e d by d a t a n e a r t h a t l e v e l ,
is q u e s t i o n a b l e .
t h e n t h e upper end of t h e c u r v e
Crippen and Bue (1977) compiled maximum f l o o d s i n t h e United
S t a t e s and p l o t t e d envelope c u r v e s of peak d i s c h a r g e v e r s u s d r a i n a g e a r e a f o r each of 17 r e g i o n s of t h e conterminous United S t a t e s .
T h e i r n a t i o n w i d e envelope
c u r v e i s i n F i g u r e 8.6.
1,000,000 m
LL 0
z
w' 100,000 0 n
4 0
v,
0
10,000
Y
a W a
A--
1000 0.1
1 10 100 1000 DRAINAGE AREA, IN SQUARE MILES
10,000
Fig. 8.6. Envelope c u r v e of maximum f l o o d s i n conterminous U n i t e Crippen and Bue, 1977).
S t a t e s (After
Under c e r t a i n c o n d i t i o n s h i s t o r i c f l o o d s t a g e s c a n be e s t i m a t e d from geologi c a l and b o t a n i c a l e v i d e n c e .
S e e S t e w a r t a n d B o d h a i n e (1961).
LaMarche (19731, C o s t a ( 1 9 7 8 ) . and B a k e r and K o c h e l ( 1 9 7 9 ) .
B e l l e y and
These h i s t o r i c
s t a g e s , when t r a n s l a t e d t o d i s c h a r g e , may p e r m i t r e a l i s t i c e x t r a p o l a t i o n s o f f r e q u e n c y c u r v e s b a s e d on s h o r t r e c o r d s .
On t h e o t h e r hand, J a h n s ( 1 9 4 7 ) con-
cluded "Because t h e C o n n e c t i c u t River h a s been engaged i n l o w e r i n g i t s bottom s i n c e t h e d r a i n i n g of t h e l a t e g l a c i a l v a l l e y l a k e , d i s c u s s i o n of s o - c a l l e d
154 1000-year
f l o o d s on t h e b a s i s of t h e i r c r e s t h e i g h t s a s r e f e r r e d t o p o i n t s along
t h e v a l l e y i s o f no v a l u e . " E r t r a p o l a t i o n s of f r e q u e n c y c u r v e s t o r e c u r r e n c e i n t e r v a l s g r e a t e r t h a n 100 years generally are not reliable. mathematically derived,
Most f r e q u e n c y c u r v e s ,
graphically or
a r e unbounded a t t h e upper end a l t h o u g h t h e r e must be
some p h y s i c a l l i m i t t o t h e f l o o d p o t e n t i a l on any stream. h a s n o t b e e n shown b y f l o o d r e c o r d s ,
Such a p h y s i c a l l i m i t
e i t h e r b e c a u s e t h e y a r e t o o s h o r t or
because t h e r e c o r d s a r e nonhomogeneous due t o changes i n t h e b a s i n s a l t h o u g h a n u p p e r l e v e l s e e m s i n d i c a t e d by e s t i m a t e s o f m a j o r f l o o d s on Han R i v e r , C h i n a , f r o m s t a g e i n f o r m a t i o n ; Chen C h i a - c h i and o t h e r s f r o m t h e M i n i s t r y o f W a t e r Conservancy and E l e c t r i c Power i n Peking r e p o r t e d i n 1974 t h a t t h e maximum f l o o d
on Han R i v e r o c c u r r e d in 1583 and a p p a r e n t l y was t h e h i g h e s t i n t h e l a s t 1000 years. Another approach t o d e f i n i n g t h e p r o b a b l e maximum f l o o d i s through e s t i m a t e s of t h e maximum p r o b a b l e p r e c i p i t a t i o n on t h e basin.
See s e c t i o n 112.7.
E v a l u a t i o n o f f r e q u e n c y c u r v e s i n t h e range below 100-year r e c u r r e n c e i n t e r v a l may be done s u b j e c t i v e l y by comparison among s e v e r a l i n a region.
I f flood
r e c o r d s a r e a v a i l a b l e a t s e v e r a l s i t e s on t h e s a m e s t r e a m a p l o t o f p e a k d i s c h a r g e s f o r s e v e r a l r e c u r r e n c e i n t e r v a l s a g a i n s t channel d i s t a n c e , a r e a , may b e u s e d t o i d e n t i f y i n c o n s i s t e n c i e s . i n f o r m a t i o n a t one s i t e .
500,00(
100,00(
1O,OO(
500(
I
'I 00
1000
I
10.oO0
DRAINAGE AREA, IN SQUARE MILES
Fig. 8 . 7 .
or drainage
F i g u r e 8.7 s h o w s q u e s t i o n a b l e
Flood c h a r a c t e r i s t i c s a t gaging s t a t i o n s on Potomac River.
155
FLOOD CEARACTEBISTICS AT UNGAGED SITES
8.10
Regression on basin characteristics
8.10.1
Refer to Chapter 4 for description of regression analysis and to Chapter 7 for its use in estimating flow characteristics of ungaged streams.
The method
is widely used to develop equations for estimating flood-frequency characteristics f r o m b a s i n characteristics.
Applications of the derived relations to
ungaged sites usually require only site data that are readily available f r o m maps or w e a t h e r records.
T h e equations developed b y T h o m a s and Corley (1977)
for Oklahoma streams are typical:
P1*92
Q2 = 0.111 = 1.00
QS
~ 0 . 6 7 ~0.26 p1.45
SE = 48% 40
Q~~
= 2.99
~ 0 . 6 8 ~ 0 . 2 8 p1.22
39
%s
=
9.49
~ 0 . 6 9 ~ 0 . 3 0 p0.97
4m
= 20.0
~ 0 . 6 9 ~ 0 . 3 1 p0.81
Q
S
~
QIOO
=:
38.6
Ao*7O
poe67
42 45
where Q is the annual flood peak in cfs at the indicated recurrence interval, A is drainage area in square miles, S is an index of main-channel slope, and P is mean annual basin precipitation in inches. sion is given.
The standard error of each regres-
The above equations are transformed from the log-linear form
in which they were solved by multiple regression. log Q = log a + bl log A + b2 log S
+ b3 log P
Various other basin characteristics have been used in regressions for estimating flood-peak characteristics.
The appropriate characteristics depend on
the hydrology of the region and the availability of data.
Rarely are more than
three basin characteristics b o t h statistically and practically significant. Although a fourth characteristic may be statistically significant and its inclusion m a y reduce the standard error a f e w percent, the results obtained b y the equations with and without this characteristics usually do not differ appreciably.
A regression on basin characteristics is defined by data from some region. and the results are considered applicable to that region.
The applicability to
all parts of the region can be appraised subjectively by plotting on a m a p at each data site the ratio of the discharge b y regression equation to the k n o w n discharge.
T h e geographic distribution of these residuals s h o u l d b e m o r e or
less random. T h e above test is l i m i t e d to sites used in defining the relation.
If these
sites do not represent the range of hydrologic conditions in the region then the
156
A regional
relation may not apply to some ungaged streams in that region. relation is commonly qualified a s to its applicability; 8.10.2
Index-flood method
The index-flood method was used for most of the regional flood-frequency analyses made by the U.S. Geological Survey prior to 1965 and is used in England (National Environment Research Council, 1975).
It consists of two parts.
The first part graphically relates mean annual flood to drainage area, and sometimes to other variables.
The mean annual flood was defined a s the 2.33
year recurrence interval flood, based on the Gumbel distribution. plotted points define several different relations.
Usually the
On the basis of these pre-
liminary relations, the geographic area being studied is divided into subareas such that a single relation of mean annual flood to drcinage area applies to each.
Thus the regionalization of the mean annual flood is attained.
The second part of the regionalization process averages the individual frequency curves to provide a regional curve.
This is accomplished after expres-
sing the flood magnitudes a t selected recurrence intervals for each curve a s ratios to the mean annual flood (the index flood).
If some of the dimensionless
individual curves are greatly different from others, the geographic area is subdivided so that each subdivision contains curves of similar shape. curves in each subdivision are averaged.
Then the
The subdivisions for this purpose are
usually not coincident with the subareas defining the various relationships of mean annual flood to drainage area.
.
Figure 8.8 shows the two parts of the
analysis
The index-flood method thus accomplishes the general purposes of a regionalization by relating the position of the frequency curve on the discharge scale to basin size, and by averaging the shapes of the individual curves. The method provides satisfactory results in many regions and is fairly simple to perform. The results are easy to apply to ungaged areas because usually only drainage area need be measured. Application of the method requires arbitrary decisions
as
to the boundaries
of subareas considered homogeneous with respect to mean annual flood or to shape of frequency curve.
No subarea should be represented by fewer frequency curves
than needed to define a meaningful regionalization, even though a close agreement among frequency characteristics in the subarea is not attained. An evaluation of the index-flood method is described by Benson (1962).
A
detailed discussion of the preparation of regional frequency curves is given by National Environment Research Council (1975, p. 170-185).
8.10.3
From channel geometry
In arid and semiarid regions and in ones with heterogeneous geology, channel geometry is
a
better indicator of flood-peak characteristics than basin
157
10
20
50
100 200
500 1000
DRAINAGE AREA, IN SQUARE MILES
1.1
1.52
5
10
20
50
100
RECURRENCE INTERVAL. IN YEARS F i g . 8.8. Relations developed by t h e index-flood Golden, 1 9 6 6 ) . characteristics.
The method,
m e t h o d ( A f t e r B a r n e s and
d e s c r i b e d i n Chapter 7,
r e q u i r e s f i e l d measure-
ments o f c h a n n e l s f o r c a l i b r a t i o n and f o r a p p l i c a t i o n t o ungaged s i t e s :
these
measurements s h o u l d b e made by p e o p l e w i t h some e x p e r i e n c e w i t h t h e technique. P r i m a r y c a l i b r a t i o n s a r e u s u a l l y made w i t h t h e 10-year f l o o d because t h a t f l o o d
is d e f i n e d a t many more s i t e s t h a n f l o o d s of h i g h e r r e c u r r e n c e i n t e r v a l .
In r e -
g i o n s where f l o o d r e c o r d s a r e long, u s u a l l y f o r t h e l a r g e r s t r e a m s , o t h e r f l o o d c h a r a c t e r i s t i c s may b e r e l a t e d t o c h a n n e l width.
F i g u r e 8.9
r e l a t i n g 50-year
158 f l o o d t o channel width, Nevada,
i s d e f i n e d by d a t a from mountain s t r e a m s i n Colorado.
Northwestern United S t a t e s ,
and Alaska.
40 10,000
t 10
5
X P
10
0
coIoraao a n d Nevada
100
1 1000
W H O L E C H A N N E L WIDTH, IN M E T E R S
Fig. 8.9.
p e l a t i o n of 50-year f l o o d t o channel width (From Riggs. 1 9 7 8 ) .
V a r i a t i o n s i n t h e r e l a t i o n s of flood peak c h a r a c t e r i s t i c s t o w i d t h occur because of d i f f e r e n c e s i n channel shapes. i n which t h e channel i s formed,
Channel shape depends on t h e m a t e r i a l
t h e amount of sediment c a r r i e d ,
r e g i m e , p a r t i c u l a r l y w h e t h e r i t i s p e r e n n i a l or ephemeral.
and on t h e f l o w Some d i f f e r e n c e s
among c a l i b r a t i o n s o n w i d t h a r e shown i n F i g u r e 8.10; t h e K a n s a s c h a n n e l s a r e deep and narrow,
t h e w e s t e r n mountain c h a n n e l s tend t o b e wide and s h a l l o w , and
t h e Kentucky c h a n n e l s a r e i n t e r m e d i a t e . Some a d d i t i o n a l measure of channel geometry i s needed f o r c a l i b r a t i o n i n a r e g i o n which c o n t a i n s c h a n n e l s o f v a r i o u s types.
Using d a t a f o r 42 c h a n n e l s of
v e r y d i f f e r e n t shapes and s i z e s i n Kansas, Alaska, Northern Canada,
and Wyoming
t h e s t a n d a r d e r r o r o f r e g r e s s i o n of t h e 1 0 - y e a r f l o o d on w i d t h a n d mean d e p t h
159
6000
1000
100
10
t 1 c
2
10
100
WHOLE-CHANNEL WIDTH, IN METERS
F i g . 8.10.
V a r i a t i o n s due t o d i f f e r e n t channel shapes (From Riggs. 1978).
was 0.22 l o g u n i t s c o m p a r e d t o 0.45 alone.
l o g u n i t s f o r a r e g r e s s i o n b a s e d on w i d t h
Even though mean d e p t h was a h i g h l y s i g n i f i c a n t and u s e f u l v a r i a b l e i n
t h i s example.
t h e s t a n d a r d e r r o r i s u n a c c e p t a b l y large.
C a l i b r a t i o n on s t r e a m s
i n a s m a l l e r r e g i o n u s u a l l y w i l l produce b e t t e r r e s u l t s .
A d i s a d v a n t a g e of t h e channel-geometry method i s t h e need f o r f i e l d measurem e n t s a t t h e s i t e s of a p p l i c a t i o n .
The u s e r n o t o n l y n e e d s t o v i s i t e a c h s i t e
where he w a n t s a f l o o d e s t i m a t e b u t he a l s o s h o u l d have some u n d e r s t a n d i n g of channel morphology i n o r d e r t o g e t a p p r o p r i a t e measurements. berg (1976) c a l i b r a t e d 10-year channel width;
Riggs and Haren-
f l o o d s a t gaged s i t e s i n Owyhee County,
Idaho on
t h e n t h e y measured channel w i d t h s a t many ungaged s i t e s ,
mined t h e 1 0 - y e a r f l o o d s a t t h e s e s i t e s , a n d p l o t t e d them on a map.
deter-
The u s e r
c a n e s t i m a t e t h e 1 0 - y e a r f l o o d s a t o t h e r s i t e s a n d on o t h e r s t r e a m s by i n t e r p o l a t i o n o r , b y u s i n g t h i s map i n c o n j u n c t i o n w i t h a t o p o g r a p h i c map, h e c a n i d e n t i f y a measured s t r e a m s i m i l a r t o t h e one f o r which a n e s t i m a t e i s wanted. I f a c a l i b r a t i o n i s a v a i l a b l e o n l y f o r t h e 10-year f l o o d , f l o o d s of l a r g e r recurrence
i n t e r v a l s may be approximated by m u l t i p l y i n g t h e e s t i m a t e d 10-year
f l o o d b y f a c t o r s b a s e d on f r e q u e n c y c u r v e s f o r t h e r e g i o n ; t h i s i s s i m i l a r t o t h e procedure used i n t h e index-flood
method.
160
8.10.4
From precipitation
Methods of estimating flood-peak characteristics directly from precipitation include the so-called Rational Method and procedures developed by the U.S. Conservation Service (SCS)
and by the U.S.
Soil
Corps of Engineers Hydrologic
Engineering Center (HEC). The Rational Method, widely used for design of storm drainage facilities, gives peak runoff rate, Q, in cubic feet per second, by Q = C I A where C is a dimensionless runoff coefficient; I is rainfall intensity in inches per hour for a period of time equal to the time of concentration of the basin, and for the s a m e recurrence interval as the discharge; and A is the drainage area in acres.
Time of concentration is usually defined as the estimated time
required for runoff to flow from the farthest point in the drainage area. The coefficient C depends on the permeability of the basin soils and other surfaces.
Its value ranges from about 0.10 for sandy soil to 0.95 for imper-
vious pavement; it is generally above 0.50 for urbanized areas.
Rainfall inten-
sity, I is obtained from an intensity-duration-frequency relation derived from precipitation records.
The duration used is the time of concentration which
must b e estimated at ungaged sites.
Anderson (1970) shows lag time (time of
concentration) as a function of basin length divided by the square root of hasin slope for natural and for fully urbanized basins. The Rational Method usually is applied only to small drainage areas. Schaake, Geyer. and Knapp (1967) examined the method and compared runoff estimates with those from runoff frequency curves for urban drainage areas.
They
found that for every five Rational Method estimates made by storm drain designers in the Baltimore, Md. area, one of them, on the average, may b e in error by more than 25%.
Ardis, Dueker. and L e n z (1969) reported a w i d e variation in
procedures used by practicing engineers for applying the Rational Method, and a consequent lack of consistency among results. Both the Hydrologic Engineering Center (HEC) of the Corps of Engineers and the Soil Conservation Service (SCS) have computer programs for estimating flood peaks of various recurrence intervals from precipitation.
These programs are
applicable to drainage areas ranging from a few to several thousand square miles. The SCS TR-55 graphical method of estimating flood-peak characteristics begins with classification of all soil units in the basin as to infiltration capacity.
This classification is used with adjustment for soil cover to define
a curve number (CN) for each.
These are area weighted and the result is used
with storm rainfall to get direct runoff in inches, usually by a graphical solution of a runoff equation.
Peak discharge is computed from direct runoff
161 computed a s above; d r a i n a g e a r e a ; t i m e of c o n c e n t r a t i o n from channel l e n g t h and slope:
a n d a c o n s t a n t (U.S.
S o i l C o n s e r v a t i o n S e r v i c e , 1 9 7 1 ) . and (McCuen.
1982). Methods f o r e s t i m a t i n g f l o o d p e a k s f r o m p r e c i p i t a t i o n u s u a l l y r e q u i r e t h e assumption t h a t t h e r e c u r r e n c e i n t e r v a l of t h e computed f l o o d i s t h e same a s t h e r e c u r r e n c e i n t e r v a l of t h e c a u s a t i v e r a i n f a l l . drainage basins.
a q u e s t i o n a b l e assumption i n some
The m e t h o d s a l s o r e q u i r e i n p u t d a t a t h a t o f t e n a r e e i t h e r
u n a v a i l a b l e or t h a t must be d e f i n e d somewhat s u b j e c t i v e l y . 8.10.5
I n t e r p o l a t i o n along channel
S t r e a m f l o w r e c o r d s and t h u s flood-peak c h a r a c t e r i s t i c s a r e a v a i l a b l e a t i n t e r v a l s along the l a r g e r streams i n t h e United States.
Better estimates
between t h e gaged s i t e s can be made by i n t e r p o l a t i o n t h a n by any of t h e methods d e s c r i b e d above, p a r t i c u l a r l y i f t h e f l o o d c h a r a c t e r i s t i c s do not change consist e n t l y along t h e channel.
The i n t e r p o l a t i o n shown i n F i g u r e 8.11 i s b a s e d on
10-year f l o o d s d e f i n e d a t 3 s i t e s on t h e main s t r e a m and on 5 t r i b u t a r i e s i n t h e
i;
20,000
2 0
g 10,000
d
0
::
L
+ 4
0
2 iooo~ n
?
e
iL tf r a W
2000
0
4
9 z
I
I
I
I
10
20
30
40
MILES ALONG CHANNEL
Fig. 8.11. Ten-year f l o o d s i n t e r p o l a t e d between gaged s i t e s , New Hampshire. F i g u r e s a r e 10-year f l o o d s a t t r i b u t a r i e s . reach.
The a b s c i s s a i s d i s t a n c e along t h e channel.
t e d and t h e mouths of major t r i b u t a r i e s a r e located.
Contocook River,
The gaged p o i n t s a r e p l o t I n t e r p o l a t i o n i s by t r i a l ,
based on t h e assumption t h a t a p p r e c i a b l e i n c r e a s e s occur o n l y where t r i b u t a r i e s enter.
The c o n t r i b u t i o n o f a g a g e d t r i b u t a r y s h o u l d b e n o t more t h a n i t s 10-
y e a r f l o o d b u t i t may be much l e s s i f t h e t r i b u t a r y f l o o d i s u s u a l l y n o t concurr e n t w i t h t h e f l o o d on t h e main stream.
162
I
I
cn
z
::
5-
I
W W
2000-
100-YR e
W'
0
5
1000-
50-YR
Y
g 2
I
-
10-YR
I
I
300
Fig. 8.12.
+ W
fi
P
0,
O
Q
0
9
0
$ v 3 a
o - lm m 1
4a
:s
><
:?I5
600 -
2
3$ z
2
I
0
O
I
0
0
I
I
Flood characteristics along Powder River, Wyoming-Montana.
Plots of flood characteristics against channel distance may be used to check the consistency of estimates at gaged sites as discussed in Section 8.9. Figure 8.12,
In
the station data indicate a large decrease from Arvada to Moorhead
for w h i c h there s e e m s to be no physical basis.
M o r e likely the difference is
due to the different periods of record on which the frequency curves are based: averaging the two discharges seems reasonable. REGULATED STBEAMS A record o f annual floods during a period w h e n f l o w w a s regulated in a
8 .ll
consistent m a n n e r is considered suitable f o r interpreting on a probability basis.
But, if during the period of record an additional reservoir or reser-
voirs w e r e added, or the pattern of regulation w a s changed, then the w h o l e record should not be used to define a frequency curve unless t h e changes are considered to have a minor effect on floods at the site of interest. Models can be used to compute homogeneous records that reflect some particular level of development in a basin, usually the present condition or a proposed future condition.
Natural streamflow records can be used as input.
These
flows are routed through storages taking into account reservoir-operating rules, evaporation losses, tributary inflows, precipitation on w a t e r surfaces, and diversions and return flows.
T h e synthesized record can then be analyzed by
conventional methods to determine the flow characteristics. (1974, 1976).
See Jeffcoat, et a1
163 See Chapter 10 for methods of estimating flood-frequency characteristics in basins modified by man. BEFERENCES Anderson, D.G.. 1970, Effects o f urban development on floods i n northern Virginia: U.S. Geol. Survey Water-Supply Paper 2001-C, 22 p. Ardis. C.V.. Dneker. K.J., and Lenz, A.T., 1969, Storm drainage practices of thirty-two cities: Journal of Hydraulics Division, ASCE, Vol. 95, NO. HY1, p. 383-408. Baker, V.R. and Kochel, R.C., 1969, Long-term flood-frequency analysis using geologic data: International Assoc. o f Hydrological Sciences Publ. NO. 128, Canberra, p. 3-9. Barnes, H.H.. Jr. and Golden, H.G., 1966, M a g n i t u d e and frequency of floods in the United States. Part 2B. south Atlantic and eastern G u l f of M e x i c o basins, Ogeechee River t o Pearl River: U.S. Geol. Survey Water-Supply P a p e r 1674. 409 p. Benson. M.A., floods:
1962, Evaluation of methods for evaluating t h e occurrence of U.S. Geol. Survey Water-Supply Paper 1580-A, 30 p.
Costa, J.E., 1978, Holocene stratigraphy in flood-frequency analysis: Resources Research, Vol. 14, No. 4, p. 626-632.
Water
Crawford. N.H. and Linsley. R.K.. 1966. Digital s i m u l a t i o n in hydrology, Stanford W a t e r s h e d M o d e l IV: Tech. Rept. No. 39, Dept. of Civil Engineering, Stanford University, Stanford, Calif. Crippen. J.B., 1978, Composite log Pearson Type 3 frequency-magnitude curve of annual floods: U.S. Geol. Survey Open-File Rept. 78-352, 5 p. Crippen. J.R and Bue, C.D., 1977, Maximum floodflows in the conterminous United States: U.S. Geol. Survey Water-Supply Paper 1887, 5 2 p. Dalrymple. T., 1960. Flood-frequency Paper 1543-A, 104 p.
analyses:
U.S.
Geol.
Survey Water-Supply
Dardy. D.R. Lichty, RW.. and Bergman. J.M.. 1972, A rainfall-runoff simulation U.S. Geol. model for estimation of flood peaks for small drainage basins: Survey Prof. P a p e r 506-B. 2 8 p. Helley, E.J. and LaMarche, V.C., 1973. Historic flood i n f o r m a t i o n for northern California s t r e a m s f r o m geological and botanical evidence: U.S. Geol. Survey Prof. P a p e r 485-E. 16 p. Jahns, RE, 1947, Geologic features of Connecticut Valley as related to recent floods: U.S. Geol. Survey Watersupply Paper 996, 158 p. and Peterson, J.B.. 1974, Lakes Marion-Moultrie Jeffcoat, H.H., Jennings, M.E., stream s y s t e m investigation: Part I - M o d e l selection. calibration and error analysis: U.S. Geol. Survey Water Resources Investigations 25-74. 55 P. Jeffcoat, H.H., Jennings, M.E.. Collins, D.L., and Shearman, J.O.. 1976, Lakes Marion-Moultrie stream system investigation: Part I1 - simulation studies: U.S. Geol. Survey Water Resources Investigations 76-11. 26 p. Jennings, M.E. and Benson. M.A., 1969, Frequency curves for annual flood series with some zero events or incomplete data: Water Resources Research, Vol. 5 . NO. 1, p. 276-280. Langbein. W.B.. 1949. Annual floods and t h e partial-duration series: American Geophysical Union. Vol. 30. McCuen, RE. 1982, A guide to hydrologic analysis using SCS methods: Prentice-Hall. Inc., 1 4 5 p. Cliffs, N.J..
Trans.
Englerood
164 National Environment Research Council, 1975, Flood studies report, 5 Vols.: Institute of Hydrology, Wallingford, Oxon, England. Pattison, A., Ed., 1977, Australian rainfall and runoff, flood analysis and design: The Institution of Engineers, Australia. Canberra, p. iii. Riggs, H.C., 1978, Streamflow characteristics from channel size: Hydraulics Division, ASCE, Vol. 104. No. HY1, p. 81-96.
Journal of
Riggs. H.C. and Harenberg. W.A.. 1976, Flood characteristics of streams in Onyhee County, Idaho: U.S. Geol. Survey Water-Resources Investigations 7688, 1 4 p. Schaake, J.C., Jr., Geyer, J.C.. and Knapp. J.W.. 1967, Experimental examination of the rational method' Journal of Hydraulics Division. ASCE, Vol. 93, No. HY6, p. 353-370. Stewart, J.E. ington:
and Bodhaine. G.L., 1961, Floods in the Skagit River basin, WashU.S. Geol. Survey WaterSupply Paper 1527, 66 p.
Thomas, W.O., Jr. and Corley. R.K., 1977. Techniques for estimating flood discharges for Oklahoma streams: U.S. Geol. Survey Water Resources Investigations 77-54. 1 7 0 p. U.S.
Soil Conservation Service, 1971, SCS National Engineering Handbook, Section
4, Hydrology, Chapters 10 and 16. Water Resources Council, 1981, Guidelines for determining flood flow frequency: Bulletin 17A of the Hydrology Committee, Washington, D.C.
165
Chapter 9
LOW-FLOW CHARACTERISTICS
9.1
INTRODUCTION The adequacy of streamflow to meet requirements for disposal of liquid
wastes, and for municipal or industrial supplies, supplemental irrigation, and maintenance of suitable conditions for aquatic life is commonly evaluated in terms of low-flow characteristics (Biggs, 1980).
Certain of these low-flow
characteristics are useful as variables in regional draft-storage studies, as the basis for forecasting seasonal low flows, and as indicators of the amount of ground-water flow to the stream.
The U.S. Environmental Protection Agency
(EPA). and some States, incorporate a low-flow characteristic into their regulations on pollution control. An annual low flow can be defined as the lowest daily mean flow in a year but it is more commonly defined as the lowest average flow for some number of consecutive days.
The 7-day low flow (Hoyt, 1938) is widely used; an average
for 7 days is less likely to be affected by minor disturbances upstream than is the minimum daily flow.
Annual low flows for 1. 3 , I, 14, 3 0 , 60, 90. 120, and
183 consecutive days can be readily obtained from a streamflow record by computer.
The climatic year, April 1 to March 31. is used because for most of the
United States it contains the entire low flow period of each year. The dependable supply of streamflow is commonly described by frequency curves of annual or seasonal low flows, or by a point on the frequency curve, such as the 7-day discharge at 10-year recurrence interval (the 7-day 10-year low flow). The rate at which streamflow recedes in the absence of precipitation is described by the recession curve (see Chapter 5 ) ; the recession rate is useful in forecasting low flows and in understanding the relation with ground water.
The
reduction in discharge of a stream may be accompanied by a degradation of water quality, principally by increased temperature, by the concentration of dissolved solids by evaporation or freezing, and by the reduced aeration capability. Recession and waterquality characteristics are not discussed further in this chapter. 9.2
FREQUENCY CURVES Frequency curves are prepared from annual low flows by methods described in
Chapter 4.
Typical graphically-defined frequency curves for 7-, 14-, 30-, and
60-day periods are shown in Figure 9.1.
The recurrence interval scale is based
on the Gumbel distribution; a normal distribution scale could have been used.
166 Most low-flow frequency curves for s t r e a m s that d o not go dry are s m o o t h curves that are concave u p w a r d on a log-probability graph.
T h e probability
RECURRENCE INTERVAL IN YEARS Fig. 9.1. Frequency curves of annual lowest mean discharge for indicated numbers of consecutive days, Spoon River, Illinois (From Riggs. 1980). distribution of annual low flows at a particular site on a stream depends on the distribution of precipitation over the basin in time and space; on the temperature regimen. which may permit storage of water as snow for considerable periods and w h i c h also influences t h e evapotranspiration rate; and on the soil and geologic characteristics which govern the recharge and discharge rates in the basin.
In addition, at a given site some of the annual low flows may be derived
entirely from ground-water inflow to the stream, whereas others may include some flow from reduction of upstream storage during those years when frequent rains occur during the low-water season.
Furthermore the base flow of a stream may be
derived from several aquifers, not all of which contribute at all times.
Conse-
quently not all low-flow frequency curves w i l l have a smooth, concave u p w a r d shape, nor should t h e h i g h annual m i n i m u m f l o w s at a site necessarily be considered as belonging to the same population as the smaller ones. For e x a m p l e s o f low-flow frequency curves having non-typical shapes s e e Figure 9.2.
The annual minimum flow of Suwannee River at White Springs consists
of (1) a f l o w ranging f r o m several hundred cubic feet per second to z e r o f r o m the headwaters in Okefenokee Swamp and (2) an inflow of 5 to 10 cubic feet per second from a limestone aquifer i n a l o w e r reach of the river.
Curve shapes
such as that o f S u w a n n e e River also result if considerable m i n e drainage or sewer effluent is included in the flow.
The shape of the Uwharrie River curve
167
i s a t l e a s t i n p a r t due t o a d i v e r s i o n f o r a c i t y supply.
A h e a v y d r a f t by
e v a p o t r a n s p i r a t i o n ( o f a m o r e or l e s s c o n s t a n t amount d u r i n g t h e low-flow period,
independent of d i s c h a r g e ) may a l s o h e l p t o produce t h e convex shape.
8N
I
I
I
I
I
I
-
-
-
-
t I
I
1.2
-
1
2
I
5
10
20
50
1.2
2
5
10
20
RECURRENCE INTERVAL, IN YEARS
F i g u r e 9.2. Frequency curves of annual minimum 7-day means f o r Suwannee River, F l o r i d a ( l e f t ) , and Uwharrie River. North C a r o l i n a ( r i g h t ) . Low-flow
d a t a such a s those f o r Suwannee River cannot b e f i t t e d a d e q u a t e l y a t
t h e lower end by any 2 or 3-parameter F i g u r e 9.1,
distribution.
Even w i t h d a t a such a s i n
a f i t t e d l o g Pearson Type 3 d i s t r i b u t i o n might be u n r e a l i s t i c a t t h e
lower end because t h e h i g h e r d i s c h a r g e s a f f e c t t h e skew. s h a p e o f t h e l o w e r end o f t h e c u r v e .
and t h u s i n f l u e n c e t h e
A graphically-fitted
c o n s i d e r e d t h e b a s i c f r e q u e n c y c u r v e f o r a n n u a l low f l o w s . Pearson Type 3 f i t i s adequate f o r most.
c u r v e should be although a log
An a l t e r n a t i v e t o g r a p h i c a l f i t t i n g i s
t h e use o f o n l y t h e l o w e r h a l f of t h e a r r a y o f low f l a w s t o d e f i n e t h e l o w e r p a r t of t h e frequency curve a n a l y t i c a l l y .
The method of f i t t i n g p a r t i a l d a t a i s
given b y J e n n i n g s and Benson (1969) and is d e s c r i b e d b r i e f l y i n Chapter 8. 9.2.1
I n t e r p r e t a t i on
R e f e r r i n g t o e i t h e r of t h e p r e v i o u s f i g u r e s , t h e 7-day 1 0 - y e a r low f l o w i s t h e d i s c h a r g e a t 10-year r e c u r r e n c e i n t e r v a l t a k e n from a f r e q u e n c y c u r v e of annual v a l u e s o f t h e l o w e s t mean d i s c h a r g e f o r 7 c o n s e c u t i v e days ( t h e 7-day low flow).
The 7-day
low flow w i l l be l e s s t h a n t h e 7-day 10-year low flow a t i n t e r v a l s
a v e r a g i n g 10 y e a r s i n l e n g t h ; or t h e p r o b a b i l i t y i s 1/10 t h a t t h e 7-day i n any one y e a r w i l l b e l e s s t h a n t h e 7-day 10-year low flow.
low flow
168 Comparable s t a t e m e n t s can be made f o r o t h e r p e r i o d s of days and r e c u r r e n c e intervals.
Note t h a t t h e p r o b a b i l i t y i s t h a t of b e i n g l e s s than:
i t i s not t h a t
of nonexceedance. The p r o b a b i l i t y i n t e r p r e t a t i o n , above, i s s t r i c t l y a p p l i c a b l e o n l y i f t h e annual low f l o w s a r e independent of each other.
A dependence may r e s u l t from a
c a r r y o v e r o f g r o u n d w a t e r f r o m one y e a r t o t h e n e x t so t h a t t h e b a s e f l o w i s somewhat d e p e n d e n t on t h e p r e v i o u s y e a r s f l o w .
Dependence may b e r e c o g n i z e d
f r o m a p l o t o f a n n u a l minimum f l o w s a g a i n s t t h o s e f o r t h e p r e v i o u s y e a r . shown i n F i g u r e 9.3,
As
t h e South Fork Obion River low f l o w s a r e h i g h l y c o r r e l a t e d
w i t h those of t h e p r e v i o u s y e a r and t h u s are. n o t independent events.
The Shoal
Creek d a t a appear t o be u n c o r r e l a t e d .
I
I
. .. .
* *
. . ..
0-
:*:
* .
.
c
SHOAL
I
50
.*
**
S.F. OBION
I 200
100
I
I 100
50
200
ANNUAL MINIMUM FLOW IN PREVIOUS YEAR, IN CFS
Fig. 9.3. 9.2.2
First-order
a u t o c o r r e l a t i o n of low flows of two Tennessee s t r e a m s .
Reliability
R e l i a b i l i t y of a low-flow of record.
frequency curve u s u a l l y i n c r e a s e s w i t h t h e l e n g t h
A r e c o r d of 15 o r 20 y e a r s may n o t p r o v i d e a r e p r e s e n t a t i v e sample
of low flows.
For example, F i g u r e 9.4 shows frequency curves based on two 15-
y e a r p e r i o d s and on t h e 3 1 - y e a r p e r i o d o f r e c o r d .
One s h o r t - p e r i o d c u r v e i s
h i g h e r and t h e o t h e r i s l o w e r t h a n t h e curve based on a l l t h e record. The tendency f o r drought y e a r s t o occur nonrandomly s u g g e s t s t h e d e s i r a b i l i t y of p r o v i d i n g a long t i m e base f o r low-flow
frequency curves.
One way t o do t h i s
would b e t o e x t e n d s h o r t r e c o r d s b y c o r r e l a t i o n w i t h l o n g o n e s and u s e t h e combined a c t u a l and s y n t h e t i c d i s c h a r g e s t o d e f i n e t h e frequency curve. of t h i s method i s r e p o r t e d by B i g g s 1972, p. 6-7). develop r a t i o s of s e l e c t e d low-flow
A test
A n o t h e r way would b e t o
c h a r a c t e r i s t i c s f o r various periods i n time
t o t h o s e f o r t h e t o t a l p e r i o d a t one o r more l o n g - r e c o r d s t a t i o n s .
The f i r s t
169 approach i s s t a t i s t i c a l l y v a l i d o n l y when c o r r e l a t i o n w i t h a long r e c o r d i s h i g h (Fiering,
1963), and t h e second h a s n o t been t h o r o u g h l y t e s t e d .
N e i t h e r method
a p p e a r s t o b e of much p r a c t i c a l value.
Fig. 9.4. E f f e c t of p e r i o d of r e c o r d on low-flow Biver. F l o r i d a (From Riggs, 1980).
frequency curve,
Ochlockonee
Seasonal r a i n f a l l averaged o v e r s e v e r a l s i t e s may h e l p t o i n t e r p r e t a lowflow record.
A p l o t o f low-flow
shown i n F i g u r e 9.5 the others.
d a t a f o r T a l l a p o o s a Biver a t Wadley,
Ala.,
is
i n which t h e 3 l o w e s t p o i n t s a p p e a r t o be "out of l i n e " w i t h
A c u r v e f i t t e d t o a l l t h e p o i n t s e i t h e r a n a l y t i c a l l y or by e y e
would be concave downward.
Such a shape on t h i s p l o t t i n g p a p e r i s unusual f o r
s t r e a m s w i t h low f l o w s of t h i s size.
Biggs (1961) r e l a t e d t h e annual minimum
f l o w s o f t h i s s t r e a m t o s p r i n g a n d summer p t e c i p i t a t i o n a n d f o u n d t h a t t h e 3 l o w e s t p l o t t e d p o i n t s corresponded t o t h e 3 s m a l l e s t p r e c i p i t a t i o n e v e n t s i n a t l e a s t 68 years.
When t h e r e c u r r e n c e i n t e r v a l s o f t h e 3 p o i n t s a r e based on t h e
68 y e a r p e r i o d a l l p o i n t s on t h e graph can b e averaged by a s t r a i g h t l i n e . 9.2.3
Seasonal frequency c u r v e s
Annual low f l o w s u s u a l l y occur i n t h e l a t e summer o r autumn i n t h e conterm i n o u s U n i t e d S t a t e s a l t h o u g h t h e r e a r e t w o low w a t e r s e a s o n s i n s o u t h e r n F l o r i d a a n d some a n n u a l low f l o w s o c c u r i n w i n t e r d u r i n g f r e e z e u p s i n t h e northern states.
I f t h e concern f o r low f l o w s i s independent of season t h e n t h e
f r e q u e n c y c u r v e o f an n u al low f l o w s i s ad equat e. monthly,
I f n o t , s e a s o n a l , or e v e n
low f l o w s s h o u l d b e u s ed t o d e f i n e a p p r o p r i a t e f r e q u e n c y cur ves.
Again, o n l y one d i s c h a r g e p e r y e a r i s u s ed t o d e f i n e a p a r t i c u l a r f r e q u e n c y curve.
170
I
1
1
*
From streamflow record
0
Based an precipitation records
RECURRENCE INTERVAL, IN Y E A R S
Fig. 9.5. Low-flow frequency plot s h o w i n g use of precipitation records to improve estimates of recurrence interval.
9.2.4
Regulated streams
Annual minimum flows of regulated streams may be considered as random events if they are all d r a w n f r o m a period in w h i c h the regulation w a s done in a consistent manner.
And of course the frequency curve derived from those minimum
flows applies only so long as that pattern of regulation continues. Where the low flow at a site is derived from substantial upstream reservoir releases, a basin m o d e l w h i c h routes those releases d o w n s t r e a m and includes estimates of inflows to the reach will simulate streamflow data under present conditions. curves.
These simulated data m a y be used to define low-flow frequency
Shearman and Swisshelm (1973) developed and applied such a model to the
Upper Kentucky River basin. LOW-FLOW CHARACTERISTICS AT UNGAGED SITES
9.3
T h e magnitudes of low base f l o w s depend on the geology of the basin and on the losses from evapotranspiration as well as on drainage area and precipitation.
Neither geology nor evapotranspiration can be reliably quantified i n a
basin.
Consequently, regression of low-flow characteristics on basin character-
istics is generally inadequate for estimating low-flow characteristics at ungaged sites.
Thomas and Benson (1970) found very high standard errors for such
regressions in 4 widely separated regions of the United States: their regression models did not include indices of geology or evapotranspiration. Various methods, including regression on basin characteristics, have b e e n used successfully in regions of limited areal extent over which the principal unmeasurable characteristics have little variation.
In other regions a regres-
sion equation w i t h a high standard error m a y provide a n acceptable tentative low-flow estimate when an answer is needed immediately.
171 9.3.1
P a r t i a l r e c o r d method
The most w i d e l y a p p l i c a b l e ,
and t h e most a c c u r a t e method o f e s t i m a t i n g low-
flow c h a r a c t e r i s t i c s a t an ungaged s i t e r e q u i r e s a few base-flow measurements a t t h e s i t e .
discharge
These measurements a r e r e l a t e d t o c o n c u r r e n t d i s -
c h a r g e s of a s t r e a m f o r which a low-flow
frequency c u r v e h a s been d e f i n e d :
then
p o i n t s on t h a t f r e q u e n c y c u r v e a r e t r a n s f e r r e d t h r o u g h t h e r e l a t i o n t o g e t e s t i m a t e s a t t h e ungaged s i t e .
F i g u r e 9.6
shows t h e procedure.
The base-flow
m e a s u r e m e n t s s h o u l d b e on d i f f e r e n t r e c e s s i o n s i n t h e s e a s o n when low f l o w s commonly occur.
20
and p r e f e r a b l y should be made i n two or more y e a r s .
50
100
200
500 1000
L
DISCHARGE OF PENN CREEK, IN CFS
F i g . 9.6. Base-flow measurements o f L o s t Creek r e l a t e d t o c o n c u r r e n t d i s c h a r g e s of Penn Creek. Low-flow c h a r a c t e r i s t i c s o f Penn Creek a r e t r a n s f e r r e d through the relation. E m p i r i c a l t e s t s u s i n g 24 p a i r s o f g a g i n g - s t a t i o n
records indicate t h a t the
r e l i a b i l i t y of a n e s t i m a t e of t h e 7-day 10-year low flow by t h i s method depends
on how w e l l t h e r e l a t i o n c u r v e i s d e f i n e d and how f a r t h e r e l a t i o n needs t o be e x t r a p o l a t e d downward. t o be ungaged,
I n t h e s e t e s t s one of each p a i r of s t a t i o n s was assumed
and low f l o w s s e l e c t e d randomly from i t s r e c o r d were assumed t o
r e p r e s e n t b a s e f l o w measurements. mean f l o w s a t t h e o t h e r s t a t i o n .
These were r e l a t e d t o t h e c o n c u r r e n t d a i l y The r e l a t i o n l i n e was drawn b e f o r e t h e known
7-day 1 0 - y e a r l o w f l o w s w e r e p l o t t e d .
F i g u r e 9.7
r e l a t i o n r e q u i r i n g a s m a l l downward e x t r a p o l a t i o n . of Moshammon Creek of about 8 c f s ,
i s a n e x a m p l e o f a good The 7-day
10-year
low flow
which would be e s t i m a t e d from t h e r e l a t i o n ,
c o m p a r e s f a v o r a b l y w i t h 9.7 c f s b a s e d on 3 2 y e a r s o f r e c o r d .
But when t h e
c o n c u r r e n t b a s e f l o w s of two s t r e a m s a r e n o t c l o s e l y r e l a t e d and when t h e 10y e a r low f l o w o f t h e i n d e x s t a t i o n i s f a r b e l o w t h e d e f i n e d r e l a t i o n ,
the
e s t i m a t e p r o b a b l y w i l l b e p o o r , e s p e c i a l l y i f i t i s l e s s t h a n one c f s .
Small
d i s c h a r g e s i n l a r g e channels a r e s u b j e c t t o s u b s t a n t i a l a b s t r a c t i o n s from evapot r a n s p i r a t i o n and t h e s e a b s t r a c t i o n s v a r y i n magnitude from y e a r t o year. r e s u l t s of a l l 24 t e s t s ,
The
in F i g u r e 9 8 . show t h a t r e l i a b l e e s t i m a t e s can u s u a l l y
be made f o r a l l b u t v e r y low discharges.
20 50 1 00 CONCURRENT FLOWS OF W.B. SUSQUEHANNA RIVER, IN CFS
F i g . 9.7. V e r i f i c a t i o n o f method o f e s t i m a t i n g 7-day 1 0 - y e a r l o x f l o w f r o m b a s e - f l o w m e a s u r e m e n t s . The X r e l a t e s t h e known v a l u e s o f 7-day 1 0 - y e a r low flows. R i g g s (1972) recommended t h a t t h e p a r t i a l - r e c o r d
method be used t o e s t i m a t e
t h e 7-day 1 0 - y e a r low f l o w e v e n i f up t o 1 0 y e a r s of c o n t i n u o u s s t r e a m f l o w record i s a v a i l a b l e .
E s t i m a t e s based on concurrent base-flows
tend t o be more
r e l i a b l e than those based on l e s s than 10 annual minimum f l o w s a t t h e s i t e . 9.3.2
Seepage runs
Ground-water i n f l o w t o , or o u t f l o w from, some c h a n n e l s i s c o n c e n t r a t e d i n p a r t i c u l a r reaches r a t h e r than being uniform along t h e channel.
Seepage r u n s
w i l l i d e n t i f y s i g n i f i c a n t channel g a i n s or l o s s e s and w i l l a i d i n i n t e r p r e t i n g
low-flow
c h a r a c t e r i s t i c s along a channel.
A seepage run c o n s i s t s of measuring
d i s q a r g e a t i n t e r v a l s along a channel reach during a p e r i o d of base flow. F i g u r e 9.9 i s a p l o t of d i s c h a r g e s m e a s u r e d on a d a y i n l a t e f a l l on a K a n s a s River.
The t r i b u t a r y flows were a l s o measured and were used t o i n t e r p r e t t h e
channel flows between measuring p o i n t s .
173
1001
10
I
'
I
I
1
U
0.1 0.1 1 10 100 7-DAY 10-YR LOW FLOW FROM GAGE RECORD, IN CFS
Fig. 9.8. stations.
Verification of the partial-record
20
"0
40 60 80 100 KILOMETERS ALONG CHANNEL
method based on 24 pairs of
120
Figure 9.9. Seepage-run data and interpretation on a Kansas River. tributaries are measured inflows. 9.3.3
Numbers at
Interpolation along a channel
Some extrapolation to ungaged sites may be achieved by plotting the low-flow characteristics at gaged sites against channel distance and by using low-flow characteristics at partial-record sites on tributaries to help interpret between gaged sites.
Figure 9.10 was prepared from information in the report by Carter
and Pntnam (1977).
Interpretation between gaged points may require estimating
low f l o w s of ungaged tributaries b y a trial-and-error process i n w h i c h the
174 objective is to d r a w a line w h i c h gives reasonable and consistent increases along the channel between tributaries and gaged points.
Gage on Ocmulgee River Gage on Oconee River 2 150 USGS gage number 0
x
Fig. 9.10. Interpolation of 7-day 10-year low f l o w s along channels, A l t a m a h a River basin, Georgia (From Riggs. 1980). If there is no significant difference between the low-flow characteristics at two gaged sites then one may assume that intervening tributaries have no flow at those times, or that the inflows and channel losses are approximately equal. Because of the lack of information between stations 2150 and 2155 on Figure 9.10, the graph s h o w s a uniform and quite large increase in l o w flow through that reach. tion.
Results of a seepage run should permit a more realistic interpreta-
175 REFERENCES Carter, R.F. and Putnam, S.A., 1977. Low-flow frequency of Georgia streams: U.S. Geol. Survey Water Resources Investigations 77-127. Fiering, M.B.. 1963. Use of correlation to improve estimates of the mean and variance: U.S. Geol. Survey Prof. Paper 434 C, 9 p. Hoyt., W.G., 1938, Drought of 1936, with discussion on the significance of drought in relation to climate: U.S. Geol. Survey Water-Supply Paper 820, p. 14. Jennings, M.E. and Benson, M.A., 1969, Frequency curves for annual flood series with some zero events or incomplete data: Water Resources Research, Vol. 5, NO. 1, p. 276-280. Riggs, EC., 1961. Rainfall and minimum flows along the Tallapoosa River, Alabama: U.S. Geol. Survey Prof. Paper 424-B, p. 96-98. Riggs, H.C., 1972, Low-flow investigations; U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 4, Chapter B1, 18 p. Riggs, Henry C., Chmn., 1980, Characteristics of low flows: Division, ASCE, Vol. 106, No. HY5, p. 717-731.
Jour. of Eydraulics
Shearman, J.O. and Swisshelm, R.V., Jr., 1973, Derivation of homogeneous streamflow records in the upper Kentucky River basin, southeastern Kentucky: U.S. Geol. Survey Open-File Rept., Louisville, Ky. Thomas, D.M. and Benson. M.A., 1970, Generalization of streamflow characteristics from drainage-basin characteristics: U.S. Geol. Survey Water-Supply Paper 1975.
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177
TEE CHANGING ENVIRONMENT 10.1
INTRODUCTION
Streamflow c h a r a c t e r i s t i c s change w i t h t i m e i n response t o n a t u r a l e v e n t s and t o man's a c t i v i t i e s .
Except f o r long-term
e v e n t s cause o n l y short-term
t r e n d s i n c l i m a t e , most n a t u r a l
changes i n s t r e a m f l o w c h a r a c t e r i s t i c s .
The e f f e c t s
of man's a c t i v i t i e s r a n g e f r o m n e g l i g i b l e t o m a j o r , b o t h i n m a g n i t u d e a n d i n dur a t ion. Knowledge o f l o n g - t e r m c l i m a t i c t r e n d s w o u l d p e r m i t b e t t e r e s t i m a t e s o f f u t u r e f l o w c h a r a c t e r i s t i c s t o b e made.
B u t r e c o r d s o f a h u n d r e d y e a r s or
a r e t o o s h o r t t o p o s i t i v e l y i d e n t i f y and q u a n t i f y a t r e n d . p e r i o d s of 30 or 40 y e a r s may be o n l y temporary. annual p r e c i p i t a t i o n r e c o r d i n F i g u r e 10.1 p a r t a n d a n upward t r e n d i n t h e l a t t e r .
SO
T r e n d s d e f i n e d by
For example,
t h e Great Lakes
shows a downward t r e n d i n t h e e a r l y L i k e w i s e , t r e n d s up t o t e n s o f y e a r s
c a n b e i d e n t i f i e d in some s t r e a m f l o w r e c o r d s b u t t h e r e i s no a s s u r a n c e t h a t t h e s e w i l l c o n t i n u e f o r an a p p r e c i a b l e time.
600
l
1860
i
I
1880
t
l
1900
On t h e o t h e r hand t h e flow of Labe
10.2) shows no t r e n d in over 100 years.
River i n Czechoslovakia (Fig.
i
1
1920
r
I
1940
I
I
1960
'
I
1980
Years F i g . 10.1.
G r e a t Lakes annual p r e c i p i t a t i o n (From Quinn. 1981).
The e f f e c t s of man's a c t i v i t i e s a r e needed for a s s e s s i n g t h e d e s i r a b i l i t y or t h e consequences of some proposed development.
Most e f f e c t s on w a t e r r e s o u r c e s
a r e d i f f i c u l t t o q u a n t i f y because t h e y tend t o be obscured by t h e n a t u r a l v a r i a b i l i t y of streamflow.
And t h e e f f e c t s d e f i n e d on one b a s i n may be only a n
a p p r o x i m a t i o n of t h a t w h i c h would o c c u r on o t h e r s u n d e r t h e same t r e a t m e n t .
178 Generalizations a r e necessary,
however,
i n p l a n n i n g ; t h e s e c a n b e b a s e d on
a n a l y s e s of b a s i n s t h a t were changed, and on an u n d e r s t a n d i n g of t h e hydrology of t h e s u b j e c t b a s i n s .
Fig.
10.2.
Annual mean f l o w s o f Labe R i v e r , Czechoslovakia,
1851-1968.
T h i s c h a p t e r d e s c r i b e s e f f e c t s on w a t e r r e s o u r c e s of n a t u r a l man's a c t i v i t i e s ,
e v e n t s and of
and c o n c l u d e s w i t h some a n a l y t i c a l methods of d e f i n i n g change.
A b r o a d e r g e o g r a p h i c c o v e r a g e of e f f e c t s of man on w a t e r r e s o u r c e s i s g i v e n by P e r e i r a (1973). 10.2
CHANGES DUE To NATURAL EVENTS
Some o b s e r v e d c h a n g e s in s t r e a m c h a n n e l s w i t h i n t h e l a s t 1 0 0 y e a r s or so m i g h t b e i n t e r p r e t e d a s i n d i c a t i o n s of c l i m a t i c c h a n g e . velopment,
One s u c h i s t h e de-
s i n c e a b o u t 1 8 5 0 . o f many a r r o y o s i n s o u t h w e s t e r n U n i t e d S t a t e s .
O p i n i o n s v a r y a s t o w h e t h e r t h i s was c a u s e d by p r e c i p i t a t i o n c h a n g e s or b y l i v e s t o c k grazing,
or b o t h (Cooke and Reeves, 1976; Schumni and Hadley, 1957).
Schumm ( 1 9 7 7 ) r e p o r t e d t h e d e s t r u c t i o n o f t h e h i g h l y s i n u o u s , r e l a t i v e l y narrow and deep Cimarron R i v e r c h a n n e l i n s o u t h w e s t e r n Kansas by t h e major f l o o d o f 1914.
W i t h i n t h e n e x t 20 or 25 y e a r s of g e n e r a l l y below a v e r a g e p r e c i p i t a -
t i o n t h e c h a n n e l widened from 50 t o 1200 f e e t .
Burkham ( 1 9 7 2 ) d o c u m e n t e d t h e
h i s t o r y of a p o r t i o n of t h e c h a n n e l o f G i l a R i v e r , Arizona.
The c h a n n e l w a s
f a i r l y s t a b l e and narrow from 1846 t o 1904 and meandered t h r o u g h a f l o o d p l a i n . Average w i d t h was l e s s t h a n 1 5 0 f e e t i n 1875 and l e s s t h a n 300 f e e t i n 1904. During 1905-17
l a r g e f l o o d s which c a r r i e d low s e d i m e n t l o a d s d e s t r o y e d t h e f l o o d
p l a i n a n d i n c r e a s e d t h e c h a n n e l w i d t h t o a b o u t 2000 f t . r e f o r m e d 1918-70
The f l o o d p l a i n w a s
due t o o c c u r r e n c e o f o n l y r e l a t i v e l y low f l o o d p e a k s c a r r y i n g
l a r g e s e d i m e n t l o a d s , and by t h e development of a dense c o v e r of s a l t c e d a r . a v e r a g e c h a n n e l w i d t h w a s 2 0 0 f e e t i n 1 9 6 4 and 400 f e e t i n 1 9 6 8 .
The
The a v e r a g e
179 annual f l o w s f o r t h e p e r i o d s 1918-64 and 1846-1904 were e s t i m a t e d t o be about t h e same.
Some o t h e r m a j o r c h a n g e s i n c h a n n e l g e o m e t r y r e s u l t i n g f r o m m a j o r
f l o o d s a r e d e s c r i b e d by Stevens, Simons, and Richardson (1975). These channel changes may have been r e s p o n s e s t o changes i n f l o w c h a r a c t e r i s t i c s b u t homogeneous s t r e a m f l o w r e c o r d s a r e t o o s h o r t t o v e r i f y t h i s .
An on-
g o i n g p r o g r a m o f g a g i n g 57 n a t u r a l s t r e a m s i n d e f i n i t e l y t o p r o v i d e t h e l o n g r e c o r d s needed t o a s s e s s n a t u r a l changes i s d e s c r i b e d i n a r e p o r t on Hydrologic Bench Marks by Cobb B B i e s e c k e r (1971). Some n a t u r a l e v e n t s produce s u b s t a n t i a l changes i n t h e hydrology of l i m i t e d geographical regions.
The e a r t h q u a k e s o f 1 8 1 1 c a u s e d l a n d s u b s i d e n c e o v e r
s e v e r a l hundred s q u a r e m i l e s i n M i s s o u r i and Tennessee, m a t i o n of t h e 20-square
r e s u l t i n g i n t he for-
m i l e R e e l f o o t Lake and many s m a l l e r lakes.
caused by e a r t h q u a k e s may a l t e r t h e topography;
Landslides
a major earthquake i n w e s t e r n
Montana i n 1 9 5 9 c a u s e d a l a n d s l i d e w h i c h f o r m e d a dam o v e r 1 8 0 f e e t h i g h on Madison R i v e r ; w a t e r was backed up 6 m i l e s .
I n a d d i t i o n t o t h e d i s r u p t i o n of
flow below t h e l a n d s l i d e , prompt i n c r e a s e s i n s t r e a m f l o w were n o t e d a t a number o f g a g i n g s t a t i o n s on o t h e r s t r e a m s i n t h e a r e a ( S t e r m i t z , 1 9 6 4 ) .
E f f e c t s of
t h e e a r t h q u a k e on s t r e a m f l o w w e r e n o t d e t e c t e d a f t e r a f e w m o n t h s , e x c e p t on Madison River. Hutchinson (1957, t h e world.
p.
42-47)
d e s c r i b e s l a k e s formed by l a n d s l i d e s throughout
Some h a v e e x i s t e d f o r many y e a r s .
O t h e r s were t e m p o r a r y and pro-
d u c e d c a t a s t r o p h i c f l o o d s when t h e dam f a i l e d . s e d i m e n t t o s t r e a m c h a n n e l s i n some r e g i o n s .
L a n d s l i d e s c o n t r i b u t e much
F i g u r e 10.3 shows a heavy accumu-
l a t i o n o f s e d i m e n t r e s u l t i n g f r o m a l a n d s l i d e on a s m a l l t r i b u t a r y t o t h e Sun Kosi i n Nepal. O c c a s i o n a l l y g l a c i e r movement c a u s e s s t o r a g e and subsequent r a p i d r e l e a s e of water.
The annual f l o o d peaks of Knik River, Alaska, were g r e a t l y i n c r e a s e d f o r
a t l e a s t 1 4 y e a r s b e c a u s e Knik G l a c i e r advanced a c r o s s Knik R i v e r each w i n t e r and t e m p o r a r i l y s t o r e d t h e s p r i n g r u n o f f .
D e s t r u c t i o n o f t h e i c e dam e a c h
summer b y m e l t i n g a n d e r o s i o n r e l e a s e d t h e s t o r e d w a t e r c a u s i n g a f l o o d p e a k about an o r d e r of magnitude g r e a t e r t h a n would have o c c u r r e d w i t h o u t t h e g l a c i e r blockage.
S e e F i g u r e 2.15 ( C h a p t e r 2 ) .
o c c u r r e d i n 1922 on I c e l a n d .
One o f t h e l a r g e s t f l o o d s o f r e c o r d
The peak d i s c h a r g e of a l m o s t 2 m i l l i o n c u b i c f e e t
p e r second r e s u l t e d from a g l a c i e r o u t b u r s t which r e l e a s e d about 1.7 c u b i c m i l e s of w a t e r o v e r a 4-day p e r i o d (Meier, 1969).
Glacier-dammed l a k e s i n o t h e r p a r t s
of t h e world a r e r e p o r t e d by Hutchinson (1957, p. 50-53). G l a c i e r s advance and r e t r e a t i n r e s p o n s e t o s m a l l b u t p e r s i s t e n t changes i n climate.
The r u n o f f of a s t r e a m f e d by a g l a c i e r w i l l be reduced i f t h e g l a c i e r
i s advancing and t h u s s t o r i n g w a t e r a s ice.
Conversely a r e t r e a t i n g g l a c i e r i s
r e l e a s i n g w a t e r and t h e r u n o f f from i t may exceed p r e c i p i t a t i o n .
E s t i m a t e s of
180 long-term
f l o w c h a r a c t e r i s t i c s o f s t r e a m s f e d by g l a c i e r s s h o u l d t a k e i n t o
account t h e e f f e c t of g l a c i e r movement d u r i n g t h e p e r i o d of record.
F i g . 10.3. E f f e c t o f a l a n d s l i d e on t h e c h a n n e l o f a s m a l l t r i b u t a r y o f Sun Kosi, Nepal. Flow C h a r a c t e r i s t i c s o f a s m a l l s t r e a m c a n be s u b s t a n t i a l l y a l t e r e d by cons t r u c t i o n of b e a v e r dams.
The impounded w a t e r promotes i n c r e a s e d e v a p o r a t i o n
and g r o u n d - w a t e r r e c h a r g e , a l b e i t o n l y t e m p o r a r i l y ; a f l o o d may w a s h o u t t h e s e r i e s o f dams a n d r e t u r n t h e s t r e a m t o i t s p r e v i o u s c o n d i t i o n e x c e p t f o r reduced r i p a r i a n timber. B r u s h and f o r e s t f i r e s o f t e n r e s u l t f r o m l i g h t n i n g s t r i k e s .
The r e d u c e d
p l a n t cover and t h e m o d i f i e d s o i l cover r e s u l t i n g from a f i r e change t h e d i s p o s i t i o n o f r a i n or snow on a b a s i n .
I n t e r c e p t i o n i s reduced b u t t h e change i n
i n f i l t r a t i o n depends on t h e o r i g i n a l s o i l cover and on t h e s o i l c h a r a c t e r i s t i c s . The r a t e and amount of r u n o f f from a s t o r m a l s o depends on t h e b a s i n topography.
On t h e San Dimas E x p e r i m e n t a l F o r e s t i n t h e San G a b r i e l Mountains of Southern C a l i f o r n i a a 2.4 s q u a r e m i l e w a t e r s h e d h a d a b o u t o n e - t h i r d o f i t s v e g e t a t i o n d e s t r o y e d by a w i l d f i r e i n December 1953.
A n a l y s i s of t h e p r e c i p i t a t i o n and
s t r e a m f l o w r e c o r d s f o r 1 7 y e a r s p r e v i o u s t o a n d 2 y e a r s a f t e r t h e f i r e showed t o t a l storm d i s c h a r g e s were t h r e e t o f i v e t i m e s a s g r e a t a f t e r t h e f i r e a s
18 1 b e f o r e , and t h a t p e a k f l o w s w e r e i n c r e a s e d b y a n o r d e r o f m a g n i t u d e o r more because of t h e f i r e ( S i n c l a i r and Hamilton,
1955).
The e f f e c t o f f i r e on t h e s m a l l s t e e p b a s i n i n t h e S a n D i m a s E x p e r i m e n t a l F o r e s t i s extreme.
Storm runoff from l a r g e r b a s i n s w i t h l o w e r topographic
r e l i e f and l e s s i n t e n s e r a i n f a l l s might show l i t t l e or no e f f e c t from f i r e . The n a t u r a l e v e n t t h a t p r o d u c e d t h e g r e a t e s t h y d r o l o g i c c h a n g e i n r e c e n t y e a r s was t h e v o l c a n i c e r u p t i o n of M t .
St. Helens i n Washington S t a t e (Findley.
1981).
The volcano e j e c t e d l a r g e q u a n t i t i e s o f a s h which m e l t e d t h e heavy snow
pack.
The r e s u l t i n g f l o o d s c a u s e d m a j o r d e s t r u c t i o n a l o n g t h e c h a n n e l s and
c a r r i e d t h e a s h and o t h e r d e b r i s f o r many m i l e s , t h e s h i p p i n g c h a n n e l of
Columbia R i v e r .
F i g u r e 10.4,
f i n a l l y clogging
After the flood receded the stream
c h a n n e l s were l e f t w i t h d e p o s i t s o f a s h (Fig. 10.5) which g r e a t l y reduced t h e i r carrying capacity.
Thus what was p r e v i o u s l y c o n s i d e r e d a minor f l o o d d i s c h a r g e
on one of t h e s e c h a n n e l s w i l l now i n u n d a t e l a r g e a r e a s along t h e s t r e a m and w i l l move more m a t e r i a l downstream and f u r t h e r reduce t h e channel c a p a c i t y i n t h e T o u t l e and C o w l i t z Rivers.
Fig. 10.4. Map of M t . St. Helens area. S t r e a m s a f f e c t e d by major mudflows a r e i n d i c a t e d by heavy l i n e s (Prom Meier and o t h e r s , 1981).
In 1877 a major e r u p t i o n of M t . Cotopaxi, Ecuador. melted t h e snow and i c e on i t s s l o p e s and produced a f l a s h f l o o d and mud f l o w t h a t inundated v a l l e y s a s f a r a s 200 m i l e s away (Morrison,
1975).
182
Fig. 10.5. Channel filled with debris as a result of Mt. St. Helens eruption (USGS photo). EFFECTS OF MAN’S ACTIVITIES
10.3
10.3.1
Surface storage
Dam construction increases evaporation l o s s e s , may increase ground-water recharge. and will change the flow regime downstream whether flow past the dam is regulated or not.
The effect of increased evaporation due to reservoirs may
b e negligible in humid regions because that evaporation is balanced by the
increased supply resulting from rainfall on the water surface rather than on the previous land surface.
But in arid regions reservoir evaporation may limit the
yield available from storage; beyond some reservoir capacity the loss from the increased reservoir surface area will b e greater than the additional yield (Langbein, 1959). Loss from a reservoir to ground water may b e larger than that in the same reach before the reservoir existed.
Ordinarily such losses are not large but as
the residual in a water-budget equation, are difficult to estimate reliably. If the ground-water table is in continuity with a stream whose level is raised by construction of a dam, then the water table will be raised accordingly.
This may direct some ground-water flow to adjacent channels and may in-
crease evapotranspiration from the ground water, both of which constitute a loss from storage. The flow regimen below a storage reservoir depends on the purpose of the impoundment, the design, and the operation.
The purpose of most impoundments is
18 3 to change the f l o w r e g i m e n to provide f l o w s w h e n needed, or to reduce flood flows.
Examples of changes due to impoundments are given in Figures 10.6,
and 10.8.
10.7
Diurnal fluctuations, not s h o w n in the examples, m a y be e x t r e m e if
the flow is regulated for power generation.
1000
0.1 1 5 20 50 80 9599 99.9
PERCENTOFTIME DISCHARGE W A S GREATERTHAN
Fig. 10.6. Duration curves for Savannah River at Augusta, Georgia, before and after construction of Clark Hill Reservoir (From Stallings, 1967).
10,000
I
O
N
D
J
F
M
A
M
J
J
A
S
MONTHS
Fig. 10.7. I n f l o w and o u t f l o w of O w y h e e Reservoir, Oregon, 1978 w a t e r year. Changes in reservoir contents and diversions for irrigation account for the differences.
184
100,000
I
\
10,000
I
INFLOW
1000
100
10
FEB
MARCH
APRIL
1978
F i g . 10.8. F l o w r e d u c t i o n d u e t o P a i n t e d Rock f l o o d - c o n t r o l R i v e r , Arizona. F i g u r e 10.9
reservoir, Gila
s h o w s t h e m o d e r a t i n g e f f e c t of a n SCS f l o o d - w a t e r
s t r u c t u r e under normal conditions.
retarding
The e f f e c t w i l l b e s l i g h t i f t h e f l o o d
o c c u r s when t h e r e s e r v o i r i s n e a r l y f u l l .
Reservoirs of t h i s type a r e u s u a l l y
b u i l t on many s m a l l s t r e a m s i n a b a s i n s o t h a t t h e i r a g g r e g a t e e f f e c t i s t o s u b s t a n t i a l l y reduce t h e peak f l o w s downstream.
A s e r i e s of r e s e r v o i r s of t h i s
t y p e was shown b y G i l b e r t a n d S a u e r ( 1 9 7 0 ) t o r e d u c e t h e a n n u a l r u n o f f a p p r e c i a b l y f o r y e a r s o f low i n f l o w b u t o n l y m o d e r a t e l y f o r y e a r s o f h i g h i n f l o w (Fig.
10.10).
Farm ponds and s t o c k t a n k s ( r e s e r v o i r s ) a r e b u i l t on many s m a l l s t r e a m s b u t few of t h e s e a r e shown on maps.
A s t u d y i n t h e 1950s o f t h e C h e y e n n e R i v e r
b a s i n ( i n Wyoming, S o u t h D a k o t a , and N e b r a s k a ) a b o v e A n g o s t u r a Dam c o n c l u d e d t h a t t h e r e were a b o u t 9,320 s t o c k r e s e r v o i r s w i t h a s t o r a g e c a p a c i t y of 52,360 acre-feet, miles.
and t h a t t h e s e r e s e r v o i r s c o n t r o l l e d a n a g g r e g a t e o f 4 , 4 4 0 s q u a r e
Based on 4-year
r e c o r d s of i n f l o w and o u t f l o w f o r a b o u t 50 r e s e r v o i r s ,
t h e e s t i m a t e s of l o s s e s chargeable t o a l l t h e r e s e r v o i r s i n t h e b a s i n ranged f r o m 19,000 a c r e - f e e t
i n a d r y y e a r t o 80,000 a c r e - f e e t
i n a very wet year.
Annual r u n o f f f r o m t h e b a s i n r a n g e s f r o m 50,000 t o 1 8 0 , 0 0 0 a c r e - f e e t ( C u l l e r , 1961). Farm p o n d s i n h u m i d r e g i o n s may n o t r e d u c e s t r e a m f l o w y i e l d a p p r e c i a b l y because pond e v a p o r a t i o n i s compensated f o r by r a i n f a l l on t h e w a t e r s u r f a c e . They may reduce f l o o d peaks o f s m a l l r e c u r r e n c e i n t e r v a l s .
185
LL
0
3
9 LL
z_
i-
look
1 000 (I)
28
30
APR.
-
OUTFLOW
...-..
10
-
2 1958
4
6
8
MAY
F i g . 10.9. M o d i f i c a t i o n o f f l o w by a f i x e d - o u t l e t s t r u c t u r e (From G i l b e r t and o t h e r s , 1 9 6 4 ) .
floodwater-retarding
(I)
W
I
u
z z
3
0
1 LL
F
3
0
2 3
z z Q
ANNUAL NET INFLOW, IN INCHES
Fig. 10.10. Graph showing r e d u c t i o n i n annual flow due t o d e t e n t i o n r e s e r v o i r s i n 7 s t u d y a r e a s in Texas. Each s t u d y a r e a had f r o m 1 t o 1 2 d e t e n t i o n r e s e r v o i r s (From G i l b e r t and Saner. 1970). Observations of runoff and sediment y i e l d were made over a p e r i o d of y e a r s a t about 200 s m a l l r e s e r v o i r s in t h e M i s s o u r i River, Colorado River, and Rio Grande b a s i n s from Montana t o s o u t h e r n Arizona.
The r e s e r v o i r s ranged i n c a p a c i t y from
0.2 t o 1,012 a c r e - f e e t and t h e c o n t r i b u t i n g d r a i n a g e a r e a s ranged from 0.1 t o 5 5 square miles.
The r e s e r v o i r s were s e l e c t e d t o sample a wide range i n c l i m a t e ,
topography, geology,
s o i l , and v e g e t a t i o n types.
Consequently a wide v a r i a t i o n
186 i n r a t e s o f r u n o f f and s e d i m e n t y i e l d w a s f o u n d ( P e t e r s o n , 1 9 6 2 ) .
S p i l l from
t h e r e s e r v o i r s ranged from z e r o t o a s much a s 95 p e r c e n t of t h e i n f l o w depending
on t h e y e a r ,
t h e s i z e and c h a r a c t e r of t h e b a s i n ,
and t h e s i z e of t h e r e s e r v o i r
r e l a t i v e t o t h e inflow. Major changes i n f l o w r e g i m e s r e s u l t from f l o w d i v e r s i o n s which may o r may not be i n conjunction w i t h storage projects.
Major d i v e r s i o n s a r e u s u a l l y
measured or t h e f l o w below t h e d i v e r s i o n i s gaged.
Occasional measurements of a
s m a l l d i v e r s i o n can be used t o a d j u s t t h e upstream monthly mean f l o w s f o r t h e diversion. An i n f r e q u e n t consequence of s u r f a c e s t o r a g e i s a d i s a s t r o u s downstream f l o o d due t o dam f a i l u r e o r some o t h e r a c c i d e n t r e l a t e d t o t h e s t o r a g e p r o j e c t .
The
w o r s t d i s a s t e r o f t h i s t y p e w a s t h e J o h n s t o w n , Pa. dam f a i l u r e o f 1889.
The
r e s u l t i n g w a l l o f w a t e r 30 t o 40 f e e t h i g h c l e a n e d o u t t h e downstream v a l l e y and took 2100 l i v e s (Hoyt and Langbein,
1955).
Some y e a r s ago a n enormous wedge of
earth s l i d into a reservoir i n northern I t a l y raising the water level t o w e l l above t h e t o p of t h e dam and c a u s i n g major damage and l o s s of l i f e downstream. The m o r e r e c e n t f a i l u r e o f T e t o n Dam i n I d a h o i n 1 9 7 6 , a n d o f some s m a l l e r s t r u c t u r e s i n o t h e r S t a t e s l e d t o programs f o r e v a l u a t i n g t h e s a f e t y of e x i s t i n g dams i n t h e U n i t e d S t a t e s .
A s i m i l a r program i s being c a r r i e d o u t i n G r e a t
Britain. The changed f l o w regime below a dam may a f f e c t t h e geometry of t h e channel and i t s b i o l o g i c and e s t h e t i c c h a r a c t e r .
Reservoir r e l e a s e s u s u a l l y c a r r y l e s s
s e d i m e n t t h a n t h e n a t u r a l f l o w : c o n s e q u e n t l y f o r some d i s t a n c e b e l o w t h e dam t h e y p i c k up s e d i m e n t b y e r o d i n g t h e c h a n n e l .
The s m a l l e r f l o o d p e a k s and
p o s s i b l y h i g h e r minimum f l o w s u s u a l l y r e s u l t i n a d j u s t m e n t t o a s m a l l e r channel f u r t h e r downstream because of s e d i m e n t d e p o s i t s and encroachment by v e g e t a t i o n . Gregory and P a r k (1974) g i v e n a n example.
Schumm (1977) d e s c r i b e s r i v e r meta-
morphoses r e s u l t i n g from flow r e g u l a t i o n , and W i l l i a m s (1978) documented changes i n t h e c h a n n e l s of t h e North P l a t t e and P l a t t e R i v e r s i n Nebraska, some of which a r e p r e s e n t l y o n l y 0.1 o r 0.2 a s wide a s they were 100 y e a r s ago. The q u a l i t y o f w a t e r r e l e a s e d f r o m d e e p r e s e r v o i r s i n t e m p e r a t e l a t i t u d e s d i f f e r s from t h a t of t h e i n f l o w n o t o n l y i n amount of s u s p e n d e d m a t e r i a l b u t a l s o i n t e m p e r a t u r e and sometimes i n d i s s o l v e d s o l i d s c o n c e n t r a t i o n .
The u s u a l
c o n d i t i o n o f t h e r m a l s t r a t i f i c a t i o n i n a r e s e r v o i r d u r i n g summer i s shown i n F i g u r e 10.11. the intake.
The t e m p e r a t u r e of r e l e a s e d w a t e r w i l l depend on t h e e l e v a t i o n of S i n c e c o n s t r u c t i o n o f Glen Canyon Dam on Colorado River, Arizona,
w a t e r t e m p e r a t u r e s a t Lees F e r r y , a few m i l e s downstream, a r e h i g h e r i n w i n t e r and c o o l e r i n summer than before. I f c h e m i c a l s t r a t i f i c a t i o n o c c u r s i n a r e s e r v o i r t h e q u a l i t y of t h e w a t e r r e l e a s e d a l s o depends on t h e d e p t h of t h e intake. s o l i d s i n Flaming Gorge R e s e r v o i r ,
Wyoming-Utah,
The d i s t r i b u t i o n of d i s s o l v e d shows c o n c e n t r a t i o n s r a n g i n g
from 450 mg/l at depths of 100 feet to I00 mgll near the 400-foot depth (Madison and Waddell, 1973).
The mean concentration of dissolved solids in Flaming Gorge
Reservoir is significantly greater than that of the inflows because of leaching from the inundated areas.
0 v)
U
W
5z
10
I' Ii
#
20 I
0
4
I
I
I
I
8
12
16
20
TEMPERATURE, IN DEGREES C
Figure 10.11.
Typical vertical distribution of lake temperature during summer.
Prior to 1964 when the Aswan High Dam went into operation, floods on the Nile River r e m o v e d domestic, industrial, and agricultural wastes annually.
Since
then floods no longer occur; the flow follows requirements for irrigation and for hydropower generation from the Dam.
Consequently the River below the Dam is
accumulating pollutants in spite of a 1962 law prohibiting disposal of industrial w a s t e s in public w a t e r bodies unless certain r e q u i r e m e n t s are met. (Mobarek, 1980). 10.3.2
Land-use changes
Modification of the land surface and of the vegetal cover affects the hydrology of a basin in varying degrees depending on the magnitude and areal extent of
the change and on t h e physical characteristics of the b a s i n and its climate. The difficulty of identifying changes in the hydrology attributable to small or moderate changes in the basin accounts for some of the conflicting reports in the literature.
Conclusions from one valid experiment may not apply to other
regions o r basins.
S o m e general statements about t h e qualitative effects of
certain land treatments, however, are widely applicable and are useful in planning and design of water-resources proj acts. (i) T i m b e r lands.
T h e m a n a g e m e n t of t i m b e r lands for b o t h w o o d and w a t e r
requires an understanding of how logging and reforestation affect streamflow. Changes m a y occur in annual yield, s u m m e r l o w flow, magnitude and r e g i m e n of floods, and distribution of flow throughout the year.
In general, removal of
188 t r e e s r e d u c e s i n t e r c e p t i o n and e v a p o t r a n s p i r a t i o n and p e r m i t s more of t h e prec i p i t a t i o n t o r e a c h t h e streams.
In humid n o r t h e a s t e r n United S t a t e s removal of
a l l v e g e t a t i o n from a f o r e s t e d w a t e r s h e d w i l l i n c r e a s e annual w a t e r y i e l d t h e f i r s t y e a r a f t e r t r e a t m e n t b y 4 t o 12 i n c h e s ( L u l l a n d B e i n h a r t , 1967).
The
wide r a n g e o f t h e s e i n c r e a s e s i s a t t r i b u t e d t o t h e methods o f l o g g i n g and t o c l i m a t i c d i f f e r e n c e s among b a s i n s . s h r u b s b e g i n s soon a f t e r logging.
In such humid r e g i o n s r e g r o w t h of t r e e s and Consequently t h e s t r e a m f l o w y i e l d t r e n d s back
toward t h e p r e c u t t i n g v a l u e s a l t h o u g h s u b s t a n t i a l i n c r e a s e s may be m a i n t a i n e d f o r years.
T h i s w a s d e m o u s t r a t e d by Swank a n d H e l v e y (1970) who r e c o r d e d t h e
a n n u a l w a t e r y i e l d f r o m a s m a l l b a s i n t h a t w a s c l e a r c u t i n 1939 a n d a g a i n i n
1962.
During t h e second r e g r o w t h p e r i o d ( a f t e r 1962) s t r e a m f l o w i n c r e a s e s a f t e r
t h e f i r s t y e a r w e r e a b o u t h a l f t h e i n c r e a s e s a t t h e same p o i n t s i n t i m e a f t e r t h e f i r s t t r e a t m e n t ( S w i f t and Swank, 1981). C l e a r c u t t i n g p a r t of a b a s i n should r e s u l t i n a n i n c r e a s e p r o p o r t i o n a l t o t h e p e r c e n t a g e of a r e a logged: fect.
s e l e c t i v e c u t t i n g p r o b a b l y would have a l e s s e r ef-
C u t t i n g o n l y 1 0 t o 20 p e r c e n t o f a b a s i n u s u a l l y p r o d u c e s e f f e c t s t o o
s m a l l t o be d e t e c t e d . Flood f l o w s may be i n c r e a s e d by logging b u t t h e change i s u s u a l l y d i f f i c u l t t o detect.
Schneider and Ayer (1961) analyzed r u n o f f from two s m a l l c e n t r a l New
York b a s i n s , one a g r i c u l t u r a l and t h e o t h e r b e i n g r e f o r e s t e d .
They c o n c l u d e d
t h a t t h e f l o o d p e a k m a g n i t u d e s d e c r e a s e d on t h e r e f o r e s t e d b a s i n a s t h e t r e e s grew and t h a t s p r i n g f l o o d s o c c u r r e d l a t e r . of a n a l y s i s .
See s e c t i o n 10.4.1
f o r t h e i r method
A n a l y s i s o f t h e same d a t a b y S a t t e r l u n d and E s c h n e r (1965) r e -
v e a l e d t h a t r u n o f f d u r i n g snowmelt p e r i o d s i s g r a d u a l l y c o n c e n t r a t e d i n a s h o r t e r t i m e f o l l o w i n g r e f o r e s t a t i o n o f o p e n l a n d s and t h a t t h e r e i s a g r a d u a l d e s y n c h r o n i z a t i o n w i t h r u n o f f from t h e a g r i c u l t u r a l w a t e r s h e d s o t h a t t h e conc e n t r a t e d snowmel t r u n o f f comes l a t e r i n t h e s e a s o n i n t h e y e a r s f o l l o w i n g ref orest a tion. Hewlett and Eelvey (1970) r e p o r t e d t h a t c l e a r c u t t i n g a m a t u r e hardwood f o r e s t i n t h e s o u t h e r n Appalachians caused i n c r e a s e s of about 11 p e r c e n t i n s t o r m f l o w volumes.
Peak d i s c h a r g e s i n c r e a s e d s l i g h t l y a f t e r l o g g i n g b u t t h e s t a t i s t i c a l
s i g n i f i c a n c e t e s t f o r peaks was n o t a s c o n c l u s i v e a s t h a t f o r volumes. S e l e c t i v e t i m b e r r e m o v a l has. b e e n f o u n d t o a f f e c t snow a c c u m u l a t i o n , t h e t i m i n g of snowmelt,
the water yield,
and t h e peak r u n o f f
t i m i n g and magnitude
b u t t h e e f f e c t s v a r y w i d e l y on v a r i o u s t o p o g r a p h i c s i t e s (Anderson and o t h e r s ,
1958). Anderson (1960) d e s c r i b e d v a r i o u s r e s e a r c h management s t u d i e s and concluded t h a t t h e r e i s no s i n g l e way o f m a n a g i n g l a n d i n t h e snow z o n e t o i m p r o v e a l l a s p e c t s of w a t e r y i e l d :
more w a t e r , b e t t e r t i m i n g of w a t e r y i e l d , b e t t e r
q u a l i t y o f w a t e r , and reduced f l o o d s and s e d i m e n t movement.
189 Replacement of hardwoods w i t h p i n e i n e a s t e r n United S t a t e s r e s u l t e d , 10 years.
i n a reduction i n water yield,
because of g r e a t e r i n t e r c e p t i o n l o s s .
on w a t e r use by t a l l r a i n f o r e s t ,
after
m o s t l y i n t h e dormant season, probably
R e s u l t s of e x p e r i m e n t s i n t r o p i c a l A f r i c a
tea plantations,
bamboo,
and p i n e and c y p r e s s
a r e g i v e n by P e r e i r a (1973). Base f l o w s c a n be s u b s t a n t i a l l y i n c r e a s e d by removing t r e e s and s h r u b s adjac e n t t o t h e s t r e a m c h a n n e l s b u t c u t t i n g on h i l l t o p s and a t i n t e r m e d i a t e elevat i o n s w e l l above t h e r a t e r t a b l e h a s l i t t l e e f f e c t .
Dunford and F l e t c h e r (1947)
r e p o r t e d t h a t c u t t i n g s t r e a m - b a n k v e g e t a t i o n on a 2 2 - a c r e
watershed i n the
Coweeta E x p e r i m e n t a l F o r e s t i n North C a r o l i n a v i r t u a l l y e l i m i n a t e d t h e d i u r n a l f l u c t u a t i o n d u r i n g t h e growing s e a s o n and i n c r e a s e d d a i l y mean f l o w s from 4 t o 1 9 percent i n a recession period.
A s t u d y o f low f l o w s i n t h e Rappahannock
River b a s i n i n V i r g i n i a l e d t o t h e f o l l o w i n g c o n c l u s i o n s :
(1) t h a t t h e d i f f e r -
e n c e s among low f l o w s ( p e r u n i t a r e a ) o f t h e n i n e s t r e a m s s t u d i e d a r e r e l a t e d t o d i f f e r e n c e s i n t h e p r o p o r t i o n s of c l e a r e d l a n d i n t h e b a s i n s , c l e a r e d land,
(2) t h a t the
m o s t l y i n p a s t u r e , g e n e r a l l y produces h i g h e r summer and f a l l b a s e
f l o w s t h a n t i m b e r e d l a n d , (31 t h a t t h e l a n d - c l e a r i n g
effects are proportionally
g r e a t e s t a t t h e l o w e r d i s c h a r g e r a t e s , and (4) t h a t f o r t h e purpose of i n c r e a s c l e a r i n g i s most e f f e c t i v e a d j a c e n t t o s t r e a m
i n g summer and f a l l b a s e flows, channels (Riggs, 1965).
Many o t h e r s t u d i e s ,
Johnson and Meginnis (1960).
some o f w h i c h a r e r e p o r t e d by
s u b s t a n t i a t e t h e s e g e n e r a l conclusions.
Grass i s t h e i m p o r t a n t r e s o u r c e i n rangelands.
( i i ) Rangelands.
Water y i e l d
from such l a n d s i n t h e United S t a t e s i s g e n e r a l l y low because of l i t t l e p r e c i p i t a t i o n or b e c a u s e t h e t o p o g r a p h y i s n o t f a v o r a b l e f o r p r o d u c i n g r u n o f f . other continents. notably Africa,
c o n s i d e r a b l e r u n o f f and ground-water
On
recharge
may o c c u r s e a s o n a l l y . Grazing by l i v e s t o c k and game a n i m a l s r e d u c e s t h e g r a s s cover and i n c r e a s e s s o i l exposure b o t h o f which i n c r e a s e t h e runoff. t i o n r a t e s (Gifford
6.
Hawkins,
1978).
Grazing a l s o r e d u c e s i n f i l t r a -
P e r e i r a (1973, p.
142-146) d e s c r i b e s t h e
e f f e c t s of g r a z i n g a n i m a l s on w a t e r s h e d s i n v a r i o u s c l i m a t i c a n d t o p o g r a p h i c regimes.
An i n t e n s i v e s t u d y o f t h e e f f e c t o f g r a z i n g on t h e h y d r o l o g i c and b i o t i c c h a r a c t e r i s t i c s o f s m a l l d r a i n a g e b a s i n s on t h e B a d g e r Wash b a s i n i n t h e C o l o r a d o P l a t e a u o f w e s t e r n U n i t e d S t a t e s w a s b e g u n i n 1953. r u n o f f from t h e g r a z e d w a t e r s h e d s averaged about 33 a c r e - f e e t per year;
From 1954-66
p e r square m i l e
r u n o f f from ungrazed ones averaged about 70 p e r c e n t of t h a t from t h e
grazed watersheds.
Sediment y i e l d from grazed w a t e r s h e d s was about 3 a c r e - f e e t
p e r s q u a r e m i l e p e r y e a r and about 2 f o r t h e ungrazed w a t e r s h e d s (Lusby, Reid, and Knipe, 1971). i n F i g u r e 10.12.
The t e r r a i n i n which t h i s e x p e r i m e n t was conducted i s shown
190
F i g . 10.12. G e n e r a l v i e w o f t h e t e r r a i n o f t h e B a d g e r Wash b a s i n . (From Lusby and o t h e r s , 1971).
Colorado
The e f f e c t of range f i r e i s t h e same a s t h a t of s e v e r e o v e r g r a z i n g i n semia r i d regions.
In w a t e r s h e d s w i t h deeply-rooted
grasses,
t h e o l d g r a s s may be
b u r n e d o f f a n n u a l l y t o p r o m o t e g r o w t h o f new g r a s s and t o p r e v e n t g r o w t h o f brush.
H e r e f i r e u s u a l l y h a s l i t t l e e f f e c t o n w a t e r or s e d i m e n t y i e l d e x c e p t
temporarily. Sagebrush i s b e i n g r e p l a c e d by c r e s t e d - w h e a t g r a s s i n some more-or-less
level
r a n g e l a n d s i n w e s t e r n United S t a t e s where annual p r e c i p i t a t i o n i s a s l i t t l e a s 1 0 inches.
Runoff from such l a n d s i s n e g l i g i b l e whether i n n a t i v e or r e p l a c e -
ment v e g e t a t i o n . T r e e s s u c h a s m e s q u i t e and j u n i p e r a r e r e m o v e d f r o m s e m i a r i d r e g i o n s o f s o u t h w e s t e r n U n i t e d S t a t e s i n o r d e r t o promot e t h e gr owt h of g r a s s f o r l i v e stock.
Any c h a n g e i n w a t e r y i e l d i s masked by t h e h i g h v a r i a b i l i y o f t h e
ephemeral flows. ( i i i ) Croplands.
C o n s i d e r a b l e i n f o r m a t i o n i s a v a i l a b l e on t h e e f f e c t s o f
v a r i o u s c u l t i v a t i o n and cropping p r a c t i c e s on r u n o f f from p l o t s of a few a c r e s . R e s u l t s o f a c o m p r e h e n s i v e i n v e s t i g a t i o n i n N e b r a s k a w a s r e p o r t e d by S h a r p , Gibbs.
and Owen (1966).
They found t h a t c o n s e r v a t i o n p r a c t i c e s reduced s u r f a c e
r u n o f f from s m a l l w a t e r s h e d s from 2 5 t o 40 p e r c e n t ,
p a r t i c u l a r l y i n dry years,
b u t t h a t no s a t i s f a c t o r y method was a v a i l a b l e f o r t r a n s f e r r i n g such r e s u l t s t o l a r g e complex watersheds.
They t r i e d numerous methods of e v a l u a t i n g t h e e f f e c t s
of watershed t r e a t m e n t on s t r e a m f l o w b u t none would c o n s i s t e n t l y a s s e s s such a f f e c t s on l a r g e b a s i n s , not e x i s t .
or even prove c o n c l u s i v e l y t h a t such e f f e c t s do or do
191 On s m a l l p l o t s t h e e f f e c t s of changing from one cropping p r a c t i c e t o another
a r e v a r i a b l e and sometimes o p p o s i t e depending on t h e p a r t i c u l a r combination of s o i l s , geology, c l i m a t e , v e g e t a t i o n , and w a t e r management p r a c t i c e s . (iv) Urbanization.
C o n s t r u c t i o n o f b u i l d i n g s , s t r e e t s , p a r k i n g l o t s , and
storm d r a i n a g e systems i n c r e a s e s t h e amount of r u n o f f by reducing i n f i l t r a t i o n , a n d t h e r a t e o f r u n o f f b e c a u s e of i n c r e a s e d v e l o c i t y o v e r l a n d a n d i n t h e i m proved channels.
Changes i n t h e r u n o f f h y d r o g r a p h r e s u l t i n g f r o m c o m p l e t e
u r b a n i z a t i o n of a b a s i n a r e shown s y m b o l i c a l l y i n F i g u r e 10.13.
The i n c r e a s e i n
peak flow depends on 1.
The r e c u r r e n c e i n t e r v a l of t h e flood.
Those of l a r g e r e c u r r e n c e i n t e r v a l s
w i l l be i n c r e a s e d l e s s t h a n t h o s e of low r e c u r r e n c e i n t e r v a l s because heavy,
p r o t r a c t e d r a i n f a l l s t e m p o r a r i l y reduce t h e i n f i l t r a t i o n of a n a t u r a l basin. 2.
The degree of development,
3.
The i n f i l t r a t i o n c h a r a c t e r i s t i c s o f t h e n a t u r a l b a s i n .
and t h e p e r c e n t of t h e b a s i n developed. Increased runoff
from impervious suri’sces depends on t h e change i n i n f i l t r a t i o n .
Paving o v e r
a sandy s o i l w i l l produce a much g r e a t e r i n c r e a s e i n runoff than paving over a t i g h t clay. 4. 5.
The d e s i g n of t h e d r a i n a g e system. Whether t h e development i n c l u d e s p r o v i s i o n f o r temporary s t o r a g e on r o o f s , i n y a r d s and p a r k i n g l o t s , and i n r e s e r v o i r s . r e q u i r e d i n some j u r i s d i c t i o n s .
P r o v i s i o n of s t o r a g e i s
Ordinances i n t h e Chicago a r e a r e q u i r e t h a t
t h e s t o r m n a t e r runoff r a t e a f t e r development be no more than i t was b e f o r e development; Talhami (1980) d e s c r i b e s methods used t o meet t h i s requirement by temporary o n - s i t e
detention.
Fig. 10.13. Flood hydrographs showing t h e e f f e c t of u r b a n i z a t i o n . A, r u r a l ; B, b a s i n s e n e r e d ; C, b a s i n s e n e r e d and w i t h an impervious s u r f a c e (After Anderson, 1970). S t o r m r u n o f f d a t a h a v e b e e n c o l l e c t e d a n d a n a l y z e d a t o n l y a few u r b a n i z e d a r e a s i n the United States.
Some r e s u l t s a r e g i v e n by A n d e r s o n ( 1 9 7 0 ) f o r
192 N o r t h e r n V i r g i n i a ; M a r t e n s (1968) f o r m e t r o p o l i t a n C h a r l o t t e . N.C.; (1974) f o r D a l l a s , Houston,
Texas,
Texas,
Dempster
m e t r o p o l i t a n a r e a ; L i s c u m and H a s s e y ( 1 9 8 0 ) f o r
metropolitan area;
and Wibben (1977) f o r N a s h v i l l e ,
Tennessee.
T h e s e r e s u l t s show r a t i o s o f f l o o d - p e a k d i s c h a r g e s f r o m u r b a n i z e d b a s i n s t o t h o s e from undeveloped b a s i n s r a n g i n g from a b o u t 1 f o r N a s h v i l l e r e s i d e n t i a l development t o about 5 i n Houston and Northern V i r g i n i a . a r e a s having s o i l s w i t h low i n f i l t r a t i o n r a t e s .
The low r a t i o s a r e f o r
Drainage-system
improvement, or
i t s l a c k , a l s o a c c o u n t s f o r some of t h e v a r i a t i o n . Leopold (1968) used a v a i l a b l e i n f o r m a t i o n t o develop a g e n e r a l i z e d r e l a t i o n f o r t h e e f f e c t s o f v a r i o u s d e g r e e s o f u r b a n i z a t i o n on t h e mean a n n u a l f l o o d ( F i g . 10.14).
T h a t g r a p h g i v e s t h e r a t i o by w h i c h t h e mean a n n u a l f l o o d p e a k
from an undeveloped b a s i n w i l l b e i n c r e a s e d because of u r b a n i z a t i o n .
The peak
f o r t h e u n d e v e l o p e d c o n d i t i o n c a n b e e s t i m a t e d f r o m a r e g r e s s i o n on b a s i n c h a r a c t e r i s t i c s ( C h a p t e r 8).
Graph s h o r i n g r a t i o o f u r b a n t o r u r a l mean a n n u a l f l o o d s (From F i g . 10.14. Leopold, 1968 )
.
Espey and Winslow ( 1 9 7 4 ) u s e d d a t a f r o m E a s t C o a s t , T e x a s , M i s s i s s i p p i , M i c h i g a n . and I l l i n o i s w a t e r s h e d s t o d e r i v e r e g r e s s i o n e q u a t i o n s f o r u r b a n f l o o d s of v a r i o u s r e c u r r e n c e i n t e r v a l s .
One of t h e i r e q u a t i o n s i s
193 w h e r e Q50 i s 5 0 - y e a r
f l o o d i n c u b i c f e e t p e r second, A is d r a i n a g e a r e a i n
I i s impervious c o v e r a s a p e r c e n t a g e ,
square miles,
s l o p e . R i s 6-hour
S i s d i m e n s i o n l e s s channel
r a i n f a l l a t 5 0 - y e a r r e c u r r e n c e i n t e r v a l , and 0 i s a f a c t o r
A, S, a n d R a r e e s t i m a t o r s of t h e p e a k f l o o d
d e p e n d i n g on c h a n n e l c o n d i t i o n s .
from t h e undeveloped b a s i n ; I, and 0 account f o r t h e e f f e c t o f u r b a n i z a t i o n . S a n e r a n d o t h e r s ( 1 9 8 3 ) c o m p i l e d a n a t i o n w i d e u r b a n f l o o d d a t a b a s e and developed e q u a t i o n s f o r e s t i m a t i n g u r b a n f l o o d f l o w c h a r a c t e r i s t i c s i n ungaged a r e a s . T h e i r e q u a t i o n s h a v e s t a n d a r d e r r o r s r a n g i n g f r o m 3 1 t o 52 p e r c e n t and a r e a p p l i c a b l e throughout t h e conterminous United S t a t e s and Hawaii. U r b a n i z a t i o n may a f f e c t ground-water
r e c h a r g e and low f l o w s b u t whether a n
i n c r e a s e , d e c r e a s e , o r no c h a n g e , o c c u r s a f t e r u r b a n i z a t i o n d e p e n d s on l o c a l conditions.
U r b a n i z a t i o n g e n e r a l l y h a s l i t t l e e f f e c t on t h e l o w f l o w s o f
s t r e a m s because t h e a r e a made impervious r a r e l y i s a s i g n i f i c a n t p e r c e n t a g e of t h e d r a i n a g e a r e a o f a b a s i n l a r g e enough t o p r o d u c e a n a p p r e c i a b l e low f l o w under n a t u r a l c o n d i t i o n s . Runoff from urban a r e a s c o n t a i n s d i s s o l v e d and suspended w a s t e m a t e r i a l s t h a t may d e g r a d e t h e w a t e r q u a l i t y o f t h e r e c e i v i n g s t r e a m s . having w a t e r - q u a l i t y
The p o s s i b i l i t y o f
p r o b l e m s a s a c o n s e q u e n c e o f u r b a n i z a t i o n d e p e n d s on
c l i m a t e . t h e t y p e o f r e c i p i e n t w a t e r body, a n d o t h e r f a c t o r s .
I n many p l a c e s
urban r u n o f f i s n o t l i k e l y t o r e s u l t i n w a t e r - q u a l i t y problems (EPA, 1982). (v) Irrigation.
I r r i g a t i o n i s a means o f p r o v i d i n g w a t e r t o p l a n t s d u r i n g
p e r i o d s of inadequate r a i n f a l l . from a stream.
Water may be pumped from t h e ground o r d i v e r t e d
Pumping of ground w a t e r a f f e c t s s t r e a m f l o w o n l y when i t removes
w a t e r t h a t w o u l d o t h e r w i s e h a v e gone t o t h e s t r e a m .
I f a w e l l is c l o s e t o a
s t r e a m , t h e e f f e c t o f g r o u n d w a t e r pumping may b e t h e same a s a s t r e a m d i v e r sion.
A t some d i s t a n c e f r o m t h e s t r e a m t h e i m m e d i a t e r e d u c t i o n w i l l b e l e s s
t h a n t h e r a t e pumped.
F i g u r e 10.15 s h o w s t h e h y d r o g r a p h o f s t r e a m d e p l e t i o n
r e s u l t i n g from pumping 10 a c r e - f e e t
p e r day f o r 3 5 d a y s from an a l l u v i a l a q u i f e r
a t a p o i n t 3600 f e e t from t h e Arkansas River i n Colorado.
Ground w a t e r pumping
d o e s n o t a f f e c t s t r e a m f l o w i n r e g i o n s where t h e w a t e r t a b l e i s a l w a y s below t h e streambeds.
Other e f f e c t s of ground-water pumping a r e d e s c r i b e d i n a f o l l o w i n g
section. More w a t e r t h a n t h e p l a n t s n e e d i s o f t e n a p p l i e d t o t h e l a n d when s u r f a c e w a t e r is used f o r i r r i g a t i o n .
The e x c e s s e i t h e r s e e p s i n t o t h e g r o u n d and
r a i s e s t h e w a t e r t a b l e o r i s d r a i n e d by s u r f a c e c h a n n e l s t o a stream.
The
p r i n c i p a l e f f e c t s of i r r i g a t i o n on s t r e a m f l o w a r e upstream r e g u l a t i o n and d i v e r s i o n s and t h e i m p a i r e d q u a l i t y of t h e w a t e r d r a i n i n g from t h e p r o j e c t . The s a l i n i t y o f
t h e d r a i n a g e w a t e r i s u s u a l l y g r e a t e r t h a n t h a t of t h e
a p p l i e d w a t e r because o f l e a c h i n g o f s a l t s from t h e s o i l . f i c i a l drainage i s u s u all y provided;
i f not,
In f l a t areas arti-
t h e w a t e r t a b l e may r i s e n e a r l y t o
194 t h e l a n d s u r f a c e and t h e consequent e v a p o r a t i o n of ground w a t e r w i l l c o n c e n t r a t e the s a l t s near the s o i l surface,
'0
100
s e v e r e l y r e d u c i n g p l a n t growth.
200
300 400 500 TIME, IN DAYS
600
700
F i g . 10.15. E x a m p l e of r e s i d u a l e f f e c t s of w e l l p u m p i n g f o r 3 5 d a y s (From J e n k i n s , 1968).
A succession of i r r i g a t i o n p r o j e c t s along a r i v e r p r o g r e s s i v e l y reduces t h e N o t a b l e examples of s t r e a m s on which t h i s h a s
flow and i n c r e a s e s t h e s a l i n i t y .
occurred a r e Colorado River (Iorns, Murray.
A u s t r a l i a (Hart,
Hembree,
and O a k l a n d .
1965) and R i v e r
1980).
I r r i g a t i o n d i v e r s i o n s from s t r e a m s f e e d i n g t e r m i n a l l a k e s c a n r e d u c e t h o s e l a k e s i n volume and s u r f a c e a r e a .
The l e v e l of t h e Caspian Sea h a s been reduced
i n r e c e n t y e a r s b e c a u s e o f i r r i g a t i o n and o t h e r c o n s u m p t i v e u s e s o f w a t e r ( F a i z i , 1980).
L i k e w i s e t h e Dead S e a l e v e l h a s b e e n d e c l i n i n g b e c a u s e o f t h e
reduced i n f l o w s o f J o r d a n R i v e r and o t h e r t r i b u t a r i e s (Sauer,
1978).
Terminal
l a k e s or swamps ( s i n k s ) i n w e s t e r n U n i t e d S t a t e s c a n b e g r e a t l y c h a n g e d , o r e l i m i n a t e d , by r e d u c t i o n of n a t u r a l i n f l o w s . Water s p r e a d i n g i s a n o t h e r form of i r r i g a t i o n . dams o n t o t h e f l o o d p l a i n s or t h e r i p a r i a n l a n d .
S t r e a m f l o w i s d i v e r t e d by low
In t h e m o u n t a i n o u s w e s t e r n
U n i t e d S t a t e s t h e s p r i n g r u n o f f i s u s e d t o i r r i g a t e h a y meadows.
I n semiarid
p a r t s of t h e w o r l d t h e c h a n n e l s o f s m a l l ephemeral s t r e a m s a r e t e r r a c e d so t h a t t h e flows, except during major floods, a r e a l l absorbed i n the t e r r a c e d a r e a (Fig.
10.16).
I n t r o d u c t i o n o f w a t e r t o d r y s o i l may produce l a n d s u b s i d e n c e through hydrocompaction.
Some o f t h e s u b s i d e n c e i n t h e S a n J o a q u i n V a l l e y , C a l i f o r n i a i s
a t t r i b u t e d t o hydrocompaction.
(See t h e s e c t i o n on Ground Water Pumping).
( v i ) Drainage and C h a n n e l i z a t i o n . uses besides agriculture.
P r o p e r d r a i n a g e i s e s s e n t i a l f o r many l a n d
The h y d r o l o g i c a l e f f e c t s of d r a i n i n g swamp l a n d s
depend on t h e g e o l o g i c and t o p o g r a p h i c s e t t i n g s .
The o u t f l o w from a w e t l a n d i s
195
F i g . 10.16.
Terraced l a n d i n t h e channel of a wadi i n North Yemen.
d o m i n a t e d by t h e s l o w movement o f w a t e r t h r o u g h t h e w e t l a n d , and by t h e h i g h evapotranspiration rate.
D r a i n a g e of a w e t l a n d r e s u l t s i n f a s t e r r e m o v a l of
water following precipitation,
and g r e a t l y reduced e v a p o t r a n s p i r a t i o n because of
t h e r e d u c t i o n i n w a t e r s u r f a c e area. low f l o w s and i n a n n u a l r u n o f f s .
These changes may r e s u l t i n i n c r e a s e s i n Klueva (19751, i n a s t u d y of 16 b a s i n s i n
B y e l o r u s s i a ranging i n a r e a from 67 t o 8770 km2, r e p o r t e d t h a t t h e minimum d a i l y w i n t e r mean d i s c h a r g e i n 8 b a s i n s i n c r e a s e d a f t e r r e c l a m a t i o n ( d r a i n a g e b y c h a n n e l i z a t i o n ) b y a n a v e r a g e o f 20 t o 1 3 0 p e r c e n t . s t u d y no s i g n i f i c a n t changes were found.
In t h e o t h e r b a s i n s u n d e r
Reclamation i n a l l b a s i n s under study
r e s u l t e d i n an i n c r e a s e of streamflow i n t h e summer and autumn period. S i m i l a r c h a n g e s w e r e f o u n d by Mustonen a n d Seuna (1975) who c a l i b r a t e d 2 n a t u r a l b a s i n s f o r 22 y e a r s ; c a l i b r a t i o n was c o n t i n u e d f o r 9 y e a r s a f t e r 40 p e r c e n t of one b a s i n was d r a i n e d f o r f o r e s t r y .
Drainage produced an i n c r e a s e of
43 p e r c e n t i n a n n u a l r u n o f f and i n c r e a s e s o f many t i m e s i n w i n t e r a n d summer annual minimums.
Heath (1975) showed t h a t deepening and widening of t h e n a t u r a l
c h a n n e l s i n t h e swampy 5 7 - s q u a r e m i l e d r a i n a g e b a s i n o f A h o s k i e C r e e k , N o r t h C a r o l i n a i n c r e a s e d t h e minimum flow from z e r o t o about 2 c f s . Although t h e r e s u l t s quoted above a r e c o n s i s t e n t , found i n o t h e r types of b a s i n s . ( v i i ) Ground-water
pumping.
d i f f e r e n t e f f e c t s may be
See P e r e i r a (1973, p. 194-200). Where ground w a t e r d r a i n s t o s t r e a m s and h e l p s
m a i n t a i n t h e i r flows, any e x t r a c t i o n of ground w a t e r w i l l reduce t h e low f l o w s and t h e y i e l d s . F i g u r e 10.15.
An e x a m p l e o f t h e e f f e c t o f t e m p o r a r y pumping was shown i n
The m a g n i t u d e of t h e e f f e c t on s t r e a m f l o w c h a r a c t e r i s t i c s of
196 ground-water
e x t r a c t i o n depends on t h e h y d r a u l i c c o n n e c t i o n between t h e a q u i f e r
and t h e s t r e a m and on t h e pumping s c h e d u l e and t h e amount pumped. S u b s t a n t i a l l o w e r i n g of t h e w a t e r t a b l e o r t h e p i e z o m e t r i c s u r f a c e i n c e r t a i n types of s o i l s r e s u l t s i n land subsidence. Valley,
Some p a r t s o f t h e S a n J o a q u i n
C a l i f o r n i a have s u b s i d e d 9 m e t e r s due t o ground-water
s t a n t i a l s u b s i d e n c e h a s a l s o o c c u r r e d i n t h e Houston-Galveston
withdrawal.
i n J a p a n , V e n i c e ( I t a l y ) and v a r i o u s o t h e r p l a c e s i n t h e w o r l d . known s u b s i d e n c e due t o ground-water
and
The maximum
pumping o c c u r r e d i n Mexico C i t y ,
w h i c h h a v e b e e n l o w e r e d a s much a s 18.7 m e t e r s i n 80 y e a r s .
Sub-
(Texas) a r e a ,
p a r t s of
Rebounds o f a few
c e n t i m e t e r s have been r e p o r t e d from J a p a n and Venice a f t e r r e c o v e r y of a r t e s i a n pressures.
See IAHS (1976) and Poland (1981).
Land S u b s i d e n c e may c h a n g e s t r e a m g r a d i e n t s , i n d u c e m o r e r e c h a r g e or more e v a p o r a t i o n from t h e channel,
and i n c r e a s e t h e r i p a r i a n a r e a s s u b j e c t t o f l o o d -
i n g i n a d d i t i o n t o i t s a d v e r s e e f f e c t s on b u i l d i n g s , h i g h w a y s , c a n a l s , a n d on agriculture. ( v i i i ) P h r e a t o p h y t e removal.
P h r e a t o p h y t e s a r e deep-rooted
p l a n t s t h a t draw
t h e i r m o i s t u r e p r i m a r i l y from ground w a t e r ; common ones a r e s a l t c e d a r , weed,
cottonwood,
saltbush,
willow,
and mesquite.
arrow-
In t h e s o u t h w e s t e r n United
S t a t e s t h e s e p l a n t s e x t r a c t l a r g e q u a n t i t i e s o f w a t e r from t h e s h a l l o w ground w a t e r a l o n g s t r e a m s and a d j a c e n t v a l l e y s .
The m o s t commotl a n d o n e o f t h e
h i g h e s t u s e r s of w a t e r i s s a l t c e d a r ( t a m a r i x ) , an i n t r o d u c e d p l a n t , which d i d n o t a p p e a r on t h e f l o o d p l a i n s u n t i l t h e 1 9 2 0 s .
By 1 9 6 5 t h e p l a n t i n f e s t e d
about a m i l l i o n a c r e s o f w e s t e r n s t r e a m v a l l e y s . The p o s s i b i l i t y of r e c l a i m i n g w a t e r used by such n o n b e n e f i c i a l v e g e t a t i o n l e d t o s t u d i e s t o d e t e r m i n e t h e a m o u n t o f w a t e r u s e d , and how some o f i t m i g h t b e salvaged.
A s t u d y b y Gatewood a n d o t h e r s ( 1 9 5 0 ) c o n c l u d e d t h a t p h r e a t o p h y t e s
used about 28,000 a c r e - f e e t G i l a River i n Arizona.
of w a t e r i n a 12-month p e r i o d i n a 46-mile r e a c h of
A six-year
o b s e r v a t i o n o f w a t e r used by s a l t c e d a r grow-
ing i n e v a p o r a t i o n t a n k s h a s shown how w a t e r use i s r e l a t e d t o p l a n t d e n s i t y and d e p t h t o w a t e r t a b l e (Van Hylckama, 1 9 7 0 ) .
Computations of p o t e n t i a l w a t e r
s a l v a g e a r e r e p o r t e d by Hughes and McDonald (1966).
A 9-year s t u d y o f a 1 5 - m i l e r e a c h o f t h e G i l a R i v e r , A r i z o n a , was b e g u n i n 1 9 6 2 ( 1 ) t o e v a l u a t e w a t e r s a l v a g e b y p h r e a t o p h y t e c o n t r o l on a f l o o d p l a i n t y p i c a l of a r e a s o f e x i s t i n g and p ro p o s ed a p p l i c a t i o n ,
(2) t o d e s c r i b e t h e
h y d r o l o g i c a l and e c o l o g i c a l v a r i a b l e s of t h e s t u d y a r e a s u f f i c i e n t l y f o r e x t r a p o l a t i o n o f w a t e r s a l v a g e d a t a t o o t h e r s i t e s , and ( 3 ) t o d e v e l o p m e t h o d s f o r e v a l u a t i n g h y d r o l o g i c v a r i a b l e s i n a l a r g e area.
The water-budget
method was
used t o e s t i m a t e e v a p o t r a n s p i r a t i o n from 5500 a c r e s of t h e f l o o d p l a i n ,
then the
f l o o d p l a i n was c l e a r e d o f v e g e t a t i o n and t h e e v a p o t r a n s p i r a t i o n a g a i n e s t i mated.
R e s u l t s show t h a t t h e average y e a r l y consumptive u s e o f 43 i n c h e s b e f o r e
c l e a r i n g w a s r e d u c e d t o 1 9 i n c h e s a f t e r c l e a r i n g ( C u l l e r and o t h e r s , 1 9 8 2 ) .
197 Water f o r m e r l y used by r i p a r i a n v e g e t a t i o n can be s a l v a g e d o n l y i f r e g r o w t h i s p r e v e n t e d o r t h e w a t e r t a b l e i s l o w e r e d b y pumping, n e i t h e r o f w h i c h may be practical. 10.3.3
Cloud s e e d i n g
Cloud s e e d i n g a s a means of inducing o r augmenting p r e c i p i t a t i o n o r of modif y i n g i t s c h a r a c t e r was proposed i n t h e l a t e 1940s.
S c h a e f e r (1946) showed t h a t
p r e c i p i t a t i o n c o u l d be induced by p r o v i d i n g n u c l e i f o r i c e f o r m a t i o n i n supercooled clouds.
He u s e d d r y i c e a s t h e s o u r c e o f t h e n u c l e i .
Silver iodide
p a r t i c l e s , p r o p o s e d by Vonnegut ( 1 9 4 7 ) . a s a s e e d i n g a g e n t , a r e now g e n e r a l l y used.
They a r e i n t r o d u c e d i n t o t h e a t m o s p h e r e by " g e n e r a t o r s " l o c a t e d on
mountain r i d g e s where t h e wind w i l l c a r r y t h e p a r t i c l e s i n t o t h e clouds.
Guide-
l i n e s f o r cloud s e e d i n g t o augment p r e c i p i t a t i o n a r e d e s c r i b e d by ASCE (1983). The p r i n c i p a l o b j e c t i v e of most c l o u d s e e d i n g i s t o p r o v i d e r a i n f o r crops. Although i t has been c l e a r l y demonstrated t h a t seeding a s u i t a b l e cloud w i l l induce p r e c i p i t a t i o n , versial.
t h e e f f e c t i v e n e s s of o p e r a t i o n a l c l o u d seeding i s contro-
Warner ( 1 9 7 4 ) s a i d t h a t s e e d i n g c l o u d s w i t h a v i e w o f s t i m u l a t i n g
a d d i t i o n a l r a i n f a l l over a r e a s of a few thousand s q u a r e k i l o m e t e r s h a s been done f o r a q u a r t e r o f a c e n t u r y and many p r o g r a m s i n o p e r a t i o n a r e c o n s i d e r e d s u c c e s s f u l , b u t when we come t o examine t h e s c i e n t i f i c b a s i s f o r t h i s assumption, t h e r e i s no g e n e r a l a g r e e m e n t a s t o w h e t h e r , o r i n w h a t c o n d i t i o n s ,
it is
justified.
Neyman a n d S c o t t ( 1 9 7 4 ) c l a i m t ' h a t e x p e r i m e n t a l d e s i g n s b a s e d on
area-to-area
comparisons a r e u n r e l i a b l e and t h a t t h e q u e s t i o n s r a i s e problems of
m a t h e m a t i c a l s t a t i s t i c s t h a t a r e f u n d a m e n t a l l y new.
WMO r e c e n t l y summarized t h e
c o n c l u s i o n s o f a p a n e l o f e x p e r t s by, "Most o f t h e p a s t w e a t h e r m o d i f i c a t i o n e x p e r i m e n t s a r e c o n s i d e r e d i n c o n c l u s i v e by t h e s c i e n t i f i c community.
Careful
e v a l u a t i o n s i n v o l v i n g b o t h e x t e n s i v e p h y s i c a l measurements of t h e clouds and p r e c i p i t a t i o n and s t a t i s t i c a l a n a l y s e s of
t h e measurements a r e now c o n s i d e r e d
mandatory i n a r r i v i n g a t sound j u d g men t s .
A t t h i s t i m e weather modification
o t h e r t h a n s u p e r c o o l e d f o g d i s p e r s a l m u s t b e c o n s i d e r e d i n t h e r e a l m of r e E n h a n c i n g p r e c i p i t a t i o n o r s u p p r e s s i n g h a i l r e l i a b l y and on demand
search.
r e m a i n d i s t a n t goals." Clond s e e d i n g i s a c o n t r o v e r s i a l a c t i v i t y beyond t h e q u e s t i o n of i t s e f f e c tiveness.
I n d u c t i o n o r augmentation of p r e c i p i t a t i o n a t a p a r t i c u l a r t i m e may
b e n e f i t some c r o p s and damage o t h e r s ; w i t h i n a r e g i o n t h e r e may be no agreement
on t h e d e s i r a b i l i t y o f w e a t h e r m o d i f i c a t i o n a t a p a r t i c u l a r time.
Even a t t e m p t s
t o i n c r e a s e t h e w i n t e r snowpack i n t h e Colorado Rockies by cloud s e e d i n g were met w i t h some o b j e c t i o n s . 10.3.4
A i r pollution
I n a d v e r t e n t cloud s e e d i n g by p a r t i c l e s i n t r o d u c e d t o t h e atmosphere from i n d u s t r i a l a c t i v i t i e s may produce l o c a l i n c r e a s e s i n p r e c i p i t a t i o n .
Huff (1977)
198 r e p o r t e d on a 5 - y e a r f i e l d a n d a n a l y s e s p r o g r a m a t S t . L o u i s , M i s s o u r i , w h e r e 225 r e c o r d i n g r a i n gages were o p e r a t e d on 5200 km2. l y a 30-percent
Data i n d i c a t e d approximate-
i n c r e a s e i n summer r a i n f a l l i n a n a r e a t h a t i s most f r e q u e n t l y
exposed t o s t o r m s c r o s s i n g t h e u r b a n - i n d u s t r i a l
region.
The e n h a n c e m e n t was
m o s t p r o n o u n c e d i n r a i n s t o r m s t h a t p r o d u c e d maxima o f 2 5 m m o r m o r e i n t h e network.
The a v e r a g e w a t e r y i e l d f o r i n d i v i d u a l r a i n c e l l s i n t h o s e s t o r m s was
o v e r 7 0 p e r c e n t g r e a t e r i n urban-exposed
c e l l s than i n surrounding r u r a l c e l l s .
The s t u d y i n d i c a t e s t h a t t h e f r e q u e n c y d i s t r i b u t i o n s of heavy r a i n f a l l s o f 5m i n u t e t o 2-hour
d u r a t i o n may v a r y s i g n i f i c a n t l y between urban,
r u r a l areas i n l a r g e urban-industrial
regions.
suburban,
and
T h i s v a r i a t i o n p r o b a b l y should
be c o n s i d e r e d i n d e f i n i n g f l o o d c h a r a c t e r i s t i c s from s m a l l w a t e r s h e d s s u b j e c t t o r a i n f a l l enhancement a l t h o u g h a d e q u a t e d a t a a r e r a r e l y a v a i l a b l e . Some p a r t i c l e s i n t r o d u c e d t o t h e a t m o s p h e r e h a v e e f f e c t s b e y o n d t h a t o f augmenting p r e c i p i t a t i o n . plants,
Man-made
other industrial a c t i v i t i e s ,
o x i d e s from s m e l t e r s ,
fossil-fueled
power
and a u t o m o b i l e e n g i n e e x h a u s t s r e a c t w i t h
m o i s t u r e t o produce a p r e c i p i t a t i o n c o n t a i n i n g c o r r o s i v e a c i d s .
O r the pollu-
t a n t s may f a l l t o e a r t h i n d r y form and be t r a n s f o r m e d i n t o c o r r o s i v e a c i d s by subsequent p r e c i p i t a t i o n o r by m e l t i n g of snow. a c i d i t y of l a k e s and s t r e a m s ,
This acid r a i n increases the
except those i n r e g i o n s r i c h i n limestone.
l a k e s i n n o r t h e a s t e r n United S t a t e s ,
Canada,
Many
and S c a n d i n a v i a no l o n g e r c o n t a i n
f i s h because a c i d r a i n h a s l o w e r e d t h e pH of t h e w a t e r below 5. Acid r a i n c a n a f f e c t p l a n t s , lation,
smelter effluents,
a n i m a l s , and i n a n i m a t e o b j e c t s .
mainly s u l f u r dioxide,
t i m b e r on l a r g e downwind a r e a s . from t h e s m e l t e r s a t Copper H i l l ,
P r i o r t o regu-
were r e s p o n s i b l e f o r k i l l i n g
In a few y e a r s b e f o r e and a f t e r 1900, e f f l u e n t Tennessee, c o m p l e t e l y denuded 17.000 a c r e s o f
f o r e s t l a n d and i n j u r e d 30,000 a d d i t i o n a l a c r e s .
The s m e l t e r a t T r a i l , B.C.,
Canada d e s t r o y e d t i m b e r f o r 40 m i l e s down t h e C o l u m b i a R i v e r v a l l e y i n t h e 1920s.
A Landsat view of t h e Wawa. O n t a r i o , Canada r e g i o n c l e a r l y shows t h e 350
s q u a r e m i l e a r e a on which v e g e t a t i o n was k i l l e d by s u l f u r d i o x i d e e m i s s i o n s from a s i n t e r i n g p l a n t (NASA, 1976. p. 1 9 9 ) .
R e c e n t e f f e c t s of a c i d r a i n a r e l e s s
s e v e r e b u t much more w i d e s p r e a d ( L a B a s t i l l e , 10.4 10.4.1
1981).
QUANTIFYING EFFECTS OF CHANGES Environmental changes
An e x p e r i m e n t c o u l d be conducted on a s i n g l e b a s i n on which p r e c i p i t a t i o n and s u r f a c e r u n o f f a r e measured f o r a number o f y e a r s u n t i l a n a c c e p t a b l e c a l i b r a t i o n i s d e f i n e d between t h e f l o w c h a r a c t e r i s t i c o f i n t e r e s t and t h e p r e c i p i t a t i o n input.
Then t h e change t h a t i s t o be e v a l u a t e d i n t h e b a s i n would be made
and d a t a c o l l e c t i o n c o n t i n u e d u n t i l a r a n g e of p r e c i p i t a t i o n i n p u t s have been recorded.
The e f f e c t of t h e b a s i n change i s t h e d i f f e r e n c e between t h e measured
199 o u t p u t a f t e r change and t h e o u t p u t f o r t h a t p e r i o d computed from t h e p r e t r e a t ment c a l i b r a t i o n . The s e n s i t i v i t y of t h i s p r o c e d u r e depends on t h e s i z e of t h e s t a n d a r d e r r o r of t h e c a l i b r a t i o n .
The e f f e c t of t h e change must a p p r e c i a b l y exceed t h e stan-
dard e r r o r i f i t i s t o be s t a t i s t i c a l l y s i g n i f i c a n t .
A s m a l l e r r e a l e f f e c t may
e x i s t a l t h o u g h i t cannot be shown by t h i s technique. Disadvantages of t h i s e x p e r i m e n t a l b a s i n approach a r e t h e c o s t of y e a r s of d a t a c o l l e c t i o n , t h e l o n g d e l a y b e t w e e n b e g i n n i n g of t h e e x p e r i m e n t and t h e a n s w e r s o u g h t , and t h e l a c k o f a f i r m b a s i s f o r a p p l y i n g t h e r e s u l t t o o t h e r t h a n t h e s t u d y basin.
S l i v i t z k y and Hendler (1965) d e s c r i b e t h e d i f f i c u l t i e s of
u s i n g e x p e r i m e n t a l b a s i n s and conclude t h a t i n most c a s e s t h e l i m i t a t i o n s outweigh t h e advantages.
Hewlett, Lull,
and R e i n h a r t (1969) d i s c u s s t h e p r o s and
cons o f t h e e x p e r i m e n t a l b a s i n approach and j u s t i f y i t s u s e f o r some o b j e c t i v e s .
A v a r i a t i o n of t h e e x p e r i m e n t a l b a s i n i s t h e p a i r e d - b a s i n
approach i n which
two s i m i l a r , n e a r b y b a s i n s a r e gaged u n t i l a r e a s o n a b l e r a n g e i n d i s c h a r g e i s obtained.
The d i s c h a r g e o f t h e o n e t h a t i s t o b e m o d i f i e d i s r e g r e s s e d on t h e
discharge of t h e other.
Then c h a n g e s a r e made i n t h e f i r s t b a s i n and d a t a
c o l l e c t i o n on b o t h i s c o n t i n u e d f o r a f e w y e a r s .
The Wagon Wheel Gap e x p e r i -
ment, d e s i g n e d and c a r r i e d o u t by B a t e s and Henry (1928) i s a n examplei Hoyt and T r o x e l l (1934) analyzed d a t a from t h i s experiment. s h e d s o f a b o u t 200 a c r e s e a c h ,
The p a i r e d c o n t i g u o u s water-
l o c a t e d i n t h e R i o Grande d r a i n a g e b a s i n of
C o l o r a d o a t a l t i t u d e s o f b e t w e e n 9000 and 1 1 0 0 0 f e e t , w e r e g e o l o g i c a l l y and t o p o g r a p h i c a l l y s i m i l a r and s u b j e c t t o t h e s a m e m e t e o r o l o g i c a l c o n d i t i o n s because of t h e i r s m a l l s i z e .
F o r e s t cover a l s o was s i m i l a r .
R e l i a b l e observa-
t i o n s of r u n o f f and p r e c i p i t a t i o n were made f o r 8 y e a r s i n t h e n a t u r a l s t a t e and f o r 7 y e a r s a f t e r c o m p l e t e d e f o r e s t a t i o n of one b a s i n . F i g u r e 10.17.
R e s u l t s a r e shown i n
A l l annual r u n o f f s o f b a s i n A f o r y e a r s subsequent t o d e f o r e s t a -
t i o n a r e s i g n i f i c a n t l y g r e a t e r s t a t i s t i c a l l y , a t t h e 95% l e v e l , t h a n b e f o r e . One might f i t a r e g r e s s i o n l i n e t o t h e a f t e r - d e f o r e s t a t i o n
p o i n t s b u t t h i s would
r e q u i r e an a s s u m p t i o n t h a t t h e c o n d i t i o n o f b a s i n A r e m a i n e d unchanged a f t e r deforestation:
t h i s a s s u m p t i o n i s u n l i k e l y because of regrowth, and i n f a c t t h e
p l o t t e d p o i n t s seem t o i n d i c a t e a c h a n g e w i t h t i m e .
Van H a v e r e n ( 1 9 8 1 ) u s e d
d a t a from t h e Wagon Wheel Gap experiment t o show t h e e f f e c t of d e f o r e s t a t i o n on a n n u a l , p e a k , and l o w f l o w s and on h y d r o g r a p h t i m i n g .
Anot her example of an
a n a l y s i s u s i n g p a i r e d b a s i n s i s g i v e n by H a r r i s (1977). The e f f e c t of a g r a d u a l b a s i n change such a s t h a t due t o r e f o r e s t a t i o n can be i d e n t i f i e d by r e l a t i n g annual f l o w s from t h e b a s i n being r e f o r e s t e d t o f l o w s f r o m a c o n t r o l b a s i n and t o number o f y e a r s f r o m b e g i n n i n g o f e x p e r i m e n t . Schneider and Ayer (1961) used t h e r e g r e s s i o n model
Rs = a + blRa
- b2
T Ra
200
w h e r e R s i s r u n o f f f r o m t h e r e f o r e s t e d b a s i n , It, basin,
i s r u n o f f from t h e c o n t r o l
T i s p o s i t i o n of t h e y e a r i n t h e n u m e r i c a l sequence b e g i n n i n g w i t h T = 1
f o r t h e f i r s t y e a r of record. magnitude of t h e change i n t h e t i m e sequence.
The f o r m o f t h e e q u a t i o n i n d i c a t e s t h a t t h e
Rs i s dependent on t h e magnitude of It, a s w e l l a s on
For t h e p e r i o d 1939-57 r e d u c t i o n s i n r u n o f f from t h e s m a l l
r e f o r e s t e d b a s i n i n c e n t r a l New York averaged about 0.36
3
5
7
i n c h p e r year.
10
BASIN B
F i g . 10.17. P a i r e d b a s i n m e t h o d o f d e f i n i n g e f f e c t o f d e f o r e s t a t i o n . Graph shows annual r u n o f f s i n inches. Circles a r e f o r calibration period; crosses a r e r e s u l t s a f t e r d e f o r e s t a t i o n o f B a s i n A. Changes t h a t have o c c u r r e d may a l s o be q u a n t i f i e d by use of a m a t h e m a t i c a l model b u t t h e p r i n c i p a l u s e of such models i s f o r e s t i m a t i n g changes t h a t w i l l r e s u l t from some proposed m o d i f i c a t i o n or development i n a basin. q u a n t i t a t i v e r e p r e s e n t a t i o n of t h e system b e i n g s t u d i e d .
A model i s a
After c a l i b r a t i o n with
b a s i n d a t a , t h e model may b e u s e d t o p r e d i c t t h e o u t p u t f r o m a g i v e n i n p u t , or t o c o m p u t e t h e c h a n g e i n o u t p u t d u e t o some m o d i f i c a t i o n o f t h e b a s i n . single-event
and c o n t i n u o u s w a t e r s h e d models a r e used t o d e t e c t change.
Both Ordi-
n a r i l y t h e change i n d i c a t e d by modeling i s n o t v e r i f i e d by d a t a : c o n f i d e n c e in t h e r e s u l t i s based on how w e l l (1) t h e model s t r u c t u r e conforms t o t h e system, ( 2 ) t h e p a r a m e t e r s d e s c r i b e s p e c i f i c e l e m e n t s of t h e system,
p a r t i c u l a r l y those
e l e m e n t s t h a t w i l l be changed, and (3) t h e c a l i b r a t i o n d a t a f i t t h e model. fundamentals of s t o r m w a t e r modeling,
The
and u s e of models f o r e v a l u a t i n g t h e e f -
f e c t s o f l a n d u s e on f l o o d f l o w s a r e g i v e n b y O v e r t o n and Meadows (1976). Feldman (1980) e v a l u a t e d t h e c a p a b i l i t y of some commonly-used h y d r o l o g i c models f o r p r e d i c t i n g peak d i s c h a r g e s of p r e s c r i b e d frequencies under v a r i o u s b a s i n conditions.
Peldman (1981) d e s c r i b e d t h e o r y and e x p e r i e n c e w i t h HEC models f o r
w a t e r r e s o u r c e s system s i m u l a t i o n .
201 A n approach used to define the effects of urbanization on flood peaks consists of gaging a dozen or more small streams whose basins encompass a range from rural to fully urbanized,
The flood frequency characteristics are defined
f r o m the gaged records, s o m e t i m e s supplemented b y information derived by a rainfall-runoff model.
Regression of a flood frequency characteristic on basin
characteristics, including a n index of urbanization, is developed.
T h e n the
changes due to urbanization can be d e t e r m i n e d b y solving the equation for various values of the index of urbanization.
If the region covered by the gaged
basins w a s reasonably h o m o g e n e o u s hydrologically before urbanization, the changes defined by this method should apply throughout that region.
For more
details see the section on Urbanization in this chapter. One of the s i m p l e r S C S (1975) models uses soils data, channel length and character, and storm rainfall of a specific recurrence interval to compute, for the urbanized condition, the peak discharge having the same recurrence interval as the rainfall. More complex models are needed for urban hydrology where lumped parameters do
not adequately describe the physical system, where many alternative development plans are to be evaluated, and w h e n various types of a n s w e r s are sought.
A
guide to urban model analysis is given by ASCE (1977). 10.4.2
Diversion and regulation
Major changes in streamflor characteristics result from storage and diversion of flow.
The modified flow characteristics can be defined by a combination of
hydrologic and hydraulic m o d e l s given suitable information on the pattern of operation of the reservoirs.
Jeffcoat and others (1974, 1976) developed a
stream-reservoir model to simulate the operation of the Lakes Marion-Moultrie reservoir system in South Carolina.
The model incorporates an inflow component,
a diversion component, and a reservoir system component and is capable of evaluating the performance of the reservoir system for a variety of operating rules. The calibrated model was used to simulate 31 years of outflow from the inflow record under an assumed operating rule.
Flow characteristics were defined from
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6
Sons, (p. 159-
Schumm, S.A. and Hadley. R.F., 1957, A r r o y o s a n d t h e s e m i a r i d c y c l e o f e r o s i o n : Am. J o u r . o f S c i e n c e , Vol. 255, March 1957, p. 161-174. SCS, 1975, Urban hydrology f o r s m a l l watersheds: Tech R e l e a s e No. 55, Washington, D.C.
U.S. S o i l C o n s e r v a t i o n S e r v i c e
S h a r p , A.L., G i b b s , A.E., and Owen. W.J., 1966, D e v e l o p m e n t o f a p r o c e d u r e f o r e s t i m a t i n g t h e e f f e c t s of l a n d and w a t e r s h e d t r e a t m e n t on s t r e a m f l o w : U.S. Dept. o f A g r i c u l t u r e Tech. B u l l . No. 1352, 57 p. S i n c l a i r , J.D. and Hamilton, EL., 1955, Streamflow r e a c t i o n s of a fire-damaged w a t e r s h e d : P r o c . ASCE, H y d r a u l i c s D i v i s i o n , Vol. 81, S e p a r a t e No. 629, 17 P. S l i v i t z k y , M.S. and H e n d l e r , M., 1965. W a t e r s h e d r e s e a r c h a s a b a s i s f o r w a t e r r e s o u r c e s d e v e l o p m e n t : N a t i o n a l R e s e a r c h C o u n c i l o f Canada, P r o c . o f Hydrology Symposium No. 4, Research Watersheds, p. 289-294. S t a l l i n g s , J.S., 1967, South C a r o l i n a s t r e a m f l o w c h a r a c t e r i s t i c s , low-flow quency and f l o w d u r a t i o n : U.S. Geol. Survey Open-File Rept., 83 p.
fre-
S t e r m i t z , F., 1964, E f f e c t s o f t h e Hebgen Lake e a r t h q u a k e on s u r f a c e w a t e r : U.S. Geol. S u r v e y P r o f . P a p e r 435-L, p. 139-150. S t e v e n s , M.A., S i m o n s , D.B., a n d R i c h a r d s o n , E.V., 1975. N o n e q u i l i b r i u m r i v e r f o r m : J o u r . o f H y d r a u l i c s D i v i s i o n , ASCE, Vol. 101, No. HY5, p. 557-566. Swank, W.T. and Belvey, J.D., 1970, Reduction i n s t r e a m f l o w i n c r e a s e s f o l l o w i n g r e g r o w t h of c l e a r c u t hardwood f o r e s t s : I n t e r n a t i o n a l A s s o c i a t i o n of Hydrol o g i c a l S c i e n c e s P n b l . No. 96, p. 346-360. S w i f t , L.W., J r . and Swank, W.T., 1981, Long t e r m r e s p o n s e s o f s t r e a m f l o w f o l lowing c l e a r c u t t i n g and regrowth: Hydrological S c i e n c e s Bull., Vol. 26, NO. 3, September 1981, p. 245-256. Talhami, A., 1980, Temporary d e t e n t i o n c u t s s t o r m flow peaks: i n g , Vol. 50. No. 12, December 1980, p. 72-75.
Civil hgineer-
Van H a v e r e n , B.P., 1981, Wagon Wheel Gap w a t e r s h e d e x p e r i m e n t r e v i s i t e d : W e s t e r n Snow Conf. Proc., Apr. 14-16, 1981, p. 131-138. Van Hylckama, T.E.A., 1970, W a t e r u s e b y s a l t c e d a r : Vol. 6 , NO. 3, p. 728-735.
Water Resources Resarch.
Vonnegut, B., 1947, The n u c l e a t i o n o f i c e f o r m a t i o n by s i l v e r i o d i d e : Applied P h y s i c s , 18, 593.
Jour.
Warner, J., 1974, Rain enhancement: A review, & Proc. of WMO/IAMAP S c i e n t i f i c Conf. on Weather M o d i f i c a t i o n , Tashkent, 1-7 October 1973: World Meteorol o g i c a l O r g a n i z a t i o n (WMO-No. 399), Geneva, 538 p.
206
Wibben, H.C., 1971. Effects of urbanization on flood characteristics in Nashville-Davidson County, Tennessee: U.S. Geol. Survey Water-Resources Invest i ga t ions 76-121. Williams, G.P.. 1978. The case of the shrinking channels - the North Platte and Platte Rivers in Nebraska: U.S. Geol. Survey Circ. 781, 48 p.
201
Chapter 11
APPLICATIONS OF HYDROLOGIC DATA
11.1 INTRODUCTION P l a n n i n g , d e s i g n , and o p e r a t i o n o f p r o j e c t s t h a t i n v o l v e or a f f e c t w a t e r resources require r e l i a b l e information.
T h i s c h a p t e r d e s c r i b e s some o f t h e
common e n g i n e e r i n g p r o b l e m s a n d t h e t e c h n i q u e s a v a i l a b l e f o r t h e i r s o l u t i o n u s i n g hydrologic i n f o r m a t i o n d e v e l o p e d i n p r e v i o u s c h a p t e r s .
The t e c h n i q u e s
given h e r e a r e r e l a t i v e l y simple, u t i l i z e a v a i l a b l e d a t a , and produce g e n e r a l l y reliable results. 11.2
RESERVOIR DESIGN
R e s e r v o i r s a r e formed t o moderate t h e range i n streamflows.
The o b j e c t i v e of
p r o v i d i n g s t o r a g e i s most o f t e n t o p r o v i d e a dependable flow g r e a t e r than t h e n a t u r a l low flow.
Another i m p o r t a n t o b j e c t i v e i s t o reduce f l o o d peaks,
common o n e i s t o p r o v i d e a l a k e f o r r e c r e a t i o n or e s t h e t i c r e a s o n s .
and a
Only t h e
h y d r o l o g i c a s p e c t s of r e s e r v o i r d e s i g n a r e t r e a t e d h e r e , p r i n c i p a l l y what storage is required t o provide a t a r g e t outflow f o r a given inflow.
Some
a s p e c t s of t h e h y d r o l o g i c d e s i g n such a s e v a p o r a t i o n l o s s e s and r e s e r v o i r sedimentation,
cannot b e q u a n t i f i e d u n t i l a s p e c i f i c l o c a t i o n f o r t h e r e s e r v o i r h a s
been proposed and surveyed.
R e s e r v o i r l o c a t i o n and dam d e s i g n a r e t h e province
of e n g i n e e r s and g e o l o g i s t s .
I n a r e a s o f low t o p o g r a p h i c r e l i e f ,
suitable
r e s e r v o i r s i t e s may n o t b e a v a i l a b l e . 11.2.1
Mass c u r v e
S t o r a g e a n a l y s e s f o r w a t e r supply have t r a d i t i o n a l l y been based on t h e mass curve of streamflow. reservoir.
Consider a long streamflow record a s the inflow t o a
Cumulative d a i l y , weekly, or monthly volumes from t h e i n f l o w record
a r e p l o t t e d a g a i n s t t i m e t o produce t h e mass curve. p o s t i o n o f a m a s s c u r v e b a s e d on m o n t h l y v a l u e s .
F i g u r e 11.1 shows a s h o r t Any d e s i r e d c o n s t a n t d r a f t
r a t e c a n b e r e p r e s e n t e d b y a s t r a i g h t l i n e of a p p r o p r i a t e s l o p e .
For example
t h e l i n e f o r a d r a f t r a t e o f 200 c f s w o u l d r i s e 1 2 x 200 = 2400 c f s - m o n t h s p e r year. I n t e r p r e t a t i o n of t h e mass c u r v e i s based on t h e f o l l o w i n g assumptions: t h a t t h e r e s e r v o i r was f u l l a t t h e beginning of t h e streamflow record,
(1)
and (2)
t h a t a s long a s t h e r e i s w a t e r i n t h e r e s e r v o i r t h e demand w i l l be met i n f u l l . I n F i g u r e 11.1 t h e most d e f i c i e n t p e r i o d of flow b e g i n s i n l a t e 1941 and extends t o t h e middle of 1943.
The s t o r a g e r e q u i r e d t o f u r n i s h 200 c f s throughout t h i s
p e r i o d i s r e p r e s e n t e d by t h e maximum v e r t i c a l d i s t a n c e between t h e mass curve
2 08
and t h e 200 c f s d r a f t r a t e l i n e .
S m a l l e r d r a f t r a t e s c o u l d have been s u s t a i n e d
during t h i s period w i t h s m a l l e r storages.
The maximum r e a l i s t i c d r a f t r a t e i s
a l w a y s l e s s t h a n t h e mean f l o w f o r t h e p e r i o d of record.
YEAR
F i g . 11.1.
Mass curve of monthly volumes, Blackwater R i v e r , V i r g i n i a .
F i g u r e 11.1 shows o n l y f o u r y e a r s of record.
E s t i m a t e s of s t o r a g e r e q u i r e d
t o s u s t a i n a g i v e n d r a f t r a t e u s u a l l y i n c r e a s e i n r e l i a b i l i t y w i t h l e n g t h of s treamf low r e c o r d used. The mass c u r v e c a n a l s o be a n a l y z e d f o r a d r a f t r a t e t h a t v a r i e s throughout t h e y e a r by p r e p a r i n g t h e a p p r o p r i a t e u s e l i n e .
11.2.2
Use of s i m u l a t e d streamflows
The mass-curve method does n o t p e r m i t assignment of a r e l i a b l e p r o b a b i l i t y of f a i l u r e t o the derived storage.
A s i n g l e r e c o r d , s a y o n e o f 25 y e a r s , may
d e f i n e t h e mean f l o w o f t h e s t r e a m r e a s o n a b l y w e l l b u t i t p r o v i d e s o n l y one sequence from which t o compute s t o r a g e r e q u i r e d .
Other sequences of monthly
volumes having t h e same means and s t a n d a r d d e v i a t i o n s would produce d i f f e r e n t storages. 50-year
Such sequences can be d e r i v e d by s i m u l a t i o n . sequences might be generated.
T y p i c a l l y 100 s e t s of
Each s e t would be analyzed by t h e mass-
c u r v e method or i t s e q u i v a l e n t t o d e t e r m i n e 100 v a l u e s of t h e maximum s t o r a g e r e q u i r e d i n 50 y e a r s f o r each of s e v e r a l d r a f t r a t e s .
Assuming a d e s i g n l i f e of
209 50 y e a r s f o r t h e r e s e r v o i r , t h e p r o b a b i l i t y o f f a i l u r e t o p r o v i d e t h e d e s i g n
d r a f t r a t e c a n b e r e l a t e d t o t h e v o l u m e of s t o r a g e by a f r e q u e n c y a n a l y s i s o f t h e s t o r a g e volumes. The u s e o f s y n t h e t i c r e c o r d s i n s t o r a g e a n a l y s i s was r e p o r t e d by Thomas and F i e r i n g (1962).
B u r g e s a n d L i n s l e y (1971) e v a l u a t e d t h e method.
It has been
w i d e l y used f o r i m p o r t a n t p r o j e c t s where s t r e a m f l o w r e c o r d s a r e a v a i l a b l e .
11.2.3
Annual mass-curve method
The mass-curve
method c a n be used t o d e f i n e t h e s t o r a g e r e q u i r e d f o r a g i v e n
d r a f t r a t e f o r e a c h y e a r o f record. f r e q u e n c y c u r v e s c a n b e prepared.
From t h e s e s t o r a g e s a s e t of d r a f t - s t o r a g e This approach i s l i m i t e d t o d r a f t r a t e s t h a t
c a n b e s u s t a i n e d by t h e s t r e a m f l o w a v a i l a b l e i n a n y o n e y e a r ; within-year
storage.
t h a t i s , by
The u s e f u l n e s s o f t h i s a n a l y s i s d e p e n d s on t h e a n n u a l
v a r i a b i l i t y of streamflow. p r o v i d e d by w i t h i n - y e a r
I n some r e g i o n s , t h e maximum d r a f t t h a t c a n b e
s t o r a g e i s l e s s t h a n a t e n t h o f t h e mean f l o w .
In
o t h e r s , n o t a b l y t h e s o u t h e a s t e r n United S t a t e s , d r a f t s o f h a l f o r more of t h e mean flow c a n be provided by w i t h i n - y e a r
storage.
D a i l y , r a t h e r t h a n monthly, d i s c h a r g e s s h o u l d be cumulated.
I n many p a r t s of
t h e United S t a t e s t h e y e a r b e g i n n i n g A p r i l 1 i s a p p r o p r i a t e because a r e s e r v o i r would most l i k e l y be f u l l on t h a t d a t e . The c o m p u t a t i o n a n d p l o t t i n g o f a m a s s c u r v e on a d a i l y b a s i s i s t i m e consuming.
The p r o c e s s of c u m u l a t i o n c a n be s i m p l i f i e d by a n a r i t h m e t i c a n a l y s i s
u s i n g monthly v a l u e s except d u r i n g t h e c r i t i c a l d a t e s o f h i g h and low storage. T a b l e 11.1 i s a n e x a m p l e o f s u c h a n a n a l y s i s .
Note t h a t i t i s n e c e s s a r y t o
c h e c k w h e t h e r t h e r e s e r v o i r w o u l d r e f i l l b y March 31. f o o t n o t e 2) i t d i d not.
I n t h e example (see
Thus t h e d r a f t r a t e of 100 c f s would r e q u i r e o v e r y e a r
s t o r a g e and t h e a n a l y s i s o f w i t h i n - y e a r
s t o r a g e s h o u l d be l i m i t e d t o a s m a l l e r
draft rate. Even a n a l y s e s o f t h e type shown i n T a b l e 11.1 a r e t i m e consuming i f s e v e r a l d r a f t r a t e s a r e s t u d i e d b u t t h e a n a l y s e s can b e made q u i c k l y by computer. T a b l e 11.2 s h o w s o u t p u t o f a c o m p u t e r p r o g r a m f o r 4 d r a f t r a t e s a n d f o r t h e same g a g i n g - s t a t i o n
r e c o r d analyzed i n Table 11.1.
Underlined f i g u r e s i n d i c a t e
t h a t t h e t a b u l a t e d s t o r a g e r e q u i r e d was n o t r e p l e n i s h e d by t h e f o l l o w i n g A p r i l 1 and t h e r e f o r e t h e c o r r e s p o n d i n g d r a f t cannot be s u s t a i n e d by w i t h i n - y e a r
storage
alone. Frequency c u r v e s o f s t o r a g e r e q u i r e d t o m a i n t a i n d r a f t r a t e s of 20, 40, and
60 c f s a r e shown i n F i g u r e 11.2.
Only t h e h i g h e r h a l f or t h i r d of t h e s t o r a g e s
c o m p u t e d i n T a b l e 11.2 n e e d b e u s e d b e c a u s e t h e l o w e r p a r t s o f t h e f r e q u e n c y curves a r e n o t of i n t e r e s t .
No c u r v e f o r a d r a f t o f 100 c f s i s shown b e c a u s e
t h a t d r a f t c o u l d n o t have been provided from within-year
1949.
A d r a f t r a t e o f 8 0 c f s s h o u l d have been included.
s t o r a g e i n 1943 and
210
TABLE 11.1 Mass analysis of daily discharges for Moosup River at Moosup, Conn., April 1. 1943, to March 31, 1944 [Draft rate is 100 cfsl
Month
Apr May June 1-4 5-30 July Aug
Sept Oct Nov Dec Jan Feb.1-14 15-2 9 Mar
Total flow in cfs-days
Draft in cfs-days
5,821 6.998 577 1,521 1,072 772 375 1,263 2,952 1.734 1,861 641 2,407 7.594
3,000 3,100 400 2,600 3,100 3,100 3,000 3,100 3,000 3.100 3,100 1,400 1,500 3,100
Cumulative Surplus plus Surplus 10,000 in in cfs-days in ofs-days 2,821 3,898 177 -1,079 -2,028 -2.328 -2,625 -1,837 -48 -1,366 -1,239 -759 +907 4,494
12,821 16,719 16,8 96 15,817 13.789 11,461 8,836 6,999 6,951 5,585 4,346 3,587 4,494 8,988
'Storage required: 16,896 (high flow) - 3,587 (low flow) = 13,309 cfs-days. [ 8 , 9 8 8 (Mar. 31) - 3,587 %eficiency on March 31: 13,309 (storage required) (low flow)] = 7,908 cfs-days.
-
11.2.4
Probability routing
An alternative to generating a long simulated streamflow record for defining the required storage is provided by a combination of the probability-routing method and the annual-mass-curve method.
Results of the probability-routing
method, after adjustment for seasonal variations, define that part of the draftstorage-frequency relation which depends on over-year storage. The annual-masscurve method is used to define the relation for lower draft rates. Probability routing is applied to a distribution of annual discharges (inflows) under the assumptions that the discharge for each year is uniform throughout that year and is equal to the mean for that year and that the annual discharges are not serially related.
The procedure was proposed by Langbein
(1958) and was described by Hardison and Furness (1963). Briefly stated, probability routing is based on assuming a distribution for start-of-year reservoir contents and then, for a given draft rate and given frequency distribution of inflow, computing the distribution of year-end reservoir contents to s e e if i t checks the assumed start-of-the-year distribution. (The end-of-year probability distribution of reservoir contents is inherently equal to the start-of-year distribution.)
The computations are begun by sub-
dividing the reservoir capacity into about 15 layers and assuming a probability for each layer as well as a probability of spill and a probability of being empty.
211 TABLE 11.2
O u t p u t o f c o m p u t e r p r o g r a m f o r w i t h i n - y e a r s t o r a g e , Moosup R i v e r a t Moosup, Conn. ( u n d e r l i n e d f i g u r e s i n d i c a t e t h a t t h e t a b u l a t e d s t o r a g e was n o t r e p l e n i s h e d by t h e f o l l o w i n g A p r i l 1 ) S t o r a g e , i n cfs-days, r e q u i r e d t o m a i n t a i n the d r a f t r a t e s i n d i c a t e d d u r i n g y e a r beginning A p r i l 1 Year 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959
20 c f s 36 82 170 80
20 10 25 19 361 25 319 301 62 24 85 113 1 39 83 34 44 378 21 29 81 1.092 14 145
The year-end
40 c f s
60 c f s
100 c f s
568 918 1.614 1,333 315 41 761 371 1,939 412 1,912 1,501 1,557 28 2 926 1,124 2,157 1,115 6 52 1,293 2,153 274 370 1,253 4,127 54 1,143
1.928 2,385 3,979 3,054 1,251 116 2,195 2,156 5,023 1,445 4.438 2,926 3,854 1.062 2.8 97 2,708 5,157 3,697 2,660 3,903 4,580 1.347 1.010 3,772 8,005 269 2.731
5.207 5,689 11,409 9,989 5,997 799 8,076 6,436 12.8 1 3 6,000 13,308 6,511 9,108 5,617 8.239 7,317 12,469 9,790 7.756 10,677 11.009 4,716 2,735 10,079 16.535 1,625 6,328
p r o b a b i l i t y f o r each s t a t e i s computed by m u l t i p l y i n g t h e as-
sumed p r o b a b i l i t y of each of t h e p o s s i b l e s t a t e s by t h e d e f i c i e n c y p r o b a b i l i t y of t h e i n f l o w r e q u i r e d t o produce t h e s e l e c t e d year-end products.
s t a t e and cumulating t h e
Agreement could be reached by t r i a l and e r r o r s o l u t i o n s t a r t i n g each
t i m e w i t h the p r e v i o u s l y computed year-end d i s t r i b u t i o n , b u t a more f e a s i b l e way i s t o s o l v e 1 5 t o 2 0 s i m u l t a n e o u s e q u a t i o n s by c o m p u t e r t o o b t a i n t h e u n i q u e
d i s t r i b u t i o n of year-end given d r a f t rate.
r e s e r v o i r c o n t e n t s f o r t h e g i v e n s t o r a g e c a p a c i t y and
Each o f t h e s e e q u a t i o n s g i v e s t h e p r o b a b i l i t y of t h e w a t e r
l e v e l being i n one of 15 t o 20 s t a t e s a t the end of t h e y e a r and t h e s o l u t i o n i s b a s e d on t h e f a c t t h a t t h e sum of t h e p r o b a b i l i t i e s m u s t e q u a l u n i t y .
The
p r o b a b i l i t y of t h e r e s e r v o i r b e i n g empty a t t h e end of t h e y e a r t h u s o b t a i n e d i s t h e d e s i r e d i n f o r m a t i o n f o r t h e d r a f t r a t e , r e s e r v o i r c a p a c i t y , and i n f l o w d i s t r i b u t i o n used i n s e t t i n g up t h e equations. P r o b a b i l i t y r o u t i n g c a n be performed f o r any d i s t r i b u t i o n of annual i n f l o w s , b u t by c h a r a c t e r i z i n g t h e i n f l o w d i s t r i b u t i o n s by a few p a r a m e t e r s ,
the r e s u l t s
212
I
I
I I l l
I
Fig. 11.2. D r a f t - s t o r a g e - f r e q u e n c y within-year s t o r a g e ) .
c u r v e s f o r Moosup R i v e r , C o n n e c t i c u t ( f o r
can be g e n e r a l i z e d so t h a t i t i s n o t n e c e s s a r y t o r e s o r t t o t h e computer f o r e a c h problem.
S o l u t i o n s have been o b t a i n e d f o r t h r e e t y p e s of two-parameter
d i s t r i b u t i o n s o f i n f l o w and t h e r e s u l t s h a v e b e e n r e l a t e d t o a v a r i a b i l i t y index.
A sample of t h e g e n e r a l i z e d computer s o l u t i o n s i s g i v e n i n Table 11.3.
These s t o r a g e r e q u i r e m e n t s a r e based on annual i n f l o w s and must b e i n c r e a s e d t o account for t h e w i t h i n - y e a r flow v a r i a b i l i t y .
Riggs and Hardison (1973) g i v e
t h e complete t a b l e s of t h e computer s o l u t i o n s and d e s c r i b e how t h e d i s t r i b u t i o n of annual i n f l o w s and t h e frequency c u r v e s of within-year
mass-curve method) a r e used t o p r e p a r e a d r a f t - s t o r a g e F i g u r e 11.3.
In t h a t f i g u r e ,
within-year
s t o r a g e (by t h e annual
r e l a t i o n such a s t h a t O f
s t o r a g e w i l l provide a dependable
d r a f t of only about 20 p e r c e n t of t h e mean flow. 11.2.5
Evaporation, sedimentation, and bank-storage
Good e s t i m a t e s of e v a p o r a t i o n l o s s e s from a r e s e r v o i r cannot be made u n t i l t h e water-surface
a r e a i s known.
Evaporation l o s s e s may a p p r e c i a b l y reduce t h e
d r a f t a v a i l a b l e from a given s t o r a g e .
e s p e c i a l l y i n a r i d regions.
An a n a l y s i s
b y Leopold (1959) c o n c l u d e s t h a t i n c r e a s e s i n s t o r a g e i n t h e Co l o r a d o Ri v e r b a s i n beyond a c e r t a i n v o l u m e w i l l a c h i e v e p r a c t i c a l l y no a d d i t i o n a l w a t e r
213 TABLE 11.3 Carryover s t o r a g e r e q u i r e m e n t s f o r normal d i s t r i b u t i o n s of annual f l o w s (Storage r e q u i r e m e n t s a r e i n r a t i o t o mean annual r u n o f f ; Cv is c o e f f i c i e n t of v a r i a t i o n of annual f l o w s ) D r a f t , i n p e r c e n t of mean flow n c
~~~
100
98
95
90
5-percent
..10 08 .12 .14 .16 .18 .20 .22 .24 .26 .28 .30 .40 .SO
1 .oo. 1.25 1 .50 1 .I5 2.01 2.26 2.52 2 .I7 3.03 3.28 3.53 3 .I9
.25 .36 .50
.65 .81 .97 1.14 1.32 1.51 1.70 1.90 2.10 3.11 4.30
.48 .I3 1.02 1.33 1.69 2.09 2.52 2.91 3.45
.21 .30 .43 .60 .80 1.02 1.24 1.47 1 .I1 1.96 2.23 2.50 3.96
I0
60
50
40
30
20
chance of d e f i c i e n c y
.ll .04 .18 .08 .26 .12 0 .34 .11 .03 .43 .23 .06 .53 .29 .10 .64 .35 .14 .I6 .42 .18 .88 .49 .23 1.01 .51 .28 1.14 .65 .34 1.28 .I4 .40 2.02 1.21 .I1 2.83 1.89 1.01
1-percent
.08 .10 .12 .14 .16 .18 .20 .22 .24 .26 .28 .30 .40 .SO
80
.02 .06 .10 .14 .18 .22 .41 -75
0 .03 .06 .09 .30 .53
0 .16 .37
.06 .24
.13
.03
0 .05 .10 .36 .65
0 .25 .52
.ll .32
chance of d e f i c i e n c y
.10 .16 .03 .24 .08 .32 .14 .03 .41 .19 .08 .51 .25 .13 .01 .62 .32 .19 .06 . I 6 .39 .24 .12 .91 .46 .30 .11 1.08 .54 .36 .23 1.26 .62 .42 .28 1.45 .71 .48 .33 2.48 1.28 .81 .64 3.65 2.04 1.32 1.01
.01 .06 .ll .16 .21 .48 .78
regulation i f evaporation l o s s is subtracted.
T h i s c o n c e p t of a p r a c t i c a l
maximum n e t flow from s t o r a g e was u t i l i z e d by Lof and Hardison (1966) i n comput i n g s t o r a g e r e q u i r e m e n t s f o r w a t e r i n t h e United S t a t e s .
B a t e s of e v a p o r a t i o n
from w a t e r s u r f a c e s a r e published; see Chapter 12. The s t o r a g e c a p a c i t y of a r e s e r v o i r w i l l be p r o g r e s s i v e l y reduced by deposi t i o n o f s e d i m e n t c a r r i e d by t h e s t r e a m .
E s t i m a t e s o f t h e annual volume of
d e p o s i t e d m a t e r i a l c a n b e made from r e c o r d s of sediment t r a n s p o r t and e s t i m a t e s o f t h e t r a p e f f i c i e n c y , t h a t i s , t h e p r o p o r t i o n o f s e d i m e n t s t r a p p e d by t h e reservoir;
see Vanoni (1975, p. 587-602).
In r e g i o n s where s e d i m e n t - t r a n s p o r t
d a t a a r e n o t a v a i l a b l e , p e r i o d i c surveys of e x i s t i n g r e s e r v o i r s w i l l provide
214 useful information.
T h e economic life of a reservoir depends on the rate of
reduction in storage capacity.
T
I
1
I
4
o C arryo ver st o rag e o Wit h in - year storage A
4
Adlustment t a carryo ver storage
x C o m b in ed st o rag e
1- ---I 1~
0 5
0
10
15
2 0
25
-
3 0
1--35
4 0
STORAGE REQUIRED, I N RATIO TO M E A N A N N U A L RUNOFF
Fig. 11.3. Draft-storage curve for 2 percent probability of deficiency, Red River, Tennessee. Reservoir storage capacity is sometimes found to be appreciably greater than that c o m p u t e d f r o m the topographic survey. storage.
returns on falling stages. this water is not lost.
11.2.6
This increase is due to b a n k
Water flows into the banks as the reservoir stage rises and much of it Thus, except for a residual in the b a n k aquifers,
See Bank Storage in Chapter 6.
Draft-storage at ungaged sites
Definition of draft-storage-frequency relations at ungaged sites is o f t e n required.
This might be done by estimating the statistics of monthly flows from
generalized relations w i t h b a s i n characteristics, synthesizing a long record from these, and analyzing that record.
It is m u c h s i m p l e r to transfer draft-
storage-frequency characteristics directly from gaged to ungaged sites. Transferring a draft-storage
relation is accomplished by use of a regional
relation in conjunction with some streamflow information collected or estimated at the site.
Two criteria must be met:
(1) draft-storage relations defined by
gaging-station records for various recurrence intervals must be closely related to flow characteristics; (2) sufficient i n f o r m a t i o n must be available at the site of application to provide good estimates of the flow characteristics needed in the regional relation.
215 Regional d r a f t - s t o r a g e
relations are u s u a l l y developed g r a p h i c a l l y because
some o f t h e m o d e l s a r e d i f f i c u l t t o e x p r e s s m a t h e m a t i c a l l y .
The c h o i c e of
v a r i a b l e s w i l l depend on flow c h a r a c t e r i s t i c s i n t h e r e g i o n and on what information i s available.
However,
t h e d r a f t and t h e s t o r a g e s h o u l d b e i n u n i t s
commonly used o r r e a d i l y computed. Various r e l a t i o n s a r e shown i n F i g u r e s 11.4, r e q u i r e d i n a l l of them.
The other variables,
11.5 and 11.6. a low-flow
Drainage a r e a i s
characteristic,
mean
f l o w , a n d a n i n d e x o f v a r i a b i l i t y o f annual. mean f l o w s , may b e e s t i m a t e d a t ungaged s i t e s by methods g i v e n i n p r e v i o u s c h a p t e r s .
IY
Y; Iy U
U
4
10 11 12 13 14 15 16 17 AVERAGE ANNUAL RUNOFF, I N INCHES
9
18
F i g . 11.4. D r a f t - s t o r a g e c u r v e s f o r a r e g i o n i n M i s s o u r i ; 2 p e r c e n t c h a n c e o f d e f i c i e n c y (From S k e l t o n , 1971). 11.2.7
Spillway d e s i g n f l o o d s
S p i l l w a y s a r e designed t o p r o t e c t t h e dam and r e s e r v o i r a g a i n s t f a i l u r e . d e g r e e o f p r o t e c t i o n provided should depend on t h e consequences of f a i l u r e .
The For
h i g h dams whose f a i l u r e would c a u s e l o s s of l i f e and e x t e n s i v e p r o p e r t y damage, t h e s p i l l w a y i s u s u a l l y designed t o p a s s t h e maximum r e a s o n a b l y p o s s i b l e flood. Where dam f a i l u r e w o u l d c a u s e m i n o r damage d o w n s t r e a m t h e s p i l l w a y may b e d e s i g n e d t o p a s s a l e s s e r flood. Streamflow r e c o r d s a r e t o o s h o r t t o p r o v i d e an adequate b a s i s f o r d e f i n i n g t h e p r o b a b l e maximum f l o o d by frequency a n a l y s i s , d i s t r i b u t i o n s used approach a l i m i t .
and none of t h e t h e o r e t i c a l
But m e t e o r o l o g i s t s a c c e p t t h e p r e m i s e of a
p r o b a b l e maximum s t o r m p r e c i p i t a t i o n , from which a maximum p r o b a b l e f l o o d oan be computed.
P r o c e d u r e s f o r e s t i m a t i n g t h e p r o b a b l e maximum p r e c i p i t a t i o n a r e
216
Draft rate of 0 . 8 m e a n flow
Draft rate of 0 . 2 m e a n flow
I
I
P
\O
0.001 0.01 0.1 MEDIAN ANNUAL MINIMUM 7-DAY AVERAGE FLOW, IN CUBIC FEET PER SECOND PER SQUARE MILE
F i g . 11.5. streams.
R e g i o n a l d r a f t - s t o r a g e r e l a t i o n s b a s e d on d a t a f o r some I l l i n o i s
d e s c r i b e d b y H e r s h f i e l d ( 1 9 6 1 ) a n d b y W Y O (1973).
Methods o f c o n v e r t i n g
p r o b a b l e maximum P r e c i p i t a t i o n i n t o e x t r e m e f l o o d f l o w s a r e g i v e n b y WMO (1969b).
P r o b a b l e maximum p r e c i p i t a t i o n a s a b a s i s f o r d e t e r m i n i n g s p i l l w a y
d e s i g n f l o o d s was e v a l u a t e d by a n ASCE Task F o r c e on t h e hydrology of s p i l l w a y d e s i g n (Banks, 1 9 6 4 ) .
The T a s k F o r c e ( 1 ) r e v i e w e d a n d s u m m a r i z e d e x i s t i n g
p o l i c y and c r i t e r i a f o r s p i l l w a y d e s i g n f l o o d s f o r dams o f a l l s i z e s ,
(2)
e x a m i n e d h y d r o l o g i c c o n s i d e r a t i o n s , p o l i c i e s , c r i t e r i a , and m e t h o d o l o g y f o r d e t e r m i n a t i o n o f d e s i g n f l o o d flows. ( 3 ) d e s c r i b e d p o l i c i e s , c r i t e r i a and methodology f o r d e t e r m i n a t i o n of s p i l l w a y c a p a c i t i e s i n r e l a t i o n t o design f l o o d flows.
and (4) e v a l u a t e d t h e a c c u r a c y o f s t a t i s t i c a l a n a l y s e s of h y d r o l o g i c d a t a
p e r t i n e n t t o f l o o d flows. 11.2.8
Storage f o r flood c o n t r o l
The i d e a l f l o o d - c o n t r o l
r e s e r v o i r i s e m p t y m o s t o f t h e t i m e so t h a t i t s
c a p a c i t y c a n be used t o reduce t h e incoming f l o o d peaks.
An a p p r o x i m a t e method
o f d e f i n i n g t h e s t o r a g e r e q u i r e d t o l i m i t o u t f l o w t o some t a r g e t d i s c h a r g e i s shown i n F i g u r e 11.7.
The hydrograph i s commonly d e r i v e d from a p r o j e c t s t o r m
b u t i t may b e t h a t o f a m a j o r r e c o r d e d f l o o d .
Release need n o t be a t t h e
217 maximum r a t e a f t e r t h e i n f l o w f a l l s below t h a t r a t e b u t t h e s t o r a g e i s u s u a l l y reduced promptly.
+ w LL w
1000 Plotted point
of variability index
O L L
C
lo0l
10
!
v
PLOT A
1
PLOT B
PL
I
Y L L
22 LL
0
0.01
0.1
1
MEAN FLOW, IN CUBIC FEET PER SECOND PER SQUARE MILE
bv,
Fig. 11.6. basin.
0.2
0.5
1
2
VARIABILITY INDEX
S t o r a g e r e l a t e d t o mean f l o w and a v a r i a b i l i t y index i n Kansas River
STORAGE REQUIRED
F i g . 11.7.
Method of d e f i n i n g s t o r a g e r e q u i r e d t o c o n t r o l a major f l o o d .
Major f l o o d s a r e n o t always w i d e l y s e p a r a t e d in time. c l o s e l y f o l l o w e d by a n o t h e r ,
I f one l a r g e f l o o d i s
t h e s t o r a g e needed t o c o n t r o l t h e d i s c h a r g e may be
2 18
l a r g e r than t h a t d e f i n e d by a n a l y s i s of a s i n g l e d e s i g n hydrograph.
The f r e -
quency mass-curve method p r o v i d e s t h e s t o r a g e needed f o r such occurrences.
From
a s t r e a m f l o w r e c o r d t h e h i g h e s t mean d i s c h a r g e s f o r v a r i o u s numbers of consecut i v e d a y s i n each y e a r a r e e x t r a c t e d , and f r e q u e n c y c u r v e s p r e p a r e d .
The ex-
amples shown i n F i g u r e 11s were d e f i n e d g r a p h i c a l l y because t h e y a r e of v a r i o u s
!!O
8000
I
I
I
I
I
80
50
30
10
5
I
1
2 1
PROBABILITY OF EXCEEDANCE, IN PERCENT
F i g . 11.8. F r e q u e n c y c u r v e s o f a n n u a l h i g h e s t mean d i s c h a r g e s f o r v a r i o u s numbers of c o n s e c u t i v e days, Toccoa River, Georgia. shapes and o n l y t h e upper ends a r e needed.
Discharges a t s e l e c t e d p r o b a b i l i t i e s
a r e t a k e n from t h e s e frequency c u r v e s and m u l t i p l i e d by t h e a p p r o p r i a t e number of d a y s t o g e t volumes.
These volumes a r e p l o t t e d a g a i n s t days t o d e f i n e a
f r e q u e n c y mass c u r v e s u c h a s t h a t o f F i g u r e 11.9.
The m e t h o d o f d e t e r m i n i n g
storages required t o l i m i t outflows t o specified discharges is s i m i l a r t o that u s e d w i t h t h e c o n v e n t i o n a l mass c u r v e : t h e s t o r a g e r e q u i r e d i s t h e maximum o r d i n a t e between t h e c u r v e and a l i n e r e p r e s e n t i n g t h e s p e c i f i e d maximum d i s charge. The amount of s t o r a g e d e f i n e d a s above may n o t be adequate a t t i m e s t o l i m i t the outflow t o the s p e c i f i e d l e v e l u n l e s s r e l e a s e s a r e near the s p e c i f i e d l e v e l u n t i l the storage i s depleted.
Such s u s t a i n e d h i g h r e l e a s e s a r e u s u a l l y unde-
s i r a b l e and need n o t be made under a l l c o n d i t i o n s .
O p e r a t i o n of a f l o o d c o n t r o l
219 r e s e r v o i r u s u a l l y i s b a s e d on a " r u l e c u r v e " w h i c h s p e c i f i e s t h e r e l e a s e s depending on r e s e r v o i r s t a g e , i n f l o w f o r e c a s t , and o t h e r r e l e v a n t i n f o r m a t i o n .
0
20
40
60
80
100
CONSECUTIVE DAYS
Fig. 11.9. Frequency mass c u r v e of annual maximum f l o o d volumes f o r 2 p e r c e n t p r o b a b i l i t y of d e f i c i e n c y . Data from F i g u r e 11.8. More s o p h i s t i c a t e d methods a r e used t o d e s i g n i m p o r t a n t f l o o d - c o n t r o l j e c t s p a r t i c u l a r l y where s e v e r a l r e s e r v o i r s a r e proposed.
pro-
Various c o m b i n a t i o n s
of s t o r a g e c a p a c i t i e s and o p e r a t i n g p l a n s a r e e v a l u a t e d u s i n g r e c o r d e d or synt h e s i z e d s t r e a m f low s. Small f l o o d - c o n t r o l
r e s e r v o i r s commonly have f i x e d o u t l e t s t h r o u g h which t h e The U.S.
r a t e of r e l e a s e d e c r e a s e s w i t h r e s e r v o i r s t a g e . S e r v i c e used many such f l o o d w a t e r - r e t a r d i n g
S o i l Conservation
s t r u c t u r e s on s m a l l subwatersheds t o
c o n t r o l f l o o d r u n o f f from t h e major watershed.
A t y p i c a l s t r u c t u r e a n d a de-
s c r i p t i o n o f t h e program i n Texas i s g i v e n by G i l b e r t and Sauer (1970). 11.3
DEPENDABLE FLOWS WITHOUT STORAGE
Many water-supply needs can be provided by t h e n a t u r a l flow of a stream.
The
adequacy of a s t r e a m f o r a p a r t i c u l a r u s e may depend on whether a t e m p o r a r i l y reduced supply can be t o l e r a t e d .
A municipal water system can provide l e s s
w a t e r than u s u a l f o r l i m i t e d p e r i o d s w i t h o u t s e r i o u s consequences t o t h e majori t y of i t s customers.
Hydropower p l a n t s and p l a n t s r e q u i r i n g p r o c e s s or c o o l i n g
w a t e r can be s h u t down f o r s h o r t p e r i o d s , b u t a t some c o s t .
But a n u c l e a r power
p l a n t must have an a s s u r e d s u p p l y of c o o l i n g water. Maintenance of c e r t a i n i n s t r e a m f l o w s i s d e s i r a b l e or l e g a l l y r e q u i r e d f o r preserving the aquatic habitat,
f o r providing d i l u t i o n f o r waste disposal,
f o r e s t h e t i c s ( A m e r i c a n F i s h e r i e s S o c i e t y , 1976).
and
R e a l i s t i c instream flows
cannot be e s t a b l i s h e d w i t h o u t i n f o r m a t i o n on streamflow.
220
Annual low-flow
frequency c u r v e s show t h e dependable f l o w w i t h o u t s t o r a g e .
The 7-day or 30-day c u r v e i s commonly u s e d , a t a p r o b a b i l i t y o f 0.1 o r l e s s a c c o r d i n g t o t h e consequences o f t h a t d i s c h a r g e n o t b e i n g a v a i l a b l e . dependable s u p p l i e s can be d e t e r m i n e d from s e a s o n a l low-flow 11.4
BRIDGE
AND
Seasonal
f r e q u e n c y curves.
CULVERT OPENINGS
The optimum s i z e and geometry of a waterway opening depends p r i n c i p a l l y on t h e d e s i g n f l o o d and t h e c h a n n e l c h a r a c t e r i s t i c s . s e l e c t i o n of t h e a p p r o p r i a t e design flood. designed t o p a s s t h e 100-year
flood.
Economic s t u d i e s l e a d t o
I n t e r s t a t e highway c r o s s i n g s a r e
Minor road c r o s s i n g s where road overflow
would r e s u l t i n l i t t l e damage a n d f o r inconvenience may be d e s i g n e d t o p a s s a 5
or 1 0 - y e a r f l o o d .
The p e a k d i s c h a r g e f o r t h e s e l e c t e d r e c u r r e n c e i n t e r v a l a t
t h e u s u a l l y ungaged s i t e i s d e t e r m i n e d a s d e s c r i b e d i n Chapter 8 . Design of t h e opening r e q u i r e s c o n s i d e r a t i o n of flow d i s t r i b u t i o n i n t h e approach channel, e s t i m a t i o n of t h e stage-discharge r e l a t i o n a t t h e c r o s s i n g s i t e , and c o m p u t a t i o n o f v e l o c i t i e s t h r o u g h t h e p r o p o s e d o p e n i n g s a n d of t h e r e s u l t a n t b a c k w a t e r ( B u r e a u o f P u b l i c Roads, 1960).
P r o c e d u r e s f o r computing
f l o w s t h r o u g h b r i d g e s and c u l v e r t s a r e g i v e n by M a t t h a i ( 1 9 6 8 ) a n d B o d h a i n e (1968) r e s p e c t i v e l y .
See Colson and S c h n e i d e r (1983) f o r f l o w s t h r o u g h m u l t i p l e
bridges. Some c u l v e r t s a r e d e s i g n e d t o t a k e advantage of t h e s t o r a g e above t h e highway fill,
t h e r e b y r e d u c i n g t h e f l o o d peak and t h e r e q u i r e d c u l v e r t s i z e .
The reduc-
t i o n a t t a i n e d depends on t h e volume a v a i l a b l e f o r s t o r a g e and on t h e volume of t h e f l o o d hydrograph. from t h e f l o o d peak.
A t ungaged s i t e s t h e hydrograph volume may b e e s t i m a t e d The r e l a t i o n
V = 0.131 Q0.878 w h e r e V i s h y d r o g r a p h v o l u m e i n a c r e - f e e t and Q i s p e a k d i s c h a r g e i n c f s , w a s d e r i v e d from hydrographs for 35 s m a l l Wyoming s t r e a m s (Craig and Rankl,
1978).
Peak d i s c h a r g e f o r t h e d e s i g n r e c u r r e n c e i n t e r v a l can be e s t i m a t e d by one of t h e methods d e s c r i b e d i n Chapter 8.
C r a i g and Rankl a l s o d e s c r i b e d a p r o c e d u r e f o r
a n a l y z i n g t h e r e d u c t i o n i n peak f l o w and t h e i n c r e a s e d head on t h e c u l v e r t f o r v a r i o u s c u l v e r t s i z e s and u p s t r e a m t o p o g r a p h i e s .
Eychaner (1976) developed a
r e l a t i o n o f v o l u m e t o p e a k f o r s t r e a m s i n s o u t h e r n U t a h and a d i m e n s i o n l e s s graph showing t h e r e d u c t i o n i n r e q u i r e d s t r u c t u r e c a p a c i t y w i t h s t o r a g e ( F i g .
11. l o )
.
11.5
FORECASTING SIBFAMFLOW
A f o r e c a s t u s e s i n f o r m a t i o n now a v a i l a b l e t h a t w i l l a f f e c t a f u t u r e f l o w . For example t h e w a t e r c o n t e n t o f a snowpack i s i n f o r m a t i o n a b o u t r u n o f f t h a t
221 w i l l r e s u l t f r o m m e l t i n g o f t h e pack.
On t h e o t h e r hand, a p r e d i c t i o n i s a n
i n f e r e n c e r e g a r d i n g a f u t u r e e v e n t based on p r o b a b i l i t y theory.
20
10
0
30
20
40
STORAGE PROW DED IN PERCENT OF INFLOW VOLUME
F i g . 11.10. Reduction i n needed waterway opening by p r o v i d i n g s t o r a g e . s o u t h e r n Utah. ( A f t e r Eychaner, 1976).
For
F o r e c a s t s a r e oommonly made o f f l o o d p e a k s o r h y d r o g r a p h s . r u n o f f v o l u m e s from s n o x m e l t ,
and r u n o f f f o r one or s e v e r a l months d u r i n g a low-flow
season.
S t r e a m f l o w and c l i m a t o l o g i c a l d a t a a r e n e e d e d t o c a l i b r a t e some f o r e c a s t i n g m o d e l s , a n d o n e or b o t h t y p e s o f d a t a may b e n e e d e d t o make t h e f o r e c a s t . Weather f o r e c a s t s a r e v a l u a b l e f o r making s h o r t - t e r m a s f o r floods.
s t r e a m f l o w f o r e c a s t s such
G u i d e l i n e s and examples of f o r e c a s t i n g methods a r e g i v e n by WMO
( 1 9 6 9 a ) , NOAA ( 1 9 7 2 ) , and b y ASCE (1980). 11.5.1
Floods
The p u r p o s e o f f o r e c a s t i n g f l o o d s i s t o p r o v i d e i n f o r m a t i o n on f l o o d d i s charges,
s t a g e s , and t i m e s of o c c u r r e n c e i n o r d e r t o e l i m i n a t e l o s s of l i f e and Another purpose i s t o p r o v i d e i n f o r m a t i o n f o r r e s e r -
reduce damage t o property. v o i r o p e r a t i o n (Nordenson
6
Richards,
1964).
Data needed i n c l u d e known or f o r e c a s t s t o r m p r e c i p i t a t i o n , flow.
and t h e s t a g e - d i s c h a r g e
r e l a t i o n a t t h e s i t e of i n t e r e s t .
c u r r e n t streamThe volume of
r u n o f f from t h e s t o r m i s e s t i m a t e d and t h e n i s d i s t r i b u t e d i n t i m e t o o b t a i n t h e hydrograph.
T h i s may be done g r a p h i c a l l y b u t d i g i t a l modeling i s w i d e l y used.
Nordenson (1969) d e s c r i b e d t h e a p p l i c a t i o n of c o n c e p t u a l c a t c h m e n t models t o river forecasting,
and S i t t n e r ( 1 9 7 6 ) r e p o r t e d r e s u l t s o f a WMO p r o j e c t on
i n t c r c o m p a r i s o n of c o n c e p t u a l models used i n h y d r o l o g i c a l f o r e c a s t i n g . of modeling a r e g i v e n by Overton and Meadows (1976).
Details
222 Hydrographs derived from precipitation, or measured at a gaging station, may be routed downstream to other points of interest (Linsley, Kohler. and Paulhus, 1975, P. 287-315).
A routing c o m p o n e n t is included in most conceptual models
used for forecasting. Discharge is forecast by most models but stage is the characteristic needed to assess the extent of flooding.
Therefore a stage-discharge relation must be
defined for transferring discharge to stage. the vicinity,
If a rated gaging station is in
its stage-discharge relation can be used although it may have to
be extended w e l l above the highest point of definition for application to unusual discharges. The time between the precipitation and the peak discharge in a stream ranges
from less than an hour to m a n y days: it depends on the size of the stream and its runoff characteristics. disseminated quickly.
To be of value the forecast m u s t b e m a d e and
Transmission of input data via satellite is most satis-
factory. Forecasts of small stream flood peaks cannot be made quickly enough following the storms to be useful.
Consequently the National Weather Service issues flood
warnings for small streams on the basis of forecasts of heavy rainfall. 11.5.2
Snowmel t runoff
The summer water supply for irrigation, hydropower, and other u s e s is derived from melting of the h i g h moun'tain s n o w p a c k in m a n y basins o f w e s t e r n United States.
Advance knowledge of the magnitude of runoff allows time to plan for
the optimum use of that often inadequate resource.
For example, forecasts as of
April 1, 1934 shored Utah to be facing the worst drought in her history; prompt implementation of a conservation program minimized its effects (Clyde, 1951). Records o f streamflow. snow surveys, and
precipitation for a n u m b e r of
concurrent years are used to develop relations for estimating runoff during the snormelt period.
Other data that may be useful include base flow of the stream
previous to the beginning of the melt, and the condition of the soil underneath the snowpack
-
frozen or unfrozen,
wet or dry.
Precipitation during the runoff
period helps to refine the relation but, of course, it cannot b e e s t i m a t e d a t time of forecast. Regression m o d e l s are w i d e l y used for forecasting seasonal runoff (Soil Conservation Service, 1972).
Figure 11.11
shows a graphical relation of April
through July runoff to maximum water content of the Spring snowpack. Seasonal runoff from melting of a snowpack also may be estimated from precipitation records at lower elevations.
In some basins, runoff estimates from
precipitation are comparable in reliability to ones made from snow-survey data. For such basins the precipitation method would be used because of the negligible cost o f low-elevation precipitation records relative to the cost of s n o w
223 surveys.
K o h l e r ( 1 9 5 9 ) s u g g e s t e d t h a t snow s u r v e y a n d p r e c i p i t a t i o n d a t a a r e
complementary and t h a t b o t h can be used t o advantage.
B a r l e y , YcCuen, and Rango
(1980) e v a l u a t e d 3 models f o r f o r e c a s t i n g snowmelt r u n o f f volumes and found t h e r e g r e s s i o n model most a c c u r a t e f o r 60 d a y s o r longer.
t; w
900-
U
w
cc
2 700-
? I c
5 U-
$
zj
500-
CT
3
3 I
F i g . 11.11. R e l a t i o n f o r f o r e c a s t i n g s n o w m e l t r u n o f f o f Rogue R i v e r , Oregon, from w a t e r c o n t e n t on Diamond Lake snow c o u r s e (From S o i l Conservation S e r v i c e , 1972). F o r e c a s t s o f r u n o f f f r o m s n o w m e l t a r e made m o n t h l y d u r i n g l a t e w i n t e r and spring.
The b e s t e a r l y e s t i m a t e of s e a s o n a l r u n o f f from a snowpack u s u a l l y i s
t h e one b a s e d on snow s u r v e y d a t a a s o f t h e d a t e f o r w h i c h t h e s n o w p a c k w a t e r c o n t e n t i s a maximum (Riggs, 1980). Autumn r u n o f f of some s t r e a m s i n s e m i a r i d r e g i o n s can be f o r e c a s t from t h e s p r i n g snowpack which p r o v i d e s t h e s o u r c e of autumn r u n o f f through r e c h a r g e of ground water.
A f o r e c a s t r e l a t i o n of t h i s t y p e i s shown i n F i g u r e 11.12.
Runoff from a snowpack i s h i g h l y r e l a t e d t o t h e t e m p e r a t u r e regime a s i n d i c a t e d by t h e h y d r o g r a p h o f d a i l y f l o w i n F i g u r e 11.13 f o r a s m a l l s t r e a m .
And
even f o r l a r g e s t r e a m s t h e hydrograph f o r t h e snow r u n o f f p e r i o d depends on t h e t e m p e r a t u r e regime (and of c o u r s e ,
on r a i n f a l l d u r i n g t h e p e r i o d ) .
Thus r e l i -
a b l e s h o r t - t e r m f o r e c a s t s of r u n o f f from snowmelt a r e l i m i t e d t o a few days f o r which w e a t h e r c a n be f o r e c a s t .
Schermerhorn (1961) used a s i n g l e t e m p e r a t u r e
i n d e x f o r m a k i n g 3-day f o r e c a s t s .
H i s i n d e x i s b a s e d on t h e u n i t - h y d r o g r a p h
p r i n c i p l e and i s c o n s t r u c t e d by w e i g h t i n g a n t e c e d e n t t e m p e r a t u r e s i n p r o p o r t i o n t o t h e o r d i n a t e s of t h e b a s i n ' s snowmelt u n i t g r a p h .
Zhidikov. e t . a l . (1976)
d e v e l o p e d a s n o w m e l t r u n o f f model f o r f o r e c a s t i n g f l o w s o f r e l a t i v e l y s m a l l r i v e r s f i v e d a y s i n advance.
Model i n p u t s a r e w a t e r e q u i v a l e n t of snow cover.
224
precipitation,
antecedent moisture content, daily snowmelt, non-uniformity
of
snow cover, retention capacity of the basin, and percent of forest cover.
5
0
~
~
20
30
40
50
SUM O F W A T E R C O N T E N T S A S OF A P R I L 1, O N FOX CREEK A N D B E A R CREEK S N O W COURSES, IN I N C H E S
Fig.
11.12.
Forecasting relations for Bruneau River, Idaho.
3
a 0
I JUNE
JULY
Pig. 11.13. Snowmelt runoff during a period of negligible precipitation. at elevation 2700 m (Riggs, 1980).
Gage
Winter and early-spring runoff from basins o f low relief providos needed water and may produce damaging floods.
The depth of snow and the areal extent
of snow cover on a basin can be analyzed with various assumed temperature and precipitation patterns to show the probability of various magnitudes of runoff volume and of peak discharge.
W M O (1969b, p. 117-135) describes some methods of
estimating the maximum floods from snowmelt and from a combination of snowmelt
225 and r a i n f a l l ,
u s i n g a n example from e a s t e r n Canada.
Baker 11972) found a h i g h
c o r r e l a t i o n b e t w e e n t h e c o l d - p e r i o d p r e c i p i t a t i o n (snow o r r a i n ) a n d e a r l y s p r i n g r u n o f f i n Minnesota where s o i l s f r e e z e annually.
R e s u l t s of h i s s t u d y
i n d i c a t e t h a t t h i s p r e c i p i t a t i o n c a n b e e n t i r e l y a c c o u n t e d f o r b y r u n o f f and s u b l i m a t i o n (or e v a p o r a t i o n ) .
The p e a k d i s c h a r g e d e p e n d s , o f c o u r s e , on t h e
t e m p e r a t u r e regime d u r i n g t h e p e r i o d of melt. Snow-survey d a t a were t h e b a s i s f o r a t i m e l y warning of t h e d i s a s t r o u s f l o o d of March 1936 on t h e Androscoggin River b a s i n i n Maine.
The snow c o n t a i n e d 250
mm of w a t e r a t low e l e v a t i o n s and up t o 450 m m a t h i g h e r e l e v a t i o n s .
The f l o o d
r e s u l t e d from m e l t i n g of t h e snowpack d u r i n g a week i n which 250 m m of r a i n f e l l
on t h e b a s i n (Church, 1949). 11.5.3
Seasonal low flows
F o r e c a s t s of monthly mean f l o w s f o r one or more months a r e u s e f u l i n managing a l i m i t e d r a t e r supply f o r domestic.
i n d u s t r i a l . and hydropower uses.
The amount of w a t e r i n t h e ground and i n n a t u r a l s u r f a c e s t o r a g e a t t h e t i m e of f o r e c a s t i s r e p r e s e n t e d b y t h e b a s e f l o w of t h e s t r e a m .
This base flow i s
In g e n e r a l , t h e
t h e i n f o r m a t i o n used i n f o r e c a s t i n g monthly or s e a s o n a l flows.
most r e l i a b l e f o r e c a s t s can b e made on s t r e a m s which have dependable b a s e f l o w s and r e c e i v e l i t t l e p r e c i p i t a t i o n d u r i n g t h e f o r e c a s t period. be e s t i m a t e d by p r o j e c t i n g t h e base-flow end of t h e f o r e c a s t period.
Assured flow can
r e c e s s i o n curve ( s e e Chapter 5 ) t o t h e
In F i g u r e 11.14 t h e r e c e s s i o n c u r v e i s p r o j e c t e d
from t h e end of May when t h e d i s c h a r g e is n e a r l y a l l b a s e flow.
I f streamflow
F i g . 11.14. E s t i m a t i n g a s s u r e d f l o w by p r o j e c t i n g t h e b a s e - f l o w curve, Potomac River.
recession
226 a t t i m e o f f o r e c a s t i s n o t e n t i r e l y b a s e f l o w t h e amount of b a s e f l o w must b e e s t i m a t e d and t h e r e c e s s i o n c u r v e p r o j e c t e d from t h a t d i s c h a r g e r a t h e r t h a n from t h e t o t a l flow.
To d e m o n s t r a t e t h i s , assume t h a t t h e hydrograph of F i g u r e 11.15
i s known o n l y t h r o u g h J u l y .
An e s t i m a t e o f t h e a s s u r e d A u g u s t b a s e f l o w r e -
q u i r e s p r o j e c t i o n of t h e base-flow
r e c e s s i o n c u r v e from e a r l y J u l y t o J u l y 31.
increasing the J u l y 3 1 base flow t o account f o r recharge during July. p r o j e c t i o n o f t h e r e c e s s i o n c u r v e t h r o u g h August.
and
But t h e t o t a l a s s u r e d f l o w
i n c l u d e s w a t e r i n c h a n n e l s t o r a g e on July 3 1 ; t h i s i s e s t i m a t e d b y u s e o f a direct-flow
g
r e c e s s i o n curve.
2000
0
I
Y U v) ~
Y
= 1000 Y Y Y
v
m
a
z
--
500
Y
0 a
U
I U v)
z
200
I I I I I JULY
1
1
1
1
1 I AUGUST
I
I
1959
F i g . 11.15. Hydrograph f o r J a m e s R i v e r , V i r g i n i a showing t h e method o f f o r e c a s t i n g a s s u r e d flow f o r August by p r o j e c t i n g d i r e c t - f l o w and base-flow r e c e s s i o n curves. The a s s u r e d f l o w w i l l b e t h e f l o w i f t h e r e i s no r a i n d u r i n g t h e f o r e c a s t period.
A d d i t i o n a l flow due t o r a i n c a n b e e v a l u a t e d from a f r e q u e n c y c u r v e of
r u n o f f i n e x c e s s o f a s s u r e d ; t h e f r e q u e n c y c u r v e s h o u l d be f o r t h e same month or p e r i o d of f o r e c a s t and c a n b e d e f i n e d by s t r e a m f l o w r e c o r d s a t t h e s i t e . d e f i n i t i o n o f e x c e s s i s shown on F i g u r e 11.15.
The
The f r e q u e n c y c u r v e b a s e d on
many Augusts i s i n F i g u r e 11.16. F o r e c a s t s f o r v a r i o u s p r o b a b i l i t i e s o f exceedance can be o b t a i n e d by adding t o the assured flow discharges a t s e l e c t e d p r o b a b i l i t i e s .
D e t a i l s of t h e f o r e -
c a s t i n g p r o c e d u r e s , and a p p l i c a t i o n s , a r e g i v e n by R i g g s ( 1 9 5 3 ) a n d R i g g s a n d Hanson ( 1 9 6 9 ) .
A s t a t i s t i c a l method o f f o r e c a s t i n g m o n t h l y f l o w i s u s e f u l w h e r e f l o w f o r some f u t u r e m o n t h or p e r i o d d e p e n d s t o some e x t e n t on t h e w a t e r i n s t o r a g e a t t i m e of f o r e c a s t .
The flow f o r t h e f o r e c a s t p e r i o d i s r e l a t e d t o t h e known f l o w
221
f o r an e a r l i e r p e r i o d u s i n g s t r e a m f l o w r e c o r d s a s shown i n F i g u r e 11.17.
Inter-
p r e t a t i o n of t h e p l o t t e d p o i n t s depends on t h e answer sought; t h e l i n e on F i g u r e 11.17 may b e u s e d t o e s t i m a t e t h e a s s u r e d f l o w ; a l i n e a v e r a g i n g t h e p o i n t s would give t h e p r o b a b l e flow.
lO,o00
5000
lo00 500
100
50
10
I
I
5
10
I l l l l l l 20 30 40 50 60 70 80
90
95
98
PROBABILITY, IN PERCENT
11.16. Fig. 11.15.
Frequency c u r v e of August excess r u n o f f a s d e f i n e d by F i g u r e
5
10
B A S E FLOW JULY 1, IN THOUSANDS CUBIC F E E T P E R SECOND
Fig.
11.17.
50
20
OF
F o r e c a s t i n g r e l a t i o n f o r Salmon River a t Whitebird.
Idaho.
228
11.6
S l R m L O W DROUGHTS
A drought i s broadly defined a s a deficiency i n p r e c i p i t a t i o n t h a t a f f e c t s man's a c t i v i t i e s and i n t e r e s t s .
The e f f e c t s depend on t h e s e v e r i t y ,
duration,
and g e o g r a p h i c a l e x t e n t of t h e p r e c i p i t a t i o n d e f i c i e n c y , and on whether p r e c i p i t a t i o n i s used d i r e c t l y , f o r example t o m a i n t a i n s o i l m o i s t u r e , or whether w a t e r s u p p l i e s a r e drawn from s t r e a m s or from ground water. I n n o n - i r r i g a t e d a g r i c u l t u r e , l a c k of r a i n f o r a few weeks d u r i n g t h e growing s e a s o n w i l l reduce t h e y i e l d or d e s t r o y t h e crop.
L i k e w i s e , r e s i d e n t i a l or
municipal w a t e r s u p p l i e s which depend on r u n o f f from r o o f s or paved a r e a s and f o r which l i m i t e d s t o r a g e i s a v a i l a b l e , frequently.
w i l l be i n a d e q u a t e i f n o t r e p l e n i s h e d
S t o c k w a t e r i n s e m i a r i d r e g i o n s i s o f t e n provided by r e s e r v o i r s ,
c a l l e d s t o c k tanks,
on s m a l l ephemeral streams.
tanks requires appreciable p erio d i c r a i n f a l l .
Maintenance of w a t e r i n t h e s e
U s e r s o f w a t e r f o r t h e s e purposes
would c o n s i d e r a r e l a t i v e l y s h o r t p e r i o d w i t h o u t r a i n f a l l a s a drought. A l a c k of r a i n f a l l f o r s e v e r a l c o n s e c u t i v e summer months w i l l n o t c o n s t i t u t e a drought i f t h e normal f o r t h o s e months i s n e a r zero,
a s i t i s i n San F r a n c i s -
co, because a drought i s a d e f i c i e n c y from normal. Lack o f r a i n f o r a f e w w e e k s or a month may h a v e no a p p r e c i a b l e e f f e c t on w a t e r s u p p l i e s d e r i v e d from s t r e a m f l o w or from ground water.
But l a c k of r a i n
f o r a n e x t e n d e d p e r i o d m i g h t r e s u l t i n s t r e a m f l o w d r o p p i n g b e l o w t h e demand; r i v e r flow r e c e d e s a t a c h a r a c t e r i s t i c r a t e d u r i n g p e r i o d s of no p r e c i p i t a t i o n a s t h e ground w a t e r r e s e r v o i r i s drained. For example, a c o u p l e of summer months w i t h no s t o r m s l a r g e enough t o produce r u n o f f might l e t t h e Potomac River flow recede t o l e s s t h a n t h e amount r e q u i r e d f o r m u n i c i p a l supply of Washington, D.C. The e f f e c t s o f r a i n d e p e n d on i t s m a g n i t u d e a n d i n t e n s i t y .
Fairly intense
r a i n f a l l i s needed t o produce r u n o f f and t h u s t o augment streamflow.
Frequent
l i g h t r a i n s may b e adequate t o s u p p o r t v e g e t a t i o n b u t may n o t produce any r u n o f f
or r e c h a r g e . Although s t r e a m f l o w drought i s caused by l a c k of normal p r e c i p i t a t i o n ,
the
e f f e c t s of p r e c i p i t a t i o n d e f i c i e n c i e s a r e delayed because of t h e i n f l u e n c e of t h e l a n d on t h e d i s p o s i t i o n of p r e c i p i t a t i o n . Streamflow d u r i n g t h e summer p e r i o d a l s o may b e a f f e c t e d by p r e c i p i t a t i o n i n t h e p r e v i o u s w i n t e r and s p r i n g when t h e g r o u n d w a t e r body, s t r e a m f l o w d u r i n g d r y weather, i s recharged.
which s u s t a i n s
I f t h e recharge i s l a r g e , the base
flow of t h e s t r e a m w i l l be l a r g e a t t h e b e g i n n i n g o f t h e summer and w i l l be l e s s l i k e l y t o b e a d v e r s e l y a f f e c t e d by d e f i c i e n t summer r a i n f a l l . Where w a t e r s u p p l i e s a r e drawn from s u r f a c e and ground-water
reservoirs,
a
l a c k o f r a i n f a l l f o r a f e w w e e k s , or e v e n a s u b s t a n t i a l d e f i c i t f o r t h e w h o l e year,
may h a v e l i t t l e e f f e c t i f t h e r e s e r v o i r s a r e o f a d e q u a t e s i z e .
The
c r i t i c a l drought under such c o n d i t i o n s i s caused by d e f i c i e n t p r e c i p i t a t i o n f o r s e v e r a l s u c c e s s i v e y e a r s so t h a t t h e u s a b l e s t o r a g e , b o t h s u r f a c e and u n d e r -
229 ground, becomes p r o g r e s s i v e l y d e p l e t e d u n t i l t h e u s u a l amount o f w i t h d r a w a l s c a n n o t b e made.
The 1976-17 d r o u g h t i n C a l i f o r n i a i s a n e x a m p l e .
Nevada snowpack.
t h e major source of supply, was l o w e s t of r e c o r d a t many s i t e s
i n 1 9 7 6 , and w a s e v e n l o w e r i n 1977. s t o r a g e was d e p l e t e d , plies,
The S i e r r a
As a c o n s e q u e n c e , s u r f a c e r e s e r v o i r
streamflow was inadequate f o r i r r i g a t i o n and o t h e r sup-
t h e r e d u c e d f l o w i n t o San F r a n c i s c o Bay a l l o w e d s a l t w a t e r t o move
upstream i n t h e D e l t a ,
and t h e ground-water
t a b l e was lowered up t o 30 f e e t by
pumping t o augment t h e reduced s u p p l i e s from t h e u s u a l s o u r c e s (Matthai.
1979).
O t h e r n o t a b l e U n i t e d S t a t e s d r o u g h t s a r e t h o s e o f t h e 1930's ( H o y t , 1936. 1 9 3 8 ) . and 1950's (Gatewood e t a l . 1960's (Barksdale e t a l , 1966).
1 9 6 4 ; Nace a n d P l u h o w s k i , 1 9 6 5 ) . and t h e
M e t e o r o l o g i c a l a s p e c t s can be d e s c r i b e d by t h e
Palmer (1965) index. 11.6.1
Seasonal streamflow drought
On an u n r e g u l a t e d s t r e a m t h e u s a b l e w a t e r supply depends on t h e magnitude of
t h e s e a s o n a l low flow which v a r i e s from y e a r t o year. b a s e f l o w s r e c e d e slowly,
Streams w i t h s u b s t a n t i a l
p e r m i t t i n g a r e a s o n a b l e e s t i m a t e of t h e base flow a
month o r m o n t h s i n t h e f u t u r e i n t h e a b s e n c e o f p r e c i p i t a t i o n ( s e e S e c t i o n 11.5.3).
S t r e a m s w i t h l i t t l e b a s e f l o w r e c e d e r a p i d l y and a r e n o t s o u r c e s o f
dependable s u p p l i e s u n l e s s r a i n f a l l o c c u r s r e g u l a r l y . The s e v e r i t y of a s e a s o n a l drought can be expressed by t h e r e c u r r e n c e i n t e r v a l of t h e 30-day ( o r o t h e r ) a n n u a l minimum f l o w . able,
of course, only a f t e r t h e drought i s over.
annual d r o u g h t s on French Broad River,
100
1
1900
F i g . 11.18. Carolina. 11.6.2
This information i s avail-
F i g u r e 11.18 shows s i g n i f i c a n t
North Carolina.
n
1910
1920
1930
1940
1950
1960
S i g n i f i c a n t a n n u a l 30-day low f l o w s . F r e n c h Broad R i v e r , N o r t h
M u l t i y e a r streamflow drought
When annual mean s t r e a m f l o w s a r e below normal f o r two o r more c o n s e c u t i v e years,
t h e d r a f t a v a i l a b l e f r o m s t o r a g e d u r i n g t h a t p e r i o d may b e g r e a t l y
230 r e d u c e d e v e n t h o u g h none o f t h e s e a s o n a l s h o r t a g e s f o r i n d i v i d u a l y e a r s (on streams without storage) a r e large.
The ground-water
supply t o t h e s t r e a m a l s o
may b e p r o g r e s s i v e l y d e p l e t e d b e c a u s e o f r e d u c e d r e c h a r g e .
Furthermore the
e f f e c t of a m u l t i y e a r d r o u g h t on d r a f t a v a i l a b l e f r o m s t o r a g e d e p e n d s on t h e s i z e of t h e s t o r a g e r e s e r v o i r ,
so t h a t t h e same p r e c i p i t a t i o n d e f i c i e n c y might
appear t o produce d i f f e r e n t e f f e c t s on a d j a c e n t s t r a m s i f t h o s e s t r e a m s d i d n o t have t h e same s t o r a g e r e l a t i v e t o t h e i r mean flows. The m a j o r d r o u g h t s t h r o u g h o u t t h e w o r l d h a v e l a s t e d f o r s e v e r a l y e a r s . During t h e drought of t h e 1930's i n United S t a t e s much farmland was abandoned i n t h e G r e a t P l a i n s because of l a c k of r a i n and t h e consequent wind erosion.
The
magnitude and d u r a t i o n of t h a t drought can be seen from t h e s t r e a m f l o w r e c o r d of Red R i v e r o f t h e N o r t h i n t h e D a k o t a s and M i n n e s o t a (Fig. 11.19);
t h e annual
mean f l o w s w e r e b e l o w a v e r a g e f r o m 1928 t o 1 9 4 1 a n d t h e f l o w s f o r 8 o f t h o s e y e a r s were lower t h a n any p r i o r t o 1928 a s f a r back a s 1884.
300
r
=z
82
200 1M)
50
z a
Y
$
20
2
z a
10
6
1890
1900
1910
1920 1930 YEAR
1940
1950
1960
F i g . 11.19. Annual mean f l o w s o f Red R i v e r , N o r t h D a k o t a - M i n n e s o t a drought of t h e 1930s.
showing
M u l t i y e a r d r o u g h t s cannot be s i m p l y d e s c r i b e d because they have 3 c h a r a c t e r istics:
magnitude,
duration,
and a r e a l extent.
E g g s (1979) proposed a method
of q u a n t i f y i n g m u l t i y e a r drought s e v e r i t y f o r use i n comparing droughts.
The
i n d i c e s a r e based on t h e d r a f t t h a t could have been o b t a i n e d through t h e drought p e r i o d under t h e assumption t h a t a s t o r a g e e q u i v a l e n t t o t h e mean annual runoff e x i s t e d i n t h e basin.
T h i s approach makes t h e i n d i c e s c o n s i s t e n t from t i m e t o
t i m e a t a s i t e a n d c o n s i s t e n t among s i t e s h a v i n g t h e same c o e f f i c i e n t o f
231 v a r i a t i o n of annual means.
The p r o c e d u r e f o r d e f i n i n g t h e d r o u g h t index i s a s
f 01lows :
1.
P l o t hydrograph of annual means f o r a n u n r e g u l a t e d stream.
2.
I d e n t i f y d r o u g h t p e r i o d s from hydrograph.
3.
P l o t a mass c u r v e of annual means encompassing each d r o u g h t p e r i o d .
4.
On each mass c u r v e draw a d r a f t l i n e l i m i t e d by a s t o r a g e e q u a l t o t h e mean
annual r u n o f f volume and by a p e r i o d o f d e f i c i e n t f l o w of 6 years. 5.
Compute d r a f t r a t e a s p e r c e n t of mean flow.
6.
Compute d r o u g h t index a s t h e p r o d u c t o f 1 0 0 minus d r a f t r a t e and t h e s q u a r e r o o t of t h e d e f i c i e n t p e r i o d i n years. The p r o c e d u r e i s i l l u s t r a t e d i n F i g u r e 11.20 u s i n g f l o w d a t a f r o m F i g u r e
11.19.
R e s u l t s f o r Red River and a n o t h e r r i v e r a r e p l o t t e d i n F i g u r e 11.21.
INDICES
v)
3
191 7-20 (100-88)fi=21 1888-92 (100-71)fi=58
z z a
1932-38 ( 1 00-2 1)&=
U
193
0
1932
YEARS
Fig. 11.20. A n a l y s i s o f a v a i l a b l e d r a f t and c o m p u t a t i o n of d r o u g h t i n d i c e s , River, North Dakota - Minnesota.
:I
L Z
k
I
r80
i
40
O
0
3
n
a a
Red
2oo -
-
Red River, North Dakota
160 -
-
120 -
-
W
-
5
-
2 3
2
I
1850
1870
I
I
I
I
1890
1910
1930
1950
1970
YEAR F i g . 11.21. M u l t i y e a r d r o u g h t i n d i c e s f o r 2 r i v e r s . shown by w i d t h of block.
Duration of drought is
232 The a b o v e i n d i c e s a p p l y t o i n d i v i d u a l s t r e a m s .
Regional i n d i c e s can be
d e r i v e d by a v e r a g i n g t h e annual f l o w s ( i n p e r c e n t of t h e i r mean) of r e p r e s e n t a t i v e s t r e a m s i n t h e r e g i o n and d e f i n i n g t h e i n d i c e s a s f o r a s i n g l e s t r e a m . F i g u r e 11.22 compares r e g i o n a l m u l t i y e a r and s e a s o n a l drought i n d i c e s f o r t h e Tennessee-Cumberland b a s i n s ,
USA.
r
1922
1930
1940
1950
1960
1970
YEAR
Fig. 11.22. I n d i c e s of s e a s o n a l and m u l t i y e a r d r o u g h t s i n t h e Tennessee-Cumberland b a s i n s . 11.6.3
A d a p t a t i o n t o drought
The b e g i n n i n g o f a h y d r o l o g i c d r o u g h t u s u a l l y i s n o t r e c o g n i z a b l e a t t h e time.
P e r i o d s of below normal flow a r e commonly t e r m i n a t e d by p r e c i p i t a t i o n
w i t h i n a few weeks or a month.
P r e c i p i t a t i o n cannot be f o r e c a s t r e l i a b l y f a r
enough i n t h e f u t u r e t o i n d i c a t e w h e t h e r a m o d e r a t e d r o u g h t p e r i o d i s t h e b e g i n n i n g o f a s e v e r e d r o u g h t or w h e t h e r t h e p e r i o d w i l l b e t e r m i n a t e d soon. Thus, a d a p t a t i o n t o a drought u s u a l l y i n v o l v e s a c t i o n s t h a t can be t a k e n q u i c k l y when t h e s e v e r i t y i s recognized.
These i n c l u d e t a p p i n g a n a l t e r n a t i v e source,
t r a n s f e r r i n g r a t e r from a low p r i o r i t y use t o a h i g h e r one, and r e u s i n g water.
r e d u c i n g w a t e r use,
M a t t h a i (1979, p. 19-23) d e s c r i b e s t h e changes i n w a t e r use
made d u r i n g t h e 1916-17 drought i n United S t a t e s . F o r e c a s t s o f some impending annual d r o u g h t s may be f e a s i b l e .
Estimates of
r u n o f f from t h e s p r i n g snowpack and e s t i m a t e s of summer low f l o w from s p r i n g p r e c i p i t a t i o n a r e r e l i a b l e on some streams. t o a d a p t t o a d e f i c i e n t supply.
These f o r e c a s t s p r o v i d e more t i m e
During a m u l t i y e a r drought s h o r t - t e r m
may be f e a s i b l e b u t ones f o r h a l f a y e a r or more a r e not.
forecasts
Probability estimates
may be used f o r p l a n n i n g and t h e s e should i n c o r p o r a t e p r e s e n t r e s e r v o i r s t o r a g e and any r e s t r i c t i o n s i n u s e t h a t w i l l be i n e f f e c t (Hirsch,
1981).
233 P r o t e c t i o n from s e v e r e w a t e r s h o r t a g e s can b e provided o n l y i f t h e n a t u r a l f l u c t u a t i o n s i n w a t e r s u p p l y a r e a c c u r a t e l y known and a r e i n c o r p o r a t e d i n t h e p r o j e c t design.
I f t h e r e g i o n a l s u p p l y is f u l l y used i n most y e a r s t h e r e w i l l
be no a l t e r n a t e temporary s u p p l y t o f a l l back on d u r i n g a dronght. 11.7
FLOOD-PRONE AREA MAPPING
D e f i n i t i o n o f f l o o d - p r o n e a r e a s i s needed f o r f l o o d p l a i n management, a means of r e d u c i n g f l o o d l o s s e s by a d a p t i n g l a n d use t o t h e f l o o d hazard.
A principal
use o f f l o o d i n u n d a t i o n maps i s t h e s e t t i n g o f r a t e s f o r f l o o d insurance.
The
N a t i o n a l F l o o d I n s u r a n c e Act o f 1 9 6 8 and t h e F l o o d D i s a s t e r P r o t e c t i o n Act of 1973 were e n a c t e d t o inform communities about t h e i r f l o o d dangers.
t o provide
new c o n s t r u c t i o n r e a s o n a b l e p r o t e c t i o n from f l o o d damage by p r u d e n t management of t h e f l o o d p l a i n ,
and t o p r o t e c t r e s i d e n t s o f f l o o d - p l a i n
f i n a n c i a l l o s s from flooding. of flood-prone
areas against
Waananen and o t h e r s (1977) d e s c r i b e how knowledge
a r e a s a f f e c t e d land-use p l a n n i n g i n t h e San F r a n c i s c o Bay area.
A f l o o d - p r o n e a r e a i s t h a t a r e a w h i c h w i l l b e i n u n d a t e d b y a f l o o d o f some specified recurrence interval,
u s u a l l y 1 0 0 years.
maps a r e shown i n F i g u r e s 11.23 and 11.24.
Fig.
11.23.
Flood-prone
Examples of f l o o d - p r o n e a r e a
The a r e a i n u n d a t e d b y t h e 1 0 0 - y e a r
a r e a d e f i n e d by an approximate method.
f l o o d i n F i g u r e 11.23 was d e f i n e d by an a p p r o x i m a t e method i n which s t r e a m d e p t h of t h e 100-year
f l o o d i s e s t i m a t e d from a r e g i o n a l r e l a t i o n w i t h d r a i n a g e a r e a
o r w i t h mean annual f l o o d d i s c h a r g e . channel shapes,
In r e g i o n s where f l o o d c h a r a c t e r i s t i c s , o r
a r e n o t c l o s e l y r e l a t e d t o d r a i n a g e area.
t h e mean annual f l o o d
d i s c h a r g e c a n b e e s t i m a t e d by o n e o f t h e m e t h o d s g i v e n i n C h a p t e r 8.
The
e s t i m a t e d d e p t h i s u s e d t o d e l i n e a t e t h e i n u n d a t e d a r e a on a t o p o g r a p h i c map. The r e l i a b i l i t y o f t h e e s t i m a t e o f t h e i n u n d a t e d a r e a c a n b e i m p r o v e d i f a
234 p r o f i l e of an observed flood, or an a e r i a l photograph of f l o o d i n g ,
is available
for t h e reach.
Fig.
11.24.
Flood-prone a r e a d e f i n e d by step-backwater a n a l y s i s .
More r e l i a b l e ,
and much more expensive,
r e s u l t s can be o b t a i n e d by d e f i n i n g
t h e w a t e r - s u r f a c e p r o f i l e through t h e r e a c h by s t a n d a r d step-backwater a n a l y s i s . This r e q u i r e s measured channel c r o s s s e c t i o n s a t i n t e r v a l s through t h e r e a c h and e s t i m a t e s of channel roughness (Davidian, a b l e f o r the analysis.
1984).
Computer programs a r e a v a i l -
The map of F i g u r e 11.24 was prepared by t h i s method.
Encroachment on f l o o d p l a i n s , such a s by a r t i f i c i a l f i l l , u s u a l l y reduces t h e f l o o d - c a r r y i n g c a p a c i t y and i n c r e a s e s f l o o d h e i g h t s , h a z a r d s i n a r e a s beyond t h e e n c r o a c h m e n t i t s e l f .
thus increasing flood
One a s p e c t o f f l o o d - p l a i n
management i n v o l v e s b a l a n c i n g t h e economic g a i n f r o m f l o o d - p l a i n d e v e l o p m e n t a g a i n s t t h e r e s u l t i n g i n c r e a s e i n f l o o d hazard.
Under t h e floodway concept t h e
a r e a i n u n d a t e d by t h e 100-year f l o o d i s d i v i d e d i n t o a p r o p o se d floodway and floodway f r i n g e s .
The floodway i s t h e channel of t h e s t r e a m p l u s any a d j a c e n t
flood-plain a r e a s t h a t must be k e p t f r e e of encroachment i n o r d e r t h a t t h e 100y e a r f l o o d be c a r r i e d w i t h o u t a s u b s t a n t i a l i n c r e a s e i n f l o o d h e i g h t (Fig. 11.25). 11.8
The floodway f r i n g e s may be c o m p l e t e l y o b s t r u c t e d . ESTIMATION OF ENVIRONMENTAL IWACT
The e f f e c t on t h e w a t e r r e s o u r c e of some proposed change i n a d r a i n a g e b a s i n depends on t h e flow c h a r a c t e r i s t i c s a t t h e p r e s e n t time. u s u a l l y must be e s t i m a t e d from r e g i o n a l r e l a t i o n s , few f i e l d measurements.
These c h a r a c t e r i s t i c s
p o s s i b l y supplemented by a
D e t e r m i n a t i o n of t h e changes i n response t o t h e a n t i c i -
p a t e d s t r e s s c a l l s f o r an u n d e r s t a n d i n g of t h e hydrology, t h e knowledge of
235 changes that occurred in other basins, and sound judgment to adjust for the different conditions.
1 OO-YR FLOOD ELEVATIONS WITHOUT AND WITH FLOODWAY
Fig.
11.25.
Channel cross section showing floodway.
REFERENCES American Fisheries Society, 1976, Instream flow needs; Proc. of Symposium by Am. Fisheries Society and Am. SOC. of Civil Engineers at Boise, Idaho, May 1976: American Fisheries Society, Bethesda, Md.. 2 Vol. ASCE, 1980, Proceedings of the Engineering Foundation Conference on Improved Hydrologic Forecasting, Why and How: New York, Am. SOC. of Civil Engineers. Baker, D.G., 1972, Prediction of spring runoff; 8, NO. 4, p. 966-912.
Water Resources Research, Vol.
Banks, H.O., Chairman, 1964, Hydrology of spillway design: Division, ASCE, Vol. 90. No. HY3, p. 235-310.
Jour. of Hydraulics
Barksdale, H.C., O'Brien, D., and Schneider, W.J., 1966, Effect of drought on water resources in the Northeast: U.S. Geol. Survey Eydrologic Atlas 243. Bodhaine, G.L., 1968, Measurement of peak discharge at culverts by indirect methods: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapt. A3, 60 p. Bureau of Public Roads, 1960, Hydraulics of bridge waterways: U.S. Dept. Commerce, Bureau of Public Roads Hydraulic Design Series 1, 53 p. Burges, S.J. and Linsley, R.K., 1971, S o m e factors influencing required reservoir storage: Jour. of Hydraulics Division, ASCE, Vol. 97. NO. HY7, p. 977991. Church. J.E., 1949, Snow and snow surveying: Ice, & Meinzer, O.E.. New York., Dover Publ., Inc.
Hydrology:
Clyde, G.D., 1951. Benefits of snow surveying: Western Snow Conf. Proc., Nineteenth Annual Meeting, p. 84-89. Colson, B.E. and Schneider, V.R., 1983, Backwater and discharge at highway crossings w i t h multiple bridges in Louisiana and Mississippi: U.S. Geol. Survey Water-Resources Investigations Rept. 83-4065, 3 9 p. Craig, G.S., Jr. and Rankl. J.G., 1978, Analysis of runoff from small drainage basins in Wyoming: U.S. Geol. Survey WaterSupply Paper 2056, 70 p. Davidian, J., 1984, Computation of water-surface profiles: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 3, Chapt. D15.
236 E y c h a n e r , J.H., 1976. E s t i m a t i n g r u n o f f v o l u m e s and f l o o d h y d r o g r a p h s i n t h e C o l o r a d o R i v e r b a s i n , s o u t h e r n Utah: U.S. Geol. S u r v e y W a t e r - R e s o u r c e s I n v e s t i g a t i o n s 76-102, 18 p. Gatewood, J.S., W i l s o n , A,, Thomas. H.E.. and K i s t e r , L.R., 1 9 6 4 , G e n e r a l e f f e c t s o f d r o u g h t on w a t e r r e s o u r c e s o f t h e S o u t h w e s t : U.S. Geol. S u r v e y P r o f . P a p e r 372-B, p. 1-55. G i l b e r t , C.R. and Saner. S.P., 1970, Hydrologic e f f e c t s of f l o o d w a t e r r e t a r d i n g s t r u c t u r e s on G a r z a - L i t t l e Elm R e s e r v o i r , Texas: U.S. Geol. Survey WaterSupply Paper 1984, 95 p. H a r d i s o n , C.H. and F u r n e s s . L.W., 1 9 6 3 , D i s c u s s i o n o f p a p e r b y J o h n B. S t a l l , “Reservoir mass a n a l y s i s by a low flow s e r i e s : Jour. of S a n i t a r y Engineeri n g D i v i s i o n , ” ASCE, Vol. 8 9 , No. SA2, p. 119-122. Hawley, M.E., McCuen, R.H., a n d Rango, A., 1980, C o m p a r i s o n o f m o d e l s f o r f o r e c a s t i n g snowmelt r u n o f f volumes: Water Resources B u l l e t i n , Vol. 16, No. 5, O c t o b e r 1980, p. H e r s h f i e l d , D.M., 1 9 6 1 , E s t i m a t i n g p r o b a b l e maximum p r e c i p i t a t i o n : J o u r . of Hydraulics D i v i s i o n , ASCE, Vol. 87, p. 99-106. Hirsch, R.M., 1981, E s t i m a t i n g p r o b a b i l i t i e s of r e s e r v o i r s t o r a g e f o r t h e upper Delaware River b a s i n : U.S. Geol. Survey Open-File Report 81-478. Hoyt, J.C., 1936, Droughts of 1930-34: 1 0 6 p. Hoyt, J.C., P.
U.S.
Geol.
Survey Water-Supply
Paper 680.
1 9 3 8 , D r o u g h t o f 1936: U.S. Geol. S u r v e y Water-Supply P a p e r 8 2 0 , 6 2
1959, P r e l i m i n a r y r e p o r t on e v a l u a t i n g t h e u t i l i t y of water-supply Kohler, M.A., f o r e c a s t s : W e s t e r n Snow Conf. Proc., 1 7 t h Annual M e e t i n g , A p r i l 1959, p. 26-33. 1 9 5 8 , Q u e u i n g t h e o r y and w a t e r s t o r a g e : J o u r . o f H y d r a u l i c s L a n g b e i n , W.B., D i v i s i o n , ASCE. Vol. 8 4 , No. HY5, p. 1811-1 t o 1811-24. L e o p o l d , L.B.. 1959. P r o b a b i l i t y a n a l y s i s a p p l i e d t o a w a t e r - s u p p l y p r o b l e m : U.S. Geol. S u r v e y C i r o . 410, 18 p. L i n s l e y , R.K., K o h l e r , M.A., New York, WcGraw-Hill,
and P a u l h u s , J.L.H., 482 p.
1975, Hydrology f o r e n g i n e e r s :
Lof, G.O.G. and H a r d i s o n , C.H., 1966, Storage r e q u i r e m e n t s f o r w a t e r i n t h e United S t a t e s : Water Resources Research, Vol. 2. No. 3, p. 323-354. M a t t h a i , H.F.. 1968‘. M e a s u r e m e n t o f p e a k d i s c h a r g e a t w i d t h c o n t r a c t i o n s by i n d i r e c t methods: U.S. Geol. Survey Techniques of Water-Resources I n v e s t i g a t i o n s , Book 3, C h a p t e r A4, 44 p. M a t t h a i , H.F., 1 9 7 9 , H y d r o l o g i c a n d human a s p e c t s o f t h e 1976-77 d r o u g h t : U.S. Geol. S u r v e y P r o f . P a p e r 1 1 3 0 , 8 4 p. Nace, R.L. and P l u h o w s k i . E.J., 1965, r e f e r e n c e t o t h e midcontinent: U.S. 1 8 p.
Drought of t h e 1950s w i t h s p e c i a l Geol. Survey Water-Supply Paper 1804.
NOAA, 1972, N a t i o n a l Weather S e r v i c e River F o r e c a s t System f o r e c a s t procedures: U.S. Dept. Commerce; NOAA TM NWS HYDRO-14. Nordenson, T.J. a n d R i c h a r d s , M.M., 1964, R i v e r f o r e c a s t i n g i n Chow, V.T., ed., Handbook of Applied Hydrology: New York, McGraw-Hill, p. 25-98 t o 25-111. Nordenson, T.J., 1969, The a p p l i c a t i o n of c o n c e p t u a l catchment models t o r i v e r f o r e c a s t i n g : H y d r o l o g i c a l F o r e c a s t i n g , World M e t e o r o l o g i c a l O r g a n i z a t i o n T e c h n i c a l Note 9 2 (WMO-No. 228. TP. 1 2 2 ) , p. 181-192. Overton, D.E. and Meadows, P r e s s , 358 p.
M.E.,
1976, Stormwater modeling:
New York, Academic
237 Palmer, W.C., 1965, Meteorological drought: U.S. Dept. Commerce Weather Bureau Research Paper No. 45, 58 p. Riggs, H.C., 1953, A method of forecasting low flow of streams: Trans. Am. Geophysical Union, Vol. 34, No. 3, p. 427-434. Riggs, H.C., 1979. Characterizing streamflow droughts: Hydrological Aspects of Droughts, International Symposium, 3-7 December 1979, New Delhi, Proc. Vol. 1, p. 331-338. Riggs, H.C., 1980, Runoff estimates from snowmelt in Pollution and Water Resources, Columbia University Seminar Series, Vol. XIII, Part 2: New York, Pergamon Press, p. 71-80. Riggs. H.C. and Hanson. R.L., 1969. Seasonal low-flow forecasting: World Meteorological Organization Tech. Note No. 92, WMO-NO. 228, TP 122, Hydrological Forecasting, Geneva, Switzerland, p. 286-289. Riggs, H.C. and Hardison, C.H., 1973, Storage analyses for water supply: U.S. Geol. Survey Techniques of Water-Resources Investigations, Book 4, Chapter B2, 2 0 p. Schermerhorn, V.P., 1961, Short-range snowmelt forecasts: Bull. of International Assoc. of Scientific Hydrology 6, No. 4, p. 75-82. Sittner, W.T.. 1976. WHO project on intercomparison of conceptual models used in hydrological forecasting: Hydrological Sciences Bull., Vol. 21, NO. 1, p. 203-213. Skelton, J., 1971, Carry over storage requirements for reservoir storage in Missouri: Missouri Geological Survey and Water Resources, Water Resources Rept. 27. 56 p. Soil Conservation Service, 1972, Snow survey and water-supply forecasting: SCS National Engineering Handbook, Section 22, USDA, Soil Conservation Service. Thomas, H.A., Jr. and Fiering, M.B.. 1962, Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation, I n Maas and others, Design of Water Resource Systems: Cambridge, Mass., Harvard University Press.
Ed., 1975, Sedimentation engineering: ASCE Manual of Engineering Vanoni, V.A., Practice, 745 p. Waananen, A.O., Limerinos, J.T., Kockelman, W.J., Spangle, W.E., and Blair, M.L., 1977, Flood-prone areas and land-use planning - selected examples from the San Francisco Bay area, California: U.S. Geol. Survey Prof. Paper 942, 75 p.
WMO, 1969a. Hydrological forecasting: World Meteorological Organization, Tech. Note No. 92, WHO-No. 228 TP. 122. Geneva, Switzerland. WMO, 1969b. Estimation of m a x i m u m floods: World Meteorological Organization Tech. Note No. 98, WYO-No. 233, TP. 126. WMO, 1973, Manual for estimation of probable m a x i m u m precipitation: World
Meteorological Organization Operational Hydrology Rept. 1, WMO-NO. 332, Geneva, Sw itzerland. Zhidikov, A.P., Levin, A.G., Nechaeva, N.S., and Popov, E.G.. 1976, A snowmelt runoff model and its application of short range forecasting of flood discharges: Hydrological Sciences Bull. 21, No. 1, p. 195-202.
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23 9
Chapter 1 2
SOURCES OF DATA AND INFORMATION 12.1
INTRODUCTION
I n t h e United S t a t e s most of t h e s i t e s f o r which w a t e r d a t a a r e a v a i l a b l e a r e l i s t e d i n t h e M a s t e r W a t e r D a t a I n d e x o f NAWDEX ( E d w a r d s , 1 9 7 9 ) .
The I n d e x
p r o v i d e s f o r e a c h s i t e t h e g e o g r a p h i c l o c a t i o n , t h e d a t a - c o l l e c t i n g organizat i o n , t h e types of d a t a a v a i l a b l e , the p e r i o d s of t i m e f o r which t h e d a t a a r e a v a i l a b l e , t h e major water-data p a r a m e t e r s f o r which d a t a a r e a v a i l a b l e , t h e frequency of measurement of t h e p a r a m e t e r s , and t h e media i n which t h e d a t a a r e stored.
L o c a l A s s i s t a n c e C e n t e r s o f NAWDEX c a n a s s i s t users i n l o c a t i n g d a t a
f o r s p e c i f i c s t r e a m s or a r e a s .
The u s e r may t h e n o b t a i n t h e d a t a f r o m t h e
o r g a n i z a t i o n s or media where s t o r e d . NAWDEX i s a f f i l i a t e d w i t h t h e W a t e r R e s o u r c e s Document R e f e r e n c e C e n t e r (WATDOC) of t h e I n l a n d Waters D i r e c t o r a t e ,
The Environment,
Canadian Department of F i s h e r i e s and
and w i t h d a t a s e r v i c e s o f s e v e r a l State-governmental organiza-
tions. F u r t h e r i n f o r m a t i o n on NAWDEX s e r v i c e s c a n be o b t a i n e d from N a t i o n a l Water Data Exchange
U.S. G e o l o g i c a l Survey 421 N a t i o n a l C e n t e r Reston. V i r g i n i a 22092 I n c o u n t r i e s o t h e r t h a n United S t a t e s ,
t h e a v a i l a b l e water-resource
d a t a may
be o b t a i n e d from t h o s e governmental a g e n c i e s whose work r e q u i r e s s u c h data. Understanding and a n a l y s i s of w a t e r - r e s o u r c e d a t a r e q u i r e s a d d i t i o n a l i n f o r mation, much o f which can b e e x t r a c t e d from c l i m a t i c r e c o r d s and maps.
Inter-
p r e t e d d a t a , and p r e v i o u s h y d r o l o g i c a n a l y s e s , a r e p a r t i c u l a r l y h e l p f u l .
The
p r i n c i p a l s o u r c e s of t h e s e t y p e s of i n f o r m a t i o n i n t h e Uni t ed S t a t e s a r e i ncluded i n t h i s c h a p t e r . 12.2
WATER-RESOURCES bATA
The p r i n c i p a l s o u r c e o f water-resource
d a t a i n t h e United S t a t e s i s t h e U.S.
G e o l o g i c a l S u r v e y w h o s e d a t a a r e p u b l i s h e d i n a n n u a l d a t a r e p o r t s on a S t a t e boundary b a s i s .
T h e s e r e p o r t s i n c l u d e r e c o r d s o f s t a g e , d i s c h a r g e , and w a t e r
q u a l i t y ( i n c l u d i n g s e d i m e n t t r a n s p o r t ) of s t r e a m s :
s t a g e and c o n t e n t s of l a k e s
a n d r e s e r v o i r s ; and w a t e r l e v e l s and w a t e r q u a l i t y o f g r o u n d - w a t e r i n w e l l s . P r e v i o u s t o 1961 such d a t a were p u b l i s h e d i n Water-Supply Papers.
Compilations
o f m o n t h l y and a n n u a l s t r e a m f l o r s and o f a n n u a l maximum a n d minimum f l o w s through 1960 a r a p u b l i s h e d i n Water-Supply P a p e r s 1301-1319, and 1721-1740 (1951-60).
1372 (through 1950)
2 40
Data of r e c o r d a l s o a r e s t o r e d i n Reston, V i r g i n i a i n t h e computerized system c a l l e d WATSTORE.
F i l e s a r e m a i n t a i n e d f o r t h e s t o r a g e o f (1) s u r f a c e - w a t e r , and g r o u n d - w a t e r d a t a m e a s u r e d on a d a i l y or a c o n t i n u o u s
quality-of-water. basis.
(2) annual peak s t a g e s and d i s c h a r g e s f o r s t r e a m f l o w s t a t i o n s ,
(3) chem-
i c a l a n a l y s e s f o r s u r f a c e - w a t e r and ground-water s i t e s , (4) r a t e r - d a t a par ameters measured more f r e q u e n t l y t h a n d a i l y , (5) g e o l o g i c and i n v e n t o r y d a t a f o r ground-water
s i t e s , and (6) summary d a t a on r a t e r use.
These d a t a can b e r e t r i e v e d from WATSTORE i n c o m p u t e r p r i n t e d t a b l e s or i n c o n j u n c t i o n w i t h programs f o r t h e s t a t i s t i c a l a n a l y s i s of c e r t a i n o f those data.
For example, programs f o r d e f i n i n g and p l o t t i n g frequency c u r v e s and f o r making r e g r e s s i o n a n a l y s e s c a n u t i l i z e d i r e c t r e t r i e v a l from WATSTORE
Information
a b o u t t h e a v a i l a b i l i t y o f s p e c i f i c t y p e s o f d a t a , t h e a q u i s i t i o n o f d a t a or products.
and u s e r c h a r g e s c a n be o b t a i n e d from l o c a l o f f i c e s o f t h e G e o l o g i c a l
Survey ( K i l p a t r i c k , 1981). Water-quality
p a r a m e t e r s c o l l e c t e d by s e v e r a l F e d e r a l o r g a n i z a t i o n s a r e i n
t h e STORET system of t h e U.S.
Environmental P r o t e c t i o n Agency.
Data i n SMRET
can be r e t r i e v e d through t h e USGS NAWDEX system. S u r f a c e Water Reference Index,
Canada 1981, l i s t s most of t h e Canadian s t a -
t i o n s f o r which s t r e a m f l o w d a t a a r e a v a i l a b l e and r e f e r s t o o t h e r p u b l i c a t i o n s f o r a d d i t i o n a l ones.
S t r e a m f l o w s and r e l a t e d r e c o r d s on i n d i v i d u a l s t a t i o n s may
be o b t a i n e d from t h e Regional O f f i c e s l i s t e d o r from D i r e c t o r ,
Water Resources
Branch. Department of t h e Environment, Ottawa. Ontario. Some s t r e a m f l o w d a t a f o r v a r i o u s p a r t s o f t h e world a r e i n p u b l i c a t i o n s of t h e World M e t e o r o l o g i c a l O r g a n i z a t i o n , Geneva, S w i t z e r l a n d . 12.3
CLIMATIC DATA
The C l i m a t i c A t l a s o f t h e United S t a t e s (ESSA, 1968) d e p i c t s t h e c l i m a t e of t h e U n i t e d S t a t e s i n t e r m s of t h e d i s t r i b u t i o n and v a r i a t i o n o f c o n s t i t u e n t c l i m a t i c elements.
P r i n c i p a l s n b j e c t s a r e t e m p e r a t u r e means a n d r a n g e s b y
months. normal t o t a l monthly and annual p r e c i p i t a t i o n , and pan and l a k e evaporation.
Other s u b j e c t s a r e s n o w f a l l , wind,
sunshine, r e l a t i v e h u m i d i t y and addi-
t i o n a l c h a r a c t e r i s t i c s of t e m p e r a t u r e and p r e c i p i t a t i o n . D e t a i l e d c l i m a t i c i n f o r m a t i o n i s a v a i l a b l e from NOAA, NCDC National Climatic Center Federal Building A s h e v i l l e , North Carol i n a
28801
which can s u p p l y a i r t e m p e r a t u r e , rainfall, tion.
snowfall.
dew p o i n t ,
h e a t i n g and c o o l i n g d e g r e e days,
b a r o m e t r i c p r e s s u r e , wind d i r e c t i o n and speed,
and s k y c o v e r f o r about 300 NWS s t a t i o n s nationwide.
s o l a r radia-
Also a v a i l a b l e a r e
d a i l y maximum a n d minimum t e m p e r a t u r e s a n d t o t a l d a i l y p r e c i p i t a t i o n f o r
241 a p p r o x i m a t e l y 12,000 s i t e s .
Monthly and y e a r l y summaries o f p r e c i p i t a t i o n a r e
a l s o available. Average annual l a k e and C l a s s A pan e v a p o r a t i o n i n i n c h e s a r e shown on maps o f t h e c o n t e r m i n o u s U n i t e d S t a t e s ( F a r n s w o r t h and o t h e r s , 1 9 8 2 ) .
Monthly,
s e a s o n a l , and a n n u a l a v e r a g e s o f e s t i m a t e d p a n e v a p o r a t i o n a r e c o m p i l e d by F a r n s w o r t h and Thompson (1982). 12.4
MAPS
The N a t i o n a l C a r t o g r a p h i c I n f o r m a t i o n Center (NCIC),
U.S.
G e o l o g i c a l Survey,
22092, m a i n t a i n s a computer index of c a r t o g r a p h i c p r o d u c t s of USGS
Reston, Va.
and o t h e r f e d e r a l agencies.
These i n c l u d e topographic,
maps, a e r i a l photographs, and s a t e l l i t e imagery.
geologic,
and land-use
Although NCIC i s p r i m a r i l y t h e
s o u r c e o f i n f o r m a t i o n , some p r o d u c t s a r e a v a i l a b l e from t h e Regional Mapping C e n t e r U n i t s (USGS, 1 9 8 1 ) . States a r e available.
P r i n t e d i n d e x e s t o t o p o g r a p h i c map c o v e r a g e b y
Although USGS i s t h e major source,
maps a r e a l s o a v a i l -
a b l e from o t h e r f e d e r a l , s t a t e , and l o c a l a g e n c i e s , and from commercial d e a l e r s . S o i l maps s h o w i n g i n f i l t r a t i o n c h a r a c t e r i s t i c s a r e p u b l i s h e d by t h e S o i l C o n s e r v a t i o n S e r v i c e of t h e U.S.
Department of A g r i c u l t u r e and where a v a i l a b l e ,
may be o b t a i n e d from t h e l o c a l S o i l C o n s e r v a t i o n S e r v i c e o f f i c e s . 12.5
CURRENT CONDITIONS AND OUTLOOKS
Streamflow d a t a a r e needed on a "real-time" b a s i s , l e s s a f t e r i t s occurrence, ment d e c i s i o n s . l i n e s , by r a d i o , t e r 3.
t h a t i s w i t h i n an hour or
f o r f l o o d f o r e c a s t i n g and f o r c e r t a i n w a t e t m a n a g e -
Data from a gaging s t a t i o n c a n be t r a n s m i t t e d o v e r telephone o r by s a t e l l i t e .
See T r a n s m i s s i o n o f Hydrologic Data i n Chap-
Data from many s t r e a m s a r e b e i n g t r a n s m i t t e d d a i l y ,
a s required.
o r more f r e q u e n t l y
S e v e r a l hundred s i t e s a r e r e p o r t i n g (1981) v i a s a t e l l i t e .
The
D i s t r i c t O f f i c e s o f USGS c a n p r o v i d e t h e n a m e s o f t h e s i t e s a n d t h e t y p e , frequency,
and method of d a t a t r a n s m i t t a l .
N a t i o n a l Water Conditions ( f o r m e r l y Water Resources Review), published s h o r t l y a f t e r t h e end o f e a c h m o n t h b y USGS, d e s c r i b e s t h e s t r e a m f l o w and ground-water c o n d i t i o n s i n United S t a t e s and s o u t h e r n Canada d u r i n g t h e month i n r e l a t i o n t o normal.
I t a l s o t a b u l a t e s t h e usable c o n t e n t s of s e l e c t e d reser-
v o i r s , t h e f l o w s o f l a r g e r i v e r s , and t h e w a t e r q u a l i t y o f a f e w l a r g e r i v e r s . D e s c r i p t i o n s of s i g n i f i c a n t f l o o d s and d r o u g h t s a r e included. Weekly W e a t h e r and Crop B u l l e t i n i s p r e p a r e d j o i n t l y by U.S. D e p a r t m e n t o f Commerce (NOAA, N a t i o n a l W e a t h e r S e r v i c e ) a n d U.S. D e p a r t m e n t o f A g r i c u l t u r e . P r i n c i p a l c o n t e n t s a r e n a t i o n a l w e a t h e r summary, w e a t h e r d a t a f o r s e l e c t e d cities,
S t a t e summaries o f w e a t h e r and a g r i c u l t u r e ,
and i n t e r n a t i o n a l weather
and c r o p summaries. Water Supply Outlook f o r t h e Western United S t a t e s i s p u b l i s h e d j o i n t l y by N a t i o n a l Weather S e r v i c e (NOAM and S o i l C o n s e r v a t i o n S e r v i c e (USDA) f o l l o w i n g
2 42 t h e p r i n c i p a l snow survey d a t e s from J a n u a r y 1 t o May 1. included.
Snow survey d a t a a r e
These r e p o r t s a l s o c o n t a i n r e f e r e n c e s t o o t h e r w a t e r s u p p l y o u t l o o k s
f o r t h e S t a t e of C a l i f o r n i a and f o r t h e w e s t e r n Canadian Provinces. A v e r a g e M o n t h l y W e a t h e r O u t l o o k , b y NOAA, N a t i o n a l W e a t h e r S e r v i c e , g i v e s mapped e s t i m a t e s of whether t h e average r a i n f a l l f o r t h e next 30 days w i l l be h e a v i e r or l i g h t e r t h a n normal; sense.
Similarly,
below,
above,
these a r e not f o r e c a s t s i n t h e meteorological
t h e o u t l o o k f o r t e m p e r a t u r e i s mapped i n t e r m s of i t s b e i n g
o r n e a r normal.
These o u t l o o k s a r e p r i n c i p a l l y f o r North America
b u t some i n f o r m a t i o n i s given f o r Europe, North A f r i c a , and Asia. 12.6
INTERPRETED DATA
Mean runoff i n United S t a t e s has been mapped by Busby (1966); h i s map i s a l s o p u b l i s h e d i n USGS (1970).
For y e a r l y v a r i a t i o n s i n runoff s e e Busby (1963).
Flood frequency c u r v e s f o r a l l gaged s i t e s i n t h e United S t a t e s t h a t had more t h a n 1 0 y e a r s of r e c o r d e d n a t u r a l ( u n r e g u l a t e d ) s t r e a m f l o w w e r e p r e p a r e d i n 1977: some of t h e s e have been updated.
They a r e a v a i l a b l e f o r i n s p e c t i o n a t t h e
D i s t r i c t O f f i c e s of t h e Water Resources D i v i s i o n of USGS. Storm-rainfall
f r e q u e n c i e s i n t h e conterminous *United S t a t e s f o r d u r a t i o n s
f r o m 112 t o 24 h o u r s and f o r r e c u r r e n c e i n t e r v a l s up t o 1 0 0 y e a r s h a v e b e e n d e f i n e d and mapped by Weather Bureau (1961) and NOAA (1973). Probable maximum p r e c i p i t a t i o n i n e a s t e r n United S t a t e s has been e s t i m a t e d by t h e N a t i o n a l Weather Service.
See S c h r e i n e r and Riedel (1978) and Eo and Riedel
(1980). 12.7
GENERAL
A bibliographic data service t h a t r e l a t e s s p e c i f i c a l l y t o water resources a c t i v i t i e s i s p r ovided by t h e Water Resourc e s S c i e n t i f i c I n f o r m a t i o n C e n t e r (WRSIC) o f t h e U.S.
G e o l o g i c a l Survey. I n 1 9 7 9 t h e s y s t e m h a d o v e r 1 0 0 , 0 0 0
computerized a b s t r a c t s t h a t r e l a t e t o water-resource subjects.
Requests t o
WRSIC may be made through NAWDEH. Water u s e d a t a a s o f 1 9 7 5 w i t h p r o j e c t i o n s t o 2000 a r e g i v e n b y WRC ( 1 9 7 8 ) f o r 106 s u b r e g i o n s of t h e United S t a t e s .
S o l l e y and
o t h e r s (1983) have tabu-
l a t e d b y S t a t e s a n d b y t h e 2 1 WRC r e g i o n s w a t e r u s e s a s o f 1 9 8 0 f o r p u b l i c supply, r u r a l , power u s e s .
irrigation,
self-supplied
industrial,
t h e r m o e l e c t r i c , and hydro-
S e p a r a t e a c c o u n t i n g s a r e made f o r f r e s h and s a l i n e w a t e r w i t h -
d r a w a l s of b o t h ground and s u r f a c e water.
USGS ( 1 9 8 3 ) r e v i e w s c u r r e n t h y d r o l o g i c c o n d i t i o n s and r e c e n t e v e n t s i n t h e U ni t e d S t a t e s and p r o v i d e s a broad overview of h y d r o l o g i c i s s u e s f a c i n g t h e nation.
The summary a l s o d e s c r i b e s w a t e r i s s u e s f o r each S t a t e .
A v a r i e t y of water-resources d a t a , j e c t s of c l i m a t e s , hydrology,
facts,
and s t a t i s t i c s c o v e r i n g t h e sub-
s u r f a c e and ground-water r e s o u r c e s ,
needs, and w a t e r q u a l i t y h a s been compiled by Todd (1970).
w a t e r use and
243 REFEBElYCES Busby, M.W., 1963, Yearly v a r i a t i o n s i n r u n o f f f o r t h e conterminous United S t a t e s : U.S. Geol. Survey W a t e r s u p p l y Paper 1 6 6 9 4 . 49 p. 1 9 6 6 , Annual r u n o f f i n t h e c o n t e r m i n o u s U n i t e d S t a t e s : U.S. Geol. Busby, M.W., Survey Hydrologic A t l a s 212. s c a l e 1 t o 1.5 m i l l i o n . E d w a r d s M.D., 1 9 7 9 , NAWDEX:A k e y t o f i n d i n g w a t e r d a t a : U.S. Geol. S u r v e y Gene r a l I n t e r e s t P u b l i c a t i o n , 1 5 p. ESSA, 1 9 6 8 , C l i m a t i c A t l a s o f t h e U n i t e d S t a t e s : U.S. Dept. o f Commerce, Environmental Science S e r v i c e s Admin., Environmental Data Service. F a r n s w o r t h . R.K. and o t h e r s , 1 9 8 2 , E v a p o r a t i o n a t l a s f o r t h e c o n t i g u o u s 48 United S t a t e s : N a t i o n a l Oceanic and Atmospheric A d m i n i s t r a t i o n Tech. Bept. UWS 33, 26 p. F a r n s w o r t h , R.K., and Thompson, E.S.. 1982. M o n t h l y , s e a s o n a l , and a n n u a l pan e v a p o r a t i o n f o r t h e U n i t e d S t a t e s : N a t i o n a l Oceanic and Atmospheric A d m i n i s t r a t i o n Tech. Rept. NWS 34, 8 2 p.
Ho, F.P. a n d B i e d e l , J.T., 1980. S e a s o n a l v a r i a t i o n o f 1 0 - s q u a r e m i l e p r o b a b l e maximum p r e c i p i t a t i o n e s t i m a t e s , United S t a t e s e a s t of t h e 1 0 5 t h meridian: H y d r o m e t e o r o l o g i c a l Rept. No. 53, NOAA, N a t i o n a l W e a t h e r S e r v i c e , S i l v e r Spring, I d . 1 9 8 1 , WATSTORE: A w a t e r d a t a s t o r a g e and r e t r i e v a l s y s t e m : K i l p a t r i c k , M.C., U.S. Geol. Survey General I n t e r e s t P u b l i c a t i o n . 15 p.
NOAA, 1913, P r e c i p i t a t i o n - f r e q u e n c y a t l a s o f t h e w e s t e r n United S t a t e s , Vols. 111: U.S. N a t i o n a l Weather S e r v i c e , S i l v e r Spring, Hd. S c h r e i n e r . L.C. and B e i d e l . J.T., 1918. P r o b a b l e maximum p r e c i p i t a t i o n e s t i mates, United S t a t e s e a s t of t h e 1 0 5 t h m e r i d i a n : Hydrometeorological Report No. 51, NOAA, N a t i o n a l Weather S e r v i c e , S i l v e r Spring, I d . C h a s e . E.B., a n d Mann. W.B., I V , 1 9 8 3 , E s t i m a t e d use of w a t e x i n t h e United S t a t e s i n 1980: U.S. Geol. Survey Circ. 1001, 56 p .
Solley, W.B.,
Todd, D.K. 1910. The r a t e r encyclopedia: P o r t Washington, N.Y., t i o n C e n t e r . 5 5 9 p.
Water Informa-
USGS, 1 9 7 0 , The n a t i o n a l a t l a s o f t h e U n i t e d S t a t e s o f A m e r i c a : U.S. Dept. of I n t e r i o r , G e o l o g i c a l Survey. USGS, 1 9 8 1 , A G u i d e t o o b t a i n i n g i n f o r m a t i o n f r o m t h e USGS 1981: U.S. S u r v e y C i r c . I l l , 42 p.
USGS, 1 9 8 3 , N a t i o n a l w a t e r summary 1 9 8 3 Geol. Survey Water-Supply
U.S.
Geol
-
H y d r o l o g i c e v e n t s and i s s u e s : U.S. Paper 2250. 243 p.
Weather Bureau, 1961, R a i n f a l l f r e q u e n c y a t l a s o f t h e Uni t ed S t a t e s f o r d u r a t i o n s f r o m 3 0 m i n u t e s t o 24 h o u r s a n d r e t u r n p e r i o d s f r o m 1 t o 100 y e a r s : U.S. W e a t h e r B u r e a u Tech. P a p e r No. 40.
WRC, 1918. The n a t i o n ' s w a t e r resourc-es, 1915-2000. U.S. Water Resources Council, Washington, D.C.
second n a t i o n a l assessment:
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245
INDEX Acid rain, 198
Control, gaging station, 27
Acoustic velocity measurement, 37
Conversion factors, British and
Acre-foot, 4
metric, 3
Active channel section, 140
Correlation, 78, 80
Anchor ice, 13
Crest-stage gage, 40
Annual floods, 145
Cropping practices, effect
Aquifer, 113, 121
on flow, 190
Arroyos, 178
Culvert sizing, 220
Artesian aquifer, 121
Cumulative distributions, 60
Assured flow, 225
Current flow conditions,
Atmospheric pollution, 198
information on, 241 Current meter, 29
Backwater at a gage, 34
Curve number, SCS, 160
Bank storage, along streams, 126 in reservoirs, 127, 214
Dam failures, 186
Base flow, 112, 126
Data transmission, 52
Base-flow recession curves, 112, 225
Debris flows, 39
Beaver dams, 180
Deflection meter, 36
Bibliographic service, 242
Degrees of freedom, 8 8
Binomial distribution, 57
Dependable flow without storage, 219
Bubble gage, 25
Design floods, for highway crossings, 220
cfs, 4 Channel changes, 178 Channel geometry, 139
for spillways, 215 Dilution methods for measuring flow, 38
flood characteristics from, 156
Discharge measurement, 28
flow estimates from, 139
Discrete distributions, 57
Climatic data, 240, 242 Climatic year, 165 Closed basin, 23 Cloud seeding, 197 Coefficient of variation, 73, 107 Confidence interval, 75 Continuous distributions, 58 Contracted-opening for flow measurement, 39
Dissolved oxygen, 118 Distributions, binomial, 57 continuous, 58 cumulative, 60 discrete, 57 Gumbel, 60, 64, 68 lognormal, 68 normal, 6 1
246 Pearson type 3, 69-70 student's t, 75
plotting formula, 146 reliability, 153
Diurnal fluctuations, 11
skewness, 149
Draft-storage-f requency
use of historic floods, 148
curves, 212, 214
Water Resources Council, 149
Drainage, effect on flow, 194 Droughts, adaptation to, 232 defining severity, 229, 230
Flood-prone area, 233 mapping, 233
definition, 228
Flood-record extension, 150
multiyear, 229
Flood stages from geological or
notable, 229 seasonal, 229
botanical evidence, 153-154 Floods, annual, 145 consistency of estimates, 162
Earthquakes, effect on flow, 179
forecasting, 221
Electromagnetic velocity
from geological and botanical
measurement, 37 Energy budget, 49 Environmental impact, 234
evidence, 153 from rainfall and snowmelt, 15, 151
Ephemeral stream, 8
interpolation along channel, 161
Evaporation from water surfaces, 47
maximum experience, 153
computation of, 49
maximum probable, 154, 215
effect on yield from storage, 212
models to estimate change, 160
Evaporation pan, 48 Evapotranspiration, 116 Experimental basin, 199
on regulated streams, 162 partial duration, 145 Floodways, 235 Plow characteristics. from channel
Farm ponds, 184 Fires, effect on flow, 180 Flood characteristics, from basin characteristics, 155 f%a% Gk%UQ-
Flood control by storage, 216 Flood forecasting, 221 Flood-frequency curves, 145-152 effect of basin characteristics, 151 extending data base, 150 from partial data, 148 outliers, 147
size, 139, 156 from rainfall, 134 interpolation between sites, 134 mean flow from measurements, 136 regression on basin characteristics, 13 1 Flow-duration curve, 111 Flow variability, 107 Fluorometer, 40 Forecasting, methods. 220 floods, 221 seasonal low flow, 225 snowmelt runoff, 222 Frequency curve, 61-62, 109
247 interpretation, 72
Indirect measurements, 39
record extension, 109
Inference, statistical, 74
Frequency factors, 70-71
Infiltration of, 16
Frequency mass curve, for flood
Instream flows, 219
control, 219
Intermittent stream, 8 Irrigation, effect on streamflow. 193
Gaging station, 25-27
Irrigation waste water, 193
Glacier dams, 179 Glaciers, effect on flow, 14, 179
Lag time, 160
Graphical regression,
Lakes, terminal, 23
procedures, 90. 93-95
Landslides, effect on flow, 179
standard error of, 92
Land-use planning, 233
Grazing, effect on flow, 189
Lognormal distribution, 68
Ground water, available to
Log Pearson type 3 distribution,
stream. 124 contribution to streamflow, 19-20
71, 147, 149, 151 Logging, effect on streamflow, 187
movement, 121, 124
Losses from channels, 123
pumping of, 193, 195
Lost rivers, 19
recharge, 116, 122
Low flow, definition, 165
storage, 17
extending record, 168
use with surface water, 128
serial correlation, 168
Gumbel distribution, 60, 66, 68, 147
Low-flow frequency curves, 165 at ungaged sites, 170
Hardness, 118 HEC models, 160, 200 Highway crossings of streams, 220 Histogram. 58 Historic floods, 148 Hydrocompaction. 194 Hydrograph, 34 interpretation, 122, 123
effect of basin characteristics, 166 interpolation along channel, 173
on regulated streams, 170 reliability, 168 seasonal, 169 statistical interpretation, 167 use of precipitation records, 169
Low-flow partial-record method, 171
relation to basin characteristics, 123
Map sources, 241
Hydrologic bench marks, 179
Mass curve, 207, 209. 219
Hydrologic data, characteristics
Mass-transfer method, 49
of, 100
Maximum floods, 153
effects on analysis, 101-103
Median, 61 Metric units, conversion
Ice, effect on flow, 11-13 Icing, 12 Index-flood method, 156 Index of variation, 73. 107
table, 3 Models, rainfall-runoff. 110, 150. 200 for estimating changes, 198 for forecasting, 221
248 Moving-boat method, 30 Mud flows, 39 Multiple regression, 80, 89 characteristics of, 97-100 graphical method, 92
Reforestation. effect on runoff, 188, 199 Regression analysis, applications, 97, 131, 155 example computation, 85 example equations, 155
NAWDEX, 239 Normal distribution, 67 Null hypothesis, 76 Outliers, 103, 147, 149
method, 77 models, 83 selection of variables, 133 use of basin characteristics, 131-134
Paired basins, 199
Reservoirs, effects of, 182
Pan coefficient, 49
Roughness coefficient, 39
Partial-duration flood series, 145
Runoff from rainfall, 5
Partial-record method, 171
Runoff, variab lity of annual, 8
Pearson type 3 distribution, 69 pE, 118
Salinity, 193, 194
Phreatophytes. 196
Saltcedar, 196
Plotting position formula, 63
Satellite data transmission, 52
Pollution, atmospheric, 198
Sediment, bed
Precipitation, as a basin
oad, 42
discharge, 42
characteristic, 52
load computation, 43
effect of man on, 47
measurement, 42
Precipitation gages, 46 Probability 3, 72. 167 Probability plotting paper, 60, 64
record, 44 reservoir deposits, 44 sampler, 43
Probability routing, 210
suspended, 42
Probable maximum flood, 215
transport, 117
Probable maximum precipitation, 215
transport curve, 45 transport data available, 239
Rain gage, 46-48 Rainfall record reliability, 151 Rainfall-runoff models, 110, 150, 162 Rating curve, 31, 34 Rational method, 160 Real time data, 241 Recession curves, 112, 126 Recharge of ground water, 122 Recorders, water stage, 26-28 Recurrence interval, 3, 63
Seepage run, 172 Serial correlation, 82, 168
SI: units, 3 Simulated streamflows, 208 Skew coefficient, 70 Skewness, 61, 149 Slope-area method, 39 simplified method, 39 Smelter effluents, 198
Snow pillow, 51
249 Snow surveying, 49
Transmission losses in streams, 123
Snowmelt runoff, 222
Transmissivity, 121
floods from, 225
Trends, 177
Snowpack, 49. 222 Soil, hydrologic classification, 51 Sounding weight, 30 Specific conductance, 117 Springs, 121 Staff gage, 25, 26 Stage, of stream or lake, 25 Stage-discharge relation, 31 Standard deviation, 61, 74 Standard error, of regression, 79,
Urbanization, effect on flow, 191 Variability, of a distribution, 73 Velocity of ground water, 121 Velocity measurement, electromagnetic, 37 by current meter, 28 acoustic, 37 Volcanic eruptions, effect on flow, 181
92, 134 of a prediction, 79 Step-backwater method, 33, 234 Stilling well, 26 Stock tank, 184 Storage, depletion by sedimentation, 213 for flood control, 216 in banks, 124. 126, 127, 214 maximum yield from, 212 to reduce culvert size, 220 within-year, 209 Stratification, therma , 186 chemical, 186 S treamf1ow, ephemeral, 123
data available, 239, 242 Streamflow record, 35 Streamflow record extension, 109 Students t distribution, 76 Subsidence, 196 Temperature of water, 118 Test for significance, 86 Time of concentration, 160 Time of travel, 40 Tracers, for discharge measurement, 38 for time of travel, 40 Transformations, 8 4
Wagon Wheel Gap, 199 Water budget, 49 Water loss, annual, 10 Water quality, 44 data, 240 Water-supply outlooks, 241 Water Resources Council, 149 Water-use data, 242 Waterway openings at highway crossings, 220 Weather outlooks, 241 Weibull formula, 63 Whole-channel section, 140
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