edited by a. sokolov t. chapman - unesdoc...

Edited by A. A. SOKOLOV and T. G. CHAPMAN

A contribution to the International Hydrological Decade

The Unesco Press Paris 1974

Studies and reports in hydrology 17

TITLES IN THIS SERIES

1. The use of analog and digital computers in hydrology: Proceedings of the Tucson Sympo- sium, June 1966 / L’utilisation des calculatrices analogiques et des ordinateurs en hydrologic: Act(= du colloque de Tucson, juin 1966. Vol. 1 & 2. Co-edition IAHS-Unesco / Coddition .4ISH- Unesco.

2. Water in the unsaturated zone: Proceedings of the Wageningen Symposium, June 1967 / L‘eau dans la zone non saturee: Actes du symposium de Wageningen, juin 1967. Edited by /edit& par P.E. Rijtema & H. Wassink. Vol. 1 & 2. Co-edition IAHS-Unesco / Coddition AISH- Unesco.

3. Floods and their computation: Proceedings of the Leningrad Symposium, August 1967 / Les crues et leur evaluation : Actes du colloque de Leningrad, aoDt 1967. Vol. 1 & 2. Co-edition I A H S - Unesco- WMO / Coddition AISH-Unesco-OMM.

,4. Representative and experimental basins: A n international guide for research and practice. Edited by C. Toebes and V. Ouryvaev. Published by Unesco.

4. Les bassins representatifs et experimentaux : Guide international des pratiques en matiere de recherche. Publie sous la direction de C. Toebes et V. Ouryvaev. Publid par I’Unesco.

5. *Discharge of selected rivers of the world / Debit de certain cours d’eau du monde. ‘ Jublished by Unesco I Publid par I‘ Unesco.

Vol. I: General and regime characteristics of stations selected / Caracteristiques gene- rales et caracteristiques du regime des stations choisies.

Vol. 11: Monthly and annual discharges recorded at various selected stations (from start of observations up to 1964) / Debits mensuels et annuels enregistres en diverses stations selectiocnkes (de l’origine des observations a I’annk 1964).

Vol. 111: Mean monthly and extreme discharges (1965-1969) / Debits mensuels moyens et debits extremes (1965-1969). t v.E pt 3 .

6. List of International Hydrological Decade Stations of the world / Liste des stations de la Decennie hydrologique internationale existant dans le monde. Published by Unesco /Publid par I’Unesco.

7. Ground-water studies: A n international guide for practice. Edited by R. Brown, J. Ineson, V. Konoplyantsev and V. Kovalevski. (Will also appear in French, Russian and Spanish / Paraitra egalement en espagnol, en francais et en russe.)

8. Land subsidence: Proceedings of the Tokyo Symposium, September 1969 / Affaisement du sol : Actes du colloque de Tokyo, septembre 1969. Vol. 1 & 2. Co-edition IAHS-Unesco / Coddition AISH- Unesco.

.9. Hydrology of deltas: Proceedings of the Bucharest Symposium, M a y 1969 / Hydrologie des deltas : Actes du colloque de Bucarest, mai 1969. Vol. 1 & 2. Co-edition IAHS-Unesco / Coddition AISH- Unesco.

10. Status and trends of research in hydrology / Bilan et tendances de la recherche en hydrologie. Published by Unesco / Publid par I‘ Unesco.

11. World water balance: Proceedings of the Reading Symposium, July 1970 / Bilan hydrique mondial : Actes du colloque de Reading, juillet 1970. Vol. 1-3. Co-edition IAHS-Unesco- WMO / Coddition AISH-Unesco-OMM.

12. Results of research on representative and experimental basins: Proceedings of the Wellington Symposium, December 1970 / RCsultats de recherches sur les bassins representatifs et experimentaux : Actes du colloque de Wellington, dbembre 1970. Vol. 1 & 2. Co-edition I A H S - Unesco / CoPdition AISH-Unesco.

13. Hydrometry: Proceedings of the Koblenz Symposium, September 1970 / Hydromktrie: Actes du colloque decoblence, septembre 1970. Co-edition I A H S - Unesco- WMO / Coddition A I S H Unesco-OMM.

14. Hydrologic information systems. Co-edition Unesco- WMO. 15. Mathematical models in hydrology: Proceedings of the Warsaw Symposium, July 1971/

Les modbles mathematiques en hydrologie : Actes du colloque de Varsovie, juillet 1971. Vol. 1-3. Co-edition IAHS-Unesco- WMO / Coddition AISH-Unesco-OMM.

16. Design of water resources projects with inadequate data: Proceedings of the Madrid Sym- posium, June 1973 / elaboration des projets d’utilisation des resources en eau sans donnCes sufisantes : Actes du colloque de Madrid, juin 1973. Vol. 1-3. Co-edition Unesco-WMO- I A H S / Coddition Unesco-OMM-AISH.

17. Methods for water balance computations. A n international guide for research and practice. Published by Unesco.

6)

The designations employed and the presentation of the material in this publication do not imply the expression of any opinion whatsoever on the part of the publishers concerning the legal status of any country or territory, or of its authorities. or concerning the frontiers of any country or territory.

Published by The Unesco Press Place de Fontenoy, 75700 Paris

Printed by Beugnet, Paris

ISBN 92- 3- 10 1227-4 0 Unesco 1974 Printed in France

P R E F A C E

The International Hydrological Decade (IHD) 1965-74 was launched by the thirteenth session of the General Conference of Unesco to pro- mote international co-operation in research and studies and the training of specialists and technicians in scientific hydrology. Its purpose is to enable all countries to make a fuller assessment of their water resources and a more rational use of them as man's demands for water constantly increase in face of developments in population, industry and agriculture. In 1974 National Committees for the Decade had been formed in 108 of Unesco's 132 Member States to carry out national activities and to contribute to regional and international activities within the programme of the Decade. The implementation of the programme is supervised by a Co-ordinating Council, composed of thirty Member States selected by the General Conference of Unesco, which studies proposals for developments of the programme, recommends projects of interest to all or a large number of countries, assists in the development of national and regional pro j ec t s and co-ordinates inter na t ional co -opera t ion.

techniques, diffusing hydrological data and planning hydrological installations is a major feature of the programme of the IHD which encompasses all aspects of hydrological studies and research. Hydrological investigations are encouraged at the national, regional and international levels to strengthen and to improve the use of natural resources from a local and a global perspective. The programme provides a means for countries well advanced in hydrological research to exchange scientific views and for developing countries to benefit from this exchange of information in elaborating research projects and in implementing recent developments in the planning of hydrological installations.

As part of Unesco's contribution to the achievement of the objectives of the IHD the General Conference authorized the Director- General to collect, exchange and disseminate information concerning research on scientific hydrology and to facilitate contacts between research workers in this field. To this end Unesco has initiated two collections of publications, 'Studies and Reports in Hydrology' and 'Technical Papers in Hydrology'.

The collection 'Studies and Reports in Hydrology', is aimed at recording data collected and the main results of hydrological studies undertaken within the framework of the Decade as well as providing information on research techniques. Also included in the collection will be proceedings of symposia. Thus, the collection will comprise the compilation of data, discussions of hydrological research techniques and findings, and guidance material for future scientific investigations. It is hoped that the volumes will fur- nish material of both practical and theoretical interest to hydrologists and governments participating in the IHD and respgnd to the needs of technicians and scientists concerned with problems of water in all countries.

Promotion of collaboration in developing hydrological research

CONTENTS

Foreword 1. Introduction

1.1 Objectives and importance of water balance studies

1.2 Purpose and scope of the report 1 3 Terminology 1.4 Symbols

2,l General form of the water balance equation 2.2 Other forms of the water balance equation 2.3 Special features of the water balance equation

for different time intervals. 2.4 Special features of the water balance equation

for water bodies of different dimensions 2.5 Closing of the water balance equation 2.6 Units for the components of the water balance

equations. Methods of computation of the main water balance components a 3.1 Basic data

3.2 Precipitation

2. The water balance equation.

3.

3.1.1 Maps and atlases

3.2.1 General 3.2.2

3.2.3

Measurement of precipitation at a point and correction of measured precipitation. Computatfon of mean precipitation over an area. 3.2.3.1 lsohyetal maps

3 2 -4 Special features.

3.3.1 Normal runoff and selection of the water

3.3-2

3.3 River runoff.

balance period. Computation of normal runoff using observational data 3.3.2.1 Graphical method 3.3 2 2 Analytical method Computation of normal runoff without observational data. 3.3.3.1

3.3.3.2

3.3.3.3

3.3.3

Computation of normal runoff from a map of isolines. Computation of normal runoff by the analogue method. Computation of normal runoff by the water and heat balance equation.

3.3.4 Maps of runoff isolines. 3.3.5 Separation of the runoff hydrograph into

components. 3.4 Evaporation.

3.4.1 General 3.4.1.1 List of symbols used only for evapor-

ation .

11 13

13 13 14 14 17 17 17

18

18 19

19

21 21 21 21 21

22

23 23 24 24

25 25 26

28

28

39

30 30

34 37 37

37

Methods /m uylter bahnce compukrtions

4.

5.

3.4.2 Evaporation from water surfaces 3.4.2.1 Computation from evaporimeter

3.4.2.2 Water balance method 3.4.2.3 Heat balance method 3.4.2.4 Aerodynamic method 3.4.2.5 Empirical formulae 3.4.2.6 Effect of aquatic plants

3.4.3.1 Computation from soil evaporimeter and lysimeter data 3.4.3.1.1 Measurements of

data

3.4.3 Evaporation from land

evaporation from snow cover by evaporimeters.

3.4.3.2 Water balance method 3.4.3.3 Heat balance method 3.4.3.4 Aerodynamic method 3.4.3.5 Empirical methods

3.4.3.5.1 The generalized combin- at ion method.

3.4.3.5.2 Other empirical methods 3.4.3.6 Methods used in the USSR

3.4.4 Maps of evaporation. Variations of water storage in river basins 3.5.1 General 3.5.2 Surface water storage.

3.5

-3.5.2.1 Detention of water in micro- depressions.

3.5.2.2 Water storage in the solid state 3.5.2.3 Water volume in lakes and reservoirs 3.5.2.4 Channel storage in a river basin

3.5.3 Soil moisture storage 3.5.4 Ground water storage

Variability of the main water balance components and accuracy of their estlmation. 4.1 4.2

Water balance of water bodies 5.1 River basins

Variability of main water balance components Estimation of the accuracy of measurement and computation of water balance components.

5.1.1 General 5.1.2 Mean water balance of a river basin 5.1.3 Water balance of a river basin for

5.1.4 Forests and forested basins specific time intervals.

5.1.4.1 Forest terrain 5.1.4.2 Forested basins

5.1.5.1 Irrigated land 5.1.5.2 Drained land

5.1.5 Irrigated and drained land

5.2 Lakes and reservoirs 5.3 Swamps

39

39 41 41 42 43 46 47

47

47 47 48 48 49

49 50 5 3 55 55 55 56

56 56 56 57 62 64

67 67

71 75 75 75 75

79 81 81 84 84 84 87 69 92

Methods for water bakznce computations

5.4 Ground-water basins 5.5 Mountain glacier basins, mountain glaciers and

ice shields. 5.6 Inland seas.

6.1 Water balance of countries. 6.2 Water balance of continents.

7.1 Main water balance equations 7.2

7.3

6. Regional water balances

7. Water balance of the atmosphere

Water balance equation for the atmosphere-soil system. Development of the water balance equation for the atmosphere. 7.3.1 Measurement systems and data sources. 7.3.2 Space scale considerations 7.3.3 Time scale considerations

atmosphere-soil system. 7.4 Estimation of the terms of the equation for the

8. Estimation of the rate of water circulation. References

LOO

104 105 107 107 108 113 113

113

116 117 118

FOREWORD

In recent years, the scientific and practical importance of water balance problems has been highlighted by predictions of fresh water shortages in many areas of the world, due to industrial development, urbanization, and increase in agricultural production. The study of these problems has therefore been given priority in the programme of the International Hydrological Decade (IW) under the sponsorship of Unesco. Water balance problems are also the active concern of the World Meteorological Organization (WMO) the Food and Agricultural Organization (FAO), and other international governmental and non-governmental organizations.

A Working Group on the World Water Balance (later re-named the Working Group on Water Balances) was established by the Co- ordinating Council for the I W at its first session in 1965, with terms of reference that included the preparation of methodological guides on water balance computations.

A 'Scheme for the Computation of Water Balance Elements' was the first step in this direction, prepared through the initiative of the USSR National Committee for the IHD at the State Hydrologi- cal Institute, under the guidance of the late Dr. V.A. Quryvaev. A paper entitled 'Summary of methods of computation of water balance' (USSR, Interdepartmental Committee for the IHD 1967) was approved by the Working Group and submitted to the Co-ordinating Council at its third session in 1967. The Council recommended that Unesco dis- tribute this paper to all the National Committees for the IW.

A WMO report on the preparation of the co-ordinated maps of precipitation, runoff and evaporation for the study of water balance (Nordenson, 1968) also contains useful guidance material.

The Working Group's Panel on the Scientific Framework of the Vorld Water Balance, at its second session (May, 1969), requested the IND Secretariat to nominate an expert for preparation of a Guide for Methods of Computation of Water Balances, taking into account Dr. Ouryvaev's document, relevant WO/IHD reports, and material submitted by National Committees. National Committee for the I W to undertake this task, and Prof. P.S. Kuzin was designated by the National Committee to prepare a draft outline of the Guide. The outline was discussed and approved by the Working Group on Water Balances at its fourth session (July, 1970). A Draft of the Guide was prepared on the basis of this outline and the guidelines set down by the Working Group, and circulat- ed to Working Group members for comment

The draft report and written comments were discussed in detail at the fifth session (December 1972) of the Working Group, Specific tasks for revision of sections which proved difficult were allocat- ed to designated authors, and it was arranged that the final manuscript would be completed at a meeting of the editors in June 1973.

The main difficulties that arose in the preparation of the report were problems of selection and consistent arrangement of the large volume of material available on methods of water balance computations. less detailed treatment has been given to sections where guidance

The Secretariat requested the USSR

While the report is intended to be complete in itself,

11

Methods for mter bokance compututions

material is already available in the international publications of WMO, UNESCO, the International Association for Hydrological Sciences (IAHS) , and other organizations.

volve a combination of scientific principles with general application, and empirical techniques restricted to specific climates, land forms, or purposes. The report attempts to indicate where these techniques may be reasonably applied, either without modif i- cation or after experimental determination of values of constants and coefficients appropriate to the specific problem. Space limit- ations have prevented more than a partial description of many techniques, and the reader is urged to study the cited references, which have been selected from the large body of international scientific literature on this subject.

at the State Hydrological Institute of the USSR headed by Prof. P.S. Kuzin, who prepared many of the sections. Sections 3.4 and 5.5 were prepared by Prof. P.P. Kuzmin; sections 3.5.2.3 and 5.2 - by Z.A. Vihlina; sections 3.5.4 and 5.5 - by O.V. Popov; sections 5.1.2 and 5.1.3 - by A.P. Bochkov; section 5.1.4 - by S.F. Fedorov; section 5.1.5 - by S.I. Kharchenko and A.S. Subbotin; section 5.3 - by L.G. Bavina; section 4 - by G.A. Plitkin, section 7 - by O.G. Sorochan. Materials for preparation of section 5.5 were kindly presented by A.N. Krenke and V.G. Khodakov from the Institute of Geography of the Academy of Sciences of the USSR.

ing Group and taken into account in the final version, were prepared by I.C. Brown (Canada), T.G. Chapman (Australia), D.R. Dawdy (USA), D. Lazarescu (Rumania), J. Nemec (WMO) and J.A. da Costa (UNESCO). D.S. Mitchell (U.K.) prepared section 3.4.2.6 om aquatic plants. M. Sugawara (Japan) prepared the revised section 4 on statistical aspects. D.W. Lawson (Inland Waterways Directorate, Department of Environment, Canada) revised section 5.4 on ground- water basins. E.M. Rasmussen (WO) contributed additional material for section 7 on atmospheric water balances.

Prof. A.A. Sokolov, Director of the State Hydrological Instit- ute of the USSR, is the senior editor of the report, assisted in the English language version by Prof. T.G. Chapman (University of New South Wales, Australia), who is Chairman of the Working Group on Water Balances.

Practical applications of the water balance method usually in-

The draft of the report was prepared by a group of scientists

3.5.2.4 - by R.A. Nezhikhovski and V.I. Babkin;

Written comments on the draft report, considered by the Work-

12

1. INTRODUCTION

1.1 Objectives and importance of water balance studies.

Water balance techniques, one of the main subjects in hydrology, are a means of solution of important theoretical and practical hydrological problems. On the basis of the water balance approach it is possible to make a quantitative evaluation of water resources and their change under the influence of man's activities.

and ground-water basins forms a basis for the hydrological substan- tiation of projects for the rational use, control and redistribution of water resources in time and space (e.g. inter-basin transfers, streamflow control, etc.). Knowledge of the water balance assists the prediction of the consequences of artificial changes in the regime of streams, lakes , and ground-water basins.

basins for short time intervals (season, month, week and day) is used for operational management of reservoirs and for the compilation of hydrological forecasts for water management.

tant for studies of the hydrological cycle. With water balance data it is possible to compare individual sources of water in a system, over different periods of time, and to establish the degree of their effect on variations in the water regime.

Further , the initial analysis used to compute individual water balance components, and the co-ordination of these components in the balance equation make it possible to identify deficiencies in the distribution of observational stations, and to discover systematic errors of measurements.

Finally, water balance studies provide an indirect evaluation of an unknown water balance component from the difference between the known components (e.g. long-term evaporation from a river basin may be computed by the difference between precipitation and runoff).

1.2 Purpose and scope of the report

This report is intended as an international manual for the computation of water balances of river basins, land areas, and surface and subsurface water bodies. most useful in developing countries and other regions where lack of data or other circumstances have prevented the computation of water balances. The background knowledge assumed in the reader is that of a graduate scientist or engineer, preferably with an elementary understanding of hydrological terms and practices.

possible, unified principles and methods which may be applied in different countries to compute the water balance and its components Such unified methods are essential for the computation of the water balances of international river basins, and of large regions covering the territory of several countries. The methods described in the report do not however account for all possible variations in environment and natural features, and therefore do not eliminate the need for tests and experimental studies in some circumstances, as

The study of the water balance structure of lakes, river basins,

Current information on the water balance of river and lake

An understanding of the water balance is also extremely impor-

It is expected that the report will be

The basic purpose of the report is to establish, as far as

13

Methods fw mater bahnce compututions

r

emphasized in the Foreword. The report describes methods of computation for both long-term

(or average) and short-term periods for the following:- - The main water balance components - precipitation, runoff , evapo- - The water balance of land areas - river basins, countries, physi- - The water balance of water bodies - lakes and reservoirs, swamps, ration, and water storage in various forms.

cal regions and continents.

ground water, glaciers and ice sheets, inland seas, and the atmos- pher e. - The water balance of areas with distinctive hydrological characteristics (which may have sufficient total area to affect large- scale water balances) - forests, irrigated land, and drained or reclaimed land.

'

1.3 Terminology

The report uses the terminology usually applied in international hydrological practice (Chebotarev, 1970; UNESCO-WMO , 1969; Gidrometeoizdat, 1970; Toebes and Ouryvaev, 1970).

Type

prescript

subscripts

1.4 Symbols

Symbols used in this report have been carefully selected to form a consistent unambiguous set that is as far as possible in conformity with other publications (UNESCO, 1971) and international standards (IUPAP, 1965).

the values of constants quoted. empirical equations may differ in appearance from the author's original f ormulat ion.

Symbols of specialized quantities, which are restricted to one section of the report, are listed separately from those which occur frequently in the text.

Many symbols are modified by the use of subscripts, to indicate a more particular meaning. listed separately below. Numerical subscripts and primes (I) have meanings which are defined locally in the text.

The units given are recommended units, and are consistent with As a result, the presentation of

Modifiers which are used frequently are

General Modifiers

Symbol

A

an ch gl I

L 0

Meaning

change in value during the water balance time interval (positive= increase; negative=decrease) analogue river and stream channels glacier, ice inflow to the water body under study lakes and reservoirs outflow from the water body undei study

Methods for water bahnce compu&tions

subscript s

superscript

obs S sn st

U -

ob served surf ace snow exchange between inland sea and ocean. underground (subsurface) mean value

General Symbols

Symbol

a A CS CV

E

g G I M

n P

Q S

S

T

V

W 11

Tr

Meaning

part of an area area (of a drainage basin) skew coefficient coefficient of variation (See

evaporation (including transpira-

acceleration due to gravity groundwater storage irrigation flow moisture in soil and unsaturated

number of terms in a series pr ec ip it at ion actually received

runoff or total flow standard deviation of water

water storage, expressed as a

water balance period conventional residence time water storage, expressed as a

water storage in the atmosphere residual term of water balance

section 4)

t ion)

zone

at the ground surface

balance component

mean depth

volume

equation

m m/sec2 m mm

mm - m

mm

mm m

various various m3

m m

15

2. THE WATER BALANCE EQUATION

2.1 General form of the water balance equation.

The study of the water balance is the application in hydrology of the principle of conservation of mass, often referred to as the continuity equation. This states that, for any arbitrary volurne and during any period of time, the difference between total input and output will be balanced by the change of water storage within the volume. In general, therefore, use of a water-balance technique implies measurements of both storages and fluxes (rates of flow) of Water, though by appropriate selection of the volume and period of time for which the balance will be applied, some measurements may be eliminated (UNESCO, 1971).

The water balance equation for any natural area (such as a river basin) or water body indicates the relative values of inflow, outflow and change in water storage for the area or body. In general, the inflow part of the water balance equation comprises precipitation (P) as rainfall and snow actually received at the ground surface, and surface and subsurface water inflow into the basin or water body from outside (QS1 and QU1). The outflow part of the equation includes evaporation from the surface of the water body (E) and surface and subsurface outflow from the basin or water body (Qso and Quo). When the inflow exceeds the outflow, the total water storage in the body (AS) increases; an inflow less than the outflow results in decreased storage. All the water-balance components are subject to errors of measurement or estimation, and the water-balance equation should therefore include a discrepancy term (11). time interval in its general form may be represented by the following equation:

Consequently the water balance for any water body and any

P + QSI + QU1 - E - Qso - QUO - As - rl = 0 (1 1 2.2 Other forms of the water balance equation.

For application to a variety of Water-balance computations equation (1) may be simplified or made more complex, depending on the available initial data, the purpose of the computation, the type of body (river basin or artificially separated administrative district, lake or reservoir, etc.), and the dimensions of the water body, its hydrographic and hydrologic features, the duration of the balance time interval, and the phase of the hydrological regime (flood, low flow) for which the water balance is computed.

In large river basins, QU1 and Quo are small compared with other terms, and are therefore usually ignored, i.e. subsurface water exchange with neighbouring basins is assumed to be zero. is no surface water inflow into a river basin with a distinct watershed divide (assuming no artificial diversions from other basins) , and therefore QS1 is not included in the water balance equation of a river basin. Thus for a river basin equation (1) is usually simplified as follows :

There

P - E - Q - AS - = 0 (2) where Q represents the river discharge from the basin.

17

Methods fbr water balance computations

On the other terms of equation pilation of water

hand, depending on the specific problem, the (1) may be subdivided. For example, in the com- balances for short time intervals, the change in

total water storage (AS) in a small river basin may be subdivided into changes of moisture storage in the soil (AM), in aquifers (AG), in lakes and reservoirs (ASL), in river channels (ASch), in glaciers (ASgl) and in snow cover (AS,,). Thus in this case the water balance equation becomes -

where QS1 represents the net surface water diversion from other basins. 2.3 Special features of the water balance equation for different

time intervals. The water balance may be computed for any time interval, but dis- tinction may be made between mean water balances and balances €or specific periods (such as a year, season, month or number of days), sometimes called current or operational water balances. Water balance computations for mean values and specific periods each have distinctive charact er ist ic s.

(calendar year or hydrological year), although they may be computed for any season or month.

simple water balance problem, since it is possible to disregard changes in water storage in the basin (AS), which are difficult to measure and compute. Over a long period, positive and negative water storage variations for individual years tend to balance, and their net value at the end of a long period may be assumed to be zero.

The reverse situation occurs when computing the water balance €or short time intervals, for which AS # 0. interval, the more precise are the requirements for measurement or computation of the water balance components, and the more subdivided should be the values of AS and other elements. This results in a complex water balance equation which is difficult to close with acceptable errors.

water balances for seasons or months.

Mean water balances are usually computed for an annual cycle

The computation of the mean annual water balance is the most

The shorter the time

The term AS must also be considered in the computation of mean

2.4 Special features of the water balance equation for water bodies of different dimensions.

The water balance may be computed for water bodies of any size, but the complexity of computation depends greatly on the extent of the area under study.

A river basin Is the only natural area for which large-scale water balance computations can be simplified, since the accuracy of computation increases with an increase in the river basin's area. This is explained by the fact that the smaller the basin area, the

18

Water bakance equation

more complicated is its water balance, as it is difficult to estimate secondary components of the balance such as ground-water exchange with adjacent basins; water storage in lakes, reservoirs, swamps, and glaciers; and the dynamics of the water balance of forests, and irrigated and drained land. The effect of these factors gradually decreases with an increase in the river basin area and may finally be neglected.

The complexity of the computation of the water balance of lakes, reservoirs, swamps, ground-water basins and mountain-glacier basins tends to increase with increases in area. This is due to a related increase in the technical difficulty of accurately measuring and computing the numerous important water balance components of large water bodies, such as lateral inflow and variations in water storage in large lakes and reservoirs, precipitation on their water surface, etc

2.5 Closing of the water balance equation.

To close the water balance equation it is essential to measure or compute all the balance elements, using independent metho ver possible. Measurements and computations of water balance elements always involve errors, due to shortcomings in the techniques used. The water balance equation therefore usually does not balance, even if all its components are measured or computed by independent methods. The discrepancy of water balance (q) is given as a residual term of the water balance equation, and includes the errors in the determination of the components considered, and the values of components not taken into account by the particular form of the equation being used. that its component parts tend to balance out.

by direct measurement OK computation, the component may be evaluated as a residual term in the water balance equation. In this case, the term includes the balance discrepancy, and therefore contains an unknown error, which may even be larger than the value of the component Similar considerations apply when measured values of one component are used to estimate the values of another component through an empirical or sani-empirical formula. estimated will include errors due to the imperfections of the formula and in the measured component, and the overall error is again unknown.

2.6 Units for the components of the water balance equations

The components of a water balance equation may be expressed as a mean depth of water over the basin or water body (nun), or as a volume of water (d), or in the form of flow rates (m3s-I). The last form is convenient for many water management computations, but is usually computed from a balance which has been derived for a specific time interval

the computation of mean precipitation over the basin, the other components are usually also expressed as depths of water. recommended units, transformations between depth and volume are

A low value of 11 may indicate only

If it is impossible to obtain the value of a balance component

The value so

AS the computation of the water balance usually begins with

In the

19

Methods for wter balance compututions

simple, e.g.

V = 1 0 0 0 A S (4 1 where S is a storage expressed as a mean depth (mm), V is the same storage expressed as a volume (m3), and A is the area of the basin or water body (lan2).

20

3. METHODS OF COMPUTATION OF THE MAIN WATER BALANCE COMPONENTS 3.1 Basic data.

Records of precipitation and runoff from the network of stations are the basic data for computation of the water balance components of river basins for long-term periods. These records are published in hydrological and meteorological year-books, bulletins, etc.

months, it is necessary in addition to have data on water storage variations in the basin. These are obtained from snow surveys, observations of soil moisture, water-level fluctuations in lakes and ground-water fluctuations in wells.

To compute the water balance of small areas with special features in the water balance (mountain glacier basins, large forest areas, irrigated land, etc.), it is necessary in most cases to or- ganize a special programme of observations, e.g. observations of glacier ablation, interception of precipitation, soil moisture, etc.

poration pans or tanks and meteorological data on temperature, humidity, wind, cloudiness, and radiation.

To compute the water balance for individual years, seasons, or

To compute evaporation it is desirable to have data from eva-

3.1.1 Maps and atlases

When there is an absence or shortage of observational data on precipitation, runoff or evaporation in a river basin, regional maps and atlases of mean values of these elements may be useful (Norden- son, 1968; GUGK and USSR Academy of Sciences 1964; WMO, 1970b; Rainbird, 1967; Sokolov, 1961; Sokolov, 1968). With the help of these isoline maps it is possible to determine the mean values of precipitation, runoff and evaporation for any area by planimetering.

The principal methods for preparing these maps are described in Sections3.2.3.1, 3.3.4 and 3.4.4; at this point it should be noted that for water-balance computations the maps of annual precipitation, evaporation and runoff must be co-ordinated, i.e. precipitation, minus evaporation and runoff, all evaluated by isoline maps, must be equal to zero in conformity with the equation for the mean water balance of a river basin (GUGK and USSR Academy of Sciences, 1964) :-

The co-ordination of the three maps is performed on the basis Usually the run- of an evaluation of the reliability of each map.

off map is the most reliable (with the exception of arid areas with ephemeral streams), since the data on discharge at a gauging section automatically integrate the depth of runoff for the basin. Runoff maps are therefore usually used for correction, as well as coordi- nation, of precipitetion and evaporation maps (Nordenson, 1968).

3.2 Precipitation

3.2.1 General

Precipitation is usually the only source of moisture coming to the land surface and thus the accuracy of measurement and computation of precipitation determines to a considerable extent the reliability

21

Methods for water balance computations

of a11 water-balance computations.

area, is determined by precipitation gauges, installed within the area under study. In the case of an insufficient number of gauges, records of precipitation gauges installed in neighbouring regions may also be used to provide a more accurate computation of precipitation. The shorter the period of water-balance computation, the more dense must be the precipitation gauge network.

Precipitation gauges used for water-balance computations must meet the usual requirements for precipitation gauges in a climato- logic and hydrometeorologic network (WO, 1962; W O , 1970a).

To compute mean water balances, long-term series of observations of precipitation are needed (about 25-50 years). To estimate missing data, it is advisable to establish graphical relations of observational data at neighbouring stations or to use the correlation method (Nordenson, 1968; Rainbird, 1967; Rodda, 1972;

The mean amount of precipitation, in a river basin or any other

Hershfield, 1965; Hershfield, 1968; Kagan, 1972a; Green, 1970a, 1970b).

When determining the mean precipitation for an area or water body, two problems arise: first, the determination of the precipitation at a point and, second, the determination of the mean precipitation depth over the area under study, using point observa- t ions.

3.2.2 Measurement of precipitation at a point and correction of measured precipitation.

It is well known that the precipitation gauges currently used in the network of meteorological stations dq not catch the total amount of precipitation, mainly because of wind effect. The catch deficiency is especially great when precipitation occurs in the form of snow and it may reach 100% due to strong winds.

In addition, a certain amount of precipitation caught by the gauge is lost by evaporation during the period between the begin- ing of precipitation and the time of measurement, and by wetting the gauge collector in each new fall, especially in the case of drizzle. cause may be considerable.

Therefore, in the computation of water balances, the mean value of precipitation for basins or water bodies must be evaluated on the basis of corrected data, to compensate for systematic errors of gauge measurements (Bochlwv, 1965; Bochkov, 1970; GGI, 1966; GGI, 1967; Struzer et al. , 1965; Struzer et al., 1968 ). In one of the latest WMO publications (WO, 1970b), the corrections for wind effect are evaluated on an average as 10-15% for rain and 40-60% for snow. gauges, installed 2 m above the ground surface. According to Nordenson (1968) , inaccuracies of measurement of tropical showers usually do not exceed 5%. Experimental investigations carried out in the USSR (Gidrometeoizdat, 1971a) show that losses from wetting the gauge collector are about 0.2 mm per measurement for rain and 0.1 mm for snow, while losses by evaporation average about 6% of the total precipitation during the summer (depending on gauge design

If drizzle occurs frequently the total loss due to this

These corrections were obtained in the USSR for 200 cm2

22

Computotion of Components

and the air temperature).

values are determined by comparison of the records of standard precipitation gauges and ground-level gauges, installed at the ground surface in places protected from wind, and designed to minimize errors due to splashing of water into or out of the collector.

surements with precipitation gauges, installed both in open and protected places (e.g. in a deciduous forest or a forest clearing), or by comparison of precipitation gauge data with the increase of snow storage, measured by detailed snow surveys during periods of no thawing a

Corrections for the reduction of measured rainfall to true

Corrections for snowfall are also determined by parallel mea-

3.2.3 Computation of mean precipitation over an area

The mean values of precipitation for river basins and administrative regions with a relatively even distribution of network stations and small variations of precipitation over the area are computed as the arithmetic mean of data available from all stations, i.e.

p = - - 1 " n pi i=P

where is the mean precipitation for the same period at the i-th station, and n is the number of stations used to compute the mean.

When the network of stations is unevenly distributed over the area, the areal precipitation is computed from the records of meteorological stations as a weighted average value, i.e.

is the mean precipitation for the given basin or region, Pi

where ai is the area, of which the i-th precipitation station is expected to be representative, A = lai is the area of the river basin or region. The area ai, adjoining the given station, may be determined by means of a map of the station network, for instance, by the Thiessen method (Rainbird, 1967; McGuinness, 1963). 3.2.3.1 Isohyetal maps

Another method for determining precipitation over a basin is the plotting of isohyetal maps. The corrected value of precipitation at each station is plotted on the map, and isolines of precipitation (isohyets) are drawn, taking into account orography and the pluviometric gradient in mountain regions (Nordenson, 1968 ; W O , 1970b). Intervals between isohyets should be not less than the mean error of interpolation.

cipitation, in areas of marked relief the spacing of isolines increases with altitude at a geometrical rate.

WMO (1970b) has recommended that maps of mean annual precipitation at the scale of 1 : 5,000,000 have isolines at 100: 200, ... 800; 1,000; ....... 1,600; 2,000; ....... 3,200; 4,000 mm.

As the standard deviation increases with the amount of pre-

23

Methods fw water balance cornputotions

3.2.4 Special features

Precipitation measurements over water surfaces and large forest areas are of a special character and demand, therefore, some additional. explanations.

When computing the precipitation that falls on the surface of lakes and reservoirs, it is necessary to take into account the fact that, due to the attenuation of ascending air currents above the water surface which aids in the formation of convective local precipitation, the amount of precipitation falling on the water surfaces, as well as on open flat islands and beaches, is less than on the land and littoral area. For instance, on flat islands in large water bodies the annual precipitation may be 15-25% less than on the shore (Natrus, 1964; Matushevski, 1960).

To take into account the reduction of precipitation over a lake or reservoir, the gauges should be installed not only around the periphery of the lake, but also at some distance from the coast on islands and light-ships.

(Corbett, 1967) precipitation gauges are installed in forest clearings. Due to aerodynamic effects, the cleared areas sometimes dis- tort the conditions under which precipitation (particularly snow) falls, increasing its amount compared to that falling over the forest area. Precipitation gauges should therefore be installed in the centre of forest clearings, where the elevation above the horizontal of the line from the gauge orifice to the tops of the nearest trees is 30° - 500 for coniferous forest and 78O - 80° for deciduous forest (Fedorova, 1966).

under the forest canopy, snow survey data may be used, in addition to precipitation observations (Costin et al., 1961).

For the computation of precipitation over a large forest area

For the determination of the total monthly solid precipitation

3.3 River runoff

3.3.1 Normal runoff and selection of the Water balance period

The mean water discharge of normal runoff is a basic characteristic of the water resources of rivers. The accuracy of runoff determination depends on the accuracy of flow measurement and computation, on the variability of the flow, on the duration of the period of observations, and on the density of the gauging network (WO, 1970a; Van der Made, 1972; Davis and Langbein, 1972).

ies of observed values, is a statistical concept. Variations of runoff with time can therefore be fitted to statistical distribu- tions and may be investigated-by means of probability theory methods. The normal runoff (Q), the variation coefficient (C ), and the skew coefficient (C,) are parameters of the distribution curve of annual runoff.

time series, i.e. the physiographic factors that affect runoff formation and the construction and management of control structures on the rivers must not change during the period to be studied. The normal or mean annual runoff should be determined for a long obser-

Normal runoff, calculated as an arithmetic mean from the ser-

For statistical treatment it is essential to have homogeneous

24

computution of ComQonents

vational period which includes several, stream flow. The normal runoff may be

1 " o = - l Qi n i=1

where 0 is the normal runoff and Qi is

wet and dry cycles of computed from

the annual runoff in the i-th year tension of the series has only a slight affect on the value of Q.

A discussion of the accuracy of estimation of normal runoff and its mean square root error is given in Section 4.2.

For the determination of mean long-term runoff it is essential to have a period of observations which involves approximately the same number of dry and wet cycles of river flow. The greater the number of complete cycles of flow, the less will be the error of estimation of normal runoff. Since cyclic runoff variations are not synchronous for rivers separated by a great distance from each other, the use of a uniform period of observations for the compilation of runoff maps is not feasible.

The appropriate period for rivers in the same hydrological re-

of a long-term period of n years, such that further ex-

~~ ~

gion, where variations of runoff by a preliminary plotting of the

against n, for n = 1, 2, 3 ... ; standard deviation of the runoff Sokolovski, 19'68).

are in phase, should be determined integrated normalized runoff

where 6 and s are the mean and (Andrejanov, 1957; Kuzin 1970;

In the computation of normal runoff three cases may occur; (a) sufficient observational data are available; (b) only short- term observational data are available; and (c) there is a complete absence of observational data.

3.3.2 Computation of normal runoff using observational data

When hydrometric data are available for a relatively long time interval, the normal runoff is computed as the arithmetic mean of the whole observation series. To this end it is essential to have a series with two or three cycles of river flow. Where the series of observations is at least 50-60 years, the mean value may be computed from the whole series without considering cyclic variations.

series (10 years or less), it is essential to extend the series. For this purpose use is made of long-term series for adjacent gauged rivers situated in similar physiographic conditions. The avail- ability of sufficiently close relations between annual runoff at the specified station and at a base station with a long-term observational series is a necessary condition for the extension of short- term series. The extension of a short series may be performed by graphical and analytical methods; the first method is preferable since it shows the type and extent of the interrelations visually.

3.3.2.1 Graphical method. The reduction to norma1 rumff is made from graphical relations plotted for the whole observation period

When computing normal runoff from a short-term observational

25

Methods for water bakame computations

on the particular river and at the base station on the river to be used as an analogue. The relations between annual runoff may be linear or curvilinear. Curvilinear relations are used when it can be established that they are explained not by a chance distribution of points but by a real difference in the variations of runoff in the two rivers.

Linear relations are most often used and in this case the points should be evenly distributed on both sides of the adopted line. The position of the line may be defined more closely when it is plotted through annual runoff values of the same frequency, i.e. of similar probability of occurrence during the period of simultaneous observations. Such plotting of equi-frequency values is admissible only when the variations of annual runoff at the two stations are synchronous.

This type of rating curve will pass through the origin of co- ordinates only when the coefficients of variation of annual runoff at both points are approximately the same. The graphs,may be considered satisfactory if the number of points on the curve is not less than 8-10? with a correlation coefficient of 0.7 - 0.8. De- viations of individual points from the rating curve should not exceed 10-15% of the computed runoff value. Reliable results will be obtained if the graph is substantiated by points related to very dry and wet years (Fig. 1).

the short-term series can be determined from the normal runoff at the site with the long-term series, without calculation of the runoff values for individual years. When the relation is curvilinear, the runoff values at the short-term site are computed for all the years in the base series, except those used in the graph, and the mean is calculated for the complete computed series at the short- term station.

on the graph, it is possible to use the correlation method (Norden- son, 1968) or the analytical method which follows.

When the relation is linear, the normal runoff at the site with

Where there are gaps in the observations or a scatter of points

3.3.2.2 Analytical method. The reduction of runoff to a long-term period depends on the assumption that the curves relating the flows at the two sites pass through the origin of co-ordinates-and the ratio of flows in the two rivers for different time periods is constant.

observation series is In this case the normal runoff at the point with a short-term

where 0 and &., indicate normal runoff at the specified site and at the analogue site, and tj and tjan obs indicate average values of runoff for simultaneous short-term observational periods.

The computation of normal runoff from equation (9) should be done only when the compared rivers are in the same physiographic region, and have approximately the same drainage areas, relatively similar proportions of base flow and similar coefficients of varia-

26

Computation of Components

Fig. 1. Relations between annual discharge per unit area of the Emba river at Araltobe and the Ilek river at Aktubinsk and the Temir river at Leninski.

27

Methods for water bakznce compututions

tion. When there are significant differences in the coefficients of variation of annual runoff for the two rivers, large errors may result.

If it is impossible to obtain a runoff analogue for the short- term site, its series may'be extended by relating runoff to meteorological elements, primarily precipitation. The use of precipitation data for runoff computation is convenient because in many countries the number of precipitation stations is higher than the number of hydrometric stations, and precipitation records are available for longer time periods. The accuracy of this method is not high, and it should therefore be applied with great caution.

3.3.3 Computation of normal runoff without observational data

An approximate evaluation of normal runoff can be made with the use of one of the following methods: (1) a map of runoff isolines (See Section 3.3.4); (2) the analogue method; and (3) the water and heat balance equation.

3.3.3.1 Computation of normal runoff from a map of isolines

Runoff maps can be used to compute the mean long-term discharge for an ungauged river. To this end, individual areas of the ungauged basin between runoff isolines are measured by a planimeter (Fig. 2), and the value of each area is multiplied by the mean runoff depth between the isolines. by the basin area, provides the mean weighted runoff of the basin. Thus the mean runoff for a basin area A is computed from the equa- t ion :

The sum of the products so obtained, divided

where 0 is the unknown normal runoff, ai is a sub-area of the basin between two adjacent isolines with an average runoff depth Qi, and n is the number of such sub-areas.

tion by means of a map for a medium sized (5000-50 000 km2) basin is about 10% in the northern region of temperate latitudes, about 15% in central areas, and about 25% in southern arid regions. In the case of large rivers, this error tends to decrease to 8-10%.

membered that the maps are mainly based on interpolations between runoff data, and may therefore be considerably in error in some areas, althoughgiving an impression of precision. It is always advisable to examine the basis of the map in some detail, otherwise past errors may be carried forward into current assessment and planning.

For small rivers of the arid zone with incomplete drainage of underground flow, data on normal runoff taken from the map may differ greatly from actual values (either increased or decreased). In the USSR, use is made of regional correction coefficients, for the transition from the normal runoff of medium-sized rivers to runoff from small basins, computed from drainage area and the degree of incision

In the USSR, the mean error of normal annual runoff determina-

In using isoline maps to compute basin runoff, it should be re-

28

ComQutution of ComQonents

Fig. 2. An example of average discharge determination from runoff isolines.

29

Methods for water balance computalions

of the stream (Fig. 3), For rivers of mountain regions, additional graphs (Fig. 4) are used, showing relations between normal runoff and basin elevation and slope exposure. effect of azonal factors for small rivers should be introduced into n o m 1 runoff , taken from the map, and compared with mean values of this factor for basins for which normal runoff isolines have been plotted on the map.

Corrections for the

3.3.3.2 Computation of normal runoff by the analogue method

The analogue method can be used to determine normal runoff for an ungauged basin when the available maps of runoff isolines are inadequate. mal annual runoff in regions with only a few runoff isolines which have been plotted from data from an inadequate number of base stations.

paid to the similarity of the basins under comparison in relation to physiographic features (topography, geology, climate, soils, vegetation), hydrographic features (lake area, river network density etc), morphometric features (drainage area, slopes, etc.) and other characteristics .

If there is sufficient similarity between the basins under comparison in relation to the above characteristics, this provides a basis for transfer of runoff values from the base station to the ungauged basin.

short-term observation series are q and F, and those for the analogue are Qan and Pan, then

This method is applied for a preliminary evaluation of nor-

When selecting analogue basins, particular attention should be

If normal runoff and normal precipitation at the site with a

This method provides an approximate normal runoff value for poorly gauged rivers.

3.3.3.3 Computation of normal runoff by the water and heat balance equation

In poorly gauged regions, an approximate evaluation of normal runoff for medium and large rivers m&y be made by use of equation (5) for the water balance of a river basin for a long-term period; the normal runoff is the difference between mean precipitation and evaporation. The normal annual precipitation required may be obtained from climatic manuals or taken from a map of mean corrected precipitation. The normal annual evaporation may be obtained from the heat balance equation or by means of empirical formulae (See Section 3.4). For small basins with a typical runoff this method may give incorrect results, and it is undesirable in any case, for reasons stated earlier, to compute a major component of the hydrological cycle as a residual in the water balance equation.

3.3.4 Maps of runoff isolines

TO characterize the distribution of runoff over an area, and to compute runoff for the large numbers of basins with gaps in the hydro-

i.e.,

30


I

Fig. 3. Variation of mean discharge with catchment area in different zones of the European territory of the USSR.

31

Methods fw water bokrnce cm~tutions

Fig. 4. The graph of dependence of mean annual runoff on the average altitude of the basin for 5 regions with different slope ex- posures in the Caucasus.

32

Computution of Components

metric record, it is useful to compile maps of isolines of mean annual runoff. liminary computation of normal runoff for individual river basins is made on the basis of direct measurements. The data obtained, unlike meteorological elements (precipitation, temperature, etc. 1 are related to the centre of gravity of the basin and not to the gauging station. To plot the isolines, the hydrometric stations are plotted on the map, the basin boundaries are drawn, and the normal runoff values are plotted in the centre of each basin. On the basis of the plotted values, lines are drawn connecting points with similar normal runoff values, taking topography and other physiographic factors into account. In mountain areas the rate of variation of areal runoff is considerable and the pattern of isolines is complex.

rivers with runoff characteristics typical of their physiographic region. Data should not be used from small rivers, with runoff mainly determined by local factors, or from large rivers, which may flow through several physiographic regions and which give rise to uncertainty as to the point where the mean runoff should be plotted. On the other hand, observational data from large basins are important as a means of checking the plotting of the runoff isolines.

To prepare maps of runoff isolines for plains areas, it is advisable with drainage areas from 500-50 000 km2, and in mountain areas with drainage areas not larger than 500 - 1000 km2. where groundwater aquifers are shallow, the lower limits of these drainage areas may be decreased (e.g. in plains down to 300 lan2, and in mountains down to 100 lad). It is undesirable to use data from ephemeral water courses, since their runoff is often underestimated due to incomplete drainage of groundwater.

possible as an approximation to use runoff values computed by the water and heat balance method. In this case the runoff isolines should be shown in the map by a dotted line.

Verification of the correct plotting of runoff isolines is done by planimetering the areas between isolines and determining the runoff in all gauged basins. Where discrepancies occur, the position of the isolines is adjusted.

The appropriate scale for a runoff map depends on the number of observational points with known normal runoff, the evenness of its areal distribution, relations of runoff between adjacent points, and the effect of topography, geology, and other factors on runoff.

To characterize the gauging intensity for a region, its area is divided by the number of gauging stations. Ideally, the scale of the map should be selected so that the mean distance between gauging stations on the map is 10 nun, which provides sufficient information to interpolate isolines every 5 mm. Thus if the gauging intensity is 1 station per 100 km2, so that the mean distance between stations is 10 km, the scale of the map should be 1 : 1 000 000. Convenient scales for various gauging intensities are shown in Table 1.

To compile the map of normal annual runoff, a pre-

For plotting runoff maps, data are taken from medium-sized

to use data from rivers with an undisturbed water regime

In some cases,

For the areas in the map without hydrological stations, it is

33

Methods for water bakance computations

Table 1. Recommended scales for runoff maps in relation to the intensity of the stream gauging network.

Gauging intensity (km2/station)

100 500

1 000 5 000 10 000

Map scale

1 : 1 000 000 1 : 1 500 000 1 : 2 500 000 1 : 5 000 000 1 :10 000 000

I I

In mountain areas the scale of the map is selected according to the rate of change of runoff with elwation in such a way that the minimum distance between runoff isolines is no less than 2 mm. Where isolines are very closely spaced, the maximum and minimum isolines are plotted, and some intermediate lines are omitted.

Maps of mean annual values of water-balance components (precipitation, runoff , evaporation) should be co-ordinated with each other (Nordenson, 1968).

3.3.5 Separation of the runoff hydrograph into components

In the computation of water balances it is often desirable to separate runoff into surface and subsurface components, ip order to compute separate water balances for different water bodies (see, for example, Section 5.4). All the methods of runoff hydrograph separation are approximate, and depend on a conceptual model of the interaction between surface water and groundwater. Each method provides a technique for drawing a line on the stream hydrograph to separate the surface from the subsurface flow. Once this line has been drawn, the subsurface runoff can be computed by planimetering the area below the line.

tion of subsurface flow and rainfall flood flow is very difficult. The most simple technique is to make a graphic separation of the runoff hydrograph on the basis of the stable discharge that occurs during the low water period when the river is mainly fed by underground water (Popov, 1967). The separation is made by a horizontal line or smooth curve passing through the ordinates of winter discharge just before spring, with a slight rise to the wave of flood recession, and through the ordinates of discharges at the start of summer low flow (Fig. 5).

decreases sharply from the start,of spring runoff, and ceases completely during the flood crest (Fig. 6). The decrease of subsurface flow in this model is caused by the increased hydrostatic pressures of the flood wave on the groundwater flow, which may result in the outflow of river water into the groundwater of the val-

In some cases, subsurface flow is divided genetically into two

For rivers in plains, with a spring snowmelt flood, the separa-

According to a different model (Kudelin, 1966), subsurface flow

ley - types: (1) perched-alluvial and (2) deep underground. The latter

34

cu

U B


35


3l I-l 0 3

W 0

?% rd U bo 0

$4 a 2 G 0 .rl U (d $4 (d a

P) CA

Compulotion of Components

flow (shown by a horizontal line in Fig. 6) is characterized by greater stability.

by snow or a glacier. is more difficult than runoff separation for plains rivers.

Other techniques of hydrograph separation have been described by Meyboom (1961) and Linsley et al. (1949), while an extensive review of the literature on base flow recession has been given by Hall (1968).

In arid zones, the water-table is usually below the level of the stream bed, and the stream flow therefore recharges the ground- water. stream chaffinel can be determined by measuring the transmission loss, which is the difference between stream inflow and outflow for this part of the channel, corrected if necessary for the effect of tributary inflows and evaporation from the stream and riparian vege- tatioffi, This fs in fact another application of the water balance approach, but errors of measurement and estimation may be unaccep- tably high unless the stream reach is sufficiently long for a large part of the inflow to become transmission loss.

Fig. 7 illustrates runoff separation for a mountain river fed The separation of runoff for mountain rivers

The inflow to the groundwater below a given length of

3.4 3.4.1 General Evaporation from water surfaces (lakes and reservoirs) and from land (river basins) may be computed by:

1) evapor @et er s ; 2) water balance method; 3) heat balance method; 4) aerodynamic method; 5) empirical formulae.

3.4.1.1 List of symbols used only for evaporation Modifiers

I Symbol I Meaning

air area (of lake) back (radiation) bottom (of lake) depth (of lake) gross (radiation) net (radiation) potential (evaporation) pan or tank roughness (vegetation) she1 t er soil water height of observation

37

Methods for urater bakrnce computations

38

Compukztion of Components

Symbols

Symbol

e e*

h H

J

k

K L

Y r

P e

Meaning

empirical coefficients specific heat of water specific heat of air at

zero plane displacement balance duration para-

water vapour pressure saturated water vapour

specific humidity sensible heat flux dens it y heat energy content per unit surface area von Karman constant (0.428)

empirical coefficient latent heat of vapori-

number of days in a month atmospheric pressure albedo radiation balance period time wind velocity Bowen ratio ration of mole weights

psychrometric constant gradient of saturation vapour pressure curve against temperature

constant pressure

met er

pressure

zation of water

of water & air (0.622)

density temperature

Units

m - mb

mb

m3/kg Joule/m2

Joul elm2

Joule/kg

mb

Joule/m2 various ml sec

- -

-

3.4.2 Evaporation from water surfaces

3.4.2.1 Computation from evaporimeter data

Evaporation (EL) from lakes and reservoirs may be estimated from evaporimeter data by

EL = K Ep (12) where Ep is the evaporation from the pan or tank evaporimeter and K is an empirical coefficient. It is normal to compute evaporimeter coefficients on an annual basis, but in many comparison trials, monthly coefficients have been computed.

39

Methodsfor water balance computations

Evaporimeters used in estimnting lake evaporation should be installed either completely within or outside the area affected by the evaporating lake surface and the coefficients to be used must be selected accordingly.

meter coefficient K due to climatic, seasonal, instrumental and observational factors, but the method can provide a useful first approximation of annual lake evaporation and is applicable in the prediction of evaporation from proposed reservoirs.

The average annual value of K for the USSR GGI-3000 evaporimeter is 0.80, and for the US class A pan is 0.70 (WMO, 1966), but observational errors and other deficiencies may give these values an error of 2 0.10 in application. The value of K also varies re- gionally in relation to climate, being lower than the quoted values in the arid zone and higher in humid areas. in selecting an appropriate value for the proposed application, and use made of local or comparable data. For the USSR 20 m2 evaporation pan the mean coefficient has been expressed in the form K = KA&jKsh, where KA depends on the lake surface area, Kd on its depth and climatic zone, and Ksh on the degree of shelter from wind; values of these ocrrection coefficients are available in tables, such as those shown in Gidrometeoizdat (1969).

Seasonal variations in the evaporimeter coefficient K are usually large enough to preclude the use of a constant value. range of monthly coefficients depends on climate and lake depth and may exceed 0.7 in extreme cases (Australian Water Resources Council, 1970a). It is therefore unwise to use equation (12) for the estimation of monthly evaporation in the absence of knowledge of the seasonal variation of K appropriate for the climatic zone and the type of evaporimeter used. A table listing Class A pan coefficients determined by various investigations for several areas in the United States is given in Gray (1970).

able for estimating monthly or even daily lake evaporation, takes account of the different water surface temperatures of lake and evaporimeter. It can be expressed in the form

There is a large range in the value of the empirical evapori-

Care should be taken

The

A refinement of the simple coefficient formula, which is suit-

*

P E Z e L - e

e* - e = K'

P Z

where K' is a coefficient which depends mainly on the type of evaporimeter (and slightly on lake area); vapour pressures corresponding to the maximum eemperatures just below the lake surface and in the evaporimeter; vapour pressure measured at a height z.

For the US Class A pan evaporimeter and an observation height z = 4 m y the value of K' is 1.50 (Webb, 1966). Computed daily values of EL are summed to give the monthly evaporation.

height z = 2 m, the value of K', given in Gidrometeoizdat (1969), is 0.88. Mean monthly values of 4, e; and e, are used to compute the

4 and e* are the saturation and e, is the mean

For the USSR GGI-3000 floating evaporimeter and an observation

40

Computotion of components

mont hl y evaporation.

references, is contained in Australian Water Resources Council

3.4,2,2 Eter balance method

The equation for the determination of evaporation from lakes and reservoirs by the water balance method (Harbeck, 1958; Harbeck et - al, 1958; 'vikulina, 1965) is as follows:

A comprehensive guide to available techniques, with over 400

E L = PL - ASL -k AQs + AQ, where EL is evaporation from the lake or reservoir, PL is precipitation on the surface of the water body, ASL is the change of water storage in the water body, AQ, = (QsI - Qso) is the difference between surface inflow and outflow from the water body, and hQu = ( Q u ~ - Quo) is -the difference between underground inflow and outflow (see Section 5.2).

The application of the water ba1anc.e method is limited, since in most cases the flow through the lake bottom cannot be measured. However geological and other considerations may indicate that this term is negligible compared with the other components of the water balance, and it can then be omitted from equation (14). Over a sufficiently long period the change in water storage also becomes negligible compared with the other components, and the equation for the total evaporation therefore becomes

E = PL + AQ S

Thi.s value can be divided by the number of years of record to obtain the mean annual evaporation. Equation (15) can also be used to determine annual evaporation values for lakes which return to approximately the same level each year, and which also have negligible water flows through the lake bottom.

3.4.2.3 Heat balance method

This method (WO, 1966) is used for the computation of evaporation from the water surface (EL) if the data necessary for the determination of heat balance components are available. The equation of heat balance for 1 m2 of the lake surface is

QQo Rn+Ha*€ib-AJ * aJs * mu * Hp - JE ) %=- where pw and L are the density and latent heat of vaporization of water, R, is the incoming net radiation, Ha and Hb are the sensible heat inflow at the lake surface and bottom, AJ is the increase in the heat content of the water body during the balance period, AJS = J,I - JSo and AJu = JU1 - J,o are the difference between heat input and output due to surface and underground inflow and outflow, Hp is the sensible heat input due to differences between the.temperature of precipitation and the lake temperature, and JE is the heat

41

Metbodsfor water balance computations

content of the water layer evaporated from the water body at the given tem erature.

the whole lake is divided by the lake surface area.

Note that all terms must be related to unit area (1 m 3 ) of the lake surface, i.e. each heat input or output for

The net radiation (%) is given by

R n = R (l-r)-R,, g

where Rg is the gross incoming radiation (sum of direct and diffuse solar radiation), r is the albedo of the water surface, and Rb is the effective back long-wave radiation from the water surface.

Equation (16) requires many careful measurements to establish the values of the different terms. At present it is more suitable for research studies than for general use.

Another application of the heat budget method, which makes use of the Bowen ratio (Anderson, 1954; Harbeck et al, 1958; Webb, 1960, 1965), can be expressed in the form

1 000 Rn - AJ + AJs + Mu 1 + B + (c/L) (eo - e,) %=c

where c is the specific heat of water, is the average temperature of the evaporating water, 8, is the average temperature of the water inflow which replaces evaporated water, and 6 is the Bowen ratio, defined by

'Cp AOa B = , L ~e

where p is the atmospheric pressure, cp, is the specific heat of air at constant pressure, E = 0.622 is the ratio of mole weights of water and air, and Aoa and A e are the differences of air temperature and vapour pressure, measured over the same height interval.

To evaluate U, temperature soundings throughout the depth of the lake (generally to 0'loC) must be made at a number of positions. For medium and large lakes, the period between soundings must generally be at least 2-3 weeks, but in small lakes a shorter balance period is possible.

cause errors in EL, which can be eliminated if an approximate mea- suremP-nt of the variation in wind speed is also available (Webb, 1964, 1965).

Variation of the Bowen ratio during the balance period can

3.4.2.4 Aerodynamic method The aerodynamic method (also known as the method of turbulent diffusion) is suitable only for sites where the necessary instruments can be properly maintained and observed. relationships connecting vertical fluxes with the mean vertical gradient, and depends on assumptions regarding the nature of the wind velocity profile above the lake surface (WMO, 1966).

culated from

It depends on aerodynamic

Applied to a short time lliterval, the evaporation may be cal-

42

cornflutotion ofcmQoonents

- 1 000 k 2pa (h2-hl) (u4 - u3) EL = In (z2/zl> . In (z4/z3>

where EL is the evaporation in mm/sec, hi and h2 are the specific air humidity at heights z1 and 22 over the evaporating surface, u3 and u4 are the wind velocities at heights 23 and 24, k = 0.43 is von Karman’s constant, and pa is the density of the air.

Equation (20) applies to a flat homogeneous surface without horizontal moisture transfer (advection), and where equilibrium conditions exist, i.e. the effects of temperature stratification in the lower layers of the atmosphere can be neglected. temperature stratification is of major importance at small wind velocities (less than 3 m/sec), and when there is a great difference (more than 5OC) between water surface temperature and air temperature at a height of 2 m. If the difference between the temperature of water and air is less than 3-4OC, then the effects of temperature stratification may be neglected at any wind velocity.

3.4.2.5 Empirical formulae

There are many empirical formulae for evaporation, that may be divided into two groups: a) surface on wind velocity and on the difference of vapour pressure at the evaporating surface and at some height above ic (method of mass transfer or bulk aerodynamic method) , b) formulae using climatological data, and usually based on the approximate solution of the simultaneous equations of water and heat balance (compl’ex or combination method).

The most useful formulae of the first group are empirical bino- mial formulae of the type

The effect of

formulae based on the dependence of evaporation from the water

= (a + bu) (e: - monomial formulae of the

E = cu (e* L s - ez) and formulae of the type

E = a (e* - e,)b L S

where U is the wind velocity, e: is the saturated vapour pressure at the water surface, e, is the vapour pressure at an observation height z, and a, b, C are empirical coefficients, which depend on the dimensions and exposure of the evaporating surface, and the climatic region.

When equation (21) is applied to the computation of daily evaporation from the water surface of the USSR 20 m2 evaporation tank, with the wind velocity and vapour pressure measured at a height of 2 m above the surface, the coefficients have the values a = 0.15 and b = 0.108. Similarly for the US Class A pan, with the wind velocity measured 150 mm above the water surface, a = 0.32 and

43

Metbodsfor water bakance computations

b = 0.161 (Kohler, Nordenson et al., 1959). Equation (22) has been applied to lakes in the United States

(Harbeck, 1962), with the wind velocity and water vapour pressure both measured 2 m above the water surface. The mean value of C (for daily evaporation) is then 0.131, but depends to some extent .on lake area, as described in the reference.

Romania, where b = 0.85 and a varies between 0.42 and 0.82 (Stoenescu, 1969; Badescu, 1974).

The formulae of the second group use climatological rather than meteorological data, and are generally applied to calculate annual evaporation for lakes of medium or large depth, due to errors caused by changes in heat storage in such lakes over shorter periods. They may be applied on a monthly basis to shallow lakes, and in the case of the combination formula, corrections may be applied (Kohler and Parmele, 1967) to enable application on a monthly basis to deeper lakes also.

Webb, 1965) are based on a combination of the energy balance and aerodynamic transport equations, assuming that information about vapour pressure and temperature at the surface is available. The best known form is that of Penman (1956), which can be used to estimate lake evaporation from

Equation (23) has been used to compute daily evaporation in

Combination formulae (Penman, 1956; Slatyer and McIlroy, 1961;

Y cu (e; - ez) (24) r 1000 Rn

T + Y P w L T + Y EL=-

where r is the gradient of the saturation vapour pressure curve against temperature, y is the psychrometric constant, R, is the net radiation received at the lake surface, pw and L are the density and latent heat of vaporization of water, C is the same constant as in equation (22) (adjusted for the length of the evaluation period), U is the wind speed at the observation height used for the evaluation of C, e: is the saturation vapour pressure at the temperature of the air at height z, and e, is the vapour pressure of the air at height z.

and in general this will differ from net radiation measured over a land surface. and diffuse short-wave radiation are available (Anderson, 1954; Van Wijk and Scholte-Ubing, 1963; Swinbank, 1963; Anderson and Baker, 1967; Kohler and Parmele, 1967). Other references give useful information on applying combination formulas In practice (Hounam, 1958; Tanner and Pelton, 1960; Fitzpatrick and Stern, 1966; Van Bavel, 1966).

Class A pans has been developed by the U.S. Weather Bureau (Kohler, Nordenson et al., 1955, 1959; Stall and Roberts, 1967).

voirs, the following formula (Gidrometeoizdat, 1969) is used in all areas of the USSR:

The net radiation (%) required is that over the lake water,

Appropriate methods of adjusting the incoming direct

A nomogram approach to compute evaporation from lakes and

To compute the mean monthly evaporation from lakes and reser-

44

Computution oj Components

* E = 0.14 n (es - ez) (1 + 0 - 72 uz) L where n is the number of days in the month, e: is the saturation vapour pressure corresponding to the water surface temperature 8 , and eZ and uz are the vapour pressure and wind speed at a height z = 2 m above the water surface. Note that e:, eZ and uz are determined from measurements taken over the water body, and averaged for the whole month over the area of the water body.

If observations over the water body are not available, observational data of meteorological stations located on land are used. The adjustment from land observations uIZt , e'Z 1 , B V z to the sorres- ponding values uz, e, and 8, for the water body is made by

uz = K K K u t 1 2 3 z' *

e = el + K4 (0.8 es - el) z e = e' + K~ (e - e; 1 z z

where U' of the anemometer (about 10 m), and K ents which depend on the laws of air tiow variation over the land- water interface. The coefficients are obtained from tables in Gidrometeoizdat (1969), relating K1 to the location and degree of wind protection of the meteorological station, K to the character of relief around the station, 4 to the mean win3 run above the water surface and the degree of reservoir protection against wind, and K to the mean wind run above the water surface and the relation between the water temperature and air temperature. The numerical values of the coefficients vary according to physiographic features. For example, for stations located in the forest zone, 5 ranges from 1.3 in grassed areas to 2.4 in the forest; and for stations in open areas, from 1.0 in the steppe to 1.5 in towns and densely populated areas. station is on top of a hill to 1.3 on the floor of a valley or de- pression. For a reservoir with the shores covered by forest 20 m high, the coefficient K3 varies, according to the area of the reservoir, from 0.25, when the mean length of wind run over the reservoir is 100 m, to 1.00 when it is more than 5 lan. The coefficient K4, under conditions of small differences between water and air temperatures, ranges from 0.02 for a mean length of wind run of 100 m to 0.34 for a mean length of wind run of 20 lan.

8 is estimated from the simplified heat balance equation

is the mean wind velocity at the standard height Z ? 2'

K2, K and K4 are coeffici- 3

4

The coefficient K2 ranges from 0.75 when the

In the absence of measurements, the water surface temperature

E = - ' Oo0 (R, + Ha + HB) pw

which is first applied to a hypothetical water body with a very small depth and with water surface temperature equal to air temperature, and then empirical corrections are introduced to adjust for

45

Methodsfor umter bakmce conrpututions

the water depth and the difference between air and water temperature, (Gidrometeoizdat, 1969). from 8.

The value of et is then obtained

3.4.2.6 Effect of aquatic plants

Transpiration through the leaves of floating and emergent aquatic plants may have a major effect on the evaporation from a lake or reservoir. This effect is difficult to measure accurately, and data derived from experiments under artificial conditions are unlikely to be reliable indicators of natural situations. measurements of transpiration by aquatic plants in natural conditions are also unlikely to be precise, if the method employed involves isolation of the whole plant, or a part of it, as this inter- f erence would almost certainly affect its transpiration rate.

covered by aquatic plants may be determined by direct application of the water balance method (Section 3.4.2.2) or the aerodynamic method (Section 3.4.2.4). The energy balance (Section 3.4.2.3), Bowen ratio (Section 3.4.2.3) and combination (Section 3.4.2.5) methods may also be adapted for this purpose, provided careful allowance is made for the possible effects of the plants on the microclimate near the water surface.

in the form of a correction coefficient Kpl, defined as the ratio of the evaporation and transpiration from a plant-covered lake or reservoir, to the open-water evaporation that would have occurred under the same. climatic conditions.

values for floating plants such as Eichhornia Crassipes (water hyacinth) or Salvinia molesta range from 0.45 to 6.6 (Penfound & Earle, 1948; Little, 1967; Timmer & Weldon, 1967; Mitchell, 1970). For these plants, values of KPl appear to increase with an increase in temperature, a decrease in humidity, and an increase in the size and vigour of the plants.

Experimental data for emergent plants, such as reeds, not directly related to open-water evaporation values, have been reported by Rudescu et al., (1965), Burian (1971), and Haslam (1970); and by Guscio et al.

In the USSK, values of Kpl have been found to be independent of the kind of vegetation, but can only be applied to mean seasonal values for small to medium lakes and reservoirs. The correction coefficients have been related to the area of the water body occupied by the emergent plants. the USSR, the values of Kp1 arel.14, 1.22 and 1.3 for 50, 75 and 100 percent cover respectively. For steppe and semi-desert zones, the corresponding values are 1.24, 1.37 and 1.5 (Gidrometeoizdat , 1969).

mites and Typha stands in an arid region in Australia, and by Rijks (1969) in African papyrus swamps indicate that E"pl may be less than 1 under conditions of lower humidity. ed that this was caused by a combination of factors, including

Direct

The total evaporation from a water surface partially or wholly

The results of experimental work may be conveniently expressed

In humid regions, KP1 is generally gi-eater than 1;

(1965) for Typha spp in the United States.

For forest and forest-steppe zones of

In contrast, measurements by Linacre et al. (1970) in Phrag-

The former workers consider-

46


sheltering of the water surface by the reed plants, their higher degree of reflectivity (albedo) and their internal resistance to water movement during dry periods. vegetation may also be significant . miking assumptions about the effect of aquatic plants on evaporation from water surfaces. In situations where the effect may be a significant component of the water balance under consideration, a special program of measurements should be undertaken.

3.4.3 Evaporation from land

When computing the mean long-term evaporation from large plains river basins, the most accurate results are obtained by the water balance method (Gidrometeoizdat, 1967). For mountain regions there are no reliable methods for measurement of evaporation, and the usual approach is to estimate the variation of evaporation with elevation and slope orientation, using direct measurements and computational methods.

3.4.3.1 Computation from soil evaporimeter and lysimeter data

Monthly evaporation from the soil in individual months may be obtained with the aid of weighing, hydraulic and other soil evaporimeters and lysimeters of various designs (Toebes and Oury~aev,1970). Since evaporation depends greatly on vegetation, soil cover and other landscape conditions, these devices should be installed as far as possible in each of the types of vegetation cover (field, forest, etc.) which occupy the river basin. The mean evaporation from the basin is computed from a knowledge of the area occupied by the various types of vegetation cover.

3.4.3.1.1

The presence of senescent and dead

It is clear from these data that caution must be exercised in

Measurements of evaporation from snow cover by evapori- met er s

For river basins in middle latitudes which are completely or partially covered by snow every year, evaporation during snow cover periods can be measured by weighing evaporimeters of special design (Toebes and Ouryvaev, 1970).

3.4.3.2 Water balance method

The water balance method gives evaporation as a residual term of the water balance equation and is therefore subject to an unknown error. The water balance method is most frequently used for the computation of the mean evaporation from large river basins using

E = P - Q S

For the determination of evaporation for a particular month the water balance equation for the upper layer of the aeration zone is

E * P - Qs - + Quc - QUP (31)

where Dl is the increase in soil water storage in the water balance period, gC is the ascending flow of water into the aeration zone

47

Methods for water balance compututions

v is the down- from the capillary fringe of the water-table, and ward flow of water from the aeration zone to the wa er-table.

Methods for computing the net drainage term Qup - Quc (Rose and Stern, 1965) involve some difficult measurements and are not suitable for routine use on the scale of a river basin. However, in low rainfall areas it may be established that percolation from rainfall does not reach the water-table and that the water-table is sufficiently deep (more than 4-5 m) so that upward flows are negligible. In these circumstances , equation (31) becomes

E = P - Qs - AM (32) Methods for estimating changes in soil moisture AM are described in Section 3.5.3. 3.4.3.3 Heat balance method

Starting from the simplified heat balance equation (29), and assuming the same eddy transfer coefficient for water vapour and sensible heat, the evaporation can be expressed as

where R, is the net radiation, Hso is the heat flux into the soil, 45 and L are the density and latent heat of vaporization of water, and B is the Bowen ratio, defined in equation (19) (Section 3.4.2.3). on a routine basis. As equation (33) does not take into account the horizontal gradient of turbulent heat exchange (advection) , it is restricted to use on large areas of flat land with uniform vegetation.

The use of the Bowen ratio does not take into consideration the influence of temperature stratification. ence, the gradients A0 and Ae should be measured as close as pract- icable to the ground (under conditions of high radiation, the height should be from 0.1 to 0.2 m and under normal conditions up to 1 m). Equation (33) is not suitable for use in arid regions.

This method is more suitable for use on research stations than

To minimize this inf lu-

3.4.3.4 Aerodynamic method

To determine evapotranspiration by the aerodynamic method, equation (18) for a water surface is recommended. In this case, however, it is necessary to take into account the influence of advection and temperature stratification. To exclude the inf hence of advection, the measurements of gradients of vapour pressure and wind speed are made on flat terrain with homogeneous vegetation. Brogmus (1952) proposes methods for determining corrections for temperature strat- if ica t ion.

tation (and soil water storage) and the difficulties of keeping instruments functioning properly over long periods, it is unlikely that these methods can be used on a routine basis.

Because of the requirements of large areas of flat uniform vege-

48


3.4.3.5 Empirical methods

Empirical methods for the determination of evaporation, unlike balance methods, are based on averaged meteorological data, such as air temperature and humidity, wind velocity, cloudiness, and duration of sunshine. Some methods also use data on evaporation from the water surface of an evaporimeter.

3.4.3.5.1 The generalized combination method

The combination formula (Tanner & Fuchsp 1968; McIlroy, 1968; Fle- ming, 1968; Australian Water Resources Council, 1970b) is derived from the energy balance equation and the transport equations for sensible and latent heat, and can be expressed as

where pw and L are the density and latent heat of vaporization of water, r is the gradient of the saturation vapour pressure curve against temperature, y is the psychrometric constant, I$, is the net radiation, Hso is the heat flux into the soil, pa and “p are the density of air and its specific heat at constant pressure, es and e, are the water vapour pressure at the surface and at a height z above it, e: and e: are the saturation vapour pressures corresponding to the temperatures at the surface and at a height z above it, T is the balance period, and f(u) is a function of wind speed. The value of r is computed for the average of the temperatures at the surface and at .a height z above it.

ticular type of vegetated surface and a limited range of climatic conditions. Examples of such equations are given in the references quoted. When the dimensions of the evaporating area are sufficiently large, f (U) can be determined from wind profile theory, as in the KEYPS profile (Sellers 1965) :

The value of f(u) is usually determin’ed empirically for a par-

where k = 0.43 is the von Karman constant, uz is the -wind speed at a height z, CP is the diabatic profile parameter, d is the zero plane displacement, and zr is the roughness length. can be determined by experimental observations of the wind profile near the vegetated surface under study. Over irrigated vegetation, it is satisfactory to put CP = 0 (Tanner and Pelton, 1960; Van Bavel, 1966) e

evaporation E, is then given by

Values of d and zp

When the evaporating surface is wet, e, = e:, and the potential

The potential evaporation is the evaporation which would occur from any surface under a given set of meteorological conditions, if there were a condition of non-limiting water supply at the surface.

49

Methods for mater balance computations

Equations (34) and (36) can be combined in such a way as to eliminate the vapour pressure es at the evaporating surface, so that the only surface measurement required is the temperature. The resulting equation relating waporation to potential waporation is

For application of combination formulae to vegetated surfaces, the net radiation Rn is usually measured directly with net radiometers (Fritschen and van Wijk, 1959; Funk, 1959), and the soil heat flux Hso is either measured directly using soil heat flux pla- tes (Monteith, 1958; Philip, 1961) or computed from the temperature profile (van Wijk, 1963).

3.4.3.5.2 Other empirical methods

In England, evaporation Eo from a large area of normally growing closed grass cover, properly supplied with water, is linearly related to evaporation E evaporimeter (Penman, f956) :

from the water surface of the British'sunken

Eo = fE P

The coefficient f for the south-eastern part of England varies between 0.6 in the winter and 0.8 in the summer, with a mean annual value of 0.75.

determination of evaporation from well-watered vegetative cover: Blaney and Criddle (1950) proposed a formula suitable for the

Eo = 45.8 KIP (e + 17.8) (39)

where Eo is ,evapotranspiration from iirigated fields for a vegetative period,K is a coefficient determined experimentally for each type of vegetation, D is the ratio of duration of daylight hours during a particular month to its annual sum, and e is the mean monthly air temp erat ur e.

ors (Blaney, 1954a, 1954b; Penman, 1963) for irrigated crops in the western USA are given in Table 2.

Table 2.

Numerical values of the coefficient K established by the auth-

Values of Blaney and Criddle's K for various crops.

Crop or Farm Land I I

Alfalfa Bean Maize Cotton Flax Cereals

Duration of the Vegetative Period (months)

Free-of-f rost period 3 4 7 7 -8 3

K

0.8 0-0.8 5 0.60-0.70 0.75-0.85 0.60-0.65 0.80 .

0.75-0.85

50


Crop or Farm Land

Sorghum Citrus Walnut Other fruit trees Pasture Clover pasture Potato Rice Sugar beet Tomato Vegetables

- -~

Duration of the Vegetative Period (months)

4-5 7 Free-of-frost period Free-of -f rost period Free-of-frost period Free-o f -f rost period 3-5 3 -5 6 4 3

K

0.70 0.50-0.65 0.70 0.60-0.7 0 0.75 0.80-0.85 0.65-0.75 1.00-1.20 0.65-0.75 0.70 0.60

The lower K value in the table for each crop corresponds to the climate of coastal areas, and the higher K value to the climate of arid zones.

evaporation from irrigated land in areas of little cloudiness. Ac- cording to approximate estimates, the error of the method for mean values of annual and growing period evaporation is of the order of 15 to 25 per cent.

Thornthwaite and Holzman (1942) developed the following equation for maximum possible monthly potential evaporation:-

Blaney and Criddle's method may be recommended for computing

Eo = 16 D' ( 7 where D' is the total monthly duration of daytime, expressed as a ratio of 360 hours, a = 0.93/(2.45 - In i), 8 is the mean monthly air temperature: dices i =(8/5)"614 for all 12 months of the year.

Turc (1955) proposed the formula

i is the sum of monthly values of temperature in-

To compute the mean annual evaporation from catchment areas,

where P is the annual precipitation and Eo is the evaporation oppor- tunity (maximum possible evaporation under given meteorological conditions and sufficient soil moisture). Turc assumes that the value of the parameter n is equal to 2 and determines Eo-as a function of the mean air temperature e (Eo = 300 + 258 + 0.05 03). equation may be used for the computation of evaporation from small areas and for short periods of time; for this purpose, in formula (41) P should be replaced by P + AM, where AM is the soil moisture lost in the form of evaporation during the balance period.

Konstantinov (1968) has proposed a method for the computation of mean evaporation in plains areas of water surplus and approximate water balance, using air temperature and humidity measured at a height of 2 m in the shelter of a meteorological station. annual evaporation is determined directly by a nomogram (Fig. 8)

The same

The mean

51

Methods for wler balance compututions

Fig. 8. Graph for the computation of annual evaporation (nrmlyear) from soil according to mean annual temperature (OC) and air humidity, measured at an altitude of 2 m.

52


relating it to mean annual values of temperature and absolute hwi- dity. The values, determined by the nomogram, characterize evaporation from an area of several square kilometers surrounding the meteorological stat ion

reliable because of the seasonal lag between temperature and radiation (which is supplying the energy). Estimating formulae should take the energy balance into account either explicitly or implicitly.

3.4.3.6 Methods used in the USSR In the USSR, Budyko (1956) has developed methods to determine mean evaporation from large areas for different types of surfaces, and also for individual months and years. The mean annual evaporation can be determined by means of

Methods which estdte evaporation from air temperature are not

where wet vegetation, and pw and L are the density and latent heat of vaporization of water.

Annual values of R, have been mapped and can be determined for any given point. The relative mean square error of computation by formula (42)is about 17%.

it is necessary to have data on precipitation (P), runoff (Q), temperature (0) and vapour pressure (e). Under conditions of water deficit, the computation for summer months uses

is the mean annual precipitation, Rn is the net radiation on

For Budyko's method for determining mean monthly evaporation,

E = E if MI + M2 2 2M0

The water storage in the upper 1 m layer of soil for the beginning of the first warm month, MI, is approximately determined by a spec- ially plotted map, while for all following months it is computed by the formula

M = M + P - Q - Eo if M1 -k M2 2 2M0 2 1

The maximum possible evaporation (E,) is computed by special nomograms, depending on the deficit of air humidity (e*2 - e2) where e2 is the vapour pressure 2m above the surface, and e2 is the saturated vapour pressure at the air temperature 2m above the surface. The critical water storage (Q) is determined by tabulated data depending on mean monthly air temperature and geobotanic zone. The

53


relative mean error of computation of monthly evaporation by this method is about 25%.

ing formulae (Kuzmin, 1953; Konoplyantsev, 1970). Daily evaporation from snow cover can be computed by the follow-

* E = (0.18 + 0.98 ul0) (esn - e2) and

* E = (0.24 + 0.04 ul0) (e2 - e2)

(45)

* * where 1110, e,,, e2, and e2 are the mean daily values of wind velocity, saturated vapour pressure corresponding to snow surface temperature and air temperature, and vapour pressure, respectively. The numbers10 and 2 below the symbols indicate the height above snow surface in metres at which the corresponding measurements are made. Monthly evaporation from snow is determined by these formulae with a relative standard error of about 30%.

diation balance of the swamp surface (Romanov, 1961):- Mean monthly evaporation from swamps is determined from the ra-

E = $Rn (47)

where the coefficient I), which varies from month to month, is taken from empirical tables, taking account of the type of swamp, while the net radiation I$, (k-cal/cm2 per month) is computed by one of the known methods using standard meteorological data.

son is computed by the equation Evaporation from forests in individual months of the warm sea-

CE = * c Eo where the coefficient $ is determined from the radiation index of aridity c%/(L 1 P); Eo has the same value as in equation (43) and is determined by the same nomograms depending on the deficit of air humidity; Q is here the net radiation of the surface with different surface covers (meadow, fallow land, etc.), measured at meteorological stations. The sums CEO, CR and CP are computed by consecu- tive summations beginning with the first warm m0nth:separately for May (V), then for two months, May and June (V-VI), then for three months, May, June and July (V-VII) , etc. up to the end of the last warm month - May-September (V-IX). equation (48), evaporation from a forest for an individual month, say for July, is determined by

From the sums CE determined by

VI1 VI

To determine evaporation from irrigated areas, the heat balance method is used. The evaporation is given by

54


where the net radiation Rn is determined directly, and the value of heat flux into the soil (€Iso) is computed from measurements of soil temperature at depths of 5,100, 150 and 200 mm. Combining the solutions of equations (33) and (49), the following is obtained:

C R ~ - H~,) A e - Ha - A0 + 1.56 Ae

which is used to compute the turbulent heat flux when (R, - Hso) > 0.10 kcal/cm2 per min, A8>0.loC, Ae >, 1 mb.

the turbulent heat flux is determined from If (G - Hs) < 0.10, or one of the valuesA0 or Ae is negative, H~ = 1.35 me (51)

The gradients A0 and de and the coefficient of turbulent exchange K are determined from experimental data on wind velocity, temperature and humidity of the air at two heights above the zero surface (0.5 and 2 m). The term ”zero surface” refers to the level at which wind velocity equals zero.

evaporation by the above heat balance method is 15%. The magnitude of errors of computed evaporation values is determined by reference to the values obtained with soil evaporimeters and lysimeters or to those calculated by the water-balance method.

3.4.4 Maps of evaporation

On the basis of computed values of evaporation obtained usually by the water balance method, maps of evaporation from river basins are drawn from which evaporation from unstudied basins is determined. Methods are described by Nordenson (1968) ; W O (1970b) ; Gidrometeo- izdat (1967).

Maps of evaporation from water surfaces are usually plotted from evaporimeter data.

3.5 Variations of water storage in river basins

3.5.1 General

As was mentioned in Section 2.2, variations of water storage in a river basin must be taken into account both when computing the water balance for short periods of time (individual year, season, month, or shorter period) and when computing mean seasonal and monthly water balances.

All the terms of the water balance equation which characterize water storage variations are determined by calculating the difference between water storage at the end and at the beginning of the balance period.

The relative standard error when determining lO-day values of

Water storage in river basins includes

55

Methods for mater balance computatiom

(a) water storage on the surface of the basin (Ss); (b) water storage in soil and in the unsaturated zone (M); and (c) ground-water storage (G) . In temperate and cold climates with stable snow cover, the

main water accumulation takes place in winter, while in warm and hot climates it occurs during the rainy season. Water balances of these two types differ in that solid precipitation accumulated in the form of snow cover in the first type forms runoff only after a long delay, while in the second type the liquid precipitation joins the hydrological process immediately upon falling or after a short delay.

3.5.2 Surface water storage

Accumulation of water on the basin surface is composed of: (1) rain water, detained in micro-depressions; (2) water storage in the solid state (snow cover, firn fields,

(3) water storage in the hydrographic network (river channels, glaciers) ;

lakes, reservoirs, swamps).

3.5.2.1 Detention of water in micro-depressions

Accumulation of water in micro-depressions (in puddles and pools after rain and showers) usually does not last long, and is therefore difficult to take into account and measure accurately. is quickly lost by evaporation and by infiltration into the soil, so that it is taken into account by other terms of the water balance equation.

This water

3.5.2.2 Water storage in the solid state

Variations of water stored in snow cover are evaluated by regular snow surveys along special routes, covering the river basin as evenly as possible and taking into account the characteristic features of the terrain.

The techniques of measurement and computation of snow storage are described in the literature (WO, 1970a; Kuzmin, 1960; Toebes & Ouryvaev, 1970).

Methods for evaluation of water storage variations in f irn fields are given in Section 5.5.

3.5.2.3 Water volume in lakes and reservoirs

Water accumulation in lakes and reservoirs depends on the capacity of the water bodies, the area of lakes in the basin and the ampli- tude of water-level fluctuations in the balance period.

Lake storage should be taken into account if there is as much as 2-3% of lake area in the basin.

To compute water volume variations in lakes and reservoirs, use is made of curves relating the water volume in the lake to the mean water-level.

lakes and reservoirs to an accuracy of 10 m, it is necessary to obtain information about water -levels from a rationally located, network of gauges, which takes into account the special features of the water body and,, if possible, excludes the distorting influence of

To ensure the computation of the mean water-level for large

56


Symbol Meaning

b p bzs 6, C, 11, (i, K empirical coefficients

relative water stage fluctuations.

and wind-induced set-up, and in reservoirs, also by long period waves caused by the unsteady operation regime of power plants. exclude the effect of wind-induced set-up and seiches, water gauges on large shallow lakes and wide reservoirs are located near the centre of gravity of the water body ("axes of equilibrium"), where relative water-level fluctuations are small. On long river reser- voirss where a considerable slope of the water surface is periodi- cally observed, the gauges are installed on the banks along the reservoir (Figs. 9, 10). For mountain lakes characterized by a complex circulation of air fluxes over the water surface and where movement of the water mass in a single direction is consequently not observed, the gauges are located on the periphery of the lake and on islands so that local level fluctuations can be excluded.

To compute the change of water volume ASz in the lake or reservoir its mean water level is determined for the given date. The mean water-level of shallow lakes and wide reservoirs is obtained directly from the readings of a gauge (or gauges) affected as little as possible by the wind. is determined separately for reaches with different slopes of the water surface. The mean water-level of deep lakes is determined as the weighted average of the readings of all operating gauges.

The volume of water in the water body for the given date is determined from the mean water-level and the curve relating volumes to wa t er-level s.

The change of water volume for the balance period is calculated as the difference between water volume at the beginning and at the end of the period.

For reservoirs with a distinct slope, separate stage-volume curves for each reach are used, i.e. the water volume is determined for separate reaches by the arithmetic mean water level obtained from readings of gauges located on the given reach.

the change of water volume is determined for each lake or reservoir separately.

where fluctuations of the water level result in large variations of the surface area, the mean water level may be accurately determined only if there is reliable altitude co-ordination of all the gauge datums. In the USSR, the method of water levelling is widely used to co-ordinate gauge datums (Karaushev, 1969). This method helps to avoid inconsistency of gauge readings and enables the establishment of a comon zero datum for all gauges operating on the water body.

3.5.2.4 Channel storage in a river basin

The following specific symbols are used in this section:

Relative fluctuations of levels of lakes are caused by seiches

To

The mean water-level of river reservoirs

If there are several lakes or reservoirs in the riser basin,

For all tater bodies, and especially for reservoirs and lakes

Units

var io ti s -

57

Methods bahnce N

S

Fig. 9. Scheme of gauge location and axes of equilibrium for the Rybinsk Reservoir. The axes of equilibrium correspond to the wind direction: 1. northern and southern; 2. western and eastern; 3. north-western and south-eastern; 4. north- eastern and south-western; 5. gauges.

3 4

e5

---- ...........

Fig. 10. Diagram of the location of gauges and axes of equilibrium on the Kuibyshev Reservoir. pond to the wind direction: 2. western and eastern;

The axes of equilibrium corres- 1. northern and southern;

3. north-western and south-eastern; 58 4. north-eastern and south-western; 5. gauges.


Meaning

slope of water surface distance of site from

drainage area ratio discharge per unit basin

stream velocity lag (travel) time for a stream reach

mouth of river

area

Units

per thousand lal

m/ sec sec

Estimates of the change of channel storage in a river basin are made only for periods of flood rises and falls and for months when there are considerably different discharges between the beginning and the end of the month.

is convenient to subdivide them into large, medium and small (Nezhi- khovski, 1967). A large drainage network is assumed to include all river channel stretches which are bounded upstream by gauge lines situated at equal distances (1) from the river mouth (where 1 is 50, 100 or 150 lan) and downstream by the outlet gauge. All the rest of the drainage network is treated as medium or small.

In drainage basins with an area between 15000 and 100000 lan2 and with a fairly dense observational network gauge lines are chosen at a distance of 100 km from the mouth. In the case of a more sparse observation network, the distance is 150 lan. For smaller basins (less than 15000 Ian2) 1 is taken as 50 km and for large basins (more than 100 000 km2) 1 is set at 150 lan.

The large drainage network so defined is subdivided in its turn into river sections without lateral inflow, with their ends at the mouths of large river arms. If such division is impossible the boundaries of the sections should be at the gauging stations.

discharge Qj in this section at the specified date, and the lag time

For the estimation of channel storage in drainage networks, it

The channel storage for a section j is estimated from the mean

Tj . To estimate Qj in a section with hydrometrical data available

(1) estimation on the basis of stream discharge Qj at the gaug- the following procedures are applied:

ing station located in a section with low lateral inflow

Q. = m QIj (52) 3

where the coefficient m represents the ratio of drainage area above the middle of the section to the area of the drainage basin above the gauging station.

(2) If there are no big tributaries in the section the mean stream discharge is estimated as the arithmetic mean, i.e.

1 Qj = T (QjI + Qjo)

59

Metbodsfor water balance compukztions

where Q and Q are the discharges at the upstream and downstream ends ofjthe sect!?on. calculated from

The storage volume Vj for the section is then

where ‘rj is the lag time (mean travel time) for the section between the gauge lines.

carrying about 50% of the total inflow, the mean stream discharge of the section is estimated with weighting coefficients, and equation (53) becomes

If there is a comparatively large tributary within the section,

V. = [KQ + (1-K) Q. 1 ‘C. (54) J jI 30 3

The weighting coefficient K is estimated from

K = 0.5 - (0.5 - 11/1) al/a (55)

where 11 is the distance from the upstream gauge line of the section to the mouth of the tributary, a1 is the drainage area of the tributary and 1 and a are the length and the area of the whole section.

At the confluence of several rivers, for instance, two of a similar size (Fig. U), V is estimated by

where Q1, Q2, Q3 are the stream discharges at the upper gauge lines of the tributaries and at the lower outlet line respectively, and the coefficients bl, b2, 6 may be estimated from the following equa- t ions :

61 bl = ‘rjl + Tj3 - b2 = Tj2 + ‘Cj, - 6 (57)

where rjl, ~ j 2 , ~ j 3 are the values of the lag times of the corresponding subsections and a1 and a2 are the drainage areas of the upper subsections.

small drainage network are obtained from Approximate estimates for channel storage in the medium and

(58)

where 4 is the mean discharge per unit area estimated for small representative rivers, and t, the mean basin stream velocity in mfsec, is estimated as the arithmetic mean of stream velocities of three or four similar rivers the length of which is < 50, 100 or 150 lan; A is


Fig. 11. Sketch of a section of river confluence explaining the procedure of channel storage estimation using equations (56) and (57).


the area of the whole basin, C and D are factors computed for plains rivers in the USSR (Table 3). velocity f may be estimated as the arithmetic mean of stream velocities U', computed for similar rivers from

More approximately, the mean stream

0.25 i 0.38 U' = 0.75 d' nhx (59)

where i is the mean slope of the water surface during the low flow period in metres per thousand metres, hax is the average maximum discharge estimated from observational data, or in their absence, from the data of similar rivers, and d is a parameter taken from Table 4. ed by summing the values of the water storage in the large, medium and small drainage network, i.e.

The total channel storage for a specified date is comput-

The change in the channel storage AVc., is calculated as the difference between the total volume of channel storage in the basin at the beginning and at the end of the balance period.

th Asch (equation (4), section 2.6) for use in the water balance equation.

commended for basins with areas over 3000-5000 km2. drainage areas the values of channel storage are generally insigni- f icant . 3.5.3 Soil moisture st.orage

Evaluation of soil-moisture storage and its variations in the unsaturated zone is done on the basis of measurements of soil moisture by weighing or neutron methods (Bell and McCulloch 1966; Cope and Trick- ett, 1965; Kharchenko, 1968; Toebes and Ouryvaev, 1970; Rode, 1967).

moisture must cover the whole depth of the soil mantle down to the water table, or when the water table is more than 4 m deep, down to the greatest depth penetrated by a wetting front. This depth depends on the climatic regime, but will not usually be less than 4 m (Kachinski, 1970). Soil moisture content may be approximately evaluated on the basis of measurements of soil moisture in the upper 1 m layer.

in different layers in the whole basin or in its separate parts, it is necessary to determine the optimum number of measurement points, which may enable the computation of mean water content with a given accuracy (Kovzel, 1972;

soil moisture during characteristic periods of the year. ing data are processed by standard statistical methods.

points established depends on the required accuracy of determination

The volume scorage AVch is then converted to an equivalent dep-

The above techniques of channel storage estimation may be re- In smaller

For accurate water balance studies, the observations of soil

To evaluate variations of total water content, or water content

McGuinness and Urban, 1964). Soil moisture observations are carried out as single surveys of

The result-

When using the gravimetric method, the number of observation

62

Compulalion of Components

0

m

rl I

0

0

0

rl I

0

0

v)

I 0

CO 0

rl

U3 W 0

0

m 0 *

0 *

0

0

In W W

r- F3 0 rd Ll a

E3

PI 0

rl

CO W

0

9

?

m

m

cu *

0

9 m 9

W

CO rl 0

0

U

m a, $4 0 Fr

0

rl rl

rl U3 0

0

1

m *

v)

m

0

9 m

v)

r-

m

rl 0

0

a, a a

a, U m I U m a, Ll 0

b

0

rl rl

CO v)

0

9

cu * *

cu m 0

0

CO

r- ?

rl rl 0

0

a, a

a

a, U

cn

rl rl rl

PI m 0

0

t m *

rl B 0 m 0

CO

rl rl 0

0

U

Ll a, m a, a I -4

cn 3

h

m

m W

g Ti U ld 3 @ a,

6

*rl

Ll U

U

rd W

la W 0

111 a, 3

rl 2 w I-1 !a 2

GWNOm

rlrlNmm

00000

.....

II

II

I

CJmmWN

00000

rlrl1cum

.. ..

ooocu?

mmrl

rl I

II

II

0v)mv)m

*curl

. rl

a, M

63

Methods for water bahnce computations

of water storage. The error in the determination of the mean water content in a lm layer of soil involving 8-10 soil samples, usually does not exceed 10-15% of the mean value.

content for selected sites (with an area ranging from several hundred to several thousand m2) is made by means of several bore holes.

The determination of the moisture variation in the upper soil layer is made at all observation points of the river basin. The water content in the zone of aeration is determined for the whole basin as a weighted average in mm of water depth.

Observations of soil moisture in the zone of aeration between the lm layer and,tlie ground-water level are rarely made, since observations are 'carried out usually in the upper root zone. sometimes in the lower layer of the ground a considerable accumulation of water may occur. For longer balance periods suchan accumulation may be transformed into other water balance components which can be measured. For shorter balance periods, the neutron method is the most satisfactory method of sampling to depth.

3.5.4 Groundwater storage

(Special symbols used in this section are listed at the beginning of Section 5.4). In computing the water balance of river basins, the variations of ground-water storage (AG) are evaluated from field data collected from observation points, usually wells, and values of the coefficient I). In the case of falling ground-water levels, v represents the coefficient of specific yield vSz, and in the case of rising ground-water levels represents the saturation deficit vuz of the ground and soil above the capillary zone. water storage variation is done separately for periods of falling or rising ground-water levels. For approximate computation, ground- water storage variations may be evaluated for any period of time provided the saturation deficit is equal to the coefficient of specific yield.

Ground-water storage variations for a homogeneous area are comput ed by

When using the neutron method the determination of the water

However,

Computation of ground-

AG = v . A5 where AG is the average variation of ground-water level for the area.

Changes of ground-water levels for a designated period in a basin are determined by computing the difference between average levels at the beginning and at the end of the designated period. Ground-water levels are measured in wells, making allowance for the effect of the topography and the characteristics of water-bearing layers. For basins with homogeneous hydrological conditions the mean level is calculated as the arithmetic mean, while for basins with heterogeneous hydrogeological conditions it is calculated as a weighted (mean. ditions there can be considerable local variations in the ground- water regime with ground-water storage increasing in some parts and decreasing in others.

In basins with heterogeneous hydrogeological con-

These differences are not taken into account

64

Compukztion of Components

by using the mean value of ground-water level changes for the whole basin. Ground-water storage variations must be evaluated for each different part of the basin within which hydrogeological conditions are homogeneous.

The division of the basin area into areas with different types of ground-water level fluctuations results in a more accurate computation of weighted mean values of level fluctuation, even when few wells are available to provide data.

Statistical techniques of data processing should be used in choosing the optimum number of observational points for evaluation of ground-water level fluctuations. This may not be possible in areas with few wells.

factors the coefficients of correlation between water-levels in wells are computed for wells situated at different distances from each other. This permits the determination of the degree of synchronism of level fluctuations in basins, for which ground-water storage variations are computed, as well as the representativeness of individual observation points for different parts of the basins. Such a regional analysis of hydrogeological observational data provides the most objective evaluation of general changes of level at the chosen observational points (Popov, 1967). Further information on networks is given in Mandel (1965) and Jacobs (1972).

water not greater than 5 m. in the forest zone of a temperate climate and under homogeneous hydrogeological conditions, the ground- water storage may be computed with 10% accuracy if there are about 10 observation points for each aquifer. If the depth to ground- water is much greater than 5 m. the number of wells may be less.

tween the total moisture capacity and the natural moisture of materials in the zone of ground-water fluctuations, determined on the basis of field data(Krestovski and Fedorov, 1970). Specific yield (Vsz) for sandy and loamy materials is determined by computing the difference between the total moisture capacity and the minimum field capacity; for sandy rocks the maximum molecular moisture capacity may be substituted for the minimum field capacity. The above values are determined by measurement of the moisture content of samples of the material taken above the level of the ground-water. When computing the specific yield Vsz it should be taken into account that even completely saturated materials may contain entrapped air, the volume of which may be 4 to 10% or more of the porosity of the material.

ered or stratified, V is computed as a weighted mean value by means of the equation

To evaluate ground-water fluctuations caused by meteorological

Thus in a basin less than 100 lan2 in area with depth to ground-

The saturation deficit (vUz) is computed as the difference be-

Where material in the zone of ground-water fluctuations is lay-

(62)

where V is the specific yield of an individual layer of material of thickness di, and Ah is the variation of water-level corresponding

65

Methods for water balance compulutions

n

i=1

ological conditions, ground-water variations are computed by divid- ing the region into relatively homogeneous sub-regions, computing the change in storage in each sub-region, and adding the sub-regional storage changes to obtain the total for the region.

In some cases the variation of ground-water storage, or mean value of Vsz for river basins, may be determined by establishing the relation of ground-water inflow to the river to the average ground- water level in the basin. For this purpose ground-water levels and discharge at the outlet are measured during stable low flow periods (periods of base flow). unit area of basin at the outlet, q, to the mean ground-water level in the basin, 5. zone of aeration is not great, the mean value of ground-water storage Vsz above the outlet may be calculated by the equation

to the thickness 1 di . For a river basin or a large region with heterogeneous hydroge-

Curves are drawn relating discharge per

If the discharge from the saturated zone into the

The mean value of ground-water swrage, vSz , is evaluated individually for different rock layers.

If no field determinations of Vsz are possible a first approximation can be obtained from the values of specific yield presented in Table 5.

More detailed information on the measurement of ground-water storage in river basins is given by Lebedev (1963), Popov (1967), Toebes and Ouryvaev (1970), VSEGINGEO (1968), and California Dept. of Water Resources (1963).

TABLE 5. Mean value of specific yield of rocks (in parts of the unit)

VSZ I

Very fine sand and loamy sand Fine sand and clayey sand Medium sand Coarse and gravely sand Sandstone with clay cement Fractured limestone

0.10 - 0.15 0.15 - 0.20 0.2 - 0.25 0.25 - 0.35 0.02 - 0.03 0.01 - 0.10

I I

66

4. VARIABILITY OF THE MAIN WATER BALANCE COMPONENTS AND ACCURACY OF THEIR ESTIMATION

4 .I Water-balance components can be considered as random variables in time and space. For example, the time series of annual precipitation or discharge is a random variable in time, and precipitation or evaporation at some point in the basin is a spatial random variable. In mathematical statistics, observed values are considered as samples of a random variable, that is, as independent samples from an infinite population. Each random variable has its own distribution, usually unknown, and in some cases it is assumed or deduced by some hypothesis, but in others it must be discovered by observation.

(i=l, 2, ..., n) relative to the mean ? = X./n is the standard deviation

Variability of main water-balance components

The measure of dispersion of a set of observed values 3 1 i=l

s = J-1-n i=l (64)

where n is the number of observed values and is called the sample size,-because we consider the Xi as samples from a population. The mean X and the standard deviation s of a set of samples tend to the population mean 11 and the population standard deviation o respectively when the sample size n tends to infinity. Therefore in the case of a large sample size (n > 25) we may assume that s is nearly equal to o and use s instead of 0. Nore precisely, it is better to use the following unbiased estimate s' for the estimation of o.

However, the difference between s and s' is negligible compared with the sampling error of s and s'. only computed when the sample size is more than 10, because s and s' are not reliable for small samples. The standard deviation 0 is expressed in the same units as the value Xi This makes the comparison of variability between different series difficult, since the value of 0 depends on the value of individual terms of the series Xi and their mean value X. variation Cv is used to indicate the relative dispersion and to compare the degree of variability of different populations. It is the ratio of the standard deviation to the mean and is a dimension- less number:

The standard deviation is usually

(mm, mm3/s, k d etc.).

The coefficient of

cv = olp (66)

The mean and the standard deviation are important because we In practice, Cv is computed by s/g or s'/x.

can see the approximate outline of the distribution from them. For example, in the case of a normal distribution where the probability density function p(x) is given by

67

Methods for water bahnce compututions

distribution

- (x-U>2 202 1 normal

distribution p(x) = E

l/a -a/2<x-p<a/2 { o Ix-pl>a/2

uniform distribution p(x) =

triangular {(:/a) (1-lx-U I /a>

exponential -(x/a) x a

distribution p(x) = x-l~ <a I x-v I >a / (:Ia) e x< 0

distribution p(x) =

- (x/a)x>,O 14""" e x< 0

a type of r distribution p(x) =

the probability that a sample falls In the interval (U-ko, p+ku) where k = 1,2,3 is:

(U-0, (U-20, (U-30, u+0) U+20) p+30:

% % 68.3 95.4 99.7%

57.7 100 100

65.0 96.6 100

86.5 95.0 98.2

73.8 95.3 98.6

It may be assumed for large samples that the relative frequency is nearly equal to probability, and X and s (or s') are nearly equal to p and CT. Therefore, for a set of numerical values of large size with a histogram of bell-type lwith or without skewness), the number of elements contained between X - s and + s is about 213 of the total, the number between ? - 2s and 2 + 2s is about 95% of the total, and almost all elements are contained between i? - 3s and + 3s.

annual precipitation or runoff shows considerable skewness and it is Usually the distribution of a hydrological time series such as

68

VatMbility and accuracy

reasonable to assume r-distribution given by

> x = 0

x c 0, where the mean 1.1, standard deviation a and coefficient of variation C,, are given as follows:

Table 7 presents the relation between the probability P and the module coefficient K = X/p, where P is the probability that a sample is greater than X = pK for the r-distribution. Table 7 shows, for example, that the module coefficient of a wet year (of 1% frequency or probability once in 100,years) equals 1.25 when the coefficient of variation is 0.10 and that it is 4.60 when the coefficient of variation is 1.00.

TABLE 7. Module coefficients of different frequencies for different coefficients of variation.

Coefficient of variation Frequency, %

1 3 10 25 5C 75 90 97 99

0.10 1.25 1.20 1.13 1.07 1.00 0.93 0.87 0.82 0.78 0.20 1.52 1.41 1.26 1.13 0.99 0.86 0.75 0.66 0.59 0.30 1.83 1.63 1.40 1.18 0.97 0.78 0.64 0.52 0.44 0.40 2.16 1.87 1.53 1.23 0.95 0.71 0.53 0.39 0.31 0.50 2.51 2.13 1.67 1.28 0.92 0.63 0.44 0.29 0.21 0.60 2.89 2.39 1.80 1.31 0.88 0.56 0.35 0.20 0.13 0.70 3.29 2.66 1.94 1.34 0.84 0.49 0.27 0.14 0.08 0.80 3.71 2.94 2.06 1.37 0.80 0.42 0.21 0.09 0.04 0.90 4.15 3.22 2.19 1.38 0.75 0.35 0.15 0.05 0.02 1.00 4.61 3.51 2.30 1.39 0.69 0.29 0.11 0.03 0.01

In the case of basins where underground water exchange with adjacent basins may be disregarded, the relation E = P - Q and Qs = Q - Q: are valid for the means of long-term periods, where QA = Quy - Qu1.1 (see Fig. 12, Section 5.2). The standard deviation and the coefficient of variation of E and Q, can be expressed as:

where rpQ and rQs; are the correlation coefficients between precipitation and total runoff, and between total runoff and underground runoff, respectively, and E and os are the mean values of wapotran-

69

Variability and accuracy

Natural sub-zones

Southern Taiga

Northern For est - Steppe Southern Forest- Steppe

spiration and surface runoff. computation using equation (71).

TABLE 8.

Table 8 presents an example of a

Example of the evaluation of space variations of normal annual surface runoff for the West-Siberian plain.

Data for computation

141 0.45 48 0.64 0.94 93

40 0.70 6.1 0.56 0.77 33.9

22 1.02 2.6 1.08 0.51 19.4

zomputat ion result by equation (71

C VQS

0.39

0.75

1.09

Equations (70) and (71) may be used for the study of spatial variability of water-balance components in any geographical zone and region and for rivers and sea basins, as well as countries and con- t inent s.

Equation (71) may also be used for the study of the variability in time of the annual surface runoff, since the same relation Qs = Q - Qu holds for annual runoff, as for a long-term period(this holds for humid zones, but may be less valid as the annual precipitation decreasas) . 4.2 Estimation of the accuracy of measurement and computation of

water balance components

There are systematic and random errors during hydrometeorological observations and during the processing of results, due to defects in instruments and methods of measurement. Systematic errors, caused mainly by the methods of observation and the design of instruments, may be avoided by correcting the observed data during processing (WO, 1970a). Random errors are dependent on many unknown causes and may be taken into account only statistically (Gid- rometeoizdat , 1970).

Systematic errors of measurements of precipitation, runoff and evaporation can be avoided with the aid of various correction coefficients obtained by comparing the readings of standard and reference instruments.

can be estimated using the following theorem:

size n from a population having a population mean vand a population standard deviation 0. Then the sample mean

After each water-balance component has been measured, its error

Let Xi (i=l ,... ,n) be a set of independent random samples of

71

Methods for water balnnce computations

n .. il = 1 Xi/n

i=l is also a random variable, that is it varies by chance, and its distribution is nearly equal to a normal distribution of mean 1.1 and standard deviation GI&.

This theorem gives an important equation for the standard deviation of the sample mean

n iz = 1 xi/"

i=1 of a sample size n.

6- = a/& X

When n becomes large, a/& becomes small, and therefore Z falls Thus for large sample, the sample mean X may be assumed near to p.

to be 1-1.

the reliability of the sample mean n

i=l

In accordance with the properties of the normal distribution,

il = 1 Xi/n

is represented by its standard deviation a/&. ion of X is the normal distribution of mean and standard deviation a/&, the probability that the difference between z and that k6/& (k'= 1,2,3) is given as follows:

As the distribut-

is less

probability that ti? - p1<0/& : 68.3% (about 213)

probability that - p1<26/6: 95.4% (nearly all)

probability that - pI<30/&: 99.7% (almost all)

Thus we can assume that the difference between i? and p is less than 36/& with very few exceptions. In most cases we do not know the true values of p and 6, which would be obtained from a very large population. (or s') instead of 6, and we represent the reliability of the sample mean by SI& or sf/&. value of 1-1 and the sample mean X will be less than 3 s l 6 (or 3sf/ &) with very few exceptions.

tage, computed from

In practice we use the sample standard deviation s

The iifference between the unknown true

Table 9 presents the relative standard error of as a percen-

where n is the sample size (or the length of a time series) and Cv is the coefficient of variation, and & is the standard error 616. Table 10 presents an example of the computation.

The above statistical methods for evaluation of random errors are equally suitable for all components of the water balance which are obtained as arithmetic means of observed values.

72

Variability and accuracy

In the study of the water balance, the areal mean of precipitation, snow storage, evaporation, soil and ground moisture, etc. are estimated from the data of point observations. is estimated either as a simple arithmetic mean or as a weighted mean. A simple arithmetic mean is used in the case where observation points are distributed evenly and the spatial variation of the given balance element is smooth over the area, usually in plains regions. A weighted mean is used in the case where the observation points are distributed unevenly and the spatial variation is great-, usually in mountain regions. To determine the weights for the weighted mean, the area A is divided into sub-areas ai corresponding to the set of observation points, such that the value Xi of the observation at each point is representative of the corresponding area ai. Then the weight wi is given by Wi = aiICai = ai/A. sub-area is determined by the Thiessen method which is convenient but has no theoretical basis. lines. A review of methods available is given by Rainbird (1967).

Generally speaking, the reliability of the weighted mean increases with the number of observation points, because random errors of different signs compensate each other while summing up weighted values.

X(x,y) can be expressed in the form of a double integral:

The areal mean

In some cases, the

Another method is by plotting iso-

Mathematically, the areal mean of a water-balance component

z = x J/x (x , y) dxdy (74) where X(x,y) is a function of the Cartesian coordinates (x,y),A is the domain of integration and A is the area of A. However, as the function is unknown, we can not determine the true value of z, and can obtain only an approximate value with some error from the existing network of observation points. Plotting the isolines of X may in some rarecases suggest a simple form for the function X(x,y) such as a plane or a conical surface, but this approach should be used with great caution.

In the simplest case the relative standard error of the areal mean value may be determined by means of equation (73), the use of which is justified when the observation points are distributed evenly and the variable at each point is equally reliable and independent. This condition holds for large homogeneous plains with an observation network in which each point is sufficiently distant from adjacent points.

errors of the areal mean value, in terms of the statistical strut- ture of fields of hydrometeorological elements (Karasseff, 1972; Kagan, 1972a,b,c; Strupczewski, 1970). To derive these techniques, some assumptions are necessary, such as homogeneity and isotropy of the field, the functional form of the correlation coefficient in terms of distance, etc. In most cases the above assumptions are only partially justified or are not justified at all, which neces- sitates an approximate evaluation of errors of areal mean.

(precipitation, snow storage, evaporation and others) are made in

There are some computational schemes for the evaluation of the

Sometimes experimental measurements of some balance components

73

Methods for water balance computntions

mean long-term value,it mm

standard error,O.mm absolute standard error of

relative standard error of

variation caef f icient , C,

Znrm

Z X

special experimental basins each with a dense network of observation points. graphs which permit the waluation of the error as a function of area and network density. applicable only under certain physiographical conditions and un- critical application to other regions may result in erroneous con- clusions concerning the error of the areal mean of the components under study.

TABLE 9.

These measurements provide computation tables or

As a rule these tables and graphs are

Relative standard errors of mean values, depending on the number of observations (n) and the coefficient of variation (Cv), expressed as a percentage of the arithmetic mean for n observations.

20 40 60 80 100 I

I

53 3 157 376 0.10 0.28 0.11 53.3 44.0 41.4

9.43 7.78 7.33

1.8 5.0 2.0

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50

3.2 6.3 9.5

12.6 15.8 19.0 22.1 25.3 28.5 31.6 34.8 37.9 41.1 44.3 47.4

2.2 1.6 1.3 1.1 4.5 3.2 2.6 2.2 6.7 4.7 3.9 3.4 8.9 6.3 5.2 4.5 11.2 7.9 6.5 5.6 13.4 9.5 7.7 6.7 15.7 11.1 9.0 7.8 17.9 12.6 10.3 8.9 20.1 14.2 11.6 10.1 22.4 15.8 12.9 11.2 24.6 17.4 14.2 12.3 26.8 19.0 15.5 13.4 29.1 20.6 16.8 14.5 31.3 22.1 18.1 15.7 33.5 23.7 19.4 16.8

1.0 2.0 3.0 4.0 5.0 6.0 7 .O 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0

TABLE 10. An example of accuracy evaluation in computing the norms of water balance components (the basin of R. Vasyugan for the period of 32 years).

I

Statistic characteristics and their symbols

Annual values

precipitation runoff evaporation

74

5. WATER BALANCE OF WATER BODIES 5.1 River basins 5.1.1 General

River basins are the main subject of water-balance research and computation. On the basis of water balances of individual river basins, generalized water balances are computed and water resources evaluated for different countries, regions and continents.

In the water balance equation of river basins all the balance elements are mean values for the basin.

To compute the water balance of a large river basin (e.g. hun- dreds of thousands km2) with different physiographic features , the basin should be divided into an appropriate number of areas (sub- basins) for which water balance computations are made individually. The water balance of the whole basin is computed from weighted average values of the main water balance components of sub-basins. If the water balance is computed for a small river basin (no more than 1000-1200 h2), characterized by balance regime (grassland, forest , irrigated or drained lands, swamps, glaciers, etc.), then the components of the water balance should be determined by taking into account the specific water balances of these areas. The computation of specific water balances for individual areas is made when these land types cover more than 20-30% of the total basin area.

fect of altitudinal zones on the distribution of water-balance component s.

5.1.2 Mean water balance of a river basin

Computation of mean water balances of river basins for a complete annual cycle (calendar or hydrological year), which is the main form of water-balance computation, provides initial information on basin water resources. As stated in Sections 2.2 and 2.3, the water balance equation of a closed river basin for a long-term period may be presented as

For mountain river basins it is necessary to consider the ef-

P-Q-E = 0 (75) In some basins which exchange a considerable volume of under-

ground water with adjacent basins, the terms QU1 of underground inflow and Quo of underground outflow must be inserted in equation (75). Ground-water exchange can be evaluated by means of special obsenra- tions (see Section 5.4).

ed from observational data; therefore, in the absence of significant ground-water exchange with adjoining basins or the sea, the value of the mean annual evaporation from the basin is reliable if it is obtained from equation (75):

Mean annual precipitation (F) and discharge (Gs) can be obtain-

a = p - q s If river water is used on a large scale for primary or second-

ary industry, the term Q, for water removal for economic purposes and the term QB for return water must be inserted in equation (75).

75

Methods for una& bakance Computations

In recent years in the USSR a differentiated water balance equation for a long-term period has been used, in which total runoff (Q) is separated into surface (flood) runoff (Q,) and underground runoff into rivers (Q:), i.e. Q = Qs + (Nauka, 1969; Lvovitch, 1973). Thus, equation (75) is presented as

On the basis of this equation it is possible to define:

E N = P - Q s = X + E ; K U =L N ; %=N (77)

where N is the total infiltration (gross moistening); efficient of river flow due to ground water, indicating the propor- tion of annual infiltration forming underground runoff into rivers; KE is the evaporation coefficient. area, with the exception-of losses of rainfall and snow melt water by infiltration, includes evaporation from the water surface and evaporation of water wetting the drainage basin surface and accumulat- ing in micro- and mezo-depressions. These two sources of precipitation losses are quite considerable in regions with a high percentage of lakes and forests, particularly in flat drainage basins with a great number of depressions.

Table 11 gives an illustration of the results of water-balance computations using equations (75) , (76) and (77). The separation of the total runoff into surface and underground runoff is made by runoff hydrograph separation (see Section 3.3.3). The total infiltration (gross moistening) is obtained by computing the difference between precipitation and surface runoff from equation (77).

The general water balance equation (1) is transformed with respect to the specific features of the water body under study and to the duration of the balance period into equations (78) and (79). The mean monthly or seasonal water balance equation of a closed river basin is

Ku is the co-

The total infiltration of an

P-Q-E-ASL - ASch - ASsn - AM - AG - % + Q g -11'0

When solving the equation it is essential to take into account the mean variation of moisture storage in the basin for these periods (see Table 12).

76

Water balance of water bodies

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In the case of an unclosed river basin, or any arbitrary land area, the surface (QS1) and underground (Qur) water inflow from adjacent areas should be added into equations (75), (76) and (77). Then the mean monthly or seasonal water balance equacion is as follows :

P-Q-E-As~-As -AS -AM-AG-Q, +Q +Q +QUI- ?') = 0 ch sn B SI (79)

where ASL is water storage variation in lakes and other closed depressions; bsch is water storage variation in river channels; AS is variation of water equivalent of snow cover; AM is variation OSn water storage in the upper lm of the soil; AG is ground-water storage variation; Qa is water withdrawal from the river for economic needs and water removal to other areas; QB is return water; QSI is surface-water inflow from adjacent areas; inflow from adjacent areas and ed balance elements and measurement errors i.e. the balance discrepancy Q = AM' + V I , where AM' is variation of water storage in the soil mantle beneath the upper lm layer and q' is the unassigned balance discrepancy.

value of undetermined elements of the water balance and the measurement errors for some seasons may be considerable. However, with an increase in the water-balance period, some undetermined balance elements can pass to subsequent seasons and become measured components of the water balance equation. The annual value of the water balance discrepancy (11) in the case described in Table 12 is 12 mm, or 2.1% of the recorded precipitation. This value includes unmea- sured water balance elements, such as underflow and the portion of sub-surface runoff which is not drained by the river channel.

measurement error. discrepancy in computed values. Even if there were no discrepancy, there still would be error. The water balance discrepancy is not a measure of the magnitude of error. If such is desired, an error analysis should be made for each component (see Section 4.2).

QU1 is ground-water includes quantitatively undetermin-

Mean water-balance computations (Table 12) indicate that the

Precipitation and all other components contain sampling and The water balance discrepancy is just that, a

5.1.3 Water balance of a river basin for specific time intervals The water balance of a closed river basin in the temperate zone, for a specific time interval, is computed from equation (78), and the water balance of an open river basin or of an arbitrary land area is computed from equation (79).

Equations (78) and (79) are suitable for water-balance computations for seasonal, monthly and shorter time intervals. When the water balance is computed for years and seasons, the term ASch is excluded from the equation since its value becomes negligible, and in the case of water-balance computation for the calendar or hydrological year, the term ASsn is equal to zero and is also excluded. Water-balance computations of a river basin for seasons of a particular year are presented in Table 13.

79

Metbods for uxrter balauce computations

TABLE 13. Seasonal water balances (mm) of a river basin. The Khoper River at Besplemianovsky. 44900 km2 1959 - 1960 Hydrological Year. Drainage Area -

Winter Spring Autumn :December (March- (Septa-

ber-No- vember

February May

Water-Balance Components

Hydrologi- cal year (December- November)

Precipitation

Runoff

Evaporation

Snow storage variations over the basin

Moisture content variations in the unsaturated zone

Ground-water storage variations

Water removal from rivers .for economic purposes

Return water into river

Quantitative1 undetermined balance elements and measurement errors

- Sym- bol s

P

QS

E

%ill

AM

AG

QU

QB

n

250

7 10

93

57

27

1.0

0

55

11 9 115

150

-93

-28

33

1.0

0

-59

162

9

23 9

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-3 7

2.0

1.0

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131

7 60

-

44

3

1.0

0

16

662 138

4 59

0

33

26

5.0

1.0

2

80

Water balance of wter bodies

As in the case of the mean water-balance computation, the annual discrepancy is not great, amounting to only 2 rnm or 0.3% of the precipitation amount.

basins in the temperate zone may vary in different months and seasons. During winter months without thaw, when evaporation is small and soil moisture is in a frozen state, the. role of these components is minor, while the role of snow storage on the basin surface is quite considerable. In spring the role of runoff due to the thawing of snow accumulated in winter is very important, as is the role of moisture storage variations in the soil, underground, and in the river channel network. In summer, evaporation is of the utmost h- portance. for an accurate computation of water-balance components averaged over different months and seasons.

5.1.4 Forests and forested basins

The scientific and practical importance of water-balance studies and computations relating to forest plots is mainly due to the necessity of determining the hydroclimatic role of the forest and of assessing the effect of forest-cutting, reforestation and forest development measures on the water regime and water resources of forested river basins (Smith et al., 1974). Such studies are also important for the estimation of possible changes in the transport of water in the atmosphere due to deforestation of large areas,

Water-balance studies of forests and forested river basins are carried out on .water-balance plots, with an area ranging from several hundred to several thousand square metres, located within the forest. The plots should be artifically isolated from the surrounding area by a watershed divide wall (from the surface down to the aquiclude). It is essential that the plots are, as far as possible, representative of the surrounding forest terrain. Depending on the variety of types of vegetation and soil within the forest terrain, one or several plots are used.

5.1.4.1 Forest terrain

The general water balance equation written for water-balance components in closed forest terrain is

The role of different components in the water balance of river

The above considerations should be taken into account

- Bo - El - E2 - E3- ASS-AM-AG- = 0 (80) - Qso P + P2 + P3 1 where PI is precipitation over the forest terrain penetrating through the canopy; is precipitation flowing down the stems of trees; surface and underground outflow respectively from the forest terrain; E1 is evaporation under the canopy; tion intercepted by the canopy; ASs is water storage variation on the forest terrain surface; water storage variation in the upper 1 m soil layer; AG is ground- water storage variation; q is water balance discrepancy ( 0 = AM' + Qup i- V', where AM' is water storage variation in the aeration zone

P2 is precipitation intercepted by the canopy, P3 Qso and Quo are

E2 is evaporation or precipita- E3 is transpiration of trees;

AM is

81

Methods for mater balance computations

*

below the upper 1 metre layer and down to the zone of saturation, Qup is percolation beyond the zone of saturation, and n' is the unassigned balance discrepancy).

Precipitation penetrating through the canopy (Pi) and precipitation flowing down the tree stems (P3) are determined by special methods (Sopper and Lull, 1967; Luchshev, 1970).

Precipitation intercepted by the canopy (Pp) is computed as the difference between precipatation falling over the forest terrain (P) (see Section 3.2.4) and the sum of precipitation penetrating through the canopy (PI) and precipitation flowing down the stems (P3), i.e.

- p3 P2 = P - PI Surface and underground outflow (QSo and Quo) from forest plots

are measured by means of weirs or measuring tanks equipped with water- level recorders (Popov, 1968; Rothacher and Miner, 1967).

water balance, heat balance and turbulent diffusion (see Section 3.4.3 and Penman, 1967).

following way:

Evaporation from the forest terrain is determined by methods of

Evaporation from the forest terrain (E) may be presented .in the

where E cipitation intercepted by the canopy; E3 is transpiration.

ponents :

is evaporation under the canopy; E2 is evaporation of pre-

Evaporation under the canopy (El) consists also of three com-

El = E; + E; + E; (83)

where Ei is evaporation from the soil; itation intercepted by the ground cover (moss, low bushes, grass); E3 is ground cover transpiration.

ristics of the forest stand (composition, age, density) the ratio between evaporation components will vary (Fedorov, 1969). In all cases, however, transpiration and evaporation of precipitation intercepted by the canopy comprise the major part of the total evaporation.

In order to determine evaporation under the canopy, weighing evaporimeters (Toebes and Ouryvaev , 1970) are installed according to the geobotanic map of the forest plot, and the evaporation is computed as a weighted mean.

Evaporation of precipitation intercepted by the canopy may be determined as the difference between precipitation over the forest canopy (P) and precipitation measured under the canopy (Pi), taking into account precipitation flowing down the stems of trees (P3);

E; is evaporation of precip-

Depending on the type of forest and on the taxonomic characte-

E2 = P - PI - P3 = P2 Treestand transpiration on the forest plot is determined by

E3 = P1 + P3 - Qso - Bo - Qup - El - A S s - ~ - ~ ' - A G (84)

(85)

82

Water bakznce oj wter bodies

The equation of evaporation for forest terrain under snow cover in winter may be written as

where E;' is evaporation from the snow cover under the canopy; is evaporation from snow intercepted by the canopy; ration of trees in winter.

by special snow evaporimeters as described by Kuzmin (1953). Its value is on the average one-third of the value of evaporation from treeless terrain.

that region, evaporation from snow intercepted by the canopy of deciduous trees may be considered equal to 2-3% of the total solid precipitation falling on the forest. Evaporation from snow intercepted by coniferous trees is determined by the equation:

Eh' E$' is transpi-

Evaporation from the snow cover under the canopy may be measured

Experimental data obtained in Valdai (USSR) indicates that, for

E;' = p - pi' (87 1

where P is precipitation over the forest and P'' is solid precipitation measured by precipitation gauges installea under the canopy.

transpiration during a warm season and may be disregarded. fore evaporation from a forest in winter may be presented as the sum of evaporation from the snow cover under the canopy and evaporation from snow intercepted by the canopy, i.e.

In the same region, winter transpiration is less than 1% of There-

Computation of evaporation from forests using the heat balance method is described by Baumgartner (1967), Penman (1967), Rauner (1.962) and Sopper and Lull (1967). (See also Section 3.4.3.3).

Use of equation (85) should be made with a certain caution. In effect, this method involves many measurements which can only be made with the greatest difficulty. The method is thus more appropriate for small-scale water balances in research projects.

Initial data for the computation of evaporation from forest ter- rains or forested basins using the heat balance method may be obtained by means of gradient masts installed in the forest and equipped with meteorological and actinometric instruments. The masts should be located in the forest at a distance from the forest edge which is 50-60 times tree height.

Observations made in the Valdai area show that monthly sums of evaporation from the forest area may be equated with potential evaporation. Empirical formulae may be used for approximate computation of potential evaporation from the forest (see Section 3.4.3.5).

In temperate zones of the USSR with distinct warm and cold seasons, evaporation from the forest area during the cold period with snow cover is computed by equations (45) and (46), developed for open land (Kuzmin, 1953). To determine evaporation of snow cover

83

Methodsfor water balance computations

under the forest canopy and of snow intercepted by the canopy from evaporation in open land, the results obtained from the above equations are multiplied by an empirical transition coefficient (1.25). Evaporation from forests in the temperate zone in the transition months (April, October, November) is equated with potential evaporation.

Moisture content in the unsaturated zone and ground-water storage are determined in accordance with the recommendations given in Sections 3.5.3 and 3.5.4. 5.1.4.2 Forested basins

The principal aspects of a water-balance study of a forested basin are essentially the same as for the forest plot.

Investigations of the water balance of a forested basin can be made if large-scale topographic, hydrogeologic, soil and geobotanic maps are available. off, ground-water level and soil moisture are made, together with lysimeter and meteorological observations and determination of the hydrophysical properties of the soil and underlying rock.

Evaporation from basins is computed as a residual term of the equations of water or heat balance, or by empirical methods (see Section 3.4.3).

In order to determine soil moisture content in the unsaturated zone, gravimetric or neutron methods are applied.

Ground-water storage variations over the basin are computed from ground-water level fluctuations and water yield coefficients of the aquifers (see Section 3.5.4).

Table 14 gives an example of the results obtained from computation of the seasonal and annual water balance of a small forested watershed in Valdai.

5.1.5 Irrigated and drained land

5.1.5.1 Irrigated land

Water-balance studies on irrigated areas are conducted with a view to : (a) improving the norms and regime of irrigation so as to enhance

(b)

Observations of the basin's precipitation, run-

the productivity of irrigated land, and assessing the changes in the water balance and water resources of river basins which provide water for irrigation. Irrigated areas may be subdivided hydrologically into well dra-

ined land with underground runoff predominating among outflow components of the balance, and poorly drained lands without underground runoff. On the basis of climatic features, it is possible to dis- tinguish between the arid irrigation areas, where irrigation water is the predominant water-balance component and the zone of approximate water balance, where precipitation may be as important as irrigation water. Every region is characterized by specific relations between the water-balance components, and their study enables the forecasting of secondary salinization and formation of swamps, and indicates measures required to prevent these events.

The water balance equation written for an irrigated field from

84

Water balance of wter bodies

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Methods /or water balance compututions

the soil surface down to the aquiclude, for any time interval, may be expressed in the form

where 13, 14, I5 are respectively the inflow of irrigation water on the field surface, outflow of irrigation water from the field and irrigation water removed through canals; 11 and I2 indicate water inflow due to filtration from arterial and from irrigation canals; QS1 and Qso are the natural inflow and outflow of surface water; QMI and QMO are inflow and outflow of soil water in the unsaturated zone; Qui and 8 2 are inflow and outflow of ground water from lower aquifers; from the water surface in canals; AS is water storage variation on the surface and underground.

QU1 and Quo are inflow and outflow of shallow ground water;

E is evaporation from the land surface; E1 is evaporation

The term AS is formed by several components:

AS = ASsn + ASs + AM + AG (90)

where ASsn is water storage variation on the soil surface due to snow accumulation; AS, is water storage variation on the soil surface due to water accumulation in depressions, AM is water storage variation in the unsaturated zone; AG is water storage variation in aquifers. AS,,, AS, and AM are computed as differences between the values of respective elements at the end and at the beginning of the balance period. is applied:

To compute AG the water balance equation for ground water

AG = QUP - Quc + ‘QUI - Quo) + (QU1 - Qu2) where Q is ground-water recharge due to infiltration of precipitation an! irrigation water, and Quc is ground-water discharge into the unsaturated zone (see Fig. 12, Section 5.4).

A brief description of the methods for estimation of the components of equations (89), (90) and (91) is given below.

Precipitation is measured by standard precipitation gauges. Irrigation water is gauged by hydrometric devices (flumes, weirs) installed in canals, or by volumetric methods, and by current-meters. Similar means are applied to determine the surface inflow and outflow of water from the field. The field is isolated by a special furrow or wall, and a gauging station is established in the lowest part of the field. Evaporation, ground-water discharge into the unsaturated zone and ground-water recharge due to infiltration of precipitation and irrigation water are important components of equations (89) and (90).

Where the water table is located at a depth of more than 3-5 m, weighing evaporimeters (Ouryvaev and Toebes, 1970) are used to study evaporation. Evaporation is computed by the heat-balance method or

All these elements are measured by lysimeters.

86

Water bahnce of water bodies

determined using lysimeters. the state of crops on the field. the evaluation of the results of lysimetric observations and i.n the application of these results to agricultural fields (taking into account the state and density of crops in the monoliths and on the field) .

cal methods. Drainage runoff is usually evaluated using hydrometric methods similar to those used in the estimation of surface runoff. In the case of ground-water recharge under pressure, the separation of drainage runoff into infiltration and pressure components is made by studying the hydraulics of the ground-water flow using large numbers of piezometers. The distribution of the network of observation wells and piezometers over the plot under study should correspond to the topography, hydrogeological conditions and the distribution of water collecting under drainage canals and irrigation networks.

Moisture storage variations LM in the unsaturated zone are usually determined by the gravimetric method or by neutron and other soil moisture meters. Soil water inflow and outflow are usually disregarded. ine methods.

On the basis of water-balance computations, measures can be taken to control water, salt and heat balances of agricultural fields.

For irrigation farming purposes the water balance equation is usually solved for the term AS or its component LM, i.e. moisture storage variations in the unsaturated zone. The result is used to determine dates and amounts of subsequent watering. In this case, for practical purposes it is sufficient to determine the main water balance by assuming that such components as inflow and outflow of surface and soil water, water exchange with lower aquifers, etc, are zero for short time intervals.

an agricultural field in the temperate zone for 10-day intervals during the growing period.

Simultaneous observations are made of Phenological observations aid in

Ground-water inflow and outflow are estimated by hydrogeologi-

Other water balance elements are determined by rout-

Table 15 gives the results of a water balance computation for

5.1.5.2 Drained land

Water-balance studies of swamps and marsh lands are conducted with the aim of providing a hydrological. basis for drainage reclamation measures and for the evaluation of their effect on the water resources and water balance of river basins and of individual regions.

impeded surface and ground-water runoff, require drainage.

out on a small river basin or on an agricultural field of the drainage system.

The water balance equation for a reclaimed basin for any period of time can be expressed as:

Swamps and mineral lands, on which water logging is caused by

Investigations of water-balance components are usually carried

87


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where QS1 and Qso are Quo are inflow and out inflow and outflow of

inflow and outflow of surface water; QU1 and .flow of shallow ground water; Qui and Qu2 are ground water from deeper aquifers (vertical

ground water exchange); E is evaporation; AS is soil moisture variation on the surface and underground; q is the balance discrepancy.

ed basin is made by methods applicable to ordinary river basins.

off (QSo + Quo) from the basin are measured on the canals of the drainage network by the same methods as applied for irrigation canals (Section 5.1.5.1).

Table 16 gives an example of the computation of the water balance of a reclaimed basin; drained swamps of the basin are used as agricultural fields (Shebeko, 1970).

off and water storage variations in the unsaturated zone were measured, while water exchange with layers below the drainage level of drainage canals (Qu2 - Qul) was computed as a residual term of the water balance equation. When this computation method is applied, the water exchange value inevitably includes errors in the determin- at ion of water-balance components.

ed agricultural field is composed of the same terms as in the equations for an irrigated field (89) and (90). The ratios of water- balance components however , will be different .

The measurement of the water-balance components of drained agricultural fields involves the same methods as for irrigated lands.

5.2 Lakes and reservoirs

According to the nature of the water balance, lakes can be divided into two main categories: open (exorheic) lakes with outflow, and closed (endorheic) lakes without outflow. Lakes with intermittent (ephemeral) outflow during high water stages constitute an intermediate category.

time interval may be written as follows:

The measurement of individual balance components of the reclaim-

Total inflow (QsI + QUI) to the basin from higher areas and run-

In the above example, precipitation, evaporation, drainage run-

The water balance equation of the unsaturated zone of the drain-

The water balance equation for lakes and reservoirs for any

Q,, + QUI + PL - EL - Qso - Quo - ASL - TI = 0 (93)

where QsI is surface inflow into the lake or reservoir; nd water inflow; EL is evaporation from the lake surface; from the lake or reservoir; percolation through the dam; age in the lake for the balance period.

For large lakes and reservoirs the surface inflow QS1 is usually subdivided into inflow Qm from the main stream and lateral inflow Q1, i.e.

QUI is grou- PL is precipitation on the surface of the lake,

Quo is underground outflow including Qso is surface outflow

and ASL is the variation of water stor-

Qs, = a, + Ql (94)

89

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Water bakance of water bodies

For lakes and reservoirs with a surface area varying considerably during water-level fluctuations, it is preferable to express the components of the water balance equation in volumetric measurements. For lakes with a constant surface area it is more convenient to express water-balance components as a depth of the water layer relative to the mean surface area of the lake.

the balance period.

reservoirs, for which it can be assumed that AsL = 0, is as follows:

The mean surface area is estimated as an arithmetic mean for

The mean water balance equation for open (exorheic) lakes and

QSI + QUI + pL = Qso + Quo + % (95)

In cases where the underground runoff components (QU1 and Quo) do not contribute significantly to the balance, they may be neglected and equation (95) may be simplified to

- QSI + pL - Qso + EL (96)

The equation for mean water balance of a closed (endorheic) lake is comprised of only three terms:

QsI + PL = EL (97)

Equation (97) may be applied for an approximate evaluation of the water resources of small endorheic lakes, using data on precipitation and runoff (inflow) only; if there are no direct measurements of these elements, they may be determined by means of regional maps indicating their long-term values. E is obtained from the water balance equation as a residual term, and includes errors due to any difference between QUI and Quo.

With the construction of numerous reservoirs on rivers, it becomes necessary to obtain daily hydrological information on the rate of inflow and water storage in these reservoirs, i.e. a compilation of current water balances for short time intervals such as months or 10 day periods (Vikulina, 1970). The shortening of the balance period requires more detailed computation and detailed accounting of additional water-balance components, such as: accumulation of water in channels and f lood-plains of submerged rivers; bank storage during the filling of the reservoir and return of this water back into the reservoir when the water-level in the reservoir is lowered; water losses due to ice left on the shore during falls of water-level in winter, and the return of these temporary losses in the form of Qoating ice in spring.

purpose of routine control of water inflow and outflow, the simplified water balance equation is used:

For an approximate computation of the water balance €or the

cI = Q + ASL where 11 is the sum of input components of the water balance equa-

91


tion; prising the sum of water discharges through the turbines, and locks, and infiltration through the dam; of water volume in the reservoir during the balance period.

Computation by the simplified equation is suitable only for small reservoirs with intensive inflow and outflow (high rate of water exchange) and for which discharge through hydroelectric power plants and surface water inflow are the most important components of the balance. For reservoirs with a large water area, the error of estimation of ASL may exceed the daily inflow and in this case the simplified scheme cannot be applied. For the water-balance computation of very large lakes a special research programme is usually developed to take into account the physiographic peculiarities of the water body.

ance of some large lakes are described by Afanasiev (1960), Baulny and Baker (1970) , Malinina (1966) , Sekachev (1970, Gidrometeoizdat , (1967), Blaney (1957), Harbeck (1958), and Harbeck et al. (1958).

tions of some lakes and reservoirs and Table 19 gives monthly water balances of one of the reservoirs for a particular year.

and the minimum allowable balance period are dependent upon the accuracy of estimation of the basic water-balance components, i.e. surface inflow and water storage in the reservoir.

inflow is expressed as a ratio

Q is discharge through the structures at the lower pool, com- spillways,

ASL is the variation

Methods for the investigation and computation of the water bal-

Tables 17 land 18 indicate the results of water-balance computa-

The accuracy of computation of the water balances of reservoirs

The relative error CL of water storage changes compared to the

where AL is the water surface area of the reservoir; of mean level estimation, and V water inflow, m3/sec, and T is hration of the balance period in days).

From investigations on large rivers and reservoirs of the USSR, the mean error of the hydrometric estimation of inflow and outflow is t 5%, and the error of mean level measurements used for the computation of storage changes is -+ 10 mm.

Equation (99) can be used to determine the length of the balance period that will ensure that the relative error CL is not more than 2 5%, i.e. it is within the limits of accuracy of hydrometric estimates of runoff.

If CL is much less than 5% due to increase of inflow (e.g. during rainfall or snow melt), it is possible to reduce the length of the balance period. In this case, T is reduced in such a way as to ensure the condition CL <5% at the given discharge.

Sh is the error = 86400 QIT is the inflow (QI is

5.3 Swamps

Investigations of the water balance of swamps are important for the selection of the most effective means of reclamation and for the

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establishment of interrelations between the water balance of the swamps and of the river basins within which the swamps are located (Costin et al., 1964).

take into account the type of swamp. Depending on the location, the conditions of water replenishment, the nature of the plant cover and its distribution over the swamp terrain, swamps may be divided into two main types: upland swamps (high bogs) and lowland swamps. Upland swamps are characterized by the following features: location on watershed divide areas; convex surface; almost exclusively atmospheric replenishment; oligotrophic vegetation. Lowland swamps are characterized by: location in depressions, river valleys or flood plains; concave or flat surface; mixed replenishment (precipitation plus surface and sub-surface inflow from surrounding dry land); eutrophic vegetation (Ivanov, 1957; Romanov, 1961).

Depending on the rate of water circulation, (see Section 8), peat deposits on natural (unreclaimed) swamps may be divided into two layers: an upper, active layer where the velocity of water flow down the surface slope is high, and a lower inert layer comprising the main peat deposit where infiltration and water exchange are very slow.

The active layer is characterized by its high porosity and high- ly variable water content. Its depth ranges from 80-100 mm in lowland swamps, up to 600-700 mm in high bogs. Water flow (runoff) in the active layer occurs partially on the swamp surface and partially as filtration flow.

efficient of permeability in this layer is the active layer) and slightly varying water content.

peat layers, almost all the horizontal runoff from swamps occurs in the active layer by surface or sub-surface flow. izontal runoff in the inert layer is less than 1% of runoff from the active layer. Thus, horizontal outflow from a swamp is practically equal to the amount of water flowing through the active layer.

comes the following (Ivanov, 1957) :

When computing the water balance of a swamp it is necessary to

The inert.layer is characterized by very low permeability (co- - 10-4 times that in Due to such differences in properties of the active and inert

The volume of hor-

The general water balance equation when applied to a swamp be-

where P is precipitation on the swamp surface; the swamp over the channel network (brooks, etc.); Q2 is horizontal flow over the active layer discharging into the adjacent dry land as a dispersed flow; 94 is inflow of surface water into the swamp from slopes of adjacent dry land, as well as ground-water inflow from aquifers intruding in- to the peat deposit at the boundaries of the swamp; water exchange between the peat deposit and the underlying mineral ground (95 2 0); E is evaporation from the swamp surface; AM is the change in moisture storage in the active layer during the balance period.

Q1 is runoff from

Q3 is inflow into the swamp from rivers and brooks;

95 is vertical

96


Equation (100) may be used for computing the annual, seasonal, monthly and 10-day water balances of swamps for particular years. For mean balances, AM is zero.

Depending on the particular conditions of swamp replenishment, equation (100) may be simplified if some of the components are eliminated or set to zero, and it may be expanded by the introduction of additional terms.

The wat er-balance components are estimated by hydrometeorological observations of the swamp. Precipitation P, evapotranspiration E, runoff Q1 and inflow 93 are measured directly. Moisture storage variation AM in the active layer is computed from data on swamp water-level fluctuations and on the specific yield of the active layer , determined experimentally (Ivanov, 1957; Romanov, 1961). Horizontal flow over the active layer 92 is estimated by examination of data on swamp water-levels and of filtration characteristics of the active layer determined experimentally (Gidrometeoizdat , 1971b). Inflow of surface water from surrounding slopes and ground-water inflow Q4, as well as vertical water exchange Q5, are usually computed jointly as the residual term of the water balance equation.

Evaporation and swamp water storage variations differ in typical parts of the swamp, in the so-called swamp micro-landscapes. A swamp micro-landscape is a part of the swamp area with homogeneous micro- relief and hydro-physical properties of the active layer, occupied by one or several plant associations with similar botanical composition and structure. Therefore, observations on evaporation and swamp water-level fluctuations and estimates of filtration characteristics of the active layer are made individually for every swamp micro-landscape. Evaporation and swamp water storage variations are then averaged for the whole swamp area, taking into account the areas covered by each type of micro-landscape.

thus computed by the formula: Water storage variations in the active layer of the swanp are

where Vi and Ahi are experimentally determined specific yield coefficient and water-level variation for an area ai of micro-landscape, and A is the total area of swamp. The mean evaporation for the whole swamp is similarly determined by

where Ei is the evaporation during the balance period from an area ai of micro-landscape.

water balance of a small high bog during a warm season (May-October) and for a hydrologic year. The water-balance components were measured or estimated. Runoff was measured in four brooks flowing down from the swamp. During high swamp water-levels, however, in spring or autumn of wet years, the outflow from the marginal parts of the

Tables 20 and 21 present the results of the computation of the

97

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swamp occurred in the form of a dispersed flow, estimated as a residual term of the water balance equation with the discrepancy of balance included. gauges; evaporation was measured by evaporimeters GGT-B-1000 (Roma- nov, 1961); moisture content variation in the active layer was computed by data on swamp water-level fluctuations and on specific yield. This computation was possible because moisture content in the unsaturated zone of the swamp was usually close to field capacity (the equilibrium distribution of moisture in the capillary fringe) due to a high porosity of the upper layers of the peat deposit and to the water table location at a shallow depth.

During dry months, however, at low water-levels in the swamp, large negative discrepancies were observed in monthly water balances (Table ZO), because the drying of the upper layers of peat deposit below field capacity was not taken into account.

5.4 Ground-water basins

The following special symbols are used for ground-water (see also Fig. 12).

Modifiers

Precipitation was measured by precipitation

Type

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Symbol

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Symbol

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saturation deficit

Meaning

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returned from other

exchange with surface

purposes

basins

flow

~

Units

m

m

100


When studying the water balance of river basins it is most important to include the upper (unconfined) aquifer in the general water-balance computation. Thus equation (1) is written for a basin whose lower boundary is delineated by the upper surface of the aquiclude upon which the unconfined ground-water is formed. Further- more, when carrying out detailed hydrological investigations, it is essential to study and compute the water balance of ground-water basins as individual water bodies. The computation of the water balance of ground-water basins is particularly important for the sub- stantiation of projects on ground-water as a source of water supply (Blaney and Criddle, 1950; Kohler, Nordenson et al., 1955; Meyboom, 1966; Freeze, 1971).

water basin or one of its parts for any time interval is as follows: The general form of the water balance equation for a ground-

Qu€J+QULI+Qu ,+g 1 -91 2 -QLly+% e-Quc -Qu2 -Quo -Qu3 = O (1 03 )

or

where Q,, is the inflow (infiltration) of precipitation to the upper surface of the ground water; Quu is the inflow of surface water a- long the design stretch of the aquifer, i.e. along the stream channel; Qu is the ground-water outflow along the channel; QU1 is the inflow og ground water through the given aquifer to the design basin; Qui is the inflow of ground water from other aquifers; artificial recharge volume (recharge wells, etc.); of underground water into the zone of aeration for moisture recovery lost by evapotranspiration; sign basin through the given aquifer; to other aquifers; Qu3 is ground-water outflow through springs; Q, is ground water withdrawn from artesian aquifers; AG is the change in ground-water storage; undetermined elements of the balance and errors of estimation of other balance elements. The last two terms of the equation, i.e. AG and 171 may be either positive or negative.

For long-term periods such as the water year, the term AG can generally be considered as zero. cludes, the balance element Qu2 representing the outflow of ground water to adjacent basins may also be excluded. ance computation is made for a confined aquifer lying within the boundaries of the underground watershed (within the whole closed underground basin), equation (103) can be simplified considerably.

It is expedient to examine the terms which have been grouped in equation (104) according to their need for data from direct observations. For instance, the first term of equation (104) represents underground water exchange across the boundary of the design basin and can be estimated by means of hydrodynamic computation of ground- water flow according to the appropriate equation of ground-water

Que is the QVc is the outflow

Quo is ground-water outflow from the de- Qu2 is ground-water outflow

and ‘11 represents quantitatively

For aquifers on hard dense aqui-

When the water-bal-

101

Metbodsfor wter balance comflukrtions

motion. water-levels and calculations of permeability from a network of observation wells. The third term in equation (104) can be estimated on the basis of discharge measurements for springs and ground-water flow calculations for Qu ments in the surface-watlr balance equation(Fig. 12).

Even in the simplest cases this requires observations of

and Qup; or by using streamflow measure-

or

Qllp - Qlly - Qu3 = QSI + Qovo - Qso - ASs - n2 where QS1 is the surface-water inflow from adjacent basin areas (artificial water transfers included); Qso is the surface-water outflow beyond the boundaries of the given area (irretrievable water intake from rivers and lakes included); Qov0 is the overland flow input to the stream channel; ASs is the change in surface-water storage; and it is assumed that there is negligible precipitation and evaporation on and from the surface of the river. the overland flow component is either estimated independently or assumed to be insignificant. The fourth term in equation (104) can be estimated from data on artesian aquifers and recharge wells (Vsegin- geo, 1968). Thus, through estimating three of the terms in equation (104) it is possible to use this equation to calculate the net value of ground-water recharge by infiltration, the term (Qup-Quc), in those situations where the change in ground-water storage can be estimated or assumed to.be insignificant.

(Qup-QUc) can also be estimated using the soil-moisture balance equation (Pig. 12)

In employing this equation

However, the net value of ground-water recharge by infiltration,

- Qup - Quc - P - Qovo - E - bf - ~3 where P is precipitation; E is evaporation, and bf is the change in soil-moisture storage. Thus if (QUp-Quc) can be calculated using equation (106) it should be possible to use equation (104) to calculate AG. Conversely, if equation (104) is used to calculate (Qup- Quc) then equation (106) should afford an estimate of AM + 113.

net ground-water recharge by infiltration could be used to advantage in the ground-water and soil-moisture balance equations (Lebedev, 1963; Vsegingeo , 1968). If detailed observations of ground-water levels are carried out at hydrogeological stations and if data on the aquifer parameters are available, then recharge by infiltration can be computed by hydrodynamic calculations based on measurements of water-level fluctuations. Independent estimates of (Qup-Quc) can also be obtained from lysimeter investigations (Lebedev, 1963).

equation, consider the special case of a natural or undeveloped (Qu, = Qup = 0) unconfined aquifer (the first ground-water body below the soil surface) overlying an essentially impervious aquiclude

It is obvious from the above that an independent estimate of the

As a further example of the utility of the ground-water balance

102


(Qui = Qu2 = 0). (104) reduces to

In this case the ground-water balance equation

If simultaneously with the determination of(QUv - Quy - Qu3) it is possible to compute the change in ground-water storage AGy and if (Qup - Quc) has been estimated independently; then an estimate can be made of the difference between the inflow QU1 and the outflow Quo of ground water in the given area without the hydrodynamic computation of these two flows. Recall that (Qup - Quc) can be calculated from the soil-moisture balance equation (105), and that Qu,, - Qur - Qu3) can be calculated from the surface-water balance equation (105), without making recourse to any hydrodynamic calculations of ground-water flow.

water recharge is taking place and augmenting the underground outflow, whereas a positive value is indicative of a net ground-water discharge in the given area. Thus the long-term value of (QU1 - Quo) is an index of the natural ground-water regime of that part of the unconfined aquifer for which the water-balance computation was made.

Underground water exchanges between river basins or their component parts, which are related by geostructural or hydrogeological characteristics to the predominant areas of recharge or discharge of the aquifer, necessitate the inclusion of ground-water exchange components in the general water balance equation (1). In this situation the water balance computations require the selection of design area boundaries based on an understanding of the direction of ground- water movement (Popov, 1967). A water balance model has been proposed which is based on the selection of design areas according to their location in areas of ground-water recharge, transmission, or discharge (Lawson, 1971).

The above concepts are perhaps best illustrated by considering the water balance equation for an artesian ground-water basin. A separation of the artesian basin into predominant recharge and discharge areas is required in order to determine the structure of the water balance equation for smaller river basins within the artesian basin. For river basins located in areaswhich receive artesian water from other areas, the water balance equation is

For AG = 0, a negative value of (QU1 - Quo) indicates that ground-

where Qul is the inflow of artesian water to the basin and Qu2 is the loss to deep aquifers which discharge ground water beyond the boundaries of the river basin under study. Other river basins would be located in areas where the artesian aquifer is being recharged and in this case the Qul term would represent an outflow and be preceded by a negative sign.

The foregoing discussion has been primarily concerned with pre- senting the structure of the ground-water balance equation, indicating

103


how the various terms can be estimated, and demonstrating the utility of this equation in water resources investigations. Little attention has been given to the accuracy with which the terms can be estimated, that is, to ground-water instrumentation and observation techniques (Gilliland, 1969), to the accuracy and precision of ground- water measurements (Hvorslev, 1951), to the nature of ground-water flow systems (Freeze and Witherspoon, 1966, 1967, 1968), to the design of ground-water observation networks (Geiger and Hitchon, 1964; Lawson, 1970), and to the strategy to be employed in'conducting ground-water basin studies (Lewis and Burgy, 1964; Meyboom, 1966, 1967; Lawson, 1970).

employment and accuracy of the ground-water balance equation. general, there is little that can be said about the accuracy of ground-water balance calculations, other than that the error term can be quite large, that it is important to base the structure of the equation on a sound understanding of the ground-water flow pattern, and that any hydrometeorological information which is used to estimate any of the terms should be as accurate as possible. It is difficult to obtain accurate estimates of the specific yield, and errors can be reduced by selecting a time period over which the change in storage approaches zero. Similarly, an inadequate knowledge of the permeability distribution often limits the accuracy of hydrodynamic computations of ground-water flow. Thus it is recommended that these hydrodynamic calculations be checked by as many independent methods as possible, e.g. by using equation (105), (106) and/or (107).

5.5 Mountain glacier basins, mountain glaciers and ice shields

The water balance equation for a mountain glacier basin for short time intervals (months, seasons) may be written as follows:

The literature cited above will provide further insight into the In

where P is precipitation; E is evaporation; Q is runoff (discharge at the outlet gauging section) from the whole mountain glacier basin; ASgl is the change in the total storage of ice and snow on the surface of all glaciers in the basin for the balance period; ASsn is the change in the seasonal snow storage over the non-glaciated basin area; AM is moisture content change in the unsaturated zone of the basin area not covered by glaciers; ground water and the unsaturated zone; unsaturated zone by ground water; Qup is percolation or infiltration into ground water from the unsaturated zone; q is the balance discrepancy.

whole mountain glacier basin if the surface and subsurface watershed divides coincide. The terms of equation (109) are estimated individually €or areas covered and not covered by glaciers. ASgl is estimated for areas occupied by glaciers and indicates the change of total ice and snow storage on the surface of all glaciers located in the given basin. All the rest of the terms of equation

Qup-QUc is water exchange between Quc is water recharge of the

This equation makes it possible to compute runoff (9) from the

The value

104

Water balance ojwater bodies

(109) are estimated for the part of the basin not covered by glaciers.

data from snow surveys and from storage precipitation gauges installed in different parts of the basin. Snow surveys are also a means of estimating the value of ASsn. The terms AS 1 may be estimated by different methods, such as by observations of t8e glacier surface melt by means of special staffs (ablation stakes) installed in the ice, by the heat balance method, or, more approximately, on the basis of air temperature data.

In order to estimate evaporation (E) it is possible to use the methods of computation given in Section 3.4.3 or observational data from evaporimeters. The estimation of AM is time-consuming since it requires soil moisture measurements by gravimetric or other methods. Since there are no methods for the measurement of water exchange between ground water and the unsaturated zone, the water exchange (Qup-Quc) is usually included in the discrepancy term.

Equation (109) expresses the water balance for particular periods of short duration (particular months, seasons). For the annual mean, it is possible to assume that LW = 0 and ASsn = 0. The value ASgl, however, unlike AM can never be assumed to be zero at any period of averaging, unless there is a sound reason for believing that the glacier is in equilibrium. Even a very low rate of advance or recession involves an appreciable annual change in AS 1.

solid phase of glacier substance and may be estimated on the basis of the following equation for the ice and snow balance of a mountain glacier :

Solid and liquid precipitation (P) is evaluated on the basis of

For every particular glacier, ASgl expresses the bafance of the

"gl = 'sn + Qgl+sn + ASsnf - ASsm - E where AS is the amount of melted snow and ice during the balance period; 'Rs ~ is the amount of snowmelt water frozen in the firn; E is evaporapion from the glacier surface; Psn is the amount of solid precipitation on the glacier surface; ice and snow on the surface of the glacier dueg&o avalanches and blizzards.

Water balances of glacier shields (ice caps) have not been ex- tensively studied, and the solution of this problem may only be obtained approximately. The water balance equation for ice and snow of the glacier shield is presented as follows:

Q +sn is the amount of

ASgl = Pin - Assn - Asice - E where ASgl is the variation of the total amount of ice and snow of the given ice shield for the balance period; melted ice and snow; Asice is the amount of ice lost by formation of icebergs; E is evaporation from the surface of the glacier shield; PAn is the amount of solid precipitation on the glacier shield.

ASsn is the amount of

5.6 Inland seas

The water balance equation of inland seas, such as the Baltic, for

105


Inflow components

mm lan3

any time interval may be expressed as

Outflow components

mm lan3

where Q runoff iischarging into the sea); sea from the shores and through the bottom of the sea; QstI is sea water inflow from the ocean through straits connecting the sea with the ocean; Ps is precipitation on the sea surface; surface; majority of cases equals zero.

charge measurements on rivers running into the sea, at gauging cross- sections nearest to the river mouth; QstI and Qsto are estimated on the basis of data of oceanographic investigations of currents in the straits connecting the sea with the ocean; P, and AS, may be determined by methods applied for the computation of these elements for large reservoirs (see Section 3.2.4 and 3.5.2.3); and E, is computed by the heat balance method. Direct measurement of underground inflow into the sea presents almost insurmountable difficulties. Underground inflow may be computed by hydrogeological methods or it may beestimated as a residual term of the water balance equation.

The approximate mean water balance of the Baltic Sea (a typical inland sea) is given in Table 22 (Sokolovski, 1968). The water balance was computed by means of the simplified equation:

is surface inflow into the sea (in general it is total river QUI is underground inflow into the

QstO is outflow from the sea through these straits; E, is evaporation from the sea

ASs is variation of water storage in the sea, which in the

Qs is determined by routine hydrometric methods, by means of dis-

Surface inflow(Qs) 1140 440

Precipitation (P,) 550 212

T o t a l : 1690 652

Qs + Ps - Es - Qsto = O

Discharge through Danish 1190 459 Straits into the North Sea (Qsto) Evaporation (Es) 500 193

T o t a l : 1690 652

The discharge (Qsto) from the Baltic sea to the North Sea through the Danish Straits was obtained by computing the difference:

The sea surface area was assumed to be 385000 IanL.

TABLE 22. Mean water balance of the Baltic Sea

106

6. REGIONAL WATER BALANCES Regional water balances (for large territories, countries, sea basins and continents) are, as a rule, determined for long-term periods only.

6.1 Water balance of countries

Determination of the water balance of countries has two aims; first, to obtain data necessary for the rational use of national water resources and second, to obtain data necessary for the preparation of generalized water balances of sea basins, continents and the globe as a whole.

cross river basins, large areas of which thus lie outside the boundaries of the country. A considerable volume of river runoff may therefore flow into the territory of a given country from another country through the channels of rivers crossing state borders.

which the variation of water storage AS and the underground water exchange with neighbouring areas Qu1-QUo may be assumed to be equal to zero) is computed by the following simplified equation:

Country boundaries seldom coincide with watershed divides; they

Therefore, the mean water balance of individual countries (for

P - E - Qs, + QsI = 0 where Q,, is the total volume of water (river runoff) carried to the country under study by rivers from foreign countries, total volume of water (river runoff) removed from the country beyond its boundaries. within the country, conventionally called local runoff.

The computation of precipitation (P) and of evaporation (E) averaged over the whole area of the country is made by methods described in Sections 3.2 and 3.4; and Qso are determined from measurements of river discharge at h:%!ometric stations nearest to the border. If the distance between the stations and the border is great, the use of graphs of variations of discharge along the river is recommended.

Local runoff Q may be determined both by calculating the difference between the values of water outflow and inflow at the border and by summarizing the runoff of individual rivers (or their stretches) situated within the country. off obtained by the two methods are approximately the same. However, if runoff which is formed on the given territory is as much as 50% or if it exceeds the difference between the volumes of outflow and inflow, the error of the difference method may be considerable. In these cases, the second method is preferable.

If there is no available information on the runoff of individual rivers, the volume of local runoff may be determined by using the map of mean annual runoff.

ance may be computed for the whole territory without division into separate river basins. For larger countries with several large river basins, the water balance of the whole country may be obtained by cal-

Qso is the

The difference Qso - QsI = Q is runoff that forms

Usually the values of local run-

If the area of the country is relatively small, the water bal-

107


culating the sum of water-balance components determined for individual river basins.

the whole country and for its individual administrative units (districts, states, provinces) or for economically important regions. The methods of water-balance computation for such territories do not differ from the above methods for countries.

Table 23 presents the results of water-balance computations by means of equation (114) for the territories of Soviet Republics and for the Soviet Union as a whole.

Table 24 presents the results of the computation of local runoff using data on inflow and outflow for the territories of two neighbouring administrative districts of the USSR.

6.2 Water balance of continents

The water balance of continents (Lvovitch, 1973) is determined by adding up the water-balance components of individual countries located on the given continent. In the same way the water-balance components of the sea or ocean surrounding the continent may be determined.

When computing the water balance of continents, special attention should be paid to the co-ordination of balance components evaluated in different countries. Discharges of large rivers crossing country borders are first co-ordinated.

Sometimes it is necessary to compute the water balance both for

108

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111

7. WATER BALANCE OF THE ATMOSPHERE The equation for the water balance of the earth, which is discussed in detail in other chapters of this report, has served as a central concept for hydrologists. A similar equation can be derived for the continuity of water substance in the atmosphere, and during the past few decades an improving network of aerological stations has produced progressively more detailed and accurate measurements of the various terms of this balance equation. The smallest areas and shortest time periods for which averages can be computed are determined by the density of observation stations and the frequency of sampling . 7.1 Main water balance equations

For a given balance period, in any selected layer of a large area (for instance, large river basins, swamp areas, etc.) and in the atmosphere above it, the water balance equations are as follows (Boch- kov and Sorochan, 1972): for the active soil layer (see equation (1) ):

Q, - Qo i- P - E - AM - Q = 0

for the atmosphere above it:

Q; - Qb - Pi- E - AW - n' = 0 (116)

Equations (115) and (116) include respectively the total inflow (QI, Qi) and outflow (90, QO) of water in the active soil layer and the atmosphere, the change in water storage (AM) in the soil down to the depth of the selected layer, and the change in water storage (AW) in the atmosphere. For a long-term balance period, the terms AM and AW may be taken as zero, but they must be included in the estimation of the water balance for a shorter time interval.

7.2 Water balance equation for the atmosphere-soil system

The,water balance equation for the atmosphere-soil system is obtained from the combined solution of equations (115) and (116):-

AQ + AQ' - AM - AW - N = 0 (117)

where AQ = Q, - Qo; AQ' = Qi - QA; N = q i- q'

Equation (117) allows atmosphere flux and storage data to be used to estimate components of the water balance equation for the earth, either as an independent check or as an indirect method of estimating components that are difficult to measure.

7.3 Development of the water balance equation for the atmosphere (For symbols see section 3.4.1.1)

The water balance equation for the atmosphere may be developed for studies of the role of water vapor in the general circulation of the atmosphere (Ramusson, 1972; Peixoto, 1973); or of the role of cum- ulus convection in the water balance of the atmosphere (Holland and

113

Methods /or water bakance cornflulotions

Rasmussen, 1973); or, as follows, so as to estimate the difference between the mean value of evaporation and precipitation averaged over an irregularly shaped area of the earth's surface (Drozdov and Grigorieva, 1963; Palmen, 1967).

pressed in the form For an area A bounded by a curve C, equation (116) can be ex-

E - P - AW- /ps <bc hu, dc ) dp - rl' = 0 gA Pt

where ps and pt are the atmospheric pressure at the earth's surface and the top of the atmosphere respectively, h is specific humidity, and un is the component of wind velocity normal to C, directed out- ward. The - symbol indicates averaging with respect to time over the balance period T.

In equation (118), the term AW is the difference between the area-averaged water vapor content W at the beginning and end of the balance period T,

Values of AW are typically a few millimetres, and the term can normally be ignored for annual or long-term balance computations, but it may be significant for seasonal averages or averages for shorter periods.

from aerological data. the atmosphere usually lies below a level of 500 mb, it is normally sufficient to take calculations A minimum vertical resolution of 50 mb is desirable in the lower levels, up to about 700 mb (Palmen, 1967).

The integral term in equation (118) represents the divergence of atmospheric vapour flux for the area A. term may be conveniently broken into a "mean" and "eddy" term, i.e.

The integral terms of equations (118) and (119) may be obtained Since more than 90 per cent of the water in

to pt = 500 or 400 mb.

The elements of this

h = G + h ' ) 1 U = u n + u ' -

n n

Since climatological summaries usually contain mean values of h and U for various averaging periods (e.g. monthly and annual), it is relatively simple to compute the mean term in equation (121). Obser- vational studies in the past 20 years (Peixoto, 1973) have shown that correlations between tem=l variations in h and U may be significant, and thus the term h'u;

7.3.1 Measurement systems and data sources

The worldwide operational rawinsonde network is the major source of

should not be neglected.

114

Atmospheric water bakance

,itmospheric data for large-scale water-balance computations. standard transmission of mandatory rawinsonde levels , which includes data at only 1000, 850, 700, 500 and 400 mb, generally does not provide adequate vertical resolution for vapor balance computations. The configuration and observational schedule of the existing rawinsonde network is designed primarily for meteorological purposes, rather than for budget computations over drainage basins, and it is often difficult to match a natural drainage system with the network; for example, rawinsonde stations are rarely located on drainage divides. Interpolation between stations may require a systematic analysis of the wind and humidity field over a large region (Cressman, 1959; Gandin, 1963). Care should also be taken to avoid errors due to instrumental differences (Flohn, Henning and Korff , 1965).

balance computations, include the Barbados Oceanographic and Meteo- rological Experiment (BOMEX) (Holland and Rasmussen, 1973) , the In- ternational Field Year for the Great Lakes (IFYGL) (Aubert, 1972; Bruce, 1972) and the GARP Atlantic Tropical Experiment (GATE). Re- mote sensing devices, particularly the geosynchronous earth satellite, offer additional sources of data.

The

Special observational projects, suitable for atmospheric water-

7.3.2 Space scale considerations

For water-balance analysis of individual cyclones or mesoscale systems, the network of aerological observations must be dense enough to resolve the major features of the disturbance. For long-term average water-balance computations, the network must resolve the variations in E-P arising from variations in the characteristics of the earth's surface. For example, over the m6untainous regions of North America, a substantial fraction of the spatial variance in the annual average value of E-P is associated with features whose dimensions range between 200 and 600 km (Rasmussen, 1971). Since the typical spacing of aerological stations in these regions is generally 250 to 350 km, it is not possible to resolve these small-scale variations with the existing network of stations.

Data from the existing network have however been used success- fully for large-scale water-balance computations in suitable areas, such as the Baltic Sea (3 x lo5 km2) (Palmen and Soderman, 1966), the Upper Colorado River Basin (2.6 x lo5 la2) (Rasmussen, 1967), and areas in the Great Plains of North America (down to 5 x lo5 lan2) (Rasmussen, 1971). The special projects noted above include water- balance computations for relatively small areas.

7.3.3 Time scale considerations

Operational rawinsonde observations are typically taken twice daily, which is probably adequate for water computations of individual cyclones, but is normally not adequate for individual mesoscale systems. However , this sampling rate is quite adequate for long-term average computat.ions, provided there are no systematic diurnal variations in the flux divergence. have been demonstrated by Hastenrath (1967), Nitta and Esbensen (1973) and Rasmussen (1966, 1967 , 1968) , and small-scale diurnal circulations,

Significant large-scale diurnal variations

115

Methods for woter balonce compututions

such as land-sea breezes and mountain-valley winds, are well known. Therefore, depending on the lcoation and the time of year, it may be necessary to sample several times dally in order to properly resolve the diurnal variation.

7.4 Estimation of the terms of the equation for the atmosphere- soil system

When the values of AQ and AQ' are given by the relevant equations and AW is known, the term AM can be estimated from equation (117). In a similar way, climatic runoff E-P or E can be estimated from the above equations if necessary.

Due to the inaccuracy of estimation of water balance terms, such estimates may include errors which depend on the 1ow.accuracy of measurements, as well as the discrepancy of estimation or the terms not taken into account.

116

8. ESTIMATION OF THE RATE OF WATER CIRCULATION To estimate the rate of water circulation in the active layer of the hydrosphere, use can be made of the criterion indicating the rate of water circulation (Kalinin, 1968), also called the residence time (UNESCO, 1971). There is not one specific residence time for a given component, and the spectrum of residence times depends on the mechanism of flow for that component. the average (conventional) residence time Tr can be expressed as the ratio or output) Q, i.e.

Regardless of this mechanism,

of ayerage storage volume ? to the average throughput (input

Tr = v/G The conventional residence time for the atmosphere can be esti-

mated with the help of the coefficients of water exchange and of water consumption, (Drozdov and Grigorieva, 1963); its average value is 8-10 days. This is low in comparison with conventional residence times for some other components of the hydrological cycle (UNESCO, 1971) , but is comparable with biological water (conventional residence time about 1 week) and water in river channels (about 2 weeks). These components provide the dynamics of the water cycle, though they together comprise only one millionth part of the earth's total water supply. the oceans (conventional residence time about 4000 years), frozen water (tens to thousands of years), deep ground water (up to tens of thousands of years) and swamps (of the order of years). Intermediate are soil water (2-4 weeks) and water in the unsaturated zone and shallow ground water (up to 1 year), which provide a link between the dynamic and stable components.

These factors are the basis of the approximations introduced in- to water-balance computations for different balances, which have been described in the report. A knowledge of the appropriate residence times for the components in a particular area is therefore helpful in planning the frequency of measurements of each component in a water- balance study. Methods of estimating the frequency distribution of residence times, based on Limiting assumptions regarding the flow mechanism, have been described by Chapman (1970).

The stabilizing components of the hydrological cycle are

117

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‘ ANDERSON, E.R.: BAKER, D.R. 1967. Estimating incident terrestrial radiation under all atmospheric conditions. Vat. Resour. Res.

ANDREJANOV, V.G. 1957. Gidrologicheskie raschety pri proyectiro- vanii malykh i srednikh gidroelektrostantsiy (Hydrological computa- tations in designing small and middle-sized water power plants). Leningrad , Gidrometeoizdat .

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storages. Canberra, Dept. of National Development, 81p. (Hydrologi- cal series No. 4).

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lacurilor de dimensiuni medii (Determination of actual evaporation from the surface of medium-sized lakes). Bucharest, IMH, vol. 45.

* BAULNY, H.L. de; BAKER, D. 1970. Water &lance of Lake Victoria. Technical Note.

* BAUXGARTNER, A. 1967. Energetic bases for differential vaporization from forest and agricultural lands. In : Sopper, W.C.; Lull, H.W. (eds.) Forest hydrology, pp. 381-390, Oxford, Pergamon Press.

the neutron scattering method in Britain. J. Hydrol. Vol. 4, p. 254

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Vol. 3, pp. 978-1005.

’ AUSTRALIAN WATER RESOURCES COUNCIL, 197Oa. Evaporation from water

BADESCU, V. 1974. Determinarea evaporatiei reale de la suprafata

Studii de hydrologie,

* BELL, J.P.; McCULLOCH, J.S.G. 1966. Soil moisture estimation by

BLANEY, H.F. 1954a. Consumptive use of ground-water by phreato-

Vol. 2, pp. 53-62. BLANEY, H.F. 1954b. Evapo-transpiration measurements in western United States. In: C.R. Ass. Int. Hydrologie Sci. Rome, Vol. 3, pp. 150-160.

BLANEY, H.F. 1957. Evaporation study at Silver Lake in the Mojave Desert, California. Trans. Am. Geophys. Un., Vol. 38, No. 2, pp.

BLANEY, H.F.: CRIDDLE, W.D. 1950. Determining water requirements in 209-215.

irrigated areas from climatological and irrigation data. U.S. Dept. of Agriculture, Soil Conservation Service, (Tech. paper 96).

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