Method of Computation of Low Streamflow - UNESCO Report

7/29/2019 Method of Computation of Low Streamflow - UNESCO Report

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Studiesand reportsinhydrology 36


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Recent titles in this series:2 0 . Hydrological m a p s . Co-edition U n e s c o - W M O .2 1 .* W orld catalogue of very large floods/Rpertoire mondia l des trs fortes crues.2 2 . Floodflow computat ion. M e t h o d s compiled from world experience.2 3 . Water quality surveys.2 4 . Effects of urbanization a n d industrialization on th e h ydrological regim^rid on w ater quality. Proceedings of the A m s t e r d a m S y m p o s i u m .October 1977/Effets de l'urbanisationet de l'industrialisationsur le rgime hydrologique et sur la qualit de l'eau. Actes d u Colloqued ' A m s t e r d a m , octobre 1 9 7 7 . Co-edition IAHS-Unesco Codition AISH-Unesco .2 5 . W orld water balance an d water resources of the earth. (English edition).2 6 . Impact of urbanization a n d industrialization on water resources planning a n d m a n a g e m e n t .2 7 . Soc io-economic aspects of urban hydrology.2 8 . Casebook of m e t h o d s of computat ion of quantitative chan ges in the h ydrological regime of river basins d u e to h u m a n activities.2 9 . Surface water a n d ground-water interaction.3 0 . A quifer contamination a n d protection.3 1 . M e t h o d s of computat ion of the water balance of large lakes a n d reservoirs.

V o l . I M ethodologyV o l . II Case studies

3 2 . Application of results from representative and experimental basins.3 3 . Groundwater in hard rocks.3 4 . Groundwater M odels .

V o l . I Concepts , problems a n d m e t h o d s of analysis with examples of their application.3 5 . Sedimentation Problems in River Basins.3 6 . M e t h o d s of computat ion of l o w stream flow.

Quadrilingual publication: EnglishFtenchSpanishRussian.

F o r details of the complete series please see the list printed at the end of this w o r k .


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Methods of computationof low streamflow

EditedbyT. A. McMahonand A. Diaz ArenasA contributionto theInternational HydrologicalProgramme

(unesoo


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T h e designations employed and the presentation of material throughout the publicationd o not imply the expression of any opinion whatsoever on the part of Unesco concerning thelegal status of any country, territory, city or area or of its authorities, or concerningthe delimitation of its frontiers or boundaries.

Published in 1982 by the United NationsEducational, Scientific and Cultural Organization,7 , place de Fontenoy, 7570D ParisPrinted byImprimerie de la Manutention, M a y e n n eI S B N 92-3-102 013-7 Unesco 1982Printed in France


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Preface

Although the total amount of water on earth is generally assumed to haveremained virtually constant, the rapid growth of population, together with theextension of irrigated agriculture and industrial development, are stressing thequantity and quality aspects of the natural system. Because of theincreasing problems, man has begun to realize that he can no longer follow a"use and discard" philosophy either with water resources or any othernatural resource. As a result, the need for a consistent policy of rationalmanagement of water resources has become evident.Rational water management, however, should be founded upon a thoroughunderstanding of water availability and movement. Thus, as a contribution to thesolution of the world's water problems, Unesco, in 1965, began the firstworld-wide programme of studies of the hydrological cycle The InternationalHydrological Decade (IHD). The research programme was complemented by amajor effort in the field of hydrological education and training. Theactivities undertaken during the Decade proved to be of great interest andvalue to Member States. By the end of that period a majority of Unesco1s MemberStates had formed IHD National Committees to carry out the relevant nationalactivities and to participate in regional and international co-operation withinthe IHD programme. The knowledge of the world's water resources hadsubstantially improved. Hydrology became widely recognized as anindependent professional option and facilities for the training ofhydrologists had been developed.Conscious of the need to expand upon the efforts initiated during theInternational Hydrological Decade, and, following the recommendations of MemberStates, Unesco, in 1975, launched a new long-term-intergovernmental programme,the International Hydrological Programme (IHP), to follow the Decade.Although the IHP is basically a scientific and educational programme, Unescohas been aware from the beginning of a need to direct its activitiestoward the practical solutions of the world's very real water resourcesproblems. Accordingly, and in line with the recommendations of the 1977United Nations Water Conference, the objectives of the InternationalHydrological Programme have been gradually expanded in order to cover not onlyhydrological processes considered in interelationship with the environment andhuman activities, but also the scientific aspects of multi-purpose utilizationand conservation of water resources to meet the needs of economic and socialdevelopment. Thus, while maintaining IHP's scientific concept, theobjectives have shifted perceptibly towards a multidisciplinarty approach to theassessment, planning, and rational management of water resources.As part of Unesco's contribution to the objectives of the IHP, twopublication series are issued: "Studies and Reports in Hydrology"and"Technical Papers in Hydrology". In addition to these publications, and in order


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to expedite exchange of information in the areas in which it is most needed,works of a preliminary nature are issued in the form of Technical Documents.The purpose of the continuing series "Studies and Reports inHydrology" to which this volume belongs,is to present data collected and the mainresults of hydrological studies, as well as to provide information onhydrological research techniques. The proceedings of symposia are alsosometimes included. It is hoped that these volumes will furnish material ofboth practical and theoretical interest to water resources scientists and alsoto those involved in water resources assessments and the planning for rationalwater resources management.


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Contents

FO REWORDLIST OF TABLESLIST OF FIGURES1. INTRODUCTION 11. 1 BACKGROUND 1

1.2 PURPOSE AND SCOPE 11.3 DEFINITIONS AND CONCEPTS 22. FACTORS AFFECTING LOW STREAMFLOW 42. 1 DESCRIPTION OF LOW FLOW PROCESS 42. 2 NATURAL FACTORS 5

2.2.1 Climatic factors 62.2. 1.1 Precipitation 62.2.1.2 Evaporation 72.2.1.3 Evapotranspiration 82.2.1.4 Air and soil temperatures 92.2.1.5 Humidity and wind 9

2.2.2 Hydrogeological factors 92.2.2.1 Geology of basin 92.2.2.2 Hydrogeological regime 102.2.2.3 Groundwater 11

2.2.3 Morphological factors 132.2.3.1 Relief... 132.2.3.2 Lakes 132.2.3.3 Swamps 142.2.3.4 Plant cover 15

2.2.4 Morphometrical factors 152.2.4.1 Basin area 152.2.4.2 Altitude 162.2.4.3 Slope 172.2.4.4 Orientation 172.2.4.5 Drainage density 172.2.4.6 Channel embedment 182.3 FACTORS DUE TO HUMAN ACTIVITY 18

2.3.1 Urbanization 182.3.2 Irrigation 202.3.3 Hydraulic works 212.3.3.1 Urban water supply 212.3.3.2 Other uses 22

2.3.4 Transfers 222.3.5 Hydroelectric stations 222.3.6 Mining 222.3.7 Navigation 222.3.8 Treatment of urban and industrial effluents...... 222.3.9 Drainage works 232.3.10 Land use changes 23

2.4 REFERENCES 243. ASSESSMENT OF DATA USED IN LOW FLOW ANALYSIS 263. 1 LOW FLOW DATA 263.2 ANALYSIS OF TRENDS AND CYCLES 26

3.2.1 Trends 273.2.2 Cycles 28


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3. 3 ERRORS 293.3.1 Measurement errors 293.3.2 Rating curve errors 293.4 HOMOGENEITY OF HISTORICAL DATA 303.5 ERRORS IN ESTIMATED DATA 303.6 STATISTICAL SAMPLING ERRORS 303.7 RELIABILITY 313.8 REPRESENTATIVENESS OF DATA SETS 313.9 REFERENCES 32COMPUTATIONAL PROCEDURES WITH ADEQUATE HYDROMETRIC DATA 334.1 SCOPE 334. 2 FLOW PARAMETERS AND PERSISTENCE 334.2.1 Central tendency 334.2.2 Variability 344.2.3 Skewness 344.2.4 Persistence 344. 3 FLOW DURATION ANALYSIS ." 344.3.1 Uses of flow duration curves 364.4 LOW FLOW FREQUENCY ANALYSES 1 364.4.1 Annual frequency series 364.4.1.1 Normal distribution 39

4.4.1.2 Log-normal distribution 404.4. 1.3 Gamma distribution 414.4.1.4 Pearson Type III distribution 424.4.1.5 Log-Pearson Type III distribution 424.4.1.6 Kritsky-Menkel distribution 434.4.1.7 Extreme Value Type I (Gumbel) distribution... 434.4.1.8 Extreme Value Type III (Weibull) distribution 444.4.1.9 Distribution choice by Goodness of Fit test.. 454.4.1.10 Comparison of distributions 454.4.2 Partial frequency series 454.4.2.1 Distribution of n-year flow 474.4.2.2 Transition probability matrix of low flows... 484.4.3 Uses of low flow frequency curves 494.5 RECESSION ANALYSIS 504.5.1 Uses of recession analysis 50

4.6 RESERVOIR CAPACITY-YIELD ANALYSIS 524.6.1 Use of reservoir capacity-yield relationships.... 534.7 STOCHASTIC MODELS 554.8 REFERENCES 55DETERMINATION OF LOW FLOW WITH INADEQUATE HYDROMETRIC DATA... 575. 1 OUTLINE 575.2 METHOD OF ANALOGY 575.2.1 Application 575.2.2 Methods of computation 585.3 EQUATIONS FOR LOW FLOW COMPUTATION 605.3.1 Principles for classifying basin sizes 605.3.2 Regionalization 615.3.3 Regional design curves oflow flow characteristics 615.4 ISOGRAM MAPS OF LOW FLOW 675.5 LOW FLOW DETERMINATION FOR LARGE RIVERS 695.6 DETERMINATION OF COEFFICIENTS OF VARIATION ANDSKEWNESS OF LOW STREAMFLOW 695.7 USE OF EMPIRICAL COEFFICIENTS 705.7.1 Determination of low streamflow forshort durations 705.7.2 Determination of low streamflow fora range of recurrence intervals 705.8 REFERENCES 71LOW FLOW FORECASTS 746. 1 PREAMBLE 746 2 REGIONAL FORECASTS 756. 3 LOCAL FORECASTS 776.4 REFERENCES 81BIBLIOGRAPHY 83INDEX 92


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Foreword

Occurring during long periods of little or no rain and in severe winter conditions, low stream-flow constitutes one of the extremes of the hydrological regime. The correct assessment of lowflows, appropriately linked with their probability of occurrence and duration, plays animportant role in the design of water supply systems, in the management of water quality and inprojects concerned with flow regulation and reservoir operations.

The methodology of low flow computations is much less reflected in the available hydro-logical literature than the theory of floods. Recognizing this, the IHD Co-ordinating Councildecided at its sixth session to broaden the terms of reference of the working group on floods inorder to include also aspects of low flow computation. Accordingly, the first session of theIntergovernmental Council of the IHP in April 1975 established a working group to prepare acasebook on methods of computation of low streamflow.The working group consisted of the following members:

T. A. McMahon (Australia) (Chairman)A. Diaz Arenas ( Cuba)J. 0. Sonuga 'Nigeria)A. M. Vladimirov (USSR).

M. Roche (France) represented the International Association of Hydrological Sciences, and Y.Bogoyavlensky (UNESCO) provided the Technical Secretariat.The working group met on three occasions:

Leningrad (USSR) 8-11 June 1976Paris (UNESCO Headquarters) 12-16 December 1977Havana (Cuba) 4-9 December 1978.Individual chapters of the book were prepared by the following members:

The book was edited by T.March 1980.

Chapter 1 : M.Chapter 2 : A.Chapter 3 : J.Chapter 4 : T.Chapter 5 : A.Chapter 6 : A.A. McMahon and A.

RocheDiaz Arenas0. SonugaA. McMahonM. VladimirovM. VladimirovDiaz Arenas, i

It should be noted that the technical terms used in the book are consistent with thosedefined in the International Glossary of Hydrology (World Meteorological Organization - UNESCO,First edition 1974).


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List o f tables

2.1 Comparison of summer minimum runoff for river basins composed of different soils.2.2 Minimum runoffs from drainage basins with lakes of different relative size.2.3 Thirty days minimum specific discharge in comparison with lake area for four USSR basins.2.4 Relation between drainage density and specific discharge for three Cuban basins.2.5 Comparison between present water consumption according to different uses and population.2.6 Seasonal variations of household and garden water use in three Australian cities.2.7 Cultivated and irrigated land in Latin America and the Caribbean.

4.1 Average low flows during consecutive periods.4.2 Examples of twenty-four months running totals of streamflow.4.3 Typical values of recession constants.

5.1 Minimum 30-day discharges for 97 per cent frequency depending on river embedment'level.5.2 Minimum 30-day discharges for 80 per cent frequency depending on mean watershed elevation.5.3 Mean minimum 30-day discharges related to values of coefficient of variation.


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List o f figures

2.1 River Niger Basin showing annual hydrographs.2.2 Discharge fluctuations in a river and associated alluvium.2.3 Relationship between low flow and annual precipitation.2.4 Relationship between low flow and annual evaporation.2.5 Relationship between annual groundwater flow and minimum summer runoft.2.6 Diagrammatic illustration of relationship between river discharge and associatedalluvial groundwater deposits.2.7 Relationship between minimum runoff and drainage area.2.8 Relationship between minimum runoff and mean basin elevation.

4.1 Relationship between frequency distribution of flows and flow duration curve.4.2 Example of annual, monthly and daily flow duration curves.4.3 Variability of monthly flow duration curves and catchment geology.4.4 Relationship between normal and extreme value probability scales.4.5 Example of annual low flow frequency curves.4.6 Typical shape of some one-day annual low flow frequency curves.4.7 Example of partial low flow frequency curves.4.8 Frequency curves based on transition matrix method and independent series.4.9 Example of hydrologie atlas of low flow characteristics.4.10 Recession analysis of a hydrograph.4.11 Derivation of recession constant.4.12 Relationship between recession constant and surficial geology.4.13 A classification of reservoir capacity-yield procedures.


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5.1 Diagrammatical illustration of the effect of geographical zones on specific minimumdischarge.5.2 Relationships between minimum 30-day specific discharge and drainage area.5.3 Relationships between minimum discharge and drainage area for permanent rivers.5.4 Relationships between minimum discharge and drainage area for intermittent rivers.5.5 Relationships between minimum specific discharge and river embedment.5.6 Relationships between minimum 30-day specific discharge and mean basin elevation forrivers of mountain regions.5.7 Isograms of summer-autumn 80% probability mean minimum monthly runoff.6.1 Relationship between minimum summer monthly specific flow and sum of winter, springsnowmelt and summer flows.6.2 Relationship between minimum summer monthly flow and sum of winter flow, losses duringspring snowmelt flood and summer rainfall.6.3 Relationship between minimum summer discharge and mean winter monthly flow.6.4 Relationships between summer low flow volumes and preceding synoptic meteorologicalindices.6.5 Determination of depletion curves.6.6 Relationship among mean September discharge, mean August discharge and precipitationdepth.


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1 Introduction

1.1 BACKGROUNDWhenever a project aims to use run-of-the-river waters, that is, when there is noregulatingreservoir, or when flow regulation is to be seasonal, orif, as a result of man's activity, theregime ofthe stream is to be substantially disturbed, itis ofvital importance to have a soundknowledge and understanding of the river's low flows and their characteristics.

This knowledge must be understood quantitatively. Furthermore, the question ofqualityofthe environment often depends on the availability of low river flows, particularly inareasofurban living, or on problems of public health, such as combating endemic diseases, as well asfor thermal orchemical pollution. Thus, the connection between quantitative and qualitativeaspects of water resources is especially sensitive during low water periods. For variousreasons (health, environmental conditions), itis necessary to maintain a minimum discharge inrivers and, consequently, this water is not available for other water users. Another exampleofthe relationship between quantity and quality concerns water salinity. Where this problemexists, salinity is much greater during low waters than during floods or mean water periods.For some projects, in addition to discharges, water levels must be considered. However,this is usuallyva high water problem and is rarely considered in low flow studies. Low waterlevels will not be treated in this book.

1.2 PURPOSE AND SCOPEA knowledge oflow flows is based normally ondirect observation of the natural flows of astream. When measured data are lacking, low flow knowledge depends upon methods ofcalculationwhich make it possible to estimate with varying degrees ofaccuracy the basic information neededfor projects. Itis necessary to know how to use these data and to extract from them thecharacteristics ofthe regime which, in any given project, will enable the parameters of thescheme to be determined. It isalso important to be able toforecast low flow volumes in theshort and medium term, since this is an essential factor in the management of some waterprojects.

This book is written for engineers, water managers and technicians. Itis a compilationof methods successfully used in different countries tocompute low streamflows and is illustrated with case studies. A chapter is also devoted to theoretical aspects ofnatural and man-induced factors affecting low flows.Following this introduction (Chapter 1 ) , Chapter 2 deals with Factors affectinglow

streamflow. After describing the low flow process, the author explains the influence on lowflows of physical factors: climate, geology and morphology. Factors affecting low flows as aresult of human activity are also discussed.Chapter 3deals with Assessment of data used in low flow analysis. The data necessary forstudying low flow characteristics are reviewed and analyses concerned with the determinationoftrends and cycles are outlined. Errors affecting data, their homogeneity and representativenessof data sets are also considered.

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Chapter 4deals with Computational procdures with adequate hydrometrio data. A greatpart ofthis chapter isdevoted to methods ofstatistical analysis with various types ofstatistical distributions, but other techniques such as recession analysis and stochastic models arealso considered. All these procedures require anadequate length oflow flow data for theresults to be reliable.

Chapter 5concerns Determinationof low flow with inadequate hydrometrio data. Direct useof statistical analysis is nolonger applicable because data are not available orthe recordistoo short. Ifthis isso, itis necessary to compare various catchments, some ofthem havingrecorded data, and hence deduce, byanalogy or bycorrelation, the low flows in anungaugedcatchment. Analogy requires extensive study ofcatchment physiography and climate. The mostobjective way is to proceed from a regional point ofview, in particular through regional mapsof low flow isograms, orelse regression equations linking low flow with catchment characteristics.

Chapter 6deals with Low flow forecasts. This kind of forecast broadly uses therelationships between rivers and groundwater, taking into account the influence ofthe precedinghydrometeorological conditions onthe soil moisture during the forecast period. For low flowforecasting at a given point on a river (that is, the provision of a local forecast) therecession ordepletion curve is widely used. For all but short forecasts itis likely that thelow flow forecast will beexpressed instatistical terms.1.3 DEFINITIONS AND CONCEPTSBefore proceeding it isimportant todefine the subject indetail, distinguishing particularlybetween the notion of low flow and that ofdrought. Low flow is defined on a seasonal basis andis linked with the annual solar cycle and its regional oreven local climatic effects. Lowflows may be absolute orrelative.

A simple regime, such as the tropical regime, has only one dry season during which thereis only one period of low flow. Anequatorial regime, on the other hand, is marked by two rainyseasons and two dry seasons, usually of unequal length; there is amain dry season with acorresponding absolute low flow, and a secondary dry season with a secondary or .relative lowflow.

In temperate and cold climates low flows also occur. Inlarge regions with extremely coldand long winters, such as in the western part ofUSSR (Siberia), rivers cease flowing duringmany months ofthe year. Whereas in temperate regions, due tothe variability ofrainfall, oneor more low flow periods may occur each year.

Seasonal irregularities -; and hence the severity of low flow -differ considerablyaccording to a basin's physiography and its climatology, and the low flow may vary from zero tohalf or more ofthe largest flow inayear.

On the other hand, drought is defined as aperiod of abnormally dry weather sufficientlyprolonged for the lack ofprecipitation tocause a serious hydrological imbalance and carriesconnotations ofamoisture deficiency with respect to man's usage ofthe water. It may involvedifferent parameters such as annual abundance. Wetherefore speak ofthe ten-year recurrenceinterval dry year when referring to the annual flow which is exceeded with a frequency of0.9.It is thus not associated with the idea oflow flow, although the statistical study oflow flowsmay lead toa drought characteristic related to a "low flow parameter".

Several concepts relating to the study of low flows are now considered. A period of lowflow is usually defined by:

- its duration, which is often equated to that ofthe dry season. This isdefined as theseason during which either there is norain orthe rainfall islow having regardtoclimate;

- the absolute minimum or lowest flow, which is almost always equated to the smallest meandaily flow during the year;a series oflow flow which expresses a correspondence between fixed lengths of time(expressed as a number ofdays) and flows which have not been exceeded during an.equivalent number ofdays, which may be either consecutive ornon-consecutive. Examplesare:

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- discharge not exceeded for 7 days or 10 days;- discharge not exceeded for 15 days;- discharge not exceeded for one month.It frequently happens that the flow of a stream ceases for one of the following reasons :

the water is frozen;the reserves supplying the streams are exhausted or insufficient to provide a surface flow, (although underflow may continue).

If there is only one major period of zero flow during the year (non-permanent streams), the lowflow, which in this case is not defined as the smallest daily flow, may be distinguished by thenumber of days when no flow is apparent. This definition can be extended without difficulty tothe case in which the period of zero flows is interrupted by small and short-lived floods.Most streams in arid and semi-arid zones, unless they are large rivers which frequentlydraw their water from less arid regions, are dry most of the time, and their flows occur sporadically in the form of floods of varying magnitude (intermittent streams). If these flows occurevery year, we can still use the analyses relating to non-permanent streams outlined in thefollowing chapters. If there is more than one year's interval between flows, another definitionof low flow will have to be sought or the study of low flows as outlined in this book will haveto be abandoned and rainfall studies carried out.The final introductory comment relates to data. We cannot stress too much the importanceof low flow measurements. Accuracy in data is especially important. Where possible, appropriate data measuring equipment should be used and this may differ from that used for medium andhigh flows.

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2 Factors affecting lo w streamflow

2.1 DESCRIPTION OF LOW FLOW PROCESSThe period of low flow, which may occur once or several times in a year, is virtually constantfor each basin or sub-basin but varies among basins. During these periods, the inflow from thebasin to the river system is substantially reduced.

During a period when discharge decreases, there is little or no precipitation contributingto flow and no water is contributed from the basin's surface-water storages; rivers are fedalmost entirely by groundwater, except supply from lakes and reservoirs.In spite of this, in temperate and cold regions it occasionally happens that snowmeltcaused by brief thaws or light showers helps to supply the flow during this period. In warmregions characterised by an incomplete differential pluvial regime, that is, one without a dryseason in the strict sense of the term, the low water period is temporarily interrupted incertain years as a result of isolated rainfall. In some extensive basins of Very longcontinental rivers, the low water period may be different from one cross- section to another

along their courses. For example, for the River Niger at Koulikoro, low water extends fromMarch to May, at Dire from April to June and at Niamey from May to July. (Locations andhydrographs are shown on Fig. 2.1.)

Fig. 2.1 River Niger Basin showing annual hydrographs.4


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During low flow periods, the groundwater regime is characterized by a gradual depletion ofseasonal storage, the capacity of which is impossible to evaluate accurately. Where there is awell defined dry season, the river flow decreases at the same rate as the seasonal groundwaterstorage decreases and, in many situations, the river attains a relatively stable minimum flowgoverned by the inflow from deep groundwater.

Depletion or recession curves can be studied to understand the regimes of watercourses andgroundwater storages. In a hydrograph, the lower part of the recession limb results fromgroundwater storage (Fig. 2.2). Castany (1967) has shown that the formulae of the depletioncurves of a river are identical to those governing water yield from an aquifer whose regime isnot subject to external influences.

P e a k

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The third category identified by Vladimirov is composed of factors that determine therelationship between river discharges and the subsequent impact of the direct and indirectfactors described above. This category includes factors that are most frequently used forpractical computation purposes and comprises the azonal characteristics of the basin (area,mean altitude, slope, drainage density, and channel embedment) and the characteristics of flow(annual runoff, annual groundwater flow to the river, self-regulation of streamflow and otherfactors).2.2.1 Climatic factors2.2.1.1 PrecipitationAll water occurring as river flow has at some time been condensed and precipitated from theatmosphere. But, as seen in the preceding paragraphs, rivers are fed during low water essen--tially from water contained below the ground surface. This storage is repleted by precipitationthat occurred prior to the period in which the surface flow has substantially diminished orceased altogether.

The effect of precipitation on streamflow can be directly observed in the basin'sdischarge characteristics. The effect can be modified to a greater or lesser extent by otherfactors. For example, natural characteristics of the basin (topography, soil^vegetationcharacteristics, hydrogeology) determine the time it takes for saturated flow to reappear inthe form of surface runoff. This may range from a short time in the case of a small karstbasin to a month or considerably longer in other types of basins. In order to determine therole of precipitation in the formation of low flow and to explain the nature of its impact, itis possible to prepare graphs showing the relation between precipitation and low flow runoff(Fig. 2. 3) . However, to establish this type of relationship, it is necessary to take into

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1 100Eu.& 80Z3DZg 60O_u.g 40O_

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400 500 600 700 800 900A N N U A L P R E C I P I T A T I O N ( m m )

Fig. 2.3 Relationship between low flow and annual precipitation.(East European Rivers).account a number of features of the basins including the uniformity of natural characteristics,the number of lakes and swamps, and the impact of man's activities (dams, irrigation systemsand other hydraulic structures) if these are of appreciable importance.

Furthermore, it is not enough to estimate actual precipitation alone in order to demons-strate its real impact upon groundwater runoff. It is also necessary to take account of losses,through direct evaporation from the ground or from plant cover and through seepage to layers sodeep that water contained in them only returns to the river after a long period of time.The plant cover of the basin, the permeability of soils and the regularity of the slopes

are factors that determine the rainfall's penetration to deep-lying horizons or its accumulationin the upper soil layers. Another important factor affecting low flows, in connection with theabove mentioned characteristics, is, therefore, the intensity of rainfall.

. Z o n e s with surplus andsufficient moisture+ Z o n e s with waterdeficit

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Precipitation as snow contributes directly to the formation of runoff only at the time ofthaw. During other times, low flows are supplied by groundwater. This process begins in springand continues throughout summer and sometimes extends to the following autumn or winter.According to Komlev (1973), in extremely cold regions such as Siberia, where the period of verylow flows during winter is stable, the correlation coefficient between winter discharge andrainfall during the same period is between 0.3 and 0.5.Low flows in Finland generally occur in winter and at the end of summer although they may

occasionally continue over a longer period as a result of low precipitation (Siren, 1960).Lazarescu (1977) states that in Romania the main periods of low flow occur during summerand autumn as a result of low precipitation during this period combined with high temperaturesand hence high evaporation losses. Low flows also occur in winter, when precipitation is lowand low temperatures prevent snow from melting.When a river's regime is mixed, that i s, when it is fed both by rainfall and by snowmelt,the occurrence of a rainy season plays an important role in low flow. For example, if rainoccurs in winter, minimum discharge will occur at the beginning of spring, which is the timewhen rainfall is diminishing and the temperature has not yet risen sufficiently for the snow tobegin melting. Such is the case in the Chilean central area.In regions where rivers are fed solely by rainfall, the low water period is governed by

the decrease or cessation of rainfall. The amount of precipitation in the preceding rainyseason has a marked effect upon the low water flow.As a result of the substantial difference in evaporation rates the effect of precipitationupon seasonal runoff is different in humid regions compared with temperate regions. But nevertheless, in both these areas rainfall is a principal meteorological element in the formationof low flows.

In small basins, and especially in those characterised by extensive karst formation, ahigh flow during the low water period will be closely related to heavy precipitation during theprior wet season.In view of the foregoing, it is fair to say that the characteristics of a basin play animportant role in the precipitation-runoff process. This is especially true for small basins.

Rivers possessing extensive basins generally traverse regions characterised by highly dissimilarfeatures, so that it is more difficult to determine their combined effects.

2.2.1.2 EvaporationHaving regard to the practical nature of this book, the term "evaporation" is used in itsbroadest sense to cover the different processes that constitute an indirect factor significantlyaffecting the flow during the low water period.

Evaporation implies the process of water emission by a free surface at a temperaturebelow its boiling point and the combined processes whereby snow dissipates from fields orice disappears from glaciers.Consequently, evaporation is an extremely important factor in the hydrologicalcycle, since it largely determines the river discharge and reduces the flow during low waterperiods (Fig. 2. 4) . The effect of evaporation is most significant at the beginning ofsummer, when a large mass of water returns from the surface soil and from open water bodies tothe atmosphere.

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120

100

80

60

40

20

n

- . ' v1 ' ' - \ Z o n e s with surplus'. \ a n d sufficientV . \ moisture \ \ \ + Z o n e s of water\ \ deficit\ . \

\ . i' 1

- > 'r- i

S-u. i - b ^i i i30 0 400 500 600 700ANNUAL EVAPORATION (mm)

800

Fig. 2.4 Relationship between low flow and annualevaporation. (East European Rivers)in regions in which the rate of evaporation cannot be compensated by a higher rate ofrainfall, an appreciable reduction in river discharge occurs. However, during low waterperiods, when rivers are fed almost exclusively by groundwater, evaporation is practicallyinsignificant. The amount of evaporation depends mainly on solar radiation, temperature ofair and water and of surface soil-water, humidity, vapor pressure, wind velocity and quality ofwater.

2.2.1.3 EvapotranspirationUnder this heading, it is essential to distinguish between two different processes; one calledtranspiration which is due to the plant cover, and the other which is related directly to thesoil. In both, the depletion of water supplies leads, initially, to a reduction in the dissi-pation of water into the atmosphere and, finally to the cessation of the process.

the intensity and duration of transpiration and evaporation differ. However, on tilledland it is very difficult to measure them individually. The climatic conditions and theavailability of water exert a similar effect on evaporation and transpiration, but in the lattercase, the type of vegetation and its stage of development take on considerable importance. Inregions where water is a limiting factor, not all plants transpire at the same rate. Moreover,crop-farming practices have a significant effect upon moisture consumption.In this context it is important to consider the influence exerted on low flow by phreato-phytes. These are plants found along streams and rivers and in areas characterised by a shallowwater table. The consumptive use of these waterloving plants is generally more than twice thatof dry crops. It is estimated that in the western region of the United States, the annual loss

of non-productive water due to these plants is equivalent to irrigating more than 2 millionhectares, a significant figure in comparison with the 235 million hectares of irrigated land inthe world (Kharchenko and Maddock, 1981). It has been demonstrated that in Uzbekistan (USSR),phreatophytes consume considerable volumes of groundwater when the water table is close to thesurface.Basov's (1941) investigations of plantations in the Kamennaya steppes of Kazakhstan (USSR)show the existence of cones of depression of the water table under the plantations during thegrowing season.


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2.2.1.4 Air and soil temperaturesThese indirect factors affect streamflow in two ways. They affect total runoff by influencingother climatic factors, especially evaporation and rainfall. Also, air temperature affects theflow distribution through freezing. Thus it is one of the principal regulatory elements intemperate and cold countries through temporary retention of water within the soil in the form ofsnow and ice. During the winter season the influence of air temperature upon minimum dischargeis largest.

The formation of ice on the surface of rivers, lakes and swamps materially reduces thequantity of water available as discharge. Szilagyi and Muszkalay (1970) explain the formationof this frozen surface with examples taken from Hungary. In the case of major river, icebegins to accumulate upstream of sections where the passage of floating ice is blocked. Thefrozen surface gradually increases in thickness upstream, and this is accompanied by anappreciable rise in backwater. For small rivers the discharge greatly diminishes once theperiod of freezing begins due to the reduced outflow of the basin. Consequently, streams thatcarry little water tend to become completely frozen over in a short period of time.In addition to freezing of surface water, enormous quantities of groundwater can alsofreeze, thereby retarding the groundwater flow and reducing the runoff that reaches the river asbase flow. This phenomenon is more evident in years when little snow is recorded. If soilfreezing progresses as deep as permafrost, base flow ceases altogether.In winter there is a relationship bet w e e n air temperature and low flow so it is possible toestablish a correlation between these two variables. Komlev C1973) has carried out an extensivestudy of Siberian rivers (USSR) and succeeded in establishing an inverse correlation between thearea of the basin and the zonal rates of the minimum mean monthly flow for the winter period.In some cold regions where air temperature during winter is sufficiently high to producethaws, the low water discharge may then be higher than it is in summer. If rises in temperaturealternate with periods of freezing, the river will flow slowly, and no high flows will occur.Such fluctuations allow a more effective percolation of water into the soil than occurs througha sudden thaw and high flow. The same temperature conditions that produce a spring flood mayalso give rise to a low flow regime during summer.In permafrost regions, an impermeable surface layer results from frozen soil water. This

phenomenon has been-studied by Popov (1968) in small and large basins. Generally, minimumrunoff is low. The effect of the permafrost layer is also evident in summer because of theresultant lack of groundwater reserves.2.2.1.5 Humidity and windHumidity and wind affect the total runoff of streams and influence other climatic factorsparticular precipitation and evaporation. Evaporation is intimately related to air moisturedeficit, and any increase therein causes an increase in evaporation, which in turn reduces soilmoisture and possible grounwater recharge. Considering its effect upon flow,air moisturedeficit plays an important role only in dry regions.

In some countries, the persistence of particular winds significantly affects the rainfalland hence the low water period. Wind also affects the distribution of the flow of rivers fed bylarge lakes. The quantity of water flowing into a river from a lake will vary with wind speedand direction.2.2.2 Hydrogeological factors2.2.2.1 Geology of basinThe continuous supply of water to rivers during low water periods is an extremely complexprocess (Roche, 1963). Nevertheless, Waugh (1970) and Riggs (1972) have pointed out that thegeology of the catchment area is the main terrestrial influence- on low flows. Areas wheresurface geology includes unconsolidated sands and gravels produce a sustained flow duringperiods of drought which contrasts to these streams in which surface formations consist of

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unfractured igneous rocks, clays or shales. In crystallized rocks where little fissuring hasoccurred, there is little groundwater flow. For two adjacent basins with the same meteorological conditions, the basin underlain by the more impervious formation will have lowerdischarges during low flow periods.Karstic rocks can have a significant influence on the rate of flow during the low waterperiod. This influence may either increase or decrease the flow, depending on the relationshipbetween the stream and the karst host rock. For example, in cases of large host rock storages

and slow water release, the low flow will be large. In those areas where karst is welldeveloped, rivers may disappear and discharge of neighbouring basins may be affected. It isdifficult, in such cases, to define the catchment area, as in Jaruco, Cuba.The influence of karst on low flow is very significant in small basins. Karst may becomesubmerged in swamps, as in Zapata, Cuba, and the study of its influence becomes very complex.

2.2.2.2 Hydrogeological regimeThe hydrogeological conditions of a basin are closely related to its geological structure, sincethe latter determines the distribution of aquifers. Most of the rainfall that percolatesthrough the soil to groundwater will eventually reach the river as groundwater flow. The typeof soil and its composition largely determine the basin absorption capacity. For soils withlarge effective porosity soil retention is low but water yield and permeability are high. Thisexplains the great dissimilarity in the behaviour of rivers in sandy or loamy areas comparedwith those that are located in clay regions. Examples of two sets of catchments are comparedin Table 2.1.

It is evident that with greater infiltration capacity, the water is able to penetratefurther into the sandy soils. Consequently there is a very clear dependence of low flow oninfiltration. At times this relation may be adversely affected by other factors that influenceinfiltration (see Section 2.3.1).Basins with friable, porous or fissured rock are mos t favourably placed for groundwaterstorage which will subsequently contribute baseflow to the river during low water periods. Butthe composition of the rock does not determine the rate of groundwater flow; this is governedto a large extent by the rocks structure.

Table 2.1 Comparison of summer minimum runoff for river basins

River

OsugaTmaVayaLinda

Basinarea(km2)

12301800601

1010

composed

DominatingSoils

clay loamssandy soils,sandy loamsclay loamssandy soils,sandy loams

of different

Forest(%)

36348070

soils.

Swamps(%)

0210

(Volga basin.

Lakes(%)

1111

USSR).

Normal annualminimum dailydischarge(Vs. km2)0.261.640.321.48

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2.2.2.3 GroundwaterGroundwater, being the main source of surface streamflow during low flow periods, is availablein two ways, namely as artesian groundwater, and as phreatic water. The volume of groundwaterdepends basically on the climate of the region and the geological structure and hydrogeologicalconditions of the basin.

During the low water season, the groundwater regime is characterised by a gradualreduction of seasonal reserves. As these diminish, the velocity of the flow and hence thegroundwater discharge decreases, and, at the end of the period, the flow reaches normally arelatively stable minimum, often determined by the inflow of artesian groundwater. Thus thegroundwater regime is governed by the nature of the hydraulic relation between the water-bearinghorizons and the river.

Investigations carried out in many countries show that there is a close relation betweenthe low flow of rivers, particularly the minimum flow, and groundwater discharge. An examplefor the Nemon basin in USSR is given in Fig. 2.5. But it should be pointed out that thisrelation is significant only in regions with uniform hydrogeological conditions.In addition to the volume of groundwater storage, the transmissivity of an aquifer alsoaffects groundwater discharge and hence river flow.

,-. ' 3"EJC~v^g soLi-CCLU1- "


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are given in Baranov et al. (1967), Diaconu (1961), Dub and Dzubak (1960), Hall (1968), Anon.(1972), Kaitera (1971), Marinov (1962), McMahon (1969), Paduraru et al. (1973), Stachy andHerbst (1970), Vladimirov and Chebotarev (1973) and Vladimirov (1976).

To construct maps showing isograms of low flow in mountain areas, it is necessary toconsider orographic effects relative to precipitation bearing winds. In some cases, isogramsmay stop at basin watersheds. Isograms are mapped as specific discharge or as runoff depth,relative to the centre of the basin. An example is given as Fig. 5.7.

Fig. 5.7 Isograms of summer-autumn'80% probability meanminimum monthly runoff (Jl/s.km^). (Caucasus, USSR),

The magnitude, of the interval between adjacent isograms should be constant in similarnatural conditions. This interval should exceed the possible error in the low flow estimate.Therefore, the interval is dependent on the low flow discharge and its standard deviation, andis given by the following equation (Vladimirov, 1976):4E'q (5.17)

where TqE*interval between isograms,value of low flow specific discharge, andstandard deviation of low flow specific discharges.

Values of E' are computed from the equation:C

(n) .5 (5.18)

where C, coefficient of variation of low streamflow, andnumber of items in the data set.The interval between isograms will vary across a region depending on the value of low streamflowand its coefficient of variation.

Low flow characteristics from isogram maps are determined- at the centre of watersheds bylinear interpolation of the isograms. If several isograms cross the watershed, a mean weightedvalue of low flow (Q_) is computed from the equation:Qi ai + Q 2 a 2 + + Q.a.

(5.19)

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where Q*IQ2IQJ = low flow specific discharge at the centre of the areasa., a n f - a j enclosed between two adjacent isograms, andA = total area of the basin upstream of the design gauging station.5.5 LOW FLOW DETERMINATION FOR LARGE RIVERSIn large rivers, the various zonal regions contribute to runoff. Therefore the low streamflowvalue at the design gauging station on a large river usually differs from the value that wouldbe determined using the geographic region about the gauging station nor can it be determinedfrom isogram maps of low flow.

However, on large rivers there are usually streamflow measurements which permit the computation of low flows at the design station by interpolating upstream gauging station data inrelation to changes in low flow and the length of the reach. Those changes are determinedmainly by intermediate inflow between gauged points and by the hydraulic structures along theriver reach.The intermediate inflow between the design station (without data) and the immediate upstream station (with permanent observations) is estimated by one of the following methods:

1. basing the estimate on the low flow of one of the major tributaries discharging into themain stream between the design and upstream stations;2. using a water balance method; or3. using an estimate of mean low flow specific discharge determined from an isogram map orfrom an equation for the sub-basin between the two stations.

The effect of hydraulic structures on low flow is a function of the type of structure.Reservoirs used for hydropower generation usually increase low flow; the longer this control,the more significant is this effect. However, dams constructed for irrigation water that issupplied to areas away from a river, greatly decrease its low streamflow. A similar effect isproduced by water diversion canals and other large water intakes from a river. All theseeffects are determined from data recorded at the structure.

5.6 DETERMINATION OF COEFFICIENTS OF VARIATION AND SKEWNESS OF LOW STREAMFLOWThis section deals with the coefficients of variation and skewness of low flow events. Forexample, the events might be the minimum 30-day discharges in each year of recorded flow.

Where a basin analogue is not available, two methods may be used to determine the coefficients of variation and skewness.1. In a hydrologically homogeneous region the magnitude of the low flow characteristic isrelated to the coefficient. An example is presented in Table 5.3. Here the design value of thecoefficient of variation is determined by interpolating between the two extreme values of theactual low flow discharge. It is essential in using this method that the adopted extreme values(of both the coefficient of variation and the discharge) are not random nor in error.2. In regions where only minor changes in the coefficient of variation occur (10-20%, say),it is possible to determine a mean coefficient of variation for the region, the value of whichis acceptable for ungauged rivers. For this situation, the relation of the coefficient to basinarea is examined. For individual regions, and particularly in zones of water deficit, adecrease in the coefficient of variation is observed with an increase in basin area from 200 to2300 km . Therefore, rivers with drainage areas exceeding this limit are used in the analysis ofthe areal distribution of the coefficient of variation.

The value of the coefficient of skewness (C ) should be determined by analogy with rivershaving a long period of observations. The ratio of the coefficient of skewness to coefficientof variation (C ) is usually used in computation because it is reasonably constant over largeregions. In regions of water surplus, C_ = 3C V, in regions of sufficient water C = 2C and inregions of water deficit C g = 1 + 1.5CV, although sometimes C g = 0.

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No.re g.

1234567

ofion

Table 5.3 Mean Minimum 30--day Discharges Related to Values oiCoefficient of Varia tion. (European part of USSR)

WinterMinimum 30-dayspecificdischarge

U/s.km2)0.5-30.0-10.01.5-61-50.5-0.31-5

seasonCoefficientofvariation

0.3-0.20.4-0.3-0.3-0.20.4-0.20.4-0.20.7-0.3

Summe r-autumnMinimum 30-dayspecificdischarge

2U/s.km )3-124-72-43-121-76-71-5

seasonCoefficientofvariation

0.5-0.30.6-0.30.6-0.40.4-0.30.5-0.30.6-0.30.6-0.3

5.7 USE OF EMPIRICAL COEFFICIENTS5.7.1 Determination of Low Streamflow for Short DurationsIn low flow analysis, a need may arise for data on minimum daily, 10-day or 30-day flows or forsimilar short durations. Normally, it is not necessary to determine each flow individually, butrather to define one in detail, for example the minimum 30-day flow, and relate the others tothat characteristic flow because they are genetically homogeneous. These relationships arelinear as follows (Anon, 1973; Vladimirov, 1968; Vladimirov and Chebotarev, 1968):

2daily ~ K Q30 (5.20)where Q, ,, = minimum daily water discharge (for mean or specific recurrence interval),Q, 0 = minimum 30-day water discharge, andK = coefficient.Curves of Q, Q would be plotted for homogeneous regions for both winter and summer-autumn (dry)seasons.5.7.2 Determination of Low Streamflow for a Range of Recurrence IntervalsIn water engineering projects, low water discharges for recurrence intervals between 4 and 100years are required. To compute these values effectively, basic relationships, equations andmaps are prepared showing low water discharge for only one given recurrence interval (usually 5years) (Anon., 1 9 7 3 ) . Discharges for other recurrence intervals are computed using an empiricalcoefficient as described below in equation (5.21) and without recourse to the mean flow or thecoefficients of variation and skewness. The value of the empirical coefficient, A , isestimated from maps on the basis of measured relations between the discharge of given recurrenceinterval and the discharge of design recurrence interval. For example, maps would be drawnshowing the relation between the minimum 30-day discharges of 5 years recurrence interval andthe 30-day discharges at 10 and 20 years recurrence interva l. Examples are given in Paduraruand Popovici ( 1 9 7 3 ) , Paduraru et al. (1973) and Vladimirov ( 1 9 7 6 ) . Such relationships arelinear and are described by the following equation:

T years T 5 years (5.21)

The coefficient A has been found to be stable over a region and is equally acceptable for dailyand up to 30-day minimum discharge irrespective of the season. Howeve r, beyond 30 days, itsvalue varies.The empirical coefficient method is very useful because it requires little effort and is

accurate. But accuracy will depend on having 15-20 years or more of data at a number of locations across the region so that an appropriate regression equation or isogram map can be drawn.

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5.8 REFERENCESAmusia, A.Z. (1972). Minimalny stok gornykh rek Srednei Asii (Minimum flow of mountain riversof the Middle Asia). Trans. GGl, Vol. 188, pp. 283-304.

(1972) Ukazania po Ooredeleniu Rasahiotnykh Gidrologicheskykh Kh.aracteristik. CH- 435-7 2 . (Instructions for the Computation of Design Hydrological Characteristics),Gidrometeoizdat, Leningrad p.l8-(1973) Rukovodstvo vo Ooredeleniu Rasahiotnykh Gidrologicheskykh Khareteristik (Handbookon Determination of Design Hydrological Characteristics). Gidrometeoizdat, Leningradp p . 64-69.

Baclo, M. (1976). Vazba plochy povodia a eho vodnosti s minimalnymi prietokami. (Ratio ofbasin surface area and its minimum flows). Vodohosp. Cas., R24, C3, s. 248-256.Baranov, V.A., Popov, L.N. and Petersen, Z.I. (1967). Karty Minimalnogo stoka riek Evropeiskoiterritorii SSSR (Maps of minimum streamflow of the European USSR). Trans. GGI, Vol. 133,

p p . 112-147.Canali, L., Giovanelli, E. (1964). Contributo preliminare alio studio dette rnagre del Vo conmtodo statistici e statistico-probabilistioi. ^preliminary contribution to the study of

low flows of the River Po using statistics and statistical probabilities). AnnaliIdrologici 1964 - Part II - Ufficio Idrografico del Po - Parma.Chow, V.T, (1964). Handbook of applied hydrology. (McGraw-Hill, New York).Diaconu, C. (1961). Unele rezultate ale calcululu scurgerii minime a riurilor din R.P.Romana. (Some results of the calculations of minimum flow of rivers in Romania). Studiide Hidvologie, Vol. 1, pp. 95-104.D u b , O. and Dzubak, M. (1960). La definition des debits d'tiage et l'illustration desuperficie de leur extension. (The definition of low waters and illustration of theirextension). IAHS General Assembly of Helskinki. pp. 151-156.Guisti, E.V. (1962). A relation between floods and drought flow in the Piedmont province in

Virginia. United States Geological Survey Professional Paper 450-c, pp. 128-129.Glos, E. and Lauterbach, D. (1972). Rgionale Verallgemeinerung von Neidriguasserdurahflussenmit Whrscheinlichkeitsaussage. (Regional generalization of low flow with probabilityprediction). "Mitteilungen des Inst, fur Wasserwirtschaft", H. 37, 88 pp . (Berlin).Gregory, K.J. and Walling, D.E. (1973). Drainage basin form and process. Edward Arnold,London . 456 pp.Halasi-Kun, G.J. (1973). Improvement of runoff records in smaller watersheds based onpermeability of the geological subsurface. Proceedings of Madrid Symposium, U N V S C O - W M D -IAHS. Vol. 1, pp. 191-204.Hall, F.R. (1968). Base-flow recession - a review. Water Resources Res., Vol. 4, No. 5,

p p . 973-983.Hely, A.G. and Olmstead, G.H. (1963). Some relations between streamflow characteristics and theenvironment in the Delaware river region. United States Geologcial Survey ProfessionalPaper, 417-B, pp. 1-25.Hmaladze, G.N. (1965). Zakonomernosti izmenienia minimalnogo stoka gornykh riek Armenii imetodika iego rascheta (Laws for the change of minimum flow of mountain rivers in Armeniaand methods for its computation). Trans. 7jakNIGVT, Vol. 18, No. 24, pp. 68-85.Huff, F.A. and Chagnon, S.A. (1964). Relation between Precipitation Deficiency and LowStreamflow. Jour. Geophys. Res., Vol. 69, No. 4, pp. 804-813. Also Huff, F.A. andChagnon, S.A. (1964), Relation between Precipitation Drought and Low Streamflow. Int. Ass.Scii Hyd. Symo. Surface Waters, pp. 167-180.

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Ishihara, T.and Takagi, F. (1965). A study on the variation oflow flow. Bull. DisasterPrevention ResearchInst., Vol. 15, No. 95, Part 2, pp. 76-98.

Kaitera R. (1971). Estimation ofthe maximum and minimum discharge in Finland. Aqua Venn.,Vol. 1, Helsinki, pp. 28-45.Kryukov, V.F. (1974). Metodika territorialnogo obobchenia statisticheskikh kharakteristik

minimalnogo stoka riek (Methods for territorial generalization of statisticalcharacteristics ofminimum streamflow). Trans. GGI, Vol. 213, pp. 102-126.

Lysenko, K.A. (1965). Groundwater flow of Ukrainian rivers. Soviet Pydrol., Vol. 6,pp. 564-571.Marinov, I. (1962). Varju plitkovodieto narequite vBulgaria (On River Low FlowinBulgaria). Hidrologuiay meteorologuia, No. 4, C3-17.McMahon, T.A. (1969). Water Yield and Physical Characteristics ofCatchments. Civil Wngg.

Trans. Inst. F.ngrs. Aust., Vol CE11, No. 1, pp. 74-81.Nikolov, Y. (1973). Varju minimalnia otox nareka Maritza vBelovo Izv. tzentrove N.I. (On

Minimum Runoff in Maritza River, Belovo). Ldboratoria hidraulikaNo. IIStranitza,pp. 107-167.Paduraru, A.and Popovici, V. (1973). Scurgerea medie zilnica minima multiannuala siasigurata80% si90%periurile Romaniei. (Mean daily multiannual minimum discharges and with 80%

and 90% exceeding probabilities onthe Romania Rivers). Sttidii deHidrologie Vol. XXXV,pp. 173-189.Paduraru, A., Popovici, V., Martian, F.and Diaconu, C. (1973). Scurgerea medie lunara minima

multiannuala siasiguraza 80% din perioada iunie-august periurile Romanei. (Mean monthlymultiannual minimum discharges and with 80% exceeding probabilities through June-Augustonthe Romanian Rivers). Studii deHidrologie, Vol. XLI, pp. 113-135.

Riggs, H.C. (1961). Rainfall and Minimum Flows Along the Tallapoosa River, Alabama. UnitedStates Geological Survey Professional Paver 424-B, pp. B96-B98.

Roche, M. (1963). hydrologie desurface. (Surface water hydrology) ParisRozhdestvenski, A.V. and Chebotarev, A.I. (1974). Statistich.esk.ie metody vgidrologii

(Statistical methods in hydrology). Gidrometeoizdat, Leningrad 422 pp.Schultz, V.K. (1965). RiU.iSriednei Azii, (Rivers ofMiddle Asia), Gidrometeoizdat,

Leningrad ,328 pp.Sokolov, A.A. (1956). Vlianie oziernogo regulirovania navelichinu minimalnogo stoka rek.

(Impact oflake regulation on minimum streamflow). Trans. GGI, Vol. 34, No. 97, pp. 89-99.Stachy, I., Herbst, M.and Orsrtynowicz, J., (1970). Przestrzenna zmiennose przeptywow srednich

niskich wPolsce. (Variation of medium and low flows inPoland). Pr. Panst, inst. hydrol.- meteorolo., No. 100, pp. 9-15.

Thomas, D.M. and Benson, M.A. (1970). Generalization ofStreamflow Characteristics fromDrainage-Basin Characteristics. UnitedStates Geological Survey Water Suvvly Paver 1975.

Visso, A., Vafin, R.and Kochiashvili, B. (1973). Formacin del escurrimiento minlmo en lasrios. (Formation ofminimum flow inrivers). Volun h.idraul., Vol. 10, No. 26, pp. 21-25.Vladimirov, A.M. (1966). Characteristics offormation and computation of the minimum flowof

small rivers inthe USSR. Soviet Hydrol., Vol. 2, p. 141.Vladimirov, A.M. (1967). Minimalny stok mallykh riek Aziatskoi territorii SSSR. (Minimum flow

of small rivers in Asiatic USSR.) Trans. GGI, Vol. 139, pp. 4-23.

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Vladimirov, A.M. (1970). Minimalny istok riek SSSR. (Minimum flow of rivers ofUSSR.)Gidrometeoizdat, Leningrad ,214 pp.

Vladimirov, A.M. (1976). Stok riek Vmxlovodny period goda (Streamflow during low waterperiod.) Gidrometeoizdat, Leningrad , 295 pp.

Vladimirov, A.M. and Chebotarev, A.I. (1973). Computation of Probabilistic Values ofLow Flowfor Ungauged Rivers. UNESCO-WyD-IAHS Symposium on the Designof Water Resources Projectwith Inadequate data, Vol. 2, pp. 561-569.

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6 L o wflowforecasts

6.1 PREAMBLELow flow forecasting is related to operational aspects of water engineering practice. Forecasting is concerned with predicting at some level of confidence the low flow state of a riverin terms of stage or discharge at some specific time in the future conditional upon the presentstate. After prediction the forecast is then used for example to operate a hydraulic structurealong the river or to allow withdrawal of water from the river. Depending on subsequent hydro-logic conditions, an amended forecast may be issued at a later date.

The methods discussed in Chapters 4 and 5 provide time independent estimates of low flowcharacteristics whereas the methods to be discussed in this chapter assume some knowledge of thepresent state of the hydrologie parameters and their related variables.Low flow forecasts should be based on the following principles:

presence of a relationship between the river and its associated groundwater storages;- effect of the preceding hydrometeorological conditions upon the river discharge at thetime under consideration;

availability of stored water from natural storage on and below the ground surface forlow flow replenishment.The latter principle has a significant effect on forecasts at a local level.The reliability of low flow forecasts depends not only on whether they are local orregional in extent but also whether they are short- or long-range forecasts. The latterincluding regional ones are less reliable.The permissible error of a long-term forecast is assumed to equal the probable deviationof the forecasted low flow from its mean value during the observational period and is determinedby the formula

H Q . - Q ) 2 1/2E' = 0.674 { } (6.1)n - mwhere E' = permissible error,

Q. = magnitude of forecast flow,Q = mean low flow discharge during the period of observations,n = number of observations, andm = number of degrees of freedom in the forecast equation.

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The short-term forecasting error is determined also by equation (6.1) where Q. and Q arereplaced by the differences between forecasted and observed values, AQ. and AQ.6.2 REGIONAL FORECASTSThree methods for making regional forecasts are outlined below.1. Forecasts of low flow may be based on graphical relationships between the forecast characteristic and functional variables. For example, it is possible to graph the interaction betweensummer minimum flow and the sum of winter flow, spring snowmelt flood flow and summer flow. Anexample is given in Fig. 6.1. Such a relation may be used to make a regional forecast (Norvatovet al., 1960).

2 KFig. 6.1 Relationship between minimum summer monthly specificflow (q) and sum of winter, spring snowmelt and summer flows(EK). (Khoper River Basin, USSR).

If both discharge and precipitation data are available, specific low discharge could berelated to the total hydrometeorological conditions. For summer minima, the independentvariables would be winter flow, water losses during spring snowmelt floods and summer rains.This is illustrated in Fig. 6.2. The method is applicable only to short-range forecasts, as thedata are not available long in advance.

Fig. 6.2 Relationship between minimum summer monthly flow (K )and sum of winter flow, losses during spring snowmelt floodand summer rainfall (EK ) . (Khoper River Basin, USSR).m

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In regions where the difference in the origin and in the value of low flow during winterand summer-autumn seasons is not great, the above relations may be simplified using only twostreamflow characteristics - winter and summer-autumn low flow. This procedure allows forecaststo be made earlier than those in the previous method. An example is given in Fig. 6.3.

Fig. 6.3 Relationship between minimum summer discharge (1^ )and mean winter monthly flow (,)

(Upper Don and Oka River Basins, USSR).

2. In addition to the use of hydrological data, synoptic meteorological indices, for example,atmospheric circulation or atmospheric gradients, may also be used in forecast methodology.Such methods are applicable to long range forecasting.

Using such methods reliable forecasts given up to 18 months prior to the low flow eventhave been made. The discharge coefficient (1 ) is used as a characteristic of low flow and itis determined as the ratio of the difference between the mean discharge for the current periodand the lowest discharge for the period of observation (Qmdischarge variations for the observation period iQmax - Q mi n ) ;Qmin) divided by the range of the

Q - Q m minmax min

(6.2)

Figure 6.4 shows an example of this relationship.(1960).The method is described by Norvatov et al.

In river basins composed of highly permeable rocks where the major portion of precipitation contributes to groundwater recharge, minimum flow may be predicted from precedingprecipitation. For example, the minimum summer-autumn flow may be associated with the meandepth of precipitation for the previous 12-15 months. Such a relation is described in Riggs(1961) and is expressed as follows:

a + b(pi-vir V v n * + c( pvin-ix- p )vni-ix' (6.3)where Q7

I-VIIpI-VIIand

5VIII-IXPVIII-IXa,b,c

summer-autumn 7-day flow,= total precipitation from January to July for the observationperiod and mean precipitation respectively,

and= total precipitation for August and September for theobservation period and mean precipitation respectively, and= empirical coefficients.

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Fig. 6.4 Relationships between summer low flow volumes andpreceding synoptic meteorological indices(a) according to Vangenheim,(b) according to Vitals.IC. = summer low flow volume defined in equation (6.2).N = number of days with C type circulation.B = atmospheric gradient regime.(See Norvatov et al., 1960).

3. For basins with natural storage (that is, high density of river network, numerous lakesor swamps), a low flow forecast may be based on a relationship between minimum winter or summer-autumn flow and the volume of stored water in the river and lake networks in the basin. Themethod uses the observed runoff curve and takes into account the basin drainage and lake areasas well as the precipitation in the month prior to the forecast and that which occurs early inthe following month. This method is explained in detail in Nezhikovsky (1956).6.3 LOCAL FORECASTSFor local forecasts, some of the above methods may be used especially for ungauged rivers.1. For gauged catchments with no tributaries runoff hydrographs at upper and low catchmentgauging stations are used to determine river discharge and lag. Graphs are then plotted asfollows:

f(Q-,) (6.4)T = f(Q 2) (6.5)

where Q., Q, = discharges at the upper and lower gauges, andT = lag time.

If there are several gauging stations, graphs of the relationshipsQ 2 = f(Q 1(L) (6.6)T = f(Q 1#L) (6.7)

may be plotted where L = distance between the lower and upper gauges. These relationships maybe used for low flow forecasting at different forecast periods.When there is no intermediate inflow, the following cases have been observed:

^ t + T f1,tand 22,t+x = f ( Q1 , t )

(6.8)(6.9)

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For river reaches where there is considerable intermediate inflow (Q.,),22,t+T = f(ei,t + Q 3 ) ( 6 ' 1 0 )

2. Depletion curves are also used for local low flow forecasts ( Bonacci, 1975; Gurevitch,1956; Indri, 1960; Martin, 1973; Toebes, 1964). The following simple form is often used:Q t = Q0Kfc (6.11)

where Q t = discharge at time t after initial time t = 0,Q = discharge at time t = 0, andK = recession constant, and its value depends on thetime interval of the analysis.Depletion curves are discussed in Chapter 4 and those often adopted in hydrological practice are given in Toebes (1964).Equation (6.11) can be transformed into

-at + SQ = Q e p (6.12)t ot -at + 8noting that K = e * (6.13)

where t = number of days,a = f ( K) , andB = f(K) .This approach is used by Bonacci (1975).

The depletion curve may also be used for the prediction of the volume of river flow thatresults from precipitation.2t = f(2t-n' V < 6' 1 4 )

where Q. = predicted value of flow at time t,Q. = flow during the forecast period, andP. = subsequent recharge of water in the basin resulting from precipitation.The prediction of these two components of streamflow is made independently, thus

Qt+At = Qt + p K ( Pm + V ( 6'15)where CL...... = predicted flow at time t + At,Q. = streamflow resulting from basin storage predicted at time t,p = streamflow coefficient characterising the effect of losses,K = empirical constant to transform rainfall depth to discharge,P = precipitation during the period equivalent to basin lag prior to forecast, andP = precipitation after forecast determined from the meteorological synoptic fore

cast. Where such forecasts are not available, an average precipitation for theperiod is adopted.Details are given in Gurevitch (1956).

Computation of the predicted flow v is made from the depletion curve with Q t__ as theknown discharge at the time of the forecast. The depletion curve is based on steep recessionsand is determined as the difference between discharge values at adjacent time intervals. Twomethods of determining depletion curves are illustrated in Figs. 4.10 and 4.11. A third methodis presented in Fig. 6.5. Here the flows at time t-1 and time t are plotted on the abscissa andordinate respectively, and an envelope curve is drawn through the lower points corresponding tothe steepest recessions. This lower envelope curve may be used to plot the recession curve forany specified initial discharge.

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o ,1500 i-

500

O,.,

1000 - /O u '

4

// 2 3" 111 i

_.

' . 'j>^ . v^ '^^. \^"^T

O 1000 2000 3000 o 4000M - 1Fig. 6.5 Determination of depletion curves.(1 : lower envelope curve; 2 : line of equal value;3 : graphical method of determining Q. ) .

The depletion curve example given in Fig. 6.5 shows the relationship between inflows for agiven point along the Volga River ( USSR) at adjacent time intervals. The lower envelope curveis accepted as the design curve. The flow value determined from the curve is a function of theamount of water in storage in the basin.3. In regions with long and stable periods of low flow, forecasts up to 6-7 months in advancemay be based on seasonal depletion laws. For a period without precipitation and for a linearrelation between groundwater outflow and river discharge, the seasonal groundwater depletion lawis as follows:

= ( Q0 " q)e ct + q (6.16)where Q t

2oqc

low flow discharge at time t,stream discharge at time t = o,discharge to the stream from groundwater at time t,coefficient characterising the intensity of seasonalsgroundwater storage depletion, andbase of natural logarithms.

Values of c and q are determined from equations (6.18) and (6.19) which are based onempirical relationships between the mean 10-day or monthly discharges:= a Q 1 + b

log a^e(6.17)

(6.18)

q = 1 - a (6.19)

where Q. and Q = mean low flow discharge (10-day or monthly) for previous andsubsequent period T,a = regression coefficient, andb = regression constant.On the basis of equation (6.16) it is feasible to estimate the mean discharge at any time

(6.20)

(6.21)

interval T as a function of initial discharge Q thus. Q T = K Q 0 + (1 - K)q

-CTwhere 1 "cT

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Popov (1964, 1968) explains this method in detail.4. For situations where the forecast period is short, mean minimum monthly flows of largerivers may be predicted on the basis of the mean discharge during preceding months estimatedfrom long term discharge data measured between the end of recorded streamflow and the forecasttime. Such a relationship is shown in Fig. 6.6.

100 300 500 700 900 Q

Fig. 6.6 Relationship among mean September discharge ( Q T y ) ,mean August discharge ( Q V I I I) and precipitation depth ( P) .In forecasting flow one month in advance for small rivers, the value of mean discharge forseveral days during the previous month, for example from 20th to 25th or from 15th to 25th, canbe used.

(1968),Examples of the procedure are given by Dumitrescu and Tuca (1974), Anon (1963) and Popov5. Where runoff data are available at a gauging station, monthly flow forecasts may be madeusing the river network water storage data and the relationship

t+1 f(wt) (6.22)The method is outlined by Lazarescu (1967) and given in Anon (1963). The relationships aredeveloped on the basis of runoff data for previous years. The value of W. , the water stored inthe river network, is calculated for all years and expressed as the mean discharge for the timeperiod for which the forecast is made. The relation (6.22) is usually linear.

If groundwater flow is taken into account, it makes the above relationship more precise.For small basins, the previous month's mean minimum specific runoff may be used as an indicatorof the value of groundwater inflow (Q_ r t ) to the river and is expressed asQ t + 1 = f(wt, Qgr#t) (6.23)

6. For rivers that are fed only by groundwater during low flows, a forecast can be made byrelating low flows to phreatic water levels (see Anon, 1963), thus:^max* (6.24)

where Q t = mean minimum monthly discharge during the dry period, andI L a x = maximum phreatic water level during wet season"in astrategically located well.

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The well should belocated outside the backwater effect ofthe river orother water body, and itshould reflect the water table fluctuation ofthe main aquifer recharging the river.7. Ifriver discharge isincreased bya significant amount ofsurface water during the lowflow period, the following regression equation can beestablished (Lazarescu, 1969):

Qt+1 = f(Qt, Qt_T) (6.25)where Qt = maximum flood flow, andQt_1 = flow prior tostart offlood wave.8. During winter seasons, when air temperature may considerably influence river flows, thelow flow forecast may bemade according to anempirical relation ofthe form:

Qt +1 =f


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Riggs, H.C. (1961). Regional Low Flow Frequency Analysis. United States Geological SurveyProfessional Paver, 424-B, pp. 21-23.Toebes, C.and Strang, D.D. (1964). Onrecession curves. 1. Recession Equations. Jour.Hydrol. (N.Z.), Vol. 3, No. 2, pp. 2-15.Tuca, I. (1974). Prognoze delunga durata aapelor mici din periodada deiarna inbazinul

riului Mures. (Long-term forecasting of winter low water inMures basin.) Studii dehidrologie, Vol. XLIII, pp. 75-97.

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