Methods of computation of low streamflow
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Transcript of Methods of computation of low streamflow
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Methods of computation of low streamflow
Edited by T. A . McMahon and A . Diaz Arenas
A contribution to the International Hydrological Programme
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Preface
Although the total amount of water on earth is generally assumed to have remained virtually constant, the rapid growth of population, together with the extension of irrigated agriculture and industrial development, are stressing the quantity and quality aspects of the natural system. Because of the increasing problems, man has begun to realize that he can no longer follow a "use and discard" philosophy — either with water resources or any other natural resource. As a result, the need for a consistent policy of rational management of water resources has become evident.
Rational water management, however, should be founded upon a thorough understanding of water availability and movement. Thus, as a contribution to the solution of the world's water problems, Unesco, in 1965, began the first world-wide programme of studies of the hydrological cycle — The International Hydrological Decade (IHD). The research programme was complemented by a major effort in the field of hydrological education and training. The activities undertaken during the Decade proved to be of great interest and value to Member States. By the end of that period a majority of Unesco1s Member States had formed IHD National Committees to carry out the relevant national activities and to participate in regional and international co-operation within the IHD programme. The knowledge of the world's water resources had substantially improved. Hydrology became widely recognized as an independent professional option and facilities for the training of hydrologists had been developed.
Conscious of the need to expand upon the efforts initiated during the International Hydrological Decade, and, following the recommendations of Member States, 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, Unesco has been aware from the beginning of a need to direct its activities toward the practical solutions of the world's very real water resources problems. Accordingly, and in line with the recommendations of the 1977 United Nations Water Conference, the objectives of the International Hydrological Programme have been gradually expanded in order to cover not only hydrological processes considered in interelationship with the environment and human activities, but also the scientific aspects of multi-purpose utilization and conservation of water resources to meet the needs of economic and social development. Thus, while maintaining IHP's scientific concept, the objectives have shifted perceptibly towards a multidisciplinarty approach to the assessment, planning, and rational management of water resources.
As part of Unesco's contribution to the objectives of the IHP, two publication series are issued: "Studies and Reports in Hydrology"and "Technical Papers in Hydrology". In addition to these publications, and in order
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 in Hydrology" to which this volume belongs,is to present data collected and the main results of hydrological studies, as well as to provide information on hydrological research techniques. The proceedings of symposia are also sometimes included. It is hoped that these volumes will furnish material of both practical and theoretical interest to water resources scientists and also to those involved in water resources assessments and the planning for rational water resources management.
Contents
FOREWORD LIST OF TABLES LIST OF FIGURES 1. INTRODUCTION 1
1. 1 BACKGROUND 1 1.2 PURPOSE AND SCOPE 1 1.3 DEFINITIONS AND CONCEPTS 2
2. FACTORS AFFECTING LOW STREAMFLOW 4 2. 1 DESCRIPTION OF LOW FLOW PROCESS 4 2. 2 NATURAL FACTORS 5
2.2.1 Climatic factors 6 2.2. 1.1 Precipitation 6 2.2.1.2 Evaporation 7 2.2.1.3 Evapotranspiration 8 2.2.1.4 Air and soil temperatures 9 2.2.1.5 Humidity and wind 9
2.2.2 Hydrogeological factors 9 2.2.2.1 Geology of basin 9 2.2.2.2 Hydrogeological regime 10 2.2.2.3 Groundwater 11
2.2.3 Morphological factors 13 2.2.3.1 Relief... 13 2.2.3.2 Lakes 13 2.2.3.3 Swamps 14 2.2.3.4 Plant cover 15
2.2.4 Morphometrical factors 15 2.2.4.1 Basin area 15 2.2.4.2 Altitude 16 2.2.4.3 Slope 17 2.2.4.4 Orientation 17 2.2.4.5 Drainage density 17 2.2.4.6 Channel embedment 18
2.3 FACTORS DUE TO HUMAN ACTIVITY 18 2.3.1 Urbanization 18 2.3.2 Irrigation 20 2.3.3 Hydraulic works 21 2.3.3.1 Urban water supply 21 2.3.3.2 Other uses 22
2.3.4 Transfers 22 2.3.5 Hydroelectric stations 22 2.3.6 Mining 22 2.3.7 Navigation 22 2.3.8 Treatment of urban and industrial effluents...... 22 2.3.9 Drainage works 23 2.3.10 Land use changes 23
2.4 REFERENCES 24 3. ASSESSMENT OF DATA USED IN LOW FLOW ANALYSIS 26
3. 1 LOW FLOW DATA 26 3.2 ANALYSIS OF TRENDS AND CYCLES 26
3.2.1 Trends 27 3.2.2 Cycles 28
3. 3 ERRORS 29 3.3.1 Measurement errors 29 3.3.2 Rating curve errors 29
3.4 HOMOGENEITY OF HISTORICAL DATA 30 3.5 ERRORS IN ESTIMATED DATA 30 3.6 STATISTICAL SAMPLING ERRORS 30 3.7 RELIABILITY 31 3.8 REPRESENTATIVENESS OF DATA SETS 31 3.9 REFERENCES 32 COMPUTATIONAL PROCEDURES WITH ADEQUATE HYDROMETRIC DATA 33 4.1 SCOPE 33 4. 2 FLOW PARAMETERS AND PERSISTENCE 33
4.2.1 Central tendency 33 4.2.2 Variability 34 4.2.3 Skewness 34 4.2.4 Persistence 34
4. 3 FLOW DURATION ANALYSIS ." 34 4.3.1 Uses of flow duration curves 36
4.4 LOW FLOW FREQUENCY ANALYSES 1 36 4.4.1 Annual frequency series 36 4.4.1.1 Normal distribution 39 4.4.1.2 Log-normal distribution 40 4.4. 1.3 Gamma distribution 41 4.4.1.4 Pearson Type III distribution 42 4.4.1.5 Log-Pearson Type III distribution 42 4.4.1.6 Kritsky-Menkel distribution 43 4.4.1.7 Extreme Value Type I (Gumbel) distribution... 43 4.4.1.8 Extreme Value Type III (Weibull) distribution 44 4.4.1.9 Distribution choice by Goodness of Fit test.. 45 4.4.1.10 Comparison of distributions 45
4.4.2 Partial frequency series 45 4.4.2.1 Distribution of n-year flow 47 4.4.2.2 Transition probability matrix of low flows... 48
4.4.3 Uses of low flow frequency curves 49 4.5 RECESSION ANALYSIS 50
4.5.1 Uses of recession analysis 50 4.6 RESERVOIR CAPACITY-YIELD ANALYSIS 52
4.6.1 Use of reservoir capacity-yield relationships.... 53 4.7 STOCHASTIC MODELS 55 4.8 REFERENCES 55 DETERMINATION OF LOW FLOW WITH INADEQUATE HYDROMETRIC DATA... 57 5. 1 OUTLINE 57 5.2 METHOD OF ANALOGY 57
5.2.1 Application 57 5.2.2 Methods of computation 58
5.3 EQUATIONS FOR LOW FLOW COMPUTATION 60 5.3.1 Principles for classifying basin sizes 60 5.3.2 Regionalization 61 5.3.3 Regional design curves of
low flow characteristics 61 5.4 ISOGRAM MAPS OF LOW FLOW 67 5.5 LOW FLOW DETERMINATION FOR LARGE RIVERS 69 5.6 DETERMINATION OF COEFFICIENTS OF VARIATION AND
SKEWNESS OF LOW STREAMFLOW 69 5.7 USE OF EMPIRICAL COEFFICIENTS 70
5.7.1 Determination of low streamflow for short durations 70
5.7.2 Determination of low streamflow for a range of recurrence intervals 70
5.8 REFERENCES 71 LOW FLOW FORECASTS 74 6. 1 PREAMBLE 74 6 • 2 REGIONAL FORECASTS 75 6. 3 LOCAL FORECASTS 77 6.4 REFERENCES 81 BIBLIOGRAPHY 83
INDEX 92
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 low flows, appropriately linked with their probability of occurrence and duration, plays an important role in the design of water supply systems, in the management of water quality and in projects 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 Council decided at its sixth session to broaden the terms of reference of the working group on floods in order to include also aspects of low flow computation. Accordingly, the first session of the Intergovernmental Council of the IHP in April 1975 established a working group to prepare a casebook 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 1976 Paris (UNESCO Headquarters) 12-16 December 1977 Havana (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.
Roche Diaz Arenas 0. Sonuga A. McMahon M. Vladimirov M. Vladimirov
Diaz Arenas, i
It should be noted that the technical terms used in the book are consistent with those defined in the International Glossary of Hydrology (World Meteorological Organization - UNESCO, First edition 1974).
List of 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.
List of 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 associated alluvial 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.
5.1 Diagrammatical illustration of the effect of geographical zones on specific minimum discharge.
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 for rivers 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, spring snowmelt and summer flows.
6.2 Relationship between minimum summer monthly flow and sum of winter flow, losses during spring 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 meteorological indices.
6.5 Determination of depletion curves.
6.6 Relationship among mean September discharge, mean August discharge and precipitation depth.
1 Introduction
1.1 BACKGROUND
Whenever a project aims to use run-of-the-river waters, that is, when there is no regulating reservoir, or when flow regulation is to be seasonal, or if, as a result of man's activity, the regime of the stream is to be substantially disturbed, it is of vital importance to have a sound knowledge and understanding of the river's low flows and their characteristics. •
This knowledge must be understood quantitatively. Furthermore, the question of quality of the environment often depends on the availability of low river flows, particularly in areas of urban living, or on problems of public health, such as combating endemic diseases, as well as for thermal or chemical pollution. Thus, the connection between quantitative and qualitative aspects of water resources is especially sensitive during low water periods. For various reasons (health, environmental conditions), it is necessary to maintain a minimum discharge in rivers and, consequently, this water is not available for other water users. Another example of the relationship between quantity and quality concerns water salinity. Where this problem exists, 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 water levels will not be treated in this book.
1.2 PURPOSE AND SCOPE
A knowledge of low flows is based normally on direct observation of the natural flows of a stream. When measured data are lacking, low flow knowledge depends upon methods of calculation which make it possible to estimate with varying degrees of accuracy the basic information needed for projects. It is necessary to know how to use these data and to extract from them the characteristics of the regime which, in any given project, will enable the parameters of the scheme to be determined. It is also important to be able to forecast low flow volumes in the short and medium term, since this is an essential factor in the management of some water projects.
This book is written for engineers, water managers and technicians. It is a compilation of methods successfully used in different countries to compute low streamflows and is illustrated with case studies. A chapter is also devoted to theoretical aspects of natural and man-induced factors affecting low flows.
Following this introduction (Chapter 1), Chapter 2 deals with Factors affecting low streamflow. After describing the low flow process, the author explains the influence on low flows of physical factors: climate, geology and morphology. Factors affecting low flows as a result of human activity are also discussed.
Chapter 3 deals with Assessment of data used in low flow analysis. The data necessary for studying low flow characteristics are reviewed and analyses concerned with the determination of trends and cycles are outlined. Errors affecting data, their homogeneity and representativeness of data sets are also considered.
1
Chapter 4 deals with Computational procédures with adequate hydrometrio data. A great part of this chapter is devoted to methods of statistical analysis with various types of statistical distributions, but other techniques such as recession analysis and stochastic models are also considered. All these procedures require an adequate length of low flow data for the results to be reliable.
Chapter 5 concerns Determination of low flow with inadequate hydrometrio data. Direct use of statistical analysis is no longer applicable because data are not available or the record is too short. If this is so, it is necessary to compare various catchments, some of them having recorded data, and hence deduce, by analogy or by correlation, the low flows in an ungauged catchment. Analogy requires extensive study of catchment physiography and climate. The most objective way is to proceed from a regional point of view, in particular through regional maps of low flow isograms, or else regression equations linking low flow with catchment characteristics.
Chapter 6 deals with Low flow forecasts. This kind of forecast broadly uses the relationships between rivers and groundwater, taking into account the influence of the preceding hydrometeorological conditions on the soil moisture during the forecast period. For low flow forecasting at a given point on a river (that is, the provision of a local forecast) the recession or depletion curve is widely used. For all but short forecasts it is likely that the low flow forecast will be expressed in statistical terms.
1.3 DEFINITIONS AND CONCEPTS
Before proceeding it is important to define the subject in detail, distinguishing particularly between the notion of low flow and that of drought. Low flow is defined on a seasonal basis and is linked with the annual solar cycle and its regional or even local climatic effects. Low flows may be absolute or relative.
A simple regime, such as the tropical regime, has only one dry season during which there is only one period of low flow. An equatorial regime, on the other hand, is marked by two rainy seasons and two dry seasons, usually of unequal length; there is a main dry season with a corresponding absolute low flow, and a secondary dry season with a secondary or .relative low flow.
In temperate and cold climates low flows also occur. In large regions with extremely cold and long winters, such as in the western part of USSR (Siberia), rivers cease flowing during many months of the year. Whereas in temperate regions, due to the variability of rainfall, one or more low flow periods may occur each year.
Seasonal irregularities -; and hence the severity of low flow - differ considerably according to a basin's physiography and its climatology, and the low flow may vary from zero to half or more of the largest flow in a year.
On the other hand, drought is defined as a period of abnormally dry weather sufficiently prolonged for the lack of precipitation to cause a serious hydrological imbalance and carries connotations of a moisture deficiency with respect to man's usage of the water. It may involve different parameters such as annual abundance. We therefore speak of the ten-year recurrence interval dry year when referring to the annual flow which is exceeded with a frequency of 0.9. It is thus not associated with the idea of low flow, although the statistical study of low flows may lead to a drought characteristic related to a "low flow parameter".
Several concepts relating to the study of low flows are now considered. A period of low flow is usually defined by:
- its duration, which is often equated to that of the dry season. This is defined as the season during which either there is no rain or the rainfall is low having regard to climate;
- the absolute minimum or lowest flow, which is almost always equated to the smallest mean daily flow during the year;
a series of low flow which expresses a correspondence between fixed lengths of time (expressed as a number of days) and flows which have not been exceeded during an .equivalent number of days, which may be either consecutive or non-consecutive. Examples are:
2
- 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 low flow, which in this case is not defined as the smallest daily flow, may be distinguished by the number of days when no flow is apparent. This definition can be extended without difficulty to the 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 frequently draw 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 occur every year, we can still use the analyses relating to non-permanent streams outlined in the following chapters. If there is more than one year's interval between flows, another definition of low flow will have to be sought or the study of low flows as outlined in this book will have to be abandoned and rainfall studies carried out.
The final introductory comment relates to data. We cannot stress too much the importance of 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 and high flows.
3
2 Factors affecting low streamflow
2.1 DESCRIPTION OF LOW FLOW PROCESS
The period of low flow, which may occur once or several times in a year, is virtually constant for each basin or sub-basin but varies among basins. During these periods, the inflow from the basin to the river system is substantially reduced.
During a period when discharge decreases, there is little or no precipitation contributing to flow and no water is contributed from the basin's surface-water storages; rivers are fed almost entirely by groundwater, except supply from lakes and reservoirs.
In spite of this, in temperate and cold regions it occasionally happens that snowmelt caused by brief thaws or light showers helps to supply the flow during this period. In warm regions characterised by an incomplete differential pluvial regime, that is, one without a dry season in the strict sense of the term, the low water period is temporarily interrupted in certain years as a result of isolated rainfall. In some extensive basins of Very long continental 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 from March to May, at Dire from April to June and at Niamey from May to July. (Locations and hydrographs are shown on Fig. 2.1.)
Fig. 2.1 River Niger Basin showing annual hydrographs.
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During low flow periods, the groundwater regime is characterized by a gradual depletion of seasonal storage, the capacity of which is impossible to evaluate accurately. Where there is a well defined dry season, the river flow decreases at the same rate as the seasonal groundwater storage decreases and, in many situations, the river attains a relatively stable minimum flow governed by the inflow from deep groundwater.
Depletion or recession curves can be studied to understand the regimes of watercourses and groundwater storages. In a hydrograph, the lower part of the recession limb results from groundwater storage (Fig. 2.2). Castany (1967) has shown that the formulae of the depletion curves of a river are identical to those governing water yield from an aquifer whose regime is not subject to external influences.
Peak
u O ce < z o CO Û
Depletion curve
Groundwater runoff
(b)
""*" ""~ — / y
fs
V ^ Depletion cur\
TIME o ce < X o ço o
Fig. 2.2. Discharge fluctuations in a river and associated alluvium.
Many factors determine the regime and discharge during a low water period. With present knowledge, the effects of the majority of these factors cannot be differentiated as a rule, since the laws governing them have not been adequately elucidated and their magnitudes are not, in general, known.
From a practical point of view, these factors can be grouped together in two main categories: climatic and azonal. Climatological factors are often more important than basin characteristics. However, the influence of man's activity on the catchment, and hence on low flow, is of enormous importance. This chapter therefore describes in detail not only the natural factors affecting the hydrology of low flows but also factors due to human activity.
2.2 NATURAL FACTORS
According to Vladimirov (1976) natural factors can be grouped into three categories taking into account their primary importance in the genesis of flow. The first category which related to the generation of flow determines directly minimum discharge. The major factor is precipitation. This is the principal source of surface flows and groundwater. Groundwater, of course, depends upon the surface flows and determines the low flow in the absence of precipitation over a prolonged period.
The second group of factors affects the regime and discharge of low flow through temporal and spatial' reduction or distribution of precipitation. These are called indirect factors and include all those that do not directly contribute to the formation of the low flow but affect the variation of its rate. This category includes: evaporation losses (temperature and air humidity deficit, wind velocity) type of soil and plant cover, relief, number of lakes and swamps, hydrogeological characteristics of the basin. With respect to the last factor, Nassar (1973) points out that the storage capacity of an aquifer mainly determines the fluctuations observed in low flow discharges.
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The third category identified by Vladimirov is composed of factors that determine the relationship between river discharges and the subsequent impact of the direct and indirect factors described above. This category includes factors that are most frequently used for practical 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 other factors).
2.2.1 Climatic factors
2.2.1.1 Precipitation
All water occurring as river flow has at some time been condensed and precipitated from the atmosphere. 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 precipitation that occurred prior to the period in which the surface flow has substantially diminished or ceased altogether.
The effect of precipitation on streamflow can be directly observed in the basin's discharge characteristics. The effect can be modified to a greater or lesser extent by other factors. For example, natural characteristics of the basin (topography, soil^vegetation characteristics, hydrogeology) determine the time it takes for saturated flow to reappear in the form of surface runoff. This may range from a short time in the case of a small karst basin to a month or considerably longer in other types of basins. In order to determine the role of precipitation in the formation of low flow and to explain the nature of its impact, it is 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
120
1 100 E
u. & 80 Z 3 DZ
g 60 O _l u. g 40 O _l
20
400 500 600 700 800 900
A N N U A L PRECIPITATION ( 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 systems and 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 so deep 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 accumulation in the upper soil layers. Another important factor affecting low flows, in connection with the above mentioned characteristics, is, therefore, the intensity of rainfall.
. • Zones with surplus and sufficient moisture
+ Zones with water deficit
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Precipitation as snow contributes directly to the formation of runoff only at the time of thaw. During other times, low flows are supplied by groundwater. This process begins in spring and 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 very low flows during winter is stable, the correlation coefficient between winter discharge and rainfall 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 summer and autumn as a result of low precipitation during this period combined with high temperatures and hence high evaporation losses. Low flows also occur in winter, when precipitation is low and low temperatures prevent snow from melting.
When a river's regime is mixed, that is, 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 rain occurs in winter, minimum discharge will occur at the beginning of spring, which is the time when rainfall is diminishing and the temperature has not yet risen sufficiently for the snow to begin 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 rainy season has a marked effect upon the low water flow.
As a result of the substantial difference in evaporation rates the effect of precipitation upon 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 formation of low flows.
In small basins, and especially in those characterised by extensive karst formation, a high flow during the low water period will be closely related to heavy precipitation during the prior wet season.
In view of the foregoing, it is fair to say that the characteristics of a basin play an important role in the precipitation-runoff process. This is especially true for small basins. Rivers possessing extensive basins generally traverse regions characterised by highly dissimilar features, so that it is more difficult to determine their combined effects.
2.2.1.2 Evaporation
Having regard to the practical nature of this book, the term "evaporation" is used in its broadest sense to cover the different processes that constitute an indirect factor significantly affecting the flow during the low water period.
Evaporation implies the process of water emission by a free surface at a temperature below its boiling point and the combined processes whereby snow dissipates from fields or ice disappears from glaciers.
Consequently, evaporation is an extremely important factor in the hydrological cycle, since it largely determines the river discharge and reduces the flow during low water periods (Fig. 2.4). The effect of evaporation is most significant at the beginning of summer, when a large mass of water returns from the surface soil and from open water bodies to the atmosphere.
7
120
100
80
60
40
20
n
- . ' v1 ' ' -• \ • Zones with surplus
'. • \ and sufficient V » . • \ moisture — • \ — \ \ + Zones of water
\ • »\ deficit \ . • \
\ . • i
' • 1
- > ' r- i
S-u. i - b ^ i i i 300 400 500 600 700
ANNUAL EVAPORATION (mm)
800
Fig. 2.4 Relationship between low flow and annual evaporation. (East European Rivers)
in regions in which the rate of evaporation cannot be compensated by a higher rate of rainfall, an appreciable reduction in river discharge occurs. However, during low water periods, when rivers are fed almost exclusively by groundwater, evaporation is practically insignificant. The amount of evaporation depends mainly on solar radiation, temperature of air and water and of surface soil-water, humidity, vapor pressure, wind velocity and quality of water.
2.2.1.3 Evapotranspiration
Under this heading, it is essential to distinguish between two different processes; one called transpiration which is due to the plant cover, and the other which is related directly to the soil. 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 tilled land it is very difficult to measure them individually. The climatic conditions and the availability of water exert a similar effect on evaporation and transpiration, but in the latter case, the type of vegetation and its stage of development take on considerable importance. In regions 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 shallow water table. The consumptive use of these water—loving plants is generally more than twice that of 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 million hectares, a significant figure in comparison with the 235 million hectares of irrigated land in the 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 the surface.
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 the growing season.
2.2.1.4 Air and soil temperatures
These indirect factors affect streamflow in two ways. They affect total runoff by influencing other climatic factors, especially evaporation and rainfall. Also, air temperature affects the flow distribution through freezing. Thus it is one of the principal regulatory elements in temperate and cold countries through temporary retention of water within the soil in the form of snow and ice. During the winter season the influence of air temperature upon minimum discharge is largest.
The formation of ice on the surface of rivers, lakes and swamps materially reduces the quantity of water available as discharge. Szilagyi and Muszkalay (1970) explain the formation of this frozen surface with examples taken from Hungary. In the case of major river, ice begins to accumulate upstream of sections where the passage of floating ice is blocked. The frozen surface gradually increases in thickness upstream, and this is accompanied by an appreciable rise in backwater. For small rivers the discharge greatly diminishes once the period of freezing begins due to the reduced outflow of the basin. Consequently, streams that carry 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 also freeze, thereby retarding the groundwater flow and reducing the runoff that reaches the river as base flow. This phenomenon is more evident in years when little snow is recorded. If soil freezing progresses as deep as permafrost, base flow ceases altogether.
In winter there is a relationship between air temperature and low flow so it is possible to establish a correlation between these two variables. Komlev C1973) has carried out an extensive study of Siberian rivers (USSR) and succeeded in establishing an inverse correlation between the area 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 produce thaws, the low water discharge may then be higher than it is in summer. If rises in temperature alternate 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 through a sudden thaw and high flow. The same temperature conditions that produce a spring flood may also 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, minimum runoff is low. The effect of the permafrost layer is also evident in summer because of the resultant lack of groundwater reserves.
2.2.1.5 Humidity and wind
Humidity and wind affect the total runoff of streams and influence other climatic factors particular precipitation and evaporation. Evaporation is intimately related to air moisture deficit, and any increase therein causes an increase in evaporation, which in turn reduces soil moisture and possible grounwater recharge. Considering its effect upon flow,air moisture deficit plays an important role only in dry regions.
In some countries, the persistence of particular winds significantly affects the rainfall and hence the low water period. Wind also affects the distribution of the flow of rivers fed by large lakes. The quantity of water flowing into a river from a lake will vary with wind speed and direction.
2.2.2 Hydrogeological factors
2.2.2.1 Geology of basin
The continuous supply of water to rivers during low water periods is an extremely complex process (Roche, 1963). Nevertheless, Waugh (1970) and Riggs (1972) have pointed out that the geology of the catchment area is the main terrestrial influence- on low flows. Areas where surface geology includes unconsolidated sands and gravels produce a sustained flow during periods of drought which contrasts to these streams in which surface formations consist of
9
unfractured igneous rocks, clays or shales. In crystallized rocks where little fissuring has occurred, there is little groundwater flow. For two adjacent basins with the same meteorological conditions, the basin underlain by the more impervious formation will have lower discharges during low flow periods.
Karstic rocks can have a significant influence on the rate of flow during the low water period. This influence may either increase or decrease the flow, depending on the relationship between 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 well developed, rivers may disappear and discharge of neighbouring basins may be affected. It is difficult, 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 become submerged in swamps, as in Zapata, Cuba, and the study of its influence becomes very complex.
2.2.2.2 Hydrogeological regime
The hydrogeological conditions of a basin are closely related to its geological structure, since the latter determines the distribution of aquifers. Most of the rainfall that percolates through the soil to groundwater will eventually reach the river as groundwater flow. The type of soil and its composition largely determine the basin absorption capacity. For soils with large effective porosity soil retention is low but water yield and permeability are high. This explains the great dissimilarity in the behaviour of rivers in sandy or loamy areas compared with those that are located in clay regions. Examples of two sets of catchments are compared in Table 2.1.
It is evident that with greater infiltration capacity, the water is able to penetrate further into the sandy soils. Consequently there is a very clear dependence of low flow on infiltration. At times this relation may be adversely affected by other factors that influence infiltration (see Section 2.3.1).
Basins with friable, porous or fissured rock are most favourably placed for groundwater storage which will subsequently contribute baseflow to the river during low water periods. But the composition of the rock does not determine the rate of groundwater flow; this is governed to a large extent by the rock•s structure.
Table 2.1 Comparison of summer minimum runoff for river basins
River
Osuga
Tma
Vaya
Linda
Basin area (km2)
1230
1800
601
1010
composed
Dominating Soils
clay loams
sandy soils, sandy loams
clay loams
sandy soils, sandy loams
of different
Forest (%)
36
34
80
70
soils.
Swamps (%)
0
2
1
0
(Volga basin.
Lakes (%)
1
1
1
1
USSR).
Normal annual minimum daily
discharge (Vs. km2)
0.26
1.64
0.32
1.48
10
2.2.2.3 Groundwater
Groundwater, being the main source of surface streamflow during low flow periods, is available in two ways, namely as artesian groundwater, and as phreatic water. The volume of groundwater depends basically on the climate of the region and the geological structure and hydrogeological conditions of the basin.
During the low water season, the groundwater regime is characterised by a gradual reduction of seasonal reserves. As these diminish, the velocity of the flow and hence the groundwater discharge decreases, and, at the end of the period, the flow reaches normally a relatively stable minimum, often determined by the inflow of artesian groundwater. Thus the groundwater regime is governed by the nature of the hydraulic relation between the water-bearing horizons and the river.
Investigations carried out in many countries show that there is a close relation between the low flow of rivers, particularly the minimum flow, and groundwater discharge. An example for the Nemon basin in USSR is given in Fig. 2.5. But it should be pointed out that this relation is significant only in regions with uniform hydrogeological conditions.
In addition to the volume of groundwater storage, the transmissivity of an aquifer also affects groundwater discharge and hence river flow.
,-. ' 3
"E JC
</> ~v
^
£ g so Li-
CC LU 1-< 5 Q Z 3 2.5 O ce ü _l < 3 z z <
—
1
+ /
/++/
•V+m**
V+r* +/•/-/ /
i
i
/ T / *
/ /
• J*
' 0
—
4- Daily runoff
• Monthly runoff
l 0 2.5 5.0
MINIMUM SUMMER RUNOFF (t/s. km2)
Fig. 2.5 Relationship between annual groundwater flow and minimum summer runoff. (Nemon River Basin, USSR).
Studies in the USSR by Koudelin (1959) and Makarenko (1948) explain the different types of groundwater regime and their relationship to low flows. Six types of groundwater are now discussed.
Phreatic water
Phreatic water is found in the active zone of groundwater storage, that is, in the shallower subsoil layers. It seeps to the river system and constitutes the main source of river replenishment during the low water period. This may involve one or more water bearing sediments. The upper aquifer has a close relation with the upper subsoil layers, its recharge being the result of precipitation that directly seeps into this horizon. The regime
11
of deep phreatic aquifers is more steady, since they are fed by deep percolation. Where phreatic water is in direct contact with surface water bodies of the basin, such as lakes and reservoirs, it has a marked influence on the discharge and runoff regime during the low water period. Phreatic water reserves are recharged mainly in spring through snowmelt in cold regions, and by rain in temperate and tropical areas. In regions with considerable precipitation and where the groundwater is near the surface, their recharge may take place even in autumn. This is illustrated diagrammatically in Fig. 2.6.
DISCHARGE LEVEL
+
O
z H I
DISCHARGE LEVEL I o +
Fig. 2.6 Diagrammatic illustration of relationship between river discharge and associated alluvial groundwater deposits.
[(a) Volga River; (b) Kazanka River].
Water in unaonsotidated sediments
From the point of view of river flow, alluvial groundwater is very important. Here the stratum water, that is, water occurring in permeable formations, is generally discharged over large areas, although in some places it may take the form of concentrated outflows. This type of groundwater is characteristic of large river valleys.
Cvack or fissure water
Crack or fissure water is formed in massive igneous rocks and is highly metamorphosed sedimentary rocks where water accumulates and circulates in fissures. This also occurs in karstic rocks with slight development of stratafied layers. Outflow from cracks or fissures is concentrated. It is of great importance in small and mountain rivers as well as in the middle reaches of valley rivers. In karstic regions concentrated outflows of groundwater predominate.
12
Artesian water
Deep groundwater storages depend on the geological structure and hydrogeological characteristics of the river basin. Artesian water is not subject to sudden changes in time and represents an important supply source for base flow. This water, confined under pressure between impervious layers or in fissures in the earth's crust, is found in horizons that are deeper than those where phreatic water is located. In small sectors of a basin, it can rise as a spring yielding a considerable amount of water. Nevertheless, during times of minimum flow of the majority of rivers, its contribution is slight.
Karstic water
Karstic water, along with permafrost groundwater discussed in the next sub-section, constitutes a special category of groundwater. Karstic groundwater varies considerably depending, among other factors, on its relation with the surface, the development of fissures and internal galleries and the storage capacity of the host rock. The importance of karstic water to river baseflow during low water periods is greatest in years of little precipitation. In basins where karst is well developed, it acts as a natural regulator, maintaining a relatively high stable flow during the low water season. In some areas, however, instead of contributing to surface runoff, it may cause the loss of part of the flow, and in small basins the total disappearance of the streamflow through sink holes, caverns or fissures may occur. It should be noted, of course, that the influence of karstic water is greatest in small basins.
Permafrost groundwater
In cold regions streamflow may also be affected by the formation of ice in permafrost zones. Here part of the undergroundflow is transformed into ice which, on thawing during the warm season, flows into the stream.
2.2.3 Morphological factors
2.2.3.1 Relief
It is logicial that the relief of a basin should have an influence on the low flow of the basin. Comer and Zimmerman (1969) analysing data from two small basins in Vermont (USA) concluded that as the land use, climate and geology were the same in both catchments, the difference in low flows was caused by the differences in topography and soils.
Variations in altitude over a basin produce variations in precipitation. Where precipitation increases with altitude., river discharge also increases and, if other factors are favourable for groundwater storage, low flows will also be larger.
2.2.3.2 Lakes
Lakes and other water bodies modify streamflow by reducing the total annual runoff while at the same time they have a stabilizing effect on discharge. In studying the role of lakes and other water bodies in the formation of low flow, other aspects, for example, their size, their location and relation to the stream, in addition to morphological and climatic conditions of the area, must be taken into account (Table 2.2).
In general, it is found thatthe greaterthe number and size of lakes in a basin, the more regular the distribution of annual runoff and the greater the discharge during low water seasons. In basins with similar physicial and geographical characteristics, those with lakes exhibit low water discharges that are higher than those in basins without lakes. The same effect is observed when water stored in a lake increases. Por this latter case the bank storage in the sediments bordering the lake may represent a considerable part of the lake volume.
The location of lakes and reservoirs relative to the outlet of a basin and to the main river affects the low water period. Lakes that are located close to the outlet yield greater specific basin discharge than those situated further away. When lakes and reservoirs are located along the main streams, the regulating influence is greatest.
Endorheic lakes, those with no discharge into a river network, accumulate surface water and groundwater, which they subsequently lose by evaporation. Consequently, their influence is negative since the catchment area of the basin supplying the river is reduced.
13
Table 2.2 Minimum runoffs from drainage basins with lakes of different relative size. (Karelia, USSR).
Drainage Lakes Minimum daily River area (% Lake runoff
(km ) of drainage location (i./s.km^) area)
1985 7.7 in the upper 2.1 part of the drainage area
1775 7.7 uniformly over 2.5 the drainage area
1715 11.9 in the lower 3.4 part of the drainage area
Study of the influence of lakes and reservoirs on low flow demands different approaches, according to whether the lakes are large or small. When they are large, the action of each storage should be considered separately. On the other hand, when the surface of each lake is no more than a few square kilometers, they should be considered as a whole although they may be many in number.
Vladimirov (1976) shows how analysis of the hydrograph facilitates a detailed study of the influence of lakes on the behaviour of a stream regime. He proposes the use of a weighted average of lake area to demonstrate the influence of a lake on the formation of low flow (Table 2.3).
Table 2.3 Thirty days minimum specific discharge in comparison with lake area for four USSR basins.
Basin Lake area Weighted Swamp area Specific area (% of river value of (% of river discharge
River (km ) basin) lake area basin) Winter Summer
U/s.km2)
Pankan-oya 15.3 3 1.6 3 1.30 1.76 Ray-oya 17.1 3 0 0 0.86 0.91
Chernaya 293 9 3.5 2 6.96 4.56 Sestra 390 1 0 6 4.08 3.46
Source: Vladimirov (1976)
2.2.3.3 Swamps
Only the water contained in the active storage zone of swamps makes a significant contribution to the yield of a river draining a swamp. Yield lasts until the water stored in the swamp reaches a specific soil depth called the inert horizon, when for practical purposes, flow ceases.
After the surface water reserve is exhausted, evaporation continues from the soil, so that part of any subsequent precipitation must replenish both reserves and therefore not all the rainfall passes into the river. This illustrates the influence on the flow from lakes and swamps of precipitation falling over them and of evaporation from their surfaces. In regions affected by hurricanes, the path taken by a storm has a marked influence on the lake flow during the subsequent low water period. This effect is more significant when the area that is waterlogged is sufficiently extensive to retain much of the resulting precipitation.
Puna
Saari
Yakhtyavan
14
In cold zones, freezing of most of the swamp water occurs in winter, thereby diminishing
its yield. Vladimirov (1976) points out that, for permafrost zones where the whole swamp
freezes, regulation of flow is much less than in other regions because the upper crust of the
peat thaws only once a year-
Waterlogging of a basin may increase or decrease the low flow of streams. This will be
affected by the location of the swamp within the basin, the thickness of the active layer, and
the vegetation.
In wet regions, evaporation from the ground is slightly less than that occurring from swamps. It is considered therefore that during low water periods swamps act as equivalent to a water-bearing horizon and, after the rainy season, they slowly release water to the river. However, in dry regions, evaporation from swamps is greater than that from the soil. During the low flow period, therefore, the supply of water from these natural sources rapidly dries up, and the flow of rivers fed from these sources may equal, or be even less than, that occurring in similar basins where such sources do not exist.
2.2.3.4 Plant cover
The vegetation of a basin affects river flow mainly through transpiration of water stored in the ground. This effect reduces the runoff.
For the purpose of examining the effect of vegetation on streamflow, plant cover can be divided into three main categories; woods, either virgin or with appreciable secondary growth; perennial or annual bushes, with small secondary growth; and cultivated plants, natural grazing plants and other native plants with little growth. The influence of these three categories extends to annual runoff, to low water flow and to the flow regime, although the magnitude is not equal in each category.
Vegetation affects streamflow in various ways. It increases soil storage and permeability by its roots breaking up the soil. Further, a surface layer of dead leaves and humus has high infiltration capacity and retards overland flow and promotes infiltration.
Annual crops with shallow rooting systems rapidly exhaust water in the upper soil layers. Also some plants extract moisture from deeper lying horizons. In both cases, water is transpired that would otherwise go to maintaining river flow, although the deeper rooting plants will have the more significant effect. The effective growing period will also affect transpiration and hence low flows.
The infiltration of rain, or water resulting from the melting of snow, is usually greater in woodland soils than in any other areas. As well, temporary retention of water in the porous layer of humus and in the upper soil zone affects the recharge of aquifers that supply rivers with water during low flow periods. The effect of forests on groundwater storage is less in sandy or unconsolidated soils, which absorb water rapidly under any conditions, than in clayey or compacted soils, where water does not penetrate easily.
In comparison with shrubs and small plants, forests provide greater surface areas for interception and re-evaporation of water, as well as providing a more effective mechanism for absorption and for the exchange of water vapor between the foliage and the atmosphere. Forests, therefore, have an important effect on streamflow patterns.
In basins where a forest covers a large area, its location is also important. If it lies in the higher parts of the basin, because of the area's higher rainfall and, thus, availability of water for transpiration, regulating influence on low streamflow will be more evident.
2.2.4 Morphometrical factors
2.2.4.1 Basin area
Studies have shown that for most rivers there is a direct relation between basin area and minimum discharge during low water periods (Fig. 2.7). This relation is used in many methods for computing low flow.
15
E JÉ
(A
ü. O z ce
i Z
I I I
+ Lower basin
A Middle basin
- • Upper basin
6
5h
1 I I I I X "
400 800 1200 1600
DRAINAGE AREA (km2)
2000
Fig. 2.7 Relationship between minimum runoff and drainage area. (Severnaya Dvina River Basin, USSR)
The surface of a basin constitutes the catchment area for precipitation. Larger areas usually mean also larger river embedment. In most cases, as the area of the watershed increases, so does the groundwater basin. However, in karst regions or areas with artesian water, the surface water divide may not coincide with the groundwater divide, and the above relation does not hold. This is particularly important in small basins with highly developed karst.
2.2.4.2 Altitude
Generally, rainfall increases with altitude thus creating more favourable conditions for groundwater recharge. The effect of altitude on a catchment is very marked in mountainous regions (Fig. 2.8). It is observed in some areas that when altitude exceeds a certain limit, precipitation occurs as snow, basin slopes are steeper, rocks are more impervious and therefore low flow is much lower than in basins lying at lower altitudes.
w 3800
< Ul
cc < UJ
o < Z 3000 < cc Q
u. O z O 2200 I-
< > UJ —I UJ
Z ¡2 1400 s
-
•
— / / •
• /
1 1
• /
i i
•/ /•
i i 0 4 8 12 16 20 24 8 10 12
MINIMUM RUNOFF (t/s. km 2 )
6 8
Fig. 2.8 Relationship between minimum runoff and mean basin elevation. (Five mountain regions of Middle Asia, USSR)
16
2.2.4.3 Slope
The slope of a basin affects mainly the quantity of infiltration that takes place and the rate of overland flow towards river channels. As a result, basins with steeper slopes allow less time for infiltration, and the supply of groundwater is therefore reduced. The importance of this factor is limited to streams in mountainous regions.
2.2.4.4 Orientation
The orientation of a basin (particularly in mountainous areas) can have a considerable influence on the characteristics of the basin's flow. Orientation determines the exposure of the basin to the prevailing water-bearing winds in the region.
Observations carried out in different parts of the world show that where mountain barriers intercept moisture laden winds, river flow is high. However, a sharp reduction in runoff can be observed at lower altitudes. In medium and high mountain regions the difference in precipitation between the windward and leeward slopes can be enormous.
The direction of the slope also has a direct influence on the quantity and intensity of solar energy reaching the soil surface and has, therefore, an indirect influence on water loss through évapotranspiration.
In Cuba, for example, where rivers are fed exclusively by rainfall, the precipitation on the windward sides of the Sierra Maestra, the Baracoa mountains and the Sierra de Cristal is higher than that on the leeward slopes, due mainly to their exposure to the wet winds prevailing in the locality, although as Trusov (1967) points out, air instability, local altitude and the direction of the coast are also influential factors. Thus on the leeward side, the rainfall regime is considerably lower than the rest of the country; this accounts for the low river regime in the area. In South America a similar influence can be seen very clearly along the Pacific slopes of the Peruvian Andean Chain.
Furthermore, Ward (1967) shows that the direction of the slope is an important factor, particularly for high lands, in the accumulation or melting of snow.
2.2.4.5 Drainage density
Drainage density expresses in quantitative terms, the drainage network of a basin. An accepted form uses the relation between the sum of the lengths of all channels and the basin area.
Climate and many physical characteristics of a basin are reflected in the nature of its drainage system. The drainage system is directly related to efficiency of water removal, in two basins with the same depth and distribution of rainfall but with different drainage systems, the basin with the denser system will provide the more efficient removal of runoff.
The greater the basin area and the more highly developed its channel system, the greater will be the probability that surface water derived from rainfall will contribute to flow during the low water period. This occurs because runoff from most distant areas is possible and the regulating capacity is increased (Table 2.4).
Table 2.4 Relation between drainage density and specific discharge for three Cuban basins.
Basin Annual Specific River Station area Drainage rainfall discharge
density (A) (B) (km2) (mm) (A/s.km2)
Yara A. Sanchez 234 0.81 1940 33.3 15.3 Baconao Trucucu 167 0.64 1600 18.0 9.6 Cauto Pilar 137 0.58 1605 18.2 7.2
(A) Annual specific discharge. (B) Specific discharge for low rainfall season. Source: Diaz Arenas (1977).
Studies carried out by Carlstone (1963) show that drainage density, surface runoff and the movement of groundwater are part of a single hydrological system controlled by the transmis-sivity of rock and its overlying soil layer. According to Carlstone, the rate of groundwater discharge to streams varies directly with the transmissivity of the aquifer. As transmissivity becomes greater, the groundwater discharge into the river increases and surface flow decreases.
In some basins, storage on the flood plain plays an important role in the regime and discharge of flow during low water periods. During flooding, a considerable volume of water is stored which subsequently is yielded to the river during the following low flow period.
* 2.2.4.6 Channel embedment
When there is a hydraulic gradient from water-bearing layers to a river, groundwater is discharged through the wetted perimeter of the channel. In rivers studied by Singh and Stall (1974) , recession curves became steeper as embedment decreased. Increased embedment of the channel throughout a river course may tap deeper water-bearing horizons and thereby the yield of the groundwater basin to streamflow increases. But in these cases an increase in contributions from deeper levels will be governed by the availability of water in the draining horizons and the hydrogeological conditions that determine the discharge and regime of groundwater flow, especially the transmissivity of the strata. If other less permeable horizons are encountered through erosion in the watercourse, the relative increase in specific river discharge is not as great as otherwise would occur.
In studies of low flow and minimum discharge, Vladimirov (1976) emphasized the importance of channel embedment, particularly in those rivers which are supplied by groundwater during low flow periods. Consequently, it is necessary to determine the depth of embedment throughout a river's course and the extent that water-bearing horizons are encountered. But as Vladimirov states, the depth of embedment is difficult to determine because the erosive capacity of a river changes appreciably with velocity. It is necessary therefore to calculate a weighted average of embedment but the methodology is little developed at present.
There is a specific relation between basin area and depth of embedment; as the area becomes larger, the depth of embedment becomes more significant.
2.3 FACTORS DUE TO HUMAN ACTIVITY
The influence of man's activity on the regime and discharge of low flows of a river varies, both in nature and intensity, according to the level of man's social, economic and technical development, the type of economic activity involved, the climatic conditions governing the basin and the hydrological regime of the river. It is sometimes very difficult to evaluate this influence because there may be different activities taking place in the basin at the same time, and some effects may offset others. An extensive investigation dealing with the hydrological and ecological effects of man's activities and their assessment has been completed by UNESCO (1980).
2.3.1 Urbanization
In most countries, the water used for residential and industrial purposes is smaller than that for agriculture (Table 2.5).
Guaranteed supplies of high quality water are extremely important for the development of present day society. In regard to residential use, McMahon and Weeks (1974) have pointed out that household consumption may be assumed constant throughout the year, but garden watering varies seasonally (Table 2.6).
Large cities and industries exert a significant influence on low water discharges downstream of water intakes or effluent outfalls. When cities use groundwater or surface water conveyed from other basins and the effluent is discharged into an adjacent river, an increase in river flow occurs during the low water period. Conversely, when water is extracted from a river, and no additional form of replenishment is available, the discharge is reduced.
In this book, embedment refers to the river bed.
18
Table 2.5 Comparison between present water consumption according to different uses and population.
Uses and Argen-population tina
Countries World level (1)
Cuba France Haiti Japan Sweden USSR 1975 2015 (3)
Residential and industrial 7.4 water use (km /year)
1.4 18.0 0.03 26.9 3.1 93.8 700 3400
Agriculture 20.3 (km /year)
Population (Millions 25.4 of persons) (2)
6.7 14.0
9.3 52.9 (2)
3.6 57.0 0.1 178.1
4.6 112 8.2 253.3 (2) (2)
2100 4700
3968 7500 (2)
Source: 1. Korzoun and Sokolov (1978); 2. UNESCO (1976); 3. Japan, National Land Agency (1978).
Table 2.6 Seasonal variations of household and garden water use
Season
Annual use
Household Garden
Spring use
Household Garden
Summer use
Household Garden
Autumn use
Household Garden
Winter use
Household Garden
in three Australian
Melbourne ($, /person/day)
69 29
69 20
69 76
69 19
69 0
cities.
Metered
supplies
Geelong
( X. /per son/ day)
63 69
63 72
63 177
63 27
63 0
Unmetered
supplies
Yallourn
(¿/person/day)
169 92
169 58
169 251
169 61
169 0
Source: McMahon and Weeks (1974).
In the case of many rivers near large cities discharges of highly polluted effluents often
exceed the natural flow of the river during the low flow season.
Where the use of groundwater resources for urban supplies is excessive, a cone of depression (which varies considerably according to the rate of withdrawal) will be formed about the withdrawal area. This results in a reduction or cessation of groundwater discharging to any
19
streams in the region of the depression and hence a decrease in their flow. If the water being extracted is from deep-lying aquifers that do not supply the rivers, an increase may occur in the river discharges during the low water period if, after use, the extracted water is disposed into the rivers. In the Playas Verdes area near Lima (Peru), the reduction of phreatic water caused by intensive pumping is visible to an observer.
With urbanization and increases in population density and in the concentration of residential, industrial and commercial buildings, impervious areas increase in size resulting in marked changes of the natural hydrological regime of an urbanizing basin. The increase in impervious area substantially alters the rainfall-runoff ratio of the natural basin and tends to reduce infiltration and évapotranspiration. The characteristics of catchment and depression storage become drastically altered as the sewer and underground drainage systems increasingly facilitate the rapid disposal of water from the catchment surface. The combination of all these factors modifies the streamflow regime to such an extent that the change is reflected in an alteration of the volume of the groundwater recharge. As a result of the increase in impervious area, the low flows of streams within city limits may decrease along with those downstream. Alternatively, low flows increase as a result of leakages from the potable water distribution system, from sewers and from the storm water drainage system.
From the foregoing, it is clear that the influence of urbanization on low water flows depends upon the climatic and hydrogeological conditions characterising the region as well as particular features of the water supply and waste water disposal system.
2.3.2 Irrigation
Irrigation is a large water consumer and is very inefficient. In 1975, in Cuba and Mexico 80% and 96%, respectively, of the total water supplied was used for irrigation. Some countries are rapidly nearing the limit of available surface water; others, particularly in arid zones, are already experiencing shortages. In Latin America and the Caribbean, irrigation annually consumes over 95,000 million cubic meters, and the areas under irrigation are constantly increasing. Data for 1975 are shown in Table 2.7.
Table
Country
Argentina Brazil Colombia Cuba Ecuador Jamaica Mexico Venezuela
2.7 Cultivated and irrigated and
Area
279.0 851.2 113.9 11.1 28.4 1.1
197.3 91.2
the Caribbean.
Cultivated land
(in millions of hectares)
40.0 70.0 4.0 3.7 3.8 0.2 18.6 1.8
land in Latin
Irrigated land
1.24 0.60 0.25 0.68 0.18 0.02 4.70 0.30
America
Irrigation Cultivation
(%)
3.1 0.9 6.3 18.4 4.7 10.0 25.3 16.7
Source: CEPAL (1976).
In order to assess the influence of irrigation on low flows, it is necessary to carry out observations at the local level, taking into account the type, the frequency and the amount of irrigation in addition to the natural characteristics of the area. The influence of irrigation will be in all cases greater in years of low rainfall than those of high rainfall because irrigation demands are higher and water applications are more frequent. On the other hand, if évapotranspiration is high such that all moisture provided by irrigation is rapidly exhausted, the influence of irrigation withdrawals on river flow increases to a point when small streams cease flowing and the flow of larger ones becomes significantly affected.
In temperate and cold countries, large-scale agriculture and irrigation depend on the beginning and duration of the warm season during which rainfall is less than at other times. In tropical countries, by contrast, agriculture continues throughout the year and the period of abundant rainfall coincides with the warmest months. Thus, in the latter countries the greater
20
demands on streamflow are made during the low water months. According to Perez (1972), in the high tablelands and mesothermal valleys of Bolivia sowing time also coincides with the low water period with the result that a reduction in streamflow becomes more acute.
The water requirement of a crop varies with different soil conditions, agricultural techniques and climate. Inefficient irrigation leads to higher water consumption, requiring the extraction of greater volumes from available sources (surface flow, reservoirs, wells). Rice is generally cultivated in floodlands that for many months of the year offer an extensive area of free water for evaporation. Fast-growing varieties have recently been developed that yield two crops per year with a consequent increase in water consumption. During an irrigation season, water returns to nearby rivers as drainage but this constitutes a very small proportion of the water consumed by rice. Sugar cane is a tall, dense crop characterised by a lengthy period of transpiration. It also has a negative effect on low water flow.
If river discharge is too low during the irrigation season, it is necessary to augment the flow from upstream reservoirs or from groundwater. But dams disturb the seasonal regime, and continuous irrigation using groundwater can also affect low flow.
Irrigation water is supplied from rivers, reservoirs and wells. Whatever the method, it results in a substantial increase in both évapotranspiration from fields and evaporation from the distribution system, hence reducing the outflow from a basin.
Very little of the water supplied to irrigation areas is returned to adjacent streams and rivers. Generally, the less sophisticated irrigation techniques return more flow. If rivers are ephemeral, the drainage from irrigation lands contributes positively to the discharge during low water. On the other hand, return flow from irrigation areas has increased mineralization which may limit its use for further irrigation.
2.3.3 Hydraulic works
In many of the world rivers, the flow is regulated or modified by means of dams built to control water for irrigation, urban supply and power generation. These hydraulic works modify the low water flow, but their effect varies according to the purpose of the works and the degree of regulation of the river in question.
Of importance, too, are the operation of the reservoir and its location in relation to the outlet of the basin. In complex systems composed of more than one reservoir, it is usually very difficult to determine the influence of each one on the low flow of the main river downstream of the system.
Generally diversion dams store little water and their effect on river discharge varies in relation to the inflow rate. For small rivers, only small dams are built. Where they produce substantial changes in the low flow regime, they generally reduce low flow. On the other hand, large reservoirs make it possible to redistribute river flow. Their influence depends on when supplementary discharge is required. As a result the discharge occasionally drops during low water, but sometimes it increases. In major rivers that are wholly or partly regulated by reservoirs, the minimum seasonal flow largely determines the system of regulation.
If the bed of the reservoir has a high hydraulic conductivity, losses to groundwater-bearing horizons become substantial. This may mean an increase in low flows as a result of groundwater recharging the river downstream. This effect is observed in karst country where recharge reservoirs located on extensive karst formations transmit through seepage large volumes of water to deeper strata.
2.3.3.1 Urban water supply
The use of hydraulic works for controlling urban water supply also results in a reduction of river flow. Often little water is returned to the river; thus the effect is greater than that observed in the case of irrigation. Nevertheless, as it has been seen in Section 2.3.1, recovery of flow may occur downstream from a city or industrial centre as a result of effluent discharge. In a fully sewered city, this discharge could amount up to 2/3 of the water supplied.
21
2.3.3.2 Other uses
Small reservoirs (ponds or farm dams) serving pisciculture, poultry farming and stock-breeding exert a large negative influence on downstream low water flow. Such reservoirs retain the entire low water runoff and great losses occur through evaporation. Cunha and Marinho (1970) point out that in the north-east of Brazil the high evaporation rate (2000 mm per year) is one of the main factors limiting the use of very small capacity reservoirs for domestic and stock breeding requirements, particularly during periods of intensive drought.
2.3.4 Transfers
The purpose of building reservoirs and their transfer systems is not only for the redistribution of streamflow in time, but also for modifying its spatial pattern.
Complex systems can transfer water to and from more than one basin. In such cases, the low flow of basins that deliver water diminishes, while that of receiving basins increases.
However, it may happen that following the establishment of a complex transfer system, no alternation occurs in the flow of the rivers affected by such works. An example of this is the Mayabeque-Mamposton system in Cuba.
2.3.5 Hydroelectric stations
The operation of a hydroelectric station affects the flow downstream of the station. For example, the discharge from a power generating station in constant operation will differ greatly from one serving to satisfy demand only during peak periods. The use of dams for purposes of power generation generally causes an increase in low water flow. In the case of pumped storage systems, flow variability is reduced through repeated use of water without producing any discharge to the river.
2.3.6 Mining
Drainage operations carried out in open-cast or open-cut mines cause the drawdown of phreatic water that normally supplies streams during low water periods and, hence, a reduction in flow occurs. The drainage of galleries in deep mines causes an alteration in the regime of groundwater flow. This may exert a positive or a negative effect on the low water flow depending on a number of factors, including: distance of the mine from nearby streams, transmissivity of the rock, and hydraulic gradient between the groundwater inflow and outflow discharge.
Continuous pumping of groundwater for the purpose of draining borrow pits eventually gives rise to the formation of a cone of depression of groundwater around the drainage basin. But if in such a case the water extracted is so deep-lying that normally it would not contribute to the groundwater supplying an adjacent river, an increase in low water flow may occur if the extracted water is disposed of in the river. If this water is conveyed to neighbouring basins, a positive influence will be exercised upon them.
2.3.7 Navigation
In some circumstances, river navigation requires the regulation of flow so that an adequate depth of water is available to allow the passage of craft throughout the navigation period of the year. When natural flows are inadequate, water stored upstream is released. This effectively increases the flow during low water. There are other ways of maintaining adequate depths for navigation, all of which, however, combine to increase the flow during the low water period.
In general, the works used to regulate streamflow for the purpose of improving navigation also benefit other users of the water. There are, however, some exceptions to this. An example is the Panama Canal which, by means of a complex system of locks and sluices, eliminates low water runoff in the lower section of the Chagres River but no other benefits are derived.
2.3.8 Treatment of urban and industrial effluents
As noted in Section 2.3.1, rivers and streams commonly receive urban and industrial wastewater. This may occasionally increase low flow. However, unless effluents are previously treated, they will be highly polluted. Normally though, effluents are treated but even so they require some dilution before they are discharged into the river. When the natural flows alone do not provide
22
adequate dilution-, which frequently occurs during low water, it is usual to augment the flows by releases from an upstream reservoir.
Another source of augmentation is suggested by Hall (1967) who recommends replacing cooling water reservoirs and towers for the removal of waste heat by discharging the hot water into streams where the temperature rise would not be too great. This, in effect, would increase low flows.
2.3.9 Drainage works
The hydrological consequences of draining swamps are determined both by geographical limits and by the surpluses or deficits of rainfall and evaporation. In localities where drainage has been carried out without proper investigation, large-scale changes in water use have occurred either by new vegetation or by regulatory effects of the drainage scheme on the streamflow. Both factors have subsequently given rise to difficulties.
Studies by Ivanov (1963) in USSR have yielded information on the hydrological consequences of draining swamps in cold regions.
Through intensive drainage of swamps, water is extracted from deep-lying horizons, thereby increasing flow during dry seasons. The role of drained swamps in supplying river flow becomes more significant as the drained area is extended. However, this positive influence on low flow is greatest in early years after a drainage scheme has been completed. It should also be mentioned that, in certain circumstances, minimum discharge can be reduced as a result of drainage works.
Draining irrigated fields tends to compensate the decrease in flow caused by irrigation, but generally its effect is slight. For rivers that stop flowing, the effect of drainage may become appreciable. However, this depends on the irrigation techniques used.
2.3.10 Land use changes
A significant change in basin land use is often followed by an alteration of the regime and discharge of the stream draining the basin. Johnston and Meginnis (1960) point out that low flows in North Carolina (USA) increased as a result of timber felling in the mountains. On the other hand, in a small basin in Ohio, due to increased transpiration, low flows diminished after the planting of pine trees. Other authors (for example Riggs, 1965) have found that in basins planted with pines the period of river flow decreased as the forest cover increased. But in the Tennessee River Valley (USA) it has been observed that a change in the amount of vegetation has not given rise to any important changes in minimum flow (Johnson, (1967). Perera (1975), working in Cuba on small experimental plots of 8 m high pines and native pasture, recorded a considerable reduction in overland flow from the pine plots compared with native pasture plots even for rain of more than 25 mm. This demonstrates the influence that increased transpiration can have on the low flow of a basin through increasing the consumption of soil water.
In various tropical regions deforestation has led to a reduction of low flows and in some cases to the cessation of flow altogether. With, replanting, low flows have been re-established. This phenomenon is due to changes in infiltration capacity that resulted from land cover modifications. Escobar and Rossi (1970) state that in wet sub-basins of the river Quiros in Peru, the basin yield reduced when natural cover (trees, bushes and perennial herbaceous plants) was replaced by commercial crops. This effect was observed up to an altitude of nearly 3000 metres.
The foregoing discussion shows that river flow depends on a balance between infiltration which is affected by plant cover and losses through transpiration.
If it is intended to study the influence of forests on low flow and on minimum discharge, it is necessary to take into consideration the use of the soil before establishing experimental plots because conditions created by forests persist in soil over a long period of time and may conceal the phenomenon under examination. In the eastern part of the United States and in Africa, direct experience shows that afforestation on a rotational basis may increase low flow contribution without losing its regulating influence on infiltration and flow (FAO, 1969).
When agricultural and land improvement measures are practised extensively in a watershed, streamflow becomes more regular and, consequently, the flow during the low water period is
23
increased. Lvovich (1973) asserts that in some regions autumn ploughing can modify the water balance of arable land by creating favourable conditions for replenishing groundwater, which supplies river flow during low water periods.
2.4 REFERENCES
Basov, G.F. (1941). The influence of shelterbelts of Kamennaya Steppe on the regulation of surface run-off. (in Russian) Lesnoe Hozyaystvo, Moscow.
Carlstone, C.W. (1965). Drainage density and streamflow. United States Geological Survey Professional Paper 422-C. Washington.
Castany, G. (1967). Traite pratique des eaux souterraines. (Handbook of Groundwater). DUNOD, France .
CEPAL (1976). Los recursos hidráulicos de America Latina; informe regional. (Water resources in Latin America). (Comisión Económica Para America Latina).
Comer, G.H. and Zimmerman, R.C. (1969). Low flow and basin characteristics of two streams in Vermont. Journal of Hydrology, Vol. 7, pp. 98-108.
Cunha, A. da y Marinho, M.E. (1972). H i â r o l o9i a d e sequias en el nordeste de Brasil.
(Hydrology of droughts in the northeastern region of Brazil). Actas del Seminario Regional sobre Hidrología de Sequias. UNESCO.
Diaz Arenas, A. (1977). Tactores Morfometricos de Algonas Cuencas Cubanas. (Morphometric factors of some Cuban basins). Informe de investigaciones 2/1977. instituto de Bidroeconomia. La Habana, Cuba.
Escobar, D. y Rossi, R. (1972). Pronostico de las disponibilidades de agua en la zona Piura-Tumbes. (Forecasting of water availability in Piura-Tumbes zone); actas del Seminario Regional sobre Hidrologia de Sequias.
FAO (1969). Report of working group on Man's influence on the hydrological cycle. SC/HYMIDEC/20.
Hull, C.H. (1967). River regulation. Maclaren, London .
Ivanov, K.E. (1963). (Hydrological computations for the drainage of swamps.) (in Russian)
Hidrometeoizdat, Leningrad.
Japan, National Land Agency (1978). The Long-Term Plan for Water demand and Supply. Government of Japan.
Johnson, E.A. (1967). Effects of multiple use on peak flows and low flows. Inter. Symp. on Forest Hydrology, pp. 545-550.
Johnston, T.E. and Meginnis, H.C. (1960). Effect of altering forest vegetation on low flows of
small streams. IAHS General Assembly of Helsinki. Pub. no. 51
Kharchenko, s.i. and Maddock, T. (eds.) (1981). Investigation of the water regime of river basins affected by irrigation. UNESCO Technical Documents in Hydrology.
Komlev, A.M. (1973). (investigation and calculation of river water flow) (in Russian) Hidrometeoizdat, Leningrad
Korzoun, V.I. and Sokolov, A.A. (1978). Will there be water in the year 2015? Unesco Courier, 31st year.
Koudelin, V.I. (1959). (present problem of groundwater supply to rivers and difficulties in long-term investigations) (in Russian) Hidrometeoizdat, Leningrad,
Lazarescu, D. (1977). Methods for calculating minimum flow in Romania.
24
Lvovich, M.I. (1973). (The worldjs water) (in Russian) Mir, Moscow
McMahon, T.A. and weeks, C.R. (1974). Climate and water use in Australian cities. Australian Geographical Studies, vol. 11, pp. 99-108.
Makarenko, F.A. (1948). (On groundwater supply to rivers), (in Russian) Gesgeoltechizdat, Moscow.
Nassar, E.G. (1973). Low flow characteristics of streams in the Paaifia slope basins and lower Columbia River basin, Washington. United states Geological Survey.
Perera, R. (1975). Influencia del bosque en la calidad de las aguas. (Influence of forest on water quality). Voluntad Hidráulica no. 36.
Pérez, M. (1972). Antecedentes sobre la sequia en Bolivia. (Background of drought in Bolivia). Aatas del Seminario Regional sobre Hidrologia de Sequías,, UNESCO.
Popov, O.B. (1968). Podzemnoe pitanie rek. (Groundwater recharge of streams) (in Russian) Gidrometeoizdat, Leningrad. 291 pp.
Riggs, H.C. (1965). Effect of land use on the low flow of streams in Rappahamock county, Virginia. United States Geological Survey Professional Paper 525, pp. 15-27.
Riggs, H.C. (1972). Low flow investigations. Techniques of water resources investigations. United States Geological Survey.
Roche, M. (1963). Hydrologie de surface, (surface Water Hydrology). Gauthier Villars Editeur, France .
Singh, K.P. and Stall, J.B. (1974). Hydrology of 7-day, 10-year low flows. Journal of Hydraulics Division, ASCE. vol. 100, No. HY12, pp. 1753-1771.
Siren, A. (1960). Occurrence of low discharge periods in rivers in Finland. IASH General Assembly of Helsinki Pub. 51.
Szilagyi, J. and Muszkalay (1970). Estimation of stream flow under the ice cover. Proceedings of the Koblenz Symposium. Unesco (Studies and Reports in Hydrology, 13), Paris.
Trusov, I. (1967). Las precipitaciones de las Isla de Cuba. (Rainfall on the island of Cuba). Institute Nacional de Recursos Hidráulicos.
UNESCO (1976). Statistical Year Book.
UNESCO (1980) Casebook on methods of computation of. quantitative changes in the hydrlogiaal regime of river basins due to human activities. Unesco (Studies and reports in Hydrology, 28), Paris.
Vladimirov, A.M. (1976) (River flow in low periods) (in Russian) Gidrometeoizdat, Leningrad.
Wall, C.H. and Youngquist, C.V. (1942). Ohio stream drainage areas and flow-duration tables. Ohio Eng. Expt. Sta. Bull. No. Ill
Waugh, J.R. (1970). The relationship between summer low flows and geology in Northland^ New Zealand. Ministry of Works - Water and Soil Division. Hydrol. Pub. No. 6.
Ward, R.C. (1967). Principles of hydrology. McGraw-Hill, England.
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3 Assessment of data used in low flow analysis
3.1 LOW FLOW DATA
In low flow analysis hydrologists are concerned with three main characteristics, namely:
1. the magnitude of low flow, 2. the duration of low flow, and 3. the frequency of occurrence of low flow.
The magnitude of low flow is the quantity of water flowing through a given section of a stream for a specified period of time and it determines the amount of water available for use. The duration depends on natural conditions as well as man-made effects and may reflect some specified water use practices (for example, irrigation cycles). The duration also depends on a period of water deficit tolerable to the user or some other requirements. The frequency of occurrence of low flow reflects the risk of failure of a water supply scheme.
For low flow studies, therefore, data are normally specified in terms of the magnitude of flow for a given period of time (the duration) within a year or a season. The given period of time is usually taken as 1 day, 7 days, 10 days or 30 days. Other periods of time may also be used. One-day flows are used as data in flow duration analyses while periods up to one year and longer are required for some storage-yield studies. For other studies, 7-day or 10-day flows are employed.
The low flow data series may be obtained from various sampling procedures. In some cases, the low flow series may comprise annual one-day low flows, that is, the series of absolute mininum or lowest one-day flow within each year or season. Thus, for a given streamflow for which N years of observations are available, N values of low flow are obtained.
Other sampling procedures are adopted depending on the type of streamflow condition and the requirement of the data. For example, in certain areas where the streams are non-perennial (that is, dry for certain periods of the year) or for some agricultural practices the low flow series may be obtained as the absolute minimum of the mean of 7, 10 or more consecutive days of the season or year.
3.2 ANALYSIS OF TRENDS AND CYCLES
Low flow data may be considered as a hydrologie time-series made up of discrete variables. In general, the time-series may be composed of random as well as non-random elements. Non-random elements in the series may appear as one or more of the following components:
1. a trend; 2. an oscillatory movement about the trend; 3. a seasonal movement; 4. a deterministic component (commonly measured by the serial correlation coefficient)•
In order to analyse the time-series properly, it is necessary to break the series into its constituents and isolate each component for individual study. In low flow analysis, trend must
26
be eliminated from the non-random component to enable proper study of the oscillatory character of the time-series. Serial correlation is treated in Chapter 4.
3.2.1 Trends
The general idea of trend is that of a smooth motion of a time series extending over a long period of time.
In hydrological time series, a trend, detected from a given sample, may be due to:
1. a slow continuous variation of meteorological conditions (climatic variations) or a long periodic cyclic variation of the climate. (The sample represents either an increasing or decreasing limb of one cycle);
2. a modification of catchment physiography especially through human activity.
The first point constitutes a topic for complex hydrological analysis, details of which may be found in references such as Yevjevich (1972). The second kind of modification is permanent so long as human activity continues at the same level. It destroys the homogeneity of the data sample and must be taken into account during data assessment.
If in a given time-series the oscillatory pattern of a sequence of values "indicates a more or less steady rise or fall, the pattern is defined as a trend" (Mátalas, 1963). The most common method of investigating trend in a time-series is that of moving averages. Given a time-series made up of N observations x.., x_, x», ...., Xj. taken at equal intervals of time, the method of moving averages involves determining overlapping means of m successive weighted values. Consider an example where m = 3. The trend values may be computed as follows:
W1X1 + W2X2 + W3X3 y2 5 o.ia)
W1 X2 + W2X3 + W3 X4 y3 (3.1b)
w„x _ + w_x . + w_x = 1 N-2 2 N-1 3_N e )
N-1 3
The weights of the moving average, w.., w,, w3, should be such that
w, + w_ + w_ 1 2 3
— \ = 1 (3.2)
Thus for moving averages of m,
n I w. = m (3.3) j=1 3
The trend values may also be computed using the general formula (Davis, 1941):
X y w .x. .
i=-X 3 1+3
y± = Sr < 3 - 4 > I w
j=-X :
where w. = weight function whose value is a constant or a binomial coefficient given by
27
,.= Cl) (3.5)
and X = parameter of the moving average chosen sufficiently large to remove any minor variations in the series.
In this case the quantity, m = 2X + 1, is called the length of the moving average.
Some properties of the moving average are:
1. the sum of the weights divided by the length of the moving average must equal unity; 2. the weights may be positive and negative; 3. the weights are symmetrical about the middle value; and 4. the same trend values are obtained whether computed forward or backward in time.
Where each of the weights equals unity, a simple moving average results. "Although a simple moving average tends to smooth out the data, it does not preserve the main features of the time-series as well as a weighted moving average." (Mátalas, 1963).
The effect of moving averages on other constituents of the time-series is of considerable importance. If the method of moving average is used to remove the trend in a time-series which can be represented by the sum of a number of harmonics, the longer period oscillation tends to be absorbed into the trend. Cyclic movements in a time-series may also be distorted by trend abstraction. The moving average can also introduce an oscillatory movement into the random element of the time series. Because of these consequences of the moving average method (referred to as the Slutzky-Yule effect) care must be exercised in discussing the oscillatory nature of a time-series after trend abstraction.
For a test of significance of a trend, the Kendall rank test may be used. Given a series, x., x-, ..., x„, the number of cases in which x. > x. for j > i is counted. Let this number be P. The expected number in a random series is N(N-l)/4. "The excess of P over this number, if significant, suggests a rising trend; a deficiency suggests a falling trend" (Kendall, 1973). The number P is simply related to Kendall's coefficient of rank correlation which is defined as
4P (3.6)
N(N - 1)
and with variance,
The coefficient T may vary from - 1 to + 1. Its expected value in a random series is zero.
3.2.2 Cycles
Another important structure of a time-series relates to cycles. One cause of cyclical variation results from the seasons within a year. Cycles may be considered as more or less regular variations about a central tendency. Strictly, the variation should be cyclical in its pattern of recurrence; that is, the peaks and troughs should occur at equal intervals of time. But because of observational errors that may alter both the amplitudes and the periods of oscillation, and due to natural variability of flow, the movement may not be entirely uniform, but may lie within some well-defined limits of statistical error.
A simple and often used algorithm to eliminate seasonal variability from monthly data is as follows:
X — X
X. . = - ^ i (3.8) i,] s
28
where X. j = transformed monthly flow for year i, month j,
xi i = untransf°rms<3 monthly flow for year i, month j;
x. = mean monthly flow for month j, and
s- = standard deviation of monthly flows for month j.
The transformation not only eliminates seasonality but also constrains monthly flows to have zero mean and unit variance.
Cyclical phenomena in time-series may be investigated by methods employing Fourier series such as spectral analysis. Spectral analysis in conjunction with correlogram analysis offers a powerful technique for detecting and separating the constituent periodic components of a time-series. The analysis identifies the frequencies at which different factors cause the data to vary. The theory of this procedure and application to hydrology have been extensively developed and a number of publications include useful algorithms for computer applications (see Davis, 1941; Chow, 1964; Ryner, 1971; Yevjevich, 1972; Kendall, 1973).
3.3 ERRORS
The true value of any observation is unknown. Errors in measured data are often introduced during the stages of observing, transmitting, recording and processing of the data. The errors can be associated with water level observations as well as with discharge measurements. Errors may creep into the data through faulty gauging equipment or measurement procedures, improper recording or reduction of data, or through changes in observational technique during the period of measurement.
Two types of errors of relative importance in low flow studies are discussed in the next section. These are measurement errors and rating curve errors.
3.3.1 Measurement errors
Generally, measurement errors are of two types:
1. systematic errors or cumulative errors, and 2. accidental errors.
Systematic errors are errors which will have a consistent magnitude and same sign under similar conditions. These types of errors may arise as:
a. instrumental errors due to imperfections in the construction or adjustment of instruments ;
b. observer errors which may be caused by the habits or physical limitations of observers;
c. method of measurements; and
d. natural phenomena.
Systematic errors can be evaluated and corrected. Many of these errors can be avoided if appropriate standards are followed.
Accidental errors are often due to observers. Such errors, which may be negative or positive, are usually random in nature and are always present in hydrologie data. In general, it is assumed that they follow a normal probability curve. For this reason, the standard deviation is used as a measurement of the magnitude of accidental (or random) errors.
3.3.2 Rating curve errors
Rating curve errors depend on the way rating curves are derived and used.
The main difficulty in constructing rating curves is insufficient gaugings at high and low discharges to enable accurate curves to be drawn. The inaccuracy of the low flow portion of
29
rating curves is often due to weed growth, underflow past the gauging station, low velocity error and shifting control» Thus, annual minimum flows are often derived from extrapolating the rating curve. This procedure may lead to the introduction of considerable errors in the data.
A number of methods are available for rating curve extension (extrapolation). A common method is to fit an equation to the curve. The equation is usually of the form
Q = k(h - a ) b (3.9)
where Q = discharge, h = stage height, a = distance between the zero elevation of the gauge and the elevation of zero flow,
and k and b = constants derived from the observed portion of the curve.
Such a curve will plot as a straight line on logarithmic paper and therefore is easily extended.
Another common source of error in the data lies in the use of an old rating curve for a long period or using a recently derived rating curve to estimate discharges from previously observed stage levels. Furthermore, care needs to be taken to differentiate between zero flow and instrument malfunction.
The reliability of data computed from a given rating curve should be assessed from the knowledge of the station history and the characteristics of the stream.
Special attention should be paid to a shifting control. This results from riverbed variations which affect the low flow stage-discharge relationship. The stage-discharge relationship may change frequently, sometimes several times a year, due to (for example):
1. a sandy bed without downstream control (especially in arid zones); and
2. a very steep stream bedslope in mountainous areas, containing very large rocks and boulders which can be moved by floods.
At sites where the relationship varies frequently, a rating curve may be of little use. It will then be necessary to carry out discharge measurements at regular time intervals (for instance weekly or monthly) and to interpolate flows by using depletion curves.
3.4 HOMOGENEITY OF HISTORICAL DATA
Homogeneity implies that data samples are taken from the same population. Non-homogeneity in data often arises from man-made developments. It is also caused by relocating gauging stations. Other examples would include modification of the basin land use, water withdrawal from rivers or from interconnected groundwater storages and return flow from irrigated areas.
Yevjevich (1972) has defined inconsistency "as systematic errors in hydrologie data. Inconsistency is the difference between the observed values, with the inherent systematic errors, and the true values". The errors can be positive or negative and can fluctuate around the true value.
Data should be checked for homogeneity before analysis (for example, see Searcy and Hardison, 1960).
3.5 ERRORS IN ESTIMATED DATA
Estimated data may result from interpolation of missing data or extrapolation to an ungauged site from a nearby gauged site. In all cases errors are caused by inaccuracy or through the use of inappropriate procedures. Both systematic and accidental errors could result (see Section 3.3).
3.6 STATISTICAL SAMPLING ERRORS
Sampling errors, which are a function of data length, also introduce uncertainties in hydrological data. Data used in hydrological studies are observed and therefore are sampled data or a subset of an infinite population of events.
30
Sampling errors depend on the number of individual events used in the computation. The equations for standard errors of estimates of parameters are listed below. It should be noted that these assume that the data are normally distributed and N is large:
standard error of mean
standard error of standard deviation
standard error of coefficient of variation
standard error of coefficient of skewness
standard error of serial correlation coefficient
where s = standard deviation of flo N = number of items of data, C = coefficient of variation, k = lag between flow events.
These expressions display the effect of data length on the sampling error.
Because of sampling errors, care should be exercised in choosing the form of a theoretical probability distribution to fit a low flow data series. Mátalas (1963) has suggested that the theoretical probability distribution be defined by no more than three parameters. This is due to the fact that N is small so that large sampling errors are associated with parameters which are defined by the fourth and higher order moments.
3.7 RELIABILITY
With all the errors inherent in hydrologie information it is often necessary to assess how the results of a prediction (a hydrologie evaluation) vary from the true values, in other words, to investigate the reliability of the analysis. Thus, reliability of an event may be viewed as a statement of the agreement between the value of a theoretical prediction derived from sampled data and the true value.
A quantitative assessment of the reliability of an analytical procedure will depend on inaccuracies arising from a number of error sources. For example, in frequency analysis, in addition to the errors discusssed in the previous sections, choice of an unsuitable distribution will lead to further error and decrease the reliability of the analytical procedure.
3.8 REPRESENTATIVENESS OF DATA SETS
Another difficulty with low flow data is that during periods of low flow, the streamflow may be seriously disturbed by the operation of sluices and pumping stations, discharges from factories and other artificial influences.
Non-homogeneities can also arise from natural effects. For example, a severe fire through a forested catchment would probably change the yield characteristics of the basin during years immediately following the fire. Alternatively, differing low flow conditions may result from flows being yielded from particular aquifers depending on general catchment dryness. This may result in apparent inconsistencies in the observed runoff. However, unless these conditions are persistent for at least five years, the usual homogeneity tests will not in normal circumstances detect such differences.
Considering these and other errors enumerated above, low flow data sets have to be carefully considered before analysis is undertaken.
=
=
=
=
'S,
and
s/N h
s/(2N)
1 c { -
v l
v2 + 2C2 1/2
v , 2 2N '
i 6N(N-1) M N - 2 )
(N - k N -
(N+l) (N+3)
- i,v* k
»*
(3.10)
(3.11)
(3.12)
(3.13)
(3.14)
31
3.9 REFERENCES
Chow, v.T. (1964). Handbook of Applied Hydrology. McGraw Hill, New York .
Davis, H.T. (1941). The Analysis of Economía Tims Series. Principia Press Indiana, USA .
Kendall, M.G. (1973). Time series. Charles Griffin, London .
Mátalas, N.C. (1963). Auto-correlation of rainfall and streamflow minimums. United States Geological Survey Professional Taper 434-B.
Mátalas, N.C. (1963). Probability distribution of low flows. United States Geological Survey Professional Paper 434-A.
Ryner, J.M. (1971). An Introduction to Spectral Analysis. Pion Ltd., London .
Searcy, J.K. and Hardison, C.H. (1960). Double-Mass Curves. Manual of Hydrology: Part 1. General Surface - Water Techniques. United States Geological Survey Water Supply Paper 1541-B.
Yevjevich, v. (1972). Probability and Statistics in Hydrology. Fort Collins, Colorado, USA .
32
4 Computational procedures with adequate hydrometric data
4.1 SCOPE
This and the following chapter deals with computational procedures relating to low flow analyses. Whereas in the next chapter the streamflow data available for use in analyses are inadequate, here it is assumed that the data are of adequate length (say approximately 30 years or more), flow estimates are for natural or unregulated conditions and they are sufficiently reliable to be used in the analyses proposed. If less than 30 years of data are available, the procedures outlined in this chapter may also be used, but it should be noted that the results will have larger probable errors than those based on the recommended data length.
The discussion of techniques covers analyses in six areas of investigation, namely:
- flow parameters and persistence; - flow duration analysis; - low flow frequency analysis using either an annual or a partial series;
- recession analysis; - reservoir capacity-yield-reliability procedures; - stochastic models.
Each of these fields of analysis is now discussed in detail. A useful literature survey of low flow studies has been made by Vasak (1977).
4.2 FLOW PARAMETERS AND PERSISTENCE
In assessing the low flow characteristics of a basin, it is often desirable to know the general flow characteristics of the stream in question. To do this several parameters need to be defined. Some or all of them are required in specifying the theoretical distribution appropriate to the flow events under consideration. The most common parameters are measures of central tendency, variability, skewness and persistence.
4.2.1 Central Tendency
In general, the mean is the most important parameter of three concerned with central tendency. It is defined as follows:
x = Zx./N (4.1)
where x. = magnitude of the flow volume or discharge, and N = number of items of data.
Often for low flow analysis the median - a second measure of central tendency - is preferred. It is the middle value or the variate that divides the frequencies of a distribution into two equal portions. It is sometimes used in the place of the mean because it is less affected by extreme values. The mode is the variate which occurs most frequently and is the third measure.
33
4.2.2 Variability
In terms of variability, the standard deviation is a common measure and is defined below:
s = [E(x.. - x)2/(N-1)] /2 (4.2)
= [(Ex.2 - Nx^/iN-D] /2 (4.3)
The coefficient of variation, C , which is defined as
C v = f (4.4) x
is a dimensionless quantity and is widely used in hydrology. It is very nearly equal to the standard deviation of the natural logarithms of the flow.
4.2.3 Skewness
The main measure of skewness is the coefficient of skewness defined as
g = — (4.5) S3
W h e r e a = (N-1HN-2) X ( xi - ^ ) 3 ( 4 > 6 )
4.2.4 Persistence
Persistence is the non-random characteristic of a time series. For example, a month with low streamflow will tend to be followed by another of low flow rather than one of high flow. This feature, which is important in storage-yield studies, is characterised by serial correlation.
Serial correlation is not a parameter specifying the distribution but it is often used in hydrologie analysis along with the moment parameters. The serial correlation coefficient between successive events, that is, the lag one serial correlation (r.,) is defined as follows:
N-1 N-1 N-1 Ex.x. - Ex. Ex.
N-1 , i i+1 ,„ M 2 - i - i + 1
'1 , N-1 , N-1
- ^ T E X . 2 1 (Lx-)2 N"1 1 X (N-1)2 X .
-.0.5 r,- Ï n S( N' 1 ) 1 Ï ^ (4.7)
' r i N-1 , N-1 1 _1_ vx 2 J (j-j. ,2
.N-Iïi+1 (N-1)2 î i + i ) J
4.3 FLOW DURATION ANALYSIS
A flow duration curve is a cumulative frequency curve that shows the percentage of time during which specified discharges were equalled or exceeded during the period of a record. It represents a non-sequential series of streamflow events and it combines in one curve the flow characteristics of a stream throughout the range of discharge without regard to the sequence of occurrence.
As shown in Fig. 4.1, the flow duration curve is a cumulative frequency distribution and can be determined by integrating the frequency distribution of historical data. Generally, the abscissa scale is such as to linearize a normal distribution and the ordinate scale is a logarithmic scale of flow magnitude.
The procedure for constructing flow duration curves is as follows:
1. For the gauging station under consideration, all measured daily (or monthly flows) are grouped into 20 to 25 class intervals of logarithmic discharge values.
2. Class frequencies are cumulated beginning with the largest discharge. Each cumulated frequency is then expressed as a percentage of the total number of days (or months) in the record.
34
(a) FREQUENCY DISTRIBUTION
(b) CUMULATIVE FREQUENCY DISTRIBUTION
MAGNITUDE MAGNITUDE
(c) FLOW DURATION CURVE
1 10 30 50 70 90 99
NORMAL PROBABILITY SCALE: PERCENTAGE OF TIME FLOWS EQUALLED OR EXCEEDED INDICATED DISCHARGE
Fig. 4.1 Relationship between frequency distribution of flows and flow duration curve.
3. Discharge is plotted against cumulated percentage frequency on log-normal probability paper. A particular advantage with log-normal paper is that it provides adequate definition of the curve at the extremities of the plotted data and tends to linearize the curve over much of the range. Furthermore, the mean flow can be easily found, the median value is that value equalled or exceeded 50% of time, and the slope of the curve is a measure of variability.
Annual, monthly and daily flow duration curves are shown in Fig. 4.2. Discharges are often expressed in units of cubic metres per second per square kilometre of catchment area or standardized with respect to the average discharge so that comparisons among catchments can be
made. But in Fig. 4 . 2 , m /s is adopted.
1 r
Mean monthly ischarge data
10u
PERCENT OF TIME INDICATED DISCHARGE WAS EQUALLED OR EXCEEDED
Fig. 4 .2 Example of annual, monthly and daily flow duration curves.
(Niger River at Koulikoro, 1908-1977, Republic of Mali. Source: O R S T O M ) .
35
For most purposes, daily discharges are used to examine duration characteristics. The relative difference between daily and monthly curves for small basins can be large, but for large basins, as shown in Fig. 4.2, daily and monthly curves are similar. However, for comparative studies differences between daily and monthly curves are normally not important. Annual curves are rarely used in analysis.
Seasonal variability can be examined by determining for each calendar month the discharge that was equalled or exceeded for a particular percentage of time of the historical record. Normally, values for 10, 50 (median value) and 90 percent of time are chosen.
Another flow characteristic that can be deduced from a flow duration curve is the percentage of time (as days or months) that cease-to-flow conditions have occurred at a gauging station. This measure is more applicable to semi-arid zones than to temperate and tropical regions. However, it has been found to apply to small tropical island catchments.
The major limitation of flow duration curves is that they do not take into account serial correlation of the discrete events that are used in their construction. However, the flows making up the discrete events do implicitly include serial correlation.
4.3.1 Uses of Flow Duration Curves
In hydrologie studies, flow duration values of 90, 95 and 99% (see Fig. 4.2) are used as measures of a stream's low flow potential. The 90% value is used as a measure of groundwater contribution to streamflow (Cross, 1949). This same value has been used as a measure of run-of-the-river hydro-power potential (Searcy, 1959). Other potential uses of the low flow portion of a duration curve include analysis relating to irrigation and urban water supplies.
The low flow portion of the curve is an index of the amount of groundwater being contributed to streamflow from natural catchment storage. If the slope of the curve in the low flow portion is flat, groundwater contributions are significant. On the other hand a steep curve indicates poor base flows and probable cease-to-flow conditions. Thus a duration curve is a valuable tool for comparing drainage basin characteristics, particularly the effect of geology on low flows. This effect is illustrated in Fig. 4.3 using data from Ontario (southern Canada) and in Fig. 2.5 using Ohio (USA) data.
Another use relates to water quality studies. The curves are used to indicate the percentage of time that various levels of stream pollution will occur following the introduction of a pollutant of given volume and strength. In cases where water quality data are inadequate, they can be used to make approximations of average conditions of other parameters so long as there is an adequate correlation between the quality parameters and discharge (Searcy, 1959).
When interpreting flow duration curve results, it is important not to imply that the stream with the highest yield per unit area is the best source of supply without considering the size of its drainage area, and not to assume that the flow varies uniformly across the basin. Year-to-year variability can be considered by constructing separate daily flow duration curves for each year and examining the overall range of curves.
4.4 LOW FLOW FREQUENCY ANALYSES
Unlike flow duration curves, low flow frequency curves use data sequences that are independent and homogeneous and therefore they can be used to determine the possibility of occurrence of a flow event of specified magnitude. In practice, two types of low flow frequency curves are used. One type - the annual series - is based on the minimum flow event in each year of record and is used for events of less than 12 months' duration. The second type - the partial series -is used where frequencies of events longer than 12 months' duration are required. Both these procedures are now discussed in detail.
4.4.1 Annual Frequency Series
The procedure for constructing annual low flow frequency curves is as follows.
1. For given durations of lengths n days, minimum consecutive n-day flows for each year of the record are ranked with the lowest flow being ranked 1.
36
MONTHLY DISCHARGE DIVIDED BY MEAN MONTHLY DISCHARGE
Fig. 4.3 Variability of monthly flow duration curves and catchment geology. A: Coarse-textured soils formed on sand and gravels; B: Moderately fine-textured soils formed on very fine sand and silts; C: Medium-textured soils on till; D: Fine-textured soils formed on till. •
Source: Adapted from Ayers and Ding (1967).
Generally n equals 1, 7, 15, 30, 60, 120, 183 and 284 days. In some analyses, 10-day consecutive flows are also considered. The processing of data is an onerous task if daily flows are not available in suitable computer format.
Sometimes, too, the analysis is concerned with seasonal flows and in such a case low flow values are selected only from the particular season under consideration.
2. Plotting positions are assigned to each flow value in terms of recurrence interval of probabi1ity, thus :
P = l = _«-T N - 2c + 1
(4.8)
where P = the estimate of probability in any year of an n-day flow being equal to or less than the recorded value,
T = the estimate of recurrence interval and equals the mean interval between years containing an event equal to or less than the n-day flow,
M = the rank of the recorded n-day flow, and N = the number of years of streamflow data.
The value of c varies with the distribution under consideration. For example, for a normal distribution c = 3/8 but as a general rule it may be taken as 0.4 (Cunnane, 1978). On the other hand, Brunet-Moret (1975) recommends c = 0.5 while Beard (1962) and Lazarescu (1976) recommend c = 0.3 when the distribution law is unknown.
37
For the case of c • 0, the following common plotting formula is obtained. However, it is recommended that equation (4.8) be used. Practical differences between equations (4.8) and (4.9) are discussed in NERC (1975).
P = M
N + 1 (4.9)
3. Observed flows for the given duration are plotted on probability paper. Various types of probability paper can be used, for example log-normal probability paper, but more often log-extreme value paper is adopted.
The relationship between the normal distribution scale as a standardized variate, which is symmetrical about the mode, and the extreme value scale as a' reduced variate, which is asymmetrical, is shown in Fig. 4.4.
— Normal (Symmetrical)
Extreme value (Asymmetrical)
3^=» +5<f
Fig. 4.4 Relationship between normal and extreme value probability scales.
4. If the recurrence interval under consideration is less than N/3 years, an eye-fitted smooth curve through the data points may be used, otherwise a theoretical curve should be calculated. An example of an annual low flow frequency curve is given in Fig. 4.5 and processed data are presented in Table 4.1. Note that it is useful to plot all durations together on one diagram.
Table 4.1 Average Low Flows during Consecutive Periods. (Brandywine Creek at Chadds Ford, Pa., USA)
Recurrence Interval (years) 7 days
Average Discharges (m /s)
30 days 120 days
1.1 2 5 10 20 50
5.35 3.26 2.35 1.98 1.64 1.43
29 79 69 24
1.83 1.59
8.66 5.38 3.74 3.03 2.41 2.01
Some authors (for example, Velz and Gannon, 1953) have noted that annual low flow-recurrence interval graphs exhibit a break in the frequency curve near the modal value. This is regarded by them as the point where a change in drought characteristic occurs so that the higher frequency flows are no longer considered as drought flows but rather are flows blending back into normal conditions. This feature is shown diagrammatically in Fig. 4.6. (An example is given by Viessman et al., 1977, Fig. 5.14).
For estimation of low flows of high recurrence interval, a number of theoretical distributions have been used to estimate the flow magnitude. These are now considered.
38
0.91 0.5 0.2 0.1 0.05
PROBABILITY 0.02
Fig. /4.5 Example of annual low flow frequency curves. (Brandywine Creek At Chadds Ford, Pa., USA, for period 1913-1952.)
0.91 0.67 0.5 0.2 0.1
PROBABILITY 0.05 0.02
Fig. 4.6 Typical shape of some one-day annual low flow frequency curves.
4.4.1.1 Normal distribution
This distribution is included for completeness rather than as a typical distribution of low flow data. Indeed considering extreme value theory, it is unlikely that short duration streamflow events could be normally distributed. However, the distribution of long duration events, say greater than 60 days, is sometimes symmetrical and a normal distribution may be appropriate. Also for partial duration events, discussed in the Section 4.4.2, a normal distribution may be -used.
The probability density function of the normal distribution is given as:
39
1 fx - x ) 2
f(x) — exp [- -^ ^- ] (4.10) s/2w 2s2
where x = the sancle mean of flow events, and s = the sample standard deviation.
Consequently, the probability of x being equal to or less than X is
X prob (x < X) = / f(x) dx (4.11)
1 t 1 o = — - / exp [ - - Z2] dZ /2ir -=o
(4.12)
where Z = X "* * (4.13) s
which is known as the standardized normal variate.
Evaluation of the parameters x and s by either moments or maximum likelihood is the same and is as follows:
x = Zx./N (4.14)
where x. = the magnitude of low flow event, and N = the number of years of data
and s = [E(x. - x)2/(N-1)]/2 (4.15)
= [(Ex.2 - Nx^/iN-l)/ 2 (4.16)
Extensive tables are available in most statistical textbooks to evaluate equation (4.12) knowing Z.
To use the method to estimate the probability of occurrence of a low flow event from an annual series, x and s are computed from the flows making up the annual series and Z, the standardized normal variate, is determined from equation (4.13). Using Z, the appropriate probability is read from tables that evaluate the cumulative normal distribution equation (4.12).
If the low flow data are plotted on linear-normal probability paper, the theoretical normal cumulative curve (which is a straight line for the axes used) can be defined by drawing a straight line through the mean (x) plotted at 50% probability and through (x + s) plotted at 16% and 84% probability respectively.
4.4.1.2 Log-normal distribution
Invariably, the distribution of low flows is skewed. By initially taking a logarithmic transformation of the flows, the log flows tend towards normality and thus a normal distribution can be applied.
To do this several options are available. One is to analyse the transformed logarithmic flows as set out in the previous section, finally exponentiating the logarithmic flow appropriate to the given probability of occurrence.
Another approach is to calculate the parameters using moment transformation equations as set out below.
x = A + exp (0.5 S2 + X) (4.17)
s2 = exp (2[S2 + X] ) - exp (S2 + 2X) (4.18)
40
g = exp (3S2) - 3 e x p (S2) + 2 ( 4 > l g )
[exp (S2) - 1]
where X, S = the log-normal moment estimates of the mean and standard deviation,
A = a lower bound value such that _ y = log (x ^ - A), and (4.20) x, s, g = the mean, standard deviation and coefficient
of skewness of annual low flows.
For a three-parameter log-normal distribution, all three equations (4.17), (4.18) and (4.19) are needed. Equation (4.19) is first solved for S by an iterative procedure and then equations (4.18) and (4.17) are solved respectively. For a two-parameter distribution, A = 0 and equation (4.19) is not required. After values for X and S (and A if the three-parameter distribution is used) are determined, the appropriate logarithmic flow value for the given probability of occurrence is estimated and then exponentiated.
Mátalas (1963) recommended that the method of maximum Likelihood rather than the method of moments be used to define the parameters. The former procedure has the advantage that the lower limit will always be less than the minimum observed values. References to the procedure are given in Mátalas (1963).
4.4.1.3 Gamma distribution
The two-parameter Gamma distribution has been used extensively in studies relating to low flow analysis and storage yield problems. The probability density function is given as:
„, , 1 a-1 -x/3 f(x) = x e (4.21)
3 r(a)
where a = the shape parameter, and 3 = the scale parameter.
Based on moments, the scale and shape parameters are related thus
x = aS (4.22)
s2 = a$2 (4.23)
The probability of x being equal to or less than X is
X prob (x < X) = / f(x) dx (4.24)
o
= ! J Xa"1 e"X/e dx (4.25)
e r(o) o
This integral is known as the Incomplete Gamma Function and tables giving the value of the integral are available (for example, Abramowltz and Stegun, 1965).
To evaluate the parameters a and f$, it is recommended that Thorn's maximum likelihood procedure (Thorn, 1958) be adopted where
1 + /1 + 4A/3 a = ^ '— (4.26)
where o = the approximate maximum likelihood estimate of a, and
A = log x - log x Í4.27)
41
where log x = the mean of natural logarithms of flows x.
There is a small correction that can be applied to a but in view of the overall errors in flow data, this can be neglected.
It follows from equation (4.22) that 3 = - . (4.28) a
Although it is possible to construct Gamma paper, it is not readily available. So the theoretical curve [the solution of equation (4.25)] is usually plotted on log-normal probability paper.
4.4.1.4 Pearson Type III Distribution
By the addition of a location parameter, the Pearson Type III distribution may be regarded as a generalised Gamma distribution. The probability density function is
-(x - x )/3 f(x) = (x - x ) e ° (4.29)
Bar«x)
where x = a location parameter.
Based on moments, the location, scale and shape parameters are related thus:
x = x + a3 (4.30) o
s2 = a32 (4.31)
g = 2//Ô (4.32)
Evaluation of the parameters by maximum likelihood procedures is not straightforward. One method is to assume a value of x and then use Thorn's procedure to estimate 3 and a by fitting a Gamma distribution to the flows less the location parameter x . The logarithmic likelihood value (LL) is then computed from the following equation:
* « E(x - x0) LL(x x ,3 ,a , ) = - N a Aoge 3 - N Jtog_ T{a.) - + (a-1) Z Zoge(x - x )
o e e 30 e O
(4.33)
for several values of x (and corresponding values of 3 an<3 « determined). Next logarithmic
likelihood values are plotted against x , and the maximum values of LL(x|x ,3,a) is estimated o o
and corresponding values of x ,3 and a are determined. Based on these computed parameters and o
using published tables for the Pearson Type III distribution, the probability of occurrence of a
low flow event can be estimated. 4.4.1.5 Log-Pearson Type III Distribution
It is not possible to calculate the parameters of this distribution in the real domain. Thus the procedure to fit a Log-Pearson Type III distribution to data by maximum likelihood is to fit a Pearson Type III distribution to the logarithms of the original flows as described in the previous section.
Another procedure (which is now being widely used in flood analysis) is to calculate a frequency factor K. for a given recurrence interval and apply it to the following equation:
42
log X = X + KS (4.34)
where X = the flow for a given recurrence interval T, X = the mean of logarithms of flows, S = the standard deviation of logarithms of flows, and K = a frequency factor and a function of the coefficient of skewness of the logarithms
of flows.
Values of K are tabulated by Benson (1968).
4.4.1.6 Kritsky-Menkel Distribution
The Kritsky-Menkel distribution is obtained from a Gamma distribution using a transformation of the form
z = axb (4.35)
The probability density function is given as
a s a b ba-1 r b, = r ( » x exp[- ax ] (4.36)
Like the Pearson Type III distribution, the Kritsky-Menkel distribution is regarded as another form of the generalised Gamma distribution. Parr and Webster (1965) describe a procedure for estimating the parameters a, b and a using maximum likelihood.
4.4.1.7 Extreme Value Type I (Gumbel) Distribution
The extreme value theory applies to the smallest (or largest) values in each of N independent sets of n independent observations each drawn from the same population. The fundamental theorem is as follows (Court, 1952):
In a set\ of N independent extremes, x«, x- ... x^, each being the extreme of one of N sets of n observations each of an unlimited, exponentially-distributed variable, as both N and n grow large the cumulative probability that any one of these N extremes will be greater than any chosen quantity x approaches the expression
$(x) = exp [-e+a(x-x)] (4.37)
where a = a parameter of the extreme value distribution, and x = the mode of all values of x.
Thus the probability density function is
f(x) = ae+a(x_x)4>(x) (4.38)
For estimating the parameters Gumbel (1954) introduced a modified least squares method by minimizing both the vertical and horizontal deviations and taking the geometric mean of the parameters from the two minimizations giving
°N a = — (4.39)
s
where x and s = the mean and standard deviation of the set of extremes, and y and a = the mean and standard deviation of a theoretical variate depending only on
sample size N.
Tables of y„ and a are available for example in Court (1952). N N
The expected extreme for any set of N extremes, that is, the extreme value for which the average recurrence interval is T, corresponds to the probability given by y where
y = - log [- log *(x)] (4.41)
An alternative method, giving a more efficient solution, for estimating the parameters is by maximum likelihood. This method is complex and requires a good deal of computation. However, a simpler procedure that gives estimates which are consistently close to the maximum likelihood estimates is estimation by sextiles. The procedure is outlined for flood analysis in World Meteorological Organization (1969). To apply the method to low flow analysis, negatived low flow values must be used as the equations given in the reference are for estimating maxima rather that minima values.
4.4.1.8 ' Extreme Value Type III (Weibull) Distribution
As observed in Fig. 4.5, annual low flows tend to be curvi-linear when plotted on log-extreme value paper. Gumbel proposed that the Extreme Value Type III distribution could be used to describe low flows. For low flows this is also known as the Weibull distribution. The cumulative probability function is given as
a $(x) = exp [- (*•-" l) ] (4.42)
y — t
where $(x) = the probability of x being equalled or exceeded, e = a lower limit either zero (for small streams) or a small positive value (for large
streams), U = the location parameter, and 1/a = the scale parameter.
Thus the probability density function is
f(x) " T^T (^T > a 1 *** [" ( ^ ) < X ] (4'43)
For estimating the parameters Gumbel (1954) proposed the method of moments, but the method is more complex than for the Type I distribution. The following equations are applicable:
/fTJ" = ii3/a3 (4.44)
U = x + a A(a) (4.45)
e = vi - a B(a) (4.46)
where x, a = the mean and standard deviation of annual minimum flows, and ^3.., A(a) and B(ot) are functions of a tabulated by Gumbel (1954).
The criterion for e > 0 is given by
x + a[A(ct) - B(a)] > or = 0 (4.47)
respectively.
If e is negative and small, it is assumed to be zero. If the lower limit turns out to be larger than the observed smallest drought or e is a large negative value, then the theory fails.
Theoretical values of low flow are obtained from the following equation:
44
log(x - e) = log (JJ - e) - 0.434 y/a (4.48)
where
y = - log [- log *(x)] (4.49)
Both the maximum likelihood and sextile methods as noted under the Extreme Value Type I procedure can also be applied here (see World Meteorological Organization, 1969 and NERC, 1975). The maximum likelihood procedure is more efficient than moments but, of course, it is more complex. Harter and Moore (1965) have presented an iterative procedure for its solution.
4.4.1.9 Distribution Choice by Goodness of Fit test
A goodness of fit test indicates the agreement between an observed sample of low flows and an assumed theoretical distribution. Two standard tests are available for this purpose namely X goodness of fit test and Kolmogorov-Smirnov procedure. It must be stressed, however, that each is concerned with how well the whole distribution fits all the data. Each is little influenced by differences in the tails of the theoretical and empirical distributions although they are the parts of the distributions that are of concern. For a description of these tests see, for example, Lindgren and McElrath (1959).
4.4.1.10 Comparison of Distributions
Two comprehensive studies of low flow distributions have been carried out using North American data. The first by Mátalas (1963) considered the Extreme Value Type III, three-parameter Log-normal, and Pearson Types III and V distributions. In the second study the Gamma, two-parameter Log-normal, square-root Normal, Normal and Weibull distributions were compared (Joseph, 1970).
Using annual minimum daily and 7-day low flows for 34 streams, Mátalas concluded that the Extreme Value Type III and Pearson Type III distributions fitted the data equally well and recommended the use of maximum likelihood estimates of parameters rather than moment estimates. Based on analysis of 37 streams, Joseph concluded that the Gamma distribution was the best of the five distributions tested.
4.4.2 Partial Frequency Series
For cases in which the independence of the annual series of low flows is in doubt, it is necessary to use a partial duration series. Two methods have been used to set up the series. This procedure may also be adopted for duration periods beyond 12 months, in which the frequency of the low flow series needs to be determined.
In the first method, all n-consecutive monthly subsequences (n > 12) out of a total of 12N months (where N = number of years in the record) are ranked, but because of the dependence between near ranks and particularly adjacent ranks, this approach is not recommended. The alternative approach is to rank in ascending order of magnitude, streamflows of n consecutive months such that overlap does not occur. This is easily carried out by a screening procedure and an example for 24 months duration is shown in Table 4.2.
The lowest 24 months running total (rank 1) for the entire record is determined and noted. Next, 23 values prior to and 23 values following the chosen value are excluded from further consideration. The number of values eliminated is equal to twice the duration period (in months) less two. From the remaining events, the lowest 24 months event (rank 2) is found, and adjacent values excluded as before. The procedure is continued until the ranked flows reach a value equal to the mean flow.
The next step is to convert the ranks to sample recurrence intervals by:
T-^4-1 {4.50)
45
Table 4.2 Example of Twenty-four Months Running Totals of Streamflow. (Hunter River at Moonan Dam Site, N.S.W., Australia).
Year JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC.
1914
1915
1916
1917
1918
1919
1920
1921
1922
-464-
444-
444-
446-
444-
-40-
-84-
444-
-454-
-448-
-444-
-446-
-444-
-39-
-84-
-446-
-454- -444- -476- - 3 * 4 - -486- J69J13 469- -446-
-444- -444- -447- -98- -94- -95- -94- -99-
-444- -444- -99- -96- -=Kr-
-444- -444- -444- 444- -444-
<3>3
-444 444
93- —94-
-444-
-444- -494- -496- -447- -448- -448- -86- -84-
-38-
-94-
-464-
-38-
-98--®1 -44- -58- -64- -65-
-454-
-444-
259
-444-
260
-474-
257
-484-
268
444-
273
-445-
276
-445-
-84-
-445-
-449-
-64-
-65-
-2-44-
278
-364-
-449-
-444-
-4+7-
-445-
-58-
-78-
-444-
270
1939
1940
1941
1942
447-
3> 64-
(S)'
-446-
-84-
-64-
-48-
-449- -444- -444- -444- -444- -98- -94-
-79-
-64-
-55-
-^7- - 76- -^4- -74- -59- -55-
-57- -55- -57- -58- -55- -54-
-94-
-54-
-54-
-54- -54- -55- -84- -45- -87- -442-
-94-
-54-
-54-
-446-
-84
-56-
-49
-444-
Source: McMahon (1969).
where T = the average recurrence interval in years of the M ranked event; N = the number of years of streamflow data; and M = the rank of the flow event.
The interpretation of equation (4.50) must be understood in the light of the duration of the event under review (n months in duration). The average recurrence interval of an n-month event (T ) of rank M is defined as
12N + 1
T = n
(4.51,
where 12N
total possible number of independent events in the sequence.
The recurrence interval T has units of n months and is converted to years thus :
T = - T 12 n
(4.52)
N + n/12 M
N + 1 (4.53)
It should be noted here that the reciprocal of equation (4.8) with c = 0.3 may be more appropriate than equation (4.50).
46
Next, the ranked flows are plotted on appropriate probability paper. It has been found that log-extreme value paper ia satisfactory. If the recurrence interval under consideration is less than N/3 years, an eye-fitted smooth curve should be adopted. An example of partial low flow frequency curves is given in Fig. 4.7.
0.91 0.5 0.2 0.1 0.05
PROBABILITY 0.02
Fig. 4.7 Example of partial low flow frequency curves (Hunter River at Moonan Dam Site, N.S.W., Australia).
Source: McMahon (1969).
4.4.2.1 Distribution of n-Year Flow
Sometimes it is necessary to determine the probability of occurrence Of a sequence of n-consecutive years of flow of specified volume, given N years of annual flow data at the site in question.
If the set of annual flows are normally distributed and independent with mean, x, and standard deviation, s, then the distribution of the sum of n-consecutive year flows is also normally distributed with
x = nx n
(4.54)
7n~ (4.55)
where the mean of n-year flows, and
the standard deviation of n-year flows.
On the other hand, if the flow distribution is skewed,it may be represented by a Gamma distribution which possesses an important additive property that can be utilized to determine the probability of occurrence of an n-year flow. The property may be stated as follows.
For a two-parameter Gamma distribution, the sum of n independent Gamma variables with ... = 3 is a Gamma variable with parameters a. = a_ a and f5. =
47
and as
then
where
x = n
a =
a n
X
n n x
*n
the s
=
=
3h
n a
a n
X
n o n ape
n
nx no
parame
(4.56)
(4.57)
(4.58)
B = the scale parameter of n-year flows.
Thus assuming the n-year flows are Gamma distributed and independent, it is possible to determine the probability of occurrence of an n-year flow of given volume. To do this one uses Thorn's procedure to calculate the scale and shape parameters of one-year flows, equations (4.56) and (4.58) to calculate the scale and shape parameters of n-year flows, and tables of the Incomplete Gamma distribution to determine the appropriate probability.
4.4.2.2 Transition Probability Matrix of Low Flows
An alternative procedure to those discussed above is to determine the steady state distribution of the n-month subsequence of flows. This can be done by first constructing a transition probability matrix based on historical data.
A transition matrix shows the probability that a variable will assume any given value at the end of a time period, given that it has any value at the beginning of the period, thus:
State at time t
State at 2 time (t+1) —
3
Prob (Zt+1= 2|Zfc = 3)
where Z. t+1' Zfc = the state of variable at times (t+1) and t.
Elements of the matrix express the conditional probabilities that result from examining in turn the value of each recorded subsequence given the value of the preceding one. The steady state distribution, obtained by powering up the transition matrix, represents the overall probability of the n-month event being in any state.
The procedure may be represented as follows:
[Pt+1] = [T] [Pt] (4.59a)
where [Pfc+<] = the column vector describing the probabilities of the n-month flow subsequences being in state 0, 1, 2, ... at the end of the t time period or at the beginning of the (t+1) time period;
[P.] = the column vector describing the probabilities of the n-month flow subsequences being in state 0, 1, 2, ... at the beginning of the t time period, and
48
[T] periods.
the transition matrix of the n-month flow subsequence between t and (t+1) time
Thus, given [P.j] ,
[P21 = [T] [P.,]/ hence [P2]
[P31 = [T] [P2] , etc.
(4.59b)
(4.59c)
As the number of iterations increases, [Ptl will approach [Pt+i] irrespective of [P.], that is, the flow distribution will reach its steady state condition which is independent of the initial condition. The steady state distribution also may be obtained by substituting [Pi.+1] • [Pfc] in equation (4.58a), and solving the resultant set of simultaneous equations after setting the coefficients of any equation equal to unity.
Results of applying the matrix technique are shown in Fig. 4.8 where the steady state solution is compared with values plotted from an independent event series. This series was obtained by dividing the historical record into N/n successive non-overlapping events of n months duration, ranking them, and plotting them in the usual manner. (N is the total number of months in the record.) The small sample sizes of the independent series (30 items of 30 months duration events and 15 items of 60 months duration events) make it difficult to define with certainty the tail of the distribution using this procedure. Nevertheless, overall the matrix results compare satisfactorily with the independent series of data.
2.0
E
I 1.0
< O Q Z cc O u.
2 Li. z <
0.5
I I I I I I I I I I I l ^ l
— Steady state (matrix method)
O Independent series
10 30 SO 70 90
PROBABILITY ( % ) 99
Fig. 4.8 Frequency curves based on transition matrix method and independent series. (Yarra River at Doctors Creek, Vic, Australia).
4.4.3 Uses of Low Flow Frequency Curves
An important use of low flow frequency curves is in reservoir capacity-yield analysis. However, this approach gives biased results in that the flows into the storage are overestimated, consequently storage need is underestimated. Hardison (1965) suggests that for small storages in which the annual series is used in the analysis, the design capacity should be increased by
49
about 10%. For the partial series, the error varies from 10% to 20%. In conjunction with duration and frequency curves, storage estimates make up a complete assessment of the streamflow characteristics of a region. An example for Illinois (USA) is given by Stall (1964).
A second major use of low flow frequency curves relates to the estimation of recurrence interval (or probability of occurrence) of low flow conditions. Curves such as those presented in Fig. 4.5 are most important in streamflow quality studies. Many countries now base their stream water quality standards on a flow condition in a stream specified as the 7-day 10-year low flow. (This is defined as the lowest average flow that occurs for a consecutive 7-day period at a recurrence interval of 10 years.)
To illustrate the application of low flow frequency analysis, reference is made to the Hydrologie Investigations Atlas published by the United States Geological Survey for the State of Wisconsin (Gebert, 1971). Part of the map is reproduced as Fig. 4.9 and shows for continuous and partial gauging stations the 7-day low flow for recurrence intervals of 2 and 10 years. Related low flow analyses are also illustrated in the atlas.
4.5 RECESSION ANALYSIS
The diminishing discharge in the recession limb of a hydrograph reflects the depletion of stored water, both surface and sub-surface, within a basin. A wide variety of methods has been used to describe the recession process. A comprehensive review is given by Hall (1968). The most widely used approach is the simple exponential form:
qt = qQ Kfc (4.60)
where q. = the discharge at time t after some initial time t = 0, a = the discharge at time t=0 (both qfc and q^ are in the same units),
and K = a recession constant, dependent in value on the units of t.
This equation implies a linear relationship between discharge and the volume of water remaining in storage, and the equation plots as a straight line on semi-log graph paper.
A common method used to determine the recession constant, K, consists of plotting daily discharge data in m /s on semi-log paper, and fitting up to three straight lines to the recession limb (Fig. 4.10). The periods should be such that replenishment of stored water by precipitation during the period for which the data are recorded is negligible. The line with least slope is assumed to represent base flow, that with medium slope to represent mainly interflow, and that with steepest slope to represent surface runoff plus a small component of interflow. As a guide in using this method, Table 4.3 shows typical daily and hourly values of the recession constant K.
Table 4.3 Typical Values of Recession Constants
Recession phase
Hourly Daily
Groundwater Interflow Surface runoff
0.999 0.99
0.99-0.95
0.97 0.9
0.8-0.3
Source: Institution of Engineers, Australia (1977).
Figure 4.11 illustrates another procedure for deriving the recession constant. It is obtained from the envelope to points on a scatter diagram of "today's flow" against the "flow n days ago" obtained from low-flow recession periods. In the United Kingdom, trials have shown that the envelope can be objectively defined by connecting the points from each recession period and by using an n value of 2 days (Beran and Gustard, 1977).
4.5.1 Uses of recession analysis
Recession analysis has a number of uses. Firstly, it is a basic tool used in the separation of base flow from flood hydrographs. Secondly, it is used in low flow forecasting during prolonged dry periods (see Chapter 6). And thirdly, as an index of base flow, the recession constant is particularly important in investigations relating to hydrogeology and geomorphology. An example
50
-5481 5 \ i v „
I L L I N O I S si»
LEGEND
Continuous - record gauging station
Partial - record station
tt2, 75(4.06)
Upper number is station number Lower left number is 7 - day Q 2 . second number is 7 - day Q1fJ(in cubic feet per second ), and third number is drainage area (in square miles)
© Ratio of growing season 7 - day Q 2 to climatic year 7-day Q 2
Area outline for which ratio applies
10 0
SCALE 10 20 30 KMS
Fig. 4.9 Example of hydrologie atlas of low flow characteristics. (Part of Wisconsin, USA). Source: Gebert (1971).
20
15
01
'— E
UJ
n5 10
< X Ü V) a
7.5
I I
X
\
1 1
\ \ K = 0.87
\ \
V ^
1 1 1
K = 0.92 > ~
N " * X
N,< * x ^ -Í. K = 0.95
1 1 1 1 1 1 1 1 1
10 12
JUNE 1969
14 16 18
Fig. 4.10 Recession analysis of a hydrograph. (Thomson River at The Narrows, Vic, Australia).
51
0.7
0.6 -
~ 0.5 ~ M
E
W 0.41-
¿ 0.8 OC CE 0.2 Ü
Envelope to recession
J_ _L _L J_ _1_ _L X 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
FLOW T W O DAYS PREVIOUSLY - (m3/s) 0.9 10
Fig. 4.11 Derivation of recession constant. (Extracted from Beran and Gustará, 1977).
15 20 25
TIME (DAYS)
30 35 40
Fig. 4.12 Relationship between recession constant and surficial geology. Source: Wright (1970).
of this latter use is given in Fig. 4.12 where generalized base flow recession curves have been related to surficial geology for the Lothians River region in Scotland (Wright, 1970).
4.6 RESERVOIR CAPACITY-YIELD ANALYSIS
Reservoir capacity-yield analysis is one of the most effective means from both a theoretical and practical point of view of quantitatively defining the low flow characteristics of a basin through the ratio of the required storage capacity to mean annual flow for given conditions of
52
reliability and yield. Reliability is often defined as the complement of the probability of emptiness or failure. Yield (sometimes termed draft or regulation) is usually expressed as a percentage of mean annual flow.
By comparing the ratios of storage to mean annual flow for various basins, one can very quickly assess the regulated yield potential of a region. From a hydrologist's point of view, this ratio multiplied by the mean annual flow gives a direct estimate of the reservoir size required to develop that potential. Such a procedure is of considerable value to developing countries. It has been found that the ratio can be easily regionalized by relating it to the coefficient of variation, which can then be used to establish a rapid means of estimating the regulated potential of ungauged basins.
A difficulty that arises with storage-yield analysis is the acceptance of a suitable procedure for calculating the required reservoir capacity to meet the design conditions or for determining the reliability of a given draft for a specified storage capacity. Fundamentally, procedures can be classified into three groups -
critical period methods, probability matrix procedures, and techniques using stochastically generated data.
Critical period methods are those in which the required reservoir capacity is equated for periods of low flow to the difference between the water released from an initially full reservoir and the inflows. For those procedures designated as mass curve, minimum flow or range, the storage is normally associated with the most severe drought sequence in the historical record. If historical data are used with these procedures, an estimate of the risk of being unable to meet the design releases cannot be made. In effect, these methods are concerned with the state of fullness of the reservoir with time.
In contrast to the above procedures, a second sub-group of critical period methods allows an assessment to be made of the reliability of the reservoir to meet the demand. The common element here is that only periods of low flow (drought) in the record are used explicitly or implicitly in the analysis.
Probability matrix is a convenient label given to the second group of procedures which are based on the work of Savarenskiy (1940) and, independently, of Moran (1954). Moran derived an integral equation relating inflow to outflow and to reservoir capacity such that the probable state of the reservoir contents at any time could be defined. However, except for idealized conditions, the solution was intractable. Then Moran considered time and flow to be discontinuous variables and showed how the reservoir capacity, release and inflow could be related by simultaneous equations, but the method has several practical shortcomings. Subsequently, Gould (1961) proposed combining the probability matrix approach on an annual basis with a within-year behaviour analysis resulting in a very practical solution to the reservoir capacity-yield-reliability problem.
Although procedures for estimating reservoir capacity-yield relationships using synthetic streamflow data generated by stochastic methods were first used more than sixty years ago, it was not until the advent of high speed digital computers in the sixties that such procedures became established in engineering hydrology. Stochastic data generation is the basis of the third group of storage-yield procedures which utilize the methods discussed above. Data generation is discussed in the next section.
A classification of storage-yield procedures is given in Fig. 4.13. Space precludes details of any procedure, but it is worth noting that no one procedure is totally adequate. Details of all procedures are given in the text of McMahon and Mein (1978).
4.6.1 Use of Reservoir Capacity-Yield Relationships
Storage-yield relationships are of direct practical importance in estimating the required size of a reservoir to regulate a stream.
In relation to low streamflow characteristics, a storage estimate by itself tells us little about the flow characteristics of a stream. If, however, the storage estimate is related to the mean flow into the reservoir, the magnitude of this ratio indicates the inability of the basin to provide water without storage. This measure is regarded as an important streamflow characteristic.
53
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4.7 STOCHASTIC MODELS
The purpose of stochastic data generation modelling is to produce synthetic streamflow sequences with the same statistical properties as the historical record. From a number of synthetic hydrological sequences, each of a given length, it is possible to examine the likely occurrence of low flows more systematically than is possible by conventional procedures and hence create a more rational basis for design. This is especially true where multi-site analysis is involved.
But this approach is dependent on being able to satisfactorily generate streamflow data using stochastic models. To date the most commonly used time series model is the Markovian approach, either with an annual or monthly (seasonal) time scale. Difficulties do arise with highly variable data (say for streams where the annual coefficient of variation is greater than one) and for streams in which zero flow conditions form a significant part of the record. It has been shown that although Markovian models can satisfactorily preserve the historical inflow parameters, for example, monthly means, coefficients of variation and serial correlation, and even skewness, long duration low flow periods are sometimes poorly modelled. On the other hand, Markovian models, that are able to preserve the long duration low flow events, do not necessarily preserve the input parameters very well.
. There are many texts and papers on the subject. For example, for methodology see Fiering and Jackson (1971), and for a comparative study, see McMahon and Mein (1978).
4.8 REFERENCES
Abramowitz, M. and Stegun, I.A. (Eds.) (1965). Handbook of Mxthematical Functions. Dover Publications, Inc.,.New York .
Ayers, H.D. and Ding, J.Y.H. (1967). Effects of Surficial Geology on Streamflow Distribution in Southern Ontario. Canadian Jour. Earth Sciences, Vol. 4, pp. 187-197.
Beard, L.R. (1962). Statistical Methods in Hydrology. United States Corps of Engineers.
Benson, M.A. (1968). uniform Flood Frequency Estimating Methods for Federal Agencies. Water Resources Research, Vol. 4, No. 5, pp. 891-908.
Beran, M.A. and Gustard, A. (1977). A Study into the Low Flow Characteristics of British Rivers. Jour. Hydrology, Vol. 35, pp. 147-157.
Brunet-Moret, Y. (1975). Distribution Gausso-logarithmique. (Log-normal distribution). Cahiers ORSTROV., ser. hydrol., Vol. XII, No. 2.
Court, A. (1952). Some New Statistical Techniques in Geophysics; Advances in Geophysics. Ed. by H.E. Landsberg, Vol. 1. Academic Press, New York .
Cross, W.P. (1949). The Relation of Geology to Dry Weather Stream Flow in Ohio. Amer. Geovhys. Union Trans., Vol. 30, No. 4, pp. 563-566.
Cunnane, C. (1978). Unbiased Plotting Positions - a Review. Jour. Hydrology, Vol. 37, pp. 205-222.
Fiering, M.B. and Jackson, B.B. (1971). Synthetic StreamflcnOS. Amer. Geophys. Union, Water Resources Mono. No. 1.
Gebert, W.A. (1971). Low Flow Frequency of Wisconsin Streams. Hydrologie Investigations Atlas HA-390. United States Geological Survey.
Gould, B.W. (1961). Statistical Methods for Estimating the Design Capacity of Dams. Jour. Inst. Engrs. Australia, Vol. 33, No. 12, pp. 405-416.
Gumbel, E.J. (1954). Statistical Theory of Drought. Proc. ASCE., Vol. 80, Sep., pp. 439.
Hall, F.R. (1968). Baseflow Recessions - A Review. Water Resources Research, Vol. 4, No. 5, pp. 973-983.
55
Hardison, C.H. (1965). Storage to Augment Low Flows. Proa. Reservoir Yield Symposium. Water Research Association.
Harter, H.L. and Moore, A.H. (1965). Maximum Likelihood Estimation of the Parameters of Gamma and Weibull Populations from Complete and from Censored Samples. Technometvics, Vol. 7, No. 4, pp. 639-643.
Institution of Engineers, Australia (1977). Australian Rainfall and Runoff Inst. Engrs., Aust.
Joseph, E.S. (1970). Probability Distribution of Annual Droughts. Proa. ASCF, Jour. Irriq. S Drain. Div., Vol. 96, No. IR4, pp. 461-474.
Lazarescu, D. Methods for calculating the minimum flow in Roumania. Manuscript forwarded to UNESCO', 1976. (unpublished).
Lindgren, B.W. and McElrath, G.W. (1959): Introduction to Probability and Statistics. Macmillan, London .
McMahon, T.A. (1969). Water Resources Research: Aspects of a Regional Study in the Hunter Valley, New South Wales. Jour. Hydrology, Vol. 7, pp. 14-38.
McMahon, T.A. and Mein, R.G. (1978). Reservoir Capacity and Yield. Advances in Water Science No. 9, Elsevier, Amsterdam .
Mátalas, N.C. (1963). Probability Distribution of Low Flows. Statistical Studies in Hydrology. United States Geological Survey Professional Paver 434-A.
Moran, P.A.P. (1954). A Probability Theory for Dams and Storage Systems. Aust. Jour. Apvl. Sci., Vol. 6, p. 117.
Natural Environment Research Council (1975). Flood Studies Report Vol. 1 Hudrological Studies, (London).
Parr, B. van, and Webster, J.T. (1965). A Method for Discriminating between Failure Density Functions used in Reliability Predictions. Technometrics, Vol. 7, pp. 1-10.
Savarenskiy, A.D. (1940). Metod rascheta regulirovaniya stoka. (Method for calculating runoff regulation). Gidrotekhnichsskoe stroitelstvo, No. 2, pp. 24-48.
Searcy, J.K. (1959). Flow Duration Curves. United States Geological Survey Water Supply Paper 1542-A.
Stall, J.B. (1964). Low Flows of Illinois Streams for Impounding Reservoir Design. Illinois State Water Survey, Bui. 51.
Thorn, H.S.C. (1958). A Note on the Gamma Distribution. Monthly Weather Review, Vol. 84, No. 4, pp. 117-122.
Vasak, L. (1977). Low Flow Studies. A Literature Survey. Free University, Amsterdam. Manuscript forwarded to Unesco Secretariat.
Velz, C.J. and Gannon, J.J. (1953). Low Flow Characteristics of Streams. Ohio State University Studies Engg. Series. Vol. xxn. No. 4, pp. 138-154.
Viessman, W., Knapp, J.W., Lewis, G.L. and Harburgh, T.E. (1977). Introduction to Hydrology, Second Edition Harper and Row, New York .
World Meteorological Organization (1969). Estimation of Mxximum Floods. Technical Note No. 98. WMO-No. 233, T.P. 126, Geneva
Wright, C.E. (1970). Catchment Characteristics Influencing Low Flows. Water and Water Engineering. Vol. 74, pp. 460-471.
56
5 Determination of low flow with inadequate hydrometric data
5. 1 OUTLINE
The methods of computation of low flow characteristics using inadequate streamflow data and the accuracy of the results depend on the hydrological knowledge of the region and on the variability of the natural factors affecting the regime and the low flows. A detailed analysis of the influence of natural factors on low flows and on design values is possible only when sufficient data are available.
Generalization of low flow characteristics over large regions with different natural features and inadequate hydrometric data is possible only by classifying runoff processes and generalizing the methods of computation.
For low flow computations with inadequate data, the following methods are used:
- determination of low flow design values with the aid of a short period of observations and data from similar nearby basins (method of analogy);
- determination of streamflow design parameters (mean, coefficients of variation and skewness) on the basis of regionalization by equations or maps;
- use of empirical coefficients based on measured data to determine the value of low flow for a specific probability of occurrence.
Depending on the size of the river, the following methods of generalization of low flow data are applied:
- relating low flow values to the important natural factors (for small rivers);
- preparing isogram maps of low flow (for medium rivers);
- interpolation of streamflow between observation points (for large rivers).
Methods of empirical analysis (empirical relations and areal interpolation) as well as probabilistic and statistic methods of computation (correlation, regression and frequency analysis) are used for generalization.
The different types of generalization are usually made for one characteristic low flow, usually the minimum 30-day low flow. Other flows are determined by correlation with this value.
5.2 METHOD OF ANALOGY
5.2.1 Application
The method of hydrological analogy is used when it is necessary to extend a short length of record or to estimate missing years of observation at a particular gauging station. To apply the method of analogy simultaneous observations during 3-5 years (or seasons) of low flows at both the station under review and the long term or analogue station are made.
57
In selecting an analogue basin, the following conditions should be taken into account:
1. The basin analogue should have a long period of low flow observations.
2. It should be climatically similar to the study basin.
3. There must be simultaneous data at both stations.
4. The basin analogue should have similar relief, soils, lithology, hydrogeology (that is, a similar number, capacity and discharge of aquifers contributing to river recharge), and similar forest, lake and swamp areas as the study basin.
5. Both basins should belong to the same category of rivers (small, medium, large) and areas should differ by no more than five times. The mean basin elevations in mountain rivers should not di ffer by more than 300 m.
6. The basin analogue should not have specific features that might affect the value of low streamflow (for example, reservoirs, offtakes to channels, industrial waste discharges or effluents from mines and quarries).
High correlations between low flows at the station under review and the analogue station are observed when both stations are located on the same stream, and there is no significant distortion of low flow along the reach between the stations.
For regions where knowledge of the hydrology is poor and/or local factors contribute significantly to low flows, it is very difficult to select an appropriate analogue basin.
5.2.2 Methods of Computation
The computation of long-term statistical parameters of low flow can be carried out graphically, analytically-graphically or using hydrometric survey data.
1. The graphical method is applied if there are more than five or six concurrent low flow values at the design gauging station and the gauging station of the analogue basin. The low flow data ase plotted on arithmetic graph paper. The correlation is considered satisfactory if the deviation of most of the points from the line of best fit does not exceed + 20% of the mean value of the dependent variable. The line may not pass through the origin because cease-to-flow conditions occur earlier in small basins than they occur in larger basins.
For a linear relation, the mean low flow at the design gauging station is read from the graph according to the mean value for the analogue station. However, for a curvilinear relation, individual values are first estimated for the design gauging station, and then the mean value computed.
The graphical method of computation is mainly used to determine the long-term mean low flow.
2. The analytical-graphical method of ctamputation permits the mean (Q) and coefficients of variation (C ) and skewness (C ) of low flows to be determined. Application of this method requires 10 to 15 years of combined observations at the design gauging station and at the analogue station.
If the relationship is linear, Q is taken from the regression between the two sets of data.
The coefficient of variation C , is computed from:
C = b -2 C (5.1) v g, v
58
where C' = design gauging station low flow coefficient of variation,
"v Q' = design gauging station low flow mean,
Q = analogue station low flow mean, and
b = coefficient based on observed low flows at both stations.
The value of the coefficient of skewness, C , is determined from an analysis of C /C ratios for a number of rivers with long records and with similar low flow conditions.
3. If the observation period at the design gauging station is less than 5 to 7 years, mean low flow discharge is computed from
Q' = Q" — (5.2) Q'"
where Q , Q = mean low flow discharge at the design gauging station and at the analogue gauging station respectively, and
Q", Q'H = mean low flow—disGha-rge at the design gauging station and at the analogue gauging station respectively determined during the combined observation period.
The use of equation (5.2) should be limited to the following conditions:
0.8 < - 2 - < 1.4
Qm
c 0.8 < — - < 1.2
v
4. When there are no data available for the river under review, information may be obtained from a hydrometric survey of both the river under review and an analogue river. Simultaneous discharge measurements are made at the outlet of the basin under review (temporary gauging station) and at the permanent gauging station on the analogue river during low flow periods. The period of stable low flow is the most favourable time for measurements. The flow measurements at the temporary gauging station are adjusted to long term mean values by an empirical coefficient developed on the basis of the simultaneous discharge measurements at the two stations. The mean value determined from several analogue stations with similar hydrogeological conditions is considered to be the design parameter.
The computation of the long-term mean is made using the empirical coefficient determined for the permanent (analogue) stations taking into account the value of the low flow of the particular year under consideration along with the long-term mean for the same station. Thus to obtain the long-term low flow mean for an ungauged river, the low flow value in a particular year is multiplied by this empirical coefficient.
To increase the reliability of the empirical coefficient its value should be determined as the mean of estimates from several analogue basins with similar natural conditions. Measurements made during several years reduce the variability of the empirical coefficient.
The above approach permits only the estimation of the mean low flow. Coefficients of variation and skewness are assumed by analogy with gauged rivers.
If an analogue basin is not available for estimating the mean, it is determined from a regional equation or map.
59
5.3 EQUATIONS FOR LOW FLOW COMPUTATION
5.3.1 Principles for Classifying Basin Sizes
The low flow of small, medium and large rivers is formed under different conditions.
Low flow discharges in small rivers with similar regional characteristics are related to the volume of groundwater drained by the river and to the importance of local effects. Medium rivers usually have abundant and stable groundwater flow. In contrast, the effect of local conditions (for example, swamps, lakes, karst) is more evident for small rivers. Therefore, for small and medium rivers, methods of low flow computation vary. For large rivers, multi-zonal effects predominate. To determine the limits of these basin areas, the effects of geographical zones on minimum specific discharge are used. These are illustrated diagrammatically in Fig, 5.1.
< x o JO Q Ü
Ü Q. CO
i.
Medium . rivers
Large rivers
Single zone regime
• + •
More humid region
Less humid region
Multi- zone regime
-+- • + •
1000 -2500 ' 50000 -75000
DRAINAGE AREA (km2)
Fig. 5.1 Diagrammatical illustration of the effect of geographical zones on specific minimum discharge.
All rivers with basins smaller than a critical area are designated as small rivers. The critical area is defined by the area of a basin for which an increase in size does not produce a change in the specific low flow discharge.
Critical basin area is determined from graphs of specific minimum 30-day discharge versus drainage area. Two examples are given in Fig. 5.2 where curves of best fit have been plotted. In some cases it has been found that a log-log plot permits easy definition of the area at which the discharge becomes constant. This point corresponds to the critical basin area.
û _ •
• / / •
/ •
I
/» • •
*y**^ o
I
•
o
I
• •
o
Basins from regions with water deficits Basins from regions with water surplus
-
1000 2000
DRAINAGE AREA (km2 )
3000
Fig. 5.2 Relationships between minimum 30-day specific discharge and drainage area. (Severnaja-Dvina River Basin, USSR).
Investigations of low flows in the USSR show that the critical basin area in wet regions with water surpluses ranges generally from 1000 to 1500 km where permanent aquifers are very deep, the critical area i arid zones and permafrost regions, the critical area increases.
For regions with water deficits, where permanent aquifers are very deep, the critical area is between 2000 and 2500 km . For
60
Of course, the critical basin area as defined above is the lower limit for medium rivers. Their upper limit is the largest basin area for which river flow is formed by consistent zonal factors. Rivers with basins exceeding this area will be characterized by a multi-zonal regime (Fig. 5.1). It has been found that zonality is limited geographically by latitude and meridian. For example, in the USSR, latitude limitations suggest that the upper limit of median sized basins is 75 000 km whereas meridian locations suggest only 50 000 km (Vladimirov, 1970, 1973). Rivers with drainage areas larger than these areas would be regarded as large rivers.
5.3.2 Regionalization
To determine low flows of small rivers in regions with large homogeneous zones, generalizations are developed by regionalization with subsequent determination of regional design curves. Consequently this approach is restricted in use to countries large enough to have homogeneous zones.
The design curves reflect the influence of one or more natural factors on the low flow discharge. These effects may be taken into account either by their inclusion in the design equation or by selecting a region with similar characteristics.
The selection of homogeneous regions by genetic features is based mainly on hydro-geological conditions which determine the groundwater flow to streams. In addition, the climatic conditions that limit the water available to the region must be taken into account. These conditions are examined both qualitatively (lithology, relief, relation' between aquifer and stream) and quantitatively (discharge of water sources and bores, depth to the groundwater table, precipitation and evaporation).
The boundaries of the regions are drawn along the line of change of hydrogeological conditions or, for medium and large rivers, along the watershed divide. The channel of a large river may also be used as a regional boundary because it is often the location of a change of physiography.
The selection of a homogeneous region may be made by cross correlation analysis or by selecting and classifying paired values of parameters from a frequency curve using homogeneity criteria (Kryukov, 1974).
For selecting homogeneous regions, it is expedient to combine the genetical approach with statistical methods (Vladimirov, 1976). Initially, using the genetical approach, a preliminary selection of homogeneous regions is made on the basis of physiography and lithology. These are then defined more clearly by statistical methods that examine the homogeneity of the low flow characteristic. This combined approach reduces the effort especially when there are a large number of gauging stations and hence many factors to take into account. Computers are, of course, an advantage in such an analysis.
It is possible to select homogeneous regions through multiple regression analysis. The homogeneity of a region may be characterized by the multiple correlation coefficient which takes into account the basic physiographic factors that determine the value of low streamflow. The closer the value of the correlation coefficient is to unity, the more complete is the account of the factors affecting low flow in the equation and the more homogeneous is the selected region. A very comprehensive study for four regions in the United States was carried out by Thomas and Benson (1970).
In the multiple regression analysis, it is recommended that both the total and partial correlation coefficients and their standard errors be determined. The values of the total and partial correlation coefficients are used as a quantitative criterion of homogeneity of the selected region. A region is considered homogeneous if the total correlation coefficient exceeds 0.80 and the partial ones exceed 0.55.
5.3.3 Regional Design Curves of Low Flow Characteristics
In establishing the relationships between low flow characteristics and natural factors, it is important to use those factors that best reflect the specific peculiarities of low flow formation in the region under review. It has been found that in plain and hilly regions, catchment area is the main factor. In mountain regions, mean elevation is also important. However, in some regions other factors should be included, for example, precipitation depth, karst development, and lake, swamp or forest areas.
61
Various low flow characteristics are used in design curves and equations. Examples are mean minimum discharge, low flow discharge at some probability of exceedance, and dry season low flow.
A range of design curves or equations is now examined.
1. For low flow calculations, the relationship between minimum discharge or specific discharge to basin area is used frequently. Basin area may be the only independent variable or it may be used together with precipitation or annual flow. Some examples follow.
Q = bAn (5.3)
Q = b(A + a ) n (5.4)
Q = bAn Pm (5.5)
Q = bAn Q Qm (5.6)
where Q = mean minimum low flow discharge or low flow «discharge at some probability of exceedance in m /s (or a specific discharge in m /s.km ) for a 30-day period (or 7, 10, 15 days) during the dry seasons,
A = basin area (km ), P = mean annual precipitation (mm), Q = mean annual discharge (m /s),
b, n, m = regional coefficients, and a = area depending on hydrogeological conditions.
For a region where part of the area does not contribute to low flow a constant "-a" will be used i equation (5.4). Where additional recharge of the river occurs due to favourable geological conditions (karst, outflow of deep artesian water, lack of coincidence of groundwater divide and watershed boundary)"+a"will be used. In regions where all rivers have permanent runoff, a = 0, and equation (5.4) is transformed to (5.3). If the area of the basin under study is less than the area without runoff within the region, that is A < a, the minimum low flow is zero.
Sometimes it is found (Halasi-Kun, 1973; Vladimirov, 1966, 1970) that when using minimum specific discharge to obtain design values, the exponent n in equations (5.3) and (5.4) becomes negative.
Values of the coefficients in equations (5.3) to (5.6) are determined by correlation analysis and the relationships Q = f(a), Q = f(A,P), Q = f(A,Q ) are plotted for regions with similar conditions of low flow development. An example of curves expressed by equation (5.3) is given in Fig. 5.3 and by equation (5.4) in Fig. 5.4. Equations of the form of (5.3) and (5.4) have been found by Ginsti (1962), Halasi-Kun (1973), Vladimirov (1966, 1967, 1970), Vladimirov and Chebotarev (1973). Chow (1964) and Hely and Olmstead (1963) adopted equations like (5.5) while Baleo (1976) and Vladimirov (1970) found equation (5.6) suitable.
When equations (5.5) or (5.6) are used, long term precipitation or mean annual discharge are required. If the analysis is for ungauged basins, regional maps of mean annual precipitation and runoff are used.
2. If precipitation significantly contributes to low flows, design equations of the form Q = f(P) may be used:
Q = aP2 + bP + K (5.7)
Q = aP« + bP, + cP, + dQ + K (5.8)
62
MINIMUM DISCHARGE (m3/s) MINIMUM DISCHARGE (m3/s)
m
D 33 > Z > O m > DO m >
*-3 to
««/
_» o o o
O o o
V >v
* \ X
1
•S
1
. •
*s •
• •
1
*-% fi>
—
•
Fig. 5.3 Relationships between minimum discharge and drainage area for permanent rivers. (a) Severnaya Dvina River (USSR); wet zone. (b) Don River (USSR); zone with water deficit.
where Q = minimum discharge (m /s), P ., P,, p3 = precipitation in three previous months (mm), a, b, c, d, = regional coefficients, and
K = regional constant.
Examples of these equations are given in Huff and Changnon (1964), Ishihara and Takagi (1965), Canali and Giovanelli (1964), Riggs (1961) and Roche (1963).
In place of precipitation, mean annual runoff may be used as an index of water stored in the basin (Schultz, 1965; Visso et al., 1965). The equation then becomes
Q = a Q„ (5.9)
where Q Q, *o a, n
= minimum specific discharge, = mean annual runoff, and = regional coefficients.
3. m regions where low flow results mainly from groundwater, the density or length of the river network (Glos and Lauterbach, 1972; Gregory and Walling, 1973) or the depth of the river embedment, may be used as the main design parameter. At the mouth of the drainage basin, depth of - river bed is sometimes used in place of embedment (Lysenko, 1965). These relationships may be represented analytically or graphically:
Q = a D" (5.10)
63
E w
LU 30 Ü
ce < X 20
O V)
û 10
5 Z>
5
_
1
(a)
+^\^r^
i i
1 1
_
—
i 1000 2000 3000
DRAINAGE AREA (km2)
» ' u • " - » .
E
LU Ü
ce < X 0.5 O V)
a 5 3
S Z
tfwnc
(b)
" ~ < 3 ^
1
' ~\r^
1
O
1
0 \ S ^
4
1
O
—
1000 2000
DRAINAGE AREA (km2) 3000
Fig. 5.4 Relationships between minimum discharge and drainage area for intermittent rivers. (a) Ob River; zone with water deficit. (b) Amur River; zone with sufficient moisture.
0.4 0.8 1.2
MINIMUM SPECIFIC DISCHARGE U/s. km2)
180
160
140
120
100
i
0.2 0.4 0.6
MINIMUM SPECIFIC DISCHARGE U/s. km2)
Fig. 5.5 Relationships between minimum specific discharge and river embedment. (Ukranian Rivers, USSR.)
64
where Q = minimum specific discharge, D = river network density determined as a ratio of the
total length of river network and the basin area, and a, n = regional coefficients.
The use of river embedment instead of network density is based on the observations that as the embedment becomes deeper, the river recharge from groundwater also increases. For plainland rivers, minimum specific discharge is related to the absolute level of the thalweg at the outlet of the basin. An example of such relationships is shown in Fig. 5.5. For practical purposes, the graphs are transformed into a table < for example Table 5.1).
Table 5.1 Minimum 30-day discharges for 97 per cent frequency depending on river embedment level. (Rivers of the Ukraine, USSR).
No. of River embedment region level
(m)
Minimum 30-day discharge for 97 per cent frequency (Vs. km )
winter
180 160 140 120
0.0 0.10 0.25 0.50
0.0 0.03 0.10 0.25
260 240 220 200 180 160
0 60 80 00 20 50
0.0 0.40 0.55 0.70 0.90 1.15
220 200 180 160 140 120 100
0.0 0.05 0.09 0.14 0.20 0.30 0.60
0 02
0.04 0.07
13 25 50
Table 5.2 Minimum 30-day discharges for 80-percent frequency depending on mean watershed elevation. (Middle Asia, USSR).
No. of region
Mean basin elevation
(m)
Minimum 30-day discharge fori 80 per cent frequency (A/s. km )
winter summer-autumn
1000 1400 1800 2200 2600 3000
40 30 20 10 00 00
0.20 1.20 2.90 5.00 7.60 11.8
1800 2200 2600 2800 3100 3200 3400 3600
,60 ,50 ,60 ,10 ,50 .40 .60
5.00
2.00 6.40 10.4 12.6 16.2 17.5 20.1 20.8
4. In mountain regions, specific low flow is often related to mean (or mean weighted) basin elevation (Amusia, 1972; Anon, 1973; Hmaladze, 1965; Nikolov, 1973; Paduraru and Popovici, 1973; Paduraru et al., 1973). Such relations may vary because it is difficult to select appropriate equations. An example is given in Fig. 5.6. For practical computations, the relation Q = f(H_) is presented as a table where values of the specific low flow discharge (Q) are related to basin elevation (ft-). An example is given in Table 5.2.
In preparing graphs like Fig. 5.6, basins are chosen with similar physiographic conditions. Particular attention should be paid to orientation of mountain slopes and direction of prevailing moisture-laden winds as well as the similarity of the hydrogeological structure of the basins.
3000 -
2600 -
< > LU
I
I
1
. •
xxx
/x J
!•
1
1 1
/ • ~
f°
1 1
z < LU 1800
2
0 2 4 6 8 10
MINIMUM 30 DAY SPECIFIC DISCHARGE (1/s. km2)
Fig. 5.6 Relationships between minimum 30-day specific discharge and mean basin elevation for rivers of mountain regions (Middle Asia, USSR).
5. Rivers flowing through lakes or with lakes in their basin are characterised by a specific regime of low flow and its value usually differs greatly from rivers without lakes. Thus, procedures outlined in (1) to (4) above are not applicable.
The effect of a lake on low flow discharge depends on the location of the lake within the basin. Where the lake is in the lower part of the basin close to the outlet, the effect on low flow is most significant. Its value is approximately 20-30% greater on average than the flow from basins where the lake is concentrated in the upper part of the watershed.
For situations where lakes are situated near the design point, low flow may be determined by equation (5.11) which takes into account the active storage volume (volume from the permanent pool to some maximum level):
Qlake Q • + cBQ *min p*o (5.11)
where Qi_i.e = mean (or given probability of exceedance of) low flow discharge during a non-flood season of a basin with a lake,
^min = m e a n (°r given probability of exceedance of) low flow discharge of a basin without a lake,
Q = mean annual discharge of river, c = coefficient, and 3 = relative regulating factor of the lake located close to the design point (that
is, storage delay time),
and e = S W
(5.12)
66
where S = lake capacity determined over a wide range of water level fluctuations, and W = mean inflow into lake.
Examples of equation (5.11) are given in Baranov et al., (1967) and Anon (1973).
When there are no data on the regulatory capacity of a lake, the following equation may be used instead of (5.11) (Sokolov, 1954):
Q'lake- a Q'o A" (flake + 1>" <5'13>
where Q'iake = minimum specific discharge,
Q' = mean annual specific discharge,
A = basin area,
^lake = l^e area in the basin, and
a,n,m = regional coefficients.
The lake area in equation (5.13) is evaluated either as the value of the ratio of lake area to river basin area or as the value of the ratio of lake area and its basin to the total river basin area.
6. Multiple linear regression analysis can be used to determine the influence of several factors on low flow characteristics. For example, to estimate the influence of drainage area (A), mean basin elevation (H ), lake area (fiaj,e)
a n d swamp area (fgw) on low flow (Qm-¡n), the equation would be
2min = a log A + b ^ + cf l a k e - dfgw - q (5.14)
where a,b,c,d = regression coefficients, and q = regression constant.
Application of multiple regression analysis requires a large amount of data. The errors in the regression coefficients increase as the number of variables increases. In view of the short length of hydrologie data, if more than four variables are used in multiple regression equations, regression coefficients will be too unreliable.
For ungauged rivers, it is sufficient to use one or two variables; more variables may be used only if a detailed regional analysis is available that will provide the additional information.
The standard error of estimate (E) characterizes the reliability of the regression equation and is defined as (Rozhdestvenski and Chebotarev, 1974):
2 Vo S(Q„ - Q > 2
E = ± [ — 2 X— ] (5.15)
where Q = observed values, = computed values = number of items in the data set
Q = computed values from regression equation, and
The values of the regression equation error may also be expressed as a percentage as follows
2 V2
K - ± "O \ \ l [ ^ " ^ ] } (5.16) o
5.4 ISOGRAM MAPS OF LOW FLOW
To determine low streamflow for medium rivers, isogram maps are used. Such maps reflect zonal changes of a particular characteristic of low flow corresponding to the changes in physiography and lithology of the region. Maps of low flow are widely used throughout the world. Examples
67
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 and Herbst (1970), Vladimirov and Chebotarev (1973) and Vladimirov (1976).
To construct maps showing isograms of low flow in mountain areas, it is necessary to consider orographic effects relative to precipitation bearing winds. In some cases, isograms may 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 mean minimum monthly runoff (Jl/s.km^). (Caucasus, USSR),
The magnitude, of the interval between adjacent isograms should be constant in similar natural 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, and is given by the following equation (Vladimirov, 1976):
4E'q (5.17)
where T q E*
interval between isograms, value of low flow specific discharge, and standard deviation of low flow specific discharges.
Values of E' are computed from the equation:
C
(n) 0.5
(5.18)
where C, coefficient of variation of low streamflow, and number of items in the data set.
The interval between isograms will vary across a region depending on the value of low streamflow and its coefficient of variation.
Low flow characteristics from isogram maps are determined- at the centre of watersheds by linear interpolation of the isograms. If several isograms cross the watershed, a mean weighted value of low flow (Q_) is computed from the equation:
Qiai + Q2a2 + + Q.a. (5.19)
68
where Q*IQ2I••«QJ = low flow specific discharge at the centre of the areas a., anf-aj enclosed between two adjacent isograms, and
A = total area of the basin upstream of the design gauging station.
5.5 LOW FLOW DETERMINATION FOR LARGE RIVERS
In large rivers, the various zonal regions contribute to runoff. Therefore the low streamflow value at the design gauging station on a large river usually differs from the value that would be determined using the geographic region about the gauging station nor can it be determined from 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 in relation to changes in low flow and the length of the reach. Those changes are determined mainly by intermediate inflow between gauged points and by the hydraulic structures along the river 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 the main stream between the design and upstream stations;
2. using a water balance method; or
3. using an estimate of mean low flow specific discharge determined from an isogram map or from 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 is supplied to areas away from a river, greatly decrease its low streamflow. A similar effect is produced by water diversion canals and other large water intakes from a river. All these effects are determined from data recorded at the structure.
5.6 DETERMINATION OF COEFFICIENTS OF VARIATION AND SKEWNESS OF LOW STREAMFLOW
This section deals with the coefficients of variation and skewness of low flow events. For example, 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 is related to the coefficient. An example is presented in Table 5.3. Here the design value of the coefficient of variation is determined by interpolating between the two extreme values of the actual 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 which is acceptable for ungauged rivers. For this situation, the relation of the coefficient to basin area is examined. For individual regions, and particularly in zones of water deficit, a decrease in the coefficient of variation is observed with an increase in basin area from 200 to
2 300 km . Therefore, rivers with drainage areas exceeding this limit are used in the analysis of the areal distribution of the coefficient of variation.
The value of the coefficient of skewness (C ) should be determined by analogy with rivers having a long period of observations. The ratio of the coefficient of skewness to coefficient of variation (C ) is usually used in computation because it is reasonably constant over large regions. In regions of water surplus, C_ = 3CV, in regions of sufficient water C = 2C and in regions of water deficit Cg = 1 + 1.5CV, although sometimes Cg = 0.
69
No. re g.
1 2 3 4 5 6 7
of ion
Table 5.3 Mean Minimum 30--day Discharges Related to Values oi Coefficient of Variation. (European part of USSR)
Winter
Minimum 30-day specific discharge
U/s.km2)
0.5-3 0.0-1 0.0 1.5-6 1-5 0.5-0.3 1-5
season
Coefficient of
variation
0.3-0.2 0.4-0.3
-0.3-0.2 0.4-0.2 0.4-0.2 0.7-0.3
Summe r-autumn
Minimum 30-day specific discharge
2 U/s.km )
3-12 4-7 2-4 3-12 1-7 6-7 1-5
season
Coefficient of
variation
0.5-0.3 0.6-0.3 0.6-0.4 0.4-0.3 0.5-0.3 0.6-0.3 0.6-0.3
5.7 USE OF EMPIRICAL COEFFICIENTS
5.7.1 Determination of Low Streamflow for Short Durations
In low flow analysis, a need may arise for data on minimum daily, 10-day or 30-day flows or for similar short durations. Normally, it is not necessary to determine each flow individually, but rather to define one in detail, for example the minimum 30-day flow, and relate the others to that characteristic flow because they are genetically homogeneous. These relationships are linear 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, and K = 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 Intervals
In water engineering projects, low water discharges for recurrence intervals between 4 and 100 years are required. To compute these values effectively, basic relationships, equations and maps are prepared showing low water discharge for only one given recurrence interval (usually 5 years) (Anon., 1973). Discharges for other recurrence intervals are computed using an empirical coefficient as described below in equation (5.21) and without recourse to the mean flow or the coefficients of variation and skewness. The value of the empirical coefficient, A , is estimated from maps on the basis of measured relations between the discharge of given recurrence interval and the discharge of design recurrence interval. For example, maps would be drawn showing the relation between the minimum 30-day discharges of 5 years recurrence interval and the 30-day discharges at 10 and 20 years recurrence interval. Examples are given in Paduraru and Popovici (1973), Paduraru et al. (1973) and Vladimirov (1976). Such relationships are linear 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 daily and up to 30-day minimum discharge irrespective of the season. However, beyond 30 days, its value 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.
70
5.8 REFERENCES
Amusia, A.Z. (1972). Minimalny stok gornykh rek Srednei Asii (Minimum flow of mountain rivers of the Middle Asia). Trans. GGl, Vol. 188, pp. 283-304.
(1972) Ukazania po Ooredeleniu Rasahiotnykh Gidrologicheskykh Kh.aracteristik. CH- 435-72. (Instructions for the Computation of Design Hydrological Characteristics), Gidrometeoizdat, Leningrad p.l8-
(1973) Rukovodstvo vo Ooredeleniu Rasahiotnykh Gidrologicheskykh Khareteristik (Handbook on Determination of Design Hydrological Characteristics). Gidrometeoizdat, Leningrad pp. 64-69.
Baclo, M. (1976). Vazba plochy povodia a ¿eho vodnosti s minimalnymi prietokami. (Ratio of basin 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 Evropeiskoi territorii SSSR (Maps of minimum streamflow of the European USSR). Trans. GGI, Vol. 133, pp. 112-147.
Canali, L., Giovanelli, E. (1964). Contributo preliminare alio studio dette rnagre del Vo con método statistici e statistico-probabilistioi. ^preliminary contribution to the study of low flows of the River Po using statistics and statistical probabilities). Annali Idrologici 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). Studii de Hidvologie, Vol. 1, pp. 95-104.
Dub, O. and Dzubak, M. (1960). La definition des debits d'étiage et l'illustration de superficie de leur extension. (The definition of low waters and illustration of their extension). 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). Régionale Verallgemeinerung von Neidriguasserdurahflussen mit Wáhrscheinlichkeitsaussage. (Regional generalization of low flow with probability prediction). "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 on permeability of the geological subsurface. Proceedings of Madrid Symposium, UNVSCO-WMD-IAHS. Vol. 1, pp. 191-204.
Hall, F.R. (1968). Base-flow recession - a review. Water Resources Res., Vol. 4, No. 5, pp. 973-983.
Hely, A.G. and Olmstead, G.H. (1963). Some relations between streamflow characteristics and the environment in the Delaware river region. United States Geologcial Survey Professional Paper, 417-B, pp. 1-25.
Hmaladze, G.N. (1965). Zakonomernosti izmenienia minimalnogo stoka gornykh riek Armenii i metodika iego rascheta (Laws for the change of minimum flow of mountain rivers in Armenia and 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 Low Streamflow. Jour. Geophys. Res., Vol. 69, No. 4, pp. 804-813. Also Huff, F.A. and Chagnon, S.A. (1964), Relation between Precipitation Drought and Low Streamflow. Int. Ass. Scii Hyd. Symo. Surface Waters, pp. 167-180.
71
Ishihara, T. and Takagi, F. (1965). A study on the variation of low flow. Bull. Disaster Prevention Research Inst., Vol. 15, No. 95, Part 2, pp. 76-98.
Kaitera R. (1971). Estimation of the 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 statistical characteristics of minimum 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 na requite v Bulgaria (On River Low Flow in Bulgaria). Hidrologuia y meteorologuia, No. 4, C3-17.
McMahon, T.A. (1969). Water Yield and Physical Characteristics of Catchments. Civil Wngg. Trans. Inst. F.ngrs. Aust., Vol CE11, No. 1, pp. 74-81.
Nikolov, Y. (1973). Varju minimalnia otox na reka Maritza v Belovo Izv. tzentrove N.I. (On Minimum Runoff in Maritza River, Belovo). Ldboratoria hidraulika No. II Stranitza, pp. 107-167.
Paduraru, A. and Popovici, V. (1973). Scurgerea medie zilnica minima multiannuala si asigurata 80% si 90% pe riurile Romaniei. (Mean daily multiannual minimum discharges and with 80% and 90% exceeding probabilities on the Romania Rivers). Sttidii de Hidrologie Vol. XXXV, pp. 173-189.
Paduraru, A., Popovici, V., Martian, F. and Diaconu, C. (1973). Scurgerea medie lunara minima multiannuala si asiguraza 80% din perioada iunie-august pe riurile Romanei. (Mean monthly multiannual minimum discharges and with 80% exceeding probabilities through June-August on the Romanian Rivers). Studii de Hidrologie, Vol. XLI, pp. 113-135.
Riggs, H.C. (1961). Rainfall and Minimum Flows Along the Tallapoosa River, Alabama. United States Geological Survey Professional Paver 424-B, pp. B96-B98.
Roche, M. (1963). hydrologie de surface. (Surface water hydrology) Paris
Rozhdestvenski, A.V. and Chebotarev, A.I. (1974). Statistich.esk.ie metody v gidrologii (Statistical methods in hydrology). Gidrometeoizdat, Leningrad 422 pp.
Schultz, V.K. (1965). RiéU.i Sriednei Azii, (Rivers of Middle Asia), Gidrometeoizdat, Leningrad , 328 pp.
Sokolov, A.A. (1956). Vlianie oziernogo regulirovania na velichinu minimalnogo stoka rek. (Impact of lake 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 w Polsce. (Variation of medium and low flows in Poland). Pr. Panst, inst. hydrol. - meteorolo., No. 100, pp. 9-15.
Thomas, D.M. and Benson, M.A. (1970). Generalization of Streamflow Characteristics from Drainage-Basin Characteristics. United States Geological Survey Water Suvvly Paver 1975.
Visso, A., Vafin, R. and Kochiashvili, B. (1973). Formación del escurrimiento minlmo en las rios. (Formation of minimum flow in rivers). Volun h.idraul., Vol. 10, No. 26, pp. 21-25.
Vladimirov, A.M. (1966). Characteristics of formation and computation of the minimum flow of small rivers in the 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.
72
Vladimirov, A.M. (1970). Minimalny istok riek SSSR. (Minimum flow of rivers of USSR.) Gidrometeoizdat, Leningrad , 214 pp.
Vladimirov, A.M. (1976). Stok riek V mxlovodny period goda (Streamflow during low water period.) Gidrometeoizdat, Leningrad , 295 pp.
Vladimirov, A.M. and Chebotarev, A.I. (1973). Computation of Probabilistic Values of Low Flow for Ungauged Rivers. UNESCO-WyD-IAHS Symposium on the Design of Water Resources Project with Inadequate data, Vol. 2, pp. 561-569.
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6 L o w flow forecasts
6.1 PREAMBLE
Low 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 river in terms of stage or discharge at some specific time in the future conditional upon the present state. After prediction the forecast is then used for example to operate a hydraulic structure along 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 flow characteristics whereas the methods to be discussed in this chapter assume some knowledge of the present 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 the time under consideration;
availability of stored water from natural storage on and below the ground surface for low 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 or regional in extent but also whether they are short- or long-range forecasts. The latter including regional ones are less reliable.
The permissible error of a long-term forecast is assumed to equal the probable deviation of the forecasted low flow from its mean value during the observational period and is determined by the formula
H Q . - Q ) 2 1/2 E' = 0.674 { } (6.1)
n - m
where E' = permissible error,
Q. = magnitude of forecast flow,
Q = mean low flow discharge during the period of observations,
n = number of observations, and
m = 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 are replaced by the differences between forecasted and observed values, AQ. and AQ.
6.2 REGIONAL FORECASTS
Three 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 between summer minimum flow and the sum of winter flow, spring snowmelt flood flow and summer flow. An example is given in Fig. 6.1. Such a relation may be used to make a regional forecast (Norvatov et al., 1960).
2K
Fig. 6.1 Relationship between minimum summer monthly specific flow (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 be related to the total hydrometeorological conditions. For summer minima, the independent variables 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 the data 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 flood and summer rainfall (EK ). (Khoper River Basin, USSR).
m
75
In regions where the difference in the origin and in the value of low flow during winter and summer-autumn seasons is not great, the above relations may be simplified using only two streamflow characteristics - winter and summer-autumn low flow. This procedure allows forecasts to 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 event have been made. The discharge coefficient (1^) is used as a characteristic of low flow and it is determined as the ratio of the difference between the mean discharge for the current period and the lowest discharge for the period of observation (Qm discharge variations for the observation period iQmax - Q mi n)
; Qmin) divided by the range of the
Q - Q • m min
max 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 preceding precipitation. For example, the minimum summer-autumn flow may be associated with the mean depth 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
ÜI-VII p I-VII
and
5VIII-IX PVIII-IX
a,b,c
summer-autumn 7-day flow,
= total precipitation from January to July for the observation period and mean precipitation respectively,
and = total precipitation for August and September for the observation period and mean precipitation respectively, and = empirical coefficients.
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Fig. 6.4 Relationships between summer low flow volumes and preceding 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 lakes or 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. The method uses the observed runoff curve and takes into account the basin drainage and lake areas as well as the precipitation in the month prior to the forecast and that which occurs early in the following month. This method is explained in detail in Nezhikovsky (1956).
6.3 LOCAL FORECASTS
For 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 catchment gauging stations are used to determine river discharge and lag. Graphs are then plotted as follows:
f(Q-,) (6.4)
T = f(Q2) (6.5)
where Q., Q, = discharges at the upper and lower gauges, and
T = lag time.
If there are several gauging stations, graphs of the relationships
Q2 = f(Q1(L) (6.6)
T = f(Q1#L) (6.7)
may be plotted where L = distance between the lower and upper gauges. These relationships may be used for low flow forecasting at different forecast periods.
When there is no intermediate inflow, the following cases have been observed:
•^t+T f1,t
and 22,t+x = f ( Q1,t )
(6.8)
(6.9)
77
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:
Qt = Q0Kfc (6.11)
where Qt = discharge at time t after initial time t = 0, Q = discharge at time t = 0, and K = recession constant, and its value depends on the
time 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 + S Q„ = Q e p (6.12) t o
t -at + 8 noting that K = e * (6.13)
where t = number of days, a = f(K), and B = 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 that results from precipitation.
2t = f(2t-n' V <6'14)
where Q. = predicted value of flow at time t, Q. = flow during the forecast period, and P. = 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, and P = precipitation after forecast determined from the meteorological synoptic fore
cast. Where such forecasts are not available, an average precipitation for the period is adopted.
Details are given in Gurevitch (1956).
Computation of the predicted flow Çv is made from the depletion curve with Qt__ as the known discharge at the time of the forecast. The depletion curve is based on steep recessions and is determined as the difference between discharge values at adjacent time intervals. Two methods of determining depletion curves are illustrated in Figs. 4.10 and 4.11. A third method is presented in Fig. 6.5. Here the flows at time t-1 and time t are plotted on the abscissa and ordinate respectively, and an envelope curve is drawn through the lower points corresponding to the steepest recessions. This lower envelope curve may be used to plot the recession curve for any specified initial discharge.
78
o, 1500 i-
500
O,.,
1000 - /
Ou ' 4
/ / 2 3
" 1 1
1 •
• i
_. •
' . • 'j>^ • . • • v^ • • '^^ . \^"^
¿T
O 1000 2000 3000 o 4000 M - 1
Fig. 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 a given point along the Volga River (USSR) at adjacent time intervals. The lower envelope curve is accepted as the design curve. The flow value determined from the curve is a function of the amount 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 advance may be based on seasonal depletion laws. For a period without precipitation and for a linear relation between groundwater outflow and river discharge, the seasonal groundwater depletion law is as follows:
= (Q0 " q)e •ct
+ q (6.16)
where Qt
2o q c
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 seasonal
sgroundwater storage depletion, and base of natural logarithms.
Values of c and q are determined from equations (6.18) and (6.19) which are based on empirical relationships between the mean 10-day or monthly discharges:
= a Q1 + 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 and subsequent period T,
a = regression coefficient, and b = 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
. QT = K Q0 + (1 - K)q
-CT
where 1 " e cT
79
Popov (1964, 1968) explains this method in detail.
4. For situations where the forecast period is short, mean minimum monthly flows of large rivers may be predicted on the basis of the mean discharge during preceding months estimated from long term discharge data measured between the end of recorded streamflow and the forecast time. 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 (QVIII) and precipitation depth (P).
In forecasting flow one month in advance for small rivers, the value of mean discharge for several days during the previous month, for example from 20th to 25th or from 15th to 25th, can be used.
(1968), Examples of the procedure are given by Dumitrescu and Tuca (1974), Anon (1963) and Popov
5. Where runoff data are available at a gauging station, monthly flow forecasts may be made using 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 are developed on the basis of runoff data for previous years. The value of W. , the water stored in the river network, is calculated for all years and expressed as the mean discharge for the time period 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 indicator of the value of groundwater inflow (Q_r t) to the river and is expressed as
Q 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 by relating low flows to phreatic water levels (see Anon, 1963), thus:
^«max* (6.24)
where Qt = mean minimum monthly discharge during the dry period, and ILax = maximum phreatic water level during wet season"in a
strategically located well.
80
The well should be located outside the backwater effect of the river or other water body, and it should reflect the water table fluctuation of the main aquifer recharging the river.
7. If river discharge is increased by a significant amount of surface water during the low flow period, the following regression equation can be established (Lazarescu, 1969):
Qt+1 = f(Qt, Qt_T) (6.25)
where Qt = maximum flood flow, and Qt_1 = flow prior to start of flood wave.
8. During winter seasons, when air temperature may considerably influence river flows, the low flow forecast may be made according to an empirical relation of the form:
Q t + 1 = f<<It'
At°> (6.26)
where Q. = flow during the autumn-winter season of the preceding year, and At" = difference in actual mean air temperature for the coldest month
and the mean long term temperature for the same month.
An example of this method of forecasting is presented by Tuca (1974).
6.4 REFERENCES
(1963) Rxik.ovod.8tVO po Gidvologicheskim Pvognozam. (Handbook of Hydrological Forecasting) Hydrometeoizdat, Leningrad, Vol. 2 & 3.
Bonacci, 0. (1975). Analyse der niedrigwasser des flusses Sava zwecks ihrer pronosierung. (Analysis of low flow of the Sava River for the purpose of forecasting). VIII "konfevenz dev Donaulander ubev hydvologisahe vovhevsagen. Regensburg.
Dumitrescu, V. and Tuca, I. (1974). Prognoza cu timp mare de anticipere a apelor mici de vara-toamna pe Dunare. (Long term forecasting of summer-fall low flow waters on Danube.) Studii de hidrologie, co. XLIII, Bucuresti, pp. 51-73.
Gurevitch, M.I. (1956). Prognozy letnego i osennego stoka ravninykh riek na osnove iego zavisimosti ot osadkov. (.Forecasting of summer and autumn streamflpw of the plain rivers on the basis of its dependence upon precipitation.) Tvans. GGI, Vol. 53, p. 107.
Indri, E. (1960). Curve di eeaurimento per alauni oorsi d'aaqua dele Alpe Venete. (curves of low flows for some rivers in the Venetian Alps). L'Acqua no luglio-agosto.
Lazarescu, D. (1967). Prognoza de lunga durata a debitului minim de vara-taomna pe únele riuri interioare din Romania. (Long-term forecasting of summer-fall minimum discharge on some inner Romanian rivers.) Studvi de hidrologie, Vol. XXVI, Bucuresti 1969, pp. 3-19
Martin, G.N. (1973). Characterization of simple exponential base flow recessions. Jour. Eydvol. (N.Z.), Vol. 12, No. 1, pp. 57-62.
Nezhikovsky, R.E. (1956). Fonovye prognozy stoka rek severo-zapada Evropeiskoi territorii SSSR (Areal forecasts of streamflow in the north west of the European part of the USSR.) Trans.
GGI., Vol. 53, (107).
Norvatov, A.M., Remizova, L.K. and Koroleva, N.P. (1960). Dolgosrochny fonovy prognoz vodnosti letnei mezhenie rek liesostiepnoi zony (Long-term areal forecasts of runoff during low water period in rivers of the forest steppe zone.) Tvans. GGI», Vol. 75.
Popov, E.G. (1964). Runoff forecasts for the dry seasons. Methods of Hydrological Forecasting for the Utilization of Water Resources. F.CkFF, WW Water Resources Ser. No. 27, 50-51.
Popov, E.G. (1968). Osnovy gidrologitaheskikh prognozov. (Principles of hydrological forecasting.) Gidrometeoizdat, Leningrad .
81
Riggs, H.C. (1961). Regional Low Flow Frequency Analysis. United States Geological Survey Professional Paver, 424-B, pp. 21-23.
Toebes, C. and Strang, D.D. (1964). On recession curves. 1. Recession Equations. Jour. Hydrol. (N.Z.), Vol. 3, No. 2, pp. 2-15.
Tuca, I. (1974). Prognoze de lunga durata a apelor mici din periodada de iarna in bazinul riului Mures. (Long-term forecasting of winter low water in Mures basin.) Studii de hidrologie, Vol. XLIII, pp. 75-97.
82
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INDEX
Altitude 16 Analogue basin 58 Annual frequency series 36 Area 15
Channel embedment 18 Climate 6 Coefficient of variation 34 Coefficient of variation - estimation of - with adequate data 34
- with inadequate data 69 Coefficient of variation - standard error of .. 31 Coefficient of skewness - estimation of - with adequate data 34
with inadequate data 69 standard error of 31
Cycles 28
Data 26 Data - accuracy 3 Data errors - see errors Data homogeneity - see homogeneity Depletion curve - see recession curve Distribution type - comparisons 45
Extreme Value Type I 43 Extreme Value Type III 44 Gamma 41 Goodness of Fit test 45 Kritsky-Menkel 43 log-normal 40 log-Pearson Type III 42 normal 39 Pearson Type III 42
Drainage 23 Drought - definition 2
Empirical coefficients 70 Errors 29 Errors - measurement 29
measurement - accidental 29 systematic 29
rating curve 29 sampling 30
Evaporation 7 Evapotranspiration 8 Extreme Value Type I (Gumbel) distribution 43 Extreme Value Type III (Weibull) distribution 44
Flow duration 34 Flow duration - analysis 34
curve 34 curve - use of 36
Forecasts 74 Forecasts - local 77
- regional 75 Frequency analysis - see low flow frequency analysis
Gamma distribution 41 - Thorn's maximum likelihood estimate 41
Geology 9 Goodness of Fit test 45 Groundwater 11
92
Groundwater - artesian 13 crack or fissure 12 karstic 13 permafrost 13 phreatic water 12 unconsolidated sediments 12
Homogeneity 30 Hydroelectric stations 22 Hydrogeology 9
Irrigation 20
Kendall rank test 28 Kritzky-Menkel distribution 43
Lakes 13 Land use change 23 Large rivers - low flow estimation 69 Local forecasts 77 Log-normal distribution 40 Log-Pearson Type III distribution 42 Low flow - definition 2
description of process 4 duration 2 factors affecting 4 factors affecting - altitude 16
area 15 channel embedment 18 climate 6 drainage 23 drainage density 17 évapotranspiration 8 evaporation 7 geology 9 groundwater 11 human activity 18 humidity 9 hydraulic works 21 hydroelectric works 22 hydrogeology 9 irrigation 20 karst 13 land use changes 23 lakes 13 mining 22 morphology 13 morphometry 15 natural 5 navigation 22 orientation 17 permafrost 13 phreatophytes 8 plants 15 precipitation 6 relief 13 reservoirs 21 sewage effluents 22 slope 17 swamps 14 temperature 9 transfers 22 urban water supply 21 urbanization 18 wind 9
Low flow - forecasts of 74 isogram maps 67 large rivers 69 period of 2 process 4 regional design curves 61
Low flows - transition probability matrix of 48 Low flow analysis - method of analogy 57
regional design curves 61 use of empirical coefficients 70
Low flow data 26 Low flow frequency 36 Low flow frequency analysis 36 Low flow frequency analysis - annual frequency series 36
partial frequency series 45 Low flow frequency curve - use of 49 Low streamflow - see low flow
Matrix analysis 48 Mean - estimation of - with adequate data 33
with inadequate data 58 standard error of 31
Median 33 Mining 22 Mode 33 Morphology 13 Morphometry 15 Moving average 27 Multi-year flow - probability of 47
Navigation 22 Normal distribution 39
Orientation 17
Partial frequency series 45 Pearson Type III distribution 42 Permafrost 13 Persistence 34 Phreatophytes 8 Plotting position 37 Precipitation 6
Rating curve - errors 29 extrapolation 30
Recession analysis 50 Recession analysis - use of 50 Recession constant 50 Recession curves ' 78 Regional forecasts 75 Regionalization 61 Regional design curves 61 Reliability 31 Relief 13 Reservoir yield analysis - see storage-yield analysis River classification 60
Sampling errors 30 Sampling procedures 26 Sewage effluent 22 Serial correlation coefficient 34 Serial correlation coefficient - standard error of 31 Skewness - see coefficient of skewness Slope 17
94
Standard deviation 34 Standard deviation - standard error of 31 Standard error 31 Standard error - coefficient of skewness 31
coefficient of variation 31 mean 31 serial correlation coefficient 31 standard deviation 31
Statistical sampling errors 30 Stochastic models 55 Storage yield analysis 52 Storage yield analysis - critical period 53
probability matrix 53 use of 53
Swamps 14 Synthetic streamflows 55
Temperature 9 Transition probability matrix 48 Trend 27 Trend - Kendall rank test 28
Urbanization 18
Variability - coefficient of variation 34 standard deviation 34
Wind 9
95
Titles in this series
1. The use of analog and digital computers in hydrology. Proceedings of the Tucson Symposium, June 1966 /L'utilisation des calculatrices analogiques et des ordinateurs en hydrologie : Actes du colloque de Tucson, juin 1966. Vol. 1 et 2. Co-edition IASH-Unesco /Coédition AIHS-Unesco.
2. Water in the unsaturated zone. Proceedings of the Wageningen Symposium, August 1967 / L'eau dans la zone non saturée : Actes dy symposium de Wageningen, août 1967. Edited by / Edité par P. E . Rijtema & H . Wassink. Vol. 1 et 2 . Co-edition IASH-Unesco / Coédition AIHS-Unesco.
3. Floods and their computation. Proceedings of the Leningrad Symposium, August 1967 / Les crues et leur évaluation : Actes du colloque de Leningrad, août 1967. Vol. 1 et 2 . Co-edition IASH-Unesco-WMO/ Coédition AIHS-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. (Will also appear in Russian and Spanish) / Les bassins représentatifs et expérimentaux : Guide international des pratiques en matière de recherche. Publié sous la direction de C . Toebes et V . Ouryvaev. Publié par ¡'Unesco. (A paraître également en espagnol et en russe).
5. Discharge of selected rivers of the world / Débit de certains cours d'eau du m o n d e / Caudal de algunos ríos del m u n d o / PacxoflM B o m a H36paHHbix peK v m p a . Published by Unesco ¡Publié par l'Unesco.
Vol. I : General and regime characteristics of stations selected / Vol. I : Caractéristiques générales et caractéristiques du régime des stations choisies / Vol. I : Características generales y características del régimen de las estaciones seleccionadas / T O M 1: 06iime H pexcHMHbie xapaKTepHcnncH H36paHm>ix d a m n ™ .
Vol. II : Monthly and annual discharges recorded at various selected stations (from start of observations up to 1964) / Vol. II : Débits mensuels et annuels enregistrés en diverses stations sélectionnées (de l'origine des observations à l'année 1964) / Vol. II : Caudales mensuales y anuales registrados en diversas estaciones seleccionadas (desde el comienzo de las observaciones hasta el año 1964) / T O M II: MecHiHbie H roflOBbie pacxoHbi BOflbi, 3aperHCTpHpoBaHHbie pa3niwHbiMH raSpaHHWMH cTamnwiMH (c Haqajia HaSmonemiH H O 1964 roria).
Vol. Ill : M e a n monthly and extreme discharges (1965-1969) / Vol. Ill : Débits mensuels moyens et débits extrêmes (1965-1969) / Vol. III : Caudales mensuales medianos y caudales extremos (1965-1969) / T O M III: Cpernte-MecHMHbie H 3KcipeManbHbie pacxoflH (1965-1969 I T . ) .
Vol. Ill (part II) : M e a n monthly and extreme discharges (1969-1972) / Vol. HI (partie II) : Débits mensuels moyens et débits extrêmes (1969-1972) / Vol. III (parte II) : Caudales mensuales medianos y caudales extremos (1969-1972) / T O M III (qacib II) : CpeflHe-MecjwHbie H 3KcipeManbHbie pacxoftbi (1969-1972 rr.).
Vol.III (part HI) : M e a n monthly and extreme discharges (1972-1975) (English, French, Spanish, Russian). 6. List of International Hydrological Decade Stations of the world / Liste des stations de la Décennie hydrologique inter
nationale existant dans le m o n d e / Lista de las estaciones del Decenio Hidrológico Internacional del m u n d o / C r m c o K CTaHmiH MesKflyHapoHHoro rHflpononrqecKoro HecarajieniH 3eMHoro m a p a . Published by Unesco / Publié par ¡'Unesco.
1. Ground-water studies. A n international guide for practice. Edited by R . Brown, J. Ineson, V . Konoplyantzev and V . Kovalevski. (Will also appear in French, Russian and Spanish / Paraîtra également en espagnol, en français et en russe).
8. Land subsidence. Proceedings of the Tokyo Symposium, September 1969 / Affaissement du sol : Actes du colloque de T o k y o , septembre 1969. Vol. 1 et 2 . Co-edition IASH-Unesco / Coédition AIHS-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 et 2 . Co-edition IASH-Unesco / Coédition AIHS-Unesco.
10. Status and trends.of research in hydrology / Bilan et tendances de la recherche en hydrologie. Published by Unesco / Publié par l'Unesco.
11. World water balance. Proceedings of the Reading Sympos ium, July 1970 / Bilan hydrique mondial : Actes du colloque de Reading, juillet 1970. Vol. 1-3. Co-edition IAHS-Unesco-WMO / Coédition AIHS-Unesco-OMM.
12. Research on representative and experimental basins. Proceedings of the Wellington ( N e w Zealand) Symposium, December 1 9 7 0 / Recherches sur les bassins représentatifs et expérimentaux : Actes du colloque de Wellington (N.Z . ) , décembre 1970. Co-edition IASH-Unesco / Coédition AIHS-Unesco.
13. Hydrometry : Proceedings of the Koblenz Symposium, September 1970 / Hydrométrie : Actes du colloque de Coblence, septembre 1970. Co-edition IAHS-Unesco-WMO / Coédition AIHS-Unesco-OMM.
14. Hydrologie information systems. Co-edition Unesco-WMO. 15. Mathematical models in hydrology : Proceedings of the Warsaw Symposium, July 1971 / Les modèles mathématiques
en hydrologie : Actes du colloque de Varsovie, juillet 1971. Vol. 1-3. Co-edition IAHS-Unesco-WMO. 16. Design of water resources projects with inadequate data : Proceedings of the Madrid Symposium, June 1973 / Elaboration
des projets d'utilisation des ressources en eau sans données suffisantes : Actes du colloque de Madrid, juin 1973. Vol. 1-3. Co-edition IAHS-Unesco-WMO/ Coédition AIHS-Unesco-OMM.
17. Methods for water balance computations. A n international guide for research and practice. 18. Hydrological effects of urbanization. Report of the Sub-group on the Effects of Urbanization on the Hydrological
Environment. 19. Hydrology of marsh-ridden areas. Proceedings of the Minsk Symposium, June 1972. 20. Hydrological maps. Co-edition Unesco-WMO. 21. World catalogue of very large floods / Répertoire mondial des très fortes crues / Catálogo mundial de grandes crecidas /
BceMHpHblH KaTajIOr ÓojIblIIHX H a B O R K O B .
22. Floodflow computation. Methods compiled from world experience. 23. Guidebook on water quality surveys. (In press.)
24. Effects of urbanization and industrialization on the hydrological regime and on water quality. Proceedings of the Amsterdam Symposium, October 1977, convened by Unesco and organized by Unesco and the Netherlands National Committee for the IHP in co-operation with I A H S / Effets de l'urbanisation et de l'industrialisation sur le régime hydrologique et sur la qualité de l'eau. Actes du colloque d'Amsterdam, octobre 1977, convoqué par l'Unesco et organisé par l'Unesco et le Comité national des Pays-Bas pour le PHI en coopération avec l'AISH. (In press /Sous presse.)
25. World water balance and water resources of the earth. 26. Impact of urbanization and industrialization on water resources planning and management. 27. Socio-economic aspects of urban hydrology. 28. Casebook of methods of computation of quantitative changes in the hydrological regime of river basins due to h u m a n
activities. 29. Surface water and groundwater interaction. 30. Aquifer contamination and protection. 31. Methods of computation of the water balance of large lakes and reservoirs. Vol. I : Methodology. Vol. II : Case studies. 32. Application of results from representative and experimental basins. 33. Groundwater in hard rocks. 34. Groundwater Models. Vol. I : Concepts, problems and methods of analysis with examples of their application. 35. Sedimentation Problems in River Basins. 36. Methods of computation of low stream flow.
SC.81/XX-36/A
