Table Of ContentStudies and reports in hydrology 36
Recent titles in this series:
20. Hydrological maps. Co-edition Unesco-WMO.
21 .* World catalogue of very large floods/Répertoire mondial des très fortes crues.
22. Floodflow computation. Methods compiled from world experience.
23. Water quality surveys.
24. Effects of urbanization and industrialization on the hydrological regimè^àrid on water quality. Proceedings of the Amsterdam Symposium.
October 1977/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. Co-edition IAHS-Unesco Coédition AISH-Unesco.
25. World water balance and water resources of the earth. (English edition).
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 ground-water 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.
Quadrilingual publication: English—Ftench—Spanish—Russian.
For details of the complete series please see the list printed at the end of this work.
Methods of computation
of low streamflow
Edited by T. A . McMahon
and A . Diaz Arenas
A contribution to the
International Hydrological
Programme
(unesoo
The designations employed and the presentation of material throughout the publication
do not imply the expression of any opinion whatsoever on the part of Unesco concerning the
legal status of any country, territory, city or area or of its authorities, or concerning
the delimitation of its frontiers or boundaries.
Published in 1982 by the United Nations
Educational, Scientific and Cultural Organization,
7, place de Fontenoy, 7570D Paris
Printed by
Imprimerie de la Manutention, Mayenne
I S B N 92-3-102 013-7
© Unesco 1982
Printed in France
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
1
value to Member States. By the end of that period a majority of Unesco s 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 AFECTING LOW STREAMFLOW 4
2. 1 DESCRIPTION OF LOW FLOW PROCES 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 1
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 Chanel embedment 18
2.3 FACTORS DUE TO HUMAN ACTIVITY 18
2.3.1 Urbanization 18
2.3.2 Irigation 20
2.3.3 Hydraulic works 21
2.3.3.1 Urban water suply 21
2.3.3.2 Other uses 2
2.3.4 Transfers 2
2.3.5 Hydroelectric stations 2
2.3.6 Mining 2
2.3.7 Navigation 2
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. ASESMENT 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 ERORS 29
3.3.1 Measurement erors 29
3.3.2 Rating curve erors 29
3.4 HOMOGENEITY OF HISTORICAL DATA 30
3.5 ERORS IN ESTIMATED DATA 30
3.6 STATISTICAL SAMPLING ERORS 30
3.7 RELIABILITY 31
3.8 REPRESENTATIVENES OF DATA SETS 31
3.9 REFERENCES 32
COMPUTATIONAL PROCEDURES WITH ADEQUATE HYDROMETRIC DATA 3
4.1 SCOPE 3
4. 2 FLOW PARAMETERS AND PERSISTENCE 3
4.2.1 Central tendency 3
4.2.2 Variability 34
4.2.3 Skewnes 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 Anual frequency series 36
4.4.1.1 Normal distribution 39
4.4.1.2 Log-normal distribution 40
4.4. 1.3 Gama distribution 41
4.4.1.4 Pearson Type I distribution 42
4.4.1.5 Log-Pearson Type I 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 RECESION ANALYSIS 50
4.5.1 Uses of recesion analysis 50
4.6 RESERVOIR CAPACITY-YIELD ANALYSIS 52
4.6.1 Use of reservoir capacity-yield relationships.... 53
4.7 STOCHASTIC MODELS 5
4.8 REFERENCES 5
DETERMINATION OF LOW FLOW WITH INADEQUATE HYDROMETRIC DATA... 57
5. 1 OUTLINE 57
5.2 METHOD OF ANALOGY 57
5.2.1 Aplication 57
5.2.2 Methods of computation 58
5.3 EQUATIONS FOR LOW FLOW COMPUTATION 60
5.3.1 Principles for clasifying 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
SKEWNES OF LOW STREAMFLOW 69
5.7 USE OF EMPIRICAL COEFICIENTS 70
5.7.1 Determination of low streamflow for
short durations 70
5.7.2 Determination of low streamflow for
a range of recurence intervals 70
5.8 REFERENCES 71
LOW FLOW FORECASTS 74
6. 1 PREAMBLE 74
6 • 2 REGIONAL FORECASTS 75
6. 3 LOCAL FORECASTS 7
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:
Chapter 1 : M. Roche
Chapter 2 : A. Diaz Arenas
Chapter 3 : J. 0. Sonuga
Chapter 4 : T. A. McMahon
Chapter 5 : A. M. Vladimirov
Chapter 6 : A. M. Vladimirov
The book was edited by T. A. McMahon and A. Diaz Arenas, i
March 1980.
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).
