Regional Flood Frequency Analysis for Zambian River Basins
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REGIONAL FLOOD FREQUENCY ANALYSIS FOR ZAMBIAN RIVER BASINS By FESSEHA WELDU Bachelor ofEngineering University of Zambia Lusaka, Zambia 1976 Master of Science Imperial College, University of London London, United Kingdom 1981 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirement for the Degree of DOCTOR OF PHILOSOPHY December, 1995 REGIONAL FLOOD FREQUENCY ANALYSIS FOR ZAMBIAN RIVER BASINS Thesis Appr_oved: 11 To Arsema 111 ACKNOWLEDGMENTS I wish to express my sincere appreciation to my co-advisors, Dr. Avdhesh K Tyagi and Dr. Charles T. Haan for their continuous guidance, assistance and encouragement. My sincere appreciation also extends to my committee members Dr. William Clarkson and Dr. John Veenstra for their valuable comments and suggestions. I thank Dr. Tyagi for allowing me to work in a project that involved the validation of water and wastewater models funded by the City of Stillwater and the Environmental Institute at Oklahoma State University. I would like to extend special recognition and deep gratitude to Dr. Haan, whose dedication to excellence and professionalism has been an inspiration to me for as long as I have been associated with him The work could not have been completed without his meticulous guidance, encouragement, constructive critici,'ffllS and patience. He truly is a great teacher! I wish to express my gratitude to the instructors, staff members, administrators and fellow graduate students in the School of Civil and Environmental Engineering for their support and advice. Last, but not least, I would like to express special appreciation to my parents and my entire extended family for their prayers, love, support and encouragement. lV TABLE OF CONTENTS Chapter Page 1 INTRODUCTION . 1 1.1 Location 1 1.2 Physical Features 2 1.2.1 Geology ..... 2 1.2.2 Drainage Patterns . 3 1.3 Climate ...... 4 1.4 Statement of problem . 5 1.5 Objectives of this study 6 2 LITERATURE REVIEW . .12 2.1 Empirical Relationships ....... .12 2.2 Statistical Methods . ....... .13 2.2.1 Delineation of Homogeneous regions .14 2.2.2 Frequency Distributions . .15 2.3 Regional Flood Frequency Models .17 2.3.1 Index-flood method . .17 2.3.2 Regression-based procedures ... .20 2.4 Regional Flood Frequency Studies in Zambia .22 3 BACKGROUND THEORY. .23 3.1 Introduction . .23 3.2 Hydrologic Models .23 3.3 Frequency Analysis .24 3.3.1 Normal Distribution . .27 3.3.2 Log normal Distribution . .28 3.3.3 Extreme Value Distribution . .30 V Chapter Page 3.3.4 Log Pearson Type III Distribution . .31 3.4 Parameter estimation ...... .32 3.4.1 Method of Moments ...... .33 3.4.2 Method of Maximum Likelihood .34 3.5 Goodness of fit Tests ...... .34 3.5.1 Chi-squared goodness of fit test (X,2) .35 3.5.2 Kolmogorov-Smirnov Test (KS Test) . .36 3.6 Cluster Analysis . .36 3.7 Regression analysis ......... .38 3.7.1 Estimation of Regression Parameters .39 3.7.2 Model validation .......... .42 4 DATA ACQIDSITION .47 4.1 Introduction . .47 4 .2 Rainfall . .48 4 .3 Stream flows .49 4.4 Basin characteristics. .50 5 METHODOLOGY AND RESULTS . .64 5.1 Outline of study . .64 5.2 Validity of Assumptions . .66 5.3 Frequency Analysis ... .68 5.4 Delineation of Homogeneous Regions . .72 5.5 Regional flood :frequency models .75 5.5.1 Index flood method . .75 5.5.2 Regression based methods .76 5.5.3 Adequacy of Models .78 5.5.4 Model Limitations . .80 6 SUMMARY AND DISCUSSION OF RESULTS . 115 7 APPLICATION OF MODELS . 120 8 CONCLUSIONS AND LIMITATIONS . 123 VI Chapter Page 9 SUGGESTIONS FOR FUTURE STUDIES . 125 REFERENCES . 127 APPENDIX A : Fitted and observed distributions . 132 APPENDIX B : Residual Analysis . 261 APPENDIX C : Dimensionless regional frequency curves . 280 Vll LIST OF TABLES Table Page 1.1 Land utilization . 7 3.1 Probability, r, that a flood with return period T will occur within the next L years. .26 4.1 Selected statistics of observed rainfall . .53 4.2 Locations of flow gaging stations ............. .56 4.3 Summary of watershed area, number of stations and average record length. .59 4.4 Watershed characteristics . .60 5.1 a Resuhs of Spearman's rank correlation test .82 5.2 Test for outliers, flows . .85 5. 3 Test for outliers, rainfall . .87 5.4 Missing data . .88 5.5 Computation of plotting positions. .89 5. 6a Fitting normal distribution to observed data . .90 5.6b Fitting log normal distribution to observed data .91 5.6c Fitting Gumbel distribution to observed data .. .92 5.6d Fitting Log Pearson type III distribution to observed data .93 5.7 Kolmogorov-Smimov Test ............. .94 5.8a Results ofKolmogorov-Smimov tests for flow data . .96 5.8b Results ofKolmogorov-Smimov tests for rainfall data .98 5.9a Estimated flows for various return periods . .99 5. 9b Estimated rainfall values for various return periods . 101 5.10a Equations for estimating magnitude and frequency of flows in Region 1. 105 5.1 Ob Equations for estimating magnitude and frequency of flows in Region 3 . 110 5.10c Equations for estimating magnitude and frequency of flows in Region 4. 112 7.1 Average QiQ2 values for Regions 1, 2, 3 and 4 . 122 Vlll LIST OF FIGURES Figures Page 1.1 Location Map . 8 1.2 Cross sections of Zambia . 9 1.3 Drainage Patterns . .10 1.4 Rainfall Distribution . .11 3.1 Residual Vs. X . .43 3.2 Residuals Vs. Estimates .43 3.3 Plot of Autocorrelations .44 4.1 Locations of rainfall measuring stations . .54 4.2 Plot of watershed and isohyets . .55 4.3 Locations of streamflow gaging stations .58 4.4 Relationships between watershed areas and record length . .62 4.5 Channel profile and average slope line .63 5.1 Methodology, Flow chart . .81 5.2 Plot of selected flow data . .84 5.3 Peak flows plotted on normal probability scale .89 5.4 Kolmogorov-Smimov Test . .95 5.5 Hydrologic regions . 102 5.6 Index flood method of regional flood :frequency analysis . 103 5.7 Dimensionless regional :frequency curves for Regions 1, 2 and 3 . 104 5.8a Frequency curves for Q2 (Region 1) . 106 5.8b Frequency curves for Q5 (Region 1) . 107 5.8c Frequency curves for Q10 (Region 1) . 108 5.8d Frequency curves for Q25, Q50 and Q100 (Region 1) . 109 5.8e Frequency curves f (Region 3) . 111 5.8f Frequency curves f (Region 4) . 113 5.9 Mean Annual Flow (Region 2) . 114 6.la Comparisons between model prediction (Region 1) . 117 6.lb Comparisons between model prediction (Region 3) . 118 6.lc Comparisons between model prediction (Region 4) . 119 lX CHAPJER 1 INTRODUCTION 1.1 Location The Republic of Zambia is a landlocked state and lies between latitudes 8 degrees 15 minutes and 18 degrees south of the equator. Formerly known as Northern Rhodesia, it is bounded by eight other countries, namely Angola, Botswana, Malawi, Mozambique, Namibia, Tanzania, Zaire, and Zimbabwe as shown in· Fig. 1.1 (given at the end of this chapter). Zambia is named after the Zambezi River, has a population of about 8 million (as at August, 1991) and covers an area of over 752,600 km2, an area equivalent to that of Texas and a third of Oklahoma combined. The total land mass amounts to 98.8% of the total area and the remaining 1.2% is covered by water bodies, such as natural lakes and man made reservoirs. A summary of the land utilization breakdown is shown in Table 1.1. Zambia's topography, with its favorable climate, enables a variety of crops to be grown. The principal crops are maize, sugar cane, cassava, millet, sorghum, cotton and tobacco. Most Zambians are traditional farmers, who grow food for their own subsistence and produce little surplus for the market. For many years, the mining of copper, which accounted for about 93% of all Zambia's foreign exchange earnings, has dominated the Zambian economy, although its contribution has declined significantly since the mid-1980's, reflecting price fluctuations on the international commodity markets. The country is the world's fifth largest producer of copper. Cobalt, a by-product of copper mining, has recently gained in significance, and Zambia has been steadily expanding its cobalt production in an attempt to offset falls in copper pnces. Despite Zambia's favorable topography, climate and relatively abundant mineral wealth, the country is still economically weak and is one of the less advantaged countries in the world. 1.2 Physical Features The topography of Zambia is dominated by the even skylines of uplifted planation surfaces and most of it lies at an altitude of over 1000 meters above sea level. The highest elevations (2165 meters) are reached on the Nyika plateau in the north eastern part of the country near the Malawi border. Elevations decline westward, where the country extends into the fringe of the vast Kalahari desert. The plateau surfaces are interrupted by localized depressions ( occupied by lakes and swamp areas, such as in the Bangweulu and Lukanga basins), and by the rifted troughs of the mid-Zambezi and Luangwa. Cross sections showing important physical features of the country are given in Fig. 1.2. 1.2.1 Geology Geologically, the Zambian plateau consists of very ancient Precambrian rock. Katangan rocks of the upper-Precambrian age yield the copper ores exploited on the Copperbelt. Younger Karoo sedimentaries floor the rift troughs of the Luangwa and the mid Zambezi rivers, while a basalt flow of this age has been incised by the Zambezi below the 2 Victoria Falls to form the spectacular gorges.