A Comparative analysis of the performance of flood frequency distributions in the Lake Victoria Basin in Kenya

Abstract

Floods have always been a major national as well as societal concern. Despite the fascinating achievements of science and technology in the 21stcentury, floods continue to hit every generation of human beings, bringing suffering, death, and material losses. The 21st century is heralded as the age of water scarcity, yet, flood losses continue to rise, soaring to tens of billions of dollars (US) in material damage and to thousands of flood fatalities a year. The primary objective of the study was to find a suitable distribution class for flood frequency analysis on the Kenyan side of Lake Victoria basin. The specific objectives included performing at-site analysis using Peak Over Threshold (POT), analyzing the shape of the distribution's tail using quantile-quantile plots, selecting appropriate distributions for modeling flood peaks, fitting extreme value distributions and determining the return periods for various flood extremes. The area of study included the catchments of Lake Victoria in Kenya, namely Nzoia sub-basin, the Nyando sub-basin, the Yala sub-basin, Sondu, Gucha-Migori and Awach. Daily discharge data for at least one station of the above sub-basins were used. The selected river gauging stations for analysis included IDA02, lEE01, lEF01, IFG01, IFG02, IGD03, IGD04, lHA14, lKC03, lKB05 and IJGOl. The methodology employed included estimating missing discharge data, quality control of data, criteria used in selection of model type, extreme value analysis, estimation of parameters, testing the goodness of fit of the chosen distribution, determining the return period and the exceedence probability. The MOVE-l (Maintenance Of Variance-Extension, Type1 method, which is a new technique of record extension was used to fill missing records of discharge data. The single mass curve was used to test on the adequacy of the data. The time series of total rainfall-runoff discharges was split into its subflows (such as the overland flow, the subsurface flow or interflow, and the groundwater flow or baseflow) using a numerical digital filter technique. To select flood series, the Peak Over Threshold approach was used as the criteria for choice of model type. Extreme value analysis was based on the quantile-quantile plots. Making use of three types of quantile

plots (UH plot, exponential Q-Q plot and pareto Q-Q plot), an analysis was made of the shape of the distribution's tail, and discrimination was made between heavy tail, normal tail and light tail behaviour. The shape, scale and location parameters of various distributions were estimated by use of method of moments, maximum likelihood, least squares and the probability plot correlation coefficient (PPCC) plot. Appropriate distributions were fitted and the goodness of fit assessed graphically and through the use of R-squared. Analysis was made on return period and exceedence probability. The results of single mass curves showed that the data was of high quality for all the river gauging stations used in the analysis. Extreme value analysis carried out based on quantilequantile plots which were used to discriminate between distributions based on their tail behaviour showed that most seven out of eleven of the river gauging stations used in the analysis had their discharge values were falling under normal tail distribution class, and only for a few stations had their discharge values were falling under heavy tail distribution class. The river gauging stations which had their discharge values falling under normal tail behaviour included .IEEOI, IFGOI, IFG02, IKB05, IJGOI, IGD03 and IGD04. Alternatively, the stations which had their discharge values conforming to heavy tail behaviour were IDA02, IEFO 1, IKC03 and IHAI4.The stations with normal tail behaviour included lEEOl, IFGOI, IFG02.; lKB05, IJGOI, IOD03 and IGD04. Alternatively, the stations conforming to heavy tail behaviour were IDA02, 1EFOI, 1KC03 and 1HA 14. After fitting appropriate distributions, EV1/Gumbel distribution proved to be the best fit for all the cases of the normal tail behaviour. For the case of heavy tail distribution class, GEV was the best fit. Finally, the return periods for various flood extremes which could be used as measure of safety (the' inverse risk') were determined. The results of return period obtained were used as measure of safety (the' inverse risk'). This study is of great significance to hydrological science and has will contribute towards filling the gap in knowledge contributed in filling the gap in knowledge. Given the wide range of probability distributions, it is' has become, easy now to generalize on the distributions to opt for flood frequency analysis in the Lake Victoria basin once the tail behaviour has been established.