Determination of regional frequency distributions of floods in West Mediterranean river basins in Turkey

Abstract

Estimation of probability distribution and return periods of flood peak flows is needed for the planning, design, and management of flood control. Much of the research on at-site and regional flood frequency analysis has focused on the determination of the best probability distribution. The first objective of this study was to determine, evaluate and compare the goodness of fit of popular probability distribution functions (PDFs) to sequences of annual maximum stream-flows measured in West Mediterranean river basins of Turkey. Besides Gumbel distribution, which is generally preferred because of its simplicity and generality in extreme hydrologic data, distributions like Pareto, Log-logistic, Pearson Type III, Log-Pearson Type III, Log-normal with two and three parameters, and Generalized Extreme Value distributions are applied to the series of annual floods with time periods ranging from 20 to 61 years for 37 gauging stations. Another objective of the study was to compare and evaluate the parameter estimation methods and goodness of fit tests for the basins. For parameter estimation, the traditionally used method of moments and, recently widely used, that of probability weighted moments were used. To make an evaluation of the suitability of the parameters obtained by both methods to the data, detailed chi-square (parametric) tests were applied twice with equal-length intervals, equal-probability intervals and Kolmogorov-Smirnov (non-parametric) goodness-of-fit tests. The results demonstrated that when chi-square goodness of fit test is applied for both parameter estimation methods (moments and probability weighted moment methods), Gumbel probability distribution was obtained as the best fitting one to the floods in West Mediterranean river basins in Turkey, according to chi-square test with equal-probability and equal-length class intervals for both of the methods. Besides, the application of chi-square goodness of fit test for both parameter estimations with average chi-square approach resulted in Log-Pearson Type III for both with equal class intervals as optimal distribution. Similar results were obtained for chi-square distribution with equal probability approach. Log-Pearson Type III distribution was the best suitable one for each of the parameter estimation methods in Kolmogorov-Smirnov goodness of fit test. These results indicated that it may be more appropriate to use Log-Pearson Type III distribution instead of the widely used Gumbel distribution for probability distribution modeling of extreme values in West Mediterranean river basins. © by PSP 2007.