Definition of the best probability distribution functions for annual minimum flows in the rivers of the Upper Euphrates River Basin, Turkey

Abstract

Abstract In this study, it is aimed to define the most suitable probability distribution functions for modelling of annual minimum flows (AM7) data for the duration 7-day that obtained from daily streamflow data of the four gauge stations located in upper part of the Euphrates River. To achieve this purpose, ten widely used distributions, namely, Gamma, Gumbel, Generalized Extreme Value, two parameter Lognormal, three parameter Lognormal, Logistic, LogLogistic, Normal, Pearson type-III and Weibull were fitted and compared. The maximum likelihood method was used to estimate parameters of the distributions. To select the most suitable distributions for AM7 series of the stations, five widely used model selection criterions (namely, the Akaike Information Criterion (AIC), Anderson Darling (AD), Bayesian Information Criterion (BIC), Cramér–von Mises (CvM) and Kolmogorov–Smirnov (KS) tests) were applied. Based on these tests/criteria, Gamma, Gumbel, Generalized Extreme Value, three parameter Lognormal, Pearson type-III were found to be the most suitable distributions for modelling data series. Finally, using the best fitted distributions that derived from these model selection methods, minimum flow estimates for various return periods (e.g. 10, 25, 50, 100, 200 and 500 years) were performed and results were discussed.