Mapping Spatial Variability of Annual Rainfall Under Different Return Periods in Turkey: The Application of Various Distribution Functions and Model Selection Techniques

Abstract

The objectives of the paper are to determine the best-fitted probability distribution functions for annual rainfall in Turkey and to provide more accurate estimates of rainfall quantiles under different return periods. To achieve these aims, 10 popular and widely used probability distributions: gamma, generalized extreme value, Gumbel, normal, logistic, log-logistic, two-parameter log-normal, three-parameter log-normal, Pearson type III and Weibull, are considered for modelling annual rainfall data covering the period 1975-2014 from 155 gauge stations uniformly distributed across Turkey. Unlike previous studies, the performances of the candidate probability distributions were evaluated by various model selection techniques: Akaike information criterion (AIC), Bayesian information criterion (BIC), Anderson-Darling (AD) criterion, the Cramer-von Mises test (CvM) and the Kolmogorov-Smirnov test (KS). According to the ranking-based scoring evaluation, the gamma, log-logistic, two-parameter log-normal, normal and Weibull distributions, which show the best fit for 78% of the data series, were mainly found to be the most suitable distributions. T year (25, 50 and 100) rainfall quantiles were then estimated using the best-fitted distributions. Finally, the universal Kriging method, which is an effective interpolation method, was used to map the estimated rainfall quantiles.