Maximum Rainfall Model Based on Archival Pluviographic Records – Case Study for Legnica (Poland)

Abstract

The scope of this study is to develop a probabilistic model for maximum rainfall in Legnica, based on a 50-year series of pluviographic records. The present authors uses Fréchet, Gamma, Generalized Exponential Distribution (GED), Gumbel, Log-Normal and Weibull distributions to describe the measurement data. Distributions parameters are estimate using maximum likelihood method. Coincidence of the analyzed theoretical distributions with measured data are inspected using the Anderson-Darling test, while the best fitting distribution is chosen by Bayesian information criterion (BIC) of Schwartz as well as by the relative residual mean square error. Among others distributions Fréchet, Gamma, GED, and Weibull distributions fulfill the compliance criterion for each of the 20 analyzed rainfall durations. BIC criterion indicates for a GED, but differences between GED, Gamma and Weibull is minor. Only RRMSE analysis revealed that in comparison to other distribution GED best describes the measurement rainfall data. At first glance maximum rainfall model was well described by the generalized exponential distribution. However, there is a substantial inconvenience to use it for engineering purposes. Generalization of the shape parameter α depended on the rainfall duration, by averaging and then recalculating remaining parameters λ and γ brought relatively simpler form of model.