Reliable estimation of high floods: A method to select the most suitable ordinary distribution in the Metastatistical extreme value framework

Abstract

Recent advances in the study of extreme values, namely the Metastatistical extreme value (MEV) framework, showed good performances for the estimation of extremes in several fields. Here we adopt MEV for flood frequency analysis and leverage its intrinsic property of allowing for the choice of the distribution which best describes ordinary peaks to improve flood estimation. To this end, we develop a non-parametric approach to select ex ante the most suitable distribution of ordinary peaks between Gamma and Log-Normal. The method relies on the tail ratio, which we define as the ratio between the empirical 99th and 95th percentile of the ordinary peaks, and is tested by using daily streamflow time series from 182 gauges in Germany. Based on the value of the tail ratio index, we choose either the Gamma or the Log-Normal distributions to represent the ordinary peaks in each gauge. The approach correctly identifies the most suitable distribution of ordinary peaks in a large majority of the analyzed basins, and is robust to changes of the considered dataset. The preliminary selection of the ordinary distribution based on the tail ratio index improves the estimation of frequent and rare floods with respect to MEV applied with a single distribution not tailored on the specific statistical properties of the ordinary peaks. Finally, by comparing the developed methodology with the standard Generalized Extreme Value (GEV) distribution, we show that we are able to reduce the estimation uncertainty of high flood quantiles.