Revisiting the use of the Gumbel distribution: A Frequency Analysis Perspective

Abstract

The manuscript presents the applicability of the Gumbel distribution in the frequency analysis of extreme events in hydrology. The advantages and disadvantages of using the distribution are highlighted, as well as recommendations regarding its proper use. A literature review was also carried out regarding the methods of estimating the parameters of the Gumbel distribution. Thus, for the verification of the methods, case studies are presented regarding the determination of the maximum annual flows and precipitations using nine methods for parameter estimation. The influence of the observed data lengths on the estimation of the statistical indicators, the parameters and the quantiles corresponding to the field of low annual exceedance probabilities (p <1%) is also highlighted. The results are compared to those obtained with the Generalized Extreme Value distribution, respectively the Burr and the Wakeby distributions with parameters estimated using the L-moments. The results highlight and reaffirm the statistical, mathematical and hydrological recommendation regarding the avoidance of using the Gumbel distribution in Flood Frequency Analysis and its use with reservations in the case of maximum precipitation, especially when the statistical indicators of the analyzed data are not close to the characteristic ones and unique to the distribution.