Statistics of extremes and estimation of extreme rainfall: I. Theoretical investigation / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: I. Recherche théorique

Abstract

Abstract The Gumbel distribution has been the prevailing model for quantifying risk associated with extreme rainfall. Several arguments including theoretical reasoning and empirical evidence are supposed to support the appropriateness of the Gumbel distribution. These arguments are examined thoroughly in this work and are put into question. Specifically, theoretical analyses show that the Gumbel distribution is quite unlikely to apply to hydrological extremes and its application may misjudge the risk, as it underestimates seriously the largest extreme rainfall amounts. Besides, it is shown that hydrological records of typical length (some decades) may display a distorted picture of the actual distribution, suggesting that the Gumbel distribution is an appropriate model for rainfall extremes while it is not. In addition, it is shown that the extreme value distribution of type II (EV2) is a more consistent alternative. Based on the theoretical analysis, in the second part of this study an extensive empirical investigation is performed using a collection of 169 of the longest available rainfall records worldwide, each having 100–154 years of data. This verifies the inappropriateness of the Gumbel distribution and the appropriateness of EV2 distribution for rainfall extremes.

Keywords:

• design rainfall
• extreme rainfall
• generalized extreme value distribution
• Gumbel distribution
• hydrological design
• hydrological extremes
• probable maximum precipitation
• risk
• pluie de projet
• précipitation extrême
• distribution généralisée de valeurs extrêmes
• distribution de Gumbel
• dimensionnement hydrologique
• valeurs extrêmes en hydrologie
• précipitation maximum probable
• risque

Additional information

Notes on contributors

Demetris Koutsoyiannis

[email protected]