A Critical Review of Probability of Extreme Rainfall: Principles and Models

Abstract

Probabilistic modelling of extreme rainfall has a crucial role in flood risk estimation and consequently in the design and management of flood protection works. This is particularly the case for urban floods, where the plethora of flow control cites and the scarcity of flow measurements make the use of rain- fall data indispensable. For half a century, the Gumbel distribution has been the prevailing model of extreme rainfall. Several arguments including theoretical rea- sons and empirical evidence are supposed to support the appropriateness of the Gumbel distribution, which corresponds to an exponential parent distribution tail. Recently, the applicability of this distribution has been criticized both on theoretical and empirical grounds. Thus, new theoretical arguments based on comparisons of actual and asymptotic extreme value distributions as well as on the principle of max- imum entropy indicate that the Extreme Value Type 2 distribution should replace the Gumbel distribution. In addition, several empirical analyses using long rain- fall records agree with the new theoretical findings. Furthermore, the empirical analyses show that the Gumbel distribution may significantly underestimate the largest extreme rainfall amounts (albeit its predictions for small return periods of 5-10 years are satisfactory), whereas this distribution would seem as an appropriate model if fewer years of measurements were available (i.e. parts of the long records were used).