Uncertainty in the estimation of extreme rainfalls around the Mediterranean Sea: an illustration using data from Marseille

The peaks-over-threshold (POT) method is a usual statistical model for hydrologists working on extreme quantiles estimation. From a theoretical point of view, the model assumes, under some general hypotheses of independence and homogeneity, that the excesses over a sufficiently high threshold are distributed as a particular family of parametric laws called generalized Pareto distributions, of which the exponential distribution is a particular case. In practice, the exponential law is often imposed while the homogeneity is assumed. As shown in the paper, such model assumptions are of real importance for applications. A set of 127 years of daily rainfalls at Marseille is used to illustrate how to apply these assumptions in practice. Usual descriptive analysis shows the heterogeneity of the data. Assuming homogeneity leads to an underestimation of high quantiles, which could induce dramatic consequences in practice. Taking into account the data heterogeneity leads to a considerable increase of the estimated values. The uncertainty attached to these values, analysed in the paper, allows one then to reach some of the historical floods recorded in the Mediterranean region. A particular result is the following: the extreme daily rainfalls at Marseille are not in the Gumbel law domain.