Spatial non-stationary extreme precipitation modelling in the Mediterranean region.

Intense precipitation events often occur in Mediterranean regions. These phenomena depend on the presence of mountainous and hilly reliefs combined with masses of humidity caused by the proximity of the sea. Floods are the most significant natural hazards in the region that may cause widespread devastation. Therefore, a proper characterization of these extreme precipitation events is crucial.

Extreme Value Theory (EVT) is a branch of statistics that provides a suitable framework for the statistical modelling of extreme events. Owing to the spatial heterogeneity of the Mediterranean area, the distribution of extreme precipitation events is non-stationary in space. To take non-stationarity into account, the parameters of the distribution can be viewed as functions of covariates that convey information on the spatial heterogeneity. Such functions may be implemented as a generalized linear model (GLM) or with more flexible non-parametric non-linear models such as Artificial Neural Networks (ANN).

In this work, we aim at evaluating and comparing several statistical models that allow to interpolate spatially the distribution of intense precipitation events. The statistical models combine the distribution of extremes with a GLM and an ANN for the spatial interpolation of distribution parameters. Key issues are the proper selection of the complexity level of the ANN (i.e. the number of hidden units) and the proper selection of geographical covariates.

Three sites that form a north-south aridity gradient are included in our study : a region in the French Mediterranean, the Cap Bon area in North-East Tunisia and the Merguellil catchment in central Tunisia. The comparative analyses aim at assessing the genericity of state-of-the-art approaches to interpolate the distribution of extreme precipitation events.

• KEYWORDS: Intense precipitation events, non-stationarity in space, extreme value theory, spatial interpolation.