Multivariate density model comparison for multi-site flood-risk rainfall in the French Mediterranean area

Abstract

The French Mediterranean area is subject to intense rainfall events which might cause flash floods, the main natural hazard in the area. Flood-risk rainfall is defined as rainfall with a high spatial average and encompasses rainfall which might lead to flash floods. We aim to compare eight multivariate density models for multi-site flood-risk rainfall. In particular, an accurate characterization of the spatial variability of flood-risk rainfall is crucial to help understand flash flood processes. Daily data from eight rain gauge stations at the Gardon at Anduze, a small Mediterranean catchment, are used in this work. Each multivariate density model is made of a combination of a marginal model and a dependence structure. Two marginal models are considered: the Gamma distribution (parametric) and the Log-Normal mixture (non-parametric). Four dependence structures are included in the comparison: Gaussian, Student t, Skew Normal and Skew t in increasing order of complexity. They possess a representative set of theoretical properties (symmetry/asymmetry and asymptotic dependence/independence). The multivariate models are compared in terms of three types of criteria: (1) separate evaluation of the goodness-of-fit of the margins and of the dependence structures, (2) model selection with a leave-one-out evaluation of the Anderson-Darling and Cramer-Von Mises statistics and (3) comparison in terms of two hydrologically interpretable quantities (return periods of the spatial average and conditional probabilities of exceedances). The key outcome of the comparison is that the Skew Normal with the Log-Normal mixture margins outperform significantly the other models. The asymmetry introduced by the Skew Normal is an added-value with respect to the Gaussian. Therefore, the Gaussian dependence structure, although widely used in the literature, is not recommended for the data in this study. In contrast, the asymptotically dependent models did not provide a significant improvement over the asymptotically independent ones.