Mapping rainfall hazard based on rain gauge data: an objective cross-validation framework for model selection

Abstract

We propose an objective framework for selecting rainfall hazard mapping models in a region starting from rain gauge data. Our methodology is based on the evaluation of several goodness-of-fit scores at regional scale in a cross-validation framework, allowing us to assess the goodness-of-fit of the rainfall cumulative distribution functions within the region but with a particular focus on their tail. Cross-validation is applied both to select the most appropriate statistical distribution at station locations and to validate the mapping of these distributions. To illustrate the framework, we consider daily rainfall in the Ardèche catchment in the south of France, a 2260 km2 catchment with strong inhomogeneity in rainfall distribution. We compare several classical marginal distributions that are possibly mixed over seasons and weather patterns to account for the variety of climatological processes triggering precipitation, and several classical mapping methods. Among those tested, results show a preference for a mixture of Gamma distribution over seasons and weather patterns, with parameters interpolated with thin plate spline across the region.