Improved regional frequency analysis of rainfall data

International audienceRainfall are subject to local orography features and their intensities can be highly variable. In this context, identifying climatically coherent regions can greatly help interpreting rainfall patterns and improve the inference of return levels. In practice, partitioning a region of interest into homogeneous sub-regions is a delicate statistical task, especially in regards to modeling heavy rainfall features. In this work, our main goal is to propose and study a fast and efficient clustering algorithm. Compared to classical regional frequency analysis techniques, a key aspect is that our algorithm does not rely on the a priori choice of covariates. The proposed numerical scheme is only based on the precipitation dataset at hand, including low, moderate and heavy rainfall. In terms of inference, our approach builds on the easy-to-compute and reliable probability weighted moments commonly used in hydrology. While being in compliance with extreme value theory, we do not impose a parametric form on rainfall distributions and, neither thresholding nor block maxima steps are required in our proposed approach. By construction, our clustering method preserves the scale invariance principle of any classical regional frequency analysis. The performance of our clustering algorithm is assessed on a detailed experimental design based on the extended Generalized Pareto distribution. Sensitivity to the number of clusters is carefully analyzed. We apply our clustering algorithm on Switzerland daily precipitation measured at 191 sites. The found homogeneous regions are consistent with local orography and our approach outperforms the classical regional frequency analysis based on normalized elevation and coordinates as covariates. To complete our analysis of Swiss rainfall, we propose three models based on our clustering outputs. A comparison between our local, semi-regional and regional models indicates that a relatively simple model with two clusters and a spatially varying scale parameter can compete very well against complex models