Extreme Rainfall Analysis at Ungauged Sites in the South of France : Comparison of Three Approaches

Carreau, Julie; Neppel, Luc; Arnaud, Patrick; Cantet, Philippe

Journal de la société française de statistique, Tome 154 (2013) no. 2, pp. 119-138.

Nous comparons trois approches pour l’estimation de la distribution des pluies extrêmes en des sites non-jaugés. Deux de ces approches reposent sur la loi des valeurs extrêmes généralisée (GEV). La méthode SIGEV interpole linéairement les paramètres de la GEV estimés localement aux sites jaugés. RFA est une méthode régionale qui définit des voisinages homogènes circulaires autour de chaque site ce qui permet d’augmenter la taille de l’échantillon. En effet, RFA fait l’hypothèse que les observations aux stations du voisinage suivent la même loi GEV à un facteur de normalisation près. Ce facteur, appelé index value doit être interpolé aux sites non-jaugés. La troisième approche se base sur un générateur de pluie horaire appelé SHYPRE. À l’aide d’un caractérisation précise des événements pluvieux, SHYPRE est en mesure de simuler de longues séries de pluie ayant des statistiques semblables aux séries d’observations. Ces trois approches sont évaluées et comparées sur un jeu de données comprenant plus de 1000 stations dans le sud de la France. La comparaison des méthodes repose sur le calcul de quantiles de haut niveau et a pour but d’évaluer la justesse et la sensibilité des méthodes. Nos conclusions sont les suivantes : SIGEV tel que mis en oeuvre ne devrait pas être retenu en raison de son manque de robustesse, RFA et SHYPRE ont des performances comparables bien que ces méthodes soient très différentes et nous concluons que le défi le plus important à relever pour ces trois approches réside dans l’interpolation spatiale des paramètres.

We compare three approaches to estimate the distribution of extreme rainfall at ungauged sites. Two approaches rely on the univariate generalized extreme value distribution (GEV). SIGEV interpolates linearly the GEV parameters estimated locally. RFA is a regional method which builds circular homogeneous neighborhood around each site in order to increase the sample size. The observations in the neighborhood, properly normalized, are assumed to follow the same GEV distribution. Then the normalizing factor (called the index value) has to be interpolated to ungauged sites. The third method is the stochastic hourly rainfall generator called SHYPRE. By characterizing precisely rainfall events, SHYPRE is able to simulate long rainfall series with statistics similar to the observed series. The distribution of extreme rainfall is estimated empirically from the simulated series. The three approaches are evaluated and compared on datasets from over 1000 rain gauges in the South of France. The evaluation framework that we follow is based on the computation of high-level quantiles and aim at assessing the goodness-of-fit of the three approaches and their sensitivity to the training data. Our conclusions are threefold : SIGEV, as implemented, should be avoided because of its lack of robustness, RFA and SHYPRE despite the fact that they are based on very different hypotheses on rainfall provide comparable performance and finally, the main challenge regarding the estimation at ungauged sites concerns the spatial interpolation of the parameters, whatever the approach taken.

Keywords: Generalized Extreme Value distribution, Regional Frequency Analysis, Stochastic hourly rainfall generator
Mot clés : Loi des valeurs extrêmes généralisée, Analyse régionale fréquentielle, générateur stochastique de pluie horaire

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