Clustering of Maxima: Spatial Dependencies among Heavy Rainfall in France

Elsa Bernard Laboratoire des Sciences du Climat et de l'Environnement, CNRS-CEA-UVSQ, Gif-sur-Yvette, France

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Philippe Naveau Laboratoire des Sciences du Climat et de l'Environnement, CNRS-CEA-UVSQ, Gif-sur-Yvette, France

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Mathieu Vrac Laboratoire des Sciences du Climat et de l'Environnement, CNRS-CEA-UVSQ, Gif-sur-Yvette, France

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Olivier Mestre Direction de la Production, Météo-France, Toulouse, France

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Abstract

One of the main objectives of statistical climatology is to extract relevant information hidden in complex spatial–temporal climatological datasets. To identify spatial patterns, most well-known statistical techniques are based on the concept of intra- and intercluster variances (like the k-means algorithm or EOFs). As analyzing quantitative extremes like heavy rainfall has become more and more prevalent for climatologists and hydrologists during these last decades, finding spatial patterns with methods based on deviations from the mean (i.e., variances) may not be the most appropriate strategy in this context of studying such extremes. For practitioners, simple and fast clustering tools tailored for extremes have been lacking. A possible avenue to bridging this methodological gap resides in taking advantage of multivariate extreme value theory, a well-developed research field in probability, and to adapt it to the context of spatial clustering. In this paper, a novel algorithm based on this plan is proposed and studied. The approach is compared and discussed with respect to the classical k-means algorithm throughout the analysis of weekly maxima of hourly precipitation recorded in France (fall season, 92 stations, 1993–2011).

Corresponding author address: Philippe Naveau, Laboratoire des Sciences du Climat et de l'Environnement, CNRS-CEA-UVSQ, Orme des Merisiers, 61190 Gif-sur-Yvette, France. E-mail: naveau@lsce.ipsl.fr

Abstract

One of the main objectives of statistical climatology is to extract relevant information hidden in complex spatial–temporal climatological datasets. To identify spatial patterns, most well-known statistical techniques are based on the concept of intra- and intercluster variances (like the k-means algorithm or EOFs). As analyzing quantitative extremes like heavy rainfall has become more and more prevalent for climatologists and hydrologists during these last decades, finding spatial patterns with methods based on deviations from the mean (i.e., variances) may not be the most appropriate strategy in this context of studying such extremes. For practitioners, simple and fast clustering tools tailored for extremes have been lacking. A possible avenue to bridging this methodological gap resides in taking advantage of multivariate extreme value theory, a well-developed research field in probability, and to adapt it to the context of spatial clustering. In this paper, a novel algorithm based on this plan is proposed and studied. The approach is compared and discussed with respect to the classical k-means algorithm throughout the analysis of weekly maxima of hourly precipitation recorded in France (fall season, 92 stations, 1993–2011).

Corresponding author address: Philippe Naveau, Laboratoire des Sciences du Climat et de l'Environnement, CNRS-CEA-UVSQ, Orme des Merisiers, 61190 Gif-sur-Yvette, France. E-mail: naveau@lsce.ipsl.fr
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