Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 14 3 2007 10.5194/npg-14-305-2007 http://www.nonlin-processes-geophys.net/14/305/2007/ http://www.nonlin-processes-geophys.net/14/305/2007/npg-14-305-2007.html http://www.nonlin-processes-geophys.net/14/305/2007/npg-14-305-2007.pdf 305 316 2007-06-25 Non-stationary extreme models and a climatic application M. Nogaj marta.nogaj@edf.fr S. Parey D. Dacunha-Castelle EDF R&D, 6 Quai Watier, 78401 Chatou, France Department of Mathematics, University Paris-XI, Orsay, France In this paper, we study extreme values of non-stationary climatic phenomena. In the usually considered stationary case, the modelling of extremes is only based on the behaviour of the tails of the distribution of the remainder of the data set. In the non-stationary case though, it seems reasonable to assume that the temporal dynamics of the entire data set and that of extremes are closely related and thus all the available information about this link should be used in statistical studies of these events. We try to study how centered and normalized data which are closer to stationary data than the observation allows easier statistical analysis and to understand if we are very far from a hypothesis stating that the extreme events of centered and normed data follow a stationary distribution. The location and scale parameters used for this transformation (the central field), as well as extreme parameters obtained for the transformed data enable us to retrieve the trends in extreme events of the initial data set. Through non-parametric statistical methods, we thus compare a model directly built on the extreme events and a model reconstructed from estimations of the trends of the location and scale parameters of the entire data set and stationary extremes obtained from the centered and normed data set. In case of a correct reconstruction, we can clearly state that variations of the characteristics of extremes are well explained by the central field. Through these analyses we bring arguments to choose constant shape parameters of extreme distributions. We show that for the frequency of the moments of high threshold excesses (or for the mean of annual extremes), the general dynamics explains a large part of the trends on frequency of extreme events. 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