## 1 Introduction

[2] The evolution of extreme rainfall events has become a major concern in the past few years because of the global warming that is expected to intensify the hydrological cycle and thus increase the precipitation intensities, even in regions where the mean annual rainfall might decrease [*Alpert*, 2002; *Trenberth et al.*, 2003; *Emori and Brown*, 2005; *Held and Soden*, 2006; *O'Gorman and Schneider*, 2009]. This prospect is clearly visible at global scale in general circulation models (GCM) and Regional Climate Models simulations [*Easterling et al.*, 2000; *Allen and Ingram*, 2002; *Milly et al.*, 2002; *Voss et al.*, 2002; *Groisman et al.*, 2005; *Kharin and Zwiers*, 2005; *Alexander et al.*, 2006; *Sun et al.*, 2007; *Min et al.*, 2011], but clear trends in that direction remain to be confirmed in observations, even though a few studies assert this to be already perceivable in some places [*Dore*, 2005; *Zhang et al.*2007].

[3] Researchers looking for possible changes in the accuracy and magnitude of extreme rainfall are facing the challenge of detecting a statistically significant trend or break in a process that is characterized by a large natural space and time variability. The core of the problem lies in the fact that there are not so many data sets spanning a sufficiently long period so as to perform meaningful statistical tests of nonstationarity on series characterized by such a high time variability. Satellite observations are still too recent in that respect, which implies that the only relevant long-term observations are rain gauge series. This explains why most studies aiming at detecting trends in extreme precipitation events during the last century are based on the analysis of daily values recorded by rain gauges [see, e.g., *Kunkel et al.*, 1999; *Manton et al.*, 2001; *Bocheva et al.*, 2009; *Costa and Soares*, 2009; *Shahid*, 2010; *Begueria et al.*, 2011].

[4] However, point rainfall series have their own weakness in terms of sampling properly the spatial variability: indeed, the strong spatial variability of extreme rainfall is another complicating factor as far as detecting trends is concerned. There is thus a need for methods allowing to combine optimally and in a robust way the time and the spatial information provided by point rainfall series covering a climatic region. The goal of this paper is precisely to propose such a method and to illustrate its efficiency by applying it to a region—the West African Sahel—where rainfall variability is notoriously high at all scales. An extensive review of literature shows that the scientific community is still lacking an integrated regional approach for characterizing extreme rainfall distribution at regional scale.

[5] A first widely used approach [*Frich et al.*, 2002; *Easterling et al.*, 2003; *Kiktev et al.*, 2003; *Klein Tank and Knnen*, 2003; *Moberg and Jones*, 2005; *Alexander et al.*, 2006] to assess trends in extreme precipitations is to describe the evolution of simple rainfall indices (as for instance the number of rainy days over a fixed threshold or the evolution of the 95th percentile of the daily rainfall distribution). By incorporating most of the recorded heavy rainfall events, this approach fairly deals with the issue of sampling effects; however, the resulting statistics are poorly informative regarding the evolution of high rainfall quantiles (typically 20 to 100 year, or larger return period values) that are of greatest interest from both a climatological and a water resources management points of view.

[6] An alternative common approach is provided by the extreme value theory (EVT) [see *Coles*, 2001 for details]. In the EVT framework, extreme series are created by extracting maxima in predefined periods (block maxima analysis: BMA) or values exceeding a given threshold (peaks-over-threshold: POT). Analytical functions are specified to infer the distributions of the extreme values as for instance the widely used generalized extreme value (GEV) distributions (used in the BMA approach) or the Generalized Pareto (GP) distributions (used in the POT approach). One of the main assumptions of the EVT is the stationarity of extremes. The detection of nonstationarity in series within the EVT framework mainly consists in examining the validity of the stationarity assumption.

[7] To that purpose, the method that has long prevailed in the literature is the use of statistical stationarity tests, designed to detect either linear or breakpoint changes in the extreme event series [*Robson et al.*, 1998; *Haylock and Nicholls*, 2000; *Manton et al.*, 2001; *Frich et al.*, 2002; *Easterling et al.*, 2003; *Klein Tank and Knnen*, 2003; *Moberg and Jones*, 2005; *Alexander et al.*, 2006; *Aguilar et al.*, 2009; *Rahimzadeh et al.*, 2009; *Costa and Soares*, 2009; *Shahid*, 2010; *Guhathakurta et al.*, 2011; *Chu et al.*, 2012]. Beyond that, there are only a few studies using regional approaches to test the stationarity of extreme precipitation; among them, we can cite *Renard* [2006], *Pujol et al.* [2007], and *Neppel et al.*[2011].

[8] More recently, parametric approaches have been proposed based on extreme value distributions incorporating time-dependent parameters or time-varying covariates [*Coles*, 2001; *Katz et al.*, 2002]. Comparing these nonstationary GEV [*Re and Barros*, 2009; *Marty and Blanchet*, 2011; *Park et al.*, 2011; *Seo et al.*, 2011] or nonstationary GP distributions [*Re and Barros*, 2009; *Sugahara et al.*, 2009; *Begueria et al.*, 2011] to their stationary counterpart is a way to assess the significance of the temporal trend in extreme rainfall distribution. The time-dependent distributions have mainly been applied to assess linear trends in extreme series, but, to our knowledge, no attempt has so far been made at adapting them to detect breakpoint changes.

[9] Among the most recent advances in the modeling of extreme events, original developments have been proposed to model the extreme events at regional scale by taking into account the spatial heterogeneities of the distributions by incorporating spatial covariates [see, e.g., *Blanchet and Lehning*, 2010; *Panthou et al.*, 2012]. *Panthou et al.* [2012] show that pooling individual point series in order to fit directly a regional model using a spatial covariate reduces significantly the impact of temporal sampling effects. Some recent studies proposed to model the spatial or spatiotemporal dependence of extremes, either using spatial latent processes [see, e.g., *Cooley et al.*, 2007; *Sang and Gelfand*, 2009] or max-stable models [see, e.g., *Padoan et al.*, 2010; *Blanchet and Davison*, 2011]. However, all these references develop and apply one single model. Among those modeling the evolution of extremes, there is no study which compares different possible approaches for describing the temporal evolution of extremes.

[10] This review of literature points to the need for studying how different approaches behave comparatively to each other. The present paper thus proposes a comparison between three methods: a classical pointwise stationarity test analysis, a pointwise time-dependent GEV model, and a regional time-dependent GEV model. Beyond the comparison itself, original methodological developments are proposed to detect both linear trends and breakpoints in the time series. The integration of these various analytical steps provides a statistically coherent way for a global analysis of extreme rainfall distribution at regional scale and for detecting changes in this distribution.