Modeling extremes of climate variables in the framework of climate change is a particularly difficult task, since it implies taking into account spatio-temporal nonstationarities. In this paper, we propose a new method for estimating extreme precipitation at the points where we have not observations using information from marginal distributions and dependence structure. To reach this goal we combine two statistical approaches of extreme values theory allowing on the one hand to control temporal and spatial non-stationarities via a tail trend function with a spatio-temporal structure in the marginal distributions and by modeling on the other hand the dependence structure by a latent spatial process using generalized `-Pareto processes. This new methodology for trend analysis of extreme events is applied to rainfall data from Burkina Faso. We show that extreme precipitation is spatially and temporally correlated for distances of approximately 200 km. Locally, extreme rainfall has more of an upward than downward trend.

18 pages 7 figures