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.

翻译：在气候变化框架内模拟极端气候变量是一项特别困难的任务,因为它意味着要考虑时空非常态因素。在本文中,我们提出一种新的方法,用于利用边际分布和依赖性结构中的信息,在没有观测到的点估计极端降水量。为实现这一目标,我们将两个极端价值理论的统计方法结合起来,一方面通过尾端趋势函数控制时间和空间非静止,另一方面通过边际分布中的时空结构,另一方面通过利用普遍`帕雷托过程'模拟潜在的空间过程来模拟依赖性结构。这种极端事件趋势分析的新方法适用于布基纳法索的降雨数据。我们表明,极端降水在空间和时间上对大约200公里的距离具有相关性。当地极端降雨是上升而不是下降趋势。