Geostatistics for spatial extremes. A case study of maximum annual rainfall in Portugal**

Spatial statistics deals with statistical methods in which spatial locations play an explicit role in the analysis of data. Spatial data are often modeled as a realization of a Gaussian process or a function of a Gaussian process. However there are events, such as rain, snow, storms, hurricanes, earthquakes, where extremes are of the main interest. Here multivariate normal distributions are inappropriate for modeling tail behavior. The natural class of processes for dealing with extremes is the max-stable processes. This work briefly reviews the approaches to the statistical modeling of spatial extremes. Models for max-stable processes will be considered in an application to the annual maxima of daily precipitation over the North of Portugal.