Modeling of Extreme Precipitation Fields on the Territoryof the European Part of Russia

Present work is devoted to the study and development of space-time statistical structures ofextreme type modeling with the use of the max-stable processes. The theory of one-dimensionalextremal values and its extension to the two-dimensional case are considered and for that max-stable processes are introduced and then the main parametric families of max-stable processes(Schlather, Smith, Brown-Resnick, and Extremal-t) are presented. By modifying the maximumlikelihood method, namely using the paired likelihood function, parameter estimates wereobtained for each of the models whose efficiency was compared using the Takeuchi informationcriterion (TIC).Resulting models are coherent with classical extreme value theory and allow consistenttreatment of spatial dependence of rainfall. We illustrate the ideas through data, based ondaily cumulative rainfall totals recorded at 14 stations in central European part of Russia forperiod 1966-2016 years. We compare fits of different statistical models appropriate for spatialextremes and select the model that is the best for fitting our data. The method can be used inother situations to produce simulations needed for hydrological models, and in particular forthe generation of spatially heterogeneous extreme rainfall fields over catchments. It is shownthat the most successful model for the data we studied is the model from the extremal-t familywith the Whittle-Matern correlation function.