Abstract
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.
Highlights
The rapidly growing number of various natural and man-made disasters that previously were considered extremely rare indicates that the global climate change of the Earth is becoming obvious
The parametrization of the generalized Pareto distribution (GPD), whose survivor function appears in the braces on the right part of equation is different from the usual one and has the advantage that the parameters τ and ξ do not depend on the choice of threshold u
Using of max-stable processes [3] is an extension of extreme value theory applied to spatio-temporal precipitation fields
Summary
The rapidly growing number of various natural and man-made disasters that previously were considered extremely rare indicates that the global climate change of the Earth is becoming obvious. The study of regional climate change peculiarities that take place in connection with global warming is a priority area of modern international research projects. Important place in this area is given to the study of changes in the frequency and intensity of extreme weather events, including extreme precipitation, as it often leads to serious economic, environmental and human losses. The archives of long-term accumulated observations and numerical model calculations of hydrometeorological parameters make it possible to study general patterns of spatiotemporal variability of extreme precipitation in Russia, caused by both environmental and anthropogenic factors over the historical observation period and to calculate the projections of their possible future changes. At the same time, such studies are important for the subsequent solution of many applied problems, including long-term planning of regional economic development
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