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Spatio-temporal analysis of the frequency of extreme daily winter temperature and precipitation in the period 1970-2015 in Russia using the data of the weather stations and in the period 2041-2060 using the projections of global climate models HadGEM and MPI-M revealed statistically significant changes in densely populated regions of European Russia, in southern Siberia and in the Far East of Russia. The statistically significant increase in the number of extremely warm days that did not exceed 1 day and the days with extremely high precipitation (by 1-3 days) prevailed in European Russia in the period 2000-2015 in comparison with 1970-1999. While frequency of extremely cold days reduced by 1 day at the most territories of Russia, a simultaneous combination of increased frequency of frosty days, extremely warm days and days with extreme precipitation in the winter at the beginning of the 21st century attracts attention in the south of Western and Eastern Siberia. According to HadGEM model projection (RCP 8.5 scenario), the extreme precipitation events in Russia may occur more often in the middle of the 21st century. The highest projected increase in the frequency of extreme daily precipitation is expected in the Altai and southeastern European Russia (by 2-3 days), in northern Siberia (4 days), in the Chukotski Peninsula (7 days). According to the MPI-M model projection (RCP 8.5 scenario), the highest increase in the frequency of days with extreme precipitation in the period 2041-2060 is expected in the center of European Russia (by 1 day) and in the Chukotski Peninsula (up to 3 days).