Statistical tests for daily and total precipitation volumes to be abnormally extremal.

In this paper, two approaches are proposed to the definition of abnormallyextremal precipitation. These approaches are based on the negative binomialmodel for the distribution of duration of wet periods measured in days. Thismodel demonstrates excellent fit with real data and provides a theoretical basefor the determination of asymptotic approximations to the distributions of themaximum daily precipitation volume within a wet period and of the totalprecipitation volume over a wet period. The asymptotic distribution of themaximum daily precipitation volume within a wet period turns out to be atempered Snedecor-Fisher distribution whereas the total precipitation volumefor a wet period turns out to be the gamma distribution. These asymptoticapproximations are deduced using limit theorems for statistics constructed fromsamples with random sizes. The first approach to the definition of abnormallyextreme precipitation is based on the tempered Snedecor-Fisher distribution ofthe maximum daily precipitation. According to this approach, a dailyprecipitation volume is considered to be abnormally extremal, if it exceeeds acertain (pre-defined) quantile of the tempered Snedecor-Fisher distribution.The second approach is based on that the total precipitation volume for a wetperiod has the gamma distribution. Hence, the hypothesis that the totalprecipitation volume during a certain wet period is abnormally large can beformulated as the homogeneity hypothesis of a sample from the gammadistribution. Two equivalent tests are proposed for testing this hypothesis.Within the second approach it is possible to introduce the notions ofrelatively abnormal and absolutely abnormal precipitation volumes. The resultsof the application of these tests to real data are presented yielding theconclusion that the intensity of wet periods with abnormally largeprecipitation volume increases.