Probability Models and Statistical Tests for Extreme Precipitation Based on Generalized Negative Binomial Distributions

Mathematical models are proposed for statistical regularities of maximum daily precipitation within a wet period and total precipitation volume per wet period. The proposed models are based on the generalized negative binomial (GNB) distribution of the duration of a wet period. The GNB distribution is a mixed Poisson distribution, the mixing distribution being generalized gamma (GG). The GNB distribution demonstrates excellent fit with real data of durations of wet periods measured in days. By means of limit theorems for statistics constructed from samples with random sizes having the GNB distribution, asymptotic approximations are proposed for the distributions of maximum daily precipitation volume within a wet period and total precipitation volume for a wet period. It is shown that the exponent power parameter in the mixing GG distribution matches slow global climate trends. The bounds for the accuracy of the proposed approximations are presented. Several tests for daily precipitation, total precipitation volume and precipitation intensities to be abnormally extremal are proposed and compared to the traditional PoT-method. The results of the application of this test to real data are presented.

Uncertainties of GPM Microwave Imager Precipitation Estimates Related to Precipitation System Size and Intensity

The uncertainties in the version 5 Global Precipitation Measurement (GPM) Microwave Imager (GMI) precipitation retrievals are evaluated via comparison with the radar–radiometer (so-called “Combined”) retrievals between 40°S and 40°N. Results show the precipitation estimates are close (~7% GMI overestimation) globally. However, some specific regions, such as central Africa, the Amazon, the Himalayan region, and the tropical eastern Pacific, show a large overestimation (up to 50%) in GMI retrievals when compared to Combined retrievals. The uncertainties are further evaluated based on precipitation system properties, such as size and intensity of the system. GMI tends to underestimate precipitation volume when the system is relatively warm (>250 K) and small (<200 km2) due to the lack of ice scattering signatures. However, for large systems (>2000 km2), GMI-derived precipitation is typically higher than Combined over all surfaces. Based on the system properties, a simple bias correction methodology is proposed to implement in the Goddard Profiling Algorithm (GPROF) to reduce GMI biases. GMI precipitation volume is adjusted in each precipitation system based on the size and minimum 89 GHz polarization-corrected temperature (PCT) over land and ocean separately. The overall GMI bias is reduced to 3%, with significant improvement over land. The GMI biases (up to 50%) over the previously mentioned regions are significantly or partially removed, becoming less than 20%. This method also shows effectiveness in removing zonal and seasonal biases from GMI estimates. These results suggest the importance of utilizing the information of whole precipitation systems instead of individual pixels in the precipitation retrieval.

Statistical Tests for Extreme Precipitation Volumes

The analysis of the real observations of precipitation based on the novel statistical approach using the negative binomial distribution as a model for describing the random duration of a wet period is considered and discussed. The study shows that this distribution fits very well to the real observations and generalized standard methods used in meteorology to detect an extreme volume of precipitation. It also provides a theoretical base for the determination of asymptotic approximations to the distributions of the maximum daily precipitation volume within a wet period, as well as the total precipitation volume over a wet period. The paper demonstrates that the relation of the unique precipitation volume, having the gamma distribution, divided by the total precipitation volume taken over the wet period is given by the Snedecor–Fisher or beta distributions. It allows us to construct statistical tests to determine the extreme precipitations. Within this approach, it is possible to introduce the notions of relatively and absolutely extreme precipitation volumes. An alternative method to determine an extreme daily precipitation volume based on a certain quantile of the tempered Snedecor–Fisher distribution is also suggested. The results of the application of these methods to real data are presented.

RELATION BETWEEN EXTENSIVE EXTREME PRECIPITATION IN POLAND AND ATMOSPHERIC CIRCULATION

The basic aim of this study was to find relations between the dates of occurrence and characteristics of extensive extreme daily (24-h) precipitation totals (EEDPTs) and pressure systems. The analysis was conducted on the basis of precipitation data from the multi-year period 1956-1980 and the Grosswetterlagen classification of circulation situations. EEDPTs were taken to embrace those cases of maximum annual daily precipitation totals that were registered on the same day at a minimum of 75 precipitation stations. In the years 1956-1980 there were 209 such events. The hypothesis about the effect of a circulation situation on the probability of occurrence of an EEDPT was verified in quantitative terms, the reference being both the entire multi-year period and the seasonal variation in the occurrence of precipitation of this type. Next, circulation situations were compared in terms of amount-related parameters of EEDPTs (mean precipitation, coefficient of variation), their spatial features (perimeter, area), and precipitation volume. The analyses performed show a statistically significant dependence between the atmospheric circulation and extensive extreme precipitation. It was demonstrated that there were circulation situations during which EEDPTs occurred much more often or much more rarely than over the entire multi-year period under study. Also identified was the connection of an atmospheric circulation with the mean amount, coefficient of variation and volume of extensive extreme precipitation.