Analysis Of The Joint Probability Characteristics Of Extreme Precipitation Based On Copula Function

Extreme precipitation is an extreme case of precipitation events,resulting in drought and flood disasters,mudslides,landslides and other secondary disasters,which cause huge economic and property losses to human society and seriously affect the safety of life.Therefore,it is necessary and urgent to study effective statistical models to analyze the law of extreme precipitation events,in order to enhance the ability to adapt to extreme climate phenomena.Extreme precipitation events are affected by many factors and the factors interact with each other.Therefore,it is often impossible to describe and reflect the characteristics of precipitation events completely with one variable,and multiple variables are needed to represent precipitation events from different angles.Therefore,it is of great significance to construct a reasonable joint probability distribution model and estimate the multi-variable joint return period accurately and effectively for analyzing the statistical law of extreme precipitation events.In order to explore the effectiveness of Copula function in constructing the joint probability distribution model of extreme precipitation events,this paper takes precipitation data of Gaoyou station as an example to conduct multivariate analysis on the characteristic values of extreme precipitation.The study area is located in the plain of the middle and lower reaches of the Yangtze River with abundant rainfall and distinct four seasons,which is representative of precipitation characteristics in this region.According to the percentile threshold method,four characteristic values(the total amount of extreme precipitation P95,extreme precipitation intensity I95,annual maximum daily precipitation Pmax and contribution rate of extreme precipitation R95)were calculated.The P-? distribution,Gamma distribution,GEV distribution and Log-Normal distribution were selected as the alternative edge distribution functions of the characteristic values of extreme precipitation,and the edge distribution function was optimized according to the Minimum Root Mean Square Error Criterion.G-H Copula,Clayton Copula and Frank Copula were selected as alternative functions to construct the joint distribution model of the characteristic values of extreme precipitation.The optimal joint distribution function was optimized by Graph Evaluation Method,Minimum Deviation Square Sum Criterion(OLS)and Akaike Information Criterion(AIC).According to the optimized Copula function,the joint return period,co-occurrence return period and Kendall return period of the characteristic values of extreme precipitation were calculated,and the corresponding design values were deduced.The results show that:1)The optimization results of edge distribution show that the optimal distribution function of P95,Pmax and I95 is P-? distribution,and the optimal distribution function of R95 is GEV distribution.2)Archimedean Copula function has a good fitting effect on extreme precipitation data in the study area.The optimization results show that:The optimal joint probability distribution functions of(P95,Pmax)and(I95,Pmax)are Frank Copula,and the optimal joint probability distribution functions of(P95,I95)and(P95,R95)are Clayton Copula.The optimal joint probability distribution function of(P95,Pmax,I95)is Frank Copula.3)Comparing the calculation methods of extreme precipitation return period,it is found that compared with the joint return period and the co-occurrence return period,the risk rate of the joint return period is higher,while the risk rate of the co-occurrence return period is lower.Kendall return period can accurately reflect the risk probability of the characteristic value of multi-variable extreme precipitation at a specific frequency.4)Compared with other methods,the design values derived from the Kendall return period calculation method and Maximum Likelihood Method are more reasonable,and the Kendall calculation results are also economical under the same return period condition.