Analysis of extreme precipitation characteristics in low mountain areas based on three-dimensional copulas—taking Kuandian County as an example

We defined the threshold of extreme precipitation using detrended fluctuation analysis based on daily precipitation during 1955–2013 in Kuandian County, Liaoning Province. Three-dimensional copulas were introduced to analyze the characteristics of four extreme precipitation factors: the annual extreme precipitation day, extreme precipitation amount, annual average extreme precipitation intensity, and extreme precipitation rate of contribution. The results show that (1) the threshold is 95.0 mm, extreme precipitation events generally occur 1–2 times a year, the average extreme precipitation intensity is 100–150 mm, and the extreme precipitation amount is 100–270 mm accounting for 10 to 37 % of annual precipitation. (2) The generalized extreme value distribution, extreme value distribution, and generalized Pareto distribution are suitable for fitting the distribution function for each element of extreme precipitation. The Ali-Mikhail-Haq (AMH) copula function reflects the joint characteristics of extreme precipitation factors. (3) The return period of the three types has significant synchronicity, and the joint return period and co-occurrence return period have long delay when the return period of the single factor is long. This reflects the inalienability of extreme precipitation factors. The co-occurrence return period is longer than that of the single factor and joint return period. (4) The single factor fitting only reflects single factor information of extreme precipitation but is unrelated to the relationship between factors. Three-dimensional copulas represent the internal information of extreme precipitation factors and are closer to the actual. The copula function is potentially widely applicable for the multiple factors of extreme precipitation.