Extraction of joint probabilistic distribution functions of characteristics of precipitation using a four-dimensional D-vine tree structure

Multivariate frequency analysis of hydrological phenomena by considering the dependence between the basic characteristics of these phenomena will lead to more their accurate estimation. Due to the high flexibility provided by vine tree copulas in problems with dimension greater than two. In this study the D-vine function is used to determine the four-dimensional probabilistic distribution function of main characteristics of the precipitation events of Cremona station in Italy (including maximum rainfall intensity, total rainfall depth, duration of wet period and dry period). First, due to the significant dependence between the main characteristics of precipitation events and also using their permutation, D-vine tree structures were obtained. After fitting the various Archimedean and elliptical copula families to the pair-copulas of each D-vine tree structure, the most suitable copula families were determined for fitting the pair-copulas of each D-vine structure by the maximum log-likelihood, Akaike (AIC) and Bayesian Information Criterion (BIC). Then, in order to evaluate the accuracy of the four-dimensional probabilistic distribution functions of the important characteristics of precipitation events, the mentioned functions were compared with the corresponding four-dimensional empirical copulas. Finally, the M-R-D-L four-dimensional D-vine structure according to the evaluation criteria of R2 = 0.991, RMSE = 0.031, and MAE = 0.024, was selected as the most appropriate structure for constructing of the joint distribution function of main characteristics of precipitation in Cremona station