Comparison of performance of C-Vine and D-Vine tree copulas in multivariate analysis of precipitation characteristics

In this study, the basic features of a tree vine copula such as the ability to decompose multivariate distributions into two-dimensional distributions, its flexibility in high-dimensional problems, and the use of conditional dependencies between variables have been considered. The purpose is to use C-Vine and D-Vine structures to determine the four-dimensional probabilistic distribution function of important characteristics of precipitation events of Cremona rain station located in Italy including maximum precipitation intensity total precipitation depth, wet period duration and dry period. So that, a combination of the most suitable Archimedean and elliptical copulas families was identified to fit the pair-copulas of each of the C-Vine and D-Vine structures. The optimal combined distribution functions of C-Vine and D-Vine structures were also calculated using chain density functions and compared with the four-dimensional experimental copula of important precipitation characteristics. Finally, the accuracy of C-Vine and D-Vine tree structures in determining the combined distribution functions of important precipitation characteristics was compared. The results showed that the RDLM C-Vine structure has a minimum value of evaluation criteria RMSE = 0.029 and MAE = 0.022, as well as a maximum of P-value = 0.35 and R2 = 0.998 among all C-Vine and D-Vine structures. As a result, it has the highest accuracy for frequency analyzing the of precipitation characteristics of Cremona station in Italy.