Modeling the Four-Dimensional Joint Distribution Function of Flood Characteristics Using C-Vine Structure

The recognition of a proper multi-dimensional copula for determination the dependence structure in multidimensional data is not easy. Because multi- dimensional copulas such as the multi-dimensional Elliptical and Archimedean copulas lack flexibility to capture dependence structure and include other limitations¡ such as parameter restrictions. To dominate these limitations¡ vine copulas have been presented and employed for simulation of hydrology variables. To realize and fully perceive the mixed and hidden dependence patterns between flood characteristics (flood volume (V)¡ peak flow (P)¡ base time (B) and peak time (TP))¡ a mixture of C-vine copulas is proposed describing the dependence structure between the main flood characteristics and then simulates them use the most proper C-vine structures. As a C-vine structure consists several parameters capturing the dependence structure through cascade of pair-copulas¡ the proposed structure can explain completely complex and hidden dependence patterns in multi- dimensional data. In the present study¡ to achieve the most suitable C-vine structures¡ first different structures were created through the permuting of flood characteristics in the C-vine structure and then the most appropriate copula family among Elliptical or Archimedean copula families was selected for each pair-copula according to Log Maximum Likelihood (LML)¡ AIC and BIC evaluation criteria. Finally¡ the obtained four-dimensional joint distribution functions were compared with empirical copula and according to RMSE¡ MAE and R2 criteria and graphical method¡ structure (B-P-V-TP) was known as the most accurate structure. Thus¡ it was found that the selection of flood base time as central variable is a appropriate selection and plays role of controlling variable for volume¡ peak discharge and peak time of flood variables.