Multivariate analysis of flood characteristics in Armand Watershed, Iran using vine copulas

Flood is one of the most devastating natural disasters that cause much damage every year in different world regions. The floods can be described by some dependent characteristics, like flood peak, volume, and duration, which are usually analyzed separately. Multivariate analysis of flood characteristics can provide a better understanding of this phenomenon for planners and engineers. This study applied the vine copula structures for a multivariate analysis of flood characteristics in the Armand watershed, Iran. For this purpose, the hydrographs of 68 flood events recorded at the Armand gauging station were selected, and the flood characteristics, including peak flow (P), flood volume (V), flood duration (D), and time to peak (T) were extracted. Then, the fitness of some commonly used univariate distributions was examined on the mentioned flood characteristics. The best fitted marginal distribution on the flood duration, peak discharge, time to peak, and flood volumes were Johnson SB, Lognormal (3P), Log-logistic, and Lognormal (3P), respectively. In the next phase, the C-vine and D-vine structures were created considering three (P, V, and T/D) and four (P, D, T, and V) variables in different orders. By examining six different copula functions (Gumbel, Frank, Joe, Clayton, Gaussian, and t-student) for creating all possible permutations of C-vine and D-vine structures, we have tested 72 cases for C-vine and 144 cases for D-vine structures. The results showed that the best permutation of C-vine in the trivariate model is PVT with Nash–Sutcliffe efficiency coefficient (NSE) of 0.994, and PVD is the best one for D-vine copulas with NSE of 0.985. In four-variate cases, the best C-vine and D-vine structures were PVTD and VPTD, respectively, with corresponding values of NSE of 0.989 and 0.990. The Frank copula has been recognized as the best-fitted copula at most of the edges and nodes in both C-vine and D-vine trees. The results indicated that the four-variate vine structures have higher concordance with the empirical copula than the trivariate structures.