Multivariate Flood Risk Analysis Using Nested Copula Functions in Bazoft Watershed

The flood risk analysis is of great importance in designing and planning to reduce flood damages. Flood is a multidimensional phenomenon that is described with correlated characteristics. Therefore, it is necessary to analyze all its characteristics simultaneously to obtain a more accurate estimate of the risk of its occurrence. In this paper, bivariate and trivariate flood frequency analysis were done in Bazoft watershed of Chaharmahal and Bakhtiari Province, Iran. For this purpose, three characteristics of flood, including flood volume (V), flood duration (D), and flood peak discharge (P) were extracted from 98 events recorded in the hydrometric station of this watershed. Nested copula functions were used to analyze the dependency structure of these three variables. Six copula functions of Clayton, Joe, Frank, t-Student, Gaussian and Gumbel were used to join the two and then the three variables. Finally, according to the obtained joint distributions, the primary, secondary and conditional joint return periods were calculated. Based on the Kolmogorov-Smirnov test, the most appropriate marginal distributions for the data of flood volume, peak flood discharge and flood duration were determined as Log-gamma, Weibull and Log-normal, respectively. The two variables of peak discharge and flood volume are the best pair to create a bivariate distribution, which were then joined with the third variable, the flood duration. Compared to the corresponding empirical copula, the Frank copula is specified as the best for PV pair (NSE = 0.996) and the Gumbel copula (NSE = 0.978) is the best option for PVD variables. Comparison of the flood variable quantiles for the univariate, bivariate and trivariate return periods corresponding to the AND and OR modes in the Bazoft watershed showed that the value of the secondary return period was less than the corresponding AND mode of that period and greater than the corresponding OR mode. Also, by comparing the period of joint conditional return period, it can be seen that the conditional return periods of the second type (i.e. the return period of the occurrence of one flood variable provided that two other flood variables occur) is greater than the values of the first type (i.e. the return period of two variables provided the third variable occurs).