Selection of the Best Copula Function in Bivariate Analysis of Water Resources Components (Case study: Siminehrood River Basin, Iran)

Abstract

The copula function is a joint distribution of correlated random variables that are defined based on univariate marginal distributions. The aim of the present study is to select the best copula function to create joint probability distributions between the pair of parameters of precipitation- river discharge, river discharge- river salinity and river discharge- groundwater level in the Siminehrood River Basin. The necessity of using copula functions is the existence of correlation between the desired pair of parameters. For review the correlation between the pair of parameters, Kendall's tau statistic was used. Correlation between the precipitation- river discharge, river discharge- river salinity and river discharge- groundwater level were obtained 0.43, 0.64 and 0.44, respectively. After correlation evaluation, the marginal distribution of the parameters was investigated. Using the Kolmogorov-Smirnov and Anderson-Darling tests, statistical distribution functions for precipitation, river discharge, river salinity and groundwater level were obtained Lognormal, Gamma, Burr and Lognormal distributions, respectively. Then, by examining the dependence structure and the structure of copulas and using NSE, RMSE and BIAS evaluation criteria, Clayton's copula function was selected for all three pair of parameters, which was used to create a joint probability distribution between the pair of parameters in the Siminehrood River Basin.