Frequency Analysis and Joint Simulation of Qualitative Variables of River Flow Using Copula Functions

In this study, in order to analyze the frequency of surface water quality variables (EC-Cl and EC-SO4) and to simulate the dependent variables, the applicability of copula-based functions was addressed. Since meteorological and hydrological variables are dependent on other variables in their surroundings, their analysis using single variable models is not able to estimate the desired results. In this regard, EC, Cl and SO4 data were used in the period of 1971-2017 at Bitas, Gardeyagoub and Kotar stations in the Mahabadchai sub-basin in the south of Lake Urmia. By choosing log logistic, generalized extreme values and also log normal marginal functions, the superior copulas regarding the mentioned pair-variables were investigated. While confirming the accepted correlation between the investigated pair-variables in Bitas stations (EC-Cl=0.39 and EC-SO4=0.38), Gardeyagoub (EC-Cl=0.81 and EC-SO4=0.78) and Kotar (EC-Cl= 0.54 and EC-SO4=0.51) and also based on RMSE, MAE and NSE criteria, Galambos copula was chosen as the best copula in all stations. The joint analysis of the mentioned pair-variables using the Galambos copula led to the presentation of typical curves regarding the estimation of Cl and SO4 values corresponding to the specific EC unit with different probabilities in the studied stations. Given that the presented curves are based on the statistical distribution of data, they are specific to the studied station.