Determination of Optimum Two-Dimensional Copula Functions in Analyzing Groundwater Changes Using Meta Heuristic Algorithms

One of the important factors in recharging the groundwater aquifers in each region is rainfall. Reducing rainfall, and even extreme values of it, can have a huge impact on reducing groundwater levels, which can cause serious damage to aquifers and their construction. Hydrological frequency analysis methods mainly consist of two steps, including selection of an appropriate sample distribution and estimation of selected distribution parameters. Using distribution functions for univariate hydrological analysis has been discussed by many researchers. Different probability distribution models have been used in hydrological studies including the two-parameter distribution such as those by Gumbel, Weibull, Gamma, and Lognormal in several studies (Du et al., 2005; Giraldo Osorio & García Galiano, 2012; Jiang et al., 2015; Villarini, 2009), the distribution of three parameters, such as GEV in other studies (Cannon, 2010; El Adlouni et al., 2007), and the Pearson-type III distribution in the studies by  Chen et al., (2010 , 2015). Therefore, due to the importance of drought and its effects on groundwater level, there are two objectives in this paper. The first is to investigate the artificial intelligence methods and meta-heuristic algorithms to determine the parameters of the copula functions, and the second is the bivariate analysis of precipitation and groundwater shortage signatures in the Nazloochai sub-basin located in the west of Lake Urmia.