Multivariate analysis of groundwater quality using Archimedean Copula functions (Case study: Shahrekord plain)

So far, various studies on the analysis of water quality parameters have been evaluated, but less multivariate analysis of quality parameters has been done. Therefore, in this study, a new approach has been proposed to multivariate analysis of water quality parameters using Copula functions. Since water quality data is skewed and the assumption of normality is not observed in the data distribution, so using the Archimedean Copula functions in this study for quality parameters (Sar, K, Mg, Na, Ca, Cl, Ec, Ph, Tds, So4 and Th, Hco3,) can be overcome by topic. For this purpose, qualitative data of 24 observation wells in Shahrekord plain were used. Then, by Coupling (pairing) the water quality parameters and determining the superior distribution, ten Copula functions were fitted on them. The results of fitting the distributions showed that the GEV (Generalized Extreme Value) distribution function is the best distribution function over the qualitative parameters and also the results of determining the copula functions showed that in the first stage the Copula search function as a function The best Copula was identified over the qualitative parameters, and then the functions of Clayton and Farley Gamble Morgan Stern were next. The results of fitting correlation analysis showed that the highest correlation based on Pearson, Spearman and Kendal correlation coefficients is related to the parameters (Sar, Na) and (Ec, Tds) with a correlation coefficient more than 0.9. so that the results of the criteria goodness of fit for them (Root Mean Square Error (RMSE), Nash Sutcliffe Efficiency coefficient (NSE) , Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC)) was respectively RMSE = 0.031,0.036, NSE = -0.0271, -0.0351, AIC = 66,65.5 and BIC = -6.4, -6.9 Awareness of qualitative pollution of groundwater resources is one of the benefits of using multivariate analysis methods in groundwater quality studies.