Copula-based geostatistical models for groundwater quality parameters

Groundwater quality parameters exhibit considerable spatial variability. Geostatistical methods including the assessment of variograms are usually used to characterize this variability. Copulas offer an interesting opportunity to describe dependence structures for multivariate distributions. Bivariate empirical copulas can be used as an alternative to variograms and covariance functions for the description of the spatial variability. Rank correlations of these copulas express the strength of the dependence independently of the marginal distributions and thus offer an alternative to the variograms. Empirical copulas for four quality parameters, chloride, sulfate, pH, and nitrate, obtained from a large-scale groundwater quality measurement network in Baden-Wurttemberg (Germany) are calculated. They indicate that the spatial dependence structure of the investigated parameters is not Gaussian. Two theoretical copula-based models are presented in this paper: a Gaussian and a non-Gaussian. Bootstrap-based statistical tests using stochastic simulation of the multivariate distributions are used to investigate the appropriateness of the models. According to the test results the Gaussian copula is rejected for most of the parameters while the non-Gaussian alternative is not rejected in most cases.