Interpolation of groundwater quality parameters with some values below the detection limit

For many environmental variables, measurements cannot deliver exact observation values as their concentration is below the sensitivity of the measuring device (detection limit). These observations provide useful information but cannot be treated in the same manner as the other measurements. In this paper a methodology for the spatial interpolation of these values is described. The method is based on spatial copulas. Here two copula models – the Gaussian and a non-Gaussian v-copula are used. First a mixed maximum likelihood approach is used to estimate the marginal distributions of the parameters. After removal of the marginal distributions the next step is the maximum likelihood estimation of the parameters of the spatial dependence including taking those values below the detection limit into account. Interpolation using copulas yields full conditional distributions for the unobserved sites and can be used to estimate confidence intervals, and provides a good basis for spatial simulation. The methodology is demonstrated on three different groundwater quality parameters, i.e. arsenic, chloride and deethylatrazin, measured at more than 2000 locations in South-West Germany. The chloride values are artificially censored at different levels in order to evaluate the procedures on a complete dataset by progressive decimation. Interpolation results are evaluated using a cross validation approach. The method is compared with ordinary kriging and indicator kriging. The uncertainty measures of the different approaches are also compared.