Interpolation of Environmental Variables Considering Additional Information Using Spatial Copulas

Copula based spatial models offer a possibility to include different information in the interpolation/simulation procedure. Prior information based on hydrogeological or land use classification can be used to assess specif and point vise different marginal distributions. After removing the marginals a copula is used to describe the spatial structure of the deviation in the quantile space. The methodology can be extended to consider values below detection limits, and also allows the simultaneous estimation/simulation of correlated variables. The model parameters can be estimated using a simultaneous maximum likelihood estimation for the marginal distributions and a multipoint maximum likelihood for the estimation of the spatial copula. The methodology is illustrated using different groundwater quality parameters measured at more than 2500 locations in South-West Germany. Cross validation and split sampling are used to compare the methodology with standard geostatistical techniques. An example on rainfall interpolation using topographical data shows another alternative application area of the methodology.