Asymmetry in Spatial Dependence Structures

The most common assumption relied on when describing spatially distributed random variables is multivariate Gaussianity. This assumption implies a connection of the variable in its middle values. The extreme values on both ends of the symmetric normal distribution, i.e. the high values and the small values, form isolated patches. We show based on measurements that such a symmetric kind of dependence is rarely found in nature, which is in accordance to the anticipated processes responsible for the formation of the variables. Even more, the degree of asymmetry is typically found to vary for different separation distances, a property that leads to non-linear scaling behaviour. We demonstrate copula based models, their parametrisation, and their capabilities to simulate such asymmetric fields of spatially distributed parameters. And we demonstrate the effects that such an asymmetric dependence has on secondary dependent variables, and compare the effects to similar fields but with a symmetric dependence. Data-sets used as examples include detailed measurements of hydraulic conductivity and field-scale as well regional groundwater quality parameters.