Definition of Spatial Copula Based Dependence Using a Family of Non‐Gaussian Spatial Random Fields

Spatial structures of natural variables are often very complex due to the different physical chemical or biological processes which contributed to the emergence of the fields. These structures often show non‐Gaussian spatial dependence. Unfortunately, there are only a limited number of approaches that can explicitly consider non‐Gaussian behavior. In this contribution, a very flexible way of defining non‐Gaussian spatial dependence is presented. The approach is based on a kind of continuous deformation of fields with different Gaussian spatial dependence. Theoretical examples illustrate the methodology for a wide variety of non‐Gaussian structures. A real‐life example of groundwater quality parameters shows the practical applicability of the geostatistical model. Key Points A method to define a wide range of non‐Gaussian spatial dependence is presented A conditional simulation approach for these non‐Gaussian structures via Monte Carlo optimization is presented A groundwater quality parameter study demonstrates the benefits of the approach