Spatial interpolation of environmental parameters with Copulas

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In the first phase of this project it has been shown that Copulas offer a great novel tool to model nongaussian dependence structures for spatially distributed parameters. Magnitude- and geometry-dependent Copula based models have successfully been applied for interpolation purposes. Copulas have started to be acknowledged by the international research community and are a key topic at the forefront of geostatistical research (Section 2).Using Copulas for interpolation purposes allows for an improved uncertainty estimate of the interpolation due to the fact that a full distribution function of the estimate can be calculated. These uncertainty estimates were validated using a split-sampling approach. An improved uncertainty estimate can prove to be beneficial for risk assessment. The possibility to express heterogeneous uncertainty can be important for value-dependent observation strategies, for example in observation network design.Within the second phase of this project it is proposed to advance Copula based models in four areas: (1) to accommodate inequality constraints for interpolation which will allow to take discrete-continuous data into account, (2) to incorporate prior information to improve interpolation both for numerical and categorical data types, (3) to find new types of theoretical Copulas to improve the fit to real-world data-sets, and (4) to find a conditional simulation technique.