17. November 2009
- Dipl. Ing. Claus Haslauer
Institut für Wasserbau, Universität Stuttgart
The first part of this talk will attempt to explain what Copulas are and how they can be used for spatial statistics, especially for describing non-Gaussian dependence structures. It will be outlined how Copulas offer a tool to describe the processes which caused the spatial distribution of the parameter of interest.The second part of this talk will show some examples how Copulas can be used to describe and model real-world data-sets of hydraulic conductivity (K). Hydraulic conductivity is a fundamental parameter that influences groundwater flow and contaminant transport. The spatial distribution of K impacts the groundwater velocity field and hence directly influences the advective spreading of a contaminant migrating in the subsurface. This spreading causes portions of the plume to advance more rapidly than the average velocity while in other zones, migration rates are slower than the average velocity. This spreading phenomenon is commonly referred to as hydrodynamic macrodispersion. The objective of the presented work is to use copulas as a novel non-Gaussian stochastic model to simulate spatially-correlated random fields of K. The spatially distributed non-Gaussian K-fields are then used to conduct a series of numerical tracer experiments using a high-resolution groundwater flow and contaminant transport model. Flow and transport characteristics are derived, particularly the rate of change of the spatial moments of the evolving contaminant plume. These characteristics are also compared with those obtained under the assumption that the underlying spatial distribution of K has a Gaussian dependence structure, a commonly made assumption. Both types of spatial K-fields were constrained to have the same variogram and the same distribution of K, but they do exhibit a different spatial dependence structure when modeled by copulas, and thus produce a different transport behavior. The outlined theory is applied to three-dimensional statistically anisotropic K-data obtained from two of the most extensively studied aquifer test-sites. Each site comprises ~1200 or more samples taken along two cross-sections. In both of these settings, non-Gaussian dependence structures of K and hence non-Gaussian transport characteristics have been found.
Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart