Copulas are multidimensional distribution functions that allow to model dependence structures independently of the marginal distribution. Copulas emerged in financial mathematics to model value at risk. They have been adopted recently in water resources engineering to model dependences of extreme events (e.g. precipitation and water level height), and in geostatistics.
A geostatistical workflow is comprised of fitting a theoretical model of the spatial structure to observations. Subsequently, this model can be used to either interpolate or simulate spatial fields. The key advantage of copulas compared with traditional geostatistical tools, is their ability to model spatial structure independent from the marginal distribution. Extreme values don't influence the estimation of the spatial structure. Even censored data can be incorporated into copula models
We developed a suite of python programs which allow:
- visualization of spatial dependence structures through empirical geostatistics (histograms, covariograms, rank correlations, empirical copula densities)
- simulation and interpolation using traditional geostatistics (Kriging, turning band simulation)
- parameter estimation, interpolation, and simulation using gaussian and non-gaussian spatial copulas
We are a group of engineering PhD students at the institute of hydraulic engineering at the University of Stuttgart, Germany. At our department we are working on hydrological issues such as flood forecasting using weather radar, climate change, solute transport phenomena in porous media. We use copulas to analyze and simulate hydraulic conductivity fields in aquifers, precipitation fields as driving factor for hydrological models, or to model river discharge time-series.
Authors: Thomas Pfaff and Claus Haslauer