Interpolation of Concentration Measurements by Kriging Using Flow Coordinates

Abstract

Groundwater contaminant plumes frequently display a curvilinear anisotropy, which conventional kriging and geostatistical simulation approaches fail to reproduce properly. In many applications, physically relevant coordinate transformations are used to modify the relationships between data points and simplify the specification of nonlinear anisotropy. In this paper, we present a kriging approach that uses a coordinate transformation to improve the interpolation of contaminant concentrations. The proposed alternative flow coordinates (AFC) consist in the hydraulic head and one (2D) or two (3D) streamline-based coordinates. In 2D, the mapping obtained using AFC is similar to that yielded by the natural coordinates of flow (i.e. hydraulic head and stream function). AFC can be generalized to 3D flow and to the presence of wells, which is not the case with the natural coordinates. The performance of the approach is investigated using a simple 3D synthetic case. Kriged concentration maps obtained with the AFC reproduce the curvilinear features found in the reference plume. Performance statistics suggest AFC improves plume delineation compared to conventional kriging on a Cartesian grid. However, the performance of the AFC transformation is limited by the fact that, while it accounts for advection, it does not consider the effects of dispersion on the shape of the plume. This aspect and further testing on complex cases is the subject of ongoing research.KeywordsStream FunctionCoordinate TransformationHydraulic HeadOrdinary KrigingInflow BoundaryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.