Ninth International Geostatistics Congress, Oslo, Norway
June 11 – 15, 2012

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Abstract No.:



Interpolation of Concentration Measurements by Kriging Using Flow Coordinates


M. Rivest, Ecole Polytechnique de Montreal (CA)
D. Marcotte, Ecole Polytechnique de Montreal (CA)
P. Pasquier, Ecole Polytechnique de Montreal (CA)


Groundwater contaminant plumes frequently display a curvilinear anisotropy, which coventional kriging and geostatistical simulations approaches fail to reproduce properly. Physically relevant coordinate transformations can be used to modify the relationships between concentration data points and to simplify the specification of nonlinear anisotropy. This paper presents a methodology, which relies on the transformation of the Cartesian grid into a flow-based grid, to improve the kriging of contaminant plumes. For 2D models, the new coordinates consist of the natural coordinates of flow: hydraulic head and stream function. Since the generalization of natural coordinates in 3D is not straightforward, streamline-based coordinates are used in that case. Both coordinate transformations straighten the streamlines in the new space. The proposed flow coordinates are themselves uncertain, as environmental studies often involve limited data and generally lead to an uncertain description of groundwater flow. Therefore, prior to the kriging of concentrations, a procedure involving kriging and inverse modeling is used to integrate all available flow information and produce calibrated heads fields and stream function for the estimation of the flow coordinates. Observation and estimation points are then mapped on the new grid and kriging is performed to estimate the contaminant concentrations. The performance of the approach is assessed using 2D and 3D synthetic test cases where it is found that kriged concentration maps reproduce the curvilinear features in the reference plume. The resulting maps are thus more realistic and accurate than those obtained with conventional kriging on a Cartesian grid. This synthetic study also highlights limitations of the approach and indicates areas where further work is required.




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