Characterization of contamination in soils or groundwater resulting from industrial activities is critical for site remediation. In this study, geostatistics and physically-based simulations are combined for estimating levels of contamination within the unsaturated zone. First, a large number of flow and transport simulations are run and their outputs are used to compute empirical non stationary variograms. Then, these empirical variograms, called numerical variograms and which are expected to reproduce the spatial variability of the contaminant plume better than a usual variogram model based on observations only, are used for kriging. The method is illustrated on a two-dimensional synthetic reference test case, with a contamination due to a point source of tritium (e.g. tritiated water). The diversity among the simulated tritium plumes is induced by numerous sets of hydraulic parameter fields conditioned by samples from the reference test case. Kriging with numerical variograms is then compared to ordinary kriging and kriging with an external drift: the results show that kriging with numerical variograms improves the estimates, all the more that few observations are available, underlining the interest of the method. When considering a relatively dense sampling scenario, the mean absolute error with kriging with numerical variograms is reduced by 52% compared to ordinary kriging and by 45% compared to kriging with an external drift. For a scarcer sampling, those errors are respectively reduced of 73% and 34%. However, the performance of the method regarding the classification into contaminated or not contaminated zones depends on the pollution threshold. Yet, the distribution of contamination is better reproduced by kriging with numerical variograms than by ordinary kriging or kriging with an external drift.
Keywords: Empirical variogram; Parameters uncertainties; Random fields; Soil hydraulic parameters; Tritium plume; Unsaturated zone.
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