Making kriging consistent with flow equations: application of Kriging with Numerical Covariances for estimating a contamination plume
Consistencia de la técnica de kriging con las ecuaciones de flujo: estimación de una pluma de contaminación con aplicación de covarianzas numéricas
Rendre le krigeage compatible avec les équations d’écoulement: application du krigeage avec des covariances numériques pour l’estimation d’un panache de contamination
Tornando a krigagem consistente com as equações de fluxo: aplicação da krigagem com covariâncias numéricas para estimar uma pluma de contaminação
Résumé
When the data are few, kriging hydraulic head or concentration with usual variogram
models can lead to physically inconsistent results, because the non-stationarity
induced by the flow or transport equations is not taken into account properly. Several
methods have been proposed to account for these equations in the geostatistical
estimation. A recent and general approach consists in incorporating them through
specific covariance models. A set of random fields sampling uncertain parameters (e.g.
conductivity) is first used as input of a flow simulator. Empirical “numerical” spatial
covariances are then calculated between pairs of points and for the variable of
interest (e.g. hydraulic head, concentration) on the corresponding set of flow simulator
outputs. These non-stationary “numerical” covariances are consistent with the specific
spatial variability of hydraulic head or concentrations. They are used in the estimation.
In this paper, flow-and-transport simulations are thus combined with kriging to estimate
contaminant concentrations in groundwater. A non-stationary Gaussian anamorphosis
in introduced for non-linear estimation so that the estimate of the concentration is
positive.
The method is first validated on synthetic data and then on real data from a twodimensional cross-section of an aquifer downstream of a trench containing radioactive
waste in the Chernobyl area. Kriging with the output of a simplified flow model as
external drift and kriging with numerical covariances reproduce the spatial variability of
the contaminant plume much better than usual (ordinary) kriging based on
observations only. The comparison between the two best estimators is discussed
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