Making kriging consistent with flow equations: application of kriging with numerical covariances for estimating a contamination plume

• Published in: Hydrogeology journal 2023-09, Vol.31 (6), p.1491-1503
• Main Authors: de Fouquet, Chantal, Le Coz, Mathieu, Freulon, Xavier, Pannecoucke, Léa
• Format: Article
• Language: English
• Subjects: Aquatic Pollution; Aquifers; Contaminants; Contamination; Covariance; Earth and Environmental Science; Earth Sciences; Environmental Sciences; Estimation; Fields (mathematics); Flow; Flow equations; Geology; Geophysics/Geodesy; Groundwater; Hydraulic conductivity; Hydraulics; Hydrogeology; Hydrology/Water Resources; Mathematical models; Mathematics; Modelling; Oceanic trenches; Parameter uncertainty; Piezometric head; Radioactive wastes; Simulation; Simulators; Spatial variability; Spatial variations; Statistics; Synthetic data; Transport equations; Variability; Waste Water Technology; Water Management; Water Pollution Control; Water Quality/Water Pollution
• ISSN: 1431-2174; 1435-0157
• DOI: 10.1007/s10040-023-02695-6

When the data are few, kriging hydraulic head or concentration with usual variogram models can lead to physically inconsistent results, because the nonstationarity induced by the flow or transport equations is not taken into account properly. Several methods have been proposed to account for these equations in geostatistical estimation. A recent and general approach consists of incorporating them through specific covariance models. A set of random fields sampling uncertain parameters (e.g. hydraulic conductivity) is first used as the input of a flow simulator. Empirical “numerical” spatial covariances are then calculated between pairs of points x and x ′ for the variable of interest (e.g. hydraulic head, concentration) on the corresponding set of flow simulator outputs. These nonstationary “numerical” covariances are consistent with the specific spatial variability of hydraulic head or concentrations, and 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 nonstationary Gaussian anamorphosis in introduced for nonlinear 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 two-dimensional cross-section of an aquifer downstream of a trench containing radioactive waste in the Chernobyl area, Ukraine. 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.