Including Conceptual Model Information when Kriging Hydraulic Heads

Abstract

A reliable hydraulic head field is a key element to many hydrogeological, environmental or geotechnical studies. It enables quick identification of areas where high hydraulic gradients could threaten an earth dam’s integrity. It also highlights probable contaminant flow paths and determines wells’ influence areas. Furthermore, some inversion algorithms (direct methods) require an initial estimation of the entire head field to compute hydraulic conductivity. Interpolation techniques, such as kriging, have the advantage of reproducing the observed values. However, the shape of the interpolated head fields often lacks realism particularly near pumping wells, boundaries and lithological contrasts. In these cases, the flow equation is poorly reproduced by interpolation. On the other hand, numerical modeling can easily integrate the hydrogeological conceptual model and generate realistic head fields. Unfortunately, the numerical model is based on uncertain hard data which poorly reproduce the head observations.

We propose an approach based on kriging that uses the “shape” information present in a numerical conceptual model as an external drift. The performance of the method is first investigated using a 2D synthetic aquifer. In this case, several numerical head fields are used in the external drift to account separately for different aspects of the phenomenon (principle of superposition). A stepwise procedure is used to select the best set of numerical head fields. Kriging with external drift (KED) shows marked improvement over ordinary kriging and universal kriging with first order polynomials. The approach is also applied to the study of two large earth dams in which monitoring data is available. Cross-validation shows again the good performance of KED compared to ordinary kriging or universal kriging with first order polynomials. The approach can be used for 3D head field estimation.