Influence of the spatial configuration of available data on hydraulic conductivity estimates for a geostatistical-Kalman filter method

Accurate hydraulic conductivity estimates are vital for groundwater evaluation. Usually, interpolations of hydraulic conductivity data are needed to obtain spatial estimates over larger areas, but the results present a high uncertainty which can be reduced by adding a secondary variable in the estimation. In this paper, the influence of the number and spatial configuration of hydraulic conductivity (K) and hydraulic head (HH) data on the estimation of K is evaluated using univariate and bivariate geostatistical-Kalman filter approaches (similar to kriging and cokriging, respectively). A synthetic case based on a transient groundwater flow model is used to generate different numbers, spatial arrays, and data. With these data, variogram models for the univariate and bivariate cases were fitted and used to calculate the corresponding covariance matrices for the Kalman filter. The results show that K estimates are more reliable when HH data is added than when only K is used, independently of the number and distribution of the data, since there is a better agreement between the calculated errors and estimate error variances. HH data provides valuable information only where K is not sampled. This evaluation could support the design of optimal sampling strategies to obtain reliable K estimates.