Estimation of Spatially Variable Aquifer Hydraulic Properties Using Kalman Filtering

Abstract

Spatial variability of aquifer properties and hydraulic heads are modeled as random fields, and their estimates are achieved by Kalman filtering. The state-space equation is developed from a quasi-analytical solution of a first-order approximation of the governing stochastic flow equation. In the state-space system, the effects of aquifer heterogeneity and uncertainty in recharge are lumped linearly into a random noise vector that is correlated in time. To account for the correlated system noise, we reformulate the problem in terms of an augmented–state-space system and use the resulting Kalman filtering recursions to estimate transmissivities, storativities, and hydraulic heads, simultaneously. The filter is applied to a numerical experiment in which the statistical parameters of log aquifer properties are assumed to be known. The results indicate that under mild head gradients, head measurements alone are of limited value if the objective is to estimate the spatial distribution of aquifer transmissivity and storativity. Ultimately, measurements of the aquifer properties may be required for reliable estimation of their unknown values.