A solution to the inverse problem in groundwater hydrology based on Kalman filtering

The paper introduces a new method for the solution of the inverse problem, that is, the estimation of parameters characterizing the hydrodynamic behaviour of aquifers given their geometrical description, the piezometric field, the net infiltration (infiltration minus abstractions) and the boundary conditions. The method, which falls in the class of Bayesian estimators, is based upon a Kalman filtering formulation which optimally combines a priori parameter values with the information contained in the observations to obtain the a posteriori parameter estimates. In that respect it can also be viewed as an extension of the subjective weighting method proposed by Neuman and Yakowitz (Water Resour. Res., 15(4), 1979). An example of the application of the proposed method to two Libyan aquifers is presented, showing the statistical adequacy of the resulting permeability estimates when compared with the permeabilities obtained at a number of points by means of pump tests.