A quick and stable algorithm for groundwater flow parameter estimation by optimization methods under steady state conditions is presented. A combination of gradient, Gauss-Newton and full Newton algorithms is used. The optimization methods are directly connected with the finite element groundwater flow computations. The sensitivity matrix is computed by a differentiation of the discretized flow equation. The gradient and the complete Hessian are computed by an adjoint state method. By formulating the inverse problem as a maximum likelihood parameter estimation problem, we are able to estimate the parameters as well as quantify the uncertainty associated with the estimates. A two parameter example is used to illustrate the parameter identification procedure. The methodology is applied to a realistic groundwater flow model and MonteCarlo analysis is used to check the results.
In recent years mathematical models for simulating groundwater flow have become standard tools of the hydrologist. The reliability of flow model predictions is based on the ability of the mathematical model to adequately represent groundwater flow in the aquifer. This requires means for estimating the unknown model parameters based upon our knowledge of the system, including measured groundwater heads and prior information about the parameters themselves. The task of an automated parameter estimation procedure is to find model parameters which are close to their prior estimates and which lead to an optimum match between the point measurements of heads and their corresponding calculated values, under consideration of input data uncertainties.
The paper consists of two parts. In the first part the mathematical formulation of the proposed methodology for simultaneously estimating different groundwater flow parameters under uncertainty is given. The methodology is only described for steady-state conditions. In general, however, the identification algorithms can be extended to transient computations. In the second part, an application of the identification procedure is presented.
The proposed methodology is based on the most comprehensive work in the area of groundwater flow parameter identification of Carrera & Neuman (1986a,b,c) and is a further developement of the work of Odenwald & Herriing (1990).