Aquifer parameter identification with optimum dimension in parameterization

This paper presents a systematic procedure whereby the functional coefficients imbedded in a two-dimensional partial differential equation which governs unsteady groundwater flow are optimally identified. The coefficients to be identified are transmissivities which vary spatially. Finite elements are used to represent the unknown transmissivity function parametrically in terms of nodal values over a suitable discretization of a flow region. A modified Gauss-Newton algorithm is used for parameter optimization. Covariance analysis is used to estimate the reliability of the estimated parameters. As the dimension of the unknown parameter increases, the modeling error represented by a least squares criterion will generally decrease, but errors in data would be propagated to a greater degree into the estimated parameters, thus reducing the reliability of estimation. The reliability of the estimated parameters is characterized by a norm of the covariance matrix. This information is used for the determination of the optimum dimension in parameterization.