Robust estimation of parameters in nonlinear subsurface flow models using adjoint state methods.

Abstract

Estimating the parameters of groundwater flow models by automatic calibration methods is an extremely difficult problem, but one which must be solved in order to produce reliable model predictions. The data upon which the model is calibrated are usually corrupted by measurement and model structure errors which can unduly affect the values of the parameter estimates. In this dissertation the statistically robust M-estimator of Huber is used to reduce the influence of large, outlying errors in the measured head data on the values of the estimated model parameters. The robust estimation procedure is implemented in a computer program which models unconfined, steady-state and transient flow as described by the Boussinesq equation for Dupuit-type flow. The program allows the user to estimate hydraulic conductivity, specific yield, specific storage, recharge rates, leakances, boundary heads and boundary fluxes. The nonlinear error criterion is minimized using conjugate gradient and quasi-Newton methods coupled with both accurate and innaccurate line search algorithms. The gradient of the error criterion is efficiently computed by using the adjoint state finite element method. Monte Carlo studies of a synthetic aquifer model are used to demonstrate the superior efficiency of the Huber M-estimator to that of ordinary least squares. The method is also applied to a large scale inverse modeling study of the Tucson basin regional aquifer.