Monte Carlo experiments with robust estimation of aquifer model parameters

Automatic calibration procedures for fitting groundwater models to measured data have almost exclusively used L₂ error norms for estimation criteria. Quadratic estimation criteria result from applying the method of maximum likelihood under the assumption of jointly normal errors in the measured head data which, for the case of uncorrelated errors with constant variance, results in the ordinary least squares criterion. Quadratic estimation criteria are extremely sensitive to errors which violate the Gaussian assumption and pose an additional source of instability for the inverse problem. We consider the use of statistically robust estimation procedures to reduce these destabilizing effects. In particular, we test the robust M-estimator of Huber with a series of Monte Carlo experiments, compute the sample mean squared error, squared bias and variance of the estimated log-hydraulic conductivities for realizations of head measurements contaminated with mixed normal noise and compare these measures to their counterparts for the OLS estimator. We show that Huber's M-estimator achieves the same estimation variance as the OLS estimator with reduced need for prior information to regularize the problem.