FITTING A GROUNDWATER CONTAMINANT TRANSPORT MODEL BY L1 AND L2 PARAMETER ESTIMATORS

This paper presents a study on the use of linear and nonlinear L1-norm parameter estimators to fit an analytical groundwater contaminant tra nsport model with nonuniform contaminant source distributions. The mod el solution is obtained as a superposition of an analytical solution d eveloped by Cleary (Cleary, R.W., Analytical Models for Groundwater Po llution and Hydrology, 208 Long Island Groundwater Pollution Study, dr aft report, vol. 3, Princeton University, NJ, 1978). Comparisons with the commonly used linear and nonlinear L2-norm estimators are conducte d. The posterior statistical inference theory by Nyquist (Nyquist, H., Commun.Statist.- Theor. Meth., 1983, 12, 2511-24) and Gonin and Money (Gonin, G. & Money, A.H., Commun. Statist. Theor. Meth., 1985, 14, 82 7-40) is used to provide the posterior covariance matrix and the proba bility distribution for the unknown parameter vector. As the conclusio n, it is suggested that in view of the nature of groundwater contamina nt transport modeling, L1-norm estimators may be preferred as robust a lternatives to L2-norm estimators in solving parameter estimation prob lems.