Parameter identification for groundwater flow and solute transport simulation: a comparison ofL1andL2estimators

Abstract

Abstract This paper presents a comparison between an L 2 estimator and an L 1 estimator for solving parameter identification problems in groundwater flow and solute transport simulation. The L 1 estimator is formulated using a weighted L 1-norm as the error measure between the vector of the observed hydraulic heads and solute concentrations and the vector of the simulated heads and concentrations. The simulation model is comprised of a finite element formulation for steady-state groundwater flow and solute transport in a two-dimensional vertically averaged aquifer system. The gradients of the state variables with respect to the parameters are computed using a state sensitivity method. Posterior statistical inferences are conducted. The solutions to two sets of hypothetical groundwater parameter estimation problems illustrate that the L1 estimator is more robust than the L2 estimator in handling observation data containing certain outliers.