This paper presents a comparison between anL2estimator and anL1estimator for solving parameter identification problems in groundwater flow and solute transport simulation. TheL1estimator is formulated using a weightedL1-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 theL1estimator is more robust than theL2estimator in handling observation data containing certain outliers.