This paper proposes a composite L1 parameter estimator to solve the inverse problems in groundwater flow and solute transport modeling. The estimator is formulated using a weighted L1 norm as the error measure between the vector of the observed hydraulic heads and solute concentrations and the corresponding vector of the heads and concentrations computed from a finite element model for steady state groundwater flow and solute transport in a two-dimensional areal confined aquifer system. The parameters currently considered are the hydraulic conductivities, the dispersivities, the porosities of the aquifer system, and the solute source concentration(s). The gradients of the state variables with respect to the parameters are computed analytically using a formulation stemming from the finite element model for the state variables. The solutions to two hypothetical groundwater parameter estimation problems are presented to illustrate that the proposed estimator does have the property of being fairly accurate and, more significantly, being robust in handling observation data containing certain outliers. ¿ American Geophysical Union 1993