Four different methods of parameterizing spatially varying log transmissivities in an inverse approach are compared with respect to prediction accuracy of simulated flow and transport. Transport parameter estimation is included by two-stage feedback optimization. In stage one the log transmissivities are estimated by fitting both head and concentration data, given initial values of the source concentration and the dispersivities. In stage two, the source concentration and the dispersivities are estimated by fitting the concentration data. With the updated transport parameters, final estimates of the log transmissivities are obtained by repeating the optimization of stage one. The formulated objective functions are minimized using Levenberg-Marquardt's algorithm. The models are applied to synthetic two-dimensional transport problems in steady state flow regimes. The "true" log transmissivity fields are generated by the turning bands method, thereby incorporating spatial variability. The test cases differ in the input variances of the generated fields and with respect to the amount and accuracy of "observed" transmissivity data.