IMPROVING PARAMETER ESTIMATION BY OPTIMIZED DATA USE

Groundwater modeling relies heavily on the reliability of the various aquifer parameters entered in the model. These parameters are usually obtained using some form of parameter estimation. It is often assumed that the model predictions can be relied upon if the measured data (mostly piezometric heads) are well-matched by the model. In addition, groundwater flows at such a small rate that errors in model predictions may not appear until years after the model has been used.

We demonstrate that a direct application of parameter estimation will not yield a reliable estimate of aquifer parameters. We mean by `direct application', parameter estimation on the basis of measurements of heads and some flow rates combined in the optimization process to produce a best fit. Considerable improvement is possible by combining the data in a special way.

We begin by defining the terms `inverse modeling' and `parameter estimation' as different procedures. We mean by `inverse modeling' the problem of solving the governing partial differential equation for the hydraulic conductivity. We define `parameter estimation' as the application of the optimization process to obtain for the best fit of aquifer parameters.

We propose an improved manner of data use in parameter estimation, and test the efficacy of our proposal against exact analytic element modeling of selected problems. Since the analytic element model satisfies the governing partial differential equation exactly, and allows access to all data of the model at each point, it is an ideal test bank for validating the procedure.