Studies in Parameter Estimation for Analytical Transport Equations II

Three new applications are presented to perform parameter estimation to assist in the calibration of a model based on Wexler's equation for his PATCHI three-dimensional analytical transport program. These join the analogous programs presented recently in this journal based on the Domenico equation. Because the Wexler equation involves the numerical evaluation of the integral of the solution to the partial differential equation for advective–dispersive solute transport, it is much more accurate than the Domenico equation, which omits the necessary numerical evaluation and is a closed-form expression. As in the “sister” paper, one of the applications studied is a quasi-exhaustive search method and the second is a successive parameter variation method. The third program is based on Box's Complex nonlinear, direct-search optimization method. The three programs and an already available calibration tool (PEST) were compared in tests using data from two different sites in southeastern Pennsylvania. These tests demonstrated the validity of the three programs for assisting the calibration of a groundwater analytical transport model based on the Wexler equation. The final estimates for the parameter values for the three methods and PEST applied to the data from each of the two sites compared reasonably closely. The three newly available programs individually should serve as calibrating tools of value for field hydrogeologists, environmental project managers, and others who have been asked to run the Wexler transport model (PATCHI). The results from the runs performed on the two sites indicate the Complex method to be the best option as a calibration tool, with the quasi-exhaustive search and the successive parameter estimation method being acceptable alternatives.