Studies in Parameter Estimation for Analytical Transport Equations

Abstract

Three new programs have been developed to perform parameter estimation to assist in the calibration of analytical contaminant transport models. The Domenico equation was chosen as an example analytical model for each of the three programs rather than a model with the exact solution, because the former is a closed‐form expression involving significantly less processing time. One of the programs 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 as examples to assist the calibration of groundwater analytical transport models. The final estimates for the parameter values for the three methods and PEST applied to the data from each of the two sites compared quite closely and, with two exceptions were well within an order of magnitude of each other. The three newly available programs individually should serve as calibrating tools indispensable for field hydrogeologists, environmental project managers, and others who have been asked to run analytical transport models. 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 method and the successive parameter estimation method being acceptable alternatives.