Parameters Estimation Using Some Analytical Solutions of the Anisotropic Advection-dispersion Model

In this paper some analytical solutions of the advection-dispersion equation are proposed and adopted to solve a non-linear parameter estimation problem. To test the robustness of the analytical solutions if adopted in inverse problems, the anisotropic dispersion coefficients are estimated using sets of experimental data simulated by Monte Carlo techniques. Cylindrical geometry is considered since large columns are the most common devices adopted to study both dispersion and kinetics mechanisms and, even if the solutions are expressed in terms of Bessel function expansion and equations solved only for particular initial and boundary conditions, they give very good results in terms of reliability and precision of our estimates. Discussion of results is based on the analysis of residuals, variance-covariance matrix and bias of parameters. The influence of location and time of sampling, number of samples and data uncertainty on the dispersion coefficients estimates is also analyzed by means of ANOVA tests.