MCMFIT: Efficient optimal fitting of a generalized nonlinear advection-dispersion model to experimental data

Abstract

The use of standard numerical schemes to solve nonlinear advective-dispersive equations for the estimation of parameters is CPU-time consuming and hence not desirable for routine use. An efficient scheme using a novel mixing cell approach has been used to estimate parameter values by nonlinear least-squares fitting for nonlinear adsorption of a single solute species coupled with one-dimensional transport. A problem with gradient methods of nonlinear least-squares fitting is that they are prone to determine best-fit parameters corresponding to local minima rather than the global minimum. As is well known, this problem can be avoided by judicious selection of the starting values. The present code, MCMFIT, includes a random search of the parameter space in order to determine a suitable set of initial parameter values. The program also includes the option of selecting user-defined initial parameter values because of possible physical considerations. These values then are passed to the nonlinear least-squares fitting program to obtain the optimal parameter values. Penalty functions have been employed to maintain user-imposed constraints on the parameter values. MCMFIT is capable of handling linear, Freundlich, Langmuir, and S-curve adsorption isotherms. The use of MCMFIT is demonstrated with the use of synthetic as well as laboratory and field data.