Virus Transport through Unsaturated Zone: Analysis and Parameter Identification

Abstract

This paper presents numerical and parameter estimation models for the analysis of virus transport and the identification of transport parameters in the unsaturated zone. The numerical model couples a mass conservative fully implicit finite difference model simulating moisture flow in the unsaturated zone with the hybrid finite volume model for virus transport. The accuracy of the numerical scheme is tested for both advection- and dispersion-dominated transport. The comparison of the numerical model with the analytical solution indicates that the numerical model’s predictions are in excellent agreement with the analytical predictions. The parameter estimation is formulated as a nonlinear least-squares minimization problem in which the parameters are estimated by minimizing the deviations between the model-predicted and experimentally observed virus concentrations. A parameter estimation procedure is developed by coupling the numerical model simulating one-dimensional virus transport in the unsaturated zone with the Levenberg-Marquard algorithm. The results of parameter estimation indicate that for the case of estimating more than two unknown parameters, the inverse procedure results in nonunique optimal estimates. Further for the case of estimating two unknown parameters, the presence of inactivation coefficients of sorbed phases with any other transport parameters also results in nonunique estimates. It is concluded that a priori estimation of the inactivation coefficient in sorbed phases is necessary for unique estimation of two unknown parameters.