Deconvolution of a nonparametric transfer function for solute transport in soils

Solute transport in soils can be described in terms of solute travel time probability density functions (pdfs). In the past, parameterized functional forms for the travel time pdf have been derived based on models of physical transport processes and the properties of the soil, or have been obtained from observed transport behavior. Alternatively, a nonparametric pdf for a particular soil can be measured experimentally. In general, this measurement requires deconvoluting the pdf, which is mathematically an ill-posed problem. In this paper we perform the deconvolution using a constrained regularization approach. The regularization method uses a basis function representation of the travel time pdf which eliminates numerical problems associated with the standard regularization approach. The method is tested using synthetic and experimental data. Regularized solutions are evaluated using Provencher's (Provencher, 1982a) F test statistic along with a visual inspection of their fit to the data. We analyze data from previously published field experiments and the results suggest multimodal travel time pdfs may be appropriate for modeling transport in soils.

Duke Scholars

Author Zbigniew J. Kabala Civil and Environmental Engineering