Generalized Transfer Function Model for Solute Transport in Heterogeneous Soils

Abstract

The convection‐dispersion (CDE) equation and stochastic–convective models are the most commonly used process representations for predicting solute transport in the field. The convection–dispersion equation assumes that the solute is perfectly mixing in the lateral direction, whereas the stochastic–convective model assumes that the solute moves at different velocities in isolated stream tubes without lateral mixing. However, solute transport in heterogeneous porous media cannot always be conceptualized as being either a convective–dispersive or a stochastic–convective process. In this study, a generalized transfer function model (GTF) was proposed to describe various solute transport processes in heterogenous soils. The model is similar to the convective lognormal transfer function model, but two parameters, λμ and λσ, are introduced to characterize the depth‐dependency of the mean (μ) and standard deviation (σ) of the logarithm of travel time, respectively. The GTF can describe well the two extremes of solute dispersion, the convective–dispersive and stochastic–convective processes, and transport processes between the two extremes. In addition, the GTF can be used to characterize other solute transport processes in heterogeneous soils, such as those in which the mean of travel time increases with depth nonlinearly, and those in which the dispersivity is a scale‐dependent function of the travel distance with any power values.