A Transfer Function Model of Solute Transport Through Soil: 3. The Convection‐Dispersion Equation

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Abstract
The two‐component convection‐dispersion equation (CDE) model is developed as a special case of the transfer function model (TFM) of solute transport. It is shown that the two‐component CDE model can be reformulated as an integral equation for the “fast” solute component which has the same form and interpretation as the TFM integral equation specialized to (1) steady water flow conditions and (2) solute input or loss restricted to the entrance or exit surface of a soil unit. The travel time probability density function (pdf) for a solute according to the two‐component CDE model then is calculated analytically as a Laplace transform. Numerical inversion of the transformed pdf is carried out for several different sets of values of the four adjustable parameters in the CDE model. The effects of convection, dispersion, and linear sorption processes, as well as the influence of the “slow” solute component, are illustrated by the numerically simulated travel time pdf. It is suggested that the fractional transport volume is the most significant physical parameter in the model in terms of impact on the shape of the travel time pdf.