Predicting preferential water flow in soils by traveling-dispersive waves

Rapid preferential drainage or by-pass flow of water and pollutants occurs in soil macropores such as burrows and channels formed by earthworm activity in soils. We show that preferential flow through these non-capillary pores can be described by a traveling-dispersive wave. This wave is the solution of a non-linear convective-dispersive equation (KDW model) that depends on three transport parameters: two are related to a convective celerity and the other one is a dispersive coefficient. We show that the flux-mobile water content relation is hysteretic and that it can be described by a non-linear function of the mobile water content and its first time derivative. By combining the latter relation with the continuity equation we derive the KDW model. This model can be viewed as a second-order correction of the purely convective kinematic wave model. The dispersive term incorporates the large-scale effects of dissipative forces without resolving the small-scale conservation equations in detail. We further present numerical solutions for the signaling problem and a direct method for estimating model parameters. The model is validated with data obtained from laboratory infiltration experiments on soil columns. The experiments were carried out in repacked soil columns inoculated with Allolobophora chlorotica earthworms. Varying rainfall intensities were applied at the top surface of the columns with a rainfall simulator. Both the mean of mobile water content within the columns and the drainage hydrograph at the bottom were recorded in time. The parameters of the model were estimated from the experimental flux-mobile water content relation. A very good agreement was found between model prediction and experimental data. (C) 2003 Elsevier Science B.V. All rights reserved.