Constant rate rainfall infiltration: A versatile nonlinear model, I. Analytic solution

Analytic solutions are presented for a nonlinear diffusion-convection model describing constant rate rainfall infiltration in uniform soils and other porous materials. The model is based on the Darcy-Buckingham approach to unsaturated water flow and assumes simple functional forms for the soil water diffusivity D(θ) and hydraulic conductivity K(θ) which depend on a single free parameter C and readily measured soil hydraulic properties. These D(θ) and K(θ) yield physically reasonable analytic moisture characteristics. The relation between this model and other models which give analytic solutions is explored. As C→ ∞, the model reduces to the weakly nonlinear Burgers' equation, which has been applied in certain field situations. At the other end of the range as C→1, the model approaches a Green-Ampt-like model. A wide range of realistic soil hydraulic properties is encompassed by varying the C parameter. The general features of the analytic solutions are illustrated for selected C values. Gradual and steep wetting profiles develop during rainfall, aspects seen in the laboratory and field. In addition, the time-dependent surface water content and surface water pressure potential are presented explicitly. A simple traveling wave approximation is given which agrees closely with the exact solution at comparatively early infiltration times.

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