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Approximate Soil Water Movement by Kinematic Characteristics

Roger E. Smith
Soil Science Society of America journal 1983 v.47 no.1 pp. 3-8
Peclet number, analytical methods, equations, layered soils, rain, soil profiles, soil water, soil water movement, unsaturated flow
Using the Richard's equation in the Fokker-Planck nonlinear diffusion form, unsaturated soil water flow may be treated as a diffusion-convection wave process. If ∂θ/∂z is assumed a function of θ alone, the unsaturated flow equation may be solved by the method of characteristics, and when ∂θ/∂z becomes sufficiently small, the Peclet number is assumed large enough to treat unsaturated flow kinematically. Changes in θ with depth in the soil profile are treated as waves, moving downward. Advancing and receding “waves” are treated differently in the approximate analytical technique described here, with advancing wetting fronts described by kinematic “shocks.” The method is compared to the complete solution to Richard's equation for a complex rain pattern and found to predict well the location of deeper moving fronts and also general θ patterns. The kinematic method is also shown to apply to root water extraction zones and to layered soil situations.