Quasi‐Analytical Solutions of the Soil Water Flow Equation for Problems of Evaporation

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Abstract
Quasi‐analytical solutions of the one‐dimensional soil water flow equation applied to problems of evaporation are derived and compared with exact numerical solutions available in the literature. Constant‐concentration and constant‐flux surface boundary conditions and semi‐infinite and finite soil columns are considered. For the semi‐infinite soils the quasi‐analytical technique of Philip and Knight (1974) is very successful in predicting the water content profiles for the constant‐concentration condition, and only moderately so for the constant‐flux condition. Their iterative procedure for the flux‐concentration function converges rapidly in the constant‐concentration case but an analogous procedure diverges in the constant‐flux case.For finite soils the simple assumption that the rate of drying of the column is independent of depth in the flow equation leads to accurate predictions of the water content profiles for the constant‐concentration case, and for the constant‐flux case if the potential evaporation is low, the soil is shallow, and/or the initial hydraulic diffusivity is high. For conditions other than these roughly accounting for the higher rate of drying that occurs near the surface in this case greatly improves the agreement.