FIRST INTEGRALS OF THE INFILTRATION EQUATION

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Abstract
Solutions of the infiltration equation have to be obtained, in general, by numerical or analytical, but approximate iterative schemes. We show here that solutions can be obtained without iterations if the diffusivity has a power law dependence on the water content and the conductivity is proportional to the water content. Even though this last condition may be too restrictive to adequately describe most soils, these solutions can be of great use to check and improve the accuracy of the iterative schemes. For a particular dependence of the surface flux on time, a solution is obtained that appears to be the only existing fully analytical solution for a realistic diffusivity. We use this particular solution to assess the accuracy of a very general optimization technique.