Small‐perturbation solution for steady nonuniform infiltration into soil surface of a general shape

A steady state solution is developed for three‐dimensional infiltration where both the water flux at the soil surface and the soil surface topography are nonuniform. By identifying a small parameter, which is defined as a ratio between the vertical and the horizontal characteristic lengths, the solution of the linearized equation can then be found by using perturbation methods. The spatial variation of both the soil surface topography and the water flux entering the profile appears only in parametric form in the equations and boundary conditions to all orders of approximation, thus allowing easy evaluation of the solution. The water accumulation due to soil surface topography is related to the inner produce between the gradients of the surface elevation and the rate of infiltration at the soil surface. Therefore the nonuniformity of the soil surface should be accompanied by a spatial nonuniformity of the applied flux in order to produce lateral variations in the solution. This method can be used to evaluate the water accumulation in the soil due to general rainfall or irrigation distributions. It can also be used for design purposes in cases where one or both sources of nonuniformities in the horizontal directions can be controlled, as for example, in an irrigation system in a field with a given topography.