Infiltration models for soil profiles bounded by a water table

Abstract

Approximate solutions of Richards' equation are developed for rational forms of the soil hydraulic conductivity and moisture retention functions using a perturbation expansion method. A novel approach is devised in the perturbation technique whereby a priori introduced parameters are estimated in an optimal context to ensure the accuracy of the perturbation solution at all times and for all flow conditions. The perturbation model describes the one‐dimensional nonlinear nonsteady infiltration for arbitrary initial conditions under either a time‐dependent surface flux or a constant head boundary condition into either a semi‐infinite or a finite medium bounded from below by a shallow water table. The optimal perturbation approach proved to be an effective method by which closed‐form linear solutions can be adapted to nonlinear soils through proper scaling factors. The results show that the first‐order linear term of the optimal perturbation solution is sufficiently accurate for practical applications, especially for shallow water table conditions. They offer the means to analyze the effect of nonuniform initial conditions and the influence of the water table on the infiltration process. Practical results in terms of well‐defined soil water parameters and the antecedent moisture content include algebraic expressions for the surface moisture content variation under variable rainfall conditions, time‐to‐ponding expressions and infiltration equations for deep and shallow water table conditions, and a prediction formula for the water table recharge rate.