Analytical results for prediction of variable rainfall infiltration

Abstract

The basic equations that govern water movement in unsaturated soils are presented for a boundary condition of variable rainfall rate at the soil surface. In particular, a differential equation for the water content at the soil surface is derived. Solutions are then obtained for the time evolution of water content at the soil surface assuming a power law form for the relative permeability to water as a function of normalized water content. Ponding time formulae are obtained and compared with other previously published relations. Water content profiles are also obtained and their shapes are displayed graphically for the case of an exponent of 2 in the power law form of the relative permeability to water for a constant rainfall rate. Formulae are also derived for the situation of a variable rainfall pattern. A methodology for the coupling of the analytical procedures with an implicit numerical solution of the water content at the soil surface is suggested as a cost-effective alternative to the strict numerical solution of the partial differential equation that governs the water content profile evolution. Postponding infiltration formulae and water content profile equations are also provided.