Derivation of equations for variable rainfall infiltration

Abstract

Formulae were derived for prediction of ponding time and cumulative infiltration following ponding under a condition of piecewise variable and even intermittent rainfall. The derivations do not assume immediate saturation at the surface or a piston displacement of air by water; they include the viscous flow of air. The results were compared with experimental data of James and Larson for two conditions: constant rainfall and intermittent rainfall. The proposed formulae are simple to use, requiring no complex solution of a partial or even an ordinary differential equation. The numerical calculations presented in the paper were performed with a small pocket calculator. The agreement with experimental data is good.