Approximate Form of Green‐Ampt Infiltration Equation

Abstract

We develop an approximation of the Green‐Ampt infiltration equation by using the first two terms of a Taylor‐series expansion of the equation. The resulting approximate equation is in the form of the Philip's equation, with an added term to account for the error in the approximation. The Taylor‐series approximation is compared with Li et al.'s 1976 quadratic approximation for the case of constant rainfall with variable time to ponding. The maximum error for the new approximation is about 3.5%; and the maximum error for the quadratic approximation is about 8%. For a range of values of the ratio of infiltrated depth to capillary potential of 0.1 to 150 the approximation of the Taylor series fits the Green‐Ampt infiltrated depth more closely than the quadratic approximation. It is shown that the approximation of the Taylor series gives less error than the quadratic approximation for coarser textured soils.