Explicit Solution to Green and Ampt Infiltration Equation

An explicit solution of the Green and Ampt infiltration equation is presented by constructing a decomposition series. Simple expressions for the cumulative infiltration depth and the infiltration rate are proposed. These expressions are valid for deep homogeneous soils under ponding conditions resulting from intense rainfall events. The solution was compared with the exact implicit solution, and with the Lambert W solution of the Green and Ampt equation. It was found that with three terms in the series, the decomposition solution has a maximum error of about 0.15%. The inclusion of additional terms in the series reduces the error. With four terms, the decomposition series yields an error of about 0.02%. The accuracy of a three-term decomposition solution seems adequate for most practical calculations. Furthermore, its simplicity of implementation makes it suitable for fast hand calculations.