An extension of the Green-Ampt model to decreasing flooding depth conditions, with efficient dimensionless parametric solution

Abstract

The theoretical formulation of the Green-Ampt infiltration model has been extended to conditions of decreasing flooding depth in an isolated system. By defining dimensionless variables of flooding depth s and time τ, an implicit dimensionless equation τ(s) was obtained, which contains a single fundamental dimensionless parameter γ controlling the process, named “infiltration delay parameter”. The characteristics and functional behaviour of γ were analysed, and its physical meaning discussed. A parametric expression s(τ) has been obtained, which uses a unique descriptive parameter a, which in turn depends only on γ and on four generic coefficients valid for a wide range of soil properties and conditions occurring in nature. By means of numerical simulations using different values of soil parameters and initial flooding depths, it was proved that the proposed parametric function generates similar infiltration rates and cumulative storages to those that are obtained starting from Darcy's equation in the extended Green-Ampt scheme.