Falling head ponded infiltration in the nonlinear limit

• Published in: Water resources research 2014-12, Vol.50 (12), p.9555-9569
• Main Author: Triadis, D.
• Format: Article
• Language: English
• Subjects: Approximation; Delta function; Falling; Green Ampt; Green-Ampt model; Hydraulic conductivity; Hydraulics; Infiltration; Mathematical analysis; Mathematical models; ponded; Ponding; Saturation; Soil; Soil analysis; Soil conductivity; Soil surfaces; Soils; Surface water; unsaturated; Wetting front
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1002/2014WR015787

The Green and Ampt infiltration solution represents only an extreme example of behavior within a larger class of very nonlinear, delta function diffusivity soils. The mathematical analysis of these soils is greatly simplified by the existence of a sharp wetting front below the soil surface. Solutions for more realistic delta function soil models have recently been presented for infiltration under surface saturation without ponding. After general formulation of the problem, solutions for a full suite of delta function soils are derived for ponded surface water depleted by infiltration. Exact expressions for the cumulative infiltration as a function of time, or the drainage time as a function of the initial ponded depth may take implicit or parametric forms, and are supplemented by simple asymptotic expressions valid for small times, and small and large initial ponded depths. As with surface saturation without ponding, the Green‐Ampt model overestimates the effect of the soil hydraulic conductivity. At the opposing extreme, a low‐conductivity model is identified that also takes a very simple mathematical form and appears to be more accurate than the Green‐Ampt model for larger ponded depths. Between these two, the nonlinear limit of Gardner's soil is recommended as a physically valid first approximation. Relative discrepancies between different soil models are observed to reach a maximum for intermediate values of the dimensionless initial ponded depth, and in general are smaller than for surface saturation without ponding. Key Points: New solutions are derived for infiltration under depleted ponded surface water Errors in using Philip's popular Green‐Ampt solution are quantified A mathematically simple “converse” to the Green‐Ampt solution is presented