An explicit, parsimonious, and accurate estimate for ponded infiltration into soils using the Green and Ampt approach

The Green and Ampt solution for vertical ponded infiltration is implicit in time, which makes the result often cumbersome to apply. Here we present a simple explicit solution for the position of the wetting front in time based on approximating the term describing early time behavior by means of the sum of gravitational flow and the exact solution for capillary imbibition. The result is within 1% of the exact implicit solution of vertical Green and Ampt infiltration. We also check the overall accuracy of the Green and Ampt approach, and find it to be within 15% of numerical simulation results for the same soils obtained with the Richards equation. Hence, the proposed approximation adds essentially no error to the Green and Ampt approach, but greatly simplifies computation of infiltration. The approximation also makes explicit the role of the representation of capillarity, which can be adjusted in ways not possible with the implicit result. We find that predictions can be markedly improved by adjusting capillary versus gravitational drivers per soil texture, revealing both a limitation of the Green and Ampt approach, but also providing a potential refinement of Green and Ampt predictions per soil type (demonstrated for sandy and clayey soils). Further, the new approximation allows for simple computation of useful quantities such as flux and cumulative infiltration. Plain Language Summary Using a physically based strategy, we allow nearly exact (< 1% error) calculation of the depth of infiltration in time based on the approach of Green and Ampt [1911]. This is useful for computing runoff following rainfall, designing irrigation systems, and in many other setting where the rate of water entry into soil is needed.