Green-Ampt Infiltration Rate

Green and Ampt built their 1911 model out of a picture rather than a curve fit. Imagine the wetting front as a sharp horizontal boundary advancing into the soil like a piston: saturated above, at the original moisture content below, nothing in between. Apply Darcy's law across the wetted zone and everything falls out. The driving head is the ponded depth plus the depth of wetting plus the capillary suction pulling at the front, the path length is the depth of wetting, and the result is $f = K(1 + \psi\Delta\theta/F)$. With K = 10 mm/h, 100 mm of suction, a moisture deficit of 0.3 and 20 mm already absorbed, the rate is $10 \times 2.5 = 25$ mm/h. This page is Darcy's law in soil clothing, which is why it belongs beside it rather than beside Horton.

The parameters are measurable, and that is the whole advantage. $K$ is the saturated hydraulic conductivity — sand around 100 mm/h, loam around 10, clay under 1. $\Delta\theta$ is the porosity minus the initial water content, so it is large on dry ground and shrinks to nothing on saturated ground. $\psi$ is the capillary suction at the front, tabulated by texture and running from about 50 mm on sand to 300 mm and more on clay, which is the counter-intuitive one: clay pulls hardest and conducts least. Notice that the driving term is $\psi\Delta\theta/F$, so as the front advances and $F$ grows the bracket collapses towards 1 and the rate decays asymptotically to $K$. No fitted decay constant is needed. The decay is a consequence of the geometry. One companion equation is worth knowing about, because this one alone does not close the problem: the rate depends on $F$, and $F$ is the integral of the rate over time. A continuous simulation therefore solves $F - \psi\Delta\theta\ln(1 + F/\psi\Delta\theta) = Kt$ implicitly for $F$ at each step and feeds the result back into this expression. What this page gives you is the rate at a stage of wetting you already know, which is the form you want for a spot check or a single design point.

Three limits, said plainly. At $F = 0$ the model predicts an infinite rate, which is its one honestly wrong answer — real soil does not accept water infinitely fast at the first drop, and every implementation starts at a small non-zero $F$ or begins with the ponding-time calculation instead. Like Horton, it returns capacity rather than actual infiltration, so before ponding the rate is whatever the rain is delivering and this equation does not apply. And the sharp-front picture is a fiction: real wetting fronts are diffuse, layered soils break the assumption of a single $K$ outright, and macropores and root channels let water bypass the matrix entirely in ways no piston model can see. Where the profile is genuinely layered, the limiting layer governs and its properties are the ones to enter. The model is still the one to reach for when you have soil data rather than infiltrometer curves, because every number in it means something about the soil.