A Simple and Accurate Explicit Form of the Green-Ampt Infiltration Model

Abstract

Abstract Note: Please see pdf for full abstract with equations. Finding a direct solution to the widely used Green-Ampt (G-A) one dimensional infiltration model has been subject of efforts for more than half a century. We derived an accurate explicit formula that appears be so far the simplest proposed model in the literature. Our approach builds upon simulating the Valiantzas’s G-A infiltration model by a second order polynomial. The proposed equation is F = Kt (0.70635 + 0.32415 √1+9.43456(S2/K2t)), with F, K, S and t being cumulative infiltration, saturated hydraulic conductivity, sorptivity and time, respectively. Relative errors (ɛ) by the application of this equation generally do not exceed ±0.3% in most practical infiltration problems faced in water resources engineering. It was both numerically and mathematically shown that absolute errors > 0.3% could only occur if Kt/F > 0.904, a criteria that could practically be the case for light textured soils like sand and loamy sand if they are exposed to long infiltration times, i.e., 6 hr and 19 hr in our examples, respectively. A simple linear adjustment model is proposed as Fadj ≅ 0.9796F + 0.335 S2/K to account for these uncommon real-World conditions. The linear adjustment assures that ɛ remains within the ± 0.3% range even under imaginary infiltration timings. Due to its simplicity and accuracy, the proposed equation here should find application among hydrologists, natural resource scientists and engineers who desire to easily derive accurate estimations of the Green-Ampt infiltration model.