A simple, accurate, and explicit form of the Green–Ampt model to estimate infiltration, sorptivity, and hydraulic conductivity

Abstract

Abstract Finding an explicit 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 explicit semiempirical approach that combines accuracy with simplicity, a concept that has been generally neglected in previous studies. The equation is F=Kst(0.70635+0.324151+9.43456(S2Ks2t)), with F (L), Ks (L/T), S (L/T0.5) and t (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 applied infiltration problems faced by water resources engineering today. We show both numerically and mathematically that │ɛ│> 0.3% could only occur if Kst/F > 0.904, a criterion that could apply to sand and loamy sand soils (i.e., coarse texture) and if they experience infiltration rates for over 6 h and 19 h, respectively. Hence, we also derived a simple linear adjustment in the model as Fadj ≅ 0.9796 F + 0.335 S2/Ks to address these longer infiltration rates, and to assure that ɛ remains within the expected ±0.3% range of uncertainty. A linearized regression technique was also developed to accurately estimate S and Ks when the G–A model is used. We numerically demonstrated that our fitting method could be used even when the G–A approach is less valid (diffusive soils), provided that the actual value of the capillary length (λ) is initially known. An added benefit of our approach is that by setting λ equal to 1/3 and 2/3, it can significantly limit the range of initializing, unknown, a priori values of S and Ks, as these two parameters are estimated through the inverse solution of implicit infiltration models. Due to the model's simplicity and accuracy, our solution should find application among hydrologists, natural resource scientists, and engineers who wish to easily derive accurate estimations from the G–A infiltration approach and/or estimate sorptivity and hydraulic conductivity without encountering divergence problems.