Comparison of two infiltration equations with three‐terms expansions consistent with the approach of Philip theory

Abstract In this study, the approximate three‐term (3 T) one‐dimensional (1D) vertical infiltration equation by Valiantzas (3 T‐V) and the 3 T approximate infiltration equation of the quasi‐exact implicit (QEI) Haverkamp equation (3T‐R) by Rahmati et al. for both direct and inverse modelling of water infiltration into soils were evaluated. The 3 T‐V equation is simpler and involves only two physically meaningful parameters, sorptivity ( S ) and saturated hydraulic conductivity ( K s ), unlike 3 T‐R, which includes an additional parameter, β . The coefficients of the second and third terms of 3 T‐V acquire the same values as those of 3 T‐R for values of the parameter β equal to 0.6 and 1.1, respectively. Both 3 T equations yielded similar cumulative infiltration results except at longer times. The inverse solution of 3 T‐V showed better accuracy in predicting S and K s, with relative error (RE) values generally below 6% and 11%, respectively. The reliability of the S and K s predictions via the 3 T equations improved over time, and both methods yielded nearly identical results across the studied soils at all infiltration times. However, longer times are needed to accurately predict K s . Analysing the contribution of each term reveals that the third term ( t 3/2 ), though minor in total infiltration, extends the validity time of the 3 T equations.