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.