This study investigates the integration of the three-term approximation of the analytical formulation of the Haverkamp infiltration equation into the Lewis-Milne framework to develop an advanced function for surface irrigation. The inverse solution of the equation allows for the estimation of fundamental soil hydraulic characteristics, specifically sorptivity (S) and saturated hydraulic conductivity \((K_s),\) provided that the advance time at two points along the furrow length is known (two-point method). The implementation of the method across various datasets has shown that the anticipated values of S and \(K_s\) closely align with those predicted by the recent approach of Kargas and Mindrinos (Irrigation and Drainage, 1–15, 2024), as well as by the method employed by Ebrahimian et al. (Irrigation Science, 28, 479–488, 2010) for the S values. If just the advance time at the furrow’s end is known, the values of S and \(K_s\) can be determined using the one-point method, assuming that the power advance exponent is 0.5. The findings showed that the one-point method’s average value for the parameter S is higher than that of the two-point method’s, while the parameter \(K_s\) shows the reverse trend.
