Soil sorptivity, S, and hydraulic conductivity, Ks, can be estimated from the inverse analysis of a disc infiltrometer cumulative infiltration curve using the quasi-exact implicit (QEI) analytical Haverkamp et al. (1994) equation, which depends on Ks, S, the β and γ parameters, the disc radius, rd, and the water content increase, ∆θ. Given the complexity to solve QEI, this paper presents alternative three-term, 3T, and four-term, 4T, QEI expansions expansions of QEI to estimate S and Ks. Firstly, the interplays between β, γ, Ks and S employing S-Ks, γ-Ks, γ-S, γ-β, S-β and Ks-β error maps generated for a synthetic infiltration curve of a loam soil were analyzed. In order to reduce the number of variables to four, Δθ, rd and γ were packed into the A=γ/(r_d (θ_s-θ_i ) ) term. Five different analyses of QEI expansions were evaluated: (i and ii) 3T leaving free the fitting of all coefficients with A, 3TA, or β, 3Tβ, as fixed variable; (iii an iv) 3T, 3TAβ, and 4T, 4TAβ, using constant β and A values; and (v) 4T leaving free the fitting of all coefficients, 4TF. The different methods were evaluated on synthetic infiltration curves of homogeneous sand, loam and silt soils, and next again tested on a loam soil with a contact sand layer. The QEI expansions were finally applied to experimental infiltration data, and the results were compared to those obtained with QEI, using the measured rd and Δθ and β and γ equal to 0.6 and 0.75, respectively. Global optimization with QEI demonstrates that γ and β were extremely linked, which made it difficult estimating these parameters. All procedures applied to synthetic homogeneous soils resulted in good Ks and S approaches. However, only 3TA, 3TAβ and 4TAβ gave accurate estimates of Ks and S when applied on a synthetic loam soil with contact sand layer. Comparison of the different expansions with QEI showed that only 3TAβ and 4TAβ allowed, in all experimental infiltration curves, accurate estimates of S and Ks.
