Three‐ and Four‐term Approximate Expansions of the Haverkamp Formulation to Estimate Soil Hydraulic Properties from Disc Infiltrometer Measurements

Soil sorptivity, S, and saturated hydraulic conductivity, K-s, 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 is a function of K-s, S, the parameters beta and gamma, the disc radius, r(d), and the water content increase, increment theta. Given the complexity of solving QEI, this paper presents three-term, 3T, and four-term, 4T, QEI expansions to estimate S and K-s. The interplays between beta, gamma, K-s and S employing S-K-s, gamma-K-s, gamma-S, gamma-beta, S-beta and K-s-beta error maps generated for a loam soil synthetic infiltration were analyzed with QEI. To reduce the number of variables, Delta theta, r(d) and gamma were packed into the A=gamma rd increment theta term. Five different QEI expansion analyses were evaluated: (i and ii) optimization of 3T using A, 3T(A), or beta, 3T(beta), as fixed variables; (iii and iv) optimization of 3T, 3T(A beta), and 4T, 4T(A beta), using constant beta and A values; and (v) optimization of 4T leaving all coefficients free, 4T(F). The different methods were evaluated with synthetic infiltrations for homogeneous sand, loam and silt soils, and for an uniform loam soil with a contact sand layer. The QEI expansions were applied to experimental infiltrations, and the results were compared to those obtained with QEI, using beta = 0.6 and gamma = 0.75. Infiltrations were performed at zero cm of soil tension. Global optimization with QEI demonstrates that gamma and beta are extremely linked. This makes it difficult to estimate these two parameters. All procedures applied to synthetic homogeneous soils resulted in good K-s and S approaches. However, only 3T(A), 3T(A beta) and 4T(A beta) obtained accurate estimates of K-s and S when applied to a synthetic homogeneous soil with a contact sand layer. Application of the different methods to the experimental infiltrations showed that 3T(A beta) and 4T(A beta) gave the most accurate and robust estimates of S and K-s.