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 β and γ , the disc radius, r d , and the water content increase, ∆θ . 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 β , γ , K s and S employing S‐K s , γ‐K s , γ‐S , γ‐β , S‐β and K s ‐ β error maps generated for a loam soil synthetic infiltration were analyzed with QEI. To reduce the number of variables, Δθ , r d and γ were packed into the A = γ r d ∆ θterm. Five different QEI expansion analyses were evaluated: (i and ii) optimization of 3T using A , 3T A , or β , 3T β , as fixed variables; (iii and iv) optimization of 3T, 3T Aβ , and 4T, 4T Aβ , using constant β 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 β = 0.6 and γ = 0.75. Infiltrations were performed at zero cm of soil tension. Global optimization with QEI demonstrates that γ and β 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 Aβ and 4T Aβ 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 Aβ and 4T Aβ gave the most accurate and robust estimates of S and K s .