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Three‐ and four‐term approximate expansions of the Haverkamp formulation to estimate soil hydraulic properties from disc infiltrometer measurements

AuthorsMoret-Fernández, David CSIC ORCID ; Latorre Garcés, Borja CSIC ORCID ; López Sánchez, María Victoria CSIC ORCID ; Pueyo, Yolanda CSIC ORCID ; Lassabatere, Laurent; Angulo‐Jaramilo, Rafael; Rahmati, Mehdi; Tormo, Jaume; Nicolau, José Manuel
Hydraulic conductivity
Disc radius
Issue DateDec-2020
PublisherJohn Wiley & Sons
CitationMoret-Fernández D, Latorre B, López MV, Pueyo Y, Lassabatere L, Angulo-Jaramilo R, Rahmat M, Tormo J, Nicolau JM. Three‐ and four‐term approximate expansions of the Haverkamp formulation to estimate soil hydraulic properties from disc infiltrometer measurements. Hydrological Processes 34 (26): 5543-5556 (2020)
AbstractSoil sorptivity, S, and saturated 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 is a function of Ks, S, the parameters β and γ, the disc radius, rd, 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 Ks. 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 loam soil synthetic infiltration were analyzed with QEI. To reduce the number of variables, Δθ, rd and γ were packed into the 𝐴=𝛾𝑟𝑑∆𝜃 term. Five different QEI expansion analyses were evaluated: (i and ii) optimization of 3T using A, 3TA, or β, 3Tβ, as fixed variables; (iii and iv) optimization of 3T, 3TAβ, and 4T, 4TAβ, using constant β and A values; and (v) optimization of 4T leaving all coefficients free, 4TF. 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 Ks and S approaches. However, only 3TA, 3TAβ and 4TAβ obtained accurate estimates of Ks 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 3TAβ and 4TAβ gave the most accurate and robust estimates of S and Ks.
Description37 Pags.- 7 Figs.- 3 Tabls. The definitive version is available at: https://onlinelibrary.wiley.com/journal/10991085
Publisher version (URL)https://doi.org/10.1002/hyp.13966
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