Explicit comprehensive models for single ring infiltration: suggestions for model application and parameterization

<p>Stewart and Abou Najm (2018) developed a comprehensive model (SA model) for single ring infiltration that consists of a couple of two-terms explicit infiltration equations similar, in form, to the approximate expansions proposed by Haverkamp et al. (1994) (HV model). Application of SA model requires the transition time, τ<sub>crit</sub>, from transient to steady state to be known <em>a-priori</em> or establishing a constraint among the four constants that figure in the infiltration equations. Estimation of soil saturated hydraulic conductivity, <em>K<sub>s</sub></em>, and capillary length, λ, from single ring infiltration measurements also needs a scaling parameter referred to “<em>a</em>” to be known. SA model assumes this scaling parameter as a constant and fixes its value at <em>a</em> = 0.45. However, there is evidence that <em>a</em> cannot be considered a constant independent of soil type and initial water content.</p><p>This study investigates some open issues related to the use of the SA model for single ring infiltration: 1) how comparable is τ<sub>crit</sub> with the maximum time, <em>t</em><sub>max</sub>, that separates transient from steady state condition in HV model; 2) how the scaling parameter <em>a</em> depends on different experimental conditions and how it can be related to HV parameters.</p><p>Preliminary theoretical considerations showed that the two characteristic times (τ<sub>crit</sub> and <em>t</em><sub>max</sub>) are related and, for relatively dry initial conditions, parameter <em>a</em> depends only on the soil type and ring radius being maximum for small ring radii or soils with high capillarity (<em>a</em> = 1) and minimum for large rings or coarse soils (<em>a</em> = 0.467).</p><p>An optimization procedure, with a constraint among the four infiltration constants, was applied to fit the SA model to both analytical and experimental infiltration data to derive  τ<sub>crit</sub> and the associated value of <em>a</em>.</p><p>The analytical data confirmed that the ratio τ<sub>crit</sub>/<em>t</em><sub>max</sub> was constant and equal to 1.495, regardless the combination of soil, ring diameter and initial water saturation. The calculated <em>a</em> values varied between 0.706 and 0.904, with a mean equal to <em>a</em> = 0.807, and were independent of the initial water content for saturation degrees up to approximately 0.50.</p><p>Application of the optimization procedure to field data was problematic given it was successful only in 29 out of 70 infiltration tests. Fixing τ<sub>crit</sub><em>a-priori</em> could be advisable in this case and it was shown that two alternative empirical criteria for selecting τ<sub>crit</sub> yielded <em>a</em> values differing by a nearly negligible mean factor of 1.10 and significantly correlated to one another (<em>R</em><sup>2</sup> = 0.997).</p><p>However, a rather high percentage of <em>a</em> values (45.5%) were greater than the theoretical maximum value (<em>a</em> = 1), and therefore were physically implausible. Excluding these values from the analysis, the mean <em>a</em> parameter (<em>a</em> = 0.735) was close to that estimated by the successful applications of the optimization procedure (<em>a</em> = 0.673).</p><p>Therefore, consistent results were obtained by field and analytical data with <em>a</em> values intermediate between the suggested values in the literature (<em>a</em> = 0.45 and 0.91). These findings can inform parameterization choices for others working with infiltration models, and should reduce uncertainty during interpretation of infiltration measurements.</p>