Explicit comprehensive models for single ring infiltration: suggestions for model application and parameterization
Authors: Iovino Massimo , Abou Najm Majdi R. , Angulo-Jaramillo Rafael , Bagarello Vincenzo , Castellini Mirko , Concialdi Paola , Di Prima Simone , Lassabatere Laurent , Stewart Ryan D. 
Published: March 2021

&lt;p&gt;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, &amp;#964;&lt;sub&gt;crit&lt;/sub&gt;, from transient to steady state to be known &lt;em&gt;a-priori&lt;/em&gt; or establishing a constraint among the four constants that figure in the infiltration equations. Estimation of soil saturated hydraulic conductivity, &lt;em&gt;K&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt;, and capillary length, &amp;#955;, from single ring infiltration measurements also needs a scaling parameter referred to &amp;#8220;&lt;em&gt;a&lt;/em&gt;&amp;#8221; to be known. SA model assumes this scaling parameter as a constant and fixes its value at &lt;em&gt;a&lt;/em&gt; = 0.45. However, there is evidence that &lt;em&gt;a&lt;/em&gt; cannot be considered a constant independent of soil type and initial water content.&lt;/p&gt;&lt;p&gt;This study investigates some open issues related to the use of the SA model for single ring infiltration: 1) how comparable is &amp;#964;&lt;sub&gt;crit&lt;/sub&gt; with the maximum time, &lt;em&gt;t&lt;/em&gt;&lt;sub&gt;max&lt;/sub&gt;, that separates transient from steady state condition in HV model; 2) how the scaling parameter &lt;em&gt;a&lt;/em&gt; depends on different experimental conditions and how it can be related to HV parameters.&lt;/p&gt;&lt;p&gt;Preliminary theoretical considerations showed that the two characteristic times (&amp;#964;&lt;sub&gt;crit&lt;/sub&gt; and &lt;em&gt;t&lt;/em&gt;&lt;sub&gt;max&lt;/sub&gt;) are related and, for relatively dry initial conditions, parameter &lt;em&gt;a&lt;/em&gt; depends only on the soil type and ring radius being maximum for small ring radii or soils with high capillarity (&lt;em&gt;a&lt;/em&gt; = 1) and minimum for large rings or coarse soils (&lt;em&gt;a&lt;/em&gt; = 0.467).&lt;/p&gt;&lt;p&gt;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&amp;#160; &amp;#964;&lt;sub&gt;crit&lt;/sub&gt; and the associated value of &lt;em&gt;a&lt;/em&gt;.&lt;/p&gt;&lt;p&gt;The analytical data confirmed that the ratio &amp;#964;&lt;sub&gt;crit&lt;/sub&gt;/&lt;em&gt;t&lt;/em&gt;&lt;sub&gt;max&lt;/sub&gt; was constant and equal to 1.495, regardless the combination of soil, ring diameter and initial water saturation. The calculated &lt;em&gt;a&lt;/em&gt; values varied between 0.706 and 0.904, with a mean equal to &lt;em&gt;a&lt;/em&gt; = 0.807, and were independent of the initial water content for saturation degrees up to approximately 0.50.&lt;/p&gt;&lt;p&gt;Application of the optimization procedure to field data was problematic given it was successful only in 29 out of 70 infiltration tests. Fixing &amp;#964;&lt;sub&gt;crit&lt;/sub&gt;&lt;em&gt;a-priori&lt;/em&gt; could be advisable in this case and it was shown that two alternative empirical criteria for selecting &amp;#964;&lt;sub&gt;crit&lt;/sub&gt; yielded &lt;em&gt;a&lt;/em&gt; values differing by a nearly negligible mean factor of 1.10 and significantly correlated to one another (&lt;em&gt;R&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt; = 0.997).&lt;/p&gt;&lt;p&gt;However, a rather high percentage of &lt;em&gt;a&lt;/em&gt; values (45.5%) were greater than the theoretical maximum value (&lt;em&gt;a&lt;/em&gt; = 1), and therefore were physically implausible. Excluding these values from the analysis, the mean &lt;em&gt;a&lt;/em&gt; parameter (&lt;em&gt;a&lt;/em&gt; = 0.735) was close to that estimated by the successful applications of the optimization procedure (&lt;em&gt;a&lt;/em&gt; = 0.673).&lt;/p&gt;&lt;p&gt;Therefore, consistent results were obtained by field and analytical data with &lt;em&gt;a&lt;/em&gt; values intermediate between the suggested values in the literature (&lt;em&gt;a&lt;/em&gt; = 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.&lt;/p&gt;