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

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_crit, from transient to steady state to be known a-priori or establishing a constraint among the four constants that figure in the infiltration equations. Estimation of soil saturated hydraulic conductivity, K_s, and capillary length, λ, from single ring infiltration measurements also needs a scaling parameter referred to “a” to be known. SA model assumes this scaling parameter as a constant and fixes its value at a = 0.45. However, there is evidence that a cannot be considered a constant independent of soil type and initial water content.

This study investigates some open issues related to the use of the SA model for single ring infiltration: 1) how comparable is τ_crit with the maximum time, t_max, that separates transient from steady state condition in HV model; 2) how the scaling parameter a depends on different experimental conditions and how it can be related to HV parameters.

Preliminary theoretical considerations showed that the two characteristic times (τ_crit and t_max) are related and, for relatively dry initial conditions, parameter a depends only on the soil type and ring radius being maximum for small ring radii or soils with high capillarity (a = 1) and minimum for large rings or coarse soils (a = 0.467).

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_crit and the associated value of a.

The analytical data confirmed that the ratio τ_crit/t_max was constant and equal to 1.495, regardless the combination of soil, ring diameter and initial water saturation. The calculated a values varied between 0.706 and 0.904, with a mean equal to a = 0.807, and were independent of the initial water content for saturation degrees up to approximately 0.50.

Application of the optimization procedure to field data was problematic given it was successful only in 29 out of 70 infiltration tests. Fixing τ_crita-priori could be advisable in this case and it was shown that two alternative empirical criteria for selecting τ_crit yielded a values differing by a nearly negligible mean factor of 1.10 and significantly correlated to one another (R² = 0.997).

However, a rather high percentage of a values (45.5%) were greater than the theoretical maximum value (a = 1), and therefore were physically implausible. Excluding these values from the analysis, the mean a parameter (a = 0.735) was close to that estimated by the successful applications of the optimization procedure (a = 0.673).

Therefore, consistent results were obtained by field and analytical data with a values intermediate between the suggested values in the literature (a = 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.