Parameterization of a comprehensive explicit model for single-ring infiltration

Abstract

Comprehensive infiltration models can simultaneously describe transient and steady-state infiltration behaviors, and therefore can be applied to a range of experimental conditions. However, satisfactory model accuracy requires proper parameterization, including estimating the transition time from transient to steady-state flow conditions (τcrit). This study focused on improving the estimation of two parameters – τcrit and a second constant called a – used in a comprehensive, explicit, two-term model for single ring infiltration (hereafter referred to as the SA model). Different studies have recommended that a should be as low as 0.45 to as high as 0.91. Furthermore, τcrit is often obtained a-priori by assuming that steady-state conditions are reached before the end of an infiltration run. However, there has not been a systematic analysis of those terms for different soils and infiltration conditions. To investigate these open issues related to the use of the SA model, here we introduce a novel, iterative method for estimating τcrit and the parameter a. We then applied this method to both analytical and experimental infiltration data, and compared it with two existing empirical methods. The analytical infiltration experiments showed that τcrit was approximately 1.5 times larger than the maximum validity time of a similar two-term transient infiltration model. Further, the iterative method for obtaining τcrit had minimal effects on the a term, which varied between 0.706 and 0.904 and was larger for finer soils and when small water sources were used. Application of the proposed method was less efficient with experimental data. Only ~ 33% of the experiments yielding plausible estimates of a (i.e., a < 1), indicating that these infiltration model parameters often have high uncertainty. The successful runs indicated that a depended on the rate at which the initial infiltration rate approached the final infiltration rate. Depending on the fitting algorithm used, a had mean values of 0.74–0.78, which were intermediate between those suggested by previous studies. Altogether, these findings expand the applicability of the SA model by providing new methods for estimating τcrit and by showing that a does not need to be fixed a-priori. We expect that these advances will result in more reliable estimations of soil hydrodynamic parameters, including hydraulic conductivity.