Assessment of the BEST-WR three-term formulation to estimate water repellent soil hydraulic properties
Authors: Yilmaz Deniz , Di Prima Simone , Lassabatere Laurent 
Published: February 2023

It&#8217;s known that certain soils surfaces may be subjected to water repellence, which prevents immediate water infiltration. With time, the water repellence vanishes and the water infiltration initiates. In such situation, the infiltration models developed for regular soils are not able to describe this early infiltration process. Recently, Abou Najm et al. (2021) proposed a simple corrector factor to deal with this problem and to account for water repellence at the beginning of the infiltration process in water-repellent soils. These authors applied their correction factor to the Philip two-term approximate transient expression. Recently, Di Prima et al. (2021) used this approach to adapt the BEST-slope algorithm (Lassabatere et al., 2006), based on the two terms transient expansion of the quasi-exact implicit (QEI) model for modelling water infiltration into regular soils for the estimation of the initial soil sorptivity (S) and the saturated hydraulic conductivity (Ks) of water repellent soils. The new model for the hydraulic characterization of soils regardless the degree of water-repellence, was named BEST-WR. It was validated using analytically generated data, involving soils with different textures and a dataset that included data from 60 single-ring infiltration tests. However, some points of the BEST-WR method deserved further investigations, especially concerning the validity time of the two-term approximate expansion used to fit the data. Indeed, if this validity time is defined for the BEST-Slope method, this is not the case for the BEST-WR method. To alleviate the issue of the limitation in time, Yilmaz et al. (2022) proposed an extension of the BEST-WR model by increasing the number of terms considered for the approximate expansions of the QEI model. They applied the correction factor to the three-term approximate expansion which is known to have a much wider validity time interval. This new formulation called BEST-WR-3T has the advantage of being valid on a very large time interval, allowing the modelling of the whole experimental datasets, without worrying about time limitations, for most practical applications. In this study, this new more robust formulation is evaluated on several examples using both analytical and field infiltration obtained with different approaches: the regular manual Beerkan method or using the automated infiltrometers developed by Di Prima et al. (2016). The robustness of the new method is observed when the BEST-WR method encounters difficulties in estimating soils parameters. &#160;References:Abou Najm et al. (2021). A Simple Correction Term to Model Infiltration in Water&#8208;Repellent Soils. Water Resources Research, 57(2), e2020WR028539.Di Prima et al. (2016). Testing a new automated single ring infiltrometer for Beerkan infiltration experiments. Geoderma, 262, 20-34.Di Prima, et al. (2021). BEST-WR: An adapted algorithm for the hydraulic characterization of hydrophilic and water-repellent soils. Journal of Hydrology, 603, 126936.Lassabat&#232;re et al. (2006). Beerkan estimation of soil transfer parameters through infiltration experiments&#8212;BEST. Soil Science Society of America Journal, 70(2), 521-532.Yilmaz et al. (2022). Three-term formulation to describe infiltration in water-repellent soils. Geoderma, 427, 116127.