Three-term formulation to describe infiltration in water-repellent soils

Modeling infiltration in water-repellent soils is difficult, as the underlying processes remain poorly quantified. However, recent work has adapted the Beerkan Soil Transfer Parameter (BEST) algorithm to include an exponential correction term for characterizing these types of soils. The original BEST-WR (WR = Water Repellent) method used a two-term approximate expansion of the Haverkamp quasi-exact implicit model. However, the BEST-WR method can have considerable inaccuracy, particularly as the time of infiltration and the soil water repellency increase. Here, we extended the BEST-WR model by adapting a three-term approximation of the Haverkamp quasi-exact implicit model to water-repellent soils. We then tested the new method using analytical data. For highly water-repellent soils, the proposed method had better performance when estimating soil sorptivity (S) and soil saturated conductivity (Ks), with respective errors of less than 1.5 % and 8 %, compared to relative errors of more than 10 % and 30 % with the two-term BEST-WR method. We also tested both approaches with experimental data. The two methods provided similar estimates for hydraulic parameters, with linear correlations between methods of R2 = 0.84 for S and R2 = 0.88 for Ks. Initial infiltration was not well modeled by either the two-term or three-term model for 33 tests, thus revealing limitations in the applied exponential model that we used to account for soil repellency. Nonetheless, the proposed three-term expression provided better fits than the two-term model for most of the infiltration runs, meaning that this new approach is more robust when modeling infiltration processes in water-repellent soils.