Scaling procedure for straightforward computation of sorptivity

Abstract

Abstract. Sorptivity is a parameter of primary importance in the study of unsaturated flow in soils. This integral parameter is often considered for modeling the computation of water infiltration into vertical soil profiles (1D or 3D axisymmetric geometry). Sorptivity can be directly estimated from the knowledge of the soil hydraulic functions (water retention of hydraulic conductivity), using the integral formulation of Parlange (Parlange, 1975). However, it requires the prior determination of the soil hydraulic diffusivity and its numerical integration between the initial and the final saturation degrees, which may be tricky for some instances (e.g., coarse soil with diffusivity functions quasi-infinite close to saturation). In this paper, we present a specific scaling procedure for the computation of sorptivity considering slightly positive water pressure heads at the soil surface and initial dry conditions (corresponding to most water infiltration on the field). The square sorptivity is related to the square dimensionless sorptivity (referred to as cp parameter) corresponding to a unit soil (i.e., unit values of all the scaled parameters and zero residual water content) utterly dry at the initial state and saturated at the final state. The cp parameter was computed numerically and analytically for five current models: delta functions (Green and Ampt model), Brooks and Corey, van Genuchten-Mualem, van Genuchten-Burdine, and Kosugi models as a function of the shape parameters. The values are tabulated and can be easily used to determine any dimensional sorptivity value for any case. We propose brand-new analytical expressions for some of the models and validate previous formulations for the other models. Our numerical results also showed that the relation between the cp\xa0 parameters and shape parameters strongly depends on the chosen model, with either increasing or decreasing trends when moving from coarse to fine soils. These results highlight the need for carefully selecting the proper model for the description of the water retention and hydraulic conductivity functions for the rigorous estimation of sorptivity. Present results show the need to understand better the hydraulic model s mathematical properties, including the links between their parameters, and, secondly, to better relate these properties to the physical processes of water infiltration into soils.