24 Mar 2021

24 Mar 2021

Review status: a revised version of this preprint is currently under review for the journal HESS.

Scaling procedure for straightforward computation of sorptivity

Laurent Lassabatere1, Pierre-Emmanuel Peyneau2, Deniz Yilmaz3, Joseph Pollacco4, Jesús Fernández-Gálvez5, Borja Latorre6, David Moret-Fernández6, Simone Di Prima7, Mehdi Rahmati8,9, Ryan D. Stewart10, Majdi Abou Najm11, Claude Hammecker12, and Rafael Angulo-Jaramillo1 Laurent Lassabatere et al.
  • 1Univ Lyon, Université Claude Bernard Lyon 1, CNRS, ENTPE, UMR5023 LEHNA, F-69518, Vaulx-en-Velin, France
  • 2GERS-LEE, Univ Gustave Eiffel, IFSTTAR, F-44344 Bouguenais, France
  • 3Civil Engineering Department, Engineering Faculty, Munzur University, Tunceli, Turkey
  • 4Manaaki Whenua - Landcare Research, 7640 Lincoln, New Zealand
  • 5Department of Regional Geographic Analysis and Physical Geography, University of Granada, Granada, 18071, Spain
  • 6Departamento de Suelo y Agua, Estación Experimental de Aula Dei, Consejo Superior de Investigaciones Científicas (CSIC), PO Box 13034, 50080 Zaragoza, Spain
  • 7Agricultural Department, University of Sassari, Viale Italia, 39, 07100 Sassari, Italy
  • 8Department of Soil Science and Engineering, Faculty of Agriculture, University of Maragheh, Maragheh, Iran
  • 9Forschungszentrum Jülich GmbH, Institute of Bio- and Geosciences: Agrosphere (IBG-3), Jülich, Germany
  • 10School of Plant and Environmental Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA, United States
  • 11Department of Land, Air and Water Resources, University of California, Davis, CA 95616, United States
  • 12University of Montpellier,UMR LISAH, IRD, Montpellier, France

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  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.

Laurent Lassabatere et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-150', Anonymous Referee #1, 05 May 2021
    • AC1: 'Reply on RC1', Laurent Lassabatere, 10 May 2021
  • RC2: 'Comment on hess-2021-150', Anonymous Referee #2, 20 May 2021
    • AC2: 'Reply on RC2', Laurent Lassabatere, 25 May 2021

Laurent Lassabatere et al.

Model code and software

Scilab script for sorptivity Laurent Lassabatere

Laurent Lassabatere et al.


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Short summary
Soil sorptivity is a crucial parameter for the modeling of water infiltration into soils. The standard equation used to compute sorptivity from the soil water retention curve, the unsaturated hydraulic conductivity, and initial and final water contents may lead to erroneous estimates due to its complexity. This study proposed a new straightforward scaling procedure for estimations of sorptivity for four famous and commonly used hydraulic models.