23 Dec 2021
23 Dec 2021
Status: a revised version of this preprint is currently under review for the journal HESS.

Mixed formulation for an easy and robust numerical 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, 18071 Granada, 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 one of the most important parameters for the quantification of water infiltration into soils. Parlange (1975) proposed a specific formulation to derive sorptivity as a function of the soil water retention and hydraulic conductivity functions, as well as initial and final soil water contents. However, this formulation requires the integration of a function involving the hydraulic diffusivity, which may be undefined or present numerical difficulties that cause numerical misestimations. In this study, we propose a mixed formulation that scales sorptivity and splits the integrals into two parts: the first term involves the scaled degree of saturation while the second involves the scaled water pressure head. The new mixed formulation is shown to be robust and well-suited to any type of hydraulic functions - even with infinite hydraulic diffusivity or positive air-entry water pressure heads - and any boundary condition, including infinite initial water pressure head, h → −∞.

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-2021-633', Anonymous Referee #1, 13 Jan 2022
    • AC1: 'Reply on RC1', Laurent Lassabatere, 25 Jan 2022
  • RC2: 'Comment on hess-2021-633', Anonymous Referee #2, 23 May 2022
    • AC2: 'Reply on RC2', Laurent Lassabatere, 31 May 2022

Laurent Lassabatere et al.

Model code and software

Scilab script for mixed formulation for an easy and robust computation of sorptivity Laurent Lassabatere

Laurent Lassabatere et al.


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Short summary
Sorptivity is one of the most important parameters for the quantification of water infiltration into soils. A specific formulation is commonly used to derive sorptivity from the soil hydraulic diffusivity, initial and final conditions. In this study, we propose a mixed formulation that avoids numerical issues and allows for the computation of sorptivity for all types of models chosen for describing water retention and hydraulic conductivity functions, and all initial and final conditions.