the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Mixed formulation for an easy and robust numerical computation of sorptivity
- 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
- 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)
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RC1: 'Comment on hess-2021-633', Anonymous Referee #1, 13 Jan 2022
Manuscript: hess-2021-633
Title: Mixed formulation for an easy and robust numerical computation of
sorptivityDear editor and authors. I read carefully the manuscript. The article is quite interesting and is well written and organized. The authors propose a new mixed formulation that scales sorptivity. The topic is relevant and gives valuable information about sorptivity. This hydraulic property is a key parameter, and there is a lack of information about it, especially in terms of the dependency with the soil water content. For these reasons, the manuscript fits into the journal’s scope and would be relevant to the readers of Hydrology and Earth Systems Science. Additionally, this manuscript complements very well the previous study of Lassabatere et al. (2021), published in this journal. However, there is one major concern that must be addressed before publication. Soil sorptivity is a function of the initial and final soil water content. Since sorptivity is an expression of the capillarity forces, the highest value corresponds to the dry condition (h=-∞) and decreases as the soil water content increases (in dry condition, the capillary forces domains the process, while near saturation there is no expression of capillarity). The authors included in the manuscript the Figures 1 and 2 in order to show an example of the of the mixed formulations. In these figures, the y axis corresponds to the sorptivity (estimated with the new mixed formulation function) and the x axis corresponds to the soil water content or water pressure head (h). The behavior of this function is the opposite to the expected one. This issue should be addressed in the manuscript. Additionally, the inclusion of hypothesis and objective will improve the manuscript. Also, it would be very interesting to include some figures with the sorptivity values as function of soil water content and water pressure head, calculated with the new mixed formulation. Below, I mention more detailed comments. I’m not English native speaker, then I will not correct language issues.
Detailed comments:
L 12-13: the first two sentences are exactly the same than the two first sentences of Lassabatere et al. (2021). Please modify.
L 20: Equation (1): Please add more information about this equation. I couldn’t find the same expression in Parlange (1975).
L 21: initial and final water contents of the soil or the water source? More detailed information about the relationship between sorptivity and water content is needed.
L 24: I couldn’t find the same expression in Ross et al. (1996). Please give more detail about the construction of this equation.
L 240-246: Please use these ideas to built hypothesis and objectives, and include them in the Introduction section.
L 363-371: this is not a conclusion. The inclusion of an explicit hypothesis will improve this section.
- AC1: 'Reply on RC1', Laurent Lassabatere, 25 Jan 2022
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RC2: 'Comment on hess-2021-633', Anonymous Referee #2, 23 May 2022
overall manuscript is well written. Authors need to include Novelty.
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AC2: 'Reply on RC2', Laurent Lassabatere, 31 May 2022
Dear Author,
Many thanks for your comment. We will elaborate on the novelty of the proposed study in the revised version.
Briefly, the novelty relies on the proposal of a new formulation that is proven to alleviate all sources of misestimation of the sorptivity. In the revised version, which also addresses the first reviewer's comments, we extend the paper to the impact of the gain in sorptivity estimation on the quality of modeling water infiltration into soils.Best regards,
Laurent on behalf of the authors.
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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 https://doi.org/10.5281/zenodo.5789111
Laurent Lassabatere et al.
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