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Shooting the Numerical Solution of Moisture Flow Equation with Root Water Uptake Models: A Python Tool

Author

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  • Fabio V. Difonzo

    (Czech Technical University in Prague
    Code Architects Automation
    Università degli Studi di Bari Aldo Moro)

  • Costantino Masciopinto

    (Consiglio Nazionale delle Ricerche)

  • Michele Vurro

    (Consiglio Nazionale delle Ricerche)

  • Marco Berardi

    (Consiglio Nazionale delle Ricerche)

Abstract

Modeling the water uptake by plant roots is a key issue in studying soil processes, which are governed by water dynamics: a comprehensive understanding and forecast of such dynamics is a relevant issue in managing water resources. Typically, movement of water in soils and uptake by roots are described by the Richards’ equation with a sink term, and numerical treatment of this problem is still a challenge, together with its practical implementations in user-friendly softwares. In order to tackle this problem, in the present paper we propose a simple and computationally fast algorithm developed as a Python code, implementing a numerical approach based on the shooting method, a classical tool for handling boundary value problems (BVPs) arising here from a discretization recently introduced for Richards’ equation: such a method is applied to the linearized Richards’ equation with Gardner’s hydraulic functions. This method is implemented also in MATLAB, in order to accomplish comparisons with built-in MATLAB solver for parabolic partial differential equations. The Python code is made available to readers, and is intended to be an easy tool for handling this problem in the framework of Gardner’s constitutive relations, filling the gap of other commercial codes, which do not provide choice of Gardner functions. Many numerical simulations are performed: the results are promising, since the proposed method behaves efficiently and in some cases it is able to converge even when the MATLAB solver fails; mass balance properties and order of accuracy issues are also investigated.

Suggested Citation

  • Fabio V. Difonzo & Costantino Masciopinto & Michele Vurro & Marco Berardi, 2021. "Shooting the Numerical Solution of Moisture Flow Equation with Root Water Uptake Models: A Python Tool," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(8), pages 2553-2567, June.
    • Handle: RePEc:spr:waterr:v:35:y:2021:i:8:d:10.1007_s11269-021-02850-2
    DOI: 10.1007/s11269-021-02850-2
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    References listed on IDEAS

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    1. Wu, Xun & Zuo, Qiang & Shi, Jianchu & Wang, Lichun & Xue, Xuzhang & Ben-Gal, Alon, 2020. "Introducing water stress hysteresis to the Feddes empirical macroscopic root water uptake model," Agricultural Water Management, Elsevier, vol. 240(C).
    2. Green, Steve R. & Kirkham, M.B. & Clothier, Brent E., 2006. "Root uptake and transpiration: From measurements and models to sustainable irrigation," Agricultural Water Management, Elsevier, vol. 86(1-2), pages 165-176, November.
    3. Stamatios Elmaloglou & Konstantinos Soulis & Nicholas Dercas, 2013. "Simulation of Soil Water Dynamics Under Surface Drip Irrigation from Equidistant Line Sources," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(12), pages 4131-4148, September.
    4. Šimůnek, Jiří & Hopmans, Jan W., 2009. "Modeling compensated root water and nutrient uptake," Ecological Modelling, Elsevier, vol. 220(4), pages 505-521.
    5. Seyed Adib Banimahd & Davar Khalili & Shahrokh Zand-Parsa & Ali Akbar Kamgar-Haghighi, 2017. "Development of a Simulation Model for Estimation of Potential Recharge in a Semi-arid Foothill Region," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(5), pages 1535-1556, March.
    6. Cundong Xu & Junjiao Tian & Guoxia Wang & Junkun Nie & Hongyang Zhang, 2019. "Dynamic Simulation of Soil Salt Transport in Arid Irrigation Areas under the HYDRUS-2D-Based Rotation Irrigation Mode," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(10), pages 3499-3512, August.
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    Cited by:

    1. Talal Alharbi & Marcos Tostado-Véliz & Omar Alrumayh & Francisco Jurado, 2021. "On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases," Mathematics, MDPI, vol. 9(17), pages 1-17, August.
    2. Sergei Stepanov & Djulustan Nikiforov & Aleksandr Grigorev, 2021. "Multiscale Multiphysics Modeling of the Infiltration Process in the Permafrost," Mathematics, MDPI, vol. 9(20), pages 1-12, October.
    3. Riya Dutta & Rajib Maity & Parul Patel, 2022. "Short and Medium Range Forecast of Soil Moisture for the Different Climatic Regions of India Using Temporal Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(1), pages 235-251, January.

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