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

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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.

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Acknowledgements

The authors wish to thank Mr. Andrea Gargaro from Code Architects for precious suggestions in organizing the code.

Funding

This work is part of the project Smart Water (grant number 5ABY6P0), funded by Regione Puglia through the Innonetwork call: all CNR-IRSA authors have been partially funded by this project.

The first author acknowledges the support of the OP RDE (OP VVV) funded project reg. No: CZ.02.1.01/0.0/0.0/16_019/0000765 - “The Research Center for Informatics”.

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Authors and Affiliations

  1. Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo nám. 13, 120 00 Nové Město, Prague, Czech Republic

    Fabio V. Difonzo

  2. Code Architects Automation, Via Campania 3, 70029, Santeramo in Colle, Italy

    Fabio V. Difonzo

  3. Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via E. Orabona 4, 70125, Bari, Italy

    Fabio V. Difonzo

  4. Istituto di Ricerca sulle Acque, Consiglio Nazionale delle Ricerche, via F. De Blasio 5, 70132, Bari, Italy

    Costantino Masciopinto, Michele Vurro & Marco Berardi

Authors
  1. Fabio V. Difonzo
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  2. Costantino Masciopinto
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  3. Michele Vurro
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  4. Marco Berardi
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Contributions

– Fabio V. Difonzo: conceptualization, methodology, software, formal analysis, writing-original draft preparation.

– Costantino Masciopinto: methodology, supervision, validation.

– Michele Vurro: funding acquisition, critical revise of the draft, visualization.

– Marco Berardi: conceptualization, methodology, writing-original draft preparation, data treatment; writing-reviewing and editing, project administration.

Corresponding author

Correspondence to Marco Berardi.

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Competing interests

The authors have no relevant financial or non-financial interests to disclose.

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Availability of Data and Materials

The Python code is publicly available at https://github.com/fdifonzo/shooting-roots-python-code

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Difonzo, F.V., Masciopinto, C., Vurro, M. et al. Shooting the Numerical Solution of Moisture Flow Equation with Root Water Uptake Models: A Python Tool. Water Resour Manage 35, 2553–2567 (2021). https://doi.org/10.1007/s11269-021-02850-2

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  • DOI: https://doi.org/10.1007/s11269-021-02850-2

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