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Border Irrigation Modeling with the Barré de Saint-Venant and Green and Ampt Equations

Author

Listed:
  • Sebastián Fuentes

    (Water Research Center, Department of Irrigation and Drainage Engineering, Autonomous University of Queretaro, Cerro de las Campanas SN, Col. Las Campanas, Queretaro 76010, Mexico)

  • Carlos Fuentes

    (Mexican Institute of Water Technology, Paseo Cuauhnáhuac Num. 8532, Jiutepec, Morelos 62550, Mexico)

  • Heber Saucedo

    (National Water Commission, Avenida Insurgentes Sur Num. 2416, Copilco el Bajo, Ciudad de Mexico 04340, Mexico)

  • Carlos Chávez

    (Water Research Center, Department of Irrigation and Drainage Engineering, Autonomous University of Queretaro, Cerro de las Campanas SN, Col. Las Campanas, Queretaro 76010, Mexico)

Abstract

In gravity irrigation, how water is distributed in the soil profile makes it necessary to study and develop methodologies to model the process of water infiltration and redistribution. In this work, a model is shown to simulate the advancing front in border irrigation based on the one dimensional equations of Barré de Saint-Venant for the surface flow and the equation of Green and Ampt for the flow in a porous medium. The solutions were obtained numerically using a finite difference Lagrangian scheme for the surface flow and the Raphson method for the subsurface flow. The model was validated with data obtained from the literature from an irrigation test and its predictive capacity was compared with another model and showed excellent results. The hydrodynamic parameters of the soil, necessary to obtain the optimal irrigation discharge, were obtained through the solution of the inverse problem using the Levenberg–Marquardt optimization algorithm. Finally, the results found here allow us to recommend that this model be used to design and model border irrigation, since the infiltration equation uses characteristic parameters of the physical soil.

Suggested Citation

  • Sebastián Fuentes & Carlos Fuentes & Heber Saucedo & Carlos Chávez, 2022. "Border Irrigation Modeling with the Barré de Saint-Venant and Green and Ampt Equations," Mathematics, MDPI, vol. 10(7), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1039-:d:778526
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    References listed on IDEAS

    as
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    2. Liu, Kun & Huang, Guanhua & Xu, Xu & Xiong, Yunwu & Huang, Quanzhong & Šimůnek, Jiří, 2019. "A coupled model for simulating water flow and solute transport in furrow irrigation," Agricultural Water Management, Elsevier, vol. 213(C), pages 792-802.
    3. Soroush, F. & Fenton, J.D. & Mostafazadeh-Fard, B. & Mousavi, S.F. & Abbasi, F., 2013. "Simulation of furrow irrigation using the Slow-change/slow-flow equation," Agricultural Water Management, Elsevier, vol. 116(C), pages 160-174.
    4. Akbari, Mahmood & Gheysari, Mahdi & Mostafazadeh-Fard, Behrouz & Shayannejad, Mohammad, 2018. "Surface irrigation simulation-optimization model based on meta-heuristic algorithms," Agricultural Water Management, Elsevier, vol. 201(C), pages 46-57.
    5. Chavez, Carlos & Fuentes, Carlos, 2019. "Design and evaluation of surface irrigation systems applying an analytical formula in the irrigation district 085, La Begoña, Mexico," Agricultural Water Management, Elsevier, vol. 221(C), pages 279-285.
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