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Simulation of Heat and Water Transport on Different Tree Canopies: A Finite Element Approach

Author

Listed:
  • Carlos E. Villarreal-Olavarrieta

    (Departmento de Oceanografía Física, Centro de Investigación Científica y de Educación Superior de Ensenada, Ensenada 22860, Mexico)

  • Néstor García-Chan

    (Departamento de Física, CU de Cs Exactas e Ingeniería, Universidad de Guadalajara, Guadalajara 44430, Mexico)

  • Miguel E. Vázquez-Méndez

    (Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, EPSE, 27002 Lugo, Spain)

Abstract

Heat and water transport modeling is a widely explored topic in micro-meteorology, agriculture, and forestry. One of the most popular models is the Simultaneous Heat and Water (SHAW) model, which includes partial differential equations (PDEs) for air-soil temperature and humidity, but with a priori discretized PDE for the foliage temperature in each canopy layer; it is solved using the finite difference method and the canopy shape is defined as a simple rule of proportionality of total quantities such as the total leaf area index. This work proposes a novel canopy shape characterization based on Weibull distribution, providing a continuous vertical shape function capable of fitting any tree species. This allows formulating a fully continuous SHAW-derived model, which is numerically solved by a finite element approach of P 1 Lagrange type. For this novel approach, several numerical experiments were carried out to understand how the shape of well distinguishable canopies influences heat and water transport.

Suggested Citation

  • Carlos E. Villarreal-Olavarrieta & Néstor García-Chan & Miguel E. Vázquez-Méndez, 2021. "Simulation of Heat and Water Transport on Different Tree Canopies: A Finite Element Approach," Mathematics, MDPI, vol. 9(19), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2431-:d:647751
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    References listed on IDEAS

    as
    1. Banimahd, S.A. & Zand-Parsa, Sh., 2013. "Simulation of evaporation, coupled liquid water, water vapor and heat transport through the soil medium," Agricultural Water Management, Elsevier, vol. 130(C), pages 168-177.
    2. Launiainen, Samuli & Katul, Gabriel G. & Lauren, Ari & Kolari, Pasi, 2015. "Coupling boreal forest CO2, H2O and energy flows by a vertically structured forest canopy – Soil model with separate bryophyte layer," Ecological Modelling, Elsevier, vol. 312(C), pages 385-405.
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    Cited by:

    1. Néstor García-Chan & Juan A. Licea-Salazar & Luis G. Gutierrez-Ibarra, 2023. "Urban Heat Island Dynamics in an Urban–Rural Domain with Variable Porosity: Numerical Methodology and Simulation," Mathematics, MDPI, vol. 11(5), pages 1-18, February.

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