Modeling and Numerical Simulation of the Thermal Interaction between Vegetation Cover and Soil

Arturo Hidalgo and Lourdes Tello
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Arturo Hidalgo: Departamento de Ingeniería Geológica y Minera, ETS de Ingenieros de Minas y Energía, Center for Computational Simulation, Universidad Politécnica de Madrid, Calle Ríos Rosas, 28003 Madrid, Spain
Lourdes Tello: Departamento de Matemática Aplicada, ETS de Arquitectura, Center for Computational Simulation, Universidad Politécnica de Madrid, Av. Juan de Herrera, 28040 Madrid, Spain

Mathematics, 2022, vol. 10, issue 3, 1-17

Abstract: In this work, we propose a mathematical model representing the thermal interaction between vegetation cover and the soil underneath it. This model consists of a one-dimensional reaction–diffusion equation describing the evolution of the temperature in the vegetation cover coupled with a two-dimensional reaction–diffusion equation to represent the evolution of the temperature in the soil. The thermal interaction between the vegetation cover and the soil is studied and the distribution of temperatures in the soil with depth is also obtained. The vegetation cover acts in this model as a dynamic and diffusive boundary condition for the soil. The developed model takes into account the latent heat of fusion, which appears when the transformation of ice into liquid water or vice versa occurs inside the soil. The numerical approach for the solution of the mathematical model conducted in this work is based on the finite volume method with Weighted Essentially Non-Oscillatory technique for spatial reconstruction and the third-order Runge–Kutta Total Variation Diminishing numerical scheme is used for time integration, which is very efficient to obtain the numerical solution of this type of model. Some numerical examples are solved to obtain the distribution of temperature both in the vegetation cover and the soil.

Keywords: vegetation cover; latent heat of fusion; climate model; soil temperature energy balance model; finite volume method; WENO reconstruction; Runge–Kutta TVD (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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