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.
Highlights
This work deals with the introduction of a mathematical model aimed at describing the thermal interaction between vegetation and soil
Soil temperature is important in seed germination and plant growth, for which the determination of the temperature in the region of the ground close to the surface is of great importance, since this is the region where the most important thermal phenomena take place
As referred to in [6] and the references therein, there is a strong dependence of soil temperature with surface cover, which affects the fraction of solar radiation reflected by the surface—that is, the albedo
Summary
This work deals with the introduction of a mathematical model aimed at describing the thermal interaction between vegetation and soil. Several aspects of the vegetation are considered in the model, such as the Leaf Area Index (LAI), the latent heat of vaporization, the sensible heat flux, the density of the foliage, or emissivities, just to name a few of them Some of these characteristics are typically used to study vegetation–soil interaction in green roof modeling, such as in [1,2]. As referred to in [6] and the references therein, there is a strong dependence of soil temperature with surface cover, which affects the fraction of solar radiation reflected by the surface—that is, the albedo. Both concepts, albedo and coalbedo, are very relevant in models accounting for thermal interaction between vegetation and soil.
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