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 P1 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.
Highlights
Forest and plant canopies have vertically varying profiles of different physical quantities related to complex transport processes
Water potential, wind velocity, longwave and shortwave radiation, photosynthesis, air and soil temperatures, and the fluxes between soil-canopy-air have vertical profiles which change in function of the vertical distribution of the canopy biomass—mainly its leaves—(see the review by [1] and references therein)
After a detailed description of the initial and boundary conditions (Section 2.3), a combination of numerical techniques is proposed to solve the model (Section 2.4). It combines a finite element approach of P1 Lagrange type for space discretization, a finite difference scheme for time discretization, and a relaxed fix-point algorithm to address the resulting non-linear system. This method is applied in several numerical experiments where the resulting vertical profiles of leaf-air-soil temperatures, and humidity and heat fluxes corresponding to four different-shaped canopies showed notable variations (Section 3)
Summary
Forest and plant canopies have vertically varying profiles of different physical quantities related to complex transport processes. After a detailed description of the initial and boundary conditions (Section 2.3), a combination of numerical techniques is proposed to solve the model (Section 2.4) It combines a finite element approach of P1 Lagrange type for space discretization (a novelty in this kind of models), a finite difference scheme for time discretization, and a relaxed fix-point algorithm to address the resulting non-linear system. This method is applied in several numerical experiments where the resulting vertical profiles of leaf-air-soil temperatures, and humidity and heat fluxes corresponding to four different-shaped canopies showed notable variations (Section 3).
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