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

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.