Mathematical Models to Estimate the Mass of Leaf and Sketch the Shape of Tree

Abstract

The mass of leaf is a key factor to estimate the magnitude of biogenic hydrocarbon emission. In this paper, following the minimum material consumption assumption and the conservation law of energy, we build a mathematical model to calculate the mass of leaf, crown and the whole tree, respectively. Also, we translate the shape of crown to match the solution of a second order differential equations with boundary value conditions. Meanwhile, we try to explore what does the climatic zone affect the shape and thickness of leaf. In the simulation section, by using the measured data for 14 trees in 3 different species, we present various simulation results through our models and formulas. Finally, following our models and formulas, we find out some hidden relationships: 1. There is an intrinsic link between the single leaf area and the hardness of the stem; 2. There is an interconnected relationship between the shape of leaf and the shape of tree; 3. There are lots of trees with large and thick leaves living in the torrid zone and few in the cold zone.

Keywords:

• leaf mass
• tree shape
• mathematical model
• conservation law of mass
• differential equation

AMS Subject Classification:

• 93A30
• 97M99
• 34M99