Exploration of Relationship between Fractal Dimension and Clumping Effect for Improving Measurements of Leaf Area Index

Abstract:

Leaf area index (LAI), defined as the one-side leaf area per unit ground area, is a key parameter in the field of agriculture, forestry and ecology. The indirect methods of the LAI estimation are mainly based on Beer-lambert law which assume the leaves are random distribution. To address the clumping effect of the leaves, clumping index (CI), accounting for the distribution of the leaves in the canopy, was introduced. Traditional methods of the CI estimation are mainly based on the one dimensional transection of the canopy which is awkward in the up-scaling. Fractal dimension (FD), as a measure of the degree to which space is filled, has been used in two dimensional image to explore the relationship between FD, CI and LAI. A strong correlation between has been proved. However, there is still a lack of a universal model to explain it. Utilized the features of the Boolean model and combined a simple Box-counting method to measure the FD of the image, a fractal model about FD, CI and LAI was established. Simulated data and field measurement data were provided to verify the fractal model and both results showed a great agreement.