Influence of the exclusion distance among trees on gap fraction and foliage clumping index of forest plantations

Abstract

A hypergeometric model is proposed explicitly instead of two previous stochastic models (the Poisson model and Neyman-A model) to describe the topological relationship of trees and the influence of the exclusion distance on gap fraction and clumping index of forest plantation canopies. Gap fraction (GF) and clumping index (CI) play key roles in plant light interception, and therefore they have strong impacts on plant growth and canopy radiative transfer processes. Trees are usually assumed to be randomly distributed in natural forests in many previous studies. However, few studies have shown how trees are distributed in forest plantations and how these distribution patterns affect GF and CI in these forests. In this paper, a simple and general distance factor defined as relative allowable shortest distance between centers of two adjacent crowns divided by the mean diameter of the crowns (RASD) is proposed to describe quantitatively the degree of mutual exclusion among trees in forest plantations of various tree distribution patterns. A hypergeometric model is proposed instead of two previous stochastic tree distribution models (the Poisson model and Neyman-A model) to describe the topological relationship of trees and the influences of the exclusion distance on the GF and CI of the forest plantation canopies. The results show that: (1) the hypergeometric model is more suitable than the Poisson model and Neyman-A model for describing the topological relationship of trees in forest plantations; (2) the exclusion distance has strong impacts on GF and CI: there are significant differences between the results of the hypergeometric model and the Poisson model. Larger RASD causes lower GF and larger CI. The simulations are verified by field measurements in four forest plantation stands. Similarly, impacts of RASD on GF and CI are also found for other two crown shapes (prolate and oblate ellipsoids).