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Received：31 October 2019，
Published：07 October 2021
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作为森林冠层结构的重要组成部分，树冠形状对冠层间隙率与聚集度指数的计算有重要影响。之前的研究通常将树冠假设为圆锥形、圆柱形、圆锥+圆柱形等形状计算了冠层间隙率与聚集度指数。然而，树冠生长受外部环境以及内部顶端优势等因素的影响，相较于上述理想化的树冠形状，半椭球形更符合树冠自然生长规律。事实上，半椭球形是一种十分常见的树冠形状。本文以树冠在空间呈泊松分布为前提，推导出半椭球形树冠的冠层间隙率与聚集度指数计算公式，并进一步扩展到双半椭球形树冠。同时，以半椭球形树冠为计算基准，对比分析了半椭球形树冠与其他树冠形状冠层间隙率与聚集度指数的相对差异。模拟计算中主要输入参数包括树冠密度、树冠高度、树冠半径以及叶面积指数等。最后通过虚拟场景对结果进行验证。结果表明：（1）半椭球形树冠与其他树冠形状的冠层间隙率有较大差异。随着观测天顶角增加，不同树冠形状与半椭球形树冠的冠层间隙率的相对差异也逐渐增大。当观测天顶角为70°时，圆锥形树冠与半椭球形树冠的冠层间隙率相对差异已接近100%。（2）树冠形状对聚集度指数同样有较明显影响。极端情况下，圆锥形树冠与半椭球形树冠的聚集度指数相对差异达到30%。（3）半椭球形树冠与其他树冠形状的半球空间聚集度指数期望值的差异不容忽视。
The structural characteristics of forest canopy directly affect the radiation interception of forest
which in turn affect the energy exchange between the canopy and the external environment. As an important part of forest canopy structure
crown shape is greatly important for calculating the gap fraction and clumping index. Researchers have calculated gap fraction and clumping index by simulating crown shape as basic geometry
such as cone
cylinder
and cone + cylinder. However
the growth of the crown is influenced by factors
such as external environment and internal apical dominance
resulting in the semiellipsoid shape of the crown. The semiellipsoid is more consistent with the natural growth low of the crowns than these crown shapes. In fact
the semiellipsoid is a very common crown shape
which is significantly different from other crown shapes with an important influence on the calculation of canopy structure parameters
such as the gap fraction of canopies and clumping index. The main objective is to exhibit the influence of the semiellipsoid-shaped crown on the gap fraction and clumping index of forest canopies.
First
assuming that the crown is an opaque geometric entity with the Poisson distribution in space
the gap fraction on crown scale was calculated. Second
considering that gaps exist in an individual crown
the formula for calculating the gap fraction of an individual crown was introduced. Then
crowns with semiellipsoid and double semiellipsoid shapes were applied to the formula of gap fraction of canopies and clumping index. Meanwhile
considering the semiellipsoid-shaped crown as the calculation criterion
we analyzed the relative differences of gap fraction of canopies and clumping index with different crown shapes. The main input parameters included crown density
crown height
crown radius and leaf area index. Finally
the results were verified by virtual scenes.
The results indicated that: (1) the gap fraction of canopies between the semiellipsoid-shaped crown and crowns with other shapes was relatively different. With the increment of view zenith angle
the relative differences of gap fraction between the semiellipsoid-shaped crown and crowns with other shapes increased. When the view zenith angle was 70°
the relative difference of gap fraction between the cone-shaped crown and the semiellipsoid-shaped crown was close to 100%. (2) The crown shape also had a significant influence on the clumping index. In extreme cases
the relative differences of clumping index between the cone-shaped crown and the semiellipsoid-shaped crown reached up to 30%. In addition
different crown densities had an important effect on the clumping index of different crown shapes. With the decrease in crown density
the relative difference in the clumping index of the semiellipsoid-shaped crown and crowns with other shapes showed an increasing trend. (3) When calculating the expectation value of the clumping index in the hemisphere space
the value of the cylinder-shaped crown was approximately 13% higher than the value of the semiellipsoid-shaped crown
and the value of the semiellipsoid-shaped crown was approximately 22% higher than that of cone-shaped crown. The value of the semiellipsoid-shaped crown and double semiellipsoid-shaped crown was close to each other
and the mixture of two crown shapes slightly influenced the results.
Therefore
the semiellipsoid-shaped crown should be considered when studying the structural characteristics of forest canopy
such as gap fraction and clumping index.
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