Attributes for structural complexity, crown dimensions, benefit-to-cost ratio, growth, and light availability
Box dimension was used for assessing structural complexity of the individual trees. Box dimension is a structural measure derived from individual tree TLS point clouds. First, one box including all TLS points of a single tree was fitted (i.e. initial box) in which the edge length of the box was tree height and then boxes of different sizes (i.e. tree height/2, tree height/4, tree height/8, tree height/16, tree height/32, tree height/64, tree height/128) were fitted to point clouds of each tree and the number of fitted boxes of each size was saved. Finally, the box dimension for each tree was defined as a slope between natural logarithm of 1/(box edge length of certain size/edge length of initial box) and natural logarithm of number of boxes including boxes of certain size (Figure 3B). Box dimension can theoretically vary between one and three, one representing pole-like objects and three solid objects such as a cube
Following examples by Seidel et al (2019a, b), the relationship between box dimension and attributes characterizing stem and crown size as well as benefit-to-cost ratio, growth, and light availability were assessed. Stem attributes included DBH, tree height, and stem volume whereas crown attributes included crown radius, crown projection area, and crown volume. Tree height was obtained using the height of the highest TLS point of each tree whereas DBH was defined from taper curve obtained with a combination of circle fitting to original stem points and fitting a cubic spline (see Yrttimaa et al. 2019, Saarinen et al. 2020). Stem volume, on the other hand, was defined by considering the stem as a sequence 10 cm vertical cylinders and summing up the volumes of the cylinders using the estimated taper curve. Crown attributes were generated from TLS points originating from branches and foliage (i.e. crown points). A 2D convex hull was fitted to envelope the crown points of each tree of which crown projection area was derived whereas crown volume was calculated from a 3D convex hull. Crown width, on the other hand, was defined as the distance between the two most outer points in xy-space.
Benefit-to-cost ratio was defined as a ratio between crown surface area and stem volume (i.e. surface-to-volume ratio), which were used as proxies for the photosynthetically active surface and building costs of a tree, respectively. The crown surface area was calculated from a 3D convex hull fitted to crown points of each tree (Figure 3A).
As TLS data were only acquired once from the study sites, growth of DBH, tree height, stem volume, and ΔH/DBH was calculated using field inventory measurements conducted in 2005-2006 and 2018-2019 for all live trees that were in the sample plots during the last field measurements.
Light availability of tree crowns was assumed to be related to the level of competition each tree is facing and the Hegyi index was used as a measure for competition and thus, a proxy for the light availability (Seidel et al. 2019a). The Hegyi’s competition index was calculated for each tree as:
\(\text{Hegy}i^{{}^{\prime}}s\ competition\ index=\ \sum_{j=1}^{n}\frac{\frac{\text{DBH}_{i}}{\text{DBH}_{j}}}{\text{dist}_{\text{ij}}}\), (1)
where i is the subject tree for which competition index is calculated, j is a competitor, \(\text{dist}_{\text{ij}}\) is the distance between the subject tree i and the competitor j , and n is the number of competitors within 5-m radius around the subject tree i . The TLS-based DBH of subject and competitor trees was used in calculating Hegyi’s competition index and the RMSE and bias are 0.7 cm (3.4%) and -0.1 (-0.6%), respectively (Yrttimaa et al. 2020).