Exploring trees in three dimensions: VoxR, a novel voxel-based R package dedicated to analysing the complex arrangement of tree crowns.

Background: Interest in tree form assessments using the terrestrial laser scanner (TLS) has increased in recent years. Yet many existing methods are limited to small-sized trees, principally due to noise and occlusion phenomena. In this paper, a novel voxel-based program that is dedicated to the analyses of large tree structures is presented. The method is based on the assumption that architectural trait variations (i.e. branching angle, bifurcation ratio, biomass allocation, etc.) influence the way a tree explores space. This method uses the concept of space exploration that considers a voxel as a portion of space explored by the tree. Once the TLS scene is voxelized, the program provides tools that extract qualitative (geometrical) and quantitative (volumetric) metrics. These tools measure (1) voxel dispersion in three dimensions (3-D), (2) projections of the voxel cloud in 2-D and (3) multi-temporal changes within a single tree crown. Scope: To test algorithm capabilities of measuring larger tree architectural traits, two application studies were conducted using point clouds that were either generated by a tree growth simulation model, thereby allowing algorithm application in a perfectly controlled environment, or acquired in the field with a TLS device. The space exploration concept makes it possible to take advantage of the volumetric nature of voxels to compensate for occlusion. The hypothesis that large-sized voxels can be used to reduce occlusion in the original point cloud was tested, as well as the consequences of voxel size on quantification of tree volume and on precision of derived metrics. Conclusions: Results show that space exploration is well adapted to highlight architectural differences among trees. They also suggest that large-sized voxels are efficient for occlusion compensation at the expense of metrics precision in some cases. The best resolution to choose depending on the research objectives and quality of the TLS scan is discussed.

Linking ice accretion and crown structure: towards a model of the effect of freezing rain on tree canopies.

BACKGROUND AND AIMS: Despite a longstanding interest in variation in tree species vulnerability to ice storm damage, quantitative analyses of the influence of crown structure on within-crown variation in ice accretion are rare. In particular, the effect of prior interception by higher branches on lower branch accumulation remains unstudied. The aim of this study was to test the hypothesis that intra-crown ice accretion can be predicted by a measure of the degree of sheltering by neighbouring branches. METHODS: Freezing rain was artificially applied to Acer platanoides L., and in situ branch-ice thickness was measured directly and from LiDAR point clouds. Two models of freezing rain interception were developed: 'IceCube', which uses point clouds to relate ice accretion to a voxel-based index (sheltering factor; SF) of the sheltering effect of branch elements above a measurement point; and 'IceTree', a simulation model for in silico evaluation of the interception pattern of freezing rain in virtual tree crowns. KEY RESULTS: Intra-crown radial ice accretion varied strongly, declining from the tips to the bases of branches and from the top to the base of the crown. SF for branches varied strongly within the crown, and differences among branches were consistent for a range of model parameters. Intra-crown variation in ice accretion on branches was related to SF (R(2) = 0·46), with in silico results from IceTree supporting empirical relationships from IceCube. CONCLUSIONS: Empirical results and simulations confirmed a key role for crown architecture in determining intra-crown patterns of ice accretion. As suspected, the concentration of freezing rain droplets is attenuated by passage through the upper crown, and thus higher branches accumulate more ice than lower branches. This is the first step in developing a model that can provide a quantitative basis for investigating intra-crown and inter-specific variation in freezing rain damage.