Assessing the scaling of the tree branch diameters frequency distribution with terrestrial laser scanning: methodological framework and issues

Lateral view of the point clouds of the three oaks, illustrating the detailed description of their woody structure

This article presents a specific methodology for assessing the scaling of the frequency distribution of the branch diameters within a tree from terrestrial laser scanning (TLS), using large oak trees ( Quercus petraea (Matt.) Liebl.) as the case study. It emphasizes the potential of TLS in assessing branch scaling exponents and provides new insights in forest ecology and biomass allometric modelling.

Context Many theoretical works invoke the scaling allometry of the frequency distribution of the branch diameters in tree form analyses, but testing such an allometry requires a huge amount of data that is particularly difficult to obtain from traditional measurements.
Aims The aims of this study were (i) to clarify the theoretical and methodological basics of this allometry, (ii) to explore the possibility of establishing this allometry from terrestrial laser scanning (TLS) and geometric modelling for the solid wood structure (i.e. diameters > 7 cm) of large trees, and (iii) to highlight the major methodological issues.
Methods Three large oak trees (Quercus petraea (Matt.) Liebl.) were digitized in leaf-off conditions from multiple points of view in order to produce accurate three-dimensional point clouds. Their woody structure was modelled using geometric procedures based on polyline and cylinder fitting. The allometry was established using basics found in literature: regular sampling of branch diameters and consideration of the living branches only. The impact of including the unpruned dead branches in the allometry was assessed, as well as the impact of modelling errors for the largest branch diameter classes.
Results TLS and geometric modelling revealed a scaling exponent of − 2.4 for the frequency distribution of the branch diameters for the solid wood structure of the trees. The dead branches could highly influence the slope of the allometry, making essential their detection in TLS data. The accuracy of diameter measurement for the highest diameter classes required particular attention, slight errors in these classes having a high influence on the slope of the allometry.
Conclusion These results could make it possible automated programs to process large numbers of trees and, therefore, to provide new insights in assessing forest structure, scaling, and dynamics for various environments in the context of climate change.

Allometry, Pipe model, Terrestrial LiDAR, Geometric modelling, Cylinder fitting, Tree architecture

Dassot, M., Fournier, M. & Deleuze, C. Annals of Forest Science (2019) 76: 66.

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Data availability
Dataset available from the corresponding author on reasonable request.

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