Annals of Forest Science

, 76:66 | Cite as

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

  • Mathieu DassotEmail author
  • Meriem Fournier
  • Christine Deleuze
Research Paper


Key message

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.


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.


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.


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.


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.


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 



This study used TLS data from the Ph.D of Mathieu Dassot, which was funded by the French National Research Agency (ANR) through the EMERGE project (ANR BIOENERGIES 2008 BIOE-003), the French Forestry Office (ONF) through the Modelfor contract (2005–2010), the French National Forest Inventory (IFN) through the contract 2008-CER-4148 and FEDER Lorraine (2007–2013).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© INRA and Springer-Verlag France SAS, part of Springer Nature 2019

Authors and Affiliations

  • Mathieu Dassot
    • 1
    Email author
  • Meriem Fournier
    • 2
  • Christine Deleuze
    • 3
  1. 1.EcoSustainEnvironmental Engineering Office, Research and DevelopmentKanfenFrance
  2. 2.Université de Lorraine, AgroParisTech, INRAUMR SilvaNancyFrance
  3. 3.ONFRDIDoleFrance

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