8th J

uly

2014

Centre for Geo-Information

Thesis Report GIRS-2014-25

USING T-LIDAR AS AN ALTERNATIVE MEASUREMENT TECHNIQUE FOR PLANT-SCALING MODELLING IN TROPICAL FOREST.

Alvaro Iván Lau Sarmiento

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Using T-LiDAR as an Alternative Measurement Technique for Plant-Scaling Modelling in Tropical Forest

Alvaro Iván Lau Sarmiento

Registration number 85 03 25 504 080

Supervisor:

dr. Harm Bartholomeus

External advisor:

Ph.D. Lisa Patrick Bentley

Ph.D. Alexander Shenkin

A thesis submitted in partial fulfilment of the degree of Master of Science

at Wageningen University and Research Centre,

The Netherlands.

July 8th, 2014

Wageningen, the Netherlands

Thesis code number: GRS-80436

Thesis Report: GIRS-2014-25

Wageningen University and Research Centre

Laboratory of Geo-Information Science and Remote Sensing

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Foreword

Terrestrial LiDAR technology applied for forestry is still in early stages, yet has a lot of potential.

This potential was one of the main reasons I chose this topic. During more than a year, I have been

involved with LiDAR technology in all stages: I joined a 6-week fieldwork in the Peruvian amazon;

four of them scanning permanent plots with a team of University of Oxford and two of them

scanning harvested trees with a team of CIFOR. This fieldwork gave me awareness of the relevance

of having an efficient data collection. I realized the advantages and limitations the LiDAR could

have and there is no one-methodology for scanning in tropical forest. Also, it gave me a deeper

understanding on how the data collection happened in tropics and how different was from previous

fieldworks. This is why my minor thesis focused on evaluating how different scan configurations in

the scanner can affect the scan procedure in tropical forest. That research reinforced my knowledge

on data processing and gave me an insight of all the capabilities LiDAR technology has.

Then, this research, supported by the School of Geography and the Environment – OUCE of the

University of Oxford, explored a new topic: branch architecture and ecological functions. This

research revealed the capabilities of LiDAR technology to derive tree parameters and plant-scaling

metabolism. Even though, this is just a first step, I think this research creates a new opportunity for

understanding ecological functions.

Finally, I’d like to express my gratefulness to God, family, all the friends and colleagues who

support me during this whole time and whole master. Especially to Yadvinder Mahli and Martin

Herold, who made this possible in the beginning; Harm Bartholomeus, who has always supported me

and many collaborators: Lisa, Jose, Allie, Walter and Karen.

Alvaro Lau,

Wageningen, July 8th 2014

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Abstract

Tropical forests are some of the most complex terrestrial ecosystems in the world. It is crucial to

assess its spatial structure, since it plays a major role in the exchange process of matter and energy

between atmosphere and terrestrial above-ground carbons stocks and influences many biophysical

processes. In order to accurate model these processes, tree allometry and branch architecture is

needed, since researches are able to construct models which statistically infer tree parameters from

these measurements. During these decades, researches regarding tropical forest have been

concentrated on developing automated algorithms for forest inventories. T-LiDAR offers a potential

for assessing vegetation structure, due to its capability to provide objective and consistent

measurements. The main objective of this research is to evaluate if T-LiDAR is an alternative for

measuring forest parameters in tropical forest. In order to do that, this research analysed the

performance of T-LiDAR in a tree model approach, the QSM approach, in order to derive tree

parameters, such as DBH, tree height, number of branches. Then, this research tested these

parameters in a plant-scaling exponent metabolism, the WBE plant-scaling model. Our results

supported the use of T-LiDAR for assessing tropical trees structure. T-LiDAR can deliver a reliable

3D point cloud, which can be used for tree modelling. The branches resulting from the QSM

approach were very accurate, compared to the original point cloud. For tree modelling, the QSM

performance showed a high accuracy, with a low RMSE (up to 1.26 cm for radius parameter) for the

first branches level, decreasing for smaller branches and top of the canopy; due to the fuzziness of

the point cloud at far distances. Finally, the tree scaling metabolism derived from T-LiDAR scans

revealed that the exponents found are not consistent with the theoretical values. This research is the

first step on using T-LiDAR data from tropical forest into plant ecology and other ecological

branches.

Keywords: tree modelling, terrestrial LiDAR, plant scaling metabolism, tropical forest

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TableofContent

Foreword ............................................................................................................................................... V 

Abstract .............................................................................................................................................. VII 

List of Pictures ...................................................................................................................................... X 

List of Figures ...................................................................................................................................... XI 

List of Tables ....................................................................................................................................... XI 

List of Graphs .................................................................................................................................... XII 

List of Appendices ............................................................................................................................ XIII 

Nomenclature .................................................................................................................................... XIV 

1.  Introduction .................................................................................................................................... 1 

1.1.  Background ............................................................................................................................. 1 

1.2.  Research overview .................................................................................................................. 4 

1.2.1.  Problem definition ........................................................................................................... 4 

1.2.2.  Research question and research objectives ...................................................................... 5 

2.  Materials and method ..................................................................................................................... 6 

2.1.  Study objects ........................................................................................................................... 6 

2.2.  Data specifications .................................................................................................................. 8 

2.3.  Quantitative structure model approach – QSM approach ....................................................... 9 

2.4.  Scaling of whole tree branch length, branch radii, and metabolism ..................................... 11 

2.5.  Methodology ......................................................................................................................... 12 

2.5.1.  Tree modelling approaches ............................................................................................ 12 

2.5.2.  Branches measurement scenario .................................................................................... 13 

2.5.1.  Digital defoliated tree scenario ...................................................................................... 15 

2.5.2.  Tropical forest tree scenario ........................................................................................... 17 

3.  Results .......................................................................................................................................... 20 

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3.1.  Tree modelling approaches ................................................................................................... 20 

3.2.  Branch measurement scenario ............................................................................................... 23 

3.3.  Digital defoliated tree scenario ............................................................................................. 29 

3.4.  Tropical Forest Tree scenario ................................................................................................ 35 

4.  Discussion .................................................................................................................................... 41 

4.1.  T-LiDAR and tropical forests trees ....................................................................................... 41 

4.2.  Details of the tree modelling approaches .............................................................................. 44 

4.3.  Limitations and improvements of the QSM approach .......................................................... 45 

4.4.  Scaling of whole tree branch length, branch radii, and metabolism ..................................... 47 

4.5.  Applications and future use ................................................................................................... 48 

5.  Conclusions .................................................................................................................................. 50 

6.  References .................................................................................................................................... 51 

7.  Appendices ................................................................................................................................... 58 

List of Pictures

Picture 1. Tree (Liquidambar styraciflua) in Wageningen Campus. Tree natural defoliated on March

2011 (left), and tree with leaves on June of the same year (right). ........................................................ 7 

List of Equations

(1) ........................................................................................................................................................... 9 

(2) ......................................................................................................................................................... 11 

(3) ......................................................................................................................................................... 15 

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List of Tables

Table 1. Settings of QSM used in this study. ....................................................................................... 10 

Table 2: Summary of methodologies. .................................................................................................. 20 

Table 3. RMSE of branches parameters per setting (in cm). ............................................................... 25 

Table 4. RMSE in metres for total branch length parameter. .............................................................. 31 

Table 5. RMSE in litres for total branch volume parameter. ............................................................... 33 

Table 6. RMSE in values for number of branches parameter. ............................................................. 34 

Table 7. Scaling exponents for branch length and radii ....................................................................... 40 

List of Figures

Figure 1. Overview of methodology. ..................................................................................................... 6 

Figure 2. (a) shows Tambopata plot in Peruvian amazon basin; (b) sample pattern used for the

fieldwork; (c) RIEGL VZ-400V-Line 3D© T-LiDAR in tilted scan configuration. .............................. 7 

Figure 3. Detailed flowchart of Branches measurement scenario. ...................................................... 15 

Figure 4. Detailed flowchart of Digital defoliated tree scenario. ........................................................ 17 

Figure 5. Detailed flowchart of Tropical forest tree scenario. ............................................................. 19 

Figure 6. (a) point cloud of branch A, (b) number of branch nodes found in branch A (3 nodes), (c)

point cloud of branch B, and (d) number of branch nodes found in branch B (16 nodes). The colour

range indicates height, from zero (blue) to 2 metres (red). .................................................................. 24 

Figure 7. (a) Tree scanned on March. This tree had no leaves and was our control dataset. (b) Same

tree scanned on June had leaves and was our tree “with leaves” dataset. From this tree, filtering out

the leaves through its reflectance was used to create two more datasets: hardwood > -5 db reflectance

(c) and hardwood > -10 db reflectance (d) respectively. Colour pattern for the first two images

showed 0 metres (blue) and 15 metres (red) height; and for the reflectance filter, red colour means

hardwood and green colour means softwood, which was filtered out. ................................................ 30 

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Figure 8. (a) Birds eye point of view of Tambopata 05 Plot with height filter from 25 (blue) to 40

(red) metres. (b), (c) and (d) show the selected trees after pre-processing (tree 01, tree 02 and tree 03

respectively). Colours mean height between 0 (blue) and 35 metres (red). ........................................ 35 

Figure 9. Cross section of Tambopata 5 plot. High vegetation density interferes with the instrument

and the object of interest (tree). ........................................................................................................... 41 

Figure 10. Point cloud density at 25 metres height. This study found out that branching point cloud

inside the crown of the tree is unclear and present structures; such as small branches or leaves are not

easily distinguish. ................................................................................................................................. 43 

List of Graphs

Graph 1. (a) Relationship between predicted and real branch A length nodes; and (b) relationship

between predicted and real branch B nodes. Y-axis shows the lengths of each branch node and X-

axis shows the measured data of the lengths of each branch node. ..................................................... 24 

Graph 2. (a) RMSE per parameter (X-axis) for different settings for branch A; (b) RMSE per

parameter (Y-axis) for different settings for branch B. ....................................................................... 26 

Graph 3. Total branch volume parameter. Boxplot showed statistics for each setting (A01 to A09 for

branch A and B02 to B09 for branch B). ............................................................................................. 27 

Graph 4. Total number of branches parameter. Boxplot showed statistics for each setting (A01 to

A09 for branch A and B02 to B09 for branch B). ............................................................................... 27 

Graph 5. DBH parameter. Boxplot showed statistics for each setting (A01 to A09 for branch A and

B02 to B09 for branch B)..................................................................................................................... 28 

Graph 6. Diameter at breast height parameter. Boxplot showed statistics for each setting (A01 to A09

for branch A and B02 to B09 for branch B). ....................................................................................... 29 

Graph 7. Total branch length per branch order for setting 04 (left) and setting 07 (right). Graph

displayed datasets with its repetitions and mean values (filled symbols). ........................................... 30 

Graph 8. Total branch volume per branch order for setting 04 (left) and setting 07 (right). Graph

displayed datasets with its repetitions and mean values (filled symbols). ........................................... 32 

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Graph 9. Number of branches per branch order for setting 04 (left) and setting 07 (right). Graph

displayed datasets with its repetitions and mean values (filled symbols).| .......................................... 34 

Graph 10.Tree profile of tree 01 (right) and, its corresponding points (left). ...................................... 36 

Graph 11. Tree profile of tree 02 (right) and, its corresponding points (left). ..................................... 36 

Graph 12. Tree profile of tree 03 (right) and, its corresponding points (left). ..................................... 37 

Graph 13. Total branch length per branch order for setting 04. Graph displayed trees with its

repetitions and mean values (filled symbols). ...................................................................................... 37 

Graph 14. Number of branches per branch order for setting 04. Graph displayed trees with its

repetitions and mean values (filled symbols). ...................................................................................... 38 

Graph 15. Total branch volume per branch order for setting 04. Graph displayed trees with its

repetitions and mean values (filled symbols). ...................................................................................... 39 

Graph 16. Branch –order scaling exponent for length (left) and radii (right) for tree 01 (black line),

02 (green line) and 03 (blue line). Theoretical WBE expected exponent for length (0.3) and for radii

are shown in red (0.5). Dashed vertical lines show the calculated mean of each tree scaling exponent.

.............................................................................................................................................................. 39 

List of Appendices

Appendix I. Tree inventory in Plot Tambopata 05. ............................................................................. 58 

Appendix II. Output results.................................................................................................................. 59 

Appendix III. Branch Measurement Protocol ...................................................................................... 60 

Appendix IV. Branch Measurement Filling Form ............................................................................... 63 

Appendix V. Real measurements: branch A and B ............................................................................. 64 

Appendix VI. Input template for WBE scaling model ........................................................................ 65 

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Nomenclature

2D Two dimensional

3D Three dimensional

cm Centimetres

db Decibel

DBH Diameter at breast height

DTM Digital terrain model

l Litres

LiDAR Light detection and ranging

m Metres

masl Metres above sea level

max maximum

min minimum

mm Millimetres

mrad Milliradians

nm Nanometres

QSM Quantitative structure model

RMSE Root mean square error

sd Standard deviation

TLS Terrestrial laser scanner

WBE West, Brown and Enquist’s model

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1. Introduction

1.1. Background

Tropical forests are some of the most structurally complex terrestrial ecosystems in the world. Their

complexity is related to the size-frequency distribution of woody stems and three dimensional

arrangement of canopy elements from the top to the ground (Saatchi et al., 2011). Due to this

complexity, it is crucial to assess its spatial structure at multiple spatial scales (Van der Zande et al.,

2006). At an ecosystem level, structure plays a major role in the exchange process of matter and

energy between atmosphere and terrestrial above-ground carbon reserves, of which tropical forests

store 13 % of global stocks (Rosell et al., 2009; Tang et al., 2012; Van der Zande et al., 2006). On

the one hand, at a tree level, structure influences many biophysical processes such as photosynthesis,

growth, CO2 uptake, evapotranspiration, light interception and radiation use efficiency (Kaggwa-

Asiimwe et al., 2013).

This spatial structure, such as number of trees, species composition, tree size, health and tree

location, provides the basis to estimate forest parameters, such as total leaf area, tree and leaf

biomass, and indirect estimation of ecosystem services, such as carbon sequestration, peak flow

attenuation and temperature regulation (Nowak et al., 2008; Rosell et al., 2009). This is why

researchers need to be able to assess spatial structure, due to their important role in biophysical

processes at different scales as it is also the main driver behind most interactions between vegetation

and the physical environment (Côté et al., 2012). In recent years, many models have been used to

estimate forest biophysical processes. These models use as basis the estimations of forest structure,

more specifically, assumptions about tree allometry and architecture.

In order to have accurate modelling in biophysical processes, tree allometry and architecture

measurements on experimental plots are needed (Allouis et al., 2012; Macfarlane et al., 2007).

However, in situ measurements are labour intensive, time-consuming, costly, destructive, susceptible

to subjective errors and sometimes impractical or dangerous owing to poor access and physical

accessibility to the terrain (Dassot et al., 2012; Hopkinson et al., 2004; Kucharik et al., 1999;

Macfarlane et al., 2007). Moreover, the number of samples available is directly influenced by the

number of harvested trees or chopped down branches (Kucharik et al., 1999). For some

measurements, destruction of the tree is necessary, to be measured on the ground or in the laboratory

(Kankare et al., 2013). For these reasons, some estimations are usually indirectly based on other

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spatial parameters, such as tree height or diameter at breast height (DBH) (Moskal & Zheng, 2011;

Watt & Donoghue, 2005). However, these estimations, especially at local level, are often poorly

suited for single-tree assessment (Dassot et al., 2012; Kankare et al., 2013; Saatchi et al., 2011).

Several innovative remote sensing techniques have been developed to characterize the 3D structure

of individual trees (Rosell et al., 2009). Ultrasonic sensors, photography, stereo images, light sensors,

high-resolution radar images, high-resolution x-ray tomography and LiDAR (Light Detection and

Ranging) offer an alternative solutions to traditional techniques (Rosell et al., 2009; Yao et al.,

2011). However, most of these methods pose practical problems under field conditions for

representing spatial patterns, because forest structure contains not only horizontal (x and y) but

vertical information (z) as well (Lefsky et al., 2002; Mathews & Jensen, 2013; Van der Zande et al.,

2006; Yang et al., 2013). Among these alternatives, Terrestrial LiDAR, or T-LiDAR, is promising as

an alternative for 3D mapping of areas with high detail (Kankare et al., 2013; Keightley & Bawden,

2010).

T-LiDAR is a non-destructive remote sensing technique for measuring distances (Rosell et al., 2009).

T-LiDAR sensors directly measure the three-dimensional distribution of the canopy, as well as sub-

canopy topography, providing a high accurate estimation of vegetation height, cover, and structure

(Lefsky et al., 2002). T-LiDAR uses a large number of laser pulses, with some divergence, emitted in

the visible or near-infrared part of the spectrum within the object’s field of view. When a pulse

comes into contact with an object, part of the energy is scattered back towards the sensor and triggers

the recording of its distance (either using time-of-flight or phase displacement) and intensity.

Knowing the direction of the emitted pulse, one can position it in a 3D space. The arrangement of

numerous of those points together is known as a point cloud (Béland et al., 2014; Henning & Radtke,

2008; Hopkinson et al., 2004).

When T-LiDAR instruments are capable of recording only one contact between the instrument and

an object in the laser’s path, are called “single return”; when it can record several contacts, it is

known as “multiple return”. Moreover, high-tech T-LiDAR instruments can measure the complete

return energy pulse, known as “full-waveform” or a set of ranges from it, “discrete return” which can

be analysed with different methods to provide significant information for more accurate processing

of laser data (Béland et al., 2014; Hancock et al., 2011; Henning & Radtke, 2008; Hudak et al., 2009;

Pirotti et al., 2013; Reitberger et al., 2009). Kankare (2013) states that scanning range from midrange

T-LiDAR allows distances between 2 and 800 metres. Moreover, measurements are highly accurate;

most 0.1 – 1 metres for airborne LiDAR and 0.05 – 10 cm for T-LiDAR (Yang et al., 2013).

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Even though the application of T-LiDAR for forestry has not been widely studied (Kankare et al.,

2013), its potential for assessing vegetation structure due, to its capability to provide objective and

consistent measurements with sufficient accuracy, been proven over time (Kankare et al., 2013;

Pueschel, 2013; Zheng & Moskal, 2012). T-LiDAR allows acquiring a forest as a dense 3D point

cloud, giving a realistic and accurate picture of a stand at a given time (Othmani et al., 2011). This

allows the quantitative analysis of the forest and the quantitative reconstruction of 3D models from

that through the scripting of algorithms capable to extract tree parameters (Raumonen et al., 2013;

Wu et al., 2013).

Most of the research on T-LiDAR in forestry (during the last decade) has been concentrated on

developing automated algorithms for plot-scaled forest inventories (Dassot et al., 2012). These tree

reconstruction algorithms provides a better understandings of the 3D organization of the structure of

plants; with ability to reconstruct and measure key attributes, such as tree location, stem density,

canopy cover, above ground biomass and diameter at breast height (DBH) with high accuracy from

point cloud data (Côté et al., 2012; Delagrange et al., 2014; Kankare et al., 2013; Pueschel, 2013;

Srinivasan et al., 2014). Moreover, these algorithms are able to reconstruct tree parameters with high

accuracy from simulated data, where potential errors; such as registration, wind or occlusion; can be

controlled or supressed (Raumonen et al., 2013). Nevertheless; for measured data, where these

potential errors cannot be controlled or suppressed, limitations exists to reconstruct properly.

This 3D organization of the structure of plants is called plant architecture (Lauri, 2007). This

architecture is the basic growth strategy of a plant or the growth pattern through which the plant

develops its shape (Rosati et al., 2013). Within this, tree architecture describes parameters such as

crown dimensions, tree height, bole diameter and crown symmetry. On the other side, branch

architecture focuses on the similarities in the patterns of branching, by measuring branch dimensions;

such as number, radius, length, number of daughter branches (Bentley et al., 2013). These detailed

measurements can provide a way to assess volume content and understanding relationships involving

tree growth, allometry, stem mechanics and canopy structure (Henning and Radtke 2006; Moskal

and Zheng 2011).

Therefore, analysing the architecture of plants is important for the understanding of plant growth,

branching pattern and yield; which exerts direct influence on key physiological processes such as

photosynthesis and radiation use efficiency (Kaggwa-Asiimwe et al., 2013; Rosati et al., 2013). From

these, researchers have constructed models that assume architecture principals that follow branching

structure and are useful to predict whole-tree functions (Bentley et al., 2013). These models are used

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to statistically infer biomass based on in situ measurements or remote sensed data for extrapolation

to bigger areas (Edson & Wing, 2011).

1.2. Research overview

1.2.1. Problem definition

Despite the advances in forest measurements, characterizing tree parameters from point cloud data in

forest environment still remains a challenge, especially over tropical rainforest (Clark et al., 2011).

Tree parameters rely on the truthful representation of the real world throughout the point cloud data,

and the accuracy of the modelling algorithm to interpret these points into tree parameters. How well

the T-LiDAR represents the real world depends on the technical constraints inherent of the scanning

device and the environmental conditions of the scanned area (Côté et al., 2009). Furthermore, the

modelling algorithms used to determine tree parameters have their own technical constraints.

The accuracy of T-LiDAR device to scan objects is limited by its own technical constraints. The

range-image point density of the beam generally decreases with distance from the sensor (from 50

m), which effectively limits the range at which certain analysis can be carried out (Henning &

Radtke, 2008; Pirotti et al., 2013; Yang et al., 2013). Moreover, the configuration of some devices

does not allow it to collect data below certain degrees zenith (not full hemispherical scans). The lack

of data above the instrument has a substantial effect for parameters such as canopy height or crown

diameter (Newnham et al., 2012). However, these constraints can be overcome by adding more

scanning points or combining multiple scans in order to achieve a full hemispherical data acquisition

(Henning & Radtke, 2008).

The accuracy of the point cloud data is also sensitive to the environment conditions, such as

geography, vegetation and weather of the tropical forest. Obscured ground and high slopes reduce

the accuracy of the measurement (Hudak et al., 2009). Also, dense vegetation, characteristic of

tropical forests, occludes the line of sight to more distant objects or surfaces. This is the main

limitation for a complete profiling of material distribution (Côté et al., 2012, 2009; Eitel et al., 2013;

Litkey et al., 2008). Extreme weather conditions, like rain and wind, greatly affect the return from

the tree canopy and other vertical objects which may sway in the wind (Parrish & Jeong, 2011)

increasing distortion and noise in the point cloud (Dassot et al., 2012). These factors limit the usage

of a single range image for analysis of a forest plot, canopy or any stand-level attribute (Henning &

Radtke, 2008; Kankare et al., 2013), which can be compensated by adding more scanning to the area.

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Moreover, tree modelling algorithms have their own constraints. Many of them need to have a clean,

without noise, point cloud (Bremer et al., 2013). Since measured data is difficult to acquire, most of

them have been tested with simulated trees or in controlled scenarios (with no adverse environmental

conditions (Côté et al., 2009). These simulated trees have a simple and predicted architecture, which

are completely different from tropical forest trees. Tropical forest constraints are related to occlusion

due to the dense vegetation, which means gaps inside the point cloud. This limits the extraction of

realistic patterns, making unrealistic connections for the constructed tree (Bremer et al., 2013; Hosoi

et al., 2013). Others required that the point cloud representation of the tree should be leaves-off in

order to give a realistic tree (Raumonen et al., 2011).

1.2.2. Research question and research objectives

The main objective of this research is to test if T-LiDAR provides a non-destructive and accurate

measurement of parameters related to tree structure in tropical forest. In order to tackle this main

objective, the following research questions (RQ) will be answered:

How can branch architecture methodologies be used to derive tree parameters from point

cloud data? (RQ1)

What is the performance of the Quantitative structure model in terms of extraction tree

parameters? (RQ2)

Is it feasible to use the Quantitative structure model on a tropical forest tree and which

problems are encountered? (RQ3)

Can the output of the Quantitative structure model be used for branch architecture modelling

and (RQ4)

What do the branching architecture parameters extracted from model of tropical trees tell us

about the scaling of whole tree metabolism? (RQ5)

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2. Materials and method

First, to understand the development of tree modelling, an exploratory literature review was done

(RQ1). This review focused on different methodologies used for extracting tree parameters such as

tree height, tree profile, branch length, wood volume from point cloud data. Then, this research

implemented the Quantitative structure model – QSM approach in three different contexts; from a

simple scheme (branches), passing into a complete defoliated tree and finally, a complex scheme a

tropical tree (RQ2), as shown in Figure 1. The details of the QSM approach are described in Section

2.3.

The first scenario, named branch measurement scenario, evaluated the QSM approach using its

different settings and assessed its reliability intervals (RQ2). Then, the second scenario, digital

defoliated tree, assessed the performance of this approach a digital defoliation (RQ2). The last

scenario tested the QSM with a tropical forest tree (RQ3). This scenario evaluated its performance

using the knowledge learned from the first and second scenario and the need to digitally defoliate the

tree or not. Finally, the extracted parameters from this scenario were used in the plant-scaling

exponent metabolism model (RQ4 and RQ5).

Figure 1. Overview of methodology.

2.1. Study objects

The branches assessed for the branch measurement scenario were collected in Wageningen

University campus from a pile of harvested branches in February 2014. The criteria of selection of

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these two branches were feasibility to measure branch parameters and uniformity of branches. The

scans were done in Wageningen Campus in May 2014. For the second scenario; a single tree dataset,

Liquidambar styraciflua (Kiliç, 2011), was scanned in Wageningen campus in 2011. The tree was

scanned two times, in March with leaves-off and in June with the leaves-on as seen in Picture 1.

Picture 1. Tree (Liquidambar styraciflua) in Wageningen Campus. Tree natural defoliated on March 2011 (left), and tree with leaves on June of the same year (right).

Finally, the tree used for the tropical Forest tree scenario was selected from the Tambopata Plot 05.

This plot is located in latitude -12.830 degrees and longitude -69.271 degrees and has an elevation of

223 masl and it is located inside Tambopata National Reserve, Madre de Dios region, Peru (Figure

2a). The plot is currently managed by Global Ecosystem Monitoring network (GEM), from the

School of Geography and the Environment (OUCE), University of Oxford, United Kingdom under

the Andes to amazon transect Project (GEM, 2014).

Figure 2. (a) shows Tambopata plot in Peruvian amazon basin; (b) sample pattern used for the fieldwork; (c) RIEGL VZ-400V-Line 3D© T-LiDAR in tilted scan configuration.

(b(a) (c)

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The plot is located in the Peruvian amazon basin, south of Madre de Dios River, dominated by

lowland humid forest (Naughton-Treves, 2004). The annual rainfall totals 3200 millimeters and is

weakly seasonal (Brightsmith et al., 2008). Due to its mature floodplain forest containing several

“giant” tree specimens, fertility of the riverside soils and highly dynamic Tambopata forests have

special interest for carbon research (Naughton-Treves, 2004). A list of the predominant tree species

found in this plot can be seen in Appendix I. The plot comprised an area of 100 by 100 m, with a

regular square sample pattern of 20 by 20 m (Figure 2b). Every intersection of the sample pattern

was considered a scan position. T-LiDAR scans of the GEM plot were collected during a fieldwork

between August and October 2013.

2.2. Data specifications

All datasets were acquired using RIEGL VZ-400V-Line 3D© T-LiDAR [RIEGL Laser Measurement

Systems GmbH, Horn, Austria, www.riegl.com], mounted on a survey tripod 1.5 m above the ground

(Figure 2c). The scanning mechanism has a rotating head for the horizontal frame. This gives a 360

degrees scan angle range in the horizontal. For the vertical frame, the scanning mechanism is a

rotating multi-facet mirror, which gives a maximum of 100 degrees scan angle in the vertical (+60

degrees and -40 degrees). This T-LiDAR is a full-waveform LiDAR, which has a near infrared

(around 1550 nm) wavelength, with an angular resolution between 0.0024 and 0.5 degrees and a

laser beam divergence of 0.35 mrad (this means a beam diameter increase of 35 mm of every 100

metres). The accuracy of the instrument is 5 mm (conformity of a measurement to its true value) and

the precision 3 mm (conformity to which further measurements shows the same result) under normal

conditions (Riegl, 2013).

For the branch measurement scenario; the two branches were placed perpendicular to the ground and

four scans were performed in order to obtain a complete 3D image from these branches. The angular

step used for these scans were 0.06 degrees. The digital defoliated tree scenario for June 2011

(leaves-on) had three scans with an angular resolution of 0.08 degrees and the March 2011 (leaves-

off) had two scans of 0.04 degrees angular resolution. For the Tropical forest tree scenario,

measurements on each scan position were done in the plot, following the 20 by 20 m sample pattern,

giving a total of 36 scan positions (Figure 2b). Since the T-LiDAR only gives you 100 degrees

vertical angle, a full-hemispherical scan was acquired by scanning two times on the same scan

position; one in an upright scan configuration (perpendicular to the ground) and one on a tilted scan

configuration (parallel to the ground, Figure 2c). The angular resolution used during the fieldwork

was 0.06 degrees.

9

Each scan produced a point cloud, from which each origin is referred to a fixed scan position of the

scanner. In order to co-register each point cloud to its neighbour, several reflectors (tie-points) were

located throughout each scan position, in a way that the tie-points can be detected from multiple scan

positions. For the first and third scenario, 5 cm cylindrical reflectors were used; while for the second

scenario, 5 cm flat reflectors were used. For all scenarios, standard deviations of co-registered tie

points were kept less than 5 mm.

2.3. Quantitative structure model approach – QSM approach

The QSM approach was developed by Pasi Raumonen1 (Raumonen, 2014) on MatLab (The

MathWorks Inc., 2014). This approach reconstructs global 3D tree architecture by covering the point

cloud with small sets corresponding to connected surface patches in the tree surface (Disney et al.,

2012; Raumonen et al., 2013). The approach results in a database of structural characteristics, which

can be used to describe trunk/branch diameter, length, location, and branch angular distribution

(Disney et al., 2012). The model is divided into six steps: a) generation of cover sets, b) derivation of

neighbour-relation and geometric characteristics of each cover sets, c) identification of tree

component based on its characteristics, d) segmentation of tree components into branches and testing

local connectivity, e) fit cylinder via least squares method and f) fill gaps between cylinder segments

(Disney et al., 2012). The model is based in the following equation (1):

_ , 0, 0, 0, , , , , , (1)

The model uses 10 variables; P is the unfiltered point cloud of the tree. This point cloud must be in a

3-column matrix and each row gives the 3D (X,Y,Z) coordinate of the point. The scale of the point

cloud gives the unit reference for the model. This research used metres as scale unit. The model uses

two covers for the generation and segmentation process. The first cover (dmin0, rcov0, nmin0) can

hold large cover sets (dmin0 = 8 to 10 cm and rcov0 = dmin0 + 1 to 2 cm). By setting this, the model

quickly separates the tree from ground and understory. Also, it defines first a rough segmentation,

which the model uses to generate a new much finer cover that also adapts into size of the smaller

details. nmin0 is the minimum numbers of points per patch; the author recommends to use at least 10

points in the first cover per patch (Pasi Raumonen, personal communication, May 7th 2014).

1 Post-doctoral researcher. Department of Mathematics. Tampere University of Technology. Finland.

10

Then, the second cover (dmin, rcov, dmin) produces a finer cover. This finer cover decreases as we

approach the tip of any branch or we are on a higher order branch. dmin is the minimum distance

between centres of the cover sets. rcov is the radius of the patches used to generate the cover sets.

These are meaningful for derivation of neighbour-relation and geometric characteristics. Raumonen

(2013) concluded that a range between 2.0 – 2.4 cm is suitable and this radius can be a little larger

than the diameter (dmin). This study set rcov = dmin + 0.005 m. nmin is the minimum number of

points per rcov. lcyl is the length/radius ratio of the cylinder and ranges from 3 to 5. Noground is a

logical value that indicates the presence (0) or absence (1) of ground in the point cloud. Finally,

string is the name of the string for saving the output files. These variables make the branching

structure much more unique and stable against different model runs and input parameters and it

reduces the maximum branching order often radically to much more realistic levels (Pasi Raumonen,

personal communication, May 7th 2014).

The model gives four output files. The first one, “cyl_data_(filename).txt”, contains the information

of each cylinder modelled at a cylinder level. Each cylinder is described in each row and the

description in the column can be seen in Appendix II. Then, “branch_data_(filename).txt” contains

the sum of each branch at branch level. Each branch is described per row and the meaning of each

column can be also found in Appendix II. The “tree_data_(filename).txt” shows the volumes and

lengths of the trunk, branches at different levels, number of branches, and other parameters. Finally,

a pdf report “results_report_(filename).txt” is generated with the settings used and the tree_data

information.

Table 1. Settings of QSM used in this study. 1 2 3 4 5 6 7 8 9 10 dmin0 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.04 0.04 rcov0 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.05 0.05 nmin0 10 10 10 10 10 10 10 10 5 5 Dmin 0.02 0.04 0.06 0.08 0.02 0.02 0.08 0.08 0.02 0.08 Rcov 0.025 0.045 0.065 0.085 0.025 0.025 0.085 0.085 0.025 0.085 Nmin 5 5 5 5 3 7 3 7 5 5 Lcyl 4 4 4 4 4 4 4 4 4 4 Noground 1 1 1 1 1 1 1 1 1 1 Variables dmin0, rcov0, nmin0, dmin, rcov, and nmin are expressed in units of the point cloud (metres).

This study assessed 10 settings as seen in Table 1, based on the suggestions and advice of the

experts. Each scenario in this study assessed all the settings and chose the best ones based on visual

evaluation. This visual evaluation was based on the similarities of the results compared to the point

cloud datasets. Then, after choosing the best settings, the model was executed 10 more times per

settings selected. Raumonen recommends from 5 to 20 times in order to get the average (Pasi

11

Raumonen, personal communication, May 7th 2014). This is needed because the cover generation is

random; thus, each cover is different. This means that if you run the code with the same inputs, the

results will be a little different each time. Therefore, it is desirable to make multiple models with the

same inputs, and then take average of these model results (Pasi Raumonen, personal communication,

May 7th 2014).

2.4. Scaling of whole tree branch length, branch radii, and metabolism

The West, Brown and Enquist (WBE) plant-scaling model is a quantitative model that explained the

essential features of transport systems, such as blood vessels in mammals, plant vascular systems in

bronchial trees and tracheal tubes in insects (West et al., 1997). This model is based on three

assumptions; the branching pattern is fractal-like, the final branch of the network is size invariant and

the energy required to distribute resources is minimized (Brown et al., 2005; West et al., 1997).

Bentley (Bentley et al., 2013) used this principle to predict the scaling of whole-tree metabolic rate

based on scaling exponents at branch level (Bentley et al., 2013). It does not measure metabolic rate,

but estimate the exponent of how metabolic rate scales with plant size from branching traits. The

scripts (SCRIPT_scaling_exponents.R, Code_maple.R, Maple_a_b_theta_ratio_based.R and

Maple_a_b_theta_tip_vol_based.R) can be executed from the R® Project “R.WEB”, see [CD ROM]:

Script/Scenario_03/R.WEB. The QSM approach provided with branch radii, length of parents and

daughter branch segments, which were used in the WEB model. The scaling exponents are calculated

at both branch level, and whole-tree level using architectural bases measurements. At both levels, the

scaling exponents for branch length and radii can be only used to estimate metabolic rate in the limit

of networks of infinite size as follows (Bentley et al., 2013):

Radii scaling ( ),

Length scaling ( ) and,

Estimated metabolic rate ( ).

The estimated metabolic rate is based from the following equation (2):

1

2 (2)

For each exponent, the median and confidence interval was calculated and compared to the

theoretical results. An R® script was written to extract the branch parameters needed for the WBE

scaling model. The parameters extracted per branch were parent branch number, number of

daughters per branch, inferior radius per branch, superior radius per branch and length per branch.

12

The input template was filled with the outcomes and the columns which were not calculated were

filled with NA values (Appendix VI).

2.5. Methodology

2.5.1. Tree modelling approaches

The exploratory literature review started with a web search in the official pages of Scopus and Web

of Science. Scopus database is developed by Elsevier (Netherlands) and has updates one-to-two

times per week. Meanwhile Web of Science database is developed by Thomson Scientific and Health

Care Corporation (US) and has a weekly update (Falagas et al., 2008). Scopus was chosen because it

includes a more expanded spectrum of journals, with a faster citation analysis. Meanwhile, Web of

science provides a better citation analysis, better than Scopus, since Web of Science was created with

this objective (Falagas et al., 2008).

Then, this study used specific keywords to describe tree modelling such as “tree modelling”, “tree

architecture”, “branch architecture” and “tree structure”. Since, our study focused on T-LiDAR,

Boolean operators were used to narrow our search (AND, AND NOT, OR). We used “Terrestrial

LiDAR”, “TLS”, “airborne LiDAR” and “ALS” with the first keywords for constraining our

searches into T-LiDAR relevant searches, e.g. (“tree modelling” AND “terrestrial LiDAR”) or (“tree

structure” AND NOT “ALS”). Also, the year of publication was taken into account; it must be

published after year 2000. Since this topic is recent, mostly all were published after year 2000.

Once the search was completed, this study looked first on the title and the abstract of the scientific

publication. If it was relevant for this study, a digital copy was saved into a local library for further

reading. The author of this study used Mendeley Desktop©, which is a free software for database

collection and reference manager. Inside this program, the metadata for each publication was looked

up through its unique Digital Object Identifier (DOI). DOI was searched in Cross Ref

(http://www.crossref.org/guestquery/). After reading several scientific publications, a general

classification was established in order to cluster different approaches. Then, the publications were

classified into the different approaches and a description, parameters measured and the accuracy

were obtained from this classification. Finally, a summarizing between these parameters was done in

order to compare the different methodologies and its results.

13

2.5.2. Branches measurement scenario

The branch measurement scenario evaluated the optimal settings of the QSM approach using sample

branches. It was divided into five components: Data acquisition, Pre-processing, Quantitative

structure model, Validation, and Reliability intervals (Figure 3). The Data acquisition component

implied the scanning of two samples branches in such a way that a complete 3D point cloud was

achieved. In parallel, measurements were taken following the Branch Measurement Protocol,

developed by Ph.D. Lisa Patrick Bentley (Appendix III). It was assumed that these measurements

had the maximum achievable accuracy and used as control. The parameters measured per branch

were:

Branch node ID,

Parent branch ID,

Tip (yes/no),

Minimum radius (cm),

Maximum radius (cm),

Node length (cm), and

Length at half node (cm).

A branch node is the section of the branch between two daughter’s branch bifurcations. Is our

smallest unit, and from this, we measured its inferior diameter, superior diameter and length. This

information was filled in the Branch measurement Form (Appendix IV). Then, the Pre-processing

component co-registered the 3 point clouds using RiScan Pro© software [RIEGL Laser

Measurement Systems GmbH, Horn, Austria, www.riegl.com]. The standard deviations of the co-

registered tie points were smaller than 0.005 m.

Then, the branches were manually selected from the point cloud and exported into a text file. The

text file only contains the three coordinate of the points with no header and using blank as separator.

The Quantitative structure model component imported the text file into the model and ran the

different settings (10) from Table 1. Visual evaluation of the outcomes gave us an insight of the

optimal settings in order to establishing an accurate evaluation.

The Reliability intervals component evaluated the variability of the outcomes per run. The QSM

approach has a random generation cover, which means that each run of the model with the same

parameters gives a small different result. In order to determine the reliability intervals of the chosen

14

settings; this study scripted a code in R© (R Core Team, 2013) using the packages “stats” (R Core

Team, 2013) and “plyr” (Wickham, 2011). The script (SCRIPT_reliability_intervals.R) can be

executed from the R® Project “R.reliability_intervals”, see [CD ROM]:

Script/Scenario_01/R.reliability_intervals. Inside this script, the model was executed ten repetitions

for each setting. Standard deviation (sd), mean, minimum (min), maximum (max) were calculated

for the following parameters:

Total branch volume (l),

Total number of branches,

DBH (cm),

Total branch length per order (m).

Finally, the Validation component compared each branch node length from the model and the

observed branch node using Root Mean Square Error - RMSE (Heuvelink, 1999). Since the model

does not give you directly each branch parameters, a script code in R© was created in order to

visually identify the cylinders belonging to each branch node. The script (SCRIPT_3D_tree.R) can

be executed from the R® Project “R.3D_view”, see [CD ROM]: Script/Scenario_01/R.3D_branches.

This script used “spatstast” (Baddeley & Turner, 2005), “scatterplot3d” (Ligges & Mächler, 2003)

and “rgl” (Adler & Murdoch, 2014) packages. This was done because the model computed the whole

branch, but the measurements were done for each branch node, having different scales. After

manually identify all the cylinders to the belonging branch node, the best settings were selected. This

evaluation was also based on visual assessment of the branches to the point cloud.

Then, a second script was written in order to assess the difference of the settings from the

measurements. The script (SCRIPT_branch_analysis.R) can be executed from the R® Project

“R.branch_analysis”, see [CD ROM]: Script/Scenario_01/R.branch_analysis. This script used

“stats”, “plyr”, and “hydroGOF” (Zambrano-Bigiarini, 2013) to evaluate RMSE for the following

parameters: minimum radius, maximum radius length and radius at half-branch node at individual

branch level. RMSE showed the difference between the measurements predicted (outcome from the

model) and measurements observed. This difference is called residual, which ranges from 0 to

infinite, with 0 being a perfect forecast to the measurement. Because it is a square quantity, RMSE is

influenced more strongly by large error than small errors and is defined mathematically as seen in

(3):

15

1 (3)

where denotes our digital measurement; denotes our measurement; and denotes the number

of verifying points.

2.5.1. Digital defoliated tree scenario

The digital defoliated tree scenario was divided in three components; Pre-processing, Quantitative

structure model, and Validation. The Pre-processing steps were executed in the same way as the

previous scenario, with a standard deviation under 5 mm. The tree scan in March was a tree with

Figure 3. Detailed flowchart of Branches measurement scenario.

BRANCH MEASUREMENT SCENARIO

Dat

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Sample branches

Pre

-pro

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ing

Qu

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Val

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Selection

Real measuringScanning

Co-registration

Manual delineation

Modelling (10 combinations)

Digital measum.

Real measurem.

RMSE

Visual assessment

Results

Rel

iab

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terv

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SD, mean, min and max

Results

Best combinations

10 repetitions

16

natural defoliation; this dataset was assumed as our “control” dataset. The second scan, in June,

scanned the tree with leaves. This scan was the “tree with leaves” dataset.

Besides the two datasets, two more datasets, containing a digital defoliated tree were created by

filtering out the softwood parts (leaves) from the hardwood parts (trunk) of the tree at different

reflectance values. T-LiDAR also recorded reflectance; therefore, an inspection of the dataset gave

us the different amplitude of the softwood (leaves) and hardwood (trunks). Using the 2D view in

RiSCAN Pro the reflectance can be determined on the softwood and hardwood by clicking on a

specified part of the object and looked into its properties. Hardwood part has different reflectance

than softwood; by analysing the data, we conclude that softwood has lower reflectance values than

hardwood. Then, we set a threshold for filtering out softwood from hardwood. For this study, and

based on the inspection of the datasets, set two thresholds were set; one kept all the values

(hardwood) with reflectance over -5 db (removing values below -5 db) and another kept all the

values with reflectance above -10 db. These filters were named: “Hardwood > -5 db” and

“Hardwood > -10 db” respectively. Thus, these filters allowed us to digitally remove the leaves from

the trunk and branches dataset.

Then, each dataset was imported into the QSM approach and the 10 settings from Table 1 were

executed. For each dataset, the best settings were selected using visual assessment, and then chose

the settings which were successfully modelled in all of them. Then, 10 repetitions of the selected

settings were ran and a script in R© took the average of the tree parameters. The scripts

(SCRIPT_main.R, SCRIPT_number_branches.R, SCRIPT_volume_branches.R and

SCRIPT_length_branches.R) can be executed from the R® Project “R.differences”, see [CD ROM]:

Script/Scenario_02/R.differences. This script used “hydroGOF” package (Zambrano-Bigiarini, 2013)

to determine RMSE. The tree parameters which were evaluated in this scenario were:

Total branch length (m) per branch order,

Total branch volume (l) per branch order, and

Number of branches per branch order.

The averages of these parameters were compared to each other in the validation component using

RMSE. The Validation compared the difference between the tree with leaves (June) and the digitally

defoliated tree against the one without leaves (our control). This assessment gave us an indication of

the relevance of using defoliated trees in order to have appropriate results from the model.

17

2.5.2. Tropical forest tree scenario

Last, the tropical forest tree scenario was divided into four components, Data acquisition, Pre-

processing, Quantitative structure model and Model Integration. The data acquisition component

involved the fieldwork in the Peruvian amazon during October 2013 explained in Section 2.2. The

Pre-processing component used the raw point cloud from the Tambopata plot scans and co-registered

each of the 72 point clouds through its tie points into one massive point cloud. In order to select a

tree, a height filter was established between 25 and 40 metres from the ground. This filter aided us to

easily visualize individual tree crowns at this height range. Bird view point of view was used to

manually delineate the crowns of the selected trees. The delineation was around the crown +20 %

more in order to assure that the whole understory was selected as well.

Figure 4. Detailed flowchart of Digital defoliated tree scenario.

18

Three trees were selected and extracted. Once extracted, the trees were cleaned manually, deleting

points which were not part of the tree. Finally, each tree was exported to a text file. In addition, an

R® script was written to determine the vertical tree profiles from the point data. The script

(SCRIPT_tree_profile.R) can be executed from the R® Project “R.tree_profile”, see [CD ROM]:

Script/Scenario_03/R.tree_profile. This vertical tree profile enabled a study of the direct influence of

the point density on the tree profile estimation, and its possible influence on the QSM approach.

The Quantitative structure model imported each tree into the QSM approach and modelled using

setting 04 (Table 1). Setting 04 was used due to its high visual accuracy during this study. Then R®

scripts were written with “plyr” package (Wickham, 2011). These scripts (SCRIPT_main.R,

SCRIPT_volume_branch.R, SCRIPT_number_branches.R and SCRIPT_length_branches.R) can be

executed from the R® Project “R.differences”, see [CD ROM]: Script/Scenario_03/R.differences and

calculate the following branch parameters from the cyl_data results per branch:

Parent branch,

Number of daughters,

Inferior radius (m),

Superior radius (m), and

Length (m).

Finally, the model integration component used these parameters and used it as inputs in the WBE

plant-scaling script in R® (Stegen, 2009). In order to fit the results from the QSM approach into the

WBE, we used a script (SCRIPT_branches.R) which can be executed from the R® Project

“R.branches” (see [CD ROM]: Script/Scenario_03/R.branches). The WBE model (Stegen, 2009) was

executed and the following exponents can be calculated:

Length ratio scaling,

Radii ratio scaling, and

Estimated metabolic rate scaling.

19

Figure 5. Detailed flowchart of Tropical forest tree scenario.

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3. Results

3.1. Tree modelling approaches

Literature review showed that most approaches for modelling individual trees rely on T-LiDAR

discrete return point cloud datasets (sequence of x, y, z coordinate combinations) and mostly leaves-

off branch reconstruction scenarios (Wu et al., 2013). These approaches (Dassot et al., 2012; Wu et

al., 2013) are based on least square circle fitting (Bienert et al., 2007; Bienert, Scheller, et al., 2006;

Maas et al., 2008), cylinder fitting (Pfeifer & Winterhalder, 2004; Thies et al., 2004), voxel-based

processing (Gorte & Pfeifer, 2004; Gorte & Winterhalder, 2004), probabilistic 3D tree branch

reconstruction (Binney & Sukhatme, 2009) and Quantitative structure model (Åkerblom et al., 2012).

The following paragraphs describe each methodology and its characteristics. A summary table of

each methodology can be found in Table 2.

Table 2: Summary of methodologies. Approach Parameters measured Methodology Accuracy Reference Circle fitting Tree height, DBH, tree

position and stem profiles.

Segmentation based on point cluster using circle fitting method.

Tree detection at 97.4%. DBH RMSE 1.8 cm Tree height RMSE 2.07 to 4.55 m Stem profiles RSME 4.7 cm

Bienert (2007; 2006). Maas (2008)

Cylinder fitting Cross sections of tree branches and stems.

Cylindrical model is fitted into given point cloud with limited height.

Stems RMSE 0.0017 m DBH 0.6 and -1.3 cm Tree height -11.5 cm

Thies (2004) Pfeifer (2004)

Voxel-based processing

Wood volume and tree parameters

Identifies structure of tree in a 3D voxel space. Uses Dijkstra’s algorithm to delineate branches.

No information available. Gorte (2004; 2004)

Probabilistic 3D branch reconstruction

Branch location, angles, radii and branch length

Probabilistic method based in a generated tree model in order to guide an iterative reconstruction process.

Tested with simulated data: segments within less than one centimetre. Radius error less than millimetre. Testes with real data: trunk radius overestimated by 0. 4 cm.

Binney (2009)

Quantitative structure model

Total and partial volume, branch size distribution, bifurcation frequency, angles, trunk and branch profiles.

Large number of cylinders whose location, topology, orientation and size locally approximate geometry of tree.

Tested with artificial trees: visual inspection verifies that branching structure is well defined. Tested with small branches: less than 1cm error. Tested with real trees: volume of trunk and large branches reconstruct accurately.

Raumonen (2013, 2011) Åkerblom (2012)

Source: Dassot (2012) and Wu (2013).

21

Bienert (Bienert et al., 2007; Bienert, Scheller, et al., 2006) developed a fully automatic point cloud

processing scheme in order to extract stems from point cloud data. In order to achieve this, first a

segmentation based on point cluster search is done and a circle is fitted into each cluster at 1.3 m

using a circle fitting method in order to detect tree diameters (Bienert, Scheller, et al., 2006). A

reliability factor: a classification method was applied in order to detect the over- and underestimated

diameters and to ensure that unreliable data did not have great impact in the fitted model (Bienert et

al., 2007).

From here, tree parameters, such as tree height, DBH, tree position and stem profiles could be

determined (Bienert et al., 2007). Tree height was defined as the difference between the highest point

and the terrain model lowest point (based of the DBH) inside of the cut cylinder (Bienert, Maas, et

al., 2006; Bienert, Scheller, et al., 2006). DBH was determined by cutting a slice at 1.30 m above the

terrain model. Tree position was defined as the coordinates of the centre point of the DBH in the

right-handed system (Bienert, Maas, et al., 2006). Finally, stem profile at different height intervals

could be determined as well (Bienert et al., 2007; Maas et al., 2008).

Validation for this approach was done with measured data. The accuracy for the determined tree

parameters was high. For multiple tree detection in the point cloud, this method had a detection rate

of 97.4% (Bienert, Scheller, et al., 2006). Also, DBH measurements had a high accuracy ratio. Circle

fitting showed an average RMSE of 1.8 cm (Bienert, Scheller, et al., 2006) and a RMSE of 4.7 cm

for the stem profiles. However, tree height parameter showed a low accuracy, between 2.07 and 4.55

m (Maas et al., 2008).

Cylinder fitting method (Pfeifer & Winterhalder, 2004; Thies et al., 2004) estimated cross sections of

tree branches and stems. The main interest of this method lied on extracting diameter and growing

direction of the stem of its parts (Thies et al., 2004). In order to achieve this; first, a digital terrain

model (DTM) was extracted into a grid of variable size. For each cell, the z-minimum value was

selected. Then, the DTM was subtracted from the point cloud and the tree reconstruction was based

from the remaining points. A cylindrical model was fitted into the given point cloud in a limited

height region of points. The detailed mathematical description of the core algorithm could be found

in Thies (2004).

Each cylinder had two parameters (radius and axis direction) which could be directly related to

diameter and growing direction of the stem. Since it was an iterative process, the next cylinder was

calculated, in an overlapped sequence. This assured a growing scheme of the cylinder. By comparing

22

the radii and axis of two consecutively fitted cylinder gave an insight of the reliability of the fitting

procedure. This algorithm stopped automatically when a RMSE of a desired threshold is exceeded

(Thies et al., 2004).

This method established RMSE as the residual of the difference between the 3D points to the

approximated cylinder surface and determined the quality of fitting (Thies et al., 2004). Validation

done with measured data showed and RMSE for stems of 1.7 mm, an average deviation between -1.3

up to 0.6 cm for DBH, accuracy of -11.5 cm difference for tree height parameter (Thies et al., 2004).

The voxel-based algorithm (Gorte & Pfeifer, 2004; Gorte & Winterhalder, 2004) identified the

structure of a tree (stem and branches) in a 3D voxel space. This method could be carried out to

calculate wood volume and tree parameters (Gorte & Winterhalder, 2004). First, a 3D raster space is

created with 3D small cubes cells called voxels (volume element). The size of the voxels determined

the space resolution. This method uses a spatial resolution between 2 and 5 cm. Using coarser spatial

resolution reduced details and by using finer resolution increased computation time (Gorte & Pfeifer,

2004). After the point cloud was transferred to the 3D raster, neighbourhood operators could be

applied to enhanced data. These operators “removed” isolated voxels and filled small holes and gaps

between voxels, mostly caused by occlusion.

Then, a line-skeletonization of the tree reduced the thickness of tree trunk and branches to a single-

voxel wide linear structure. This aimed to identify branches and revealed topological relations

between the objects. Finally, in order to find the structure of the tree, segmentation based on

Dijkstra’s algorithm helped to find the shortest route from the tip to the destination node (root). This

provided a logical model for a tree and helped to assign parent and daughter nodes.

Binney (2009) presented a probabilistic method for reconstructing trees from sensor data. It used a

generated model of a tree in order to guide an iterative reconstruction process. The main parameters

which could extract are branch location, angles, radii and lengths of branches. This method used a

generative statistical model to fit likely hypothesis, and then used a sensor model to evaluate the

likelihood of each hypothesis. It is iteratively done from the base of the trunk and after the trunk was

reconstructed, it reconstructed each branch. The process was iterative, and after each branch was

reconstructed, the same process occurred to find sub-branches. The mathematical details of this

method could be found in Binney (2009).

Sometimes real-world parameters were hard to acquire (Côté et al., 2009); thus, validation was done

with simulated data. The probabilistic 3D branch reconstruction method was validated first with

23

simulated data, showing that the outcome segments were less than 1 cm from where should be

(Binney & Sukhatme, 2009). Trunk radius was overestimated by 0.4 cm with measured data,

compared to millimetre errors with simulated data (Binney & Sukhatme, 2009).

Finally, the Quantitative structure model - QSM (Åkerblom et al., 2012; Raumonen et al., 2013,

2011) is an approach for automatically approximating above-ground volume and branch size

distribution of trees from point cloud data. This method assumed that the point cloud is a sample of a

surface in 3D space and that this surface is locally like a cylinder. Each point cloud must describe

one single tree. This approach covered the point cloud with small patches, creating a surface. Then,

these patches were characterized geometrically (size, shape and orientation) into their neighbour,

leading into a classification of these patches into a tree component (trunk, ground, branches, sub-

branches). Components which were not part of the tree (e.g. ground) were removed and the base of

the trunk was defined.

Segmentation divided the components of the tree into small segments, which must be straight so

cylinders must fit. This segmentation defined tree structure and branching-relationship. Finally, each

segment could be reconstructed with successive cylinders locally approximating the radius and

orientation of each segment. This method also interpolated with accurate estimates parts which were

not present in the dataset. The validation was first evaluated with small branches. This gave us less

than 1 cm error; meanwhile when it was tested with artificial trees, visual inspection verified that the

branching structure was well defined (Raumonen et al., 2013).

3.2. Branch measurement scenario

Two samples branches (branch A and branch B) were scanned (Figure 6a & Figure 6c) and measured

in Wageningen Campus on May 2014. Measurements were taken following the protocol in Appendix

III. Diameters were taken at the inferior and superior tip of each branch node, at half-length of the

branch nodes and the length of each branch node. Branch A had 3 branch nodes meanwhile branch B

had 16 branch nodes (Figure 6b & Figure 6d). The detailed measurements of each section were

described in Appendix V.

24

Figure 6. (a) point cloud of branch A, (b) number of branch nodes found in branch A (3 nodes), (c) point cloud of branch B, and (d) number of branch nodes found in branch B (16 nodes). The colour range indicates height, from zero (blue) to 2 metres (red).

This study ran the model using the 10 settings established by Table 1. The 3D results were inspected

visually to see if they resembled the original point cloud. Settings 01, 02, 05, 06, 09 were chosen for

branch A and setting 02, 05, 08 and 09 were chosen for branch B. A script in R© used the

cyl_data_A_branch.txt and cyl_data_B_branch.txt to visualize in 3D each of the cylinders. Cylinders

were not related to the nodes in the measured data; therefore, this study linked each cylinder to the

corresponding branch node. Once we defined all the nodes, we sum all the small cylinder’s radius

and length, in order to fit with the template. We also defined the first cylinder as the one with the

maximum radius and the last cylinder of the branch node the one with the minimum radius. In order

to determine the radius at half-length, we calculated which cylinder was at half-way and chose its

radius.

Graph 1. (a) Relationship between predicted and real branch A length nodes; and (b) relationship between predicted and real branch B nodes. Y-axis shows the lengths of each branch node and X-axis shows the measured data of the lengths of each branch node.

Graph 1 described the accuracy between the lengths of each branch node from the settings selected

(Y axis) against the values of the measured data (X-axis). In case of branch A (Graph 1a), the

(a) (b) (c) (d)

25

settings selected were 01, 02, 05, 06 and 09. This graph showed a high accuracy between the

predicted values from the model and the measured data. The measured data (Appendix V) for branch

node 0, 1 and 2 were 0.41, 0.60 and 1.49 m respectively. Predicted values were accurate to the

measured one; which can be evidenced by the value alignment to the 1:1 dashed line (which

represents symmetric data). It is noticeable the formation of three clusters, representing each branch

node.

The second branch, branch B, had 4 settings selected: 02, 05, 08 and 09. Graph 1b displayed data

alignment for short nodes, below 0.5 meters. Predicted values showed accuracy for branch nodes’

length below 0.5 meters. For branch nodes’ length larger than 0.5 m there was an overestimation of

the predicted values, evidenced by values above the 1:1 dashed line. Setting 09 had the most

overestimated values for branch nodes larger than 0.5 m.

Table 3. RMSE of branches parameters per setting (in cm). A branch

Setting 01 02 05 06 09 Minimum radius 1.32 1.56 1.26 1.31 1.87 Maximum radius 2.92 2.34 2.35 2.94 3.04 Sum lengths 4.90 9.11 4.83 5.25 13.45 Half-length radius 3.12 2.71 2.92 3.11 3.28

B Branch Setting 02 05 08 09 Minimum radius 1.49 1.45 1.57 1.52 Maximum radius 1.48 1.04 1.34 1.25 Sum lengths 40.12 32.97 44.53 36.13 Half-length radius 1.37 1.01 1.34 1.24

This study also evaluated the different settings with RMSE to determine how deviated were the

predicted branch nodes of the model from the real nodes (Table 3). For branch A (Graph 2a), the

overall setting with lowest deviation was 05, followed by setting 06 and 02. RMSE for minimum

radius revealed that setting 05 had the lowest deviation (1.27 cm); meanwhile setting 09 had the

highest RMSE (1.87 cm). This pattern was also seen for the maximum radius and sum of lengths. For

half-length radius parameter; setting 02 showed the lowest RMSE (2.72 cm), followed by setting 05

with 2.92 cm. The highest values for this parameter could be found in setting 09 with 3.29 cm.

26

Graph 2. (a) RMSE per parameter (X-axis) for different settings for branch A; (b) RMSE per parameter (Y-axis) for different settings for branch B.

Graph 2b showed that setting 05 had the smallest overall RMSE, followed by setting 09 for branch

B. Setting 05 had the lowest RMSE on each parameter; while setting 08 displayed the highest

deviation among these parameters (RMSE). Table 3 evidenced that setting 05 had the lowest RMSE

in the minimum radius parameter (1.46 cm), against the maximum value: 1.58 cm (setting 08). The

maximum radius and half radius parameters with the lowest RMSE was setting 05 (1.04 cm and 1.02

cm respectively) and the most deviated RMSE was setting 02 (1.48 cm and 1.38 cm respectively).

The total sum of lengths parameter exhibited the lowest RMSE was setting 05 (32.98 cm) and the

highest RMSE was setting 8 (44.54 cm).

The reliability interval component showed the variability of the repetitions per different settings.

This analysis was done in order to understand the randomness of the cover generation of the QSM

approach. This study ran 10 repetitions for each setting. Then, standard deviation, mean, minimum

and maximum values were calculated to determine variability. A number of branch parameters were

evaluated within this scope, such as total branch volume (l), total number of branches, total length of

branches (m) and DBH (cm). Graph 3 showed the total branch volume for branch A (left settings

with prefix “A”) and branch B (right settings with prefix “B”). For branch A, the standard deviations

between the repetitions were least variable, ranging from 0.186 (A05) up to 0.205 litres (A06). Also,

the minimum value from branch volume ranged from 0.14 (A01) up to 0.167 litres (A05) for branch

A. The maximum value ranged from 0.681 (A09) up to 0.725 litres (A02) for branch A. However,

branch B was more variable, standard deviations ranged from 0.274 (B05) up to 0.482 litres (B08),

with minimum values for volume ranged from 0.995 (B05) up to 1.44 (B08) litres and maximum

values ranged from 1.76 (B05) up to 3.11 litres (B08).

27

Graph 3. Total branch volume parameter. Boxplot showed statistics for each setting (A01 to A09 for branch A and B02 to B09 for branch B).

The total number of branches parameter showed a consistent results for branch A, where all the

settings and its repetition displayed only 1 branch as seen in Graph 4. Nevertheless, for branch B

standard deviations ranged from 1 (B02, B08 and B09) to 2 (B05) branches, with a minimum of

branches between 3 (B08) and 9 (B09). The maximum of branches ranged from 6 (B08) to 11 (B09).

Also, mean values on branch B ranged from 5 to 10. Branch B showed more dispersion between its

repetitions and among its different settings.

Graph 4. Total number of branches parameter. Boxplot showed statistics for each setting (A01 to A09 for branch A and B02 to B09 for branch B).

Graph 5 showed the variability of results for diameter at DBH, for branch A (left) and branch B

(right) at different settings. Branch A revealed that standard deviations fluctuated from 0.168 (A05)

28

up to 0.255 cm (A02). Minimum values of DBH ranged from 6.72 (A02) up to 7.33 cm (A09).

Maximum values oscillated from 7.59 (A02) up to 7.97 cm (A05); finally mean values ranged from

7.11 (A02) up to 7.79 cm (A05). On the other hand, branch B showed more variability in setting

B08, with a standard deviation of 0.83 cm, compared to setting B09, with 0.05 cm. Minimum values

between 3.2 (B02) and 3.36 cm (B08) and maximum values between 3.57 (B05) and 5.65 (B08) were

obtained. Mean values ranged from 3.391 (B05) and 4.024 (B08) cm.

Graph 5. DBH parameter. Boxplot showed statistics for each setting (A01 to A09 for branch A and B02 to B09 for branch B).

Finally, this study also evaluated the variability within the total branch lengths’ on the first and

second order of branches (Graph 6). Branch A only got 1 branch order, while branch B got two

branch orders. The first order of branches (Graph 6a) evidenced that standard deviation were small

compared to Graph 6b and Graph 6c. Standard deviations of 0.03 (A02) up to 0.09 cm could be

found in the first order. Minimum values between 0.23 and 0.43 m were obtained for A06 and A02

respectively. In addition, maximum values for DBH between 0.51 and 0.58 m were found in A09 and

A05 as well. Mean values were ranged from 0.42 (A09) up to 0.48 cm (A02).

29

Graph 6. Branch length parameter. Boxplot showed statistics for each setting (A01 to A09 for branch A and B02 to B09 for branch B).

Branch B had two orders (Graph 6b and c), for the first order of branches; the standard deviation of

the lengths oscillated between 0.18 (B05) and 0.81 m (B08). For the second order, it ranged from

0.214 (A09) up to 1.13 m (B02). For the first order of branches (Graph 6b) minimum values of

lengths fluctuated from 1.5 (B05) up to 2.35 m (B09). Maximum values ranged from 2.14 (B05) up

to 3.67 m (B08). Mean values were variable, from 1.68 m (B05), up to 2.85 m (B09). For the second

order branches, Graph 6c, minimum values ranged from 0 (B08) up to 2.51 m (B09). Maximum

values ranged from 2.82 m (B08) up to 3.28 m (B09). Mean values ranged from 1.11 m (B08) up to

2.87 m (B09).

3.3. Digital defoliated tree scenario

Four datasets were analysed as seen in Figure 7. Figure 7a showed the tree scanned in March,

without leaves, due to winter season. This was our “control dataset” as the most accurate

representation of branches. Figure 7b showed the same tree scanned on June of the same year. This

dataset was our tree “with leaves” dataset. Two more datasets “hardwood > -5 db” and “hardwood >

-10 db” were created from the latter (Figure 7c and d respectively).

The QSM approach ran these datasets for all the settings. Visual inspection of the output model

against the point cloud was our evaluation method in order to discard a setting. Big branches missing

or weird branching pattern were used to reject settings. For the control dataset; settings 03, 04, 07

and 08 were visual accurate. For the tree with leaves dataset; settings 02, 03, 04 and 07 had an

acceptable representation of the point cloud. Finally, for the digital defoliated trees; only settings 04

30

and 07 had an acceptable accuracy. Therefore, the common settings from all the datasets; 04 and 07

were selected for further analysis.

Figure 7. (a) Tree scanned on March. This tree had no leaves and was our control dataset. (b) Same tree scanned on June had leaves and was our tree “with leaves” dataset. From this tree, filtering out the leaves through its reflectance was used to create two more datasets: hardwood > -5 db reflectance (c) and hardwood > -10 db reflectance (d) respectively. Colour pattern for the first two images showed 0 metres (blue) and 15 metres (red) height; and for the reflectance filter, red colour means hardwood and green colour means softwood, which was filtered out.

In order to compare datasets, the QSM approach was executed 10 times with each setting. Then, we

obtained the mean values. The parameters were extracted from file “tree_data” text file. Graph 7

through Graph 9 showed the parameters evaluated (branch length, branch volume and number of

branches). These graphs showed all the repetitions per datasets for two settings (04 and 07) and

displayed by branch order (X-axis). It is noticeable through the parameters assessed, that the dataset

with hardwood > -5 db had the lowest values compared to hardwood > -10 db.

Graph 7. Total branch length per branch order for setting 04 (left) and setting 07 (right). Graph displayed datasets with its repetitions and mean values (filled symbols).

(a) (b) (c) (d)

31

Graph 7 showed the results for the total branch length in meters parameter for the first six branch

orders. This study assumed that the data from the scans of March had the most achievable accuracy

(black squares). Also, to see variability, each repetition was also plotted. For both settings, 04 and

07, the dataset with the most accuracy was the one scanned with leaves (red circles). Then it was

followed by hardwood > -10 db dataset (blue diamonds). Finally, the hardwood >-5 db dataset had

the lowest accuracy (green triangles).

The graph also indicated that at trunk level, all the datasets represented the trunk with high accuracy.

However, a difference between the datasets could be seen from the 1st up to the 3rd branch order,

which the hardwood >-10 db reflectance threshold had the lowest accuracy. This graph also showed

a bigger dispersion between the repetitions, between the 2nd and the 4th branch order. Moreover, the

3rd branch order had the largest length; then it went down from the 4th order. This implied that

beyond the 3rd branch order, the model might be not capable of modelling branches properly.

Table 4. RMSE in metres for total branch length parameter. Setting 04 Setting 07

Hardwood

> -5db Hardwood

> -10db Tree with

leaves Hardwood > -

5db Hardwood > -

10db Tree with

leaves Global 251.19 - 59.25 - 29.40 - 253.06 - 54.55 - 27.80 +

Trunk 1.25 - 3.38 + 1.83 + 1.19 - 1.99 + 2.03 +1st order 42.29 - 17.50 - 12.87 + 47.15 - 24.80 - 10.58 - 2nd order 271.02 - 87.20 - 68.54 - 287.71 - 97.24 - 54.96 - 3rd order 458.82 - 123.20 - 66.35 - 465.89 - 108.81 - 55.89 - 4th order 362.16 - 64.67 - 33.30 + 353.99 - 51.57 - 45.97 +5th order 162.54 - 38.39 + 54.96 + 151.74 - 41.34 + 54.50 +6th order 41.17 - 31.98 + 30.76 + 39.90 - 31.60 + 28.56 +(-) means underestimated values and (+) means overestimated value (against control).

Further analysis with RMSE also confirmed our results (Table 4). Global RMSE for total branch

length parameter showed that tree with leaves dataset had a lower RMSE (29.40 and 27.80 metres for

setting 04 and 07 respectively). This, followed by hardwood > -10 db reflectance threshold dataset

(59.25 and 54.55 metres for the same settings) and, finally hardwood > -5 db reflectance threshold

dataset with 251.19 metres (setting 04) and 253.06 metres (setting 07) respectively. Individual

RMSE analysis per branch order also supported the global RMSE results. This analysis evidenced

that both digital defoliated datasets had larger deviations compared to the complete dataset (with

leaves) in the global RMSE. Table 4 displayed RMSE for the trunk and for each branch orders.

RMSE per individual order for the tree with leaves datasets were smaller compared to both digital

defoliated datasets. And the dataset at hardwood > -5 db reflectance threshold had the largest

deviations, meaning a higher RMSE for both settings.

32

The largest deviation could be seen in 3rd and 4th branches orders; where the RMSE reached 465.89

metres as the highest for the hardwood > -5 db reflectance dataset, compared to 55.89 metres in trees

with leaves dataset (setting 07). Then, at 2nd and 4th branch order still RMSE of both digital

defoliated datasets indicated larger deviation. Only the trunk variable showed a consistent RMSE

throughout the datasets, as shown in Table 4. Also, most of the QSM approach underestimated the

total length of the branches, as most of the results were below our control dataset. This could be seen

for hardwood > -5 db dataset for both settings. For tree with leaves dataset, only the 3rd and 4th

branch order had underestimated values, while the other levels were overestimated.

The total branch volume parameter (Graph 8) also showed a similar pattern to the previous

parameter. Hardwood > -10 db reflectance threshold dataset had the lowest accuracy compared to the

other datasets. For volume, the dataset with hardwood > -10 db reflectance threshold (blue

diamonds) was closer to the control dataset than the dataset with leaves (red circles).

Graph 8. Total branch volume per branch order for setting 04 (left) and setting 07 (right). Graph displayed datasets with its repetitions and mean values (filled symbols).

This graph also showed that the trunk, even though was just the main trunk, had more volume than

the whole branches. Also, this graph evidenced a high variability of volume for the branches,

between the different datasets and among its own repetitions. Bigger dispersion between its

repetitions per order could be distinguished, especially in the trunk and the first three branch orders.

We took the average of the repetitions, since the average data had less variability than individual

repetitions. In addition, it was noticeable that the volume of branches decayed after the 2nd branch

order, from over 1 200 litres in average up to almost 0 litres at the 6th branch order.

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Table 5. RMSE in litres for total branch volume parameter. Setting 04 Setting 07

Hardwood

> -5db Hardwood

> -10db Tree with

leaves Hardwood > -

5db Hardwood > -

10db Tree with

leaves Global 365.94 - 59.84 + 130.72 + 374.90 - 144.42 - 159.87 +

Trunk 252.99 - 195.69 - 231.29 - 305.51 - 345.91 - 298.96 - 1st order 309.01 - 195.68 - 165.83 - 326.39 - 230.25 - 115.22 - 2nd order 583.37 - 120.54 + 257.41 + 609.13 - 165.45 + 213.85 +3rd order 645.40 - 86.19 + 221.39 + 630.03 - 142.35 + 255.19 +4th order 296.40 - 90.28 + 153.72 + 276.57 - 108.60 + 136.53 +5th order 65.73 - 69.58 + 77.74 + 62.91 - 49.47 + 53.17 +6th order 7.43 - 20.28 + 19.94 + 8.01 - 13.36 + 12.05 +(-) means underestimated values and (+) means overestimated value.

Also supporting our results, RMSE for this parameter was also calculated (Table 5). Global findings

also stated that hardwood > -10 db reflectance threshold had least deviation (59.84 litres for setting

04 and 144.42 for setting 07), followed by tree with leaves dataset (130.72 for setting 04 and 159.87

for setting 07) and finally hardwood > -5 db reflectance threshold (365.94 litres for setting 04 and

374.90 litres for setting 07). A more detailed analysis of individual branch level (up to 6th branch

order) also held that hardwood > -10 db reflectance threshold had the lowest deviation in every

branch order, except the 6th one, in which the hardwood > -5 db reflectance threshold showed lowest

deviation.

Larger deviations could be seen from 1st up to 4th branch order, for both setting; up to 645.40 litres

deviated (for hardwood > -5 db dataset) in the 3rd branch order. Individual RMSE showed that

branch volume parameter had larger deviations as a whole, ranging from 7.43 litres up to 645.40

litres. Predicted outcomes also showed and underestimated values, especially for hardwood > 5 db

dataset. For the other datasets, QSM approach overestimated the volume of the branches, especially

in higher branch orders.

34

Graph 9. Number of branches per branch order for setting 04 (left) and setting 07 (right). Graph displayed datasets with its repetitions and mean values (filled symbols).|

The last parameter, number of branches, detailed the number of branches per branch order. As seen

in Graph 9, the dataset with > -10 db reflectance threshold got the lowest accuracy (farthest to the

control dataset). For this parameter, the dataset with leaves achieved the most accurate

representation. The number of branches, for both settings, achieved its maximum in the 3rd order

branches (with a range from 500 up to 900 branches per repetition) and diminished until the 6th

branch order (with less than 200 branches per repetition). This parameter showed a high variability,

shown by the spread of it repetitions throughout the Y-scale. This variability was strong in the 3rd

and 4th branch orders.

Table 6. RMSE in values for number of branches parameter. Setting 04 Setting 07

Hardwood

> -5db Hardwood

> -10db Tree with

leaves Hardwood > -

5db Hardwood > -

10db Tree with

leaves Global 450 - 142 - 76 - 459 - 128 - 70 -

1st order 30 - 20 - 13 - 33 - 22 - 15 - 2nd order 314 - 148 - 107 - 342 - 170 - 112 - 3rd order 721 - 260 - 176 - 755 - 241 - 140 - 4th order 689 - 191 - 63 - 686 - 144 - 53 +5th order 351 - 74 - 80 + 326 - 68 - 87 +6th order 98 - 60 + 63 + 92 - 55 + 57 +(-) means underestimated values and (+) means overestimated value.

Finally, RMSE for this parameter also supported our visual findings, as seen in Table 6. For this

parameter, RMSE was rounded to analyse branch numbers. Global RMSE supported that tree with

leaves had the highest accuracy, and therefore lowest residual and RMSE, it is followed by

hardwood > -10 db dataset, and finally the hardwood > -5 db dataset got the highest RMSE. This

pattern occurred as well in setting 07. Individual RMSE detailed each RMSE per branch order,

35

indicating a larger deviation for hardwood > -5 db dataset, which ranged from 324 up to 755

branches at its maximum. For this parameter, the QSM approach underestimated the number of

branches constructed. Only in the higher branch orders, the approach overestimated them.

3.4. Tropical Forest Tree scenario

Three trees were analysed for this scenario (Figure 8). These trees were located in Tambopata 05 plot

and were scanned during the fieldwork in Peru. Details from the fieldwork were explained in Section

2.1. Figure 8a showed the complete Tambopata plot with the 72 scans. Due to software limitations, a

height filter between the range of 25 and 40 metres was created in order to visualize individual tree

crowns and eased its individual extraction. Figure 8b, c and d showed the selected trees (01, 02 and

03 respectively) after manual extraction and point cloud cleaning.

Figure 8. (a) Birds eye point of view of Tambopata 05 Plot with height filter from 25 (blue) to 40 (red) metres. (b), (c) and (d) show the selected trees after pre-processing (tree 01, tree 02 and tree 03 respectively). Colours mean height between 0 (blue) and 35 metres (red).

Tree profiles were obtained from the point cloud data for each tree. Graph 10 showed the tree profile

for tree 01. This graph showed the reconstructed tree formed from each point data (left) and its

corresponding point density for every 5 cm (right). From this profile, some tree parameters can be

inferred. The height of the tree went up to 30 metres, with a crown diameter up to 22 metres. The

tree profile showed the point density; with a high amount of points from 20 to 30 metres, defining

the tree crown. The main trunk of the tree could be seen on the first 20 metres. It was noticeable the

higher density of points the first 5 metres, and the decay after the first 5 metres.

(a) (b) (c) (d)

36

Graph 10.Tree profile of tree 01 (right) and, its corresponding points (left).

On the same way, Graph 11 displayed the vertical tree profile for tree 02. This tree had a different

vertical profile pattern, with more than the main trunk, and a less dense canopy. The height of this

tree was 25 metres, smaller than the other trees. Also, the crown diameter was a bit smaller, 16

metres. This tree had a less dense canopy, with two differentiated peaks between 20 and 25 metres.

This could be seen in the point cloud, where there were two main tree crowns. As explained before,

this tree also presented a denser point cloud the first 5 metres, which decay after the first 5 metres.

Graph 11. Tree profile of tree 02 (right) and, its corresponding points (left).

Tree 03 vertical profile is displayed in Graph 12. This tree was the tallest of the displayed tree, with

32 metres height. Also had the widest crown, with a 20-meter diameter crown. The canopy was

37

between 25 and 30 metres above. Also, it had a fewer point cloud, with a peak of 3 000 points in the

canopy, compared to the other trees, which had over 6 000 point at its peaks.

Graph 12. Tree profile of tree 03 (right) and, its corresponding points (left).

Using QSM approach, the model was able to determine the total branch length (metres) per branch

order, the number of branches and the branch volume (litres) of the trees. This study also evaluated

the randomness of the model, as seen in Graph 13, Graph 14 and Graph 15 (for branch length,

number of branches and volume parameter respectively).

Graph 13. Total branch length per branch order for setting 04. Graph displayed trees with its repetitions and mean values (filled symbols).

Graph 13 displayed the total branch length in metres for the three trees. This graph showed that tree

01 had more branches from the 3rd branch order, compared to tree 02 and 03. This also confirmed a

38

denser canopy for tree 01, compared to the other trees. However, this graph also showed that data is

very variable, getting differences of 200 metres long among its repetitions (4th branch order of tree

01 for example). The variability of the repetitions was more noticeable in tree 01 than tree 02 and 03.

Tree 02 had the least variable output for this parameter.

Graph 14. Number of branches per branch order for setting 04. Graph displayed trees with its repetitions and mean values (filled symbols).

Graph 14 displayed the number of branches per tree. Tree 01 had more branches, especially after the

3rd branch order, which meant a denser canopy structure compared to the other two trees. The range

of branches at these orders ranged from 500 up to 800 branches per branch order for tree 01. In the

same branch orders, tree 02 and tree 03 had between 100 to 300 branches per different orders. We

could distinguish also variability among each repetition, especially more noticeable in tree 01, with

more than 300 branches at the 4th branch order.

Graph 15 showed the branch volume in litres at different branches order. Tree 03 trunk had a volume

of 12 000 litres, compared to tree 01 and 02. This meant an overestimation of the trunk volume. This

applied for trunk volume of tree 02, which had a volume of 6 000 litres.

39

Graph 15. Total branch volume per branch order for setting 04. Graph displayed trees with its repetitions and mean values (filled symbols).

For all trees extracted, branch-level scaling exponents for length and radii were Gaussian densities

and not significantly different among trees (Graph 16):

Graph 16. Branch –order scaling exponent for length (left) and radii (right) for tree 01 (black line), 02 (green line) and 03 (blue line). Theoretical WBE expected exponent for length (0.3) and for radii are shown in red (0.5). Dashed vertical lines show the calculated mean of each tree scaling exponent.

Across all trees, the calculated branch-level length scaling exponent varied from 0.30 to 0.38 and the

calculated branch-level radii scaling exponent ranged from 0.44 to 0.51 (Table 7). Using Equation 3,

the calculated (estimated) metabolic rate scaling exponent was 0.70, 0.78 and 0.81 for tree 01, 02 and

03 respectively. All calculated exponents overlapped with the predicted exponents from the WBE

model.

40

Table 7. Scaling exponents for branch length and radii

Length scaling

Confidence interval

Radii

scaling Confidence

interval

Estimated metabolic rate

scaling Tree 01 0.38 0.36 - 0.41 0.51 0.49 - 0.54 0.7 Tree 02 0.38 0.33 - 0.42 0.44 0.4 - 0.49 0.78 Tree 03 0.3 0.25 - 0.36 0.46 0.4 - 0.52 0.81

41

4. Discussion

4.1. T-LiDAR and tropical forests trees

Several authors, such as Lovell (2011), Saatchi (2011) and Thies (2004) had already described the

advantages of using T-LiDAR scans for delivering point cloud data in a reliable, accurate and non-

destructive way compared to traditional forestry measurements. Nevertheless, this study reveals that

scanning trees in tropics and extracting tree parameters means new challenges to overcome due to

characteristics of the tropical forest; such as (1) dense vegetation causing high occlusion, (2) strong

wind on the top of canopies, (3) high presence of cellulose and lignin in leaves, and (4) the high

humidity content.

Figure 9. Cross section of Tambopata 5 plot. High vegetation density interferes with the instrument and the object of interest (tree).

One of the most difficult challenges to overcome using T-LiDAR was occlusion due to vegetation

(Figure 9). Even more in tropical forest, where hyper-diverse communities compete for nutrients and

light in a highly dynamic environment. Our results support the idea that occlusion is significant in

tropical forest and might cause the loss of part of the trees. This was reported as well by Zhao

(2013), who found that T-LiDAR may miss canopy tips of dominant trees due to occlusion. Bienert

(2007) also reported that occlusion caused misdetection of trees; and Pfeifer (2004) stated that it is

impossible to get all the points around the crown branches.

This limitation can be improved by taking scans from different positions. This is a strategy widely

used in order to minimize occlusion; even though, it does not eliminate it. To minimize it, this study

took several scans from different positions in order to increase the visibility of trees from different

angles and distances. The plot was covered with 36 scan positions, every 20 meters to complete 1 ha

42

plot. Other studies also employed the same strategy; Bienert (2006) stated that having only one view

position can restrict the amount of data collected. Kankare (2013) also reported the use of multiple

scans results in a highly reconstruction of individual trees.

Another challenge encountered during the fieldwork and the analysis of data was the presence of

wind during the scan collection. Salis (2012) reported wind between 69 and 90 km/h in the Brazilian

amazon rainforest. During scans, the presence of wind moved the upper branches and canopy, adding

uncertainty to the point cloud by distorting the scan. This has been already reported by Henning

(2006). This certainly affects the analysis of tree parameters. This was observed by Xu (2013) who

found that wind might explained the deviation in measurements in trees. Hence, it is not recommend

scanning trees when it is very windy, since the uncertainty added might cause deviations in the

calculations.

Relevant characteristics of tropics are the content and lignin in its vegetation and the high humidity

of the environment. The laser beam of T-LiDAR is close to the NIR water-absorption band and is

heavily influenced by water content. High content of water outside the leaves (from a rain shower,

for example) reduces the reflectance of the object, acquiring fewer data back per scan. On fieldwork,

scans needed to wait until the most of the leaves were dry in order to begin the scan.

With respect of the presence of high content of cellulose and lignin in the leaves of tropical trees is a

limitation for setting a threshold for reflectance values. Lovell (2011) found that the reflectance of

trunks varies between species and age. However, further researches evidenced a consistent threshold

for his study. Our results also showed that the tree scanned in Wageningen campus had a well-

defined threshold (-10 db reflectance threshold), compared to the amazon tree forest, which the same

threshold was not able to extract softwood. Even, no threshold was able to successfully extract

softwood from hardwood in this study. The presence of this metabolite was observed by Bloomfield

(1993), who stated that in tropical forest, many tissues contains secondary chemicals, which helped

them to be less vulnerable to attackers. Also, Asner (2011) found greater concentrations of lignin and

other secondary metabolites in foliage. The high content of these metabolites might interfere with the

softwood filtering.

On the other hand, fieldwork done for this research revealed that correct T-LiDAR settings used for

scanning must be taken into account for an accurate measurements in tropics. There is no standard

methodology, and this varies upon different variables; such as, parameter measured, tree type,

43

environment, instrument settings. It is relevant to (1) evaluate T-LiDAR different settings, and (2)

design a proper scan pattern adapted to tropical forest environment.

Figure 10. Point cloud density at 25 metres height. This study found out that branching point cloud inside the crown of the tree is unclear and present structures; such as small branches or leaves are not easily distinguish.

Point density is a relevant factor associated with tree modelling. This study observed that occlusion

and distance from the instrument influenced the point cloud data and its further analysis. The

presence of high dense vegetation limited the tree coverage and made difficult to scan inside tree

crown. Also, distance from the scanner limited the coverage of points (Figure 10). The tree profiles

from the tropical trees support this argument. Our results evidenced that there was a loss of point

density across the trunk after 5 metres height (Figure 1 to Graph 12). This might be caused by the

occlusion from the surrounding vegetation, which caused an incomplete point cloud of the tree.

Similar findings were reported by Henning (2006), who founded a loss of accuracy after 10 metres

height, by a reduced amount of points in such heights. He effectively quadrupled the point density by

increasing the point density up to 0.027 degrees and got more points up to 10 metres height.

Setting the most appropriate configuration for scanning tropical forest is ideal. Tropical forests are

already a challenging environment; dense occlusion caused by vegetation, strong winds moving trees

and among other variables had to be taken into account in order to have a reliable scan. Due to this, it

was relevant to design a scan pattern which could systematically scan a complete plot. This research

scanned 72 times Tambopata 05 plot with two scan modes, one in upright mode and a tilted mode.

This two combined, assembled a full-hemispherical scan. Besides that, we created a scan a complete

1 ha plot with 72 scans. We used at least 16 tie points per scan to link to each other. A similar study

by Bienert (2007) reported that at least 3 tie points were necessary to merge point clouds, but the

more the more accurate.

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4.2. Details of the tree modelling approaches

Every approach analysed by this study supported the potential of T-LiDAR scans for extracting tree

parameters. Each of these approaches analysed the point cloud in different ways. The first two

approaches use only sections of the tree for its analysis. This is the case of the circle fitting approach

(Bienert et al., 2007) which uses a best circle fitting method on a point cluster based on segments.

Also, the cylinder fitting approach (Thies et al., 2004) uses cylinder fitting methods instead of circles

based on segments. In a very different approach, identifying a complete volume structure, the voxel-

based processing (Gorte & Pfeifer, 2004), constructs the tree structure in a 3D voxel space. In the

same way, the Probabilistic 3D branch reconstruction (Binney & Sukhatme, 2009) generates a

complete tree model from a probabilistic method and, finally the QSM (Raumonen et al., 2013) used

patches to create cylinders throughout the whole tree.

As expected, different approaches result in different parameters calculated. The first two approaches,

circle fitting and cylinder fitting, can measure cross sections of tree, DBH, and stems. Circle fitting

also calculates tree height and tree position in the plot. The other three approaches, voxel-based,

probabilistic 3D branch reconstruction and QSM, are able to extract more parameters; volumes,

distribution of branches, tree height, DBH, and even angle and bifurcation frequency from the point

cloud data.

Most of the approaches analysed by this study are on-going researches, which have their own

limitations and need to be refined and improved in several characteristics. The biggest limitation

founded throughout the approaches is occlusion. Algorithms needed a minimum number of points all

over the study model in order to interpolate data. This point density depends on the distance of the

tree, the scan resolution and the thickness of the branches. Pfeifer (2004) reported that reconstruction

process performed very well with four scans, but some small branches were grouped into larger

segments. Also, Bienert (2007) reported to reduce occlusion and improve accuracy with three scans

around a tree.

Another limitation founded during this research was the one tree analysis per batch. The cylinder

fitting, voxel-based, probabilistic 3D branch and QSM approaches still need a single clean tree to

execute their algorithms. As a pre-processing step, manual delineation of the tree is necessary. The

tree needs to be identified, separate from the point cloud, and cleaned from points which do not

belong to the tree. This task can be tough, especially in dense vegetation such as tropical trees, where

vegetation density is very high and complicates the extraction of a single tree. Circle fitting is able to

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extract DBH from an area with several trees; however, false positive occurs when the algorithm

identifies tree parameter in point cluster where there are no trees.

A key topic which all approaches addressed is validation. It is hard to validate a complete branching

modelling scheme since it is practically impossible to measure all the branches for a whole tree. For

example, Binney (2009) tested his algorithm with simulated data. When tested with measured data,

his results were based from a leafless branch instead of a tree in a controlled environment. Another

study, conducted by Bienert (2006) only had tree height reference measurements from two trees in

the plot; moreover, these measurements were calculated by extrapolations from DBH. The height

differences between digital and measured data were 0.22m and 1.47 m. On another research, this

author used a tachymeter and measured four trees. RMSE indicated a deviation of 0.80 m. He stated

his doubts about using conventional hand-held tachymeter as reference data. On a summary,

approaches to extract tree parameters from T-LiDAR data are still on a young stage, however, they

already pointed out the relevance of T-LiDAR scans as an accurate alternative source.

4.3. Limitations and improvements of the QSM approach

This research exploits the potentialities of the QSM approach for branch architecture modelling.

Throughout the whole research, the QSM was used to model individual branches, a European tree

and tree tropical trees with an acceptable visual accuracy. However, the QSM is still an algorithm in

constant development and improvement; thus some remarks need to be taken into account such as,

(1) the robustness of the approach is linked to the quality of the point cloud, (2) the intrinsic

randomness of cover generation, (3) the number of variables used for executing the algorithm, and

(4) the lack of control data for validation.

We already discussed in the first section about the challenges of getting a reliable point cloud from a

T-LiDAR. This has a direct impact in the modelling approach, since the robustness of the model is

function of the quality of the measurements. The model based its function on the point cloud data,

and if there are parts are not covered or if there is a low density of points, the algorithm might not be

able to reconstruct that part correctly. This issue has been already addressed by Raumonen (2013),

who reported issues with T-LiDAR data concerning missing parts which were not reconstructed. One

issue this study addressed was the presence of leaves; our results indicated that there is no difference

to filter out the leaves from the tropical tree point cloud before running the algorithm. Nevertheless,

Åkerblom (2012) indicated that the presence of leaves on a coniferous tree added noise and increase

the diameter of branches in the output model.

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The version of the QSM approach used 10 variables. From these variables, this study used 6 to assess

the performance (Table 1). In order to understand the behaviour of each of the parameters, a

literature research and conversations with experts gave us an insight on the influence of some

variables in the result model. The variables which had a strong influence over the outcome model

tree are dmin, rcov and nmin. The dmin ranged from 0.02 up to 0.08 m, rcov ranged from 0.025 up to

0.085 m and nmin ranged from 3 up to 7.

For the first scenario, the branch measurement scenario ran the 10 settings and visual inspection

selected the ones which resembled the most to the point cloud. Setting 01, 02 05, 06 and 09 were

selected for analysing branch A. These settings had dmin between 0.02 and 0.04 m; rcov between

0.025 up to 0.045 m and nmin between 3 and 5. For branch B, this research found out that settings

02, 05 08 and 09 were the most visually accurate ones. The dmin ranged from 0.02 up to 0.08 m,

rcov from 0.025 up to 0.085 and nmin from 3 to 7. In both branches, setting 05 was the one with

lowest deviation compared to the real measured branches. This setting had a dmin of 0.02 m and rcov

of 0.025 with an nmin of 3. The small values of the variables used would help the accurate definition

of the fine branches, since fine branches needed a fine cover to proper execute the model.

In the same way, for the Digital defoliated tree and tropical tree forest scenario, visual inspection

selected setting 04 and 07 for the first scenario and setting 04 for the latter. Both settings used 0.08,

0.085 for dmin and rcov respectively; however, nmin varies from 3 to 5 for each one. In both

scenarios, an increase in dmin and rcov was necessary in order to model wider branches, compared to

the first scenario. Another study conducted by Disney (2012) showed that branches smaller than

dmin was not be recognized at all, and merged with its parent’ branch or deleted. This supported our

finding that smaller values of dmin influenced the threshold of calculating the minimum branching

diameter. By decreasing the dmin variable, you were be able to model branches with smaller size, a

and captured more detail; however you were adding more noise to the output model and required

more computational time.

Another strong point into consideration in the QSM was the randomness of the algorithm. The

algorithm used two cover sets which are randomly generated; therefore every execution of the QSM

model using the same point cloud and variables returned different results; in most of the cases, just

slight differences between them. This could be observed in the branch measurement scenario, where

we compared the variability of branch volume, number of branches, length of branches and DBH.

The standard deviations showed slight variability for these parameters for these branches. For the

digital defoliated tree, the randomness showed a variation between each run from an average of 800

47

litres for the branch volume, 200 branches per execution and 200 metres total length. In order to

tackle this variability, it is recommend averaging between 5 – 20 repetitions and using the average of

the data.

Lastly, one issued found during the research, was the validation of the QSM. For the sample

branches analysed in the first scenario, validation with manual measurements was feasible because of

the few samples; 3 and 16 branches for A and B branches. For the second scenario, since measure the

complete tree was not feasible, validation was done by comparing with a complete modelled tree as

our “control” dataset. However, visual validation was done in order to see if the reconstructed tree

was accurate against the point cloud. Similar methodology was also conducted by Raumonen (2011).

In his study, he used visual assessment as validation control, since he was not able to use reference

data.

4.4. Scaling of whole tree branch length, branch radii, and metabolism

For the three trees scanned in the Peruvian Amazon rainforest, calculations of tree scaling

metabolism derived from T-LiDAR scans showed consistent and similar values, between 0.3 up to

0.38 for length ratio exponent, between 0.44 up to 0.51 for radii ratio exponent and between 0.70 and

0.81 for the estimated metabolism rate respectively Since the three scanned trees were most likely

different species, these results provide evidence to support the WBE assumption of similarities in

branching structure and common set of branching rules across trees. In empirical analyses of inter-

specific tree branching patterns, similar branch-level exponent estimations were also observed by

Bentley (2013) and Vasseur (2012).

In an examination of 9 different trees from temperate and tropical regions, Bentley (2013) showed

that the scaling of branch radii was less variable than the scaling of branch length. These results

support the WBE assumption that energy minimization for water transport leads to minimization of

hydrodynamic resistance. More specifically, this assumption implies that changes in radius lead to

bigger changes and more use of energy than changes in length; thus trees are more able to respond to

their environment through changes branch length compared to branch width. This suggests a

constraint in space-filling branching, linked directly to crown gaps or light competition.

Nevertheless, the current study could not find a strong evidence of this variability; length and radii

were equally variable. While it might be possible that Bentley’s (2013) results were driven by the

inclusion of a large number of temperate trees, it is more likely that increased variability in length

scaling was not observed here because the trees studied were large, canopy trees. Thus, these mature,

48

emergent trees did not have high light competition and as such their branching structure could

potentially be in close equilibrium with the demands from the surrounding environment. In the

future, it would be useful to analyse more trees and their surrounding light environment demands to

further explore this variability.

Importantly, not only were calculated scaling exponents similar for all trees, calculated scaling

exponents were not statistically different from WBE model predictions. Deviations from the WBE

exponents were observed by Bentley (2013), especially for the calculated expected metabolic rate

exponents. It is possible that these deviations from the WBE predictions were not observed here due

to the maturity of the sampled trees. It has been shown that the WBE model predictions apply more

closely to trees that are larger and closer to the limits of an infinitely sized network (Savage et al.,

2008).

Lastly, these above findings are extremely relevant to field of ecology for the scaling of whole tree

carbon and water use. Currently, the only way to extract these branch-level parameters from trees is

to painstakingly measure each branch part by hand. This procedure can take hours and only extracts

parameters from part of the tree. Here, by coupling T-LiDAR with image processing codes in

Matlab® and R®, we are able to extract branch-level parameters from a much larger percentage of the

whole tree (and even in some cases from the whole tree). Thus, this fast and relatively easy way to

calculate branch-level scaling exponents has the potential to revolutionize the ability to calculate the

scaling of whole tree carbon and water use. Not only will researchers be able to calculate exponents

for trees of much greater sizes than possible by hand, it will be possible to process a greater number

of trees in much less time.

4.5. Applications and future use

This research revealed that using T-LiDAR for extracting parameters it is on its early steps; yet, so

far has shown a lot of potential for different approaches and interests. This study focused on branch

modelling approach and its relation with plant scaling exponent metabolism; but combining ground

measurements with airborne LiDAR and other remote sensing imaging and ranging sensors open a

whole new opportunity for developing novel techniques and more accurate algorithms to understand

the ecological processes in tropical forests.

In addition, present tree modelling approaches are still in experimental phase or haven’t been tested

in a different range of trees, such as tropical trees. By expanding their use towards new and different

49

approaches will make these algorithms more accessible to the scientific community. this will

increase their interest and continuous feedback, improving the understanding of the modelling

processes of trees.

50

5. Conclusions

T-LiDAR scans, in combination with automatic branch architecture algorithms, may shorten the

existent breach between conventional forestry allometry (which are based on small plots, and

estimated from extrapolation techniques) and airborne LiDAR (which acquires wide areas, but

limited to some tree parameters derived from terrain and crown height model). Our results supports

that (1) T-LIDAR can deliver a reliable 3D point cloud of the tropical forest, (2) this point cloud can

be used and processed by tree modelling approaches, and (3) there is potential number of tree

parameters which can be calculated with high accuracy from the T-LiDAR scans.

The tree modelling approaches reviewed in the exploratory literally review (1) support and

encourage the use of T-LiDAR point cloud data as input parameter for tree modelling, (2) analyse

the point cloud through different methodologies and successfully calculate tree parameters, (3) are

still on-going researches and can be used knowing beforehand its own limitations and boundaries,

and (4) still needs to be refined and improved to get more accurate results.

The tree 3D models resultant from the Quantitative Structure Model approach and T-LiDAR scans in

the study support that (1) QSM approach is a stable model, able to model tropical trees from T-

LiDAR scans, (2) the model is sensitive to different input parameters, (3) point density needs to

enough for deriving tree parameters at higher distances, and (4) randomness plays has to be taken

into account in the modelling.

The tree scaling metabolism derived from T-LiDAR scans in this research evidenced that (1) length

ratio exponent, radii ratio exponent and estimated metabolic rate converge between the tropical trees

analysed, (2) there is no strong evidence to support that tropical trees has more ability to respond to

change branch length than branch width, and (3) length ratio exponent, radii ratio exponent and

estimated metabolic rate from the tropical trees analysed are not consistent with their predicted

values.

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7. Appendices

Appendix I. Tree inventory in Plot Tambopata 05.

Top 40 trees

1. 'Cedrelinga cateniformis' 2. 'Pseudolmedia laevis' 3. 'Bertholletia excelsa' 4. 'Roucheria punctata' 5. 'Pourouma minor' 6. 'Brosimum lactescens' 7. 'Pseudolmedia laevigata' 8. 'Leonia glycycarpa' 9. 'Jacaranda copaia' 10. 'Clarisia racemosa' 11. 'Ocotea bofo' 12. 'Pterocarpus indet' 13. 'Huberodendron swietenioides' 14. 'Hebepetalum humiriifolium' 15. 'Bixa arborea' 16. 'Eschweilera coriacea' 17. 'Calophyllum brasiliense' 18. 'Acalypha indet' 19. 'Licania heteromorpha' 20. 'Iriartea deltoidea' 21. 'Enterolobium schomburgkii' 22. 'Iryanthera juruensis' 23. 'Hevea guianensis' 24. 'Coussapoa trinervia' 25. 'Anthodiscus peruanus' 26. 'Alchornea triplinervia' 27. 'Pouteria torta' 28. 'Pseudolmedia macrophylla' 29. 'Micropholis guyanensis' 30. 'Minquartia guianensis' 31. 'Hymenaea parvifolia' 32. 'Helicostylis tomentosa' 33. 'Pourouma guianensis' 34. 'Hymenaea oblongifolia' 35. 'Sclerolobium bracteosum' 36. 'Sterculia tessmannii' 37. 'Ouratea indet' 38. 'Rollinia centrantha' 39. 'Tachigali polyphylla' 40. 'Meliosma herbertii'

Source: Alexander Shenkin2

2 Post-Doctoral Research Assistant. School of Geography and the Environment. University of Oxford, United Kingdom.

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Appendix II. Output results

cyl_data _(filename).txt

Radius Length X-coordinate Y-coordinate Z-coordinate

Radius of the cylinders

Length of the cylinders

X-coordinate of the starting point of the cylinder

Y-coordinate of the starting point of the cylinder

Z-coordinate of the starting point of the cylinder

X-component Y-component Z-component Index1 Index2

X-component of the cylinder axis

Y-component of the cylinder axis

Z-component of the cylinder axis

(row number in this file) of the parent cylinder

(row number in this file) of the extension cylinder

Branch Branch order Belonging Added

(row number in the branch data-file) of the cylinder

Branch order of the branch the cylinder belongs

Running number of the cylinder in the branch it belongs

Indication if the cylinder is added after normal cylinder fitting (=1 if added)

branch_data _(filename).txt

Branch order Index Volume of the

branch (L) Length of the branch (m)

Branching angle (degrees)

0 for trunk, 1 for branches originating from the trunk, etc.

(Row in this file) of the parent branch

Sum of the volumes of the cylinders forming the branch

Sum of the lengths of the cylinders

Angle between the branch and its parent at the branching point

tree_data_(filename).txt

Attribute Attribute 1. total_volume 2. Trunk_volume 3. Branch_volume 4. Total_height 5. Trunk_length 6. Branch_length 7. Number_of_branches 8. Maximum_branch_order 9. Total_cylinder_area 10. DBH_(cylinder) 11. DBH_(triangulation) 12. Trunk_volume_(cylinders) 13. Trunk_volume_(triangulation) 14. Trunk_length_(cylinders) 15. Trunk_length_(triangulation) 16. Number_of_1-order_branches 17. Number_of_2-order_branches 18. Number_of_3-order_branches 19. Number_of_4-order_branches 20. Number_of_5-order_branches 21. Number_of_6-order_branches 22. Volume_of_1-order_branches 23. Volume_of_2-order_branches 24. Volume_of_3-order_branches 25. Volume_of_4-order_branches 26. Volume_of_5-order_branches 27. Volume_of_6-order_branches 28. Length_of_1-order_branches 29. Length_of_2-order_branches 30. Length_of_3-order_branches 31. Length_of_4-order_branches 32. Length_of_5-order_branches 33. Length_of_6-order_branches

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Appendix III. Branch Measurement Protocol

Protocol by D.Phil. Lisa Bentley3

Summary

This document briefly outlines a methodology to comprehensively measure the branching architecture of an individual tree or branch. At the core of this methodology is the relationship between a uniquely numbered branching node and its parent. From this relationship and measurements associated with branch segments much of the plant’s architecture can be reconstructed.

Goals

Central goals of this measurement scheme are the calculation of lengths and radii ratios and branching ‘furcation’ (i.e., how many branches arise at a given node). However, we can extract a number of other important quantities of the network if we;

give each branching node a unique ID,

if we relate each new ID to its parent ID (the larger diameter node that preceded it, and

if we associate branch measurements to each node unique to that branch.

This scheme will allow us to measure branching generations and total lengths along each path from the base to particular tip as well as the variability of these characteristics. Also, a variety of more complex network characterization schemes may be applied to these data (e.g., Turcotte et al. 1998. J. Theor. Biol.).

Theoretical background

Consider the following diagram, we starting at the bottom (base)

assigning each node a new ID number,

noting the parent node (could be recorded as ‘base’ at the bottom),

determining the number of branches at the node, i.e., furcation, n (though this could be

calculated later from the information in 1 and 2 but it is simple to collect and may be used for

quality control),

determining whether the node is a branch or a branch tip (which must be numbered uniquely

like a node but may have special measurements such as leaf area or number),

3 Post-Doctoral Researcher. School of Geography and the Environment. University of Oxford, United Kingdom.

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and by associating branch or tip measurements such as length, radius, or leaf number with the

node, a vector we could call v.

We can record all of this as the following vector (Node ID, Parent ID, Tip?, n, v), as shown in the figure (where v is indexed to the node).

Note that “P-” indicates “Parent” node just for clarity. Please also note that there is no specific importance to the assignment of node IDs and that the example tree above has been ‘chopped off’ and does not show the tips on the major branches. The spread sheet would look something like the following where we have included columns for the number of leaves at tips and notes:

Node ID Parent Is Tip n (furcation) # of Leaves at tip Branch Measurement columns, v…

Aa Base NO 2 NA vAa Ab Aa NO 2 NA vAb Ad Ab YES NA 0 vAd Ac Ab NO 2 NA vAc Ba Aa NO 3 NA vBa

To be more specific regarding branch measurement columns, we are interested in branch diameters, internode lengths, and the number of leaves at each node (if available).

This method includes no (or almost no) assumptions about side branching. Since we can easily reconstruct the relationships between branches of this tree from our dataset, we can go back and apply whatever scheme for classifying lateral branches that we would like, e.g., if the smaller branch is less that 1/10 the larger branch(es) it is a ‘side branch.’ This—our ability to unambiguously ‘reconstruct’ the tree—is the power of the proposed approach.

Field methods: Equipment needed:

Sharpie pen and/or tape for marking branch segments

Ruler or calipers for measuring diameters and lengths

Envelopes or bags for sample preservation

Hand pruners or hand saw for cutting branches

Data book for recording measurements

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Field methods: Measurement protocol

1) Label each node starting with the bottommost branch by attaching a piece of tape or writing directly on the branch using a Sharpie pen with the node identification number. Use a numbered (1, 2, 3, …) or lettered (Aa, Ab, Ac…) scheme depending on what you think is easier. Focus one branch at a time. Carefully work your way through every node of your selected branch. Here is another diagram as an example:

2) Record the node ID number, parent node to which it is attached, if the node is a tip, the node’s branching furcation number, the number of leaves at the node (if available). Also label if a leaf is missing because it was used for photosynthesis measurements. See example table above and photo below. Two people can be very useful for this process; one to write the number on the node, and one to record the data in data book.

3) Once the whole branch is labelled, cut each major branch; take measurements and record in book:

Distal diameter (the diameter at the

beginning of the internode)

Proximal diameter (the diameter at

the end of the internode) *Note: Diameter

tends to flare at the nodes so take your measurements slightly away from the flare.

Internode length (length measured from centre to centre of each node)

4) Note that branch may not have to be cut to be measured. It might be easier to measure on the branch. Once done measuring, use branch for wood density/anatomy analyses and then discard.

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Appendix IV. Branch Measurement Filling Form

Based on the work of Ph.D. Lisa Patrick Bentley

Place Branch Date N° of scans Evaluator Angle Node Parent Tip Inferior radius

(cm) Superior radius (cm)

Length (m)

Half-length radius (cm)

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Appendix V. Real measurements: branch A and B

Place Wageningen Branch A Date May 2nd 2014 N° of scans 4 Evaluator Alvaro Lau Angle 0.06 Node (sections)

Parent Tip Inferior radius (cm) (maximum radius)

Superior radius (cm) (minimum radius)

Length (m)

Half-length radius (cm)

0 Base N 0.0579 0.0568 1.492 0.0224 1 0 N 0.0500 0.0471 0.414 0.0482 2 0 N 0.0267 0.0205 0.604 0.0535

Place Wageningen Branch A Date May 2nd 2014 N° of scans 4 Evaluator Alvaro Lau Angle 0.06 Node (sections)

Parent Tip Inferior radius (cm) (maximum radius)

Superior radius (cm) (minimum radius)

Length (m)

Half-length radius (cm)

0 base N 0.0433 0.0470 0.3010 0.0433 1 0 Y 0.0279 0.0221 0.3800 0.0245 2 0 N 0.0403 0.0393 0.0840 0.0388 3 2 N 0.0053 0.0041 0.1460 0.0049 4 3 Y 0.0032 0.0013 0.6730 0.0021 5 3 Y 0.0032 0.0013 0.4410 0.0022 6 2 N 0.0377 0.0376 0.1930 0.0374 7 6 N 0.0105 0.0054 1.6700 0.0076 8 7 Y 0.0048 0.0005 0.8500 0.0030 9 7 Y 0.0038 0.0003 0.7210 0.0016 10 6 N 0.0393 0.0393 0.0550 0.0393 11 10 Y 0.0371 0.0032 0.4900 0.0045 12 12 N 0.0393 0.0371 0.0590 0.0390 13 12 Y 0.0067 0.0016 0.4510 0.0056 14 12 N 0.0371 0.0355 0.2230 0.0379 15 14 Y 0.0201 0.0172 0.1860 0.0186 16 16 N 0.0355 0.0342 0.1210 0.0352

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Appendix VI. Input template for WBE scaling model

Node ID Parent Is Tip/Scar?

n (furcation)

Length (cm)

# of leaves (per node)

Weight of leaves (g)

…

1 0 NA 29 4189.53 NA NA

2 1 NA 0 47 NA NA

3 1 NA 33 3299.38 NA NA

… … … … … … …

… Average weight of

each leaf (g)

dlow (mm) dhigh (mm) Age (Proximal yr)

Age (Distal yr)

Leaf area (cm2)*

NA 2.5 344.8 NA NA NA

NA 20.1 40.2 NA NA NA

NA 24.8 133.2 NA NA NA

… … … … … …