Dissertation

i
Determining Carbon Content in a
North England Sitka Forest Using
Terrestrial and Airborne Laser
Scanning
Darcy Glenn
11,997 words
Thesis submitted for consideration towards a degree of
MSc Climate Change,
Dept of Geography,
UCL (University College London)
September 2016

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UNIVERSITY COLLEGE LONDON
MSc Climate Change
Please complete the following declaration and hand this form in with your MSc Research
Project.
I, Darcy Glenn
hereby declare :
(a) that this MSc Project is my own original work and that all source material
used is acknowledged therein;
(b) that it has been prepared specially for the MSc in Climate Change of University
College London;
(c) that it does not contain any material previously submitted to the Examiners of this
or any other University, or any material previously submitted for any other
examination.
Signed : ....................................................................................
Date : .....................................................................................

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Abstract
Climate change is driving a focus on carbon budgets as nations work to make human activities
carbon neutral (United Nations, 2015). Great Britain can use the carbon absorption from its
Sitka Spruce forests to offset some of its emissions. This would require large scale monitoring
to ensure the carbon budget was accurate. Airborne Laser Scanning (ALS) data provided the
ability to take height measurements over an entire forest (Calders et al., 2014), however an
equation to convert from height to volume was not easily accessible for North England Sitka
Spruce. Therefore highly detailed measurements were taken in June of 2016 using a Terrestrial
Laser Scanner (TLS) (Raumonen et al., 2013) at Harwood Forest, a lumber plantation in
Northumberland, England (Zerva and Mencuccini, 2005). These TLS scans allowed height and
volume to be determined for a 46 trees of varying sizes. An allometric equation of the form
V=ahb
was found to be the best fit for the data (Fowenban et al., 2012). The equation was
applied to ALS data from Harwood Forest previously collected by the Natural Environment
Research Council (Www2.geog.ucl.ac.uk, 2003) and to Keilder Forest’s ALS data provided by
the Environmental Agency (Environment.data.gov, 2016). Using a basic density of 350kg/m3
(+50 kg/m3 or -20 kg/m3) and a percentage carbon content of 47.5% (+5.5% or -1.91),
Harwood was found to hold the equivalent of 3,050 tonnes (+838 tonnes or -351 tonnes) of
carbon dioxide emissions. Assuming that Kielder Forest is made up of only Sitka Spruce and
the allometric equation holds for tree heights outside the allometric training set, Kielder Forest
could be sequestering the equivalent of 36,200 tonnes (+10,000 tonnes or -4,140 tonnes) of
carbon dioxide emissions of carbon dioxide. These uncertainties do not consider uncertainties
in TLS and ALS data. Reducing uncertainties will require relating the Harwood ALS data
schedule to be taken later this year to the recent TLS ground measurements. The carbon content
of the forests are relatively small compared to Great Britain's over 500 million tonnes of carbon
dioxide annual emissions (Department of Energy and Climate Change, 2015), but hopefully
the height based equation developed in this study can be applied to other forests along the
English-Scottish border. The equation's viability in other forests will require both ALS and
TLS from those forests. Regardless, the method described in this paper is a potential option for
wide spread carbon monitoring in Great Britain.
Word Count: 11,997

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Acknowledgements:
Firstly, I would like to thank my advisor Professor Mat Disney for giving me the opportunity
to work on such a fascinating topic. Without you guidance and support none of this would have
been possible.
Secondly, I’d like to thank Dr. Phil Wilkes, Dr. Andy Burt, and Dr. Kim Calders. Without your
help I would not have known how to start, let alone finish, this project. Thanks for putting up
with all of my questions.
I would also like to thank the NERC via the NCEO and the NERC GREENHOUSE Project
who provided the funding for the fieldwork in Northumberland.
To my Climate Change and Linux Room colleagues, thanks for your friendship and support.
Hard to believe, but we made it through!
Last but not least, to my family. You have kept me sane through this whole process. Your
friendly ears, advice, and proof-reading were invaluable. I couldn’t have done it without you.

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Contents
1 Introduction.........................................................................................................................1
2 Methods................................................................................................................................5
2.1 Terrestrial Laser Scanning ..............................................................................................5
2.1.1 Terrestrial Laser Scanning Data Collection ..............................................................5
2.1.2 Registering Point Clouds.........................................................................................10
2.1.3 Extracting Tree Parameters From Point Clouds......................................................12
2.2 Allometric Equation .......................................................................................................15
2.2.1 Equation Development............................................................................................15
2.2.2 Allometric Training Set Sensitivity Tests ...............................................................17
2.3 Airborne Laser Scanning Data Collection .....................................................................18
2.3.1 Previously Collected Data.......................................................................................18
2.3.2 Data Processing .......................................................................................................19
2.3.3 Kielder Forest ..........................................................................................................20
3 Results................................................................................................................................22
3.1 Terrestrial Laser Scanning Tree Extraction ...................................................................22
3.2 Allometric Equation .......................................................................................................25
3.2.1 North and South Stands...........................................................................................25
3.2.2 Harwood Forest’s Allometric Equation...................................................................27
3.2.3 Effects of Bias .........................................................................................................29
3.2.4 Minimum Sample Size ............................................................................................30
3.3 Airborne Laser Scanning Tree Extraction......................................................................34
3.4 Carbon Content of Forests..............................................................................................36
3.4.1 Carbon Content of Trees Within Allometric Range................................................38
3.4.2 Emissions and Uncertainties....................................................................................39
4 Discussion...........................................................................................................................40
4.1 Terrestrial Laser Scanning ............................................................................................40
4.1.1 Benefits of TLS .......................................................................................................40
4.1.2 Comparison to Previous Allometric Equations .......................................................40
4.1.3 Lessons From Data Collection ................................................................................42
4.2 Allometry .......................................................................................................................43
4.2.1 Sampling Method ....................................................................................................43
4.2.2 Future Sampling ......................................................................................................44

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4.3 Airborne Laser Scanning ...............................................................................................44
4.3.1 Uncertainties............................................................................................................44
4.3.2 Role in Carbon Monitoring .....................................................................................45
5 Conclusion .........................................................................................................................46

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Chapter 1
Introduction
Climate change is one of the most comprehensive and widespread problems faced by the
international community (Kirtman et al., 2013). The primary driver of this current climate
change is the anthropogenic release of carbon dioxide into the atmosphere at a faster rate than
the Earth system can sequester it into less harmful reservoirs (Broadmeadow and Matthew,
2003). To combat the imbalance between carbon release and absorption, the international
community came together at the 2015 Paris Climate Conference and called for nationally
imposed carbon budgets (United Nations, 2015). The ultimate goal of these budgets is to make
human activities carbon neutral, only releasing the amount of carbon dioxide that could be
absorbed by the world’s reservoirs, such as its landscape. As Great Britain begins to create its
carbon budget to account for over 500 million tonnes of carbon dioxide released per year
(Department of Energy and Climate Change, 2015), it is looking for ways to increase its carbon
sequestering power in an effort to offset some emissions. One of the simplest and quickest
ways for the land to capture carbon is through forests (Houghton et al., 1993; Silver et al., 2000;
Minounno, 2010).
Trees naturally capture carbon dioxide from the atmosphere during photosynthesis and then
store it in the form of cellulose and lignin, the building blocks for tree growth (Broadmeadow
and Matthew, 2003). In this way, biomass in a living tree sequesters carbon that would
otherwise be a greenhouse gas. If the percentage of wood that is composed of carbon is known,
then biomass can be used to calculate carbon content. As the focus on carbon budgets increases,
there is a need to determine a forest’s biomass and the amount of carbon it stores to ensure the
calculations are accurate.
Determining the amount of biomass in a forest is not a new challenge; indeed, the forestry
industry has been asking this question for over 100 years (Newnham et al., 2015). During this
time, they have established allometric equations that relate an easily measurable variable, such
as a tree’s diameter at breast height (DBH), to less measurable variables, such as its above-
ground biomass (Calders et al., 2014). These DBH measurements can be taken and processed

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quickly with low technology tools such as Biltmore sticks, callipers, and clinometers (Newham
et al., 2015; Liang et al., 2016). While DBH is a simple measurement, it is time-consuming to
perform over a whole forest (Kankare et al., 2013).
Airborne Laser Scanning (ALS), an aerial form of Light Detection and Ranging (LIDAR)
(Hakenberg et al., 2015), offers an alternative to ground measurements for large scale data
collection (Calders et al., 2014). During ALS data collection, an aircraft flies over the forest
while emitting a laser pulse (Lim et al., 2003; Anderson et al., 2015). When the laser hits a tree
or the ground, the laser pulse reflects back to the aircraft where the signal is recorded (Lim et
al., 2003; Anderson et al., 2015). The distance to the reflective surface is determined by the
time it takes for the laser pulse to return to the receiver (Anderson et al., 2015). Because light
travels at a relatively constant and known speed through the atmosphere, a difference in return
time indicates a difference in the distance to the reflective surface (Anderson et al., 2015;
Newnham et al., 2015). If a laser point is only partially interrupted, for example by the edge of
a branch, part of the laser pulse will move further down the canopy before being completely
interrupted (Disney et al., 2010). This will lead to a single laser pulse being reflected off
multiple surfaces and registering multiple returns (Lim et al., 2003; Disney et al., 2010;
Anderson et al., 2015). The ALS data in this analysis registered the first and last returns from
the laser pulses. The first return represents the tallest reflective surface, e.g. the top of the
canopy, and the final return represents the lowest elevation the laser could reach before being
completely reflected, e.g. the ground. Depending on canopy thickness there may have been
some ground points within the first return data set and some non-ground points in the last return
data set (Lim et al., 2003; Khosravipour et al., 2014). In this study, the first and last pulse data
collected by Natural Environment Research Council (NERC) (Www2.geog.ucl.ac.uk, 2003)
were combined to maximize the amount of information available while extracting all possible
ground points and creating a typographical map. The typographical map was then used to
normalize the rest of the data, and create a Canopy Height Model (CHM) (Khosravipour et al.,
2014). The CHM enabled the volume of the trees to be calculated using allometric equations
based on tree height instead of DBH and then converted into biomass and carbon storage.
Allometric equations have been refined by destructively measuring a sampling of trees (Calders
et al., 2014). This method is accurate and taken as the ‘ground truth’ (Hackenberg et al., 2014).
However, errors in biomass calculations can occur if the logs become wet before measurement
(Hackenberg et al., 2014). This process is also expensive and labor intensive, so larger trees

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are often underrepresented in the sample set, calling the allometric relationship into question
(Raumonen et al., 2013; Calders et al., 2014; Calders et al., 2015). Additionally, if the purpose
of determining the amount of carbon stored in a forest is for a climate-related carbon budget,
then destructive measuring may be seen as counterproductive.
Alternatively, allometric equations can be verified or recalculated using Terrestrial Laser
Scanning (TLS), a tripod based form of LIDAR (Raumonen et al., 2013; Hakenberg et al.,
2015). As discussed with ALS, TLS measures distance by timing laser pulses, however the
RIEGL VZ-400 scanner used in this experiment recorded four returns instead of just the first
and last. If multiple TLS scans are taken of the same area from different angles, the resulting
data clouds can be stitched together for a three-dimensional rendering of specific trees
(Raumonen et al., 2013). These renderings have enough detail that the tree volume can be
directly extracted from the data (Newnham et al., 2015). In the past, TLS volumes extracted
from conifer forests have been comparable to the best field measurements and allometric
equations (Astrup et al., 2014; Liang et al., 2016). The volume can be compared to other tree
characteristics, such as DBH or tree height, extracted from the same three-dimensional
rendering. The characteristics extracted can then be combined to independently verify existing
allometric equations or create new ones (Calders et al., 2014).
This project focused on quantifying the carbon in Harwood Forest in Northumberland,
England, a timber plantation growing Sitka Spruce (Picea sitchensis) (Zerva and Mencuccini,
2005). This is an ideal equation-training location as a single tree species forest allows for easier
computation and more accurate verification of allometric equations. Ensuring that the
allometric equations for Sitka Spruce are correct is vital for estimating Great Britain's carbon
budget. Sitka Spruce is the species with the largest share of Great Britain’s carbon stocks in
woodlands trees (National Forest Inventory, 2011a). Currently, Sitka Spruce trees make up
25.8% of the total carbon stocks contained in the Great Britain’s principal woodland trees
(National Forest Inventory, 2011a). That percentage jumps to 50.0% when focusing on
Scotland (National Forest Inventory, 2011a).
In this study, TLS data were taken for a half hectare of the forest in 2016, encompassing the
area TLS data were taken the previous year. The half hectare spanned across two stands of
trees, or groups of trees sharing the same characteristics (Jenkins et al., 2012), that were
separated by a road. The trees north and south of the road had slight differences in topography.

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They were considered separate stands for the sake of examining the role of topography on tree
growth. It should be noted that all trees in this study were considered part of the same sub-
compartment, b 22 73, by the Forestry Commission (Ash, 2016). The trees were planted at the
same time under the same conditions (Jenkins et al., 2012; Data.gov.uk, 2016a).
In this dissertation, the TLS data were then used to verify the Sitka Spruce allometric equations
and, if necessary, adjust them. The TLS-supported allometric equations were applied to ALS
data collected from Harwood in 2003 to determine its carbon content. The allometric equations
were then applied to ALS data from Kielder Forest, a nearby Sitka Spruce dominant forest
(McIntosh, 1995), to determine its carbon content. Harwood and Kielder could then be
compared based on both tree height characteristics and carbon content. The comparison tests
the created allometric equation’s viability outside of its training forest.

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Chapter 2
Methods
Determination of the carbon content of Harwood Forest involved using Terrestrial Laser
Scanning (TLS) data to create a mathematical model (Zianis and Mencuccini, 2004) and
Airborne Laser Scanning (ALS) survey data to apply the model over the surveyed portion of
Harwood Forest’s wooded area. First, TLS data was collected and processed to find the heights
and volumes of trees from two stands with different topographic properties. Then, the heights
and volumes of those trees were combined to create Harwood-specific allometric equations.
The equation was applied to ALS data from 2003 to determine the wood volume from
individual tree heights. Following this, the amount of stored carbon in Harwood Forest was
determined by converting wood volume to carbon mass using the density and chemical makeup
of the wood. The allometric equation developed for Sitka Spruce in Harwood was also applied
to ALS data from Kielder Forest in an effort to compare the two forests.
2.1 Terrestrial Laser Scanning
2.1.1 Terrestrial Laser Scanning Data Collection
TLS data were recorded in timber sub-compartment b SS 73 in Harwood Forest,
Northumberland, England, on June 3 and 4, 2016 (Figure 1) (Ash, 2016). Before TLS
measurements were taken a 50m x 50m array was incrementally measured out using a tape
measure and compass. Every 10m a marker was placed to indicate the general scan position of
the laser scanner. Slight deviations from a precisely measured 10m grid were acceptable as the
spacing was dense enough to ensure multiple overlapping data point clouds for each sampling
position. The laser scanner used was a RIEGL VZ-400 with an accuracy of 5mm, a precision
of 3mm, and an angular resolution less than 1.8arcseconds (Datasheet RIEGL VZ-400, 2014).

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Figure 1: a) Harwood Forest (Ordinance Survey, 2003) with an embedded map (Jones, 2010)
showing the approximate location of Harwood (green tree) in Northumberland. The larger of
the two boxes shows the area of the ALS scan, subplot b, and the smaller box is seen in subplot
c. Source: Ordinance Survey, 2003; Jones, 2010. b) The ALS data collected by the Natural
Environment Research Council (Www2.geog.ucl.ac.uk, 2003). c) The tower plot where the
TLS was scanned (teal box) (Ash, 2016). Notable features include the tower access road and
car park. Source: Ash, 2016. d) The trees scanned with TLS.
Navigational reflectors were set up so that the data point clouds could be ‘stitched’ together.
Point clouds are a collection of all the individual locations in the Cartesian coordinate system
where trees or other objects reflected the scanner’s laser. The azimuthal plane was taken as the
xy-plane. The navigational reflectors were custom-made white plastic cylinders 0.1m long with
a diameter of 0.054m (Figure 2a). They were placed on 5ft garden poles, and staked into the

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ground (Figure 2c). Four reflectors were placed at the front of the first position grid cell (Figure
2b). Each reflector was individually visible from both the first and second position’s grid cell.
When the scanner moved to the second position, four additional reflectors were added to the
front of the second position. The original four reflectors located at the back of the second scan
position’s grid cell were left untouched (Figure 2b). Except for the start and end of a scan path,
every scan position had at least eight reflectors spread around it. This allowed each scan to be
‘stitched’ to the point clouds taken in the scan positions before and after it. Scan positions at
the end of a column had an extra reflector placed outside of the array to mark its edge (Figure
2b).

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Figure 2: a) A close up of the handmade reflector. b) Reflectors placement for different parts
of the scan path. The circles represent reflectors and the tripods represent the different scan
positions. The colors of the circles reflect which scan positions used them. If a reflector has
two colors it indicates that two scan positions used those reflectors. If a circle has only one
color, then the reflector was only needed for the corresponding scan. c) Setup of reflectors and
scanner for scan position 24, looking west from scan position 25, on the road separating the
north (right) and south (left) stands of trees.

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Two point clouds were taken in every scan position. One 360° shot in the xy-plane, and one
100° shot (+60°/-40°) perpendicular to the xy-plane (Datasheet RIEGL VZ-400, 2014). The
laser was placed on a tripod and oriented so that the shot in the perpendicular captured the
previous scan positions. In general the path of the data collection moved southward snaking
east and west (Figure 3). The stand of trees north of the road (scan positions 1-36) was first
measured on a 40m x 40m grid (scan positions 1-25) to ensure that a previously measured
section was rescanned. TLS data had been taken from the area encompassed by scan positions
1-25 in 2015. Afterwards, the grid was expanded to 50m x 50m (scan positions 1-36). The last
3 scan positions (34-36) were measured the morning of the second day, which had windier
conditions than the first day. This is not ideal as the scanning process for creating a point cloud
is slow enough that swaying trees can lead to blurs or duplicate branches (Hackenberg et al.,
2015; Liang et al., 2016).

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2.1.2 Registering Point Clouds
RiSCAN PRO 64 bit v2.3 (RiSCAN PRO, 2016) was used to register the point clouds (Figure
4). Point clouds were stitched together by translating and rotating one point cloud until it was
a seamless continuation of the point clouds before it. To ensure a good fit, a minimum of four
overlapping tie points were required to be matched with a tolerance of 0.0500m between scans.
If no acceptable data cloud position was found, then the minimum number of overlapping
points was reduced to three. If there was still no match, the tolerance was increased to 0.1000m
for first four and then three overlapping points. If increasing the tolerance did not reveal a
match, then the point cloud was temporarily skipped. The following point cloud was then
Figure 3: The scan path used to collect TLS data in Harwood Forest. The numbers indicate the
scan locations while the arrows show the path taken through those locations. The light green
and brown numbers indicate scan positions where only 8 reflectors were used. The dark green
and brown numbers are scan positions at the edge of a column so an extra reflector was used.
For scan positions 1, 36, and 66, this means 5 reflectors were in use. Scan postion 26 had 13
reflectors, and the rest of the dark numbers had 9 reflectors. The scan positions within the
dotted box were measured on June 3, 2016 and the rest were measured the following day. The
brown numbers indicate scans taken on the road, and green indicates that scans taken under the
canopy. The north stand is to the right of the road and the south stand is to the left of the road.

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registered and optimized. This allowed registration of the skipped point cloud to be attempted
when there was a greater chance of successfully located tie points. More registered reflectors
increased the number of available tie points. One point cloud was registered and optimized at
a time while all previous point clouds were held constant.
Optimization was performed by running a Multistation Adjustment (MSA) multiple times. The
MSA created a fit using all available point clouds, resulting in a more holistic solution. Each
time the MSA was run it started where the last adjustment ended. When the difference between
adjustments was less than ±0.003m in any direction, the point cloud was considered optimized.
Once an end of a column was reached, all point clouds, except the first, were allowed to vary
and optimized against each other. The MSA was performed twice at the end of each column to
ensure best fit. The first data cloud was held constant throughout to anchor the plot. The choice
of the first scan as the anchor was for convenience when locating items in the point cloud. The
scan choice to anchor the plot does not affect the end results.
The method of registration was changed for scan positions 37-66 (Figures 3&4) because of the
challenges aligning them with the previous day’s data. Each position went through multiple
Figure 4: Flowchart of the method used to register each TLS data point cloud with RiSCAN
PRO (RiSCAN PRO, 2016). MSA is the Multistation Adjustment process that allows for a
holistic fit to be found.

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MSAs where it could freely align itself with a smaller number of ‘locked’ data clouds. ‘Locked’
data clouds could not move their position or orientation during the MSA. The locked data
clouds used for a single scan’s adjustment included all previously registered scans in its column
and all neighboring scan positions in the previous column. If a scan was not properly aligned
through registration and MSA, it was temporarily unregistered and skipped. Once the following
position was registered the problematic scan was re-registered and re-run through an MSA.
This greatly improved the accuracy of the problematic scan’s alignment. When a column was
registered the whole column went through two MSA cycles against the locked previous two
columns. Then all scans, except the first, were allowed to vary against each other once. The
MSA over the whole dataset was performed an extra time after the final column was registered.
Once all points were registered, the Sensor’s Orientation and Position matrices (SOPs) were
exported as DAT files (RiSCAN PRO, 2005). These SOP matrices allowed each scan to be
translated and rotated to the proper location within the composite point cloud.
2.1.3 Extracting Tree Parameters From Point Clouds
A semi-automated collection of C++ and Python codes, described in Calders et al. (2014) and
written by Andy Burt and Kim Calders, was used to process the SOPs produced by RiSCAN
PRO along with the individual scans (Figure 5). First all the individual position and orientation
matrices were combined into a single DAT file (Burt, 2016a). Then the single position file and
individual scans were used to break the point cloud into voxels ensuring the entire tree canopy
was captured (Calders et al., 2014). Then every point was checked in an effort to determine if
a data point was part of a tree (close nearest neighbors) or noise (far nearest neighbors) (Burt,
2016b). This information was used when downsizing the data.

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Figure 5: a) A flowchart describing the process of extracting individual tree heights and
volumes from a data point cloud of a forest. b) The gap in a point cloud that signifies a tree
stem when separating clusters. c) The cross section of the downsampled forest before (left) and
after (right) 1800 trees were separated. d) Removing secondary branches from the base of the
stem. e) Removing foliage and branches from the tree stem. The code recognises all branches
and stems as being the same tree (first) when it can actually include parts of other trees as seen
in the cross section (second). Only the stem (third) was used in the calculations.
The point density within the data cloud was gradated, decreasing as the distance from the TLS
grew. Thus the ground and low sections of stems had the highest point density due to their
proximity to the scanner. Here the term ‘stem’ refers to the primary, vertical part of the tree,
i.e. the trunk. Moving up the trees results in a lower density of returns. This is due to the scanner
emitting laser pulses at a constant angular density (Datasheet RIEGL VZ-400, 2014). Moving
further away from the scanner decreases the density in the Cartesian coordinates. Downsizing
can reduce this effect (Burt, 2016c). When downsizing the point cloud is divided into a grid of

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voxels (Burt, 2016c). Then all the points within a voxel are reduced to one representative point
within the box (Burt, 2016c). The extent of downsizing depends on the size of the box. The
choice of box size was dependent on the diameter of the scanner's laser at its furthest distance.
The maximum distance was taken to be 50m. The REIGL laser exits with a diameter of 7mm
and a divergence of 0.00035 radians (Datasheet RIEGL VZ-400, 2014). Equation 1 was used
to calculate the diameter of the laser at a specific point along its trajectory. The voxel edge
length should be a least the size of the laser diameter at its maximum distance, so 0.025m was
used.
Equation 1: D=DExit+rtanθ
D=0.007m+(50m*tan(0.00035 radians))
D=0.007m+(50m*tan(0.00035 radians*180º/radian))
D=0.007m+(50m*tan(0.0201º))
D=0.0245m
Once downsized, a cross-section was taken of the point cloud that was created (Burt, 2016d).
The cross-section spanned from 0.5m to 1.5m in the z-direction. Then the cross-section was
sliced into boxes that were 2mx2m in the xy-plane. This created a cross-section of the point
cloud allowing easier identification and separation of individual trees from the point cloud.
Then individual trees were found by locating clusters of nearest neighbors. The code did not
capture all the trees of interest (Burt, 2016e), therefore, tree separation was also performed by
hand using CloudCompare v2.7.0 (CloudCompare, 2016). The signature ‘trunk gap’ (Figure
5b) was used to find trees. The tree gap is a circle with no return within a cloud of returns. The
lack of return indicates something, here the tree stem, is causing the laser to reflect and is solid
enough that the laser cannot penetrate it. Judgment calls need to be made on whether to include
two close trunks as one or two trees. If the two trunks could not be easily separated, then they
were said to be one trunk. Additionally, trunks with an extreme tilt were assumed to be one of
the many fallen trees. The cross-section also includes trees that were not within the measured
array, which were avoided. Their trunks were only partially measured which would have made
the next step of fitting the trunk gaps with cylinders more difficult. A total of 1828 trees were
separated from the point cloud and exported as ASCII files. Those files were then converted
into binary PCD files (Burt, 2016f; 2016g).

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The bases of the stems were then extracted (Calders, 2016a). Due to time constraints, only the
bases of 200 trees, 100 per stand, were extracted. The hundred from the southern stand were
grouped closer together than the trees from the northern stand. The bases were cleaned in
CloudCompare (Figure 5d) to ensure there was no additional ground or branches included.
Again, time constrains prevented all trees from being used. Twenty five trees were selected
from each stand to provide a range of tree types (Green at al., 2005). As the height of the trees
were not discernable from the stem bases, DBH was used to roughly gauge tree size. Trees
were separated by eye into one of five size categories: small, small-medium, medium, medium-
large, and large. Five trees from each category were used to represent a stand. Once all 50 stem
bases had been cleaned of extra data points, they became the foundation on which the rest of
the tree was built. Then the foliage was removed using the C++ code (Calders, 2016b). This
piece of code could take a day to run, and was only completed for 46 trees. The foliage and
branches at the top of the tree were so thick that the code had difficulty knowing what to include
as part of a single tree. Extra branches and foliage had to be removed by hand in CloudCompare
(Figure 5e).
The newly cleaned stems were then imported back into the C++ code. The heights and volumes
of the stems were calculated by fitting cylinders inside the tree gap for the entire tree (Burt,
2016h). Each iteration of the cylinder fitting created a unique model that varies in height, DBH,
and volume (Calders et al., 2014). To ensure tree measurements were as accurate as possible
the model was run at least ten times per tree (Calders et al., 2014). The reported tree
measurements were the average of the results. The standard deviation was also determined for
each measurement and taken to be an estimation of error. The volumes of the branches were
not considered because the majority of the tree’s total volume is in its stem (Tobin and
Nieuwenhuis, 2005; Kankare et al. 2013). Additionally, the lower branches of the tree were
dead, making them sources and not sinks of carbon dioxide (Kim et al., 2009). The stem heights
and volumes were then used to create a Harwood Forest Sitka Spruce allometric equation.
2.2 Allometric Equation
2.2.1 Equation Development

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Allometric equations have been used to describe the relationship between the volume, diameter
and height of trees during their growth phase (Zianis and Mencucci, 2004). The volume of the
main stem of a tree can be approximated by a cone (Equation 2). Here V is Volume, r is the
base radius, h is the tree height, and D is the base diameter. The stem’s widest diameter is at
its base and it is narrowest at the top. The cross sectional area at any point along the stem is
taken to be a circle. The diameter of the tree is rarely measured at the ground. A more
convenient field measurement is DBH, causing it to appear in many allometric equations
describing the volume of a tree stem.
Equation 2: V=1/3*π*r2
*h=1/12*π*D2
*h
Fonweban et al. (2011) tested four allometric equations (Equation 3-6) on Sitka Spruce in North
England and Scotland. Here a, b, and c are constants found by fitting the equation to the data.
Three of the locations included in their sample set lay between the areas scanned in Kielder
and Harwood forests. The use of similar sample datasets when evaluating equations is
important because location can alter growth patterns (Black et al., 2004). All four of Fonweban
et al.’s (2011) equations were DBH dependent. To remove the dependency on DBH, a height
to DBH equation (Equation 7), based on the generic allometric power function y=axb
(Hackenberg et al., 2014), was substituted into all four of Fonweban’s equations. Equations
3-5 all reduced to Equation 8 and Equation 6 reduced to Equations 9. Equations 8 and 9 were
used to create a height to volume allometric equation.
Equation 3: V=a(DBH)2
h+b
Equation 4: V=a(DBH)2
+b
Equation 5: V=a(DBH)b
hc
+d
Equation 6: V=a(DBH)b
hc
Equation 7: DBH= ahb
Equation 8: V=ahb
+c
Equation 9: V=ahb
Both equations were fit using nonlinear least-squares (Fonweban et al., 2012). The error was
estimated to be the Root Mean Square Error (RMSE) derived during cross validation

17
(Fonweban et al., 2012) found using the leave-one-out method. In the leave-one-out method
each tree is individually excluded from one in a series of best fit calculations (Muukkonen,
2007). The allometric equation resulting from that iteration’s best fit was then applied to the
excluded tree’s height (Muukkonen, 2007). Then the RMSE for individual trees was found by
comparing each tree’s actual volume and its allometrically derived volume. The RMSE of cross
validation (Equation 10) was taken as the RMSE for the whole allometric equation
(Muukkonen, 2007).
Equation 10: RMSE = √
1
n
∑ (Vi − Vpredicted,i)2n
i=1
i=leave-one-out iteration
n=number of trees
Both measured and allometrically-determined volumes were converted to biomass using Sitka
Spruce’s basic density. Basic density refers to the dry weight of wood divided by its green
volume (Moore, 2011). Sitka Spruce average basic density for the UK is 350 kg/m3
, although
it has been known to range from 330kg/m3
to 400kg/m3
(Moore, 2011). Once the dry biomass
was known it could be converted into carbon. The carbon content based on the dry weight of
North England Sitka Spruce averages 47.5% of the total mass (Matthew, 1993). However
spruce’s carbon content has been known to range from 45.1%±0.49% to 52%±1% (Matthew,
1993; Tobin and Niewnhuis, 2005; Green et al., 2007). Because reforestation is being used as
a climate change mitigation tactic to offset emissions (Minunnoet et al., 2010), the carbon
content of Sitka Spruce forests were compared to the Great Britain’s annual emissions
(Department of Energy and Climate Change, 2015). To ensure an accurate comparison, the
carbon dioxide from emissions was converted to the proportion that was carbon (Equation 11)
so the total mass of the same carbon element was being compared.
Equation 11: MassCO2=MassC*MolarMassCO2/MolarMassC= MassC*3.66
2.2.2 Allometric Training Set Sensitivity Tests
If TLS informed allometric equations are to become more wide-spread, the collection process
should be as efficient as possible. One way to speed up the collection process is to reduce the
number of trees scanned. Therefore the minimum number of scans needed to accurately

18
reproduce the allometric relationship was explored. Accuracy was examined at ±10% and
±30% of the volumes predicted by the allometric equation produced using all 46 trees. The
accuracy of the allometric equation is not solely dependent on the number of trees chosen; it
can be affected by how those trees are selected. Three methods of tree selection were also
tested.
The first method was randomly sampling the trees across the full spectrum of heights. No tree
was duplicated within a single sample set. Five samples of random, unique trees were created
with five trees in the sample set. The allometric equations were then compared to the 46 tree
allometric equation. The process was repeated for 10, 20, 30 and 40 trees.
The second method of sampling broke the 46 trees into five bins based on height. The bins
were <10m, 10m-15m, 15m-20m, 20m-25m, and >25m. Sample sets were created containing
5, 10, 15, 20, and 25 trees. Each bin provided one-fifth of the random, unique trees used in the
sample set. The largest sample set could only be 25 trees total, because the 15m to 20m bin
only contained 5 trees. Bins were sampled five times for each sample set size to provide more
information on the possible outcomes.
The third sampling method divided the 46 trees into two bins based on whether it was at least
15m tall. The sample set sizes ranged from 5 to 35 trees increasing in increments of 5 trees.
One fifth of the sample set came from trees chosen randomly without repetition from the lower
than 15m bin. The other four-fifths came from random, unique trees from the taller than 15 m
bin. This test was designed to see if purposefully focusing on the trees with the largest volumes
would reduce the number of trees needed to be sampled.
2.3 Airborne Laser Scanning
2.3.1 Previously Collected Data
ALS data was collected over Harwood Forest (Figure 1b) on June 15, 2003 by the Natural
Environment Research Council (NERC) (Www2.geog.ucl.ac.uk, 2003). They used the Optech
ALTM-3033 scanner from a helicopter to collect 17,338,895 points of data from 16.3171km2
of Harwood. This resulted in a point density of approximately 1point/m

19
(Www2.geog.ucl.ac.uk, 2003). The NERC researchers processed the raw ALS data using
Applanix PosPac version 3.02 and output text files for the first and last pulse containing
location, height, and intensity of the pulse (Www2.geog.ucl.ac.uk, 2003).
2.3.2 Data Processing
The data from NERC’s text files was processed into a Canopy Height Model (CHM) using
LAStools (Isenburg, 2016a). Before any calculations were made, the first and last pulse data
were combined into a single LAS file using lasmerge. To continue working in LAStools the
data needed to be reversibly broken into 750m x 750m tiles using lastiles (Isenburg, 2016b).
Tiles allow large point clouds (over 1.5 million points) to be broken into small point clouds. If
they are left large LAStools will slightly perturb the results. Tiles include buffers around them
to avoid increasing the number of edge effects. Edge effects tend to manifest as spikes when
categorizing ground points. This is because lasground considers neighbors when categorizing
points, and the edges have fewer neighbors (Isenburg, 2016c). Buffers extend the tiles into the
neighboring tiles, here by 0.25m on each edge, when preforming calculations. This removes
the increased risk of edge effects associated with tiling (Isenburg, 2015). Buffers are then
excluded when reporting the CHM of the tile to prevent repeats in data (Isenburg, 2015).
All tiles were then run through lasground, lasheight, and lasgrid. Lasground was used in
wilderness mode to classify which parts of the dataset were ground points (Isenburg, 2016c).
Lasheight set the ground points to be zero, normalizing the dataset (Isenburg, 2016d). Lasgrid
creates a raster where the LAZ file is broken into boxes and the boxes are condensed into a
single pixel (Isenburg, 2016e). The highest return from the box was represented in the pixel
creating a CHM. This simplified version of creating a CHM ignored pit reduction
(Khosrvaipour et al., 2014). However it achieved the best results in the waterfall-based script
(Wilkes, 2016) that was used to find individual trees (Figure 6).

20
Figure 6: This image was produced by Wilkes’s (2016) waterfall script. It shows a 250m x
250m section of Harwood Forest’s Canopy Height Model (CHM). The color bar indicates the
height [m] of the CHM. The black dots indicate the location of a tree apex.
2.3.3 Kielder Forest
LIDAR composite data for Kielder Forest was downloaded from the Environmental Agency’s
Survey Open Data (Figure 7) (Environment.data.gov.uk, 2016b). The composite data
combined the data from various LIDAR surveys within the area of the Ordinance Survey

21
gridbox (Data.gov.uk, 2016b). Ordinance Survey grid NY68 had data from a 2009 1m-
resolution survey and a 2003 50cm-resolution survey. The composite datasets had a resolution
of 1m. Using data from a single year would have been preferable, as 6 years can significantly
affect tree height (Moore 2011). However, the tiles from the individual years did not produce
a usable CHM for this method of height extraction. While both a Digital Terrain Model (DTM)
and Digital Surface Model (DSM) were available, only the DSM was used to create a CHM. A
DTM is a representation of the ground topography while a DSM shows the returns with the
highest elevation (Hyyppä, 2008). If the DTM was subtracted from the DSM (Hyyppä, 2008)
the resulting CHM was unrealistically choppy. The DTM and DSM could not be merged into
a single file, as done for Harwood’s ALS data, because they had different starting points along
their z-axis. Following the rest of Harwood’s ALS procedure, the ground of the DSM was
found, then normalized. During the normalization any points above 40m were taken to be
clouds and therefore excluded. Then, the Kielder data was made into a CHM and its trees’
apexes were found.
Figure 7: a) The Environmental Agency collected ALS data for Geological Survey grid NY68
(Enviroment.data.gov, 2016). The embedded map (Jones, 2010) shows the approximate
location of Kielder (green tree) in Northumberland. Source: Enviroment.data.gov, 2016; Jones,
2010. b) The Digital Surface Model (DSM) of the composite data was used to create a
normalized Canopy Height Model (CHM) for NY68.

22
Chapter 3
Results
3.1 Terrestrial Laser Scanning Tree Extraction
The height and volume of 46 distinct trees successfully extracted from the TLS data are shown
in Table 1. Heights ranged from 3.44m to 26.5m, DBH ranged from 5.25cm to 33.9cm and
volume ranged from 7.11 liters to 3014.5 liters. The distribution of height was even from 3m
to 20m, but numbers increased from 20m to 26.5m (Figure 8). The height averaged 17.3m and
the median height in the sample set was 20.3m. Stem length was also included in the table. It
tended to be slightly longer than the stem height depending on how much a tree bent or was
tilted. This data set demonstrates the importance of using as many trees as possible for the
training set to reduce biases in the allometric equations. Without a large amount of data, an
individual tree can skew the allometric equations. For example there was a sharp increase and
decrease in volume between Trees 20, 21, and 23 (Table 1).
Tree
number
Height
(m)
Standard
Deviation
of Height
(m)
Length
(m)
Standard
Deviation
of Length
(m)
DBH
(cm)
Standard
Deviation
of DBH
(cm)
Volume
(liters)
Standard
Deviation
of
Volume
(liters)
1 3.44 0 3.45 0 5.48 0.219 7.11 0.211
2 4.04 0.00405 4.06 0 9.41 0.077 22 1.59
3 5.89 0 5.91 0 5.25 0.0221 8.9 0.538
4 5.98 0 5.98 0.0332 5.72 0.117 10.2 0.104
5 6.1 0.0557 6.12 0.0479 7.61 0.157 17.3 0.379
6 7.73 0 7.74 0 8.29 0.196 23.3 0.542
7 7.74 0.00302 7.76 0.00302 8.7 0.11 25.4 0.473
8 8.06 0.0275 8.09 0.0276 9.87 0.0951 29.1 0.194
9 8.4 0 8.41 0 7.95 0.643 24.5 1.25

23
10 8.71 0.0603 8.72 0.00405 5.89 0.0437 13.5 0.238
11 9.44 0.00302 9.51 0.00674 14.9 0.448 102.1 2.02
12 10.9 0 10.9 0 7.82 0.0687 30.4 0.0688
13 10.9 0.0302 10.9 0 7.83 0.0519 30.4 0.143
14 12.1 0.0467 12.1 0 13.2 0.0539 108.3 0.786
15 13.2 0.11 13.4 0.117 11 0.0422 72.9 1.11
16 14.0 0.0786 14.0 0.0522 9.35 0.0693 63.5 0.361
17 14.2 0.0924 14.2 0.0467 9.46 0.0902 51.7 0.427
18 15.1 0.211 15.1 0.211 19.4 0.309 163.3 1.79
19 16.4 0.857 16.5 0.857 39.5 2.92 970.4 16.7
20 18.4 0.306 18.7 0.333 18.5 0.535 240.1 3.00
21 19.1 0.284 19.1 0.295 36.0 0.66 1192.1 17.9
22 19.2 0.227 19.3 0.23 29.7 0.0789 850.4 8.95
23 20.1 0.2 20.14 0.24 15.2 0.15 179.9 0.96
24 20.5 0.403 20.7 0.429 36.9 0.0972 1302.7 17.8
25 20.7 0.561 20.7 0.575 20.1 0.396 348.1 6.86
26 21.1 0.0302 21.1 0.0302 18.2 0.338 266.8 1.25
27 21.4 0 21.5 0 18.5 0.148 245.6 0.924
28 21.4 0.245 21.9 0.441 28.2 0.166 683.9 6.02
29 21.5 1.32 21.5 1.3 20.3 0.92 371.5 14.2
30 21.9 0.47 22 0.502 27.4 0.0701 771.8 11.1
31 22.3 0.406 22.3 0.406 29.4 0.301 706.5 6.65
32 22.6 0.145 22.7 0.112 21.4 0.458 373.7 3.10
33 22.6 0.0924 23.3 0.234 35 2.21 950.1 5.38
34 22.7 0.158 23.1 0.277 23.5 0.224 543.1 4.81
35 23.2 0.348 23.5 0.37 32.9 0.141 987.5 7.74
36 23.5 0.332 23.8 0.429 31.4 1.2 1012.5 11.6
37 23.6 0.419 23.6 0.427 40.7 2.3 1302.3 40.6
38 23.7 0.189 23.8 0.223 28.1 0.193 746.9 3.91
39 25 0.647 25.1 0.635 35.4 1.85 1096.7 12.7
40 25.1 0.629 25.2 0.634 35.1 1.68 1197.7 17.3
41 25.5 0.305 25.7 0.467 28.9 0.143 908.9 9.17
42 25.5 2.27 25.6 2.26 58.5 0.4228 3014.5 101.3

24
43 25.7 0.291 26.5 0.622 35 1.95 1415.4 22.5
44 26.3 0.543 26.4 0.581 26.1 0.175 716.2 7.32
45 26.4 0.266 26.5 0.27 38.4 2.93 1361.1 10.2
46 26.5 1.66 26.7 1.76 39.9 1.4 1749.8 28.9
Table 1: The means and standard deviations of the 46 trees extracted from the TLS data. The
shaded numbers are trees from the southern stand.
Figure 8: The 46 trees used to create the allometric equations.
The standard deviation of each tree measurement was also included in Table 1. Because of the
diversity in tree size it is hard to directly compare standard deviations. Therefore standard
deviation was examined in terms of its size compared to the mean measurement size. The
percentages of the standard deviation related to the mean were plotted against that tree’s
volume, height and DBH (Figure 9) in order to detect any patterns in the distributions. The
average percentage standard deviation for height, DBH, and volume were 1.4%, 2.3%, and
1.6% respectively. All standard deviations for all trees remained below 9% for all
measurements. This indicates that the cylinder fitting provided consistent quality in volume

25
estimation for all tree types. DBH had a higher percentage standard deviation than the heights,
but the standard deviation for DBH was never higher than 3mm (Table 1). This means that TLS
DBH readings are comparable to field measurements taken by hand (Black et al., 2004). The
percentage standard deviation for volume does not seem to increase with the size of the tree,
whether the size is measured by volume, height or DBH. However trees with the highest
volumes have the largest standard deviation. This variability can be equivalent to the volume
of multiple smaller trees (Table 1). Reducing the large tree’s variability is important if the
allometric equations are expected to produce accurate predictions of carbon content.
Figure 9: The percentage standard deviation of each tree’s volume, height, and Diameter at
Breast Height (DBH) have been plotted against that tree’s a) volume, b) height, and c) DBH
3.2 Allometric Equations
3.2.1 North and South Stands

26
In order to detect any possible effect of the soil on tree growth, allometric equations were
created and tested for the north and south stands (Figure 10). An allometric equation was fitted
to the north stand’s tree data and then tested on the south stand. Then the process was reversed,
testing a southern stand allometric equation on the north stand trees. For the southern stands,
the leave-one-out RMSE’s from the development stand were larger than the RMSE’s from the
adjacent stand. This shows that the north’s trees were, on average, within the uncertainty of the
south’s allometric equation. The north equation did preform worse on the southern trees. The
different RMSE seem to highlight the importance of including large trees in the training set.
More trees will be needed before the effects of soil and typography will be detected.

27
3.2.2 Harwood Forest’s Allometric Equation
All 46 trees were used to calculate the allometric equation that was used to find forest-wide
tree volumes (Figure 11). As seen in the individual stands, the equation in the form of y=axb
was more accurate (Equation 12), with an RMSE of 0.405m3
. So, it was used to determine the
volume of Harwood Forest trees. The northern and southern stands both contributed trees with
volumes above and below the allometric prediction.
Figure 10: a&c) The allometric equations created by non-linear least squares using data from
25 (21) trees from the northern (southern) stand. The Root Mean Square Error (RMSE) was
calculated by testing the northern (southern) allometric equation on 21 (25) southern (northern)
stand trees. The calculated volumes were compared to the southern (northern) trees’ actual
volumes. b&d) The volume of the southern (northern) trees derived from the northern
(southern) allometric equations were plotted against the actual volumes. The points that fit the
best with the allometric equation were the closest to the y=x line.

28
Figure 11: The allometric equations fit by non-linear least squares using all available trees
from the northern and southern stands. A total of 46 trees were used with heights ranging from
3.44m-26.5m, volumes ranging from 0.00711m3
to 3.015m3
, and calculated carbon content
ranging from 0.0000232 tonnes to 0.344 tonnes. This assumes a basic density of 350kg/m3
and
47.5% of the dry weight of Sitka Spruce being carbon (Matthew, 1993; Moore, 2011).
Equation 12: V=1.55*10-5
[m-0.59
]*h3.59
After a tree reached 15m there was a significant increase in its potential volume. Trees under
15m were all very close to the allometric predicted volumes. Trees above 15m varied in volume
much more and could be much larger than the equation predicted. Therefore, 15m was taken
to be Harwood’s height of ‘carbon maturity’, the point at which an individual tree could have
a significant carbon contribution.
When comparing Equation 12 to the individual stand equations, Equation 12 split the difference
between the northern and southern stands’ allometric equations (Figure 12). The difference
between the stand-wide equations and the total allometric equation grew as height increased.

29
This demonstrates the importance of tall trees when creating allometric equations, because the
tall trees have the greatest potential of experiencing bias.
Figure 12: a) The allometric equation created by the northern stand (blue), the southern stand
(yellow), and both stands (green) were plotted for the allometric height range of 3.44m-26.5m.
b) The difference taken between the north/south stands and the 46 tree equation.
3.2.3 Effects of Bias
Throughout this process, uncertainties in height measurements have been a concern. The tops
of the tallest trees were difficult to capture with TLS due to the number of overlapping branches
from other trees. When the cylinder model was fit to the TLS measured trees, heights had some
of the largest standard deviations. ALS measurements also tend to report lower tree heights
than TLS (Anderson, 2015). The first return will always register slightly below the exact top
of the canopy, due to the ALS’s required threshold that it needs to receive from the laser pulse
before it registers the first return (Disney et al., 2010; Anderson et al., 2015; Liang et al., 2016).
Additionally, the tree apex has a small cross-sectional area compared to the rest of the tree’s

30
crown. The likelihood of the ALS laser hitting it is relatively low. Therefore errors in height
are important to examine.
To examine the result of a potential bias in height, the allometric equation for Harwood was
recreated twice (Figure 13), first with a standard deviation of each height added to it, and
second where each height had the standard deviation subtracted from it. The allometric
equation created when the standard deviation was added crossed into the 30% envelope of the
standard allometric equation by 15m. The equation were one standard deviation was subtracted
did not cross into the 30% envelope until 18m. By 23m, both equations were within the 10%
envelope. The resulting allometric equations were applied to Harwood’s ALS data. The ALS
data was assumed to be accurate and unbiased. Adding one standard deviation to the height
decreased the total carbon 23%. There was a 37% increase in the total carbon when the height
had one standard deviation subtracted.
Figure 13: The allometric equation based on the mean heights (black) plotted against the
allometric equations when one standard deviation was added to (blue) and subtracted from
(red) the mean heights. a) The mean height values are plotted, the edges of the height error bars
were used as the heights in the other two allometric equations. b) The 10% envelope (dashed)
and 30% envelope (dotted) of the standard allometric equation.
3.2.4 Minimum Sample Size

31
Three different sampling methods were tested to see if they could produce accurate results,
within 10% or 30%, when compared to the Equation 12. The 10% envelope was ideal, but 30%
accuracy was included. It reflected the 23% and 37% changes in carbon when the effects of
height bias were examined. The equations, their differences, and their percentage differences
were all studied (Figures 14-16). The absolute differences between the training data sensitivity
runs and the 46 tree equation made the runs’ performances seem better than they actually were
(Figure 14-16). The percentage difference showed that even when the absolute difference was
small the sensitivity runs could still be outside the desired 30% accuracy range. Trees smaller
than 10m tended to have some of the largest percentage differences. This is due to the volume
difference being divided by an actual volume number approaching zero. The large percentage
differences for trees less than 10m is not as important as those above 10m. The small trees
absolute difference is small enough that the forest’s total carbon will not be affected. The
percentage difference also diverges above 26.5m. While some of the equations could be applied
to trees outside the allometric range, the results must be treated with caution.
Figure 14: Different numbers of trees (5, 10, 20, 30, and 40 trees) were randomly sampled five
times and used to create five allometric equations (blue). They were plotted against the 46 tree

32
allometric equation (black) and its 10% envelope (dashed line) and 30% envelope (dotted line).
a) The equations were plotted as well as their b) difference from the 46 tree equation, and their
c) percentage difference with respect to the 46 tree equation.
Figure 15: Different numbers of trees (5, 15, 10, 20, and 25 trees) were sampled five times
using the five-bin method and used to create five allometric equations (blue). They were plotted
against the 46 tree allometric equation (black) and its 10% envelope (dashed line) and 30%
envelope (dotted line). a) The equations were plotted as well as their b) difference from the 46
tree equation, and their c) percentage difference with respect to the 46 tree equation.

33
Figure 16: Different numbers of trees (5, 10, 15, 20, 25, 30, and 35 trees) were sampled five
times using the two-bin method and used to create five allometric equations (blue). They were
plotted against the 46 tree allometric equation (black) and its 10% envelope (dashed line) and
30% envelope (dotted line). a) The equations were plotted as well as their b) difference from
the 46 tree equation, and their c) percentage difference with respect to the 46 tree equation.
The sampling methods produced different behaviours when generating the five runs for each
sensitivity test. The random method’s five runs could produce completely different outcomes
each time the model was run. This lack of precision was reduced with the addition of more
trees, although it was still present even when 40 trees were used. The binning models produce
two curve groupings for all model runs. The first curve grouping crossed out of the +30%
envelope between 20m and 26m. The second curve grouping crossed out of the 10% envelope
around 26.5m. The first curve grouping was the less accurate of the two groupings, but it
improved with the addition of more trees. The first curve grouping indicates a sample set that
included one or more of the largest volume trees and could lead to a significant bias. The
numbers of trees available in each height bin stayed the same even as the number of trees being
randomly selected from each bin increased. Therefore, sensitivity tests with larger number of

34
trees were more likely to include the trees that produced allometric equations in the first curve
grouping. Depending on which five runs were produced, the size of the groupings could vary.
The only graph (Figure 14-16) with little to no perceivable change was the 35 trees sampled
using the two-bin method. Therefore, the percentage of successful runs either within 30% or
10% accuracy may not be exactly what is shown in Figures 14-16. This is an area that requires
further investigation.
Some general patterns can still be found. The random method was able to produce five runs
where four of them were within the 30% accuracy envelope for trees in the 15m to 26.5m height
range. This covers the carbon mature trees in the allometric range. When 40 trees were sampled,
three out of five runs were within the 10% envelope for tree heights of 15m to 26.5m.
Unfortunately, this method could produce a wide variety of equations, so the accuracies were
not consistent. The binning method allowed for precision in the produced allometric equations.
The two-bin method seemed to be more precise than the five-bin method. The precision for
both increased as more trees were added. The two-bin method had a slightly different behaviour
in its curve grouping. Its first curve grouping only needed 15 trees for it to cross the +30%
curve at 26.m. The five-bin method needed 20 trees. The two-bin method also seemed to delay
the first curve grouping’s dominance to when 20 or more trees were used. In the five-bin
method the first curve grouping became dominant at 15 trees. Unfortunately, with the addition
of more trees, the range of accuracy reduced to heights from 20m to 26.5m. The inclusion of
25 trees in the five-bin method and 35 trees in the two-bin method did not produce accurate
results for all carbon mature trees in the allometric range. Both binning methods under
predicted the volumes of trees shorter than 20m.
3.3 Airborne Laser Scanning Tree Extraction
The 16.3171km2
of Harwood Forest that was scanned (Www2.geog.ucl.ac.uk, 2003) contained
36,415 trees (Figure 17). This excluded tree heights lower than 2m and higher than 30m. The
trees lower than 2m were excluded to avoid including brush. This assumption will not have a
significant effect on forest wide carbon calculations because their total volume is so small. The
single tree above 30m was excluded as it was assumed to be indicating a cloud that may have
interfered with the measurements. Harwood Forest is a plantation, and it is unlikely for a tree
to be 9m taller than any trees around it. Harwood’s distribution of tree heights is bimodal

35
(Figure 17) peaking at 6m-7m and 14m-15m with an average height of 11.2m. The number of
the larger trees above the second peak tapers off rapidly. This is possibly due to the tallest tress
being harvested. In the UK, harvested Sitka Spruce tend to be between 16m-28m tall depending
on age and yield class (Moore 2011).
Figure 17: The height of the considered tree apexes for both Harwood and Kielder forests. In
both cases tree heights below 2m were excluded to avoid brush. a) In Harwood the single tree
above 30m was taken to be a cloud. b) A 40m height cap was used for Kielder Forest. 40m is
within a normal growing range from Great Britain (Moore, 2011).
Kielder Forest has a similar bimodal distribution in the heights of its 173,276 trees. Its second
peak is the same as Harwood, 14m-15m, but its first peak is slightly lower, 4m-5m. As in
Harwood, tree apexes lower than 2m were excluded to avoid brush. The cap for tree heights
was increased to 40m because it is a typical growth height for Sitka Spruce in Great Britain
(Moore, 2011). Bins above 37m contained less than 12 trees each, so any trees over 40m would
be rare and have a minimal impact on the forest’s carbon content.

36
3.4 Carbon Content Of Forests
The 46 tree, y=axb
form of the allometric equation was applied to the entire forest to provide a
general picture of the distribution of carbon over all tree heights. There are some tree heights
that were not represented in the sample set used to create the allometric equations. The volumes
produced from these trees are more likely to be biased than volumes from trees that were
represented, as demonstrated by the northern and southern stands allometric equations (Figure
10). Since the 3 out of the 24 height bins that contained zero trees were spread throughout the
height range, the risk of bias is lower than if unrepresented bins were clumped together (Figure
8). With this in mind, the application of the allometric equation across all trees allows for a
more complete understanding of the forests’ carbon content.
In Harwood Forest, the 824 tonnes (+227 tonnes or -94 tonnes) of carbon from trees with
heights within the allometric range represent 99.2% of the forest-wide allometrically-predicted
carbon (Figure 19b). In Kielder Forest, assuming all trees captured by the ALS were Sitka
Spruce (McIntosh, 1995), the 7,130 tonnes (+1,962 tonnes or -816 tonnes) of carbon
represented in the allometric sample set only accounted for 75% of the forest-wide
allometrically-predicted carbon content (Figure 19d). Therefore, if the large trees experience a
bias in the allometric equation, it is more likely to affect Kielder Forest’s carbon budget than
Harwood Forest’s carbon budget. Therefore, it is important to collect height and volume data
from the largest trees in Kielder, so that, like Harwood, the tallest trees are represented in the
allometric training set.

37
The carbon content of the forest binned by tree height (Figure 19a) can be compared to the
number of trees in each bin (Figure 17). Despite Harwood’s bimodal distribution in height, the
carbon content exhibited a more normal distribution when sorted by height. Trees between
16m-17m had peak carbon storage despite the fact that they have fewer trees than other height
Figure 18: The allometric equations were applied to all trees in Harwood Forest (top row)
and Kielder Forest (bottom row). Dark green represents trees with heights encompassed
by the allometric training set and yellow represents trees that were not represented. a)
Harwood’s carbon content of all the trees sorted into 1m height bins. b) In Harwood, 99.2%
of the forest’s carbon, as predicted by the allometric equations, was in trees with heights
encompassed by the allometric range. c) Kielder’s carbon content of all the trees sorted
into 1m height bins. d) In Kielder, the percentage of carbon within the allometric range
drops to 75%.

38
categories. Trees under 10m contributed a relatively small amount to the total carbon,
considering that 6m-7m was the larger of the two peaks in the bimodal distribution of
Harwood’s tree heights. Kielder Forest also has a normal distribution of carbon content when
sorted by height, but it was a more gradual decay than Harwood and had a later peak (Figure
19c). In both forests, a peak in carbon content occurring after a peak in height indicates that
the increasing volume of large trees initially overwhelms the effect of their decreasing
quantities.
3.4.1 Carbon Content Of Trees Within Allometric Range
The distribution of carbon content for only the trees within the allometric range was also
examined for Harwood Forest and Kielder Forest (Figure 20). In Harwood Forest, the 15m-
20m range made the largest contribution to carbon content of trees within the allomteric range.
Trees less than 10m cannot be neglected as they contribute 9% of the carbon content of trees
within the allometric range. In Kielder, taller trees were more imporatnt to the carbon budget.
Kielder Forest’s largest contributing range was between 20m-25m, while trees less than 10m
contirbuted less than 1%.
Figure 19: The pie charts consider only the carbon content of trees in a) Harwood and b)
Kielder whose heights were within the range of the sample set that created the allometric
equations.

39
3.4.2 Emissions and Uncertainties
The total carbon in Harwood Forest is 833 tonnes (+229 tonnes or -96 tonnes). This is
equivalent to 3,050 tonnes (+838 tonnes or -351 tonnes) of carbon dioxide emissions. The same
calculations were made for Kielder woods, assuming that all the trees were Sitka Spruce.
Kielder stored 9890 tonnes (+2,740 tonnes or -1130 tonnes) of carbon equivalent to 36,200
tonnes (+10,000 tonnes or -4,140 tonnes) of carbon dioxide emissions. The calculations have
been made without considering the ALS uncertainties or TLS volume uncertainties. The
uncertainties may interact in such a way that the actual amount of carbon stored might have
been higher or lower than the numbers reported here. If the same conversion holds for the
170,012m3
total Sitka Spruce volume in Great Britain (National Forest Inventory, 2011b), the
forest stored an estimated 28,300 tonnes (+7,780 tonnes or -3,240tonnes) of carbon that would
have been 103,500 tonnes (+28,500 tonnes or -11,800 tonnes) of carbon dioxide emissions.
If forests are to be used to offset yearly emissions, only the carbon added to the forest that year
should be considered. The carbon already in the forest is storing the offset carbon from previous
years. A range of different densities would need to be applied to the yearly carbon increases,
because younger Sitka Spruce grow faster (Moore, 2011) and have higher densities than older
Sitka Spruce (Tobin and Nieuwenhuis, 2005). The effect of branches must also be considered.
For the two stands studied here, the thick top canopy of the tallest trees prevents much light
from penetrating through to the understory. As a result the main tree stems contained the largest
percentage of biomass for the trees, likely on the order of similar spruce forests. Examples
include 71% in a Sitka Spruce forest in Ireland (Tobin and Nieuwenhuis, 2005) and 74.6% in
a Norway Spruce forest in Finland (Kankare et al., 2013). However, branches can play a
significant role in younger stands where the main stems may only contribute 26% of the total
carbon (Tobin and Nieuwenhuis, 2005). One way to account for branches would be to
painstakingly separate the entire tree from the point cloud. However, interwoven branches
would lead to a lot of guesswork. Other options are to destructively measure trees, or to collect
TLS data during timber harvesting when a tree’s neighbors have been removed.

40
Chapter 4
Discussion
This experiment combined two relatively new forestry technologies, Terrestrial Laser Scanning
(TLS) and Airborne Laser Scanning (ALS), to lay the groundwork for wide scale carbon
sequestration monitoring in Great Britain. TLS captured high quality data on the volume,
height, and diameter of individual trees that were used to formulate the necessary allometric
equation to enable rapid wide scale ALS forest monitoring. While both technologies open up
new possibilities in carbon sequestration monitoring, the large computational processing
needed may limit TLS’s applicability to those who have the resources to develop allometric
equations. Costs of ALS may limit the amount of forest-wide data that monitoring groups can
afford to collect. Both issues of time and money must be addressed for the benefits of the
technology to be fully realized.
4.1 Terrestrial Laser Scanning
4.1.1 Benefits of TLS
TLS data taken over a half hectare allowed individual trees to be selected so the entire range
of heights was represented in the allometric training set. The large number of trees fully
captured in the point cloud allowed for additional criteria to be applied to the trees included in
the sample set. Here, the straightest trees were chosen. This ensured that the reported average
volume for each height was the actual average volume of straight trees at that height. Trees
with bends and trees that grew tilted will have larger volumes than straight trees with the same
apex height. If actually offsetting carbon emissions is the goal, the underestimation of carbon
content by assuming every tree is straight is preferable to the overestimation of carbon. An
overestimation of carbon sequestered by forests in carbon budgeting would allow for smaller
cuts in emissions than actually necessary.
4.1.2 Comparison To Previous Allometric Equations
An equation suitable for ALS-based carbon monitoring was not easily accessible for Harwood
Forest. As the largest trees play a vital role in determining the shape of the allometric curve,
TLS is a practical and accurate method of determining the necessary parameters. The high

41
quality data provided by TLS allowed for the creation and testing of allometric equations by
directly extracting desired variables from individual trees in the point cloud. New allometric
equations were tailored to the available input, height, and the desired output, volume, for wide
scale monitoring by ALS. The other two available methods were destructive measuring and the
use of field measurements and DBH-based allometric equations. Destructive measuring, while
accurate, would have been expensive and time consuming. Using field measurements of tree
heights and DBHs, and entering them into Fowenban et al.’s (2012) most accurate equation
(Equation 6) would have produced accurate volumes, but the resulting height based allometric
equation might have propagated biases. Their equation performed well, with an
RMSE=0.1246m3
; the use of both height and DBH created a better fit. However, they were
slightly biased, and consistently underestimated the volumes of the 46 trees extracted from the
point cloud (Figure 21).
Figure 20: The heights and diameters at breast height (DBH) were extracted from the 46 TLS
trees and entered in the Fonweban et al.’s (2012) equation, V=a(DBH)b
hc
.
4.1.3 Lessons From Data Collection

42
As carbon monitoring becomes more widespread, lessons from this experiment can be used to
inform future TLS data collection. The first lesson is the importance of plot and tree choice.
While the whole range of possible heights need to be included in the training set, there should
be an additional focus on capturing the range of large trees. Compared to the trees below 15m,
the carbon mature trees showed more variation in volume and contribute a larger portion of the
overall carbon content of the forest despite their lower numbers. As demonstrated by the
individual stands allometric equations, if the full range of tall trees’ volumes is not represented,
a significant portion of a forest’s carbon budget may be biased.
Including enough trees in the training set to ensure an accurate representation of heights and
volumes is a time consuming process. If monitoring is to be done on a large scale, then the
computational time needs to be reduced. In this experiment time constraints limited the amount
of TLS data able to be processed. One way to reduce computation time would be to make
registration easier with the use of additional reflectors. The method of reflector placement used
here only linked a scan position to the positions immediately before and after it. While
decreasing setup time, this method occasionally made registration more difficult. If there was
a troublesome scan position there was no alternative registration path for the remainder of the
scans. The use of permanent reflectors placed between the columns of scan positions would
increase the registration paths available to poorly aligned scans. The path of registration could
use the neighbouring column to go around the troublesome scan. This would increase the
number of tie points available and help with the initial registration of the problematic scan.
Additionally, surrounding the unaligned scan with registered scan positions would help with
the holistic optimization. The use of additional reflectors would have meant that fewer field
measurement were taken within the same amount of time, however, more of those
measurements would have been able to be processed. More processed data would have made
the allometric equations even more accurate and helped examine the effects of soil and
topography on tree growth.
The best method to create an allometric training set is not easily identified. Random sampling
can achieve accuracy, but lack the precision needed for consistency. Binning provided
consistency, but introduces a potential bias that prevents accuracy. This was most pronounced

43
when the full range of larger tree volumes was not represented, allowing a single tree to
dominate the best fit calculations. As more trees are added the positive aspects of both methods
improved. Trees have a wide variety of growth patterns (Figure 21) and a large number of trees
are needed to adequately capture the range of growth. The only tested combination able to get
within the 10% error bars was the 40 randomly sampled trees. This indicates that high accuracy
equations are more dependent on the number of trees being sampled than how those trees are
sampled.
Figure 21: The growth rates of the Sitka Spruce’s yield classes 6-24. Source: Moore, 2011
4.2 Allometry
4.2.1 Sampling Method
TLS was able to deliver the data needed to create new allometric equations that were only
dependent on height. When assembling the 46 trees to include in the allometric training set the
heights of the trees were still unknown. The trees were included in the sample using an
approximate five-bin method based on DBH. The resulting distribution of tree heights for those

44
46 trees (Figure 8) is closer to a two-bin method. However, the ratio is closer to a 1:2
distribution than the 1:4 distribution tested. The resulting equation is likely precise, however it
may be slightly biased for tree heights below 20m and above 26.5m.
4.2.2 Future Sampling
Equation 12 was the best equation for this data (Figure 11). It had an RMSE of 0.405m3
, which
is higher than Fowenban et al.’s (2012) Sitka Spruce allometric equations using both height
and volume. Their RSME was only 0.1246m3
. Fowenban et al.’s (2012) equation provided a
better fit for 46 of Harwood’s trees than the height only equation made with those same 46
trees, but it produced a low bias. This shows that the forests sampled by Fowenban et al. (2012)
had similar growth patterns to Harwood. However, if this equation is to cover all possible tree
heights in those forests, more height and volume data will need to be collected. The resulting
allometric equation should be used with caution, because generalized allometric equations for
European conifer stem’s volumes have been less accurate than site-specific equations
(Muukkonen, 2007).
4.3 Airborne Laser Scanning
4.3.1 Uncertainties
Biases from ALS and TLS can interact and alter the carbon content estimates, so the
relationship between TLS and ALS must be understood. The accuracy of applying the
allometric equation to ALS data will be tested later this year when another round of ALS data
will be taken over Harwood. Additionally, Kielder’s findings must be tested to ensure the
volumes derived by applying the allometric equation to ALS data reflected the ground truth.
This could be done using either TLS or destructive measuring, but as previously discussed is
expensive. If TLS data is being collected in Kielder Forest, additional scans should be taken of
trees between 26.5m and 40m. Adding the additional scans to the training set would create a
more robust allometric equation. Nearly all of Harwood and Kielder’s trees and carbon content
would then be represented in the new equation. Furthermore, this would make the application
of the allometric equation to other forests more likely to produce accurate carbon contents.
Reported differences in height must be accounted for and incorporated into the allometric
equation if the carbon reported from different forests is to be accurate. Results of bias are

45
significant and must be addressed. ALS remeasurement will allow TLS to be further evaluated
as a method of creating ALS-friendly allometric equations.
4.3.2 Role in Carbon Monitoring
The demand for accurate carbon accounting may increase the use of ALS when determining
carbon budgets. With new height-based allometric equations, ALS can help monitor patterns
and changes in carbon storage over large areas. Changes could be caused by altered growth
patterns, harvesting timber, or reforestation. When Harwood’s ALS data is remeasured it will
create a time series of Harwood’s carbon content and help to determine how much carbon is
added to forests each year. Pairing ALS data with TLS derived allometric equations can provide
responsive and accurate carbon measurements needed when determining Great Britain’s
carbon budget.
The allometric equation that has been developed for Harwood hopefully will be applicable for
similar forests throughout Great Britain (Fowenban et al., 2012). The nearby Kielder Forest is
a logical place to determine if the equations derived with Harwood’s TLS data can be applied
to other forests. This will require destructive measurements or TLS data from Kielder Forest
and ALS from the same year to ensure volumes match the ground truth. During the
comparisons all heights, not just those under 40m, should be considered. If Kielder and other
forests have similar growth patterns to Harwood, Equation 12 can be applied to the ALS data
available from both NERC (Browse.ceda.ac.uk, 2016) and the Environmental Agency
(Data.gov.uk, 2016c). The carbon content for other Sitka Spruce forests in Great Britain can
be readily determined.
The costs of ALS scanning may be a barrier to scanning for some forests, so other surveying
technologies should be explored. In 2003, aerial photographs were collected along with the
LIDAR data. If height information, comparable to LIDAR data, can be extracted from photos,
it opens up the possibility for drone based data collection. Unmanned drones are already
equipped with cameras and could allow a quick, cheap, readily available alternative to
helicopter based ALS data collection. This would enable more frequent aerial readings and
create a more detailed carbon budget.

46
Chapter 3
Conclusion
The Harwood Forest experiment demonstrated the value of combining two modern forestry
technologies, Terrestrial Laser Scanning (TLS) and Airborne Laser Scanning (ALS), when
determining a forest’s carbon content. The TLS was able to capture and process 46 highly
detailed TLS scans of trees. The trees’ height and volume data were extracted from these scans,
and combined to create a previously unavailable ALS-friendly allometric equation for
Harwood forest. When the equation was applied to ALS data from both Harwood and Kielder,
it showed that both forests had a normal distribution of carbon content when sorted by tree
height. This was in spite of the bimodal distribution of the quantities of trees sorted by height.
In both forests, the trees over 15m had a larger effect on the carbon content than the trees below
15m, despite both peaks in quantity of trees occurring below 15m. The total carbon content for
the forest was 833 tonnes (+229 tonnes or -96 tonnes) for Harwood and 9890 tonnes (+2,740
tonnes or -1130 tonnes) for Kielder. However, biases in height caused a +37% or -23%
uncertainty in Harwood carbon content. Uncertainties in TLS volumes and ALS heights must
also be considered. Understanding how all the uncertainties interact will involve a comparison
between the TLS data collected in the study and the ALS data scheduled to be collected from
Harwood later this year.
If wide scale carbon monitoring is to be performed over the whole of Great Britain, then the
process must be as streamlined as possible. One way to optimize the collection of TLS data is
to scan as few trees as possible that will still allow the data to achieve the desired accuracy.
For example, if the desired volume accuracy is only 30%, similar to the uncertainty resulting
from height measurements, then a five binning method can reach this accuracy about 40% of
the time using only ten trees. If a 10% accuracy is desired, the number of trees included in the
training set matters more than the method used to select them. The pursuit of large quantities
of trees should be undertaken so that the computational time afterwards is minimized. This will
involve the use of additional reflectors when taking field measurements. While fewer trees will
be able to be scanned in the same amount of field time, the time needed to register the point

47
clouds will decrease. The result is an increase the number of trees processed and able to be
used in the allometric training set.
As of 2003, Harwood Forest stored the equivalent of 3,050 tonnes (+838 tonnes or -351 tonnes)
of carbon dioxide in 16km2
. Alone this forest has little impact on the national emissions level,
which as of 2014, was estimated at over 500 million tonnes of carbon dioxide (Department of
Energy and Climate Change, 2015). This is especially the case when considering that carbon
offsets calculated on a yearly basis should only include the carbon that has been added to the
forest within that year. However, Sitka Spruce is the most common tree in Great Britain
(National Forest Inventory, 2011a), and, based on the estimation of basic density (Moore, 2011)
and percentage carbon content (Matthew, 1993; Tobin and Nieuwenhuis, 2005) used in this
paper, they contain the equivalent of 103,500 tonnes (+11,800 tonnes or -28,400) tonnes of
carbon dioxide. This is a meaningful impact on the carbon budget, and as such must be
effectively monitored. Harwood’s TLS-derived allometric equation, combined with
widespread, periodic ALS surveys, can be used to effectively monitor carbon and increase the
accuracy of Great Britain’s carbon budget.

48
Auto-critique
I wanted to work on a dissertation topic that had implications for climate change mitigation or
adaptation. Mat Disney showed me the detailed mapping potential of TLS, and I was excited
to be able to utilize some of my modelling background from my undergraduate degrees in
Physics and Mathematics. The forestry aspect was particularly appealing, because of my time
spent as an outdoor educator.
One of the primary strengths of this paper is the use of field measurements that I helped collect
when calculating a previously inaccessible allometric equation. The equation was applied to
Harwood and Kielder ALS data as a test run for when ALS data is collected from Harwood
later this year. Both forests were able to be compared. When the allometric equation was
applied to trees outside the training set it was noted due to possible biases. This paper offered
an alternative method to Tobin and Nieuwenhuis (2005) study on the amount of carbon in an
Irish Sitka Spruce plantation. They created their equation by destructively harvesting 36 trees.
This study had an additional 10 trees to use when creating the allometric equation. I was able
to examine how some sources of uncertainties might affect the allometric tree volumes, the
TLS measured heights and the sampling method used to create the allometric training set.
Sampling methods and their implications for potential bias were examined, and their findings
were applied to my own sampling method. This allowed me to acknowledge some potential
biases in my equation.
Due to time limitations, only 46 trees were able to be extracted from the 1000’s of trees in the
TLS data. The use of more trees would have made the equation more robust. Additionally, it
would have been better if uncertainties in TLS height and volume, ALS height, and their
interactions were examined. Kielder’s calculations assumed that it was a Sitka Spruce forest.
The presence of other trees could have been considered. One basic method would have been to
multiply the carbon content by the percentage of Sitka Spruce. Additionally, the methods
section involving Andy Burt’s code was a little vague. I only had a basic understanding of how
the code actually worked, and there was limited resources written on it.
If I were to recollect the TLS data I would have used additional scanners to make the
registration process easier. It took three tries to register the data, which used up all the time that

49
Andy Burt was still in the country. I then processed the TLS data before the ALS data, to take
advantage of Phil Wilkes’s presence. As a result Andy Burt’s model was still generating trees
a week and a half before the deadline. This limited the number of trees captured by the model
and the amount of time available for final data analysis. If the TLS data was processed first,
the model could have run while the ALS data was being processed. This would have produced
more trees and may have allowed more time for data analysis.

50
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