Towards Small-footprint Airborne LiDAR-assisted
Large Scale Operational Forest Inventory
- A case study of integrating LiDAR data into Forest Inventory and
Analysis in Kenai Peninsula, Alaska
Yuzhen Li
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
University of Washington
2009
Program Authorized to Offer Degree: College of Forest Resources
University of Washington
Graduate School
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Yuzhen Li
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examining committee have been made.
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_____________________________________________________
Gerard F. Schreuder
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______________________________________________________
Gerard F. Schreuder
______________________________________________________
David G. Briggs
______________________________________________________
Eric C. Turnblom
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Abstract
Towards Small-footprint Airborne LiDAR-assisted
Large Scale Operational Forest Inventory
-A case study of integrating LiDAR data into Forest Inventory
and Analysis in Kenai Peninsula, Alaska
Yuzhen Li
Chair of the Supervisory Committee:
Professor Gerard F. Schreuder
College of Forest Resources
Many studies have already demonstrated that small-footprint airborne LiDAR has the
capacity to measure forest biophysical characteristics and the accuracy of the results is
relatively consistent and independent of specific LiDAR systems. However, most
previous studies were conducted in small research areas. To date, there have been
relatively few examples of applying LiDAR to large area operational forest inventory
because of the high cost and lack of methodology and expertise. The main objective of
this research is to develop processing and analysis techniques to facilitate the use of
small-footprint LiDAR data for large-scale Forest Inventory and Analysis (FIA) on the
Kenai Peninsula of Alaska. Results from this study indicate that it is possible to
develop parsimonious regression models for different forest types using three primary
LiDAR metrics - mean height, coefficient of variation of height and canopy point
density. LiDAR mean height represents canopy height in the field, coefficient of
variation of height represents canopy depth, and canopy point density represents
canopy cover. These three LiDAR metrics succinctly describe the 3D canopy structure
and have clear biological interpretation. Forest aboveground biomass models using
these three LiDAR metrics have R2 values ranging from 0.68 to 0.87 for three
different forest types. This research also assessed plot position error and plot size on
these three LiDAR metrics and predicted forest biomass through simulation. Results
show that the accuracy of plot position and plot size are important factors affecting the
accuracy and precision of LiDAR metrics and predicted biomass in heterogeneous
forest stands. Results suggested that small position error is acceptable in homogeneous
forest stands, but accurate field plot positions are necessary in heterogeneous forest
stands. In the context of FIA, acquiring accurate coordinates for the subplots is not
currently part of the standard plot protocol. If it is not possible to obtain accurate GPS
locations for each subplot, linking LiDAR data with field measurements using larger
plots, which encompass four subplots, may provide a way to characterize forest
condition at similar scale as the combination of the four subplots. Finally, maps of
predicted plot-level forest height over the whole study region were produced from
both LiDAR data and field measurements, and the distribution of predicted stand
height from field data is very similar to the distribution of predicted LiDAR mean
height.
In conclusion, the methodology and results presented in this dissertation demonstrate
that it is feasible to integrating LiDAR data with existing FIA field plot network.
Table of Contents
List of Figures............................................................................................................iii
List of Tables.............................................................................................................. v
Chapter 1 Introduction................................................................................................ 1
1.1 Current FIA inventory scheme ......................................................................... 2
1.2 Using airborne LiDAR in forest inventory....................................................... 4
1.3 Research objective............................................................................................ 7
Chapter 2 Literature Review ...................................................................................... 9
2.1 LiDAR system .................................................................................................. 9
2.1.1 Airborne LiDAR system.......................................................................... 10
2.2 Airborne LiDAR application in forestry ........................................................ 12
2.2.1 Creating Digital Terrain Models in forested area.................................... 12
2.2.2 Deriving forest structure characteristics for forest inventory.................. 13
2.2.3 Applying LiDAR data in operational forest inventory............................ 18
Chapter 3 LiDAR-derived Metrics Selection ........................................................... 25
3.1 Introduction .................................................................................................... 25
3.1.1 LiDAR metrics selection ......................................................................... 25
3.1.2 Generality of LiDAR-based forest structure prediction models.............. 27
3.2 Data and methods ........................................................................................... 29
3.2.1 Study sites................................................................................................ 29
3.2.2 LiDAR data ............................................................................................. 31
3.2.3 LiDAR metrics selection methods........................................................... 33
3.3 Results ............................................................................................................ 35
3.3.1 LiDAR metrics selected by principal component analysis...................... 35
3.3.2 Model comparisons ................................................................................. 38
3.4 Discussion....................................................................................................... 40
i
Chapter 4 Effects of Plot Position Error and Plot Size on LiDAR-derived Metrics
and Predicted Biomass ............................................................................................. 44
4.1 Introduction .................................................................................................... 44
4.2 Data and methods ........................................................................................... 46
4.2.1 Unsupervised classification ..................................................................... 47
4.2.2 The contagion spatial variation index...................................................... 48
4.2.3 Simulation................................................................................................ 49
4.3 Results ............................................................................................................ 50
4.3.1 LiDAR patch classification and spatial variation.................................... 50
4.3.2 Effects of plot location error and plot size on LiDAR-derived metrics .. 56
4.3.3 Effects of plot location error and plot size on predicted biomass ........... 64
4.4 Discussion....................................................................................................... 65
Chapter 5 Forest Height Prediction from Field Measurement and LiDAR Data via
Spatial Models .......................................................................................................... 70
5.1 Introduction .................................................................................................... 70
5.2 Study area and data description...................................................................... 71
5.3 Methods .......................................................................................................... 73
5.4 Results ............................................................................................................ 74
5.4.1 Empirical semivariogram model fitting................................................... 74
5.4.2 Spatial prediction..................................................................................... 76
5.4.3 Difference in predicted plot-level heights between field-based
measurements and LiDAR-based measurements ............................................. 81
5.5 Discussion....................................................................................................... 83
Chapter 6 Conclusions.............................................................................................. 86
List of References..................................................................................................... 94
ii
List of Figures
Figure 1.1 The FIA national hexagon array (Bechtold and Patterson 2005).................. 2
Figure 1.2 FIA Phase 2 plot design (Bechtold and Patterson 2005) .............................. 3
Figure 3.1 Location of three study sites (denoted by black stars) ................................ 29
Figure 3.2 Results of plot-level LiDAR-based estimation of aboveground biomass for
Capitol Forest (CF), Mission Creek (MC), Kenai Peninsula (KE) and the combined
dataset with mean height, coefficient of variation of height and canopy point density
as predictor variables.................................................................................................... 40
Figure 4.1 LiDAR patches classification results based on 5X5m grids without field
plot location .................................................................................................................. 52
Figure 4.2 LiDAR patches classification results based on 5X5m grids with field plot
center indicated by black asterisk................................................................................. 53
Figure 4.3 LiDAR patches clumped classification results based on 5X5m grids without
field plot location.......................................................................................................... 54
Figure 4.4 LiDAR patches clumped classification results based on 5X5m grids with
field plot center indicated by black asterisk ................................................................. 55
Figure 4.5 Contagion value for classified LiDAR patches........................................... 56
Figure 4.6 Mean of the differences between LiDAR-derived mean height from
simulated plots and from original plots over 100 simulations. .................................... 57
Figure 4.7 Standard deviation of the differences between LiDAR-derived mean height
from simulated plots and from original plots over 100 simulations............................. 59
Figure 4.8 Mean of the differences between LiDAR-derived canopy cover from
simulated plots and from original plots over 100 simulations. .................................... 60
Figure 4.9 Standard deviation of the differences between LiDAR-derived canopy
cover from simulated plots and from original plots over 100 simulations................... 61
Figure 4.10 Mean of the differences between LiDAR-derived coefficient of variation
of height from simulated plots and from original plots over 100 simulations. ............ 62
iii
Figure 4.11 Standard deviation of the differences between LiDAR-derived coefficient
of variation of height from simulated plots and from original plots over 100
simulations.................................................................................................................... 63
Figure 4.12 Ratio of average residual from simulated plots versus the mean of fieldestimated biomass over 100 simulations ...................................................................... 65
Figure 5.1 Map of study area. Picture in the middle is LANDSAT ETM+ image for
the study area and red circles indicate field plot locations ........................................... 72
Figure 5.2 Empirical semivariogram fitting of four aggregated plot-level height ....... 75
Figure 5.3 Maps of predicted plot-level heights from field measurements along with
their standard error estimates........................................................................................ 78
Figure 5.4 Maps of predicted plot-level heights from LiDAR data along with their
standard error estimates................................................................................................ 79
Figure 5.5 Empirical cumulative distribution function and kernel density function of
predicted plot-level heights .......................................................................................... 80
Figure 5.6 Differences of predicted plot-level heights between field-based
measurements and LiDAR-based measurements ......................................................... 82
Figure 5.7 Empirical probability density function of the differences of predicted plotlevel heights.................................................................................................................. 83
iv
List of Tables
Table 3.1 . Summary of field plots for three study sites............................................... 29
Table 3.2 LiDAR system specification for three study sites ........................................ 32
Table 3.3 Correlation between principal components and original LiDAR metrics .... 37
Table 3.4 Final above ground biomass regression models from different statistical
methods......................................................................................................................... 39
Table 4.1 Proportion of classes in classified LiDAR patches (5mX5m resolution) .... 53
Table 4.2 Biomass regression models for 30 selected FIA plots based on original plot
location for two different plot sizes.............................................................................. 64
Table 5.1 Summary of predicted plot-level height....................................................... 77
v
ACKNOWLEDGEMENTS
I would like to express my sincere appreciation to my major professor, Dr. Gerard F.
Schreuder, for his time, patience and contributions to the successful completion of this
research. I have been very privileged to get guidance and support from Dr. Schreuder,
even after his retirement.
My appreciations are also extended to Dr. Hans-Erik Andersen and Mr. Robert
McGaughey for their valuable insights, technique support and constructive challenges
they raised through this project. They made my graduate study the most enriching
professional experience I have had so far.
I also would like to thank the members of my supervisory committee, Professor David
Briggs and Professor Eric Turnblom for their long-term profession and personal
support. They both were on my Master committee before. Without their trust and
support, I probably won’t be here today.
My thanks also go to Stephen Reutebuch of the USDA Forest Service for his
guidance. I also would like to thank Mr. Ken Winterberger from the Anchorage
Forestry Science laboratory, USDA Forest Service PNW station, for helping with field
data and answering many of my questions. I also would like to thank my graduate
student friends - Jacob Strunk, Tobey Clarkin, Andrew Cooke, Akira Kato, Joowon
Park, Tracey Marsh, Alicia Sullivan, Rapeepan Kantavichai and Nora Konnyu for
their technical or mental support.
I appreciate the financial support provided by Forest Inventory and Analysis program
and Precision Forestry Cooperative.
vi
Finally, my deepest appreciation goes to my family, especially to my husband, my
son, my parents for their love, support and sacrifices over this long journey.
I thank you all from the bottom of my heart.
vii
1
Chapter 1 Introduction
Operational forest inventory collects information relating to forest resources at large
landscape, regional, or national level. It includes estimating forest area, species
composition, growth, mortality, and harvesting. The USDA Forest Service Forest
Inventory and Analysis (FIA) is one example of operational forest inventory at
national level. The FIA program of the USDA Forest Service conducts periodic
surveys of forestland in the United States to determine its extent, condition, growth
and removal both on private and public lands. As national and regional interest in
assessing and monitoring ecosystem sustainability has grown in recent years, FIA is
being asked to provide information on the distribution and trends of forest structure
and diversity at more detailed levels with higher accuracy and shorter inventory cycle
(American Forest Council 1992). This represents a significant challenge for the
traditional ground-based forest inventory, especially in remote areas like Alaska where
costs to install and remeasure ground plots are prohibitive. Airborne Light Detection
and Ranging (LiDAR) is an active remote sensing technique that offers the potential to
capture detailed three-dimensional information describing tree canopies over large
area in a very short time. It has been reported repeatedly in the literature that airborne
LiDAR can produce reliable and useful estimates of tree-level, average plot-level and
stand-level forest inventory parameters, such as tree height, tree diameter distribution,
stand volume, and biomass, especially in scientific projects conducted in forest types
with relatively simple composition and structure, such as boreal forest. Attempts are
also being made to introduce airborne LiDAR to operational forest inventory,
especially in Nordic countries with promising results (Naesset et al. 2004, Naesset
2007). Integrating LiDAR into large-scale operational FIA may provide an efficient
way to reduce the inventory cycle and increase the accuracy of estimates compared
with the current FIA inventory design.
2
1.1 Current FIA inventory scheme
Current FIA, as conducted by the US Forest Service, consists of three Phases. In Phase
1, remote sensing imagery, mostly aerial photographs, are used to stratify lands into
forest and nonforest. Phase 2 involves field data collection. Permanent field plots are
established based on a national array of approximately 6000-acre hexagons with each
containing one permanent ground plot (Figure 1.1) (Bechtold and Patterson 2005). All
vegetated plots that fall on National Forest Systems land and forested plots on other
lands will be ground sampled. At each ground plot, a cluster of four circular subplots
arranged in a fixed pattern is established (Figure 1.2). Tree and plot measurements are
collected. Phase 3 is designed to assess forest health by sampling a subset of Phase 2
plots. Approximately one out of every 17 Phase 2 plots is identified as a Phase 3 plot
and measures related to forest ecosystem health, such as tree crown, soil, lichen and
down woody debris, are collected.
Figure 1.1 The FIA national hexagon array (Bechtold and Patterson 2005)
3
Figure 1.2 FIA Phase 2 plot design (Bechtold and Patterson 2005)
The Phase 2 plot design consists of a cluster of four circular subplots (Figure 1.2). The
subplots are 1/24 acre in size with a radius of 24.0 ft. The center subplot is subplot 1.
Subplots 2, 3 and 4 are located 120.0 ft horizontal at azimuth of 0, 120 and 240
degrees, respectively from the center of subplot 1. The center of subplot 1 (plot center)
is obtained using a Global Positioning System (GPS) receiver while the centers of
other subplots are often obtained using tape and compass based on the horizontal
distance and azimuth among subplots. Data on trees with diameter of 5.0in or greater
is collected on each subplot. Each subplot contains a microplot of approximately 1/300
acre in size with a radius of 6.8ft. The center of the microplot is offset 90 degrees and
12.0 ft horizontal from each subplot center. Sapling and seedlings are measured on
each microplot. Field plots may also include annular plots of ¼ acre in size with a
radius of 58.9 ft with annular plot center coinciding with each subplot center. Annular
plots are used to sample rare events, such as very large tree (USDA Forest Service
2003). This clustering pattern was designed to sample more local variation and at the
same time overcome the constraints of cost and time associated with simple random
4
sampling, since travel expenditures makes up most of the inventory cost (Birdsey1995,
Bechtold and Patterson 2005).
Currently, the FIA inventory design is essentially ground-plot based and inventory
parameters for large areas are estimated by applying statistical estimating models. This
involves logistically-complex labor-intensive field work and often incorporates
intricate sampling schemes and extrapolation efforts due to the inherent complexity of
forest areas. The costs in terms of money, time and labor are huge. In addition, FIA’s
sampling design has an intensity of one plot per approximately 6000 acres and is
assumed to produce a random, equal probability sample. Traditionally, the FIA
program has reported estimates of forest attributes for states and counties. Due to the
low sampling rate (1/24*4/6000*100 =0.003%), FIA sample design may not be
adequate to capture the forest spatial variability at large scales. Some studies already
indicate that current FIA plot size is not big enough to capture density of large trees
and snags, species richness and mortality in mature old-growth Douglas-fir stands
(Gray 2003). Finally, the number of FIA field plots available for model development
is often constrained by accessibility and cost.
1.2 Using airborne LiDAR in forest inventory
LiDAR actively transmits beams of light toward an object of interest, and receives the
light that is scattered and reflected by objects in its path. The difference in time from
transmission to reception is used to calculate the distance (range) of the object by
multiplying the time differential by the speed of light. Unlike passive remote sensing,
LiDAR does not image reflected or emitted solar radiance from objects in a given
scene, instead it systematically emits near infrared laser pulses and records the georeferenced x, y, and z coordinates and intensity of the reflections, resulting in a highdensity and high-accuracy 3D point cloud (Flood and Gutelius 1997).
5
In a forested area, the ability of some laser pulses to penetrate partly into and possibly
through the forest canopy to produce several separately recordable reflections provides
the theoretical basis for analysis of three-dimensional (3-D) forest structure using
LiDAR measurements (Ackermann 1999). The 3-D characteristics of LiDAR data
make it possible to measure the vertical dimension of the canopy, which is difficult to
measure in ground surveys or using aerial photographs. At the same time, it is easy to
filter out the ground returns in LiDAR data to avoid mixing ground and canopy
reflections, which is a common problem in 2D photograph and satellite image. In
addition, compared to field-based inventory, LiDAR data has other advantages, such
as the short data acquisition and processing time, extensive area coverage, precise
georeferenced location and highly accurate measurements. All these features make it
very attractive to the forestry community.
In recent years, the topic of using of airborne LiDAR to describe forest structure
characteristics has been widely studied. Numerous studies have shown that mean tree
height and canopy height distribution can be directly retrieved from LiDAR data at the
plot level. Other important structure characteristics, such as stem volume, basal area,
stand density, aboveground biomass and canopy fuel parameters can be estimated by
regression techniques at acceptable accuracy and precision (Naesset 2002, Andersen
2003, Holmgren 2004, Maltamo et al. 2004, Naesset et al. 2004, Andersen et al. 2005).
Also there have been some attempts to extract individual tree attributes from LiDAR
measurements (St-Onge 2000, Young et al. 2000, Hyyppa et al. 2001, Lim et al. 2001,
Magnussen et al. 2001, Popescu et al. 2002, 2003 and Holmgren et al. 2003,
Brandtberg 2007), including species classification (Brandtberg et al. 2003), individual
tree measurements (Persson et al. 2002) and growth (Yu et al. 2004a). Many
experiments have already demonstrated that LiDAR has the capacity to measure forest
biophysical characteristics and the accuracy of the results is relatively consistent and
independent of specific LiDAR systems. Before transiting from research to practical
6
application, more comprehensive research efforts are needed to assess LiDAR
performance over large area.
Study over large area is necessary to determine the actual accuracy of predictions of
forest stand attributes using LiDAR measurements. However, it is unusual to have
accurately georeferenced field plots available over large regions. The USDA Forest
Service FIA provides a unique opportunity because FIA establishes and maintains
nationwide field plot network and collects field data using the same field protocol. In
addition, FIA ground plots distributed over all forested area in the nation (with a few
exceptions, such as interior Alaska and Hawaii) cover a complete range of forest
condition and these existing plots are measured over time. Field measurements
collected by FIA can be used to develop and validate LiDAR analysis models,
whereas LiDAR techniques make the data that previously was available only for a few
ground plots available for a much larger region, providing information on spatial
variability which is hard to capture using field plots alone.
However, there are some problems integrating LiDAR data with FIA field plots. The
common procedures using LiDAR data require accurate locations for field plots.
Traditional ground-based FIA plots are not designed to provide spatially explicit
information, and the plot location information recorded in the field only serves as an
approximate reference for locating the plot for the next visit. The accuracy of these
locations is usually poor. In addition, because of the canopy interference with GPS
reception, it is often difficult to obtain accurate ground positions, especially under
dense canopy. Errors of 10 meters in current FIA plot records are not uncommon and
some plots may have position error as high as 50 meters (Reutebuch et al. 2005). For
example, investigators in the North Central FIA unit found the average separation
distance of 1145 remeasured FIA plots was 13.6m with standard deviation of 46.2m
(Hoppus and Lister 2006). This makes it difficult to georeference LiDAR data with
FIA field plots and presents a challenge to integrate LiDAR data with FIA field
7
measurement. There are some studies acknowledging the possible position error of the
ground reference plots (Brandtberg et al. 2003, Holmgren et al. 2003) and their
recommendation is to use high-precision GPS units. For the FIA field plot network,
considering the large number of plots involved, the cost of GPS equipments and
weight for field crews to carry them are high, thus acquiring the accurate plot location
using high-precision GPS is expensive, especially for the remote areas.
1.3 Research objective
This study explores the feasibility of using multiple-return small-footprint LiDAR data
to support large scale forest inventory in southcentral Alaska USA, where field work
is expensive and useful satellite imagery is not easy to obtain due to persistent cloud
cover. The main objective was to investigate the utility of small-footprint LiDAR data
in the context of large-scale assessment and monitoring of forest height and biomass,
especially in remote regions such as Alaska. This study examined three important
questions regarding the use of LiDAR in the context of operational forest inventory: 1)
is it possible to select a small set of LiDAR metrics which have strong prediction
power and also have clear biological interpretation? 2) what are the effects of plot
position error and plot size on derived LiDAR metrics and predicted plot-level
biomass? 3) what are the differences between predicted plot-level heights based on
operational field inventory and on LiDAR measurements when compared over a large
region using spatial modeling? This study attempts to make a contribution to the
boarder field of forest measurements through the innovative application and analysis
of LiDAR for forest inventory, especially for large-scale operational forest inventory
where accurate field plot positions are not available. Results from this study will
provide valuable information regarding the usability of LiDAR for the US forest
Service FIA program given the operational constraints of the current FIA field plot
design.
8
The main study area is located in the west of the Kenai Mountains, Kenai Peninsula, in
south central Alaska. This area covers approximately 3000 square miles and primary
forest types are white spruce (Picea glauca), black spruce (Picea mariana), paper
birch (Betula papyrifera) and mixed spruce and birch. A total of 105 FIA permanent
field plots located in this area were used in this study. In addition, two other small
areas were also used as supplementary samples. One is a 5.2 km2 study area within the
Capitol State Forest, western Washington State. This area is dominated by Douglas-fir
(Pseudotsuga menziesii) and western hemlock (Tsuga heterophylla). The other area is
located in the Mission Creek watershed, in the eastern Cascade Mountains of
Washington State. The main species are Douglas-fir and Ponderosa pine (Pinus
ponderosa) with scattered grand-fir (Abies grandis).
The remainder of this dissertation is organized as follows: Chapter 2 reviews the
relevant literature on LiDAR systems and methods used to apply LiDAR in forest
measurement and inventory. Chapter 3 describes three methods to select LiDAR
metrics-stepwise regression, principal component analysis and Bayesian Model
Averaging and presents forest aboveground biomass models using selected LiDAR
metrics. Chapter 4 describes a simulation approach to examine the effects of plot
position error and plot size on derived LiDAR metrics and predicted plot-level
biomass. Chapter 5 applies spatial modeling techniques to produce maps of predicted
plot-level height over western Kenai, and then compares predicted heights from
operational field inventory and LiDAR measurements. Chapter 6 summarizes the main
conclusions and implications of the research. The limitations of this study are also
discussed in Chapter 6.
9
Chapter 2 Literature Review
2.1 LiDAR system
LiDAR is an active laser remote sensing technology. It transmits laser pulses typically
in the infrared wavelengths toward an object of interest at high frequencies, and
receives the light that is scattered and reflected by objects in its path. The difference in
time from transmission to reception is used to calculate the distance (range) of the
object by multiplying the time differential by the speed of light. A typical LiDAR
system consists of three main components: a Global Positioning System (GPS) to
provide position information, an Inertial Navigation System (INS) for attitude
determination and a laser scanner to provide the range from the laser-beam firing point
to its footprint (Bang et al. 2008). By varying the wavelength of the light transmitted,
pulse frequency and duration, and other factors, LiDAR can be used in a variety of
applications to detect numerous substances.
Scanning laser systems may be mounted on different platforms: on a tripod (terrestrial
LiDAR system), on aircraft (airborne LiDAR system), or on satellite (space-borne
LiDAR system). Ground-based laser scanning is used to capture very high-resolution
data describing architectural details in construction projects. Ground-based laser
scanning systems have been used in forestry research, and they can provide detailed
reconstructions of trunk, branch and leaf distribution from which tree locations,
diameter and height, timber volume and canopy gap fraction can be quantified
(Hopkinson et al. 2004, Danson et al. 2008, Litkey et al. 2008), but the complexity of
forest scenes makes analysis very complicated. Space-borne LiDAR systems have
often been used in atmospheric research and a few large-scale ecosystem studies (Blair
et al. 2001, Lefsky et al. 2002, Boudreau et al. 2008). Due to limited data availability
and coarse resolution, there are not many studies that apply space-borne LiDAR data
10
for forest inventory (Pflugmacher et al. 2008, Pang et al. 2008). Airborne LiDAR
systems are commercially available and have been used to map and model terrain
elevation. In the past two decades, airborne LiDAR systems have been used to model
forest canopy structure and function, mostly in the scientific research projects (Lefsky
et al. 1999, 2002, Næsset 2002, Drake et al. 2003, Holmgren 2004, Lim and Treitz
2004, Maltamo et al. 2004, Mean et al. 1999, Næsset et al. 2004, Andersen et al.
2005). There are also some efforts to promote airborne LiDAR system in operational
forest inventory, especially in Scandinavia counties (Naesset 2007).
2.1.1 Airborne LiDAR system
In airborne laser scanning, a swath of terrain under the aircraft is surveyed through the
lateral deflection of the laser pulses and the forward movement of the aircraft. The
scanning pattern within the swath is established by an oscillating mirror or rotating
prism which causes the pulses to sweep across in a consistent pattern below the
aircraft (Baltsavias 1999b). Baltsavias (1999a) and Wehr and Lohr (1999) presented
the basic principles and formulas of airborne LiDAR. Baltsavias (1999b) compared
laser scanning to photogrammetry in the following aspects: sensors, platforms, flight
planning, data acquisition conditions, imaging, object reflectance, automation,
accuracy, flexibility and maturity, production time and costs, and concluded that the
two technologies are fairly complementary and their integration can lead to more
accurate and complete products.
There are two main categories of airborne LiDAR systems: small-footprint discretereturn LiDAR and large-footprint, waveform-recording LiDAR. Small-footprint
discrete-return LiDAR devices measure either one (single-return systems) or a small
number (multiple-return systems) of heights by identifying, in the return signal, major
peaks that represent discrete objects in the path of the laser illumination. The distance
corresponding to the time elapsed before the leading edge of the peak(s), and
sometimes the power of each peak, are the typical measurements recorded by this type
11
of system (Wehr and Lohr 1999). Large-footprint waveform-recording devices record
the time-varying intensity of the returned energy from each laser pulse, providing a
record of the height distribution of the surfaces illuminated by the laser pulse.
Small-footprint discrete-return LiDAR systems have a small Instantaneous Field Of
View (IFOV) which is usually between 0.2m and 0.9m. The small diameter of their
footprint and the high repetition rates of these systems together can yield dense
distributions of sampled points. Thus, discrete-return systems are preferred for
detailed mapping of ground and canopy surface topography (Flood and Gutelis 1997).
Another advantage is their ability to aggregate the data over areas and scales specified
during data analysis, so that specific locations on the ground, such as a particular
forest inventory plot or even a single tree crown, can be characterized. Finally,
discrete-return systems are readily available, with ongoing and rapid development.
Large-footprint waveform LiDAR systems have a large IFOV which is usually 5m or
larger (although small-footprint waveform LiDAR systems are starting to emerge).
Waveform-recording LiDAR systems record the entire time-varying power of the
return signal from all illuminated surfaces and are therefore capable of collecting more
information on canopy structure than all but the most spatially dense collections of
small-footprint LiDAR. In addition, waveform-recording LiDAR integrates canopy
structure information over a relatively large-footprint and is capable of storing that
information efficiently, from the perspective of both data storage and data analysis.
Finally, waveform-recording LiDAR is currently being collected globally from the
spaceborne ICESat system (Lefsky et al. 2002).
Means et al. (2000) gives a good comparison between small and large footprint
LiDAR by examining them with respect to their design, capabilities and uses,
especially in the context of forestry application. The primary differences between
small- and large-footprint LiDARs involve the scale and resolution of terrain and
vegetation characterization.
12
The technical capabilities of LiDAR systems have increased rapidly. Baltsavias
(1999a, 1999b) reviewed existing commercial systems and firms ten years ago. All
systems have been improved since then. For example, for small-footprint LiDAR
systems, the industry standard has advanced from systems emitting 5000 pulses per
second and measuring a single return to those emitting between 75,000 and 250,000
pulses per second, and measuring up to seven returns, with most recording the
intensity of each return (Moffiet et al. 2005). Today most LiDAR systems can record
multiple pulses. Some systems have an integrated digital camera to provide digital
images that can be used in bare earth modeling and feature classification procedures.
2.2 Airborne LiDAR application in forestry
Over forested areas, most of the laser pulses are reflected by the leaves and branches
of the trees, but a certain fraction of the laser pulses can pass partly or through forest
canopy and reach the forest floor through small gaps in the canopy. Thus it is possible
to reconstruct both the three dimensional structure of forest canopy and the terrain
surface under canopy using LiDAR point cloud data.
2.2.1 Creating Digital Terrain Models in forested area
To generate Digital Terrain Models (DTM), terrain LiDAR points have to be separated
from vegetation LiDAR points. Various filtering algorithms have been proposed.
Kilian et al. (1996) generated a DTM based on mathematical morphology operations
for comparing height differences. Kraus and Pfeifer (1998) used a discriminate
function and introduced linear prediction into the DTM generation. Axelsson (1999,
2000) described a method based on progressive densification of a triangular irregular
network (TIN), a surface is allowed to fluctuate within certain values and points from
the point cloud are added to the TIN during iteration, these iterations proceed until no
further low ground points can be added. Vosselman (2000) proposed a slope based
13
filtering method. The basic idea behind his algorithm is that a large height difference
between two nearby points is unlikely to be caused by a steep slope in the terrain,
therefore the higher point has a high probability of being a non-ground point, such as a
vegetation hit. Wang et al. (2007) introduced a Guassian-fitting model to identify
ground returns.
The filtering algorithm used by the commercial software TopScan is an iterative
procedure that first computes a rough terrain model from the lowest LiDAR points
found in a moving window of a rather large size. All points with residuals exceeding a
given threshold are filtered out, and a new DTM is calculated from the remaining
points. This step is repeated several times, reducing the window size with each
iteration (Petzold et al. 1999).
In terms of terrain model accuracy, Kraus and Pfeifer (1998) report a vertical root
mean squared error (RMSE) of 57 cm for a wooded area in Austria. In a study over
open areas with flat hard surfaces, Pereira and Janssen (1999) report accuracies of 15
cm. In a study under a conifer forest canopy in western Washington, Reutebuch, et al.
(2003) reported overall ground surface errors of 22 cm with a standard deviation of 24
cm under a variety of canopy densities.
Despite intense efforts in the creation of high-resolution DTMs from LiDAR data, the
characterization of terrain topography under dense forest conditions remain
challenging.
2.2.2 Deriving forest structure characteristics for forest inventory
There are two main approaches for deriving forest characteristics using small-footprint
discrete LiDAR: individual tree delineation approach and plot-level regression model
based on LiDAR canopy height distribution approach (Reutebuch et al. 2005,
Packalen et al. 2008). The former approach is usually used for high resolution LiDAR
14
data with 5-10 LiDAR returns per square meter, and the latter is used for low
resolution LiDAR with about one LiDAR return per square meter (Packalen et al.
2008).
2.2.2.1 Individual tree identification and single-tree properties derivation
A common method in individual tree delineation is to detect trees from an interpolated
canopy height model by locating local maxima of the height values. After that, trees
are segmented around the local maxima using some kind of region growing algorithm
(St-Onge 2000, Young et al. 2000, Hyyppa et al. 2001, Magnussen et al. 2001,
Popescu et al. 2002, 2003 and Holmgren et al. 2003). Once treetops are located, tree
height can be obtained by subtracting corresponding heights from the DTM. Tree
diameter and crown area can be predicted using their relationship with tree height and
tree volume can be calculated using estimated diameter and height (Hyyppa and
Inkinen 1999, Persson et al. 2002). Other individual tree parameters, such as the height
to crown, are also derived from LiDAR points (Maltamo et al. 2006, Popsecu and
Zhao 2008).
Estimated height using individual tree extraction approaches is usually lower than
field measured tree height (Nilsson 1996, Perssson et al. 2002, Andersen et al. 2006).
Hyyppa and Inkinen (1999) reported a standard error of less than 1m for the estimated
height of overstory coniferous trees, and Perssson et al. (2002) reported much less than
1m and Brandtberg (1999) reported slightly more than 1m for a test using Norway
spruce. Tendency of underestimation of height is probably due to 1) light transmitted
by the laser will usually penetrate the outer surface of the tree crowns before a
significant return signal is recorded and 2) a large portion of the pulses will be
reflected from the lower part of the visible tree crowns.
Factors that influence the quality of the 3D single tree extraction algorithm are the
density of the raw point cloud and the forest condition. Higher point density will
15
improve the accuracy of tree extraction and better results can be expected for a less
dense forest stands. Magnussen et al. (1999) proposed that if 6–10 laser hits per tree
crown are obtained, individual trees may be detected.
The biggest challenge when using a canopy height models to identify individual trees
is that neighboring trees are often not separated so a tree group instead of a single tree
is often formed (Young et al. 2000). Moreover, only the dominant tree layer can be
detected, and smaller trees in the intermediate and lower height level cannot be
recognized since they are invisible in the canopy height model. Some attempts have
been made to improve this. In the study by Maltamo et al. (2004), a theoretical
distribution function was used to produce estimates of timber volume and number of
stems. Assuming a Weibull distribution of the tree height, large trees were obtained
with individual tree delineation whereas the number of undetected small trees was
predicted from the Weibull distribution. They reported that the accuracy of estimated
stand volume and stand density were improved. There are some new efforts to extract
individual trees using raw LiDAR points instead of canopy height model. Wang et al.
(2007) claimed that their procedure can detect trees in the lower canopy layer. But
they didn’t test the accuracy due to the lack of field data.
There are some studies on species differentiation using LiDAR data. Brandtberg et al.
(2003) classified three deciduous species: oaks, red maples and yellow poplars using
LiDAR intensity data and relative height differences between the first and last
vegetation returns. Holmgren and Persson (2004) classified Scots pine and Norway
spruce using the structure and shape of the tree crowns and intensity data. Moffiet et
al. (2005) conducted exploratory data analysis to assess the potential of laser return
type and return intensity as variables for classifying white cypress pine and poplar
box. Brandtberg (2007) presented a new approach - directed graph for tree species
classification and tried to develop a theoretical framework based on the laser
interaction with trees. An improved classification accuracy of 64% was reported for
16
three leaf-off individual tree species: oak, red maple and yellow poplar. However,
Holmgren et al. (2008) reported that laser scanner data alone do not provide enough
information to enable tree species classification at the individual tree-level and the
best discrimination can be obtained when using a combination of LiDAR and multispectral data. The identification of a range of species or of distinct trees in more
heterogenerous forests has yet to be demonstrated using LiDAR data.
Most individual tree based approaches have been applied in coniferous managed
forests and moderate success has been achieved in delineating trees and predicting
certain metrics. However, it is still difficult in natural forests since the distribution of
trees on different species and size classes is complex.
2.2.2.2 Plot-level regression-model-based forest structure measurement
Three dimensional LiDAR data represent measurements of reflecting surfaces within
forest canopy. Canopy structure characteristics, such as canopy height profile and
canopy LiDAR point density distribution, have been successfully derived and used to
estimate forest stand characteristics, such as basal area, stand density, tree diameter
distribution, stand volume, aboveground biomass, and canopy fuel parameters (Lefsky
et al. 1999, 2002, Næsset 2002, Drake et al. 2003, Holmgren 2004, Lim and Treitz
2004, Maltamo et al. 2004, Næsset et al. 2004, Andersen et al. 2005, Bollandsas and
Naesset 2007). The most popular procedure described in the literature is to apply
multiple linear regression techniques to relate the spatial distribution of LiDAR returns
to coincident plot-level stand inventory variables.
Naesset (2002) presented a two-stage LiDAR-based stand inventory procedure that
has been widely adopted. In the first stage, individual canopy height distributions of
LiDAR points were created for each training plot and regression relationships between
stand structure variables and LiDAR metrics extracted from canopy height distribution
were developed. In the second stage, all forest stands in the LiDAR acquisition area
17
were divided into a grid of cells with cell size equal to the training plot size. Based on
the developed empirical regression model, stand structure variables were predicted for
each cell and final stand estimates were computed as the average or total values of the
individual cell prediction.
In studies carried out across a wide variety of different forest types in North America,
Japan, Europe, Australia, and Canada, LiDAR-derived canopy structure metrics have
been shown to be highly correlated with forest inventory variables and most reported
coefficient of determinations are greater than 0.6 (Lefsky et al. 1999, 2002, Næsset
2002, Drake et al. 2003, Wulder 2003, Holmgren 2004, Lim and Treitz 2004, Maltamo
et al. 2004, Næsset et al. 2004, Andersen et al. 2005, Tickle et al. 2006, Bollandsas
and Naesset 2007). Experiences from leading research conducted in Scandinavia
indicate that laser-based stand inventory is able to produce stand information with
accuracies superior to those of conventional methods based on fieldwork and aerial
photo-interpretation (Naesset 2007).
Besides deriving inventory variables in structurally homogeneous single-layer forests,
there are some attempts to quantify forest structure in heterogeneous multi-layer
forests. Zimble et al. (2003) studied the possibility of using height variance from
LiDAR data and field data to distinguish the single story and multi-story forest. Riano
et al. (2003) used cluster analysis to separate understory trees and overstory trees.
Maltamo et al. (2005) applied a histogram thresholding method to the height
distribution of laser hits to separate different tree layers.
Current research shows a trend toward a combination of laser data and spectral
imagery. LiDAR can be used to locate and describe properties of tree crowns while
spectral imagery is used to enhance species classifications (Lim et al. 2001, Holmgren
et al. 2003, St-Onge 2003, Popescu et al. 2004). Using a combination of LiDAR data
and aerial photograph, Packalen and Maltamo (2007) tried nonparametric k-most
18
similar neighbor method to predict species specific forest variables such as volume,
stem density, basal area median diameter and tree height. The results showed similar
accuracy to results from the current stand-level field inventory in Finland. The
characteristics of Scots pine and Norway spruce were predicted more accurately than
those of deciduous trees.
2.2.2.3 Comparing individual tree and plot-level regression model approaches
Individual tree identification-based approaches offer the possibility of providing
individual tree-level parameters for all trees and are operationally preferable since
most existing inventory systems rely on individual tree information. In addition,
individual tree approaches represent an improvement over current inventory sampling
methods based on data collected on a small number of intensively monitored plots and
then applied broadly across the forested landscape. However, there is still a long way
to go before the individual tree-based approaches can be used in operational practice.
Plot-level regression modeling is straightforward and suitable for operational use.
Many plot-level regression models have been developed for different forest types. One
disadvantage is that accurate ground plot position is required for model development.
Packalen et al. (2008) compared an individual tree detection approach and plot-level
regression modeling using the same dataset from managed boreal forests in Finland.
They concluded that both approaches produced equally accurate estimates of stem
volume and Lorey’s height. However, stem density estimates were less accurate with
both approaches. In particular, the individual tree approach had a large bias and RMSE
and underestimated stand density.
2.2.3 Applying LiDAR data in operational forest inventory
So far LiDAR applications in forestry are concentrated largely in scientific research
projects. Application of LiDAR for operational forest inventories has been relatively
limited because of the high cost involved, and the lack of methodology and expertise.
19
The increasing availability of commercial LiDAR systems, decreasing cost, and
recognition of the wide range of information that can be obtained from LiDAR data
have led to an increase in utilization. Operational applications have occurred in recent
years, especially in Northern Europe.
The first operational application in the world was developed in Norway by Prof. Erik
Naesset from Agricultural University of Norway (Naesset 2002, 2004). Now this
method is commercially marketed and implemented in Norway. A survey company in
Norway called Prevista (http://www.prevista.no/) offers services using LiDAR for
large area operational forest surveys and it claims deliver many important forest stand
characteristics at competitive price, such as volume per acre, mean diameter, diameter
distribution, dominant and mean height, basal area and number of stems. It has
completed several projects for Norway and Sweden.
The method they use is a two-stage procedure (Naesset 2002). In the first stage,
georeferenced field plots and LiDAR plots were used to develop stratum-specific
empirical relationships between various metrics derived from the laser data and tree
characteristics measured in the field. Such relationships are extrapolated in the second
stage to provide corresponding estimates for each stand. Their method is intended for
use in area-based inventories where the aim is to provide estimates of growth and
volume in each stand for the purposes of forest management planning. So far six
projects have been conducted using this method with the largest project covering a
total area of 49,000ha (Naesset 2007). It was reported that the differences between
LiDAR predicted and ground reference values are from -0.58 to -0.85m for mean
height (standard deviation: 0.64 to 1.01m), -0.60m to -0.99m for dominant height (sd:
0.67 to 0.84m), 0.15 to 0.74cm for mean diameter (sd: 1.33 to 2.42cm), 34 to 108ha-1
for stem number (sd: 97 to 466ha-1), 0.43 to 2.51m2ha-1 for basal area (sd: 1.83 to
3.94m2ha-1), and 5.9 to 16.1 m3ha-1 for volume (sd: 15.1 to 35.1m3ha-1) (Naesset
2004). This procedure depends on precise locations of field plots in the first stage
20
(Naesset 2002, 2004). The main conclusion from Nordic countries is that the tested
procedures, although slightly different between countries and validated with data from
different laser instruments, seem to be robust for use in practical inventories over large
areas, at least if the forest is dominated by coniferous species. Topographic variability
and variability in laser sampling density seem to have limited impact on the
applicability of the stand based procedures. The bias seems to be at an acceptable
level, and the precision for most of the evaluated stand characteristics is higher than
those obtained using traditional inventory methods. The methods are also superior to
conventional inventory methods as far as inventory costs and data utility are
concerned (Nesset et al. 2004).
In the USA, Parker and Evans (2004) proposed a double sampling method of using
LiDAR for forest inventory and they applied this method in a 1,200 acre forest in
Louisiana (Parker and Glass 2004, Parker and Mitchel 2005) and 5,000 acre
timberland in central Idaho (Parker and Evans 2004). Unlike Naesset’s methods,
Parker’s method is essentially individual-tree based. Individual trees were selected
from LiDAR data using a focal filter procedure from a smoothed LiDAR canopy
surface and tree height was calculated as the difference between interpolated canopy
and DTM surface (Parker and Mitchel 2005). Relationships between Diameter at
Breast Height (DBH) and height, estimated from field data, were applied to LiDAR
tree heights to predict DBH for LiDAR trees. Basal area and volume were then
calculated on both coincident LiDAR and field plots, and they are used as auxiliary
variables in the double-sampling to predict the variable of interest, such as volume of
the total area. They reported that there was no statistical difference on adjusted mean
volume estimates between high density (four hits per 1m2) versus low-density (one hit
per 1m2) LiDAR data, even though it appears that tree heights from high-density
LiDAR more closely approximate ground-measured height. They also reported
sampling errors of 8.16% versus 7.60% without height adjustment and 8.98% versus
8.63% with height adjustment on the Lousiana site for height and low-density LiDAR,
21
and 11.5% sampling error on the Idaho site for low-density LiDAR. In their study,
using adjusted height increases sampling error of the double-sample volume
regression estimates, which is kind of unusual. Their explanation is that the doublesample procedure adjusts the bias between phase 1 (LiDAR plots) and phase 2
(Ground plots) volume estimates and any additional error introduced by the height
adjustment affects the regression estimation. The height adjustment removed the bias
in the LiDAR height estimate, thus dampening the inherent variation in heights and
volume that is normally adjusted by the regression estimator. In addition, they used a
Monte Carlo simulation to randomly assign LiDAR height measurements to species
group and achieved volume distribution across species, which is an interesting
approach to provide species information in LiDAR data applications. However, they
didn’t provide complete validation for their methods.
Nelson et al. (2004) used first-return data from an airborne laser profiler combined
with a video camera to estimate forest volume and biomass by line intercept sampling
method in Delaware (5205 km2).
Instead of depending on accurate registration
between airborne laser and ground transects, they defined an inventory procedure
based on a canopy simulator which uses mapped ground tree data to recreate a canopy
model of the ground plots at 0.25m*0.25m resolution. Then linear and multiple
regression equations were fit between ground measurements and simulated laser
measurement on ground transect. Finally these relationships were used in conjunction
with airborne laser data acquired over the study site to produce regional estimates
(Nelson et al. 1997). The original test in tropical forest of Costa Rica didn’t produce
good results. On two of three study sites, the laser estimates of basal area, volume and
biomass grossly misrepresented ground estimates. Estimations on the third site were
within 24% of ground estimates. In the test in Delaware (Nelson et al. 2004), they
reported that merchantable volume estimates from the LiDAR profiler were less than
US Forest Service estimates by 15% statewide and 22% at the county level. Total
above-ground dry biomass estimates were within 22% of USFS estimates at the
22
county level and within 20% at state level. In general the relationships developed in
their study are not as strong as those obtained in most other LiDAR studies. Some of
the reasons are probably because they only used first return from LiDAR profiling
system, while others use multiple returns from a LiDAR scanning system. The
profiling system only collects data from a narrow strip beneath the platform.
Recording only first returns limited their capability to extract accurate digital terrain
model. In addition the first returns only contains information on canopy height, not on
canopy vertical structure.
In Australia, LiDAR, combined with large scale photography, was used to quantify the
species distribution and forest structure in a 220,000 hectare area (Tickle et al. 2006).
LiDAR and photography were acquired over 150 primary sampling units of size 7.5 ha
(500m*150m). Photography was used for species interpretation and forest type
stratification, and LiDAR was used for extracting canopy height information. Each of
the 150 primary sampling units was then subdivided into 30 systematically numbered
secondary sampling units which were 50m*50m in area. Based on the stratification
results, and considering access condition and travel time, a total of 34 secondary
sampling units were established as ground plots. Regression relationships on height,
foliage/branch projected cover and foliage projected cover were developed between
coincident LiDAR plots and ground plots at individual tree and stand level. The R2
values are were high and the regression relationships were then extrapolated to the
whole area. After comparison with several existing survey systems, they claimed
sampling with photography and LiDAR, either singularly or in combination, provided
similar estimates at the broad levels but also allowed access to more detailed record.
For example, based on species interpretation from large scale photography and
structure estimates from LiDAR, they found that Callitris and Angophora dominated
higher height classes while Acacias generally dominated the lower height classes. This
kind of detailed information is impossible to get from the traditional inventory.
23
Similar efforts on large-scale LiDAR forest inventory are also reported in Canada
(Wulder 2003). Among all such efforts, the only operational application is the one in
Norway. Olsson (2003) attributed Norway’s success to several positive factors, such
as coniferous dominated landscape; researchers working with laser scanning of forest
resources; a surveying company owning a modern laser scanner and the presence of
state subsidies to help coordinate large forest mapping efforts among many land
owners. For most other places, despite the promising results from intensive research
efforts, there is still a long way to go before applying LiDAR to large-area forest
survey operationally. There are several reasons. First, the current cost of LiDAR data
is still high especially for high point density (about $1 per acre); second, there is a lack
of documented relationships between forest canopy structure measured by LiDAR and
the forest structure measured in the field over large areas (Lefsky et al. 1999). Most
previous studies have a relatively small number of field plots from a restricted area,
the accuracy and precision in predicting forest stand attributes may be overestimated,
both by the small sample size and the relative uniformity of species composition and
environmental condition over these small study areas; third, the lack of knowledge on
the relationship between LiDAR system settings and measurement precision. Studies
so far have concentrated on linking coincident LiDAR and field plots together and
testing what measurements LiDAR is best suited for (Popescu et al. 2003). There
haven’t been many efforts on studying how to take full advantage of the wall-to-wall
mapping of forest structure provided by LiDAR, such as assessing spatial variability
across large area to guide field plot distribution.
There are three main advantages when using LiDAR data in large-scale operational
forest inventory. First, LiDAR data can be collected quickly over large areas and is
readily amenable to automated processing and analysis, so information can be quickly
updated when changes happen. Second, laser data can be used to extend a limited
ground sampling effort over areas that may not be easily accessible by ground
24
inventory crews. Third, LiDAR data don’t have saturation problems (Nilson &
Peterson, 1994), commonly seen in passive sensed image products.
25
Chapter 3 LiDAR-derived Metrics Selection
3.1 Introduction
Given the anticipated decline in the cost of LiDAR data collection in the near future, it
is expected that LiDAR data will be an increasingly useful tool in forest inventory. In
a few years, the use of LiDAR data may be as commonplace as the use of aerial
photos and topographic maps today. However, most published LiDAR studies focus
on developing empirical regression relationships between LiDAR metrics and forest
structure field measures and do not consider LiDAR metric selection and biological
interpretation explicitly. In addition, most LiDAR-based models were developed
within a relatively small study area. Little work has been done to assess the generality
of these models across different forest types and regions. In order for LiDAR data to
be useful as an operational tool in forest management, these questions have to be
addressed.
3.1.1 LiDAR metrics selection
Forest canopy is the photosynthetic powerhouse of forest productivity and it is closely
related to what is commonly referred to as stand structure - defined as the size and
number of woody stems per unit area, and related statistics (Oliver and Larson 1996).
The close connection between canopy structure and woody stems provides the
biological basis for the strong regression relationship between LiDAR-derived
(canopy-based) structural metrics and field measurements of stand structure (woody
stem-based). However, due to the complex 3D structure (position and orientation) of
forest canopy components and the variation in reflectivity between leaves, branches,
and twigs within tree crowns, interactions between canopy and laser pulses are very
complex. A few exiting studies have attempted to describe the laser photon interaction
26
with forest canopy using SLICER large-footprint waveform data (Ni-Meister et al.
2001), but physical models using small-footprint discrete-return LiDAR data are not
yet available, although with increases in pulse rate and data density this might become
possible in the future. The most popular procedure described in the literature is to
apply multiple linear regression techniques to link LiDAR canopy structure metrics
with coincident forest stand field measurements.
The large number and complex spatial arrangement of LiDAR returns over forest
canopies can result in a large set of potential predictor variables for regression
analysis. As an example, a total of 46, 44 and 39 LiDAR metrics were used in the
regression models in Næsset (2002), Næsset (2004), and Hall et al. (2005),
respectively. LiDAR data are 3D measurements of tree components: stems, branches,
and foliage; thus most LiDAR metrics are related to canopy height and often highly
correlated. Regression models with highly-correlated independent variables are not
stable from a statistical perspective and hard to interpret from the biological
perspective. Model parsimony – minimizing the number of LiDAR metrics and
avoiding redundant information – needs to be seriously considered in model building.
Næsset et al. (2005) reduced the number of LiDAR variables from 34 original LiDAR
metrics to 7, 5 and 3 non-correlated principal components for the young forest, mature
forest on poor sites, and mature forest on good sites respectively. Although this
method ensured that there was no correlation between predictor variables, it is difficult
to interpret the models because principal components themselves are a linear
combination of the original LiDAR metrics and they don’t have a clear physical
meaning. Hudak et al. (2006) applied best-subset regression on a suite of 26 predictor
variables derived from LiDAR, Advanced Land Imager multispectral and
panchromatic data and geographic (X, Y, Z) location, and identified small sets of
variables for predicting tree basal area and tree density. Best-subset regression uses the
branch-and-bound algorithm to find a specified number of best models containing a
specified number of predictor variables. The problem with the best-subset regression
27
is the number of predictors has to be defined in advance, so the best model is for a
given number of predictor variables instead of for all possible models. Hall et al.
(2005) selected LiDAR predictor variables from a pool of 39 LiDAR metrics based on
mechanistic hypotheses of why these metrics should be good predictors for each stand
structural variable considered. The problem is that the relationships between LiDAR
canopy measurement and field stand structure are very complex and it is difficult to
validate their mechanistic hypotheses. Lefsky et al. (2005a) explored LiDAR metrics
selection using large-footprint SLICER data in western Oregon and Washington states.
The correlations between LiDAR canopy structure and field stand structure indices
was analyzed using canonical correlation analysis. Mean height, cover (or leaf area
index) and height variability were found to represent the fundamental data structure,
contained the majority of data variability, and were associated with physical
characteristics. This method provided a way to place both LiDAR canopy metrics and
field stand indices within the overall covariance structure and can be used as a guide
for model selection. Since the description of LiDAR canopy structure developed in
their study was designed specifically for large-footprint SLICER waveform data, it is
not clear how this method can be adapted to small-footprint LiDAR point data.
3.1.2 Generality of LiDAR-based forest structure prediction models
Many site-specific empirical relationships have been developed across a variety of
forest types in both Europe and North America, but published models are very
different in terms of model precision, model form and the LiDAR predictor variables
included. As high-resolution LiDAR data become increasingly available, there is a
great need for simple, accurate, and physically meaningful prediction models that can
be used or easily adapted to different regions and sensor systems. Næsset et al. (2005)
studied the effect of inventory site on estimating mean tree height, dominant height,
mean diameter, stem number, basal area, and timber volume. Separate regression
models were developed for each inventory area as well as common models using two
inventory areas simultaneously. He concluded that the coefficients of LiDAR-based
28
models do not differ significantly across two tested inventory sites except for the mean
height. Lefsky et al. (2002) found that a single regression model based on mean
canopy height and mean canopy cover derived from large-footprint waveform
SLICER data was sufficient to model aboveground biomass across three biomes:
temperate deciduous, temperate coniferous and boreal coniferous. Lefsky et al.
(2005b) compared the relationship between LiDAR-measured canopy structure and
coincident field measurements of forest stand structure using data from five locations
in the Pacific Northwest of the USA with contrasting composition. Of the 17 stand
structure variables considered, they reported eight equations that were valid for all
sites, including aboveground biomass and leaf area index. Instead of dividing data into
training and testing samples, data from all study sites were used to develop prediction
models and the predicted values from the overall regression model were compared
with the observed values for each site to check the generality of the model, so the
RMSE values reported in their paper were not truly RMSE, but residual standard
deviation. It is highly possible that RMSE values were underestimated and the
generality of the overall model was overestimated. In contrast, Drake et al. (2003)
reported that the relationship between LiDAR metrics and aboveground biomass were
significantly different between two study areas using Laser Vegetation Imaging
Sensor (LVIS) data. Besides different LiDAR systems applied, reasons for these
inconsistent results are not clear, and further work is needed to investigate the
generality of LiDAR-based prediction models.
This study tested three different variable selection methods (Stepwise regression,
principal component analysis and Bayesian Modeling Averaging) to develop LiDARbased aboveground biomass prediction models for three different forest types –a moist
Douglas-fir (Pseudotsuga menziesii) / western hemlock (Tsuga heterophylla) forest in
western Washington state, dry Ponderosa pine (Pinus ponderosa) forest in the eastern
Cascade Mountains of Washington state, and a birch/spruce forest on the Kenai
peninsula of Alaska. As an exploratory study, the objectives were to investigate: 1)
29
whether it is possible to develop LiDAR-based aboveground forest biomass models
with a small set of LiDAR metrics that have a clear biological interpretation; and 2)
whether models from different variable selection methods are significantly different in
terms of the goodness of the model fit.
3.2 Data and methods
3.2.1 Study sites
Both LiDAR and field data were collected over three study areas: 1) Capitol Forest in
western Washington State, 2) Mission Creek in eastern Washington State, and 3)
Kenai Peninsula in south-central Alaska (Figure 3.1). A summary of the field plots for
these study sites are shown in Table 3.1.
Figure 3.1 Location of three study sites (denoted by black stars)
Table 3.1 . Summary of field plots for three study sites
Study
Location
Forest type
Stand age
sitea
(yr)
CF
western
Douglas-fir and western 70
Washington state hemlock, moist site
MC
Eastern
Douglas-fir and
25
Cascades,
Ponderosa pine, dry site
Washington state
KE
South-central
Spruce and birch
74
Alaska
a
CF: Capitol Forest; MC: Mission Creek; KE: Kenai Peninsula.
Plot size
(ac)
0.2
Number
of plots
98
Trees
per acre
60
0.62
66
112
0.167
105
66
30
Area 1 was a 5.2 km2 study area within the Capitol State Forest, western Washington
State (122.990W to 123.323W, 46.828N to 47.087N). The area is dominated by
Douglas-fir and western hemlock. Additional species include western red cedar (Thuja
plicata), red alder (Alnus rubra), and maple (Acer spp.). A total of 98 field inventory
0.2-acre plots were used in this study. Field inventory was conducted in the fall of
1998 and spring of 1999 and measurements acquired at each plot included species and
diameter at breast height (DBH) for all trees greater than 14.2 cm in DBH. In addition,
total height and height-to-base-of-live crown were measured on a representative
selection (47%) of trees over the range of diameters using a hand-held laser
rangefinder. This site is in the location of an ongoing experimental silvicultural trial,
and a detailed description of the plot measurement protocol can be found in a previous
report (Curtis et al. 2004).
Area 2 was located in the Mission Creek watershed, in the eastern Cascade Mountains
of Washington State (120.450W to 120.631W, 47.383N to 47.477N). The main
species are Douglas-fir and Ponderosa pine with scattered grand-fir (Abies grandis). A
total of 66 plots with plot size 50 m by 50 m were used in this study. Data collected at
each plot included tree species, DBH, and three height measurements for all trees:
height to dead crown, height to live crown, and total height. Canopy closure, the
proportion of open sky obscured by vegetation, was measured using a Lemmon
Spherical Densiometer Model-A at each sampled grid point. This site is part of an
ongoing forest fire and fire surrogates experiment carried out by the US Forest
Service, and a detailed description of the plot measurement protocol can be found in a
previous paper (Lolley 2005). Field measurements were collected in the summer of
2003 and all trees were stem-mapped in the summer 2004 using an Impulse laserrangefinder and Trimble GPS system.
Area 3 was located in the west of the Kenai Mountains, Kenai Peninsula, south central
Alaska (149.498W to 151.804W, 59.580N to 61.456N). The area covers
approximately 3000 square miles and elevation ranges from sea level to 600 m.
31
Primary forest types are white spruce (Picea glauca), black spruce (Picea mariana),
paper birch (Betula papyrifera) and mixed spruce and birch. A total of 105 Forest
Inventory and Analysis (FIA) permanent field plots located in this area were used in
this study. Each field plot consists of a cluster of four circular subplots approximately
1/24 acre in size with a radius of 24.0 ft. Most plots were measured by FIA crews in
the summers of 2001-2003. Trees greater or equal to 5 inch in DBH were tallied and
tree height was measured for several site trees within the plot. For detailed plot and
tree measurement information, please refer to the Forest Inventory and Analysis
National Core Field Guide (2005).
Plot-level aboveground biomass (including leaves, branches and stem) was estimated
for Capitol Forest and Mission Creek study areas using BIOPAK (Means et al. 1994).
For the Kenai study area, aboveground biomass of individual trees was estimated
using equations developed in Washington, Oregon and the British Columbia (Shaw
1979, Alemdag 1984, Manning et al. 1984, and Singh 1984) and plot-level
aboveground biomass was then calculated by summing all trees within the four
subplots.
3.2.2 LiDAR data
3.2.2.1 LiDAR system specification
High-density LiDAR data were acquired over the Capitol Forest study area with a
SAAB TopEye system mounted on a helicopter platform in March 1999. LiDAR data
for Kenai Peninsula and Mission Creek study areas were acquired with an OPTECH
ALTM 30/70 kHz LiDAR system mounted on a twin-engine Cessna 320 in May and
August 2004 respectively. The system settings and flight parameters are shown in
Table 3.2.
32
Table 3.2 LiDAR system specification for three study sites
Study LiDAR system
Flying
Flying
Swath
sitea
speed
heightb
width
(m/s)
(m)
(m)
Laser pulse
density
(points/m2)
Beam
Footprint
(diameter, cm)
CF
MC
4
>4
40
84
>4
84
SAAB TopEye
750
25
70
OPTECH ALTM
1200
50
300
30/70 kHz LiDAR
KE
OPTECH ALTM
1200
50
300
30/70 kHz LiDAR
a
CF: Capitol Forest; MC: Mission Creek; KE: Kenai Peninsula.
b
Flying height is above ground level height.
3.2.2.2 Derivation of LiDAR metrics
For each study site, the vendor provided raw LiDAR point data consisting of XYZ
coordinates and return intensity information for all LiDAR points in ASCII text
format. In addition, the vendor provided “filtered ground” data representing ground
returns isolated via a proprietary filtering algorithm. These filtered ground returns
were used to generate a digital terrain model (DTM). All return observations (points)
were spatially registered to the DTM according to their coordinates. The relative
height of each point was computed as the difference between its Z coordinate and the
terrain surface height. Points with a relative height value less than 2 m were excluded
to eliminate ground hits and the effect of stones, shrubs, etc. and the remaining points
were considered to be laser canopy hits. A set of variables that describe the canopy
height distribution (the 10th, 25th, 50th, 75th, 90th height percentiles, maximum height,
mean height and coefficient of variation of height) were calculated from all returns of
the laser canopy hits for each field plot. In addition, the canopy point density (d) was
calculated as the percentage of the first return canopy hits divided by the total number
of first returns (both canopy hits and ground hits). At the Kenai Reninsula study site,
LiDAR metrics were calculated at the big plot level, which contains all four subplots,
instead of individual subplot level. The list of plot-level LiDAR metrics was then
33
merged with the plot-level field-based aboveground biomass estimates and imported
into the R statistical analysis software.
3.2.3 LiDAR metrics selection methods
3.2.3.1 Stepwise regression
Multiple linear regression models, which include all extracted LiDAR metrics as
predictor variables, were first applied for each study area. Based on residual plots and
variable transformations suggested by the Alternating Conditional Expectations
method (Raftery and Richardson 1996), logarithm transformed forest biomass was
used as the dependent variable. Standard backward stepwise regression was then
conducted and the best fitting models were selected based on the lowest Akaike
Information Criterion (AIC) value.
3.2.3.2 Bayesian model averaging
Bayesian Model Averaging (BMA) is a Bayesian method that involves averaging over
all possible combinations of independent variables and accounts for uncertainty about
model form and assumptions (Raftery et al. 2005). Under BMA, all possible models
are considered and predictor variables are selected based on the posterior probability.
The posterior distribution of predictor variable is a weighted average of its posterior
distribution under each of the models considered, where a model’s weight is equal to
the posterior probability that it is correct, given that one of the models considered is
correct. This method avoids the problem that the selected model depends on the order
in which variable selection and outlier identification are carried out. Suppose we have
data D and we want to make inference about an unknown quantity χ. If there are p
possible predictors in the regression model, the number of models K could be quite
large
(as
many
as
2p).
The
BMA
P( x | D) = ∑i =1 P( x | D, M i ) * P( M i | D) ,
k
posterior
distribution
of
χ
is
34
where P(χ | D, Mi) is the posterior distribution of χ given the model Mi, and P(Mi|D) is
the posterior probability that Mi is the correct model, given that one of the models
considered
P( M i | D) =
is
correct.
The
posterior
model
probability
is
given
by
P( D | M i ) * P( M i )
∑
k
i =1
P( D | M i ) * P( M i )
where P(D| Mi) is the integrated likelihood of model Mi and it could be approximated
by Bayesian Information Criterion (BIC). BICi = n * log(1 − Ri ) + Pi * log(n) , where
2
R2i is the value of R-square, Pi is the number of predictors for the i-th regression
model and n is the sample size (Raftery et al. 1997). The sum over all models is
approximated by finding the models with the highest posterior probability using the
fast leap and bounds algorithm. As an attempt to select both LiDAR metrics and
models at the same time, BMA was used and the model with the highest model
posterior probability was selected.
3.2.3.3 Principal component analysis
Principal component analysis describes the variation of a set of multivariate data in
terms of a set of uncorrelated variables, each of which is a particular linear
combination of the original variables. The first principal component accounts for as
much variation of the original data as possible, the second component is chosen to
account for as much remaining variation as possible subject to being uncorrelated with
the first component and so on (Everitt and Dunn 2001). Using principal component
analysis, a subset of variables that explain the majority of variation can be selected
from a large set of (possibly highly correlated) predictor variables. The procedure is as
follows: 1) Decide how much of the total variation contained in the original variables
needs to be accounted for, where values between 70% and 90% are usually suggested
(Jolliffe 1972); 2) Find the number of components which explain such variation. This
number indicates the effective dimensionality of the data and is the size of the subset
of original variables to be retained; and finally, 3) Original variables are selected, one
35
associated with each component, as the one not already chosen which has the greatest
absolute coefficient value on the component.
Principal component analysis was used to select LiDAR metrics from the pool of
available LiDAR metrics, such as maximum height, mean height, 10th, 25th, 50th, 75th,
90th height percentiles, coefficient of variation of height and the canopy point density.
The minimal variation that needed to be explained was set to 95%. Two kinds of
principal component regression models were developed. One was using the most
significant principal components as predictor variables (denoted as PCA_1) and the
other was using selected LiDAR metrics from principal component analysis as
predictor variables (denoted as PCA_2).
Separate aboveground biomass regression models were developed using the selection
methods described above for each study site as well as common models using three
study sites simultaneously.
3.3 Results
3.3.1 LiDAR metrics selected by principal component analysis
Principal component analysis indicated that the first three principal components
accounted for more than 95% of the total variation contained in the original set of
LiDAR metrics. This is true for three individual study sites and the combined dataset.
To be specific, the first three principal components explained 98.5%, 96.0%, 97.6%
and 98.6% of the total variation contained in the original LiDAR metrics for the
Capitol Forest, Mission Creek, Kenai Peninsula study sites and the combined dataset
respectively. Based on the criteria set for variable selection, this means that only three
original LiDAR metrics are needed to explain the majority of the variation contained
in the LiDAR data. The coefficients defining the nine principal components with the
original LiDAR metrics are shown in Table 3.3. These coefficients were scaled so that
36
they represent correlations between LiDAR metrics and the principal components. For
all three study sites, mean height had the largest absolute correlation with the first
principal component, coefficient of variation of height had the largest absolute
correlation with the second principal component, and canopy point density had the
largest absolute correlation with the third principal component. Therefore, mean
height, coefficient of variation of height and canopy point density explain most of the
variation in the original LiDAR metrics set and they were selected as the most
predictive variables for regression model PCA_2. After combining three study sites
together, mean height, canopy point density and coefficient of variation of height were
selected again as the most predictive variables, but their order is slightly different from
that for the individual sites (Table 3.3). For the individual study sites, coefficient of
variation of height had the largest correlation with the second principal component and
canopy point density had the largest absolute correlation with the third principal
component, while for the combined dataset, the coefficient of variation of height had
the largest absolute correlation with the third principal component and canopy point
density had the largest absolute correlation with the second principal component.
37
Table 3.3 Correlation between principal components and original LiDAR metrics
Study site
PC1
PC2
PC3
PC4
PC5
PC6
PC7
PC8
PC9
CF
Maxht
-0.368 -0.221 -0.174 0.247 0.595 0.600
Meanht -0.392
-0.141
-0.443 0.785
CV
0.133 -0.776
0.373 -0.468 0.120
P10
-0.298 0.511
0.720 -0.353
P25
-0.385
-0.491 -0.486 0.515 0.271 0.129 -0.124
P50
-0.388 -0.110
-0.155 -0.132 -0.189 -0.751 -0.227 -0.380
P75
-0.383 -0.170
-0.394
0.795 0.182
P90
-0.378 -0.206
0.152 -0.381 0.594 -0.315 -0.429
D
0.128
-0.146
-0.979
MC
Maxht
-0.334 -0.357 -0.120 -0.473 0.662 -0.279
Meanht -0.434
0.119 0.883
CV
-0.158 0.627 0.408
-0.637
P10
-0.179 0.546
-0.696 -0.218 0.246 0.247
P25
-0.360 0.325
0.361 0.493 0.580 -0.135
-0.158
P50
-0.427
0.293
-0.313 0.604 0.400 -0.301
P75
-0.427
0.109 -0.331 -0.162
-0.797 -0.141
P90
-0.405 -0.216
-0.143 -0.343
-0.623 0.423 -0.271
D
-0.975 0.184
KE
Maxht
-0.330 -0.391
-0.313 0.789
Meanht -0.391
0.167
0.894
CV
-0.232 -0.486 -0.274 0.100
-0.788
P10
-0.343 0.334
-0.686 -0.305 0.341 0.256 -0.123
P25
-0.372 0.244
-0.212
-0.597 -0.447 0.427 -0.111
P50
-0.386 0.112
0.276
-0.412 0.264 -0.654 -0.292
P75
-0.386
0.114 0.406
0.171 0.506 0.585 -0.193
P90
-0.378 -0.187
0.243 -0.169 0.493 -0.629 -0.157 -0.249
D
-0.191
-0.971
Combined Maxht
-0.351
-0.350
0.709 0.492
Meanht -0.365
-0.147
0.906
CV
0.274
-0.843 -0.365 -0.275
P10
-0.342 -0.135 0.269 -0.869
-0.165
P25
-0.363 -0.113
-0.566 0.611 0.304 -0.142 -0.220
P50
-0.364
0.188 -0.231
-0.677 0.505 -0.217
P75
-0.362
-0.164 0.192
-0.397 -0.195 -0.766 -0.129
P90
-0.360
-0.227 0.158 0.110 -0.437 0.631 0.362 -0.244
D
-0.167 0.974
-0.101 -0.105
* PC1: the first principal component; PC2: the second principal component; … ; PC9: the ninth
principal component; Maxht: maximum height of all LiDAR returns above 2m within plot boundary
(m); Meanht: mean height of all LiDAR returns above 2m within plot boundary (m); CV: coefficient of
variation of height based on all LiDAR returns above 2m within plot boundary; P10: 10 percentile
height of all LiDAR returns above 2 meters within plot boundary (m); P25: 25 percentile height of all
LiDAR returns above 2 meters within plot boundary (m); …; P90: 90 percentile height of all LiDAR
returns above 2 meters within plot boundary (m) D: canopy point density (D) was calculated as the
percentage of the first return canopy hits divided by the total number of first returns (both canopy hits
and ground hits). Canopy hits have height greater or equal to 2 meters.
38
3.3.2 Model comparisons
Table 3.4 lists final biomass models selected from different variable selection methods
for the individual study sites and the combined study sites. All models have high Rsquare values ranging from 0.67 to 0.88. R-square values in the Kenai site were lower
than those in the Mission Creek site, which were a little lower than those in the Capitol
Forest site. Within each study site, Stepwise models had slightly higher R-square
values than BMA and PCA models, which means that Stepwise models explained
slightly more variation in aboveground biomass than BMA models and models from
principal component analysis (PCA_1 and PCA_2). BMA models explained almost
the same amount of variation as models containing the first three principal
components (PCA_1) and models containing only mean height, coefficient of
variation of height and canopy point density (PCA_2). Despite the similar R-square
values within each study site, the number of LiDAR metrics selected by different
statistical methods was different and Stepwise models tended to contain more LiDAR
metrics than BMA and PCA models (Table 3.4).
Canopy point density was the only LiDAR metric selected by Stepwise, BMA and
PCA_2 models for all three study sites. The coefficients of canopy point density were
consistent (i.e. approximately the same) within each study site, but not consistent
across study sites. For other LiDAR metrics selected, their coefficients were very
different across different selection methods and different study sites (Table 3.4), which
indicated that the common model using the combined dataset was not good enough to
capture individual variation within each study site.
Across different study sites, PCA_2 models contain the same set of LiDAR metrics:
mean height, coefficient of variation of height and canopy point density. Figure 2
shows LiDAR-based biomass prediction from PCA_2 models versus field-based
biomass estimate for three separate models and the common model from the combined
dataset. As indicated in Figure 3.2, overall model fit was good for both separate
models and the common model as the relationship was not far from the 1:1 line.
39
However, the coefficients for these three LiDAR metrics were very different across
study sites. The coefficient of mean height was 0.04 at Capitol Forest, 0.05 at Mission
Creek, 0.34 at Kenai Peninsula and 0.11 for the combined dataset. The model
coefficient of the coefficient of variation of height was 0.03 at Capitol Forest, 2.29 at
Mission Creek, 9.36 at Kenai Peninsula and 5.66 for the combined dataset. Finally for
the canopy point density, the coefficient was 2.35 at Capitol Forest, 1.85 at Mission
Creek, 2.61 at Kenai Peninsula and 3.14 for the combined dataset.
Table 3.4 Final above ground biomass regression models from different statistical methods
Study site
Method
Final Model
Number of
R2
predictor
variables
CF
Step
LN(Bio b) = 9.50+0.097*Meanht +1.47*CV 4
0.88
0.05*P90+2.42*D
BMA
LN(Bio) = 9.97+0.03*P25+2.39*D
2
0.87
LN(Bio) = 12.46-0.02*PC1+0.01*PC2 0.61*PC3
3
0.87
PCA_1a
PCA_2
LN(Bio) = 9.88+0.04*Meanht +0.03*CV+2.35*D
3
0.87
MC
Step
LN(Bio) = 7.97-0.03*Maxht +0.47*Meanht
6
0.76
+4.73*CV-0.10*P25-0.23*P75+1.89*D
BMA
LN(Bio) = 8.83+0.05*Meanht +2.29*CV+1.85*D
3
0.74
PCA_1
LN(Bio) = 11.70-1.0*PC1 -0.09*PC2 -0.39*PC3
3
0.73
PCA_2
LN(Bio) = 8.83+0.05*Meanht +2.29*CV +1.85*D
3
0.74
5
0.70
KE
Step
LN(Bio) = 1.58 -2.72*Meanht +14.03*CV
+1.48*P25 +1.48*P75 +2.90*D
BMA
LN(Bio) = 2.83+8.70*CV+0.25*P75 +2.70*D
3
0.69
PCA_1
LN(Bio) =9.89-0.49*PC1 -0.55*PC2 -0.41*PC3
3
0.67
PCA_2
LN(Bio) = 2.41+0.34*Meanht +9.36*CV +2.61*D
3
0.68
6
0.75
Combined Step
LN(Bio)=5.49+0.42*Meanht+ 5.18*CV0.66*P50+0.66*P75-0.30*P90 +2.98*D
BMA
LN(Bio)=5.49+0.42*Meanht+ 5.18*CV 6
0.75
0.66*P50+0.66*P75-0.30*P90 +2.98*D
PCA_1
LN(Bio)=11.23-0.42*PC1+0.70*PC2-0.64*PC3
3
0.71
PCA_2
LN(Bio)=5.64+0.11*Meanht + 5.66*CV+3.14*D
3
0.72
a
PCA_1 is regression models using the first three principal components: PC1, PC2 and PC3 as
predictor variables; PCA_2 is regression models using mean height, coefficient variation of height and
canopy point density as predictor variables.
b
LN(Bio): log transformed above ground biomass (kg/ha).
40
MC
11.5
12.0
12.5
12.0
11.5
13.0
10.5
11.0
11.5
12.0
Field LN(Biomass)
KE
Combined
12.5
13
12
11
10
6
8
9
8
9
Predicted LN(Biomass)
14
10 11 12 13
Field LN(Biomass)
7
Predicted LN(Biomass)
11.0
11.0
Predicted LN(Biomass)
13.0
12.5
12.0
11.5
Predicted LN(Biomass)
12.5
CF
4
6
8
10
Field LN(Biomass)
12
4
6
8
10
12
Field LN(Biomass)
Figure 3.2 Results of plot-level LiDAR-based estimation of aboveground biomass for Capitol
Forest (CF), Mission Creek (MC), Kenai Peninsula (KE) and the combined dataset with mean
height, coefficient of variation of height and canopy point density as predictor variables. Lines
represent 1:1 relationship.
3.4 Discussion
As expected, there is a significant relationship between field-based aboveground
biomass estimates and LiDAR metrics for our three study sites. The biological basis
behind this is the ecological and biomechanical links between canopy vertical
41
structure and forest stand structure parameters. From the perspective of tree form and
function development, there is usually a connection between the differences in vertical
canopy structure and differences in forest biomass both through forest succession and
across areas with contrasting environmental conditions. For example, Larson (1963)
reported that crown geometry and crown position exert considerable control over bole
form and vertical distribution of stem increment. LiDAR sensors directly measure
three-dimensional characteristics of forest canopy structure, which provides a good
foundation for high correlations between LiDAR metrics and forest biomass.
However, trees might develop different stem and crown shape relationships across
different environmental conditions and geological regions, even for the same species.
This might explain why model coefficients were different across the three study sites.
In this study, mean height, coefficient of variation of height and canopy point density
were selected by principal component analysis as the most predictive variables with
the same order for all three LiDAR datasets tested, and biomass models developed
using these three metrics had high R-square values. LiDAR mean height represents
canopy height in the field, coefficient of variation of height represents canopy depth,
and canopy point density represents canopy cover. These three LiDAR metrics
succinctly describe the 3D canopy structure, which provides explanation why these
metrics capture the majority of variation contained in LiDAR data. From a resource
management standpoint, these kinds of LiDAR-based forest structure models would be
analogous to the use of aerial stand volume tables that have been widely used in forest
inventory for a long time. Aerial stand volume tables present (in tabular form) the
relationship between forest structure variables easily estimated from aerial photos often mean tree height and percent canopy cover - and stand volume (Paine and Kiser
2003). Because aerial photos are passively-sensed, these methods cannot account for
variation in stand volume associated with the vertical structure of the canopy. Previous
studies have indicated that crown ratio, defined as the ratio of the crown length to total
stem length, is an important indicator of the growth history of the tree and
42
significantly influences the allometric scaling between foliage and wood biomass
(Makela and Valentine 2006). The use of three-dimensional forest structure
information provided by LiDAR has the potential to provide reliable estimation for
variation associated with the canopy vertical structure. The most predictive LiDAR
metrics set (mean height, coefficient of variation of height, and canopy point density)
found in this study is consistent with the mean tree height and percent canopy cover
used in the aerial stand volume table while the third variable, coefficient of variation
of height, is a measure of canopy vertical variation. Because most LiDAR returns are
from the dominant trees, especially from the outer canopy of the dominant trees, the
distribution of LiDAR return heights is weighted toward the tallest trees. As a result,
the LiDAR mean height likely represents the height of the overstory trees. On the
other hand, field-derived forest stand structure parameters are calculated using all trees
in the plot. So the inclusion of the coefficient of variation of height helps to account
for intermediate tree crowns in the overstory and suppressed trees in the understory.
Within each study site, LiDAR canopy structure information summarized by mean
height, coefficient of variation of height and canopy point density did explain a similar
amount of variation compared to other models. The predictive ability of these three
LiDAR metrics is good for forest biomass across all three forest types, which indicates
that the combination of mean height, coefficient of variation of height and canopy
density represents a sufficient and concise quantitative description of the canopy
structural content and therefore provides a good representation of stand structure
characteristics. Models using these three LiDAR metrics likely capture the
fundamental allometric relationships between foliage volumes and stem biomass. This
finding is consistent with results from large foot print SLICER data (Lefsky et al.
2005a), in which mean height, cover or leaf area index and height variability were
found to explain the most of variability in forest physical characteristics.
43
After combining our three datasets together, mean height, coefficient of variation of
height and canopy point density were again found to explain the majority of variation.
However, the coefficients from the combined model were different from the individual
models, which suggests that the general model representing all study sites may
produce more bias for each individual site than models developed for the specific site.
In comparison to stepwise and BMA models, models containing mean height,
coefficient of variation of height and canopy point density (PCA_2) explained similar
levels of variation in aboveground biomass, but PCA_2 models are relatively simple in
model format and have clear biological interpretation. The straightforward prediction
models described in this study will greatly facilitate the application of LiDAR to
practical forest inventory and management.
To characterize forest stand structure, a remote measurement of canopy structure that
is rapid, reproducible, and with a spatial resolution commensurate with the scale of
structural variation is needed because existing ground-based approaches are slow,
inexact, or highly-averaged spatially. As a rapidly-growing remote sensing
technology, LiDAR offers great potential to capture detailed three-dimensional canopy
information rapidly. Findings from this study indicate that it is possible to develop
straightforward regression models for different forest types using three primary
LiDAR metrics - mean height, coefficient of variation of height and canopy point
density. If this is true for a wide range of forest types and LiDAR systems, the
operational use of LiDAR for forest inventory may become common in the future.
44
Chapter 4 Effects of Plot Position Error and Plot Size on
LiDAR-derived Metrics and Predicted Biomass
4.1 Introduction
The most popular approach to using small-footprint discrete LiDAR data in a forest
inventory is to develop empirical regression relationships between forest stand
structure parameters measured in the field and LiDAR metrics extracted from laser
canopy hits within corresponding field plots. Accurate field plot location is crucial for
successfully linking LiDAR data with field-measured forest biophysical variables.
Field plot locations are often obtained using a global positioning system (GPS). The
accuracy of GPS locations depends on survey environment, survey parameters and
methodology (Piedallu and Gegout 2005). Currently, GPS manufactures only provide
accuracy specifications under clear sky conditions. It is known that the accuracy of
GPS under a forest canopy is much lower than under clear sky conditions because
trees attenuate or completely block the GPS satellite signals. There are some studies
acknowledging the error in the position of ground reference plots in forest conditions
(Bolduc et al. 1999, Brandtberg et al. 2003, Holmgren et al. 2003) and their
recommendation is to use relatively expensive, survey-grade high-accuracy GPS units.
Due to the cost concern, this could be done when only a small number of field plots
are involved and the plots are in single-layer forests without dense canopy. In large
area operational inventories, less accurate easy-to-carry, recreational-grade GPS
receivers are commonly used. For example, FIA plots were originally located with a
variety of handheld GPS units, ranging from military-grade Rockwell PLGR units to
recreational-grade units, which provided a wide range of positional error sometimes
exceeding 20 meters in the horizontal direction (Hoppus and Lister 2006).
Traditionally, plot location in the large scale forest inventory is intended to assist the
field crews in relocating the plots, as well as to document their general location, so
45
obtaining plot locations with several meters of error is acceptable. However, in the
context of a double-sampling inventory design, error in the position of the ground
reference plots may result in a mismatch between field plots and LiDAR data, which
could weaken the empirical relationship between field measurements and LiDARderived metrics, which may, in turn, influence the estimation of forest inventory
variables.
A variety of techniques have been used in the past to obtain more accurate field plot
positions. In a study in Australia, average inventory field plot position error is
approximately 10 meters (Hollaus et al. 2007), and manual co-registration of the forest
inventory data to the LiDAR data has been carried out. The position of each sample
plot center is adjusted so that the measured single-tree positions best fit the visually
detectable tree positions in the LiDAR canopy height model and the measured tree
height best fit the canopy height model. Only 103 of the 143 sample plots could be
clearly co-registered to the LiDAR data (Hollaus et al. 2007). In addition, this method
is time-consuming and subjective.
Gobakken and Naesset (2008) assessed the effects of positioning errors on LiDARderived metrics and biophysical stand properties through simulation. Nine different
levels of field position errors were assessed. It was reported that the standard deviation
of the differences between various LiDAR-derived metrics generated at incorrect plot
positions and those generated at the true positions increased with increasing plot
position error. However, the mean of the differences between incorrect plot positions
and ground-truth positions was not reported. They also concluded that plot position
errors had a larger effect in poor sites with more scattered trees compared to more
productive sites with denser canopies and more evenly-distributed trees. Breidenbach
et al. (2007) examined plot position error on predictions of Lorey’s tree height. First,
thirty simulated plot locations were generated with plot centers a specified distance
away from the true plot center and an angle between these simulated plots of 12
46
degree. Then the 3rd quartile of LiDAR point height was derived for each of simulated
plots. Finally Lorey’s tree height was calculated from linear regression models with
the 3rd quartile height as the covariate. The conclusion was that the root mean squared
error for tree height increased only slightly with increasing distance to the plot center.
Is accurate plot location absolutely necessary? Under what condition this requirement
can be relaxed? Depending on forest condition and field plot size, a small position
error may be acceptable. Slight mismatches between field plots and LiDAR data may
not make a significant difference in the estimation. It maybe reasonable to expect that
LiDAR-derived metrics are relatively stable with large plot sizes and in homogenous
forest stands, but not with small plots or in heterogeneous stands. This hypothesis
could be tested by relocating and resizing LiDAR virtual plots, and then comparing
LiDAR metrics extracted from new plots with the original one. The objective of this
chapter is to assess the effects of plot location error and plot size on selected LiDARderived metrics and predicted biomass through simulation.
4.2 Data and methods
LiDAR data from ninety-five 300m*300m patches from western Kenai Peninsula,
Alaska were used for this study. In chapter 3 and Li et al (2008), it was shown that
three LiDAR-derived metrics, mean height, coefficients of variation of heights and
canopy LiDAR point density, explained the majority of variation contained in LiDAR
data. These three LiDAR metrics were calculated for each patch at 1m*1m, 5m*5m,
10m*10m, and 15m*15m resolution. Then, unsupervised classification was conducted
and a spatial variation index, contagion, was computed for each LiDAR patch. Forest
stands often contain clusters of trees which are distinctly different, in terms of
horizontal and vertical structure, from surrounding trees. This may be due to species
differences, age differences, site factors or silvicultural treatments. It is suspected that
the spatial variation index would be sensitive to these differences. Based on contagion
47
value on each LiDAR patch, LiDAR patches were then grouped into three categories:
homogeneous, medium, and heterogeneous. Ten FIA plots from each category were
selected and simulations were made on these thirty plots.
4.2.1 Unsupervised classification
Registered maps at four different resolutions (1m*1m, 5m*5m, 10m*10m, and
15m*15m) were generated in ENVI© based on LiDAR-derived mean height,
coefficient of variation of height, and canopy LiDAR point density. For each
resolution, maps were combined into a multiband raster image with each cell in the
raster has a three-dimensional attribute vector of LiDAR metrics. ISODATA
algorithm was used to classify the raster image (Tou and Gonzalez 1974). ISODATA
first randomly chooses k initial cluster centers, or means, then classifies each pixel to
the closest cluster. The new cluster mean vectors are calculated. The process is
iterated and these initial cluster centers are updated until the "change" between the
iterations is small. The objective of the ISODATA algorithm is to minimize the
within-cluster variability. The ISODATA algorithm implemented in ENVI© follows
fourteen principle steps detailed in Tou and Gonzalez (1974). In this study, the number
of iterations was set to ten, the minimum number of classes was set to one and the
maximum number of classes was set to ten. The minimum number of pixels in each
class was set to one and the maximum class deviation was set to one. The minimum
class distance was set to five and maximum number of merged pairs was set to two.
Typically classified images suffer from a lack of spatial coherency (speckle or holes in
classified areas). Adjacent similar classified areas were then smoothed using
morphological operators. The selected classes were clumped together by first
performing a dilate operation and then an erode operation on the classified image
using a kernel of size 3*3.
48
4.2.2 The contagion spatial variation index
Here we borrow the concept of spatial variation from landscape ecology to assess the
classified LiDAR image. Spatial variation is a function of spatial scale which
encompasses both extent and grain. Extent is the overall area encompassed by an
investigation. Grain is the size of the individual units of observation. Any inferences
on spatial variability in a system are dependent on the scale and are constrained by the
extent and grain of investigation. Here we would like to assess spatial variation in the
classified LiDAR map and the extent is the fixed 300m*300m LiDAR patch. The
grain is the grid size used to calculate LiDAR metrics. Metrics describing spatial
variation usually fall into two categories: those that quantify the composition of
features without reference to spatial attributes and those quantify the spatial
configuration requiring spatial information (Cushman & McGarigal 2003).
Composition metrics associate with the variety and abundance of the attribute of
interest, such as richness, evenness and diversity. Spatial configuration refers to the
spatial character and arrangement, position, or orientation of the experimental units
within the landscape (Cushman & McGarigal 2003). Contagion is one of the common
metrics used to describe spatial configuration and it is used here to quantify spatial
variation contained in the LiDAR patches. Contagion index is defined as
⎡
⎤⎡
⎤
⎢
⎥
⎢
gik
gik ⎥
⎢
⎥
⎢
⎥
P
P
*
ln(
)
*
i
i
∑∑
m
m
⎥
⎢
i =1 k =1 ⎢
gik
gik ⎥
∑
∑
⎢⎣
⎥
⎢
⎥⎦
k =1
k =1
⎦⎣
Contagion = (1 +
) *100
2 * ln(m)
m
m
where Pi is proportion of LiDAR patch occupied by class i, gik is the number of
adjacencies between pixels of class i and class k, and m is the number of classes
present in the LiDAR patch. Contagion approaches 0 when the distribution of
adjacencies (at the level of individual cells) among unique classes becomes
increasingly uneven and it equals 100 when all classes are equally adjacent to all other
patch types. FRAGSTAT (McGarigal and Marks 1995) was used to calculate
contagion indexes.
49
For 95 classified LiDAR maps, the contagion index was calculated at the grid level.
After visual examination of the classified map, the raw LiDAR point clouds, and the
photos taken on field visits, LiDAR patches with contagion index less than 30 were
considered to be heterogeneous in terms of spatial variation, 30-60 were considered to
be medium, and greater than 60 were consider to be homogenous.
4.2.3 Simulation
Thirty field plots and corresponding LiDAR patches, ten from each spatial variation
category, were selected for the simulation study. To investigate the effects of position
errors on metrics derived from the laser data, the position errors of field plots were
simulated. This was done by introducing a horizontal shift to the field plot coordinates
prior to extracting laser points within the new plots. Horizontal distance shifts from
the original field plot positions were altered using a sequence of distances from 1m to
20m in increments of 1m, and the direction shifts from the original field plot positions
were altered randomly. For each fixed shift distance, 100 simulated plots were
generated. Mean height, coefficient of variation of height and canopy point density
were computed from LiDAR points within the original plot boundary and LiDAR
points within the shifted plot boundary. The differences between corresponding
metrics derived from the plots with simulated positions and plots with original
positions were computed for each sample plot at each simulation. The mean and
standard deviations of these differences were summarized for each spatial variation
category.
For LiDAR-derived metrics, three plot sizes were tested: 0.04 acre (corresponding to
FIA subplot size), 0.08 acre (corresponding to the doubled FIA subplot size) and 1.5
acre (corresponding to the big plot which contains four FIA subplots). For each plot
size considered, sixty thousand simulated plots (100 simulations * 20 distances * 30
50
plots) were generated. LiDAR points within these simulated plots were clipped and
LiDAR-derived metrics were calculated for each simulated plot.
The effects of plot position errors and plot size on predicted biomass were also
assessed using the following procedure: 1) biomass estimates were calculated using
field-measured DBH and height; 2)
regression models were developed with log
transformed biomass as a dependent variable, and LiDAR-derived mean height,
canopy LiDAR point density and coefficient of variation of height from original plots
as predictive variables; 3) biomass was predicted for each simulated plot using
coefficients of developed regression models and LiDAR-derived metrics from
simulated plots; 4) the residuals between back-transformed predicted biomass and
original biomass estimates were calculated; 5) residuals were summarized according
to simulated distances and LiDAR patch spatial variation categories.
Since FIA only measures trees within the four subplots, only plot size 0.04 acre and
1.5 acre were considered when assessing the effects on predicted biomass.
4.3 Results
4.3.1 LiDAR patch classification and spatial variation
Four different grid cells were used to calculate LiDAR-derived mean height,
coefficient of variation of height, and canopy point density: 1m*1m, 5m*5m,
10m*10m, and 15m*15m, and an ISODATA unsupervised classification was
implemented on the raster maps with different resolution. The classification maps at
1m*1m had a salt and pepper appearance and classification maps at 10m*10m and
15m*15m appeared too smoothed (not shown here). Considering that the average tree
crown radii in this sample dataset is 2.8m, classification maps at 5m*5m was selected
for further investigation. Figure 4.1 and 4.2 show raw classification results at 5m*5m
51
resolution without and with field plot locations, and Figure 4.3 and 4.4 show
corresponding smoothed classification results.
In total, six classes were produced and their proportions of total area are listed in
Table 4.1. Since no ground training dataset is available for classification, biological
interpretation of the classes is impossible. However, this doesn’t matter in this study
where the main objective of classification is to stratify areas in the LiDAR patches.
Since it was found in Chapter 3 that the three LiDAR-derived metrics used for
classification have the capability to capture the majority of variation contained in the
LiDAR data, the classification results should provide information useful when
stratifying areas within the LiDAR patch. Assuming LiDAR data accurately captures
forest stand structure, LiDAR image classification results should indicate forest
structure strata in the field. Considering that numerous previous studies have shown
that LiDAR can collect highly detailed measurements of three-dimensional forest
structure (Lefsky et al. 1999, 2002, Næsset 2002, Drake et al. 2003, Holmgren 2004,
Lim and Treitz 2004, Maltamo et al. 2004, Næsset et al. 2004, Andersen et al. 2005,
Bollandsas and Naesset 2007), this assumption seems very reasonable. In addition,
field visits to 24 plots during the summer of 2007 confirmed that the classification
results make sense.
Classification results clearly indicate that some forest areas characterized by the
LiDAR patches are more uniform than others (Figure 4.1, 4.3). In general, the
majority of field plots are near the center of LiDAR patches though there are a few
exceptions (Figure 4.2 and 4.4). Some field plots are located within the main class of
their LiDAR patches while other field plots are located near the boundary of different
classes. The contagion index based on clumped classes ranges from 23.3 to 90.9 with
the mean of 44.1. Larger contagion value indicates more homogeneous spatial
arrangement of classes within the boundary. Twelve LiDAR patches have a contagion
52
value less than 30, ten LiDAR patches have a contagion value greater than 60, and
seventy-three LiDAR patches have a contagion value between 30 and 60 (Figure 4.5).
Figure 4.1 LiDAR patches classification results based on 5X5m grids without field plot location
53
Figure 4.2 LiDAR patches classification results based on 5X5m grids with field plot center
indicated by black asterisk
Table 4.1 Proportion of classes in classified LiDAR patches (5mX5m resolution)
Class
Class 1
Class 2
Class 3
Class 4
Class 5
(red)
(green)
(blue)
(yellow)
(cyan)
Proportion (%)
26.54
36.43
19.09
11.74
5.39
Class 6
(pink)
0.84
54
Figure 4.3 LiDAR patches clumped classification results based on 5X5m grids without field plot
location
55
Figure 4.4 LiDAR patches clumped classification results based on 5X5m grids with field plot
center indicated by black asterisk
56
100
Contagion
90
80
70
60
50
40
30
20
10
SLD0153
SLD0103
SLD0082
SLD0063
SLD0040
SLD0024
KNI0334
SLD0006
KNI0320
KNI0299
KNI0293
KNI0278
KNI0258
KNI0232
KNI0214
KNI0200
KNI0188
KNI0180
KNI0169
KNI0152
KNI0141
KNI0129
KNI0119
KNI0112
KNI0097
KNI0089
KNI0080
KNI0070
KNI0062
KNI0050
KNI0042
KNI0026
KNI0020
KNI0012
KNI0002
0
Plot ID
Figure 4.5 Contagion value for classified LiDAR patches
4.3.2 Effects of plot location error and plot size on LiDAR-derived metrics
Thirty field plots and their corresponding LiDAR patches, ten from each category,
were selected for simulation. Mean and standard deviation of the differences between
LiDAR-derived metrics from simulated plots and from original plots are shown in
Figure 4.6-4.11, in which the homogenous category is colored in orange, the medium
category is colored in green and the heterogonous category is colored in blue.
Figure 4.6 shows boxplots of the average differences between corresponding LiDARderived mean height computed from the simulated plots and from the original plots for
three different LiDAR patch types over 100 simulations. For plot size of 0.04 acre and
0.08 acre, the averaged differences for LiDAR-derived mean height are within ±0.5m
for homogenous LiDAR patch which is colored in orange. This increase to ±2m for
the medium and the heterogeneous LiDAR patches which are colored in green and
blue. It is clear from Figure 4.6 that as the distance between simulated plot position
and original plot position increases, the averaged differences for LiDAR-derived mean
height in the homogenous LiDAR patches are small and stay relatively stable. In
contrast, the averaged differences in the medium and heterogeneous LiDAR patches
increase until the position error is around 10m. For the largest plot size of 1.5 acre, the
averaged differences of LiDAR-derived mean height between simulated plots and
original plots are very small in all three types of LiDAR patches and they don’t change
much as the position error increases.
57
Figure 4.6 Mean of the differences between LiDAR-derived mean height from simulated plots
and from original plots over 100 simulations.
58
Figure 4.7 shows the standard deviation of the differences between corresponding
LiDAR-derived mean height computed from the simulated plots and from original
plots across a sequence of distances over 100 simulations. The standard deviation of
the differences increases as the distance between simulated plot center and original
plot center increases. For fixed position error, the standard deviation of the differences
in the homogenous LiDAR patch is smaller than those in the medium and
heterogeneous LiDAR patches. Comparing plot size 0.04 acre, 0.08 acre and 1.5 acre,
standard deviation increases as plot size decreases.
Figure 4.8 and 4.9 shows the mean and standard deviation of the differences between
LiDAR-derived canopy cover (represented in percentage) computed from simulated
plots and from original plots. LiDAR canopy cover here has the same definition as
canopy point density, and the only difference is that canopy cover is represented as a
percentage while canopy point density is represented as a ratio. Similar to mean
height, the averaged differences of LiDAR canopy cover in the heterogeneous LiDAR
patches are greater than those in the medium and homogenous LiDAR patches. As
distances between simulated plots and original plots increases, the mean of the
differences of LiDAR-derived canopy cover gently increases. As plot size increases,
the averaged differences decrease. A similar pattern exists for the standard deviation
of the differences on LiDAR canopy cover.
Figures 4.10 and 4.11 show the mean and standard deviation of the differences
between LiDAR-derived coefficient variation of height from simulated plots and from
original plots. Similar to LiDAR-derived mean height and canopy cover, the average
difference of coefficient of variation of height increases as LiDAR patches become
more heterogeneous; it also increases as the distance between simulated plots and
original plots increases; and decreases when plot size increases from 0.04 acre to 0.08
acre to 1.5 acre.
59
Figure 4.7 Standard deviation of the differences between LiDAR-derived mean height from
simulated plots and from original plots over 100 simulations.
60
Figure 4.8 Mean of the differences between LiDAR-derived canopy cover from simulated plots
and from original plots over 100 simulations.
61
Figure 4.9 Standard deviation of the differences between LiDAR-derived canopy cover from
simulated plots and from original plots over 100 simulations
62
Figure 4.10 Mean of the differences between LiDAR-derived coefficient of variation of height
from simulated plots and from original plots over 100 simulations.
63
Figure 4.11 Standard deviation of the differences between LiDAR-derived coefficient of variation
of height from simulated plots and from original plots over 100 simulations
64
4.3.3 Effects of plot location error and plot size on predicted biomass
Table 4.2 shows the regression model of biomass based on LiDAR metrics from the
original plot position at subplot level and at the 1.5acre plots level which contain all
four subplots.
Table 4.2 Biomass regression models for 30 selected FIA plots based on original plot location for
two different plot sizes
Plot size
Model
R2
0.04 acre
LN(Biomassa) = 7.004+0.113*meanht +0.014*cv+1.484*d
0.498
1.5 acre
LN(Biomass)=10.246+0.024*meanht -0.702*cv+2.700*d
0.634
a
Biomass: above ground biomass (kg/ha); meanht: LiDAR-derived mean height (m);
cv: coefficient of variation of LiDAR-derived height; d: canopy point density represented by ratio
Figure 4.12 shows boxplots of the ratio of the averaged residual versus the mean of
estimated biomass from field measurement for each category over simulated distances.
The residual is the difference between estimated biomass from field measurement and
predicted biomass that is obtained using regression models in Table 4.2 and LiDARderived metrics from simulated plots. For each LiDAR patch category, the mean of
estimated biomass from field measurements is fixed across position error distances
and simulations, so changes in the ratio indicate changes in the residual. For plot size
0.04 acre, the ratio in the homogenous LiDAR patches is within 15% of the mean of
estimated biomass from field measurement and it stays relatively stable as the
simulated plot is moved away from the original plots, while ratios in the medium and
heterogeneous LiDAR patches show increasing residual as distance increases. Most
residuals in the medium and heterogeneous categories are within 50% of the mean of
the estimated biomass from field measurement; however, a few residuals are nearly
100% of the mean biomass (Figure 4.12). In addition, the majority of ratios in the
medium LiDAR patches are negative, which indicates predicted biomass in the
medium category tends to be less than the estimated biomass from field measurement.
For plot size of 1.5 acre, all three categories have a small ratio. As position error
65
increases, the ratio in the homogeneous patches barely changes while the ratio in the
medium and heterogeneous patches slightly increases.
Figure 4.12 Ratio of average residual from simulated plots versus the mean of field-estimated
biomass over 100 simulations
4.4 Discussion
This study presents an automatic procedure to assess plot position error and plot size
on LiDAR-derived metrics. First, grid-level LiDAR metrics were extracted from the
3D LiDAR point cloud, and a multi-band LiDAR image was created with each band
66
consisting of a single LiDAR metric. Then, unsupervised classification was
implemented to stratify LiDAR patches. Finally, simulation was conducted and
LiDAR metrics from simulated plots and from original plots compared. One
advantage of this method is that only LiDAR data were used to assess spatial
variation. No ground information is necessary. LiDAR data usually cover a larger area
than field plots, thus using LiDAR data for classification could capture more spatial
variation information, which could provide information on using LiDAR data as a
sampling tool to guide where to locate field plots. However, further validations are
needed before application in operational forest inventories.
The results in this study have shown that three important LiDAR-derived metrics –
mean height, canopy point density and coefficient of variation of height- are sensitive
to plot position error, especially in the LiDAR patches of homogeneous forests. As the
distance between simulated plots and original plots increases, the mean and the
standard deviation of the differences between LiDAR-derived metrics from simulated
plots and from original plots increase. In addition, plot size greatly affects the
differences between these three LiDAR-derived metrics from simulated plots and from
original plots. As plot size increases, the mean and standard deviation of the
differences decrease. At plot size of 1.5 acre, the averaged difference of LiDARderived metrics between simulated plots and original plots are small for LiDAR
patches of homogeneous to heterogeneous forest. The findings are consistent with
results from Gobakken and Naesset (2008), who reported that the standard deviation
of the differences for the LiDAR height percentiles, LiDAR density-related metrics,
maximum laser canopy height, arithmetic mean laser canopy height and coefficient of
variation of laser canopy height increased with increasing plot position error.
The effects of plot size on LiDAR-derived metrics are not surprising. For a fixed
simulated distance, larger plot size means more overlap area between simulated plots
and original plots thus increasing the chance for small differences between LiDAR-
67
derived metrics from simulated plots and from original plots. For example, if the
simulated plot centers are 5 meters away from original plot center, the common area is
57.3% for a plot size of 0.04 acre, 69.4% for a plot size of 0.08 acre and 92.7% for a
plot size of 1.5 acre. Beyond the distance of 14 meters, there are no overlaps between
simulated plots and original plots for a plot size of 0.04 acre, but 20.7% overlap for a
plot size of 0.08 acre and 79.8% overlap for a plot size of 1.5 acre.
In this study, LiDAR metrics derived from LiDAR patches of homogeneous forest are
found to stay relatively stable as the distance between simulated plot centers and
original plot center increases, but not in LiDAR patches of heterogeneous forest,
especially for the small plot size. It should be emphasized here that the definition of
homogeneous and heterogeneous is based on the contagion value for the classified
LiDAR patch (300m*300m) of forest and not based on forest structure measured in
the field plots, even though these two are closely correlated. Due to the financial
limitations and inability to accessing some FIA plots, it was not possible to check the
consistency of spatial variation between LiDAR patch and forest structure in the field
for all plots studied. However, field visits to 24 field plots during summer 2007
confirmed that classification results and spatial variation grouping were reasonable. In
addition, numerous previous studies have shown that LiDAR-derived metrics can
capture three-dimensional forest structure. Thus spatial variation in LiDAR patch
should provide a good indication of the spatial variation in terms of forest structure.
Since LiDAR-derived metrics are shown to be subject to errors if the plot location is
not accurate, especially in LiDAR patches of heterogeneous forest, it is likely that
stand properties predicted from LiDAR metrics will be affected by plot position error.
However, since regression models linking stand properties and LiDAR-derived
metrics usually contain several LiDAR metrics and models often involve variable
transformation, it is hard to quantify the effects of position errors on predicted stand
properties. Nevertheless, biomass estimates from FIA subplot 1 and from large plots
68
which contain four FIA subplots were used to assess the effect of plot location error
and plot size. The results indicate that for plot size of 0.04 acre, the ratio of the
averaged residual versus the mean of field estimated biomass is small in the
homogenous LiDAR patches. This means that the averaged predicted biomass in the
simulated plots doesn’t differ much from estimated biomass based on field
measurements in the original plots. In the LiDAR patches of heterogeneous forest, the
ratio increases with increasing distance. This means that the differences between
predicted biomass in the simulated plots and estimated biomass based on field
measurements in the original plots increases. This is consistent with results from
Gobakken and Naesset (2008), who report that the mean and standard deviation of the
differences for mean tree height, stand basal area and stand volume increased with
increasing plot position error especially on poor sites where there were normally few
stems. For large plots (1.5 acre), only small ratios were obtained over the whole
sequence of simulated distances indicating that the average predicted biomass doesn’t
differ much from the actual field plot biomass even as positional error increases. It
should be noted here that biomass estimates for the large plot (1.5acre) actually are the
average of the four subplots, not the mean of the large plot (1.5acre) since FIA only
measures trees within four subplots, not the whole large plot.
The findings from this study imply that as plot size increases, the effect of plot
location error on LiDAR metrics is decreasing. Small position errors are acceptable in
homogeneous forest stands, but it is important to have accurate plot position in
heterogeneous forest stands with high spatial variation. Whenever possible, using
larger plot sizes will reduce the effects of plot position error on LiDAR-derived
metrics. In the context of FIA, if plot location is obtained with recreational-grade GPS,
which is true in most area, matching LiDAR data with field measurements at the
subplot level is risky because of the inaccurate plot locations and the small subplot
size, especially in forest stands with high spatial variation. In this case, linking LiDAR
data with field measurements using larger plots, which encompass four subplots, may
69
provide a way to characterize forest condition at the similar scale as the combination
of four subplots. Because FIA only measures trees within four subplots, not within the
whole large plot (1.5acre), if plot location is obtained with survey-grade GPS, the use
of smaller subplots is probably better since there is high chance to accurately
georeference LiDAR data with field subplot while large LiDAR plot covers more area
than four subplots combined.
70
Chapter 5 Forest Height Prediction from Field Measurement
and LiDAR Data via Spatial Models
5.1 Introduction
Forest height is a crucial inventory attribute for calculating timber volume, forest
biomass, site potential, and scheduling silvicultural treatment. Measuring height by
current photogrammetric or field survey techniques is time consuming and expensive.
As a new emerging remote sensing tool, airborne LiDAR data have been studied to
derive height information. Two different approaches have been used to obtain height
measurements from LiDAR data. The first approach is to identify individual trees
using a canopy height model and extract their height, and the second approach is to
regress plot-level or stand-level height on LiDAR-derived metrics which describe
vertical and horizontal distribution of forest canopy (Hyyppä et al. 2000, Næsset 2002,
Persson et al. 2002, Maltamo et al. 2004, Andersen et al. 2006). Many studies have
reported that the accuracy of height estimates from LiDAR data is comparable to field
height measurement, while others found LiDAR tends to underestimate individual tree
height because of the low probability that the small-footprint laser pulses will intercept
the apex of tree top (Hyyppä et al. 2000, Gaveau and Hill 2003, Yu et al. 2004,
Andersen et al. 2006). Though these results are promising, most of reported studies
were conducted over small areas and field heights were measured carefully or using
more expensive and accurate instruments than the hand-held rangefinder commonly
used in forest inventory practices such as the US Forest Service Forest Inventory and
Analysis (FIA) program. The accuracy of LiDAR-derived height when compared to
field height measurement is not clearly understood in an operational forest inventory
setting.
71
Another issue with large-area operational forest inventory is the accuracy of plot
positions. As stated in Chapter 4, less accurate, easy-to-carry GPS receivers are often
used to get the position of field plots. This may introduce inaccurate geographical coregistration of field plots with LiDAR data. If field plots are poorly georeferenced, it is
likely that the empirical regression relationship between field height and LiDAR
metrics will be affected.
Models describing spatial correlations have been used to determine forest biophysical
parameters and characterize forest ecosystem structure (Biging and Dobbertin 1995,
Stoyan and Stoyan 1998, Stoyan and Penttinen 2000, Lappi, J. 2001, Zawadzki et al.
2005). In this study, instead of linking field plots with LiDAR data directly, a
stationary spatial process was assumed for plot-level height, and then spatial models
were applied to predict plot-level height at unobserved locations both from field
inventory and LiDAR data respectively. The particular objective is to produce maps of
predicted plot-level height over a large region, and then compare the distributions of
heights predicted from operational field inventory and from LiDAR measurements.
5.2 Study area and data description
As in chapters 3 and 4, a set of 95 FIA field plots located in the west of the Kenai
Mountains, Kenai Peninsula, Alaska are used for this study. Each field plot consists of
a cluster of four circular subplots approximately 1/24 acre in size with a radius of 24.0
ft, and each subplot contains a 6.8-foot fixed-radius microplot (Bechtold and Patterson
2005). Within each subplot, the height of trees with diameter at breast height of 5.0
inches or greater were measured; within each microplot, the height of saplings (1.0-4.9
inches DBH) and seedlings were measured. At each subplot center, a polygon type,
which is a unique combination of land cover type, forest density, forest stand size and
forest stand origin, was determined and the size of the polygons was collected (field
procedures for coastal Alaska inventory 2003). Two aggregated plot-level heights, plot
72
tree height and stand height, were defined and calculated for the purpose of this study.
Plot tree height is defined as the average height of individual trees on the plot with
DBH equal or greater than 5 inches weighted by polygon area. Stand height is defined
as the average height of trees with DBH equal or greater than 5 inches, seedlings, and
sapling on the plot weighted by polygon area.
As described in chapter 3 and 4, LiDAR data were collected over each field plot and
the surrounding area. For each 300m by 300m LiDAR patch, a digital terrain model
(DTM) was generated using returns classified by the data provider as bare-earth
points. Then all LiDAR returns were spatially registered to the DTM using their
coordinates. The relative height of each return was calculated as the difference
between its vertical Z coordinate and the terrain surface height. Returns with a relative
height value less than 2 meters were excluded to eliminate ground returns, rocks,
stumps and low vegetation. The remaining points were considered to be laser canopy
hits. Finally, the laser canopy hits within the boundary of a 144-foot fixed-radius plot
containing the four subplots were extracted, and LiDAR plot mean height and 90th
percentile height were calculated. The reason that the large plot was used instead of
four individual subplots is to decrease the effect of inaccurate field plot positions that
results from poor GPS positions or azimuth and distance errors when locating the
individual subplots.
Figure 5.1 Map of study area. Picture in the middle is LANDSAT ETM+ image for the study area
and red circles indicate field plot locations. Picture in the right is the LiDAR coverage over one
example field plot and colored by height.
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5.3 Methods
Four aggregated plot-level heights (plot tree height and stand height from field
measurements, LiDAR plot mean and LiDAR 90th percentile height) from 95 plots
were assumed to be a partial realization of a stationary Gaussian process. That is
{Z ( s) : s ∈ D ⊂ ℜ 2 }, Z = (Z(s1 ), , … Z(s n )) T
has a multivariate normal distribution, where Z(s) represents aggregated plot-level
height at location s, D is a fixed subset of 2-dimensional Euclidean space;
D ⊂ ℜ 2 contains spatial coordinates s={s1,…,sn} and si is the longitude and latitude
coordinates at location i. n is the number of locations, 95 in this case. Stationary
means that for any set of n sites {s1,…,sn} and any h ∈ ℜ 2 , the distribution of
(Z(s1),…, Z(sn)) is the same as that of (Z(s1+h),…, Z(sn+h)), which implies that the joint
distribution doesn’t change when shifted in space. Further, an isotropic process was
assumed, which means that the semivariogram function depends upon the separation
vector h only through its length ||h||. For the sake of simplicity, the Gaussian process
was assumed to have a constant mean, that is Z(s) =µ + ω(s) + ε(s), where µ is the
mean component of the model, and ω(s) is a zero-centered stationary Gaussian spatial
process, which captures the residual spatial association, and the ε(s) is an uncorrelated
pure error term. The ω(s) introduces the partial sill and range parameter and ε(s) adds
the nugget effect (Banerjee et al. 2004).
Empirical semivariograms of plot-level heights were first fitted by four theoretical
parametric models: Gaussian, exponential, Matern and Spherical class. Model
parameters were estimated by restricted maximum likelihood methods. For detailed
differences between theoretical semivariogram models, refer to Banerjee et al. (2004).
The theoretical models allow us to calculate semivariance values for any h that are
necessary for other geostatistical calculations and analyses such as kriging. Finally
ordinary kriging was applied and maps of predicted height were produced over the
74
entire region along with its standard error. All computations were conducted in the
geoR package in R (Ribeiro Jr. and Diggle 2001).
5.4 Results
5.4.1 Empirical semivariogram model fitting
Figure 5.2 shows empirical semivariograms as fit using four theoretical models for
both
field-measurement-based
and
LiDAR-based
plot-level
heights.
The
semivariogram is the function describing the degree of spatial dependence of
aggregated plot-level heights and the empirical semivariogram is a nonparametric
estimate of the semivariogram. The empirical semivariance for a vector of separation h
is derived by calculating one-half the average squared difference in plot-level height
for every pair of plots locations separated by h. These values are then plotted against
the distances between data pairs. Field plots in our sample were spread over the
western Kenai region with the maximum distance of about 163,500 m. It is common
not to compute the empirical semivariogram up to the largest possible distance due to
the fact that shrinking number of available pairs for larger distances increases the
variability of the empirical semivarogram. A general recommendation is to compute
the empirical semivariogram up to about one half of the maximum separation distance
in the data (Schabenberger and Gotway 2005). In addition, since field plots don’t fall
on a regular grid, the distances between pairs are all different. The distance considered
needs to be divided into regular bins. The distance values represent the bin midpoints.
At least 30 pairs per bin were used to calculate empirical semivariogram (Banerjee et
al. 2004).
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Figure 5.2 Empirical semivariogram fitting of four aggregated plot-level height
Figure 5.2 shows that semivariance of aggregated plot-level heights has a similar
pattern over distance. All semivariograms rise to a distance around 40,000 m then
level off or decrease, which implies that aggregated plot-level heights from two plots
may not be correlated when their distance is beyond 40,000 m. No semivarigrams pass
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through the origin, which suggests that the nugget effect is not zero for all cases. The
estimated sill is not the same for four different heights. Estimated sill values are 8, 30,
8, 17 for plot tree height, stand height, LiDAR mean height and LiDAR 90th percentile
height respectively. The estimated sill is the sum of total variation explained by the
spatial structure and nugget effect.
Four different semivariogram models - Gaussian, exponential, Matern and spherical
model were fit to empirical semivariograms. The main differences among these
theoretical models are the curve smoothness and whether sill can be reached or not.
The smooth parameter is infinity for Gaussian model, 1 for Matern model and 0.5 for
exponential model. These models were fit interactively "by eye" and curves based on
the best fitting model parameters were drawn in Figure 5.2. Within small distances,
the spherical curve rises quickly and reaches the plateau in a short distance. The
curvature of the Gaussian curve changes sign within a short distance. There is not
much difference between exponential (red dash line) and Matern (green dot line)
models. From visual examination, none of the models fit well. The better fitting Matern model was finally chosen to be the covariance function.
5.4.2 Spatial prediction
Using the Matern covariance model, ordinary kriging was applied and height
prediction and standard error over the region were computed at 300m by 300m pixel
resolution. Contour maps of predicted height and standard error are displayed in
Figure 5.3 and summary statistics are shown in Table 5.1. Empirical cumulative
distribution functions and probability density functions of predicted plot-level height
are plotted in Figure 5.4. As expected, predicted plot tree height is higher than
predicted stand height and predicted LiDAR 90th percentile height is higher than
predicted LiDAR mean height. The mean of predicted plot tree height is very similar
to the mean of predicted LiDAR 90th percentile height, but predicted plot height has
much less range than predicted LiDAR 90th percentile height. This is confirmed by
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distribution curves in Figure 5.4 in which the predicted LiDAR 90th percentile height
represented by blue line spreads more widely than the predicted plot tree height
represented by black line. Predicted stand height has similar mean and range as
predicted LiDAR mean height. In fact their empirical distributions (green and red lines
in Figure 5.4) seem very close. However, predicted stand height has much larger
kriging standard error (5.05-5.37 m) than predicted LiDAR mean height (1.94 to 2.78
m).
Table 5.1 Summary of predicted plot-level height
Mean
Median
(m)
(m)
Plot tree height
12.34
12.41
Stand height
7.66
7.72
LiDAR mean height
7.37
7.49
12.00
12.22
LiDAR 90th percentile height
Minimum
(m)
10.12
4.62
4.12
6.05
Maximum
(m)
14.62
10.96
11.25
17.18
Contour maps shown in Figure 5.3 reveal similar spatial patterns for height predicted
from field measurements and LiDAR data. A circular area of low height is shown in
the north-east of the Kenai Peninsula. Maps of kriging standard error also show the
same pattern among different types of plot-level heights except that standard error of
predicted stand height is a slightly larger. As expected, all standard error maps indicate
that standard error near the location of the observed points is small.
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Figure 5.3 Maps of predicted plot-level heights from field measurements along with their
standard error estimates
79
Figure 5.4 Maps of predicted plot-level heights from LiDAR data along with their standard error
estimates
80
Figure 5.5 Empirical cumulative distribution function and kernel density function of predicted
plot-level heights
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5.4.3 Difference in predicted plot-level heights between field-based measurements
and LiDAR-based measurements
Three groups of comparisons were made: predicted plot tree height vs predicted
LiDAR mean height, predicted plot tree height vs predicted LiDAR 90th percentile
height, and predicted stand height vs predicted LiDAR mean height. Maps of the
differences are shown in Figure 5.5. On average, predicted plot tree height is much
higher than predicted LiDAR mean height with mean difference of 4.97m. The
differences between predicted plot tree height and predicted LiDAR 90th percentile
height, and between predicted stand height and predicted LiDAR mean height, are
very small. For the majority of grids, these differences are within 1m as shown in
Figure 5.6. On average, predicted plot tree height is higher than predicted LiDAR 90th
percentile height by 0.34m and predicted stand height is higher than predicted LiDAR
mean height by 0.28m.
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Figure 5.6 Differences of predicted plot-level heights between field-based measurements and
LiDAR-based measurements
83
Figure 5.7 Empirical probability density function of the differences of predicted plot-level heights
5.5 Discussion
Semivariogram results indicate that aggregated plot-level heights in this dataset seem
to spatially correlate until the distance between locations exceeds about 40,000m.
However, since few pairs are located within short distances due to the fact that FIA
plots are established based on an array of approximately 6,000-acre hexagons with
each hexagon containing only one plot (Bechtold and Patterson 2005), the results may
have been different if field plots had a different distribution pattern.
Spatial prediction results show that at 300m by 300m pixel resolution, the distribution
of predicted stand height is comparable to the distribution of predicted LiDAR mean
height with the mean difference of only 0.28m, but predicted plot tree height is much
higher than predicted LiDAR mean height with the mean difference of 4.97m. As
described earlier, stand height is calculated from trees, saplings and seedlings, while
plot tree height is calculated from trees only. In the literature, mean tree height from
field measurements is often reported to be higher than corresponding averaged laser
canopy height due to the fact that the majority of laser returns would miss tree tops
84
and would be reflected from the side of the crowns of dominant and co-dominant
trees. The magnitude of difference depends on forest conditions and the LiDAR
acquisition specifications used and varies from study to study, but the majority of the
difference is usually within 3 meters (Næsset et al. 2004). The big difference between
predicted plot tree height and predicted LiDAR mean height in our results is probably
because forests in the western Kenai region have very low stand density (mean stand
density is 66 trees per acre), low height and relatively open canopies, the laser can
easily pass through the upper canopy and some laser returns are indeed reflected from
saplings and seedlings. This also explains why average height from trees, saplings and
seedlings is very similar to the predicted LiDAR mean height (Li 2008). In addition,
field plot height is the weighted average of tree height from four surveyed subplots
while LiDAR mean height is the average of the canopy return heights within the big
plot containing all four subplots. This might explain why the minimum and maximum
of field plot height and LiDAR mean height are different.
The mean of predicted plot tree height is comparable to the mean of predicted LiDAR
90th percentile height, but predicted plot tree height tends to have smaller standard
error and range than predicted LiDAR 90th percentile height. Both field-based plotlevel height and LiDAR-based height display similar spatial patterns across the whole
region.
The choice of the covariance function impacts the kriging prediction. Since our
primary interest is spatial prediction, the correctness of the covariance model is
important. Unfortunately the selected parametric Matern model doesn’t fit the
empirical semivariogram well even though cross validation results indicate it is
acceptable. Consequently spatial prediction results may not be highly accurate. In
addition, the distance between field plots is large and spatial correlation indicated in
the semivariogram is not strong, which may also contribute to inaccurate spatial
predictions. Nevertheless, kriging surface maps produced in this study provide a visual
85
display describing the spatial distribution of height, which is very useful information
for forest inventory and monitoring. For the sake of simplicity, a constant mean model
of Gaussian process was assumed. Considered the large area coverage, adding some
covariant variables, such as weather parameters and site conditions, may improve
prediction precision.
Reliable tree height mapping is useful to support forest inventory and monitoring.
Most vegetation mapping today is conducted by manual photo-interpretation or
satellite imagery combined with field surveys. The manual photo interpretation
technique is costly and the results are dependent on the interpreter. Mapping based on
optical satellite imagery requires that the area of interest is cloud-free. In Alaska,
nearly persistent cloud cover precludes acquisition of useful optical satellite images
for a particular time period. A remote measurement of forest structure that is rapid,
reproducible and that provides reasonable spatial resolution is needed. As a rapidlygrowing remote sensing technology, LiDAR offers great potential to capture canopy
structure. However, due to high costs to apply LiDAR data in operational forest
inventory, LiDAR data are primarily acquired over specific project areas that are
typically much smaller than the spatial extent at which most satellite image datasets
are routinely acquired. In addition, it is unusual to have accurately georeferenced field
plots available over large regions. These factors may limit the operational use of
LiDAR. In this study, instead of developing regression models assuming accurate field
plot location, a new approach was developed that uses discontinuous LiDAR coverage
and spatial models. This new approach produced estimates of plot-level height over a
large region using discontinuous LiDAR data that are comparable to those obtained
using field inventory. The results are particularly useful for remote areas like Alaska
where field work is expensive and optical satellite imagery is not easy to obtain. This
approach could save time when greater accuracy is not needed, but quick assessment
is necessary.
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Chapter 6 Conclusions
The results presented in this dissertation provide valuable information regarding the
utility of LiDAR data for operational forest inventory given field plot design and
inaccurate plot location. The processing and analysis techniques described contribute
to solve methodology challenges on how to use small-footprint airborne LiDAR to
facilitate large-scale operational forest inventory, especially when accurate plot
locations are not available.
Overall, this research proved that small-footprint airborne LiDAR has a promising
future in forest inventory and analysis. Results of this study offer solutions to three
important questions regarding the use of LiDAR in the context of operational forest
inventory:
1) Is it possible to select a small set of LiDAR metrics which have strong prediction
power and also have clear biological interpretations?
In chapter 3 of this dissertation, three variable selection methods - stepwise regression,
principal component analysis (PCA), and Bayesian Modeling Averaging (BMA) were
compared using LiDAR data from three very different forest types: Douglas-fir and
western hemlock forest in moist western Washington State, Douglas-fir and Ponderosa
pine forest in dry central Washington State, and Spruce and birch forest in Kenai
Peninsula in south central Alaska. Separate aboveground biomass regression models
were developed for each study site as well as common models using the three study
sites combined. Results from principal component analysis indicate that three LiDAR
metrics - mean height, coefficient variation of height and canopy LiDAR point
density- explain the majority of variation contained within a larger set of LiDARderived metrics, and this is true for three different study sites and the combined
87
dataset. Thus these three metrics were selected as predictive variables for biomass
PCA regression models.
Final biomass models based on three variable selection methods have R2 values
ranging from 0.67 to 0.88 and models contain different sets of LiDAR-derived
metrics. Within each study site, the stepwise models had slightly higher R-square
values than the BMA and PCA models, but the stepwise models tended to contain
more LiDAR metrics than the BMA and PCA models. The BMA models had similar
R-square values to the PCA models. However, the BMA models contain different
LiDAR metrics across three study sites whereas PCA models contain the same set of
LiDAR metrics: mean height, coefficient of variation of height and canopy point
density, for the three study sites.
It is encouraging to find that the same set of LiDAR-derived metrics was found to be
the most predictive across the different forest types. In the literature, many sitespecific empirical relationships have been developed across a variety of forest types,
but published models are very different in terms of model form and the LiDAR
metrics included. To apply LiDAR data in an operational forest inventory, there is a
great need for simple, accurate, consistent, and physically meaningful prediction
models that can be used or easily adapted to different regions and sensor systems.
Results from this study indicate that it is possible to develop straightforward
regression models for different forest types using three primary LiDAR metrics - mean
height, coefficient of variation of height and canopy point density. These kinds of
LiDAR-based forest structure models would be analogous to the use of aerial stand
volume tables that have been widely used in forest inventory for a long time. If this is
true for a wide range of forest types and LiDAR systems, it is expected that the
operational use of LiDAR in forest inventory will become common.
88
Another appealing aspect of these three LiDAR metrics is their biological
interpretation. By definition, LiDAR mean height represents canopy height in the
field, coefficient of variation of height represents canopy depth, and canopy point
density represents canopy cover. The three LiDAR metrics succinctly describe the 3D
canopy structure, which explains why these metrics capture the majority of variation
contained in LiDAR data. Forest canopy structure closely correlates with stand
structure which is defined as the size and number of woody stems per unit area. Thus
models using these three LiDAR metrics likely capture the fundamental allometric
relationships between foliage volumes and stem biomass.
It is possible to select a small set of LiDAR metrics which have strong prediction
power and also have clear biological interpretations. However, due to the different
coefficients at different study sites, individual site models using these three variables
are recommended.
2) What are the effects of plot location error and plot size on LiDAR-derived metrics
and predicted biomass?
Traditionally, field plot positions recorded in a large-scale forest inventory program,
such as FIA, are intended to assist field crews in relocating the plots, as well as to
document their general location. Plot locations with small errors (several meters) are
acceptable. However, when using LiDAR data in forest inventory, plot position errors
may result in mismatch between field plots and LiDAR data, and thus may affect the
empirical relationship between field measurements and LiDAR-derived metrics, which
may then influence the prediction of forest inventory variables. The most challenging
aspect of integrating LiDAR data into the US Forest Service FIA program is the
inaccuracy of field plot locations. In Chapter 4 of this dissertation, an original
automated procedure to assess plot location error and plot size on LiDAR-derived
metrics and predicted biomass is presented. First grid-level LiDAR metrics were
89
extracted from 3D LiDAR points, and a multi-band LiDAR image was created with
each band representing each metric. Second, unsupervised classification was used to
stratify the LiDAR patches. Finally, simulation was conducted and LiDAR metrics
from simulated plots and from original plots were compared.
The results show that for small plot size of 0.04 acre and 0.08 acre, the averaged
differences of three LiDAR-derived metrics - mean height, canopy cover and
coefficient of variation of height - are small in the LiDAR patches of homogenous
forest, and these differences don’t change much as the distance between simulated plot
position and original plot position increases. In the LiDAR patches of the medium and
heterogeneous forests, these differences increase with increasing distance between
simulated plot position and original plot position. For a plot size of 1.5 acre, the
average differences of LiDAR-derived metrics between simulated plots and original
plots are very small in all three types of LiDAR patches and these changes don’t
change much as the position error increases.
The effects of plot position error and plot size on above ground biomass estimates
were assessed using the residual between field estimated biomass and biomass
predicted using regression models developed from original plots and simulated
LiDAR metrics. The results indicate that for small plots (0.04 acre), the averaged
predicted biomass in the simulated plots for LiDAR patches of homogeneous forest
doesn’t differ much from estimated biomass based on field measurement in the
original plots, but in the LiDAR patches of heterogeneous forest the differences
between predicted biomass in the simulated plots and estimated biomass based on
field measurement in the original plots increases with increasing position error.
In summary, the results show that the accuracy of field plot position and the size of
field plot are important factors affecting the accuracy and precision of LiDAR-derived
metrics and predicted biomass in heterogeneous forest stands. The logical conclusion
90
is that it is important to have accurate field plot position in these types of stands. On
the other hand, in homogenous stands, small position errors are acceptable. Whenever
possible, using larger plots will reduce the effects of plot position error on LiDAR
metrics and predicted stand biophysical variables. In the context of US Forest Service
FIA, georeferenceing LiDAR data with field measurements at subplot level is risky
due to inaccurate plot position records and the small subplot size, especially in the
forest stands with high spatial variation. In this case, linking LiDAR data with field
measurements using larger plots, which encompass four subplots, may provide a way
to characterize forest condition at the similar scale as the combination of four subplots.
3) What are the differences between predicted plot-level height based on operational
field inventory and heights based on LiDAR measurements when compared over a
large region using spatial models?
In chapter 5, four aggregated plot-level heights (plot tree height and stand height from
field measurements, LiDAR plot mean and LiDAR 90th percentile height) were
defined and compared. Plot tree height is defined as the average height of individual
trees with DBH equal or greater than 5 inches weighted by polygon area. Stand height
is defined as the average height of trees with DBH equal or greater than 5 inches,
seedlings, and sapling weighted by polygon area. LiDAR plot mean height and 90th
percentile heights are based on the laser canopy hits within the boundary of a 144-foot
fixed radius plot containing the four subplot plots. A stationary Gaussian process with
constant mean was assumed and empirical semivariograms of plot-level heights were
fit by theoretical parametric models. Then ordinary kriging was implemented and
contour maps of predicted plot-level height from field height measurements and from
LiDAR data were produced over the entire region along with maps of estimated
standard error. Results indicate that, at a 300m by 300m pixel resolution, the spatial
trends of predicted plot-level height are similar between field measurements and
LiDAR measurements. The distribution of predicted stand height is very similar to the
91
distribution of predicted LiDAR mean height with mean difference of only 0.28m. The
mean of predicted plot tree height is comparable to the mean of predicted LiDAR 90th
percentile height, but the distribution of predicted LiDAR 90th percentile height has
much heavier tails.
In this study, instead of developing regression models assuming accurate field plot
location, a new approach that uses discontinuous LiDAR coverage and spatial models
was developed and maps of predicted plot-level height over a large region were
produced. Forest height is a crucial forest inventory variable and forest height
mapping is important in forest inventory and monitoring. The method and results are
particularly useful for remote areas like Alaska where field work is expensive and
optical satellite imagery is difficult or impossible to obtain.
In conclusion, the methodology and results presents in this dissertation demonstrate
that it is feasible to integrate LiDAR data into large scale forest inventory. Three
LiDAR-derived variables - mean height, coefficient of variation of height and canopy
point density, which quantify canopy height, canopy depth and canopy cover,
respectively, have strong prediction power for forest biophysical structure parameters.
When matching field measurements with potentially large location errors with LiDAR
data, large plots are recommended due to plot position error and plot size concerns.
Using LiDAR data alone, it is possible to stratify forest stands and map forest height.
Methodologies developed in this dissertation can be automated with little manpower
involved. After these methods are streamlined, it should be possible to provide results,
such as regression models and maps over large area, within a few weeks of the LiDAR
acquisition.
There are some limitations with this study. First of all, the LiDAR data used is not
continuous wall-to-wall coverage, but limited to small patches centered on field plots.
Classification over these small patches may not represent forest stand condition over
92
the larger spatial extent. Secondly, the above ground biomass is the total weight of
oven-dried biological material present above the soil surface in a specified area and
the biomass estimates from field measurements in this study were obtained using
previously developed allometric relationships with field measured DBH and height.
The individual tree biomass was calculated using allometric equations and plot-level
biomass is the sum of all measured trees converting to mass per unit area. Majority of
the existing allometric equations don’t account for wood density, which is a known
factor affecting precise estimate of individual tree biomass, due to the complicity that
wood density varies among individuals of a given species, among geographic
locations, and within the vertical and radial dimensions of individual trees (Fearnside
1997). Using these allometric equations smoothes out tree to tree variations and results
may be different from the true biomass obtained through destructive harvest method.
Thus the coefficients of the developed regression models between biomass and
LiDAR metrics in this study may change if using true biomass. However, true biomass
is difficult to obtain at present, if not possible. In addition, depending on the
objectives, true biomass estimates over large area may be not necessary since variation
among individual trees may average out. Thirdly, no other image data were used in
this study. Fusion of LiDAR data with other optical data, such as aerial photos and
satellite images may help characterize the forest canopy, since LiDAR data only
provide structure information while optical data can record reflectance properties
indication of forest composition which can be used for species recognition. More
research is clearly needed to test different sensor and flight parameters, combining
LiDAR data with other hyperspectral images.
Given the anticipated decline in the cost of LiDAR data collection, it is expected that
LiDAR data will be an increasingly useful tool in forest inventory. This study may
lead to further advancements and efficiencies in large-scale forest inventories in the
following areas: 1) LiDAR data may be used to measure a broad range of structural
attributes to quickly update existing forest structure maps. 2) Well-calibrated LiDAR
93
data could be used to capture inventory attributes in remote or inaccessible regions.
All of these may lead to more meaningful and ecologically relevant measures of forest
composition, structure and function.
94
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106
VITA
Name:
Education
Ph D (2009)
Yuzhen Li
Quantitative Resource Management (Remote Sensing),
University of Washington, Seattle, WA, USA
MS (2008)
Statistics, University of Washington, Seattle, WA, USA
MS (2005)
Quantitative Resource Management (Forest Biometrics),
University of Washington, Seattle, WA, USA
MS (1998)
Silviculture, Chinese Academy of Forestry, Beijing, China
BS (1995)
Forest Science, ShanDong Agriculture University, TaiAn, China
Professional Experience
Graduate Intern, June 2008 – Sep. 2008, Biometrics & Statistics group, Western
Timberlands Research Department, Weyerhaeuser Company, Federal way, WA
Graduate Teaching Assistant, Jan. 2008 - June 2008
Department of Statistics, University of Washington, Seattle, WA
Graduate Research Assistant, Sep. 2001- Dec. 2007, Sep. 2008- Mar. 2009
College of Forest Resources, University of Washington, Seattle, WA
Assistant Researcher, July 1998- Mar. 2001
Chinese Academy of Forestry, Beijing, China