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USING LIDAR TO ESTIMATE THE TOTAL ABOVEGROUND LIVE BIOMASS OF
REDWOOD STANDS IN SOUTH FORK CASPAR CREEK WATERSHED,
JACKSON DEMONSTRATION STATE FOREST, MENDOCINO, CALIFORNIA
By
Hai Hong Vuong
A Thesis Presented to
The Faculty of Humboldt State University
In Partial Fulfillment of the Requirements for the Degree
Master of Science in Natural Resources: Forest, Watershed and Wildland Sciences
Committee Membership
Dr. Mahesh Rao, Committee Chair
Dr. John-Pascal Berill, Committee Member
Dr. Yoon G Kim, Committee Member
Dr. Anil Kizhakkepurakkal, Committee Member
Dr. Alison O’Dowd, Graduate Coordinator
May 2014
ABSTRACT
The overall objective of this study is to develop a method for estimating total
aboveground live (ABGL) biomass of redwood stands in South Fork Caspar Creek
Watershed (SFCCW), Jackson Demonstration State Forest (JDSF), Mendocino, California
using airborne LiDAR data. The study focused on two major species: redwood (Sequoia
sempervirens or SESE) and Douglas-fir (Pseudotsuga menziesii or PSME). Specifically,
the objective includes developing statistical models for tree diameter at breast height
(DBH) on LiDAR-derived height for both species. From twenty-three 0.1-ha plots
randomly selected within the study area, field measurements (DBH and tree coordinates)
were collected for a total of 429 trees of SESE and PSME. Field measurements were taken
for all trees having DBH equal to or greater than 25.4cm. In case of LiDAR-derived tree
the height, a minimum height of 15m was used for this study. Software programs
TreeVaW and FUSION/LDV were used to develop Canopy Height Models (CHM), from
which tree heights were extracted. Based on LiDAR-derived height and ground-based
DBH, linear regression models were developed. The linear regression models explained
62.65% of the total variation associated with redwood’s DBH and 82.58% of Douglas fir’s
DBH. The predicted DBH was used to estimate the ABGL biomass using Jenkins’ formula
(Jenkins et al., 2003A). At a single tree level, the average ABGL biomass of 257 SESE
trees using predicted DBH was underestimated by about 10.1% compared with that of
ABGL biomass using the ground-based DBH. The average ABGL biomass of 172 PSME
trees using predicted DBH was underestimated by about 8.0% compared with that of using
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ground-based DBH. For both species, there was a statistically significant difference in the
mean ABGL-biomass between using predicted DBH and ground-based DBH. In case of
the twelve randomly-sampled plots, biomass estimates for both species on the rough terrain
( ≥ 15% slope) were significantly lower and more varied than those on the flat terrain (<
15% slope). The 95% confidence interval for the mean ABGL-biomass of the two species
combined was 369.5±128.8 ton/ha while that of all species included was 583.1± 165.5
ton/ha. This study demonstrates that LiDAR data plays an important role in estimating the
ABGL biomass of the second-growth redwood stands and Douglas fir. Thus, this method
can make a significant contribution to forestry inventory by reducing time and labor cost in
the timber industry.
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ACKNOWLEDGEMENTS
I was able to complete this thesis thanks to the generous support and help of many
professors, researchers, friends, and fellow students. I am very much honored to
acknowledge their contributions.
Thanks to Dr. Mahesh Rao for providing me with many suggestions and advices
both in terms of methodology involved and in terms of proofreading the draft. I am also
very much indebted to Dr. Berrill for many valuable advices in silviculture, about the
relationship between DBH and LiDAR-derived height, in particular. Thanks to Dr. Kim for
his many statistical advices and editing help, and to Dr. Kizhakkepurakkal for GIS help.
I have been much encouraged and helped by the JDSF staff; Lynn Webb, Brian
Barrett, and Shawn Headley, in particular, who provided me with valuable GIS
information about the study area. Thanks also for the housing help when I was collecting
data. Special thanks to Brian Barrett for his enthusiastic help during the difficult times.
Thanks also to Diane Sutherland and Sue Hilton of the Pacific Southwest Research
Station in Arcata for LiDAR raw data and GIS information.
I am also much grateful to George Pease and Gayleen Smith for providing me
with the needed equipment and various administrative supports.
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TABLE OF CONTENT
ABSTRACT ...................................................................................................................... ii
ACKNOWLEDGEMENTs.............................................................................................. iv
TABLE OF CONTENT .................................................................................................... v
LIST OF TABLES ........................................................................................................... ix
LIST OF FIGURES .......................................................................................................... x
TERMS & ABBREVIATIONS ...................................................................................... xii
INTRODUCTION ............................................................................................................ 1
LITERATURE REVIEW ................................................................................................. 5
MATERIALS AND METHODS ...................................................................................... 9
Materials……………………………………………………………………………..9
Study area.............................................................................................................. 9
GIS and remote sensing data............................................................................... 11
Ground Data ........................................................................................................ 12
Software .............................................................................................................. 15
Instruments .......................................................................................................... 16
LiDAR overview ................................................................................................. 18
How does LiDAR work? .................................................................................... 20
Overview of the FUSION/LDV analysis and visualization ................................ 22
Methods…………………………………………………………………………….23
Outline of study procedures ................................................................................ 23
Sensitivity analysis.............................................................................................. 27
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Spatial analysis of TreeVaW and LDV .............................................................. 30
Biomass estimate at a single tree level ............................................................... 31
Biomass estimate at plot level ............................................................................. 32
Statistical analysis ............................................................................................... 33
RESULTS AND DISCUSSION ..................................................................................... 34
Sensitivity Analysis Using Summer 2012 Data………………………....................34
Spatial Analysis Using Summer 2013 Data………………………………………...............................................................39
Regression Model for Ground-Based DBH on H_LDV…………………………...43
Regression model for SESE ................................................................................ 43
Regression model for PSME ............................................................................... 49
Biomass Analysis……………………………………………………......................56
Single tree level................................................................................................... 56
Plot level ............................................................................................................. 59
Terrain effect on biomass dispersion .................................................................. 62
Significant factors for the total biomass ............................................................. 65
Biomass in SFCCW ............................................................................................ 67
SUMMARY .................................................................................................................... 69
Future Research…………………………………………………………….............71
REFERENCES ............................................................................................................... 73
APPENDIX 1 .................................................................................................................. 77
Data: 429 Paired Trees of SESE and PSME from 23 Randomly Sampled Plots…..77
APPENDIX 2. REDWOOD LINEAR REGRESSION MODELS…………………….78
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SESE Linear Regression Model of Log(DBH) on Log(H_LDV) without “Terrain” Variable…………………………………………………………………………….78
SESE Linear Regression Model of Log(DBH) on Log(H_LDV) with “Terrain” Variable…………………………………………………………………………….78
APPENDIX 3. DOUGLAS-FIR REGRESSION MODELS .......................................... 79
PSME Linear Regression Model of Log(DBH) on Log(H_LDV) without “Terrain” Variable…………………………………………………………………………….79
PSME Linear Regression Model of Log(DBH) on Log(H_LDV) with “Terrain” Variable…………………………………………………………………………….79
APPENDIX 4…………………………………………………………………………..80
Appendix 4-1: SESE Individual Tree Biomass…………………………………….80
Appendix 4-2: PSME Individual Tree Biomass…………………………………....81
APPENDIX 5…………………………………………………………………………..82
Variance Test and t.Test for SESE Biomass at a Single Tree Level……………….82
APPENDIX 6…………………………………………………………………………..83
Variance Test and t.Test for PSME Biomass at a Single Tree Level……………....83
APPENDIX 7…………………………………………………………………………..84
Comparison Mean of H_LDV to Mean of H_Gr…………………………………..84
APPENDIX 8…………………………………………………………………………..85
Distance (D) Between Tree Tip and Tree Position of 429 Paired Trees…………...85
APPENDIX 9…………………………………………………………………………..86
Distances D ( D= ) Between Tree Tip and Tree Base of 429 Paired Trees……….86
APPENDIX 10………………………………………………………………………....87
Spatial Analysis of the Square Rooted Distance…………………………………...87
APPENDIX 11…………………………………………………………………………88
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Number of 0.1 Ha Plots Required for an Error of ±50 (Ton/Ha) of the True Mean Biomass…………………………………………………………………………….88
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LIST OF TABLES
Table 1.Dates of field work during summer 2013 ............................................................ 14
Table 2. Image processing, geospatial and statistical software ........................................ 15
Table 3. Instruments used for the study ............................................................................ 17
Table 4. DBH and Height values by TreeVaW and LDV for a total of 55 trees (summer 2012) ................................................................................................................................. 38
Table 5. Summary of 257 redwood trees .......................................................................... 44
Table 6. Summary of 172 Douglas-fir trees...................................................................... 50
Table 7. SESE biomass analysis at single tree level (Appendix 4) ................................. 57
Table 8. PSME biomass analysis at single tree level (Appendix 4) ................................. 58
Table 9. ABGL biomass of redwood/Douglas-fir stands on twelve 0.1 ha plots ............. 60
Table 10. Predicted and ground biomass on different terrain ........................................... 63
Table 11. The contribution of red wood clumps, grand fir, and western hemlock to the biomass difference between ground DBH-based biomass and predicted DBH-based biomass ............................................................................................................................. 66
Table 12. Summary of biomass research in California ..................................................... 68
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LIST OF FIGURES
Figure 1. South Fork Caspar Creek Watershed, Jackson Demonstration State Forest, Mendocino County, California ......................................................................................... 10
Figure 2.Tree-base position and tree-tip position within a threshold distance of 4 m ...... 13
Figure 3. Field instruments ............................................................................................... 16
Figure 4. Schematic of an airborne laser scanning system and one pulse has many returns........................................................................................................................................... 19
Figure 5. LiDAR Data Viewer (LDV) .............................................................................. 21
Figure 6. Outline of study procedures............................................................................... 24
Figure 7. Measurement marker tool indicating the highest point (48.31 m) of a tree in the cylinder and its associated coordinate............................................................................... 26
Figure 8. Model builder for iterative task of creating the CHM for each combination of cell size and filter window size ......................................................................................... 28
Figure 9. Correlation between ground-based height (H_gr) and LiDAR-derived height with FUSION interface or LDV ....................................................................................... 35
Figure 10. TreeVaW-paired tree ratio compared with LDV-paired tree ratio .................. 36
Figure 11. LDV-derived height (m) and ground-based DBH of 172 Douglas-fir ............ 40
Figure 12. LDV-derived height (m) and ground-based DBH of 257 redwoods ............... 40
Figure 13. Distribution of D and the square rooted D ( Dd = ) ....................................... 42
Figure 14. SESE model ..................................................................................................... 45
Figure 15. log(DBH) vs. log(H_LDV) ............................................................................. 46
Figure 16. Homogeneity of variance ................................................................................ 47
Figure 17. Diagnostic plots of the residuals...................................................................... 48
Figure 18. PSME model .................................................................................................... 51
x
Figure 19. log(DBH) vs. log(H_LDV) ............................................................................. 52
Figure 20. Homogeneity of variance ................................................................................ 53
Figure 21. Diagnostic plots of the residuals...................................................................... 54
Figure 22. Predicted biomass and ground-based biomass ................................................ 64
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TERMS & ABBREVIATIONS
ABGL Aboveground Live
ABGR Grand fir (Abies grandis)
CHM Canopy Height Model
CI Confidence Interval
CSM Canopy Surface Model
DBH Diameter at Breast Height
DEM Digital Elevation Model
F Flat terrain with slopes less than 15%,
FIA Forest Inventory Analysis
GPS Global Positioning System
JDSF Jackson Demonstration State Forest
LDV LiDAR Data Viewer
LiDAR Light Detection And Ranging
NSSDA National Standard for Spatial Data Accuracy
PSME Douglas-fir (Pseudotsuga menziesii)
R Rough terrain with slopes equal to or greater than 15%,
SESE Redwood (Sequoia sempervirens)
SFCCW South Fork Caspar Creek Watershed
TreeVaW Software for measuring individual trees using LiDAR data
TSHE Western hemlock (Tsuga heterophylla)
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USDA United States Department of Agriculture
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1
INTRODUCTION
A growing forest removes greenhouse gases from the atmosphere and lessens the
impact of global climate change. Global vegetation removes carbon from the atmosphere at
a rate of (4.7±1.2) Gt/year whereas industries using fossil fuel emitted carbon into the
atmosphere at the rate of (8.7±0.5) Gt/year and deforestation contributed more carbon
(1.2±0.7 Gt/year) to the atmosphere (Le Quéré et al., 2009). Thus, the speed of carbon-
related emission was about twice as fast as carbon-sinking speed. This imbalance between
atmospheric carbon emission and removal can be corrected more by a better forest
management for more aboveground-live (ABGL) biomass. The more effectively the forest
management practices, the higher the carbon sequestration is. Effective monitoring of
forest carbon poses serious challenges to forest managers (Golinkoff et al., 2011), and
scientists. It requires robust methods to better quantify forest carbon storage over time
across extensive landscapes (Gonzalez et al., 2010). Such a demand can be met with
remote sensing techniques such as LiDAR.
There are a variety of methods for calculating tree volume and tree biomass based
on the principle of “dimensional analysis” such as the study described by Whittaker and
Woodwell (1968). Their study relies on the consistency of allometric relationship between
tree attributes (usually diameter at breast height (DBH) and/or height) and biomass for a
given species or a group of species. Many stems are sampled for a range of involved
variables (DBH or height), then a regression model is extracted to model tree biomass on
one or more tree characteristics such as DBH, height, crown width, etc. Currently, various
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biomass estimation methods are being applied to forest lands in the United States. The
USDA Forest Service has recently used the Jenkins’ model designed for the national-scale
biomass estimation (Jenkins et al., 2003B). This model uses the ground-based diameter at
breast height as the input for the biomass estimation. Another method for tree biomass
estimation on the-national scale is the component ratio method (CRM). CRM was
proposed for consistent national projection of tree biomass based on the forest inventory.
Detailed calculation and examples are described by Heath et al. (2008). Both of these
national-scale methods have produced generalized biomass estimates compared with
regional allometric equations (Zhou and Hemstrom, 2010). Consequently, regional volume
and biomass models were developed for regional tree species (Waddell and Hiserote,
2005). In general, these models have been developed from local tree studies. These models
are direct functions of either tree diameter or both diameter and height based on species-
level data. Different regions sometimes manipulate data such as logarithmic
transformation, linear or quadratic models to model local characteristics better. The forest
inventory analysis (FIA) program of the Pacific Northwest Research Station uses separate
sets of models for bole, branch, and bark biomass. Tree bole biomass is estimated from
volume via species-specific wood density factors. Each tree species is associated with a set
of specific volume and biomass equations. All these models using ground-based methods
for tree attributes are based on extensive field data, which are labor intensive, costly, time
consuming, and often result in destruction of materials. Furthermore, the low accuracy of
the height measurement in a dense stand complicates the issue even more. These
disadvantages can be resolved with the use of LiDAR and GPS (global positioning system)
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technology. GPS provides the high accuracy in the positioning, and LiDAR is well-known
for both of its vertical and horizontal accuracy in the mapping community (Renslow,
2000). Field research has demonstrated the high accuracy of LiDAR in estimating canopy
height, and high correlation between LiDAR height and field-measured aboveground
biomass (Andersen et al., 2006). In this study, available LiDAR data in the study area
acquired from the National Oceanic and Atmospheric Administration (NOAA) has vertical
positional accuracy of less than or equal to 18 cm (equivalent to root mean square error
(RMSE) of 9 cm if errors were normally distributed) based on the National Standard for
Spatial Data Accuracy (NSSDA). Hence, the high accuracy of LiDAR-derived height
makes it a good predictor variable for DBH. This predicted DBH forms an input to
estimating ABGL biomass using Jenkins’ formula (Jenkins et al., 2003A).
The main goal of this study is to develop a LiDAR-based model to estimate ABGL
biomass of Redwood/Douglas-fir stands in the South Fork Caspar Creek Watershed
(SFCCW) within the Jackson Demonstration State Forest (JDSF) in Mendocino County of
California.
Objectives of this study also include:
1. Optimization of the LiDAR-derived Canopy Height Model (CHM) using sensitivity
analysis.
2. Optimization of matching ground-based tree positions (tree base) with LiDAR-derived
tree positions (tree tip) using spatial analysis.
3. Developing linear regression models for DBH on LiDAR-derived tree height for two
dominant species: redwood and Douglas-fir, and estimating ABGL biomass using the
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Jenkins’ allometric model based on the predicted DBH. In addition to LiDAR height,
terrain was also added in developing better models.
4. Evaluation of the biomass estimates.
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LITERATURE REVIEW
LiDAR applications in forest management have been increasing around the world.
Since 2000, compared with traditional ground methods, reduced cost and greater accuracy
are turning LiDAR into such a useful tool for forest applications.
In Queensland, Australia the retrieval of tree and forest structural attributes (mainly
stem height, tree density, and crown cover) using LiDAR have been used with CHM in
addition to the Height-Scaled Crown Openness Index (HSCOI) (Lee et al., 2007). The
LiDAR applications in New South Wales, Australia included topographic mapping, wood
resource assessment, carbon accounting, harvest planning, forest health assessment and
fuel assessment (Turner, 2007).
In Europe, LiDAR was used for timber production and estimation of forest
attributes. Both of the airborne LiDAR and satellite multispectral data were applied to the
estimation of timber volume at a plot level in Trento, Southern Italian Alps (Tonolli et al.,
2011). In Norway, forest structural attributes such as tree height, diameter, stem number,
basal area, and timber volume were estimated from various canopy heights and canopy
density derived from a small-footprint laser scanner over both young and mature forest
stands (Naesset, 2004).
In the United States, LiDAR was used to estimate the aboveground live biomass as
well as below-ground biomass. It can be also used to estimate forest structural attributes. In
McDonald-Dunn Research Forest of Oregon, LiDAR was found quite useful in measuring
total aboveground biomass (TAGB) based on individual stems. The accuracy of LiDAR-
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TAGB was assessed by stem counts and heights (Edson, et al., 2011). A 4,800-ha forested
area in eastern Texas was selected to develop methods for scale-invariant estimation of
forest biomass using LiDAR. Researchers proposed a linear functional model and an
equivalent nonlinear model for biomass estimation using LiDAR-derived canopy height
distributions (CHD) and canopy height quantile (CHQ) functions, respectively. The study
looks promising for estimating some forest characteristics such as below-ground biomass,
timber volume, crown weight, and Leaf Area Index (Zhao et al., 2008). In the Pacific-
Northwest of the US, LiDAR was used to predict forest stand structural attributes, carbon
storage in particular, which took the geographic variability into account (Lefsky et al.,
2005). In Western Oregon, researchers combined LiDAR estimates of aboveground
biomass and LANDSAT estimates of stand age to spatially validate the model of forest
productivity. The productivity estimates looked good when compared with field estimates
(Lefsky et al., 2004). Airborne LiDAR was also used to estimate aboveground biomass of
Loblolly pine stands (Pinus taeda) in Sam Houston forest, Texas, and it is a proven
technology that can be used to accurately assess aboveground forest biomass (Popescu,
2007).
In California carbon stock was analyzed in two areas: Blodgett Forest Research
Station (BFRS) in Sierra Nevada, CA and Jackson Demonstration State Forest (JDSF) in
Mendocino County of California (Brown et al., 2004). Since October 2003, researchers at
BFRS have collected plot-level data for carbon analysis across permanent plots. Litter and
duff depth, biomass, soil carbon stocks and dead wood densities were part of the data
collected. In 2004, field data were collected at the JDSF for biomass estimation. Various
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tree attributes were measured in and around clear-cut plots, and the measurements were
also taken in plots using group selection method. Researchers also calculated the
aboveground live tree biomass based on the yield tables of Lindquist and Palley (1963)
using “empirical data” of redwood stands. All individual trees of DBH over 4.5” were used
to calculate the individual biomass using Jenkins’s formula (2004), and then they were
added up to get the stand biomass per acre (Brown et al., 2004).
Gonzalez et al., 2010 argued, “Greenhouse gas inventories and emission reduction
programs require robust methods to quantify carbon sequestration in forest. We compare
forest carbon estimates from Light Detection and Ranging (LiDAR) data and QuickBird
high-resolution satellite images, calibrated and validated by field measurements of
individual trees. We conducted the tests at two sites in California: (1) 59 km2 of secondary
and old growth coast redwood (Sequoia sempervirens) forest (Garcia–Mailliard area) and
(2)58 km2 of old-growth Sierra Nevada forest (North Yuba area). Regression of above live
tree carbon density, calculated from field measurements, against LiDAR height metrics
and against QuickBird tree crown diameter generated equations of carbon density as a
function of remote sensing parameters. Employing Monte Carlo method (*), we quantified
uncertainties of forest carbon estimates from uncertainties in field measurements, remote
sensing accuracy, biomass regression equations, and spatial autocorrelation. … . Large
sample sizes in the Monte Carlo analyses of remote sensing data generated low estimates
of uncertainty. LiDAR showed lower uncertainty and higher accuracy than QuickBird, due
to high correlation of biomass to height, and undercounting of trees by the crown detection
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algorithm. …. The method that we tested, combining field measurements, LiDAR, and
Monte Carlo, can produce robust wall-to-wall spatial data on forest carbon.”
This study also attempts bivariate regression models to predict DBH for more
accurate biomass estimation using ground DBH and LiDAR-derived height. Main focus is
on the intelligent use of FUSION/LiDAR DATA VIEWER to find the best CHM when
random points are used as the center points of data collection. Other study ( Popescu,
2007) has estimated biomass using DBH as a function of LiDAR-derived tree height and
LiDAR derived tree crown; another study (Gonzalez et al., 2010) estimated LiDAR
biomass as a multivariate regression model of LiDAR-derived height, and QuickBird
biomass as a bivariate regression model of tree-crown diameter.
(*): Monte Carlo simulation methods (or Monte Carlo procedures) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results; typically thousands of iterations are done to obtain the distribution of an unknown entity. .
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MATERIALS AND METHODS
Materials
Study area
The study site is located in the South Fork Caspar Creek Watershed (SFCCW) at the
coordinate of 123o 44’W, 39o 20’N within the Jackson Demonstration State Forest (JDSF)
in Mendocino County, California (Figure 1). The total area is about 460 ha, and the study
site has two dominant species: redwood (Sequoia sempervirens), and Douglas-fir
(Pseudotsuga menziesii). These two species are thought to be representative of young-
growth stand being managed in the area. The topography of the study site has an
elevation ranging from 4 m to 200 m, and typically steep slopes (> 15%). The stand age
in the South Fork watershed would be 40 and 147 years old. The 40-year old component
comes from uneven-aged selection. It removed about 65 % of the standing volume of the
redwood second growth and some older white wood. The second-growth red wood stands
on the south side of Route 408 and Route 409 (Figure 1) were first harvested using clear-
cut system before 1900 (L. Webb, personal communication, Nov. 18, 2013).
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Figure 1.
R 409
Figure 1. South Fork Caspar Creek Watershed, Jackson Demonstration State Forest, Mendocino County, California
11 GIS and remote sensing data
GIS and remote sensing data pertaining to roads, streams, SFCCW, cut blocks and
silvicultural systems were provided by the GIS staff of JDSF and Pacific Southwest
Research Station in Arcata, California. 2011 LiDAR raw data set for SFCCW was
obtained from the National Oceanic and Atmospheric Administration (NOAA) in the
format *.LAS and *.TIF. NOAA imagery − ALS Leica 40-Coastal California Digital
Imagery of 0.3 m resolution (Geo TIFF files) was also obtained from the website of
NOAA. 2011 LiDAR metadata file provides the following information about accuracy:
Horizontal_Positional_Accuracy and Horizontal_Positional_Accuracy_Report. The
minimum expected horizontal accuracy was tested to meet or exceed the National
Standard for Spatial Data Accuracy (NSSDA). Horizontal accuracy is 50 cm RMSE or
better.
The minimum expected vertical accuracy (from Vertical_Positional_ Accuracy of
LiDAR data and Vertical_Positional_Accuracy_Report) was also tested to meet or
exceed the NSSDA. When compared to GPS survey grade points in generally flat, non-
vegetated areas, at least 95% of the positions had an error less than or equal to 18 cm
(equivalent to root mean square error (RMSE) of 9 cm if errors were normally
distributed).
Fugro Earth Data, Inc. in Frederick, Maryland collected ALS60-derived LiDAR
data over Coastal California with a 1 m nominal post spacing using two Piper Navajo
airplanes. Data collection was done between October 2009 and August 2011 with a total
12 of 1,546 flight lines in 108 lifts. The flight lines were at an average altitude of 6,244 feet
above terrain and 121,300 pulses per second were used. They used Leica ALS60 MPiA
LiDAR systems.
Ground Data
Survey 1. To perform the sensitivity analysis, field data were collected during summer of
2012 with the following protocol:
• Plot center position was recorded by a GPS device called Trimble Juno at the
maximum accuracy of 3 m.
• MapStar Compass Module II was used to measure the Azimuth and the distance from
the plot center to the tree base to calculate the tree base position.
• NAD1983, UTM, Zone 10N coordinate system was used for this study.
• Tree DBH, height (when possible), and terrain characteristics were collected to build
good regression models.
Fifty-five trees were measured from the plot of 75 m radius in May and July of 2012 (See
Figure 2).
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Figure 2.Tree-base position and tree-tip position within a threshold distance of 4 m
14 Survey 2. The quality of field data in summer 2013 improved a lot with the new GPS
device (Trimble GEO XH 6000 Series), which has ten times higher accuracy (0.3 m vs. 3
m) than Trimble Juno. A total of 548 trees were measured over 23 randomly selected
plots (Figure 1) in June, July, and August of 2013 (See Table 1).
Table 1.Dates of field work during summer 2013 Plot No. June Plot # July Plot # August
20 5, 6, 10, 12 24 9, 10, 11 16 1
8 7, 8, 11 14 10, 11 11 4, 5
10 8, 9 21 13, 14 18 12, 13
12 13 9 15, 16 22 14, 15
4 14 17 17, 18
25 15, 16 2 19
7 17, 19 15 25
23 20, 22 19 29, 31
3 22 5 28
1 24
15 Software
Table 2. Image processing, geospatial and statistical software Software Source Application Fusion/LDV http://forsys.cfr.washington.edu/fusion/fusionlatest.html USDA Forest
Service software to analyze LiDAR data.
ArcMap http://www.esri.com/ Viewing, editing, creating, and analyzing geospatial data. ArcMap allows users to explore data, and create maps.
TreeVaW http://ssl.tamu.edu Analyzes LiDAR data. Handles individual tree location, tree height, and crown widths.
Erdas http://geospatial.intergraph.com/products/ERDAS-Extensions-for-ArcGIS/Details.aspx
Image processing and classification of digital image for mapping use in GIS or in CAD.
IDL 8.2 with ENVI 5.2
http://www.exelisvis.com/ Analyzes geospatial imagery. IDL 8.2, ENVI 5.2 with TreeVaW are used to extract tree tip.
R http://www.r-project.org/ Powerful statistical software.
16 Instruments
Figure 3 shows two most important instruments used for the study. They are used
to accurately find tree tips in the ArcMap and tree base on the ground.
MapStar Compass Module II Trimble GeoExplorer 6000 Series Figure 3. Field instruments
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Table 3. Instruments used for the study
Instrument Function Manufacturer
MapStar compass module II Measures azimuth and distance Laser Technology Inc.
Logger tape Measures distance and diameter Forestry Suppliers Inc.
D-tape, Biltmore Stick Measures diameter Forestry Suppliers Inc.
GeoXH 6000 Series Determines the coordinates of plot
centers at the accuracy of 1 m
Trimble Inc.
18
LiDAR overview
LiDAR system uses laser light to measure distances. They are used for a variety
of applications, for example, estimating atmospheric aerosols by shooting a laser
skyward, and measuring speed of cars on a highway. Airborne laser-scanning technology
is a specialized, aircraft-based type of LiDAR that provides extremely accurate, detailed
3-D measurements of the characteristics on the ground including vegetation and
buildings. Developed in the last 15 years, one of LiDAR’s first commercial uses in the
United States was in survey of power line corridors to identify invading vegetation. Other
uses include mapping of lands and coastal areas. Ground contours can be measured from
an aircraft which provides an accuracy of within 6 inches of the actual elevation when
used in wide open and flat areas. When used in steep and forested areas, the accuracy is
typically in the range of 1 to 2 feet and it also depends on other factors, such as density of
canopy cover and the spacing of laser shots. The speed and accuracy of LiDAR make it
feasible to map large areas with so much detail that were possible in the past with time-
consuming and expensive ground crews. LiDAR has been used to create highly detailed
contours across large flood plains, and it can pinpoint areas of high risk. In some cases,
LiDAR was used to produce more accurate digital terrain data over entire states, which
are valuable information for emergency planning and timely response. LiDAR mapping
of terrain uses a technique called “bare-earth filtering”. The method strips away all the
data about trees and buildings and leaves just the bare-ground data. Fortunately for
foresters and other natural resource researchers, the data being “thrown away” by
19 geologist can provide detailed information about vegetation conditions and structure
(McGaughey, 2012).
Figure 4 showed the Airborne Laser Scanning (ALS) system and sending one
laser pulse may have many returns.
Source of image: USDA Forest Service, Fusion manual pdf (McGaughey, 2012)
Figure 4. Schematic of an airborne laser scanning system and one pulse has many returns
20 How does LiDAR work?
LiDAR measures how long it takes each pulse to travel from the emitter (on
aircraft) to the object and reflects back to the receiver (on aircraft). These times are used
to compute the distance each pulse travels from scanner to ground. The global positioning
system (GPS) units (both on aircraft and on the ground) with the inertial measurement
unit (*) (IMU) on the aircraft determines the precise location and altitude of the laser
scanner as the pulses are emitted, and an exact coordinate is calculated for each point.
Once distance and location information is accurately determined, the laser pulses provide
all the needed information for 3-D measurements of the ground characteristics, such as
surface structure, vegetation, roads, and buildings. Millions of data points are recorded by
LiDAR; they are so many that LiDAR can create a 3-D data cloud of ground
characteristics.
Figure 5 showed one such example of 3-D image of a specific rectangular plot
which used FUSION/LDV analysis and visualization (McGaughey, 2012).
(*)IMU is an electronic device that measures and reports on a craft's velocity, orientation, and gravitational forces. Precise kinematic positioning by differential GPS and orientation by the IMU of the scanner is critical to the performance of the LIDAR system. GPS provides the coordinates of the scanning laser and IMU provides the direction of the pulse. With the range and time, the position of the “return point” can be accurately calculated (Renslow et al., 2000).
21
Figure 5. LiDAR Data Viewer (LDV)
22 Overview of the FUSION/LDV analysis and visualization
LiDAR produces huge amount of data, which needs to be divided into small samples for
a particular research project. Scientists both at the Pacific Northwest Research Station
and at the University of Washington have decided to design a more practical system to
support their research, which came to be called the analysis and visualization system. It
consists of two main programs: FUSION/LDV (LiDAR Data Viewer), and a collection of
task-specific command line program. The primary interface, provided by FUSION,
consists of a graphical display window and a control window. The FUSION display
presents all the data in a 2-D display similar to the GIS. It supports a variety of data types
and formats including shape files, images, digital terrain models, canopy surface models,
and LiDAR data. LDV provides the 3-D visualization environment for the spatially-
explicit data. Command line program provides specific analysis and data processing
capabilities to make FUSION suitable for processing large amount of LiDAR data
(McGaughey, 2012).
In this study two DOS command lines: “GridSurfaceCreate” and “GroundFilter”
were, in that order, used to create the Canopy Surface Model (CSM) using the first return
of LiDAR raw data and the Digital Elevation Model (DEM or bare-earth model) using
the last return of LiDAR data. Canopy Height Model (CHM) was the result of subtracting
DEM from CSM using "Map Algebra" in ArcMap.
23
Methods
Outline of study procedures
Two approaches were used to study SESE/PSME-stand biomass: TreeVaW
method and LDV method. Both methods required that for each observable tree, its
LiDAR-derived height must associate with its ground-based DBH to develop the linear
regression model. Ground based DBH was a reliable measurement on the field while the
accuracy of CHM-derived height sensitively varied with two parameters: cell size
(desired grid cell size in the same units as LiDAR data) and (n x n) cell median filter or
mean filter or both for smoothing of the surface models. Hence, it created the need for a
sensitivity analysis. This analysis dealt with the effect of cell size and window filter size
on grid values of CHM. The purpose of sensitivity analysis was to look for a specific
CHM from which the derived height was the closest to the correspondent ground height.
Additionally, for each observable tree, the LiDAR-derived tree tip position and ground-
tree base position did not inherently coincide due to the uncertainties with individual tree
mapping on the ground using the global positioning system (GPS), to the close canopy
conditions, and to structural properties of the tree crown. Hence, for the same tree in a
specific projected coordinate system, its tree tip coordinate was mostly different from its
tree base coordinate. Consequently, the problem was how big the distance between tree
tip and tree base was acceptable as a threshold below which the tree tip and tree base
were considered to belong to the same tree. This was done using spatial analysis in
ArcMap.
24
Figure 6. Outline of study procedures
25
Figure 6 shows that it begins with the use of FUSION to extract CSM, DEM from
two FUSION parameters: cell size and window filter size. ArcMap is then used to create
the CHM together with the CSM and DEM for sensitivity analysis. TreeVaW is used next
for the best CHM to glean information about tree tip heights, coordinates, and crown
widths. Finally, spatial analysis (process of matching tree) is performed based on the
threshold distance between tree-tip coordinates and tree-base coordinates. In addition to
the TreeVaW method, LDV also extracts the same shape file as the TreeVaW, but it uses
its own CHM derived from LDV. LDV used “measurement marker” tool to get a shape
file of tree tip heights with their coordinates (Figure 7). Each method yields its own set of
paired trees and attributes. Ground-based DBH and LiDAR-derived height are used for
statistical modeling for each species.
26
Figure 7. Measurement marker tool indicating the highest point (48.31 m) of a tree in the cylinder and its associated coordinate.
27 Sensitivity analysis
Using primary interface of FUSION, two important models are extracted: CSM
from the first return of LiDAR data and DEM from the last return of LiDAR data. Both
models are in the *.*dtm format and they are converted to the grid format (*.*asc)
and added to ArcMap, which then converts them to raster files. CHM is then derived by
subtracting DEM from CSM using the “Map Algebra” of ArcMap. For a specific set of
ground-based tree coordinates, a set of associated tree height is extracted from CHM, and
then it is compared with associated set of ground-based height to analyze the accuracy of
CHM. There were eight CHM’s associated with eight combinations of cell size and
window filter sizes (1 m and 3×3 m, 1 m and 5×5 m, 1 m and 7×7 m, 1 m and 9×9 m, 2 m
and 3×3 m, 2 m and 5×5 m, 2 m and 7×7 m, 2 m and 9×9 m). When analyzing the effect
of these two parameters on the accuracy of LiDAR height, ArcMap Model Builder is
useful in generating CHM from each combination (See Figure 8). The coefficient of
determination (R2) between CHM-derived height and ground-based height is used to find
the best CHM for TreeVaW application (Figure 6).
28
Figure 8. Model builder for iterative task of creating the CHM for each combination of cell size and filter window size
29
What’s common for both of the two methods is a set of ground-based height from
the following process. The attributes and position of each observable tree*1 on the field is
determined by its ground-based height and DBH, its Azimuth, and distance from a
specific plot center (random point) using MapStar compass module II and Trimble
instrument (GeoXH 6000 Series). The set of tree base coordinates is then used to extract
LiDAR-derived heights from either FUSION-derived CHM or LDV-derived CHM.
Associated with observable trees are two sets of tree heights: the ground-based-
height and the LiDAR-derived-height. These sets are used to calculate the R2 from the
relationship between the two types of height for each CHM. Eight R2 values
corresponding to the eight CHM’s are calculated. Finally, the CHM with the highest R2 is
called the best CHM, which is used for TreeVaW applications.
Sensitivity analysis is simpler for LDV than FUSION because it uses the only set
of height from LDV-derived CHM for the same set of ground-based height.
For both methods, the most appropriate CHM for further spatial analysis must
have a high R2 between ground-based height and LiDAR-derived height.
Observable tree*1 is identifiable by either TreeVaW or LDV and it was possible to take
their ground measurements including azimuth, distance from plot center to tree base,
height, and DBH.
30 Spatial analysis of TreeVaW and LDV
DBH and LiDAR-derived height must come from the same tree for this study. So,
spatial analysis focuses on how to pair LiDAR-derived tree tip with tree base.
To obtain LiDAR-derived tree tip positions using TreeVaW, the most appropriate
CHM needs to be in the ENVI format, 32-bit image, which consists of a binary file and a
header file. TreeVaW runs without any problems on computer with IDL Virtual Machine
8.2. Its output is a text file with location and dimensions (i.e., height and crown radius) of
each tree identifiable on the CHM. CHM is derived from the set of LiDAR data. A shape
file is created from this text file containing dominant or co-dominant-tree height, and it’s
called the TreeVaW-derived height (H_TreeVaW).
Obtaining LiDAR-derived tree tip position using LDV was quite different from
TreeVaW. Instead of the text file for the whole LiDAR area, the output of LDV is the
*.csv file containing the coordinates and height for each tree identifiable with a specific
CHM. This CHM is extracted on a specific area. For example, CHM can be extracted on
an area within 50 m radius of a random point using LDV window. LDV-measurement
marker tool is used to build a *.csv file and then a shape file containing the tree tip
position and its correspondent height was created using ArcMap. Height derived from
LDV is called H_LDV. This method turns out to be very helpful for random or
systematic sampling when plot centers are designated before field survey.
Following the LiDAR-derived height and tree tip position is creating a set of tree
base coordinate and ground-based DBH. The GPS unit is used for each random point
(control plot center). In addition to tree DBH, azimuth and distance from a specific plot
31 center to each LiDAR observable tree are collected. Based on the distance and azimuth,
the tree base coordinates are computed and added to the shape file for either TreeVaW or
LDV in ArcMap. That is, there are two set of coordinates: one identified by TreeVaW or
LDV (tree tip coordinates), and another calculated from ground based data (tree base
coordinates). Distance between two coordinates is calculated using “measure tool” of
ArcMap. If the distance is less than 4 m, the distance threshold value, the two different
coordinates are considered to belong to the same tree, and such a tree is called a paired
tree. The quotient, (number of paired trees ÷ Total number of observed trees), is the ratio
of paired trees. It represents the ratio of LiDAR identified trees for fitting regression
models. The process of matching LiDAR-derived tree tip to its tree base is called “tree
pairing process” or “tree matching process” (Popescu, 2007).
Biomass estimate at a single tree level
Out of 23 randomly selected 0.1 ha plots, all paired trees are separated into two
groups depending on species: redwood and Douglas-fir. For each species, paired trees are
used to fit regression models for ground-based DBH on the LiDAR-derived height.
Statistical software R is used to fit models and to validate necessary assumptions of
regression analysis (Grafen et al., 2006). It turns out there is a good linear regression
model to fit DBH on LiDAR-derived height for each species. Then, for a single tree level,
the predicted DBH with the LiDAR derived height become an input of the following
formula to estimate biomass (Jenkins et al., 2003A).
bm = exp{ + log (DBH)},
32 where bm = total aboveground live biomass (kg) for tree of 2.5 cm DBH or larger,
, = parameters associated with species
DBH = diameter at breast height (cm)
Jenkins’ formulas produce the following models for redwood and Douglas-fir.
Estimated biomass for redwood = exp{-2.0336+2.2592×log (DBH)}
Estimated biomass for Douglas-fir = exp{-2.2304+2.4435×log (DBH)}
Biomass estimate at plot level
Twelve 0.1 ha plots are studied. Regression model for each species are again used
to predict DBH from the LiDAR-derived height. Again, this predicted DBH is used as an
input for the Jenkins’ formula to estimate an individual-tree biomass. Biomass of all
LiDAR-derived trees for both species within 0.1 ha plot is then added up to estimate the
biomass of the plot (ton/ha), which is then compared with the true ground truth biomass.
The true ground biomass is calculated using ground-based DBH (greater than or
equal to 25.4 cm) of trees for all species (SESE, PSME, TSHE, ABGR, etc.) on the 0.1 ha
plots. For LiDAR-derived trees, DBH-limit is not applied and 15 m is the lower limit of
LiDAR derived height. The predicted biomass on the plot is evaluated and compared with
the ground biomass. It’s also compared with that reported in earlier study about the
Pacific coastal redwood.
33
Statistical analysis
Statistical software R is used to fit the linear regression models for SESE
(Appendix 2) and PSME (Appendix 3). DBH is the dependent variable and the LiDAR-
derived height is the explanatory variable. In addition to the LiDAR height, “terrain”
variable in the PSME model is also examined.
At a single tree level, variance test (var.test) and paired t-test are also carried
out to compare the average ABGL between using predicted DBH and using ground DBH
for each species. These tests are also used to compare H_LDV and H_gr* (i.e., LDV-
derived height and height measured on the ground).
H_gr* is the height of LiDAR-derived tree measured by the ground crew. It is also called the ground-based height while H_LDV is the LiDAR-derived height using CHM of Fusion/LiDAR Data Viewer.
34
RESULTS AND DISCUSSION
Sensitivity Analysis Using Summer 2012 Data
The goal of the sensitivity analysis was to identify the Canopy Height Model
(CHM) appropriate for spatial analysis. Out of the 55 trees measured during the first field
survey in summer 2012, there were 34 paired trees using LDV compared with 14 paired
trees using TreeVaW. It turns out I was able to measure only 18 paired tree heights# for
both FUSION-sensitivity analysis and LDV-sensitivity analysis.
# Tree height is measured on the ground using impulse laser Range Finder.
35
Figure 9. Correlation between ground-based height (H_gr) and LiDAR-derived height with FUSION interface or LDV
36
TreeVaW ratio = 14/55 = 25%
LDV ratio = 34/55 = 62 %
Figure 10. TreeVaW-paired tree ratio compared with LDV-paired tree ratio
37
Figure 9 shows that FUSION-derived CHM from the combination of 2 m cell size
and 5×5 window filter size was the most appropriate with the highest R2 = 77.6% among
eight candidate models. However, it was still lower than LDV-derived CHM (R2 =
83.5%). This shows that H_LDV is more strongly correlated with ground-based height
(H_gr) than the FUSION-derived height. Also, comparison between H_LDV and H_gr
shows that that there is no significant difference in the mean values (p-value = 0.9978)
(See Appendix 7 for variance test and the paired t-test).
LDV also shows greater matching ratio of paired trees than TreeVaW (62 % vs.
25 %, see Figure 10).
In addition to the advantage over TreeVaW in terms of greater paired-tree ratio
and stronger relationship with ground-based height, LDV shows greater range of values
than of TreeVaW. Table 4 showed that the range of DBH_LDV (95.5 cm) was larger
than the range of DBH_TreeVaW (67.8 cm) and H_LDV also had the higher range than
H_TreeVaW (21.9 m vs. 13.1m).
LDV approach was selected as the main tool to extract tree tip positions and its
associated ground based DBH for summer 2013 survey 2 because it was better than
TreeVaW method in terms of the height accuracy, the paired tree ratio, and the range of
interest.
38 Table 4. DBH and Height values by TreeVaW and LDV for a total of 55 trees (summer 2012)
DBH (or LiDAR derived Height)
using LDV (or using TreeVaW )
Minimum Maximum Range
LDV-based DBH or DBH_LDV (cm) 42.9 138.4 95.5
TreeVaW-based DBH or DBH_TreeVaW (cm) 66.3 134.1 67.8
LDV-derived height or H_LDV (m) 37.4 59.3 21.9
TreeVaW-derived height or H_TreeVaW(m) 47.4 60.5 13.1
39
Spatial Analysis Using Summer 2013 Data
Out of 548 trees from 23 randomly selected plots using LDV, 429 trees of the two
species were paired (429/548 = 78%). They were separated into two groups: Douglas-fir
and redwood as shown in Figure 11 and Figure 12.
40
Figure 11. LDV-derived height (m) and ground-based DBH of 172 Douglas-fir
0
50
100
150
200
1 19 37 55 73 91 109
127
145
163
181
199
217
235
253H_l
dv i
n m
eter
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sti
ck)
DBH
in c
enti
met
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lue
stic
k)
Tree numbered
Data of 257 redwood tree collected in summer 2013
dbh
H_ldv
Figure 12. LDV-derived height (m) and ground-based DBH of 257 redwoods
41
Spatial analysis was applied to the 429 distance values (Appendix 8) to check if
the 4 m threshold distance was appropriate. The distances (D) did not follow the normal
distribution (Figure 13 and Shapiro test in Appendix 10), square root transformation was
used to transform D, and it’s called “d” (i.e., Dd = ).
It turns out about 95% of the d values are between 0.533 and 1.917 m, or
equivalently, D values are between 0.284 and 3.676 m (See Appendix 10). Using 3.68 m
as the threshold value, there are 419 distances (See Appendix 8) that meet the pairing
condition ( ≤ 3.68 m) and they covered 419/429 = 97.7% of the total paired trees (Figure
13). That is, 3.68 m (or rounded to 4 m) is considered as a reasonable threshold for
pairing these trees.
42
Figure 13. Distribution of D and the square rooted D ( Dd = )
43
Regression Model for Ground-Based DBH on H_LDV
Regression model for SESE
• Summary statistics of the 257 redwood trees are shown in Table 5.
• Using these 257 paired trees, I find the best model as
(1) DBH = 0.5243 × (H_LDV)1.3292 (Figure 14)
or equivalently
(2) log(DBH) = -0.645629 + 1.32924×log(H_LDV) (Figure 15)
Estimated model (2) seems to reasonably satisfy all the statistical assumptions
(Figure 15) including important homogeneous variance assumption (Figure 16). Figure
17 shows residuals and Shapiro test verifies that the residuals are normal (p-value =
0.0743) (See Appendix 2).
• 62.65% of the variation in log(DBH) is explained by the model (p-value < 0.001)
(Appendix 2). Also, “terrain” is not significant (p-value > 0.05). (Appendix 2).
44
Table 5. Summary of 257 redwood trees
SESE statistical description
Ground DBH (cm) H_LDV (m) Predicted DBH (cm)
Mean 76.1 41.2 74.3
SD 27.1 9.1 21.7
SE 1.7 0.6 1.4
CV (%) 35.7 22.0 29.2
Min 10.8 17.1 22.8
First Quartile 56.1 34.6 58.2
Median 73.4 40.9 72.7
Third Quartile 92.2 47.9 89.6
Max 173.2 69.8 148.2
45
Figure 14. SESE model
46
2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2
2.5
3.0
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log(H_ldv)
log(
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Figure 15. log(DBH) vs. log(H_LDV)
47
3.5 4.0 4.5 5.0
-3-2
-10
12
diameter at breast height
modelSESE$fitted.values
scal
e(m
odel
SE
SE
$res
idua
ls)
Figure 16. Homogeneity of variance
48
Figure 17. Diagnostic plots of the residuals
49 Regression model for PSME
• Summary statistics of 172 Douglas-fir paired trees are shown in Table 6.
• Using these 172 paired trees I find the best model as
(3) DBH = 0.2569×(H_LDV)1.4622 with R2=79.4% (Figure 18)
or equivalently
(4) log(DBH) = -1.3591 + 1.4622×log(H_LDV) (Figure 19)
• 79.4% of total variation in log(DBH) is explained by the model (p-value < 0.001)
(Appendix 3). But, “terrain” is highly significant (p-value < 0.001). (Appendix 3).
When both variables (i.e., terrain and log(H_LDV)) are used in a model, R2
increased to 82.6% as shown below.
• The estimated coefficients are somewhat different depending on “flat” terrain and
“rough” terrain for PSME as shown in the following equations.
(5) Flat terrain: log(DBH_F) = -1.09925 + 1.41875×log(H_LDV)
(6) Rough terrain: log(DBH_R) = -1.25765 + 1.41875×log (H_LDV)
• Both of the models for PSME, (5) and (6), satisfy all the assumptions of a linear
model (Figure 19).
Models R2 p-value
log(DBH) vs. log( H_LDV) 79.4% < 0.001
log(DBH) vs. log(H_LDV) + Terrain 82.6% < 0.001
50
Table 6. Summary of 172 Douglas-fir trees
PSME statistical description
Ground DBH (cm) H_LDV (m) Predicted DBH (cm)
Mean 75.9 47.7 74.8
SD 27.6 10.7 23.8
SE 2.1 0.8 1.8
CV (%) 36.3 22.5 31.9
Min 18.3 20.4 24.0
First Quartile 58.7 44.3 64.0
Median 77.4 50.5 78.9
Third Quartile 94.7 54.8 93.1
Max 169.6 64.8 119.7
51
Figure 18. PSME model
52
3.0 3.2 3.4 3.6 3.8 4.0 4.2
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Figure 19. log(DBH) vs. log(H_LDV)
53
Figure 20. Homogeneity of variance
54
Histogram of scale(mo
scale(modelPSME$residuals
Fre
qu
en
cy
-2 -1 0 1 2 3
01
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0
-2 -1 0 1 2
-2-1
01
23
Normal Q-Q Plot
Theoretical Quantiles
sta
nd
ard
ize
d r
esid
ua
ls
Figure 21. Diagnostic plots of the residuals
55
Figure 20 shows the model satisfies homogeneous variance assumption. Figure 21
shows residuals and Shapiro test verifies that the residuals are normal (p-value = 0.3969)
(See Appendix 3). Also, 82.6 % of log(DBH) variation is explained by the model (p-
value < 0.001 (Appendix 3). Figure 19 also shows strong positive correlation between
LiDAR-derived height and DBH. I also find that DBH on flat terrain (F) tends to be
greater than that on the rough terrain (Equations (5) and (6)). Simple algebra can convert
equations (5) and (6) into the following equivalent forms.
______________________________________________________________________________ (5)* and (6)* are equivalent expressions to (5) and (6), respectively, because of the following simple algebra. When ( ) ( ) ( )baba xexexbay logloglog)log()log( =+=⋅+= , we have
ba xey =
(5)* Flat terrain: DBH_F = 0.33312×(H_LDV)1.41875
(6)* Rough terrain: DBH_R = 0.28432×(H_LDV)1.41875
56
Biomass Analysis
Single tree level
Jenkins’ formula is used to estimate the biomass using the predicted DBH from
regression models shown in the previous section. For the purpose of simplicity, models
(5)* and (6)* are used to for PSME and model (1) was used for SESE. That is, the
following models are used to estimate DBH, which will then be entered into the Jenkins’
formula.
(1) Redwoods: DBH = 0.5243×(H_LDV)1.3292
(5)* Douglas-fir on flat terrain: DBH_F = 0.33312×(H_LDV)1.41875
(6)* Douglas-fir on rough terrain: DBH_R = 0.28432×(H_LDV)1.41875
Appendix 4 (SESE in table 4.1, PSME in table 4.2) shows the estimated biomass from
Jenkins’ formula. At a single tree level, using the predicted DBH shows the average of
ABGL biomass of 257 SESE tree is lower by about 10.1% (i.e., 2750 vs. 2473) than the
average ABGL biomass using ground-based DBH (Table 7).
In case of Douglas-fir, the average ABGL predicted biomass of 172 PSME trees
is lower by about 8.0% than the average ABGL biomass using ground-based DBH
(Table 8).
57
Table 7. SESE biomass analysis at single tree level (Appendix 4)
SESE When predicted
DBH is used
When ground-based
DBH is used
Mean ABGL biomass (kg of dry weight per tree) 2,473.0 2,750.0
SD 1,658.3 2,243.3
CV (%) 67.1 81.6
58
Table 8. PSME biomass analysis at single tree level (Appendix 4)
PSME When predicted
DBH is used
When ground-based
DBH is used
Mean ABGL biomass (kg of dry weight per tree) 4,779.0 5,195.0
SD 2,965.7 4,182.6
CV (%) 62.1 80.5
59
Also, in both species, the average ABGL biomass shows greater CV using
ground-based DBH, which means that biomass shows more variability when ground-
based DBH is used.
At a single tree level for both species, there is a significant mean difference
between the two types of ABGL biomass. For PSME, t-test shows p-value = 0.04572
(Appendix 6) and for SESE, t-test has p-value = 0.0060 (Appendix 5).
Plot level
In case of LiDAR, all the individual biomass estimates of the two species (SESE
and PSME) are added to find the biomass per plot. In case of ground-based DBH,
biomass of individual trees of all kinds of species (i.e., SESE, PSME, TSHE, ABGR, and
others) are estimated and the sum of them becomes the true ground biomass per plot.
Summary of these estimates and related statistics per plot is shown in Table 9.
60 Table 9. ABGL biomass of redwood/Douglas-fir stands on twelve 0.1 ha plots
Plot Biomass of SESE and PSME
(ton/ha) using predicted DBH
Biomass of all species (ton/ha)
using ground-based DBH
Terrain
1 222.6 274.3 Rough
3 259.7 391.8 Rough
7 127.6 317.0 Rough
2 403.1 560.3 Rough
23 141.8 378.7 Rough
21 113.1 235.1 Rough
4 544.8 824.0 Flat
8 473.2 857.1 Flat
10 545.7 841.3 Flat
12 545.1 821.6 Flat
20 319.9 562.0 Flat
25 737.0 934.1 Flat
Mean 369.5 583.1
SD 202.6 260.5
SE 58.5 75.2
CV (%) 54.8% 44.7%
CI 128.8 165.5
range 240.7~498.2 417.6~748.6
61
At the plot level, ABGL predicted biomass using predicted DBH is lower by
about 36.6% (583.1 vs. 369.5) than that of using the ground-based DBH. The predicted
biomass using predicted DBH has about 35%* precision and biomass using the ground-
based DBH has 28.4 % precision within the true mean. In order to increase the precision,
more plots need to be taken. For example, if the desired half-width of the confidence
interval (i.e., E) is required to be within ±50 (ton/ha) of the true mean, 66 of 0.1 ha plot
will be needed (See Appendix 11).
* I calculated the error, E, as shown by Avery and Burkhart (2002) as follows. Using
predicted DBH, 7585.1285.58201.211025.0 =×=×= = SEtE df (ton/ha), i.e., about 34.9% (128.7585
/ 369.5 = 0.3485); Using ground-based DBH, 5152.1652.75201.211025.0 =×=×= = SEtE df
(ton/ha), i.e., about 28.4% (165.5152 / 583.1 = 0.2839)
62 Terrain effect on biomass dispersion
Table 10 shows the type of DBH used to estimate the ABGL biomass does not
matter much when it comes to terrain. The mean biomass on the flat terrain is greater
than that of the rough terrain. Also, biomass on the rough terrain shows greater variation
than that on the flat terrain.
63
Table 10. Predicted and ground biomass on different terrain
Biomass Rough terrain Flat terrain
predicted biomass ground
biomass
predicted
biomass
ground biomass
mean 211.3 359.5 527.6 806.7
SD 110.2 115.1 134.8 126.8
SE 45.0 47.0 55.04 51.76
CV (%) 52.1 32.0 25.6 15.7
CI 95.7~327.0 238.7~480.3 386.1~669.1 673.6~939.8
64
Figure 22. Predicted biomass and ground-based biomass
65 Significant factors for the total biomass
Redwood clumps and two other large size species such as grand fir and hemlock
contribute hugely to the total ground biomass (Table 11). LDV records only the tallest
one of the stems of redwood clumps, which causes the estimated biomass using predicted
DBH much less than the ground biomass. Redwood clumps make up about 40.9% of the
total underestimated biomass (Table 11), while two other species (grand fir and western
hemlock) add 19.9% to the underestimated biomass. On average these two factors make
up 60.8% of the underestimated biomass. Some species like tanoak (Lithocarpus
densiflorus) and Bishop pine (Pinus muricata) appear at a low frequency. They are
presented in plots 1, 4, 12, and 23 and make up about 3.8% of the underestimated
biomass. The remaining percentage 35.4% (i.e., 100 − 60.8 − 3.8) of the underestimated
biomass can be explained by trees of all kinds of species (DBH ≥ 25.4 cm) within plots,
but they are shadowed by the dominant or co-dominant trees’ crowns (LDV-derived
trees) and are also different from the redwood clumps. It is easy for LDV to miss the
intermediate stratum of the forest, resulting in the underestimation of the biomass of
redwood/Douglas-fir stands.
It is also noted that the four plots, 4, 8, 10, and 12, show noticeable ground
biomass (Figure 22 and Table 11). These plots are in the clear-cut area which was
harvested during 1860-1890 while other plots used group selection method (L. Webb,
personal communication, Nov. 18, 2013). It raises another question: whether significant
difference in biomass is caused more by terrain or more by the silvicultural system?
66
Table 11. The contribution of red wood clumps, grand fir, and western hemlock to the biomass difference between ground DBH-based biomass and predicted DBH-based biomass
(*) Underestimated biomass is the difference between ground biomass and predicted biomass.
Plots 1, 3, 7, 2, 23, and 21 are on rough terrain; Plots 4, 8, 10, 12, 20, and 25 are on flat terrain.
Plot Biomass (ton/ha) Underestimated biomass(*)
Biomass Underestimated biomass (%)
Predicted DBH
Ground DBH Redwood
clumps Grand fir, and
Western Hemlock
Redwood clumps
Grand fir,
Western Hemlock
Redwood clumps,
Grand fir, and
Western Hemlock
1 222.60 274.29 51.69 25.03 24.3 48.4 47 95.4
3 259.66 391.76 132.10 55.30 50.6 41.9 30.3 72.2
7 127.59 317.03 189.44 2.70 164.9 1.4 46.6 48.0
2 403.08 560.26 157.18 134.31 0.0 85.4 0.0 85.4
23 141.84 378.69 236.84 102.91 25.4 43.5 10.7 54.2
21 113.15 235.12 121.97 46.22 9.60 37.9 7.9 45.8
4 544.77 824.04 279.27 166.97 0.0 59.8 0.0 59.8
8 473.18 857.09 383.91 198.14 82.23 51.6 21.4 73.0
10 545.73 841.31 295.58 59.74 27.24 20.2 9.2 29.4
12 545.11 821.64 276.53 84.65 26.9 30.6 9.7 40.3
20 319.90 562.01 242.11 79.74 8.63 32.9 3.6 36.5
25 736.97 934.15 197.18 73.15 8.88 37.1 4.5 41.6
mean 369.47 583.12 213.65 85.74 35.73 40.9 19.9 60.8
67 Biomass in SFCCW
Biomass at SFCCCW biomass was taken from earlier research (Table 12). The
LiDAR derived height of stands and age of stands are two factors that affect the biomass
of a stand. A complete inference about biomass in the area can only be done with enough
detailed information about species composition, soil types, knowledge about dominant or
co-dominant species, information about silvicultural methods applied, and the number of
sampled plots, etc.
68
Table 12. Summary of biomass research in California
California sites
of redwood stands
Average
ABGL
biomass
(ton/ha)
error
(ton/ha)
Average
LiDAR
height of
the
redwood
stands (m)
Age
(years)
SFCCW
Secondary Growth
369.5 128.8 43.8±10 40~150
Garcia River Forest Secondary
growth
(Gonzalez et al., 2010)
200.0 12.2 29.5±5 20~80
Mailliard Forest*
old growth coastal redwood
(Gonzalez et al., 2010)
640.0 70.0 53.0±9 >= 200
Bull Creek
old growth forest,
Humboldt Redwood SP
3,300~5,800 >= 90 > 500
* Aboveground carbon density (ACD) of the second growth redwood forest at Garcia
River was 100±6.1 (ton/ha), and the ACD at Mailliard Forest was 320±35 (ton/ha). The
ratio of ACD to biomass is thought to be 0.5 and this calculation is used to estimate the
biomass shown here.
69
SUMMARY
The goal of this study is to develop an intelligent way to estimate biomass of the
redwood/Douglas-fir stands in the South Fork Caspar Creek Watershed of JDSF in
Mendocino County of California via sensitivity analysis and spatial analysis. Sensitivity
analysis was conducted to evaluate the accuracy of CHM derived from LiDAR using
TreeVaW or LDV. LDV is better than TreeVaW in terms of the accuracy, the ratio of
paired trees, and variables that we are interested in (i.e., DBH and LiDAR-derived
height). Spatial analysis shows that LDV has a higher ratio of paired trees than TreeVaW.
Based on the statistical analysis of separate distances between the ground-tree bases and
LDV-tree tips, a threshold of 4 m is justified in pairing trees.
Better way to estimate biomass using linear regression models of redwood and
Douglas-fir is shown. For both species, LDV-derived tree tips are matched with tree
bases to create paired trees, which come with the ground-based DBH and LDV-derived
height. A set of 257 SESE trees and separate set of 172 PSME trees are used for the
study. Using statistical software R, linear regression models for DBH on H_LDV are
developed for both species. Predicted DBH’s from such models are then entered into of
Jenkins’ formula to estimate biomass at a single tree level. The models used are
summarized below.
• Linear regression model from 257 redwood paired trees:
log(DBH) = -0.645629 + 1.32924×log(H_LDV)
70 62.65% of the total variation of redwood log(DBH) is explained by this model.
• Linear regression models from 172 Douglas-fir paired trees for flat terrain and for
rough terrain:
log(DBH_F) = -1.09925 + 1.41875×log(H_LDV)
log(DBH_R) = -1.25765 + 1.41875×log (H_LDV)
82.6 % of the total variation of Douglas-fir log(DBH) is explained by the model. Terrain
has a significant effect on Douglas-fir DBH, and inclusion of the variables improves R2
to 82.6 % from 79.4 %.
At single tree level, there is a significant difference in mean biomass between
average ABGL biomass of SESE (or PSME) using predicted DBH and that using ground-
based DBH. The SESE biomass when predicted DBH is used is lower by about 10.1%
than when the ground-based DBH is used. In case of PSME, predicted DBH produces
underestimated biomass by about 8.0%.
At the plot level, the study finds that ABGL biomass on flat terrain is be greater
and less dispersed than that on the rough terrain. ABGL predicted biomass was
underestimated by about 36.6% when predicted DBH is used instead of ground-based
DBH.
71
Future Research
After having modeled DBH on H_LDV for grand fir and western hemlock,
relationship between H_LDV and biomass of the whole redwood clumps also need to be
investigated. Both studies will help estimate biomass more accurately.
It is also important to do research about identifying major species of trees: SESE,
PSME, ABGR (Abies grandis), and TSHE (Tsuga heterophylla) using multi-spectral
images. Species identification and corresponding H_LDV can be quite cost effective in
terms of time and man power.
Further research in biomass at North Fork Caspar Creek Watershed (NFCCW)
should be done because it is a post-harvest redwood experiencing clear-cut system
whereas SFCCW underwent the group selection system. In-depth study of such
silvicultural practices would provide valuable information about biomass variability.
Studying old-growth redwood stands using LiDAR will span upper end of the
range of H_LDV. The 1 m post spacing of such LiDAR data might not be fine enough to
identify the tree tip. Hence, it is worthwhile to research the effect of LiDAR data post
spacing with varying threshold values. The finer post spacing may improve the accuracy
of CHM.
Based on the field observation, the best positional accuracy of Trimble GeoXH
6000 Series is from 0.7 to 1 m, not its nominal accuracy of 0.3 m. On a flat terrain it takes
about 2 hours to log in the coordinate of a specific plot center using 1 m accuracy and
72 800 logging-interval counts on GPS instrument. However, on a very rough terrain (slope
> 30%), it can take a whole day to log in the center coordinate with much fewer counts or
no count at all on GPS. Based on my experience, the precision of a plot center-coordinate
on a steep slope is from 3 to 7 m instead of 1 m. As a result, the “ratio” of paired trees
decreased considerably on such a terrain. It would be interesting to find some ways to
improve the horizontal and positional accuracy of the GPS instrument and the precision
of plot center coordinates regardless of dense canopy or rough terrain.
73
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77
APPENDIX 1
Data: 429 Paired Trees of SESE and PSME from 23 Randomly Sampled Plots
origin species DBH (cm) H_LDV (m) PLOT Terrain Distance (m)*
1 7 SESE 69.4 44.42 10 F 1.08 2 19 SESE 137 54.4 10 F 0.71 3 22 SESE 99 56.26 10 F 1.03 4 27 SESE 64.3 42.62 10 F 0.73 5 28 SESE 61.6 43.54 10 F 0.24 6 30 SESE 51.5 39.41 10 F 0.99 7 31 SESE 85.7 49.37 10 F 0.25 8 32 SESE 43.8 44.85 10 F 1.73 9 35 SESE 152.8 57.19 10 F 1.34 10 38 SESE 173.2 54.56 10 F 1.79 … … … … … … … …
420 14 PSME 55.1 51.95 22 R 3.28 421 15 PSME 67.2 60.85 22 R 2.28 422 16 PSME 77.5 64.4 22 R 0.88 423 17 PSME 87.6 64.75 22 R 1.25 424 18 PSME 73.4 53.02 22 R 1.94 425 19 PSME 50.8 43.24 22 R 1.95 426 20 PSME 74.1 44.26 22 R 2.60 427 1 PSME 51.2 36.89 22 R 4.08 428 2 PSME 50.9 39.96 22 R 2.59 429 3 PSME 47.7 38.05 22 R 2.47
(*) Distance (m) between LDV tree tip and tree base. … Complete data are available upon request.
78
APPENDIX 2. REDWOOD LINEAR REGRESSION MODELS
SESE Linear Regression Model of Log(DBH) on Log(H_LDV) without “Terrain”
Variable
> lm(formula = log(GroundTruth_DBH) ~ log (H_LDV))
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.64562 0.23785 -2.714 0.00709 **
log (H_LDV) 1.32924 0.06427 20.682 < 2e-16 ***
Residual standard error: 0.2326 on 255 degrees of freedom
Multiple R-squared: 0.6265, Adjusted R-squared: 0.625
F-statistic: 427.7 on 1 and 255 DF, p-value: < 2.2e-16
> shapiro.test(scale(model2$residuals))
Shapiro-Wilk normality test
data: scale(model2$residuals)
W = 0.99, p-value = 0.0743
SESE Linear Regression Model of Log(DBH) on Log(H_LDV) with “Terrain” Variable
> lm(formula = log(GroundTruth_DBH) ~ log (H_LDV) + ter)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.69838 0.24311 -2.873 0.00441 **
log (H_LDV) 1.33850 0.06487 20.635 < 2e-16 ***
terR 0.03118 0.02983 1.045 0.29700
Residual standard error: 0.2325 on 254 degrees of freedom
Multiple R-squared: 0.6281, Adjusted R-squared: 0.6252
F-statistic: 214.5 on 2 and 254 DF, p-value: < 2.2e-16
79
APPENDIX 3. DOUGLAS-FIR REGRESSION MODELS
PSME Linear Regression Model of Log(DBH) on Log(H_LDV) without “Terrain”
Variable > lm(formula = log (DBH) ~ log (H_LDV))
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.35888 0.21944 -6.192 4.31e-09 ***
log (H_LDV) 1.46220 0.05709 25.612 < 2e-16 ***
Residual standard error: 0.1978 on 170 degrees of freedom
Multiple R-squared: 0.7942, Adjusted R-squared: 0.793
F-statistic: 656 on 1 and 170 DF, p-value: < 2.2e-16
> shapiro.test(scale(model2$residuals))
Shapiro-Wilk normality test
data: scale(model2$residuals)
W = 0.9914, p-value = 0.3969
PSME Linear Regression Model of Log(DBH) on Log(H_LDV) with “Terrain” Variable > lm(formula = log (DBH) ~ log (H_LDV) + ter)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.09925 0.20781 -5.290 3.75e-07 ***
log (H_LDV) 1.41875 0.05325 26.643 < 2e-16 ***
terR -0.15840 0.02858 -5.542 1.13e-07 ***
Residual standard error: 0.1825 on 169 degrees of freedom
Multiple R-squared: 0.8258, Adjusted R-squared: 0.8238
F-statistic: 400.7 on 2 and 169 DF, p-value: < 2.2e-16
80
APPENDIX 4
Appendix 4-1: SESE Individual Tree Biomass
Species Ground DBH (cm)
H_LDV (m)
Predicted DBH (cm)
Terrain Dist(*)
(m) Ground DBH
Biomass
Predicted DBH Biomass
1 SESE 69.4 44.42 81.2 F 1.08 1891.6 2696.8 2 SESE 137 54.4 106.3 F 0.71 8792.2 4956.5 3 SESE 99 56.26 111.2 F 1.03 4220.4 5483.0 4 SESE 64.3 42.62 76.9 F 0.73 1591.9 2381.8 5 SESE 61.6 43.54 79.1 F 0.24 1444.9 2539.6 6 SESE 51.5 39.41 69.3 F 0.99 964.1 1882.7 7 SESE 85.7 49.37 93.4 F 0.25 3046.6 3703.8 8 SESE 43.8 44.85 82.2 F 1.73 668.7 2776.0 9 SESE 152.8 57.19 113.6 F 1.34 11251.0 5759.7
10 SESE 173.2 54.56 106.7 F 1.79 14933.0 5000.4 … … … … … … … … …
252 SESE 73.1 36.16 61.8 R 1.14 2127.1 1453.9 253 SESE 92.2 35.86 61.1 R 0.91 3593.7 1418.0 254 SESE 92.8 43.59 79.2 R 4.23 3646.7 2548.3 255 SESE 43.2 34.08 57.1 R 1.86 648.2 1217.0 256 SESE 84.1 52.91 102.4 R 1.26 2919.6 4559.9 257 SESE 53 46.56 86.4 R 0.64 1028.7 3106.1
(*) Distance (m) between LDV tree tip and tree base. Biomass is in kg dry weight per tree. … Complete data are available upon request.
SESE biomass
summary(x) for ground biomass Min. 1st Q. Median Mean 3rd Q. Max.
28.3 1170.0 2147.0 2750.0 3594.0 14930.0
summary(y) for predicted biomass using R Min. 1st Q. Median Mean 3rd Q. Max.
153.4 1269.0 2103.0 2473.0 3372.0 10500.0
81 Appendix 4-2: PSME Individual Tree Biomass
Species Ground DBH (cm)
H_LDV (m)
Terrain Dist(*)
(m) Predicted DBH (cm)
Predicted DBH Biomass
Ground DBH Biomass
1 PSME 123.6 55.96 F 1.37 100.6 8398.9 13905.8 2 PSME 109.7 56.29 F 2.59 101.4 8571.8 10389.5 3 PSME 119.2 58.49 F 1.00 107.1 9790.3 12727.1 4 PSME 83.7 53.76 F 1.83 95.0 7308.6 5364.5 5 PSME 72.3 52.02 F 0.93 90.7 6520.8 3751.1 6 PSME 169.6 59.5 F 3.93 109.7 10389.0 30126.7 7 PSME 103.5 52.52 F 1.36 91.9 6740.7 9012.7 8 PSME 92.1 56.03 F 1.60 100.7 8435.4 6776.7 9 PSME 101.4 54.16 F 0.27 96.0 7498.9 8572.4 10 PSME 89.5 49.93 F 2.80 85.5 5656.7 6318.7 … … … … … … … … …
163 PSME 55.1 51.95 R 3.28 77.2 4407.4 1931.3 164 PSME 67.2 60.85 R 2.28 96.7 7625.3 3137.1 165 PSME 77.5 64.4 R 0.88 104.8 9281.7 4444.9 166 PSME 87.6 64.75 R 1.25 105.6 9457.7 5996.0 167 PSME 73.4 53.02 R 1.94 79.5 4730.2 3892.0 168 PSME 50.8 43.24 R 1.95 59.5 2332.8 1583.5 169 PSME 74.1 44.26 R 2.60 61.5 2529.2 3983.4 170 PSME 51.2 36.89 R 4.08 47.5 1345.1 1614.2 171 PSME 50.9 39.96 R 2.59 53.2 1774.7 1591.2 172 PSME 47.7 38.05 R 2.47 49.7 1497.5 1357.7
(*) Distance between LDV tree position and ground tree position. Biomass unit is in kg dry weight per tree. … Complete data are available upon request. PSME biomass summary(x) for ground biomass Min. 1st Q. Median Mean 3rd Q. Max.
130.7 2257.0 4424.0 5195.0 7258.0 30130.0
summary(y) for predicted biomass
Min. 1st Q. Median Mean 3rd Q. Max.
253.6 2786.0 4646.0 4779.0 6955.0 12860.0
82
APPENDIX 5
Variance Test and t.Test for SESE Biomass at a Single Tree Level
x = Biomass using ground DBH
y = Biomass using predicted DBH > var.test(x,y)
F test to compare two variances
data: x and y
F = 1.83, num df = 256, denom df = 256, p-value = 1.637e-06
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
1.431562 2.339297
sample estimates:
ratio of variances
1.829986
> t.test(x,y,paired=T)
Paired t-test
data: x and y
t = 2.769, df = 256, p-value = 0.006033
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
79.90379 473.39738
sample estimates:
mean of the differences
276.650
83
APPENDIX 6
Variance Test and t.Test for PSME Biomass at a Single Tree Level
x = Biomass using ground DBH
y = Biomass using predicted DBH > var.test(x,y)
F test to compare two variances
data: y and x
F = 1.989, num df = 171, denom df = 171, p-value = 8.727e-06
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
1.472390 2.686982
sample estimates:
ratio of variances
1.989041
> t.test(x,y var.equal=FALSE, paired=T)
Paired t-test
data: y and x
t = 2.0127, df = 171, p-value = 0.04572
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
8.012896 824.133615
sample estimates:
mean of the differences
416.0733
84
APPENDIX 7
Comparison Mean of H_LDV to Mean of H_Gr
x = Ground-based height (H_gr)
y = LiDAR Data Viewer height (H_LDV) > var.test(x,y)
F test to compare two variances
data: x and y
F = 1.2142, num df = 18, denom df = 18, p-value = 0.6849
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.4677958 3.1515865
sample estimates:
ratio of variances
1.214207
> t.test(x, y, var.equal= T, paired=T)
Paired t-test
data: x and y
t = 0.0028, df = 18, p-value = 0.9978
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-1.378488 1.382192
sample estimates:
mean of the differences
0.00185177
85
APPENDIX 8
Distance (D) Between Tree Tip and Tree Position of 429 Paired Trees
[1] 0.03 0.13 0.21 0.23 0.24 0.25 0.26 0.27 0.27 0.27 0.28 0.29 0.29 0.31 0.31 0.32 [17] 0.32 0.33 0.36 0.36 0.37 0.37 0.37 0.40 0.44 0.44 0.47 0.49 0.50 0.50 0.50 0.52 [33] 0.53 0.55 0.57 0.57 0.58 0.59 0.61 0.63 0.64 0.64 0.64 0.64 0.67 0.67 0.67 0.67 [49] 0.68 0.68 0.68 0.69 0.70 0.71 0.71 0.71 0.71 0.72 0.72 0.73 0.73 0.73 0.73 0.74 [65] 0.75 0.76 0.76 0.76 0.77 0.77 0.78 0.78 0.78 0.78 0.80 0.80 0.81 0.81 0.81 0.82 [81] 0.84 0.85 0.85 0.86 0.87 0.87 0.87 0.88 0.88 0.88 0.89 0.89 0.90 0.91 0.91 0.91 [97] 0.92 0.92 0.92 0.93 0.93 0.94 0.94 0.94 0.94 0.94 0.95 0.95 0.96 0.99 0.99 0.99 [113] 1.00 1.00 1.01 1.01 1.01 1.03 1.03 1.03 1.04 1.05 1.06 1.07 1.07 1.07 1.08 1.08 [129] 1.09 1.09 1.10 1.10 1.10 1.11 1.11 1.11 1.11 1.11 1.11 1.12 1.13 1.13 1.14 1.14 [145] 1.14 1.15 1.15 1.17 1.17 1.18 1.18 1.18 1.18 1.19 1.20 1.21 1.21 1.21 1.21 1.21 [161] 1.23 1.23 1.23 1.24 1.24 1.24 1.25 1.25 1.26 1.27 1.27 1.27 1.27 1.28 1.29 1.30 [177] 1.30 1.31 1.31 1.31 1.31 1.31 1.32 1.32 1.32 1.32 1.32 1.32 1.33 1.34 1.34 1.36 [193] 1.36 1.37 1.37 1.38 1.38 1.39 1.40 1.41 1.41 1.42 1.42 1.43 1.44 1.44 1.44 1.45 [209] 1.45 1.45 1.46 1.47 1.47 1.47 1.47 1.49 1.49 1.50 1.50 1.52 1.53 1.55 1.56 1.57 [225] 1.57 1.57 1.58 1.58 1.58 1.58 1.60 1.60 1.60 1.61 1.62 1.62 1.62 1.62 1.62 1.63 [241] 1.63 1.64 1.65 1.67 1.67 1.68 1.68 1.69 1.70 1.70 1.71 1.72 1.72 1.72 1.73 1.73 [257] 1.74 1.74 1.74 1.74 1.75 1.76 1.76 1.77 1.77 1.79 1.79 1.79 1.80 1.81 1.82 1.82 [273] 1.82 1.83 1.83 1.84 1.84 1.85 1.86 1.86 1.86 1.86 1.87 1.87 1.87 1.88 1.88 1.89 [289] 1.89 1.89 1.89 1.90 1.90 1.91 1.91 1.92 1.93 1.94 1.94 1.95 1.95 1.95 1.96 1.96 [305] 1.96 1.97 1.98 1.99 2.00 2.01 2.02 2.04 2.05 2.07 2.08 2.08 2.09 2.10 2.11 2.11 [321] 2.12 2.13 2.14 2.16 2.17 2.17 2.19 2.19 2.22 2.23 2.26 2.28 2.28 2.29 2.29 2.29 [337] 2.30 2.30 2.30 2.31 2.32 2.34 2.34 2.37 2.39 2.39 2.39 2.41 2.43 2.45 2.45 2.45 [353] 2.46 2.47 2.47 2.48 2.49 2.50 2.50 2.52 2.53 2.54 2.54 2.55 2.56 2.59 2.59 2.60 [369] 2.61 2.62 2.63 2.63 2.64 2.64 2.65 2.67 2.72 2.74 2.74 2.80 2.82 2.82 2.82 2.84 [385] 2.85 2.86 2.86 2.86 2.88 2.92 2.92 2.93 2.94 2.94 2.94 2.96 2.97 2.98 3.03 3.06 [401] 3.08 3.08 3.10 3.13 3.15 3.16 3.20 3.25 3.28 3.28 3.34 3.35 3.35 3.40 3.51 3.56 [417] 3.57 3.58 3.62 3.69 3.81 3.82 3.87 3.87 3.89 3.93 4.07 4.08 4.23
86
APPENDIX 9
Distances D ( D= ) Between Tree Tip and Tree Base of 429 Paired Trees
[1] 0.18 0.36 0.45 0.48 0.49 0.50 0.51 0.52 0.52 0.52 0.53 0.54 0.54 0.56 0.56 0.56 [17] 0.57 0.57 0.60 0.60 0.61 0.61 0.61 0.63 0.66 0.66 0.68 0.70 0.71 0.71 0.71 0.72 [33] 0.73 0.74 0.76 0.76 0.76 0.77 0.78 0.80 0.80 0.80 0.80 0.80 0.82 0.82 0.82 0.82 [49] 0.82 0.83 0.83 0.83 0.84 0.84 0.84 0.84 0.84 0.85 0.85 0.85 0.86 0.86 0.86 0.86 [65] 0.86 0.87 0.87 0.87 0.88 0.88 0.88 0.88 0.88 0.89 0.89 0.89 0.90 0.90 0.90 0.91 [81] 0.92 0.92 0.92 0.93 0.93 0.93 0.93 0.94 0.94 0.94 0.94 0.95 0.95 0.95 0.95 0.96 [97] 0.96 0.96 0.96 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.98 0.99 1.00 1.00 [113] 1.00 1.00 1.00 1.00 1.00 1.01 1.01 1.02 1.02 1.03 1.03 1.03 1.03 1.04 1.04 1.04 [129] 1.04 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.06 1.06 1.06 1.06 1.06 1.07 1.07 [145] 1.07 1.07 1.07 1.08 1.08 1.08 1.08 1.09 1.09 1.09 1.10 1.10 1.10 1.10 1.10 1.10 [161] 1.11 1.11 1.11 1.11 1.12 1.12 1.12 1.12 1.12 1.13 1.13 1.13 1.13 1.13 1.14 1.14 [177] 1.14 1.14 1.14 1.14 1.14 1.14 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.16 1.16 1.17 [193] 1.17 1.17 1.17 1.17 1.17 1.18 1.18 1.19 1.19 1.19 1.19 1.20 1.20 1.20 1.20 1.20 [209] 1.20 1.20 1.21 1.21 1.21 1.21 1.21 1.22 1.22 1.23 1.23 1.23 1.24 1.24 1.25 1.25 [225] 1.25 1.25 1.26 1.26 1.26 1.26 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27 [241] 1.27 1.28 1.28 1.29 1.29 1.30 1.30 1.30 1.30 1.30 1.31 1.31 1.31 1.31 1.32 1.32 [257] 1.32 1.32 1.32 1.32 1.32 1.33 1.33 1.33 1.33 1.34 1.34 1.34 1.34 1.34 1.35 1.35 [273] 1.35 1.35 1.35 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.37 1.37 1.37 1.37 1.37 1.38 [289] 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.39 1.39 1.39 1.39 1.40 1.40 1.40 1.40 1.40 [305] 1.40 1.40 1.41 1.41 1.41 1.42 1.42 1.43 1.43 1.44 1.44 1.44 1.44 1.45 1.45 1.45 [321] 1.45 1.46 1.46 1.47 1.47 1.47 1.48 1.48 1.49 1.49 1.50 1.51 1.51 1.51 1.51 1.51 [337] 1.52 1.52 1.52 1.52 1.52 1.53 1.53 1.54 1.55 1.55 1.55 1.55 1.56 1.56 1.56 1.57 [353] 1.57 1.57 1.57 1.57 1.58 1.58 1.58 1.59 1.59 1.59 1.59 1.60 1.60 1.61 1.61 1.61 [369] 1.62 1.62 1.62 1.62 1.62 1.62 1.63 1.63 1.65 1.65 1.66 1.67 1.68 1.68 1.68 1.69 [385] 1.69 1.69 1.69 1.69 1.70 1.71 1.71 1.71 1.71 1.72 1.72 1.72 1.72 1.73 1.74 1.75 [401] 1.76 1.76 1.76 1.77 1.78 1.78 1.79 1.80 1.81 1.81 1.83 1.83 1.83 1.85 1.87 1.89 [417] 1.89 1.89 1.90 1.92 1.95 1.95 1.97 1.97 1.97 1.98 2.02 2.02 2.06
87
APPENDIX 10
Spatial Analysis of the Square Rooted Distance
D = Distance (values are in APPENDIX 8)
d D= (Appendix 9).
• Calculation of SD2d ×±
=±=×±=×± 0.69221.22520.3461)(21.2252SD2d (0.5331, 1.9173) (m)
This is the interval that contains about 95% of the d’s. Equivalent interval for D is
(0.28, 3.68) (m). > shapiro.test(D)
Shapiro-Wilk normality test
data: D
W = 0.9645, p-value = 1.122e-08
We conclude that D does not follow the normal distribution.
> shapiro.test(d)
Shapiro-Wilk normality test
data: d
W = 0.9957, p-value = 0.2934
We conclude that d is considered normally distributed.
88
APPENDIX 11
Number of 0.1 Ha Plots Required for an Error of ±50 (Ton/Ha) of the True Mean Biomass
• The number of 0.1 ha plots required to have the average biomass (ton/ha) of South
Fork Caspar Creek forest within ±50 ton/ha of the true mean at 95 % confidence can
be calculated as follows.
• Introductory statistics book shows that the necessary sample size under given
scenario can be found from2
025.0
×=
ESDt
ndf
. SD=202.6 from Table 10 is used here.
We have 667.6550
6.2022 2
≈=
×
≈n , so about 66 plots are needed to have the desired
precision.