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

ii

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

v

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

vi

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

vii

Number of 0.1 Ha Plots Required for an Error of ±50 (Ton/Ha) of the True Mean Biomass…………………………………………………………………………….88

viii

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

ix

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

xi

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)

xii

USDA United States Department of Agriculture

xiii

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

2

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)

3

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

4

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.

5

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-

6

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

7

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

8

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. .

9

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).

10

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).

13

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

17

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

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200

1 19 37 55 73 91 109

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Tree numbered

Data of 257 redwood tree collected in summer 2013

dbh

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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

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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

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Figure 19. log(DBH) vs. log(H_LDV)

53

Figure 20. Homogeneity of variance

54

Histogram of scale(mo

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Theoretical Quantiles

sta

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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.