ABSTRACT HALL, KEVIN BROWN. Modeling The

ABSTRACT

HALL, KEVIN BROWN. Modeling the Actual Productivity of Eucalyptus benthamii in the Southeastern United States. (Under the direction of Jose Stape).

Eucalyptus species have been investigated as viable production forest species in the southeastern United States for more than 40 years. A frost tolerant Eucalyptus species with reduced climatic limitations would allow forest companies and landowners to plant

Eucalyptus on a larger scale over a greater geographic range. Initial trials in the 1960s resulted in the establishment of Eucalyptus plantations in southern Florida with tropical species such as E.grandis, E.robusta, E.camaldulensis and E.tereticornis. Later trials in the

1970s and 1980s showed some promising growth and survival of E.viminalis, E.nova- anglica, E.macarthurii and E.camphora in states such as Georgia, Alabama and South

Carolina. However, several hard, freezes in 1983 and 1984 caused severe damage to many of the trials ultimately ending these efforts. Since that time, forest companies around the world have had success with Eucalyptus in temperate and subtropical areas. As demand hardwood fiber grew, the planted area expanded into colder regions (e.g. southern region of Latin

America, Europe and South Africa), resulting in breeding efforts focused on frost tolerant

Eucalyptus.

In recent Eucalyptus frost tolerant trials established by NCSU/ Forest Productivity

Cooperative (FPC), E.benthamii has shown superior growth rates as well as frost tolerance for USDA Cold Hardness Zones 8 to 9. Also, the current research efforts of the NCSU/FPC, several US based companies have shown interested in E.benthamii as a feed stock resulting in a variety of research trials and pilot plantations across the SE US. Similarly, available plot-level data for E.benthamii are disjunct. The aggregation of these data can provide valuable information for assessing the growth of E.benthamii across the SE US. The aim of this project is to develop volumetric and biomass growth and yield models to characterize the current performance of E.benthamii in the SE US. During 2012-2013, a network of one hundred permanent inventory plots of E.benthamii ranging from ten months to 13 years in age across seven states (AL, GA, LA, SC, TX and NC) were established. These plots range in size from 100 to 400 m2 and all diameters at breast height and total stem height were measured. Site quality was established by developing a site index guide curve using age and mean dominant height. Site index with a base age of six years for E.benthamii in the SE US ranged from six to 21 meters. Functions for mean dominant height and stand basal area based on age were developed to project each stand variable through time. Yield tables for volume, green weight and biomass, in metric units, were developed by using the combined- variable of mean dominant height and stand basal area for each age class.

Eucalyptus benthamii and six other cold-tolerant Eucalyptus species were measured weekly for one-year while climate data during the winter months was measured hourly. The behavior of Eucalyptus cold-tolerant species was evaluated to obtain insight on growth controls over the winter months in the SE US. Eucalyptus species have shown little lag time in expressing the fixed carbon as stem growth. Temperature is the leading climate variable that controls growth of cold-hardy Eucalyptus species. The objective of this study was to examine differences in cold tolerant Eucalyptus rate of biomass accumulation through the winter months and to develop biomass gain by species and the weekly average minimum temperature.

Modeling the Actual Productivity of Eucalyptus benthamii in the Southeastern United States

by Kevin Brown Hall

A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Master of Science

Forestry and Environmental Resources

Raleigh, North Carolina

2015

APPROVED BY:

______Jose Stape Bronson Bullock Committee Chair

______Douglas Frederick Jeff Wright

BIOGRAPHY

Kevin Brown Hall, son of Walter and Mary Kay Hall, was born in Raleigh, North

Carolina on May 14, 1987. When considering an undergraduate degree focus, Kevin’s passion for outdoors and sciences drew his attention to undergraduate Forest Management program at North Carolina State University. Kevin capitalized on opportunities during his undergraduate career at NCSU to gain experience in forest plantations systems by traveling abroad to participate in undergraduate research. In 2012 immediately after completing his undergraduate degree, Kevin began graduate school at NCSU by accepting a study abroad program in Curitiba, Brazil to learn about silvicultural practices of plantation forests in southern Brazil. Kevin completed his graduate work for Master of Science in Forestry with a focus in growth and yield modeling and frost-tolerant Eucalyptus silviculture.

ACKNOWLEDGMENTS

Firstly, I would like to thank my parents, Walter and Mary Kay Hall, for their support and encouragement throughout this process. Without their guidance and support I would not be where I am today. I am very fortunate to have the support of my family and friends and their encouragement, advice and humor.

I would also like to thank my committee for the guidance and support; Dr. Jose Stape,

Dr. Bronson Bullock, Dr. Doug Frederick, and Dr. Jeff Wright. A special thanks to Dr. Stape for accepting me as his graduate student, encouraging me to pursue my interest in Eucalyptus through a Master’s project, and giving me the opportunity to grow as a forest professional. I would also like to acknowledge the Forest Productivity Cooperative (FPC), its members, fellow graduate students and undergraduate interns for all of their encouragement, advice, willingness to collaborate and help in achieving the goals of my Master’s thesis project. I would like to specifically acknowledge Henrique Ferraço Scolforo, Marcello Bontempi Pizzi,

Caroline Rodrigues, Carolina Mata Machado and Nathan Thomas for their help with data collection in the field.

Finally, I would like to acknowledge the Southeastern Partnership for Integrated

Biomass Supply Systems (IBSS) and Dr. Steve Kelley for their support to realize this project.

The IBSS project is supported by the Agriculture and Food Research Initiative (AFRI)

Competitive Grant no. 2011-68005-30410 from the USDA National Institute of Food and

Agriculture.

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TABLE OF CONTENTS LIST OF TABLES ...... vi LIST OF FIGURES ...... viii

CHAPTER ONE: INDIVIDUAL STEM VOLUMETRIC, GREEN WIEGHT AND BIOMASS EQUATIONS FOR EUCALYPTUS BENTHAMII AND OTHER SPECIES WITHIN THE SECTION MAIDENARIA PLANTED IN THE SOUTHEASTERN UNITED STATES ...... 1 Introduction ...... 1 Eucalyptus in exotic environments ...... 2 Eucalyptus in the United States ...... 3 Stem allometric equations and biomass partitioning...... 7 Materials and Methods ...... 9 Individual stem volume, green weight and biomass ...... 10 Biomass partitioning of Eucalyptus benthamii ...... 14 Statistical Analysis ...... 15 Results and Discussion ...... 16 Individual stem volume, green weight and biomass ...... 16 Merchantable ratio of frost tolerant Eucalyptus ...... 20 Biomass partitioning of Eucalyptus benthamii ...... 21 Conclusion ...... 24 References ...... 26

CHAPTER TWO: A GROWTH AND YIELD MODEL FOR EUCALYPTUS BENTHAMII IN THE SOUTHEASTERN UNITED STATES ...... 49 Introduction ...... 49 Eucalyptus silviculture in the southeastern United States ...... 53 Developing a growth and yield model for Eucalyptus benthamii ...... 54 Materials and Methods ...... 55 Site index classification for Eucalyptus benthamii in SE US ...... 56 Stand density as a function of basal area for Eucalyptus benthamii in the SE US...... 58 Statistical Analysis ...... 59 Results and Discussion ...... 60 Site index for Eucalyptus benthamii in SE US ...... 61 Stand density as a function of basal area for Eucalyptus benthamii in the SE US...... 61 iv

Yield model for Eucalyptus benthamii in SE US ...... 62 Projecting yield and recovering growth of Eucalyptus benthamii in the SE US ...... 63 Conclusion ...... 66 References ...... 68

CHAPTER THREE: THE TEMPERATURE-RADIATION EFFECT ON SEVEN COLD- HARDY EUCALYPTUS SPECIES PLANTED IN THE PIEDMONT REGION OF NORTH CAROLINA ...... 99 Introduction ...... 99 Materials and Methods ...... 103 Frost-tolerant Eucalyptus species growth ...... 104 Effects of climate variables on frost-tolerant Eucalyptus growth ...... 104 Temperature lag-time response on growth of frost-tolerant Eucalyptus ...... 108 Results and Discussion ...... 110 Frost-tolerant Eucalyptus species growth ...... 110 Effects of climate variables on frost-tolerant Eucalyptus growth ...... 112 Temperature lag-time response on growth of frost-tolerant Eucalyptus ...... 116 Conclusion ...... 118 References ...... 120

LIST OF TABLES

Table 1.1. Summary statistics for total stem volume, green weight and biomass of frost tolerant Eucalyptus...... 29

Table 1.2. Summary statistics for total tree biomass by compartment of Eucalyptus benthamii (n = 6)...... 31

Table 1.3. Analysis of variance for the combined-variable model form for each response variable...... 33

Table 1.4. Parameter estimates for the combined-variable model form for each response variable...... 34

Table 1.5. Analysis of variance for the generalized logarithmic model form for each response variable...... 36

Table 1.6. Parameter estimates for the generalized logarithmic model form for each response variable...... 37

Table 1.7. Analysis of variance for the logarithmic model form for each response variable.

...... 39

Table 1.8. Parameter estimates for the logarithmic model form for each response variable. 40

Table 1.9. Analysis of variance for merchantable ratio (dob) model form for each response variable...... 42

Table 1.10. Parameter estimates for the merchantable ratio (dob) model form for each response variable...... 43

Table 1.11. Analysis of variance for the merchantable ratio (ht) model form for each response variable...... 44

Table 1.12. Parameter estimates for the merchantable ratio (ht) model form for each response variable...... 45

Table 1.13. Analysis of variance of the logarithmic (dbh only) model form for each tree compartment...... 46

Table 1.14. Parameter estimates for the logarithmic (dbh only) model form for each tree compartment...... 47

Table 2.1. Summary statistics of plot attributes (trees per hectare, basal area, mean dominant height, volume outside-bark (VOB) and inside-bark (VIB), green weight outside-bark

(GWOB) and inside-bark (GWIB) and stem biomass outside-bark (DWOB) and inside-bark

(DWIB)) by age class (year)...... 74

Table 2.2. Analysis of variance and parameter estimates for the simple linear regression of the reciprocal of age (year) as a predictor of the logarithm of mean dominant height (m). ... 76

Table 2.3. Mean dominant height (m) and base age 6-years and number of observations per

Site Index class...... 79

Table 2.4. Analysis of variance for the simple linear regression of the reciprocal of age

(year) as a predictor of the logarithm of basal area (m2 ha-1) by Site Index classes...... 81

Table 2.5. Parameter estimates for the simple linear regression of the reciprocal of age

(year) as a predictor of the logarithm of basal area (m2 ha-1) by Site Index classes...... 82

Table 2.6. Analysis of variance for the simple linear regression of the combined-variable basal area-mean dominant height as a predictor of yield...... 88

Table 2.7. Parameter estimates for the simple linear regression of the combined-variable basal area-mean dominant height as a predictor of yield...... 89

vii

Table 2.8. Summary of mean annual increments by Site Index class for E.benthamii in the

SE US for all yield variables (bold indicates rotation age)...... 92

Table 3.1. Cold-tolerant Eucalyptus species stem biomass (kg tree-1)...... 121

Table 3.2. Weekly mean stem biomass growth by month of cold-tolerant Eucalyptus species...... 123

Table 3.3. Analysis of variance to test for significance among cold-tolerant Eucalyptus species...... 125

Table 3.4. Mean climatic variables, minimum, mean and maximum temperature (C), vapor pressure deficit (kPa), photosynthetically active radiation (MJ m-2 d-1), and total precipitation

(mm) during the sampling period...... 127

Table 3.5. Thirty-year (1981-2010) monthly mean climatic variables (minimum, mean and maximum temperature (C), and total precipitation (mm)) of Raleigh, North Carolina provided by the National Oceanic and Atmospheric Administration (NOAA)...... 128

Table 3.7. Analysis of variance and parameter estimates for the prediction on weekly average minimum temperature and study period intervals...... 140

Table 3.8. Analysis of variance and parameter estimates for the prediction on weekly average minimum temperature and study period intervals...... 141

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LIST OF FIGURES

Figure 1.1. Scatter plot of sample trees for each species...... 30

Figure 1.2. Biomass partitioning of 9-year old Eucalyptus benthamii in South Carolina. ... 32

Figure 1.3. Scatter plot of actual versus predicted A) volume, B) green weight and C) dry weight for the combined-variable model form...... 35

Figure 1.4. Scatter plot of actual versus predicted A) volume B) green weight and C) dry weight for the generalized logarithmic model form...... 38

Figure 1.5. Scatter plot of actual versus predicted A) volume B) green weight and C) dry weight for the logarithmic model form...... 41

Figure 1.6. Root and stem biomass ratio. Linear regression with fixed intercept through the origin...... 48

Figure 2.1. Eucalyptus benthamii inventory plot network across the southeastern United

States...... 72

Figure 2.2. Scatter plot of all sample trees within the southeastern United States for the

Eucalyptus benthamii inventory plot network...... 73

Figure 2.3. Scatter plot of mean dominant height (m) of each inventory plot by age (years).

...... 75

Figure 2.4. Linear regression of inverse age (year) as a predictor of natural logarithm of mean dominant height (m) to determine Site Index Guide Curve for E.benthamii in SE US.

Coefficient of determination = 0.4283...... 77

Figure 2.5. Anamorphic site index guide curves and mean dominant height (m) of inventory plots for Eucalyptus benthamii in the southeastern United States...... 78

Figure 2.6. Scatter plot of basal area (m2 ha-1) of each inventory plot by age (years) by Site

Index class...... 80

Figure 2.7. Linear regression of inverse age (year) as a predictor of natural logarithm of basal area (m2 ha-1) by Site Index class for E.benthamii in SE US. SI – I R2 = 86.73. SI – II

R2 = 0.6839. SI – III R2 = 0.5342. SI – IV R2 = 0.3487...... 83

Figure 2.8. Scatter plot of actual versus predicted basal area...... 84

Figure 2.9. Projected mean basal area by site index classes for all plots over time...... 85

2 -1 Figure 2.10. Scatter plots of A) mean dominant height (Hdom; m), B) basal area (G; m ha ) and C) combined-variable Hdom*G as predictors volume...... 86

Figure 2.11. Scatter plots of the combined-variable Hdom*G as a predictor of A) volume, B) green weight and C) dry weight with (OB) and without (IB) the presence of bark...... 87

Figure 2.12. Scatter plots of observed and predicted yield variables...... 90

Figure 2.13. Projected yields (A) VOB, B) VIB, C) GWOB, D) GWIB, E) DWOB, F)

DWIB) for Eucalyptus benthamii in the SE US...... 91

Figure 2.14. Projected current (CAI) and mean (MAI) annual increments and observed for volume with the presence of bark (VOB) by Site Index class (A) SI-I; B) SI-II; C) SI-III; D)

SI-IV) of E.benthamii in SE US...... 93

Figure 2.15. Projected current (CAI) and mean (MAI) annual increments and observed MAI for volume without the presence of bark by Site Index class (A) SI-I; B) SI-II; C) SI-III; D)

SI-IV) of E.benthamii in SE US...... 94

Figure 2.16. Projected current (CAI) and mean (MAI) annual increments and observed MAI for green weight with the presence of bark by Site Index class (A) SI-I; B) SI-II; C) SI-III; D)

SI-IV) of E.benthamii in SE US...... 95

Figure 2.17. Projected current (CAI) and mean (MAI) annual increments and observed MAI for green weight without the presence of bark (GWOB) by Site Index class (A) SI-I; B) SI-II;

C) SI-III; D) SI-IV) of E.benthamii in SE US...... 96

Figure 2.18. Projected current (CAI) and mean (MAI) annual increments and observed MAI for biomass with the presence of bark by Site Index class (A) SI-I; B) SI-II; C) SI-III; D) SI-

IV) of E.benthamii in SE US...... 97

Figure 2.19. Projected current (CAI) and mean (MAI) annual increments and observed MAI for biomass without the presence of bark by Site Index class (A) SI-I; B) SI-II; C) SI-III; D)

SI-IV) of E.benthamii in SE US...... 98

Figure 3.1. Total mean stem biomass (kg) of seven cold-tolerant Eucalyptus species planted in the Piedmont of North Carolina...... 122

Figure 3.2. Weekly mean stem biomass growth (kg) for each cold-tolerant Eucalyptus species planted in the Piedmont of North Carolina...... 124

Figure 3.3. Mean stem biomass growth (kg tree-1 week-1) of all cold-tolerant Eucalyptus species with an initial mean stem biomass of 5.69-kg and E.benthamii with an initial mean stem biomass of 8.45-kg...... 126

Figure 3.4. Thirty-year mean climate data for Raleigh, North Carolina from 1981 through

2010. Daily mean observations provided by NOAA summarized to weekly observations to compare climate during study period using equal time intervals...... 129

Figure 3.5. Weekly mean minimum, mean and mean maximum temperature (C) observed hourly from the CRONOS database at the Reedy Creek Field Laboratory during the study period...... 130

Figure 3.6. Weekly precipitation accumulation (mm) calculated from hourly observations of the CRONOS database at the Reedy Creek Field Laboratory during the study period...... 131

Figure 3.7. Weekly mean daylight vapor pressure deficit (kPa) calculated from the relative humidity (%) and temperature (C) observed hourly from the CRONOS database at the

Reedy Creek Field Laboratory during the study period...... 132

Figure 3.8. Weekly mean photosynthetically active radiation (PAR) (MJ m-2 d-1) from the

CRONOS hourly observations collected at the Reedy Creek Field Laboratory during the study period...... 133

Figure 3.9. Relation between normalized weekly mean stem biomass growth (%) of all cold tolerant Eucalyptus species (initial and final mean stem biomass of 5.69-kg and 31.77-kg respectively) and weekly mean minimum (A), mean maximum (B) and mean (C) temperature(C), weekly precipitation (D) (mm), mean daylight vapor pressure deficit (E)

(kPa) and mean photosynthetically active radiation (F) (MJ m-2 d-1)...... 134

Figure 3.10. Relation between normalized weekly mean stem biomass growth (%) of

E.benthamii (initial and final mean stem biomass of 8.45-kg and 43.29-kg respectively) and weekly mean minimum (A), mean maximum (B) and mean (C) temperature (C), weekly precipitation (D) (mm), mean daylight vapor pressure deficit (E) (kPa) and mean photosynthetically active radiation (F) (MJ m-2 d-1)...... 135

Figure 3.11. Residuals for the normalized weekly stem growth for each prediction equation based on the dummy variables of winter/spring and summer/autumn...... 137

Figure 3.12. Observed data and prediction curves by season showing the fit of normalized weekly stem growth of cold tolerant Eucalyptus species and the weekly mean temperature in the piedmont of North Carolina...... 138 xii

Figure 3.13. Weekly mean minimum temperature (C) and normalized weekly stem biomass growth (%) during the study period...... 139

Figure 3.14. Observed and predicted weekly mean minimum temperature in Raleigh, NC during the study period...... 142

Figure 3.15. Observed and predicted normalized weekly stem growth of cold tolerant

Eucalyptus species (initial mean stem biomass = 5.69-kg) in Raleigh, NC during the study period...... 143

Figure 3.16. Fitted sinusoidal prediction curves for weekly mean minimum temperature and normalized weekly stem growth of cold tolerant Eucalyptus species in Raleigh, NC during the study period...... 144

Figure 3.17. Residuals of sinusoidal curves for weekly biomass growth of cold tolerant

Eucalyptus species and weekly average minimum temperature ...... 145

xiii

CHAPTER ONE: INDIVIDUAL STEM VOLUMETRIC, GREEN WIEGHT AND

BIOMASS EQUATIONS FOR EUCALYPTUS BENTHAMII AND OTHER SPECIES

WITHIN THE SECTION MAIDENARIA PLANTED IN THE SOUTHEASTERN

UNITED STATES

Introduction

The desire for greater energy independence and security is a key part of legislation passed in the United States (Energy Independence and Security Act (EISA) of 2007) and the

European Commission’s binding renewable energy target of 2020 (Berndes and Hansson,

2007). EISA outlines the need for 137 billion liters of biofuels in the United States by 2022 with at least 80 billion liters from cellulosic and advanced biofuels. To meet this future demand, new crops and residue collection systems are required to efficiently, economically and sustainably convert lignocellulosic materials to ethanol and other transportation fuels

(McLaughlin and Kszos, 2005; Perlack et al., 2005).

Lignocellulosic feedstocks are the cellulose, hemicellulose and lignin components of plant material. Examples of lignocellulosic feedstocks include municipal wastes, agricultural residues (corn stover, wheat straw or sugarcane bagasse), dedicated energy crops (fast- growing perennial grasses or trees), wood residues from logging operations and fuel- treatment thinnings from forest lands (Dale et al., 2011). Perlack et al. (2005) explains that dedicated bioenergy crops have greater potential when comparted to crop residues for providing a large, sustainable feedstock resource in the United States. The environment, local economy and climatic conditions in regions of the United States will dictate specific crops that are best suited for a specific region. Dedicated bioenergy feedstocks such as

Eucalyptus and tropical grasses in the southern United States, coppicing willow systems in the northern US and Lake States, and a variety of energy sorghum, sudangrass, or agave in the western and southwestern regions, show that a variety of perennial woody and grass species are adapted to all regions of the United States (Dale et al., 2011).

Land-use decisions regarding types of bioenergy crops, farm locations and management practices have a direct impact on carbon sequestration, native plant diversity, food production, greenhouse gas emissions, water and air quality, and other environmental and social attributes (Dale et al., 2011). The majority of dedicated energy crops are perennial crops which inherently have low environmental impacts compared to annual crops.

Furthermore, perennial crops can often be planted on marginal lands that are not suited for food crops. Establishing perennial crops on marginal lands would reduce the land-use conversion from food to dedicated energy crops. Perennial energy crops include trees grown purposely for bioenergy applications (Hinchee et al., 2009).

Eucalyptus in exotic environments

Of the Myrtaceae family, more than 700 species of Eucalyptus are indigenous to

Australia and some surrounding islands. Eucalyptus species grow from 10 N to 44 S latitude, from sea level to 2000 meters in elevation, with rainfall ranging from 250 to 3800 mm per year (Davidson, 1996). The broad range of geographic and climatic conditions have resulted in immense diversity within the genus Eucalyptus. As a result, Eucalyptus have been successfully introduced to other tropical, subtropical and warm-temperate zones of the world as a feedstock for fuel wood, pulp and timber production (Davidson 1996). While there are more than 700 species of Eucalyptus, less than 20 are widely planted in exotic 2

environments (Gonzalez et al. 2011). The successful introduction of exotic species can result in superior growth performance due to ideal climatic conditions and lack of pests within the new environment, as is the case for E.grandis, E.urophylla and their hybrids (i.e. Brazil,

Colombia, Venezuela, South Africa), E.globulus (i.e. Chile, Portugal, Spain),

E.camaldulensis (i.e. Israel, Nigeria, India), E.nitens (i.e. Chile, New Zealand), E.viminalis

(i.e. Argentina, Brazil), E.gunnii (i.e. France) and E.benthamii (i.e. Brazil). (Davidson, 1996;

Madgwick et al., 1991).

As the demand for Eucalyptus fiber has increased in recent years around the world, forest companies have expanded their management area into cooler regions that require the expansion of breeding programs to incorporate cold tolerant Eucalyptus species.

Eucalyptus in the United States

Eucalyptus was first introduced in the United States during the California gold rush during the late 1840s and early 1850s (Kellison et al., 2012). The barren Californian landscape during this period is described as treeless with occasional oak groves, lines of trees and brush along larger streams, with brown mountains covered with grass or wild oats during the winter and spring (Hittel, 1863; Cronise, 1868). Cooper (1876) described how European countries such as Germany and France are allocating twenty and thirty-two percent of land in forests to maintain farming conditions respectively. Cooper elaborated that the establishment of forests in regions with less than suitable climates could be used to moderate winds and increase rainfall (1876). Cooper (1876) explained that the Eucalyptus globulus planted on his homestead near Santa Barbara, California had exhibited adequate growth characteristics following three years of growth and had shown drought resistance through the summer

months. Cooper (1876) continued to depict the utilization of Eucalyptus wood to meet the demand for timber production in the United States by referring to the annual consumption of timber products such as fencing, railroad ties, gunships, wagon wheels and other purposes.

Introduced to the southern United States as early as 1878, Eucalyptus species would not be utilized beyond windbreaks, ornamentals and shade trees in central and southern

Florida and Texas until the 1950s and 1960s when forest-based organizations such as St.

Regis Company and Champion International Corporation trial-planted Eucalyptus in Florida and Texas, respectively (Moultin, 1999). The Florida Forests Foundation (FFF) began research in 1959 to determine if Eucalyptus could be utilized for hardwood pulpwood production on rangeland or other low quality sites south of Tampa, Florida (Rockwood,

2012). In 1968, the USDA Forest Service and the Florida Division of Forestry became focused on continuing the efforts of the FFF (Kellison et al., 2012). In the early 1970s, the first Eucalyptus Research Cooperative (Florida Group) was formed consisting of more than five industrial members and the USDA Forest Service scientists in Lehigh Acres, Florida

(Geary et al., 1983). The Florida Group, working with E.grandis, E.robusta,

E.camaldulensis, E.tereticornis, E.amplifolia and C.torelliana, outlined two main objectives; to develop practices to raise seedlings and to establish commercial plantations. There was also a focus by Dr. Carlyle Franklin and Mr. George Meskimen, of the USDA Forest Service, to conduct a four-phase genetic improvement program for E.grandis (Geary et al., 1983). In

1971, Dr. Bruce Zobel and others, with the support of the Hardwood Research Cooperative at

North Carolina State University (NCSU), began a systematic evaluation of species and sources of Eucalyptus to determine their success in the southern US (Hunt and Zobel, 1978).

The Florida Group joined the Hardwood Research Cooperative in 1978 and continued the study until 1985, following three severe freezes (Kellison et al., 2012).

During the 14-year study, 569 Eucalyptus seed sources representing 103 species were planted in 141 sites across the southeastern US. Seed material was obtained in native environments of Australia and surrounding islands as well as from exotic locations. Three types of tests were installed; (1) screening trials consisting of six-tree row plots replicated six times, (2) in-depth trials consisting of four replications of 25-tree plots of the promising species/sources from the screening trials and (3) semi-operational trials of one to five-acres of the most promising species/sources from the screening trials (Kellison et al., 2012). The screening trial measured survival, height and subjectively assessed cold-tolerance based on canopy damage. At the end of two years, over 80 percent of the sources had less than 40 percent survival, and the remaining 113 sources advanced to the in-depth trials (Kellison et al., 2012). The Hardwood Research Cooperative continued the study with Eucalyptus until

1985 when efforts were abandoned following severe freeze events of December 24, 1983,

January 20, 1984 and January 9, 1985 (Kellison et al., 2012). Although the Hardwood

Research Cooperative did not continue to search for a cold tolerant Eucalyptus species for the southern US, the semi-operational plantations of central and southern Florida remained.

Beginning in the 1980s, the University of Florida (UF) conducted Florida-wide

Eucalyptus research with many collaborators such as The Short Rotation Woody Crops

Program of the US Department of Energy (1980 to 1988), the Gas Research Institute (1981 to

1991) and other federal, academic and corporate institutions (Rockwood, 2012). UF developed a cost-effective tree improvement program for E.grandis in Florida by utilizing the short generation time and rapid growth of Eucalyptus with a combination of provenance

and progeny testing, with early selection to achieve steady genetic gains (Rockwood, 2012).

This breeding strategy resulted in a 16 percent gain of mean stem volume per generation from the second to the fourth within one genetic base population (Rockwood, 2012).

Following the severe freezes from 1983 through 1985, UF was able to successfully identify five cultivars (E.nergy series E.grandis G1, G2, G3, G4 and G5) based on genetic tests established on a variety of sites and climatic characteristics in Florida (Rockwood 2012,

Rockwod and Tamang 2010). The E.nergy cultivars were patented and released for commercial use in 2009 (Rockwood and Tamang, 2010).

Several aforementioned Eucalyptus species under investigation by the Florida Group had varying results. E.robusta were selected and clonally tested in the early 1980s where clones had poor performance ratings and were no longer considered for commercialization.

Seed production of E.camaldulensis and E.tereticornis was problematic. A few were commercially propagated in California in the 1990s but are no longer available (Rockwood et al., 1994; Rockwood et al., 1995). E.amplifolia and C.torelliana have been retained by the

Florida Division of Forestry for their ornamental properties and have shown tolerance to freeze events in northern Florida. (Rockwood, 2012).

In 2010, the NCSU/ Forest Productivity Cooperative (FPC) began to investigate the potential of Eucalyptus in the southeastern United States (Stape et al., 2011). The current initiative was proposed and accepted due to the growing biomass markets in the US. The nation’s current goal for biofuels is to displace 15 percent of gasoline usage by 2017. In order to achieve this goal, the renewable fuel supply must increase from 18.9 million m3 of corn grain ethanol to approximately 132 million m3 of alternative fuels from plant materials such as grasses, woodchips and agricultural residues (ArborGen, 2012). Also, there are a

large number of Eucalyptus genotypes that have yet to be tested, and new breeding and propagation techniques and a well-established silvicultural protocol from Latin America that had not yet been established during the trials of the early 1980s (Graça et al., 1999; Higa and

Carvalho, 1990). With new protocols, genotypes and a sound conservative research approach, the FPC and cooperators believe that there is great potential in establishing forest plantations of cold-tolerant Eucalyptus in the southern United States. This region wide initiative encompasses three main objectives; (1) identify Eucalyptus species/sources that have sufficient cold tolerance to survive and grow on a variety of sites across the southern

US, (2) quantify and model the biomass growth and yield of these species based on a six-year rotation and (3) investigate the environmental factors related to Eucalyptus cold tolerance and determine cold-risk zoning and region-wide productivity mapping.

Stem allometric equations and biomass partitioning

A strong research initiative has focused on establishing Eucalyptus plantations across the southern United States. Freezing winter temperatures have proven to be the primary climatic variable that limits the range of Eucalyptus species in North America. As a result, an emphasis has been placed on frost tolerant Eucalyptus species. It is necessary to be able to predict individual stem volume and biomass (dry weight) for the principal species of interest to accurately assess growth rates. Individual total stem volume and biomass are powerful dependent variables compared to individual tree measurements when evaluating the performance of species/sources. Also, detailed individual stem volume and biomass equations are necessary when estimating total volume and biomass on a plot or stand level.

The transportation of raw materials is a key component in the economic analysis for the production of bioproducts (Seary et al., 2007). Although transportation of raw materials is generally limited by the allowable tonnage on roads, the consumable material for the production of bioproducts is the dry weight. Therefore, a greater emphasis is focused on the dry weight of raw material for bioproducts than volume when harvesting for dimensional lumber. This requires increased accuracy in the estimation of bole green weight and dry weight. This information provides insight to the relative moisture content. Low moisture content of the raw material used for bioproducts is desired in the conversion process, and the reduced moisture content of the raw material also increases the amount of consumable biomass per load (Acuna et al., 2012; Seary et al., 2007). Therefore, reduced moisture content of raw materials with higher densities can ultimately reduce transportation costs (per actual metric ton) or allows for increased haul distances (Seary et al., 2007).

The objectives of this research were; (1) to develop widely applicable total and merchantable individual stem volume, green weight and biomass outside- and inside-bark allometric equations for frost tolerant Eucalyptus species, in both metric and English units, and (2) to quantify the biomass partitioning of E.benthamii for both above- and belowground compartments. The motivation for developing allometric equations with and without the presence of bark are related to the ash content of bark, and ash contents less desirable properties in the conversion process of biofuels. The data set consists of forty frost tolerant

Eucalyptus trees within the section Maidenaria. Trees were selected among six species

(E.badjensis, E.benthamii, E.dorrigoensis, E.macarthurii, E.nitens and E.viminalis) that have shown significant frost tolerance and growth characteristics in preliminary results of screening trials. The equations predict total or merchantable (to a given upper diameter or

height limit) stem volume, green weight or biomass outside- or inside-bark. In a more detailed and elaborate study, total biomass partitioning for above- and below-ground compartments of E.benthamii was estimated for six, nine-year old trees. This set of equations will be the initial equations developed to estimate individual total and merchantable stem volume, green weight and biomass for frost tolerant Eucalyptus in the SE

US and total biomass of E.benthamii for above- and below-ground compartments.

Materials and Methods

Two sites were selected to represent size classes through the anticipated rotation age

(six-years). Study trees ranged in age from two to nine years. A total of 40 trees were sampled within six species (E.badjensis, E.benthamii, E.dorrigoensis, E.macarthurii,

E.nitens and E.viminalis) that exhibited superior growth and cold tolerance following three winters. A variety of cold tolerant Eucalyptus species will likely be necessary to meet the hardwood fiber demand in the SE US resulting in multiple Eucalyptus species selected for a set of allometric equations that will be universally useful for estimating yields of different cold tolerant species within the section Maidenaria. Trees were selected based on the median, first and third quartiles of the diameter at breast height (dbh) from a temporary plot within the study site. This selection criteria ensured the capture of the size distribution across the site without making assumptions based on normality. Additional trees were selected to fill gaps between the first and third quartiles in the size distributions and species per site.

Individual stem volume, green weight and biomass

The purpose of destructive sampling was to obtain accurate outside- and inside-bark diameter measurements as well as determining the volume, green weight and dry weight of each stem section. Sampling protocol was similar to that described by da Silva et al. (2004) with the exception of diameter measurements taken in one-meter increments to 2.5-cm top rather than a 4-cm top. Following the felling of each tree, all branches were removed, total height was measured and a disc was collected from the stem at 0.3 m, 1.3 m and every 1.0 m to a 2.5 cm outside-bark diameter. A disc was removed from the base of each long section along the stem. Each disc was weighted and diameter measure with- and without-bark. Each stem section was also weighed in the field to determine green weight. The summation of the disc and section weights yield total individual stem green weight. Smalian’s equation was used for each section based on the disc outside- and inside-bark diameters. Base-section volume was estimated using the volume equation of a cylinder, and top-section volume was estimated using the volume formula of a cone. The summation of the volume of each section yields the total individual stem volume outside- and inside-bark. Each disc along with the bark sampled was dried at 60 Celsius to a constant weight and weighed to determine moisture content and bone dry weight of the disc and bark samples. The dry weight of each section inside-bark was estimated using the green weight and moisture content of each disc inside-bark and the green weight of the section. The sectional bark dry weight was estimated using the section bark green weight and the moisture content of the bark sample to determine the sectional bark dry weight. The summation of each sectional wood and bark dry weight pair yield the total individual stem outside-bark dry weight. This sampling protocol allowed

the determination of the estimated wood density of each stem section with- and without-bark, as well as the total stem weighted mean wood density.

The analysis allows for comparison of two equations forms to predict total individual stem volume, green weight and biomass outside- and inside-bark. The two equation forms of interest are the combined-variable (Avery and Burkhart, 2002) and logarithmic (Schumacher and Hall, 1933). The logarithmic equation form does not have a slope-intercept term, therefore it is necessary to investigate a generalized logarithmic form with a slope-intercept term to test the significance of this particular parameter estimate before concluding the term can be removed from the equation form. The general form of the combined-variable equation used is given in the equation

2 푉푡 , 퐺푊푡 표푟 퐷푊푡 = 훽0 + 훽1퐷 퐻 + 휀 (1.1)

3 where 푉푡, 퐺푊푡 and 퐷푊푡 are the total stem volume (m ), total stem green weight (kg) and total stem dry weight (kg) respectively, 훽0 and 훽1 are coefficients to be estimated, 퐷 is tree dbh (cm), 퐻 is total stem height (m) and 휀 is the error term. The general equation form for the generalized logarithmic equation is given in the equation

훽4 훽5 푉푡 , 퐺푊푡 표푟 퐷푊푡 = 훽2 + 훽3퐷 퐻 + 휀 (1.2)

3 where 푉푡, 퐺푊푡 and 퐷푊푡 are the total stem volume (m ), total stem green weight (kg) and total stem dry weight (kg) respectively, 훽2, 훽3, 훽4 and 훽5 are coefficients to be estimated, 퐷 is tree dbh (cm), 퐻 is total stem height (m) and 휀 is the error term. The general form of the logarithmic equation is given in the equation

훽7 훽8 푉푡 , 퐺푊푡 표푟 퐷푊푡 = 훽6퐷 퐻 + 휀 (1.3)

3 where 푉푡, 퐺푊푡 and 퐷푊푡 are the total stem volume (m ), total stem green weight (kg) and total stem dry weight (kg) respectively, 훽6, 훽7 and 훽8 are coefficients to be estimated, 퐷 is tree dbh (cm), 퐻 is total stem height (m) and 휀 is the error term.

Merchantable volume, green weight and biomass vary greatly due to the upper diameter restriction imposed by different processing facilities. Therefore, in order to accurately estimate the merchantable portion of stem wood, a ratio function is required in conjunction with the total stem wood equations. Furthermore, being able to estimate merchantable height based on a given upper stem diameter can be useful as well when processing facilities require specific log lengths. Sectional stem data for the forty sample trees were used consisting of 449 observations. SAS 9.3 software was used to perform a nonlinear regression with the Gauss-Newton estimation method.

By creating merchantable stem wood functions based on upper stem diameter or height ratios, it is possible to set these equations equal and solve for the imposed limit. The following equation form (eq. 1.4) estimates the merchantable ratio based on a given upper diameter (Burkhart, 1977)

푑표푏훼2 푅 = 1 + 훼 ( ) + 휀 (1.4) 푑표푏 1 퐷훼3 where 푅푑표푏 is the proportion of merchantable stem wood for a given 푑표푏, 훼1, 훼2 and 훼3 are coefficients to be estimated, 퐷 is tree dbh (cm), 푑표푏 is the upper stem diameter outside-bark

(cm) and 휀 is the error term. The following equation form (eq. 1.5) for the “Modified

Burkhart” estimates the merchantable stem wood as a proportion of merchantable height as it relates to total height (Cao et al., 1980)

(퐻−ℎ)훼5 푅 = 1 + 훼 ( ) + 휀 (1.5) ℎ푡 4 퐻훼6

where 푅ℎ푡 is the proportion of merchantable stem wood at a given ℎ, 훼4, 훼5 and 훼6 are coefficients to be estimated, 퐻 is total tree height (m), ℎ is the merchantable stem height (m) and 휀 is the error term.

Merchantable stem wood is a function of total stem wood and the merchantable ratio.

The generic equation forms for merchantable stem wood are

푌푚 = 푓(푌푡, 푅푑표푏) (1.6) and

푌푚 = 푓(푌푡, 푅ℎ푡) (1.7)

These equations can be set equal to each other and solved for the unknown merchantable limit requirement. The following equations show the prediction equations for upper limit diameter outside-bark (푑표푏) and merchantable height (ℎ).

1 훼 (퐻−ℎ) 5 훼2 훼4∗( 훼6 ) 푑표푏̂ = [( 퐻 ) ∗ 퐷훼3] (1.8) 훼1 and

1 훼2 푑표푏 훼5 훼1∗( 훼3 ) ℎ̂ = 퐻 − [퐻훼6 ∗ ( 퐷 )] (1.9) 훼4

This allows the user to predict the missing merchantable variable based on a given restriction necessary in calculating merchantable volume, green weight or biomass. The merchantability ratio also allows the user to estimate the percentage of merchantable stem wood pending on the dbh and total height of a given tree or stand of trees.

The deliverables for this analysis are total and merchantable stem wood (volume, green weight and dry weight outside- and inside-bark) equations for cold tolerant Eucalyptus species within the section Maidenaria for the southeastern United States. 13

Biomass partitioning of Eucalyptus benthamii

To determine the aboveground biomass partitioning of six, nine-year old E.benthamii trees, all leaves were separated from the branches following the stem sampling. All leaves and branches were weighed separately in the field to determine the green weight of each compartment. A one-kilogram green weight sample of both branches and foliage were collected from each tree and dried at 60 Celsius to a constant bone dry weight to determine moisture content. Total green weight and moisture content of each compartment was used to estimate the total biomass of each compartment.

Belowground biomass sampling was performed for each of the six E.benthamii sample trees. Prior to beginning root excavation, the leaf litter and duff was removed from the forest floor surface. Sampling and processing protocol was adapted from the protocol outlined by Albaugh, Allen and Kress (2006) for Pinus taeda. A one by one-meter wooden frame was set squarely around each stump. The ground-line was marked on each stump. All soil and roots were then excavated in 20-cm depth increments. All the extracted material at each depth increment was sieved through a four millimeter screen to separate roots and soil.

All roots removed from the tap root during excavation were collected and labeled by sampled tree and depth increment (0-20 cm, 20-40 cm, 40-60 cm, 60-80 cm, 80-100 cm and 100+ cm). Roots were excavated to a depth of one-meter. The tap root was then excavated and any remaining roots were excavated and labeled accordingly. Tap roots were cut according to the depth from the marked ground line. All root samples were cleaned and dried at 60

Celsius to a constant bone dry weight. The total biomass of the six E.benthamii sample trees

can be estimated using the dry weight estimations of each compartment (canopy, branch, stem, stem bark and root).

The allocation of biomass for Eucalyptus benthamii was examined. Using the green weight and moisture content from a one-kilogram sample of each above-ground compartment, the total biomass (dry weight) was estimated. Roots were collected, dried to a constant weight and weighed at each sample depth. In total, the biomass of five compartments were examined: canopy, branches, stem bark, stem wood and coarse roots.

The biomass of each compartment can be estimated using a logarithm equation form for each compartment. By definition, the summation of each compartment can then be used to estimate the total biomass for a given tree. The following equation form for each compartment is

훽 2𝑖 푊𝑖 = 훽1𝑖퐷 + 휀 (1.10)

푡ℎ where 푊𝑖 is the dry weight (kg) for the 𝑖 compartment, 훽푛𝑖 are parameters to be estimated for the 𝑖푡ℎ compartment, 퐷 is the diameter at breast height (cm) and 휀 is the error term. The summation of the prediction equations of each compartment yields the total biomass accumulation.

Statistical Analysis

Statistical analyses for each total stem response variable, volume outside-bark (VOB), volume inside-bark (VIB), green weight outside-bark (GWOB), green weight inside-bark

(GWIB), dry weight outside-bark (DWOB) and dry weight inside-bark (DWIB), for the combined-variable model form were performed utilizing SAS PROC REG (SAS Institute

Inc., 2012). Statistical analysis for each total stem response variable (VOB, VIB, GWOB, 15

GWIB, DWOB, DWIB) for the generalized logarithm and logarithm model forms were performed utilizing SAS PROC NLIN (SAS Institute Inc., 2012). Statistical analysis for each merchantable ratio model forms were performed utilizing SAS PROC NLIN (SAS

Institute Inc., 2012). Statistical analysis for each tree compartment for the logarithmic equation form were performed utilizing the SAS PROC NLIN (SAS Institute Inc., 20012).

Gauss-Newton convergence method was used for each nonlinear model form.

Results and Discussion

The performance of three model forms were evaluated to select the most appropriate model form for a prediction equation of frost tolerant Eucalyptus species in the southeastern

United States. The comparison of various components of the statistical results indicated that the logarithmic model form was the most statistically significant as well as fitting the biological constraints of the system modelled. While the prediction equation of stem wood with and without bark provide a practical application when modelling on larger scales (plot

& landscape), the parameter estimates of volume outside-bark are useful in describing the form or shape of the stem as it deviates from that of a cone.

Individual stem volume, green weight and biomass

All stem volume, green weight and biomass both outside- and inside-bark were found to be statistically significant (alpha level = 0.05). The objective of the work is to determine the most appropriate model form (combined-variable or logarithmic). Therefore, the coefficient of determination and pseudo-coefficient of determination values were examined

for each model for each response variable. The residual plots were also examined for each response variable to be considered in conjunction with the coefficient of determination as well as the significance of each parameter estimate.

The descriptive statistics for various bole attributes pertaining to the complete observed dataset have been compiled in Table 1.1. The harvested trees ranged from 4.0 to

32.3-cm and 6.6 to 25.5-m in diameter at breast (dbh) and total height respectively. The mean dbh is 13.8-cm with a standard error of 0.98-cm. The mean total height is 11.8-m with a standard error of 0.84-m. Double bark thickness ranged from 1.2 to 14.0-cm with a mean of 5.4-cm. Volume outside-bark ranged from 0.0051 to 0.8210-m3 with a mean of 0.1190- m3. Volume inside-bark ranged from 0.0045 to 0.6660-m3 with a mean of 0.0992-m3. Green weight outside-bark ranged from 3.0 to 825.0-kg with a mean of 113.8-kg. Green weight inside-bark ranged from 2.6 to 701.3-kg with a mean of 98.89-kg. Stem biomass with bark ranged from 2.1 to 349.9-kg with a mean of 53.2-kg. Stem biomass without bark ranged from 1.8 to 310.9-kg with a mean of 46.3-kg.

A simple linear regression (SLR) was performed using the combined-variable (D2H) model form for each response variable (VOB, VIB, GWOB, GWIB, DWOB and DWIB).

All models were found to be statistically significant beyond the alpha-level 0.05 (Table 1.3).

The combined-variable D2H model explained more than 97.6% of the variation for each response variable. The residual plots in figure 1.3 show that the combined-variable model form is adequate at predicting stem volume, green weight and dry weight both inside- and outside-bark for cold tolerance Eucalyptus species. The parameter estimates, standard errors, t-value and p-value for each response variable are reported in table 1.4. The slope parameter estimate, 훽1, was found to be significant for each response variable. The slope parameter

estimate decreased without the presence of bark for each response variable volume, green weight and dry weight. However, the y-intercept parameter estimate, 훽0, was significant for only the VOB and VIB response variables. Furthermore, the combined-variable model form yielded negative estimates for the y-intercept parameter of GWOB and GWIB failing to conform to the biological system under investigation.

A nonlinear regression was performed for both the generalized logarithmic and logarithmic model forms to develop prediction equations for each response variable (VOB,

VIB, GWOB, GWIB, DWOB and DWIB). The inclusion of the generalized logarithmic model form was necessary to ensure it was not necessary to include a y-intercept parameter estimate.

All generalized logarithmic models were found to be statistically significant beyond the alpha-level 0.05 (Table 1.5). The parameter estimates for the generalized logarithmic model form show that the y-intercept terms for each response variable is not significant at the alpha-level 0.05 (Table 1.6). By concluding the y-intercept parameter estimate is not significantly different from zero, the y-intercept parameter estimate can be “fixed” at zero.

This analysis method conforms to the biological system rather than accepting potential negative y-intercept parameter estimates. A conclusion can be drawn that the logarithmic model form would be more appropriate to compare to the combined-variable model form.

A nonlinear regression was performed for the logarithmic model form to develop prediction equations for each response variable (VOB, VIB, GWOB, GWIB, DWOB and

DWIB). All models were found to be significant beyond alpha level 0.05 (Table 1.7). The logarithmic model form explained more than 99.1% of the variation for each response variable. The residual plots (Figure 1.5) show the logarithmic model form does a good job

predicting volume, green weight and dry weight both outside- and inside-bark with no patterns in the residuals. The estimates, approximate standard errors and approximate 95% confidence interval of each parameter for each dependent variable (Table 1.8). Examining the parameter estimates for volume outside- and inside-bark shows that the logarithmic model form decreased the parameter estimate of diameter at breast height (dbh) while the slope and height parameter estimates remain similar. This shows the logarithmic model excelling in remaining consistent between models. The green weight and dry weight logarithmic model parameter estimates begin to diverge from the theoretical concepts as confounding elements such as moisture content and wood density are introduced respectively. The logarithmic model form performs well when comparing the outside- and inside-bark for both green weight and dry weight parameter estimates. However, the model accounts for the absence of bark for both green weight and dry weight by decreasing the estimate of total height and dbh estimates remain relatively consistent.

The performance of three allometric model forms were examined to determine the best set of prediction equations of volume, green weight and dry with and without the presence of bark for E.benthamii in the southeastern United States. Based on the coefficient of determination and the residual plots, the logarithmic model form consistently outperformed the combined-variable and generalized logarithmic model forms. The logarithmic model was the best for developing a prediction equation for each response variable when compared to the combined-variable and generalized logarithmic model forms.

The significance at alpha level 0.05 was examined for each parameter estimate for each model and response variable. The y-intercept parameter estimate was not significant for the volume response variables using the combined-variable model form and also for all response

variables using the generalized logarithmic model form. The parameter estimates associated with the dbh and height of the logarithmic model form allowed for increased sensitivity to the resultant prediction equation compared to the combined-variable model form.

Merchantable ratio of frost tolerant Eucalyptus

Merchantable stem wood can be more powerful than total stem wood when predicting available stem wood for the mill or performing economic valuations. Merchantable ratio can be used in conjunction with total stem wood to determine merchantable stem wood. A nonlinear regression was performed to develop a merchantable ratio based on diameter outside-bark (Burkhart merchantable ratio) up the stem for each response variable. All models were significant at or beyond the alpha level 0.05 (Table 1.9). The Burkhart merchantable ratio model explained more than 93.1% of the variation for each response variable. The parameter estimates, approximate standard errors and approximate 95% confidence intervals of each parameter for each dependent variable are reported in Table

1.10. Based on the confidence limits of each parameter estimates for each dependent variable, all parameter estimates were found to significant at the alpha-level 0.05.

A nonlinear regression was performed to develop a prediction equation based on merchantable height (Modified Burkhart merchantable ratio) for each response variable. All models were found to be significant at or beyond the alpha level 0.05 (Table 1.11). The

Modified Burkhart merchantable ratio model explained more than 98.3% of the variation for each response variable. Based on the confidence limits of each parameter estimates for each dependent variable, all parameter estimates were found to be significant at the alpha-level

0.05 (Table 1.12.

The coefficient of determination showed that the Modified Burkhart merchantable ratio model form based on the relative height performed better at predicting the ratio of the stem dependent variables compared to the Burkhart merchantable ratio using diameter outside-bark. Therefore, from a practical perspective, the Modified Burkhart merchantable ratio prediction equation in conjunction with the logarithmic model prediction equation are best suited for estimating merchantable volume, green weight or dry weight both outside- and inside-bark for cold tolerance Eucalyptus species in the southeastern United States.

However, the power of functions is realized by setting them equal and solving for the limiting merchantable value, diameter outside-bark or merchantable height, to estimate the missing value.

Biomass partitioning of Eucalyptus benthamii

The logarithmic model from with diameter at breast height (dbh) as the independent variable was able to accurately predict the biomass (kg) for each Eucalyptus benthamii compartment (coarse root, stem wood, stem bark, branch and foliage). Furthermore, dbh was found to have a significant correlation with total aboveground woody material. There was also positive linear relationship between stem biomass and root biomass.

The descriptive statistics for various growth attributes of the complete tree biomass per compartment dataset have been compiled in Table 1.2. Diameter at breast height (dbh) ranged from 14.1 to 32.3-cm with a mean of 21.6-cm. The total height ranged from 18.1 to

25.5-m with a mean of 23.3-m. The double bark thickness at breast height ranged from 5.5 to 14.0-cm with a mean of 8.4-cm. Foliage biomass ranged from 1.6 to 21.6-kg with a mean of 8.4-kg. Stem biomass ranged from 40.0 to 310.9-kg with a mean of 162.2-kg. Stem bark

biomass ranged from 6.5 to 39.0-kg with a mean of 21.1-kg. Branch biomass ranged from

2.9 to 98.6-kg with a mean of 30.2-kg. Coarse root biomass ranged from 7.7 to 62.3-kg with a mean of 31.0-kg.

Aboveground biomass was estimated by summing the stem wood, stem bark and branch compartments. Aboveground biomass ranged from 49.4 to 448.5-kg with a mean of

213.5-kg and standard error of 56.64-kg. Total biomass was estimated by summing aboveground biomass and coarse roots compartments. Total biomass ranged from 57.1 to

510.7-kg with a mean of 244.5-kg and standard error of 64.27-kg. The average aboveground and belowground breakup of total biomass was 88% and 12% respectively. Of the total observed aboveground biomass; 73.1% was allocated to stem wood, 9.5% was allocated to stem bark, 13.6% was allocated to branches and 3.8% was allocated to foliage. Of the total observed woody biomass; 66.4% was allocated to stem wood, 8.6% was allocated to stem bark, 12.3% was allocated to branches and 12.7% was allocated to coarse roots. The ratio of biomass allocation between coarse roots and stem wood was found to be 19.1%.

A nonlinear regression was used to develop a logarithmic prediction equation (dbh only) for each compartment (bole, bole with bark, branches, foliage, coarse roots, aboveground woody and total woody). All models were found to be significant beyond the alpha level 0.05 (Table 1.13). The logarithmic model form explained more than 96.4% of the variation for each response variable. The slope parameter estimates, approximate standard error and 95% confidence interval for each response variable can be seen in table 1.14. The parameter estimates of the logarithmic model of foliage varied in significance with the exponential parameter estimate of diameter at breast height (dbh) being significant at alpha level 0.05 based on the 95% confidence interval. Stem wood was modeled with and without

the presence of bark. The increase in the slope parameter estimate, while the parameter estimate of dbh remained relatively constant, with the presence of stem bark biomass explained the increase in bole biomass. The branch parameter estimates varied greatly compared to other compartments. The slope parameter estimate was the smallest and the parameter estimate for dbh was the greatest when compared to prediction equations of the other compartments. The logarithmic model of total aboveground woody biomass was found to be significant beyond alpha level 0.05 and explained more than 97.7% of the variation based on the coefficient of determination. The total aboveground woody biomass prediction equation is a valuable allometric equation when determining whole tree harvesting yields.

The coarse root logarithmic model parameter estimate of dbh was the only significant parameter estimates. The coarse root prediction equation can provide information related to belowground carbon stocks as well as investigation the root to shoot ratios. Total woody biomass was with the inclusion of coarse roots with the aboveground woody biomass components. The logarithmic model for explained more than 97.8% of the variation in total woody biomass based on the coefficient of determination.

The biomass partitioning of the above-ground components (stem wood, bark, branches and foliage) of nine-year old Eucalyptus benthamii planted near Ravenel, South

Carolina, USA were consistent with four-year old E.benthamii planted in Guarapuava,

Paraná State, Brazil reported by da Silva et al. (2004). While the partitioning of the aboveground components are similar, it is important to understand that the significant difference in age of the sample trees suggest that it is necessary to further investigate the allocation of biomass by compartment for each age class of E.benthamii planted in the southeastern United

States. The root:shoot ratio of the E.benthamii trees sampled at the Ravenel, SC site was

estimated to be 0.17. This is consistent with high productive E.grandis plantations examined in northeastern Bahia, Brazil (Stape et al., 2004). Comparing these findings with those reported from Brazilian studies that there are indeed similarities in the allocation of biomass.

However, extrapolating this information to examine the complete rotation of these systems is not recommended. Aside from estimating biomass by compartment outside the sample distribution used in the modeling process, comparing allocation of biomass at a given age with previous Brazilian studies, may suggest that E.benthamii is allocating biomass at a different rate which could suggest there is an edaphic, climatic and other effects.

Conclusion

Using data from 40 cold tolerant Eucalyptus species of the section Maidenaria grown in the southeastern United States, three allometric model forms (combined-variable, generalized logarithmic and logarithmic) were examined to select the best prediction equation for volume, green weight and dry weight both outside- and inside-bark. The logarithmic model form yielded the best results for the estimation of the response variables previously stated. The logarithmic model form was able to explain more of the variability within the data set based on the coefficient of determination, and the parameter estimates of the prediction equations for each response variable were significant (at or beyond alpha-level

= 0.05) while not violating any of the assumptions of the biological system. The Modified

Burkhart merchantable ratio model form using the merchantable and total heights explained more of the variation within the data compared to the Burkhart merchant ratio model form using the upper limit diameter outside-bark and diameter at breast height based on the

coefficient of determination. However, both merchantable ratio model forms explained more than 93% of the variation in the data showing that both methods are applicable.

Estimating the biomass of each compartment of six nine-year old E.benthamii trees in

South Carolina provided insight to the distribution and allocation of resources by this tree species. The modified (dbh only) logarithmic model performed well at estimating the biomass for each compartment of E.benthamii. The ability to estimate the total woody biomass aboveground is useful for harvesting systems such as whole-tree chipping that could become more common for biomass production. Also, understanding the belowground allocation of biomass when assessing carbon stocks and sustainability of the forest systems.

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McLaughlin, S.B. and L.A. Kszos. 2005. Biomass and bioenergy development of switchgrass (Panicum virgatum) as a bioenergy feedstock in the United States. Biomass and Bioenergy 28: 515-535.

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Table 1.1. Summary statistics for total stem volume, green weight and biomass of frost tolerant Eucalyptus.

Variables n Mean Standard error Minimum Maximum Skewness Kurtosis Bole attributes Dbh (cm) 40 13.9 0.98 4.0 32.3 0.5679 0.5826 Height (m) 40 11.8 0.84 6.6 25.5 1.6263 1.7635 Bark thickness (cm) 40 5.37 2.87 1.2 14.0 0.7413 0.7577 Volume (m3) Outside-bark 40 0.1190 0.0248 0.0051 0.8210 2.9867 10.5760 Inside-bark 40 0.0992 0.0202 0.0045 0.6660 2.9148 10.0923 Green weight (kg) Outside-bark 40 113.8 26.2 3.0 852.0 3.0460 10.5705 Inside-bark 39 98.9 22.1 2.6 701.3 2.9403 9.9533 Biomass (kg) Outside-bark 39 53.2 11.3 2.1 349.9 2.7718 8.6416 Inside-bark 39 46.3 10.0 1.8 310.9 2.7923 8.7477

15 Total height (m) height Total 10

0 0 5 10 15 20 25 30 35 Diameter at breast height (cm)

Figure 1.1. Scatter plot of sample trees for each species.

Table 1.2. Summary statistics for total tree biomass by compartment of Eucalyptus benthamii (n = 6).

Biomass by compartment (kg tree-1) dbh height Bark thickness Stem Stem Branch Aboveground Foliage Coarse Total Attribute (cm) (m) (cm) wood bark woody roots woody Mean 21.6 23.3 8.4 162.2 21.1 30.2 213.5 8.4 31.0 244.5 Standard error 2.55 1.14 1.22 37.44 4.91 15.10 56.64 2.89 7.67 64.27 Minimum 14.1 18.1 5.5 40.0 6.5 2.9 49.4 1.6 7.7 57.1 Maximum 32.3 25.5 14.0 310.9 39.0 98.6 448.5 21.6 62.3 510.7 Skewness 0.947 -1.640 1.586 0.602 0.562 1.655 0.972 1.607 0.837 0.960 Kurtosis 1.238 2.854 2.873 0.880 -0.719 2.352 0.995 2.841 0.933 0.998

500 Stem_wood 450 Stem_bark 400 Branch Canopy 350 root 300

250

200

Biomass Biomass (kg) 150

100

-50

-100

Figure 1.2. Biomass partitioning of 9-year old Eucalyptus benthamii in South Carolina.

Table 1.3. Analysis of variance for the combined-variable model form for each response variable.

Source df Sum of squares Mean square F value Pr > F VOB Model 1 0.95352 0.95352 4881.52 < 0.0001 Error 38 0.00742 0.00019533 Total 39 0.96094 VIB Model 1 0.63363 0.63363 4022.07 < 0.0001 Error 38 0.00599 0.00015754 Total 39 0.63962 GWOB Model 1 1052834 1052834 2133.58 < 0.0001 Error 38 18751 493.45857 Total 39 1071585 GWIB Model 1 710085 710085 2281.20 < 0.0001 Error 37 11517 311.27688 Total 38 721602 DWOB Model 1 184393 184393 1601.71 < 0.0001 Error 37 4259.53043 115.12244 Total 38 188652 DWIB Model 1 145117 145117 1561.13 < 0.0001 Error 37 3439.37222 92.95601 Total 38 148556

Table 1.4. Parameter estimates for the combined-variable model form for each response variable.

Parameter Estimate Standard error t Value Pr > |t| VOB Intercept 0.00681 0.00273 2.49 0.0171 d2h 0.00003176 4.546091E-7 69.87 < 0.0001 VIB Intercept 0.00783 0.00245 3.19 0.0028 d2h 0.00002589 4.082671E-7 63.42 < 0.0001 GWOB Intercept -4.01517 4.34103 -0.92 0.3608 d2h 0.03338 0.00072256 46.19 < 0.0001 GWIB Intercept -0. 33258 3.50673 -0.09 0.9250 d2h 0.02753 0.00057644 47.76 < 0.0001 DWOB Intercept 2.66100 2.13260 1.25 0.2200 d2h 0.01403 0.00035056 40.02 < 0.0001 DWIB Intercept 1.44192 1.91632 0.75 0.4565 d2h 0.01245 0.00031501 39.51 < 0.0001

0.90 ) 3 A 0.75 0.60 0.45

0.30 1:1 line 0.15 VOB

Predicted volume (m volume Predicted VIB 0.00 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 3 Observed volume (m )

900 B 750 600 450 300 1:1 line 150 GWOB

Predicted green wt. (kg) wt. green Predicted GWIB 0 0 100 200 300 400 500 600 700 800 900 Observed green weight (kg)

400 350 C 300 250 200 150 1:1 line 100 DWOB 50 Predicted dry wt.(kg) Predicted DWIB 0 0 50 100 150 200 250 300 350 400 Observed dry weight (kg) Figure 1.3. Scatter plot of actual versus predicted A) volume, B) green weight and C) dry weight for the combined-variable model form.

Table 1.5. Analysis of variance for the generalized logarithmic model form for each response variable.

Source df Sum of squares Mean square F value Pr > F VOB Model 3 0.9568 0.3189 2771.29 < 0.0001 Error 36 0.00414 0.000115 Corrected Total 39 0.9609 VIB Model 3 0.6368 0.2123 2748.63 < 0.0001 Error 36 0.00278 0.000077 Corrected Total 39 0.6396 GWOB Model 3 1064262 354754 1743.87 < 0.0001 Error 36 7323.4 203.4 Corrected Total 39 1071585 GWIB Model 3 715738 238579 1423.95 < 0.0001 Error 35 5864.2 167.5 Corrected Total 38 721602 DWOB Model 3 187322 62440.6 1642.82 < 0.0001 Error 35 1330.3 38.0083 Corrected Total 38 188652 DWIB Model 3 147560 49186.8 1728.93 < 0.0001 Error 35 995.7 28.4493 Corrected Total 38 148556

Table 1.6. Parameter estimates for the generalized logarithmic model form for each response variable.

Approx. Approximate 95% Parameter Estimate Standard Error Confidence Limits VOB

훽2 0.00185 0.00360 -0.00546 0.00916 훽3 0.000049 9.531E-6 0.000029 0.000068 훽4 1.7419 0.0495 1.6415 1.8422 훽5 1.1367 0.0479 1.0396 1.2337 VIB

훽2 0.00127 0.00302 -0.00485 0.00740 훽3 0.000049 9.531E-6 0.000030 0.000069 훽4 1.6818 0.0490 1.5824 1.7811 훽5 1.1338 0.0472 1.0382 1.2295 GWOB

훽2 1.5803 4.6128 -7.7748 10.9355 훽3 0.0260 0.00721 0.0114 0.0406 훽4 1.6602 0.0621 1.5343 1.7861 훽5 1.4304 0.0736 1.2811 1.5796 GWIB

훽2 -0.2995 4.3866 -9.2048 8.6059 훽3 0.0313 0.00913 0.0128 0.0499 훽4 1.6635 0.0682 1.5251 1.8019 훽5 1.3103 0.0743 1.1594 1.4612 DWOB

훽2 -0.2354 2.2109 -4.7237 4.2529 훽3 0.0259 0.00693 0.0119 0.0400 훽4 1.4870 0.0612 1.3628 1.6112 훽5 1.3448 0.0679 1.2070 1.4827 DWIB

훽2 -0.2048 1.8920 -4.0458 3.6362 훽3 0.0199 0.00528 0.00913 0.0306 훽4 1.4856 0.0598 1.3643 1.6069 훽5 1.3912 0.0686 1.2520 1.5305

0.90 )

3 A 0.75 0.60 0.45

0.30 1:1 line 0.15 VOB

Predicted volume (m volume Predicted VIB 0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 3 Observed volume (m )

900 B 750 600 450 300 1:1 line 150 GWOB

Predicted green wt. (kg) wt. green Predicted GWIB 0 0 100 200 300 400 500 600 700 800 900 Observed green weight (kg)

400 350 C 300 250 200 150 1:1 line 100 DWOB

Predicted drywt. (kg) Predicted 50 DWIB 0 0 50 100 150 200 250 300 350 400 Observed dry weight (kg) Figure 1.4. Scatter plot of actual versus predicted A) volume B) green weight and C) dry weight for the generalized logarithmic model form.

Table 1.7. Analysis of variance for the logarithmic model form for each response variable.

Source df Sum of squares Mean square F value Pr > F VOB Model 3 1.5228 0.5076 4500.47 < 0.0001 Error 37 0.004174 0.000113 Uncorrected Total 40 1.5269

Corrected Total 0.9609436 VIB Model 3 1.0308 0.3436 4550.58 < 0.0001 Error 37 0.00279 0.000076 Uncorrected Total 40 1.0336

Corrected Total 0.6396188 GWOB Model 3 1582456 527485 2656.47 < 0.0001 Error 37 7347.0 198.6 Uncorrected Total 40 1589803

Corrected Total 1071584.98 GWIB Model 3 1097121 365707 2244.78 < 0.0001 Error 36 5864.9 162.9 Uncorrected Total 39 1102986

Corrected Total 721602.44 DWOB Model 3 297796 99265.2 2685.43 < 0.0001 Error 36 1330.7 36.9644 Uncorrected Total 39 299126

Corrected Total 188652.05 DWIB Model 3 231153 77050.9 2784.82 < 0.0001 Error 36 996.1 27.6682 Uncorrected Total 39 232149

Corrected Total 148556.21

Table 1.8. Parameter estimates for the logarithmic model form for each response variable.

Approx. Approximate 95% Parameter Estimate Standard Error Confidence Limits VOB

훽6 0.000053 5.761E-6 0.000041 0.000065 훽7 1.7307 0.0435 1.6426 1.8187 훽8 1.1236 0.0398 1.0430 1.2042 VIB

훽6 0.000053 5.601E-6 0.000041 0.000064 훽7 1.6726 0.0429 1.5857 1.7595 훽8 1.1231 0.0391 1.0439 1.2023 GWOB

훽6 0.0281 0.00438 0.0192 0.0370 훽7 1.6527 0.0567 1.5378 1.7675 훽8 1.4149 0.0571 1.2992 1.5306 GWIB

훽6 0.0308 0.00504 0.0206 0.0410 훽7 1.6653 0.0615 1.5406 1.7900 훽8 1.3134 0.0598 1.1922 1.4346 DWOB

훽6 0.0253 0.00365 0.0179 0.0327 훽7 1.4894 0.0552 1.3775 1.6014 훽8 1.3494 0.0532 1.2415 1.4574 DWIB

훽6 0.0194 0.00280 0.0137 0.0251 훽7 1.4880 0.0543 1.3778 1.5981 훽8 1.3960 0.0533 1.2880 1.5040

0.90 ) 3 A 0.75 0.60 0.45

0.30 1:1 line 0.15 VOB

Predicted volume (m volume Predicted VIB 0.00 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 3 Observed volume (m )

900 B 750 600 450 300 1:1 line 150 GWOB

Predicted green wt. (kg) wt. green Predicted GWIB 0 0 100 200 300 400 500 600 700 800 900 Observed green weight (kg)

400 350 C 300 250 200 150 100 1:1 line DWOB

Predicted drywt. (kg) Predicted 50 DWIB 0 0 50 100 150 200 250 300 350 400 Observed dry weight (kg)

Figure 1.5. Scatter plot of actual versus predicted A) volume B) green weight and C) dry weight for the logarithmic model form.

Table 1.9. Analysis of variance for merchantable ratio (dob) model form for each response variable.

Source df Sum of squares Mean square F value Pr > F VOB Model 3 223.8 74.6049 12151.7 < 0.0001 Error 406 2.4926 0.00614 Uncorrected Total 409 226.3

Corrected Total 38.9975740 VIB Model 3 222.8 74.2508 11623.3 < 0.0001 Error 406 2.5936 0.00639 Uncorrected Total 409 225.3

Corrected Total 39.7149258 GWOB Model 3 229.8 76.6043 12114.3 < 0.0001 Error 406 2.5673 0.00632 Uncorrected Total 409 232.4

Corrected Total 38.0417308 GWIB Model 3 224.7 74.9012 11593.0 < 0.0001 Error 396 2.5585 0.00646 Uncorrected Total 399 227.3

Corrected Total 37.3653544 DWOB Model 3 214.4 71.4544 12193.0 < 0.0001 Error 396 2.3207 0.00586 Uncorrected Total 399 216.7

Corrected Total 37.6479979 DWIB Model 3 213.8 71.2751 12075.9 < 0.0001 Error 396 2.3373 0.00590 Uncorrected Total 399 216.2

Corrected Total 37.9687271

Table 1.10. Parameter estimates for the merchantable ratio (dob) model form for each response variable.

Approx. Approximate 95% Parameter Estimate Standard Error Confidence Limits VOB

훼1 -0.3272 0.0182 -0.3630 -0.2914 훼2 2.4053 0.0454 2.3159 2.4946 훼3 2.1541 0.0445 2.0666 2.2416 VIB

훼1 -0.3322 0.0187 -0.3689 -0.2955 훼2 2.3965 0.0459 2.3064 2.4867 훼3 2.1478 0.0449 2.0595 2.2362 GWOB

훼1 -0.3176 0.0184 -0.3539 -0.2814 훼2 2.4894 0.0483 2.3945 2.5843 훼3 2.2372 0.0471 2.1447 2.3298 GWIB

훼1 -0.3144 0.0187 -0.3512 -0.2776 훼2 2.4987 0.0494 2.4017 2.5958 훼3 2.2436 0.0480 2.1493 2.3379 DWOB

훼1 -0.3647 0.0196 -0.4023 -0.3262 훼2 2.3355 0.0437 2.2496 2.4214 훼3 2.1230 0.0428 2.0388 2.2071 DWIB

훼1 -0.3731 0.0199 -0.4123 -0.3339 훼2 2.3310 0.0436 2.2453 2.4168 훼3 2.1253 0.0427 2.0413 2.2093

Table 1.11. Analysis of variance for the merchantable ratio (ht) model form for each response variable.

Source df Sum of squares Mean square F value Pr > F VOB Model 3 225.9 75.3017 76035.7 < 0.0001 Error 406 0.4021 0.000990 Uncorrected Total 409 226.3

Corrected Total 38.997574 VIB Model 3 224.9 74.9832 76782.0 < 0.0001 Error 406 0.3965 0.000977 Uncorrected Total 409 225.3

Corrected Total 39.7149258 GWOB Model 3 231.8 77.2690 54755.1 < 0.0001 Error 406 0.5729 0.00141 Uncorrected Total 409 232.4

Corrected Total 38.0417308 GWIB Model 3 226.6 75.5446 47617.3 < 0.0001 Error 396 0.6283 0.00159 Uncorrected Total 399 227.3

Corrected Total 37.3653544 DWOB Model 3 216.2 72.0820 65196.8 < 0.0001 Error 396 0.4378 0.00111 Uncorrected Total 399 216.7

Corrected Total 37.6479979 DWIB Model 3 215.7 71.9014 62114.1 < 0.0001 Error 396 0.4584 0.00116 Uncorrected Total 399 216.2

Corrected Total 37.9687271

Table 1.12. Parameter estimates for the merchantable ratio (ht) model form for each response variable.

Approx. Approximate 95% Parameter Estimate Standard Error Confidence Limits VOB

훼4 -0.8871 0.0194 -0.9251 -0.8490 훼5 2.7607 0.0236 2.7143 2.8070 훼6 2.7191 0.0249 2.6702 2.7680 VIB

훼4 -0.8871 0.0190 -0.9246 -0.84975 훼5 2.7468 0.0231 2.7014 2.7922 훼6 2.7025 0.0244 2.6545 2.7504 GWOB

훼4 -0.8830 0.0236 -0.9294 -0.8366 훼5 2.9064 0.0302 2.8470 2.9658 훼6 2.8655 0.0317 2.8032 2.9278 GWIB

훼4 -0.8537 0.0248 -0.9025 -0.8049 훼5 2.9526 0.0329 2.8878 3.0173 훼6 2.8975 0.0345 2.8297 2.9654 DWOB

훼4 -0.9351 0.0220 -0.9783 -0.8919 훼5 2.6800 0.0245 2.6319 2.7281 훼6 2.6624 0.0259 2.6115 2.7133 DWIB

훼4 -0.9477 0.0227 -0.9923 -0.9030 훼5 2.6732 0.0249 2.6242 2.7221 훼6 2.6595 0.0263 2.6077 2.7112

Table 1.13. Analysis of variance of the logarithmic (dbh only) model form for each tree compartment.

Source df Sum of squares Mean square F value Pr > F Stem wood Model 2 198540 99270.1 275.71 < 0.0001 Error 4 1440.2 360.0 Uncorrected Total 6 199980

Corrected Total 42060.97 Stem wood & bark Model 2 253215 126608 264.96 < 0.0001 Error 4 1911.3 477.8 Uncorrected Total 6 255127

Corrected Total 53548.16 Branch Model 2 12081.0 6040.5 107.01 0.0003 Error 4 225.8 56.4486 Uncorrected Total 6 12306.8

Corrected Total 6839.08 Foliage Model 2 671.3 335.7 255.43 < 0.0001 Error 4 5.2565 1.3141 Uncorrected Total 6 676.6

Corrected Total 251.3205900 Root Model 2 7471.9 3736.0 325.85 < 0.0001 Error 4 45.8617 11.4654 Uncorrected Total 6 7517.8

Corrected Total 1763.29 Aboveground woody Model 2 367565 183783 343.84 < 0.0001 Error 4 2138.0 534.5 Uncorrected Total 6 369703

Corrected Total 96258.85 Total woody Model 2 479795 239897 358.80 < 0.0001 Error 4 2674.4 668.6 Uncorrected Total 6 482469

Corrected Total 123934.32

Table 1.14. Parameter estimates for the logarithmic (dbh only) model form for each tree compartment.

Approx. Approximate 95% Parameter Estimate Standard Error Confidence Limits Stem wood

훽1 0.6174 0.36860 -0.4061 1.6409 훽2 1.7993 0.1820 1.2940 2.3047 Stem wood & bark

훽1 0.7065 0.4300 -0.4873 1.9004 훽2 1.7953 0.1856 1.2801 2.3105 Branch

훽1 0.000168 0.000286 -0.00063 0.000962 훽2 3.8283 0.4985 2.4441 5.2124 Foliage

훽1 0.00148 0.00117 -0.00176 0.00472 훽2 2.7600 0.2340 2.1105 3.4096 Root

훽1 0.0747 0.0423 -0.0427 0.1921 훽2 1.9432 0.1717 1.4664 2.4200 Aboveground woody

훽1 0.3303 0.1878 -0.1909 0.8516 훽2 2.0833 0.1718 1.6064 2.5601 Total woody

훽1 0.4002 0.2217 -0.2155 1.0158 훽2 2.0656 0.1675 1.6004 2.5307

30 Root biomass (kg) biomass Root 20

10 y = 0.1714x R² = 0.9852 0 0 50 100 150 200 250 300 350 400 Stem biomass (kg)

Figure 1.6. Root and stem biomass ratio. Linear regression with fixed intercept through the origin.

CHAPTER TWO: A GROWTH AND YIELD MODEL FOR EUCALYPTUS

BENTHAMII IN THE SOUTHEASTERN UNITED STATES

Introduction

The southern United States consists of 86.9 million hectares of forestland in which nearly 21 percent are planted timberlands (Smith et al., 2009). Furthermore, there are approximately 2 million hectares of idle agricultural fields in the southeastern United States

(SE US) that could be converted to short-rotation woody crops (SRWC) (Kline and Coleman,

2010). Perlack et al. hypothesized that a change in the land use of agricultural fields (while meeting the USDA baseline projection for food and feed demands) to perennial crops could range from 16 to 24 million hectares when yields reach 10 and 19 dry tons ha-1 yr-1 respectively (2005).

In order for perennial crops to meet the demand of the biomass market as outlined by the “30 x ‘30” goal for a 30 percent replacement of United States petroleum consumption with biofuels by 2030, a variety of species and management practices are necessary in the

United States. Furthermore, haul distances must be minimized for raw materials and refined bio-oils and -fuels costs. This will require the matching of species and management practices to a variety of edaphic and climatic conditions across all regions of the United States

(Simmons et al., 2008). In the northeastern United States, the Salix Consortium has established over 280 hectares of shrub willow (native cultivars) research varying from research- to commercial-scale (Volk et al., 2006). Current efforts of shrub willow biomass systems in northeastern United States have average yields of 7.5 dry tons ha-1 yr-1 for first- rotation commercial-scale plantings compared to fertilized and irrigated willow grown in

Europe on three-year rotations yielding 10 dry tons ha-1 yr-1 (Volk et al., 2006; Christersson 49

et al., 1993). Populus clones were found to outperform willow clones under coppice management in Michigan by approximately 30 percent (Wang and MacFarlane, 2012).

Hybrid poplar clones have been planted in the north central United States on marginal agricultural fields (Headlee et al., 2013; Goerndt and Mize, 2008). Netzer et al. (2002) reported the yield of hybrid poplar total aboveground biomass (25-tree blocks) on better sites

(former agricultural fields) in Wisconsin, Minnesota and the eastern Dakota averaging 9 Mg ha-1 yr-1 on sites with current annual increment maximized between years seven and 11 at

1736 trees per hectare.

The southern United States is often referred to as the wood basket of the United

States as a result of pine plantation success and producing more industrial timber than any other region in the world (Schultz, 1997; Allen et al., 2005). Pine plantation forestry has been practiced in the southern United States for more than 50 years which has resulted in intensive silvicultural regimes and tree improvement programs (Fox et al., 2007). Federal, academic and industrial forest research related to seedling production, site establishment, weed control and fertilization have increased the production of southern pine forests from approximately 6 m3 ha-1 yr-1 in the 1950s to nearly 30 m3 ha-1 yr-1 in the 2000s (Fox et al.,

2007). Leveraging the forest industry infrastructure of the southeastern United States to establish, manage and harvest short-rotation hardwood crops would increase available biomass for fuel production.

Eucalyptus has been planted extensively outside its’ native range of Australia and surrounding islands to meet a variety of demands including pulp and paper production, sawn timber and energy. Eucalyptus species have desirable wood properties including short fibers and high wood densities best for the production of pulp and paper, charcoal, fuel and sawn

timber (Rockwood et al., 2008). Eucalyptus species were first introduced in Brazil to meet the demand of fuelwood imposed by railroads following the exploitation of the Atlantic and

Araucaria (Araucaria angustifolia) Forests for agriculture and pasture lands, lumber and fuelwood (Brito, 1997). The Eucalyptus plantations of Brazil have increased productivity from 12 m3 ha-1 yr-1 to 40 m3 ha-1 yr-1 through intensive silviculture and matching improved genetic material with proper edaphic and climatic conditions (Stape et al., 2001). The Congo has also planted Eucalyptus species primarily for the production of fuelwood, pulp and sawn timber (Rockwood et al., 2008). From 1985 to 1995, the government of Ethiopia established

2.9 million hectares of fuelwood plantations mainly planted with Eucalyptus globulus to meet the demand of household energy demands (40 percent from wood) (Pukkala and

Pohjonen, 1990) E.globulus established in Ethiopia on eroded hillsides (1850 to 3500 m) with depleted nutrients achieved mean annual increments ranging from 9 to 44 m3 ha-1 yr-1

(Pukkala and Pohjonen, 1990). More than 8 million hectares of Eucalyptus plantations have been established in India, producing low yields ranging from 6 to 10 m3 ha-1 yr-1, have failed to meet the country’s growing demand for pulp and fuelwood due to inferior genetic selections, improper management and the little available nutrients in the soils (Sankaran et al., 2008). While Eucalyptus species have been revered as a genus that thrives in exotic environments, several common themes persists. The genetic selection should consider the similarities of the selected species with the native climate, proper silvicultural regimes including weed control and sufficient fertilization are required to achieve desirable yields from Eucalyptus plantations (Zalesny et al., 2008).

Eucalyptus species have been grown commercially in central and southern Florida primarily for the production of mulch wood since the 1970s (Rockwood, 2012). Eucalyptus

short-rotation woody crops have also been implemented on clay settling areas following the mining of phosphate in southern Florida to reclaim the sites from invasive cogongrass

(Langholtz et al., 2007). However, the cold tolerance of certain Eucalyptus species, such as

E.grandis, has limited the expansion of these plantation forests further north beyond central

Florida. The 2012 United States Department of Agriculture (USDA) Plant Hardiness Zone

Map (PHZM) provides insight to the geographic distribution of perennial plant species based on injury as a result of extreme cold (Daly et al., 2012). The 2012 USDA PHZM employs the Plant Hardiness (PH; the lowest temperature recorded in a year) statistic from 1976 to

2005 (30 year sample size) to provide thirteen 5.6C full zones (1 being coldest and 13 being warmest) that are separated in to 2.8C half zones, “a” or “b” (Daly et al., 2012). The current

USDA PHZM shows that Eucalyptus plantations in Florida occur in the 9b zone were the average annual extreme temperature (1976-2005) has ranged from -3.9 to -1.1C.

Cold-tolerant Eucalyptus species have been investigated in the SE US for more than forty years (Kellison et al., 2012). However, since these trials ended in the mid-1980s, there has been a continued effort to investigate the growth and cold tolerance of several Eucalyptus species in Brazil (Higa and Carvalho, 1990). A study in Dois Vizinhos, Paraná state Brazil showed that E.benthamii along with E.dunnii and the hybrid E. “cambiju” were the best performers (based on survival, total height and diameter at breast height) out of twelve species 45-months after planting (Higa and Carvalho, 1990). Eucalyptus benthamii has shown tolerance to drought, frost and low temperatures and has survived in absolute minimum temperatures ranging from -6 to -10C in Hunan Province, China (Mujiu et al.,

2003). E.benthamii was first introduced in southern United States during the 1990s by

Westvaco Corporation and has shown good tolerance to freezing temperatures (Zalesny et al., 52

2011). Expanding the range for Eucalyptus plantations with in the southeastern United States with E.benthamii can provide a desirable raw material for bioproducts, pulp and paper.

Eucalyptus silviculture in the southeastern United States

In a recent publication from ArborGen, Eucalyptus benthamii and Eucalyptus macarthurii were reported to have fast growth and sufficient frost tolerance characteristics for the greater portion of the Gulf and Atlantic Coast in the southern US (ArborGen, 2012).

Due to the vast differences between pine and hardwood management, it was fundamental for the success of Eucalyptus planation forests to have a unique, often comparatively more intensive, silvicultural regime. Tree stress caused by lack of available nutrients and weed competition (especially grasses) will reduce productivity without a unique silvicultural regime for Eucalyptus species in the SE US. By reducing stresses caused by weed competition and increasing nutrient availability, Eucalyptus are healthier with greater vigor and are less susceptible to freeze damage (Kellison et al., 2012).

Little attention was devoted to developing a silvicultural prescription for Eucalyptus species in the southeastern United States prior to the 1970s (Gonzalez et al., 2011).

ArborGen has outlined an adequate silvicultural management regime for Eucalyptus species in the southern US. Site selection, avoid excessively well-drained and poorly-drained sites, and seedlings purchases should be in preparation for a fall planting (ArborGen, 2012).

Planting densities may range from 1482 to 2964 trees per hectare based on desired product class of pulpwood or bioenergy, respectively (ArborGen, 2012). Mechanical site preparation

(i.e. subsoiling and/or bedding) is required to optimize soil texture, and chemical site preparation with a summer application of glyphosate prior to planting should be used to

reduce weed competition (ArborGen, 2012). ArborGen recommends containerized seedlings for fall planting which contradicts International Paper Company and Brunswick Paper

Company that claim bareroot seedlings could be planted with success if planted immediately after being removed from the nursery bed flowing the last spring frost (ArborGen, 2012;

Kellison et al., 2012). Fertilization at planting of 170 to 224 kg ha-1 of triple super phosphate on P-deficient sites and a broadcast application of 224 kg ha-1 of urea is recommended after canopy closure (two to three years) (ArborGen, 2012). Prior to canopy closure, direct application of glyphosate is recommended to completely control weed competition

(ArborGen, 2012).

Developing a growth and yield model for Eucalyptus benthamii

The demand of short-rotation hardwood plantations for pulp and paper as well as the potential of a biomass market has increased interests in a cold-hardy Eucalyptus species suitable for the fluctuating winter weather of the southeastern United States (SE US). This has resulted in Eucalyptus species screening and biomass trials (RW24) being installed across the SE US to examine the frost tolerance and biomass potential. The NCSU/ Forest

Productivity Cooperative (FPC) cold tolerance Eucalyptus species screening trial was established with 150 species. After three years, seven species showed sufficient cold- hardiness through the 2010, 2011 and 2012 winters with Eucalyptus benthamii being the best performer. Permanent plots were subsequently installed across the SE US in range of stand sizes, from small research plots to pilot commercial plantations, to be used in conjunction with the FPC screening trials to assess the actual productivity of E.benthamii.

With support of the Integrated Biomass Supply System (IBSS), the FPC and members of the FPC, a network of E.benthamii permanent inventory plots have been installed across the SE US. Standard inventory measurements, leaf are index estimation and soil and foliage samples were taken to provide yield and nutrition information for each plot. The objective of the permanent inventory plot network is to encompass all growing conditions to provide a realistic view of production. E.benthamii plots within the RW24 study were also used as foundation to the permanent plot network resulting in a total of 100 permanent plots.

The objectives of this study are to (1) install a permanent inventory plot network for

E.benthamii in the SE US to be measured biannually, (2) develop initial site quality classification for E.benthamii in the SE US using site index, (3) develop an empirical growth model to estimate the total volume, green weight and biomass of E.benthamii and (4) produce yield tables based on age, stocking and site index.

Materials and Methods

A network of permanent inventory plots were installed to examine the actual productivity of Eucalyptus benthamii across the SE US (Figure 2.1). Sites ranged in latitude from -77.48 (eastern North Carolina) to -94.48 (eastern Texas) latitude degrees west and

26.86 (southern Florida) to 35.82 (central North Carolina) longitude degrees north. Sites ranged in United States Plant Hardiness Zones 7b (central North Carolina) to 9b (south

Florida). Site elevations ranged from six to 160-meters. Stand ages ranged from 10-months to 13-years in age.

Twenty-six permanent plots have been installed ranging in size from 113 to 314 square meters depending on parcel size. An additional seventy-four Eucalyptus benthamii 55

plots were included from the FPC RW24 screening and biomass trials to yield a total of 100 permanent inventory plots. Diameter at breast height (dbh) was measured for all trees and total height was measured for the four largest dbh trees and the first six trees, thus defining the dominant trees, within the plot excluding those that may have been previously measured.

Remaining tree heights were estimated using a linear regression following logarithmic transformations of dbh and total height of the ten measured trees for each plot. The family of allometric equations previously presented were used to estimate total volume, green weight and biomass for each sample tree within each plot based on the inventory data.

Site index classification for Eucalyptus benthamii in SE US

Site index is the mean height of the dominant portion of the stand at an arbitrarily chosen age and is most commonly used as an indicator of site quality (Burkhart and Tomé,

2012). Historically, site quality of forest systems were considered to be a static site characteristic as it related to soil and site characteristics (Fox, 2000). However, intensive silvicultural practices, improved genetics and matching genetics and site conditions have increased site quality for forest systems utilizing both hardwoods and softwoods as the growing stock. Therefore, site index can be manipulated based on a range of stand characteristics such as climate, intensive management regimes and genetic stock to reflect the changes in site quality (Scolforo et al., 2013).

In this study, trees were defined as being in the dominant portion of the stand based on the one-hundred largest dbh trees per hectare (minimum two dominant trees per plot)

(Assmann, 1970). This study developed a family of anamorphic site index curves for cold tolerant Eucalyptus benthamii in the southeastern United States to assess site quality. The

estimation of site index for each inventory plot was then incorporated into the growth and yield model as the site quality parameter.

A simple linear regression (SLR) was performed using dominant height (meter) and age (year) following logarithmic transformations for each variable. The transformation was necessary because mean dominant height has a logarithmic relationship with age; therefore, the reciprocal of age and the logarithm of mean dominant height were used to provide a linear relationship for statistical analysis. The logarithm of height-reciprocal of age model presented by Schumacher (1939) is

−1 ln ℎ푑표푚 = 훽0 + 훽1푡 (2.1) where ℎ푑표푚 is the mean height of the dominant trees (meter), 훽0 and 훽1 are parameters to be estimated and 푡 is age (year) of the tree since planting. By definition, mean height of the dominant trees at base age (푡푏) is the site index (푆), seen in the following equation form.

−1 ln 푆 = 훽0 + 훽1푡푏 (2.2)

Therefore, by substituting the definition of 훽0 into the initial logarithm of height-reciprocal of age model and simplifying, gives

−1 −1 ln 푆 = ln ℎ푑표푚 + 훽1(푡 − 푡푏 ) (2.3) which can be used to generate mean height of dominant trees at a given age for specific values of 푆 and 푡푏 (Burkhart and Tomé, 2012). Equation 2.3 can be transformed to estimate the site index at a given mean height of dominant trees (ℎ푑표푚) and age (푡). The slope coefficient (훽1) was estimated from equation 2.1, and the site index was then estimated with equation 2.3 for each plot using a base age of 6 years.

Stand density as a function of basal area for Eucalyptus benthamii in the SE US

Basal area is the metric used by forest managers to implement silvicultural practices such as thinnings. Basal area in conjunction with trees per unit area also provides information related to mean individual tree girth (Burkhart and Tomé, 2012). Furthermore, basal area has shown to be highly correlated with stand growth and yield with the inclusion of stand age and site index (Burkhart and Tomé, 2012). Due to the heterogeneous nature of basal area (m2 ha-1) across time for the E.benthamii inventory plot network, it was necessary to stratify the plots into more homogeneous stands which was done by each site index (Avery and Burkhart, 2002). The following logarithm of basal area- reciprocal of age model was used to estimate basal area for each site index class

−1 ln 퐺𝑖 = 훽0𝑖 + 훽1𝑖푡 (2.4)

2 -1 푡ℎ where 퐺𝑖 is the basal area (m ha ) of the plot for the 𝑖 Site Index class, 훽0 and 훽1 are parameters to be estimated and 푡 is age (year) of the tree since planting.

Yield model for Eucalyptus benthamii in the SE US

Yield models have been used extensively to forecast yields of forest systems. These models have been primarily developed as a prediction tool to aid forest managers and investors in the decision-making process. The objective of this empirical model is for predicting actual productivity of Eucalyptus benthamii in the SE US.

Burkhart and Tomé (2002) describe a study examining different stand density measurements (SDI, CCF, basal area and trees per hectare) used within the Clutter model from an unpublished research report in 1982. In the work of Burkhart et al. (2002), CDI,

CCF and basal area had parameter estimates of 0.970, 0.984 and 0.992 respectively which all 58

three stand density measurements performed better than trees per hectare, and basal area was the superior to all with a coefficient of determination of 0.990. Revisiting equation 2.5, setting 훽3 = 1.0 based on the findings of Burkhart et al. (1982) and taking the antilogarithm of each side gives,

−1 푉 = 푒훽0푒훽1푆푒훽2퐴 퐺 (2.5) where 푉 is cubic volume and 퐺 is basal area (ha-1). Based on the understanding of site index and age (equation 2.3), specifying age (퐴) and site index (푆) is equivalent to the dominant

훽0 height (ℎ푑표푚). By setting 푒 = 퐹, the stand form factor, equation 2.6 can then be rewritten as

푉 = (퐹)(ℎ푑표푚)(퐺) (2.6) which is, by definition, the stand volume (Burkhart and Tomé, 2012). This approach was adopted to estimate a variety of yield types (volume, green weight and biomass) for

E.benthamii in the SE US which resulted in the following generic equation form

푌 = 훽0 + 훽1(ℎ푑표푚 ∗ 퐺) + 휀 (2.7) where 푌 is a measure of yield per hectare, 훽0 and 훽1 are parameters to be estimated, 퐺 is

2 -1 basal area (m ha ) for each plot, ℎ푑표푚 is the mean dominant height of each plot and 휀 is the error term. The inclusion of the intercept parameter (훽0) was included to reduce the error sum of squares.

Statistical Analysis

Statistical analysis of site index, projected basal area and the yield model were performed in SAS 9.3 using PROC REG (SAS, 2012). The yield equation 2.7 was modeled for each yield variable volume outside- (VOB) and inside-bark (VIB), green weight outside- 59

(GWOB) and inside-bark (GWIB) and dry weight or biomass outside- (DWOB) and inside- bark (DWIB). A combination of model variables were used to assess the goodness of fit for each model. When using the same model for multiple units of yield, the significances of the

Y-intercept parameter and the relationship of the resultant estimates as they work within the biological system is critical.

Results and Discussion

The summary statistics for each age class for all sample plots (n = 100) can be seen in table 2.1. Plots ranged in age class from one to 13 years. Stocking was reported in trees per hectare (TPH) as well as basal area (G; m2 ha-1) for all plots. Mean TPH per age class ranged from 1503 (2-year) to 828 (13-years). Mean TPH per age class had a negative correlation with age. This trend may be the result of self-thinning but more practically is the result of improved silvicultural practices such as soil preparation and weed control. Mean basal area per age class ranged from 0.15 to 21.1 m2 ha-1. Mean dominant height per age class had a positive correlation with age. Mean dominant height ranged from 2.5 (1-year) to 21.1 (13- years) meters. Mean volume outside-bark for all sample plots was 22.9 m3 ha-1 yr-1 with

13.6% of the volume consisting of bark. Mean green weight outside-bark for all sample plots was 20.0 Mg ha-1 yr-1 of which bark accounted for approximately 11.2% of the green weight.

Mean dry weight outside-bark for all sample plots was 10.2 Mg ha-1 yr-1 of which bark accounted for approximately 14.7% of the dry weight.

Site index for Eucalyptus benthamii in SE US

Site quality was found to be highly variable across all plots. Prior to performing the analysis, plotting logarithm of mean dominant height and the reciprocal of age there was a negative correlation between the two variables (figure 2.4). The logarithm of dominant height-reciprocal of age linear model was to be significant beyond alpha level 0.005 (table

2.2). The coefficient of determination was found to be 0.4283 for the linear model. The slope coefficient parameter estimate from the simple linear regression was used in equation

2.2 to generate the site index guide curve using a base age of six-years for Eucalyptus benthamii in the southeastern United States. The site index guide curve yielded 13.6-meters at a base age of six years.

The Schumacher-type model was successful in producing a site index guide curve for the height-age paired plot data for the development of top height growth model of

E.benthamii. Using the slope parameter estimate from the linear regression of equation 2.1, the defined base age of six years and equation 2.3, a family of anamorphic site index curves

(Figure 2.5) was developed by increased and decreased the site index of the guide curve in

33% increments to capture the range mean dominant heights observed in the data set. This resulted in a family of anamorphic site index curves for E.benthamii in SE US, ranging from

4 to 19 meters at a base of six years. A site index class (I, high; II, medium-high; III, medium-low; IV, low) was assigned to each inventory plot (table 2.3).

Stand density as a function of basal area for Eucalyptus benthamii in the SE US

The observed stratification of observed basal area (m2 ha-1) by site index class for each plot, seen in figure 2.6, suggested the necessity of individual basal area projection

equations for each site index class. The figure also shows that variance across ages is heterogeneous with leverage points at age 8 for Site Index Class II and at age 13 for Site

Index Class I. Attempts to model with the growth and yield of E.benthamii in the SE US with the Clutter model were unsuccessful primarily due to the heterogeneous variance of basal area. Projecting basal area using the natural logarithm of basal area – inverse of age while stratifying by Site Index class was found to be significant (table 2.3), and the homogenous nature of the variance of residuals was found to be acceptable (figure 2.8). The analysis resulted in the following basal area prediction equations,

3.48345−3.01793푡−1 퐺̂푆퐼−퐼 = 푒 (2.9)

3.71789−4.22567푡−1 퐺̂푆퐼−퐼퐼 = 푒 (2.10)

3.97887−5.87933푡−1 퐺̂푆퐼−퐼퐼퐼 = 푒 (2.11)

3.24377−5.16204푡−1 퐺̂푆퐼−퐼푉 = 푒 (2.12) where all coefficients were found to be significant beyond alpha level 0.05 (Table 2.4).

The coefficients of determination (R2) for the prediction equations of basal area for each site index ranged from 0.8673 to 0.3487, decreasing with site quality. The reduction in

R2 values from an empirical perspective seem to be primarily attributed to the high variance in basal area per age class as well as the limited age range for SI classes III and IV. Figure

2.7 shows the observed basal area (transformed to the logarithmic scale) for each plot and trend line for each Site Index class.

Yield model for Eucalyptus benthamii in SE US

There is a strong positive relationship with volume (m3 ha-1) and stand yield variables such as dominant height and basal (Figure 2.10); however, these relationship are exponential 62

in natural and would require transformations with modeling purposes. Combining mean dominant height and basal area into one variable for each inventory plot showed a strong positive linear correlation with volume (Figure 2.10). This strong, positive linear correlation was also seen for all other yield metrics (Figure 2.11). A simple linear regression was performed based on equation 2.5 to estimate volume, green weight and dry weight both outside- and inside-bark. All models were found to be significant for each response variable

(Table 2.5).

Projecting yield and recovering growth of Eucalyptus benthamii in the SE US

The actual productivity of Eucalyptus benthamii in the southeastern United States was projected to determine growth and potential yields at rotation age. The mean dominant height (m) and the basal area (m2 ha-1) at ages 1 through 9-years were projected for each inventory plot using the prediction equations 2.3 and 2.4 respectively. The yield equation form 2.7 was then used to estimate the yield for a variety of metrics including volume, green weight and biomass with and without bark. The mean yields at each age was determined for each site index class based on the projected yields.

Based on the given site index and initial stand-density, yield (per hectare) plotted over time results in a sigmoid curve (Burkhart and Tomé, 2012). Yield curves for Eucalyptus benthamii in the southeastern United States were developed for each yield metric by site index class (Figure 2.13). For all yield metrics, volume, green weight and dry weight, the total yield was reduced by approximately 8.7 percent from SI-I to SI-II, 17.5 percent from SI-

II to SI-III and 59.3 percent from SI-III to SI-IV. Comparing the site index curves (Figure

2.5) and the basal area projection curves (Figure 2.9) with the projected yield curves (Figure

2.13), the large reduction of yield between SI-III and SI-IV seem to be highly correlated with the basal area projection curve. This severe reduction in basal area for SI-IV is likely to be related to high mortality. Yield for volume outside-bark ranged from approximately 60 (SI-

IV) to 190 (SI-I) m3 ha-1 at age 9-years. An approximate reduction of 15.5 percent in volume was realized with the removal of bark with yields ranging from 50 (SI-IV) to 160 (SI-I) m3 ha-1 at age 9-years. Yield for green weight outside-bark ranged from approximately 55 (SI-

IV) to 180 (SI-I) Mg ha-1 at age 9-years. An approximate reduction of 14 percent in green weight was realized with the removal of bark with yields ranging from 50 (SI-IV) to 155 (SI-

I) Mg ha-1 at age 9-years. Yield for dry weight outside-bark ranged from approximately 26

(SI-IV) to 85 (SI-I) Mg ha-1 at age 9-years. An approximate reduction of 13.3 percent in dry weight was realized with the removal of bark with yields ranging from 23 (SI-IV) to 74 (SI-I)

Mg ha-1 at age 9-years.

The growth curve, or current annual increment (CAI), is the derivative of the yield function which increases until the inflection point in the yield curve and then continues to decrease. The mean annual increment (MAI), another important quantity, is the total yield of a given year divided by the years of accumulation (typically since planting for plantation forests) (Burkhart and Tomé, 2012). The CAI and MAI curves intersect at the MAI maximum. This intersection point of CAI and MAI defines the optimum rotation length; harvesting later would allow the current forest to produce less yield than an newly established plantation and harvest prior to this point would remove a system that would produce in excess of the mean increment in a year. The MAI of Eucalyptus benthamii in the southeastern United States was calculated for each yield metric by site index class (Table

2.7). The table shows the maximum MAI (bold) for each site index class by yield metric

(volume, green weight and dry weight with- and without-bark). The table shows that as site index class increases, the MAI increases and MAI reaches its maximum earlier in age for all yield types. The maximum MAI is reached in the same year for all yield metrics because the model is only changing the parameter estimates for each yield type as seen previously. Site index class IV and III reached maximum MAI in the eighth year, and site index classes II and

I reached maximum MAI at year six and five respectively. The projected current and mean annual increments were plotted against the observed mean annual increments for each inventory plot by site index class for each yield metric (Figures 2.14-2.19). By plotting the observed MAI, the influence of leverage points, as seen for SI-I beyond year 7, can be observed on the modeled growth trend. These results show that growth is likely underestimated for SI classes I and IV based on observed MAI values beyond year four (with the exclusion of the leverage points in SI-I). However, these results show this modeling approach was accurate at projecting growth for SI classes II and III.

Mean annual increments reported by Dougherty and Wright (2012) estimated yields for E.benthamii, with appropriate silviculture, of 18 to 36 green Mg ha-1 yr-1 with rotation ages ranging from six to eight years for the Lower Gulf Coast Region of the southern United

States. While the growth and yield model encompassed a much larger region and varying levels of management intensities, results were not conflicting. The model estimated MAI ranging from approximately 6 to 23 green Mg ha-1 yr-1 with rotations from 8 to 5-years respectively. However, several inventory plots with the E.benthamii network observed MAI of more than 25 green Mg ha-1 yr-1 between ages 3 and 4-years.

Eucalyptus species have been found to perform well in exotic environments (Stape et al., Albaugh et al., 2013). The southeastern United States is no different, with areas in the

SEUS realizing mean annual increments at projected rotation ages of 8 to 6 years ranging from approximately 7 (SI-IV) to 25 (SI-I) cubic meters per hectare per year outside-bark respectively pending on site quality. In comparison, southern pines, predominantly loblolly pine (Pinus taeda L.) and slash pine (P.elliottii Englem.) but including shortleaf (P.echinata

Mill.), longleaf (P. palustris Mill.), pond (P.serotina Michx.), sand (P.clausa Chapm.), and

Virginia (P.virginiana Mill.) pines typically produce 7 to 15 m3 ha-1 and as much as nearly

30 m3 ha-1 over a 25 to 30-year rotation under plantation management in the same region of the United States (Allen et al., 1990; Fox et al., 2007). Eucalyptus production in other regions of the world range with a MAI as much as 40 m3 ha-1 yr-1 for E.grandis in Brazil, 18 to 30 m3 ha-1 yr-1 for E.nitens and E.globulus in Chile and 13 to 14 m3 ha-1 yr-1 for E.nitens in

South Africa (Stape et al., 2001; Tibbits et al., 1997). Invariably, empirical data of current

Eucalyptus benthamii trials and pilot plantations in the SE US show that the actual productivity is promising. While the potential productivity of E.benthamii in the SE US is defined by factors such as genotype, edaphic and climatic conditions, the reduction of reducing factors, such as pests, diseases and competing vegetation, and limiting factors, such as nutrition, through improved precision silvicultural practices will narrow the gap between the actual and potential productivity of E.benthamii.

Conclusion

The Eucalyptus benthamii inventory plot network in the southeastern United States, the subsequent site index guide curve and growth and yield model show that there is a wide range of productivity for E.benthamii across varying edaphic and climatic conditions. Site index at base age 6-years ranged greatly from 6 to 21-meters at base age 6-years capturing 66

the variability in site quality. The E.benthamii inventory plot network in the SE US show an average mean annual increment of 15 m3 ha-1 yr-1 ranging from 6 to 35 m3 ha-1 yr-1 or 6 dry

Mg ha-1 yr-1 ranging from 3 to 16 dry Mg ha-1 yr-1 between ages of 3 and 13 years. The growth and yield model developed showed that mean annual increments can range from 6 to

25 m3 ha-1 yr-1 or 3 to 11 dry Mg ha-1 yr-1 at rotation ages ranging from 8 to 5 years respectively.

Using an array of stem wood metrics with and without bark and also investigating a whole tree system has allowed this Schumacher-type model the flexibility to estimate yields of E.benthamii for the SE US based on a variety of different constraints as they could be imposed by either transportation or conversion process limitations.

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Figure 2.1. Eucalyptus benthamii inventory plot network across the southeastern United States.

10 Stem height Stem(meter) height

0 0 5 10 15 20 25 30 35 Diameter at breast height (centimeter)

Figure 2.2. Scatter plot of all sample trees within the southeastern United States for the Eucalyptus benthamii inventory plot network.

Table 2.1. Summary statistics of plot attributes (trees per hectare, basal area, mean dominant height, volume outside-bark (VOB) and inside-bark (VIB), green weight outside-bark (GWOB) and inside-bark (GWIB) and stem biomass outside-bark (DWOB) and inside-bark (DWIB)) by age class (year). Age Plots Trees Basal area Dom. height VOB VIB GWOB GWIB DWOB DWIB (year) (ha-1) (m2 ha-1) (meter) (m3 ha-1) (m3 ha-1) (Mg ha-1) (Mg ha-1) (Mg ha-1) (Mg ha-1) 1 1 2078 4.5 7.6 14.6 13.2 13.2 11.5 6.9 5.7 2 63 1621 4.6 7.6 15.6 13.8 13.8 12.4 7.0 5.8 3 25 1502 9.0 9.6 39.8 34.5 34.2 34.2 17.7 15.1 4 8 1549 13.6 12.2 70.6 60.7 62.8 62.8 31.5 27.0 7 1 637 17.0 20.4 125.4 104.8 120.9 120.9 54.7 47.8 8 1 864 19.5 19.2 144.9 122.2 139.8 139.8 65.0 56.7 13 1 732 24.4 21.5 192.9 160.3 189.1 189.1 83.7 73.3

10 Mean dominant height (meter) height Mean dominant 5

0 0 2 4 6 8 10 12 14 Age (year)

Figure 2.3. Scatter plot of mean dominant height (m) of each inventory plot by age (years).

Table 2.2. Analysis of variance and parameter estimates for the simple linear regression of the reciprocal of age (year) as a predictor of the logarithm of mean dominant height (m).

Source df SS MS F value Pr > F Model 1 3.92337 3.92337 73.42 < 0.0001 Error 98 5.23678 0.05344 Total 99 9.16015

Parameter Symbol Estimate St.Error t value Pr > |t| Intercept Β0 2.92367 0.09528 30.68 < 0.0001 invA Β1 -1.89098 0.22069 -8.57 < 0.0001

3.5

3.0

2.5

2.0

(m)) dom

1.5 Ln(Ht

1.0

0.5 R² = 0.4283 0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Inverse Age (yr)

Figure 2.4. Linear regression of inverse age (year) as a predictor of natural logarithm of mean dominant height (m) to determine Site Index Guide Curve for E.benthamii in SE US. Coefficient of determination = 0.4283.

25 I

20 II

15 III

IV Mean dominant height (meter) height Mean dominant

0 1 2 3 4 5 6 7 8 9 10 11 12 13 Age (year)

Figure 2.5. Anamorphic site index guide curves and mean dominant height (m) of inventory plots for Eucalyptus benthamii in the southeastern United States.

Table 2.3. Mean dominant height (m) and base age 6-years and number of observations per Site Index class.

SI Class Mean Hdom (m) Plots I 8 13 II 12 33 III 16 44 IV 20 10

30 SI - I SI - II 25 SI - III SI - IV

) 20

ha 2

Basal area (m area Basal 10

0 0 2 4 6 8 10 12 14 Age (year)

Figure 2.6. Scatter plot of basal area (m2 ha-1) of each inventory plot by age (years) by Site Index class.

Table 2.4. Analysis of variance for the simple linear regression of the reciprocal of age (year) as a predictor of the logarithm of basal area (m2 ha-1) by Site Index classes. Source df Sum of squares Mean square F value Pr > F SI – I Model 1 3.08027 3.08027 52.28 < 0.0001 Error 8 0.47133 0.05892 Total 9 3.55160 SI – II Model 1 7.03324 7.03324 90.85 < 0.0001 Error 42 3.25151 0.07742 Total 43 10.28475 SI – III Model 1 8.07697 8.07697 35.55 < 0.0001 Error 31 7.04335 0.22720 Total 32 15.12032 SI - IV Model 1 2.63328 2.63328 5.89 0.0336 Error 11 4.9188 0.44716 Total 12 7.55209

Table 2.5. Parameter estimates for the simple linear regression of the reciprocal of age (year) as a predictor of the logarithm of basal area (m2 ha-1) by Site Index classes. Parameter Estimate Standard error t Value Pr > |t| SI – I Intercept 3.48345 0.18008 19.34 < 0.0001 Inv(age) -3.01793 0.41738 -7.23 < 0.0001 SI – II Intercept 3.71789 0.19204 19.36 < 0.0001 Inv(age) -4.22567 0.44334 -9.53 < 0.0001 SI – III Intercept 3.97887 0.43746 9.10 < 0.0001 Inv(age) -5.87933 0.98608 -5.96 < 0.0001 SI – IV Intercept 3.24377 0.84042 3.86 0.0027 Inv(age) -5.16204 2.12719 -2.43 0.0336

3.5 R² = 0.6839

3.0 )

1 2.5

- ha 2 R² = 0.3487 2.0

1.5 SI - I SI - II R² = 0.8673 SI - III 1.0 SI - IV Linear (SI - I) R² = 0.5342 Linear (SI - II) Natural log basal area (m area log Natural basal 0.5 Linear (SI - III) Linear (SI - IV) 0.0

-0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Inverse age (year)

Figure 2.7. Linear regression of inverse age (year) as a predictor of natural logarithm of basal area (m2 ha-1) by Site Index class for E.benthamii in SE US. SI – I R2 = 86.73. SI – II R2 = 0.6839. SI – III R2 = 0.5342. SI – IV R2 = 0.3487.

25 1:1 line Basal area

)

ha 2 15

Predicted basal area (m area Predicted basal 5

0 0 5 10 15 20 25 2 -1 Observed basal area (m ha )

Figure 2.8. Scatter plot of actual versus predicted basal area.

30 SI - I 25 SI - II

SI - III

) 1 - SI - IV

ha 20 2

10 Mean basal area area Mean (m basal

0 0 2 4 6 8 10 Age (year)

Figure 2.9. Projected mean basal area by site index classes for all plots over time.

250

) A 1

- 200 ha

3 150

100

Volume (m Volume 50

0 0 5 10 15 20 25 Mean dominant height (m)

250

) 1

- 200 B ha 3 150 100

50 Volume (m Volume 0 0 5 10 15 20 25 30 Basal area (m2 ha-1)

250 )

1 C

- 200 ha 3 150 100

50 Volume (m Volume 0 0 100 200 300 400 500 600

Hdom * G

2 -1 Figure 2.10. Scatter plots of A) mean dominant height (Hdom; m), B) basal area (G; m ha ) and C) combined-variable Hdom*G as predictors volume.

250

) A

1 200

- ha

3 150

100 OB

Volume (m Volume 50 IB 0 0 100 200 300 400 500 600 Hdom * G

200

)

1 - B 150

100

50 OB IB Green weight (Mg (Mg weight ha Green 0 0 100 200 300 400 500 600 H * G dom

) 1 - 75 C 60 45 30 OB 15

Dry weight ha Dry (Mg IB 0 0 100 200 300 400 500 600

Hdom * G

Figure 2.11. Scatter plots of the combined-variable Hdom*G as a predictor of A) volume, B) green weight and C) dry weight with (OB) and without (IB) the presence of bark.

Table 2.6. Analysis of variance for the simple linear regression of the combined-variable basal area-mean dominant height as a predictor of yield. Source df Sum of squares Mean square F value Pr > F VOB Model 1 105687 105687 10570.0 < 0.0001 Error 98 979.88116 9.99879 Total 99 106667 VIB Model 1 74567 74567 8127.25 < 0.0001 Error 98 899.14248 9.17492 Total 99 75466 GOWB Model 1 97309 97309 14597.5 < 0.0001 Error 98 653.28322 6.66616 Total 99 97962 GWIB Model 1 70920 70920 13253.6 < 0.0001 Error 98 524.39888 5.35101 Total 99 71444 DWOB Model 1 20641 20641 7082.45 < 0.0001 Error 98 285.60866 2.91437 Total 99 20927 DWIB Model 1 15673 15673 7848.04 < 0.0001 Error 98 195.70564 1.99700 Total 99 15868

Table 2.7. Parameter estimates for the simple linear regression of the combined-variable basal area-mean dominant height as a predictor of yield.

Parameter Estimate Standard error t Value Pr > |t| VOB Intercept 1.55428 0.42134 3.69 0.0004 (G*Hdom) 0.38971 0.00379 102.81 < 0.0001 VIB Intercept 2.09979 0.40361 5.20 < 0.0001 (G*Hdom) 0.32734 0.00363 90.15 < 0.0001 GWOB Intercept -1.47817 0.34403 -4.30 < 0.0001 (G*Hdom) 0.37394 0.00310 120.82 < 0.0001 GWIB Intercept -0.26452 0.30823 -0.86 0.3929 (G*Hdom) 0.31924 0.00277 115.12 < 0.0001 DWOB Intercept 0.78372 0.22747 3.45 0.0008 (G*Hdom) 0.17222 0.00205 84.16 < 0.0001 DWIB Intercept 0.41025 0.18830 2.18 0.0317 (G*Hdom) 0.15007 0.00169 88.59 < 0.0001

210 180 180 150 150 120 120 90

90 Predicted

Predicted 60 60 1:1 line 30 VIB 30 VOB 1:1 line 0 0 0 30 60 90 120 150 180 210 0 30 60 90 120 150 180 Observed Observed

200 180

160 150 120 120 90

80 Predicted Predicted 60 40 1:1 line 30 GWIB GWOB 1:1 line 0 0 0 40 80 120 160 200 0 30 60 90 120 150 180 Observed Observed

100 90

80 75 60 60 45

40 Predicted Predicted 30 1:1 line 1:1 line 20 15 DWOB DWIB 0 0 0 20 40 60 80 100 0 15 30 45 60 75 90 Observed Observed

Figure 2.12. Scatter plots of observed and predicted yield variables.

250 180 S-I SI-I B S-II A 160 SI-II 200 S-III 140 SI-III

) S-IV )

1 SI-IV -

1 120 -

ha 150 ha

3 100 3 80

100 VIB (m VIB

VOB VOB (m 60 50 40 20 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Age (year) Age (year) 200 180 SI-I SI-I C 160 D SI-II SI-II 140 SI-III

) 150 SI-III

)

1 -

1 SI-IV SI-IV - 120 100 100 80

60 GWIB GWIB ha (Mg GWOB GWOB (Mg ha 50 40 20 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Age (year) Age (year) 90 80 SI-I SI-I 80 E 70 F SI-II SI-II 70 SI-III

) 60 SI-III

)

- 1 60 SI-IV - SI-IV 50 50 40 40

30 30 DWIB DWIB ha (Mg DWOB DWOB ha (Mg 20 20 10 10 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Age (year) Age (year)

Figure 2.13. Projected yields (A) VOB, B) VIB, C) GWOB, D) GWIB, E) DWOB, F) DWIB) for Eucalyptus benthamii in the SE US.

Table 2.8. Summary of mean annual increments by Site Index class for E.benthamii in the SE US for all yield variables (bold indicates rotation age).

Age Presence of bark Absence of bark (year) SI - IV SI - III SI - II SI - I SI - IV SI - III SI - II SI - I Volume (m3 ha-1) 1 1.66 1.70 2.31 3.99 2.19 2.22 2.74 4.14 2 2.65 4.28 8.86 14.95 2.62 3.99 7.84 12.95 3 4.55 9.03 15.45 21.93 4.09 7.85 13.24 18.68 4 5.84 12.59 19.03 24.56 5.10 10.78 16.18 20.83 5 6.51 14.71 20.56 25.03 5.63 12.51 17.43 21.18 6 6.80 15.81 20.95 24.52 5.84 13.41 17.73 20.73 7 6.85 16.26 20.74 23.59 5.87 13.77 17.53 19.93 8 6.83 16.31 20.22 22.52 5.79 13.80 17.08 19.01 9 6.62 16.13 19.55 21.42 5.65 13.64 16.51 18.08 Green weight (Mg ha-1) 1 0.00 0.00 0.00 0.86 0.00 0.00 0.36 1.73 2 1.05 2.62 7.01 12.86 1.40 2.73 6.49 11.47 3 3.38 7.68 13.83 20.05 3.22 6.89 12.14 17.45 4 4.86 11.34 17.52 22.82 4.40 9.93 15.20 19.73 5 5.65 13.52 19.13 23.42 5.03 11.74 16.53 20.19 6 6.03 14.67 19.61 23.03 5.31 12.69 16.90 19.83 7 6.15 15.17 19.47 22.21 5.39 13.10 16.77 19.11 8 6.13 15.28 19.03 21.23 5.36 13.17 16.37 18.25 9 6.02 15.15 18.43 20.22 5.25 13.04 15.84 17.37 Dry weight (Mg ha-1) 1 0.83 0.85 1.12 1.86 0.45 0.47 0.70 1.35 2 1.22 1.94 3.96 6.65 0.92 1.55 3.32 5.66 3 2.04 4.02 6.86 9.72 1.69 3.42 5.89 8.38 4 2.60 5.59 8.43 10.88 2.20 4.80 7.28 9.41 5 2.90 6.52 9.10 11.08 2.47 5.63 7.88 9.60 6 3.02 7.00 9.27 10.85 2.59 6.06 8.04 9.41 7 3.04 7.20 9.18 10.44 2.61 6.23 7.96 9.06 8 3.00 7.22 8.95 9.96 2.58 6.26 7.76 8.65 9 2.94 7.14 8.65 9.47 2.53 6.19 7.51 8.23

40 35 A Obs. MAI B Obs. MAI 35 MAI 30 MAI

CAI CAI )

30 )

1 -

- 25

1 1

- 25

- 20

ha 3 20 3 15

15 VOB (m 10 VOB (m 10 5 5 0 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 Age (year) Age (year) 25 14 C D 12

)

1 -

- 10

1 - 15 -

ha 8

3 3 10 6

4 VOB (m 5 Obs. MAI VOB (m Obs. MAI MAI 2 MAI CAI CAI 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Age (year) Age (year)

Figure 2.14. Projected current (CAI) and mean (MAI) annual increments and observed for volume with the presence of bark (VOB) by Site Index class (A) SI-I; B) SI-II; C) SI-III; D) SI-IV) of E.benthamii in SE US.

35 30 A Obs. MAI B Obs. MAI 30 MAI 25 MAI

CAI CAI

)

1 -

25 -

1 -

20 -

ha 3 3 15 15

10 VIB (mVIB

10 VIB(m 5 5

0 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 Age (year) Age (year) 25 12 C D

20 10

) )

1 1 -

- 8

yr yr

1 1 -

- 15

ha ha 3 3 6 10

VIB(m VIB(m 5 Obs. MAI Obs. MAI MAI 2 MAI CAI CAI 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Age (year) Age (year)

Figure 2.15. Projected current (CAI) and mean (MAI) annual increments and observed MAI for volume without the presence of bark by Site Index class (A) SI-I; B) SI-II; C) SI-III; D) SI-IV) of E.benthamii in SE US.

40 35 Obs. MAI Obs. MAI 35 A B

MAI 30 MAI

)

1 1

- CAI

30 CAI - yr

yr 25

1 - 25 - 20 20 15 15

10 10

GWOB (Mg ha GWOB(Mg ha 5 5 0 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 Age (year) Age (year) 25 10

C D )

20 ) 8

- - 15 6

10 4

Obs. MAI GWOB (Mg (Mg GWOBha 5 GWOB (Mg ha 2 Obs. MAI MAI MAI CAI CAI 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Age (year) Age (year)

Figure 2.16. Projected current (CAI) and mean (MAI) annual increments and observed MAI for green weight with the presence of bark by Site Index class (A) SI-I; B) SI-II; C) SI-III; D) SI-IV) of E.benthamii in SE US.

35 30 A Obs. MAI B Obs. MAI

30 MAI 25 MAI

)

) 1

1 CAI -

- CAI

yr 1

1 20

- - 20 15 15 10

GWIB (Mg ha GWIB (Mg ha 5 5 0 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 Age (year) Age (year) 25 10 C D

20 ) 8

)

1 - - 15 6

10 4 GWIB (Mg ha GWIB (Mg ha 5 Obs. MAI 2 Obs. MAI MAI MAI CAI CAI 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Age (year) Age (year)

Figure 2.17. Projected current (CAI) and mean (MAI) annual increments and observed MAI for green weight without the presence of bark (GWOB) by Site Index class (A) SI-I; B) SI-II; C) SI-III; D) SI-IV) of E.benthamii in SE US.

18 16 Obs. MAI Obs. MAI A 14 B

15 MAI MAI

)

1 -

CAI - 12 CAI

1 - 12 - 10 9 8

6 6

4 DWOB (Mg ha 3 (Mg DWOBha 2 0 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 Age (year) Age (year) 12 5 C D

10 )

) 4

1 -

- 8 3 6 2

4 DWOB (Mg ha DWOB (Mg ha Obs. MAI 1 Obs. MAI 2 MAI MAI CAI CAI 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Age (year) Age (year)

Figure 2.18. Projected current (CAI) and mean (MAI) annual increments and observed MAI for biomass with the presence of bark by Site Index class (A) SI-I; B) SI-II; C) SI-III; D) SI-IV) of E.benthamii in SE US.

16 14 A Obs. MAI B Obs. MAI

14 MAI 12 MAI

) ) 1 CAI

- CAI

12 1 -

yr 10

- 1 10 - 8 8 6 6

4 4

DWIB (Mg ha DWIB (Mg ha 2 2 0 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 Age (year) Age (year) 10 5 C D

8 ) 4

)

1 - - 6 3

4 2

DWIB (Mg ha Obs. MAI DWIB (Mg ha 2 Obs. MAI 1 MAI MAI CAI CAI 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Age (year) Age (year)

Figure 2.19. Projected current (CAI) and mean (MAI) annual increments and observed MAI for biomass without the presence of bark by Site Index class (A) SI-I; B) SI-II; C) SI-III; D) SI-IV) of E.benthamii in SE US.

CHAPTER THREE: THE TEMPERATURE-RADIATION EFFECT ON SEVEN

COLD-HARDY EUCALYPTUS SPECIES PLANTED IN THE PIEDMONT REGION

OF NORTH CAROLINA

Introduction

The Eucalyptus genus has more than 800 species, which occur in their native range in

Australia-Indonesia from the equator to 40S. In the southeastern United States, many

Eucalyptus initiatives are trying to identify cold-hardy species that can be used for fiber, biomass, biofuels or mulch production, with the ability to coppice after harvesting. Based on the varying climatic and edaphic in southeastern United States, a variety of Eucalyptus species have potential to be grown commercially to provide a feedstock for a variety of final products.

The NCSU/Forest Productivity Cooperative (FPC) began a special Eucalyptus species study in 2010. The study consisted of a region wide approach to screen for suitable cold tolerant Eucalyptus species, evaluate the yield associated with the most promising species and understand the environmental factors and physiological controls of cold tolerant

Eucalyptus species to evaluate cold-risk zoning and productivity across the southeastern

United States (SE US). Following two years of species screening in the northern-most site, seven Eucalyptus species have exhibited significant cold tolerance and superior growth.

Eucalyptus badjensis, commonly known as Badja gum or Big Badja gum, is a large, excurrent (40-m tall) tree that occurs naturally in the high altitude plateaus and hills of southeastern New South Wales state in Australia. The species has moderate moisture needs in its natural cultures growing in soils textures such as gravels, loams or sandy loams with

pH ranging from 5.5 to 6.4. E.badjensis natural range coincides with the USDA plant hardiness zone 8.

Eucalyptus benthamii Maiden & Cambage, commonly known as Camden White

Gum, grows naturally in the coastal region of New South Wales in an area southwest of

Sydney in Australia (Benson, 1985). With the construction of dams and clearing of land for agriculture, much of the habitat for E.benthamii has been lost in Australia with the arrival of

Europeans. Today, E.benthamii remains naturally in two populations along the Nepean

River and Kedumba Creek, the latter being that larger of the populations (Benson, 1985).

Trials in southern Brazil during the 1990s showed that E.benthamii was one of the best performers as it was related to survival and growth (Higa & Carvalho, 1990).

Eucalyptus dalrympleana, commonly known as Mountain White Gum, is large, excurrent (40 meters) tree that occurs naturally in southeastern Australia and Tasmania in grassy or sclerophyll woodlands on loamy or sandy soils at higher elevations. Booker and

Evans observed that E.dalrympleana could survive periods of -6 to -9C after a hardening period in the British Isles (1983). A close relative of E.gunnii, E.dalrympleana has exhibited superior cold tolerance than E.nitens and increased growth compared to E.gunnii in United

Kingdom plantings (Leslie et al., 2012).

Eucalyptus dorrigoensis, commonly known as Dorrigo white gum, is large tree that is native to eastern Australia. E.dorrigoensis is most closely related to E.benthamii and was once was consider to be a variety of the species, but is not consider to be a different taxon

(Benson, 1985). E.dorrigoensis exhibited better growth along with E.benthamii and E.dunnii in a species trial established in northern Fujian provenance, China; however, the

E.dorrigoensis plots, while having favorable growth, did not have similar mortality rates

100

following a 1999 cold event consisting of seven consecutive daily minimums below 0C with an absolute minimum of -8C (Hesheng et al., 2003).

Eucalyptus macarthurii, commonly known as Paddy’s River Box or Camden

Woollybutt, is a large excurrent (40-m tall) tree when grown in forest plantations or medium, decurrent (20 to 30-m) tree, by retaining basal branches, when grown in isolated conditions.

In its natural habitat, E.macarthurii is restricted to the Blue Mountains and Southern

Highland Tablelands of New South Wales in Australia. In this region, precipitation ranges from 700 to 1000 mm annually with the inclusion of occasional snowfall, and with 20 to 40 frost events per annum, E.macarthurii experiences annual minimum temperatures of -7C.

Eucalyptus nitens, commonly known as Shining gum, is a large, excurrent tree (60-m tall) native to Victoria and New South Wales, with a latitude range of 30 to 38S, in

Australia and is found on fertile soils in cool areas with high precipitation (Tibbits et al.,

1997). E.nitens is a preferred hardwood species for plantation forestry in temperate regions and is considered to be more frost tolerant than other suitable Eucalyptus species such as

E.globulus (Misra et al., 1998). E.nitens has been planted in exotic environments, such as

China, Chile, New Zealand and South Africa, to produce sawn timber, pulp and paper in temperate climates frequently occurring at elevations between 400 and 800-m where frequent cold events prevent establishment of other Eucalyptus species (Tibbits et al., 1997). The mean annual increment varies greatly across the exotic environments with plantations of

E.nitens ranging from 13 (in South Africa) to 30 (in Chile) m3 ha-1 yr-1 (Tibbits et al., 1997).

Eucalyptus viminalis, commonly known as Manna Gum or White Gum, is a large

(40-m tall) excurrent tree native to southern Australia and Tasmania ranging in latitudes from

28 to 43S and elevation from sea level to 1300-m (Cappa et al., 2010). Mean temperature 101

ranges from 18 to 32C during the summer months and -7 to -3C during the winter months with annual precipitation ranging from 500 to 1700 mm per year (Cappa et al., 2010). The frequency of frost varies greatly with none near sea level and more than 100 days year in the high altitude areas (Cappa et al., 2010). The high growth and frost tolerance of E.viminalis has become highly desirable for plantation forestry in the Pampeana region of Argentina (33 to 39S) with areas producing a mean annual increment as much as 25 to 35 m3 ha-1 yr-1 for high-quality wood for pulp and fiber board (Cappa et al., 2010).

Each of these species have exhibited potentially economically viable growth characteristics and cold tolerance when established in exotic environments. While all of the species of interest originate in the same general region of Australia, their individual distribution and also disjunct populations have resulted in an array of responses to climatic conditions. The response of Eucalyptus species to climatic conditions such as precipitation, photosynthetically active radiation (PAR), vapor pressure deficit (VPD) and extreme high temperatures are well known. However, as the demand for forest products increases, the planting range of commercial forest species, such as Eucalyptus, have expanded into regions less suitable for optimal growing conditions. Therefore, understanding the effects of climatic variables on the growth of exotic species is paramount in the development of zoning potential areas for forest plantation establishment.

To investigate the potential of new species and how their growth rates are affected by the radiation-temperature effect, a screening and detailed measurement trial were installed in a typical Piedmont area of North Carolina. The objectives of this study are to (1) determine if there a significant difference in weekly growth among species, (2) describe the effects of

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major climate variables on the weekly growth of cold tolerant Eucalyptus species, and (3) examine potential lag time effect on weekly growth as it relates to temperature.

Materials and Methods

A Eucalyptus frost tolerant screening trial was installed in Raleigh, NC (35.79N,

78.70W) in 2010 consisting of 150 different species on a clayey alfisol soil (fertile). Site selection was intended to provide intensive screening of Eucalyptus species based on climate variables in a northern. The close proximity of the study site provided opportunities for detailed growth measurements during the screening process. Winters of 2010 and 2011 in

Raleigh, NC had absolute minimum temperatures of -7C resulting in sixty percent of the

150 Eucalyptus species surviving with healthy canopies. Of the remaining species, seven species (E.badjensis, E.benthamii, E.dalrympleana, E.dorrigoensis, E.macathurii, E.nitens and E.viminalis) were not only frost tolerant but had high growth rates.

Stem biomass accumulation of Eucalyptus species can be measured weekly because of their shorter lag time following the fixation of carbon through photosynthesis. Unlike pines that store the majority of fixed carbon as carbohydrates during the winter months,

Eucalyptus species immediately use a large portion of a fixed carbon growth when climate factors allow. This is referred to as indeterminate growth. The indeterminate growth allows

Eucalyptus species to continuously produce merchantable biomass as well as canopy development through the otherwise dormant season compared to native species. However, this phenomenon also allows the succulent new growth such as leaves and terminal buds to be susceptible to frost damage.

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In this experiment, seven cold tolerant Eucalyptus species were selected and measured weekly for 58 weeks to examine the effects of cold temperatures on stem biomass growth. Beginning October 2012, diameter at breast height (dbh) was measured and recorded weekly, using a diameter tape to the 1/100th of an inch to closely examine changes in dbh each week. Total height and height to canopy were measured monthly using a telescopic height pole. Between measurements, a linear relationship was used to estimate change in height on a weekly basis. Stem dry weight outside-bark was estimated for each sample tree using a logarithmic prediction equation. A Schumacher-type allometric prediction equation was developed using thirty-nine cold tolerance Eucalyptus species ranging in age from ten-months to nine-years in age. There are 21 individual trees in this experiment with each of the seven species having weekly observations (individuals) ranging from two to four individuals per species.

Frost-tolerant Eucalyptus species growth

A univariate approach, time as a factor, was used to develop a statistical model to test for differences among species throughout the study period. Species was tested against individual nested within species to determine if there is a significant difference between species. This statistical analysis was performed using the PROC GLM procedure in SAS

(SAS, 2012).

Effects of climate variables on frost-tolerant Eucalyptus growth

Climate data was used from the Climate Retrieval and Observations Network of the

Southeast (CRONOS) database developed by the State Climate Office of North Carolina 104

from the Reedy Creek Field Laboratory (35.81N, 78.74W), approximately 4.4 kilometers from the study site. Climate variables such as ambient temperature (C), precipitation (mm), relative humidity (%), solar radiation (W m-2) and photosynthetically active radiation (PAR)

(W m-2) were measured hourly by the Reedy Creek field lab.

Photosynthesis is temperature dependent and different species exhibit a different temperature optimum as seen by Battaglia, Beadle and Loughhead when comparing the response of photosynthetic rates of E.globulus and E.nitens to a range of temperatures

(1996). The following temperature variables were calculated using the CRONOS database to determine the driving temperature variable for cold-tolerant Eucalyptus species growth in the

SE US. The absolute minimum and maximum ambient temperature per day was averaged across each sample period (week) to determine the weekly average minimum and maximum temperature. The average of all hourly ambient temperature measurements for each sample period calculated the weekly average ambient temperature. The summation of observed precipitation determined the total precipitation for each sample period. This resulted in the three temperature variables: weekly 1) average-maximum, 2) average and 3) average- minimum temperature.

Photosynthesis is the basis of tree growth and is driven by the radiant energy from the sun that is absorbed by leaves (and for other species, other photosynthetic surfaces)

(Landsberg and Sands, 2011). However, photosynthetic organisms are only able to use solar radiation in the spectral range from 400 to 700 nanometers, which corresponds with the range of light visible to the human eye, in the process of photosynthesis. This spectral range of solar radiation is called photosynthetically active radiation (PAR). The ratio of PAR to total solar radiation (150 to 3200 nanometers) outside the Earth’s atmosphere is 0.44; however, 105

due to atmosphere effects such as the presence of clouds, the ratio of PAR to total solar radiation ranges from 0.4 to 0.6 (nominally taken to be 0.5) (Landsberg and Sands, 2011).

Climate data is often more concerned with the total solar radiation (thus reports measurements in (W m-2) as it is more related to energy balance of bodies (atmosphere, sun, ground, plants) and also processes such as transpiration (Landsberg and Sands, 2011).

Landsberg and Sands (2011) explain that for photochemical processes, such as photosynthesis, the actual number of photons (fundamental quantum particle of radiation) is also important, and the unit used for PAR is the mole (one mole of photons is called an

Einstein (E)). The advantage of using photon-flux density (with units of mols m-2 s-1) opposed to the energy-flux density (W m-2) is that photosynthetic efficiency can be expressed in terms of the numbers of moles or CO2 fixed per mole of photons in the visible waveband in which radiation with activate photosynthesis (Landsberg and Sands, 2011). While it is not strictly correct to convert from energy flux to photon flux to the energy of a photon is dependent on the respective wavelength, in normal sunlight 1 J of PAR contains approximately 4.6 μmol (i.e. for solar radiation 1000 W m-2 ≈ 2300 μmol m-2 s-1 PAR)

(Landsberg and Sands, 2011).

Relative humidity is the percentage of water vapor in the air as it relates to the water vapor capacity at that temperature, and the water vapor capacity of the air increases as ambient temperature increases. In other words, relative humidity (퐻푟) is the ratio of the vapor pressure of unsaturated air to saturated vapor pressure of the air at the same air

푒푎 temperature (i.e. 퐻푟 = ). Murray explains that for most meteorological purposes the 푒푠(푇) saturation vapor pressure is expressed as

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17.269 푇 (237.3+푇) 푒푠(푇) = 0.6108 푒 , (3.1) where 푇 is the temperature in C and 푒푠 is given in kPa, is acceptable (1967). The partial pressure of water vapor in unsaturated air (vapor pressure) can be calculated from the standard psychrometric equation

푒푎 = 푒푠(푇푊) − 훾(푇 − 푇푊) (3.2) where 푇푊 is the wet-bulb temperature, 푒푠(푇푊) is the saturation vapor pressure 푇푊, and 훾 is

푐 푃 the psychrometric constant (훾 = 푝푎 (Pa K-1)) based on 푃 (Pa) is atmospheric pressure, 휀

-1 -1 -1 푐푝푎 = 1004 J kg K is the specific heat of dry air,  = 2.454 MJ kg is the latent heat of vaporization of water and 휀 = 0.622 is the ratio of the molecular weights of water and air

(Landsberg and Sands, 2011).

Vapor pressure deficit (VPD) is the amount of moisture in the air and how much moisture the air can hold when it is saturated. As a result, VPD is a function of both ambient temperature and relative humidity. Considering transpiration, the vapor pressure difference

(e, Pa) between the inside of the leaves and the ambient air is the important variable which depends on the vapor pressure of the air and the foliage temperature (푇푓). Assuming that air in sub-stomatal cavities is saturated with water vapor, then ∆푒 = 푒푠(푇푓) − 푒푎. Generally, vapor pressure deficit (퐷) (Pa) is an important measure of the drying power of air. It is given by

퐻 퐷 = 푒 (푇) − 푒 = 푒 (푇) (1 − 푟 ) (3.3) 푠 푎 푠 100 where 푇 is the observed diurnal temperature (Landsberg and Sands, 2011). VPD and relative humidity have an inverse relation (as increases VPD, 퐻푟 decreases). High daylight VPD demands moisture from the foliage, increasing transpiration and ultimately contributing to 107

water stress at the foliar level of the plant. This water stress for prolonged periods of time can adversely impact the plant growth.

Each climatic variable was examined against weekly biomass growth. The objective was to examine the effect of temperature on growth during optimal growing conditions.

Climatic variables found to be not limiting growth were noted and removed from further analysis. Observations made during exposure to limiting climatic variables, excluding temperature, were removed from further analysis. The resulting growth data were analyzed against the previously described temperature variables to determine the influence of temperature on cold tolerant Eucalyptus growth in the SE US.

Temperature lag-time response on growth of frost-tolerant Eucalyptus

Ogle et al. (2014) elaborates four types of memory lengths as they relate to current condition: short, intermediate, long and long with minor lag. These weighted memory types can be seen as the duration a past event effects the current state of a plant or ecosystem, or the lag-time response of a past event. Ogle et al. (2014) explains that there are two principle effects on the current state: (1) exogenous, effects of external factors (environmental) and (2) endogenous, the previous state of the plant or system (size). This study focuses on the effect of weekly average minimum temperature (푇푚𝑖푛) on the weekly stem biomass accumulation for cold tolerant Eucalyptus species for 58 weeks. This study period has resulted in the effects of seasonal variation of 푇푚𝑖푛 of larger or coarser time step as well as the weekly effect on the variation of 푇푚𝑖푛 on a finer time step.

The response of growth to weekly temperature was examined using a sinusoidal modeling approach to examine initially the seasonal effects on growth as they relate to 108

weekly average minimum temperature. Due to the influence of tree size (endogenous effect) on growth rate, the weekly growth was divided by the tree size of the previous week to mitigate the influence of tree size on growth rate. This resulted in a normalized weekly growth reflecting the percent increase in stem biomass per week. The following model form was used to estimate the weekly average minimum temperature (C) as well as normalized weekly mean stem biomass growth (kg)

∆푛퐵(푡) 표푟 푇푚𝑖푛(푡) = 퐴 cos[휔(푡 − 훼)] + 퐶 + 휀 (3.4) where ∆푛퐵(푡) is the response variable for the normalized weekly mean stem biomass growth as a function of time (푡) and 푇푚𝑖푛(푡) is the response variable for weekly mean minimum temperature as a function of time, 퐴 is the amplitude (height of each peak form the baseline),

2휋 휔 is the angular frequency (휔 = ) based on the period (푃), 훼 is the phase shift (horizontal 푃 offset), 퐶 is the vertical offset (height of the baseline) and 휀 is the model error. A fixed value of 52 (weeks per year) was used for the period to remain consistent with seasonal factors.

The Gauss-Newton convergence method was performed using the PROC NLIN procedure for each response variable in SAS to minimize the sum of squares error for the overall model

(SAS, 2012).

Using the residuals from the sinusoidal model for normalized weekly mean stem biomass growth and temperature, a lag time analysis was conducted to determine the growth response at a fine temporal resolution of one week for cold tolerant Eucalyptus species weekly growth as it is influenced by 푇푚𝑖푛.

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Results and Discussion

Mean weekly stem biomass accumulation for each of the seven species can be seen in

Figure 3.2. The graph shows that cold tolerant Eucalyptus species will continue to add stem biomass through the winter months as long as the weekly minimum temperature allows. This gives Eucalyptus the advantage over pine species and native hardwoods that store fixed carbon as carbohydrates or remain dormant during the winter months, respectively. The graph also shows that during summer months there are other climate factors that are limiting the growth of the cold tolerant Eucalyptus.

Frost-tolerant Eucalyptus species growth

The total stem biomass (kg) was calculated for each individual based on the weekly dendrometric measurements (Table 3.1). The overall mean stem biomass at the initial measurement was 5.59-kg. Of the seven species, E.benthamii had the greatest average stem biomass of 8.45-kg, and E.dalrympleana, with a 62.6% reduction, had the smallest average stem biomass of 3.16-kg at the initial measurement on September 14, 2012 with an age of approximately 1.4-years. Figure 3.1 shows that during the study period, there was not any apparent changes in mean stem biomass ranking among the species. Species with smaller mean stem biomass (E.dalrympleana and E.viminalis) did not change ranking between the two species, and the intermediate performers (E.dorrigoensis, E.badjensis and E.nitens) did change mean stem biomass ranking with the exception of E.badjensis remaining superior to

E.nitens throughout the study period.

E.benthamii had the greatest mean stem biomass throughout the study period, and

E.macarthurii was the only species to close the gap in mean stem biomass. The overall mean

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stem biomass at the end of the study period was 30.69-kg, an approximate 5.5-fold increase.

As outlined, the mean stem biomass ranking did change; and, as a result, E.benthamii has the greatest mean stem biomass of 42.28-kg, and E.dalyrmpleana, with a 63.8% reduction, had the smallest mean stem biomass of 15.32-kg at the end of the study period of 58 weeks.

The first objective of this work was to determine if there is a significance difference in growth behavior among cold tolerant Eucalyptus species. The hypothesis was that all cold tolerant Eucalyptus species respond in a similar manner. If there is no significant difference in growth, then the growth of different cold tolerant Eucalyptus species will respond in a similar manner as it relates to climatic variables.

By examining the potential significant differences in the growth rates among cold tolerant Eucalyptus species, we can determined that the cold tolerant Eucalyptus species selected for this research react to climatic changes and stresses in a similar matter.

The difference in mean stem biomass per species was used to examine the effect of temperature on growth. The mean weekly stem biomass growth (kg tree-1) is presented in

Table 3.2 for each study tree by month through the study period. January, February and

March 2013 observed the lowest weekly stem growth across all species with all individuals in the study averaging 15-g or less for this three-month period with the exception of one

Eucalyptus benthamii growing less than 50-grams in February and March. Beginning June

2013 all cold tolerant Eucalyptus species had one or more individuals growing more than one kilogram per week through October with the exception of Eucalyptus dalrympleana.

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Effects of climate variables on frost-tolerant Eucalyptus growth

Climate data from a weather station in close proximity to the study site was used during the study period to compare the influences of climatic variables to growth. Data was collected in hourly intervals and summarized as weekly data to remain consistent with the growth measurements. Table 3.4 summarized these weekly climatic variables at the monthly scale. The climate data collected during the sampling period was compared to the daily means of thirty-year data collected by the National Oceanic and Atmospheric Association

(NOAA) from 1981 to 2010 (Table 3.5). During the study period, weekly mean minimum

(Tmin), weekly mean (Tavg), and weekly mean maximum (Tmax) temperatures were on average

1C warmer than the observed historical data. Precipitation during the study period (Figure

3.5) greatly was found to be evenly distributed throughout the year with the exception of

April and May 2013 where only 7-mm of precipitation was recorded. During the 58-week study period, 2128-mm of precipitation was recorded (averaging 1907-mm per year) which greatly exceeded the historical average of 1100-mm per year. Weekly mean daylight vapor pressure deficit (VPD) (Figure 3.6) averaged 0.81-kPa across the study period and peaked in

April through September with weekly values reaching as high as approximately 1.4-kPa.

The increased precipitation during the study period reduced the atmospheric demand of water from vegetation which likely contributed to the reduced VPD values observed. Weekly mean photosynthetically active radiation (PAR) (Figure 3.7) averaged 6 MJ m-2 day-1 during the study period peaking in April through June at approximately 12 MJ m-2 day-1.

Weekly temperature variables (Tmin, Tavg and Tmax) observed during the study period were closely compared with the historical data for Raleigh, North Carolina. Across all temperature variables (weekly mean minimum, weekly mean, and weekly mean maximum)

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January 2013 was found to be approximately 3C warmer than the 30-year average, while

February and March 2013 were only average 2C colder across all temperature variables.

When comparing the temperature variables of April through July 2013 to the historical mean, these months showed less variance (approx. 1.5C) in temperature with weekly mean minimums and weekly mean maximums being cooler than the historical data. August 2013 was consistently cooler across all temperature variables compared to historical data by approximately 2C. Observations during September 2012 and 2013 were cooler than the historical average with September 2012 being more divergent from the historical trend.

Observations during October 2012 and 2013 were consistent with those of September in that

2012 weekly temperatures of October were cooler; however, the weekly temperature variables of October 2013 can be considered normal with the exception of a cooler weekly mean maximum temperature by approximately 3C. Measurements during November 2012 were much cooler compared to the historical data by as much as 4C for Tmax and as little as

2C for Tmin with the weekly mean temperature approximately 3.5C cooler. Contrastingly,

December 2012 was found to be overall warmer compared to historical data with Tmin being nearly 4.5C warmer and Tmax being slightly more than 1C warmer and the weekly mean temperature being more than 2.5C warmer.

Climate variables were categorized for regression analysis based on the astronomical seasons where spring spans from the March equinox to the June solstice, summer spans from the June solstice to the September equinox, fall spans from the September equinox to the

December solstice, and winter spans from the December solstice to the March equinox. The weekly stem biomass growth (kg tree-1) was normalized as percent gain as it related to the

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previous weeks stem biomass (kg tree-1). This provided the removal of endogenous effects

(tree size), and were able to examine the exogenous weekly climate effects for all cold tolerant Eucalyptus species (Figure 3.9) and E.benthamii (Figure 3.10).

The weekly mean stem growth (% stem biomass increase) of cold tolerant Eucalyptus species was compared to six climate variables (Figure 3.9): weekly mean minimum temperature (Tmin), weekly mean temperature (Tavg), weekly mean maximum temperature

(Tmax), precipitation, weekly mean daylight vapor pressure deficit (VPD; kPa), and weekly mean photosynthetically active radiation (PAR; MJ m-2 day-1). The three temperature variables showed a positive correlation with normalized weekly stem growth. Examining the temperature variables within seasons it showed that the combined seasons of winter and spring have a stronger correlation with normalized weekly mean stem growth compared to the combined seasons autumn and summer. Normalized weekly mean stem biomass growth appeared to stop at Tmin=-2.5C, Tavg=2.5C or Tmax=7C and reached at maximum normalized growth of approximately 7% at Tmin=22C, Tavg=25C or Tmax=30C. However, at maximum temperature there was great variation in range of growth likely influenced by other climate variables. Weekly precipitation and mean PAR did not appear to correlation.

Weekly mean daylight vapor pressure deficit (VPD) showed a parabolic shape as it relates to the normalized weekly mean stem biomass growth. VPD ranged during the study period from approximately 0.48 to 1.5-kPa where stem growth reached a climate at approximately

1.10-kPa. A decline in stem growth was observed when VPD increased beyond 1.10-kPa.

Using the weekly mean stem biomass growth from all individuals in the study, the major climatic variables were compared to growth to examine potential correlations. A multiple linear regression approach was used to explore the climate variables best suited to 114

explain the variation in growth of cold tolerant Eucalyptus species in the southeastern United

States. The data was organized categorically by seasons and incorporated in the multiple regression model using dummy variables for each season. All climate variables previously described were considered in the formation of the regression analysis. However, multicollinearity became problematic when apply multiple climate variables and/or using dummy variables for individual seasons.

Weekly mean temperature and normalized weekly stem growth were transformed using inverse and logarithm functions to linearize the data and provide an asymptotic effect to the upper limits. The dummy variable was applied by grouping winter and spring together which results in two unique prediction equations for each season pair. Examining the relationship between Tavg and nB in Figure 3.9 shows that the winter/spring data and summer/autumn data have similar y-intercept with unique slopes suggesting the necessity for an interaction term with the dummy variable and Tavg. The analysis of variance and parameter estimates can be seen in table 3.5 which yielded the following predictions equations:

−1 Winter/Spring: ∆̂푛퐵 = exp (−3.0067 − 10.8494 ∗ 푡푎푣푔) (3.5)

−1 Summer/Autumn: ∆̂푛퐵 = exp (−3.0067 + (5.1830 − 10.8494) ∗ 푡푎푣푔). (3.6)

The residual plot (Figure 3.11) and the fit plot (Figure 3.12) show that while the prediction equations do an excellent job with weekly stem growth rates below 3%. The increased variation in growth rates beyond 15C resulted in the heterogeneous nature of the residuals for the summer/fall prediction equation. While the inclusion of other climate variables reduced the overall performance of the model with increasing the accuracy during the summer and autumn season, the potential for a lag time response or a decoupling of growth 115

rates from temperature may be present during the growing seasons for cold tolerant

Eucalyptus species in the piedmont of North Carolina.

Temperature lag-time response on growth of frost-tolerant Eucalyptus

Based on the examination of weekly mean stem biomass growth (kg tree-1) and a range of climate variables, it is apparent that temperature is more correlated with cold tolerant Eucalyptus growth than other major climate variables during the study period. The weekly mean temperature and normalized weekly mean stem biomass growth is presented in

Figure 3.11 showing that during the study period the Eucalyptus species responded weekly to the abrupt changes in weather. A sinusoidal function was used for weekly growth and temperature the neutralized the seasons effects and more closely examine the weekly variation.

The analysis of variance and parameter estimates for weekly mean minimum temperature (Tmin) and normalized weekly mean stem biomass growth (nB) can be seen in

Table 3.7 and Table 3.8 respectively. Both models had high levels of significances and all parameter estimates being statistically significant at the alpha-level 0.05. The Tmin parameter estimates for equation 3.4 show that the amplitude (A) of Tmin is approximately 9.86C during the study period with a baseline (C) temperature of approximately 10.9C. The baseline temperature of the predicted curve is consistent with the overall observed Tmin value seen in Table 3.4. The nB parameter estimates for equation 3.4 show that the amplitude (A) of nB is approximately 0.0181 during the study period with a baseline (C) temperature of approximately 0.029. These parameter estimates of normalized growth show that throughout

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the study period that the stem biomass of cold tolerant Eucalyptus species increased by approximately 2.9% with a peak and trough at approximately 4.7% and 1.1% respectively.

The fit of the prediction equations for weekly mean minimum temperature and normalized stem growth are shown with the observed data in Figures 3.14 and 3.15 respectively. Both predictions equations are plotted in Figure 3.16 to observe potential effects of seasonal lag time on growth. Figure 3.16 shows that the peak and trough of Tmin and nB are not consistent by week. The empirical evidence of this seasonal lag time is realized when comparing the phase shift (α) parameter estimates. Weekly mean temperature has a phase shift parameter estimate of 6.27 while normalized weekly stem growth is 4.87.

This is interrupted as the previous year’s peak in Tmin and nB was approximately 6.3 and

4.9 weeks prior to when the sampling period began. This suggests that there is a seasonal lag time of approximately 1.4 weeks in maximum and minimum stem growth as it relates to the highest and lowest weekly mean minimum temperature during the year.

The residuals (Figure 3.17) of the fitted sinusoidal curves for Tmin and nB were examined for potential lag time responses in growth as a result of changing weekly mean minimum temperature. The figure shows several points where nB decouples from and converges with the weekly mean minimum temperature during the study period. The convergence of mean stem growth with weekly mean minimum temperature begins in mid-

December and divergence is observed in April. However, during the period from December through April, we observed that the weekly mean minimum temperature is driving the weekly stem biomass growth on a weekly basis. This observation is consistent with the multiple linear regression analysis a showing improved distribution of residuals during the

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winter and spring weeks while the residuals increases dramatically during the weeks of summer and autumn.

Conclusion

The growth of seven cold tolerant Eucalyptus species were tested against demanding climatic conditions to understand the potential limiting climate variables of these promising exotic species. Site selection for this trial was based on optimal soil conditions near the northern limit of the estimated zone of commercial plantations to increase the likelihood of adverse weather conditions. We observed that all the cold tolerant Eucalyptus species tested did not have any significant differences in weekly growth rates throughout the 58 week study period.

When comparing six climate variables to the normalized weekly mean stem growth, multiple regression techniques showed that temperature is the predominant driver of growth for cold tolerant Eucalyptus species. The effects of temperature on growth were seasonally dependent through the incorporation of dummy variables into the regression analysis. The sensitivity of cold tolerant Eucalyptus species was examined through a lag time study to determine the response of weekly stem growth to the weeks mean minimum temperature. A seasonal lag time of approximately 1.4 weeks was observed from peak growth and mean minimum temperature and least growth and mean minimum temperature. However, examining the residuals of the seasonal growth and temperature trends indicated that cold tolerant Eucalyptus respond on a weekly basis to the change in mean minimum temperature throughout the winter months of January through March during the study period.

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The establishment of forest plantations using exotic species requires matching the site and climatic characteristics of the exotic environments with the natural environments. Soil treatments such as site preparation and fertilization allows forest managers to mitigate some undesirable soil conditions for exotic species. However, the unpredictable nature of climatic variables requires careful examination while matching exotic species to sites across regions.

Historical climate data provides insight to species selection; but, rigorous field trials near zoning limits are required to test the performance of exotic species with demanding climatic conditions.

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Hesheng, L., Q. Jingqing, X. Guoyang, H. Delong, Z. Shirong and L. Wenge. 2003. Review of Cold-Tolerant Eucalyptus Improvement in Fujian Province. In: Proceedings of the ACIAR international conference No. 111, Eucalypts in Asia, Turnbull, J.W., April 7-11, 2003. Zhanjiang, Guangdong, People’s Republic of China. 117-122.

Higa, A.R. and P.E.R. Carvalho. 1990. Sobrevivência e crescimento de doze espécies de eucalipto em Dois Vizinhos, Paraná. Congresso Florestal Brasilierio, EMBRAPA. Curitiba, Brasil: 459-461.

Landsberg, J. and P. Sands. 2011. Weather and energy balance. In Physiological ecology of forest production: Principles, processes and models. (First edition, p. 331). Burlington, MA: Academic Press.

Leslie, A.D., M. Mencuccini and M. Perks. 2012. The potential for Eucalyptus as a wood fuel in the UK. Applied Energy 89: 176-182.

Misra, R.K., C.R.A. Turnbull, R.N. Cromer, A.K. Gibbons and A.V. LaSala. 1998. Below- and above-ground growth of Eucalyptus nitens in a young plantation: I. Biomass. Forest Ecology and Management 106: 283-293.

Murray, F.W. 1967. On the Computation of Saturation Vapor Pressure. J. Appl. Metor. 6: 203-204.

Ogle, K., J.J. Barber, G.A. Barron-Gafford, L.P. Bentley, J.M. Young, T.E. Huxman, M.E. Loik and D.T. Tissue. 2014. Quantifying ecological memory in plant and ecosystem processes. Ecology letters: 1-15 p.

SAS. 2012. SAS/STAT 9.3 User’s Guide, second edition.

Table 3.1. Cold-tolerant Eucalyptus species stem biomass (kg tree-1).

E.badjensis E.benthamii E.dalrympleana E.dorrigoensis E.macarthurii E.nitens E.viminalis

Date No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Sep-12 3 6.1 7.5 7.1 10.1 5.4 13.2 7.4 5.1 2.5 2.4 5.1 7.1 7.0 4.7 9.0 6.2 3.2 7.7 2.7 3.9 4.4

Oct-12 4 7.8 9.1 8.7 11.9 6.4 15.2 8.7 6.2 3.1 2.8 6.0 8.4 8.1 6.1 10.2 8.0 3.7 8.7 3.2 4.7 5.1

Nov-12 4 8.9 10.7 9.8 13.6 7.7 17.0 9.9 7.7 3.7 3.6 7.1 9.7 9.1 7.4 11.6 9.6 4.3 10.1 4.2 5.4 5.7

Dec-12 5 9.7 11.8 10.7 15.6 8.1 19.0 11.1 8.6 4.0 3.9 8.0 10.3 10.6 8.2 12.6 10.6 5.2 12.2 5.9 5.8 6.5

Jan-13 4 10.5 12.9 11.3 16.5 8.3 20.6 12.0 9.0 4.2 3.9 8.6 10.6 11.0 8.8 13.4 11.4 5.8 12.9 6.1 6.1 6.8

Feb-13 4 10.8 13.1 11.6 17.7 8.5 20.9 12.1 9.1 4.2 4.0 8.9 10.9 11.2 9.1 13.6 11.7 6.0 13.2 6.3 6.2 7.0

Mar-13 4 11.1 13.4 11.9 19.7 8.7 21.1 12.2 9.4 4.3 4.0 9.2 11.1 11.5 9.5 14.0 12.2 6.1 13.5 6.4 6.3 7.2

Apr-13 5 12.0 14.8 12.9 21.2 9.0 22.3 12.6 10.5 4.9 4.1 9.7 12.0 12.4 10.2 15.5 13.6 6.7 14.9 7.2 7.1 8.0

May-13 5 13.7 17.1 14.7 24.1 9.5 25.4 13.4 13.1 6.2 4.4 11.5 14.7 15.3 12.4 18.6 16.5 7.9 17.9 8.6 8.8 10.5

Jun-13 4 15.6 19.8 17.7 28.6 10.6 28.5 16.4 16.0 7.7 5.0 14.8 17.9 20.1 16.3 23.9 20.0 9.9 21.2 11.0 12.1 13.7

Jul-13 4 17.5 25.2 21.8 37.0 13.0 34.7 23.4 18.5 9.3 6.3 17.9 21.3 25.7 20.0 29.4 22.8 11.7 26.1 13.7 15.0 18.6

Aug-13 5 18.9 29.0 26.7 43.3 15.4 42.5 28.1 20.2 10.0 7.8 21.1 24.1 28.6 23.2 35.7 25.5 13.6 29.9 16.9 17.3 22.0

Sep-13 4 21.2 32.7 29.5 49.4 17.7 46.9 31.6 22.9 11.0 8.2 27.0 28.9 31.2 28.8 38.7 27.7 16.0 33.4 18.0 18.4 23.8

Oct-13 3 24.8 37.0 32.2 58.1 20.2 52.0 34.7 24.8 12.3 8.3 31.7 33.1 32.3 34.5 42.3 30.4 17.7 39.3 18.8 19.3 26.0

121

45 E.badjensis 40 E.bentahmii E.dalrympleana E.dorrigoensis 35 E.macarthurii E.nitens 30 E.viminalis

15 Mean stem biomass (kg) biomass stem Mean 10

0 0 10 20 30 40 50 60 Week

Figure 3.1. Total mean stem biomass (kg) of seven cold-tolerant Eucalyptus species planted in the Piedmont of North Carolina.

122

Table 3.2. Weekly mean stem biomass growth by month of cold-tolerant Eucalyptus species.

E.badjensis E.benthamii E.dalrympleana E.dorrigoensis E.macarthurii E.nitens E.viminalis

Date No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Sep-12 2 0.73 0.53 0.53 0.65 0.28 0.95 0.61 0.30 0.21 0.04 0.30 0.44 0.35 0.44 0.52 0.52 0.21 0.28 0.22 0.30 0.27

Oct-12 4 0.42 0.50 0.42 0.48 0.33 0.52 0.28 0.40 0.19 0.16 0.29 0.39 0.29 0.39 0.39 0.53 0.14 0.32 0.14 0.23 0.17

Nov-12 4 0.15 0.27 0.19 0.47 0.24 0.32 0.27 0.26 0.11 0.15 0.25 0.18 0.33 0.24 0.24 0.25 0.18 0.48 0.42 0.11 0.17

Dec-12 5 0.24 0.32 0.22 0.32 0.04 0.55 0.30 0.14 0.04 0.04 0.12 0.13 0.19 0.16 0.24 0.25 0.21 0.28 0.18 0.08 0.13

Jan-13 4 0.09 0.08 0.05 0.11 0.05 0.11 0.05 0.04 0.02 0.01 0.12 0.04 0.06 0.08 0.09 0.07 0.06 0.13 0.02 0.05 0.05

Feb-13 4 0.07 0.05 0.09 0.45 0.05 0.08 0.04 0.07 0.01 0.00 0.07 0.10 0.06 0.09 0.04 0.11 0.03 0.04 0.04 0.01 0.05

Mar-13 4 0.08 0.10 0.11 0.36 0.04 0.02 0.02 0.05 0.03 0.01 0.05 0.02 0.05 0.08 0.14 0.11 0.05 0.13 0.05 0.07 0.05

Apr-13 5 0.31 0.47 0.29 0.52 0.09 0.47 0.15 0.42 0.21 0.04 0.19 0.38 0.39 0.26 0.50 0.49 0.18 0.48 0.24 0.23 0.37

May-13 5 0.35 0.46 0.45 0.54 0.09 0.70 0.13 0.58 0.28 0.09 0.53 0.58 0.65 0.60 0.87 0.64 0.32 0.56 0.38 0.51 0.47

Jun-13 4 0.43 0.87 0.67 1.56 0.45 0.75 1.31 0.60 0.38 0.18 0.78 0.81 1.40 0.91 1.01 0.65 0.46 0.97 0.47 0.71 0.97

Jul-13 4 0.40 1.16 1.24 1.96 0.58 1.93 1.51 0.50 0.30 0.38 0.63 0.65 1.01 0.80 1.76 0.83 0.41 1.19 0.85 0.73 1.15

Aug-13 5 0.30 0.77 0.84 1.07 0.50 1.20 0.88 0.50 0.15 0.24 0.99 0.86 0.72 0.90 0.85 0.40 0.48 0.60 0.49 0.35 0.55

Sep-13 4 0.84 1.08 0.72 2.06 0.61 1.35 0.93 0.60 0.37 0.04 1.33 1.14 0.43 1.48 0.97 0.74 0.55 1.29 0.25 0.30 0.48

Oct-13 3 0.95 1.12 0.75 2.37 0.68 1.34 0.76 0.44 0.28 0.03 1.33 1.21 0.29 1.54 0.93 0.71 0.45 1.65 0.19 0.21 0.62

123

2.25 E.badjensis 2.00 E.benthamii E.dalrympleana 1.75 E.dorrigoensis E.macarthurii E.nitens 1.50 E.viminalis

1.25

1.00

0.75

0.50 Weekly mean stem biomass growth (kg) growth biomass meanstem Weekly 0.25

0.00 0 10 20 30 40 50 60 Week

Figure 3.2. Weekly mean stem biomass growth (kg) for each cold-tolerant Eucalyptus species planted in the Piedmont of North Carolina.

124

Table 3.3. Analysis of variance to test for significance among cold tolerant Eucalyptus species.

Source df Sum of squares Mean square F value Pr > F Model Species 6 19.138 3.190 2.42 0.0812 Plant(species) 14 18.454 1.318 Week 56 135.882 2.426 34.19 < 0.0001 Species*Week 336 43.313 0.129 1.82 < 0.0001 Error 784 55.641 0.071 Total 1196 277.363

125

Sep-12 Dec-12 Mar-13 Jul-13 Oct-13 2.25

All species 2.00

E.benthamii

) 1

- 1.75

week

1 -

1.50 kg kg tree 1.25

1.00

0.75

0.50 Mean stem Meanstem biomass growth(

0.25

0.00 0 10 20 30 40 50 60 Week

126

Table 3.4. Mean climatic variables, minimum, mean and maximum temperature (C), vapor pressure deficit (kPa), photosynthetically active radiation (MJ m-2 d-1), and total precipitation (mm) during the sampling period.

Tmin Tavg Tmax VPD PAR Precip. Year month season Weeks (C) (C) (C) (kPa) (MJ m-2 d-1) (mm) 2012 Sep. Fall 3 15.7 19.9 24.8 0.84 4.68 197 2012 Oct. Fall 4 8.7 13.6 19.1 0.75 4.16 167 2012 Nov. Fall 4 3.1 8.4 14.5 0.64 3.21 43 2012 Dec. Fall 3 8.1 12.1 16.6 0.55 2.10 79 2012 Dec. Winter 2 1.9 5.9 10.0 0.43 2.21 131 2013 Jan. Winter 4 3.1 7.6 12.9 0.47 2.74 145 2013 Feb. Winter 4 0.8 5.5 10.6 0.47 4.46 249 2013 Mar. Winter 2 3.1 8.8 14.4 0.70 5.75 66 2013 Mar. Spring 2 1.9 6.7 11.4 0.65 6.96 83 2013 Apr. Spring 5 10.8 15.6 20.7 0.89 7.50 7 2013 May Spring 4 14.6 20.2 25.7 1.13 9.63 6 2013 Jun. Spring 3 18.9 23.4 28.2 1.14 9.29 91 2013 Jun. Summer 2 21.2 24.7 29.4 0.94 8.57 208 2013 Jul. Summer 4 21.5 25.3 30.1 1.13 8.70 135 2013 Aug. Summer 5 19.5 23.8 28.8 1.04 8.19 349 2013 Sep. Summer 2 16.7 21.7 27.3 1.19 7.97 83 2013 Sep. Fall 2 13.1 18.4 24.5 0.94 7.34 42 2013 Oct. Fall 3 12.2 16.0 19.7 0.58 4.06 45 Grand Total/Mean 58 11.0 15.6 20.7 0.81 6.00 2128

127

Tmin Tavg Tmax Precip Month Weeks (C) (C) (C) (mm) January 4 -0.6 4.9 10.4 80 February 4 0.8 6.6 12.5 82 March 5 4.1 10.6 17.1 114 April 4 8.7 15.5 22.3 70 May 4 13.0 19.5 26.0 72 June 5 18.4 24.3 30.3 105 July 4 21.1 26.7 32.4 108 August 4 20.6 26.1 31.6 99 September 5 17.1 22.7 28.4 130 October 4 10.4 16.7 23.0 76 November 4 5.6 12.1 18.5 74 December 5 1.2 6.9 12.6 94 Grand Total/Mean 52 10.0 16.1 22.1 1101

128

35 35 Precip Tmax 30 30 Tmin

25 25

20 20

15 10

Weekly Weekly precipitaitontotal (mm) 10 5 Weekly mean temperature (deg. C)

5 0

0 -5

1-Jul 8-Jul

7-Jan

3-Jun

7-Oct

8-Apr 1-Apr

4-Feb 2-Sep 9-Sep

2-Dec 9-Dec

5-Aug

15-Jul 22-Jul 29-Jul

4-Nov

4-Mar

6-May

14-Jan 21-Jan 28-Jan

10-Jun 17-Jun 24-Jun

14-Oct 21-Oct 28-Oct

15-Apr 22-Apr 29-Apr

11-Feb 18-Feb 25-Feb 16-Sep 23-Sep 30-Sep

16-Dec 23-Dec 30-Dec

12-Aug 19-Aug 26-Aug

11-Nov 18-Nov 25-Nov

11-Mar 18-Mar 25-Mar

13-May 20-May 27-May Week ending date

Figure 3.4. Thirty-year mean climate data for Raleigh, North Carolina from 1981 through 2010. Daily mean observations provided by NOAA summarized to weekly observations to compare climate during study period using equal time intervals.

129

Sep-12 Dec-12 Mar-13 Jul-13 Oct-13 35.0 Tmax 30.0 Tavg

Tmin C)

 25.0

20.0

15.0

10.0

5.0 Weekly Weekly temperature mean (

0.0

-5.0 0 10 20 30 40 50 60 Week

Figure 3.5. Weekly mean minimum, mean and mean maximum temperature (C) observed hourly from the CRONOS database at the Reedy Creek Field Laboratory during the study period.

130

250

200

150

100 Precipitation (mm) Precipitation

0 1 11 21 31 41 51 Week

Figure 3.6. Weekly precipitation accumulation (mm) calculated from hourly observations of the CRONOS database at the Reedy Creek Field Laboratory during the study period.

131

Sep-12 Dec-12 Mar-13 Jul-13 Oct-13 1.8

1.6

1.4 kPa) 1.2

1.0

0.8

0.6

Weekly Weekly daylight mean ( VPD 0.4

0.2

0.0 0 10 20 30 40 50 60 Week

Figure 3.7. Weekly mean daylight vapor pressure deficit (kPa) calculated from the relative humidity (%) and temperature (C) observed hourly from the CRONOS database at the Reedy Creek Field Laboratory during the study period.

132

Sep-12 Dec-12 Mar-13 Jul-13 Oct-13 12.0

10.0

)

d 2

- 8.0 MJ MJ m

6.0

4.0 Weekly Weekly PAR mean (

2.0

0.0 0 10 20 30 40 50 60 Week

Figure 3.8. Weekly mean photosynthetically active radiation (PAR) (MJ m-2 d-1) from the CRONOS hourly observations collected at the Reedy Creek Field Laboratory during the study period.

133

0.08 0.08 0.07 Winter 0.07 Winter Autumn Autumn 0.06 0.06 Spring Spring 0.05 Summer 0.05 Summer 0.04 0.04 0.03 0.03 0.02 0.02

0.01 A 0.01 D Stem Stem biomass growth (%) Stem Stem biomass growth (%) 0.00 0.00 -5 0 5 10 15 20 25 30 35 0 50 100 150 200 250 Mean min. temperature (C) Weekly precipitation (mm)

0.08 0.08 Winter 0.07 Winter 0.07 Autumn Autumn 0.06 Spring 0.06 Spring 0.05 Summer 0.05 Summer 0.04 0.04 0.03 0.03 0.02 0.02

0.01 B 0.01 E Stem Stem biomass growth (%) Stem Stem biomass growth (%) 0.00 0.00 0.0 0.5 1.0 1.5 2.0 0 5 10 15 20 25 30 35 Mean max. temperature (C) Mean vapor pressure deficit (kPa)

0.08 0.08 Winter Winter 0.07 Autumn 0.07 Autumn 0.06 Spring 0.06 Spring 0.05 Summer 0.05 Summer 0.04 0.04 0.03 0.03 0.02 0.02

0.01 C 0.01 F Stem Stem biomass growth (%) Stem Stem biomass growth (%) 0.00 0.00 0 5 10 15 20 25 30 35 0 4 8 12 Mean temperature (C) Mean PAR (MJ m-2 d-1)

134

0.09 0.09 0.08 Winter 0.08 Winter Autumn 0.07 0.07 Autumn Spring Spring 0.06 0.06 Summer Summer 0.05 0.05 0.04 0.04 0.03 0.03 0.02 0.02

0.01 A 0.01 D Stem Stem biomass growth (%) Stem Stem biomass growth (%) 0.00 0.00 -5 5 15 25 35 0 50 100 150 200 250 Mean min. temperature (C) Weekly precipitation (mm)

0.09 0.09 0.08 Winter 0.08 Winter E Autumn Autumn 0.07 Spring 0.07 Spring 0.06 Summer 0.06 Summer 0.05 0.05 0.04 0.04 0.03 0.03 0.02 0.02

0.01 0.01 Stem Stem biomass growth (%) B Stem biomass growth (%) 0.00 0.00 0 5 10 15 20 25 30 35 0.0 0.5 1.0 1.5 2.0 Mean max. temperature (C) Mean vapor pressure deficit (kPa)

0.09 0.09 Winter 0.08 Winter 0.08 F Autumn Autumn 0.07 0.07 Spring Spring 0.06 0.06 Summer Summer 0.05 0.05 0.04 0.04 0.03 0.03 0.02 0.02

0.01 0.01 Stem Stem biomass growth (%) Stem Stem biomass growth (%) C 0.00 0.00 0 5 10 15 20 25 30 35 0 4 8 12 Mean temperature (C) Mean PAR (MJ m-2 d-1)

Figure 3.10. Relation between normalized weekly mean stem biomass growth (%) of E.benthamii (initial and final mean stem biomass of 8.45-kg and 43.29-kg respectively) and weekly mean minimum (A), mean maximum (B) and mean (C) temperature (C), weekly precipitation (D) (mm), mean daylight vapor pressure deficit (E) (kPa) and mean photosynthetically active radiation (F) (MJ m-2 d-1).

135

Table 3.6. Analysis of variance and parameter estimates for the multiple linear regression analysis of weekly mean temperature as a predictor of normalized weekly stem growth of −1 −1 cold tolerant Eucalyptus species. 푙푛 ∆푛퐵 = 훽0 + 훽1푡푎푣푔 + 훽2푑1푡푎푣푔. Source df SS MS F value Pr > F Model 2 36.5747 18.2874 86.0181 < 0.0001 Error 55 11.6930 0.2126 Total 57 48.2677

Parameter Estimate St. error t stat P-value 훽0 -3.0067 0.1210 -24.8471 < 0.0001 훽1 -10.8494 0.9009 -12.0432 < 0.0001 훽2 5.1830 1.5931 3.2533 0.001952

136

0.04 Winter/Spring 0.03 Summer/Autumn

0.02

0.01

Residual 0

-0.01

-0.02

-0.03 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 Predicted weekly stem growth per tree (%)

Figure 3.11. Residuals for the normalized weekly stem growth for each prediction equation based on the dummy variables of winter/spring and summer/autumn.

137

0.08 Predict Summer/Fall 0.07 Predict Winter/Spring Winter/Spring 0.06 Summer/Fall

0.05

0.04

0.03

0.02 Normalized stem growthper tree (%)

0.01

0 0 5 10 15 20 25 30 Weekly mean temperature (C)

138

25.0 0.08 Avg.Tmin_C

ALL.NormdB 0.07 20.0

0.06

15.0 0.05

10.0 0.04

0.03 5.0

0.02 Weekly Weekly temperature mean (deg. C) 0.0 0.01 Normalized growth biomass stem weekly (%)

-5.0 0.00 0 10 20 30 40 50 60 Week

Figure 3.13. Weekly mean minimum temperature (C) and normalized weekly stem biomass growth (%) during the study period.

139

Table 3.7. Analysis of variance and parameter estimates for the prediction on weekly average minimum temperature and study period intervals. 푇푚𝑖푛(푡) = 퐴 푐표푠[휔(푡 − 훼)] + 퐶, 2휋 where 휔 = . 52 Source df SS MS Approx. F value Pr > F Model 2 2615.7 1307.9 160.74 < 0.0001 Error 55 447.5 8.1366 Corrected Total 57 3063.2

Parameter Approx. estimate St. error Approx. 95% Confidence Limits 퐴 9.8575 0.5508 8.7537 10.9613 훼 6.2675 0.4340 5.3977 7.1372 퐶 10.8932 0.3782 10.1352 11.6511

140

Table 3.8. Analysis of variance and parameter estimates for the prediction on weekly average minimum temperature and study period intervals. ∆푛퐵(푡) = 퐴 푐표푠[휔(푡 − 훼)] + 퐶, 2휋 where 휔 = . 52 Source df SS MS Approx. F value Pr > F Model 2 0.00883 0.00441 20.58 < 0.0001 Error 55 0.0116 0.000214 Corrected Total 57 0.0204

Parameter Approx. estimate St. error Approx. 95% Confidence Limits 퐴 0.0181 0.00282 0.0124 0.0237 훼 4.8749 1.2371 2.3946 7.3552 퐶 0.02942 0.00195 0.0255 0.0334

141

25 Tmin Model

C) 20 

Weekly mean minimum emperature ( emperature minimum mean Weekly 0

-5 0 10 20 30 40 50 60 Week

Figure 3.14. Observed and predicted weekly mean minimum temperature in Raleigh, NC during the study period.

142

0.08 dBiomass 0.07 Model

0.06

0.05

0.04

0.03

0.02 Weekly stem biomass growth (%) growth biomass stem Weekly 0.01

0.00 0 10 20 30 40 50 60 Week

Figure 3.15. Observed and predicted normalized weekly stem growth of cold tolerant Eucalyptus species (initial mean stem biomass = 5.69-kg) in Raleigh, NC during the study period.

143

25 0.05

C)  20 0.04

15 0.03

10 0.02 Weekly biomass growth (%) growth biomass Weekly 5 0.01

Tmin model Weekly mean minimum temperature ( temperature meanminimum Weekly dB model 0 0.00 0 10 20 30 40 50 60 Week

Figure 3.16. Fitted sinusoidal prediction curves for weekly mean minimum temperature and normalized weekly stem growth of cold tolerant Eucalyptus species in Raleigh, NC during the study period.

144

14-Sep-12 13-Nov-12 12-Jan-13 13-Mar-13 12-May-13 11-Jul-13 9-Sep-13 0.04 10 NormdB_res 0.03 8

Tmin_res )

C 

) 6 0.02

4 0.01 2 0.00 0 -0.01 -2

-0.02

Weekly Weekly stem biomass growth (% -4 Weekly mean minimum minimum Weekly mean temperature ( -0.03 -6

-0.04 -8 0 10 20 30 40 50 60 Week Figure 3.17. Residuals of sinusoidal curves for weekly biomass growth of cold tolerant Eucalyptus species and weekly average minimum temperature

145