Modeling Crown Characteristics of

Loblolly Pine Trees

Modeling Crown Characteristics of

Loblolly Pine Trees

Harold E. BurkhartHarold E. BurkhartVirginia TechVirginia Tech

Outline

• Importance of crown measures

• Review two studies aimed at modeling loblolly pine crowns

– Measurements– Modeling methods

• Challenges and opportunities

Context

Loblolly Pine Plantations Managed for Wood Production

Variety of Products Intensive Silviculture• Pulpwood

• Sawtimber

• Peelers

• Poles

• Genetic selection

• Vegetation control

• Fertilizer applications

• Thinning (and possibly pruning) treatments

Crown characteristics important for:

• Making genetic selections– Crown width, branch size and angle

• Estimating response to silvicultural treatments

– Thinning, fertilizer

• Quantifying wood quality– Number, size, location of branches

Loblolly pine crowns are highly variable

Typically 2-5 whorls per year

Most commonly used crown variable crown ratio

Plot MeasurementsIndividual trees• Dbh• Total height• Height to base of crown

StandAge, site index, stand density, etc.

Model height to crown base or crown ratio

CR = 1 – exp (-())

CR constrained between 0 and 1

() is a function of tree and stand attributes

Crown Development

From: Liu, et al. 1995. For. Sci. 41:43-53.

Thinning Response Modifier

From: Liu, et al. 1995. For. Sci. 41:43-53.

I = BAa/BAb

More Detailed Descriptions of Tree Crowns

Approximate with geometric shapes

Model crown shape

Model crown morphology (branch diameter, location, angle, and length)

Efforts to Model Loblolly Pine Crown Morphology

Southern Global Change Project1990s

Subsequent work focused on wood quality modeling

Development of a Static Model of Loblolly Pine Crowns

1. Quantify foliage distribution

2. Model number, size, location of branches

3. Provide link between G&Y and process model

Southern Global Change Program

Felled sample trees across a range of stand ages and densities

28 in Virginia Piedmont40 in North Carolina Coastal Plain

Field Measurements

Tree Characteristics

1. DBH and diameter at base live crown

2. Total height and height to base live crown

3. Stump age and age at base live crown

4. Crown class

Summary of Measurements

Branch Characteristics

1. Height above ground to each branch

2. Diameter of each branch

3. Azimuth of each branch

4. Total length of the branch

5. Angle of the branch

Detailed measurements on a sample of

branches

Mapping foliage distribution in X-Y-Z space

Foliage divided into inner, middle, and outer thirds

Modeling Branches

• Total number of branches

• Diameter distribution of branches

• Vertical location of whorls

• Number of branches per whorl

• Circular location of branches in each whorl

• Branch length

• Branch angles

AnalysisTotal Number of Branches

Recursive system involving number of whorls and number of branches

No. whorls = 3.93 + 0.43 (dbh) + 0.94 (crown length)

No. branches = 7.29 + 2.26 (No. whorls)

Diameter Distribution of BranchesModel average, minimum, and maximum branch diameters as functions of dbh and

whorl height

Vertical Location of BranchesAssumed fixed spacing of whorls

Number of Branches in a WhorlUtilize overall percentages and random assignment

No. branches Percent of total whorls

1 19

2 28

3 29

4 15

5 6

6 2

7 1

Total Branch Length

Model total branch length as afunction of branch diameter

))diameterbranch(20.1-(e55.16+158.3

Total branch

length=

Branch Angle

Model branch angle from vertical as afunction of relative whorl height

Branch angle = 64.7 – 28.47 (relative whorl height)2.73

Circular Patterns of Branches

• Use circular statistics to examine rotational patterns of branches in consecutive whorls

• Found for consecutive whorls with the same number of branches, a positive rotation exists

Doruska and Burkhart. 1994. CJFR 24:2362-2376.

Doruska and Burkhart. 1994. CJFR 24:2362-2376.

Foliage Weight and Surface

Area Distributions

From: Baldwin, et al. (1997) CJFR 27:918-927.

Foliage Distribution Used inLinked Model

PTAEDA2Growth & Yield Model

MAESTROProcess Model

From: Baldwin, et al. (2001) For. Sci. 47:77-82.

SI = b1 (log(A2) – log (A1))

+ b2 (NPS2 – NPS1)

+ b3 (1/N2 – 1/N1)

BiasObserved Predicted

ft3/ac. m3/ha ft3/ac. m3/ha ft3/ac. m3/ha

4891 342.2 4284 299.8 4875 341.1

No SIAdjustment

SI Increase

Dynamic Model of Knot Size, Frequency, and Distribution

Sampling of whorlsLongitudinal data from a spacing study

214 whorl sections

January 2005

• DBH• TH• Stem height and diameter of every visible whorl

Stem dissection techniqueRecovering information on knot morphology and branch development

Branch dissection

Ring widthMarch-May 2005

Results

• Vertical trend of branch diameters and location along and around the stem

• Model of knot shape

• Volume of knots (live/dead portions)─ live branches─ non-occluded dead branches─ occluded dead branches

• Branch model linked to growth and yield model (PTAEDA)

Model of Live Portion of Knots

)(K=Rr

L2

2l

r = radius at length l

R = maximum radius

L = total length

From: Trincado and Burkhart. (2008) Wood and Fiber Sci. 40:634-646.

Branch Model

From: Trincado and Burkhart. 2009. Can. J. For. Res. 39:566-579.

Number of Whorls

From: Trincado and Burkhart. 2009. Can. J. For. Res. 39:566-579.

Multicategory logistic regression (h)

From: Trincado and Burkhart. 2009. Can. J. For. Res. 39:566-579.

Location of Whorls

No predictive equation possible

Used observed relative mean location

Number of Branches per Whorl

Stochastic procedure using double-truncated Poisson distribution with a,b = minimum and maximum number of branches per whorl observed

Branch Orientation around the Stem

Adapted methods of Doruska and Burkhart (1994)

Angle of Branch Inclination

Generated by sampling from a three-parameter Weibull distribution

Initial Branch Diameter

Assigned from a three-parameter Weibull distribution

Diameter Growth of First-Order Branches

BD = 0.780BL0.827 exp(-1.53RCH)

Link to Growth and Yield ModelPTAEDA

Challenges and Opportunities

• Determining which crown characteristics affect response to silvicultural treatment

• Modeling crown response to silviculture

Mass Control Pollinated

Challenges and Opportunities

ClonalOpen pollinated

Developing Models for a Rangeof Genetic Stocks

Four-Year-Old Planting of aLoblolly Pine Clone

Land ClassificationSoil Mapping System

GIS-Based Precision

Silviculture

Remote Sensing of LeafArea and Plantation Health

Thanks!

Questions?