Modeling Crown Characteristics of Loblolly Pine Trees Modeling Crown Characteristics of Loblolly Pine Trees Harold E. Burkhart Virginia 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 ProductsIntensive 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 Measurements Individual trees Dbh Total height Height to base of crown Stand Age, 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 For. Sci. 41:43-53.

Thinning Response Modifier From: Liu, et al For. Sci. 41: I = BA a /BA b

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 Project 1990s 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 Piedmont 40 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

Analysis Total Number of Branches Recursive system involving number of whorls and number of branches No. whorls = (dbh) (crown length) No. branches = (No. whorls)

Diameter Distribution of Branches Model average, minimum, and maximum branch diameters as functions of dbh and whorl height Vertical Location of Branches Assumed fixed spacing of whorls

Number of Branches in a Whorl Utilize overall percentages and random assignment No. branchesPercent of total whorls

Total Branch Length Model total branch length as a function of branch diameter Total branch length =

Branch Angle Model branch angle from vertical as a function of relative whorl height Branch angle = 64.7 – (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 CJFR 24:

Foliage Weight and Surface Area Distributions From: Baldwin, et al. (1997) CJFR 27:

Foliage Distribution Used in Linked Model PTAEDA2 Growth & Yield Model MAESTRO Process Model From: Baldwin, et al. (2001) For. Sci. 47:77-82.

 SI=b 1 (log(A 2 ) – log (A 1 )) +b 2 (NPS 2 – NPS 1 ) +b 3 (1/N 2 – 1/N 1 )

Bias ObservedPredicted ft 3 /ac.m 3 /haft 3 /ac.m 3 /haft 3 /ac.m 3 /ha No SI Adjustment SI Increase

Dynamic Model of Knot Size, Frequency, and Distribution

Sampling of whorls Longitudinal data from a spacing study 214 whorl sections January 2005 DBH TH Stem height and diameter of every visible whorl

Stem dissection technique Recovering information on knot morphology and branch development Branch dissection Ring width March-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 r=radius at length l R=maximum radius L=total length

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

Branch Model From: Trincado and Burkhart Can. J. For. Res. 39:

Number of Whorls From: Trincado and Burkhart Can. J. For. Res. 39: Multicategory logistic regression (  h)

From: Trincado and Burkhart Can. J. For. Res. 39:

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 =  BL exp(-1.53RCH)

Link to Growth and Yield Model PTAEDA

Challenges and Opportunities Determining which crown characteristics affect response to silvicultural treatment Modeling crown response to silviculture

Mass Control Pollinated Challenges and Opportunities Clonal Open pollinated Developing Models for a Range of Genetic Stocks

Four-Year-Old Planting of a Loblolly Pine Clone

Land Classification Soil Mapping System GIS-Based Precision Silviculture Remote Sensing of Leaf Area and Plantation Health

Thanks! Questions?