Transcript Modeling Crown Characteristics of Loblolly Pine Trees Harold E

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 Products
• Pulpwood
• Sawtimber
• Peelers
• Poles
Intensive Silviculture
• 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. 1995. For. Sci. 41:43-53.
Thinning Response
Modifier
I = BAa/BAb
From: Liu, et al. 1995. For. Sci. 41:43-53.
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
Southern Global Change Program
1. Quantify foliage distribution
2. Model number, size, location of
branches
3. Provide link between G&Y and
process model
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
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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 = 3.93 + 0.43 (dbh) + 0.94 (crown length)
No. branches = 7.29 + 2.26 (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. branches
1
2
3
4
5
6
7
Percent of total whorls
19
28
29
15
6
2
1
Total Branch Length
Model total branch length as a
function of branch diameter
Total branch
length
=
3.58
1 + 16.55 e
( -1.20 ( branch diameter ))
Branch Angle
Model branch angle from vertical as a
function 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 in
Linked Model
PTAEDA2
MAESTRO
Growth & Yield Model
Process 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)
Bias
Observed
Predicted
No SI
Adjustment
SI Increase
ft3/ac.
m3/ha
ft3/ac.
m3/ha
ft3/ac.
m3/ha
4891
342.2
4284
299.8
4875
341.1
Dynamic Model of Knot Size,
Frequency, and Distribution
Sampling of whorls
Longitudinal data from a spacing study
January 2005
• DBH
• TH
• Stem height and diameter of every visible whorl
214 whorl sections
Stem dissection technique
Recovering information on knot morphology and branch development
March-May 2005
Ring width
Branch dissection
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
2
r = K ( l )
2
L
R
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
Multicategory logistic regression (h)
From: Trincado and Burkhart. 2009. Can. J. For. Res. 39:566-579.
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 doubletruncated 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 = 0.780BL0.827 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
Challenges and Opportunities
Developing Models for a Range
of Genetic Stocks
Open pollinated
Mass Control Pollinated
Clonal
Four-Year-Old Planting of a
Loblolly Pine Clone
Remote Sensing of Leaf
Area and Plantation Health
Land Classification
Soil Mapping System
GIS-Based
Precision
Silviculture
Thanks!
Questions?