A COMPATIBLE STEM TAPER-

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A COMPATIBLE STEM TAPER-
VOLUME-WEIGHT SYSTEM
FOR INTENSIVELY MANAGED FAST GROWING LOBLOLLY PINE
YUJIA ZHANG
BRUCE E. BORDERS
ROBERT L. BAILEY
WARNELL SCHOOL OF FOREST RESOURCE
A UNIT OF THE UNIVERSITY OF GEORGIA
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INTRODUCTION
Geometry-oriented methodology yields a stem
taper function and associated compatible volume
and weight equations.
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STUDY MATERIALS
Our data came from the Consortium for Accelerated
Pine Production Studies (CAPPS) maintained by our
school.
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TREATMENTS

• H - complete vegetation control throughout the
  life of the stand using herbicides
• F - annual fertilization treatment
• HF - both H and F
• C - check plot

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Destructive stem samples were collected from the
lower coastal plain of Georgia and measured in
field and lab.
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STEM TAPER FUNCTION
d
(dob? dob)/2
dob/2
? V
o
h
l
? l
V f (dob, l)
? Vf(dob? dob, l? l)-f(dob, l)
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i.e.
(1)
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Using Newtons formula, ?V can be expressed as
(2)
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By Eqs. (1) and (2), we derived
(3)
Assume
V a dob2 l
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Eq. (3) can be written as
(4)
where ? is a constant
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Integrating Eq. (4) yields the taper function
(5)
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Using l H - h and p h / H in Eq. (5)
(6)
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The stem taper most likely changes abruptly at
some points. Two segments seem to be sufficient
for our stems.
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The derived taper function is
(7)
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where
(8)
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Replacing dob using dbh in Eq. (7) results in
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The taper equation can be written as
(9)
?0 for 0ltp ltp and ?1 for pltp lt1
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The derived taper function (insider bark) is


(10)
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STEM VOLUME
In the form of integration of the taper function
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The resultant segmented volume equation is
(11)
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and (for stem inside bark)
(12)
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STEM MERCHANTABLE WEIGHT
Figure 2 shows specific gravity (SG) versus stem
ratio, suggesting that a quadratic equation form
may work well for SG prediction.
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Figure 2. Specific gravity distributions versus
stem ratio for dry wood only (SGDW), green
wood and bark (SGGWB), and green wood only (SGGW)
from one of the stems at age 12.
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• Data analysis showed
• age is a predictor of the SG of stem dry wood
  only
• no significant treatment impacts on SG detected

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SG prediction equations
(13)
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The segmented weight equation in integration
form
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(14)
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(15)
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(16)
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TREATMENT IMPACTS
Data analysis was done using form quotients at
height proportion 0.25, 0.5, 0.6, 0.75, and 0.9
(q25, q50, q60, q75, and q90)
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• no significant impacts from herbicide
• significant impacts of fertilization only on q75
  and above

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To reflect this fact, the value of the upper form
factor should be different from fertilized and
unfertilized trees.
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RESULTS
Nonlinear system mixed-effects modeling technique
was applied for obtaining efficient estimates and
localizing parameters for each subject (stem).
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The modeling efficiency (EF), root mean square
error (RMSE), and mean bias (MB) were applied for
fit statistics. The estimates obtained are listed
in Table 1 with the fit statistics in Table 2.
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DISCUSSION
The taper function can be readily transformed
into a ratio (PD) taper equation (outside bark)
by dividing dbh
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or (inside bark)
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Likewise, the ratio (PV) volume equation (outside
bark) can be obtained by dividing the total
volume
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or (inside bark)
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Figs. (3) and (4) show the profiles of dob and
dib, respectively, using a 18 m long stem with
dbh 20 cm.
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Figure 3
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Figure 4
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Fertilization slightly increased stem volume
outside and inside bark subject to the reduction
of upper taper (Fig. (5)).
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Figure 5
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Stem weight profiles (green weight wood and bark,
green weight wood only and dry weight wood only)
are displayed in Fig. (6).
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Figure (6)
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We concluded that fertilization did not
significantly reduce the specific gravity of
wood, which agrees with the results of data
analysis and conclusions derived by other wood
scientists using the same data.
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Questions and comments