Smaller
pines, better model 
Robert
Leverett 
Oct
31, 2005 07:50 PST 
Will,
Jess, Lee, et al:
The weather gods smiled on Gary and me
this past weekend and we were
able to volume model several more white pines.
The number of trees modeled thus far has
started to provide us with
an intuitive feel for what to expect for broad diameter and
height
classes. But most of the work remains to be done. We're just at
the
beginning. Hopefully, the dominant patterns of how volume is
acquired
for white pine over time and for various combination of heights
and Diameters
and growing conditions will become steadily clearer as we add
more
sample points.
To date, 41 trees have been modeled for
volume. One is the Thoreau
Pine, which was actually modeled by BVP. So I don't have
Diameters
at 50 and
100 feet. A second trees is the huge threetrunked Conway pine
that has
only been partially modeled for volume. Four trees of the 41 are
not
white pines. That leaves 35 trees for the current all white pine
model.
As of yesterday, the model
evolved. The regression coefficient is
0.9535. That's very high and will likely remain high, but can be
expected to drop as more large trees are added. The regression
equation
for the existing data is:
Y = 359.1724 1.243018X1 + 61.757745X2
+ 9.4596238X3 + 9.6177308X4
where:
Y = trunk and limb volume in cubic feet
X1 = Total height in feet
X2 = CBH in feet (could have been DBH in
inches to have been consistent)
X3 = Diameter at 50 feet in inches
X4 = Diameter at 100 feet in inches
Obviously, the above model has limitations. It
won't accommodate
trees
under 100 feet in height. A future model will regress
volume
against total
height and Diameter at 2.5 and 4.5 feet and at 33% and
67% of total
height. A better result might be obtained by adding Diameter at
6 feet.
Also, as more measurements are added for smaller diameter trees
and a
few for the largest ones, the coefficients of the regression
model will
change dramatically. I'll feel more secure when I see the
coefficients
begin to stabilize. At present, when a few more trees are added,
the
coefficients can change wildly even though the regression
coefficient
remains quite high. It is the risk carried of having a
relatively small
sample size. By the time 100 trees have been modeled
satisfactorily,
I'll begin to feel more confident.
In the above model, Diameters at 50 and or
100 feet had to be
interpolated for a few situation where visibility prevented
Diameter
measurements at those exact heights. Visibility often figures
into where
Diameter measurements are actually taken. Field conditions
necessitate being
flexible.
The data collected so far shows that the
requirement to be very
accurate on Diameters at heights above 100 feet is not great. That's
good
because accurate Diameters at near 100 feet are often extremely
difficult to
get. More to the point, volumes from points where the Diameter has
dropped to
16 inches or less on to the tops of the pines is on the order of
20 to
40 cubes for most of the pines. So an error of even 50% of the
volume
where the trunk has slendered down to 16 inches or less on to
the top is
likely not to exceed 20 cubes.
Robert T. Leverett
Cofounder, Eastern Native Tree Society
dbhg@comcast.net wrote:

Will,
Jess, John, Lee, et al:
Today Gary Beluzo
and I are going to spend a couple of hours in Monica's
Woods. Although Gary
is well acquainted with the general area, to
include Broad Brook
and Fitzgerald Lake, I am anxious for him to see the
area on Broad Brook
behind Monica's house. We'll also model a couple
slimmer white pines
to get more volume determination measurements of
pines in the 6 to
7.5 foot circumference class. I plan to take the
modeling down to the
45 foot class and of course up to the very
largest. The
regression model I now have has a regression coefficient
of
0.938. That is high
and adding smaller, symmetrical trees will likely
increase the
coefficient by 0.1 or 0.2. But adding large, irregular
bulky trees will
likely decrease the coefficient. I suspect that a
regression
coefficient of around 0.90 will be the long term result
of
many modelings. At
this point, there are two hemlocks, one tuliptree,
and one red oak in
the sample. The nonwhite pines will be removed for
an all white pine
model. I'll eventually develop an all hemlock model
and then a
combination of the two.
In a way, all this is practice
for modeling the Smoky Mountain giants.
That will occur next year.
Bob Leverett 

