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 three-trunked 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


    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

   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 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 4-5 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 non-white 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