Weekend Modeling   Robert Leverett
  Nov 07, 2005 06:36 PST 

ENTS,

   Two topics are presented below. The first is for dendromorphometrists
and the second for those disinclined to want to wade through my usual
gobs of numbers. So the first topic deals with the measuring stuff. The
second turns more to the mystical side of trees.

MEASURING STUFF:

   For the past 3 days the great Ents in the sky have witnessed their
very mortal and humble subject Bob modeling tree volumes like a fiend. I
am now up to 45 white pines. Included in this weekends catch were the
12.6-foot CBH, 121.3-foot tall giant (Spencer Pine) in Quabbin and the
12.6-foot CBH, 136-foot tall hulk in Belchertown. I didn't have time to
model the 12-foot CBH sister tree to the Spencer Pine. It would have
been about 125 to 150 cubes less.

   Today, I modeled what may be Mt Tom's largest single-stemmed pine at
11.7-feet around and 130 feet in height. It has a limb that measures 44
feet. Very conspicuous to say the least. I also modeled a 5.1-foot
circumference tree on Mt Tom to collect more data at the lower end of
the volume scale. I need more trees in the 5 - 6-foot CBH range. The
single tree is acting like a statistical outlier rather than a
well-behaved member of the sample. In fact, the new tree slightly
reduced the multiple linear regression coefficient. It was up to 0.9582.
It is now 0.9576. While this change is not statistically significant, it
does reflect the impact of the small tree. The regression equation now
utilizes 5 independent variables. The equation is:

Y = -319.22901-1.1565991(X1)
-2.5708427(X2)+17.54586(X3)+8.9927451(X4)+10.72667(X5)

Where Y = trunk and limb volume in ft^3
          X1 = Total height in feet
          X2 = Diameter in inches at 2.5'
          X3 = Diameter in inches at 4.5'
          X4 = Diameter in inches at 50'
          X5 = Diameter in inches at 100'

    I did switch exclusively to inches for diameters. Although the
multiple linear regression coefficient is quite high, this equation
needs a lot more data points. It fails miserably to predict volume at
the low end of the volume scale and misses the high end enough to cause
concern. For instance, at the low end of the scale, the equation
predicts a volume of -19.3 cubes (yes negative) for the Mt Tom WP #6, a
skinny tree that is 19.6 inches DBH and 101.3 feet tall. I modeled the
tree to 97 cubes. Treating it as a perfect cone with a base diameter of
23.7 inches, its measured diameter at 0 feet, yields a volume of 104
cubes. That is pretty remarkable. However, the tree’s form is quite
conical and the volume calculation suggests that other young pines in
the stand may follow suit. How interesting if volume modeling with the
RD 1000 for young white pines validate use of nothing more than the
simple cone formula:

      V = h/3(A), where A = cross-sectional area of the base of the
cone.

    But, I suspect that the modeling mission will eventually lead to a
family of formulas driven by both size and age. If that's where the
data takes us, so be it.

   There are several bulky great whites that now need to be added to the
sample. They include two 12-foot circumference pines on the land of J.
Healey in Shelburne Falls Mass, and of course, the 11.2-foot
circumference beauty that John Eichholz mentioned, also in Shelburne
Falls. There are others. I'll begin to feel safe when the sample
includes no less than 300 pines, 30 in each CBH class 1 foot wide and
starting at 5 feet and going to 15.

Bob    


Robert T. Leverett
Cofounder, Eastern Native Tree Society
Back to Ed   Robert Leverett
  Nov 08, 2005 12:32 PST 

Ed,

   I, like most of my tree-measuring comrades on this list, believe that
conifers like spruce, hemlock, and most species of pines undergo
predictable form changes as they mature as keyed to the conditions in
which they are growing. The operative word here is "predictable". We can
see that the forms change, but how predictable are those changes?
Determining to what extent there is predictability in form and volume
change is what the multiple linear regression analysis is all about. At
this point age is not being factored it.

   After enough sample points in various diameter classes ahve been
collected, a comparison will be made of the volume obtained from
applying an individual class model for a diameter class relative to that
from applying a broad model that incorporates all the data. There are
other variations on this theme, but discussion of them will be held for
later.

   I am hoping that the results of the above kinds of comparisons will
quantify what many know intuitively. For instance, when Lee Frelich
looks at a bulky hemlock from a distance, and gives it an age projection
of 400+ years, he has quickly scanned its crown architecture, assessed
its limb to trunk mass, and its overall trunk and limb forms. If he is
up close, he will the observe age cues that are held in the bark color
and texture. Lee has cored so many hemlocks that he has an efficient
built in mental model of the typical form changes that can be expected
with time and growing conditions - such as prolonged suppression,
continuous competition, crowding, etc.

   Through the modeling and the various kinds of statistical analysis
that will be performed, I'm hoping to eventually be able to quantify the
form changes undergone by a species and gain predictability over those
form changes as a product of time and dimension. Somewhere in this age
or at least age class will need to become a variable. Each species will
have its own set of volume formulas. No mixes species here.

   Beyond the pure research aspect, I admit that I do have ulterior
motives. I believe that species like white pine in good growing
conditions gain significant volume for a much longer time period than
some of the local timber specialists here in Massachusetts seem to
think. Some of these folks believe that white pines in the 40 to 60 age
range have done most of their growing, and consequently, are ready for
harvest. Others have a diameter cut off such as 24 or 25 inches.
However, white pines in the Northeast are growing machines and those on
good sites continue to add significant bulk aloft after radial expansion
at breast height may suggest that the tree has slowed down its growth so
much as to be stagnant.

   I admit that I don't know nearly enough about the relative and
absolute growth rates of white pines in good growing conditions, to
defend any particular belief, assumption, or hypothesis. But I'm
determined to find out. I have researched volume formulas developed by
silviculturists, but so far have not found anything useful. I have no
interest in trying to apply an nth degree polynomial or use data from
young plantation trees unless I want to treat a 30 to 40 year old tree
as mature. The question for me isn't just how much volume is explained
by a set of independent variables, but how that volume was achieved over
time. I'd like to eventually be able to profile the white pine in terms
of how a "typical" one on a good site might look at say 50, 100, 150,
and 200 years in terms of its progressive gain in overall volume,
overall height, and its diameter at different heights. Silhouette
drawings could reflect what the numbers say, but with a pleasing visual
impact.

   I am reasonably satisfied with the diameters now being obtained with
the RD 1000 for heights up to 80 feet and for diameters in the 12 inches
and over class. To improve accuracy beyond 80 feet and for small
diameters will require a lot more work.

   Incidentally, a goal of Will Blozan and mine for years has been to
model the great Smoky Mountain hemlocks. By next summer, we should be
ready to roll. What has been learned to date and what will be learned in
the next few months from the white pine modeling hopefully will allow me
to avoid my early mistakes. Following Will as he crashes through the
rhodo hells of the southern Apps isn't something that I want to often
repeat. I want to get it right the first time.

   More on the specifics of the regression process in future e-mails.

Bob
Quabbin    Bob Leverett
Nov 14, 2005

Bruce,

The attached Excel spreadsheet includes the 3 trees we modeled in Quabbin a week ago Friday. The general model I use as applied to the Spencer pine gives 756 cubes. However, lack of good data for the upper crown has likely led to an understatement of the huge tree's full volume. Based on my experience, I suspect that the volume of the Spencer pines is closer to 775 cubes. Had it not been zapped by the hurricane, I suspect its volume would be close to 800 cubes. 

For comparison purposes, you'll note that the smallest tree modeled with dimensions of 16.0 inches dbh and a height of 100 feet yields only 59 cubes. So the Spencer pine is nearly 13 times the volume of the young Mount Tom tree. 

I look forward to when we can stomp the woods together looking for and at big pines.

Bob 

Database Developer and Systems Analyst
Information Technologies

Quabbin