Ed,
Young white pines hold to a conical shape with surprising consistency and
the conical volume using BH comes pretty close to a more thoroughly modeled
form. The number of pines I have modeled to arrive at this conclusion numbers
around 150.
Often the pines in a stand will show great consistency of form. Increasing
sample size dramatically doesn't add much new information. As pines age and the
root structure develops, the volume implied by using the area calculated at RH
overcomes any change in trunk shape toward the paraboloid form.
I will have to do a lot more work before I'd take any formula to the bank,
but the formulas and range of F values boxes in the true volumes pretty well.
It is a start.
In terms of what species fall within the formulas and F values, well, I'd
be reluctant to go beyond the white pine at this point. The formulas probably
don't apply to the hemlock, at least not without changing the F value range.
The use of one predominant shape for young trees, another for old-growth
pines, and a third for intermediate age trees follows from the data I have, but
there are lots of exceptions. I'll discuss them in future communications. The
age criteria is just a starting point. Overall shape or form really drives the
volume, but pines change shape over time along the lines indicated by the
formulas. More to come on this topic.
Bob
-------------- Original message --------------
From: "Edward Frank" <[EMAIL PROTECTED]>
Bob,
An interesting article. I especially liked the background summary and the
concept for your specialized list. looking at the volume formulas you
suggested as a rough estimate, I have some questions. In the final set of
equations the basic difference between the three formulas is based upon the
difference in area of a section at breast height versus the area of the trunk
at the root collar. I am sure you have run statistics on the numbers and these
produce meaningful results on a first pass. What bothers me about the process
is that the entire trunk is being characterized by the differences in the tree
diameter at breast height and at the root collar. Is this relatively tiny
fraction of the total volume of the tree really an adequate basis for
projecting the volume of the entire tree? I really have my doubts in a broad
sampling that it does. First we really don't seem to know why some trees have
more of a flared base than others.&n bsp; Across species it seems, based upon
obs
ervations only and not any modeling, that species that grow on a more unstable
substrate have a larger flair at the base of their trunk. Does this
observation stand up to analysis - I don't know. Does it also apply within a
single species - would it apply to pine trees - again would think so, but I
don't actually know, but I think it should be considered. So if the amount of
flair between breast height and the root collar is not dependant on overall
trunk shape, but upon some other factor, such as the nature of the substrate,
then it would not serve as a good indication of overall volume.
The second question that comes to mind is that you are characterizing young
trees as having one shape, old growth trees as having another shape, and also
an intermediate category. I wonder if these generalizations are valid over a
larger sampling size. Is is age that affects the shape, is it the size of the
tree, is it the history of suppression and rapid growth, is it dependant on age
or the history of a particular tree?
In the final formulas you present you essentially are adjusting the
cross-sectional area used in a basic formula by considering whether to use the
breast height area, the root collar area, or something in between. I would
feel a more appropriate approach would be to keep the position of the
cross-section are at breast height and adjust the Form Factor between the
suggested ranges, 0.33 to 0.50 based upon visual observation of the taper of
the trunk, whether or not the tree has excessive flair extending above breast
height, and whether or not the tree appears to have been topped. Your formulas
may provide a good estimate, I am just wondering if a different approach that
just included a form factor might yield better results, as the role of trunk
basal flair in overall trunk volume is unclear (at least to me.)
Ed Frank
"Two roads diverged in a yellow wood, And sorry I could not travel both. "
Robert Frost (1874–1963). Mountain Interval. 1920.
----- Original Message -----
From: [EMAIL PROTECTED]
To: [email protected]
Cc: Rick VanDePoll ; Sam Stoddard ; Steve [EMAIL PROTECTED] ; Laurie Sanders &
Fred Morrison ; David Govatski ; Robert Carr
Sent: Tuesday, November 11, 2008 5:26 PM
Subject: [ENTS] Rejuvenated White Pine Lists and Volume Modeling
ENTS
The recent ENTS rendezvous in western Massachusetts has energized
me to return to specialized big/tall tree lists. Beyond an interest in the
knowledge encapsulated by the lists, my efforts are motivated by an awareness
of informational gaps that need to be filled if the public is to understand and
support our heritage big trees and stands of trees. In the case of the various
white pine lists that Will Blozan, Dale Lutheringer, and I have conceived over
the years, those lists are in recognition of the historic role of the white
pine. This role especially applies to New England, but awareness of the history
of the species has been diluted by a variety of fac tors, most of which work
against preserving the impressive stands of white pine that we have remaining.
In a nutshell, if people do not know what is significant or what will soon
become significant, then preservation efforts will not likely be successful.
To look backward in time, Pinus strobus was THE tree species in
colonial New England. White pines were coveted for ship masts by the English
monarchy and were widely used for construction purposes by the colonists.
However, for a period of decades, the great whites lost most of their value due
to the white pine weevil and the white pine blister rust, but the species has
largely survived those threats and is still the eastern United States’s tallest
species. The white pine is definitely New England’s flagship species for
stature. Without it, our site Rucker Indexes would suffer greatly. In my humble
view, because of its historical importance an d stature, the species deserves
our respect beyond the mundane valuing of it for timber purposes. But for the
public to value our heritage white pines, reliable information must be
available on individual trees and stands of trees - information that has
heretofore been very sparse.
To acknowledge what has been done, there are a few New England
sites that have been preserved because of their large and/or old white pines.
Sites that come immediately to mind include the Bradford and Tamworth Pines in
New Hampshire, the Carlisle Pines in Massachusetts, the Cathedral and Gold
Pines in Connecticut, and the Scott Fisher Memorial and Cambridge Pines in
Vermont. Exemplary sites such as MTSF, Ice Glen, and the Bryant Homestead, all
in Massachusetts, escaped notice until recently. Now thanks to the ENTS
website, masterfully created and maintained by our webmaste r Ed Frank, people
who do Internet research can find dimension-based information and qualitative
narratives on the white pine that put into context our beliefs about what may
have grown in yesteryear as well as what is out there today. We are actively
documenting white pine sites and gradually homing in on the genetic
capabilities of the species across its geographical range. The latter mission
has t
he greatest scientific value.
I believe it is in our interest to expand our white pine database
and organize it for convenient web-based maintenance and for general public
access, but this mission will take time and needs our collective input. For the
present, we can construct a list of important trees. To this end, I recently
proposed to Will a criteria for inclusion of white pines in a list that for the
present is aimed predominantly at the Northeast. He tentatively agreed. We
would like the input from others. Basically, a pine would be included in the
list if it meets any of the following criteria:
1. Is 150 feet tall or more (maybe less in northern New England),
2. Is 12 feet in circumference or more,
3. Earns 1500 ENTS points or more (ENTS Pts = girth^2 * height/10),
4. Has a modeled trunk volume of 500 cubic feet or more.
These criteria are sufficiently strict in terms of what is growing
now that the list, at least in the Northeast, isn’t in danger of becoming so
extensive as to give the idea that trees meeting any of the above criteria are
everywhere common. That certainly is not the case and the point will need to be
emphasized.
The most difficult of the above criteria to apply is #4, the
modeled trunk volume, which is the subject of the remainder of this email.
Fortunately, there are shortcuts to allow us to approximate volume based on the
general formula:
V = F * A * H
where A = area of the base at a designated height (such as 4.5
feet),
H = full height of tree, and
F = the form factor that lies between 0.333 and 0.50.
For those who want to review the calculation of A, it can be done
through any of the following formulas:
A = PI * R^2
A = PI * D^2/4
A = C^2/(4 * PI)
Where R is radius, D is diameter, and C is circumference (or girth).
For forest-grown pines in the age-class of 150 years or more, the F
factor will commonly be between 0.38 and 0.44. Stocky old-growth outlier pines
may achieve a factor between 0.45 and 0.47. I doubt any pine will be 0.5, which
is the factor that determines the paraboloid shape. The overall shape of a
trunk of a mature pine characteristically begins as a neiloid (F=0.25), change
to paraboloid (F=0.5), and then into a cone (F=0.333), but a single F value can
be used to calculate the volume of a pine. Determining the value of F for a
particular tree is our challenge.
For initial inclusion of a pine in the list, the F factor can be
estimated if a more exacting determination can’t be made such as through use of
the Macroscope 25/45. I acknowledge that a lot of work remains to be done on
figuring out how to derive the F factor for a pine to get a quick volume
approximation, but at this juncture, we are not helpless. We have a good head
start.
From data we’ve collected thus far, it is safe to assume all but
the highly columnar pines will have a trunk volume that is less than the
calculated value achieved by taking the cross-sectional area just above the
root collar, the full height of the tree, and an F value of 0.333. By contrast,
single-trunk old-growth specimens are proving to have volumes very close to the
calculated volume using the base set at the root collar, with some trees
requiring an F value as high as 0.35 or even 0.37.
At the least, we presently have a strategy for homing in on the
trunk volume by first surrounding it with high and low volume estimates. We
then can refine the estimate by choosing an F value that appears to match the
trunk. Judgment is involved, but with experience, we can eventually reduce the
error to an acceptable level without being forced to fully model a tree. A fact
obvious to me now that was not several years ago is that relatively few of us
in ENTS are driven to calculate trunk volumes through full trunk modeling and
do other kinds of tree modeling that is numerically intensive. So, if the few
of us want volume-based lists created by more than just ourselves, we are going
to have to come up with handy ways of calculating volumes that involve a
minimum of calculations and that means refining the application of the F value.
Today we are a lot closer to doing that than we were a couple of years ago.
At this point, I feel confident in saying that for young pines, a
straightforward trunk volume calculation using DBH, full height, and an F
between 0.333 and 0.35 will give a close approximation for the junior class of
pines. For old-growth specimens with straight trunks, DRH (R=root), full
height, and an F between 0.30 and 0.40 will do the job in most cases. F values
as low as 0.30 can be required where root flare is extreme and the tree tapers
fast. For white pines of intermediate age, the volume calculation is equally
challenging and we can approach it in several ways. Using BH (breast height), F
can vary between 0.35 and 0.40. Using RH (root collar height), F will be
between 0.30 and 0.36. Occasionally, the trunk will be so stocky that the F
value for RH needs to be as high as 0.37, but that will not often occur on
intermediate- aged pines. In general, the volume of a single-trunk,
intermediate-aged white pine will usually lie between the two methods just
described
and often near the midway point. Let’s now examine some specific trees.
Jake Swamp Pine
The average of the two volumes (CBH and CRH with F = 0.333) for the
Jake Swamp tree is 574 cubes. This uses a CBH of 10.4 feet, which is what
Will’s model uses, as opposed to my more liberal 10.5 feet, Will’s full
modeling of Jake on November 1st yielded 573 cubes. This is an amazing match,
and it is not accidental. The shape of Jake falls between that of young and old
pines. Let us formalize these volume calculations.
Let ABH = area of trunk at breast height,
ARH = area of trunk at root collar height,
H = full height of tree,
F = form factor,
VEI = volume estimate of intermediate-aged pine.
VEI = F*H*(ABH + ARH)/2
Where F = 0.333
Tecumseh Pine
Let’s try the VEI formula on the Tecumseh Pine, an older, stockier
tree, but not yet truly old growth. The circumference at the root collar is
13.24 feet and at breast height is 11.9 feet. The full height of the tree is
163 feet as determined by Will on his November 2nd climb.
VEI = 693 cubes. Compared to the modeled volume of 779 cubes this is
significantly low. However, the Tecumseh Tree is a stocky pine. Consequently,
its volume can be better approximated by: VE = F*H*ARH, which yields 788 cubes
and that is much closer. The F value for RH needed to reach the modeled volume
is 0.35675, which falls between or 0.333 and 0.37 parameters.
So, the volume estimation process works pretty well provided
adjustments are made to the F value and the base area is calculated as either
the lower, upper, or mid-point of collar to breast height span. I stress that
the choices are dependent on the overall form of the tree.
Saheda Pine
As the last example, the Saheda Pine was modeled in 2007 by Will.
It is comparably aged pine to Tecumseh Pine, but less stocky in its upper
portion. Its measurements in 2007 were CBH = 11.8 feet, Height = 163.6 feet.
Its girth at root flair, as determined by Will was CRH = 13.3 feet. Will
modeled Saheda at 695 cubes. The RH volume is 767 cubes and its BH volume is
604 cubes. The average of the two is 685 cubes, which is close to the modeled
volume of 695 cubes. The averaging method works for Saheda. The more slender
upper portions of the Saheda Pine virtually guarantee that the RH volume will
over-estimate the modeled volume. The greater age of the pine guarantees that
the BH volume will under-estimate the modeled volume. The F value needed to
produce the modeled volume using BH is 0.3835 . The F value needed at RH is
0.302. This latter value is necessitated because of the slender double trunk
near the top of Saheda in combination with the root flare.
Summary
ABH = area of trunk at breast height,
ARH = area of trunk at root collar height,
H = full height of tree,
F = form factor,
There is lots more to come on this topic along with lists of pines based on the
proposed criteria, but to summarize. As a first cut, if the pine is young use:
VEY = 0.333 * ABH * H.
If the tree is a stocky old-growth specimen, use:
VEO = 0.333 * ARH * H
If the tree is intermediate in form and age, use:
VEI = 0.333 * H * (ABH + ARH)/2
For a particular tree, as more measurements are taken, the F value can adjusted
to better fit the observed form.
Bob
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