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TOPIC: Rejuvenated White Pine Lists and Volume Modeling
http://groups.google.com/group/entstrees/browse_thread/thread/e37922c4f666f795?hl=en
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== 1 of 6 ==
Date: Tues, Nov 11 2008 2:26 pm
From: dbhguru@comcast.net
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 factors,
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 and 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 webmaster Ed
Frank, people who do Internet research can find dimensionbased
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 th
e greatest scientific value.
I believe it is in our interest to expand our white pine database
and organize it for convenient webbased 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 forestgrown pines in the ageclass of 150 years or more, the F
factor will commonly be between 0.38 and 0.44. Stocky oldgrowth
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 crosssectional area
just above the root collar, the full height of the tree, and an F
value of 0.333. By contrast, singletrunk oldgrowth 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 volumebased 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 oldgrowth 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 intermediateaged pines. In
general, the volume of a singletrunk, intermediateaged white pine
will usually lie between the two methods just described a
nd 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 intermediateaged 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 midpoint 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
overestimate the modeled volume. The greater age of the pine
guarantees that the BH volume will underestimate 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
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 oldgrowth 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
== 2 of 6 ==
Date: Tues, Nov 11 2008 3:05 pm
From: "Edward Frank"
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. Across species it seems, based upon observations 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
crosssectional 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 crosssection 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.
== 3 of 6 ==
Date: Tues, Nov 11 2008 4:15 pm
From: dbhguru@comcast.net
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
oldgrowth 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
== 6 of 6 ==
Date: Tues, Nov 11 2008 9:40 pm
From: "Edward Frank"
Bob,
What I am thinking is that really what you are looking at is a
change in shape of the trunk in different trees. In your summary
formulas you are mimicking the change in shape by substituting the
cross sectional area of the trunk at either breast height, root
collar height, or somewhere in between into a formula while the
shape factor is represented as a constant (0.33). Then you suggest
that the F factor should be modified to fit other situations. By
substituting crosssectional area for shape, you are approaching the
same values, the trend of the calculations are going in the same
direction,as would be obtained by adjusting the F shape factor. So
there should be a statistical correlation in what you are doing but
that doesn't mean it is an optimal solution. I think the logic of
the substitution is flawed as I don't see any direct reasonable
relationship to the amount of basal flair to total tree trunk
volume. The correlation is coincidental because it is going in the
same direction as the tree shape parameter is going. If this
parameter must be modified further by changing the F shape factor in
certain cases, then what is gained?
You are creating an artificial variable (changing the
crosssectional area) that is in the same direction as the actual
variable  shape, so that you have two variables instead of one. To
me it seems much more reasonable to keep the crosssectional area a
constant at one height  say breast height in the formulas  and to
manipulate the one true variable  the F shape factor  in the
general formula. One variable that is real, instead of two  one
fake (crosssectional area) variable that approaches the same volume
as the trunk and second fake variable (an F factorlike factor that
really doesn't represent anything measurable in the tree) that is
essentially a fudge factor to make the first fake variable better
match the actual trunk volume. It is like you are saying in your
summary formulas  the tree really isn't this shape, but if we
adjust the basal area in this way, and throw in a fudge factor when
needed the resulting generated form will be somewhat similar in
volume to the actual trunk.
What I would suggest is to instead develop a standard Protocol to
assign a tree specific F shape depending on the general shape of the
trunk. It likely will fall into broad groups like you suggest, I
believe you are on the button in that regard. However the
methodology is more sound when you are manipulating the formula
based upon variations trunk shape, rather than generating an
artificial variable value by changing the basal cross section.
Ed Frank
"Two roads diverged in a yellow wood, And sorry I could not
travel both. "
Robert Frost (1874–1963). Mountain Interval. 1920.
== 2 of 2 ==
Date: Tues, Nov 11 2008 11:27 pm
From: "Edward Frank"
ENTS, Bob,
First let me apologize for the two empty posts that appeared from.me
regarding this matter. I was having some computer problems, and it
appears that the problem was simply my mouse going bad and was
multiclicking everything.
Mathematical discussions are hard to articulate and I am never
satisfied with the explanations and arguments that I present. Bob,
this is mostly directed at you, please forgive my referring to you
in the third person. as I am not sure how else to state it. In Bob's
original post he provided these three formulas:
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 oldgrowth 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.
These represent the general equations for volume calculations in
white pines in his data sets. The first formula: VEY = 0.333 * ABH *
H. the volume is equal to the form factor for a cone (0.33) x (the
crosssectional area at breast height) x (tree height). Bob reports:
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. I believe this a a
reasonable formulation that is supported by a large data set. I have
no complaints on this matter.
In the second formula presented Bob says: If the tree is a stocky
oldgrowth specimen, use: VEO = 0.333 * ARH * H This is the formula
I am trying to discuss. In the initial characterization the tree is
described as a "stocky oldgrowth." It is not conical in
shape, yet in the formula Bob has chosen to use the F or shape
factor for a cone as the first parameter. Since this tree is larger
in volume than a cone, if you keep the F or shape factor for the
cone, one of the other parameters must be increased to represent the
increased volume of the tree. The height is pretty straight forward,
so it was left alone. In the formula, instead of changing the F
value Bob has opted to change the crosssectional area used in the
tree. He is using the crosssectional area of the tree at the root
collar instead of at breast height. This number will be bigger than
the crosssectional area at breast height, therefore will generate a
bigger number for volume. We know the volume of the stocky
oldgrowth tree is larger, this manipulation generates a bigger
volume number, therefore there will be a positive correlation
between the two. This is exactly what the formulas say....
The problem is that by changing the crosssectional area instead of
the F or shape factor for the tree, the volume modeled is not the
same shape as the tree. The lower portions of the trunk will be
exaggerated in volume, while the upper portions will be
underestimated. The hope is that the amount of exaggeration at the
bottom is exactly the same as the amount the top is underestimated,
thus yielding a good volume for the tree. For example a cone with a
crosssectional area of its base three times larger than that of a
cylinder of the same height, will have exactly the same volume as
the cylinder, even though they have a different shape. What I don't
see is why the crosssection at the top of the root collar should be
that balancing point where the bottom exaggerations and the upper
underestimates match. There surely is some place where they do
match, but why should it be this crosssectional area of the tree at
the root collar?
The third formula suggests that some trees are intermediate in shape
between the conical young trees and the stocky oldgrowth trees.
Sure I can buy that, but the formula states that the value for the
intermediate form will be a crosssectional area somewhere between
that at breast height and that at the root collar. Why should breast
height and root collar be the boundaries? Breast height is
reasonable as it can be demonstrated by field measurements, but as
far as I can see the root collar crosssection is an arbitrary value
that may be higher or lower than is appropriate for a given set of
trees. If you are just picking out a crosssectional area from a
given range, knowing that the number you pick out does not actually
represent the shape of the tree but a hoped for balance point of
errors, would it not be better to pick out from a range a value that
actually represented the shape of the tree? A range of F shape
factors? Bob says: For a particular tree, as more measurements are
taken, the F value can adjusted to better fit the observed form.
Would this be an adjustment to F as used in the first formula, or
does he mean an adjustment as a fudge factor to the F in the second
equation, and therefore not really representing the overall form of
the tree at all?
What I am suggesting is that instead of picking the crosssectional
area at the root collar and hoping it is somewhere close to the
theoretical balance point between lower exaggerations and upper
underestimates, it would be better to find some repeatable protocol
for estimating the F or shape factor for a given species of trees in
an area, and keep the basic crosssectional are at breast height as
a constant in the formula. That way you are changing the true
variable in the formula, shape of the trunk, to fit the tree being
examined, instead of just picking a value at the root collar and
hoping it will be OK. This would be a simpler way to deal with the
different shapes of trees and a sounder approach in my opinion. I
anticipate that there will be a different F shape factor for each of
the different classes of trees being examined and that a pattern
will emerge. I am not sure, and don't believe that this same pattern
will be observable if volume is calculated by manipulating the
crosssectional area. Another advantage of developing a protocol for
assigning an F value would be that trees with unusually wide basal
flairs or those who have had their tops broken out will tend to fall
into separate ranges of F, rather than being intermixed as might be
the case using formula 2.
Ed Frank
from Don Bertolette, Nov 12, 2008
Bob
I wondered if your tree library had any of the following references
on eastern white pine volume data :
PART B. DIAGNOSTIC CRITERIA
VOLUME TABLE/EQUATIONS
 FormClass Volume Tables (2nd Edition). 1948. Department of
Mines and Resources, Mines, Forests, and Scientific Services
Branch, Dominion Forest Service, Ottawa, Canada.
SITE INDEX EQUATIONS
 Beck, Donald E. 1971. Polymorphic Site Index Curves for White
pine in the Southern Appalachians. Dept. of Agriculture Forest
Service, Southeastern Forest Experiment Station, Asheville,
North Carolina.
YIELD TABLES
 Normal
 Leak, William B. 1970. Yields of Eastern white pine in New
England Related to Age, Site, and Stocking. USDA Forest
Service Research Paper, Northeastern Forest Experiment
Station, Upper Darby, PA.
 Empirical
 Leak, William B. 1970. Yields of Eastern white pine in New
England Related to Age, Site, and Stocking. USDA Forest
Service Research Paper, Northeastern Forest Experiment
Station, Upper Darby, PA.
 Variable Density
 Leak, William B. 1970. Yields of Eastern white pine in New
England Related to Age, Site, and Stocking. USDA Forest
Service Research Paper, Northeastern Forest Experiment
Station, Upper Darby, PA.
