New
Formula (Sneak Preview) 
dbhg@comcast.net 
Aug
21, 2007 15:16 PDT 
ENTS,
A new ENTS
formula is in the works. At this point, it is simple and may
prove very useful to those of us woking with trunk volumes.
Over the past several years of modeling, I've consistently seen
that the computing the conical volume of singlestemmed white
pines using the cone's base as the area just above the trunk
flare (old root collar) and the full height of the tree
overshoots the volume on young and middleaged pines and
understates the volume on old growth trees. I've also observed
that the conical volume using the area of the base of the cone
as the area at breast height of the trunk along with the full
tree height consistently understates the volume. In a sample of
30 modeled pines, the conical volume using breast height area
understated the volume in 29 cases. By contrast, the turnk flare
base yielded an overstatement in 21 of the 30 cases. For my
Taking an average of the two bases yielded a volume that
overstated the modeled volume in 12 of the 30 cases and
understated 17 and equaled in 1. The average percent of the
averaged volumes of the modeled volumes was 98 with standard
deviation of 10. Yes,
that's high, but if we introduce a form factor of 1.1 for old
growth, columnar forms, and 0.95 for forms that taper extremely
fast, and 1.00 for trees that appear just right  a judgment
call in each case. Then the average of the ratios of the new
volumes versus the modeled volumes remains at 98 and the
standard deviation drops to 9. Changing the factors to 1.10,
0.90, and 1.00 yields an average ratio (turned into a percent)
of 99 with the standard deviation remaining at 9. SOLD!
The formula needed to estimate the volume of singestemmed pines
is:
V =
H*F*(C1^2 + C2^2)/75.4
where:
V = Trunk volume
H = full tree height
F = form factor (1.1, 1.0, 0.9)
C1 = circumference at trunk flare height
C2 = circumference at breast height.
I'm sure Will, Jess, myself, and others interested in trunk
modeling can refine this formula, but even as it stands, it is
pretty good. Its algebraic derivation follows for those who
wantit.
D1 = diameter at trunk flare height
D2 = diameter at breast height.
C1 = circumference at trunk flare height
C2 = circumference at breast height.
A1 = crosssectional area at trunk flare
A2 = crosssectional area at breast height
V1 = trunk volume using cone base area as the area at trunk
flare height
V2 = trunk volume using cone base area as the area at breast
height.
H = full tree height
F = form factor (1.1, 1.0, 0.9)
V = averaged trunk volume
V1 = H/3*A1
V2 = H/3*A2
V = (V1 + V2)/2
V = (H/3*A1 + H/3*A2)/2
V = H/6*(A1 + A2)
A1 = PI*D1^2/4 = (PI*(C1/PI)^2)/4 = C1^2/(4*PI)
A2 = C2^2/(4*PI)
V = H/6*[C1^2/(4*PI) + C2^2/(4*PI)]
V = H/(24*PI)*(C1^2 + C2^2)
V = H*(C1^2 + C2^2)/75.4 where 24*PI = 75.4
Introducing the form factor F, we arrive at the final formula:
V =
H*F*(C1^2 + C2^2)/75.4.
This formula
does not replace a full modeling, but should give a pretty good
approximation of trunk volume for singlestemmed white pines and
I presume other conifers. I particularly like this formula
because it does not require the use of either the RD1000 or
Macroscope 25. The formula won't apply to most hardwoods.
However, hardwoods such as young tuliptrees with a still
symmetrical crown may fit well enough.
My current objective is to develop an easy way of obtaining high
and low estimates of trunk volume for singlestemmed white pines
using simple calculations and avoiding the extra gadgets that
some of us use. Once we have the simple method nailed down, we
can then search for refinements. As a first cut, the simple
formula presented above seems to fit the bill.
Bob

RE:
Sneak Preview 
DON
BERTOLETTE 
Aug
22, 2007 04:26 PDT 
Bob
Looks like a good first cut solution...you may recall that we've
had conversations in the past over how badly USFS estimates of
oldgrowth tree volumes are...that's because they have a uniform
formula for the broad array of diameters/heights/form factors
that they encounter across a broad geographic area.
What you've done, is narrow the population's size diversity,
and are now averaging species diversity within the
constrained population of oldgrowth trees...further refinement
could be achieved through similar factors for specific
species that typically fall outside the "oldgrowth
unnormal norm"...cypress comes to mind as an obvious
'outlier'
I noticed your use of the word 'judgement (call)'...while it can
add confusion to the 'confidence level' when user judgement
isn't of 'expert quality', constraining estimates to 'expert
quality users' would likely improve quality of estimates.
DonB

Back
to Don Bertolette 
dbhg@comcast.net 
Aug
22, 2007 10:47 PDT 
Don,
Yes, you're quite right. I saw no other way to
get a handle on volume calculations via a simple process than to
narrow the field of investigation. I expect most of the eastern
conifers, certainly the pines, spruces, and firs, will lend
themselves to the outlined modeling process. I'd love to perfect
it more in the coming months and then see how well it applies to
the ponderosas and other Rocky Mountain conifers next summer.
Lots more to do though in the interim.
Bob

New
Formula 
dbhg@comcast.net 
Aug
23, 2007 19:36 PDT 
Don,
Don, Ed, Will, Jess, et. al.
Today I modeled two more old pines
in Childs Memorial Park, Northampton. My sample now consists of
32 pines. Using the formula:
V = H*F*(C1^2 + C2^2)/75.4
Where V = trunk volume
H
= full tree height
F
= a choice from the set { 0.90, 1.00, 1.10)
C1
= girth at trunk/root flare (TF)
C2
= girth at breast height (BH)
and modeling the volumes using the
Macroscope 25, I got the following results.
Tree 1 2
VolTF 481.6 409.2
VolBH 287.3 307.5
VolAvg 384.4 355.3
VolAdj Avg 346.0 390.9
VolModeled 350.0 371.3
Adj Avg/MV 0.99 1.05
I applied the factor 0.9 to the first
tree and 1.1 to the second. The first tree has a large trunk
flare that leads to much too high of a volume. The second
confirms to the old growth white pine model, so I used 1.1.
The ratio of the adjusted average to
modeled volume (MV) for all 32 sample points is a surprising
0.99 with a standard deviation of 0.09. I can't beat the average
ratio value, but the standard deviation could be tighter.
However, it is what it is. I could cheat and bring down the
standard deviation for the smaple by including a lot of younger
trees. But my purpose is to investigate the range of values we
can expect using plenty of trees in all ages classes. So far,
I'm satisfied with the results and believe the formula has
value.
Tomorrow, I'll model a few younger pines
and present the results. Oh yes, the stats on the modeled pines
are (120.0, 9.5) and (120.8, 9.7). Despite their closeness in
the two common measures, the first has a girth at trunk flare
height of 12.3 feet. The second has a girth at trunk flare of
11.3 feet.
Bob

New
Formula Continued 
dbhg@comcast.net 
Aug
24, 2007 12:10 PDT 
ENTS,
With respect to the new trunk
volume estimating formula, the sample size for testing the trunk
volume now consists of 38 trees. To refresh everyone on the
formula, which I now refer to as the adjusted averaged trunk
volume formula (AATV), the variables and formula are given by:
V = F*H*/3*(C1^2 +
C2^2)/75.4
where H = full tree height
C1
= circumference at trunk/root flare point
C2
= circumference at breast height (4.5 feet above base)
F
= form value (0.90, 1.00, 1.10)
If we denote the modeled
trunk volume by MV, for the 38 sample trees, the current ratio
of AATV/MV stands at 0.993 with a standard deviation of 0.088
pretty impressive. The numbers for the unadjusted averaged trunk
volume are 0.984 and 0.101  not bad either. Basically, if there
is a large trunk flare and a faster than expected taper, then F
= 0.9. If the trunk flare is small to moderate and the taper is
very slow, then F = 1.1. All intermediate forms have F = 1.00.
This form adjustment requires experience and equally qualified
modelers will likely disagree on more than a few trees. So, I
hope to replace the form adjustment factor in time, but for the
present, it serves a useful purpose. It allows us to compensate
for obvious shape exaggerations such as a big trunk flare
followed by a quick taper. Not making the adjustment would lead
to an overestimation of trunk volume. On the other hand, a
small or modest trunk flare followed by a very columnar form
would lead to underest
imating. The use of only 3 factor values is admittedly
arbitrary, but so far the three have proven sufficient and avoid
the invocation of too many arbitrary form evaluations that the
modeler would face. A future refinement will include diagrams
showing forms that call for one factor value or another.
As an example of a
spectacular success, the Jake Swamp tree provides a clear case
of the process working exceptionally well. Jake's taper is slow,
but Jake's trunk flare borders on the high side. With a factor
of 1.00, the AATV is 571 versus a MV of 570. That is as good as
it gets. However, if I were to introduce a refinement for the
Jake tree, I'd probably use an F value of 0.95 to adjust for the
"almost too much" trunk flare. This would lead to an
AATV value of 542 versus the modeled 570.
As I see it, the especially
attractive features of the AATV formula are that it uses
familiar measurements. It employs girth at breast height and
full tree height. These are measurements that are normally
taken. The measurer need only add one additional measurement 
girth at the trunk flare point and then make a judgment call of
form by choosing a value for F, which can simply be left at 1.00
if the modeler sees no exaggerated trunk features.
The AATV formula currently
applies only to singletrunked pines. However, I expect it will
fit eastern hemlocks, red spruce, loblolly pines, etc. quite
well. It won't fit bald cypress. It may also fit singletrunked,
narrowcrowned oaks, young tuliptrees, and probably many species
of hardwoods grown in close competition with other trees – if
they maintain narrow crowns. However, additional factors or
alternative formulas will ultimately be needed to expand to a
wider range of tree forms.
So, why are we going through this
process? Well, the most obvious reason is because we want to.
It’s what we do, i.e. finding better ways to measure and model
trees. Computer methods will ultimately render these simple
field techniques obsolete for the experts with plenty of
computing experience, but the simper field methods will continue
to have a place for both researchers and amateurs, at least for
supplying interim measures.
Well, tomorrow, I will add a
couple or three more trees. The time consuming part is modeling
with the Macroscope 25. BTW, for the trees being modeled, there
is an average 14% reduction in girth going from trunk flare
girth to girth at 4.5 feet with a standard deviation of 7%. That
is a big variation, but on that is to be expected.
Bob 
New
Formula Cont' 
dbhg@comcast.net 
Aug
25, 2007 20:05 PDT 
Will,
Jess, Don, Don, Ed, Lee, et. al.:
I am up to 41 white pines modeled for testing
the new trunk volume fomula. With the inclusion of 3 more pines,
the ratio of AATV/MV stands at 0.992 and the standard deviation
is 0.089. The unadjusted ATV/MV is 0.982 and the standard
deviation is 0.102. Two of the added pines are old growth and
one is mature. Adding young pines would improve the ratio and
standard deviation, but that is not the purpose. I expect the
long run ratio to stabalize around 0.98 with a standard
deviation of probably 0.095. We'll see.
In an experiment, I applied the formula to the
big Dunbar Brook hemlock and the AATV fell well short of that
modeled. The old growth hemlock form will require an F value of
1.2, if not more. Applying the formula to old growth hemlocks is
going to be a challenge.
Well about an hour ago, I went and did it. I
ordered the Macroscope 45. I wanted a backup instrument to the
indispensible Macroscope 25 and elected to upgrade to the 45.
The telescope version works the same for both models, but the
microscope feature has a magnification factor of 45 for the
Macroscope 45 instead of 25. One can't have too many gizmos.
I'm anxious to purchase one of those extremely
accurate laser rangefinders that Paul Jost is tracking. The
TruPulse 200 is useful, but falls well short of shooting the
holes like the Nikon Prostaff 440 does. It is the real work
horse of the laser clan.
While scanning the Ben Meadows catalog, I saw
new entries in the one instrument to do everything competiton,
but all their tree height routines are the flawed tangent
method. So, for now, I'll stick with the simpler instruments and
do the math through the ENTS formula package.
Bob 
RE:
Back to Don again 
dbhg@comcast.net 
Aug
26, 2007 05:56 PDT 
Don,
C1 is at the point of trunk/root flare, which
is usually from 1.0 to 2.5 feet from ground contact point, at
least for eastern trees. C2 is at breast height. I realize that
the C1 point is often debatable  a weakness in the method, but
not a significant flaw for the vast majority of white pines. It
remains to be seen how well the method will hold up for other
conifers. For spruce, I think it will be even more accurate, but
probably less so for hemlock.
Bob
 Original message 
From: DON BERTOLETTE <FoResto@msn.com>;
Bob
You said "I'd say it is safe to conclude that the breast
high determination consistently underestimates the trunk
volume." By the volume amount due to the flare? Are C1 and
C2 circumferences at base and breast height? Seems
'calculable'...
DonB

Onward
marching volumes 
dbhg@comcast.net 
Aug
26, 2007 10:30 PDT 
ENTS,
I just finished modeling Monica's
tuliptree. I wanted to see how well the AATV formula fit that
slender, graceful tree. I believed the match would be close. The
rest of you can be the judges. Here are the numbers.
Monica's Tuliptree
CRH 7.95' (Girth at the
trunk flare)
CBH 6.60' (Girth at 4.5
ft above base)
Height 123.0' (full height)
V1 206.2 (volume
using the cone's base as the area computed at the trunk flare
point)
V2 142.1
(volume using the cone's base as the area computed at 4.5 feet
above base)
VC 180.2 (volume
modeled with the reticle)
AATV 174.2
Note: AATV = 1.00*123*(7.95^2+6.6^2)/75.4
AATV/VC = 0.97
This obviously is a very good trunk volume
estimation for Monica's tuliptree. Her tree is arrow straight,
has a gradual, even taper and a noticeable, but not exaggerated
trunk flare. So, I set the F value to 1.00.
Adding Monica's tree to the sample, I
now have 42 modeled trees. My contention continues to be that
the formula fits young forestgrown trees very well. Old trees
are the rascals. No surprise there, but I think for trees in the
1.0 to 5.0ft diameter range, the AATV formula will prove
valuable. For example, the huge Grandfather white pine in Monroe
SF has an AATV value of 976 cubes. Past modeled volumes run from
930 to 1020 cubes, with the most likely value being around 950.
Why the variation? Well, it is very difficult to see the trunk
in the crown region from the ground. As soon as my toe heals
sufficiently and the insect population crashes, it is of the
Dunbar Brook I go to remodel the Grandfather pine. I expect to
spend the entire day, circling the tree to get more and more
points. Hopefully, when Will comes in October, we'll put the
issue to rest with a climb.
Bob 
RE:
New Formula Cont' 
DON
BERTOLETTE 
Aug
28, 2007 13:37 PDT 
Bob/et al
As I read your post below, realizing how accurate your
procedures have become, I couldn't help but think that there
probably needs to be different levels of measuring devices for
different levels of accuracy needed.
Conceptually, I would suggest there are three levels...that of
1)approximation,
2)estimation, and
3)exacting (for the lack of a better word.
Respectively, these would be purposely for
1) a measurement triage, taken with lightweight field gear [as
defined by absence of gear belt/overloaded day or
fannypack...;>] such as a clinometer and rag tape;
2) a measure of candidacy for superlative listing, taken with
extensive/expensive digital field gear [defined as the array
needed to induce field duct tape repairs due to equipment
overload and repeated face plants...;>]; and
3) an exacting, undeniably accurate and precise measure that
stands up to the highest scrutiny, and only needed for trees of
such superlative dimension that they are likely to be eligible
for state or national tree champion status. This third level
would necessarily have to be precise (capable of replication by
independent measurement) and field going (though not necessarily
awkward, but probably so...:>}.
I'm thinking something that has precise control of vertical and
horizontal axis, like a 'Total Station' or such. There's
just too much 'loss of control' in handheld electronics, at the
level of accuracy that ENTS procedures can muster. Stand to the
side of anyone measuring the angle to the top and bottom, and
you'll see more 'movement' vertically than the accuracy striven
for (tenths of a foot).
DonB

Re:
New Formula Cont' 
Edward
Frank 
Aug
28, 2007 17:17 PDT 
Don,
Bob, et al,
The fourth level of accuracy would be called excruciating....
Ed Frank

Back
to Don 
dbhg@comcast.net 
Aug
30, 2007 22:18 PDT 
Don,
I think you are on to something. By
recognizing and formalizing the 3 levels of measurement, we
would be making a definitive statement about accuracy while
making room for those to participate who may be just starting
out and intimidated by all the expensive equipment and/or math
required to go to the extremes. We would be emphasizing the
lesser level of accuracy of Type I measurements and drawing
attention to them without rejecting them outright  although
Type I measurements would not be ENTScertified. Let's continue
this thread.
With respect to equipment, LaserTech is
delivering a TruePulse 360 to my doorstep this morning at
9:00AM. Way cool! Then the testing will begin.
Bob

Re:
New Formula Cont' 
dbhg@comcast.net 
Aug
30, 2007 22:42 PDT 
Ed,
Don, et al:
Or exhilarating. The 4th stage is where
we call in Will to climb the tree. Then depending on how the
climb goes, it is excruciating or exhilarating  maybe both. For
us landlubbers remaining on the ground, probably just
fascinating.
Bob

Comparisons
and modeling 
dbhg@comcast.net 
Sep
12, 2007 01:39 PDT 
ENTS,
Much
of our ENTS Internet time is spent discussing the big trees that
we've measured and what we want to see. From time to time, we
discuss historically significant big trees and often wonder if
their reported dimensions are anywhere near accurate. There is
much food for thought here that calls in not only reports of the
past, but also the concept of bigness.
Ents
who are involved in champion tree programs, directly
administering or suppoting them, use the American Forests
champion tree formula as the arbiter of tree size when working
within the context of the champion tree programs. However, we in
ENTS have other systems for measuring and judging tree size.
Will Blozan's TDI system is an alternative to the champion tree
formula. I prefer it, but there is a place for both systems and
I don't deprecate the former.
Trunk
modeling is another method for getting at tree size  at least
trunk size for the trees of a compliant form, i.e. where trunk
form is distinguishable. But modeling trunk volumes is labor
intensive and requires another instrument beyond the standard
laser rangefinder, clinometer, and scientific calculator. Laser
Tech's dendrometer the RD1000 and/or the Macroscopes 25 and 45
are instruments that can be productively employed in trunk
modeling. Several of us are now into trunk modeling in a big
way.
Despite
our zeal and Will Blozan's extensive modeling of the great
southern hemlocks not withstanding, in most ways, ENTS trunk
(and limb) modeling is still in its infancy. Tree forms such as
that of the humugus live oaks that our friend Larry is
confirming are beyond simple modeling techniques. These giant
spreaders need a team headed by the likes of Bob Van Pelt and
Will Blozan to do them justice. However, for eastern conifers,
like the pines, spruces, and hemlocks, we are getting closer to
calculating acceptable trunk volumes with far simpler methods.
The fromula that I've now presented a number of times holds
increasing promise. I repeat it below.
V
= F*H*(C1^2 + C2^2)/75.4
Where:
V
is volume,
C1
is circumference at 4.5 feet above the tree's base,
C2
is circumference at the trunk/root flare,
H
is full height, and
F
is a factor that an be applied if the situation calls for it to
compensate for exaggerated trunk forms such as:
a.
Extreme trunk flare,
b.
A very columnar form,
c.
A very fast trunk taper,
d.
Broken trunk,
e
A combination of the above.
We also define:
V1
as the conical volume based on the full height H and a basal
area equal to the area at 4.5 feet above ground level,
V2
as the conical volume based on H and a basl area equal to the
area at the trunk flare point.
Vm
as modeled trunk volume.
We can state that:
a.
V1 <=V <= V2
b.
V1 <= Vm <= V2 in a high percentage of trees and almost
always in young to mature trees, but not old trees.
c.
0.97 <= average(V/VM) <= 1.03 with almost 100% certainty
where the sample of trees ranges over young to old trees..
So, the formula for V
is holding up well and we won't be misrepresenting what it does
so long as we clearly state that it provides a means of
estimating trunk volume and does not replace modeling methods.
So what can we glean in the
way of information that might give us new insights about trunk
volumes and as a derivative  tree bigness? One piece of
information that I think is not tree trivia is that provides an
easy way to investigate common tree size for comparison purposes
to place things into perspective. For instance, in central and
northern New England, second growth forests are heavily stocked
with trees in the CBH range of 4 to 7 feet and height ranges of
70 to 100 feet. Trees in the size range of 16 to 20 inches DBH
and 75 to 100 feet tall are everywhere abundant in regrowth
forests and those trees are considered economically mature.
Trees in the quoted size range have a trunk volume range of
about 50 to 175 cubic feet. A big tree person walking through
these young, nondescript forests sees little to get excited
about. But with many,many trees in the 75 to 150 cubic foot
trunk volume range here in New England's forests, it is easy to
lose sight of the fact that the forests are still ecologically
immature. Except for a relatively few big tree locations and
riparian zones, people are now accustomed to a reduced standard.
The big trees are in towns.
On the big tree sites,
white pines and hemlocks with trunk volumes in the 400 to 600
cubic foot ranges stand out as large to very large and an
800foot cube tree is a monster. Yet an 800foot cuber is only
half the volume of the largest eastern hemlock modeled by Will
and Jess in the Smokies. And 1600 cubes, as large as that is, is
not even half the size of the biggest tuliptrees in the southern
Appalachians and only a quarter of the size of the largest live
oaks down Larry's way. Scale and perspective are important.
Consider the General Sherman
Tree in California. Based on BVP's work, we know that it has
over 50,000 cubic feet of wood. Obviously the scale for tree
size is very wide. Taking a respectible 150cuber in a regrowth
New England forest as an example that satisfies modern timber
professionals, it would take 333 New England trees to equal the
General Sherman tree. Obviously, scales and ranges are far
broader for trees than for the characteristics of people  which
I suspect effects the way we make and understand comparisons. A
125lb adult human male is usually considered small. A 375lb
adult human male is huge. The ratio here is 1 to 3 on weight.
Yes, there are superobese people who weigh 500 to 800 lbs and
occasionally over 1,000 lbs, but they are not representatives of
the human species that inspire any of us. A 100 lb to 400 lb is
about the range we can expect and respect. That's 1 to 4, not 1
to 333. So, people comparisons don't provide us with a broad
enough scale to fully appreciate tree comparisons.
So where is this
going? Well, I'm unsure except that when it comes to the
comparison game, we need to do a lot of thinking about what is
ordinary, unusual, exceptional, and very exceptional when it
comes to trees and what we do with the information. The ranges
for trees are all over the place and that can obscure what is
exceptional at the local level. Sometimes a comparatively little
is a actually lot for a species. For instance, a 140foot tall
tuliptree is not exceptional throughout much of the range of
that species where growing conditions are good, but 170 feet is.
That is a 1 to 1.214 ratio. Now, in terms of volume, a 200
cubic foot tuliptree is very ordinary, but at the other end of
the volume range, we have the 4000cube monsters. That is a a
ratio of 1 to 20 for the same species. So, in terms of
comparisons, we need all the help we can get to recognize when
to get excited with intraspecies and interspecies comparisons.
Presently, I get excited when a great white goes over 500 cubes.
That's a benchmark of significant size for that species for me,
north or south.
Will, Jess, Ed, Lee,
etc.your turn with the comparison ratios.
Bob 
Re:
Comparisons and modeling 
Dean
Hedin 
Sep
12, 2007 20:56 PDT 
I
don't like F. It seems to make the rest of the formula almost
meaningless if you can just multiply a constant to everything
to make it come out nice.
In my line a work we call that a "Fudge Factor".
I'll be honest, I haven't measured many trees, but I don't need
that experience not to like F.
I understand the difficulty of the problem. You would like to
get a very good estimate of volume from a minimal set of
measurements.
Such a problem may not have a simple solution (or any).
I know how I would find out. I presume you have a set of data
that consist of the "simple measures" along with
data of tree volumes measured in some careful manner and are
relatively accurate.
I would then write a genetic algorithm that tries different
"formula combinations" and then runs these across the
data set as a test for fitness of the formula. This process is
repeated many times over with the "formula
combinations" crossbred until a formula of required
accuracy is found (or not).
It's a brute force method. In other words, let the computer find
the best formula (or let it tell you it can't find one).
I would think that one could get good estimate of tree volume
for an "isolated" deciduous tree by merely taking a
high resolution digital picture of the tree against a clear
background (like the sky) in the winter, when the leaves have
fallen. So long as a scale is indicated in the image an
algorithm could then count up the dark pixels in the image and
then estimate the volume.

Modeling 
dbhg@comcast.net 
Sep
17, 2007 17:43 PDT 
Dale, Will, Jess, Howard, et al:
On Friday I went
to MTSF for a brief period, but long enough to model the Mirror
tree, a handsome white pine that stands 156.6 feet tall and has
an 11.0foot girth. It models to 533.0 cubes. The AATV formula
yields 516.5 cubes for the Mirror Tree. The difference of 3.3%
in volume resulting from use of the formula is acceptable as an
estimate of the tree's volume. This morning, I modeled a
neighbor's pine, a gorgeous tree 8.1 feet in girth and 120.0
feet tall. My neighbor's white pine yields 232.0 cubes and
computes on the formula to 239.1. The difference is 3.1 percent.
This afternoon, I modeled a pine on Monica's land. It models to
237.1 cubes. The unadjusted formula gives 244.7 and the adjusted
formula gives 232.5.
I have now modeled 46 pines
and applied the formula to the same. The volume yielded by the
formula averages 98.3% of modeled volume with a standard
deviation of 9.6%. Using the adjusted volumes by applying the
shape factor to the situations that I've previously described,
the formula yields 99.2% of modeled volume with a standard
deviation of 8.6%. The very old trees and trees on steep slopes
are the ones that predictably produce the high standard
deviation. Nonetheless, The formula is proving its worth as a
tool for ENTS to use. The beauty of it is that it gives us a
good estimate of volume for singletrunk eastern conifers with
very little measuring. However, as it underestimates the volume
of old growth forms, the Seneca Pine's volume would be
underestimated by between 10% and 20% unless the shape factor
is applied.
Dale, will you have any time to
experiment with the formula in the coming months? Similarly,
Will, Jess, and Howard, will you be able to give it a fair test
on conifers in your region? I am especially interested in how
the formula would work if tweaked it with one extra measurement
taken at halfway up the trunk? A measurement at that point would
negate the need for the subjectively applied shape factor, but
would require the reticle and finding the midway point of the
trunk. That would deter its wide spread usage, but allow us to
catalog many more trees.
Bob 
RE:
Modeling 
DON
BERTOLETTE 
Sep
18, 2007 01:32 PDT 
Bob
I'm thinking that you may end up with a formula adjustment
factor (FAF) that may be effective within species, ie, og white
pines would have xx.x FAF, whereas hemlocks might likely have a
somewhat different one, etc., etc. As well as
age, growth habit (steep slopes, creeping soils, etc.), and
other peculiarities affecting base.
Don

RE:
Modeling 
dbhg@comcast.net 
Sep
18, 2007 07:30 PDT 
Dale,
The formula is as follows:
H = full tree height,
C1 = Circumference at root flare
C2 = Circumference at 4.5 feet
F = shape factor
V = volume
V = H*F*(C1^2 + C2^2)/75.4
If the difference between C1 and C2 is
over 2 feet, you can set F to either 0.95 if the taper is slow
or 0.9 if the taper is fast. If the taper is extremely slow as
with an OG tree, F could be as high as 1.2 for a normal root
flare. Big root flare and extremely slow taper would cancel one
another, if you get the idea. You be the judge. Young white
pines with out a pronounced root flare have F=1.00.
Bob
 Original message 
From: Dale Luthringer <djluth@pennswoods.net>;
Bob,
I’d like to try it out on a couple of pines, and maybe compare
it a couple of hemlocks as well. Can you please send me the
formula again?
Sorry, I’m just starting to get my head above water over here
after the busy summer season.
Dale

Back
to Dale 
dbhg@comcast.net 
Sep
18, 2007 11:05 PDT 
Dale,
We will need to experiment with
the form factor to cut down on the element of judgement. Making
it species specific as Don Bertolette suggests will be required.
Hemlocks will most likely have a wider range for the form
factor.
It will be interesting to
see if we can get this approach to really work and with John
Eichholz coming back on board in the not too distant future,
we'll have a good team to work on the process. As it stands now,
the formula does work for a limited range of white pine shapes,
but that's all I can say for sure.
Now as to Anthony's Mohawk
haircut, well even though he doesn't think he would look
handsome in a nice new Mohawk, I think he would be mobbed by the
ladies. He'd owe us big time. What do you think?
Bob

RE:
Modeling 
dbhg@comcast.net 
Sep
18, 2007 14:33 PDT 
Don,
Yes, that's the direction all this seems to be
pointed. I think the formula will apply well to spruce in Alaska
 hint, hint.
Bob

#49
and counting 
dbhg@comcast.net 
Sep
20, 2007 12:34 PDT 
Will,
Dale, Howard, Jess, Lee, Don, et al:
I just returned from modeling white pine
#49  a very mature tree growing near upper Broad Brook. Its
stats are as follows:
Girth at Trunk Flare: 10.3 '
Girth at 4.5 feet: 9.1'
Girth at 6 feet: 8.8'
Total Hgt: 115.3'
The modeled volume with reticle is
289.5 cubes
The unadjusted formula volume is
288.9 cubes.
What can I say? I didn't apply an
adjustment because the taper is normal and the trunk flare is
under 1.5 feet. This tree is a dream match to the fromula, but
of course, other trees aren't. The unadjusted percentage of the
average of the formulacalculated volumes to the equivalent
averaged modeled volume stands at 98.7% with a standard
deviation of 9.7%. The comparable stats for the adjusted formula
are 99.3% and 8.4% respectively. Although, I'll continue
modeling pines, I think the case for that species has been made.
It's mainly a question of tewaking the adjustment factor. Anyone
have thoughts on the best way to proceed?
Bob 
#51,
counting and adding species 
dbhg@comcast.net 
Sep
20, 2007 12:45 PDT 
ENTS,
After the success with #49, I added two northern red oaks. One I
had previously modeled but had excluded from the data. The other
is an blackscarlet hybrid in Monica's front yard. The tree's
vital stats are:
Girth at 1.0 ft = 7.6'
Girth at 4.5 ft = 6.3'
Height = 84.0 feet
The modeled volume is 107.2 cubes. The
main trunk holds true to near the top branches, so the overall
form is right for formula application. The unadjusted formula
volume is 108.6 cubes. Wow! Two tight matches in one day of
different species. This is starting to get way cool.
Bob 
#53 
dbhg@comcast.net 
Sep
21, 2007 13:00 PDT 
ENTS,
I just modeled a slender white oak across the
street from Monica's house. Its stats are:
Height: 95.9 ft
CFH: 6.59 ft
CBH: 4.58 ft
Its modeled volume is 88.5 cubes and the
formula volume computes to 82.0 cubes. The 6.5cube difference
seems a lot, given the prior close matches, but not unexpected.
I am going to turn my attention to
hemlocks now and see if the younger ones conform as well as the
younger white pines.
Don Bertolette,
Don, any chance of applying the formula
to some of the straight young to mature spruce in your neck of
the woods? My current belief is that spruce should be most
compliant.
Bob 
Back
to Don 
dbhg@comcast.net 
Sep
22, 2007 13:48 PDT 
Don,
#54 was modeled an hour ago  a fine black oak
in a neighbors yard. The modeled volume was 159.8 cubes. The
formula gave 158.9. Since the species is an oak there is a lot
of branching, as you would expect. So, what the formula means or
produces when applied to such a form, is unclear. The close of
numbers match is very interesting. More on this later.
Bob

Bob
I would guess that boles with branching may have more hidden
mass/volume than those without, the way that many trees will
buttress their limbs for strength...
Don

#54
and #55 
dbhg@comcast.net 
Sep
25, 2007 13:23 PDT 
ENTS,
Yesterday, I modeled Baaby's Hemlock on
Petticoat Hill in Williamsburg, MA ((yes, that's two A's in
Baaby). The stats for the tree are:
CRH: 9.8 '
CBH: 8.1'
Height: 127.1'
The modeled volume of Baaby's
Hemlock is 277.3 cubes. The unadjusted formula volume is 271.1.
The difference represents 2.2% of modeled volume, which is quite
acceptable. The F value in the formula was left at 1.00, because
the fast taper of the tree appears to be offset by the slightly
high trunk flare (1.7 feet more girth than at 4.5 feet).
The primary reason I’ve modeled
Baaby's Hemlock is to establish an ENTS record of significant
hemlocks in New England before they succumb to the adelgid.
Baaby's Hemlock has lost a lot of foliage and may be past the
point of no return. It is significant because its 127.1foot
height makes it the tallest measured so far in the eastern
Berkshires. Its age appears to be between 130 and 180 years,
probably in the 140150 range.
Baaby’s Hemlock becomes
#54 modeled and compared to the calculated volume via the trunk
volume formula, which continues to perform well when applied to
singletrunk conifers up to 200 years in age and not growing on
extremely steep slopes or in excessively wet areas, where trunk
flare becomes exaggerated.
Today, Gary Beluzo and I
searched for tuliptrees and I modeled another hemlock along
Broad Brook. Stats are:
CRH = 9.35’
CBH = 8.2’
Height = 117.0’
Modeled Volume = 229.1 cubes
Adjusted Formula Volume =
228.0 cubes
Unadjusted Formula Volume = 240.0
cubes
The tree had a normal root
flare, but a very fast taper, so F was set to 0.95.
The reason the formula works
well is that the volume of the trunk of eastern conifers usually
falls between two conical forms. The upper limit form is the
cone formed by using its basal area equal to that of the
tree’s crosssectional trunk area taken at the trunk flare
point. The lower limit is the conical form with the cone’s
basal area equal to the tree’s crosssectional area at 4.5
feet up. In both cases, the cone height equals the full height
of the tree. Trees that taper extremely fast or extremely slow
and trees that have an extreme trunk/root flare can fall outside
the above range. A modest compensating factor can be applied
that will capture about 3/4ths to 4/5ths of these trees, but
some trees will fall out side the range of +/ 10%. We can
eventually derive factors to capture most of eastern conifers
and perhaps a lot in the West, at least the Rocky Mountain West.
To repeat the formula:
C1 = circumference at
trunk/root flare
C2 = circumference at
4.5 feet above base
H =
full height of tree
F = trunk form
adjustment factor
V = trunk volume
V =
F*H*(C1^2+C2^2)/75.4
The adjusted formula volume
averages 99.33% of the modeled volume with a standard deviation
of 7.94%. This is after 55 modelings.
Bob

New
formula 
dbhg@comcast.net 
Sep
25, 2007 16:37 PDT 
Will,
Dale, Jess, Don, et al:
I modeled another white pine
today  a slender one on Broad Brook that exhibits the trunk
form that works well in the formula. The modeled volume came out
to be 147.3 cubes and the formula, unadjusted, yielded 144.7
cubes. The difference of 2.6 cubes is pretty minimal. The Broad
Brook pine becomes number 48 modeled with reticle to test the
formula. I won't be content until I have 100 pines modeled. My
guess is that the unadjusted volume via the formula will be
about 98% of modeled volume with a standard deviation of around
10%. The adjusted version will be about 99.5% and 8.5%.
Bob 
