| Weekend
modeling, Nov 28 |
Robert
Leverett |
| Nov
28, 2005 06:43 PST |
ENTS
Yesterday, John Eichholz and I modeled 3
more MTSF white pines for
volume, bringing the total number of modeled pines to 58. Per
agreement
with Will Blozan, I've dropped limb volume estimates out of the
totals
and settled for trunk volume. The latest regression equation is:
Y = -53.38829012 - 2.25714004(X1)
+ 2.100125255(X2) + 5.904026908
(X3) + 11.82357878(X4) + 14.04687849(X5)
where Y = trunk volume in cubic feet
X1
= total height in feet
X2
= diameter in inches at 2.5 ft
X3
= diameter in inches at 4.5 ft
X4
= diameter in inches at 50 ft
X5 = diameter in inches at 100 ft
The multiple linear regression coefficient
from the 58 sample points
is 0.963. As explained in a previous e-mail, this very high
regression
coefficient is misleading in terms of using it as a reliable
predictor
of trunk volume. For example, using the equation, two small
trees in the
sample have a computed negative volume and the volumes of the 8
largest
trees are all understated. A nonlinear equation is needed, but
one based
on multiple independent variables. The regression programs I
have are
for multivariate linear or bivariate nonlinear.
By excluding limbs, of the 58 pines modeled,
only the Grandfather
pine in Monroe State Forest exceeds 1000 cubes. The question of
whether
or not subsequent measurements of the tree will continue
supporting a
thousand cubes begs to be answered. What must be done is to
volume model
the trunk from two vantage points that are 90 degrees apart,
i.e. test
for elliptical sections of the trunk.
There is no question that the Grandfather tree
is huge. It's CBH is
13.7 or 13.8 feet depending on where the midpoint of the slope
is
located. Personally, I do believe the tree has a good crack at
being
confirmed as a legitimate thousand cuber, but not by much. On
the next
available weekend date with good weather, it will be back to
Monroe I
will go.
One of the 3 pines John and I modeled in
MTSF was a very slender
tree. Its CBH is only 4.6 feet or 17.7 inches DBH. In this
dimension,
the slender tree compares to one modeled in Mt Tom reservation.
That
tree is 17.8 inches DBH. The volumes are virtually identical. A
side by
side comparison follows:
Tree Height Diam
at 2.5' Diam at 4.5' Trunk
Volume
MTSF 133.3 18.5' 17.7" 76
cubic
ft
Mt Tom 106.6 18.8' 17.8" 75
cubic
ft
The 26.7 ft height difference
illustrates the dramatic height
advantage that Mohawk's pines enjoy over stands that are more
typical of
what one commonly sees around New England.
In an exercise to compare conical volume
to computed volume I took
the diameter at 2.5 feet as opposed to on the ground and used
that as
the base diameter. When the conical volume is compared to that
computed
with the RD 1000, the results are all over the place, revealing
the many
trunk departures from a regular cone shape. Interestingly,
though, the
cone shape exceeds far more than trails the computed volume. So
root
flare is still too much of a distorting factor at 2.5 feet.
Using the
diameter at 4.5 feet, the cone shape understates the volume in
47 of the
58 sample trees. Using the diameter at 2.5 feet, the cone shape
overstates the volume in 40 of the 58 trees. A lot seems to be
happening
between 2.5 and 4.5 feet above the base, though this is seldom
obvious
from simple eye observation. Trees that have a big root flare
start the
cone well outside the general space taken up by the trunk. That
much is
obvious to the eye. For trees that remain cylindrical for a long
trunk
distance and then take a nosedive to the top, the conical shape
stays
within the space of the trunk for a long time.
It would be extremely useful to
find two diameters, taken at
standard heights, one of which fairly consistently overstates
and the
other of which fairly consistently understates the modeled
volume. The
diameters at 2.5 and 4.5 feet come fairly close to doing this.
Perhaps
2 feet and 5.5 feet would accomplish this. Getting closer to the
base
than 2 feet often gets one into so much root mass, that
circumference/perimeter determinations start to be challenging
and when
a big tree is on a steep slope – forget it. However, to
illustrate the
idea, the Jake Swamp tree cubes out to 561 cubic feet. The
volume based
on the diameter at 2.5 feet is 588 cubic feet. The volume based
on the
diameter at 4.5 feet is 480 cubic feet. The computed volume lies
within
these boundaries. The Seneca and Grandmother trees have computed
volumes
that fall within their 2.5 and 4.5 boundaries. However, the
Grandfather
and Ice Glen pines do not. Oh well, onward with the mission.
Bob
Robert T. Leverett
Cofounder, Eastern Native Tree Society |
| RE:
Weekend modeling |
Don
Bragg |
| Nov
28, 2005 13:17 PST |
Bob--
Did you ever run your model without the intercept (the -53
value)?
Given how regression models are optimized, I would be surprised
if it
would affect your regression coefficient much, and it would give
you
another intuitive data point (volume = 0 cubic feet when total
height =
0) that may improve the fit for smaller diameter trees.
I'm not sure how you fit your regressions, but I have seen a
program on
the market (TableCurve, http://www.systat.com/products/TableCurve2D/)
that can fit a massive number of models quickly if you'd like to
play
model form more. I believe they offer a preview version for
people to
try for free, a good thing given its $500 price tag.
Just some thoughts...
Don Bragg
|
| RE:
Weekend modeling |
dbhg-@comcast.net |
| Nov
29, 2005 03:54 PST |
Don,
Thanks for the ideas and the info on the
regression software. I've just been using what is built into the
Data Analysis package of Excel.
I did put in an arbitrary 0 origin point
inot my data, but that didn't cure the problem. So long as the
model remains linear, the result seems yield negative
intercepts. I'll drop the negative constant and recalculate the
regression result.
Bob |
| RE:
Weekend modeling and Excel problems |
Don
Bragg |
| Nov
30, 2005 13:19 PST |
I wondered if you were using Excel...there has been considerable
consternation in some Ecology email lists (e.g., ECOLOG) about
using
Excel for statistical analysis, including some definite errors
due to
how things are calculated. Type 'regression problems in excel'
into
Google, and you will find multiple webpages on this topic. I use
other
programs to do regression in part to avoid the weaknesses of
Excel--I
don't know if it will affect your outcomes, but it is worth
investigating.
If you'd like, I'd be happy to run some regressions using my
statistical
software, and see what comes up (you'd have to email me your
data)...
Don Bragg
|
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