Modeling to commence   Robert Leverett
  Aug 04, 2005 06:50 PDT 

ENTS:

   Will Blozan and I are laying plans to measure the volumes of the
great Smoky Mountain hemlocks while some of the largest are still
standing. Will climbed a giant that he named the Long Branch hemlock. At
its absolute base, this huge tree has a 25-foot perimeter foot print. At
4.5 feet up, it is 16 feet around. It reaches a very respectable height
of 143 feet and some inches. Will climbed the tree and took 32
circumferential measurements. Modeling the volume the way we have in the
past (using frustums of cones), the volume computes to around 1,335
cubic feet. That's huge, but Will thought it would be more as did I,
given what we computed the now dead Yonaguska hemlock's volume to be. On
his climb of that tree, Will took measurements at 3-foot intervals all
the way up. The Yoni tree splits into two trunks. Will climbed both, so
we have measurements that reflect the entire tree. The Yonaguska and
Tsali hemlocks have both been modeled as have several other giants and
1,500 cubic feet seems to be the upper volume limit for the Smoky
Mountain giants. The Long Branch giant was to be the record breaker, but
so far it hasn't been. The answer seems to be in the large amount of
wood in the Yonaguska's double trunks that start well up the tree.

   Modeling these trees requires a lot of measurements and some sporty
assumptions about shape. Always assuming circularity overstates volume.
We know that, but by how much is the question. One thing we know is that
if we want to model the volumes with a high degree of accuracy, we
cannot rely on built-in algorithms that make assumptions about shape and
overall volume that just aren't fulfilled for old-growth forms.

Bob       

Robert T. Leverett
Cofounder, Eastern Native Tree Society
Possible Solution (Private Email)   Robert Leverett
  Aug 04, 2005 06:50 PDT 

Will:

I think I have a possible way to handle trunk anomalies. First, though, I've attached a spreadsheet that more clearly shows the interpolated diameter or circumference calculation. The calculation is central to figuring out how many and where to take diameter measurements with the RD 1000. 

So here is my thinking. We would start out with a DBH level diameter measurement. Then we would go to an area beneath the first significant limb bulge and take a second diameter. The interval could be long or short. We would then go to the mid-point of the interval and take a diameter measurement and then do the interpolated calculation from the formula in the spreadsheet at that mid-point and compare the measured with the interpolated results. If the numbers are very close, we would accept the single section as sufficiently conical and just apply the frustum formula once. If not, we would break the trunk into two sections at the mid-point determination and apply the above procedure in binomial fashion to each half. Sections that are sufficiently conical would not be split further. In this way we divide only the trunk sections that deviate from conical. We would have to proceed slowly so as not to lose our place or skip a section. We would take as many measurements as we felt needed between DBH level and the base. Dealing with areas from the first major branching point to the crown would have to be by the seat of our pants for obvious reasons. 

I'm going to try the above method on the Ice Glen Pine on Saturday. Wish me luck.


Bob
Re:  Possible Solution   Edward Frank
  Aug 04, 2005 06:50 PDT 
Bob,

I don't understand why if you are going to take a midpoint reading anyway, why you don't just break the trunk section into two segments instead of worrying whether or not the entire column can be calculated as a single cone. Using the measurements to define two conical sections isn't any harder as it is simply a cell in the spreadsheet. It also would assure a consistency of methodology rather than sometimes treating the section below the first limb as a single section and sometimes treating it as two or more sections.

Is it because you are going to apply a different formula (conical) if the trunk is considered in one section and binomial if considered in two sections? How much of a difference is this going to make? And how are you going to deal with the problem af comparing information between trees whose volumes were derived using different formulas? Will it make a difference? Since the trunk above the branching is going to be done "seat of the pants" will the estimated errors be bigger or smaller than the variations between the two methods of calculating the lower trunk volumes? I am asking what you feel about these variables, not looking for a detailed numerical analysis.

I wonder if some method could be determined to deal with the asymmetry of the diameter - oval versus circular. I am thinking that the volume variation from this type of asymmetry may be greater than the variation between using conical versus other assumptions about tree tapering, so long as you are dealing with shorter trunk segments.

Anyway, good luck with your experiments. Looks like I will be off on my trip again Saturday, so I will be out of the loop.

Ed
Re: Modeling to commence   Don Bertolette
  Aug 04, 2005 18:24 PDT 

Bob-
A few thoughts/questions...
You've chosen circumference as a measure of the base cross-section.
Why circumference instead of diameter? Is this to eliminate a mathematical
step (dividing by Pi)?

When you begin your modelling of the Long Branch hemlock, will you be using
your new laser hypsometer?
Will you not be measuring the tree cross-section by diameter, as you go up
the tree? How will you correct error due to parallax   <O    ?
Ideally you'd be able to back off sufficiently far to minimize effect of
parallax, but I suspect that GSMNP woods are rather dense to get very far
away?
Comparing Will's actual measurements to the new laser would provide a way to
factor out parallax in level to near level readings, but as you go up the
tree and down in cross-sectional units (tree narrows), the factor would
change?
-DonB
Re: Modeling to commence   Don Bertolette
  Aug 04, 2005 18:24 PDT 

Bob-
A few thoughts/questions...
You've chosen circumference as a measure of the base cross-section.
Why circumference instead of diameter? Is this to eliminate a mathematical
step (dividing by Pi)?

When you begin your modeling of the Long Branch hemlock, will you be using
your new laser hypsometer?

Will you not be measuring the tree cross-section by diameter, as you go up
the tree? How will you correct error due to parallax   <O    ?
Ideally you'd be able to back off sufficiently far to minimize effect of
parallax, but I suspect that GSMNP woods are rather dense to get very far
away?

Comparing Will's actual measurements to the new laser would provide a way to
factor out parallax in level to near level readings, but as you go up the
tree and down in cross-sectional units (tree narrows), the factor would
change?

-DonB
RE: Modeling to commence    Robert Leverett
   Aug 05, 2005 07:18 PDT 

Don:

   I tend to use circumference and diameter interchangeably, since one
is a multiple of the other. Conversions through linear relationships has
never caused me problems. I tend to use circumference a lot in our
discussions because it is what we directly measure.

   You are, of course, correct. The dendrometer will be measuring
cross-sectional distance, a surrogate for diameter when thinking of the
cross-sectional area as circular.

    Looking up a trunk from a fixed spot, I don't believe parallax will
be much of a problem when maintaining the same vertical plane. So far as
the diameter line is concerned that will be the subject of measure,
looking up to it is somewhat equivalent to just being farther away from
it. While the cross-sectional area from the plane through the eyes up
through the tree to include the diameter line is elliptical, the
diameter (or ellipse axis) is a two-dimensional figure. I don't think it
is distorted so long as there is no lateral movement. Thought of another
way, whether the target diameter is viewed from a position below it,
level with it, or from above it, the subtended angle of the diameter is
the same, provide the distance to the target diameter remains the same -
rather like traveling around the circumference of a large circle
oriented in the vertical plane. Stay within the same vertical plane and
there is no lateral distortion of a fixed diameter line. Move left or
right and you are no longer seeing the same tangent points to the sides
of the trunk that define the diameter line. With lateral movement, the
original diameter line, were it actually visible as a line, would become
foreshortened as points on the sides of the subtended angle. The new
diameter line based on the distance between tangent points from the eye
to either side of the trunk might or might not be the same length as the
original line, depending on whether the left-right shift was linear or
circular (keeping a fixed distance) and whether or not the
cross-sectional area was circular. Oh my aching head!    

   All good stuff to think about. However, Will and I, and others I
presume, are going to be fiddling with these measurements for a long
time. But, the call of those ancient Great Smoky Mountain hemlocks to be
accurately modeled while they still live is a powerful incentive that
both Will and I need to stay focused. The priority with us isn't so much
a scientific investigation of why the Smoky Mountain hemlocks grow so
large as it is the historical documentation of those trees. Call us
obsessed. We clearly are.   

Bob