Tree Form Analysis    Edward Frank
   Jan 22, 2005 12:30 PST 


Will Blozan's proposed big tree formula is independent of tree shape
between species. The AF big tree formula and the formula I suggested
a(height) + b(cbh) + c(crown spread) = Points where a, b, and c are
constant weighting factors are dependant on tree form. It strikes me that
an equation of this form could be used to analyze tree shape.

Some trees, such as spruce, tend to be tall with a small canopy spread.
Others, like Live Oak, tend to have a broad canopy compared to their
overall height. Other trees fall somewhere in between. The first step
would be to calculate what the proper weighting factors should be for each
parameter. A tree of average proportions would be measured. The factors
of height, cbh, and crown spread would each be weighted so that all of
these parameters would be equal. These weighting factors, designated a, b,
and c would then be applied to other trees with differing forms.

For the base tree the (a)height/total points = 33.3%, the (b)cbh/total
points = 33.3%, and (c)crown spread/total points = 33.3%. On a ternary
diagram (triangular graph) this generic tree would plot dead square on the

The same weighting factors would then be used to calculate the total points
for the tree in question. Using the same formulas as above, then the
weighted values would be calculated as a percentage of the total points.
These would all plot as a single unique point on the ternary diagram.
Trees with a broad crown would plot toward the crown apex of the graph,
tall trees would plot toward the tall apex, fat trees would plot toward the
girth apex. The form of the tree would be expressed as a list of these
three percentages.

This format would allow comparisons to be made between trees of different
forms, between forest versus open grown trees, and similar analysis. The
advantage is that it uses existing measurements to calculate these form
parameters and does not require any additional measurements.

Initially some measurements of select trees might need to be made to
determine what the base "neutral shape" ratios would be in order to
calculate the weighting factors. But beyond that initial step it would only
amount to a few cells in a spreadsheet to calculate a form factor.

I have a small stand alone program that plots ternary diagrams. I know
that when in school one of the technicians was using Excel to plot ternary
diagrams. I don't know if this was a base ability of Excel, or if a
particular macro was used force a ternary diagram. I can check if someone
is interested. Excel would be a better choice as it should be able to
import the raw data from the ENTS database.

Ed Frank
Re: Tree Form Analysis
   Jan 22, 2005 13:31 PST 


Definitely... Ternary (triad) graphical data presentation is well known in
environmental sciences - soil constituents (is it sand/silt/clay?) and aquatic
sediment health (chemistry/toxicity testing/health of biota in situ) are just
two examples. Tree forms would be evident, just as soil types are, by such an

Re: Tree Form Analysis   Edward Frank
  Jan 30, 2005 18:58 PST 


I have been thinking about this problem: How to calculate what the average
dimensions of a typical tree would be in order to determine the weighing
factors? The other question is how does the shape of the tree change over
time as the tree grows taller and matures?

We can't simply average the crown spread, height, and girth of the trees in
our dataset (this is something I ask Bob about), because our trees
measurements are dominated by lots of some trees - white pine - and few
examples of many others. So averaging the numbers would produce a value,
but that value would produce something closer to the typical white pine
shape than the shape of an average tree.

The other consideration is how the shape changes as the trees grow larger.
We are generally looking at the tallest trees when me measure them, so if
the form varies, we should calibrate our weighting numbers for the larger
trees. It is like calibrating a pH meter. If you are measuring acid
solutions you calibrate using a pH 4 buffer, so that the measurements will
be most accurate in the range you are measuring. If we were looking at the
shape of saplings, or young trees, we would need to calibrate to determine
appropriate weighing parameters for trees in that size range.

It occurs to me that using a given set of weighing factors, you could plot
a large number of tree of the same species representing different ages and
sizes and see if there is a consistent pattern of shape change over time as
the tree matures.   You would need to compare forest grown with forest
grown instead of mixing open and forest grown on one plot for this purpose.

How to determine a good weighting factor to characterize an "average" tree
shape. One possibility would be to take say three to five examples per
species of a wide variety of trees, including both forest grown and open
grown if possible, and averaging them together. This would offset sampling
bias caused by one species being sampled more often than another.

It doesn't really matter if a particular tree is larger or smaller than the
average, the same weighting factor would be applied to each parameter, and
the result calculated as a percentile of the total. Distinct shape
differences should be seen between species, between open grown and forest
trees, or between trees of different ages. This is a way to characterize
tree shape in a mathematical way, rather than simple description.

Does anyone know how to do a ternary diagram with excel?

Ed Frank

TernPlot - Excel Ternary Diagram Spreadsheet  ternplot.xls