Crown Volume    Edward Frank
   Feb 11, 2007 06:59 PST 


Last night I was talking with Will over the internet and the subject of
crown volume came up. I put forth a suggestion on how to approximate
this value. Well overnight the idea rattled around in the large open
space inside my head. The calculations are really simpler than I first
suggested. I wrote to Will the following:
Crown volume.   My ideas on this are to measure average crown spread,
measure thickness of crown (live crown ratio), and then match the
general shape of the crown to a series of shape diagrams. You look in
tree books and they show the typical shape of the tree crown. A grid of
these with shapes down one side from flat (donut shaped) to pointy -
open grown pines on one axis. The other axis would be from round
footprint to oval to one sided windswept. Most anything can be
expressed as an integral of a shape - so in each box would be a formula
for the volume of this shape. Punch in the crown spread measurement,
punch in the crown thickness, and out comes a volume. It would be basic
integration that could be handled by excel (I think).
The thing is that a particular tree profile really represents a family
of profiles. You can stretch the profile taller, squish it flatter,
make it bigger or smaller, or wider or narrower and it will still be
recognizable so long the branches at different heights maintain their
relative proportions. That means for a particular profile shape, an
average branch length can be calculated that is some constant proportion
of the maximum length regardless of how the profile is stretched. If
the footprint of the tree was round then rotating the profile around the
tree would give you a solid with the volume of the crown, Similarly
rotating the average branch length across the height of the crown around
the axis of the tree will give you a cylinder equal to the volume of the
tree. This is a much simpler volume to calculate.

Fore every canopy profile there will be an average branch length, which
spread across the length of the crown will equal the area of the crown
in that dimension. If this value is rotated about the axis of the tree
(major and minor axis radii would need to be measured as a typical tree
is more over in footprint than round, that value would equal the volume
of the crown. This isn't a nasty calculation at all.

What do people think about the idea? At this stage I don't see any
practical way of measuring crown volume without extensive labor, and
there still is the question of density of material in the crown, but
this is a start.

Ed Frank
Re: Crown Volume   Lee Frelich
  Feb 11, 2007 09:16 PST 


Sounds like a good alternative to the way Lorimer and I did it. We
measured the crown radius in 4 directions, the height to the base of the
crown and to the widest part of the crown, and top of the tree, and then
divided the crown into 8 ellipsoids, kind of like 4 wedges of pie above the
wide point and 4 below. Each ellipsoid is 3-D and defined by three radii,
the vertical from wide point to top or bottom of crown, and the two
adjacent horizontal radii. You then use the formula 1/8 x 4/3 Pi x R1 x R2
x R3 for each of the 8 pieces and sum the 8 to get total volume. It takes
into account different shapes because of the four radii often very a lot
for trees with a crown mainly pointing one way.

Re: Crown Volume
  Feb 12, 2007 05:21 PST 

A friend of mine at the Anchorage Forestry Science Lab is working with
a software package for LIDAR that quantifies tree crown mass,
conceptually "immersing" the tree crown and measuring
displacement...fairly good resolution, fairly high cost solution at
this stage of the research.
Re: Crown Volume   Edward Frank
  Feb 13, 2007 14:00 PST 


I hope you are not being facetious, but I think the idea I suggested has
some merit. There are various ways to document crown structure,
configuration, and volume. The detailed maps of the canopy that Bob Van
Pelt has done for the Giant Sequoia and redwoods out west are amazing. He
maps the intersection of every branch and its orientation down to a very
small size. This enables him to create 3D diagrams of every branch in the
tree. These can be rotated and viewed from different sides. Some of this
was completed in the Middleton oak Project. The artistry of his tree
diagrams is amazing. For people not familiar with them, I encourage you to
visit his website:    Similarly Roman Dial,
BVP, and others they were mapping the canopy openings in the big Eucalyptus
forest in Victoria Australia. (National Geographic March 2003) Sort of the
polar opposite of mapping the canopy itself but related.

In your process I am sure you could develop a much more detailed view of the
canopy structure than my suggested basic process. There would be openings
and breaks between branches to consider. How large must an opening be
before it is no longer considered part of the canopy volume? In my idea I
am painting the canopy of the tree with a broad brush. Within the general
shape all of the openings are considered part of the canopy and small
branches sticking out are not included. The value of the idea is that it
can be done relatively quickly, and does not require any expensive
equipment, or require someone to climb the tree. There are a handful of
ground-based measurements that can be done with a rangefinder and
clinometer. People must match the shape of a tree to a series of choices.
People are generally good at pattern matching so I think the results would
be pretty consistent. It would produce a good approximation of the total
volume of the canopy and would specify a general shape to the canopy. The
weakness is the lack of small detail, and problems characterizing the
average with trees that are odd shaped.

Ed Frank
Re: Crown Volume   Lee Frelich
  Feb 13, 2007 16:46 PST 


I was not being facetious. There is room for a lot of exploration into new
ways to measure crown volume, especially for easy ways to do it without a
lot of equipment. The way Lorimer and I did it is not necessarily the
best, in fact he has experimented with a number of other methods.

RE: Crown Volume   Roman Dial
  Feb 14, 2007 11:37 PST 

BVP did a lot of his PhD work modeling crown volumes. He generally used
variously shaped volumes to approximate them.

If he is lurking about, perhaps he can be drawn forth to provide us some