Crown Volume    Edward Frank    Feb 11, 2007 06:59 PST  ENTS, 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  Ed: 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. Lee Re: Crown Volume   foresto-@npgcable.com   Feb 12, 2007 05:21 PST  Ed/Lee- 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. -DonB Re: Crown Volume   Edward Frank   Feb 13, 2007 14:00 PST  Lee, 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: http://www.forestgiants.com/    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  Ed: 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. Lee 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 citations. Roman   Home