Percent Cylinder Occupation  

TOPIC: Back to tree modeling

== 1 of 1 ==
Date: Tues, Aug 19 2008 9:27 pm
From: "Edward Forrest Frank"


Nice to see you back at tree modeling and preparing to scare people off the list with mathematics.

I have mentioned this before but I want to suggest cylinder occupation again in this context. In the study of the volumes of hemlocks in the Tsuga Search Project a ration could be determined between the actual volume of the tree and the volume of a cylinder of the same height as the tree and of the same diameter as the tree at breast height. What was found was that at the lower end of the scale were outlier percentages representing trees with an abnormally fat base. The unusually large base diameter would yield a lower than average % cylinder occupation. Above this was the normal range of trees with a normal girth to height ratio and generally uniform tapers. Those at the lower end of the spectrum are tree which taper rapidly, while at the upper end of the normal spectrum are those trees that have a slower taper for a much greater portion of the trees height before tapering to a point. The third group of trees were those that had their tops damaged or removed. Since these trees had the profile in their lower portion more representative of larger and taller trees, and a foreshortened top segment representing the least cylinder occupation of any portion of the tree, these tree had an anomalously high % cylinder occupation.

The same could be done for the pine volumes you are measuring. I would expect, if this tree you measured in Bryant Woods has had its top removed and regrown that it would be in the anomalously high outlier or at least in the upper end of the normal spectrum.

What can this tell you? By itself it can indicate that a particular tree has been damaged in the past. it is a measure nor of size of the tree but of shape. I am wondering if there would be a general trend in this value from younger to older trees in an area indicating that the trees basic shape changes with time and as it grows? I am also wondering wonder if there might be a regional trend from south to north that could be determined? The other thing is would there be a clustering of values from trees in a particular environment? For example, would the trees nearer the coast that Andrew Joslin thinks are kept short because of winds, form a meaningful cluster of data points?

This goes along with the idea of plotting three parameters on a triangular ternary plot. Initially I was thinking about plotting girth - height - and average crown spread. This would be a shape diagram for different species of trees, perhaps also show a distinction between young and old trees in a species, and perhaps variations in shape with location or environment. Perhaps the plot of height - girth - and volume would also be interesting. I have a basic ternary plot program posted in the measurement section of the website. Does anyone know or have a macro to create ternary plots in excel?

I certainly think this is something worth pursuing, and you may have enough volume measurements at this point to do some preliminary calculations and plots.

Ed Frank

== 2 of 6 ==
Date: Wed, Aug 20 2008 8:07 am


Yea, I'm loading up for bear. A set of volume formulas is tumbling around in my noodle getting ready to spill out and find their way into e-mails. I hope that none of the 231 ENTS members will be driven way, but remind the intimidated, that's what the e-mail delete button is for.

You make a compelling case for calculating the percentage of a cylinder occupied by a trunk. Each time you present your ideas on the subject, they become more appealing. Let's call it the Frank Volume Index (FVI). I particularly like the way it would help to capture the volume for of "decapitated" pines that have recovered enough to present us with very bushy, indistinct tops. Good stuff.


== 3 of 6 ==
Date: Wed, Aug 20 2008 8:43 am
From: "Edward Forrest Frank"


The concept should be called PCO or %CO for percent cylinder occupation. I am all for descriptive names rather than names that make people puzzle over what they mean. 


== 4 of 6 ==
Date: Wed, Aug 20 2008 8:55 am
From: "Edward Forrest Frank"

Bob, ENTS,

The Percent Cylinder Occupation concept may not prove to be that useful after we look at the numbers being generated. But the thing is, at this point, it is a fairly simple number to calculate once you have the tree volumes, so why not add a column to the spreadsheet as see what the numbers reveal?


== 5 of 6 ==
Date: Wed, Aug 20 2008 10:50 am

A few nearly random thoughts...I was thinking that the index you are labeling FVI, should stand for Forrest Volume Index, still giving Ed appropriate credit...and yes, I too have in the past recommended such a seems to me that statistically the population of each species' old-growth form is not quite normal, but more reflective of the increased likelihood of the environmental/climatic variables over increased periods of time.