Revisiting the tree dimension index

General discussions of measurement techniques and the results of testing of techniques and equipment.

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Jess Riddle
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Revisiting the tree dimension index

Post by Jess Riddle » Sun Nov 03, 2013 6:38 pm

NTS,

The recent discussions about what “average” crown spread represents and how crown spread should be weighted in the American Forests formula made me wonder about how we treat the variables in the TDI system.

All other things being equal, if tree 1 is twice the diameter of tree 2, tree 1 gets twice as many points for the stem component in the TDI system. However, tree 1 will have four times as much wood. Why not use diameter squared for the TDI system? That would make difference in the diameter score directly proportional to differences in tree size, which seems like a desirable characteristic.

You could take this one step further and weight the scores of the different TDI components. Since diameter represents two dimensions of space while height represents one, you could argue that the diameter component should be counted twice.

So there is some mathematical basis for altering the TDI system, but would these changes work in the real world? Thanks to the Tsuga Search, we can test that idea. I took the 37 trees from Tsuga Search and looked at how well TDI predicted volume using: the traditional equal weighting linear dimensions formula; equal weighting, but with diameter squared; and with both diameter squared and the diameter component counting twice as much as height.
TDI comparison.JPG
Differences in TDI score do a much better job of reflecting differences in tree size when the diameter is squared. Giving the diameter component twice as much weight produces modest additional improvement. Together, these changes improve the fit by 22%.

There are, of course, drawbacks to these changes. The loss of simplicity is significant and should not be disregarded. Adding spread will make the situation messier, but I have some ideas on how to deal with that issue. However, these changes would make the TDI system better reflect differences in tree size without compromising the ability to put all species on the same scale or requiring additional measurements.

Jess

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Matt Markworth
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Re: Revisiting the tree dimension index

Post by Matt Markworth » Sun Nov 03, 2013 8:54 pm

Jess,

Thanks for posting this, it's very intriguing.

I think that single-stem volume is the ultimate tree measurement for many purposes including a champion tree list, therefore a proxy for volume using commonly measured dimensions is very desirable. Do you have thoughts on what formula is the most reliable proxy for volume without going to extreme measuring efforts? Would additional diameter measurements at say 15% of height and 50% of height be needed to weed out "bell bottom" trees and to reach an acceptable level of deviation from the true volume?

Matt

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Josh Kelly
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Re: Revisiting the tree dimension index

Post by Josh Kelly » Mon Nov 04, 2013 12:19 am

Jess,

Thanks for doing some needed testing of methods for scoring big trees. One question I have is how less-exceptional trees than those found in Tsuga search would fare with the diameter squared approach? Would a diameter squared situation tend to over-score shorter individuals or species? Just a thought. Overall, I love the concept linking a squared relationship to diameter.

Josh

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Don
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Re: Revisiting the tree dimension index

Post by Don » Mon Nov 04, 2013 1:25 am

Josh/Matt/Jess-
Without sounding Clintonian, may I ask how TDI defines "big"? It seems to be a somewhat elusive answer in our arena over at AF. I gather in part that with TDI it has to do with volume (but is it of the bole, of bole up to branching, how do conifers and deliquescent forms achieve parity in the overarching all-forms competition)? And is crown volume the biomass measure, or the 'space' it takes up?
And do you think there's a synergy possible in a AF/TDI database pairing (or I guess in my old-school way I'm asking if a information needs analysis were done of the two, are there 'common denominators' that would go a long ways towards some amalgamation), while as Jess cautions, retaining 'simplicity?
-Don
Don Bertolette - President/Moderator, WNTS BBS
Restoration Forester (Retired)
Science Center
Grand Canyon National Park

BJCP Apprentice Beer Judge

View my Alaska Big Tree List Webpage at:
http://www.akbigtreelist.org

Joe

Re: Revisiting the tree dimension index

Post by Joe » Mon Nov 04, 2013 5:32 am

Josh Kelly wrote:Jess,

Thanks for doing some needed testing of methods for scoring big trees. One question I have is how less-exceptional trees than those found in Tsuga search would fare with the diameter squared approach? Would a diameter squared situation tend to over-score shorter individuals or species? Just a thought. Overall, I love the concept linking a squared relationship to diameter.

Josh
foresters routinely measure the full volume of the stem using different formulas and tables- certainly volume increases by the square of the diameter but height of the tree is indeed a factor- though I doubt any of these methods would be useful for the tallest trees you folks find as most foresters would probably think such trees don't exist- and these tables/formulas are NOT very accurate- yet it would be the best possible science to get an accurate determination of total tree volume, stem plus branches- but doing that will never be easy

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Will Blozan
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Re: Revisiting the tree dimension index

Post by Will Blozan » Mon Nov 04, 2013 7:44 am

Don wrote:Josh/Matt/Jess-
Without sounding Clintonian, may I ask how TDI defines "big"? It seems to be a somewhat elusive answer in our arena over at AF. I gather in part that with TDI it has to do with volume (but is it of the bole, of bole up to branching, how do conifers and deliquescent forms achieve parity in the overarching all-forms competition)? And is crown volume the biomass measure, or the 'space' it takes up?
And do you think there's a synergy possible in a AF/TDI database pairing (or I guess in my old-school way I'm asking if a information needs analysis were done of the two, are there 'common denominators' that would go a long ways towards some amalgamation), while as Jess cautions, retaining 'simplicity?
-Don
Don,

TDI has nothing whatsoever to do with total tree volume. However, tree volume can be a component of a TDI comparison. Jess is simply using tree data that have trunk volume already known as a factor to see how it may work as a proxy for champion tree status (as in a large volume tree of any species).

Personally, I think he may be on to something here and will ponder more later. Off to work!

Will

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dbhguru
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Re: Revisiting the tree dimension index

Post by dbhguru » Mon Nov 04, 2013 12:33 pm

Joe, et al.

I believe that at least three concepts of size are involved here. One is overall mass and a second is volume. Neither of these measures can be determined simply. The third is the appearance or perception of size, i.e. 'bigness" in the eye of the beholder. I expect that bigness is more closely associated with volume than mass in the public's mind. In the AF program, as well as the state counterparts, we are partially dealing, though not intentionally, with the third concept. I don't know what the original thinking was for capturing size, probably mostly aimed at volume, but through an arbitrary, problem-plagued formula that leads to results that few of us like. But this is why the AF MGWG was created and Don and I are members. And while we're making excellent progress in tightening the measuring process, we're a long way from resolving the basic issue of how to put the separate measurements together in a way that satisfies our collective sense of bigness.

So, I keep cycling back to the basic concept. If we were to ask John Q. Public, which is the bigger of two identically sized cubes, one of gold and one of aluminum, I'd bet we'd get differing answers (cubes are not places beside one another). The dimensions, and thus volumes, are the same, but the gold cube is far more massive, and some people who understand specific gravity or density might instinctively go with the gold. If we painted both cubes the same color, then I would guess most people would see them as the same size, i.e. equally big. But change the color of one, and the perception of size would change for some people, again, unless the cubes were placed side by side.

If we kept the same volumes, but changed shapes, as in different rectangular dimensions, we would probably get differing answers as to which was bigger. We have then "perceived bigness" to accompany actual volume, mass, maximum, minimum, and average dimensions. So, we need to come to grips with what it is that we mean by big, or intend to mean, when dealing with the variant shapes of trees, and what it is that we think others mean by the common terms. This is especially relevant for the National Register because AF always emphasizes the public's role in the champion tree program.

Will's TDI produces a point winner through comparisons to species maximums. The system makes a lot of sense so long as we are careful not to assert that it captures the idea of bigness in all cases. For example, I'm unsure of how well TDI performs relative to our individual perceptions of bigness (if in the end that matters). Attached is an Excel evaluation of 17 white pines in the Northeast on the AF and TDI systems along with my perception of their "bigness". I've updated the dimensions to what I think they currently are. Crown spreads are the weak link, but within the ball park.

My preferred order in this spreadsheet of psychological size proves nothing, but does demonstrate the subjective nature of bigness in the eye of this beholder. I find that interesting in and of itself. Notice where Yo Mama sits in the three lists according to my eye. Actual dimensions put Yo Mama high on the AF and TDI lists, but until you get close to this graveyard pine that splits into multiple trunks at about 7 or 8 feet, it doesn't have a visual impact commensurate with its statistics. By contrast, the Thoreau Pine in MSF makes a heck of a visual impact, and consequently, is 4th on my list versus 5th and 7th on the other two. The Ice Glen Pine also has a big visual impact. I recall BVP being very impressed with the Ice Glen Pine. I think Will, who climbed it, feels similarly. BVP said that it reminded him of sugar pines in California. However, the Ice Glen Pine makes only 8th and 10th places on the AF and TDI lists.

I could go on, but I trust my point is clear. An awkward shape for a tree can cause us to devalue its "bigness". Trunk color matters. Root flare can have an over-sized effect. The list of subjectives goes on that presumably AF needs to keep in mind.

So, in the end, what is it that we are measuring when we use a compromise point system such as the current AF formula? Should our perceptions/preferences even enter into the design of the method? Unless, we go strictly on volume or mass, I don't see how perceptions can be eliminated. The 1/4th weighting factor for crown spread and the use of inches for girth in the AF system are perception-based. We've searched for justifications on purely objective grounds and found none.

I'll close by saying that the devaluation of crown spread makes less and less sense in judging size. Why would we ever reduce the crown spreads of Larry Tucei's magnificent live oaks by 3/4ths? I believe that TDI minimizes personal preference. However, the AF system is so entrenched that completely replacing it in the near future is not likely to happen. We can make improvements, though.

(Note: I'm revising the attachment)

Bob
Robert T. Leverett
Co-founder, Native Native Tree Society
Co-founder and President
Friends of Mohawk Trail State Forest
Co-founder, National Cadre

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Don
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Re: Revisiting the tree dimension index

Post by Don » Mon Nov 04, 2013 3:56 pm

Bob-
After viewing your AF-TDI Comparison spread sheet, I couldn't help but wonder if it would be possible to put Jess's/Josh's thoughts about girth into play, in the AF/TDI/Bob's Biased Perception columns for Girth x 2 and for Girth squared, to see how these trees you guys are familiar with faired, with such a computational change? I hope we all can put our definitions for bigness out there, as I wonder if we all qualify/quantify bigness the same way!
-Don
Don Bertolette - President/Moderator, WNTS BBS
Restoration Forester (Retired)
Science Center
Grand Canyon National Park

BJCP Apprentice Beer Judge

View my Alaska Big Tree List Webpage at:
http://www.akbigtreelist.org

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dbhguru
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Re: Revisiting the tree dimension index

Post by dbhguru » Mon Nov 04, 2013 5:14 pm

Don,

I added girth^2 to the TDI and rearranged the tables a bit. The comparison is attached. I'll have comments later.

Bob
Attachments
AF-TDIComparison.xlsx
(98.38 KiB) Downloaded 65 times
Robert T. Leverett
Co-founder, Native Native Tree Society
Co-founder and President
Friends of Mohawk Trail State Forest
Co-founder, National Cadre

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Will Blozan
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Re: Revisiting the tree dimension index

Post by Will Blozan » Mon Nov 04, 2013 6:25 pm

Bob,

I am reminded of the drawings Jack Sobon did for "Stalking the Forest Monarchs" that had trees of vastly different forms that had the same AF point score. I don't have the time now to scan them but they could help with this discussion- especially when their respective TDI scores could be visualized...

In this day of the Smartphones and iPhone apps it seems a tree hunter could easily enter the dimensions into a formula and know how the tree she has found would rank...

Will

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