Revisiting the tree dimension index

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dbhguru
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Re: Revisiting the tree dimension index

Post by dbhguru » Tue Nov 05, 2013 7:58 pm

Hi folks

Below is a comparison of 20 northeastern white pines. In the dark beige table, the pines are arrayed in descending order by trunk volume. The factor column is the multiplier. Cross-sectional area at 4.5 feet is multiplied by height and the factor. A factor of 1/3rd produces a cone. A factor of 1/2 produces a paraboloid, etc. The values in the factor column are based on past climbs and volume modelings done by Will and/or are my best judgement. The factors are not perfect, but okay for these purposes. The last 4 columns show where individual trees fall in descending order of volume based on their AF Pts, AF Adjusted Pts (no weighting of crown), TDI, and adjusted TDI (CBH^2). For example, the Elder Pine is in #2 place in Volume order, but #3 based on its TDI-Adj points, #1 in regular AF order, etc. As another example, the Ice Glen tree is #8 in volume order, but #11 in AF points, Adj AF points, and regular TDI points order, and #12 on the Adj TDI order. I first found it strange that the Ice Glen tree ranks 8th in volume, but makes only #12 on the Adj TDI list. The reason is that while the tree is tall, big-girthed, and broad-crowned, it isn't sufficiently close to any maximum to push it high on the list. As a result, its Adj-TDI score is modest. Note also that Thoreau is 10th in volume and 10th in Adj-TDI points.
COMP FULL.png
All in add, the adjusted TDI does well at predicting volume. Notice below how close the position of a tree in the Adjusted TDI list comes to the position of the tree in the volume list. The location of a tree in the Adjusted TDI list averages only one position removed from its location in the volume order. This is a pretty good match of the Adjusted TDI points system to volume.
COMP CLOSE.png
Note that the comparable average for regular TDI is also only one position removed from the volume order. It would seem that we don't gain from the adjustment, however, with the adjusted TDI, 10 positions are exact matches between the two lists. For example, the tree that is in 10th place according to volume is also in 10th place in the Adjusted TDI list. The tree (Thoreau) that is in 15th place in the volume list is in 15th place in the Adjusted TDI list. This kind of match occurs 10 times for Adj TDI, 7 time for regular TDI, 5 times in Adj AF formula, and only once with the regular AF formula. I find this approach very telling with respect to how far the current AF formula deviates from reflecting volume - at least for 20 northeastern white pines. Well, it's a start. Jess may have really launched us on a new direction.

Bob
Robert T. Leverett
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Co-founder and President
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Don
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Re: Revisiting the tree dimension index

Post by Don » Tue Nov 05, 2013 11:48 pm

Does the addition of AF values for crown spread tighten the comparison between AF, TDI?
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Jess Riddle
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Re: Revisiting the tree dimension index

Post by Jess Riddle » Wed Nov 06, 2013 8:23 pm

Matt,
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?
My thinking is along much the same lines as yours, and I hope volume numbers become much more widely available as ground based LiDAR and photometric technology continue to improve. For now though, I think practical difficulties with volume measure and even volume estimates create a need for other systems, like TDI.

The standard approach for estimating volume from a few easily obtainable measurements would be to do some kind of regression analysis. The analysis would give you a set of coefficients that you would multiply your measurements by to give you the best estimate of volume. In the current example, instead of multiplying diameter^2 by 2/max diameter^2 and multiplying height by 1/max height, we would multiple diameter^2 and height by a pair of numbers that would give us the best estimate of volume, and when we sum those numbers together the resulting estimate would be in volume untis (e.g. cubic feet).

While that approach works great on paper, there are a couple related practical problems. First, you need to know the volume of a bunch of trees to be able to work out what the coefficients should be. In the East, we’ve only got that for hemlock. Second, the formula would only be valid for trees like the ones you used to make it. That later issue is why we can’t use the allometric equations Joe is referring and the issue that Josh is getting at. A formula made with normal sized trees may not be valid for record sized trees, and a formula made with forest grown trees probably wouldn’t work well for open grown trees. And of course a formula that works well for one species may do a terrible job with another species. Hence, we need something like TDI that can give us reasonable rankings without requiring a mountain of data.

Yes, diameters higher up the stem would improve volume estimates. If you have a copy of Bob Van Pelt’s Forest Giants of the Pacific Coast, check out appendix three. He develops equations to estimate volume from diameter^2 for a handful of species, and lists which height gives the best volume estimate. Dbh tells you almost nothing about the volume of a big sequoia, but it does a decent job for grand fir. However, diameter at 100’ gives you an excellent volume estimate with grand fir.

Sorry if I've gone overboard on the explanation.

Josh,
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.
These modifications would definitely make shorter trees more competitive and rank higher. I’m not sure that they would be over-scored though. I think it’s more likely that they have been under-scored until now. I realized that the Tsuga Search trees were not a very typical population, but they seemed like an appropriate group to test since TDI is intended for use with near record sized trees.

Don,

I’m having a little trouble following some of your questions, but I’ll take a stab at each of them.
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 don’t think TDI defines “big” per se, but I don’t think that’s a problem either. TDI is a ranking system, so each individual is big or small relative to its peers. Also, since TDI is a relative system, the score is unitless. Another way to look at your question is that “big” is whatever you relativize by. In that case, we have always defined “big” as the maximum known dimensions of each species.
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)?
TDI does not explicitly deal with volume, unless volume is included as a factor (which I would never do). However, there is a correlation between TDI and volume, as there is between any two data sets. I think a high correlation between TDI and volume would be a desirable trait for the TDI system, because that would mean that differences in TDI score reflect differences in the size of the trees. As far as what parts of the tree are included in the volume, that would likely depend on what data you have available.
And is crown volume the biomass measure, or the 'space' it takes up?
I always thought mass was the biomass measure, in a crown or anywhere else, but maybe you’re referring to some use of “biomass” that I’m not familiar with? As far as evaluating crown volume, I think that would depend on your purpose. Wood volume (re-scaled as biomass) would work best if you want to look at carbon storage while the space occupied by the crown would probably be more useful if you were modeling tree competition or bird habitat. For a champion tree program, I would go with wood volume since I’m more interested in the size of a tree rather than its shape, but it would really depend on what values the program is trying to capture.
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?
The AF points system and TDI certainly have different strengths and weaknesses, but I’m having a hard time seeing how one could compensate for the other. I see simplicity as the primary strength of the AF system, so I don’t see how bringing in another system would help. My imaginations pretty limited though.

Did I get at what you were asking about?

Bob,

Great to see more data in the discussion. I'm still digesting your posts.

One quick questions. In comparing the systems, why look at rankings and throw out the differences between the trees? The Elder pine went to so much work and effort to corral all those jumpy CO2 molecules to make 172 more cubic feet of wood than the Grandfather pine. Shouldn't it get full credit for all that additional wood. On the other hand, our measurements aren't even accurate enough to be sure the Thoreau pine is bigger than the Sobon. Correlations would take all that info into account.

Okay, enough of that. I'll address the meat of your post next time. I really am glad to have another species and more ranking systems to test.

Jess

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dbhguru
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Re: Revisiting the tree dimension index

Post by dbhguru » Wed Nov 06, 2013 10:08 pm

Jess,

I was curious as to how the 4 methods of evaluating trees would serve to predict the volumes of those pines. The. Sobon pine is a weeviled tree. It has a mass of limbs just a few feet above ground, about 5.5 if I remember. I probably shouldn't have included it. The factor is too much of a guess. I also did linear regressions. The regular AF method is the poorest predictor of the volumes.

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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Larry Tucei
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Re: Revisiting the tree dimension index

Post by Larry Tucei » Thu Nov 07, 2013 11:59 am

Jess, Don, Bob, Matt, all- Hi everyone, after reading the postings lately on Tree measuring perhaps it’s time to break the process into a different method. All trees do not grow the same and should be measured accordingly. Pine crowns tend to be smaller than Oaks, there are exceptions. Live Oaks have as much wood by volume as tall Pines, Tulips, other Oaks, etc. Bottom line is Old Growth trees have lots of volume. A 300 year old Live Oak, Red Oak, White Oak, Cypress, Tulip, Pine, all are HUGE trees. How best to measure them would be based on what? Would you include Height, Dia, Cir, Crown Spread, Maximum Spread, Average Spread, Crown Volume, Wood Volume, Trunk Volume, Limb Volume. I don't know what is best I just thought I would throw this in the mix for you guys to think on. Found this link for you all. http://en.wikipedia.org/wiki/Tree_measurement Larry

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Don
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Re: Revisiting the tree dimension index

Post by Don » Fri Nov 08, 2013 1:32 am

Jess-
Thanks for your reply. My questions I think were getting at something simpler. I've started to develop an idea that Fred Besley (the guy who initially championed what is now AF's Point Formula) might have been using average crown spread and height as a proxy for crown volume (as defined as the 'space' that the crown takes up, as opposed to biomass); and diameter/girth and height as a proxy for bole volume. I believe Besley, as early as 1925, was using these proxies in order to enable the public to participate, much as AF became (not odd, Besley was on the earliest Board of Directors of AF), as an advocate for conservation and protection of our forests.

This would be consistent with the national concern about the decimation of our nation's forests by an unregulated timber industry, prior to the 1900's...I'm sure you're familiar with the dialogues of Muir and Pinchot. By engaging the public with values of big trees, for NON-commercial purposes, conservation principles could become ingrained in the American public.

Even more basic, I'd ask you what measure of bigness occupies your mind as you walk up on large tree? For me, I think, it's the crown, whether emergent (as often is the case with conifers) or of significant breadth (which in deliquescent forms) to dominate those around it.

As one who's hiked through the classic old-growth mixed conifer forests of the Sierra Nevada range in California, since the 1970's, I'm not at all immune to cylindrical boles 25' around and rising more than a hundred feet before branching and tapering begin. They absolutely gobsmack me. And seeing a ponderosa pine whose rounded stag-horned crown emerges well above its cohorts, stops me in my tracks. These are part of what defines bigness for me.

So measures such as TDI, modified TDI, AF's and others interest me. So do 'wireframes', and aerial photogrammetry/satellite imagery, LiDar, Structure from Motion, and cloud mapping. Relative to LiDar and SfM, the images of crowns and the possibilities of quantifying 'crown space' I find especially intriguing. Girth by cloud mapping...these sound impractical now, but guys like you are working through them and it won't be far in the future before they're second nature to Dendromorphometrists.

Just saying....
Don Bertolette - President/Moderator, WNTS BBS
Restoration Forester (Retired)
Science Center
Grand Canyon National Park

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View my Alaska Big Tree List Webpage at:
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gjschmidt
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Re: Revisiting the tree dimension index

Post by gjschmidt » Tue Mar 25, 2014 9:11 pm

I am a little late in this conversation, but I thought about this problem many years ago. I never understood the significance of the AF points system. It assumes certain ratios between the dimension that are simply artifacts of the units of measure and would not make sense in metric. Think about it, it is all linear, a 4.5 foot stump of a has the the potential to outrank a fairly large volume tree under the AF ranking system.

Instead I favor the proposed "tree dimension index" in that it does relate more directly to mass and volume, and will rank the trees the same way regardless of the choice of units. Alternatively, if we are really interested in how impressive a tree "looks", perhaps just multiplying height by width (without squaring) to get a surface area equivalent, since a 2 dimensional surface is what all that we can see of the tree at any one time.
Greg Schmidt

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