Tuliptree Modeling - bold new NTS project

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#1)  Tuliptree Modeling - bold new NTS project

Postby dbhguru » Wed Feb 14, 2018 10:19 am

Ents,

  Recent email communications between Erik, Elijah, Jared, and myself are pointing us toward a project to volume model tuliptrees over a wide range of ages and shapes. It is our growing belief that the ratio of limb to trunk volume changes dramatically over the life of the tuliptree. You might say, Duh! Doesn't just looking at tuliptrees from youth to full maturity and beyond tell us that? It certainly appears to, but we have almost no hard data on the change of the ratio of limb volume to trunk volume, and now thanks to the reticle and our volume models, we are finally equipped with those tools to calculate limb volumes without spending an eternity of time on each tree. Trunks have never been a problem, but limbs?

  A practical result of the project could be getting a better handle on how the species accumulates mass over time. Larger, older trees may be a lot more important for carbon sequestration than would be apparent from modeling just the trunk. Getting an answer to the question is of interest to Erik. He expressed as much just the other day.

  How do we go about the project? We have a number of regular geometrical forms to use in volume modeling: frustums of circular and elliptical cones, paraboloids, and neiloids to name the main ones. We can consider other trunk/limb taper models, but the amount of work quickly gets out of hand. We could apply them only where they would lead to significantly greater accuracy for important trees. For the present, we'll stick with the principal forms and look for ways to apply them ever more efficiently. For example,a more complete modeling of a conspicuous limb or limb segment could be used as a shortcut to modeling similarly shaped limbs. Lots of possibilities. Ideas are welcomed.

   One of the first steps for me is to assemble the formulas for the frustums named above and present them in a single document for easy access by all. The formulas are presently scattered all over cyberspace. Heretofore, there wasn't the impetus to create a single document because it wasn't clear that it would be used, and I've long be a champion of creating stuff that nobody uses, including myself. I realize that limb and trunk volume modeling is never going to make it to the top of the popularity charts. But at least we now we have some committed volume modelers. Presently, they include Erik, Elijah, Jared, Dale, Michael, and myself. We're hoping others will join us. Our Mississippi buddy Larry comes to mind. In the past, Will Blozan and Jess Riddle did groundbreaking work that immortalized them in the annals of NTS. Maybe we can persuade them to rejoin us. Jess has more recently measured some humdinger tulips in northern Georgia.

   The invitation is open to all who would throw in with us. We'll get you through the initial period of pain. Ooh, did I say that?

Bob
Robert T. Leverett
Co-founder and Executive Director
Native Native Tree Society
Co-founder and President
Friends of Mohawk Trail State Forest

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#2)  Re: Tuliptree Modeling - bold new NTS project

Postby Erik Danielsen » Wed Feb 14, 2018 1:27 pm

Bob, a quick thought- I reread some of the early reports on volume modeling this morning and as I think about it, I think we're unlikely to find a consistent relationship between trunk volume and crown volume across trees of similar age. I say this because, if we compared two hypothetical trees, both with identical dbh and identical diameter at the highest point below the crown dividing, with identical limb architecture and with both crowns occupying the same amount of vertical space, but due to site factors one tree has a main trunk 15 or 20 feet taller than the other (a realistic scenario comparing zoar's upland tulips to those in the canyon) both trees might have identical crown volumes but very different trunk volumes, and therefore different ratios of trunk to crown volume.

An alternative avenue for predicting tulip crown volumes might be finding an average percentage of cylinder occupation for crowns of tulips in different age categories, using the trunk diameter where the crown diverges and the vertical height of the crown as the inputs. We'll need to model plenty of trees, of course!
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#3)  Re: Tuliptree Modeling - bold new NTS project

Postby dbhguru » Wed Feb 14, 2018 8:13 pm

Erik,

 Good points. I have no doubt that you're right about the lack of a reliable ratio that would relate limb to trunk volume across a range of ages and tree shapes. There's just too much variability, and we can see it without ever calculating it. However, might we be able to establish a range of ratios, and particular establish some maximums? I'm not aware of any statistics that do that. We could model a sample of young versus mature trees over a range of ages and shapes and perhaps determine statistically reliable trends. As we discussed in a prior email communication, the implications of this kind of analysis for carbon sequestration are considerable.

  I expect that methods are being developed (or have been) that predict the biomass contained in crowns versus lower trunks for whole stands of trees, but I seriously doubt that any method intended for large numbers of trees in fairly uniform stands would ever be applicable to individual trees.  

Bob
Robert T. Leverett
Co-founder and Executive Director
Native Native Tree Society
Co-founder and President
Friends of Mohawk Trail State Forest
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#4)  Re: Tuliptree Modeling - bold new NTS project

Postby Erik Danielsen » Mon Feb 19, 2018 6:40 pm

Two Tulips, modeled and compared.

February 12, 2018 I modeled two tuliptrees, one (145.05' tall, 11.48'cbh) located on an old-growth alluvial terrace within Zoar Valley's canyon and the other 139.09' tall, 10.1'cbh) on the slope of a minor ravine at the edge of an upland old-growth stand near Holcomb Pond.

The two trees have similar bark characteristics that may suggest similar age, though the smaller tree's multiple relatively slender similar-sized crown leaders lend a more youthful impression than the larger tree's more complex crown with varied reiterations of differing size. Higher growth rates within the canyon on one hand and increased shelter from wind for the upland tulip tucked into a ravine surrounded by a canopy of hardwoods on higher ground compared to an emergent crown in the broad main canyon could be conjectured to make up the difference in a variety of imaginary scenarios. Suffice to say that their crown structures are rather different but tree age class may be more similar than not.

The smaller upland tree's trunk tapers slowly from cbh to the highest measurement below crown divergence, at 65' high. The bole is fairly circular, so I modeled with a circular cross-section. From base to 65, the trunk's modeled volume is 451.3 ft3. There is a major “kink” where some limbs emerge just above this, but the main leader continues, reduced in girth, to a height of about 70' where it finally diverges entirely. This last stretch was modeled as a simple paraboloid to save time, figuring that the swelling associated with the kink and the taper above it should more or less even out. The section adds another 21.7 ft3 to the trunk, so the true variance should be more than several ft3 in either direction. Full trunk volume= 472.96 ft3
               
                       
DSC_3723.jpg
                       
The upland tree viewed in full.
               
               

Above 70', the crown diverges into four relatively upright leaders of similar size. I modeled the most directly visible one to a height of 109.5'. Above this point the leader diverges into two more sub-leaders of almost the same diameter, so my paraboloid projection from 109.5' to the highest one's end at 134' is likely conservative, basically representing just one leader and excluding all additional branching including those that diverged lower on the main modeled leader. Total modeled volume for this leader is 64.48 ft3.
               
                       
DSC_3743annotated.jpg
                       
The crown above 70', with the modeled leader pointed out and the segment of direct measurement (divided into several frustums, not shown) designated by two lines.
               
               

Because of the relative similarity of the other three leaders (two a bit larger, one a bit smaller) I decided to substitute the modeled leader's volume for each one. As you can see in the image, this still leaves out some substantial branching, so the model should be conservative. Additionally the trunk kink produces four major leaders, probably a little less long than the modeled leader but at least one is thicker and two others not much thinner- I substituted another 2x the modeled leader to conservatively account for these. In total, the crown volume modeled in this fashion comes to 386.88 ft3.
               
                       
DSC_3740.jpg
                       
The crown from a little further back, including the lower leaders that diverge between 65' and 75' up the trunk.
               
               

Total modeled volume is 859.84 ft3. Perfect modeling would include a bit more crown volume but is impractical- compromises should be kept consistent across compared trees.
               
                       
DSC_3815.jpg
                       
Trunk of the Knife-Edge Terrace Tulip. Not quite exactly a nice neat pillar...
               
               

The canyon terrace tree (one of the most impressive tulips in the valley) is somewhat more elliptical and complex in its shape, so I devoted more time to modeling the trunk up to 55' in two axes. Between 55' and 60' high the trunk flares out considerably to its crown divergence, so I measured the top of the flare at a point that seemed representative and modeled this last 5 feet as a nieloid. The total volume of the trunk up to 60' high came to 554.92 ft3.
               
                       
DSC_3811.jpg
                       
The Knife-Edge Terrace Tulip in full (hard to find a single clear view)
               
               

To model the very full crown, first I sketched a side view of the crown and gave letter designations to different sections. The most upright thick leader was section A until it divided again significantly, then became section B, with the main leader from division of that modeled in many segments as section C. Visual assessment counted 4 more limbs similar in size to C. Later I realized that one more substantial lower limb (E) had been left out of my modeling. This limb was significantly longer and thicker than C, so I substituted another 2x C for that limb. A third major leader from the main point of divergence was section D. Calculating and adding A, B, Cx7, and D came to a total of 456.48 ft3.
               
                       
DSC_3826.jpg
                       
Looking up into the crown.
               
               

Total modeled volume is 1011.4 ft3 (I used a different number in the Zoar Valley thread that multiplied Cx4 to model E, which is probably closer to reality, but for comparing to the other tulip in this thread I'm aiming for a similar degree of conservatism).

The Crown to Trunk volume ratio for the upland tree is 0.817997. For the terrace tree the ratio is 0.822605. These are very close. The ratio of crown height to trunk height for the upland tree (0.9866) and the terrace tree (1.4175) are very different, however, and they have very different crown architecture. More modeled trees will be needed to suss out relationships between these components.

Taking a slightly different approach and calculating the percent of occupation of a cylinder for the crowns above the highest point of relatively uniform bole as measured on the trunk (at 65' on the upland tree, just below the kink, and at 55' on the terrace tree, before the swell towards crown divergence), we have 108.82% for the upland tree and 82.94% for the terrace tree.

Would a larger dataset of modeled tulips show trees of similar form having similar crown to trunk volume ratios? Similar cylinder occupation percentages? Or perhaps some form factor normalizing a certain crown to trunk volume ratio against crown height to trunk height ratio? Would crown spread or a count of the number of dominant leaders help us develop and refine a good model for estimating tulip crown volume from more basic measurements, like the form factors we have for conifers? Are hardwood crowns so individually variable that anything we come up with will have to be more general?

On this occasion I also treated all modeled limbs as vertical sections in terms of "length," rather than directly measuring segment length with the reticle using the trapezoidal method. The primary effect in this case would be to underestimate the length (and calculated volume) of certain limb segments in the Knife-Edge Terrace Tulip (the modeled leader on the upland tulip was fairly vertical). Strict use of the trapezoidal method in the future will improve modeling.

We'll just have to measure more trees!
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