Re: Crown spread weighting, tree biology, and path length

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Jess Riddle
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Crown spread weighting, tree biology, and path length

Post by Jess Riddle » Sun Nov 17, 2013 6:02 pm

NTS,

Bob Leverett’s recent explorations of different crown weightings in the American Forests big tree formula have made me reconsider how I view crown spread and its role in big tree formulas. The biology of growth and tree volume provide interesting perspectives for examining how to treat crown spread.

A tree’s growth rate is directly proportional to the total area of its leaves. All things (water, nutrients, light, temperature) being equal, trees with larger crowns grow faster. Hence, most large trees have large crowns. A large tree can have a small crown, either by being old and growing at a moderate rate for a long time, or by have a crown reduced by storms and disease after most of the growth is done. But those scenarios probably account for a minority of champion trees.

Consequently, when crown spread is explicitly added to a tree’s big tree points, spread is being partially double counted. The size of the crown is already reflected in the diameter of the trunk, and possibly to a lesser extent the height. If more precise information on the size of the crown is desired, crown spread is probably not the best measure for many species. Narrow crowned conifers, like many spruces and firs, may vary much more in crown length than in crown width. Crown spread has the additional down side of being a much less repeatable measure than diameter in many situations. On the other hand, if the lower trunk is influenced by burls, buttresses, or other unusual growths, including crown spread in the overall score would diminish the influence of those eccentricities.

One way to think of tree volume is as the average cross section area times the average path length from base to leaf. Or to simplify things a bit, cross section area at some point times the maximum path length with some characteristic rate of taper thrown in. The rate of taper would probably be fairly strongly dependent on the species, and be constrained by things like wood strength and xylem characteristics. I visualize this as a tree folding up all its branches and fusing together, kind of like a squid folding up its arms.

From that perspective, diameter and path length should be a good base for estimating volume/tree size, at least for comparisons within a species. Height should provide a good estimate for maximum path length in most species. The exception would be short trees with large spreads, live oaks being the obvious example. In that case, maximum path length could be approximated as half of the maximum spread. The tree would be short changed a little, because the length from the base to base of the limb wouldn't be included, but half the spread is probably the best option without taking additional measurements.

I tried to make a simulation incorporating these ideas to test each version of the AF and TDI systems by seeing how consistent they would be for trees of the same size but different shapes. Ultimately, I was never satisfied that the simulation realistically captured how trees’ shapes could vary, the trade-offs between height, spread, and dbh, but the exercise did suggest a few relationships. For trees with narrow crowns, awarding a point for each foot of crown spread seemed to work better than quarter weighting. The opposite was true for species with broad crowns; full weighting biased the results towards the short, thick trees with broad crowns. I was generally surprised by how consistently the AF system treated trees with different shapes. Doubling the diameter weighting in TDI did not work well. Squaring the diameter in the TDI system created a slight bias towards short, think trees, but using raw dbh created a slight bias toward tall, skinny trees. The simulation was an evaluation of how different shapes were handled, and I suspect the primary value of squaring diameter is in the treatment of different sized trees.

These physical relationships don’t address the perception of size. If American Forests wants to factor in how big a tree seems, I wonder why they don’t address that issue directly by doing what everyone else does online, have a vote. Lighting and background would certainly influence perceived size, which might or might not be a problem, but Photoshop could probably take care of those issues.

Finally, trying to make a simulation to better understand the different versions of the current tree ranking systems brought me back to an old idea. About a decade ago, someone (Bob Leverett?), came up with ENTS Points, which were simply circumference times height. If we instead take diameter squared times height (or better yet, path length), we should have a very simple system that would be well correlated with the amount of wood in a tree. I tried that system with the Tsuga Search hemlocks. The result was an R^2 of 0.66, which compares favorably with any version of the TDI system I tried.

Jess

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dbhguru
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Re: Crown spread weighting, tree biology, and path length

Post by dbhguru » Sun Nov 17, 2013 7:50 pm

Jess,

Thanks for weighing in with some original thinking about alternative champion tree ranking systems. I vacillate between systems that are weighted toward volume and ones that try to capture visual impact. Take a look at the following.
CrownSpreadComparisonSilhouettes.png
I realize these scaled images don't really prove any thing, but the visual impact of a large crowned tree is not to be denied. I have long held the belief that from a biological standpoint, crown spread is reflected to a large degree in girth. So, it seemed like including full crown spread would be tantamount to double counting, and to a degree I still believe that is true, but the range of shapes of trees within and across species leaves so much room for dissatisfaction with any simple formula. I recently compared 27 white pines with which I have considerable familiarity through 6 different formulas. See the attachment.

There is a lot of judgement going on here. For the NTS-Vol formula, 0.42 is an average form factor - half way between a cone and a paraboloid. For the NTS-VolAdj formula, the form factor column reflects different form factors for the included trees. A few of the factors are just plain guesses on my part.

The NTS-VolAdj list comes closest to how I would intuitively rank them, but not by much. This type of analysis is a very much a work in progress.

Bob
Attachments
AFPointComparison.xlsx
(208.69 KiB) Downloaded 48 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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Don
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Re: Re: Crown spread weighting, tree biology, and path lengt

Post by Don » Sun Nov 17, 2013 8:53 pm

Jess/Will/Bob-
This dialogue once again opens up the 'open grown' versus 'forest grown' competition fairness issue...no clear cut answers here yet. This question has come up in AF Measuring Guidelines discussions, and will continue to...

In the future, and not too far off at that, lies an increasingly reasonable solution...fellas like Mike Taylor and others are investigating the use of Structure for Motion (SfM) and LiDar composites to measure tree features such as tree height, crown height (from crown base to crown tip), crown width, crown volume, species, and stress on increasingly smaller scales (single-trees-in-small-stands size versus large-scale broad landscapes - witness Michael Taylor's SfM study of the large northern California oak). Pie in the sky? For now. But I'm hearing that it's closer than we might think both in terms of cost and practicality.
-Don
Last edited by Don on Sun Nov 17, 2013 11:33 pm, edited 1 time in total.
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edfrank
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Re: Re: Crown spread weighting, tree biology, and path lengt

Post by edfrank » Sun Nov 17, 2013 9:43 pm

I must say I am firmly not in the "volume is the way to go camp." Yes wood volume is a nice measurement, but it is not inherently better than any of the other measurements. So comparing how various changes to the weighting of parameters of height, girth, and crown spread vary with respect to volume are only valid if you accept that volume is a superior measure. If you don't accept that basic premise, then the discussion is spurious. With volume you are considering the wood volume of the trunk and branches. Most of that volume is is just dead tissue. It is not a representation of the living mass of the tree. Hollows in the trunk - the absence of wood - are treated in the same way as if the wood had not rotted away.

If you want to think of alternative measures, then perhaps an approach would be to measure the amount of living tissue or the volume of space the living tissue takes up rather than the mass of dead tissue present. The bark is alive and can be characterized by a surface area times a nominal thickness. The crown could be calculated as a crown volume, and I have presented formulas to do so. You might argue that crowns have different densities of leaves and branches. This could also be calculated using a densiometer. One that can be printed out on paper or even on clear plastic is available for download from the USFS. I gave links before.

But what are we really talking about in a champion tree? Are we talking about some discrete mathematical measurement? Are we talking about how impressive a tree might be? Is it something that is really quantifiable or is it something that is emotional and not readily amenable to quantification? I think the latter is the case. A tree can be impressive because of a massive trunk. A tree can be impressive because of its height. A tree can be impressive because of its large crown. I think the crown aspect is denigrated too much in this forum by people primarily considering volume as the key criterion on their thinking. In my opinion this is wrong. You cannot deny that Larry Tucei's live oaks with fat trunks an 150 foot crown spreads gain much of their impressiveness through the size of their crown. This aspect is easily as, and arguably more, impressive as the thick trunks of the trees. The heights involved are nothing to shout about, but yet the trees are impressive.

The American Forests formula of 1 point per inch of girth, 1 point per foot of height, and 1/4 point per foot of crown spread is a compromise that attempts to balance these aspects of impressiveness with values that can easily be measured. Sure some trees that are deserving may not be the point champion while other visually less impressive trees win on points. No matter how the factors are weighted, there will be these discrepancies between numerical champions and those trees that miss out. I think the existing formula is pretty fair overall and do not think it should be changed.

The real solution lies not in tweaking the formulations ad nauseum, but to recognize that impressiveness is more subjective and there is in most cases not just one tree that is clearly the champion of impressiveness, but several that all deserve recognition, no matter what the points say.

In 2003, Colby Rucker and others put out a big tree list. In the list there is not just one tree per species listed, but multiple trees of large size listed. The same is true of the listings on the PA Big Trees website. There is one tree that has the most points at the top, but other trees worth noting are listed as well. Determining a single champion will always be arbitrary and to a degree flawed. What needs to be done is to recognize multiple large trees as equally valid champions, and multitrunk trees as a form with separate champions of their own, rather than designating a single champion.

Picking a single champion based upon arbitrary weighting of parameters will always be a flawed process and ultimately futile, unless you recognize that it is just a game whose purpose is to motivate the players.

Edward Forrest Frank
"I love science and it pains me to think that so many are terrified of the subject or feel that choosing science means you cannot also choose compassion, or the arts, or be awe by nature. Science is not meant to cure us of mystery, but to reinvent and revigorate it." by Robert M. Sapolsky

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Matt Markworth
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Re: Crown spread weighting, tree biology, and path length

Post by Matt Markworth » Sun Nov 17, 2013 10:55 pm

Hi All,

Perception of big is very important for anything that is called the biggest. As an exercise, I listed several objects and then thought about what determines my perception of big.

Painting, Lake, Leaf – Surface Area

Elephant, Planet, Rock, Mountain, Tree Trunk, Tree Branch, Tree Roots, Fruit – Volume

Tree Crown, Pine Cone – The space it occupies

If an object appears 2-dimensional, then my perception of big is based on surface area. If an object is 3-dimensional without the appearance of being porous, then my perception of big is based on volume. If an object is 3-dimensional and porous, then my perception of big is based on the space that the object appears to occupy. I don't know if there are standard measuring protocols for measuring porous objects in other fields of study.

Matt

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Don
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Re: Re: Crown spread weighting, tree biology, and path lengt

Post by Don » Sun Nov 17, 2013 11:41 pm

Matt-
Not to go to extremes (but here I go...; > ) but at the molecular and atomic levels, all objects that you considered above and more, are porous.
It then becomes logically an issue of density, and then, weight for any given volume.
The problem I think is that we haven't done the first most basic thing. We haven't defined "big" yet to everybody's satisfaction...
-Don
Don Bertolette - President/Moderator, WNTS BBS
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dbhguru
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Re: Crown spread weighting, tree biology, and path length

Post by dbhguru » Wed Nov 20, 2013 9:50 am

Don, Matt, Jess, Will, Ed, et. al.,

In the animal kingdom, weight is usually used to define big. The African elephant is universally considered to be the largest land mammal. Giraffes are a good bit taller, but their great height doesn't override the weight advantage of the elephant. Internet lists of the biggest animals invariably turn to weight as the deciding factor. For instance, the American bison is usually considered to be larger than the moose. Although an Alaskan moose is a formidable animal and taller, it is not quite as heavy as the bison. So, the latter gets the nod.

For 'bigness' in trees, at least in the eye of the public, an argument can be made for the surface area presented in the direction of the viewer. Great height is important, but usually only in combination with other features such as a wide base, a huge trunk, or an expansive crown. In fact, height alone, at least total height, is probably the least important feature in defining size in the public eye. Although arguments can be made for factoring in weight and density, I doubt that they are important to most people. If we painted four identically sized cubes of osmium, gold, iron, and aluminum and presented them to the public, they would look the same. Osmium, being the densest, would be considered the biggest - only if the definition of big were based on mass and the judges were allowed to pick up the cubes. Were volume used to define big, the cubes would be considered equal. It we changed the shapes of the formerly four equal dimensioned cubes, all hell would break loose. We'd be in the fix that we are in now.

In the case of trees, people don't pick them up and test their weights, so I think volume would trump mass as the more important attribute in the public's eye. However, if the mass of an object is distributed in such a way as to present the appearance of great size by being spread out in several directions, as opposed to be condensed, I believe this would form the basis of a judgement on size - again in the public's eye. This is where crown spread assumes a larger role, and it then doesn't matter if crown spread is reflected in trunk volume. From a distance, it is the silhouette effect. Up close, the trunk takes over. If it is is a form like a live oak, it is the interplay of crown spread and trunk. Height shrinks to insignificance.

As a person's tree knowledge increases, or different tree/forest associated professions come into the picture, the competing weighting systems for judging champions rear their heads. The players become more conscious of the tradeoffs, and we find ourselves questioning what we mean by big in a tree. It is a natural evolutionary process of thought.

As major players in the game, we need to retain an awareness of the separate stakeholders and where each is coming from when discussing size. The current system began in Maryland with a forestry consultant who was trying to raise public awareness on the plight of Maryland's woodlands, which had been severely over-harvested. We will never know exactly what was in the mind of Fred Besley who thought up the present system. But it has been in place all these years and to change it in a direction that would merely shuffle the list of champions with no clear pattern isn't a good idea. We need to weigh the benefits of changes to the various stakeholders. Exactly what outcome are we looking for? Who are we trying to please? Well, these are a couple of questions we are trying to answer.

We will probably never achieve agreement on a definition of big that will satisfy all. However, American Forests has decided to revisit the issue and explore the thinking behind the current formula, and so, that is what we are doing in the MGWG. Don and I want to give NTS members a chance to weigh in. There is a benefit to continuing the discussions, even though much of it is plowed ground. Talking about it keeps the arguments and points of view fresh in our minds.

On a related matter, AF has given members of the AF MGWG a large download from the National Register database to sort through. As an exercise, we'll lift the 1/4th crown weighting factor and see how many champion trees get shuffled around. This is more an effort to see what the overall effects will be than to rationalize particular switches as favorable or unfavorable. In my first crack at looking at the data, my concern is with the accuracy and credibility of the measurements. Shuffling mis-measured trees around in a list is of dubious value. I could give examples of obviously mis-measured trees in the database, but that would come as no surprise to any of you. The frequency I'm encountering apparently mis-measured trees is now my issue. We in NTS have a role to play.

We need to continue our work at assembling the best set of maximums that we can. So far, Matt Markworth's growing maximum height list fits the need. Next, we need to establish a direct connection with AF to help them catch obviously mis-measured trees before they get into the database. That will be Don's and my job. No organization other than NTS can do the job, and fortunately, Don and I are in an increasingly better position to bring about the connection.

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: Re: Crown spread weighting, tree biology, and path lengt

Post by Don » Sat Feb 22, 2014 11:58 pm

Some great discussions of 'bigness'!
In reading Bob's post where he commented on height being one of the lesser measurers of bigness perceptually, I was initially surprised. But after thinking about it, I believe it's not surprising, what is surprising though, is how poorly the general public estimates size.
My two primary 'careers' (forestry and surveying) both involved extensive measuring, the former in height, dbh, crown size; and the latter in distances (horizontal, slope, vertical). During those years where I had 9-12 months of field time, my estimation of those kinds of measurements were, by those who were my peers and bosses, very good. I suspect that some of you are the same way in your own careers.
The point is, 'we' are in the minority, and need to remember that John Q. Public sitting at a desk, is just not "going to measure up"...and that's okay...getting good measurements is what "WE" are here for!
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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