Don, Such an instrument is what I see in my dreams.
Bob -------------- Original message -------------- From: DON BERTOLETTE <[EMAIL PROTECTED]> Bob/Ed- The DBH as a standard has as its primary recommendation as that of being convenient (almost anybody can reach that high, and MANY (non-oldgrowth) trees have 'cylindered up' by then). Determining volume as a subset of all measurements of a tree, it makes all the sense in the world to measure only at points of inflection. Those diameters and the heights they were taken at may at some point in the future (when enough measures of the population are taken) would then be useful (when compared to DBHs) in form class determinations. -DonRB Wouldn't it be nice if there were to be a laser hypsometer that could lock onto the distance of a tree, and follow the edges up, providing a 'continuous' record of height/diameter? From: [EMAIL PROTECTED] To: [email protected] Subject: [ENTS] Re: Rejuvenated White Pine Lists and Volume Modeling Date: Thu, 13 Nov 2008 00:18:54 +0000 Ed, I basically agree with what you are saying. Determining upper and lower boundaries for the volume at the outset by using a cross-sectional area that leads to over-estimation and another that leads to under-estimation with a common F value is just a first step. I apply it when I really don't have a simple way of refining the F value applied for a particular height (BH) on the trunk. My preference really is to manipulate F from a standard spot. The big challenge for us is to find ways of refining F, which we agree conveys critical information about trunk shape. In general, the value for all pines will fall between 0.3 and 0.5 using BH to establish the basal area. However, this is a very wide range. We know that the canonical form of the trunk, courtesy of the forestry profession's past modeling efforts, starts as a neiloid (F=0.25), changes to paraboloid for a section, then goes to a cone (F=0.33), and in some cases back to a paraboloid. An F value we would select for a particular tree would have to reflect the proper averaging of these forms for the tree being modeled, but we are not very far along in refining the process. A point I would make about the BH standard for modeling purposes. On some trees, 4.5 feet up is still in the neiloid zone. On other trunks, 4.5 feet is in the zone of the paraboloid or cone shape. Seldom will the 4.5-foot height coincide with an inflection point. If it did, it would be far more useful in tree modeling. BVP likes to go much higher up the trunk to get a circumference in order to volume model. He wants to be clear of the root flare influence - a point you well understand, Ed. Of course, if we are modeling the tree with a reticle or through a climbing, we can look for inflection points and establish frustums that correspond to the same kind of curvature, but in lieu of detailed modeling, maybe we should choose the height where the point of inflection occurs. Just a thought. Bob -------------- Original message -------------- From: "Edward Frank" <[EMAIL PROTECTED]> ENTS, Bob, First let me apologize for the two empty posts that appeared from.me regarding this matter. I was having some computer problems, and it appears that the problem was simply my mouse going bad and was multi-clicking everything. Mathematical discussions are hard to articulate and I am never satisfied with the explanations and arguments that I present. Bob, this is mostly directed at you, please forgive my referring to you in the third person. as I am not sure how else to state it. In Bob's original post he provided these three formulas: Summary ABH = area of trunk at breast height, ARH = area of trunk at root collar height, H = full height of tree, F = form factor, There is lots more to come on this topic along with lists of pines based on the proposed criteria, but to summarize. As a first cut, if the pine is young use: VEY = 0.333 * ABH * H. If the tree is a stocky old-growth specimen, use: VEO = 0.333 * ARH * H If the tree is intermediate in form and age, use: VEI = 0.333 * H * (ABH + ARH)/2 For a particular tree, as more measurements are taken, the F value can adjusted to better fit the observed form. These represent the general equations for volume calculations in white pines in his data sets. The first formula: VEY = 0.333 * ABH * H. the volume is equal to the form factor for a cone (0.33) x (the cross-sectional area at breast height) x (tree height). Bob reports: Young white pines hold to a conical shape with surprising consistency and the conical volume using BH comes pretty close to a more thoroughly modeled form. The number of pines I have modeled to arrive at this conclusion numbers around 150. I believe this a a reasonable formulation that is supported by a large data set. I have no complaints on this matter. In the second formula presented Bob says: If the tree is a stocky old-growth specimen, use: VEO = 0.333 * ARH * H This is the formula I am trying to discuss. In the initial characterization the tree is described as a "stocky old-growth." It is not conical in shape, yet in the formula Bob has chosen to use the F or shape factor for a cone as the first parameter. Since this tree is larger in volume than a cone, if you keep the F or shape factor for the cone, one of the other parameters must be increased to represent the increased volume of the tree. The height is pretty straight forward, so it was left alone. In the formula, instead of changing the F value Bob has opted to change the cross-sectional area used in the tree. He is using the cross-sectional area of the tree at the root collar instead of at breast height. Th is number will be bigger than the cross-sectional area at breast height, therefore will generate a bigger number for volume. We know the volume of the stoc ky old-growth tree is larger, this manipulation generates a bigger volume number, therefore there will be a positive correlation between the two. This is exactly what the formulas say.... The problem is that by changing the cross-sectional area instead of the F or shape factor for the tree, the volume modeled is not the same shape as the tree. The lower portions of the trunk will be exaggerated in volume, while the upper portions will be under-estimated. The hope is that the amount of exaggeration at the bottom is exactly the same as the amount the top is under-estimated, thus yielding a good volume for the tree. For example a cone with a cross-sectional area of its base three times larger than that of a cylinder of the same height, will have exactly the same volume as the cylinder, even though they have a different shape. What I don't see is why the cross-section at the top of the root collar should be that balancing point where the bottom exaggerations and the upper under-estimates match. There surely is some place where they do match, but why should it be this cross-sectional area of the tree at the root collar? The third formula suggests that some trees are intermediate in shape between the conical young trees and the stocky old-growth trees. Sure I can buy that, but the formula states that the value for the intermediate form will be a cross-sectional area somewhere between that at breast height and that at the root collar. Why should breast height and root collar be the boundaries? Breast height is reasonable as it can be demonstrated by field measurements, but as far as I can see the root collar cross-section is an arbitrary value that may be higher or lower than is appropriate for a given set of trees. If you are just picking out a cross-sectional area from a given range, knowing that the number you pick out does not actually represent the shape of the tree but a hoped for balance point of errors, would it not be better to pick out from a range a value that actually represented the shape of the tree? A range of F shape factors? &am p;am p;nb sp;Bob says: For a particular tree, as more measurements are taken, the F value can adjusted to better fit the observed form. Would this be an adjustment to F as used in the first formula, or does he mean an adjustment as a fudge factor to the F in the second equation, and therefore not really representing the overall form of the tree at all? What I am suggesting is that instead of picking the cross-sectional area at the root collar and hoping it is somewhere close to the theoretical balance point between lower exaggerations and upper under-estimates, it would be better to find some repeatable protocol for estimating the F or shape factor for a given species of trees in an area, and keep the basic cross-sectional are at breast height as a constant in the formula. That way you are changing the true variable in the formula, shape of the trunk, to fit the tree being examined, instead of just picking a value at the root collar and hoping it will be OK. This would be a simpler way to deal with the different shapes of trees and a sounder approach in my opinion. I anticipate that there will be a different F shape factor for each of the different classes of trees being examined and that a pattern will emerge. I am not sure, and don't believe that this same pattern will be observable if volume is calculated by manipulatin g the cross-sectional area. Another advantage of developing a protocol for assigning an F value would be that trees with unusually wide basal flairs or those who have had their tops broken out will tend to fall into separate ranges of F, rather than being intermixed as might be the case using formula 2. Ed Frank "Two roads diverged in a yellow wood, And sorry I could not travel both. " Robert Frost (1874–1963). Mountain Interval. 1920. <BR --~--~---------~--~----~------------~-------~--~----~ Eastern Native Tree Society http://www.nativetreesociety.org You are subscribed to the Google Groups "ENTSTrees" group. To post to this group, send email to [email protected] To unsubscribe send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/entstrees?hl=en -~----------~----~----~----~------~----~------~--~---
