Bob, What I am thinking is that really what you are looking at is a change in shape of the trunk in different trees. In your summary formulas you are mimicking the change in shape by substituting the cross sectional area of the trunk at either breast height, root collar height, or somewhere in between into a formula while the shape factor is represented as a constant (0.33). Then you suggest that the F factor should be modified to fit other situations. By substituting cross-sectional area for shape, you are approaching the same values, the trend of the calculations are going in the same direction,as would be obtained by adjusting the F shape factor. So there should be a statistical correlation in what you are doing but that doesn't mean it is an optimal solution. I think the logic of the substitution is flawed as I don't see any direct reasonable relationship to the amount of basal flair to total tree trunk volume. The correlation is coincidental because it is going in the same direction as the tree shape parameter is going. If this parameter must be modified further by changing the F shape factor in certain cases, then what is gained?
You are creating an artificial variable (changing the cross-sectional area) that is in the same direction as the actual variable - shape, so that you have two variables instead of one. To me it seems much more reasonable to keep the cross-sectional area a constant at one height - say breast height in the formulas - and to manipulate the one true variable - the F shape factor - in the general formula. One variable that is real, instead of two - one fake (cross-sectional area) variable that approaches the same volume as the trunk and second fake variable (an F factor-like factor that really doesn't represent anything measurable in the tree) that is essentially a fudge factor to make the first fake variable better match the actual trunk volume. It is like you are saying in your summary formulas - the tree really isn't this shape, but if we adjust the basal area in this way, and throw in a fudge factor when needed the resulting generated form will be somewhat similar in volume to the actual trunk. What I would suggest is to instead develop a standard Protocol to assign a tree specific F shape depending on the general shape of the trunk. It likely will fall into broad groups like you suggest, I believe you are on the button in that regard. However the methodology is more sound when you are manipulating the formula based upon variations trunk shape, rather than generating an artificial variable value by changing the basal cross section. Ed Frank "Two roads diverged in a yellow wood, And sorry I could not travel both. " Robert Frost (1874–1963). Mountain Interval. 1920. ----- Original Message ----- From: [EMAIL PROTECTED] To: [email protected] Sent: Tuesday, November 11, 2008 7:15 PM Subject: [ENTS] Re: Rejuvenated White Pine Lists and Volume Modeling Ed, 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. Often the pines in a stand will show great consistency of form. Increasing sample size dramatically doesn't add much new information. As pines age and the root structure develops, the volume implied by using the area calculated at RH overcomes any change in trunk shape toward the paraboloid form. I will have to do a lot more work before I'd take any formula to the bank, but the formulas and range of F values boxes in the true volumes pretty well. It is a start. In terms of what species fall within the formulas and F values, well, I'd be reluctant to go beyond the white pine at this point. The formulas probably don't apply to the hemlock, at least not without changing the F value range. The use of one predominant shape for young trees, another for old-growth pines, and a third for intermediate age trees follows from the data I have, but there are lots of exceptions. I'll discuss them in future communications. The age criteria is just a starting point. Overall shape or form really drives the volume, but pines change shape over time along the lines indicated by the formulas. More to come on this topic. Bob -------------- Original message -------------- From: "Edward Frank" <[EMAIL PROTECTED]> Bob, An interesting article. I especially liked the background summary and the concept for your specialized list. looking at the volume formulas you suggested as a rough estimate, I have some questions. In the final set of equations the basic difference between the three formulas is based upon the difference in area of a section at breast height versus the area of the trunk at the root collar. I am sure you have run statistics on the numbers and these produce meaningful results on a first pass. What bothers me about the process is that the entire trunk is being characterized by the differences in the tree diameter at breast height and at the root collar. Is this relatively tiny fraction of the total volume of the tree really an adequate basis for projecting the volume of the entire tree? I really have my doubts in a broad sampling that it does. First we really don't seem to know why some trees have more of a flared base than others.&a mp;n bsp; Across species it seems, based upon observations only and not any modeling, that species that grow on a more unstable substrate have a larger flair at the base of their trunk. Does this observation stand up to analysis - I don't know. Does it also apply within a single species - would it apply to pine trees - again would think so, but I don't actually know, but I think it should be considered. So if the amount of flair between breast height and the root collar is not dependant on overall trunk shape, but upon some other factor, such as the nature of the substrate, then it would not serve as a good indication of overall volume. The second question that comes to mind is that you are characterizing young trees as having one shape, old growth trees as having another shape, and also an intermediate category. I wonder if these generalizations are valid over a larger sampling size. Is is age that affects the shape, is it the size of the tree, is it the history of suppression and rapid growth, is it dependant on age or the history of a particular tree? In the final formulas you present you essentially are adjusting the cross-sectional area used in a basic formula by considering whether to use the breast height area, the root collar area, or something in between. I would feel a more appropriate approach would be to keep the position of the cross-section are at breast height and adjust the Form Factor between the suggested ranges, 0.33 to 0.50 based upon visual observation of the taper of the trunk, whether or not the tree has excessive flair extending above breast height, and whether or not the tree appears to have been topped. Your formulas may provide a good estimate, I am just wondering if a different approach that just included a form factor might yield better results, as the role of trunk basal flair in overall trunk volume is unclear (at least to me.) Ed Frank "Two roads diverged in a yellow wood, And sorry I could not travel both. " Robert Frost (1874–1963). Mountain Interval. 1920. ----- Original Message ----- From: [EMAIL PROTECTED] To: [email protected] Cc: Rick VanDePoll ; Sam Stoddard ; Steve [EMAIL PROTECTED] ; Laurie Sanders & Fred Morrison ; David Govatski ; Robert Carr Sent: Tuesday, November 11, 2008 5:26 PM Subject: [ENTS] Rejuvenated White Pine Lists and Volume Modeling 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. Bob --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
