Radial versus Volume Growth Bob Leverett
January 14, 2009


      A challenge presented to ENTS from tree land is how to compute plausible increases in trunk volume that accompany increases in radial growth. The calculations depend on not so obvious assumptions about trunk form. Canonical forms such as neiloid, cone, and paraboloid may serve as guides, but like people, trees are individuals and defy easy classifying with respect to their exact form. However, for conifer species like pine, hemlock, and spruce, we can do a pretty fair job of calculating trunk volume of individual trees if we can first establish good trunk form factors for the trees being measured. For the white pines on which I have specialized, F values typically range from 0.333 to 0.45, with mature trees usually between 0.38 and 0.42. The F value for old growth specimens can reach 0.45, but can also be as low as 0.35. The volume implication is considerable for a change of only 0.1 in the form factor.

      A problem that I have been dealing with for some time now is the mistaken perception that the big pines in places like MTSF that exhibit narrow annual rings such as 1/20th of an inch have basically stopped growing. However, a narrow ring on a big tree can still represent a significant increase in volume. I think smart tree people know this, but there are a heck of a lot of dumb tree people out there.

     The attached Excel workbook tackles the problem of computing and comparing volume increases on the basis of radial increases. Like previous Excel workbooks, I've set this one up to allow operator input in green cells and protect the rest. Calculations are all automatic. So anyone can use the spreadsheet without understanding how it was built or the included formulas. The example shown in the spreadsheet is as follows.

      Suppose we have two trees with the following dimensions.


            Tree #1                                   Tree #2


             Radius       = 1.75 ft               Radius       = 1.0 ft    

             Height        =  149 ft               Height        = 85 ft

             Form Fac  =  0.38                  Form Fac   = 0.35


        Suppose that for a new season of growth, tree #2 grows radially 0.020833 ft (0.25 inches) and 1.1 feet in height. Further suppose that tree #1 grows 0.8 ft in height. If the overall volume increase is the same for the two trees, what must be the radial increase of tree #1? The attached spreadsheet allows this and similar problems to be easily solved.

            The answer for the above example is 0.003624 ft (0.043484 inches) of new radial growth for tree #1. At the example rates of radial growth, tree#2 will increase its radius by an inch in just 4 years. By contrast, it will take tree#1 a surprising 23 years to add an inch of radial growth. However, for the year in question, the volume increase is the same for the two trees.  

       I can imagine some one looking at a stump of a tree comparable to tree #1 and believing that for all practical purposes, the tree had stopped growing. The increase in height would not be obvious from the ground except to an observer that recognizes new candle growth on pines, but even then, it wouldnít look like much. However, from the standpoint of carbon sequestration, the two trees are performing equally. Like Rachel Maddow says on MSNBC, talk me down. Maybe Iím missing something.

      The patterns of annual increase in radial growth and height versus the corresponding volume increase is what I am investigating for the white pines in MTSF, on Mt Tom State Reservation, Broad Brook in Florence, and at selected sites elsewhere in Massachusetts. Iím attempting to do the job in a way that allows me to  manipulate the inputs to spreadsheet-based models and then with the help of others, independently test the results. Past tree climbs of Will Blozan, and hopefully in the future of Jeff Lacoy and Andrew Jostlin, will be invaluable to ground-truthing. I know the time will come when computer modeling will supply all the answers, but I believe that we will still need field techniques at least for a decade or two.

      On a different topic, the big tree reports from our valued European Ents are making me salivate. I never even thought of places like the Czech Republic, Bosnia, Bulgaria, etc. as the locations of great trees. Two of my wife Monica's pianos were built in the Czech Republic. I am beginning to think more seriously about a trip to that part of the world. I must confess that the political situations in some of those places leave me nervous, but if ENTS is going to do the job that we are destined to do, the risks may have to be taken.   





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