Zane,

I'm trying to wrap my head around the issues, explicit and implicit, in your new approach to volume for species like redwoods. So, here goes. The starting point for me is your discussion of competing forms: (1) a redwood that we interpret to be a main stem plus one or more coppice shoots that have fused to the main stem with a separation at below 1/3rd the height of the main stem, and (2) what we interpret as a single stem that then divides into two stems at 1/3rd or more of the height of the taller stem. As I understand your point, in the case of (1), we expect these coppice stems to increasingly fuse to the main stem and the bark to grow around the assemblage so that the fused region is indistinguishable from a single trunk to the naked eye. Many of the redwood giants are of this form. From this starting point, I understand that you wanted to develop a method to compute a "functional volume" for (1) versus (2), principally to establish parity for big tree competition purposes. So one challenge became how to compensate for the extra stems in a way that balances the factors. One consideration was how the tree might have developed had it continued as a single trunk. So, how do we reduce complex forms to single-trunk equivalents, doing justice to both? We've not been blind to these issues as we continue to work on the American Forests measuring guidelines, but we had not considered the approach that you outlined.

In your equations, where you show the expression V1 + V2 for what is treated as a single-trunk form (split occurs at or above 1/3rd the height of the tallest stem), I assume that you actually calculate the volume of each stem above the split and then add the single stem portion below the split. Or do you mean to do the actual volume calculation as though two stems were involved below the area of separation? Under the first approach, we might express the total volume symbolically as V1 + V2 + V3, where V1 and V2 are the stem volumes above the separation and V3 is the single trunk portion. In the case where the form is considered to be two trunks (separation at below 1/3 the height of the tallest stem) all the way down to near the base, V1 and V2 would represent the whole volumes of those stems. In the latter case, you then discount part of V2 per your 3(S/H) factor. As I understand it, you arrive at V1 and V2 by using the cross-sectional areas of the stems at separation. I presume that you first computed the volume below separation as a single trunk, i.e. V3, and then calculated V1 and V2 as: V1 = V3(A1/(A1+A2)) and V2 = V3(A2/(A1+A2)). The volume of V2 is then adjusted, using your factor. We might create a 4th variable V4: V4 = 3(V2)(S/H). Is this the way you do the calculations?

The reason I ask is that for many eastern trees, the line of separation distinguishing the individual trunks remains discernible, except for maybe a small section near the base. This allows us to measure the individual diameters of the trunks and compute V1 and V2 separately, as opposed to an apportioning strategy from a whole. We would likely do this if we considered the trees to be separate individuals as opposed to a coppice. We would determine which of the two possibilities (a coppice or separate trees) using the pith test. Given the size of redwoods and their giant forms, I expect that pith tests are pretty much out of the question.

Now for some history. When we began rewriting the American Forest measuring guidelines, we wanted to correct a big problem with the then system. As you know, the National Register had become saturated with multi-stem forms, often clearly more than one tree. We wanted the best of the single-trunk specimens to receive the attention they deserved. Don's pith test was a cornerstone for determining if a candidate was one or more trees. However, this left species prone to coppicing like redwoods, cottonwoods, silver maples, willows, live oaks, etc. in an in-between state. We didn't want to discredit these forms (Don's Gobsmackers), but were unsure of how to handle specimens where coppicing was at the root collar. This is still the case for the complicated forms like live oak. We continue to test different strategies.

One point I make for the group of readers as a whole. Suppose we have a clump of individual stems that are fused, but separate out at some point. We can compute the cross-sectional area of each at the location where all the stems have split from each other. We can compute each cross-sectional area as a percentage of the whole and then apply the each percentage the cross-sectional area where all stems have fused at a lower point on the trunk, ideally 4.5 feet above the ground. However, we might have to go lower, wherever. This allows us to treat each fused trunk separately in subsequent calculations. For example, following Zane's redwood method, we could discount the area or volume contribution for each of the coppice stems.

There are hurdles to be faced, and they are what we will continue working on. For example, if the two trunks of a coppice are touching, but individually discernible, we would want to calculate cross-sectional areas at various points of measurement (and subsequent volumes) separately as opposed to apportioning them via the above method. It is only if we cannot distinguish where one trunk stops and another starts that we would resort to the apportioning method.

Here is something else we want to keep in mind. It occasionally has relevance where attempting to deal with a total cross-sectional area of a fused pair versus handling them separately.

If A1 = area of one trunk of diameter D1

A2 = area of a second trunk of diameter D2

A = area of a trunk of diameter D, where D = D1 + D2

Then A - (A1+A2) = (PI/2)(D1)(D2). This expression quantifies the amount that the larger single trunk exceeds the sum of the two smaller ones subject to the constraint D = D1+D2. I realize that the actual trunks are compressed together, so the actual geometry doesn't fit exactly.

Bob