Should Foresters Believe in Logs?

The logarithmic transformation is used frequently in forestry calculations. The reason for this is obvious, and true: we deal with LOGS.

Specifically, we deal with the volume of logs, and therefore, the value of logs.

Many foresters assume that a log is cylindrical. Well... logs are somewhat cylindrical, but ask anyone who has been to a pole mill: a good pole tree is hard to find. In other words, it is rare that a perfectly cylindrical tree is found, or even a perfectly cylindrical log cut from a tree. Trees taper off at their upper ends. In fact, we measure tree height in what is called merchantable height, which means "a certain minimum width at the top"-- usually 4-6 in. The bole of the tree could be 22 inches... somewhere up high, it will be 4-6 inches.

Let's say we're walking through the woods and we want to know "how much is this tree worth for timber?" You can look at a 70 foot pine with a 15 inch DBH, but that means that 16 feet up that tree you aren't looking at a 15 inch DBH-- you may only have a 12 inch DBH. So how do we measure the tree? Let's simply consider the case of a perfectly straight, but tapered tree. First of all, we've got to make an estimate of the tree's diameter at some height above DBH in all of these methods-- and let me tell you right now: no economical forester is going to go climb every tree to get this measurement. When you've got to survey 200 acres in a day, you learn to eyeball it, or, if you're lucky, maybe get a good laser gator. Next, you've got to figure out what cuts you are going to make-- you can get 8, 10, 12 and 16 foot logs at most places, plus crappy wood like rail tie and pulpwood. These cuts represent the "height" of your cylinder. Usually at this point you will cut the tree. Then you choose a log rule: Doyle's, Scribner's, or International-- you can make an arguement for any of the three rules (each has advantages and disadvantages) to determine the merchantable volume from the log, and hope you get a good estimate....

It seems like, in theory, foresters should believe in "logs." That is, if the volume of a tree is ROUGHLY cylindrical, we can use the cylinder volume equation: (pi/4)*(d^2)*h in a logarithimic form: log(volume) = log (pi/4) + 2 log (d) + log(height) which could convert to log(volume) = b0 + b1D + b2H where D = log(d) and H = log(h) to estimate the proper equation given lots of data about diameter and height... but we forget something magical and terrible about logs: where there is a logarithmic transformation, there is also the ability for the data variance to be increased and the distribution to be non-normal. And over here, we do not do non-normal distributions. Well... we try not to!

Increase variance: decrease ability of the equation to work for large values of d and h... and who wants an equation that only works accurately on small, crappy trees...

So I wonder... what's a forester to do? The answer many mills use is actually.. well, calculus. New laser scanners can actually integrate the shape of a log and provide an accurate measurement of a cut logs volume-- they can even suggest optimal cuts to get the best grain and least knots. Got to love technology, but I admit: it seems awfully ironic that foresters really can't believe in LOGS.