Good question, Jared!
At one level, you can measure anyway you want, define your system of measurement, and seek agreement with those you encounter.
At the national champion tree register level, you imagine you're lowering a completely horizontal plane until it first contacts the tree being measured.
Simlarly, you establish a horizontal plane at the base of the subject tree, and then you measure the vertical distance between the two horizontal planes, which is by American Forests definition of the height of the tree. Leaning, bent, it doesn't matter...two horizontal planes at tip top, and tree's bottom (defined as the root collar, or point where it was apparent that the original seed level was (point where tree bole turns into root system)).
Mark brings up a good point...you may lose a couple of tenths (of a foot) measuring winter's height leaf off, versus spring/summer's height with leaf on...but that probably can be obfuscated by the seasonal growth that trees can be capable of.
For the really picky...I maintain that the tree's respiration/transpiration during diurnal and seasonal variations can easily vary in the tenths of a foot realm.
Don Bertolette - President/Moderator, WNTS BBS
Restoration Forester (Retired)
Grand Canyon National ParkBJCP Apprentice Beer Judge
View my Alaska Big Tree List Webpage at:http://www.akbigtreelist.org
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