Compatible systems of total tree cubic volume, volume ratio, and stem taper curves are developed based on four well known volume equations: the constant form factor, the combined variable, Schumacher's, and Honer's. These systems are constructed to insure that the volume obtained for a portion of the tree bole by integrating the stem taper curve will be equal to the volume for the same portion of the bole obtained using the compatible volume ratio equation. Both methods produce total tree volumes equal to that obtained from the total tree volume equation. Each system was fitted to black oak ( Quercus velutina ) data from New Jersey. The overall system estimation error was reduced substantially by fitting the equations simultaneously as opposed to fitting the taper equation and algebraically solving for the coefficients of the other equations. No differences in performance were noted between the four volume estimation systems on this small data set. Forest Sci. 30:977-990.
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Reed et al. (1984) studied this question.