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Estimating Truncated Tree Volumes with the Behre Hyperboloid and Existing Total Volume Equations

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An analytical procedure is presented for estimating truncated tree volumes when direct measurement of volume is not feasible, and neither a taper-based volume equation nor a volume ratio model is available for estimating volume to variable merchantability limits. The procedure essentially estimates a taper curve (Behre's hyperbola) for each tree, which is then integrated to estimate the truncated volume between any two merchantability limits, or the volume below the point of top-kill. The one parameter of the Behre hyperboloid can be estimated directly from the cylindrical form factor of the tree; this may require a local height-diameter curve if the tree has been top-killed. The procedure has the advantage of producing truncated volume estimates that are compatible with any total volume equation, without the disadvantage of requiring taper data to estimate the "free" parameters in the procedure proposed by Demaerschalk (1972, Forest Sci. 18:241-245). Furthermore, only information normally available from a standard timber inventory is required. The procedure is evaluated using 4,623 "truncated" Douglas-fir tree sections, from northern Idaho and northwestern Montana. Although Behre's taper curve lacks the flexibility to account for butt swell near the base of the tree, the procedure nevertheless promises to provide an acceptable means of estimating truncated volumes when conventional alternatives are either not feasible or unavailable. Forest Sci. 27:253-265.

Keywords: Douglas-fir; Pseudotsuga menziesii; compatible taper curve; mensuration; merchantable volume; top-kill; variable-top; volume ratio model

Document Type: Journal Article

Affiliations: Principal Mensurationist, USDA Forest Service, Ogden, Utah

Publication date: June 1, 1981

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
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