Integrated Systems for the Estimation of Tree Taper and Volume

Abstract

The desirability and the advantages of deriving taper equations from existing volume equations are discussed. It is demonstrated that the most common types of volume equations can be converted to compatible taper equations. These mathematical stem profile expressions yield tree volumes for any desired stump height and top diameter outside bark from inputs of diameter breast height outside bark and total height.

Compatible taper-volume models of Quercus variabilis Blume forests in north China

“…According to several studies in the literature (Diéguez-Aranda et al 2006, Oytunemre et al 2008, Hjelm 2013, taper equations can be grouped in three types: (1) simple taper equations (Bruce et al 1968, Kozak et al 1969, Demaerschalk 1972, Demaerschalk 1973, Ormerod 1973, Goulding & Murray 1976, Fang & Bailey 1999, Sharma & Oderwald 2001; (2) segmented taper equations (Max & Burkhart 1976, Cao et al 1980, Parresol et al 1987, Fang et al 2000, Jiang et al 2005; (3) variable exponent taper equations (Kozak 1988, Newnham 1992, Bi 2000, Lee et al 2003, Kozak 2004. Some researchers have pointed out that segmented taper equations and variable exponent taper equations can sometimes provide more flexible descriptions of tree profiles than simple taper equations; variable exponent taper equations usually have the least bias and best predictive abilities among the three kinds of models (Kozak 1988, Newnham 1992, Muhairwe 1999, Oytunemre et al 2008.…”

Compatible systems for the estimation of tree and stand volume

“…Therefore, a search for different stand volume solutions based on estimates obtained from the same tree volume equation will become unnecessary. The third advantage derives from the integrated systems for the estimation of tree taper and volume developed by Demaerschalk (1973). In a compatible system, consistent results can be obtained in tree taper, three volume and stand volume analyses.…”

Compatible volume-taper equations for predicting merchantable volume to variable merchantable limits for <i>Cupressus lusitanica</i>, Ethiopia

“…The volume (V2) of the solid of revolution is obtained by summing up the volumes of a series of thin cross sectional slices and lengths along the entire stem height. This is achieved by integrating d with respect to L. Some of the previous works from Bruce et al ( 1968), Kozak et al (1969), Demaerschalk (1973), Clutter (1980) and Reed and Green (1984) could be cited as examples. This taper equation can also be used to compute sectional volumes at any part of the tree if integrated between the appropriate limits.…”

“…However, as noted by Demaerschalk (1973), although many taper equations developed by mensurationists have resulted in a good estimate of taper, the estimation of volume was usually less satisfactory because of bias. The biases on taper estimates vary considerably with the position in the tree and with the size of the tree.…”

“…In contrast when this is not fulfilled, the system is said to be 'incompatible'. Demaerschalk (1973), Munro and Demaerschalk (1974), and Evert (1976) discussed the advantages of a volume-taper estimation system. According to Munro and Demearschalk (1974) the m ost important benefit of a compatible system is to obtain consistent results from both volume and taper equations.…”