A variable-exponent taper equation

Abstract

A different approach to fitting taper equations has been developed, which eliminates the necessity of using several functions to predict diameter inside bark at different parts of the stem. The variable form taper function is easy to develop and saves computing time. For the data used in this study, it predicted tree profile as a function of height, diameter at breast height, and height from the ground with less bias than many of the taper-estimating systems found in the literature.

Un modèle pour l’estimation du volume commercialisable du pin sylvestre dans les principales régions de montagne d’Espagne

“…Although a large number of taper functions of these kinds have been developed and many describe the diameter along the stem quite well (e.g., Bi, 2000;Bruce et al, 1968;Kozak, 1988;Max and Burkhart, 1976;Muhairwe, 1999;Newnham, 1992;Riemer et al 1995), the segmented function of Fang et al (2000) and the variable exponent function of Kozak (2004) have shown very good results in many studies of several species of pinus and other species in Spain (Barrio et al, 2007;Castedo-Dorado et al, 2007;Diéguez-Aranda et al, 2006;Rojo et al, 2005) and in Mexico (Corral-Rivas et al, 2007), and behaved better than others in preliminary analyses. They were therefore selected for further analysis.…”

“…Variable-exponent taper equations were introduced by Kozak (1988), and describe the stem shape with a changing exponent or variable, from the ground to the top of the tree, to represent the neiloid, paraboloid, conic and several intermediate forms (Kozak, 1988;Newnham, 1988). They are basically allometric functions of the form y = kx c , where y and x are the dependent and independent variables, respectively, k a constant and c is the exponent term descriptive of tree form.…”

“…This approach is based on the assumption that the stem form varies continuously along the length of a tree and eliminates the need to develop segmented taper functions for different portions of the stem. In comparison with single and segmented taper models, this approach usually provides the lowest degree of local bias and the greatest precision in taper predictions (e.g., Bi, 2000;Kozak, 1988;Sharma and Zhang, 2004), although they have the disadvantage that cannot be analytically integrated to calculate total stem or log volumes. Kozak (2004) developed two new models based on his original 1988 model in order to reduce the associated multicollinearity.…”

“…Accurate estimation of stem volume makes it possi-equations predict merchantable volume as a percentage of total tree volume (e.g., Burkhart, 1977;Clutter, 1980;Reed and Green, 1984). Taper equations (e.g., Kozak, 1988Kozak, , 2004Newnham, 1992) are mathematical formulae that describe the stem shape; integration of the taper equation from the ground to any height provides an estimate of the volume to that height. In both cases, merchantable stand volume is obtained by summing the merchantable volume of all the trees within a stand.…”

“…Although tree taper has long been studied through the development of taper functions by many forest researchers throughout the world (e.g., Bi, 2000;Demaerschalk, 1972;Kozak, 1988;Max and Burkhart, 1976;Newnham, 1992), the topic is still relevant, perhaps because no single theory has been developed that adequately explains the variation in stem form for all kinds of trees (Newnham, 1988).…”