My last words on taper equations

Abstract

A brief review of the nearly half century of research related to taper equations in the Faculty of Forestry at the University of British Columbia is presented. Two new variable-exponent taper models, the 2001 and 2002 models, are introduced and compared to Kozak's 1988 and models. This comparison, based on 38 species groups consisting of 53 603 trees, demonstrated that the 2002 model is consistently the best overall model of the four, and the 2001 model is the simplest in form and the best for estimating merchantable height. The results of this study also indicate that several fit statistics and lack-of-fit statistics should be used to create indices for ranking taper models for practical applications, instead of only a few.

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

“…Under certain conditions it is still possible to do simultaneous fitting when one of the models is an integral (e.g., Parresol and Thomas, 1996;Thomas et al, 1995); however, as actual volumes are rarely known, because they are usually calculated by Smalian's or Huber's formula, which provide only approximations of the actual volume and have been shown to overestimate the volumes, especially in the butt region (Husch et al, 1982;Kozak, 1988;Martin, 1984), the option of estimating the parameters of the taper function and recovery of the implied total volume equation was finally used for fitting the compatible system of Fang et al (2000). This also allowed a more rigorous comparison between the estimations of this system and the variable-exponent taper equation of Kozak (2004), as in both cases the same variable (d) was optimized during the fitting process.…”

“…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.…”

“…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. The comparison of these models against the original and another one proposed by the same author in 1997 (Kozak, 1997) verified that the most stable, and therefore the most consistent taper model was the following:…”

“…Taper functions not only provide estimates of diameter at any height along the stem and total stem volume, but also the merchantable volume and height to any top diameter from any stump height, and individual volumes for logs of any length at any height from the ground (Kozak, 2004).…”

“…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.…”