Theoretical Derivation of a Two-way Volume Equation in Coniferous Species.

Abstract

A two-way volume equation in coniferous species is theoretically derived. The Kunze equation is used as a relative stem profile equation. Based on earlier studies, we assume that the normal form-factors at 0.7 and 0.5 in relative height are steady at 0.7 and 1.0, respectively. From these assumptions, two methods for estimating coefficients of a relative stem profile equation are derived. Assuming that the coefficients estimated by these methods are equivalent to each other, we obtain the following two-way volume equation ; v=πd_b²h/4{2(1-h_b/h)}^1.060, where v, stem volume ; d_b, diameter at breast height ; h, total tree height ; and h_b, breast height (=1.2m). This equation is fitted to Japanese cedar and Japanese cypress data. Standard errors of estimated stem volume for Japanese cedar and Japanese cypress are 0.028 m³ and 0.025 m³, respectively. Based on the assumptions and functional form, the features of the derived two-way volume equation are discussed.