Compatible taper and volume systems for Larix olgensis and Larix kaempferi in northeast China

Accurate estimation of tree stem form and merchantable volume is an important prerequisite for forest management and economic evaluation. A system of compatible taper-volume equations was constructed for estimating the upper stem diameter and merchantable volume of different larch species in northeast China using Larix olgensis (LO) and Larix kaempferi (LK) as examples. Five common compatible taper-volume systems were evaluated by using the diameter, height, and cumulative volume data of 262 LO and 86 LK trees. The seemingly unrelated regression (SUR) was used for parameter estimation of the nonlinear simultaneous equations, and the power function was applied to eliminate the heteroscedasticity of the volume equations. Subsequently, the tree species were used as dummy variables to construct generalized equations suitable for the two species. Finally, the adjusted coefficient of determination (Ra2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{a}^{2}$$\end{document}), root mean square error (RMSE), Akaike information criterion (AIC), RMSE%, condition number (CN), mean absolute bias (MAB) and mean percentage of bias (MPB) were used to evaluate the performance of the model. The segmented model outperformed the simple model, and in particular, the model presented by Fang (FS 46:1–12, 2000) exhibited the best performance in predicting diameter and volume. The Fang (FS 46:1–12, 2000) model explained the difference in stem form between both larch species, that is, LO had a higher upper inflection point and a lower inflection point than LK. The dummy variable model provides an effective approach to accurately predict stem diameter and volume variables for both species. The generalized equation can be used for simultaneous estimation of stem taper and merchantable volume for LO and LK in northeast China. Under the same conditions, LO has longer middle segments and better stem form than LK.