A compatible system of biomass equations for three conifer species in Northeast, China

A compatible system of biomass equations was developed for three major conifer species, Korean spruce (Picea koraiensis Nakai), Korean pine (Pinus koraiensis Sieb. et Zucc), and Dahurian larch (Larix gmelinii Rupr) in northeastern China. The model error structure (additive vs multiplicative) of the power function (Y = a Xb) was evaluated using a likelihood analysis. The results indicated that the assumption of multiplicative error structure was strongly supported for the biomass equations of total, sub-total, and tree components. Thus, a system of log-transformed biomass equations was developed using nonlinear seemly unrelated regression (NSUR), with three constraints on the structural parameters to account for the cross-equation error correlations between four tree component biomass (roots, stems, branches, and foliage), two sub-total biomass (aboveground and crown), and total tree biomass. The effectiveness of three anti-log correction factors for predicting the expected biomass in original scale was also assessed. Our results indicated that (1) the likelihood analysis can be used as a tool for rigorously evaluating the error structures of tree biomass equations and choosing an appropriate model form for the given biomass data; (2) the additive or compatible system of biomass equations with three constraints can be developed by NSUR to obtain favorable model fitting and prediction performance; and (3) the anti-log correction may not be necessary and sometimes can be ignored.