Key message We developed two additive systems of biomass equations based on diameter and tree height for nine hardwood species by SUR, and used a likelihood analysis to evaluate the model error structures. Abstract In this study, a total of 472 trees were harvested and measured for stem, root, branch, and foliage biomass from nine hardwood species in Northeast China. Two additive systems of biomass equations were developed, one based on tree diameter (D) only and one based on both tree diameter (D) and height (H). For each system, three constraints were set up to account for the cross-equation error correlations between four tree component biomass, two sub-total biomass, and total biomass. The model coefficients were simultaneously estimated using seemly unrelated regression (SUR). Likelihood analysis was used to verify the error structures of power functions in order to determine if logarithmic transformation should be applied on both sides of biomass equations. Jackknifing model residuals were used to validate the prediction performance of biomass equations. The results indicated that (1) stem biomass accounted for the largest proportion (62 %) of the total tree biomass; (2) the two additive systems of biomass equations obtained good model fitting and prediction, of which the model R a 2 was [0.89, and the mean absolute percent bias (MAB %) was \35 %; (3) the system of biomass equations based on both D and H significantly improved model fitting and performance, especially for total, aboveground, and stem biomass; and (4) the anti-log correction was not necessary in this study. The established additive systems of biomass equations can provide reliable and accurate estimation for individual tree biomass of the nine hardwood species in Chinese National Forest Inventory.

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A total of 138 Dahurian larch (Larix gmelinii Rupr.) trees and 108 white birch (Betula platyphylla Suk.) trees were harvested in the eastern Daxing'an Mountains, northeast China. We developed four additive systems of biomass equations as follows: the first additive model system (MS-1) used the best combination of tree variables as the predictors; the second additive model system (MS-2) included tree diameter at breast height (D) as the sole predictor; the third additive model system (MS-3) included both D and tree height (H) as the predictors; and the fourth additive model system (MS-4) included D, H, and crown attributes (crown width (CW) and crown length (CL)) as the predictors. The model coefficients were simultaneously estimated using seemingly unrelated regression (SUR). The heteroscedasticity in model residuals was addressed by applying a unique weight function to each equation. The results indicated that: (1) the stem biomass accounted for the largest proportion of the total tree biomass, while the foliage biomass had the smallest proportion for the two species; (2) the four additive systems of biomass equations exhibited good model fitting and prediction performance, of which the model R a 2 > 0.81, the mean prediction error (MPE) was close to 0, and the mean absolute error (MAE) was relatively small (<9 kg); (3) MS-1 and MS-4 significantly improved the model fitting and performance; the ranking of the four additive systems followed the order of MS-1 > MS-4 > MS-3 > MS-2. Overall, the four additive systems can be applied to estimate individual tree biomass of both species in the Chinese National Forest Inventory.

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