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.

Accurate quantification of tree biomass is critical and essential for calculating carbon storage, as well as for studying climate change, forest health, forest productivity, nutrient cycling, etc. Tree biomass is typically estimated using statistical models. In this study, a total of 289 trees were harvested and measured for stem, root, branch, and foliage biomass from three coniferous plantation species in northeastern P.R. China. We developed two additive systems of biomass equations based on tree diameter (D) only and both tree diameter (D) and height (H). For each system, 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. The model coefficients were simultaneously estimated using seemingly unrelated regression (SUR). The results indicated that stem biomass had the largest relative contribution to total biomass, while foliage biomass had the smallest relative proportion for the three species. The root to shoot ratio averaged 0.27 for Korean pine, 0.25 for larch, and 0.23 for Mongolian pine. The two additive biomass systems obtained good model fitting and prediction performance, of which the model R a 2 > 0.80, and the percent mean absolute bias (MAB%), was <17%. The second additive system (D and H) had a relatively greater R a 2 and smaller root mean square error (RMSE). The model coefficient for the predictor H was statistically significant in eight of the twelve models, depending on tree species and biomass component. Adding tree height into the system of biomass equations can marginally improve model fitting and performance, especially for total, aboveground, and stem biomass. The two additive systems developed in this study can be applied to estimate individual tree biomass of three coniferous plantation species in the Chinese National Forest Inventory.

Accurate quantification of tree biomass is critical and essential for calculating carbon storage, as well as for studying climate change, forest health, forest productivity, nutrient cycling, etc. Tree biomass is typically estimated using statistical models. Although various biomass models have been developed thus far, most of them lack a detailed investigation of the additivity properties of biomass components and inherent correlations among the components and aboveground biomass. This study compared the nonadditive and additive biomass models for larch (Larix olgensis Henry) trees in Northeast China. For the nonadditive models, the base model (BM) and mixed effects model (MEM) separately fit the aboveground and component biomass, and they ignore the inherent correlation between the aboveground and component biomass of the same tree sample. For the additive models, two aggregated model systems with one (AMS1) and no constraints (AMS2) and two disaggregated model systems without (DMS1) and with an aboveground biomass model (DMS2) were fitted simultaneously by weighted nonlinear seemingly unrelated regression (NSUR) and applied to ensure additivity properties. Following this, the six biomass modeling approaches were compared to improve the prediction accuracy of these models. The results showed that the MEM with random effects had better model fitting and performance than the BM, AMS1, AMS2, DMS1, and DMS2; however, when no subsample was available to calculate random effects, AMS1, AMS2, DMS1, and DMS2 could be recommended. There was no single biomass modeling approach to predict biomass that was best for all aboveground and component biomass except for MEM. The overall ranking of models based on the fit and validation statistics obeyed the following order: MEM > DMS1 > AMS2 > AMS1> DMS2 > BM. This article emphasized more on the methodologies and it was expected that the methods could be applied by other researchers to develop similar systems of the biomass models for other species, and to verify the differences between the aggregated and disaggregated model systems. Overall, all biomass models in this study have the benefit of being able to predict aboveground and component biomass for larch trees and to be used to predict biomass of larch plantations in Northeast China.

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Unmanned aerial vehicle laser scanning (UAVLS) systems present a relatively new means of remote sensing and are increasingly applied in the field of forest ecology and management. However, one of the most essential parameters in forest inventory, tree diameter at breast height (DBH), cannot be directly extracted from aerial point cloud data due to the limitations of scanning angle and canopy obstruction. Therefore, in this study DBH-UAVLS point cloud estimation models were established using a generalized nonlinear mixed-effects (NLME) model. The experiments were conducted using Larix olgensis as the subject species, and a total of 8364 correctly delineated trees from UAVLS data within 118 plots across 11 sites were used for DBH modeling. Both tree- and plot-level metrics were obtained using light detection and ranging (LiDAR) and were used as the models’ independent predictors. The results indicated that the addition of site-level random effects significantly improved the model fitting. Compared with nonparametric modeling approaches (random forest and k-nearest neighbors) and uni- or multivariable weighted nonlinear least square regression through leave-one-site-out cross-validation, the NLME model with local calibration achieved the lowest root mean square error (RMSE) values (1.94 cm) and the most stable prediction across different sites. Using the site in a random-effects model improved the transferability of LiDAR-based DBH estimation. The best linear unbiased predictor (BLUP), used to conduct local model calibration, led to an improvement in the models’ performance as the number of field measurements increased. The research provides a baseline for unmanned aerial vehicle (UAV) small-scale forest inventories and might be a reasonable alternative for operational forestry.