Developing Two Additive Biomass Equations for Three Coniferous Plantation Species in Northeast China

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. 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 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.

Biomass is a basic quantitative character of forest ecosystem. Biomass data are foundation of researching many forestry and ecology problems. 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. Constructing biomass models is considered a good approach to estimate forest biomass. Based on biomass data of 97 sampling trees of natural Tilia Linn. in Xiaoxing'an Mountains and Zhangguangcai ranges, three additive systems of individual tree biomass equations were developed: based on tree diameter at breast height (D) only, based on tree diameter at breast height and height (H), and based on the best models. The nonlinear seemly unrelated regression was used to estimate the parameters in the additive system of biomass equations. The heteroscedasticity in model residuals was addressed by applying a unique weight function to each equation. The individual tree biomass model validation was accomplished by Jackknifing technique. The results showed that three additive systems of individual tree biomass equations could fit and predict the biomass of Tilia Linn. well (adjusted coefficient of determination Ra2>0.84, mean predicted error percentage MPE<8.5%, mean absolute error MAE<16.3 kg,mean standard error percentage MPSE<28.5%). The biomass equations of stem and aboveground were better than biomass equations of branch, foliage and crown. Adding total tree height and crown factor in the additive systems of biomass equations could significantly improve model fitting performance and predicting precision (Ra2 improved from 0.01 to 0.04, MAE decreased from 0.01 to 4.55 kg), narrow the confidence interval of the predicted value and the biomass of stem, foliage and aboveground were increased more than the biomass of branch and crown. In general, the equations of the additive system based on the best models produced the best model fitting, followed by that of the additive system based on D and H, and that based on D. It was essential to develop biomass model by adding total tree height and crown factor.

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 Ra2 &gt; 0.81, the mean prediction error (MPE) was close to 0, and the mean absolute error (MAE) was relatively small (&lt;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 &gt; MS-4 &gt; MS-3 &gt; 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 estimation of tree biomass is required for accounting for and monitoring forest carbon stocking. Allometric biomass equations constructed by classical statistical methods are widely used to predict tree biomass in forest ecosystems. In this study, a Bayesian approach was proposed and applied to develop two additive biomass model systems: one with tree diameter at breast height as the only predictor and the other with both tree diameter and total height as the predictors for planted Korean larch (Larix olgensis Henry) in the Northeast, P.R. China. The seemingly unrelated regression (SUR) was used to fit the simultaneous equations of four tree components (i.e., stem, branch, foliage, and root). The model parameters were estimated by feasible generalized least squares (FGLS) and Bayesian methods using either non-informative priors or informative priors. The results showed that adding tree height to the model systems improved the model fitting and performance for the stem, branch, and foliage biomass models, but much less for the root biomass models. The Bayesian methods on the SUR models produced narrower 95% prediction intervals than did the classical FGLS method, indicating higher computing efficiency and more stable model predictions, especially for small sample sizes. Furthermore, the Bayesian methods with informative priors performed better (smaller values of deviance information criterion (DIC)) than those with the non-informative priors. Therefore, our results demonstrated the advantages of applying the Bayesian methods on the SUR biomass models, not only obtaining better model fitting and predictions, but also offering the assessment and evaluation of the uncertainties for constructing and updating tree biomass models.

Accurate estimation of tree and forest biomass is key to evaluating forest ecosystem functions and the global carbon cycle. Allometric equations that estimate tree biomass from a set of predictors, such as stem diameter and tree height, are commonly used. Most allometric equations are site specific, usually developed from a small number of trees harvested in a small area, and are either species specific or ignore interspecific differences in allometry. Due to lack of site-specific allometries, local equations are often applied to sites for which they were not originally developed (foreign sites), sometimes leading to large errors in biomass estimates. In this study, we developed generic allometric equations for aboveground biomass and component (stem, branch, leaf, and root) biomass using large, compiled data sets of 1203 harvested trees belonging to 102 species (60 deciduous angiosperm, 32 evergreen angiosperm, and 10 evergreen gymnosperm species) from 70 boreal, temperate, and subtropical natural forests in Japan. The best generic equations provided better biomass estimates than did local equations that were applied to foreign sites. The best generic equations included explanatory variables that represent interspecific differences in allometry in addition to stem diameter, reducing error by 4-12% compared to the generic equations that did not include the interspecific difference. Different explanatory variables were selected for different components. For aboveground and stem biomass, the best generic equations had species-specific wood specific gravity as an explanatory variable. For branch, leaf, and root biomass, the best equations had functional types (deciduous angiosperm, evergreen angiosperm, and evergreen gymnosperm) instead of functional traits (wood specific gravity or leaf mass per area), suggesting importance of other traits in addition to these traits, such as canopy and root architecture. Inclusion of tree height in addition to stem diameter improved the performance of the generic equation only for stem biomass and had no apparent effect on aboveground, branch, leaf, and root biomass at the site level. The development of a generic allometric equation taking account of interspecific differences is an effective approach for accurately estimating aboveground and component biomass in boreal, temperate, and subtropical natural forests.

Developing generalized single-tree biomass models suitable for forest biomass estimation is an effective way to provide scientific approaches. To simplify biomass modeling and improve the accuracy of model estimation for better understanding of biomass, carbon stocks, and dynamics in large-scale forests and to precisely estimate tree biomass, this study used stem, bark, needle, branch, and root biomass of Larix kaempferi of 161 sample trees in Gansu, Hubei, and Liaoning Provinces to generalize single-tree biomass equations suitable for different organs and regions using seemingly unrelated regression and dummy variable modeling methods. Results showed that the generalized biomass equations not only solved compatibility problems with different components but also increased accuracy with an average increase of 0.28%-0.44% in R2, decreased 0.40%-6.61% in the root mean square error (ERMS), and decreased 1.63%-6.61% in the mean abosolute bias (BMA). Effects due to region increased accuracy more than effects due to developmental stages. When both region and developmental stages were added to the dummy variable model, it was more accurate and produced the best equation. Therefore, we suggest that both regional and developmental stages be considered as dummy variables to establish generalized biomass equations in order to solve the compatibility problem with different components as well as for overcoming problems of generalizing with different regions.

Applying allometric equations in combination with forest inventory data is an effective approach to use when qualifying forest biomass and carbon storage on a regional scale. The objectives of this study were to (1) develop general allometric tree component biomass equations and (2) investigate tree biomass allocation patterns for Pinus massoniana, a principal tree species native to southern China, by applying 197 samples across 20 site locations. The additive allometric equations utilized to compute stem, branch, needle, root, aboveground, and total tree biomass were developed by nonlinear seemingly unrelated regression. Results show that the relative proportion of stem biomass to tree biomass increased while the contribution of canopy biomass to tree biomass decreased as trees continued to grow through time. Total root biomass was a large biomass pool in itself, and its relative proportion to tree biomass exhibited a slight increase with tree growth. Although equations employing stem diameter at breast height (dbh) alone as a predictor could accurately predict stem, aboveground, root, and total tree biomass, they were poorly fitted to predict the canopy biomass component. The inclusion of the tree height (H) variable either slightly improved or did not in any way increase model fitness. Validation results demonstrate that these equations are suitable to estimate stem, aboveground, and total tree biomass across a broad range of P. massoniana stands on a regional scale.

Accurate estimation of forest biomass is of great significance for carbon stock assessment and forest resource management. Hierarchical Bayesian methods, as a statistical approach that can effectively enhance parameter stability, have large potentials in the precise estimation of forest biomass. Based on data from 143 sample trees of Larix olgensis in the Mengjiagang Forest Farm of Heilongjiang Province, we adopted hierarchical Bayesian see-mingly unrelated regression (SUR) to develop a univariate seemingly unrelated mixed-effects model (SURM1) with diameter at breast height (DBH) as the independent variable and a bivariate seemingly unrelated mixed-effects model (SURM2) with DBH and tree height as independent variables. We compared the fitting and predictive performance of restricted maximum likelihood estimation (REML) with three hierarchical Bayesian methods: no prior information (Br1), data-derived prior information (Br2), and historical prior information (Br3). The results showed that the SURM2 model significantly outperforms SURM1 in predicting stem biomass and total individual tree biomass, with mean absolute percentage errors (MAPE) reduced by 7.8% and 7.6%, respectively. The hierarchical Bayesian method utilizing data-derived prior information (Br2) demonstrated notably superior parameter estimation stability (with standard deviations ranging from 0.003 to 0.108) compared to REML (standard deviations from 0.052 to 0.540), Br1 (standard deviations from 0.033 to 0.819), and Br3 (standard deviations from 0.038 to 0.771). Predictions based on Br2 yield superior accuracy, with MAPE for SURM1 model predictions of stem, branch, leaf, root, and total biomass being 17.6%, 45.1%, 48.3%, 25.2%, and 17.1%, respectively. The SURM2 model improved the prediction accuracy for stem biomass and total biomass, reducing MAPE by 7.3% and 6.7%, respectively, compared to SURM1. Furthermore, when sample size was small (fewer than 60), incorporating effective prior information could enhance the stability of predictions. The use of data-derived prior information in the Bayesian method demonstrated significant advantages in improving both the accuracy and stability of biomass predictions for L. olgensis, providing valuable support for the precise estimation of biomass in the Heilongjiang Pro-vince.

Accurate estimation of forest biomass in China is crucial for the study of carbon cycle and mechanisms underlying carbon storage in global terrestrial ecosystems. Based on the biomass data of 376 individuals of Larix olgensis in Heilongjiang Province, we used seemingly unrelated regression (SUR) method to build a univariate biomass SUR model with diameter at breast height as the independent variable and considering the random effect at the sampling site level. Then, a seemingly unrelated mixed effect (SURM) model was constructed. As the calculation of random effects of SURM model did not require the empirically measured values of all dependent variables, we analyzed the deviations from the following four types in detail: 1) SURM1, the random effect was calculated according to the measured biomass of stem, branch and foliage; 2) SURM2, the random effect was calculated according to the measured value of tree height (H); 3) SURM3, the random effect was calculated according to the measured crown length (CL); 4) SURM4, the random effect was calculated according to the measured values of H and CL. The results showed that the fitting effect of branch and foliage biomass models was improved significantly after considering the horizontal random effect of the sampling plot, with R2 being increased by more than 20%. The fitting effect of stem and root biomass models were improved slightly, with R2 being increased by 4.8% and 1.7%, respectively. When using five randomly selected trees to calculate the horizontal random effect of the sampling plot, the prediction performance of SURM model was better than that of SUR model and SURM model considering only fixed effects, especially SURM1 model (MAPE% of stem, branch, foliage and root was 10.4%, 29.7%, 32.1% and 19.5%, respectively). Except for SURM1 model, the deviation of SURM4 in predicting stem, branch, foliage and root biomass was smaller than that of SURM2 and SURM3 models. In actual prediction, although the prediction accuracy of SURM1 model was the highest, it needed to measure aboveground biomass of several trees, and the use cost was relatively high. Therefore, the SURM4 modelled on measured H and CL was recommended to predict the standing tree biomass of L. olgensis.

IntroductionAccurate biomass estimation is crucial for quantifying forest carbon storage and guiding sustainable management. In this study, we developed four biomass modeling systems for natural white birch (Betula platyphylla Sukaczev) in northeastern China using field data from 148 trees.MethodsThe data included diameter at breast height (DBH), tree height (H), crown dimensions, and biomass components (stem, branch, foliage, and root biomass), as well as soil and climate variables. We employed Seemingly Unrelated Regression (SUR) and mixed-effects models (SURM) to account for component correlations and spatial variability.ResultsThe base model (SURba), using only the DBH variable, explained 89-96% of the biomass variance (RMSE%: 1.34-19.94%). The second model (SURbio) incorporated H for stem/branch biomass and crown length (CL) for foliage, improving the predictions of stem, branch, and foliage biomass (R2 increased by 1.69–4.86%; RMSE% decreased by 10.76-59.04%). Next, the SURba-abio and SURbio-abio models integrated abiotic factors, including soil organic carbon content (SOC), mean annual precipitation (MAP), degree-days above 18°C (DD18), and soil bulk density (BD). Both models showed improvement, with the abiotic factor model SURba-abio performing similarly to the biotic factor model SURbio (ΔR2 &amp;lt; 4.36%), while the SURbio-abio model performed the best. Subsequently, random effects were introduced at the sampling point (Forestry Bureau) level, developing seemingly unrelated mixed-effects models (SURMba, SURMbio, SURMba-abio, SURMbio-abio), which improved model fitting and prediction accuracy. The gap between the SURMba-abio model (with abiotic factors) and the SURMbio-abio model (including both biotic and abiotic factors) was minimal (ΔR2 &amp;lt; 2.80%). The random effects model stabilized when calibrated with aboveground biomass measurements from four trees.DiscussionIn conclusion, these models provide an effective approach for estimating the biomass of natural white birch in northeastern China. In the absence of biotic factors, the SURba-abio and SURMba-abio models serve as reliable alternatives, emphasizing the importance of abiotic factors in biomass estimation and offering a practical solution for predicting birch biomass.

Regressive models of the aboveground biomass for three conifers in subtropical China—slash pine (Pinus elliottii), Masson pine (P. massoniana) and Chinese fir (Cunninghamia lanceolata)—were established. Regression analysis of leaf biomass and total biomass of each branch against branch diameter (d), branch length (L), d3 and d2L was conducted with functions of linear, power and exponent. A power law equation with a single parameter (d) was proved to be better than the rest for Masson pine and Chinese fir, and a linear equation with parameter (d3) is better for slash pine. The canopy biomass was derived by adopting the regression equations to all branches of each individual tree. These kinds of equations were also used to fit the relationship between total tree biomass, branch biomass, foliage biomass and tree diameter at breast height (D), tree height (H), D3 and D2H, respectively. D2H was found to be the best parameter for estimating total biomass. However, for foliage biomass and branch biomass, both parameters and equation forms showed some differences among species. Correlations were highly significant (P<0.001) for foliage biomass, branch biomass and total biomass, among which the equation of the total biomass was the highest. With these equations, the aboveground biomass of Masson pine forest, slash pine forest and Chinese fir forest were estimated, in addition to the allocation of aboveground biomass. The above-ground biomass of Masson pine forest, slash pine forest and Chinese fir forest was 83.6, 72.1 and 59 t/hm2 respectively, and the stem biomass was more than the foliage biomass and the branch biomass. The underground biomass of these three forests which estimated with others’ research were 10.44, 9.42 and 11.48 t/hm2, and the amount of carbon-fixed were 47.94, 45.14 and 37.52 t/hm2, respectively.

Biomass functions were established to estimate above-ground biomass of Siberian larch (Larix sibirica) in the Altai Mountains of Mongolia. The functions are based on biomass sampling of trees from 18 different sites, which represent the driest locations within the natural range of L. sibirica. The best performing regression model was found for the equations y = (D 2 H)/(a+bD) for stem biomass, y = aD b for branch biomass, and y=aD b H c for needle biomass, where D is the stem diameter at breast height and H is the tree height. The robustness of the biomass functions is assessed by comparison with equations which had been previously published from a plantation in Iceland. There, y=aD b H c was found to be the most significant model for stem and total above-ground biomasses. Applying the equations from Iceland for estimating the above-ground biomass of trees from Mongolia resulted in the underestimation of the biomass in large-diameter trees and the overestimation of the biomass in thin trees. The underestimation of thick-stemmed trees is probably attributable to the higher wood density, which has to be expected under the ultracontinental climate of Mongolia compared to the euoceanic climate of Iceland. The overestimation of the biomass in trees with low stem diameter is probably due to the high density of young growth in the not systematically managed forests of the Mongolian Altai Mountains, which inhibits branching, whereas the plantations in Iceland are likely to have been planted in lower densities.

A new system of additive tree biomass equations was developed for juvenile white birch plantations based on tree diameter at breast height (DBH) and tree height (HT). Compared with previous equations developed for natural white birch forests, the new system included one more biomass component and provided more accurate predictions. Accurate estimates of tree component and total biomass are necessary for evaluating alternative forest management strategies for biomass feedstock, carbon sequestration, and products. Previous biomass equations developed for white birch trees in natural stands provided substantially biased predictions for white birch plantations. A new system of additive tree biomass equations was developed for juvenile white birch plantations in the northeastern China. With destructive biomass sampling data from 501 trees sampled from white birch provenance and family trails at ages 7, 9, 10, and 13 in three provinces, a system of nonlinear additive tree biomass equations based on DBH and tree height was developed using the nonlinear seemingly unrelated regressions (NSUR) approach. Compared with previously published equations developed for natural white birch forests, the new system provided more accurate predictions of white birch tree component and aboveground and total biomass, especially of branch, foliage, and root biomass. The new system extended the applicability of biomass equations to white birch plantations in the northeastern China.

Silvicultural manipulation and site effect on above and belowground biomass equations for young Pinus radiata

The ability of mangrove to sequestrate carbon dioxide (CO2) is becoming part of the methods for climate change mitigation due to the ability of plants to absorb and store CO2from the atmosphere as biomass. Therefore, this research aimed to estimate CO2 sequestration and litter production by Avicennia alba planted in mangrove rehabilitation area. The data collection method was field observation which was used to measure tree parameters and litter on the observation plot. Tree biomass was estimated using the allometric equation and converted to carbon sequestration. Moreover, a one-way Analysis of Variance (ANOVA) test was applied to assess biomass and litter production differences in the observed stations. Regression analysis was also used to diagnose the relationship between tree diameter, biomass, and carbon sequestration. The results showed that the average biomass and carbon storage at tree level were directly proportional to tree diameter and age. At the stand level, biomass and carbon sequestration in the three stations were not significantly different at the 95% confidence level. It was also observed that stem density affected mangrove biomass. The results showed that more mangrove mortality occurred with older ages at the observed stations and this lowered the stem density and biomass. Furthermore, the relationship between diameter, biomass, and carbon sequestration was directly proportional. Litter production also increased directly with tree age and diameter but the trend was insignificant. The leaf part was found to be the most significant contributor to litter production, and the proportion increased with age and diameter. These results were essential information for future sustainable mangrove rehabilitation plans.Received: 2024-04-02 Revised: 2024-06-21 Accepted: 2025-03-07 Published: 2025-04-28