With the development of national-scale forest biomass monitoring work, accurate estimation of forest biomass on a large scale is becoming an important research topic in forestry. In this study, the stem wood, branches, stem bark, needles, roots and total biomass models for larch were developed at the regional level, using a general allometric equation, a dummy variable model, a mixed effects model, and a Bayesian hierarchical model, to select the most effective method for predicting large-scale forest biomass. Results showed total biomass of trees with the same diameter gradually decreased from southern to northern regions in China, except in the Hebei province. We found that the stem wood, branch, stem bark, needle, root, and total biomass model relationships were statistically significant (p-values < 0.01) for the general allometric equation, linear mixed model, dummy variable model, and Bayesian hierarchical model, but the linear mixed, dummy variable, and Bayesian hierarchical models showed better performance than the general allometric equation. An F-test also showed significant differences between the models. The R² average values of the linear mixed model, dummy variable model, and Bayesian hierarchical model were higher than those of the general allometric equation by 0.007, 0.018, 0.015, 0.004, 0.09, and 0.117 for the total tree, root, stem wood, stem bark, branch, and needle models respectively. However, there were no significant differences between the linear mixed model, dummy variable model, and Bayesian hierarchical model. When the number of categories was increased, the linear mixed model and Bayesian hierarchical model were more flexible and applicable than the dummy variable model for the construction of regional biomass models.

Accurate biomass estimations are important for assessing and monitoring forest carbon storage. Bayesian theory has been widely applied to tree biomass models. Recently, a hierarchical Bayesian approach has received increasing attention for improving biomass models. In this study, tree biomass data were obtained by sampling 310 trees from 209 permanent sample plots from larch plantations in six regions across China. Non-hierarchical and hierarchical Bayesian approaches were used to model allometric biomass equations. We found that the total, root, stem wood, stem bark, branch and foliage biomass model relationships were statistically significant (p-values < 0.001) for both the non-hierarchical and hierarchical Bayesian approaches, but the hierarchical Bayesian approach increased the goodness-of-fit statistics over the non-hierarchical Bayesian approach. The R² values of the hierarchical approach were higher than those of the non-hierarchical approach by 0.008, 0.018, 0.020, 0.003, 0.088 and 0.116 for the total tree, root, stem wood, stem bark, branch and foliage models, respectively. The hierarchical Bayesian approach significantly improved the accuracy of the biomass model (except for the stem bark) and can reflect regional differences by using random parameters to improve the regional scale model accuracy.

The characteristics and distribution of foliage biomass are important aspects of the crown structures of trees. In this study, we developed a foliage biomass distribution model at the branch level and annual shoot level (i.e., all branches on an annual increment of the main tree bole) using a sample of 51 Korean pine trees that were destructively sampled in Liaoning Province, northeast China. A variety of independent variables, including branches, trees, and forest competition, were used as explanatory variables in the model development. Our results indicated that foliage biomass at the branch level increased with an increasing relative distance from the tree tip into the crown. The peak of the foliage biomass distribution shifted to the tree tip with increasing tree age. A power function, including branch diameter and competition variables, showed excellent performance in modeling branch foliage at the branch level. The final model, which included branch diameter, competition variables, and relative distance to branch base for the relative foliage density, showed best performance. The trees that showed advantageous growth ability also had a larger amount of foliage biomass.