Construction of Compatible Volume Model for Populus in Beijing, China

The accurate assessment of tree volume is crucial for developing forest management plans, and this can be achieved using tree volume models. In this study, data on individual trees were collected and calculated, including the diameter at breast height (D), ground diameter (DG), tree height (H), and tree volume (V). A total of 400 Populus × tomentosa Carrière, 400 Populus tomentosa Carr, and 400 Populus × canadensis Moench trees were sampled. Two compatible volume model systems were established using corresponding methods. The models consisted of the following five types: V-DH, V-D, V-DG, H-D, and DG-D. In our calculations, before the horizontal line was the dependent variable, and behind the horizontal line was the independent variable. Variations in preferences for the H-D models were observed among the tree species, with the logistic function proving the most suitable for Populus × tomentosa Carrière, Chapman–Richard function for Populus tomentosa Carr, and power function for Populus × canadensis Moench. Among the three volume models, the V-DH model exhibited a superior performance, with its R2 values ranging from 0.965 to 0.984 and mean estimated error (MPE) values ranging from 1.26% to 1.78%. Following this was the V-D model, with R2 values between 0.9359 and 0.9704 and MPE values between 1.71% and 2.46%. The V-DG model ranked third, with R2 values ranging from 0.8746 to 0.9501 and MPE values ranging from 2.33% to 3.16%. In the H-D model, the R2 and MPE values ranged from 0.4998 to 0.7851 and from 1.31% to 1.45%, respectively. For the DG-D model, the R2 values ranged from 0.9563 to 0.9868 and the MPE values ranged from 0.47% to 0.68%. Comparing both compatible methods, the nonlinear seemingly uncorrelated regression (NSUR) was more effective. The three volume models demonstrated high levels of accuracy and compatibility, providing a reliable scientific foundation for forest management and the formulation of harvesting plans in Beijing, with significant practical implications.