Objective: The purpose of this article was to use the Random Forest method and nonlinear mixed-effects method to develop a model for determining tree height–diameter at breast height (DBH) for a natural coniferous and broad-leaved mixed forest in Jilin Province and to compare the advantages and disadvantages of the two methods to provide a basis for forest management practice. Method: Based on the Chinese national forest inventory data, the Random Forest method and nonlinear mixed-effects method were used to develop a tree height–DBH model for a natural coniferous and broad-leaved mixed forest in Jilin Province. Results: The Random Forest method performed well on both the fitting set and validation set, with an R² of 0.970, MAE of 0.605, and RMSE of 0.796 for the fitting set and R² of 0.801, MAE of 1.44 m, and RMSE of 1.881 m for the validation set. Compared with the nonlinear mixed-effects method, the Random Forest model improved R² by 33.83%, while the MAE and RMSE decreased by 67.74% and 66.44%, respectively, in the fitting set; the Random Forest model improved R² by 9.88%, while the MAE and RMSE decreased by 14.38% and 12.05%, respectively, in the validation set. Conclusions: The tree height–DBH model constructed based on the Random Forest method had higher prediction accuracy for a natural coniferous and broad-leaved mixed forest in Jilin Province and had stronger adaptability for higher-dimensional data, which can be used for tree height prediction in the study area.

Tree height–diameter relationship is very important in forest investigation, describing forest structure and estimating carbon storage. Climate change may modify the relationship. However, our understanding of the effects of climate change on the height–diameter allometric relationship is still limited at large scales. In this study, we explored how climate change effects on the relationship varied with tree species and size for larch plantations in northern and northeastern China. Based on the repeated measurement data of 535 plots from the 6th to 8th national forest inventory of China, climate-sensitive tree height–diameter models of larch plantations in north and northeast China were developed using two-level nonlinear mixed effect (NLME) method. The final model was used to analyze the height–diameter relationship of different larch species under RCP2.6, RCP 4.5, and RCP8.5 climate change scenarios from 2010 to 2100. The adjusted coefficient of determination $R_{adj}^2$, mean absolute error (MAE) and root mean squared error (RMSE) of the NLME models for calibration data were 0.92, 0.76 m and 1.06 m, respectively. The inclusion of climate variables mean annual temperature (MAT) and Hargreaves climatic moisture deficit (CMD) with random effects was able to increase $R_{adj}^2$ by 19.5% and reduce the AIC (Akaike’s information criterion), MAE and RMSE by 22.2%, 44.5% and 41.8%, respectively. The climate sensitivity of larch species was ranked as L. gmelinii > the unidentified species group > L. principis > L. kaempferi > L. olgensis under RCP4.5, but L. gmelinii > L. principis > the unidentified species group > L. olgensis > L. kaempferi under RCP2.6 and RCP8.5. Large trees were more sensitive to climate change than small trees.

Background: Tree height-diameter relationship is very important in forest investigation, understanding forest ecosystem structure and estimating carbon storage. Climate change may modify the relationship. However, our understanding of the effects of climate change on height-diameter allometric growth is still limited at large scale.Methods: In this study, we explore how the climate change effects on height-diameter allometric relationship vary with tree species and size for larch plantations in northern and northeastern China. Based on the repeated measurement data of 535 plots from the 6th to 8th national forest inventory of China, climate-sensitive tree height-diameter models of Larix plantations in north and northeast China were developed by two-level nonlinear mixed effect (NLME) method. The final model was used to analyze the height-diameter relationship of different Larch species under RCP2.6, RCP 4.5, and RCP8.5 climate change scenarios from 2010 to 2100.Results: The values of B(adjusted coefficient of determination), MAE(mean absolute error) and RMSE(root mean squared error) of the NLME models for calibration data were 0.92, 0.76m and 1.06m, respectively. The inclusion of climate variables MAT (Mean annual temperature), CMD (Hargreaves climatic moisture deficit) with random effects was able to increase a by 19.5% and reduce the AIC (Akaike’s information criterion), MAE and RMSE by 22.2%, 44.5% and 41.8%, respectively. The climate sensitivity was ranked as L. gmelinii > the unidentified species group > L. pincipis-rupprechtii > L. kaempferi > L. olgensis under RCP4.5, but L. gmelinii > L. pincipis-rupprechtii > the unidentified species group > L. olgensis > L. kaempferi under RCP2.6 and RCP8.5. Conclusion: According to the climate sensitivity, tree species could be classified as group I(L. gmelinii, L. pincipis-rupprechtii and the unidentified species group) with large c (from -4.77% to 18.17%) and group II (L. kaempferi and L. olgensis) with small k (from -6.37% to 9.4%).Large trees were more sensitive to climate change than small trees.