Incorporating stand parameters in nonlinear height-diameter mixed-effects model for uneven-aged Larix gmelinii forests

Tree attributes, such as height (H) and diameter at breast height (D), are essential for predicting forest growth, evaluating stand characteristics and developing yield models for sustainable forest management. Measuring tree H is particularly challenging in uneven-aged forests compared to D. To overcome these difficulties, the development of updated and reliable H-D models is crucial. This study aimed to develop robust H-D models for Larix gmelinii forest by incorporating stand variables. The dataset consisted of 7,069 Larix gmelinii trees sampled from 96 plots at Northeast China, encompassing a wide range of stand densities, age classes, and site conditions. Fifteen widely recognized nonlinear functions were assessed to model the H-D relationship effectively. Model performance was assessed using root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R2). Results identified the Ratkowsky model (M8) as the best performer, achieving the highest R2 (0.74), the lowest RMSE (16.47%) and MAE (12.50%), at statistically significant regression coefficients (p < 0.05). Furthermore, M8 was modified into 5 generalized models (GMs) by adding stand-variables (i.e., mean height, mean diameter and volume and their combination), the results indicate that GM2 was the best model achieving R2 of 0.82% and RMSE of 13.7%. We employed generalized nonlinear mixed-effects modeling approach with both fixed and random effects to account for variations at the individual plot level, enhancing the predictive accuracy. The model explained 71% of variability with significant trends in the residuals. The model was calibrated using response calibration method, through EBLUP theory. Our findings suggest that incorporating stand-level variables representing plot-specific characteristics can further improve the fit of mixed- effects models. These advancements provide forest authorities with enhanced tools for supporting sustainable forest management.