Height–diameter modeling of tree species in boreal and mixed forests using a mixed-effects approach and stand-level variables

Forests are ecologically complex, and trees play a structural and functional role in ecosystem dynamics. Tree height–DBH (diameter at breast height) relationships serve as a key indicator of forest productivity, competition, and succession, fundamental to sustainable forest management. This study develops height–DBH models for eight ecologically important tree species in boreal and mixed forests by applying nonlinear mixed-effects modelling approach to improve the predictive accuracy of height estimations. We evaluate height–DBH functions, including the two-parameter power function and Chapman–Richards function, incorporating stand-level variables—stand height based on dominant or co-dominant trees (SHT), basal area (BAH), and tree density (TPH) to refine predictions. Results indicate that mixed-effects models significantly improved model performance, with M4 (Chapman–Richards with mixed-effects) and M5 (Chapman–Richards function with mixed-effects and stand-level variables)–showing lowest AIC (Akaike Information Criterion) across species. Incorporating stand-level variables significantly enhanced performance, though improvements varied by species. The high accuracy of model M5 was further confirmed by validation process. Among stand-level variables, SHT contributed the most to height predictions (25.3 – 53.0%), while BAH (≤ 0.36%) and TPH (≤ 0.01%) had negligible effects. Still M4 can be a reliable alternative when stand-level variables are unavailable. This study highlights the effectiveness of a mixed-effects modelling framework complemented by stand-level variables in improving tree height estimation. Our research improves decision-making in growth and yield estimations of mixed stands and enhances the reliability of forest vegetation simulator outputs, thereby supporting ecological integrity.