Provenance-Specific Height–Diameter Modeling for Chinese Fir: A Clustered Mixed-Effects Approach

Chinese fir is the predominant afforestation species in southern China, exhibiting distinct provenances due to long-term climatic adaptation. This study utilized data from four surveys conducted at different ages in a provenance trial forest at Zhangping Wuyi Forest Farm, Fujian Province, to classify Chinese fir provenances using cluster analysis based on growth metrics. The resulting clusters were integrated as random effects into height-diameter models. Model performance was enhanced by incorporating age parameters and validated through five-fold cross-validation. The findings reveal that: (1) the Logistic model best captured the fundamental height-diameter relationship of Chinese fir; (2) the inclusion of provenance-clustering random effects improved model fit and predictive accuracy, with height-based clustering outperforming other methods; (3) the addition of age parameters further refined the base models beyond the clustering effects, and the combination of both approaches achieved the highest precision. Among clustering techniques, height-based clustering surpassed combined height-diameter at breast height (DBH) clustering, while DBH-based clustering was the least effective. The developed models facilitate precise growth predictions for multi-provenance Chinese fir across extensive geographic ranges, offering a theoretical basis for provenance-specific management.