Combining allometric equations and machine learning approaches for more reliable tree height estimation

We present the first national-scale implementation of a species-specific hybrid workflow combining allometric equations with machine-learning (ML) bias correction, applied to the individual tree heights data in Korean National Forest Inventory (NFI). Our dataset includes 141,669 trees representing 50 major species across the country. On average, the hybrid approach reduced RMSE by 9.1 % and increased R² by 10.5 % compared to allometric estimates alone. Tree height is a key variable in forest science, intrinsically linked to individual tree biomass, stand productivity, and carbon dynamics. However, dense canopy conditions often limit direct measurement, necessitating reliance on allometric equations based on diameter at breast height (DBH). Although practical, these equations can introduce significant bias, compromising forest inventory accuracy. We address this by learning the residual bias between measured and allometically estimated height with a Random Forest model using 5-fold cross-validation and tree-, stand-, and site-level predictors. The hybrid approach consistently outperformed allometry alone. For instance, in Pinus densiflora , coefficient of determination (R 2 ) improved from 0.72 to 0.81, and root mean square error (RMSE) decreased from 1.92 m to 1.58 m. Similar improvements were observed for Quercus mongolica (R 2 : 0.70–0.84, RMSE: 1.71 m to 1.24 m) and Acer ginnala (R 2 : 0.41–0.65; RMSE: 1.93 m to 1.18 m). Across all species, ML-based correction improved accuracy (before correction: r = 0.60–0.92, RMSE = 0.92–2.86 m; after correction: r = 0.64–0.95, RMSE = 0.95–2.39 m). Variable importance analysis revealed that site conditions (e.g., distance to roads, slope, altitude) and stand characteristics (e.g., mean DBH, basal area, structural diversity) were key predictors of bias, though their importance varied by species. Integrating ML with allometric models significantly enhances the reliability of NFI height estimates and could improve forest biomass and carbon stock assessments. • Machine learning model effectively corrects allometric height bias in NFI data. • Hybrid "Allo + ML" boosted height accuracy/precision for 50 Korean tree species. • Site conditions and stand structure were key predictors of height bias. • Bias correction variable importance varied by tree species. • Improved height estimates could enhance biomass and carbon stock assessments.