LiDAR-Based Modeling of Individual Tree Height to Crown Base in Picea crassifolia Kom. in Northern China: Comparing Bayesian, Gaussian Process, and Random Forest Approaches

This study compared hierarchical Bayesian, mixed-effects Gaussian process regression, and random forest models for predicting height to crown base (HCB) in Qinghai spruce (Picea crassifolia Kom.) forests using LiDAR-derived data. Both modeling approaches were applied to a dataset of 510 trees from 16 plots in northern China. The models incorporated tree-level variables (height, diameter at breast height, crown projection area) and plot-level spatial competition indices. Model performance was evaluated using leave-one-plot-out cross-validation. The Gaussian mixed-effects process model (with an RMSE of 1.59 and MAE of 1.25) slightly outperformed the hierarchical Bayesian model and the random forest model. Both models identified LiDAR-derived tree height, DBH, and LiDAR-derived crown projection area as primary factors influencing HCB. The spatial competition index (SCI) emerged as the most effective random effect, with the lowest AIC and BIC values, highlighting the importance of local competition dynamics in HCB formation. Uncertainty analysis revealed consistent patterns across the predicted values, with an average relative uncertainty of 33.89% for the Gaussian process model. These findings provide valuable insights for forest management and suggest that incorporating spatial competition indices can enhance HCB predictions.