Small area estimation of forest volume using mixed effects random forests and multi-source remote sensing data

Accurate estimation of forest growing stock volume (GSV) at fine spatial scales is essential for sustainable management, carbon accounting, and local decision-making. However, traditional inventories often lack sufficient sampling density for small areas. This study evaluates two small-area estimation (SAE) approaches: the Empirical Best Predictor (EBP), based on a nested-error linear regression model, and the Mixed-Effects Random Forest (MERF), using multi-source remote sensing data. The analysis was conducted in the Vallombrosa Nature Reserve (Italy), integrating field measurements from 101 plots with auxiliary variables from Sentinel-2 and airborne LiDAR. Both methods estimated mean and total GSV across 658 forest stands, many lacking direct observations. Performance was assessed via spatial cross-validation, and uncertainty was quantified using root-mean-square error (RMSE). Results show that MERF outperformed EBP in predictive accuracy, achieving higher R² (0.67 vs. 0.37) and lower RMSE (151 vs. 202 m³ ha⁻¹). MERF produced more stable uncertainty estimates with improved coverage. While both methods yielded comparable total GSV, EBP exhibited greater sensitivity to model assumptions. Conversely, MERF effectively captured non-linear relationships and handled multicollinearity, despite reduced interpretability and higher computational demand. Overall, findings highlight the advantages of integrating machine learning with mixed-effects modeling for SAE under sparse sampling.