Small Area Estimation of Forest Volume Using Mixed Effects Random Forests and Multi-Source Remote Sensing Data

Abstract

Accurate estimation of forest growing stock volume (GSV) at fine spatial scales is essential for sustainable forest management, carbon accounting, and local decision-making. However, traditional forest inventories often lack sufficient sampling density to provide reliable estimates for small areas. This study evaluates the performance of two small area estimation approaches: the Empirical Best Predictor (EBP) based on a nested-error linear regression model, and the Mixed-Effects Random Forest (MERF) for estimating GSV at the forest stand level 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 derived from Sentinel-2 imagery and airborne LiDAR. Both methods were applied to estimate the mean and total GSV across 658 forest stands, many of which lacked direct observations. Model performance was assessed using 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{square}1). MERF also produced more stable and precise uncertainty estimates, with improved coverage of observed values. While both methods yielded comparable total GSV estimates, EBP exhibited greater variability and sensitivity to model assumptions. In contrast, MERF effectively captured non-linear relationships and handled multicollinearity among predictors, though at the cost of reduced interpretability and higher computational demand. Overall, findings highlight the advantages of integrating machine learning with mixed-effects modeling for SAE in forestry, particularly under conditions of sparse sampling and complex ecological variability.