Hierarchical Bayesian models for small area estimation of forest variables using LiDAR

Light detection and ranging (LiDAR) data have become almost ubiquitous as a remote sensing tool in forestry estimation and mapping applications. Such initiatives commonly rely on spatially aligned forest inventory plot measurements and LiDAR covariates to inform model-based estimators for small area estimation. There are many examples where such linking models provide the desired accuracy and precision of forest parameter estimates for small areas where paucity of inventory plot observations preclude design-based inference. This paper builds on previous small area estimation (SAE) work by linking LiDAR covariates with variable radius forest inventory plot measurements within a hierarchical Bayesian framework. Using this framework, we compare SAE of forest aboveground biomass using: i) Fay-Herriot (FH); ii) FH with conditional autoregressive random effects (FHCAR); and iii) FHCAR with smoothed sampling variance (FHCAR-SMOOTH) models. Candidate models and the direct estimate based on plot measurements alone were compared using coefficient of variation (CV). On average, the FH model reduced the CV by 52.3% compared to the direct estimate. Incorporating spatial structure via the FHCAR model reduced the CV by 56.9% and 10.8% relative to the direct and the FH model estimates, respectively. Overall, these results illustrate the applicability and utility of using a SAE framework for linking LiDAR with typical forest inventory data.