A spatially varying model for small area estimates of biomass density across the contiguous United States

Abstract

The USDA Forest Service, Forest Inventory and Analysis (FIA) program constructs area estimates of forest attributes through a quasi-systematic sample of field plots distributed across the contiguous US. The program is under increasing pressure to provide estimates over small areas, for which the precision of FIA estimates is limited by small sample sizes. Small area estimation (SAE) models can improve the precision of estimates by leveraging relationships between forest attributes and auxiliary data across multiple small areas of interest. SAE models with large model domains are challenged by requiring auxiliary data encompassing the large domain and by spatially varying relationships between the auxiliary data and forest attributes. We implement a Fay–Herriot SAE model that accounts for spatial variation to make estimates of forest above-ground biomass density (AGBD) within 64,000 hectare hexagons across the contiguous US. Model inference is conducted through a Bayesian paradigm, providing AGBD estimates and quantification of uncertainty through posterior standard deviations and credible intervals. We compare the utility of data from the Global Ecosystem Dynamics Investigation (GEDI) and the National Land Cover Database 2016 Tree Canopy Cover (TCC) product as auxiliary data within the model. Results show that models using GEDI data provide more precise estimates of AGBD than direct estimates using FIA plot data alone while giving accurate quantification of uncertainty. The model using only the TCC product as auxiliary data also reported more precise estimates, but a cross-validation study revealed the reported uncertainty to be overly optimistic for high-biomass areas. We demonstrate that accounting for spatial variation in the model is crucial, and that doing otherwise leads to poor quantification of uncertainty and locally biased estimates. This study not only provides an effective model for small area estimates of AGBD with a large model domain, but also emphasizes the importance of validating models and their reported errors.