Multivariate spatial models for small area estimation of species-specific forest inventory parameters

National Forest Inventories (NFIs) provide statistically reliable information on forest resources at national and other large spatial scales. As forest management and conservation needs become increasingly complex, NFIs are being called upon to provide forest parameter estimates at spatial scales smaller than current design-based estimation procedures can provide. This is particularly true when estimates are desired by species or species groups, which is often required to inform wildlife habitat management, sustainable forestry certifications, or timber product assessments. Here we propose a multivariate spatial model for small area estimation of species-specific forest inventory parameters. The hierarchical Bayesian modeling framework accounts for key complexities in species-specific forest inventory data, such as zero-inflation, correlations among species, and residual spatial autocorrelation. Importantly, by fitting the model directly to the individual plot-level data, the framework enables estimates of species-level forest parameters, with associated uncertainty, across any user-defined small area of interest. A simulation study revealed minimal bias and higher accuracy of the proposed model-based approach compared to the design-based estimator. We applied the model to estimate species-specific county-level aboveground biomass for the 20 most abundant tree species in the southern United States using Forest Inventory and Analysis (FIA) data. County-level biomass estimates from the proposed model had high correlations with design-based estimates, yet the model-based estimates tended to have a slight positive bias relative to design-based estimates, particularly for abundant and managed species. Importantly, the proposed model provided large gains in precision across all 20 species. On average across species, 91.5% of county-level biomass estimates had higher precision compared to the design-based estimates. Future work should explore incorporation of additional auxiliary data sources that can help explain fine-scale variation in biomass of managed species. The proposed framework is an attractive solution for NFI data users to generate species-level forest parameter estimates with reasonable precision at management-relevant spatial scales.