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National Forest Inventory (NFI) programs can provide vital information on the status, trend, and change in forest parameters. These programs are being increasingly asked to provide forest parameter estimates for spatial and temporal extents smaller than their current design and accompanying design-based methods can deliver with desired levels of uncertainty. Many NFI designs and estimation methods focus on status and are not well equipped to provide acceptable estimates for trend and change parameters, especially over small spatial domains and/or short time periods. Fine-scale space-time indexed estimates are critical to a variety of environmental, ecological, and economic monitoring efforts. Estimates for forest carbon status, trend, and change are of particular importance to international initiatives to track carbon dynamics. Model-based small area estimation (SAE) methods for NFI and similar ecological monitoring data typically pursue inference on status within small spatial domains, with few demonstrated methods that account for spatio-temporal dependence needed for trend and change estimation. We propose a spatio-temporal Bayesian model framework that delivers statistically valid estimates with full uncertainty quantification for status, trend, and change. The framework accommodates a variety of space and time dependency structures, and we detail model configurations for different settings. Through analysis of simulated datasets, we compare the relative performance of candidate models and a traditional direct estimator. We then apply candidate models to a large-scale NFI dataset to demonstrate the utility of the proposed framework for providing unique quantification of forest carbon dynamics in the contiguous United States. We also provide computationally efficient algorithms, software, and data to reproduce our results and for benchmarking.

Spatially explicit quantification of forest biomass is important for forest-health monitoring and carbon accounting. Direct field measurements of biomass are laborious and expensive, typically limiting their spatial and temporal sampling density and therefore the precision and resolution of the resulting inference. Satellites can provide biomass predictions at a far greater density, but these predictions are often biased relative to field measurements and exhibit heterogeneous errors. We developed and implemented a coregionalization model between sparse field measurements and a predictive satellite map to deliver improved predictions of biomass density at a 1-by-1 km resolution throughout the Pacific states of California, Oregon and Washington. The model accounts for zero-inflation in the field measurements and the heterogeneous errors in the satellite predictions. A stochastic partial differential equation approach to spatial modeling is applied to handle the magnitude of the satellite data. The spatial detail rendered by the model is much finer than would be possible with the field measurements alone, and the model provides substantial noise-filtering and bias-correction to the satellite map.