  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.
