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Fine-resolution maps of forest aboveground biomass (AGB) effectively represent spatial patterns and can be flexibly aggregated to map subregions by computing spatial averages or totals of pixel-level predictions. However, generalized model-based uncertainty estimation for spatial aggregates requires computationally expensive processes like iterative bootstrapping and computing pixel covariances. Uncertainty estimation for map subregions is critical for enhancing practicality and eventual adoption of model-based data products, as this capability would empower users to produce estimates at scales most germane to management: individual forest stands and ownership parcels. In this study we produced estimates of standard error (SE) associated with spatial averages of AGB predictions for ownership parcels in New York State (NYS). This represents the first model-based uncertainty estimation study to include all four types of uncertainty (reference data, sample variability, residual variability, and auxiliary data), incorporate spatial autocorrelation of model residuals, and use methods compatible with algorithmic modeling. We found that uncertainty attributed to residual variance, largely resulting from spatial correlation of residuals, dominated all other sources for most parcels in the study. These results suggest that improvements to model accuracy will yield the greatest reductions to total uncertainty in regions like the northeastern and midwestern United States where forests are divided into smaller spatial units. Further, we demonstrated that log-log regression relating parcel characteristics (area, perimeter, AGB density, forest cover) to parcel-level SE can accurately estimate uncertainty for map subregions, thus providing a convenient means to empower map users. These findings support transparency in future regional-scale model-based forest carbon accounting and monitoring efforts., Comment: 22 pages, 8 figures, 4 tables

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.

The United States (US) Forest Service Forest Inventory and Analysis (FIA) program operates the national forest inventory of the US. Traditionally, the FIA program has relied on sample-based approaches -- permanent plot networks and associated design-based estimators -- to estimate forest variables across large geographic areas and long periods of time. These approaches generally offer unbiased inference on large domains but fail to provide reliable estimates for small domains due to low sample sizes. Rising demand for small domain estimates will thus require the FIA program to adopt non-traditional estimation approaches that are capable of delivering defensible estimates of forest variables at increased spatial and temporal resolution, without the expense of collecting additional field data. In light of this challenge, the development of small area estimation (SAE) methods for FIA data has become an active and highly productive area of research. Yet, SAE methods remain difficult to apply to FIA data, due in part to the complex data structures and inventory design used by the FIA program. Thus, we argue that a new suite of estimation tools (i.e., software) will be required to accommodate shifts in demand for inference on large geographic areas and long time periods to inference on small spatial and/or temporal domains. Herein, we present rFIA, an open-source R package designed to increase the accessibility of FIA data, as one such tool. Specifically, we present two case studies chosen to demonstrate rFIA's potential to simplify the application of a broad suite of SAE methods to FIA data: (1) estimation of contemporary county-level forest carbon stocks across the conterminous US using a spatial Fay-Herriot model; and (2) temporally-explicit estimation of multi-decadal trends in merchantable wood volume in Washington County, Maine using a Bayesian mixed-effects model.

Forest Inventory and Analysis (FIA) is a US Department of Agriculture Forest Service program that aims to monitor changes in forests across the US. FIA hosts one of the largest ecological datasets in the world, though its complexity limits access for many potential users. rFIA is an R package designed to simplify the estimation of forest attributes using data collected by the FIA Program. Specifically, rFIA improves access to the spatio-temporal estimation capacity of the FIA Database via space-time indexed summaries of forest variables within user-defined population boundaries (e.g., geographic, temporal, biophysical). The package implements multiple design-based estimators, and has been validated against official estimates and sampling errors produced by the FIA Program. We demonstrate the utility of rFIA by assessing changes in abundance and mortality rates of ash (Fraxinus spp.) populations in the Lower Peninsula of Michigan following the establishment of emerald ash borer (Agrilus planipennis).