Gretchen G. Moisen’s research while affiliated with United States Postal Service and other places

Comparing and evaluating small area estimation (SAE) models for a given application is inherently difficult. Typically, we do not have enough data in many areas to check unit-level modeling assumptions or to assess unit-level predictions empirically; and there is no ground truth available for checking area-level estimates. Design-based simulation from artificial populations can help with each of these issues, but only if the artificial populations (a) realistically represent the application at hand and (b) are not built using assumptions that could inherently favor one SAE model over another. In this paper, we borrow ideas from random hot deck, approximate Bayesian bootstrap (ABB), and k nearest neighbor (kNN) imputation methods, which are often used for multiple imputation of missing data. We propose a kNN-based approximation to ABB (KBAABB) for a different purpose: generating an artificial population when rich unit-level auxiliary data is available. We introduce diagnostic checks on the process of building the artificial population itself, and we demonstrate how to use such an artificial population for design-based simulation studies to compare and evaluate SAE models, using real data from the Forest Inventory and Analysis (FIA) program of the US Forest Service. We illustrate how such simulation studies may be disseminated and explored interactively through an online R Shiny application.

Ecologists are increasingly relying on national forest inventories to address a wide variety of issues. The ‘FIESTA' R package (Forest Inventory ESTimation and Analysis) is a tool that enables customized investigations using the extensive sample‐based inventory data collected across all lands in the US by the US Dept of Agriculture, Forest Service, Forest Inventory and Analysis (FIA) Program. To date, the complex nature of the FIA inventory constrains many users to conduct only limited analyses through existing tools with pre‐specified geographic boundaries, timeframes, and auxiliary data under a single statistical estimation process. Yet, the rapid evolution of available remotely sensed data and statistical methods present the opportunity to conduct spatial and temporal analyses of forest attributes that are much more relevant to many pressing ecological, environmental, economic, and social issues in the US, The ‘FIESTA' package was developed to augment the current set of available tools by providing a flexible platform that accommodates evolving technologies and leading‐edge estimation techniques. The package contains a collection of functions that can query FIA databases, summarize sample‐based inventory data, extract and aggregate auxiliary spatial data, and generate estimates with associated variances. The ‘FIESTA' R package is available on CRAN ( https://cran.r‐project.org/package=FIESTA ).

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.

This paper demonstrates a process for translating a database of forest measurements to interactive dashboards through which users can access statistically defensible estimates and analyses anywhere in the conterminous US. It taps the extensive Forest Inventory and Analysis (FIA) plot network along with national remotely sensed data layers to produce estimates using widely accepted model-assisted and small area estimation methodologies. It leverages a decade’s worth of statistical and computational research on FIA’s flexible estimation engine, FIESTA , and provides a vehicle through which scientists and analysts can share their own tools and analytical processes. This project illustrates one pathway to moving statistical research into operational inventory processes, and makes many model-assisted and small area estimators accessible to the FIA community. To demonstrate the process, continental United States (CONUS)-wide model-assisted and small area estimates are produced for ecosubsections, counties, and level 5 watersheds (HUC 10) and made publicly available through R Shiny dashboards. Target parameters include biomass, basal area, board foot volume, proportion of forest land, cubic foot volume, and live trees per acre. Estimators demonstrated here include: the simplest direct estimator (Horvitz–Thompson), model-assisted estimators (post-stratified, generalized regression estimator, and modified generalized regression estimators), and small area estimators (empirical best linear unbiased predictors and hierarchical Bayes both at the area- and unit-level). Auxiliary data considered in the model-assisted and small area estimators included maps of tree canopy, tree classification, and climatic variables. Estimates for small domain sets were generated nationally within a few hours. Exploring results across estimators and target variables revealed the progressive gains in precision using (in order of least gain to highest gain) Horvitz–Thompson, post-stratification, modified generalized regression estimators, generalized regression estimators, area-level small area models, and unit-level small area models. Substantive gains are realized by expanding model-assisted estimators beyond post-stratification, allowing FIA to continue to take advantage of design-based inference in many cases. Caution is warranted in the use of unit-level small area models due to model mis-specification. The dataset of estimates available through the dashboards provides the opportunity for others to compare estimators and explore precision expectations over specific domains and geographic regions. The dashboards also provide a forum for future development and analyses.

Small area estimation is a growing area of research for making inferences over geographic, demographic, or temporal domains smaller than those in which a particular survey data set was originally intended to be used. We aimed to review a body of literature to summarize the breadth and depth of small area estimation and related estimation strategies in forest inventory and management to-date, as well as the current state of terminology, methods, concerns, data sources, research findings, challenges, and opportunities for future work relevant to forestry and forest inventory research. Estimation methodologies explored include direct, indirect, and composite estimation within design-based and model-based inference bases. A variety of estimation methods in forestry have been applied to extensive multi-resource inventory systems like national forest inventories to increase the precision of estimates on small domains or subsets of the overall populations of interest. To avoid instability and large variances associated with small sample sizes when working with small area domains, forest inventory data are often supplemented with information from auxiliary sources, especially from remote sensing platforms and other geospatial, map-based products. Results from many studies show gains in precision compared to direct estimates based only on field inventory data. Gains in precision have been demonstrated in both project-level applications and national forest inventory systems. Potential gains are possible over varying geographic and temporal scales, with the degree of success in reducing variance also dependent on the types of auxiliary information, scale, strength of model relationships, and methodological alternatives, leaving considerable opportunity for future research and growth in small area applications for forest inventory.

The national forest inventory within the US has been experiencing a greater need to estimate forest attributes over smaller geographic areas than the inventory was originally designed for. Producing reliable estimates for these areas may require the use of estimation methods beyond post-stratification. Staying within the dominant design-based paradigm, this research explores how model-assisted estimation is impacted by leveraging data outside the area of interest. In particular, we compare the performance of the post-stratified estimator, the generalized regression estimator (GREG), and a modified GREG. Typically the assisting model of the modified GREG is fit over a sample comprising all of the areas of interest. Here we introduce a modified GREG, denoted as GREGORY, which gives the practitioner a high degree of flexibility in selecting the sample subset for constructing the assisting model. We use these estimators to produce county level estimates of the mean of four forest attributes in the Interior Western US. Comparing the relative efficiencies of the estimators, we find that the more complex estimators, GREG and GREGORY, generally improve the precision of the estimates, especially in regions with a high degree of forested land. When using all the data from a 10-year measurement, fitting the model over a larger region does not lead to efficiency gains. To explore the impact of smaller sample sizes, we conduct a simulation study and find that as the sampling intensity decreases, the GREGORY tends to produce more efficient estimates than the GREG, and its variance estimator exhibits less negative bias. The GREG and GREGORY can easily be computed and compared using a new R package, gregRy, available on CRAN.

The U.S. Forest Inventory and Analysis Program (FIA) collects inventory data on and computes estimates for many forest attributes to monitor the status and trends of the nation's forests. Increasingly, FIA needs to produce estimates in small geographic and temporal regions. In this application, we implement area level hierarchical Bayesian (HB) small area estimators of several forest attributes for ecosubsections in the Interior West of the US. We use a remotely-sensed auxiliary variable, percent tree canopy cover, to predict response variables derived from ground-collected data such as basal area, biomass, tree count, and volume. We implement four area level HB estimators that borrow strength across ecological provinces and sections and consider prior information on the between-area variation of the response variables. We compare the performance of these HB estimators to the area level empirical best linear unbiased prediction (EBLUP) estimator and to the industry-standard post-stratified (PS) direct estimator. Results suggest that when borrowing strength to areas which are believed to be homogeneous (such as the ecosection level) and a weakly informative prior distribution is placed on the between-area variation parameter, we can reduce variance substantially compared the analogous EBLUP estimator and the PS estimator. Explorations of bias introduced with the HB estimators through comparison with the PS estimator indicates little to no addition of bias. These results illustrate the applicability and benefit of performing small area estimation of forest attributes in a HB framework, as they allow for more precise inference at the ecosubsection level.

Globally, forests are a crucial natural resource, and their sound management is critical for human and ecosystem health and well-being. Efforts to manage forests depend upon reliable data on the status of and trends in forest resources. When these data come from well-designed natural resource monitoring (NRM) systems, decision makers can make science-informed decisions. National forest inventories (NFIs) are a cornerstone of NRM systems, but requires capacity and skills to implement. Efficiencies can be gained by incorporating auxiliary information derived from remote sensing (RS) into ground-based forest inventories. However, it can be difficult for countries embarking on NFI development to choose among the various RS integration options, and to develop a harmonized vision of how NFI and RS data can work together to meet monitoring needs. The NFI of the United States, which has been conducted by the USDA Forest Service's (USFS) Forest Inventory and Analysis (FIA) program for nearly a century, uses RS technology extensively. Here we review the history of the use of RS in FIA, beginning with general background on NFI, FIA, and sampling statistics, followed by a description of the evolution of RS technology usage, beginning with paper aerial photography and ending with present day applications and future directions. The goal of this review is to offer FIA's experience with NFI-RS integration as a case study for other countries wishing to improve the efficiency of their NFI programs.

Throughout the last three decades, north central Georgia has experienced significant loss in forest land and tree cover. This study revealed the temporal patterns and thematic transitions associated with this loss by augmenting traditional forest inventory data with remotely sensed observations. In the US, there is a network of field plots measured consistently through time from the USDA Forest Service’s Forest Inventory and Analysis (FIA) Program, serial photo-based observations collected through image-based change estimation (ICE) methodology, and historical Landsat-based observations collected through TimeSync. The objective here was to evaluate how these three data sources could be used to best estimate land use and land cover (LULC) change. Using data collected in north central Georgia, we compared agreement between the three data sets, assessed the ability of each to yield adequately precise and temporally coherent estimates of land class status as well as detect net and transitional change, and we evaluated the effectiveness of using remotely sensed data in an auxiliary capacity to improve detection of statistically significant changes. With the exception of land cover from FIA plots, agreement between paired data sets for land use and cover was nearly 85%, and estimates of land class proportion were not significantly different for overlapping time intervals. Only the long time series of TimeSync data revealed significant change when conducting analyses over five-year intervals and aggregated land categories. Using ICE and TimeSync data through a two-phase estimator improved precision in estimates but did not achieve temporal coherence. We also show analytically that using auxiliary remotely sensed data for post-stratification for binary responses must be based on maps that are extremely accurate in order to see gains in precision. We conclude that, in order to report LULC trends in north central Georgia with adequate precision and temporal coherence, we need data collected on all the FIA plots each year over a long time series and broadly collapsed LULC classes.

National monitoring of forestlands and the processes causing canopy cover loss, be they abrupt or gradual, partial or stand clearing, temporary (disturbance) or persisting (deforestation), are necessary at fine scales to inform management, science and policy. This study utilizes the Landsat archive and an ensemble of disturbance algorithms to produce maps attributing event type and timing to > 258 million ha of contiguous Unites States forested ecosystems (1986–2010). Nationally, 75.95 million forest ha (759,531 km2) experienced change, with 80.6% attributed to removals, 12.4% to wildfire, 4.7% to stress and 2.2% to conversion. Between regions, the relative amounts and rates of removals, wildfire, stress and conversion varied substantially. The removal class had 82.3% (0.01 S.E.) user’s and 72.2% (0.02 S.E.) producer’s accuracy. A survey of available national attribution datasets, from the data user’s perspective, of scale, relevant processes and ecological depth suggests knowledge gaps remain.