Review and Synthesis of Estimation Strategies to Meet Small Area Needs in Forest Inventory

Abstract

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.

Composite estimation to combine spatially overlapping environmental monitoring surveys

“…Synthetic estimates are acquired by applying statistical relationships developed between auxiliary variables (e.g., biophysical attributes, airborne and satellite data products) and observations in the subset and in some portion or all of the remaining population. The estimator balances the unbiasedness of direct and the precision of synthetic estimates to provide improved estimates for the subset [19]. The forest inventory community over the past 20 years has researched SAE techniques to acquire more reliable estimates of forest attributes at smaller spatial scales (county level, national forests, foreststand level) than those provided by national forest inventories, such as the USDA Forest Inventory and Analysis (FIA) program, and by state forest inventories [17][18][19].…”

“…The estimator balances the unbiasedness of direct and the precision of synthetic estimates to provide improved estimates for the subset [19]. The forest inventory community over the past 20 years has researched SAE techniques to acquire more reliable estimates of forest attributes at smaller spatial scales (county level, national forests, foreststand level) than those provided by national forest inventories, such as the USDA Forest Inventory and Analysis (FIA) program, and by state forest inventories [17][18][19]. The nationwide sampling intensity of one FIA plot per 2,438 ha on multiple ownerships provides insufficient data at within-state scales for reliable estimates but at the same time provides a large regional sample for SAE applications.…”

“…Incorporating composite estimation into an existing monitoring program can be challenging and requires statistical expertise. There can be many statistical considerations in developing composite estimation applications, such as discerning appropriate methods to correct for under coverage and obtaining MSE weightings when necessary, and selecting between modelassisted (design-based) and model-based (not design-based) methods in SAE applications (e.g., [19]). An extensive technical literature details the statistical issues and options.…”

“…Composite estimator applications have used spatially overlapping local and regional surveys to improve estimates of the smaller scale area [7] and at both scales [8], and even to composite temporally repeated observations of a survey to improve estimates of different time periods [9][10][11]. Composite estimators are commonly used in what is formally called small area estimation to bolster subpopulation estimates with low sample sizes and precisions by combining them with more precise synthetic (often modeled) estimates derived from a larger portion of the surveyed population [12][13][14][15][16][17][18][19] or a similar population [20]. Composite estimation with complementary data offers environmental monitoring efforts an analytical approach to improve assessments of resource conditions without costly modification of an ongoing monitoring design, such as increasing the number of sampling sites.…”

Sampling and Estimation Documentation for the Enhanced Forest Inventory and Analysis Program

“…Synthetic estimators are being implemented through an Amazon Web Services cloud computing environment using Esri's Raster Analytics platform as described in the BIGMAP project in the Computing Resources section. Guldin (2021) and Dettmann et al (2022) provide recent reviews of small area estimation in forest inventory applications, and investigations into improving precision in FIA estimates over small domains continues to rise. For example, in the Pacific Northwest, Bell et al (2022)…”