Simplifying Small Area Estimation With rFIA: A Demonstration of Tools and Techniques

Abstract

The United States (US) Department of Agriculture 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—estimation techniques that support inference on small domains—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 survey design used by the FIA program. Herein, we present the potential of rFIA, an open-source R package designed to increase the accessibility of FIA data, to simplify the application of a broad suite of SAE methods to FIA data. We demonstrate this potential via two case studies: (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 multi-level model. In both cases, we show the application of SAE techniques offers considerable improvements in precision over FIA's traditional, post-stratified estimators. Finally, we offer a discussion of the potential role that rFIA and other open-source tools might play in accelerating the adoption of SAE techniques among users of FIA data.

A Note on Simultaneous Confidence Intervals for Direct, Indirect and Synthetic Estimators

“…However, they rely on other data requirements, complex assumptions and methods, and, in the case of model misspecification, adverse effects on further inference can become substantial [4]. In contrast, design-based estimators are quite simple, work with weaker assumptions, do not necessarily need auxiliary information and can be assumed nearly design-unbiased [5,6]. The lack of auxiliary information-especially on the unit level-is a major problem in many cases and countries.…”

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

“…In addition to the temporally indifferent method, rFIA can produce estimates for individual annual panels and implements multiple forms of a moving average estimator, providing flexibility in the temporal specificity of estimates. InStanke et al (2022), rFIA was recently used to develop spatial Fay-Herriot models of forest carbon stocks for counties across the conterminous United States. rFIA-related material can be found in the dynamic content, here: https:// www.fia.fs.usda.gov/library/sampling/index.php.GEEGoogle Earth Engine's (GEE) cloud-based archive and programming interface eliminate image acquisition and processing tasks that previously took up most of the budget for large land cover mapping projects.…”