Updating annual state- and county-level forest inventory estimates with data assimilation and FIA data

The United Nations Framework Convention on Climate Change requires annual estimates for forestry and ecological indicators to monitor the change in forest resources, the sustainability of forest management, and the emission and sink of forest carbon. It is particularly important to update estimates of forestland area in a timely fashion and at flexible geographical scales, not only for its value in monitoring biological diversity at the ecosystem scale, but also because of its close association with other indicators such as forest biomass and carbon. However, in the US, the Forest Survey Handbook advises that the sampling error should not exceed 3% per 404686 ha (one million acres) of forestland area, a demanding standard barely met by pooling the Forest Inventory and Analysis (FIA) panel data measured in an inventory cycle of 5-10 years. Consequently, this study aims to propose and illustrate an updating procedure using data assimilation that integrates a design-based estimator with a model-based mixed estimator for updating annual estimates at two population levels, the stateand county-levels. The three states in the USA, Minnesota (MN), Georgia (GA) and California (CA), representing the Northern, the Southern and the Pacific Northwest FIA programs, constitute the study areas. FIA data collected were based on a 5-year inventory cycle for MN (2006-2010) and GA (2005-2009), and a 10-year cycle for CA (2001-2010). The total number of sample plots was 17764 for MN, 6323 for GA, and 16740 for CA. Distinguishing features attribute to this procedure include: (1) unbiasedness: the integration of design-based estimates into the mixed estimator introduces a favorable property - unbiasedness, which could be the property national forest inventories concern the most; (2) efficiency: considerable improvements in estimation precision greater than 55%, achieving sampling errors as small as those relying on using 5-10 years pooled FIA data; (3) time: compared with the temporal trends reflected by design-based estimates, the updated trends were of much smoother trend lines and narrower confidence intervals that would better depict temporal changes for a population at flexible spatial scales; (4) space: this procedure is scale-invariant, meaning its efficiency is not affected by an inventory employing either a largeor small-area estimation, which was demonstrated at the two population levels; and (5) generalizability: this procedure is unbiased and efficient, 100% compatible with the FIA database which is readily available to the public, and thus suitable for various official reporting instruments.

Automated summary

This study proposes and demonstrates an updating procedure using data assimilation that integrates design-based and model-based estimators to update annual estimates at state and county levels. The method achieves unbiasedness, efficiency, smooth trend lines, and flexibility in spatial scales, and is compatible with the readily available FIA database for official reporting.