Small Area Estimation of Postfire Tree Density Using Continuous Forest Inventory Data

Abstract

Wildfire activity in the western United States is expanding and many western forests are struggling to regenerate postfire. Accurate estimates of forest regeneration following wildfire are critical for postfire forest management planning and monitoring forest dynamics. National or regional forest inventory programs can provide vegetation data for direct spatiotemporal domain estimation of postfire tree density, but samples within domains of administrative utility may be small (or empty). Indirect domain expansion estimators, which borrow extra-domain sample data to increase precision of domain estimates, offer a possible alternative. This research evaluates domain sample sizes and direct estimates in domains spanning large geographic extents and ranging from 1 to 10 years in temporal scope. In aggregate, domain sample sizes prove too small and standard errors of direct estimates too high. We subsequently compare two indirect estimators—one generated by averaging over observations that are proximate in space, the other by averaging over observations that are proximate in time—on the basis of estimated standard error. We also present a new estimator of the mean squared error (MSE) of indirect domain estimators which accounts for covariance between direct and indirect domain estimates. Borrowing sample data from within the geographic extents of our domains, but from an expanded set of measurement years, proves to be the superior strategy for augmenting domain sample sizes to reduce domain standard errors in this application. However, MSE estimates prove too frequently negative and highly variable for operational utility in this context, even when averaged over multiple proximate domains.