A Multi-Metric Approach to Fay-Herriot Small Area Estimation of Forests

Forest managers are tasked with decisions regarding silvicultural practices that require detailed information about the environments they serve. Managing complex structures like forests demands consideration of many interrelated variables characterizing the overall condition of a forest. Success in these management initiatives includes not only maximum production from the timber assets, but also proof that these operations accord with modern sustainable practices. Small area estimates obtained from a National Forest Inventory (NFI) dataset lack necessary statistical certainty due to a relatively small sample of forest plots. These inventory datasets are spatially sparse, yet attribute-rich. Given these properties, research efforts in this field focus on improving the quality of estimates by balancing the sample data with spatially abundant, but often attribute-sparse, auxiliary data. Small area estimation is a family of methods that have been implemented to improve estimation of forest inventories. This thesis considers the multivariate nature of forests by estimating volume, basal area, mortality, and biodiversity using the Fay- Herriot small area estimation framework. Estimates are obtained using univariate models borrowing strength from one of the following remotely sensed datasets: 1) a new National Agriculture Imagery Program (NAIP) Canopy Height Model (CHM), 2) National Land Cover Database Tree Canopy Cover (TCC), or 3) US Forest Service’s Landscape Change Monitoring System (LCMS). Optimal estimates were selected via performance criteria, yielding estimates of net cubic volume and basal area using NAIP data, net cubic mortality volume using LCMS, and species diversity using TCC. These county-level estimates were combined to provide a multi- metric representation of the forests, revealing new patterns across space within the forests of Virginia. Mortality proved to be a sparse enough occurrence that estimate certainties exhibited over shrinkage, warranting extra care when interpreting these estimates. Volume estimates showed strong trends with Basal Area and Biodiversity estimates. This multi-metric approach introduces a new way to examine variance reduction in forest inventories. Reducing variance in a multi-dimensional estimate provides greater complexity and greater explainability. This thesis provides a case study of some pitfalls regarding variable selection and highlights the potential for more explainability of forest conditions using inventory estimates.