A Separable Bootstrap Variance Estimation Algorithm for Hierarchical Model-Based Inference of Forest Aboveground Biomass Using Data From NASA's GEDI and Landsat Missions

The hierarchical model-based (HMB) statistical method is currently applied in connection with NASA's Global Ecosystem Dynamics Investigation (GEDI) mission for assessing forest aboveground biomass (AGB) in areas lacking a sufficiently large number of GEDI footprints for employing hybrid inference. This study focuses on variance estimation using a bootstrap procedure that separates the computations into parts, thus considerably reducing the computational time required and making bootstrapping a viable option in this context. The procedure we propose uses a theoretical decomposition of the HMB variance into two parts. Through this decomposition, each variance component can be estimated separately and simultaneously. For demonstrating the proposed procedure, we applied a square-root-transformed ordinary least squares (OLS) model, and parametric bootstrapping, in the first modeling step of HMB. In the second step, we applied a random forest model and pairwise bootstrapping. Monte Carlo simulations showed that the proposed variance estimator is approximately unbiased. The study was performed on an artificial copula-generated population that mimics forest conditions in Oregon, USA, using a dataset comprising AGB, GEDI, and Landsat variables.