Propagation of plot location uncertainty through unit-level small area estimation in operational forest inventory

Contemporary sources of remotely sensed data (e.g. Sentinel-2, LiDAR) invite reconsideration of forest cruising methodology through model-based estimation such as small area estimation (SAE). The unit-level nested error regression model is attractive because it exploits fine-grained auxiliary data to model within-stand variation, but it depends on accurate co-registration between field plots and the auxiliary surface. We consider the common operational case in which recorded plot locations are uncertain and no surveyed truth exists. Rather than estimating error relative to an unknown true location, we frame the problem as uncertainty propagation, investigating how the inability to precisely locate a plot contributes to total uncertainty in model outputs. Using a Monte Carlo framework applied to fixed-radius plots in Oregon, we resample auxiliary covariates at perturbed locations and trace the resulting distribution of estimated coefficients, variance components, and stand-level empirical best linear unbiased predictions (EBLUP). We give particular attention to a pathway specific to SAE. Location error preferentially degrades covariates that carry fine-scale forest signal, inflating within-stand residual variance and driving the shrinkage weight down. Each stand-level estimate is thus pulled away from its own field data and toward a synthetic model built on those same degraded covariates—a behavior with no analogue in the ordinary regression models examined previously. Despite this internal sensitivity, propagation to the stand-level estimate is largely buffered, with uncertainty dominated by sample size.