Remote sensing-assisted data assimilation and simultaneous inference for forest inventory

Data assimilation (DA) has a broad category of mathematical procedures for updating and calibrating existing predictions or parameter estimates using new observations. Typical DA procedures such as the Kalman filter require that the observations of a variable of interest used in a forecast of this variable to be collected just prior to the updating procedure and that they continue to be collected over time, a requirement that is not always practical for forest inventory problems. Distinct from the Kalman filter, the best linear unbiased predictor (BLUP) circumvents this time constraint, because it can calibrate the predicted values of a variable of interest using observations from other variables correlated with this variable of interest. Remote sensing played a major role in this study by providing the latter observations. The objective of this study was threefold: (1) to propose and illustrate a DA calibration procedure that incorporates simultaneous predictions and BLUP to improve prediction accuracy; (2) to expand this procedure in the framework of model-based inference; and (3) to compare the inferential properties before and after DA calibration for multiple scenarios. Four major conclusions are relevant. First, the prediction accuracies for all variables of interest were consistently increased by 10%–74% after implementing the DA procedure. Second, the DA procedure supported simultaneous inference, and the precision of the simultaneously estimated population means for the variables of interest were increased by 55%–76% after implementing this procedure. Third, the parametric bootstrap procedures used to estimate the inferential precisions for this complex estimation problem were effective and converged rapidly. In addition, this DA calibration procedure is universally applicable for DA calibrations using other data sources such as airborne or terrestrial laser scanning and spectral data, given that cross-model correlations exist. Overall, the proposed procedure demonstrated considerable potential for better serving forest inventory with respect to both simultaneous inference and inferential precision.