Hybrid three-phase estimators for large-area forest inventory using ground plots, airborne lidar, and space lidar

Previous studies have utilized ground plots, airborne lidar scanning or profiling data, and space lidar profiling data to estimate biomass across large regions, but these studies have failed to take into account the variance components associated with multiple models because the proper variance equations were not available. Previous large-domain studies estimated the variances of their biomass density estimates as the sum of the GLAS sampling variability plus the model variability associated with the models that predict airborne lidar estimates of biomass density (Y) as a function of satellite lidar measurements (X). This approach ignores the additional variability associated with the predictive models used to estimate ground biomass density as a function of airborne lidar measurements. This paper addresses that shortcoming. Analytic variance expressions are provided that include sampling variability and model variability in situations where multiple models are employed to generate estimates of biomass. As an example, the forest biomass of the continental US is estimated, by forest stratum within state, using a space lidar system (ICESat/GLAS). An airborne laser system (ALS) is used as an intermediary to tie the GLAS measurements of forest height to a small subset of US Forest Service (USFS) ground plots by flying the ALS over the ground plots and, independently, over individual GLAS footprints. Two sets of models are employed to relate satellite measurements to the ground plots. The first set of equations relates USFS ground plot estimates of total aboveground dry biomass density (Y1) to spatially coincident ALS forest canopy measurements (X1). The second set of models predicts those ALS canopy height measurements (X1) used in the first set of models to GLAS waveform measurements (X2). The following important conclusions are noted. (1) The variability associated with estimation of the plot-ALS model coefficients is significant and should be included in the overall estimate of biomass density variance. In the continental US, the total variance of mean forest biomass density (98.06t/ha) increases by a factor of 3.6×, i.e., from 1.91 to 6.94t²/ha², when plot-ALS model variance is included in the calculation of total variance. (2) State-level results are more variable, but on average, the percent model variance at the state level, i.e., (model variance/total variance)∗100, increases from 16% to 59% when plot-ALS model variance is included. (3) The overall model variance is driven in large part by the number of plots overflown by the ALS and the number of GLAS pulses overflown by the ALS. Given a choice of improving precision by either increasing the number of plot-ALS observations or increasing ALS-GLAS observations, there is no obvious benefit to selecting one over the other. However, typically the number of ground plots overflown is the limiting factor. (4) If heteroskedasticity is evident in either the ground-air or air-satellite models, it can modeled using weighted regression techniques and incorporated into these model variance formulas in straightforward fashion. The results are unambiguous; in a hybrid three-phase sampling framework, both the ground-air and air-satellite model variance components are significant and should be taken into account.