A simulation approach for accuracy assessment of two-phase post-stratified estimation in large-area LiDAR biomass surveys

Auxiliary information provided by airborne laser scanners (ALS) is expected to increase the accuracy of biomass estimation in large-scale forest surveys. Because acquisition of “wall-to-wall” ALS data over large areas is not economically feasible, a systematic sampling approach using ALS as a strip sampling tool was used to supplement a conventional field-based inventory in a large-scale biomass survey in Hedmark County (HC), Norway. However, the complexities of these surveys render prohibitive the analytical determination of the properties of the resulting estimators and of the estimators of their sampling variances. To overcome the problem, the statistical properties of the estimators were empirically investigated in this paper using simulated sampling from an artificial population. Through this approach, estimators with desirable properties can be identified and used for inference in real applications. By combining biomass estimates from Norwegian National Forest Inventory plots in HC, ALS measurements and Landsat 5 TM imagery, an artificial population at the scale of HC was created. Using this artificial population as “ground-truth”, we demonstrate how simulated sampling can be used for assessing the statistical properties of regression estimators and of their variance estimators under two-phase post-stratified systematic sampling (SYS) and simple random sampling without replacement (SRSwoR) designs, considering design- and model-dependent inferential frameworks. The results were assessed using a purely ground-based systematic design with a Horvitz–Thompson (HT) estimator as benchmark. The real overall precision of the ALS-aided systematic survey was nearly five times overestimated when using the design-based variance estimators developed for SRSwoR, while under model-dependent inference the overestimation of the real standard errors was around 40%. Compared to ground-based inventory, the estimated standard errors of the systematic ALS survey doubled while in reality the standard errors were 55% lower. Using successive differences variance estimators greatly improved the precision of the systematic ALS-aided survey and produced valid 95% confidence intervals under the design-based inference. The most satisfactory results for the ALS-aided survey in terms of analytical variances occurred under design-based inference with successive difference variance estimator, closely followed by the model-dependent estimators. Using simulations, the cost efficiency of the ground based and ALS-aided surveys was assessed by evaluating accuracy against inventory cost for various sampling intensities. The results indicated that the ALS-aided surveys can be a cost-efficient alternative to traditional field inventories.