Analysis of area level and unit level models for small area estimation in forest inventories assisted with LiDAR auxiliary information

Abstract

Forest inventories require estimates and measures of uncertainty for subpopulations such as management units. These units often times hold a small sample size, so they should be regarded as small areas. When auxiliary information is available, different small area estimation methods have been proposed to obtain reliable estimates for small areas. Unit level empirical best linear unbiased predictors (EBLUP) based on plot or grid unit level models have been studied more thoroughly than area level EBLUPs, where the modelling occurs at the management unit scale. Area level EBLUPs do not require a precise plot positioning and allow the use of variable radius plots, thus reducing fieldwork costs. However, their performance has not been examined thoroughly. We compared unit level and area level EBLUPs, using LiDAR auxiliary information collected for inventorying 98,104 ha coastal coniferous forest. Unit level models were consistently more accurate than area level EBLUPs, and area level EBLUPs were consistently more accurate than field estimates except for large management units that held a large sample. For stand density, volume, basal area, quadratic mean diameter, mean height and Lorey’s height, root mean squared errors (rmses) of estimates obtained using area level EBLUPs were, on average, 1.43, 2.83, 2.09, 1.40, 1.32 and 1.64 times larger than those based on unit level estimates, respectively. Similarly, direct field estimates had rmses that were, on average, 1.37, 1.45, 1.17, 1.17, 1.26, and 1.38 times larger than rmses of area level EBLUPs. Therefore, area level models can lead to substantial gains in accuracy compared to direct estimates, and unit level models lead to very important gains in accuracy compared to area level models, potentially justifying the additional costs of obtaining accurate field plot coordinates.