A three-phase sampling strategy for large-scale multiresource forest inventories

This article considers a two-phase estimation for the areal extent of K land categories partitioning a study region and a three-phase estimation for the biomass of W forest categories out of the K. In the first phase, a sample of N points is selected according to the unaligned systematic sampling. In the second phase, the selected points are partitioned into L strata on the basis of aerial photos. Then, a total sample of n < N points is selected by stratified sampling and the selected points are visited on the ground and correctly classified into one of K categories. The information achieved in the second phase is sufficient for obtaining an unbiased estimator of the areal extent vector together with a conservative estimator of its variance-covariance matrix. As to the estimation of the biomass of the W forest categories, in the third phase the second-phase sample is further partitioned into substrata on the basis of ground information. Finally, a total sample of m < n points is selected by stratified sampling. Then a plot of adequate radius centered at each point is considered and the biomass is recorded within. An unbiased estimator of the biomass vector is derived together with a conservative estimator of its variance-covariance matrix. The proposed strategy also makes it possible to obtain the calibrated estimator of the areal extent vector as well as estimators for the sums or ratios of the areal extents and biomasses. The application of the strategy in the Italian National Forest Inventory is considered.