Usually forest inventories are performed by adopting two phases sampling strategies. In the first phase, the study region is partitioned into spatial subset of equal size and a point is randomly and independently selected in each subset. Then, these points are classified as forest and non-forest by means of satellite or aerial information and, in a second phase, a sample of points is selected, generally by means of a stratified design. Finally, forest attributes are recorded within plots centered at any second-phase points. Descriptive summaries such as forest cover, total tree volume and basal area can be unbiasedly estimated and conservative estimation of the design-based variances can be obtained. Commonly, spatially explicit estimation for constructing forest maps for geographically depicting resource location can be performed by adopting model-depending predictors, such as kriging. Nevertheless, recently Fattorini et al. (Biometrika, 2018) proposed a design-based spatial prediction that, under some conditions, ensure design-based consistency of the resulting maps. The use of systematic grid sampling or tessellation stratified sampling and the nature of the data collected by plots are sufficient to achieve the consistency of the maps that would be obtained if plots were centred in all the points selected in the first phase.

The aim of this work is to extend the consistency results from one- to two-phase sampling, giving sufficient conditions that must be shared by the scheme adopted to select points in the second phase for achieving consistency of the maps. In order to check the mapping performance, some simulation studies are performed from artificial and real populations and a real case study in a forested area of Italy is reported. Simulations results highlight that the most common schemes adopted in the second phase satisfy the consistency condition.

References:

Fattorini, L., Marcheselli, M., Pisani, C., Pratelli, L. (2018) Designed-based maps for continuous spatial populations. Biometrika, 105, 2: 419-429.