Two-phase sampling strategies for design-based mapping of continuous spatial populations in environmental surveys

The estimation of a surface throughout a continuum of points in a study area is addressed by means of two-phase sampling strategies. To this aim, a family of two-phase inverse distance weighting interpolators is introduced, and their design-based asymptotic properties are derived when the surface re-mains fixed and the number of sample points approaches infinity. In particu-lar, conditions ensuring asymptotic unbiasedness and consistency are derived and are proven to hold for some of the most widely applied environmental sampling schemes. Furthermore, a computationally simple mean squared error estimator is proposed. Finally, a simulation study is performed to assess the theoretical results. The proposed strategy is adopted to provide the map of basal area in a forested region of Casentino Valley (Central Italy).