Mapping the diversity of forest attributes: a design-based approach

Forest attributes such as volume or basal area are concentrated at tree locations and are absent elsewhere. It is, therefore, more meaningful to consider the amount of forest attributes at a prefixed spatial grain, within regular plots of prefixed size centered at the points of the study area. In this way, the diversity of attributes within plots also can be considered and quantified by suitable indexes, giving rise to a diversity surface defined on the continuum of points constituting the area. We analyze the estimation of diversity surfaces when a sample of plots is selected by a probabilistic sampling scheme and diversity within nonsampled plots is estimated using an inverse distance weighting interpolator. We discuss the design-based asymptotic properties of the resulting maps when the survey area remains fixed and the number of sampled points increases. Because diversity surfaces share suitable mathematical properties, if the schemes adopted to select sample points ensure an even coverage of the study areas avoiding large portions of non-sampled zones, it can be proven that the estimated maps approach the true maps.