The variance quadtree algorithm: use for spatial sampling design

Spatial sampling schemes are mainly developed to determine sampling locations that can cover the variation of environmental properties in the area of interest. Here we proposed the variance quadtree algorithm for sampling in an area with prior information represented as ancillary or secondary environmental data, and the covariance structure of the ancillary variable is non-stationary. The algorithm is based on the idea of a quadtree decomposition, where an area is successively divided into strata so each stratum has more-or-less equal variation. An observation point is then placed inside each stratum. This scheme samples sparsely in relatively uniform areas and more intensively where variation is large. It samples in the feature space and also takes into consideration the spread in the geographic space. We describe the algorithm, its software implementation, and present some examples of applications.