Spatial scale problems and geostatistical solutions: A review

The concept of spatial scale is fundamental to geography, as are the problems of integrating data obtained at different scales. The availability of GIS has provided an appropriate environment to re-scale data prior to subsequent integration, but few tools with which to implement the re-scaling. This sparsity of appropriate tools arises primarily because the nature of the spatial variation of interest is often poorly understood and, specifically, the patterns of spatial dependence and error are unknown. Spatial dependence can be represented and modelled using geostatistical approaches providing a basis for the subsequent re-sealing of spatial data (e.g., via spatial interpolation). Geostatistical techniques can also be used to model the effects of re-scaling data through the geostatistical operation of regularization. Regularization provides a means by which to re-scale the statistics and functions that describe the data rather than the data themselves. These topics are reviewed in this paper and the importance of the spatial scale problems that remain is emphasized.