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A Typology of Spatial and Temporal Scale Relations

A simple typology of relations between any two geographical scales is established by qualitatively comparing their respective grains and extents. This typology is applied to spatial, temporal, and spatiotemporal scales. It describes seven relations between any two scales in either space or time. These basic relations yield a set of 169 qualitatively different spatiotemporal scale relations, a subset of which is portrayed diagrammatically. If it is possible to transform processes or patterns from one scale in the relation to the other, up to four scaling methods may need to be simultaneously applied, depending on the relation. Scaling methods might be classified as forms of grain generalization, grain decomposition, extent extrapolation, or extent selection. This typology may also provide a framework for investigations of dependencies between scales, as well as a reference scheme for observations of scale nonstationarity. The possibility is offered that any relation that forms a nonintersecting hierarchy in either space or time is a relation between essentially independent scales. However, the use of this typology is contingent on a number of factors, and it is offered as a tool, rather than a solution, for problems of scale.