The Role of Spatial Scale in Geomorphic Systems

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Abstract
Geomorphic systems are characterized by numerous, complex interrelationships between system components, and by processes and controls which may operate over different spatial scales. Factors operating at any given spatial scale can be viewed as an abstracted subset of all relationships operating at all scales. The theory that relationships which operate over spatial scales an order of magnitude different are effectively independent of each other is formally stated in terms of abstracted systems. An example is given to illustrate the use of spatial statistics to determine what constitutes a significant spatial scale difference in controls over hydraulic geometry of a desert wash.