Multiple scales in river basin morphology

Abstract

Existing data reveal that the steepness S of many river basins with mountainous headwaters, defined as the ratio of total relief to total length of a basin, is related to the logarithm of basin size. The relief of these same river basins is observed to be non-linearly related to basin steepness, with maximal values of relief occurring iu basins for which the value of S is about 0.03 or, equivalently, in basins in which die average slope is about 2 degrees, These systematic relationships between size, relief, and steepness of some basins, which span nine orders of magnitude of area, are interpreted in terms of an intermediate limit process bounded by well separated spatial scales. The lower-limiting scale corresponds to a threshold between channel formation and significant mass wastage, and the upper-limiting scale corresponds to the size of the largest landmass, If the observed relationships between basin size, relief, and steepness indeed reflect a limit process, then they are independent of the details of the physics contributing to landscape development and instead result from the constraints imposed by the bounding, spatial scales. Exceptions to the limiting relationships explored here are readily noted, however, and are interpreted to reflect regional geological and temporal controls. The delineation of the importance of multiple scales provides a potentially powerful basis for the examination of morphological relationships in river basins.