Influence of Valley Type on the Scaling Properties of River Planforms (original) (raw)

1996, Water Resources Research

Scaling properties of 44 individual river planforms from the Cascade and Olympic Mountains of Washington State were defined using the divider method. Analysis of the standardized residuals for least squares linear regression of Richardson plots reveals systematic deviations from simple self-similarity that correlate with the geomorphological context defined by valley type. A single fractal dimension describes rivers flowing through bedrock valleys. Those flowing in inherited glacial valleys exhibit two distinct fractal dimensions, with a larger fractal dimension at small scales. Rivers flowing in alluvial valleys are also described by two fractal dimensions, but with a larger dimension at large scales. We further find that the wavelength of the largest meander defines an upper limit to the scaling domain characterized by fractal geometry. These results relate scaling properties of river planforms to the geomorphological processes governing valley floor morphology. GoodchiM, 1980; Mark and Aronson, 1984; GoodchiM and Mark, 1987; Klinkenberg, 1992], few studies relate D to processes governing these forms [Woronow, 1981; Phillips, 1993]. Indeed, the relatively narrow range of fractal dimensions describing a variety of natural patterns suggests the futility of searching for ties with physical processes [Turcotte, 1992]. Some geomorphic features, however, exhibit scale-dependent variations in D, motivating examination of physical causes of such variations [Church and Mark, 1980; GoodchiM, 1980; Dutton, 1981; Lam and Quattrochi, 1992; Beauvais et al., 1994]. Efforts to evaluate potential connections between geomorphological process and scaling properties of river planforms are complicated by the many ways to calculate D. Some workers calculate the fractal dimension of river planforms from the relation between mainstream length and basin area [Hack, 1957]: L -= I3A • (1) where oe is the length of the river planform,/3 is a constant of proportionality, andA is the drainage area. Mandelbrot [1977], and later Church and Mark [1980] and Hjelmfelt [1988], interpreted the exponent a as being half the fractal dimension of the river planform (i.e., a -D/2). The relatively small range of a for most drainage basins (see data compiled by Montgomery and Dietrich [1992]) implies that D defined in this manner is equal to approximately 1.2 for rivers in general [Mandelbrot, 1983; Tarboron et al., 1988; Turcotte , 1992]. This implies that the D derived from length-area relations is not useful for examining differences among rivers. Furthermore, Robert and showed the unreliability of using a to infer the fractal dimension of rivers due to the effect of cartographic generalization.