Fractal Sinuosity of Stream Channels

Snow, R. Scott

doi:10.1007/978-3-0348-6389-6_6

Cited by 30 publications

(37 citation statements)

References 8 publications

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“…Their conclusions must be tempered by the lack of fit apparent in some land surfaces. Further studies which link the theoretical work of Newman and Turcotte (1990) and Lovejoy and Schertzer (1985) with the more practical work reported in this paper and by Skoda (1987), Snow (1989) and others is required in order to provide a more complete basis for understanding the fractal nature of the land surface and the processes which shape that surface ( c j Thornes, 1990). …”

Section: Discussionmentioning

confidence: 90%

The fractal properties of topography: A comparison of methods

Klinkenberg

Goodchild

1992

Earth Surf Processes Landf

176

132

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In this study the fractal characteristics of fifty-five digital elevation models from seven different United States physiographic provinces are determined using seven methods. The self-similar fractal model tested in this analysis is found to provide a very good fit for some landscapes, but an imperfect fit for others. Thus, outright rejection of this model does not appear to be warranted, but neither does a blind application.The three implementations of the dividers methods considered in this study consistently produce lower dimensions than those produced by the other methods, and those dimensions consistently do not vary much between surfaces. Although the dimensions produced by the cell counting method (applied to the digital elevation model itself) display consistent intersurface variation, the dimensions are generally lower than those produced by the variogram-based methods. Among the variogram-based methods, the dimensions of the quarter-sections of the digital elevation models are generally greater than the dimensions obtained from the other variogram-based methods. The dimensions produced by the variogram method which considered the surfaces on a directional basis are very similar, on average, to the dimensions produced by the entire-surface variogram.

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Section: Discussionmentioning

confidence: 90%

The fractal properties of topography: A comparison of methods

Klinkenberg

Goodchild

1992

Earth Surf Processes Landf

176

132

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“…Snow (1989) applied fractal analysis to stream channels and related the fractal dimension to sinuosity. Sinuosity is the ratio of real channel length to some general river course length.…”

Section: Channels (Caves and Streams)mentioning

confidence: 99%

Fractal Surfaces: Measurement and Applications in the Earth Sciences

1993

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Earth scientists have measured fractal dimensions of surfaces by different techniques, including the divider, box, triangle, slit-island, power spectral, variogram and distribution methods. We review these seven measurement techniques, finding that fractal dimensions may vary systematically with measurement method. We discuss possible reasons for these differences, and point to common problems shared by all of the methods, including the remainder problem, curve-fitting, orientation of the measurement plane, size and direction of the sample. Fractal measurements have been applied to many problems in the earth sciences, at a wide range of spatial scales. These include map data of topography; fault traces and fracture networks; fracture surfaces of natural rocks, both in the field and at laboratory scales; metal surfaces; porous aggregate geometry; flow and transport through heterogeneous systems; and various microscopic surface phenomena associated with adsorption, aggregation, erosion and chemical dissolution. We review these applications and discuss the usefulness and limitations of fractal analysis to these types of problems in the earth sciences.

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“…These approaches often have little relationship with the actual drainage. As such, these methods can only investigate the simple geometric configurations (Snow, 1989) and poorly describe natural features of complex river networks (Mandelbrot, 1977;Schuller et al, 2001;Hassan and Kurths, 2002;Guillermo et al, 2004). Several studies have recognized the importance of the irregular components in river networks (e.g.…”

Section: Introductionmentioning

confidence: 99%