Fat fractal scaling of drainage networks from a random spatial network model

Water Resources Research
By:  and 



An alternative quantification of the scaling properties of river channel networks is explored using a spatial network model. Whereas scaling descriptions of drainage networks previously have been presented using a fractal analysis primarily of the channel lengths, we illustrate the scaling of the surface area of the channels defining the network pattern with an exponent which is independent of the fractal dimension but not of the fractal nature of the network. The methodology presented is a fat fractal analysis in which the drainage basin minus the channel area is considered the fat fractal. Random channel networks within a fixed basin area are generated on grids of different scales. The sample channel networks generated by the model have a common outlet of fixed width and a rule of upstream channel narrowing specified by a diameter branching exponent using hydraulic and geomorphologic principles. Scaling exponents are computed for each sample network on a given grid size and are regressed against network magnitude. Results indicate that the size of the exponents are related to magnitude of the networks and generally decrease as network magnitude increases. Cases showing differences in scaling exponents with like magnitudes suggest a direction of future work regarding other topologic basin characteristics as potential explanatory variables.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Fat fractal scaling of drainage networks from a random spatial network model
Series title Water Resources Research
DOI 10.1029/92WR00805
Volume 28
Issue 7
Year Published 1992
Language English
Publisher American Geophysical Union
Description 7 p.
First page 1975
Last page 1981