Premium
Fractal relation of mainstream length to catchment area in river networks
Author(s) -
Rosso Renzo,
Bacchi Baldassare,
La Barbera Paolo
Publication year - 1991
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/90wr02404
Subject(s) - fractal , fractal dimension , scaling , drainage basin , mathematics , hydrology (agriculture) , mandelbrot set , fractal analysis , drainage network , geometry , geology , mathematical analysis , geography , cartography , geotechnical engineering
Mandelbrot's (1982) hypothesis that river length is fractal has been recently substantiated by Hjelmfelt (1988) using eight rivers in Missouri. The fractal dimension of river length, d , is derived here from the Horton's laws of network composition. This results in a simple function of stream length and stream area ratios, that is, d = max (1, 2 log R L /log R A ). Three case studies are reported showing this estimate to be coherent with measurements of d obtained from map analysis. The scaling properties of the network as a whole are also investigated, showing the fractal dimension of river network, D , to depend upon bifurcation and stream area ratios according to D = min (2, 2 log R B /log R A ). These results provide a linkage between quantitative analysis of drainage network composition and scaling properties of river networks.