Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A physical explanation of the cumulative area distribution curve

A physical explanation of the cumulative area distribution curve A physical explanation for the behavior of the cumulative area distribution (CAD) based on the Tokunaga channel network model is given. The CAD is divided into three regions. The first region, for small areas, is dependent on hillslope flow accumulation patterns and represents the catchment average of the hillslope flow accumulation in the diffusive erosion‐dominated areas, upstream reaches, of the catchment. The second region represents that portion of the catchment dominated by fluvial erosion. This region is well described by a log‐log linear power law, which results from the scaling properties of the channel network. The scale exponent, ϕ, is highly sensitive to a parameter of the Tokunaga stream numbering scheme. The exponent ϕ converges to −0.5 for higher order Tokunaga networks for parameters consistent with topological random networks. Small networks have lower values of ϕ, which asymptotic converges to ϕ=−0.5 as the catchment scale increase. The third region reflects the lowest reaches of the channel network, the scale of the catchment, and is a boundary effect. An explicit analytical solution to the scaling properties in the second region is derived on the basis of the Tokunaga network model. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

A physical explanation of the cumulative area distribution curve

Loading next page...
 
/lp/wiley/a-physical-explanation-of-the-cumulative-area-distribution-curve-4ZJLHcvWKt

References (30)

Publisher
Wiley
Copyright
Copyright © 1998 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
DOI
10.1029/98WR00259
Publisher site
See Article on Publisher Site

Abstract

A physical explanation for the behavior of the cumulative area distribution (CAD) based on the Tokunaga channel network model is given. The CAD is divided into three regions. The first region, for small areas, is dependent on hillslope flow accumulation patterns and represents the catchment average of the hillslope flow accumulation in the diffusive erosion‐dominated areas, upstream reaches, of the catchment. The second region represents that portion of the catchment dominated by fluvial erosion. This region is well described by a log‐log linear power law, which results from the scaling properties of the channel network. The scale exponent, ϕ, is highly sensitive to a parameter of the Tokunaga stream numbering scheme. The exponent ϕ converges to −0.5 for higher order Tokunaga networks for parameters consistent with topological random networks. Small networks have lower values of ϕ, which asymptotic converges to ϕ=−0.5 as the catchment scale increase. The third region reflects the lowest reaches of the channel network, the scale of the catchment, and is a boundary effect. An explicit analytical solution to the scaling properties in the second region is derived on the basis of the Tokunaga network model.

Journal

Water Resources ResearchWiley

Published: May 1, 1998

There are no references for this article.