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
Publisher
Wiley
Copyright
Copyright © 1998 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
D.O.I.
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

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off