Premium
A physical explanation of the cumulative area distribution curve
Author(s) -
Perera Hemantha,
Willgoose Garry
Publication year - 1998
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 - 10.1029/98wr00259
Subject(s) - exponent , scaling , erosion , catchment area , drainage basin , boundary (topology) , channel (broadcasting) , hydrology (agriculture) , fluvial , geology , streams , scale (ratio) , flow (mathematics) , geometry , mathematics , structural basin , geography , geomorphology , mathematical analysis , computer science , geotechnical engineering , cartography , computer network , philosophy , linguistics
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.