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References (17)
-
A. Abrahams (1984)
Channel Networks: A Geomorphological PerspectiveWater Resources Research, 20
-
V. Gupta, Oscar Mesa (1988)
Runoff generation and hydrologic response via channel network geomorphology — Recent progress and open problemsJournal of Hydrology, 102
-
T. Móri, G. Székely (1985)
A note on the background of several Bonferroni–Galambos-type inequalitiesJournal of Applied Probability, 22
-
D. Gray (1961)
Interrelationships of watershed characteristicsJournal of Geophysical Research, 66
-
B. Troutman, M. Karlinger (1984)
On the expected width function for topologically random channel networksJournal of Applied Probability, 21
-
J. Hack (1957)
Studies of longitudinal stream profiles in Virginia and Maryland -
Jerry Mueller (1972)
Re-evaluation of the Relationship of Master Streams and Drainage BasinsGeological Society of America Bulletin, 83
-
W. Feller (1959)
An Introduction to Probability Theory and Its Applications -
M. Church, D. Mark (1980)
On size and scale in geomorphologyProgress in Physical Geography, 4
-
Werner Werner, Smart Smart (1973)
Some new methods of topological classification of channel networksGeogr. Anal., 5
-
V. Gupta, E. Waymire (1983)
On the formulation of an analytical approach to hydrologic response and similarity at the basin scaleJournal of Hydrology, 65
-
C. Werner (1972)
MODELS FOR HORTON'S LAW OF STREAM NUMBERS*Canadian Geographer, 16
-
R. Shreve (1967)
Infinite Topologically Random Channel NetworksThe Journal of Geology, 75
-
L. Jolley, A. Donkin, H. Piggott, D. Ferguson, C. Durell, R. Fawdry, R. Gibbs (1925)
Summation of Series.Mathematics of Computation, 16
-
J. Moon (1980)
On the expected diameter of random channel networksWater Resources Research, 16
-
R. Shreve (1974)
Variation of mainstream length with basin area in river networksWater Resources Research, 10
-
R. Shreve (1966)
Statistical Law of Stream NumbersThe Journal of Geology, 74
- Publisher
- Wiley
- Copyright
- Copyright © 1987 by the American Geophysical Union.
- ISSN
- 0043-1397
- eISSN
- 1944-7973
- DOI
- 10.1029/WR023i011p02119
- Publisher site
- See Article on Publisher Site
Abstract
Motivated by the empirical relationship between the main channel length and the basin area for river networks, a similar equation is derived analytically using the random model postulates and the additional assumption that link lengths have a common exponential probability distribution. Specifically, it is shown that in networks with large magnitude m, the main channel length l(m), and the magnitude are related by l(m) ∼ β(2π)½(2π)½, where β is mean link length. This result is utilized to explain another empirical relationship between the distance to the center of gravity lc(m) and the main channel length; lc(m) ∼ l(m)/2. The observed deviations of the random model prediction regarding the main channel length from empirical observations is used to discuss some important open problems.
Journal
Water Resources Research – Wiley
Published: Nov 1, 1987