# Statistical self‐similarity in river networks parameterized by elevation

Statistical self‐similarity in river networks parameterized by elevation A stochastic theory is developed to describe spatial variability in link heights in topologically random river networks. Both the systematic and random spatial variability in link heights are reflected in a scaling invariance property of their probability distributions with drainage area serving as a scale parameter. Tests of theoretical predictions against empirical observations show that link height distributions exhibit scaling invariance under magnification or reduction of the scale parameter. This invariance property is referred to as statistical “self‐similarity.” It provides a fundamental theoretical basis for some existing empirical relationships on gradients and other river geometries in channel networks and points to important research directions in river basin hydrology. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

# Statistical self‐similarity in river networks parameterized by elevation

Water Resources Research, Volume 25 (3) – Mar 1, 1989
14 pages

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Publisher
Wiley
Copyright
Copyright © 1989 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
DOI
10.1029/WR025i003p00463
Publisher site
See Article on Publisher Site

### Abstract

A stochastic theory is developed to describe spatial variability in link heights in topologically random river networks. Both the systematic and random spatial variability in link heights are reflected in a scaling invariance property of their probability distributions with drainage area serving as a scale parameter. Tests of theoretical predictions against empirical observations show that link height distributions exhibit scaling invariance under magnification or reduction of the scale parameter. This invariance property is referred to as statistical “self‐similarity.” It provides a fundamental theoretical basis for some existing empirical relationships on gradients and other river geometries in channel networks and points to important research directions in river basin hydrology.

### Journal

Water Resources ResearchWiley

Published: Mar 1, 1989

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