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.
Water Resources Research – Wiley
Published: Mar 1, 1989
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