SPATIAL UNIFORMITY OF POWER AND THE ALTITUDINAL GEOMETRY OF RIVER NETWORKS

It is hypothesized that river networks adjust their geometries in the altitudinal space to achieve a state of maximum spatial uniformity of power. A model developed to study the spatial variability of power shows that the notion of uniformity is linked to both minimum variance and maximum information theoretic entropy. Recent descriptions of link heights and streamflows (Gupta and Waymire, 1989, 1990) are applied to formulate the power of a link in a network. The hypothesis relates the scaling exponent of link heights to the scaling exponents of instantaneous flows. It also predicts the superiority of the self‐similar model over alternative models of link heights in channel networks. Copyright 1990 by the American Geophysical Union.