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Spatial uniformity of power and the altitudinal geometry of river networks
Author(s) -
Kapoor Vivek
Publication year - 1990
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/wr026i010p02303
Subject(s) - scaling , exponent , statistical physics , link (geometry) , mathematics , entropy (arrow of time) , channel (broadcasting) , geometry , computer science , physics , telecommunications , combinatorics , linguistics , philosophy , quantum mechanics
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.