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On Hack's Law
Author(s) -
Rigon Riccardo,
RodriguezIturbe Ignacio,
Maritan Amos,
Giacometti Achille,
Tarboton David G.,
Rinaldo Andrea
Publication year - 1996
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 - 10.1029/96wr02397
Subject(s) - fractal , power law , law , scaling , scaling law , character (mathematics) , interpretation (philosophy) , exponent , affine transformation , mathematics , physics , statistical physics , geometry , computer science , mathematical analysis , statistics , political science , philosophy , linguistics , programming language
Hack's law is reviewed, emphasizing its implications for the elongation of river basins as well as its connections with their fractal characteristics. The relation between Hack's law and the internal structure of river basins is investigated experimentally through digital elevation models. It is found that Hack's exponent, elongation, and some relevant fractal characters are closely related. The self‐affine character of basin boundaries is shown to be connected to the power law decay of the probability of total contributing areas at any link and to Hack's law. An explanation for Hack's law is derived from scaling arguments. From the results we suggest that a statistical framework referring to the scaling invariance of the entire basin structure should be used in the interpretation of Hack's law.