Premium
River network fractal geometry and its computer simulation
Author(s) -
Nikora Vladimir I.,
Sapozhnikov Victor B.
Publication year - 1993
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 - 10.1029/93wr00966
Subject(s) - fractal , hurst exponent , fractal dimension , scaling , drainage basin , geometry , hydrology (agriculture) , basis (linear algebra) , mathematics , exponent , dimension (graph theory) , statistical physics , statistics , geology , geography , physics , combinatorics , mathematical analysis , cartography , geotechnical engineering , linguistics , philosophy
The hierarchical ordinal and statistical models of river networks are proposed. Their investigation has been carried out on the basis of river networks computer simulation as well as on empirical data analysis. The simulated river networks display self‐similar behavior on small scales (the fractal dimension D ≈ 1.52 and Hurst's exponent H = 1.0) and self‐affine behavior on large scales (the lacunary dimension D G ≈ 1.71, H ≈ 0.58). Similar behavior is also qualitatively characteristic for natural river networks (for catchment areas from 142 to 63,700 km 2 we obtained D G ≈ 1.87 and H ≈ 0.73). Thus in both cases one finds a region of scales with self‐affine behavior ( H < 1) and with D G < 2. Proceeding from fractal properties of the river networks, the theoretical basis of scaling relationships L ∼ A β and ℒ ∼ A ε , widely used in hydrology, are given ( L , ℒ and A denote the main river length, the total length of the river network, and catchment area, respectively); β = 1/(1+ H ) and ε= D G /2.