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Horton Horton (1945)
Erostonal development of streams and their drainage basinsGeol. Soc. Amer. Bull., 56
Liao Liao, Scheidegger Scheidegger (1968)
A computer model for some branching type phenomena in hydrologyBull. Int. Ass. Sci. Hydrol., 13
Strahler Strahler (1957)
Quantitative analysis of watershed geomorphologyTrans. Amer. Geophys. Union, 38
Scheidegger Scheidegger (1967)
A stochastic model for drainage patterns into an intramontane trenchBull. Int. Ass. of Sci. Hydrol., 12
J. Smart, A. Surkan (1967)
The relation between mainstream length and area in drainage basinsWater Resources Research, 3
H. Schenck (1963)
Simulation of the evolution of drainage‐basin networks with a digital computerJournal of Geophysical Research, 68
A. Scheidegger (1967)
A STOCHASTIC MODEL FOR DRAINAGE PATTERNS INTO AN INTRAMONTANE TREINCHHydrological Sciences Journal-journal Des Sciences Hydrologiques, 12
M. Morisawa (1963)
Distribution of Stream-Flow Direction in Drainage PatternsThe Journal of Geology, 71
L. Milton (1966)
THE GEOMORPHIC IRRELEVANCE OF SOME DRAINAGE NET LAWSAustralian Geographical Studies, 4
A. Strahler (1957)
Quantitative analysis of watershed geomorphologyEos, Transactions American Geophysical Union, 38
Smart Smart, Surkan Surkan, Considine Considine (1967)
Digital simulation of channel networksInt. Ass. Sci. Hydrol. Publ., 75
R. Horton (1945)
EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGYGeological Society of America Bulletin, 56
R. Shreve (1967)
Infinite Topologically Random Channel NetworksThe Journal of Geology, 75
K. Liao, A. Scheidegger (1968)
A COMPUTER MODEL FOR SOME BRANCHING-TYPE PHENOMENA IN HYDROLOGYHydrological Sciences Journal-journal Des Sciences Hydrologiques, 13
R. Shreve (1966)
Statistical Law of Stream NumbersThe Journal of Geology, 74
A random walk model of a drainage network is generated on an underlying matrix by selecting at random the drainage direction out of the elementary areas. In a random roughness model, roughness heights of the elementary areas rather than drainage directions are assigned at random. The resulting topography of that model then uniquely determines the drainage pattern. An equivalence of the two models is suggested by the similarities, found in the mode of construction and by the equality of the probabilities of occurrence of some simple configurations. The random roughness model can yield values of primary probabilities, i.e., probabilities which can be used in the construction of a random walk model. The various types of drainage patterns are classified by the sets of primary probabilities which would generate them. Thus outcomes of homogeneous and isotropic matrices are classified as pure dendritic patterns. Outcomes of homogeneous matrices with probability sets derived from a sloping plane roughness model are classified as general dendritic (including parallel) patterns. Trellis, annular, and other patterns are considered as subgroups of the class of patterns generated on all other possible matrices.
Water Resources Research – Wiley
Published: Jun 1, 1969
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