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A. Strahler (1952)
Hypsometric (area-altitude) analysis of erosional topography.Geological Society of America Bulletin, 63
S. Schumm (1956)
EVOLUTION OF DRAINAGE SYSTEMS AND SLOPES IN BADLANDS AT PERTH AMBOY, NEW JERSEYGeological Society of America Bulletin, 67
Schumm Schumm (1956)
Evolution of drainage systems and slopes in badlands at Perth Amboy, New JerseyBull. Geol. Soc. Am., 67
Strahler Strahler (1952)
Hypsometric analysis of erosional topographyBull. Geol. Soc. Am., 63
H. Schenck (1963)
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K. Bowden, J. Wallis (1964)
EFFECT OF STREAM-ORDERING TECHNIQUE ON HORTON'S LAWS OF DRAINAGE COMPOSITIONGeological Society of America Bulletin, 75
A. Broscoe (1959)
QUANTITATIVE ANALYSIS OF LONGITUDINAL STREAM PROFILES OF SMALL WATERSHEDS
L. Leopold, John Miller (1956)
Ephemeral streams; hydraulic factors and their relation to the drainage net
Horton Horton (1945)
Erosional development of streams and their drainage basins: Hydrophysical approach to quantitative geomorphologyBull. Geol. Soc. Am., 56
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
M. Melton (1957)
analysis of the relations among elements of climate, surface properties, and geomorphology
M. Morisawa (1962)
Quantitative Geomorphology of Some Watersheds in the Appalachian PlateauGeological Society of America Bulletin, 73
R. Shreve (1966)
Statistical Law of Stream NumbersThe Journal of Geology, 74
Morisawa Morisawa (1962)
Quantitative geomorphology of some watersheds in the Appalachian PlateauBull. Geol. Soc. Am., 73
Two basic assumptions are employed in this treatment of the statistics of stream lengths: (1) All topologically distinct networks with a given number of sources are equally likely (after Shreve). (2) Lengths of interior links in a given network are independent random variables drawn from the same population. The mathematical development leads to an approximate expression for L¯ω that contains no adjustable parameters and that depends only on the stream numbers and the mean link length. This expression gives somewhat better agreement with data on actual stream systems than does Horton's law of stream lengths; other advantages over Horton's law are cited. Quantitatively, our procedure appears to account for about 65% of the variance in mean stream length data for third‐ and fourth‐order basins. If exact values of the link numbers are introduced into the calculation, the unexplained variance is reduced to about 15%. For a complete statistical description of stream lengths, it is necessary to know the distribution of interior link lengths. Results of computer simulation studies suggest that this distribution is negative exponential. Data taken on two small watersheds (140 links) show reasonable agreement with this hypothesis.
Water Resources Research – Wiley
Published: Oct 1, 1968
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