Access the full text.
Sign up today, get DeepDyve free for 14 days.
A. Strahler (1952)
Hypsometric (area-altitude) analysis of erosional topography.Geological Society of America Bulletin, 63
Woldenberg Woldenberg (1969)
“Spatial Order in Fluvial Systems: Horton's Law Derived from Mixed Hexagonal Hierarchies of Drainage Basin Areas,”Bull. Geol. Soc. Amer., 80
S. Schumm (1956)
EVOLUTION OF DRAINAGE SYSTEMS AND SLOPES IN BADLANDS AT PERTH AMBOY, NEW JERSEYGeological Society of America Bulletin, 67
Morisawa Morisawa (1962)
“Quantitative Geomorphology of Some Watersheds in the Appalachian Plateau,”Bull. Geol. Soc. Amer., 73
Kenneth Smith (1958)
EROSIONAL PROCESSES AND LANDFORMS IN BADLANDS NATIONAL MONUMENT, SOUTH DAKOTAGeological Society of America Bulletin, 69
A. Scheidegger (1966)
Stochastic branching processes and the law of stream ordersWater Resources Research, 2
Schumm Schumm (1956)
“Evolution of Drainage Systems and Slopes in Badlands at Perth Amboy, New Jersey,”Bull. Geol. Soc. Amer., 67
C. Werner (1969)
Networks of Minimum LengthCanadian Geographer, 13
A. Strahler (1957)
Quantitative analysis of watershed geomorphologyEos, Transactions American Geophysical Union, 38
Strahler Strahler (1957)
“Quantitative Analysis of Watershed Geomorphology,”Amer. Geophys. Union, Trans., 38
M. Melton (1959)
A Derivation of Strahler's Channel-Ordering SystemThe Journal of Geology, 67
Werner Werner (1969b)
“Topological Randomness in Line Patterns,”Proc. Assoc. Amer. Geogr., 1
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
A. Scheidegger (1968)
Horton's Law of Stream NumbersWater Resources Research, 4
M. Woldenberg (1969)
Spatial Order in Fluvial Systems: Horton's Laws Derived from Mixed Hexagonal Hierarchies of Drainage Basin AreasGeological Society of America Bulletin, 80
J. Smart (1968)
MEAN STREAM NUMBERS AND BRANCHING RATIOS FOR TOPOLOGICALLY RANDOM CHANNEL NETWORKSHydrological Sciences Journal-journal Des Sciences Hydrologiques, 13
Horton Horton (1945)
“Erosional Development of Streams and Their Drainage Basins: Hydro‐physical Approach to Quantitative Morphology,”Bull. Geol. Soc. Amer., 56
Smith Smith (1958)
“Erosional Processes and Landforms in Badlands National Monument, South Dakota,”Bull. Geol. Soc. Amer., 69
K. Liao, A. Scheidegger (1968)
A COMPUTER MODEL FOR SOME BRANCHING-TYPE PHENOMENA IN HYDROLOGYHydrological Sciences Journal-journal Des Sciences Hydrologiques, 13
M. Morisawa (1962)
Quantitative Geomorphology of Some Watersheds in the Appalachian PlateauGeological Society of America Bulletin, 73
Strahler Strahler (1952)
“Hypsometric (Area‐Altitude) Analysis of Erosional Topography,”Bull. Geol. Soc. Amer., 63
R. Shreve (1966)
Statistical Law of Stream NumbersThe Journal of Geology, 74
ACCORDING to Hortonâs law of stream numbers, the bifurcation ratio in a drainage network is fairly constant with an average value between 3.5 and 4, so that the stream numbers tend to form a geometric progression. This paper investigates drainage networks whose structure is controlled by chance only. The mathematical analysis shows that the expected stream numbers also approach a geometric progression, and that the corresponding bifurcation ratios approximate the value 3.6 18. INTRODUCTION A scientific investigation of real world phenomena usually concentrates on selected properties and disregards all others. An example is the sequential pattern of merging rivers in a drainage network. The apparent hierarchy of their mergers can be studied disregarding all other components (topography, hydrology, morphometry). What remains is the information regarding the number of tributaries the system contains, and how they are interconnected, i.e., the topological structure of the network. This structure is the subject of Hortonâs famous law. To understand its content, a few network parameters have to be defined. Since the original concept of stream order introduced by Horton (1945, p. 281) still contains a geometrical element (angles), the refined version of Strahler (1952, p. 1120) will be used here. The stream
The Canadian Geographer/Le Geographe Canadien – Wiley
Published: Mar 1, 1970
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.