Applications of the random model of drainage basin composition

Smart, J. S.; Werner, Christian

doi:10.1002/esp.3290010304

Cited by 32 publications

(27 citation statements)

References 25 publications

(21 reference statements)

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“…This prediction is supported by the results of various investigations, particularly that of Werner and Smart (1976). The first step in our analysis of channel network composition, then, is an attempt to gain some insight into the topologic properties of the networks.…”

Section: Topologic Analysismentioning

confidence: 68%

“…Unfortunately, the data which he presented in its behalf were scant and not very convincing, and there has been little if any later work which supported it. Early work by Strahler and his students led Strahler (1952Strahler ( , p. 11361957, p. 914), to conclude that the bifurcation ratio was essentially independent of environment except in regions that have certain types of strong geological controls. Chorley (1957), in a morphometric study of three areas with widely different reliefs and drainage densities, found no significant differences in the bifurcation, length, or area ratios.…”

Section: Composition Implies the Numbers And Lengths Of Streams And Tmentioning

confidence: 97%

“…Finally, the model could be completed and its value greatly enhanced by the addition of a fourth postulate concerning channel slopes and their relation to the planimetric properties of basins; see, for example, a recent contribution by Flint (1976). Smart and Werner (1976) demonstrated the effectiveness of the random model in estimating the values of geomorphic variables and in explaining and predicting geomorphic relationships. The use of link-associated variables and link data vectors was mentioned but not emphasized.…”

Section: The Random Modelmentioning

confidence: 99%

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The analysis of drainage network composition

Smart

1978

Earth Surf. Process.

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SUMMARYThe Horton method of analyzing drainage network composition is reviewed, with the conclusion that it has not been very effective either in improving understanding or in developing useful methods of characterizing drainage basins. New methods which are based on the link rather than the Horton (or Strahler) stream are described. A number of detailed examples of the application of these new methods to the topologic and geometric properties of networks are provided. The results are compared with the predictions of the random model.Data used in the analysis were obtained from 1 :24,OOO U.S.G.S. topographic maps of eastern Kentucky. Thirty drainage basins were selected and their channel networks were outlined first by the contour-crenulation (CC) method and then by another, more objective, method (SC) in which stream sources were identified by a quantitative slope criterion. The CC and SC samples comprise about 8,700 and 1,700 links, respectively.The three most important results of the analysis are: (1) the channel networks are slightly but significantly more elongated than predicted by the random model, (2) there are fewer second magnitude links than predicted, and (3) the length distribution for interior links depends upon the kind of link (interior or exterior) joined downstream. These features are found in both CC and SC networks.

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Section: Topologic Analysismentioning

confidence: 68%

Section: Composition Implies the Numbers And Lengths Of Streams And Tmentioning

confidence: 97%

Section: The Random Modelmentioning

confidence: 99%

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The analysis of drainage network composition

Smart

1978

Earth Surf. Process.

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“…III Data structure Since Shreve (1966; identified the link as the fundamental network element it has become apparent that all the information extracted from a drainage network should be referenced to individual link locations. Some recent studies have reported very large link data sets: over 8700 link lengths by Smart and Werner (1976), and over ig6oo link lengths and azimuths by Jarvis (ig75). It is appropriate to devise some general data structure model, so that future link data sets may be both comparable between studies, and also, as far as possible, amenable to re-use when further new parameters are defined.…”

Section: Terminology and Conceptsmentioning

confidence: 99%

Drainage network analysis

Jarvis

1977

Progress in Physical Geography: Earth and Environment

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The investigation of drainage network systems would seem to address the essential focus of a geographical approach to landform analysis. Drainage networks identify organized transport systems in space, and also operate as dynamic space-filling systems in temporal landscape evolution. The drainage network defines a drainage basin, and thus provides both a framework for integrating spatial elements of the land surface, and also a structure for dissecting sampling space into functional areas. These functional areas are units amenable to statistical treatment as sample replicates, and serve as spatial modules for physical systems analysis of fluvial landscapes.The stream ordering approach to drainage networks, proposed by Horton ( i g45) and Strahler (1952), has generated many applications. Stream ordering has been described by Bowden and Wallis (1964, 767) as '... the touchstone by which drainage net characteristics could be related to each other and to hydrologic and erosional processes'. Haggett and Chorley ( ig6g, 302) applaud the '... success of the Horton-Strahler approach in the recognition of fundamental regularities in drainage systems ...' However, since 1966 there has been a marked change in the nature of drainage network models, with the appearance of a radically different approach in the work of Shreve (1966; 1967; i g6g), Smart ( i g6ga) and Scheidegger ( i g67a) .In the io years that have elapsed since Shreve's presentation of a random topology model for drainage network composition there has been a steady succession of fresh insights and new theory generation. The methodological stagnation of the first two decades following Horton (1945), when study after study simply related morphologic parameters of the drainage basin to stream order, has given way to a series of newly developed models, incorporating many new parameters of geomorphologic significance. Virtually all of the acclaimed successes of the Horton-Strahler stream ordering approach have been explained by random model theory, including the distribution of bifurcation ratios (Shreve, 1966), the distribution of stream length ratios (Shreve, 1967;1969;Smart, 1968), the o.6 power relation between mainstream length and basin area (Shreve, 1974;Smart, 1973), andMelton's (1958) discovery of the approximate proportionality of Strahler stream frequency and the square of drainage density (Shreve, 1967). Further applications of the ran-

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“…It is possible to argue that it is a theory, since work by the drainage network topology school (cf. Smart and Werner, 1976) appears to show the persistence of random patterns which are largely uninfluenced by variations in lithology, history or present-day intensity of processes.…”

mentioning

confidence: 93%

A question of scale?

Kennedy¹

1977

Progress in Physical Geography: Earth and Environment

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Applications of the random model of drainage basin composition

Cited by 32 publications

References 25 publications

The analysis of drainage network composition

The analysis of drainage network composition

Drainage network analysis

A question of scale?

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