- ∗ This study was carried out while the author was at the University of Exeter on study leave from the University of New South Wales. Financial assistance from the University of New South Wales and the generous provision of facilities by the Department of Geography, University of Exeter, are very much appreciated. H. Lorraine Oak assisted in the field, and Richard S. Jarvis and Michael J. Woldenberg offered helpful comments on an early draft of the manuscript.
- 1 R. E. Horton, “Erosional Development of Streams and their Drainage Basins; Hydrophysical Approach to Quantitative Morphology,”Bulletin of the Geological Society of America, Vol. 56 (1945), pp. 275 370.
- 2 Horton, op. cit., footnote 1, p. 290.
- 3 Deficiencies in Horton's maps were first noted by A. N. Strahler, “Hyposometric (Area-Altitude) Analysis of Erosional Topography,”Bulletin of the Geological Society of America, Vol. 63 (1952), pp. 1117 42, see p. 1136. Examples of investigators who failed to corroborate Horton's conclusion are Strahler, ibid., p. 1136; and D. R. Coates, Quantitative Geomorphology of Small Drainage Basins of Southern Indiana, Technical Report No. 10 (New York: Columbia University Department of Geology, 1958), p. 21. Examples of the application of the concept of steady state are provided by R. J. Chorley, Geomorphology and General Systems Theory, Professional Paper 500B (Washington, D.C.: U.S. Geological Survey, 1962); and J. J. Hack, “Interpretation of Erosional Topography in Humid Temperate Regions,”American Journal of Science, Vol. 258-A (1960), pp. 80 97.
- 4 Examples of studies which were inconsistent with the notion that relief has little or no effect on basin planimetry are S. A. Schumm, “Evolution of Drainage Systems and Slopes in Badlands at Perth Amboy, New Jersey,”Bulletin of the Geological Society of America, Vol. 67 (1956), pp. 597 646, see pp. 613–14, 617; M. A. Melton, “Geometric Properties of Mature Drainage Systems and their Representation in an E4 Phase Space,”Journal of Geology, Vol. 66 (1958a), pp. 35 56, see pp. 39, 47; and M. A. Melton, “Correlation Structure of Morphometric Properties of Drainage Systems and their Controlling Agents,”Journal of Geology, Vol. 66 (1958b), pp. 442 60, see pp. 450, 455–56. Examples of authors writing in the early 1970s who maintained that relief has little or no effect on basin planimetric properties are R. C. Flemal, “The Attack on the Davisian System of Geomorphology: A Synopsis,”Journal of Geological Education, Vol. 19 (1971), pp. 3 13, see p. 10; and E. D. Ongley, “Fluvial Morphometry on the Cobar Pediplain,”Annals, Association of American Geographers, Vol. 64 (1974), pp. 281 92, see pp. 287, 292. Recent evidence supporting the view that relief influences basin planimetry has been presented by A. D. Abrahams, “Factor Analysis of Drainage Basin Properties: Evidence for Stream Abstraction Accompanying the Degradation of Relief,”Water Resources Research, Vol. 8 (1972), pp. 624 33;A. D. Abrahams, “Evolutionary Changes in Link Lengths: Further Evidence for Stream Abstraction,”Transactions, Institute of British Geographers, Vol. 1 (1976), pp. 225 30;A. D. Abrahams, “The Factor of Relief in the Evolution of Channel Networks in Mature Drainage Basins,”American Journal of Science, Vol. 227 (1977), pp. 626 46; and D. N. Wilcock, “Relations between Planimetric and Hypsometric Variables in Third- and Fourth-Order Drainage Basins,”Bulletin, Geological Society of America, Vol. 86 (1975), pp. 47 50.
- 5 Schumm, op. cit., footnote 4.
- 6 J. S. Smart, “Quantitative Characterization of Channel Network Structure,”Water Resources Research, Vol. 8 (1972), pp. 1487 96, see p. 1495.
- 7 A channel link is a section of channel extending from either a source in the case of an exterior link or a fork in the case of an interior link to the next fork downstream. An exterior link that joins another exterior link at its downstream end is a source link, whereas one that joins an interior link is a tributary-source link. In large, topologically random channel networks, approximately 50 percent of the exterior links are tributary-source links. The figure of 55.14 percent tributary-source links was obtained from an examination of the topographic map of the Perth Amboy drainage basin and not from Table 1 in Schumm's paper which incorrectly shows the number of second-order streams as being 45.
- 8 See Abrahams (1977), op. cit., footnote 4, pp. 633–34.
- 9 Smart, op. cit., footnote 6, p. 1490.
- 10 Smart, op. cit., footnote 6, p. 1490.
- 11 Melton (1958a), op. cit., footnote 4, p. 36.
- 12 Smart, op. cit., footnote 6, p. 1491.
- 13 Melton (1958a), op. cit., footnote 4, pp. 39, 41, 47; and Melton (1958b), op. cit., footnote 4, p. 450.
- 14 The magnitude of a drainage basin is equal to the number of exterior links it contains.
- 15 Abrahams (1977), op. cit., footnote 4, pp. 630–32.
- 16 M. A. Poole and P. N. O'Farrell, “The Assumptions of the Linear Regression Model,”Transactions of the Institute of British Geographers, No. 52 (1971), pp. 145–58.
- 17 J. C. Maxwell, Quantitative Geomorphology of the San Dimas Experimental Forest, California, Technical Report No. 19 (New York: Columbia University Department of Geology, 1960), pp. 1–8, 37–41, 55–57; and M. E. Morisawa, Relation of Quantitative Geomorphology to Stream Flow in Representative Watersheds of the Appalachian Plateau Province, Technical Report No. 20 (New York: Columbia University Department of Geology, 1959), pp. 1–5.
- 18 Abrahams (1977), op. cit., footnote 4, p. 636.
- 19 M. G. Kendall and A. Stuart, The Advanced Theory of Statistics, third edition (London: Charles Griffin and Company, 1973), Vol. 2, pp. 393–94; D. M. Mark and M. Church, “On the Misuse of Regression in Earth Science,”Mathematical Geology, Vol. 9 (1977), pp. 63 75; and J. Durbin, “Errors in Variables,”Review of the International Statistical Institute, Vol. 22 (1954), pp. 23 32.
- 20 Horton, op. cit., footnote 1, p. 319.
- 21 The source area of an exterior channel link refers to the area that would contribute overland flow to the head of the link if overland flow occurred over the entire ground surface.
- 22 Schumm, op. cit., footnote 4, p. 614; M. E. Morisawa, “Quantitative Geomorphology of Some Watersheds in the Appalachian Plateau,”Bulletin, Geological Society of America, Vol. 73 (1962), pp. 1025 1046, see p. 1041; and R. L. Shreve, “Stream Lengths and Basin Areas in Topologically Random Channel Networks,”Journal of Geology, Vol. 77 (1969), pp. 397 414, see p. 413.
- 23 M. J. Kirkby and R. J. Chorley, “Throughflow, Overland Flow and Erosion,”Bulletin of the International Association of Scientific Hydrology, Vol. 12, No. 3 (1967), pp. 5 21, see pp. 6–8.
- 24 Kirkby and Chorley, op. cit., footnote 23; and R. P. Betson, “What is Watershed Runoff?”Journal of Geophysical Research, Vol. 69 (1964), pp. 1541 52.
- 25 T. Dunne and R. D. Black, “Partial Area Contributions to Storm Runoff in a Small New England Watershed,”Water Resources Research, Vol. 6 (1970), pp. 1296 311; and T. Dunne, T. R. Moore and C. H. Taylor, “Recognition and Prediction of Runoff-producing Zones in Humid Regions,”Hydrological Sciences Bulletin, Vol. 20 (1975), pp. 305 27.
- 26 Schumm, op. cit., footnote 4, pp. 600–01, 629–34.
- 27 W. R. Dearman, “Dartmoor: its Geological Setting,” in I. G. Simmons, ed., Dartmoor Essays (Exeter: The Devonshire Association, 1964), pp. 1–29.
- 28 R. S. Waters, “The Significance of Quaternary Events for the Landform of South-West England,” in K. J. Gregory and W. L. D. Ravenhill, eds., Exeter Essays in Geography (Exeter: University of Exeter Press, 1971), pp. 23–31, quotation from p. 28.
- 29 Rainfall over the Areas of the Devon and Cornwall River Boards, 1916–1950, Hydrological Memoranda No. 12 (London: Meteorological Office, 1963); and R. J. Chorley and M. A. Morgan, “Comparison of Morphometric Features, Unaka Mountains, Tennessee and North Carolina, and Dartmoor, England,”Bulletin, Geological Society of America, Vol. 73 (1962), pp. 17 34.
- 30 B. Clayden and D. J. R. Manley, “The Soils of the Dartmoor Granite,” in I. G. Simmons, ed., Dartmoor Essays (Exeter: The Devonshire Association, 1964), pp. 117–40.
- 31 S. D. Ward, A. D. Jones and M. Manton, “The Vegetation of Dartmoor,”Field Studies, Vol. 3 (1972), pp. 505 33.
- 32 A. Werritty, “Accuracy of Stream Link Lengths Derived from Maps,”Water Resources Research, Vol. 8 (1972), pp. 1255 64, quotation from p. 1263.
- 33 K. J. Gregory, “Drainage Network and Climate,” in E. Derbyshire, ed., Geomorphology and Climate (London: John Wiley and Sons, 1976), pp. 289–315.
- 34 For example, the correlation coefficient between the relief ratio and source-area slope (after log-transformation of both variables) is r=+0.875 for the 206 exterior basins at Perth Amboy. Source-area slope was determined by dividing the difference in altitude between the highest and lowest points in the source area by the straight-line distance (measured in the same units) from the channel head to the farthest point on the perimeter of the source area.
- 35 That the hypsometric integral is a crude index of ground slope distribution was suggested by Strahler, op. cit., footnote 3, pp. 1125–28.
- 36 The data for drainage density and the relief ratio for the eleven second-order basins at Perth Amboy are given by Schumm, op. cit., footnote 4, p. 616, Table 8. The hypsometric integral for each basin was derived by measuring the area under the appropriate hypsometric curve depicted on p. 615, Figure 18; Wilcock, op. cit., footnote 4, p. 49; and Coates, op. cit., footnote 3, pp. 51, 55, 58, 62.
- 37 For example, see M. J. Selby, “Aspects of the Geomorphology of the Graywacke Ranges Bordering the Lower and Middle Waikato Basins,”Earth Science Journal, Vol. 1 (1967), pp. 37 58, see pp. 43, 51; and R. G. Bailey and R. M. Rice, “Soil Slippage: An Indicator of Slope Instability on Chaparral Watersheds of Southern California,”Professional Geographer, Vol. 21 (1969), pp. 172 77, see p. 176.
- 38 Bailey and Rice, op. cit., footnote 37, p. 176; and L. Band, personal communication, 1979.
- 39 Abrahams (1977), op. cit., footnote 4, p. 645.
Annals of the Association of American Geographers
Volume 70, 1980 - Issue 1