Statistical moments of the hypsometric curve and its density function

  • John M. Harlin


A method, applicable to multivariate designs, describing the form of the percentage hypsometric curve is developed in this research. Emphasis is placed on the quantitative aspects of curve form, rather than on average slopes, inflection points, or hypsometric integrals. A question of uniqueness arises when values, like the integral, are used as landform surrogates in process-response models involving drainage basins. It is demonstrated that the hypsometric curve has a much greater potential for quantitative landform analysis than can be realized through employment of the integral value alone. Unlike the integral, the functional form of the curve is unique to a particular area, depicting, among other things, evolutionary changes in the form of drainage basins. The technique involves treating the “decumulation” of the hypsometric curve in its mirror image as a cumulative distribution function. Statistical moments of the curve, and expectations of (x)for the curve's density function are derived, projecting a vector of curve-form attributes.

Key words

geomorphology hypsometric analysis statistical moments 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allen, R., Jr., 1975, Polynomial regression analysis of beach profiles: Prof. Geographer, v. 27, no. 2, p. 189–193.Google Scholar
  2. Carson, M. A., and Kirkby, M. J., 1972, Hillslope form and process: University Press, Cambridge, 475 p.Google Scholar
  3. Chorley, R. J., and Kennedy, B. A., 1971, Physical geography: A systems approach: Prentice-Hall, Englewood Cliffs, 375 p.Google Scholar
  4. Coates, D. R., 1956, Quantitative geomorphology of small drainage basins of southern Indiana: Office of Naval Research, 389-042, Technical Report no. 10.Google Scholar
  5. Evans, I. S., 1972, General geomorphometry, derivatives of altitude, and descriptive statistics:in Spatial analysis in geomorphology, p. 17–90.Google Scholar
  6. Langbein, W. B.,et al., 1947, Topographic characteristics of drainage basins: U.S. Geological Survey, Water Supply Paper 968-C, p. 125–157.Google Scholar
  7. Miller, V. C., 1953, A quantitative geomorphic study of drainage basin characteristics in the Clinch Mountain Area, Virginia, and Tennessee: Office of Naval Research, 389-042, Technical Report no. 3.Google Scholar
  8. Scheidegger, A. E., 1961, Theoretical geomorphology: Prentice-Hall, Englewood Cliffs, 333 p.Google Scholar
  9. Schumm, S. A., 1956, Evolution of drainage systems and slopes in badlands at Perth Amboy, New Jersey: Bull. Geolog. Soc. Amer., v. 67, p. 597–646.Google Scholar
  10. Strahler, A. N., 1952, Hypsometric (area-altitude) analysis of erosional topography: Bull. Geolog. Soc. Amer., v. 63, p. 1117–1141.Google Scholar
  11. Tanner, W. F., 1959, Examples of departure from the gaussian in geomorphic analysis: Amer. Jour. Science, v. 257, p. 458–460.Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • John M. Harlin
    • 1
  1. 1.Department of GeographyUniversity of Maryland (Baltimore County)BaltimoreUSA

Personalised recommendations