Advertisement

Mathematical Geology

, Volume 26, Issue 1, pp 83–97 | Cite as

The angle measure technique: A new method for characterizing the complexity of geomorphic lines

  • Robert Andrle
Articles

Abstract

A new method for characterizing the complexity of geomorphic phenomena is presented. This method, termed the angle measure technique, involves measuring the angularity of a digitized line for a wide range of scales. In this manner, the technique is capable of delineating changes in the complexity of geomorphic lines with scale, from which the characteristic scale(s) of the lines can be identified. Unlike fractal analysis, values produced by the angle measure technique correspond to single scales. Therefore, no assumptions are made concerning the relationship between complexity and scale, and the technique can resolve variations in complexity over small ranges of scale. The technique is illustrated using both computer-generated curves and natural lines, including the trace of a river channel, and is compared to fractal analysis on a contour line crossing two lava flows.

Key words

geomorphometry scale fractal river lava flow 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andrle, R. 1992, Estimating fractal dimension with the divider method in geomorphology: Geomorphology, v. 5, p. 131–141.Google Scholar
  2. Andrle, R., and Abrahams, A. D. 1989, Fractal techniques and the surface roughness of talus slopes: Earth Surface Proc. Landforms, v. 14, p. 197–209.Google Scholar
  3. Burrough, P. A. 1985, Fakes, facsimiles and facts: Fractal models of geophysical phenomena,in S. Nash (Ed.), Science and Uncertainty: Sheridan House, Dobbs Ferry, New York, p. 219.Google Scholar
  4. Goodchild, M. F. and Mark, D. M. 1987, The fractal nature of geographic phenomena: Ann. Assoc. Am. Geogr., v. 77, n. 2, p. 265–278.Google Scholar
  5. Lam, N. S., and Quattrochi, D. A. 1992, On the issues of scale, resolution, and fractal analysis in the mapping sciences: Prof. Geogr., v. 44, n. 1, p. 88–98.Google Scholar
  6. Mandelbrot, B. B. 1967, How long is the coast of Britain? Statistical self-similarity and fractal dimension: Science, v. 156, p. 636–638.Google Scholar
  7. Mark, D. M. and Aronson, P. B. 1984, Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping: Math. Geol., v. 16, n. 7, p. 671–683.Google Scholar
  8. McMaster, R. B. 1986, A statistical analysis of mathematical measures for linear simplification: Am. Cartogr., v. 13, n. 2, p. 103–116.Google Scholar
  9. Orford, J. D., and Whalley, W. B. 1983, The use of fractal dimension to quantify the morphology of irregular-shaped particles: Sedimentology, v. 30, p. 655–668.Google Scholar

Copyright information

© International Association for Mathematical Geology 1994

Authors and Affiliations

  • Robert Andrle
    • 1
  1. 1.Department of Geography U-148University of ConnecticutStorrs

Personalised recommendations