Geomorphic application of the hausdorff-besicovich dimension
Abstract
An algorithm was developed and tested to produce a useful description of natural terrain texture. First, orthogonal calculation of the variance spectrum of an elevation matrix of a square terrain sample was made using a variation of standard methods to eliminate directional effects. Second, the slope of the log-log spectrum-wavelength diagram was used to calculate the Hausdorff-Besicovitch (H-B) dimension of the terrain sample according to Voss' formula.The algorithm was tested on samples from a 60 km × 60 km digital terrain model from Death Valley, California, and Las Vegas, Nevada, U.S.A. Three 12 km × 12 km samples showed systematic variations in both the spectral signature and H-B dimension. One of the terrain samples was manipulated by smoothing and simulated erosion to test the sensitivity of the dimension. A sloping artificial surface was subjected to several cycles of synthetic fluvial erosion with dimension increasing with erosion duration (age). A smoothed 60 km × 60 km terrain model was subjected to extended cycles of synthetic erosion which produced a Pali-type landscape typical of the Island of Kauai.
- Publication:
-
Earth Surface Processes and Landforms
- Pub Date:
- December 1992
- DOI:
- 10.1002/esp.3290170805
- Bibcode:
- 1992ESPL...17..775O