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Geomorphic application of the hausdorff‐besicovich dimension
Author(s) -
Outcalt Samuel I.,
Melton Mark A.
Publication year - 1992
Publication title -
earth surface processes and landforms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.294
H-Index - 127
eISSN - 1096-9837
pISSN - 0197-9337
DOI - 10.1002/esp.3290170805
Subject(s) - terrain , geology , digital elevation model , smoothing , fractal dimension , erosion , fluvial , dimension (graph theory) , elevation (ballistics) , geometry , fractal , mathematics , remote sensing , geomorphology , statistics , geography , cartography , combinatorics , mathematical analysis , structural basin
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.