Journal of the International Association for Mathematical Geology
, Volume 16, Issue 7, pp 671683
First online:
Scaledependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping
 David M. MarkAffiliated withDepartment of Geography, State University of New York at Buffalo
 , Peter B. AronsonAffiliated withEnvironmental Systems Research Institute
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Fractional Brownian surfaces have been widely discussed as an appropriate model for the statistical behavior of topographic surfaces. The fractals model proposes that topographic surfaces are statistically selfsimilar, and that a single parameter, the fractal dimension, applies at all scales. This paper presents the results of empirical examinations of 17 topographic samples. Only one of these samples shows the statistical behavior predicted by the fractals model; however, in 15 of the 17 samples, the surfaces' variograms could be adequately described by ranges of scales having constant fractal dimension, separated by distinct scale breaks. For scale ranges between adjacent breaks, surface behavior should be that predicted by the fractals model; the breaks represent characteristic horizontal scales, at which surface behavior changes substantially. These scale breaks are especially important for cartographic representations and digital elevation models, since they represent scales at which there is a distinct change in the relation between sampling interval and the associated error.
Key words
Fractals variograms topography stochastic models Title
 Scaledependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping
 Journal

Journal of the International Association for Mathematical Geology
Volume 16, Issue 7 , pp 671683
 Cover Date
 198410
 DOI
 10.1007/BF01033029
 Print ISSN
 00205958
 Online ISSN
 15738868
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Fractals
 variograms
 topography
 stochastic models
 Industry Sectors
 Authors

 David M. Mark ^{(1)}
 Peter B. Aronson ^{(2)}
 Author Affiliations

 1. Department of Geography, State University of New York at Buffalo, 14260, Buffalo, New York, USA
 2. Environmental Systems Research Institute, 380 New York Street, 92373, Redlands, California, USA