Use of the fractal dimension in characterization of terrestrial surfaces

Abstract

This thesis investigates the feasibility of using certain descriptive parameters that have been determined to be independent of scale over certain ranges to define the texture and roughness of terrestrial surfaces. The parameters employ the concept of a "fractal dimension" as described by Benoit Mandelbrot and utilized by many others in various cartographic applications. Relationships involving the resolved surface area and volume of digital elevation models were utilized in evaluating the fractal dimension. Three digital elevation models (DEM) were examined with respect to area and volume. Changes in scale and grid data resolution were simulated by decreasing the grid sampling interval of the DEMs in a systematic manner. The three DEMs examined were of a homogeneous character and were sampled on a 3 arc second latitude and longitude grid interval. The DEMs represented three distinct terrain types, subjectively described as smooth, rolling, and rough. The results of the characterization provided distinct terrain roughness differentiation among the DEMs examined. The determined values of fractal dimension were, however, considerably lower than had been predicted in the literature examined. The low fractal dimension values were attributed to the course resolution of the DEM data sets.