The effects of scale on fractal dimension of topography: a case study from Sudbury, Ontario, Canada

摘要

An issue of concern when analyzing remotely sensed data is the impact of data resolution on the results of the analysis and on the conclusions that are subsequently drawn. We investigate the effects of spatial resolution on fractal dimension of digital elevation models (DEMs) generated at various spatial resolutions. The DEMs used in this study were created from three sources: 2-m resolution derived from LiDAR altimetry data, 20-m resolution derived from 1:20000-scale topographic maps, and 100-m resolution derived from National Topographic Series (NTS) maps of Canada at 1:250000 scale. Directional variograms were used to determine the fractal characteristics of the study area for each scale. In addition, the 2-m LiDAR data, which show detailed lithological and structural textures, were resampled to simulate lower resolutions of 50-m and 100-m. The results of the study indicate that, while the three data sources display a multifractal surface, the fractal dimension (D) at range-scale shows a consistent decrease with increasing cell size. The lower resolution, therefore, appears to cause a smoothing of the topographic surface, thereby reducing the fractal dimension in all directions. In contrast, the results from the resampled LiDAR data are less consistent This suggests that the detailed lithological information present in the high-resolution LiDAR data is sufficiently retained, even at degraded resolutions, to influence the fractal characteristics.