Comparison of slope estimates from low resolution DEMs: scaling issues and a fractal method for their solution

• Published in: Earth surface processes and landforms Vol. 24; no. 9; pp. 763 - 779
• Main Authors: Zhang, Xiaoyang, Drake, Nick A., Wainwright, John, Mulligan, Mark
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.08.1999; Wiley
• Subjects: Bgi / Prodig; DEM resolution; downscaling; Earth sciences; Earth, ocean, space; Exact sciences and technology; fractal dimension; Geomorphology; Geomorphology, landform evolution; Physical geography; regional to global scale; slope; Slopes; Surficial geology; Iberian Peninsula; Southern Europe; Spain; fractal dimension; digital terrain models; algorithms; slope angle; Asia; Europe; Fractal geometry; Methodology; Numerical model; Slope gradient; Topography; Scale; Spatial variation; Algorithm; Slope
• ISSN: 0197-9337; 1096-9837
• DOI: 10.1002/(SICI)1096-9837(199908)24:9<763::AID-ESP9>3.0.CO;2-J

Five different algorithms for calculating slope from digital elevation models (DEMs) have been compared from regional to global scales. Though different methods produce different results, the most significant outcome is that slope varies inversely with the DEM grid size. Thus, slopes estimated from coarse resolution data can be considered to produce significant underestimates of the true slope. A fractal theory is adapted to solve this problem. The variogram technique for the definition of fractal parameters is demonstrated to provide a relationship between slope and the spatial resolution of measurement. The variation of fractal parameters is discussed at various scales, and a model is developed to estimate the high resolution slope based on the coarse resolution DEM by using fractal parameters. The fractal parameters are estimated from the standard deviation of elevation in a 3 × 3 window of the DEM to account for local variability in the surface. Standard deviation of elevation is found to be the most invariant property of different scale DEMs of the same area. The model is validated using different resolution DEMs in southern Spain and it is used to estimate the high resolution slope values at global scales based on a coarse resolution DEM. The slopes estimated using the technique outlined are a significant improvement on those estimated directly from the coarse resolution data. Slopes estimated in this way allow the more effective use of available coarse resolution data in regional and global scale modelling studies. Copyright © 1999 John Wiley & Sons, Ltd.