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Zonal analysis in geographic information systems is a useful and convenient tool to study the accuracy of the digital elevation model ͑DEM͒ in terms of topographic complexity, which is defined in this paper as the change in terrain slope or slope change. The accuracy of the U.S. Geological Survey 1-degree DEM over two test areas is studied by comparing it with the USGS 7.5-min DEM. The statistical quantities of the DEM errors are studied and modeled using various mathematical functions. It is shown that the standard deviation of the 1-degree DEM can be largely approximated with a linear function of the slope change, while its minimum and maximum errors remain almost unchanged and occur in all slope change zones as a behavior independent of the terrain complexity.

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