Assessing the Spatial Characteristics of DEM Interpolation Error

Stephen Wise
Department of Geography, University of Sheffield, Sheffield, UK

Abstract: Studies of the detailed characteristics of DEM error have been hampered by the difficulty of obtaining a large sample of error values for a DEM. The approach proposed in this paper is to resample a DEM to a lower resolution and then re-interpolate back to the original resolution which produces a large sample of error values well distributed across the DEM. It is argued that this is analogous to creating a DEM from low- density data sources such as spot height and contour data. This method is applied to a sample area from Scotland which contains a variety of terrain types. The results show that the standard measure of error, the Root Mean Square Error (RMSE) of elevation shows only moderate correlation with a visual assessment of the quality of DEMs produced by a range of interpolation methods. The usual assumptions that elevation error has a Gaussian distribution and is strongly correlated are thrown into doubt. The distribution is much more strongly clustered around zero than the Gaussian, and the level of spatial autocorrelation varies markedly depending on the density of the source data and the interpolation method. At the level of the individual DEM point, elevation error is shown to be a poor predictor of error in slope derivatives which depend on the spatial pattern of elevation errors around the point and are also sensitive to differences in terrain. At the level of a whole DEM however, RMSE of elevation is a good predictor of RMSE in gradient and aspect.

Keywords: Error modelling, terrain analysis, spatial interpolation, spatial statistics

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