Cross-validation as a means of investigating DEM interpolation error

Studies of the detailed characteristics of DEM error have been hampered by the difficulty in 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 reinterpolate back to the original resolution which produces a large sample of error values well distributed across the DEM. 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 frequency distribution and strength of spatial autocorrelation are shown to vary with the initial data density and interpolation method. When the source data density is low, the error has strong spatial autocorrelation and a distribution that is close to being Gaussian. However, as the data density increases, levels of spatial autocorrelation drop and the distribution becomes leptokurtic with values very strongly clustered around zero. 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 but not of curvature.