Investigating DEM error patterns by directional variograms and Fourier analysis

Abstract

In many spatial analyses and GIS applications, a Digital Elevation Model (DEM) is often used to derive a variety of new variables and parameters. Previous research shows that the accuracy of derived variables is affected, not merely by the magnitude of DEM errors and the algorithms applied to derive these variables, but also by the spatial structure of DEM errors. However, the lack of knowledge and understanding of the spatial structure of DEM errors often handicaps the analysis of error propagation. This paper investigates the spatial autocorrelation and anisotropic pattern of DEM error by using directional variograms in the spatial domain and Fourier analysis in the frequency domain. Based on an empirical study, it is concluded that the spatial autocorrelation pattern of DEM errors is anisotropic and scale-dependent, and that the maximum direction and range of the autocorrelation depends upon the orientation and wavelength of the terrain features. For a smooth terrain, the magnitude of DEM errors is correlated to surface slope. For a rugged terrain, the elevation values in DEMs tend to be underestimated in ridges, and overestimated in valleys, but the correlation between the DEM error and surface slope is quite low.