Accuracy Assessment of DEM Slope Algorithms Related to Spatial Autocorrelation of DEM Errors

Digital elevation models (DEM) are representations of topography but with unavoidable inherent errors, which result in DEM uncertainty. Entities are spatially dependent and with autocorrelation related to distance. The spatial autocorrelation of the DEM error will systematically affect the result of terrain analysis. It should be taken into account when calculating slope from a grid-based DEM. The effect of the accuracy of slope calculation models on terrain analysis based on quantitative models could be very significant. DEM uncertainty and error propagation is hard to describe with a single, fixed and analytical error based on spatial databases. The Monte Carlo simulation technique is an effective method to simulate error fields and can be used to research the DEM error’s spatial autocorrelation and DEM uncertainty. The accuracy of slopes is studied and four commonly used slope algorithms, namely, the 2

nd

Finite Difference, 3

rd

order Finite Difference, 3

rd

order Finite Difference Weighted by Reciprocal of Squared Distance, and 3

rd

order Finite Difference Weighted by Reciprocal of Distance, are compared theoretically in this paper based on the error being spatially dependent and autocorrelated. The theoretical results are confirmed by Monte Carlo simulation experiments using three digital elevation model data sets.