Accuracy Assessment of Digital Elevation Models based on Approximation Theory

Empirical research in DEM accuracy assessment has observed that DEM errors are correlated with terrain morphology, sampling density, and interpolation method. However, theoretical reasons for these correlations have not been accounted for. This paper introduces approximation theory adopted from computational science as a new framework to assess the accuracy of DEM.; interpolated from topographic maps. By perceiving DEM generation as a piecewise polynomial simulation of the unknown terrain, the overall accuracy of a DEM is described by the maximum error at any DEM point. Three linear polynomial interpolation methods ore examined, namely linear interpolation in ID, TIN interpolotion, and bilinear interpolation in a rectangle. Their propagation error and interpolation error, whose sum is the total error at a DEM point, are derived. Based on the results, the theoretical basis for the correlation between DEM error and terrain morphology and source data density is articulated for the first time.