Estimating the propagation error of DEM from higher-order interpolation algorithms

The accuracy of a DEM is critical to its applications, such as spatial analysis. Error in an interpolated DEM is related to two factors: (1) a model error of the applied interpolation algorithm and (2) a propagated error from the error of the original nodes of the network. In this study, we focus on the second type of error in biquadratic and bicubic interpolation algorithms. Representations of a DEM surface by the biquadratic interpolation and bicubic interpolation models from regular grids are derived first. Based on these, the formulae of error propagation in terms of the mean elevation error of DEM constructed by both biquadratic and bicubic interpolations are derived, respectively, according to a mathematical proof. It is found that the single propagation errors of both the biquadratic and bicubic models are identical to each other-as in the bilinear model. Combining the formula and the result of Kidner, who found that both the biquadratic and bicubic model bicubic interpolation reduce the rms error by up to 20 % of the bilinear interpolation, it is concluded that the biquadratic and bicubic interpolation algorithms are more accurate than the bilinear interpolation in terms of their total error including both the propagation error and the model error of the generated DEM surface.