The cumulative error at a point in a LiDAR-derived DEM consists of three components: propagated LiDAR-sensor error, propagated ground error, and interpolation error. To combine these error components so as to assess the vertical accuracy of a  LiDAR-derived DEM, statistical methods based on the error propagation theory are often used. Due to the existence of systematic error, statistical methods are only effective if a large number of checkpoints are available, which may not be affordable in many practical applications. This paper presents approximation theory as an alternative methodology that departs from error propagation theory in fundamental ways. Using approximation theory, an error bound of the cumulative error at any point in the study site can be obtained, thus informing users conservatively of the spatial variation of DEM accuracy and pointing out the weakly determined areas. The new method is illustrated from DEM users’ perspective by assessing whether a publicly available LiDAR-derived DEM meets FEMA’s accuracy standard for flood risk mapping. The paper calls for a change in the existing methods of assessing and reporting the errors in a LiDAR-derived DEM, in particular those introduced during the ground  filtering process.
['XiaoHang Liu', 'Hai Hu', 'Peng Hu']
Accuracy Assessment of LiDAR-Derived Digital Elevation Models Based on Approximation Theory