Assessing slope precision from numerical propagation of DEM (Digital Elevation Model) vertical errors

Digital Elevation Models (DEM) are widely used tools in planetary sciences. Geometric parameters such as pixel orientations and local slopes can be derived from these DEM. However, as any data, DEM have a limited precision (i.e. errors), which yields to the propagation of errors on geometric parameters. Assessing local slopes is necessary for many morphological studies: then, how do the DEM vertical errors propagate on the slope values? To answer to this question, we develop a simple and fast numerical method based on the addition of noise on synthetic DEM. We evaluate the different components of slope errors to define the relationship between input DEM noise and output slope errors. Results can be used as first order estimations to discuss slope maps precision.