In order to characterize the morphology of a triangulated terrain, we define several discrete estimators that mimic mean and Gaussian curvatures in the discrete case. We start from concentrated curvature, a discrete notion of Gaussian curvature for polyhedral surfaces, defined by Troyanov . Since concentrated curvature does not depend on the local geometric shape of the terrain, we introduce Ccurvature that allows us to obtain discrete counterparts of both Gaussian and mean curvature. Finally, we define distortion, which behaves as an approximation of mean curvature. We apply all such measures to the analysis of the morphology of triangulated terrains.