We address the problem of morphological analysis of real terrains. We describe a morphological model for a terrain by considering extensions of Morse theory to the discrete case. We propose a two-level model of the morphology of a terrain based on a graph joining the critical points of the terrain through integral lines. We present a new set of generalization operators specific for discrete piece-wise linear terrain models, which are used to reduce noise and the size of the morphological representation. We show results of our approach on real terrains.