We consider the problem of extracting the morphology of a terrain represented as a Triangulated Irregular Network (TIN). Our reference framework to model terrain morphology is given by the descending and the ascending Morse complexes, which define a decomposition of the terrain through its critical points and integral lines. We review several algorithms proposed in the literature to extract descending and ascending Morse complexes, which we have implemented for TINs. We analyze the behavior of such algorithms on real data sets by comparing the output decomposition they produce, based on different metrics.