Terrain modeling is a fast growing field with many applications such as computer graphics, resource management, Earth and environmental sciences, civil and military engineering, surveying and photogrammetry and games programming. One of the most widely used terrain model is the Digital Elevation Model (DEM). A DEM is a simple regularly spaced grid of elevation points that represent the continuous variation of relief over space. DEMs require simple storage and are compatible with satellite data. However, they do not easily account for overhangs. In this work we report on the Grounded Heightmap Tree, a new data structure for terrain representation built as a generalization of the DEM. The new data structure allows to naturally represent terrain overhangs. We illustrate the performance of the Grounded Heightmap Tree when applied to represent terrains that undergo big changes.