We present the PM2-Triangle quadtree (PM2T-quadtree), a new hierarchical spatial index for triangle meshes which has been designed for performing spatial queries on triangle-based terrain models. The PM2T-quadtree is based on a recursive space decomposition into square blocks. Here, we propose a highly compact data structure encoding a PM2T-quadtree, which decouples the spatial indexing structure from the combinatorial description of the mesh. We compare the PM2T-quadtree against other spatial indexes by considering the structure of the underlying domain subdivision, the storage costs of their data structures and the performance in geometric queries.