Abstract: We present an algorithm for simplifying terrain data that preserves topology. We use a decimation algorithm that simplifies the given data set using hierarchical clustering. Topology constraints, along with local error metrics, are used to ensure topology-preserving simplification and to compute precise error bounds in the simplified data. The earth's mover distance is used as a global metric to compute the degradation in topology as the simplification proceeds. Experiments with both analytic and real terrain data are presented. Results indicate that one can obtain significant simplification with low errors without losing topology information.