I/O-Efficient Hierarchical Watershed Decomposition of Grid Terrains Models

Recent progress in remote sensing has made massive amounts of high resolution terrain data readily available. Often the data is distributed as regular grid terrain models where each grid cell is associated with a height. When terrain analysis applications process such massive terrain models, data movement between main memory and slow disk (I/O), rather than CPU time, often becomes the performance bottleneck. Thus it is important to consider I/O-efficient algorithms for fundamental terrain problems. One such problem is the hierarchical decomposition of a grid terrain model into watersheds–regions where all water flows towards a single common outlet. Several different hierarchical watershed decompositions schemes have been described in the hydrology literature. One important such scheme is the Pfafstetter label method where each watershed is assigned a unique label and each grid cell is assigned a sequence of labels corresponding to the (nested) watersheds to which it belongs. In this paper we present an I/O-efficient algorithm for computing the Pfafstetter label of each cell of a grid terrain model. The algorithm uses O(sort(T )) I/Os, the number of I/Os needed to sort T elements, where T is the total length of the cell labels. To our knowledge, our algorithm is the first efficient algorithm for the problem. We also present the results of a experimental study using massive real life terrain data that shows our algorithm is practically as well as theoretically efficient.