Depressions-inwardly draining regions of digital elevation models-present difficulties for terrain analysis and hydrological modeling. Analogous "depressions" also arise in image processing and morphological segmentation, where they may represent noise, features of interest, or both. Here we provide a new data structure-the depression hierarchy-that captures the full topologic and topographic complexity of depressions in a region. We treat depressions as networks in a way that is analogous to surface-water flow paths, in which individual sub-depressions merge together to form meta-depressions in a process that continues until they begin to drain externally. This hierarchy can be used to selectively fill or breach depressions or to accelerate dynamic models of hydrological flow. Complete, well-commented, open-source code and correctness tests are available on GitHub and Zenodo.
Bibliographical noteFunding Information:
Acknowledgements. Richard Barnes was supported by the Department of Energy’s Computational Science Graduate Fellowship (grant no. DE-FG02-97ER25308), the Gordon and Betty Moore Foundation through the Berkeley Institute for Data Science’s PhD Fellowship (grant GBMF3834), and the Alfred P. Sloan Foundation (grant 2013-10-27).
Kerry L. Callaghan was supported by the University of Minnesota Department of Earth & Environmental Sciences Junior F. Hayden Fellowship, start-up funds awarded to ADW by the University of Minnesota, and by the National Science Foundation under grant no. EAR-1903606.
Empirical tests and results were performed on XSEDE’s Comet supercomputer (Towns et al., 2014), which is supported by the National Science Foundation (grant no. ACI-1053575). Portability and debugging tests were performed on the Mesabi machine at the Minnesota Supercomputing Institute (MSI) at the University of Minnesota (http://www.msi.umn.edu, last access: 20 May 2020).
Financial support. This research has been supported by the U.S. Department of Energy, Krell Institute (grant no. DE-FG02-97ER25308); the National Science Foundation, Office of Advanced Cyberinfrastructure (grant no. ACI-1053575); the Gordon and Betty Moore Foundation (grant no. GBMF3834); the National Science Foundation, Geomorphology and Land-use Dynamics program (grant no. EAR-1903606); and the Alfred P. Sloan Foundation (grant no. 2013-10-27).