Computing water flow through complex landscapes - Part 3: Fill-Spill-Merge: Flow routing in depression hierarchies

Richard Barnes, Kerry L. Callaghan, Andrew D. Wickert

Research output: Contribution to journalArticlepeer-review

Abstract

Depressions - inwardly draining regions - are common to many landscapes. When there is sufficient moisture, depressions take the form of lakes and wetlands; otherwise, they may be dry. Hydrological flow models used in geomorphology, hydrology, planetary science, soil and water conservation, and other fields often eliminate depressions through filling or breaching; however, this can produce unrealistic results. Models that retain depressions, on the other hand, are often undesirably expensive to run. In previous work we began to address this by developing a depression hierarchy data structure to capture the full topographic complexity of depressions in a region. Here, we extend this work by presenting the Fill-Spill-Merge algorithm that utilizes our depression hierarchy data structure to rapidly process and distribute runoff. Runoff fills depressions, which then overflow and spill into their neighbors. If both a depression and its neighbor fill, they merge. We provide a detailed explanation of the algorithm and results from two sample study areas. In these case studies, the algorithm runs 90-2600 times faster (with a reduction in compute time of 2000-63 000 times) than the commonly used Jacobi iteration and produces a more accurate output. Complete, well-commented, open-source code with 97 % test coverage is available on GitHub and Zenodo.

Original languageEnglish (US)
Article number7
Pages (from-to)105-121
Number of pages17
JournalEarth Surface Dynamics
Volume9
Issue number1
DOIs
StatePublished - Mar 2 2021
Externally publishedYes

Bibliographical note

Funding Information:
Kerry L. Callaghan was supported by the National Science Foundation under grant no. EAR-1903606, the University of Minnesota Department of Earth Sciences Junior F Hayden Fellowship, the University of Minnesota Department of Earth Sciences H.E. Wright Footsteps Award, and start-up funds awarded to Andrew Wickert by the University of Minnesota.

Funding Information:
Acknowledgements. Richard Barnes was supported by the Department of Energy’s Computational Science Graduate Fellowship (grant no. DE-FG02-97ER25308) and, through the Berkeley Institute for Data Science’s PhD Fellowship, by the Gordon and Betty Moore Foundation (grant GBMF3834) as well as by the Alfred P. Sloan Foundation (grant 2013-10-27).

Funding Information:
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 Alfred P. Sloan Foundation (grant no. 2013-10-27), and the National Science Foundation Division of Earth Sciences (grant no. EAR-1903606).

Funding Information:
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: 6 February 2021).

Funding Information:
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 Alfred P. Sloan Foundation (grant no. 2013-10-27), and the National Science Foundation Division of Earth Sciences (grant no. EAR-1903606).

Publisher Copyright:
© Author(s) 2021.

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