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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/esurf-2020-31
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esurf-2020-31
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 05 May 2020

Submitted as: research article | 05 May 2020

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This preprint is currently under review for the journal ESurf.

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

Richard Barnes1,2,3, Kerry L. Callaghan4,5, and Andrew D. Wickert4,5 Richard Barnes et al.
  • 1Energy & Resources Group (ERG), University of California, Berkeley, USA
  • 2Electrical Engineering & Computer Science, University of California, Berkeley, USA
  • 3Berkeley Institute for Data Science (BIDS), University of California, Berkeley, USA
  • 4Department of Earth & Environmental Sciences, University of Minnesota, Minneapolis, USA
  • 5Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, USA

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 a Fill-Spill-Merge algorithm that utilizes our depression hierarchy 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 as well as results from two sample study areas. In these case studies, the algorithm runs 90–2600× faster (with a 2000–63 000× reduction in compute time) than the commonly-used Jacobi iteration and produces a more accurate output. Complete, well-commented, open-source code is available on Github and Zenodo.

Richard Barnes et al.

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Status: final response (author comments only)
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AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

Richard Barnes et al.

Model code and software

Fill-Spill-Merge Source Code R. Barnes and K. Callaghan https://doi.org/10.5281/zenodo.3755142

Richard Barnes et al.

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Latest update: 09 Jul 2020
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Short summary
Existing ways of modeling the flow of water amongst landscape depressions such as swamps and lakes take a long time to run. However, as our previous work explains, depressions can be quickly organized into a data structure – the depression hierarchy. This paper explains how the depression hierarchy can be used to quickly simulate the realistic filling of depressions including how they spill over into each other, and, if they become full enough, how they merge into one another.
Existing ways of modeling the flow of water amongst landscape depressions such as swamps and...
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