Articles | Volume 9, issue 1
https://doi.org/10.5194/esurf-9-105-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esurf-9-105-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
02 Mar 2021
Research article |
| 02 Mar 2021
| 02 Mar 2021
Computing water flow through complex landscapes – Part 3: Fill–Spill–Merge: flow routing in depression hierarchies
Richard Barnes
CORRESPONDING AUTHOR
Energy & Resources Group (ERG), University of California, Berkeley, USA
Electrical Engineering & Computer Science, University of California, Berkeley, USA
Berkeley Institute for Data Science (BIDS), University of California, Berkeley, USA
Kerry L. Callaghan
Department of Earth & Environmental Sciences, University of Minnesota, Minneapolis, USA
Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, USA
Andrew D. Wickert
Department of Earth & Environmental Sciences, University of Minnesota, Minneapolis, USA
Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, USA
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Cited
20 citations as recorded by crossref.
- Modified Priority-Flood algorithm for hydrologic modelling-based digital terrain analysis using a hash heap structure L. Ma et al. https://doi.org/10.1080/19475683.2026.2617191
- Transfer learning with convolutional neural networks for hydrological streamline delineation N. Jaroenchai et al. https://doi.org/10.1016/j.envsoft.2024.106165
- Depression detection in billion-scale DEM grids in digital terrain analysis using HRBTree L. Ma et al. https://doi.org/10.1007/s12145-025-02050-1
- Persistent flow-division imbalance in a tidal river network under climate stress and engineering intervention: a case study from the Sai Gon–Dong Nai system N. Chung & N. Dang Tinh https://doi.org/10.2166/wpt.2026.288
- Thalweg and Ridge Network Extraction From Unaltered Topographic Data as a Basis for Terrain Partitioning G. Moretti & S. Orlandini https://doi.org/10.1029/2022JF006943
- Example-based terrain synthesis with pit removal J. Scott & N. Dodgson https://doi.org/10.1016/j.cag.2021.06.012
- Land-surface parameters for spatial predictive mapping and modeling A. Maxwell & C. Shobe https://doi.org/10.1016/j.earscirev.2022.103944
- From data modification to preservation: evolution of DEM depression processing algorithms in hydrological modelling L. Ma et al. https://doi.org/10.1007/s12665-026-12971-9
- A network-based analysis of critical resource accessibility during floods M. Preisser et al. https://doi.org/10.3389/frwa.2023.1278205
- CHONK 1.0: landscape evolution framework: cellular automata meets graph theory B. Gailleton et al. https://doi.org/10.5194/gmd-17-71-2024
- The Water Table Model (WTM) (v2.0.1): coupled groundwater and dynamic lake modelling K. Callaghan et al. https://doi.org/10.5194/gmd-18-1463-2025
- c-HAND: near real-time coastal flood mapping M. Wang et al. https://doi.org/10.3389/frwa.2024.1329109
- The role of climate and population change in global flood exposure and vulnerability J. Rogers et al. https://doi.org/10.1038/s41467-025-56654-8
- Evaluation of Priority Queues in the Priority Flood Algorithm for Hydrological Modelling L. Ma et al. https://doi.org/10.3390/w17223202
- Drainage integration in extensional tectonic settings P. Larson et al. https://doi.org/10.1016/j.geomorph.2021.108082
- Topological Relationship‐Based Flow Direction Modeling: Stream Burning and Depression Filling C. Liao et al. https://doi.org/10.1029/2022MS003487
- Fill‐spill‐merge terrain analysis reveals topographical controls on Canadian river runoff N. Wagle & L. Smith https://doi.org/10.1002/hyp.15238
- GraphFlood 1.0: an efficient algorithm to approximate 2D hydrodynamics for landscape evolution models B. Gailleton et al. https://doi.org/10.5194/esurf-12-1295-2024
- GDBM: A database of global drainage basin morphology S. Grieve et al. https://doi.org/10.1371/journal.pone.0320771
- Short communication: Learning how landscapes evolve with neural operators G. Roberts https://doi.org/10.5194/esurf-13-563-2025
20 citations as recorded by crossref.
- Modified Priority-Flood algorithm for hydrologic modelling-based digital terrain analysis using a hash heap structure L. Ma et al. https://doi.org/10.1080/19475683.2026.2617191
- Transfer learning with convolutional neural networks for hydrological streamline delineation N. Jaroenchai et al. https://doi.org/10.1016/j.envsoft.2024.106165
- Depression detection in billion-scale DEM grids in digital terrain analysis using HRBTree L. Ma et al. https://doi.org/10.1007/s12145-025-02050-1
- Persistent flow-division imbalance in a tidal river network under climate stress and engineering intervention: a case study from the Sai Gon–Dong Nai system N. Chung & N. Dang Tinh https://doi.org/10.2166/wpt.2026.288
- Thalweg and Ridge Network Extraction From Unaltered Topographic Data as a Basis for Terrain Partitioning G. Moretti & S. Orlandini https://doi.org/10.1029/2022JF006943
- Example-based terrain synthesis with pit removal J. Scott & N. Dodgson https://doi.org/10.1016/j.cag.2021.06.012
- Land-surface parameters for spatial predictive mapping and modeling A. Maxwell & C. Shobe https://doi.org/10.1016/j.earscirev.2022.103944
- From data modification to preservation: evolution of DEM depression processing algorithms in hydrological modelling L. Ma et al. https://doi.org/10.1007/s12665-026-12971-9
- A network-based analysis of critical resource accessibility during floods M. Preisser et al. https://doi.org/10.3389/frwa.2023.1278205
- CHONK 1.0: landscape evolution framework: cellular automata meets graph theory B. Gailleton et al. https://doi.org/10.5194/gmd-17-71-2024
- The Water Table Model (WTM) (v2.0.1): coupled groundwater and dynamic lake modelling K. Callaghan et al. https://doi.org/10.5194/gmd-18-1463-2025
- c-HAND: near real-time coastal flood mapping M. Wang et al. https://doi.org/10.3389/frwa.2024.1329109
- The role of climate and population change in global flood exposure and vulnerability J. Rogers et al. https://doi.org/10.1038/s41467-025-56654-8
- Evaluation of Priority Queues in the Priority Flood Algorithm for Hydrological Modelling L. Ma et al. https://doi.org/10.3390/w17223202
- Drainage integration in extensional tectonic settings P. Larson et al. https://doi.org/10.1016/j.geomorph.2021.108082
- Topological Relationship‐Based Flow Direction Modeling: Stream Burning and Depression Filling C. Liao et al. https://doi.org/10.1029/2022MS003487
- Fill‐spill‐merge terrain analysis reveals topographical controls on Canadian river runoff N. Wagle & L. Smith https://doi.org/10.1002/hyp.15238
- GraphFlood 1.0: an efficient algorithm to approximate 2D hydrodynamics for landscape evolution models B. Gailleton et al. https://doi.org/10.5194/esurf-12-1295-2024
- GDBM: A database of global drainage basin morphology S. Grieve et al. https://doi.org/10.1371/journal.pone.0320771
- Short communication: Learning how landscapes evolve with neural operators G. Roberts https://doi.org/10.5194/esurf-13-563-2025
Saved (final revised paper)
Latest update: 13 Jun 2026
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...
