the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 May 2024
GraphFlood 1.0: an efficient algorithm to approximate 2D hydrodynamics for Landscape Evolution Models
Abstract. Computing hydrological fluxes at the Earth's surface is crucial for landscape evolution models, topographic analysis, and geographic information systems. However, existing formalisms, like single or multiple flow algorithms, often rely on ad-hoc rules based on local topographic slope and drainage area, neglecting the physics of water flow. While more physics-oriented solutions offer accuracy (e.g. shallow water equations), their computational costs limit their use in term of spatial and temporal scales. In this conrtibution, we introduce GraphFlood, a novel and efficient iterative method for computing river depth and water discharge in 2D on a digital elevation model (DEM). Leveraging the Directed Acyclic Graph (DAG) structure of surface water flow, GraphFlood iteratively solves the 2D shallow water equations. This algorithm aims to find the correct hydraulic surface by balancing discharge input and output over the topography. At each iteration, we employ fast DAG algorithms to calculate flow accumulation on the hydraulic surface, approximating discharge input. Discharge output is then computed using the Manning flow resistance equation, similar to the River.lab model. Iteratively, the divergence of discharges increments flow depth until reaching a stationary state. This algorithm can also solve for flood wave propagation by approximating the input discharge function of the immediate upstream neighbours. We validate water depths obtained with the stationary solution against analytical solutions for rectangular channels and the River.lab and Caesar Lisflood models for natural DEMs. GraphFlood demonstrates significant computational advantages over previous hydrodynamic models, with approximately a 10-fold speed-up compared to the River.lab model. Additionally, its computational time scales slightly more than linearly with the number of cells, making it suitable for large DEMs exceeding 106–108 cells. We demonstrate the versatility of GraphFlood in integrating realistic hydrology into various topographic and morphometric analyses, including channel width measurement, inundation pattern delineation, floodplain delineation, and the classification of hillslope, colluvial, and fluvial domains. Furthermore, we discuss its integration potential in landscape evolution models, highlighting its simplicity of implementation and computational efficiency.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(15807 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-1239', Anonymous Referee #1, 09 Jun 2024
The manuscript by Gailleton et al. presents a suite of algorithms designed to solve the shallow water equation over gridded topographic data, utilizing graph theory-related data structures and associated tree scanning algorithms. By doing so, the authors leverage advancements and overcome some challenges of two existing approaches for hydrologic and landscape evolution calculations. Specifically, the authors combine (1) recent advances in applying graph theory-related algorithms in large-scale Landscape Evolution Models, which speed up computations of drainage area and consequently erosion/sedimentation rates (e.g., Braun and Willett, 2013) but commonly assume that flow occurs as 1D lines, and (2) shallow water equation solvers that more realistically represent flow routing over complex topography but commonly suffer from high computational costs, limiting their usage to small length scales and short time scales.
The presented numerical advances are impressive and substantial. The manuscript makes convincing arguments that their utility could be fundamental for specific hydrologic and landscape evolution problems. However, the manuscript remains in the realm of model development and, as such, doesn't provide new insights into natural processes (including what models' emergent dynamics teach us about how nature could work). Consequently, the manuscript reads more like (an impressive) technical report. If expanding the analysis toward more physical insights is desired, the current manuscript holds some threads that could be pulled to produce new, insightful understandings.
For example, the analysis presented in figure 7 could potentially be utilized to produce preliminary (and possibly case-specific) insights about the relationship of flow width as a function of bedforms and local relief (and precipitation input, of course). There are more opportunities like this in the manuscript.
Specific comments:
- Lines 53-54 list several studies demonstrating the advantages of integrating 2D hydrodynamics to inform the study of landforms. What is missing in these studies?
- Fig 1. What are the arrows? How are they scaled?
- Line 70. What does "remains hampered by the physics behind which explicitly simulates wave propagation" mean?
- Line 120. The text about xmax is out of context.
- Line 146. Unsure if z was defined?
- Line 164. Since the hydraulic surface is a crucial concept, readers might benefit from a formal definition and possibly a demonstration (relative to topography).
- Line 182. "The magnitude of Qout flux is the same for MFD and SFD schemes." Is this an assumption (represented by the correction factor) or a fact? Is it also valid for the transient case? Since this is such a central corollary, perhaps the authors can expand on this issue.
- Line 207. What does "while in reach mode, given entry nodes receive an arbitrary Qin" mean?
- Fig 2. Can't understand the comparison. Which of the panels are a and c?
- Line 215. What does "(then determined in respect to CFL conditions)" mean?
- Fig. 3. It is possible to guess from the context, but readers will benefit from using different symbols for the stationary and transient solutions. I would also be interested in the actual time represented by these simulations (perhaps multiple time axes are needed). It is interesting to understand the time necessary for the transient solution to converge to the analytic solution, as this represents (gives a hunch for) the time scale over which the transient solution is important. Additionally, consider adding a graphical representation of the rectangular channel.
- Fig. 8. Wrong caption. Duplication of fig 7.
- Fig. 9. S−a_s. The interpretation of the colluvial sections is surprising. Are the white pixels (channels) in the left-hand side, lower relief landscape truly colluvial? The different types of slope break from colluvial to fluvial (lower slope on the LHS and higher slope on the RHS) could indicate that the interpretation should be more complex. Additionally, the slope increase at the high S – s_a end is surprising. While mentioned in line 327, its source is still not clear.
- Line 412. Q_{out} and Q_{in}
- Consider reducing the use of acronyms. Acronyms are useful for the authors but less for casual readers (specifically those not from the same field).
Citation: https://doi.org/10.5194/egusphere-2024-1239-RC1 - RC2: 'Comment on egusphere-2024-1239', Anonymous Referee #2, 22 Jul 2024
- AC1: 'Authors responses to reviewers', Boris Gailleton, 30 Aug 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-1239', Anonymous Referee #1, 09 Jun 2024
The manuscript by Gailleton et al. presents a suite of algorithms designed to solve the shallow water equation over gridded topographic data, utilizing graph theory-related data structures and associated tree scanning algorithms. By doing so, the authors leverage advancements and overcome some challenges of two existing approaches for hydrologic and landscape evolution calculations. Specifically, the authors combine (1) recent advances in applying graph theory-related algorithms in large-scale Landscape Evolution Models, which speed up computations of drainage area and consequently erosion/sedimentation rates (e.g., Braun and Willett, 2013) but commonly assume that flow occurs as 1D lines, and (2) shallow water equation solvers that more realistically represent flow routing over complex topography but commonly suffer from high computational costs, limiting their usage to small length scales and short time scales.
The presented numerical advances are impressive and substantial. The manuscript makes convincing arguments that their utility could be fundamental for specific hydrologic and landscape evolution problems. However, the manuscript remains in the realm of model development and, as such, doesn't provide new insights into natural processes (including what models' emergent dynamics teach us about how nature could work). Consequently, the manuscript reads more like (an impressive) technical report. If expanding the analysis toward more physical insights is desired, the current manuscript holds some threads that could be pulled to produce new, insightful understandings.
For example, the analysis presented in figure 7 could potentially be utilized to produce preliminary (and possibly case-specific) insights about the relationship of flow width as a function of bedforms and local relief (and precipitation input, of course). There are more opportunities like this in the manuscript.
Specific comments:
- Lines 53-54 list several studies demonstrating the advantages of integrating 2D hydrodynamics to inform the study of landforms. What is missing in these studies?
- Fig 1. What are the arrows? How are they scaled?
- Line 70. What does "remains hampered by the physics behind which explicitly simulates wave propagation" mean?
- Line 120. The text about xmax is out of context.
- Line 146. Unsure if z was defined?
- Line 164. Since the hydraulic surface is a crucial concept, readers might benefit from a formal definition and possibly a demonstration (relative to topography).
- Line 182. "The magnitude of Qout flux is the same for MFD and SFD schemes." Is this an assumption (represented by the correction factor) or a fact? Is it also valid for the transient case? Since this is such a central corollary, perhaps the authors can expand on this issue.
- Line 207. What does "while in reach mode, given entry nodes receive an arbitrary Qin" mean?
- Fig 2. Can't understand the comparison. Which of the panels are a and c?
- Line 215. What does "(then determined in respect to CFL conditions)" mean?
- Fig. 3. It is possible to guess from the context, but readers will benefit from using different symbols for the stationary and transient solutions. I would also be interested in the actual time represented by these simulations (perhaps multiple time axes are needed). It is interesting to understand the time necessary for the transient solution to converge to the analytic solution, as this represents (gives a hunch for) the time scale over which the transient solution is important. Additionally, consider adding a graphical representation of the rectangular channel.
- Fig. 8. Wrong caption. Duplication of fig 7.
- Fig. 9. S−a_s. The interpretation of the colluvial sections is surprising. Are the white pixels (channels) in the left-hand side, lower relief landscape truly colluvial? The different types of slope break from colluvial to fluvial (lower slope on the LHS and higher slope on the RHS) could indicate that the interpretation should be more complex. Additionally, the slope increase at the high S – s_a end is surprising. While mentioned in line 327, its source is still not clear.
- Line 412. Q_{out} and Q_{in}
- Consider reducing the use of acronyms. Acronyms are useful for the authors but less for casual readers (specifically those not from the same field).
Citation: https://doi.org/10.5194/egusphere-2024-1239-RC1 - RC2: 'Comment on egusphere-2024-1239', Anonymous Referee #2, 22 Jul 2024
- AC1: 'Authors responses to reviewers', Boris Gailleton, 30 Aug 2024
Peer review completion
Journal article(s) based on this preprint
Model code and software
Supporting code for GraphFlood 1.0: an efficient algorithm to approximate 2D hydrodynamics for Landscape Evolution Models Gailleton Boris and Steer Philippe https://doi.org/10.5281/zenodo.11065794
Supporting code for GraphFlood 1.0: an efficient algorithm to approximate 2D hydrodynamics for Landscape Evolution Models Gailleton Boris and Steer Philippe https://doi.org/10.5281/zenodo.11065794
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Cited
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Discussed
Boris Gailleton
Philippe Steer
Philippe Davy
Wolfgang Schwanghart
Thomas Guillaume Adrien Bernard
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(15807 KB) - Metadata XML