the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Nov 2024
Multiple Equilibrium Configurations in River-Dominated Deltas
Abstract. The morphological evolution of river deltas is a complex process influenced by both natural forces and human interventions. As hubs of human settlement and economic activity, deltas face unique challenges that necessitate integrated management strategies to balance development with ecological sustainability. This study investigates multiple equilibrium states within deltaic systems, revealing key internal feedback mechanisms between delta branches through a novel theoretical model tailored to river-dominated delta channels. Focusing on the Po River Delta as a case study, we analyze equilibrium variability and identify potential avulsion sites. These findings provide a valuable framework for predicting future shifts in deltaic morphology and supporting adaptive management strategies.
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Preprint
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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.
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RC1: 'Comment on egusphere-2024-3552', Matthew Hiatt, 20 Jan 2025
Review of “Multiple Equilibrium Configurations in River-Dominated Deltas”
Review date: Jan 20, 2025
Review by: Matt Hiatt
Conflicts: This is my first review of the manuscript and I identify no conflicts of interest.
Assessment: The manuscript is well-presented, relatively easy to read and follow, and is free of grammatical errors. Overall, I found the paper interesting and the results showing the variable effects of downstream length, in the channels immediately downstream or downstream of the second bifurcations, follows well-understood phenomena based on models from these authors and others. The comparison to the Po River delta is a welcomed piece, and the model does provide some interesting insights into the dynamics of that system. I have some criticisms of the contextualization of the results, especially with the assumption that flow is contained completely within channels. I am not suggesting that the authors redo anything, but it is my opinion that this assumption warrants some consideration and discussion. The abstract also needs to be edited to provide more substance and detail. At the moment it is very short and general to the point it is difficult to tell what novel insights this paper provides, and there are plenty of interesting results the authors could include to improve it.
Major points:
Abstract: The abstract lacks substantive information on the results of the paper. It I clear that equilibrium configurations are analyzed, but it’s not clear what novel information or insights this manuscript provides. These authors have published several papers on equilibrium configurations in bifurcations, deltas, etc. and it would be beneficial to add specificity to the abstract.
It appears that there is no overbank flow allowed in such a model. If my understanding of the way these models work is correct, there cannot be an internal outlet. Is perfect flow conservation within the channel deltaic network to the seaward boundary realistic? For eg., see Allison et al (2023; 2012), Feizabadi et al., 2024; Gao et al., 2023; Hiatt & Passalacqua (2015;2017); Hiatt et al., (2018); Shaw et al., 2016. Even if it is not realistic, how does this assumption affect the results? Several studies suggest that connectivity with the floodplain is a primary driver of morphology in river deltas (e.g., Coffey and Shaw, 2017; Olliver and Edmonds 2021), and it stands to reason that this should affect bed morphology, etc. I recognize many of these examples are from Wax Lake Delta, but nevertheless this is often considered a prototype river dominated delta. I think this should be explained in the context of the assumption/limitations of the model design and in the discussion section to understand how containing flows to the channel network influences predictions of morphology/stability. This point may be important when considering the results shown in Figure 5. Water level asymmetry can drive lateral flow (Gao et al., (2023)) and may have implications for the results showing disagreement with the Po system, especially in the more downstream reaches (Tolle), where I assume the assumption of conserved channelized flow fails (I am not sure of this, of course, but there certainly looks to be connections in Figure 1b).
Minor points and edits:
Line 10-11: Is the quantity and quality of sediment relative to the accommodation space really the key driver? In other words, even if the quantity of sediment is very small, if the space that needs to be filled is very small then a delta will be formed. The opposite is also true for large sediment loads with lots of space to fill. I suppose the point is moot because the authors mention this is in the next sentence, essentially.
Figure 1b: If the bathymetry of the channels is shown, we likely need a colorbar to distinguish elevations, otherwise it should be removed to match the birdsfoot. Also, I know the Po is the focus of the manuscript, but there should probably also be an inset map for the Birdsfoot. The inset map in Figure 1b is also not supremely helpful to those that are not familiar with northern Italy, so I’d recommend showing the full country and political boundaries.
Lines 21-22: “…drains a significant amount of water and carries a substantial quantity of sediment…” I’d recommend just reporting those annual figures here instead of using qualifying adjectives. Just give the quantities.
Lines 30-32: This statement should be modified or removed: There are many studies focused on deltas that consider things other than flow routes and bio-ecology (not even sure what bio-ecology is). I would recommend a rewrite of this whole paragraph, giving proper consideration to the literature. Deltaic science is multidisciplinary are there are myriad studies across disciplines, so saying that most studies related to deltas “…focus merely on hydrodynamics…” is incorrect. The second argument also may not be correct – there are quite a number of detailed morphological modeling studies in the Mississippi River Delta, for example (e.g., Meselhe et al., (2021) cited below).
Lines 36-42: While I am familiar with these models and agree that they are useful , I recommend being more objective and removing words such as “easier” and “powerful insight.”
Line 57-58: There is some work on the bed morphology in Wax Lake Delta from Ehab Meslhe’s group using a Delt3D Morpho model (Meselhe et al., 2021).
Line 182: What is the critical threshold for R_Up? Can the authors please present an example for on of the L’tot values so the reader can more easily contextualize the results in Figure 4?
Citations
Allison, M. A., Meselhe, E. A., Kleiss, B. A., & Duffy, S. M. (2023). Impact of water loss on sustainability of the Mississippi River channel in its Deltaic Reach. Hydrological Processes, 37(10), e15004.
Allison, M. A., Demas, C. R., Ebersole, B. A., Kleiss, B. A., Little, C. D., Meselhe, E. A., ... & Vosburg, B. M. (2012). A water and sediment budget for the lower Mississippi–Atchafalaya River in flood years 2008–2010: Implications for sediment discharge to the oceans and coastal restoration in Louisiana. Journal of Hydrology, 432, 84-97.
Coffey, T. S., & Shaw, J. B. (2017). Congruent bifurcation angles in river delta and tributary channel networks. Geophysical research letters, 44(22), 11-427.
Gao, W., Wang, Z. B., Kleinhans, M. G., Miao, C., Cui, B., & Shao, D. (2023). Floodplain connecting channels as critical paths for hydrological connectivity of deltaic river networks. Water Resources Research, 59(4), e2022WR033714.
Feizabadi, S., C. Li, and M. Hiatt (2024), Response of river delta hydrological connectivity to changes in river discharge and atmospheric frontal passage, Frontiers in Marine Science, 11, https://doi.org/10.3389/fmars.2024.1387180
Hiatt, M. and P. Passalacqua (2015), Hydrological connectivity in river deltas: The first-order importance of channel-island exchange, Water Resources Research, 51, 2264–2282, https://doi.org/10.1002/2014WR016149
Hiatt, M. and P. Passalacqua (2017), What controls the transition from confined to unconfined flow? Analysis of hydraulics in a coastal river delta, Journal Hydraulic Engineering, 60th Anniversary Reviews,143(6), https://doi.org/10.1061/(ASCE)HY.1943-7900.0001309
Hiatt, M., E. Castañeda-Moya, R. Twilley, B.R. Hodges, and P. Passalacqua (2018), Channel-island connectivity affects exposure time distributions in a coastal river delta, Water Resources Research, 54, https://doi.org/10.1002/2017WR021289
Meselhe, E., Sadid, K., & Khadka, A. (2021). Sediment distribution, retention and morphodynamic analysis of a river-dominated deltaic system. Water, 13(10), 1341.
Olliver, E. A., & Edmonds, D. A. (2021). Hydrological connectivity controls magnitude and distribution of sediment deposition within the deltaic islands of Wax Lake Delta, LA, USA. Journal of Geophysical Research: Earth Surface, 126(9), e2021JF006136
Shaw, J. B., Mohrig, D., & Wagner, R. W. (2016a). Flow patterns and morphology of a prograding river delta. Journal of Geophysical Research: Earth Surface, 121, 372–391. https://doi.org/10.1002/2015JF003570Citation: https://doi.org/10.5194/egusphere-2024-3552-RC1 -
RC2: 'Comment on egusphere-2024-3552', Anonymous Referee #2, 21 Jan 2025
This research article presents a numerical framework that schematizes a delta channel network as a series of connected bifurcations. The research builds on a large body of work that considers “stability of bifurcations”, or what configuration of water and sediment partitioning at a bifurcation enables the bifurcation to persist (i.e., be in equilibrium) rather than abandon one of the branches. This work extends that framework to multiple bifurcations, wherein the upstream leg of a bifurcation is treated as one of two downstream branches of another bifurcation; this is considered to be analogous to a delta network. Through a system of equations derived for any initial delta configuration, system parts and variables are isolated, and their stability is determined. A key finding, per the article title, is that there are multiple flow-partitioning configurations of given planform delta configuration that are stable. The framework is then initialized with data from the real-world Po River delta system, and the stability of this system is explored. Through this analysis, the authors have identified new insights into the possible controls on avulsion and bifurcations stability, as well as potential futures for the Po River delta system.
Overall, the article is fairly well written, interesting, and will be well received by the readers of Earth Surface Dynamics. The introduction and discussion could benefit from clarification to contextualize the research. The model description and presentation of results are excellent. In particular, I enjoyed reading the Po River delta application, and exploration of possible avulsions in the system (Figure 9). I recommend some minor revisions before publication.
Main comments:
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The motivation in the Introduction could be made more specific to this research. At present, it is very general about anthropogenic modification and “proper management” but does not specifically talk about channels or avulsions. For example, there is discussion of levees reducing flow onto interdistributary basins (line 27) but it is not clear how this relates to channel stability. The authors mention “navigability and downstream infrastructure” (line 388) in the discussion, which may be more relevant motivations for this study.
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I am not incredibly familiar with the Salter 2018 2020, Barile 2023, Ragno 2022, and Durante 2024 papers and the framework described in each (lines 36–54). It would help the reader understand the advance of this study if it could be clarified how each of these models/stability frameworks differs (or not) from the one presented here. This will, overall, help to contextualize this study in the wider literature.
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a. The organization of the discussion could be improved. The Discussion could be improved by reducing the number of paragraphs and grouping logically-related ideas into subsections. Subsections could break apart the analysis of (i) internal bifurcation feedback, (ii) system planimetric effects, (iii) and Po River delta application.
b. I also suggest the authors revisit the logical organization of their paragraphs in the Discussion section. For example, there are several times that the discussion mentions seaward effects (lines 382, 393), but these ideas span a few (sometimes short) paragraphs. -
The idea of adjustment timescales and equilibria introduced in lines 307–312 is not revisited when discussing the channel abandonment (line 344–348), or soft avulsion (line 354–360), or delta lobe progradation (line 382–390). In my opinion, this discussion of timescales is the most important aspect of applying this numerical framework to the real world in any meaningful way, which seems to be of interest to the authors. I realize the framework is not fully morphodyanmic and does not explicitly include a temporal evolution, but the authors could identify terms in the framework that would be compared against real world processes and rates mentioned above (abandonment, soft avulsion, lobe progradation) to determine the scales at which this framework is useful. To me, this is a major limitation to understanding whether this framework has any predictive power.
Minor comments/corrections:
- The meaning of “multiple equilibrium states” on line 4 of the abstract is not clear at this point. I suggest revising the abstract to be more specific about the “unique challenges” facing deltas (see Main Comment 1) and more specific about the numerical approach before stating what exactly the study identifies.
- The actual description of the numerical framework, including relevant terms and their relationships, is excellent. Thank you.
- The analysis beginning on line 168 assumes a symmetrical planform delta (Lb1=Lc1), correct? This was not clear to me at first: even though it does say symmetrical on line 171/172, the sketch in Figure 3 is not depicting a symmetrical delta, but this sketch is referenced on line 172. Moreover, what does Figure 3 depict that is not already covered in Figure 2? I found this to be a sort of confusing point, because I couldn’t understand how Lb1=Lb2 in Figure 3 when they are clearly different, until I reread a few times and realized the sketch did not match the description. I suggest the authors consider revising Figures 2/3/4c/4d to show the necessary components and only one time, for both a case of symmetric delta asymmetric delta. This will also help clarify how a delta can be planform symmetrical but have asymmetrical discharge partitioning.
- Suggest to indicate the meaning of the dashed lines in Figures 6 and 7 in either the figure itself or the figure caption.
- “the concept of long-term morphodynamic equilibrium in river deltas may be inherently transient” was a confusing statement to me. I don’t think the authors mean the concept is transient. Suggest revising to be more specific.
Citation: https://doi.org/10.5194/egusphere-2024-3552-RC2 - AC2: 'Reply on RC2', Lorenzo Durante, 19 Feb 2025
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- AC1: 'Reply on RC1', Lorenzo Durante, 19 Feb 2025
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-3552', Matthew Hiatt, 20 Jan 2025
Review of “Multiple Equilibrium Configurations in River-Dominated Deltas”
Review date: Jan 20, 2025
Review by: Matt Hiatt
Conflicts: This is my first review of the manuscript and I identify no conflicts of interest.
Assessment: The manuscript is well-presented, relatively easy to read and follow, and is free of grammatical errors. Overall, I found the paper interesting and the results showing the variable effects of downstream length, in the channels immediately downstream or downstream of the second bifurcations, follows well-understood phenomena based on models from these authors and others. The comparison to the Po River delta is a welcomed piece, and the model does provide some interesting insights into the dynamics of that system. I have some criticisms of the contextualization of the results, especially with the assumption that flow is contained completely within channels. I am not suggesting that the authors redo anything, but it is my opinion that this assumption warrants some consideration and discussion. The abstract also needs to be edited to provide more substance and detail. At the moment it is very short and general to the point it is difficult to tell what novel insights this paper provides, and there are plenty of interesting results the authors could include to improve it.
Major points:
Abstract: The abstract lacks substantive information on the results of the paper. It I clear that equilibrium configurations are analyzed, but it’s not clear what novel information or insights this manuscript provides. These authors have published several papers on equilibrium configurations in bifurcations, deltas, etc. and it would be beneficial to add specificity to the abstract.
It appears that there is no overbank flow allowed in such a model. If my understanding of the way these models work is correct, there cannot be an internal outlet. Is perfect flow conservation within the channel deltaic network to the seaward boundary realistic? For eg., see Allison et al (2023; 2012), Feizabadi et al., 2024; Gao et al., 2023; Hiatt & Passalacqua (2015;2017); Hiatt et al., (2018); Shaw et al., 2016. Even if it is not realistic, how does this assumption affect the results? Several studies suggest that connectivity with the floodplain is a primary driver of morphology in river deltas (e.g., Coffey and Shaw, 2017; Olliver and Edmonds 2021), and it stands to reason that this should affect bed morphology, etc. I recognize many of these examples are from Wax Lake Delta, but nevertheless this is often considered a prototype river dominated delta. I think this should be explained in the context of the assumption/limitations of the model design and in the discussion section to understand how containing flows to the channel network influences predictions of morphology/stability. This point may be important when considering the results shown in Figure 5. Water level asymmetry can drive lateral flow (Gao et al., (2023)) and may have implications for the results showing disagreement with the Po system, especially in the more downstream reaches (Tolle), where I assume the assumption of conserved channelized flow fails (I am not sure of this, of course, but there certainly looks to be connections in Figure 1b).
Minor points and edits:
Line 10-11: Is the quantity and quality of sediment relative to the accommodation space really the key driver? In other words, even if the quantity of sediment is very small, if the space that needs to be filled is very small then a delta will be formed. The opposite is also true for large sediment loads with lots of space to fill. I suppose the point is moot because the authors mention this is in the next sentence, essentially.
Figure 1b: If the bathymetry of the channels is shown, we likely need a colorbar to distinguish elevations, otherwise it should be removed to match the birdsfoot. Also, I know the Po is the focus of the manuscript, but there should probably also be an inset map for the Birdsfoot. The inset map in Figure 1b is also not supremely helpful to those that are not familiar with northern Italy, so I’d recommend showing the full country and political boundaries.
Lines 21-22: “…drains a significant amount of water and carries a substantial quantity of sediment…” I’d recommend just reporting those annual figures here instead of using qualifying adjectives. Just give the quantities.
Lines 30-32: This statement should be modified or removed: There are many studies focused on deltas that consider things other than flow routes and bio-ecology (not even sure what bio-ecology is). I would recommend a rewrite of this whole paragraph, giving proper consideration to the literature. Deltaic science is multidisciplinary are there are myriad studies across disciplines, so saying that most studies related to deltas “…focus merely on hydrodynamics…” is incorrect. The second argument also may not be correct – there are quite a number of detailed morphological modeling studies in the Mississippi River Delta, for example (e.g., Meselhe et al., (2021) cited below).
Lines 36-42: While I am familiar with these models and agree that they are useful , I recommend being more objective and removing words such as “easier” and “powerful insight.”
Line 57-58: There is some work on the bed morphology in Wax Lake Delta from Ehab Meslhe’s group using a Delt3D Morpho model (Meselhe et al., 2021).
Line 182: What is the critical threshold for R_Up? Can the authors please present an example for on of the L’tot values so the reader can more easily contextualize the results in Figure 4?
Citations
Allison, M. A., Meselhe, E. A., Kleiss, B. A., & Duffy, S. M. (2023). Impact of water loss on sustainability of the Mississippi River channel in its Deltaic Reach. Hydrological Processes, 37(10), e15004.
Allison, M. A., Demas, C. R., Ebersole, B. A., Kleiss, B. A., Little, C. D., Meselhe, E. A., ... & Vosburg, B. M. (2012). A water and sediment budget for the lower Mississippi–Atchafalaya River in flood years 2008–2010: Implications for sediment discharge to the oceans and coastal restoration in Louisiana. Journal of Hydrology, 432, 84-97.
Coffey, T. S., & Shaw, J. B. (2017). Congruent bifurcation angles in river delta and tributary channel networks. Geophysical research letters, 44(22), 11-427.
Gao, W., Wang, Z. B., Kleinhans, M. G., Miao, C., Cui, B., & Shao, D. (2023). Floodplain connecting channels as critical paths for hydrological connectivity of deltaic river networks. Water Resources Research, 59(4), e2022WR033714.
Feizabadi, S., C. Li, and M. Hiatt (2024), Response of river delta hydrological connectivity to changes in river discharge and atmospheric frontal passage, Frontiers in Marine Science, 11, https://doi.org/10.3389/fmars.2024.1387180
Hiatt, M. and P. Passalacqua (2015), Hydrological connectivity in river deltas: The first-order importance of channel-island exchange, Water Resources Research, 51, 2264–2282, https://doi.org/10.1002/2014WR016149
Hiatt, M. and P. Passalacqua (2017), What controls the transition from confined to unconfined flow? Analysis of hydraulics in a coastal river delta, Journal Hydraulic Engineering, 60th Anniversary Reviews,143(6), https://doi.org/10.1061/(ASCE)HY.1943-7900.0001309
Hiatt, M., E. Castañeda-Moya, R. Twilley, B.R. Hodges, and P. Passalacqua (2018), Channel-island connectivity affects exposure time distributions in a coastal river delta, Water Resources Research, 54, https://doi.org/10.1002/2017WR021289
Meselhe, E., Sadid, K., & Khadka, A. (2021). Sediment distribution, retention and morphodynamic analysis of a river-dominated deltaic system. Water, 13(10), 1341.
Olliver, E. A., & Edmonds, D. A. (2021). Hydrological connectivity controls magnitude and distribution of sediment deposition within the deltaic islands of Wax Lake Delta, LA, USA. Journal of Geophysical Research: Earth Surface, 126(9), e2021JF006136
Shaw, J. B., Mohrig, D., & Wagner, R. W. (2016a). Flow patterns and morphology of a prograding river delta. Journal of Geophysical Research: Earth Surface, 121, 372–391. https://doi.org/10.1002/2015JF003570Citation: https://doi.org/10.5194/egusphere-2024-3552-RC1 -
RC2: 'Comment on egusphere-2024-3552', Anonymous Referee #2, 21 Jan 2025
This research article presents a numerical framework that schematizes a delta channel network as a series of connected bifurcations. The research builds on a large body of work that considers “stability of bifurcations”, or what configuration of water and sediment partitioning at a bifurcation enables the bifurcation to persist (i.e., be in equilibrium) rather than abandon one of the branches. This work extends that framework to multiple bifurcations, wherein the upstream leg of a bifurcation is treated as one of two downstream branches of another bifurcation; this is considered to be analogous to a delta network. Through a system of equations derived for any initial delta configuration, system parts and variables are isolated, and their stability is determined. A key finding, per the article title, is that there are multiple flow-partitioning configurations of given planform delta configuration that are stable. The framework is then initialized with data from the real-world Po River delta system, and the stability of this system is explored. Through this analysis, the authors have identified new insights into the possible controls on avulsion and bifurcations stability, as well as potential futures for the Po River delta system.
Overall, the article is fairly well written, interesting, and will be well received by the readers of Earth Surface Dynamics. The introduction and discussion could benefit from clarification to contextualize the research. The model description and presentation of results are excellent. In particular, I enjoyed reading the Po River delta application, and exploration of possible avulsions in the system (Figure 9). I recommend some minor revisions before publication.
Main comments:
-
The motivation in the Introduction could be made more specific to this research. At present, it is very general about anthropogenic modification and “proper management” but does not specifically talk about channels or avulsions. For example, there is discussion of levees reducing flow onto interdistributary basins (line 27) but it is not clear how this relates to channel stability. The authors mention “navigability and downstream infrastructure” (line 388) in the discussion, which may be more relevant motivations for this study.
-
I am not incredibly familiar with the Salter 2018 2020, Barile 2023, Ragno 2022, and Durante 2024 papers and the framework described in each (lines 36–54). It would help the reader understand the advance of this study if it could be clarified how each of these models/stability frameworks differs (or not) from the one presented here. This will, overall, help to contextualize this study in the wider literature.
-
a. The organization of the discussion could be improved. The Discussion could be improved by reducing the number of paragraphs and grouping logically-related ideas into subsections. Subsections could break apart the analysis of (i) internal bifurcation feedback, (ii) system planimetric effects, (iii) and Po River delta application.
b. I also suggest the authors revisit the logical organization of their paragraphs in the Discussion section. For example, there are several times that the discussion mentions seaward effects (lines 382, 393), but these ideas span a few (sometimes short) paragraphs. -
The idea of adjustment timescales and equilibria introduced in lines 307–312 is not revisited when discussing the channel abandonment (line 344–348), or soft avulsion (line 354–360), or delta lobe progradation (line 382–390). In my opinion, this discussion of timescales is the most important aspect of applying this numerical framework to the real world in any meaningful way, which seems to be of interest to the authors. I realize the framework is not fully morphodyanmic and does not explicitly include a temporal evolution, but the authors could identify terms in the framework that would be compared against real world processes and rates mentioned above (abandonment, soft avulsion, lobe progradation) to determine the scales at which this framework is useful. To me, this is a major limitation to understanding whether this framework has any predictive power.
Minor comments/corrections:
- The meaning of “multiple equilibrium states” on line 4 of the abstract is not clear at this point. I suggest revising the abstract to be more specific about the “unique challenges” facing deltas (see Main Comment 1) and more specific about the numerical approach before stating what exactly the study identifies.
- The actual description of the numerical framework, including relevant terms and their relationships, is excellent. Thank you.
- The analysis beginning on line 168 assumes a symmetrical planform delta (Lb1=Lc1), correct? This was not clear to me at first: even though it does say symmetrical on line 171/172, the sketch in Figure 3 is not depicting a symmetrical delta, but this sketch is referenced on line 172. Moreover, what does Figure 3 depict that is not already covered in Figure 2? I found this to be a sort of confusing point, because I couldn’t understand how Lb1=Lb2 in Figure 3 when they are clearly different, until I reread a few times and realized the sketch did not match the description. I suggest the authors consider revising Figures 2/3/4c/4d to show the necessary components and only one time, for both a case of symmetric delta asymmetric delta. This will also help clarify how a delta can be planform symmetrical but have asymmetrical discharge partitioning.
- Suggest to indicate the meaning of the dashed lines in Figures 6 and 7 in either the figure itself or the figure caption.
- “the concept of long-term morphodynamic equilibrium in river deltas may be inherently transient” was a confusing statement to me. I don’t think the authors mean the concept is transient. Suggest revising to be more specific.
Citation: https://doi.org/10.5194/egusphere-2024-3552-RC2 - AC2: 'Reply on RC2', Lorenzo Durante, 19 Feb 2025
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- AC1: 'Reply on RC1', Lorenzo Durante, 19 Feb 2025
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Lorenzo Durante
Nicoletta Tambroni
Michele Bolla Pittaluga
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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