The effect of operational discharge capacity of pumps and sluices on flood hazards &ndash; A case study on discharging the Rhine and Meuse under sea level rise

van Gijzen, Laurie; Bakker, Alexander M.; Jonkman, Sebastiaan N.

doi:10.5194/egusphere-2025-5801

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https://doi.org/10.5194/egusphere-2025-5801

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23 Dec 2025

| 23 Dec 2025

The effect of operational discharge capacity of pumps and sluices on flood hazards – A case study on discharging the Rhine and Meuse under sea level rise

Laurie van Gijzen, Alexander M. Bakker, and Sebastiaan N. Jonkman

Abstract. Future sea level rise will likely hamper the discharge of excess water from low-lying water systems all around the world. One example of such a water system is the Rhine-Meuse delta in the Netherlands, which discharges to the North Sea. A possible mitigation strategy involves closing off the delta from the North Sea with large dams and to discharge the incoming river discharge with large pumping stations. In this study, we determine the required amount of pump capacity by including the new concept of operational discharge capacity. This way we can account for the variations in the available pump and sluice discharge capacity due to variations in the head difference between the sea and water system and possible technical malfunctions. The effect of variations in the operational discharge capacity on return periods of extreme water levels in the water system is assessed within a probabilistic and hydraulic model framework.

We find that variations in operational discharge capacity substantially increase maximum water levels in the water system and increase flood frequencies compared to simulations with the assumption of a constant and fully available discharge capacity. In one scenario of our case study, including the effect of operational discharge capacity leads to an increase in flood frequency from 1/10,000 years to 1/75 years. In our case study, most of the increase can be attributed to including sluice reliability. Including pump reliability increases the frequency of higher water levels in the reservoir, until a water level is reached at which the sluices are available. However, available sluices can prevent a further increase of reservoir water levels. The precise effect of operational discharge capacity will vary per water system and design set-up. Yet, the examples in this paper show a clear effect for most design scenarios. Therefore, the operational discharge capacity is a crucial parameter that should be taken into account in the design of pumping stations.

Received: 21 Nov 2025 – Discussion started: 23 Dec 2025

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Laurie van Gijzen, Alexander M. Bakker, and Sebastiaan N. Jonkman

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-5801', Anonymous Referee #1, 31 Jan 2026

This manuscript reported a study on the flooding frequency in Rhine-Meuse delta in the Netherlands under sea level rise and considering the failure of pumps and sluice. The topic fulfills with the journal and is quite interesting. However, the study was very technical and the manuscript read like a technical report and was far from an academic journal paper. I would not support its publication in the present version. Below are suggestions for further revision.
(1) The introduction was long but most was related to the background of the problem. Discussion on the related academic topics was not enough. Besides, most of the cited references were published many years ago, not recent.
(2) The writing, formulas, and figures should be improved to reach the standard of an academic journal paper. For example,
(2.1) Figure 4 showed three sketches of the variation of pump head with flow rate. It read so confusing that how the authors obtained this relations and which situation they were used for. In the main text, for Figure 4(a), it was claimed that “The amount of energy loss varies with the flow velocity. Higher velocities cause higher friction losses, while eddies are more prominent at lower velocities. This results in a practical pump curve (Figure 4.a)”. Were there any references to support this sketch? “Eddies are more prominent at lower velocities” read strange, as the a faster velocity corresponds to a higher turbulent flow and more eddies. For what the eddies were ‘more prominent’?
(2.2) Besides, in Figure 4, the mathematical symbols were not standard, like Hdyn and Hstat.
(2.3) Similarly, in Figure 5, H_crit was also not a standard mathematical symbol.
(2.4) Figure 5, it is suggested to use subfigures to separate the figure into three subfigures and clarify what the subfigure shows. For example, the authors have not mentioned what the below-right part of the figure mean and used for.
(2.5) There were many errors related to mathematical expressions. For example, Line 236, “A peak discharge with a 2 year frequency”. Frequency has a unit of year?
(2.6) Moreover, line 240, “Both experiments correspond to 30,000 years (our return period of interest being 10,000 years x 3)”. It is hard to understand the meaning of the sentence in the bracket, especially “10,000 years x 3”.
(2.7) More, lines 316-317, “f(Fail)(= 7.2) is the frequency” and “f(Qex)(= 0.5)”? What were their meaning of these two mathematical expression?
(2.8) Figure 7 is a typical figure of this manuscript. There was no explanation of each subfigure. Even in the subfigure, there was not x and y titles of the plot like in Figure 7(a).
(3) The description of the method was not straightforward. There were a lot of wordy and useless descriptions. However, critical information should be provided but the authors did not. For example, Line 125, “for 2 meter and 5.4 sea level rise. In this study we only consider 2 meter sea level rise”. The authors should at least mention what scenario the “2 meter” and “5.4 meter” cases were used for? Why the authors only considered 2 meter in this study.
(4) Typos or grammar errors. For example,
(4.1) Line 42, “Haringvlietsluices” should be “Haringvliet sluices”.
(4.2) Line 116, “The northern outlet is the Nieuwe Waterweg is”. Delete one of the two “is”.
(4.3) Line 155, it should be Figure 4(a), not 4(c).
(4.4) Line 136, “buffer (V_buffer) with a an incoming river discharge”. Delete “a”;
(4.5) Lines 125, “for 2 meter and 5.4 sea level rise” changed to be “2- and 5.4-meter sea level rise”

Citation: https://doi.org/10.5194/egusphere-2025-5801-RC1
- AC1:
  'Reply on RC1', Laurie Van Gijzen, 21 May 2026
  Dear reviewer,
  Thank you for the critical review and the valuable comments. Like the other review comment, this review emphasizes the importance and novelty of the subject, but also states that the presentation needs improvement. Subsequently, the review presents a number of useful suggestions that helped us to substantially improve the manuscript. In the remainder of this response, we explain how we dealt with each issue.
  The introduction was long but most was related to the background of the problem. Discussion on the related academic topics was not enough. Besides, most of the cited references were published many years ago, not recent.
  
  We substantially revised the introduction to improve focus and readability. In particular, we shortened the introductory section and critically evaluated the necessity of the case-study descriptions. Several elements that are introduced later in the manuscript and non-essential for the introduction have been moved or streamlined to avoid repetition with later sections, in line with the reviewer’s observation. Furthermore, we clarified the problem statement by more explicitly emphasizing that tidal dynamics and operational malfunctions are highly relevant for discharge capacity assessments. We agree with the reviewer that the used citations are relatively old and few in number. However, despite an extensive literature search, we found that only a limited body of research is currently available on this specific topic, particularly studies that closely align with the scope and focus of our work because such considerations are not yet standard practice in operational applications. We have tried to include the most relevant and applicable references available in the literature.
  The writing, formulas, and figures should be improved to reach the standard of an academic journal paper. For example:
  2.1 : "Figure 4 showed three sketches of the variation of pump head with flow rate. It read so confusing that how the authors obtained this relations and which situation they were used for. In the main text, for Figure 4(a), it was claimed that “The amount of energy loss varies with the flow velocity. Higher velocities cause higher friction losses, while eddies are more prominent at lower velocities. This results in a practical pump curve (Figure 4.a)”. Were there any references to support this sketch? “Eddies are more prominent at lower velocities” read strange, as the a faster velocity corresponds to a higher turbulent flow and more eddies. For what the eddies were ‘more prominent’?
  
  We used the chapter by Wijdieks and Bos (1994), which was cited in the text for the information on pumps discussed in paragraph 3.1.1. We have included an extra citation in the caption. A similar figure to Figure 4.a can be found in that document. In this case the eddies do not refer to smaller eddies related to friction induced turbulence, but to eddies resulting from a backflow within the pump which can occur under lower velocities. We have changed the term eddies into backflow, to account for the confusion.
  2.2: Besides, in Figure 4, the mathematical symbols were not standard, like Hdyn and Hstat. Similarly, in Figure 5, H_crit was also not a standard mathematical symbol.
  
  We agree that we should conform to the relevant literature. Yet, we see that the use of symbols is not always consistent. So, we decided to conform as much as possible to most related studies. We have changed the mentioned symbols to H_dyn, H_stat and H_crit.
  2.3: Figure 5, it is suggested to use subfigures to separate the figure into three subfigures and clarify what the subfigure shows. For example, the authors have not mentioned what the below-right part of the figure mean and used for.
  
  We have included subfigures for the upper and lower left figure. The lower right figure is a legend, explaining the meaning of each color in the flow diagram. This is made clear in the figure and we have included an extra description in caption.
  2.4: There were many errors related to mathematical expressions. For example, Line 236, “A peak discharge with a 2 year frequency”. Frequency has a unit of year?
  
  We mean it to have the unit [1/year]. The text changed to 1-in-2 year frequency.
  2.5: Moreover, line 240, “Both experiments correspond to 30,000 years (our return period of interest being 10,000 years x 3)”. It is hard to understand the meaning of the sentence in the bracket, especially “10,000 years x 3”.
  
  We mean that our return period of interest( 1/10,000 years) should be multiplied by 3. This has been changed in the text.
  2.6: More, lines 316-317, “f(Fail)(= 7.2) is the frequency” and “f(Qex)(= 0.5)”? What were their meanings of these two mathematical expression?
  
  In these cases f(Fail) refers to the failure frequency of the pumps, being 7.2 times per year. f(Q_ex) refers to the frequency of an extreme discharge event, being 1/2 years. These are constant stochasts in our model. We have rephrased this sentence in the text, so the symbols are not written in this form.
  2.7: Figure 7 is a typical figure of this manuscript. There was no explanation of each subfigure. Even in the subfigure, there was not x and y titles of the plot like in Figure 7(a).
  
  We understand the reviewers comment and have rigorously revised the lay-out of Figure 7. We have included explanations for all subfigures in the caption and made sure all plots included the proper elements such as axis titles.
  The description of the method was not straightforward. There were a lot of wordy and useless descriptions. However, critical information should be provided but the authors did not. For example, Line 125, “for 2 meter and 5.4 sea level rise. In this study we only consider 2 meter sea level rise”. The authors should at least mention what scenario the “2 meter” and “5.4 meter” cases were used for? Why the authors only considered 2 meter in this study.
  
  To improve the description of the method we have:
  removed redundant phrasing, there are occasionally sentences that do not add substantial information or contain repetition.
  
  verified whether the methodological description is sufficiently detailed to allow reproduction of the study. The summary provided by Reviewer 2 already seems to suggest that this is largely the case.
  
  Check whether all methodological choices and assumptions have been adequately explained and justified.
  
  We have included an explanation why only the 2 meter case was implemented in this study. The 2 meter case was applied to all scenarios described in table 3.
  
  Typos or grammar errors
  
  We have corrected the mentioned typos and grammar errors and double checked the manuscript for any other typos and errors.
  
  Citation: https://doi.org/10.5194/egusphere-2025-5801-AC1
RC2:
'Comment on egusphere-2025-5801', Anonymous Referee #2, 10 Apr 2026

Review of the paper “The effect of operational discharge capacity of pumps and sluices on flood hazards - A case study on discharging the Rhine and Meuse under sea level rise” by van Gijjzen et al.

The study addresses a very important and relevant issue concerning the design of coastal flood defense systems to cope with storm surges and river floods at estuary outlets. The case study refers to the Rhine–Meuse delta in the Netherlands, a region particularly vulnerable to flooding.
The main element of novelty in the authors’ proposal is the inclusion of operational discharge capacity in the reliability assessment of coastal defense infrastructures in such low-lying water systems. Operational discharge capacity takes into account possible technical malfunctions of both pumps and sluices. The frequency of failure events for pumps and sluices is introduced, together with storm surge and peak river discharge, as stochastic inputs in a simple mass balance model of the Rhine–Meuse delta.
A Monte Carlo approach is used to simulate water levels in the Rhine–Meuse delta for three adaptation designs with different buffer capacities. The main goal is to calculate the frequency of exceedance of a predefined critical level for the different configurations of the water system, characterized by pumping, buffer, and sluice capacity.
I found the paper interesting and, to my knowledge, it addresses issues that are generally not taken into account in the design of such flood defense systems. This makes the manuscript potentially suitable for publication. However, I also believe that the quality of the manuscript could be significantly improved by reducing its length and removing figures that are not strictly necessary. There are several redundancies in the text, while at the same time some relevant aspects are not sufficiently developed.
For instance, paragraphs 3.1.1 and 3.1.2 could be merged into a single, more concise paragraph. Figure 4 could be omitted, or only subplot 4c retained.
Paragraph 3.1.3 (“Failure events”) should discuss more thoroughly the issue that represents the core of the study. What types of failure events are considered? How is the frequency of pump and sluice failures evaluated? Are there criteria to guide pumping station design? In the specific case of the Rhine–Meuse delta, are there historical records that could support the representation and mathematical formalization of the type and frequency of failures? I suggest integrating paragraph 4.3 into paragraph 3.1.3. In addition, the derivation of the parameters reported in Table 1 is unclear and should be better explained.
I also suggest integrating paragraph 3.2 (“Water system dynamics including pumps and discharge sluices”) with paragraph 4.2 (“Reservoir model”). The representation of the water system dynamics and its mathematical formalization could be better harmonized within a single paragraph.
Figures 5, 6, and 8 could also be combined into a single figure.
Regarding paragraph 4.5 (“Design Scenarios”), a brief discussion explaining how these scenarios were identified and providing some justification would be useful. Otherwise, the proposed solutions may appear somewhat arbitrary. Some assumptions, such as the 30-day flood duration and the independence of storm surge and flood events, should be justified.
The results are sound, but I suggest improving and better organizing their presentation. Figure 14 should be checked: there is a dot on the right-hand side whose corresponding scenario is unclear, and there is no reference explaining the size of the dots.
Finally, in the present study, the authors use a heuristic approach to investigate the influence of operational discharge capacity and buffer capacity on water levels in the delta, by comparing a priori assumed configurations of the water system design. A possible further development of this work would be to integrate the reservoir model into a multi-objective optimization framework (for instance, a genetic algorithm), in which buffer, pumping, and sluice capacities are decision variables; water level is the state variable; and failure events, floods, and storm surges are stochastic inputs.
Objective functions could include minimizing the frequency of exceedance of critical water levels in the delta and the costs of construction and maintenance of defense infrastructures. The outcome of such a model would be a Pareto front of optimal solutions, from which the trade-off between the two objective functions, and relative solutions in terms of buffer, pumping and sluice capacity, could be inferred.

Citation: https://doi.org/10.5194/egusphere-2025-5801-RC2
- AC2:
  'Reply on RC2', Laurie Van Gijzen, 21 May 2026
  Dear reviewer,
  We want to thank you for your time reviewing our paper and your constructive feedback and comments. The comments acknowledge the scientific relevance of the study while also pointing out areas where the manuscript could be strengthened, particularly in terms of presentation and clarity. The suggestions offered by the reviewer were very helpful and have guided several important revisions to the manuscript. Below, we respond to each comment in detail and describe the corresponding changes that were made.
  There are several redundancies in the text, while at the same time some relevant aspects are not sufficiently developed.
  
  We critically reviewed the different sections to prevent redundant information. For instance, we reduced the length of the introduction and reconsidered the extent to which the case-study descriptions were necessary at this stage of the manuscript, as they are also fully introduced in section 2. In addition, the problem statement has been refined to more clearly highlight the importance of tidal dynamics and operational failures in the assessment of discharge capacity.
  
  1.1: For instance, paragraphs 3.1.1 and 3.1.2 could be merged into a single, more concise paragraph.
  
  We have merged the paragraphs and rewritten some passages.
  1.2: Figure 4 could be omitted, or only subplot 4c retained.
  
  For the full comprehension of the working of pumps, we think 4.b and 4.c should remain in the paper. We agree that figure 4.a might be less important.
  1.3: Paragraph 3.1.3 (“Failure events”) should discuss more thoroughly the issue that represents the core of the study. What types of failure events are considered? How is the frequency of pump and sluice failures evaluated? Are there criteria to guide pumping station design? In the specific case of the Rhine–Meuse delta, are there historical records that could support the representation and mathematical formalization of the type and frequency of failures?
  
  Specifically large pump failures occur very rarely, which also explains why clear and universally accepted quantitative estimates are limited in literature. There are no historical records that support the frequency of large failures. Therefore, we used values that were based on the reliability models currently applied by Rijkswaterstaat. These are internal reports, due to the sensitivity of the information.
  1.4: I suggest integrating paragraph 4.3 into paragraph 3.1.3. In addition, the derivation of the parameters reported in Table 1 is unclear and should be better explained. I also suggest integrating paragraph 3.2 (“Water system dynamics including pumps and discharge sluices”) with paragraph 4.2 (“Reservoir model”). The representation of the water system dynamics and its mathematical formalization could be better harmonized within a single paragraph."
  
  We agree with this suggestion. The new setup of section 3 will be:
  A Operational discharge capacity (3.1.1 and 3.1.2)
  B water system dynamics,
  C Technical malfunctions (3.2 and 4.2)
  C Malfunctions and reliability (3.1.3 and 4.3)
  D Sea water level and river discharge (4.3)
  
  1.5: Figures 5, 6, and 8 could also be combined into a single figure.
  
  We think Figure 5 and 6 have distinct functions in the paper. Figure 5 introduces the more high-level conceptual model and shows all the interactions between the different elements in the pump-sluice-water system. Figure 6 has a different goal by explaining the used probabilistic methodology to compute the exceedance curves. Figure 8 explains the steps taken within the reservoir model to compute the water level for the next timestep. Therefore, the different figures show our approach at different detail levels and we think the figures all have their own concepts to inform the reader.
  Regarding paragraph 4.5 (“Design Scenarios”), a brief discussion explaining how these scenarios were identified and providing some justification would be useful. Otherwise, the proposed solutions may appear somewhat arbitrary. Some assumptions, such as the 30-day flood duration and the independence of storm surge and flood events, should be justified.
  
  We have included the extra explanation mentioned by the reviewer and verified whether the methodological description is sufficiently detailed to allow replication of the study, including our assumptions made in the methodology. As we are replicating the study by Knowledge Program Sea-level Rise, we did not make many of these choices/assumptions ourselves, and we do not always know the reasons behind all assumptions and model choices. We have added the specification if this was the case.
  The results are sound, but I suggest improving and better organizing their presentation. Figure 14 should be checked: there is a dot on the right-hand side whose corresponding scenario is unclear, and there is no reference explaining the size of the dots.
  
  We have included the extra explanation in the text and in the figure.
  Finally, in the present study, the authors use a heuristic approach to investigate the influence of operational discharge capacity and buffer capacity on water levels in the delta, by comparing a priori assumed configurations of the water system design. A possible further development of this work would be to integrate the reservoir model into a multi-objective optimization framework (for instance, a genetic algorithm), in which buffer, pumping, and sluice capacities are decision variables; water level is the state variable; and failure events, floods, and storm surges are stochastic inputs. Objective functions could include minimizing the frequency of exceedance of critical water levels in the delta and the costs of construction and maintenance of defense infrastructures. The outcome of such a model would be a Pareto front of optimal solutions, from which the trade-off between the two objective functions, and relative solutions in terms of buffer, pumping and sluice capacity, could be inferred.
  
  We acknowledge the reviewer’s suggestion and agree that the case is indeed well suited for a multi-objective optimization framework, given the multiple competing interests involved, including navigation, flood safety, water supply, and spatial constraints. However, a comprehensive multi-objective optimization approach falls outside the scope of the present study. The focus of this work is therefore limited to the specific research objectives addressed here. In our next studies we expand on our current scope by also considering the life-cycle of the pumps in relation to functions, performance and investment costs.
  
  Citation: https://doi.org/10.5194/egusphere-2025-5801-AC2

Laurie van Gijzen, Alexander M. Bakker, and Sebastiaan N. Jonkman

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Short summary

Future sea level rise will likely challenge many low-lying deltas in the world. A possible mitigation strategy discharging the incoming river discharge with large pump-sluice stations. In this study we determine the required pump and sluice capacity by including the new concept of operational discharge capacity. We found that including operational discharge capacity led to an significant increase in flood frequency, making it crucial to account for in the design of pump-sluice stations.


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