the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Nov 2025
A Fluvial Flood Risk Model for Quantifying the Benefit of Mitigation Measures under Uncertainty
Abstract. We present a dynamic probabilistic flood risk model that addresses key challenges in the implementation of integrated flood risk management. These include the need for holistic, large-scale risk assessments that adopt a system-based perspective, and a decision-making framework based on benefit-cost analysis. The proposed model allows for the explicit simulation and dynamic coupling of the flood process components, including downstream flood wave propagation and possible dike failures, in a computationally efficient and data-sparse manner. It enables the consideration of aleatory and epistemic uncertainties in a 2-level Monte Carlo framework. By separating these uncertainties, the model supports robust risk assessments and facilitates the uncertainty-aware evaluation of the benefit of mitigation measures. The model is applied to the Bavarian Danube, demonstrating its ability to estimate the flood risk reduction potential from mitigation measures.
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RC1: 'Comment on egusphere-2025-4875', Anonymous Referee #1, 02 Dec 2025
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AC1: 'Reply on RC1', Mara Ruf, 05 Dec 2025
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Dear reviewer,
Thank you for the detailed and extremely valuable feedback!
We will incorporate your comments and address the questions you raised (also those directly in the manuscript) in our final version. Regarding your general comments:
1) We will make sure to point that out in the abstract and introduction of the paper.
2) Good point — We will state the limitations more clearly in the paper. The large uncertainties introduced by this simplification are, however, accounted for in the uncertainty analysis. The rationale for this model choice is that we wanted to run a very large number of simulations (which requires runtimes far shorter (~1sec per simulation) than any hydraulic model can provide, as far as we can judge) in order to holistically quantify the influence of epistemic and aleatory uncertainties (and therein also dike breaches) and to use this model in subsequent studies, f.e.x in optimization problems. Independent of that, we found your judgement very interesting: We had considered all model components to be in a roughly comparable degree of process representation…
3) Yes, we agree and struggled with this while writing the paper. On the one hand, the uncertainty and sensitivity analysis deserves a much larger share of the manuscript, since this is one of the main contributions of our work. On the other hand, the description of the flood risk model has already become quite long, and we wanted to avoid further inflating the paper. As a consequence, we chose to illustratively focus on only three epistemic uncertainties and therewith intended to show how the model — and the hierarchical structure — can incorporate and support UA and SA, without going into all modeling choices and background assumptions. I will try to shorten the flood risk model chapter (if possible) and expand the UA section.
4) In our case study, we limited the assessment to scenarios with recurrence intervals > 100 years because the mitigation measure we assess is only activated beyond that threshold. I realize this was not clearly described in the paper: we will add a description of the detention basin to the study area section and emphasize it again in the hydrological load and results sections. If other mitigation measures are evaluated, the catalogue of flood scenarios has to, of course, be extended
5) We agree and will add a short discussion in the end. Despite the more advanced approaches pursued in more recent studies (e.g. fully coupled model chains, like the benchmark study by Sairam et al. 2021), we believe that there are use cases where the development or application of these models is not feasible or, in the case of AI approaches, more useful. The model was developed in a fairly short time frame and with limited data available. Applying more advanced (and thus computationally more demanding) approaches to problem settings like feasibility studies, cost benefit analyses or optimization problems could be, out of our perspective, challenging. For these use cases, a simpler, computationally cheaper model based on surrogates can be advantageous. We will emphasize the model’s intended use but also its limitations in the paper.
Thanks again for your feedback and comments!
Citation: https://doi.org/10.5194/egusphere-2025-4875-AC1
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AC1: 'Reply on RC1', Mara Ruf, 05 Dec 2025
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RC2: 'Comment on egusphere-2025-4875', Anonymous Referee #2, 19 Jan 2026
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The paper presents a flood risk model to enable quick appraisal of flood mitigation measures. The model calculates expected benefits of a measure as a reduction in flood damage with respect to the ‘no measure’ baseline. The key feature of the model is its computational efficiency, which is obtained through an implementation that allows to pre-calculate a range of systems relationships, so that run time is faster. Such computational efficiency in turn enables a comprehensive quantification of output uncertainty and sensitivity through Monte Carlo simulations. I think the paper is potentially an interesting and valuable contribution, but it needs revision in order to clarify its novelty, scalability and transferability.
General remarks
1. The Introduction does not do enough to clarify the key focus and contribution of the study.
The description of the “three key necessary developments” on page 1-2 is very broad and potentially misleading. It raises a wide set of issues but after reading the full paper I think only the first one is addressed in this work. For example, the conclusions of point 2 and 3 that “integration into official practice is still lacking” and “practical implementation often remains fragmented across various professional sectors that focus on local flood protection planning” are certainly true but there is no follow up on them in the remainder of the paper. Point 3 on page 2 talks about “cross-border approaches” and “large spatial scales” but the proposed method is demonstrated here on a 380 km section of the Danube river in Germany, which is neither “cross-border” or necessarily “large scale”. The literature review on L. 57 onwards includes studies at very different scales, from national flood risk assessment (in the UK and Germany) to regional studies within Germany or even reach-level studies, for example the 50 km reach of the Po River of Domeneghetti et al. (2013). Hence, throughout the Introduction it is unclear what the paper focus is, in terms of spatial scale.
The statement of the study contribution (L.85-90) could be better connected to the previous literature review, so to clarify how exactly the proposed model differs or advance on the methods reviewed in previous lines 57-84. A much clearer statement is given in Sec 3.6: “The developed flood risk model differs from other methodologies, such as those presented by Vorogushyn (2008) and Domeneghetti et al. (2013), primarily in that ….” and in the Conclusions: “A key element enabling this independence is the developed flood routing method, along with segment-specific lookup tables that store the relationships between inundation elevation, floodwater volume, and damages.”. It might be useful to have these or similar statements made earlier on in the Introduction and not left at such later stages into the paper.2. Section 3 is very long and it is difficult to grasp which parts are a description of approaches that have been previously used and published by others, and which are the truly novel steps. Considering that the key contribution is the way the model is implemented (=with pre-computed look-up tables instead of dynamic coupling at runtime) it seems strange that “Sec. 3.6 - Model Implementation” takes only 8 lines out of a 12-pages “Sec 3 – Flood risk model” section! Indeed, novel ideas on how to perform pre-calculations are also spread out across Secs 3.1-3.5, but they are less obvious to find out. In summary, I suggest re-organising materials in this Section so that the key differences from previous studies and novel ideas are easier to identify.
3. The transferability and scalability of the proposed approach should be discussed. Could the approach sketched out in Figure 10 be applied to the entire Danube river or Germany-wide? What would be the challenges in terms of data availability, software implementation, run-time, etc.? Could the approach be applied in other regions of the world with different climatic and landscape characteristics? What are the critical assumptions underpinning the approach that may hinder its application elsewhere?
4. I am also confused by the organisation of materials through sections 3 and 5. “Sec. 5 - Results” only includes Figures of the aggregate loss estimates and their uncertainty and sensitivity to three selected parameters. This draws the reader’s attention to the UA&SA part of the paper, which is the least “interesting” as there is no novel contribution here (all the definitions and methods used for the UA&SA have been published before, as also acknowledged in Sec. 4). If the paper’s key contribution is the computationally-efficient implementation of the flood risk model, I would have expected the Results to mainly report on the behaviour of the model, and how its predictions compare to those of a dynamically coupled but more computationally expensive model - maybe at different river sections and under different scenarios with or without a dyke breaches. I suspect Fig. 7 and. 8 partially do this, but oddly they are embedded in Section 3 (“Flood risk model”), which somehow becomes both a description of the method and (implicitly) results section. In summary, I would suggest a better organisation of the materials and expanding results that demonstrate the “success” of the proposed approach for efficient implementation of flow routing and flood risk calculations, and less on the UA&SA results – where the authors apply standard methods instead of suggesting new ones.
Other specific points
Lines 150: why was the RCP8.5 scenario chosen, and does this means that everything that follows about hazard estimation only applies under such scenario? Please clarify.
Lines 153: “The detention basin evaluated in this study (5 is designed to be activated only when the discharges exceed the threshold of a 100-year event” Something wrong with this sentence, what does “(5” mean?
Line 204: “A breach resistance value — defined as the maximum water level the segment can withstand before failure — is randomly sampled from the fragility function”
What does this mean? How is the breach resistance value sampled from the fragility curve? UnclearLine 240 onwards: Does the approach to derive D use roughness, or not? First the authors say “This study employed a DEM with a 50x50 m grid cell resolution and average, land-use-specific roughness values based on literature data” but they do not mention how in the subsequent description, and in the end they conclude “However, this approach neglects the influence of various parameters such as terrain roughness, …” Please clarify
Line 396: “The reduction of risk associated with these factors is communicated as an additional benefit of the measures implemented, but it is not included in the formal benefit-cost analysis”
What does “communicated” mean? Are these factors quantified or assessed in any other qualitative way? If not, is this point even worth raising?Line 399: “The developed flood risk model differs from other methodologies, such as those presented by Vorogushyn (2008) and Domeneghetti et al. (2013), primarily in that the flood simulation model is executed independently of a coupling with hydraulic and hydrodynamic simulation models”
Confusing. I understand from Fig.2 that the “flood simulation model” is exactly the coupling of the hydraulic (=inundation) and hydrodynamic module, so the wording “is executed independently of a coupling with…” is confusing. Maybe the authors mean something along the lines of: “The developed flood risk model differs … primarily in that the execution of the flood simulation model does not require a dynamic coupling of the hydraulic and hydrodynamic simulation modules at runtime, but rely on reading from pre-computed lookup tables of …”?Sec. 4.1 “Xa is a set of multiple hundreds of aleatory random variables, which represent the flood scenarios, the resistance of all dike segments and the breach widths of failed dike segments”. Unclear. What is the flood scenario? How many options are there? How are the resistance and breach widths sampled (according to which distribution?) and what is the space explored (I assume proportional to the number of segments but this should be clarified also to get an idea of whether using 3,600 samples is enough or too little given the dimension of the space explored!)
Table 1: How are the epistemic uncertainties sampled? For example, I suppose that “breach width PDF” or “V-E relation dike segment” are functions, so how are they sampled? How can you represent the uncertainty in a function through a “beta distribution”? Unclear
Line 444: “This is shown in Fig. 12 for a0, no measure, and the implementation of the measure under study, aM” Unclear. I guess this result is obtained for a given realisation of the epistemic uncertainty? please clarify
Line 456: “To approximate E[Ye|Xe,i] based on the samples, a one-dimensional linear regression Sis applied” – linear assumption seems ok in the three examples provided here but may not in others, and is unnecessary – it is easy to use other non-linear approximators – see for example: https://doi.org/10.1016/j.envsoft.2015.09.011
Figure 2: add legend or info in the caption about the meaning of variables Q, W, V, E, D
Figure 10: fonts are very small and hardly readable
Figure 13: what does “No numbers are shown on the x-axis due to the preliminary nature of the results.” mean!? What is the point of showing results if they are so preliminary that their physical interpretation is still impossible/unclear?
Citation: https://doi.org/10.5194/egusphere-2025-4875-RC2
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Review of manuscript „A Fluvial Flood Risk Model for Quantifying the Benefit of Mitigation Measures under Uncertainty” by Mara Ruf et al., submitted to NHESS
The manuscript presents an interesting extension to the existing flood risk estimation and uncertainty quantification methods, with the aim of quantifying flood risk in economic terms for large river reaches. It applies a concept of simple surrogate models to the required flood model chain (rainfall-runoff simulation, river routing, dike breach/overtopping, inundation and damage estimation). It builds on the probabilistic flood risk assessment concepts developed about 20 years ago, including an uncertainty estimation using the concept of aleatory and epistemic uncertainty. The main advancement of the work is the inclusion of dike failures in a probabilistic manner and to include this in the risk and uncertainty estimation by a2-staged Monte Carlo analysis. Moreover, the work also presents the framework for a cost-benefit analysis of large-scale flood protection measures, like flood retention basins. This is possible because the model concept enables the downstream effect of flood protection measures in a river reach.
The proposed concept is valid and the work takes large scale flood estimation a step further, mainly by including probabilistic dike failures in the risk assessment. The manuscript is properly structured and the work is well presented. Overall, I recommend the publication in NHESS, but some issues should be addressed beforehand:
Next to these more general points I made some comments in the attached annotated manuscript.