Review of “Impact of wave-water level non-linear interactions for the projections of mean and extreme wave conditions along the coasts of western Europe” by Chaigneau et al.

The aim of this paper is to assess the impact of including time dependent water level variations in the external forcings of a regional wind-wave model of the IBI domain (i.e., an area of the northeastern Atlantic including the Iberian-Biscay-Ireland regions) on the wave setup estimated from modelled mean and extreme sea state statistics.

Two configurations of the same regional wind-wave model differing only in the water level forcing (i.e., one uses it while the other one does not) are compared. Numerical experiments include hindcast integrations covering the period 1950-2014 and projected simulations spanning the period 1950-2100 under two climate change scenarios.

I believe the idea behind the study is intriguing and of interest for the broad environmental-scientific community and I think the topic of the manuscript is relevant to Ocean Science journal. However, I do have few major concerns listed below that I think the authors should address before the study could be suitable for publication.

General major comments

1. Methodology:

• As stated by the authors (L60-61), “wave characteristics used to estimate wave setup are sensitive to water level changes in shallow waters, where waves interact with the ocean bottom.” From section 2.2.4 I understand that the wave model considers water-level variations only for the wave propagation (i.e., group velocity and wave number) while “coastal (depth-induced) breaking is not included” in the model (L92-95). My concern is that by not including the depth-induced wave-breaking the authors are missing a fundamental depth-dependent process, which can have a first order effect on the wave statistics in shallow water and hence on the wave setup. In addition, as the authors also explain in the introduction (L35-36), the wave setup is in fact due to the depth-induced wave breaking. So what I cannot understand is how the authors can assess the impact of water-level variations on the wave setup if the leading order physical mechanism driving the wave setup is not included in the model. I think the authors should carefully address this point in their manuscript.
• When assessing the impact of water-level forcing on the wave setup at a domain level the authors report an impact in few coastal locations. My doubt is: how much can we trust these results given the 6m minimum depth approximation?
• Also, could it be that the authors found a generally small (very few locations) impact because the depth-induced breaking is neglected and the minimum depth approximation is applied?

 2. Validation:

• The title of section 3 is “Validation and projections of IBI-CCS-WAV, without waves-sea level interactions” and in fact the figures of this section report data only for IBI-CCS-WAV. However, at L259-261 the authors state that “The ability of IBI-CCS-WAV and IBI-CCS-WAV_ssh to reproduce observed distributions is assessed for the mean state and the 99th percentile of the significant wave height and peak period since these variables are then used to compute the wave setup scaling”. Is the IBI-CCS-WAV_ssh validated as well? If not (as I believe is the case), then I think the authors should also include the validation for the experiment using water-level forcing since, apart from the impact on the wave setup, it is also interesting and useful to know for the wave modelling community whether including this forcing can help to improve the accuracy of the model.

3. Manuscript structure:

• In general, I think the structure of the paper should be substantially improved before being suitable for publication. Below, a list of possible changes:
• Section 2: this section is quite confused and not logically structured in my opinion. I would first move L101-112 as in intro of Sec. 2, improving the text and Fig 2 (the colours are to weak). Then, I think the authors could

            a) describe the numerical wave model (sec 2.1), avoiding the references to global and regional simulations (e.g. L85), since I think can confuse the reader.

            b) describe the regional wave configuration IBI-CCS-WAV (sec 2.2): this is the real focus of this paper, all the other models are used to force this model in my opinion. In addition, I would move L185-190 at the beginning of this section just to state at the beginning what is the aim of this model.

            c) describe the external forcings (sec 2.3) with three subsections:

                *) Atmospheric forcing (sec. 2.3.1), describing and validating (L138-152) CNRM-CM6-1-HR model and the fields used to force IBI-CCS-WAV. Also, please avoid the acronym GCM which is typically used for General Circulation Model instead.

                *) Hydrodynamic forcing (sec 2.3.2), describing IBI-CCS and the fields used to force IBI-CCS-WAV.

                *) Wave forcing (sec 2.3.3), describing CNRM-HR-WAV and the fields used to force IBI-CCS-WAV.

            d) Inclusion of water level variations in the regional wave model: IBI-CCS-WAV_ssh (sec 2.4)

            e) Wave setup calculation (sec. 2.5): Please check the definition of the wave setup scaling – there is a delta in the definition (L243) that I think should not be there.

• Section 4: I would first describe the impact on the entire coastal domain and after on the specific locations. Also, I think the authors should clarify better what is the rational behind the choice of those two specific locations. Why not for example the Bristol channel? The tidal range there is almost as large as in Mont-Saint Michel. Also, I would rewrite Sec. 4.2 and 4.1 (which are the most important sections in my opinion), trying to discuss more in depth what is the impact and to contextualise it, maybe moderating a bit the wording (e.g., “highly impacted”) which I think it is not fully reflecting the results of the authors.
• I would describe a bit better in the Conclusions and Abstract the limitations of your study.

Specific comments

• L13: you don’t need the acronym EWL here, since you don’t use it anymore in the abstract.
• The authors may want to add some references at L170 – 173. Here I am suggesting some possible references for the North Atlantic (which is the area I am more familiar with): the Atlantic coasts are subject to very energetic events in terms of significant wave heights, wave periods and energy flows (e.g., Masselink et al. 2016, Bruciaferri et al. 2021) whereas the Mediterranean Sea and North Sea are more sheltered areas. In addition, the zone also contains very different tidal regimes with both macro and micro tidal regimes respectively in the English Channel/Celtic Sea (Valiente et al. 2018, Stokes et al. 2021) and in the Mediterranean Sea.
• L219-220: “Limitations related to the use of parameterizations have been extensively discussed in Melet et al., 2020” -> can the authors do a summary of those limitations here so that the reader is aware?
• L224: please define “foreshore”.
• L355: Figure 7 illustrates “projected changes” -> changes respect to what? Please clarify
• L422-425: please rephrase it.
• L453: the most significant impact -> quite strong wording, you have an impact (not so strong) only in one location out of two in Fig. 10.
• L461: however small -> to me seems nihil
• L484-485: I would be careful here. If what the authors are saying is true, then why it is not valid everywhere, e.g. Mont-Saint Michel? Please clarify.

References

• Masselink, G. et al. 2016: The Extreme 2013/2014 Winter Storms: Hydrodynamic Forcing and Coastal Response along the Southwest Coast of England, Earth Surface Processes and Landforms, https://doi.org/10.1002/esp.3836
• Bruciaferri, D. et al. 2021 - The Impact of Ocean-Wave Coupling on the Upper Ocean Circulation During Storm Events, Journal of Geophysical Research: Oceans, https://doi.org/10.1029/2021JC017343
• Valiente, G. N. et al. 2018: Role of waves and tides on depth of closure and potential for headland bypassing, Journal of Marine Geology, https://doi.org/10.1016/j.margeo.2018.10.009
• Stokes et al. 2021: Forecasting coastal overtopping at engineered and naturally defended coastlines, Journal of Coastal Engineering, https://doi.org/10.1016/j.coastaleng.2020.103827 

Summary

This paper analyses the impact of nonlinear interactions between wind-waves and water level changes using numerical modelling projections. The study is focused on the IBI region, and the methods involve running different experiments accounting (or not) for water level variations, under different SLR scenarios. The focus is on the wave set up, which is calculated by deriving the wave setup scaling (without beach slope); the latter can then be scaled based on different empirical formulae or slopes. This allows calculation of the wave set-up over different potential beach slopes. Results show projected changes in significant wave height, peak periods, and wave set-up scaling. The inclusion of water level variation in the wave model has little (but some) impact over the mean sea state, however it does have an important impact during extreme event periods, particularly in high tidal range regions. Here, including the water-level changes can lead to an increase of significant wave height and wave setup.

General comments

The interaction between waves and ocean are bound by complex feedback effects, which are difficult to represent in models, yet increasingly important to consider in the light of future sea level rise predictions.  This paper therefore tackles a very current issue, of interest to the scientific community and within the scope of the journal; that of the impact of water-level changes over wind-wave projections in regional climate models.

This work gives a new, good picture of changes induced by water-level changes to both the significant wave height and the wave period at the coast. The study also shows changes to the wave set up scaling, in a way which can be easily re-used and adapted to future studies considering specific beach slopes.

Details on the models used and methodology are thoroughly detailed. The paper is overall well written with strengths as well as weaknesses of the method explained clearly and objectively outlined.  The limitation of the study however could be better explained in the discussion.

The discussion brings up important points to consider when analyzing results but could be better written by developing what the implications of the paper’s findings are.

I thinks this paper brings an interesting contribution to the field, but before publication I would like the authors to clarify the following major point:

• The model used does not include shallow water processes such as wave breaking (line. 93), and cannot represent important interactions with the seabed in shallow regions, as the minimum depth is 6m (line. 206). These shallow water processes, as stated by the authors in the introduction, are important for wave setup and set down; yet this work estimates the setup from data that exclude them. Can the estimation of the setup, calculated excluding important shallow water processes, be trusted? Is it a reliable approximation?

Detailed comments

Section 2 Methods: model and simulations: I find this section hard to read. I appreciate that all information required on the models are provided in section 2, and figure 1 is helpful to understand the simulation used, however it is easy to get lost in the nomenclature of the multiple simulations, and in the mere amount of information laid out. It may be worth considering simplifying the reader’s work by adding a table containing a list of all simulations ran, including which forcing were used and the main details (resolution, period etc.) for each. This would improve the readability.

Line 217-223: ‘Therefore, at first order, wave setup and runup can be predicted via empirical formulations […] wave setup estimates are based on an empirical formulation (Stockdon et al., 2006).’ This is the paragraph where you should convince the reader that runup estimation is reliable, despite the model’s approximation. Please give more details on the parametrization limitations and how the empirical formulation you use affects results (i.e. what processes you are missing out). Explain why you think this first order approximation is good enough, even though you are not including sallow water processes.

Line 243:  When referring to the wave setup scaling the author sometimes use (eg. Line 243) and sometimes don’t use (eg. Figur10 description, Line 433) the delta sign. Please be consistent with it.  

Line 259-261 ‘The ability of IBI-CCS-WAV and IBI-CCS-WAV_ssh to reproduce observed distributions is assessed for the mean state and the 99th percentile of the significant wave height and peak period since these variables are then used to compute the wave setup scaling (Sect. 3.2, 4).’ Has the IBI_CCS_WAV_ssh been validated?  The section title seems to imply it hasn’t (‘Validation and projections of IBI-CCS-WAV, without waves-sea level interactions’).

Section 5. Discussion: Important points are discussed, but I would strongly recommend adding a section on the implications of your results. For example:

The authors found an increase in the wave set up and a large impact on the wave-water level interaction in regions of extreme tidal range.  In the introduction, the authors talk about coastal hazards and flooding during extreme water level to motivate the study. You cannot quantify hazards based on wave setup alone, but there is a lot to discuss. Considering that the tidal range will also be affected by sea level rise, are the regions where you predicted an increase in wave setup the same regions that are at risk from extreme wave events today?   Are there other regions in the world that these finding could be relevant for (eg. Regions where the tidal range is expected to increase significantly)? The number of extreme events is also expected to increase in future, and your results show that these are periods in which the wave setup is particularly affected by the water-level changes; this could also be discussed. Which are the limitations of this study?

Line 587, Impact of waves on sea level.  Please discuss what this means in relation to your results: how would you expect the impact of waves on sea level to affect your results?   

Line 605: The new paragraph starts with ‘However’, it would be better to remove and start the sentence with ‘The’.  

Section 6. Conclusion. The main conclusion is not clear. I would rephrase it a way that answers your main aim reformulated as a question. For example, answer specifically: How is the sensitivity of historical and projected sea states for the IBI region coastlines affected by the non-linear interactions between wind-waves and water level changes, notably during extreme events?