Reply to general comment

We express our sincere appreciation to the Reviewer for conducting a thorough review of our manuscript and for providing valuable feedback that has greatly contributed to the enhancement of our work. We fully understand the importance of addressing the major comments raised by the Reviewer before resubmission. In terms of the organization and clarity of the manuscript, we acknowledge the Reviewer’s valid point about the need for further editing and refinement of the text. We would like to clarify that the issue raised in lines 102-107 occurred during a minor revision phase, during which we were specifically instructed to change only the title and availability statement. Regrettably, an erroneous copy-paste during the final submission inadvertently included internal notes from another manuscript. We deeply regret this oversight. However, we want to assure the Reviewer that, apart from this isolated issue, the manuscript underwent multiple reviews and revisions by the authors prior to the initial submission to ensure its quality and coherence.

We concur with the Reviewer that certain relevant prior work was initially overlooked. Building upon the Reviewer’s citations, we will incorporate references to pertinent previous studies and emphasize the specific contributions of our study in light of these works, particularly in terms of our utilization of full spectral representation of wave quantities. We also recognize the importance of highlighting the unique aspects of our work. To achieve this, we will revise the introduction to better underscore the novelty and distinctiveness of our study within the broader context of wave-current interaction modeling. This will encompass a discussion of how our approach differs from previous efforts, both within our modeling system and in other modeling systems. We firmly believe that our study provides valuable insights and advancements in the field of wave-current interaction modeling, and we are committed to conveying this effectively in the revised manuscript.

We are fully committed to address these comments and resubmit a revised manuscript that meets the necessary standards for publication.

Reply to first major comment

We highly appreciate the valuable comment provided by the Reviewer, which has guided us in improving the quality of our manuscript with the refinement of the referenced literature and the introduction of our model developments. In response to the Reviewer’s observations, we have addressed the omission of references to previous model developments within the same modelling framework and those from other model systems. Of particular significance is the

inclusion of reference to the work initiated by Kumar et al. (2017). These references have been thoughtfully incorporated into the introduction of our manuscript to provide a more comprehensive context for our research. To effectively underscore the unique contributions of our manuscript in relation to the works

mentioned by the reviewer, we provide a detailed discussion of each specific work, highlighting both connections and distinctions with our study.

Works Within the Same Modelling System

Kumar et al. (2017) proposed a significant advancement in modelling wave-current interactions through the advocacy of spectral reconstruction for the forcing and coupling of wave-current models. This approach, rooted in the partitioning of WaveWatchIII, delivers more accurate estimates of the Stokes drift when compared to the spectral peak monochromatic approximation of Uchiyama et al. (2010), which often results in underestimations. Later, Liu et al. (2021) confirmed the need of spectral estimates of the Stokes drift for both deep- and intermediate-water applications. Our study aligns with this methodology by employing full spectra from a regional spectral model to force our wave model and incorporating spectral estimates of the Stokes drift. Moreover, we have introduced additional spectral field exchanges to further refine the description of wave-current interactions, thereby distinguishing our novel approach.

Romero et al. (2021) introduced a novel ROMS WEC (Wave Effects on Currents) framework that extended the monochromatic approach of Uchiyama et al. (2010). This extension encompassed spectral approximations of Stokes drift, Bernoulli head, and wave-induced vertical mixing, achieved through iterative computations and a switching mechanism between deep- and shallow-water formulations. Hypolite et al. (2021) used this framework to explore the impacts of the spectral approach on ocean mesoscale circulation variability, revealing relatively modest wave effects despite larger Stokes drift estimates. In consonance with their work, we have incorporated the exchange of spectral Bernoulli head in our model coupling. Additionally, our enhancements encompass novel spectral field exchanges designed to provide a more precise representation of the wave-induced bottom boundary layer. This includes the exchange of spectral bottom wave orbital velocity, which we have demonstrated to have a comparable impact on macro-tidal current profiles to that of the Stokes drift in our specific application. Notably, our study accentuates the significant influence of wave effects on macro-tidal currents, further distinguishing our research from prior investigations.

Works on Different Model Systems Incorporating Full Spectral Wave Quantities

While the references cited by the Reviewer describe developments akin to ours, all aimed at achieving a more comprehensive description of wave-current interactions, our study delves into aspects specific to the employed modelling system, setting it apart from the frameworks mentioned by the Reviewer in several key ways.

Regarding technical aspects, our coupled model uses different hydrodynamic and wave spectral models than the cited systems. These models are not integrated with each other, requiring a third model for coupling and thus introducing associated complexities and advantages. To do so, the CROCO coupled system uses the OASIS-MCT coupler, which is a set of libraries allowing for parallel exchanges and grid interpolations between different models. This framework has multiple advantages such as the possibility of choosing different grids for the different models (and eventually different nesting strategies), the possibility of choosing the coupling frequency, the exchanged variables, etc. This interface is thus particularly flexible and allows coupling CROCO with any model included in the OASIS-MCT library. Furthermore, the computational grids used by CROCO (which is not necessarily the same of the wave model) are structured rather than unstructured as the cited modelling systems.

Regarding historic aspects, ROMS was originally designed for regional oceanic applications. CROCO inherited from ROMS and recent model developments added up new capacities to link the regional, coastal and nearshore scales. Our work, in line with these recent advances, concentrates on its adaptation for intermediate-water macro-tidal conditions, distinguishing it from the cited modelling frameworks which are more nearshore-oriented.

These distinctions underscore the specific contributions and relevance of our study within the context of the CROCO modelling framework and the broader field of wave-current interactions.

Reply to second major comment

We sincerely appreciate the reviewer’s valuable comments, which have raised important concerns regarding the numerical setup and the discussion of the numerical results to assess the added value of employing a full spectral representation of wave quantities.

In our research, we used a numerical model that incorporates wind stresses at the free surface, tidal currents and levels as well as full wave spectra at the offshore boundaries to simulate the hydrodynamics within the macro-tidal bay of Somme in the English Channel. This choice of setup was grounded in our belief that these specific forcing terms are the most pertinent factors for capturing the dynamics of the study area.

We duly acknowledge the reviewer’s concern regarding the influence of wave boundary conditions on our simulation. It is indeed true that the hindcast data used to force the wave model exhibit some biases in our study area. Nevertheless, it is crucial to emphasize that the use of full spectra at the boundaries was made because is the best (and most computationally demanding) practice in modelling spectral waves, particularly when investigating complex phenomena such as spectral Stokes drift and wave-current interactions (as highlighted in Kumar et al., 2017, and Liu et al., 2021, both now cited in the revised manuscript).

Addressing the concern related to water levels and currents, we acknowledge the possibility that the proximity of the southern boundary to the measurement sites could result in an appearance of excessive control by the imposed forcing. To investigate this, we conducted an additional numerical simulation with an extended computational grid in the south and west directions, effectively placing the measurement sites further from the open boundaries. In this new simulation, we limited the forcing to only the west and north offshore boundaries to assess the independence of the hydrodynamic model results from the relative distance between the forcing boundary and the measurement locations (refer to Figure 1). The results of this supplementary simulation align closely with the outputs of the original simulation which solely employed tidal forcing. This congruence is evident in terms of circulation patterns (as illustrated in the tidal flood snapshot, Figure 2, which can be compared with Figure 6 of the submitted manuscript), time series of near-bottom currents (Figure 3), and

discussed vertical profiles (Figure 4). These additional results convincingly demonstrate that the boundary was situated at a sufficient distance from the measurement locations where vertical velocity profiles were examined. It is vital to emphasize also that the discrepancies observed in the modelled tidal currents between different tidal forcing setups are approximately one order of magnitude lower than those found when comparing pure tidal profiles with those influenced by wind and waves (as evident if comparing Figure 4 with Figure 13 of the submitted manuscript), particularly as we approach the free surface.

Based on these additional results, we assert with confidence that the choice of tidal forcing in our simulations does not exert undue control over the modelled hydrodynamics. This support our validation of the macro-tidal currents influenced by wind and waves in the bay of Somme and the discussion of the substantial added value derived from the incorporation of additional spectral wave field exchanges.

Reply to third major comment

We concur with the Reviewer’s perspective that the use of a spectral representation is more significant in wave-dominated shallow waters. In such environments, the effects of waves on currents can manifest with particular prominence, a factor that is less pronounced in intermediate water depths, as the locations of the measurements discussed in this study.

To provide a comprehensive context for our study and elucidate the rationale for our choice of modelling application, it is essential to place our research within the framework of its funding project. The DEMLIT project, funded by SHOM in collaboration with the University of Caen Normandy, is dedicated to investigate the sand filling dynamics in the Bay of Somme. The submitted manuscript represents the initial phase of this project, focusing on the macro-tidal circulation off the bay and its interactions with offshore winds and waves. To do this we employed available tidal atlases and low-resolution bathymetric data from SHOM complemented by in-situ measurements from the University. It is important to note that we did not account for wave effects on currents below 2 meters water depth, as the interpolation of the low-res bathy data within the bay resulted in steep seabed gradients, leading to numerical instabilities in the surf zone.

This model will serve as a nest model, providing a foundation for higher-resolution, shallower-water nested applications. These forthcoming applications will explore hydrodynamics and sediment transport processes within the bay. Notably, we have collected new shallow-water, high-resolution bathymetric data and ADCP measurements in the surf zone to inform and validate this forthcoming phase of the modeling.

We understand the significance of accurately reproducing wave processes in shallow waters, especially while striving to improve the representation of wave effects on currents, and we acknowledge that previous versions of our model have been applied in such settings, as highlighted by Uchiyama et al. (2010) and Marchesiello et al. (2015). However, it is crucial to underscore the primary objective in our current study, which is centered on model the interactions of macro-tidal currents with offshore winds and waves. Given this clarification, we will remove from the section dealing with the assessment of modelled wave the last paragraph discussing wave breaking in shallow waters. These aspects, though undeniably important, will be reserved for the future extensions of our modelling efforts, as we focus on the fundamental objective of our study.

Reply to fourth major comment

We appreciate the Reviewer’s feedback and agree that a more detailed description of the coupling procedure is warranted.

All the additional spectral fields required for the proposed advanced coupling were already incorporated into the WAVEWATCH-III model, and we simply added the necessary exchanges in CROCO to compute the wave forcing terms. These modifications have been available in CROCO since the v1.2 release. Both the ’monochromatic’ and ’full’ coupling procedures are accessible for comparison in different configurations, and users can easily switch between them

by activating or deactivating a preprocessing key.

The OASIS coupler handles all data exchanges, including interpolations on different grids. Coupling information is specified in a parameter file exclusively used by OASIS. Therefore, applying this new coupling to another configuration and assessing the impact of our developments should not pose significant challenges. These information will be added to the section dealing with the coupling procedure.

Replies to specific comments

1) Following the Reviewer’s suggestion, we will carefully reconsider the wording in the abstract to accurately reflect the main outcomes of our study while taking into account its limitations in terms of nearshore modelling and the primary scope of our work.

2) In response to the Reviewer’s valuable feedback, we will carefully revise the text throughout the entire manuscript to eliminate any ambiguity regarding the study’s objective. We will explicitly narrow down the study objective from ’modelling wave-current interactions in coastal areas’ to ’modelling interactions of macro-tidal currents with winds and waves’. This adjustment will ensure greater clarity and alignment with the primary goals of our research.

3) The text will been corrected.

4) As we clarified in our response to the third major comment, the specific focus of our study does not revolve around ’wave-dominated environments.’ We will take extensive measures to overhaul the entire introduction section, ensuring that the text provides a clear and accurate representation of the paper’s objective. This comprehensive revision will guide the reader toward a precise understanding of our research goals.

5) The sentence will be modified in accordance with the primary objective of our study. We appreciate the Reviewer’s suggestion, and it’s essential to note that even in intermediate waters within macro-tidal environments, the resolution of the vertical current profile is crucial for understand and model the transport of sediment, particles, and tracers. While the effects of winds and waves may be comparatively less pronounced, the accuracy of the vertical current profile remains instrumental in capturing these important aspects even in the discussed intermediate-water setting.

6) The text will be update to specify that these theories derive depth-dependent expressions of the wave-averaged flux of momentum due to waves to study the interaction of currents and waves in water of finite depth.

7) We acknowledge the importance of providing a comprehensive overview of the state of the art of the modelling of wave-current interaction in 3D. In response to the Reviewer’s valuable suggestion, we will enhance the end of the introduction section to ensure a more thorough and detailed presentation of the current state of the field. By incorporating the references suggested by the Reviewer in his/her general comment, we will be able to enhance the comprehensiveness

of our manuscript.

8) We agree with the Reviewer and will revise the sentence in question to better reflect the contributions of the cited works.

9) See above point. This part of the introduction will be modified to better reflect the contributions of the cited works.

10) See the response to the third major point.

11) We agree with the Reviewer that, despite well in line with the funding project of our research work, the description of the sedimentary environment in the Bay of Somme does not include relevant information for the scope of the present study. We will then remove from the section the paragraph describing sediment transport, seabed features and infilling sedimentary process characterising the bay.

12) Yes, the Reviewer is right.

13) Please, see our response to the general comment.

14) The Reviewer is right. The text will be corrected.

15) The equation is identical to the one found in the WAVEWATCH-III manual, with the only distinction being that it is expressed in terms of wave energy and frequency, as opposed to wave action.

16) Wetting and drying in the spectral wave model operates in a manner consistent with the hydrodynamic model. It refrains from computation in grid cells where the instantaneous water depth falls below a specified threshold value.

17) The typo will be corrected throughout the text and in the schematic of Figure 2.

18) The text ill be corrected.

19) We agree with the Reviewer that our discussion of the results depends very much on the vertical shear observed at the instrument position to do not investigate the control exerted by the imposed tidal forcing on the results. As discussed in detail in the response to the second major comment, we conducted an additional numerical simulation with an extended computational domain, placing the measurement sites further from the boundaries where we imposed tidal levels and currents. These supplementary results indicated the independence of our previous results from the relative distance between the forcing boundary and the measurement locations.

20) We did not account for wave effects on currents below 2 meters water depth because the interpolation of the low-resolution bathymetric data resulted in steep seabed gradients within the bay, leading to numerical instabilities in the surf zone. We have recently collected accurate shallow-water high-resolution bathymetric data within the bay. In the forthcoming phases of our modelling of the Bay of Somme, we will use these new data and test the reliability of our

model in the nearshore context.

21) We appreciate the Reviewer’s consideration of the potential impact of the model domain’s scale on the representation of wind contributions. While it is true that the wind contribution near the boundary may be subject to some uncertainty due to the reduced extension of the model domain, we would like to emphasise that the identified tendency observed in our results remains valid. The key point is that the identified tendency, specifically the acceleration of the current profile when accounting for additional spectral wave field exchanges, is not contingent on the specific uncertainties related to wind contributions. Even though some uncertainty may exist due to the scale of the model domain and its influence on the reproduction of a realistic 3D profile, the observed tendency is consistent and supported by the data.

22) Here we are referring to the Beaufort wind scale, where fresh to strong breeze are classified depending on the wind speed.

23) We used both significant wave height and its root-mean-square value throughout the manuscript due to the fact that the wave model provides results in terms of significant wave height, while the hydrodynamic model gives root-mean-square values. We acknowledge the Reviewer’s concern regarding the discrepancy in wave energy representation during the peak of the discussed event. It is important to note that this limitation does not arise from the specific model developmentspresented in our study but is associated with the spectral wave model used to provide boundary conditions with full spectra, a computationally demanding yet best practice in wave modelling. Furthermore, it’s worth emphasizing that the representation of tidal currents is much more accurate than that of waves in our model. The primary focus of our study is to assess the added value of the spectral terms introduced in the representation of wind and wave effects on macro-tidal currents, which can still be meaningfully discussed with the current model configuration. We observe that the predicted current values, when considering these additional terms, tend to be closer to the measurements, resulting in differences of approximately 10% of the current magnitude (2-3 cm/s in 20-30 cm/s currents, see bottom left panel of Figure 13). Nonetheless, we agree with the Reviewer that addressing the issue of wave energy representation in future modeling efforts is important. We appreciate the Reviewer’s feedback, which will guide our ongoing work to further enhance the accuracy and reliability of our model, especially regarding wave-current interactions.

24) This part of the text will be removed.

25) This part of the text will be removed.

26) Please see the response to the second major point.

27) True, but a better match is systematically obtained with the coupled wind-wave-current configuration during the remaining phases of the tidal cycle, resulting in the same R2 and RMSE values on which this sentence is based.

28) The sentence will be modified without referring to the presence of sub-grid scale bedforms. Regarding the forcing, as discussed in our response to the second major point, we checked the forcing and we assessed that it does not overly control the obtained results.

29) The wind drag coefficient is computed according to the formulation of Smith (1988), which estimates the coefficients for sea surface wind stress as a function of wind speed while accounting for a constant Charnock coefficient. In the present study, the latter is computed assuming fetch-limited coonditions. In the discussion of the results, our aim was to methodically isolate the distinct contributions stemming from various forcing factors. To achieve this, we conducted a series of simulations in which we incrementally introduced different metocean forcings while ensuring that their effects remained as isolated as possible. As part of this approach, we deliberately did not consider the influence of waves on winds through adjustments to the Charnock coefficient. In other words, we kept the wind contribution consistent, irrespective of whether waves were factored into the model. This deliberate choice allowed us to scrutinise and quantify the impact of other variables while minimising the confounding effects of altered wind conditions due to wave effects and viceversa.

30) We did not perform sensitivity tests on the impact of the mixing length parameterisation employed. In Section 3.3.5 we introduced the turbulence model to highlight the difference in its choice with respect to former versions of ROMS, which include some of the additional spectral wave terms discussed in our study while using a different turbulence model.

31) The Reviewer is right. We will modified the text accordingly.

32) The results using the new spectral field exchange show an improved matching with the measurements both close to the free-surface and the bottom. Also, since the entire paper is focused on the 3D modelling of wave-current interactions, we do not see the point in computing stats associate to depth-averaged values.

33) The figure will be modified according to the Reviewer’s comment.

34) We removed te speculative sentence from the text.

35) Probably there is a typo in the line numbers. At these lines, we just observed how wind aligned with tidal propagation accelerates further the free-surface velocity.

36) To understand why we focus on this particular data set, please see the response to the third major point. It’s crucial to emphasise that the primary focus of our paper is to evaluate the added-value of incorporating additional spectral wave terms in the computation of wave-current interactions, rather than concentrating on the details of turbulence modelling in these interactions. We employed a standard turbulence model with standard boundary conditions to ensure a fair and consistent comparison between simulations with and without the spectral terms.

37) The sentence will be removed from the text.

38) We agree with the Reviewer that directly comparing these terms may not be suitable, given that the bulk representation has primarily been applied in the context of depth-induced wave breaking rather than whitecapping, which is the dominant dissipative process for waves in our study area. However, we would like to clarify that our intention was not to compare bulk and full spectral representations of wave breaking. Instead, our objective was to assess the improvement resulting from our model developments, which include the representation of whitecapping dissipation in addition to depth-induced breaking. Since no depth-induced breaking occurs in the measuring location where the data discussed in this study have been collected, the observed changes in the solution are primarily due to the consideration of whitecapping effects. To make this point clearer, we will revise the corresponding text to better express the purpose of this comparison.

39) Please consider that the disparities in current magnitude are, in certain instances, greater than 3 cm/s. Also, when addressing variations slightly below 1 cm/s in a Stokes drift that fluctuates between 10 and 5 cm/s, this accounts for approximately 10% of the overall value.

40) Figure 17 will be changed to clarify the representation of water levels.

41) The Reviewer is right, and we will remove the sentence from the manuscript. Initially, this section aimed to elucidate the distinctions between one-way and two-way coupled simulation outcomes. However, we later decided to exclude the one-way simulations from the paper to enhance conciseness.

42) Since we will removed from the text the parts dealing with wave processes in shallo waters, the depth-induced refraction process will be described only as likely misrepresented. We will deal with this issue using higher resolution nested models in shallow waters in our future modelling works.

43) Please see the response to the third major comment.

44) We will modified the text replacing the use of the term 'surf zone' to avoid any confusion.

45) The observed slight phase shift in tidal floods between modelled and measured currents does not depend on random metocean forcing. As it is not related with wind and wave forcing, it does not impede our ability to assess the effects of wind and wave forcing on macro-tidal currents, which is the primary focus of our study. Thus, this phase shift is not a hindrance to the evaluation of our model developments related to wave and wind influences on currents.

Reply to the general comment

 We would like to thank the Reviewer for her/his positive feedback on our manuscript. We appreciate the Reviewer’s thorough review and are pleased to hear that she/he found the work well-written and the experiments appropriately designed. In the following, we address both major and minor points raised.

Reply to the first major point

 Thank you for the feedback regarding the concern about the performance of the newly implemented version of the model. It’s important to note that results in Figure 3 show that the predicted bulk wave parameters from the fully coupled model are very similar to those of the previous version of the coupled model, with comparable RMSE and R2 values. However, as for Figures 7, 8, and 9, these results are only from previous versions of the model. We have deliberately chosen not to include results from the newly implemented version in these particular figures, as our focus here was to compare the effects of the different forcing employed.

Reply to the second major point

The extra computational cost of including the additional spectral term exchanges in the fully coupled version is negligible in the present model configuration, accounting for less than 1% of the computational time required by the previous version of the coupled model. However, it is important to note that the impact of these additional exchanges on computational cost may vary in larger domain configurations. We will include information on the extra computational costs

in the manuscript.

Reply to minor points

1)  The exceptional tides were not simulated due to the unavailability of relevant data for that timeframe (september and march).

2)  The current configuration of the CROCO model with a 100-meter horizontal resolution is not suitable for resolving small-scale features such as small dunes and ripples, which can be as small as a few centimeters in size. Our focus in this study is primarily on larger-scale processes, such as the interactions between currents and waves. However, we acknowledge the limitations in resolving fine sediment patterns. In future phases of our modelling efforts, we plan to enhance the model resolution through nesting, reaching a horizontal resolution of 10 meters and increasing the number of vertical layers. This approach will enable us to better represent tidal dunes, while smaller-scale wave ripples will be parameterised as bottom roughness.

3)  The text between lines 105-106 will be cleaned up. We acknowledge that the issue occurred during a minor revision phase when we were instructed to change only the title and availability statement. Unfortunately, an erroneous copy-paste during the final submission included internal notes from another manuscript. We apologise for this oversight.

4)  We have decided to replace the equation in question with the original one found in the WWIII manual to avoid any potential confusion. Any detailed information about its unknown variables and solution methods is available in the WWIII manual.

5)  These equations are wave-averaged equations that CROCO solves specifically when wavecurrent interactions are considered. The original hydrodynamic model in CROCO solves the hydrostatic Navier-Stokes equations. To maintain clarity and consistency, we chose to include these wave-averaged equations in the section dedicated to the introduction of wave-current interactions rather than in the section on the hydrodynamic model.

6)  The text will be modified as suggested to improve clarity.

7)  We agree with the Reviewer’s observation, and we will include a comment in the text to address this gap.

8)  Yes, when we refer to ’mean grain size,’ we are indeed referring to d50, which represents the mass median diameter of sediment particles. We will make this clarification in the text.

9)  The improved fit with observations in the flow is attributed to the inclusion of waves propagating in the direction opposite to the wind stresses. This addition helps smooth out the overly sharp wind-induced current vertical profile at the free surface, a mechanism that is explained in detail in Groeneweg and Klopman (1998).

We appreciate the reference to Hsu et al.'s recent work on wave model performance during tropical cyclones. It's indeed an interesting avenue for further exploration, and we're pleased to note that researchers, including Kumar and his team, have already started testing model developments similar to the ones discussed in this paper in the context of tropical cyclones. Their initial work involved a test case that included a reconstruction of the spectral Stokes drift, and given the capabilities of our model, we believe it has the potential to provide additional insights and improvements in modeling hurricanes. We look forward to further research and collaboration in this area.