Bottom topography effects on the internal wave climate in the Ionian Sea

Kokoszka, Florian; Sparnocchia, Stefania; Cavaliere, Davide; Artale, Vincenzo; Borghini, Mireno; Giambenedetti, Beatrice; Falcini, Federico

doi:10.5194/os-22-2249-2026

Articles | Volume 22, issue 4

https://doi.org/10.5194/os-22-2249-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/os-22-2249-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 22, issue 4

Research article

|

27 Jul 2026

Research article |

| 27 Jul 2026

Bottom topography effects on the internal wave climate in the Ionian Sea

Florian Kokoszka, Stefania Sparnocchia, Davide Cavaliere, Vincenzo Artale, Mireno Borghini, Beatrice Giambenedetti, and Federico Falcini

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Final revised paper (published on 27 Jul 2026)
Supplement to the final revised paper
Preprint (discussion started on 09 Oct 2025)
Supplement to the preprint

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4762', Anonymous Referee #1, 18 Nov 2025

Please see attached pdf.

Citation: https://doi.org/10.5194/egusphere-2025-4762-RC1
- AC1: 'Reply on RC1', Federico Falcini, 09 Jan 2026
  
  Dear Reviewer,
  please find our revision notes in the attached file.
  Best regards
  Federico Falcini (on behalf of all co-authors)
  
  Citation: https://doi.org/10.5194/egusphere-2025-4762-AC1
RC2:
'Comment on egusphere-2025-4762', Gunnar Voet, 04 Jan 2026

The authors present an analysis of CTD/LADCP measurements from 2007 to investigate internal wave properties in the deep waters of the Ionian Sea. The major focus of the study are the ratios of integrated shear and strain variances, which, for linear waves, allow to infer wave frequencies, and their relationship to bottom depth, bottom slope, and bottom roughness. The major result of the study is that shear-to-strain ratio R_omega varies with bottom slope and roughness. Bottom slope and roughness appear to be closely related in this region.
The presented research is an interesting piece of analysis on the internal wave climate in the deep Ionian Sea using existing CTD/LADCP observations. This type of analysis has been carried out before, but I believe it is of interest in the regional context (if the authors can show that these results are new for the Ionian Sea).
Based on my review below I suggest a major revision of the paper.

Major Points

------------
The study lacks details on the regional context of both the regional circulation and the regional internal wave climate. Are there other studies on the internal wave climate of the Ionian Sea? There are papers showing how the low stratification of the deep Ionian Sea can support vertical inertial oscillations (e.g. van Haren & Gostiaux, 2007, GRL). Possibly related, why are shear variance spectra so much larger than GM spectra while strain spectra are much closer to GM?
The study does not address the impact of temporal variability of the internal wave field on the results. Instead, results are framed as an investigation into spatial variability of the shear-to-strain ratio. However, other studies have shown that "Temporal variability in R_omega is observed at daily, weekly, and monthly scales." (Chinn et al., 2016, p. 3299)
The study lacks a comparison with other papers investigating shear-to-strain ratios outside of Kunze et al. (2006). Is Kunze et al the only paper that looked into shear-to-strain ratios? If not, do results presented here align with other studies?
Much of the motivation is framed in terms of diapycnal mixing and its importance for the Mediterranean and global ocean circulation. However, the bulk of the analysis focuses on the internal wave climate in the Ionian Sea. I suggest keeping the focus on the internal wave climate without trying to branch out too much. Otherwise more ground will have to be covered along questions of, e.g., how well the does the finescale parameterization work for estimating dissipation rate of turbulent kinetic energy in these lowly stratified regimes? Is a mixing efficiency of 0.2 applicable here? Why not remove calculation of diapycnal diffusivity (the results are not further analyzed) and maybe even turbulent dissipation and just focus on internal wave dynamics? I am not convinced that the study presents results on regional patterns or the influence of bottom slope on these turbulence parameters.

Minor Points

------------
I suggest changing the title as the study is less about abyssal diapycnal mixing but rather on the internal wave climate. How about "Bottom topography effects on the internal wave climate in the Ionian Sea"?

Typos and Small Comments

------------------------
12f: I sugest removing "diapycnal mixing" and "turbulent kinetic energy" from the keywords and adding "finescale parameterization".
18: Spatial patterns of diapycnal mixing are not really the focus of the study (see my comment above).
21f: I believe you show that bottom slope and seafloor roughness are linked to absolute values of shear-to-strain ratio, not variability.
28: Specify what you refer to with large-scale and small-scale.
29ff: The concluding sentence reads very generic and is not suported by the study. I suggest being more specific in why your results matter.
43ff: I suggest not going into details of where upwelling and downwelling happens but rather state that where turbulent mixing happens matters.
54ff: Rephrase. It is well quite established by now that rough bathymetry leads to enhanced IW generation, scattering, and breaking, and thus increased levels of turbulent dissipation.
61ff: This would be good to expand on as it lays the groundwork for your study!
65: Mixing processes are not studied in this paper. You are investigating the composition of the internal wave field or the internal wave climate.
68ff: Consider reducing the discussion on the Mediterranean overturning circulation and adding a review of what is known about internal waves in the region.
69f: "one of the most interesting" - rephrase
86: Strait of Gibraltar not shown in Fig. 1a.
103f: Why does this matter?
105: What "flow" is this?
106f: More information in internal-wave-driven turbulence in the region is needed here.
109: What is unique here?
121: "impulsive" - Does this mean temporally variable? If so, on what scales?
133f: "showing the role..." - Can you be more precise and state their central result in this regard?
135: I am guessing you mean "synergetic", but why not simply state here that you expand the Artale et al analysis by including LADCP measurements to investigate shear variance in addition to strain variance?
140f: See my other comments suggesting removing diapycnal diffusivity estimates.
150: "Hydrological" - The term does not include velocity measurements, see below.
151: Move the reference to Borghini et al to the end of the sentence.
153: Does this refer to CTD/LADCP? The term hydrological does not include velocity measurements.
155: have -> had
158: in -> at
160: have been preset -> were set
161: 10.00 -> 10
162: Move the link to the "Data and Code Availability" section and add reference to Visbeck (2002, JTECH).
162f: Were shipboard ADCP data available to include in the processing? What about bottom tracking velocities from the downlooker?
182: a recent -> the form of the
186: Brunt-Väisälä (buoyancy frequency is much easier!)
195: buoyancy-normalized
206ff: It would be better to point out (as Chinn et al) that the error associated with not having the right W_omega is not symmetric and therefore it is better to use shear variance for R_omega > 3 and strain variance for R_omega < 3.
211: Remove "ideally".
228: shear -> shear variance
248f: Do you implicitly apply a shear-to-strain ratio of 3 here?
259: more robust than?
260: Remove "Conveniently".
263: Shouldn't this be the Visbeck reference I mentioned above and not Polzin?
263: It is unclear what "single bin error profile" refers to.
265: "distributed on the spectral domain" - what does this mean?
269: highlighted -> highlight
273: Remove "then".
282ff: Why calculate vertical diffusivity? How is N^2 calculated? Is the use of gamma=0.2 justified?
285: Does this refer to the code used for your calculations? Move this to the data and code availability section at the end.
292: spatial or temporal
293: "near mixing hotspots" - is this the only case where it deviates?
313: and temporal?
325: ration -> ratio
328f: This has just been stated on line 326.
329ff: "Even..." - "Even" makes no sense here - best to remove this statement.
332: What does "realistic" mean here? Observed?
334: Do you have a reference for this statement?
343ff: Can you rephrase this? What spatial variability? What does sinusoidal sense mean in this context?
345: Do you have a reference for this statement?
366: on -> in
368: bathymetrical -> bathymetric
379: Does this mean internal waves on line 376 refer only to tides?
385f: Reference? If you merge this paragraph with the next one then you have your reference in Kunze et al. Also, what does large-scale refer to in this case?
394: It would be good to show your results for slope and roughness with two extra panels in Fig. 1. I suggest moving current 1b to its own figure and adding slope and roughness here.
399f: How is roughness calculated in other studies, e.g. Kunze et al 2006? Does your method diverge from these?
404: to surface -> towards the surface (otherwise this implies you are investigating the full water column)
406: into -> in
406: Remove "then".
407: The figure reference is not helpful here as so far you have only discussed your binning procedure.
409: 1 -> 1b
409: Smaller -> Small
411: Unclear where the Malta escarpment is.
411f: I suggest moving this to the discussion section (where you already talk about this).
413: increase with depth?
417: Move this to where you describe roughness calculation on lines 399f.
418: Remove "it results that".
421ff: Remove sentence "Correspondingly, ..." as this just repeats what has been stated already.
423: Slope and roughness appear to be almost linearly related. Are you sure your method for estimating these is good and without any errors?
425: Are you sure that "dispersion" is a good term to use here?
429: You have highlighted this in your theory section, i.e. no analysis necessary.
431: There are lots of vertical lines in Fig. 3a.
434: What does "bulk" stand for?
436: In Fig. 3b and c supercritical is marked as delta slope < 0. Which one is right?
437: "Once scattered through this quantity" - what does this mean? A scatter plot against delta slope? If so, just remove this.
437f: Remove "a clear pattern appears i.e.".
438: clearly -> generally
449: "characterized by elevated roughness" - Yes, for the highest roughness (bin 5.1). However, bins 4.5 and 4.0 show relatively low strain variance which is not supportive of your statement.
450: "shear variance diminishes at low wavenumbers" - Not clear. Are any differences here statistically significant?
454f: Yes for the highest roughness but not generally, see comment above.
459: "shear spectra in Fig. 4b show a clear dependence on delta slope" - Yes!
459f: Not sure why you talk about R_omega here?
461f: "Spectra [...] support what we observed" - not a surprise as R_omega is calculated from shear and strain spectra!
462: "critical threshold" - please explain this further
464: "Fig. 5" - why not refer to Fig. 3c showing the same?
465f: Need to define Richardson number and detail calculation. From a, b it is not immediately clear that delta slope approaching zero aligns with more critical (negative? why negative?) Richardson number events.
466: This has been evident in previous figures as well!
468: What does vice-versa mean here?
469: What is diffusion rate of TKE?
483ff: This whole paragraph is not needed here.
498: "Values of R_omega are necessary" - in the finescale parameterization.
504ff: Please rephrase, this is incredibly hard to read and make sense of.
509f: I don't think you show this.
511: This whole paragraph is very hard to follow.
513f: I thought you show that roughness leads to low R_omega and thus high strain variance?
517: What does "Although" mean here?
521: "shallow areas" - or rough?
524: would -> could
526f: Please explain why this reference would be appropriate here - it does not appear to be on mesoscale eddies.
530: Can you show this?
531: How do these lines connect to the previous? Should this be a new paragraph?
542ff: How so? How do you know internal waves you observe have been generated by geostrophic currents?
546ff: Remove or be more specific.
553: What is "additional abyssal flow"?
553f: Unclear why all these references. Can you be more specific in how your results will help refine mixing parameterizations?
594: Mediterranean Sea -> Ionian Sea?
594: Please add some labels for those not familiar with the region.
596: What about the transect marked with circles?
596: I suggest moving 1b to be its own figure and adding a panel for bottom roughness, possibly also for bottom slope.
602: dotted -> dashed
609f: "low (high)..." - Leave this for results / discussion section.
611: over the study area -> at the cast sites
611: Remove "Scatterplot of"
611: Here and elsewhere remove "z-axis" and call this "color".
647: It seems you are averaging over less spectra here than in Fig. 1b. Why? What is the difference?
690: Richardson number not defined.
690f: Why is the ratio of observed to GM strain shown in log scale but shear not?

Citation: https://doi.org/10.5194/egusphere-2025-4762-RC2
- AC2: 'Reply on RC2', Federico Falcini, 15 Feb 2026
  
  Please find our revision notes in the attached file.
  Best regards
  Federico Falcini
  
  Citation: https://doi.org/10.5194/egusphere-2025-4762-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

AR by Federico Falcini on behalf of the Authors (15 Feb 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (25 Feb 2026) by Katsuro Katsumata

RR by Anonymous Referee #1 (25 Mar 2026)

RR by Anonymous Referee #1 (31 Mar 2026)

Suggestions for revision or reasons for rejection

Review of MS#egusphere-2025-4762 entitled “Bottom topography effects on abyssal diapycnal mixing in the Eastern Mediterranean Sea”by Florian Kokoszka et al.

In the first review round, I provided the following specific comments:

L86: I cannot find the Strait of Gibraltar in Fig. 1.

Fig. 1: It would be helpful to overlay the circulation pattern on the map.

L113-124: are tidal flows much weaker than the mean flow?

L125-134: It would be helpful to explicitly state what is lacking in Artale et al. (2018) in order to better motivate the present study. Clarifying the gaps or limitations in that work will strengthen the rationale for your research.

L206, 208: I suggest reconsidering the use of “overestimate” and “underestimate” in the text. In this context, terms like “increase” and “reduce” may be more accurate and appropriate.

L208-210: I cannot understand this argument. Please explain more.

L249: 0.22, not 0.22N2

L258-261, L403-407: I’m confused with the statements. Could you clarify what “80 m” refers to in this context? Bin size should be larger than 640m?

L268-275: “from 640 to 107 m” It would be easier to understand if you rewrite them in rad/m

L314-373: I think the descriptions are very redundant. For example, equations 7 and 8 are identical. Please rewrite.

L435-438: I think the description is not accurate. The internal-wave frequency or propagating angle doesn’t change during the reflection, but wavenumber changes.

L453: is this spectral increase statistically significant?

L480: I cannot discern a clear coherent pattern in the figure. The authors should clarify which aspects they consider coherent and provide an explanation to support this interpretation.

L513: “suppression of the strain in rougher area” is correct?

In the authors’ response to my comments, I acknowledge that authors provided their response to my major comments. However, the specific comments raised above have not been answered, and most of these issues also remain unaddressed in the revised manuscript. Addressing them is essential, as they directly relate to the interpretation of results and the clarity of the manuscript. It is unusual to receive such an incomplete response to detailed reviewer comments. I am sorry for the short comment but am disappointed with the response.

In response to the editor’s request, below are my additional comments on the authors’ response to my major comments:

First, the author cited the well-known diagram of internal waves generated by “tide”- topography interactions (St. Laurent and Garrett 2002, note this is incorrectly cited as St. Laurent et al., 2012) to argue that tidally-driven lee waves are not significant. However, this does not address my original concern. My comment specifically referred to the potential generation of lee waves by “mean flows”, not tidal flows. My original specific comments (Fig. 1: It would be helpful to overlay the circulation pattern on the map. L113-124: are tidal flows much weaker than the mean flow?) relates to this point. Without a clear response to these points, I remain unconvinced by the authors’ argument.

Second, on the Δ-slope, I am convinced that the bathymetry slope does affect the calculation of Δ-slope. However, the validity of calculating β using the single-wave approximation is not addressed at all. Moreover, it remains unclear how the criticality of the bottom slope affects internal-wave frequencies (and Rω). This is related to the unanswered comment (L435-438: I think the description is not accurate. The internal-wave frequency or propagating angle doesn’t change during the reflection, but wavenumber changes).

Third, regarding the calculation of topographic roughness and steepness: I acknowledge the authors’ clarification that the roughness derived from the GEBCO product is relatively insensitive to horizontal scale and correlates well with the topographic slope. However, roughness and steepness represent distinct physical properties and are expected to play different roles in internal wave dynamics. At present, I am confused about how each of these two parameters individually influences the observed variations of Rω. The manuscript does not provide a clear physical interpretation that distinguishes their respective effects.

Lastly, regarding the blue strain spectra at high wavenumbers: I acknowledge that the potential inclusion of double-diffusive layers, excluded from the analysis, could contaminate the strain spectra. The authors now present strain spectra restricted to the data used in the analysis; however, they apply a low-pass filter that artificially suppresses high-wavenumber signals. This approach does not fully address my concern. I would expect to see the behavior of the strain spectra at high wavenumbers without the application of a low-pass filter, in order to properly assess whether the used signals are not contaminated. For comparison, Ferron et al. (2014), which the authors argue to follow, present shear and strain spectra without applying such filtering, and their strain spectra do not exhibit a blue slope at high wavenumbers. This point needs to be explicitly addressed; otherwise, I remain unconvinced by the interpretation of the high-wavenumber strain spectra.

Overall, as my comments remain largely unaddressed, I am unable to recommend this manuscript for publication.

Hide

ED: Reject (27 Mar 2026) by Katsuro Katsumata

Thank you for revising the manuscript. I must thank you for your patience, too.
Reviewer #1 found that the revision failed to address the issues raised for the initial version (version 1) of the manuscript.
Reviewer #2 was not available for this round but the recommendation for version 1 was to "reconsider after major revision".

Based on these opinions and on my own reading, I am sorry but I have to agree with Reviewer #1; I find the manuscript not suitable for publication even in the revised form.
I am not certain if further revision on the same line would make sufficient improvement.

I explain my opinion along with the comments from Reviewer #1 for version 1.

The first point the reviewer raised was the effect of lee-wave generation. In reply, the authors introduced
the Bell's linear theory to come up with a conversion rate of 1E-5 to 1E-3 W/m2. The authors called this "small values"
but it was not clear to what number this should be compared. Typical kinetic energy dissipation rate in the ocean
is 1E-10 to 1E-8 W/m3, which becomes comparable if integrated in a 1000m-high water column, which does not appear small.
Even if these lee-waves are "small", these are propagating internal waves and possibly contribute to the shear and strain to affect R_ω.
It still seems necessary to demonstrate that whatever the wave field the authors are assuming is much stronger than
these lee waves.

The second point was the interpretation of "Δ-slope". The reviewer pointed out
[1] the strong constraint from the dispersion relationship (the equation for β = tan^{-1}...), and
[2] assumption of dominance by a single frequency wave.
In addition, I have a question with the way topographic slope was calculated (L.451-454 in egusphere-2025-4762-manuscript-version3.pdf). It seems that
average of the bottom slope in eight directions was used. When topographic scattering/reflection is considered,
the slope is usually calculated along the direction of the wavenumber vector. On a meridional slope (sloping north-south),
I think an eastward propagating wave feels the slope only in a narrow width of the fluid particle movement across the wavenumber vector.
It is not clear to me how one can compare the average slope with the bottom slope that the travelling wave feels.
I see that if R_\omega is plotted against "Δ-slope", the dots scatter depending on the roughness
but they collapse on a single line when plotted against β. Here, again, I failed to see how the difference
offers an explanation for [1] and [2] above. (I do not expect it answers my question.)
I agree with Reviewer #1 that [2] is a central assumption behind using a simple dispersion relation such as Eqs.(7)(8)(9) and needs a justification.

I see the authors' reply to the third point, re: calculation method for the slope and roughness, is valid and found Fig.R4 convincing.

I also think the next point (re: blue strain spectra) is addressed by new Fig.4(a), or Fig.R5.

Moreover, in the course of looking up the strain spectra for fine scale parameterisation, I have come across a paragraph
in Polzin et al. (2014, JGR, P.1398);

"The use of shear-strain ratios as a metric of the variable aspect ratio of the internal wavefield only makes
physical sense if shear and strain are estimated over the same bandwidth. While some authors have calculated
this ratio by evaluating shear variance and strain variance over different vertical wave number ranges
(using the GM model as a common reference), we recommend that a common wave number band is used
to avoid biasing the estimation of Rx for nonwhite (i.e., non-GM-shaped) shear and strain spectra."

This point also needs to be explained. Chinn et al. (2016) used the same wavenumbers for shear and strain (P.3302, left column).

I find the comments from Reviewer #2 have been mostly addressed appropriately.

All in all, the science in this manuscript seems in need for more work. Rather than restricting the work
to a month or so, I believe a longer time frame would be beneficial for revision. I reject the
manuscript at this stage but re-submission is not precluded after these scientific issues are addressed appropriately.
When resubmitting, you could include in the cover letter that Katsumata will handle the manuscript.

Hide

ED: Reconsider after major revisions (02 Apr 2026) by Katsuro Katsumata

Following my decision on 27 March 2026, the authors submitted a rebuttal letter and formally requested a review of the decision. This appeal was based on a one-line report from Reviewer #1.
In response, I have requested that the reviewer revise the report. I attach their rebuttal letter as Supplement.

As the authors have not yet replied to 14 specific comments from Reviewer #1, I believe the review process is not yet complete. It is imperative that the authors respond to ALL comments from the reviewer. Please also be advised that the reviewer explicitly states that the responses (egusphere-2025-4762-authors_response-version2.pdf) did not adequately address most of the major comments. I would like to emphasise the seriousness of the last major point. In the responses, the caption to Fig.R5 states that "Strain spectra were low-pass filtered at high wavenumbers (cutoff at 10 m) to remove potential noise contamination." Fig.R5 appears very similar to Fig.3a in the revised manuscript (version 3), but I could not find any indication of the use of a low-pass filter. Should the filter have been applied surreptitiously, it is difficult to believe other figures -- we have an ethical issue here.

In the revised version, please ensure that the authors' responses address the specific scientific issue raised by the reviewer. For instance, in response to the second comment regarding β and the 'single frequency' assumption, the authors initiated a discussion on the merits of the Δ-slope plot. I do not believe that it responds to the reviewer's request for justification of the use of single frequency. Merits do not overwrite physics.

It is no longer necessary to reply to Reviewer #2.

I would like to express my gratitude to the authors for their rebuttal letter, which has been instrumental in clarifying the various perspectives we hold. I would like to raise the following points in response. In the next revision, please give due consideration to the following comments. The line numbers refer to those on egusphere-2025-4762-manuscript-version3.pdf. C16 and RL refer to Chinn et al. (2016) and the rebuttal letter, respectively.

(1) The parameter "Rw"
As the fourth paragraph of RL shows, the parameter "Rw" differs from $R_\omega$ (LaTeX notation). The former "Rw" is a new quantity introduced in this manuscript and its physical meaning needs to be clearly explained. The latter $R_\omega$ has a clear physical meaning (shear-to-strain ratio of internal wave as superposition of linear waves (Eq.(10) of C16) or the frequency ratio (Eq.(6) of C16) if interpreted as a single wave (explicitly noted before Eq.(6) on C16)).
I even find it confusing to use the symbol $Rw$ for a distinct quantity from $R_\omega$ and would recommend using a different symbol.
It is evident that "Rw" is employed as a "statistical" parameter here ("designed as statistical exploration", last paragraph RL), however its physical significance remains ambiguous. As illustrated in Eq.(6), the ratio is calculated as
'shear relative to GM from waves with wavelengths between 107 and 640 m'
divided by
'strain relative to GM from waves with wavelengths between 10 and 128 m'.
Despite gauging shear and strain against GM, the authors state that they do not intend to characterise departures from GM itself (4th paragraph RL).

In this sense, Fig. 3 was an interesting attempt to characterise the internal wave field ("low-pass filter" problem aside), and it has potential to be physically fruitful.
It may be possible to justify the use of "Rw" as a proxy for $R_\omega$ using a scientific argument based on these figures. However, I am unable to interpret Figs. 2 and 4.
It is essential to clarify how one can "diagnose bathymetric effects on the internal wave field from variance estimates" (4th paragraph RL).
It appears unfeasible to estimate the local energy level of the IW field and to modulate a canonical value of the dissipation rate of turbulent kinetic energy using "Rw" without first defining its physical meaning. (L.208-) The same remark applies to L.365. It is necessary to explain why this "Rw" is being used as a statistical parameter but compared to GM's canonical value of 3 (see L.463).
The quantity "Rw" is not significantly related to the finescale parameterisation of the dissipation rate. It appears that Section 2.2 is not appropriate in this particular context. As stated in RL, 'interpreting estimates of ε or K (which is not our objective)' is not the objective of this project.

(2) Single-frequency assumption
This issue has also been raised by Reviewer #1 (second major point). In RL, the authors state in paragraph 2 that "Rw estimates ... capture coherent large-scale variations in the internal wave frequency content". However, in order to achieve this objective, it appears that the second equality in Eq.(11) in L.418 must be satisfied. This is precisely the single-frequency assumption. Without the single frequency assumption, the ratio of kinetic to potential energy is calculated as follows:

Rw = (u^2 + v^2) / (b^2 / N^2) = {∫a^2(ω) cos^2 φ(ω) (ω^2 + f^2) / ω^2 dω} / {∫a^2(ω) sin^2 φ(ω) N^2 / ω^2 dω} (#)

where (u, v) are the horizontal velocities, b is the buoyancy and N^2 is the buoyancy frequency, a^2(ω) is the amplitude as function of frequency ω, and φ is the heading angle of the wavenumber vector from the horizontal. Please note that the integration frequencies will be different for the denominator and numerator of "Rw" in this manuscript because different wavenumbers were used for the kinetic and potential energies (see Eq. (6), L.342). If the spectrum of a^2(ω) has a clear peak, one can approximate the integration around the peak. This will result in the right-hand side being approximated as (ω^2 + f^2) (N^2 - ω^2) / (ω^2 - f^2) / N^2. Assuming ω^2 << N^2, this is the second equality in Eq.(11) in L.418 of the manuscript. If the spectrum of a^2 does not display a clear peak, however, I am unable to see how the "coherent large-scale variations" in "Rw" can be connected to "internal wave frequency content", particularly when the integration ranges of the denominator and numerator are different in equation (#). It is not possible to take the integration out of the equation.
It is evident that the arguments presented in the following places all require the single-frequency assumption (L.422-, L.442-, L.472-, L.470-, Fig.2a, Fig.2c, L.486-, L.513-, L.518-, and so on).

Comments to the Author: PDF

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AR by Federico Falcini on behalf of the Authors (19 May 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (22 May 2026) by Katsuro Katsumata

RR by Anonymous Referee #1 (30 May 2026)

Suggestions for revision or reasons for rejection

Review of MS#egusphere-2025-4762 entitled “Bottom topography effects on the internal wave climate in the Ionian Sea” by Florian Kokoszka et al.

I have reviewed the Author’s Response. While the authors have responded to the editor's comments, there is no direct response to my second additional comments:

---(comments provided before)---
First, the author cited the well-known diagram of internal waves generated by “tide”- topography interactions (St. Laurent and Garrett 2002, note this is incorrectly cited as St. Laurent et al., 2012) to argue that tidally-driven lee waves are not significant. However, this does not address my original concern. My comment specifically referred to the potential generation of lee waves by “mean flows”, not tidal flows. My original specific comments (Fig. 1: It would be helpful to overlay the circulation pattern on the map. L113-124: are tidal flows much weaker than the mean flow?) relates to this point. Without a clear response to these points, I remain unconvinced by the authors’ argument.

Second, on the Δ-slope, I am convinced that the bathymetry slope does affect the calculation of Δ-slope. However, the validity of calculating β using the single-wave approximation is not addressed at all. Moreover, it remains unclear how the criticality of the bottom slope affects internal-wave frequencies (and Rω). This is related to the unanswered comment (L435-438: I think the description is not accurate. The internal-wave frequency or propagating angle doesn’t change during the reflection, but wavenumber changes).

Third, regarding the calculation of topographic roughness and steepness: I acknowledge the authors’ clarification that the roughness derived from the GEBCO product is relatively insensitive to horizontal scale and correlates well with the topographic slope. However, roughness and steepness represent distinct physical properties and are expected to play different roles in internal wave dynamics. At present, I am confused about how each of these two parameters individually influences the observed variations of Rω. The manuscript does not provide a clear physical interpretation that distinguishes their respective effects.

Lastly, regarding the blue strain spectra at high wavenumbers: I acknowledge that the potential inclusion of double-diffusive layers, excluded from the analysis, could contaminate the strain spectra. The authors now present strain spectra restricted to the data used in the analysis; however, they apply a low-pass filter that artificially suppresses high-wavenumber signals. This approach does not fully address my concern. I would expect to see the behavior of the strain spectra at high wavenumbers without the application of a low-pass filter, in order to properly assess whether the used signals are not contaminated. For comparison, Ferron et al. (2014), which the authors argue to follow, present shear and strain spectra without applying such filtering, and their strain spectra do not exhibit a blue slope at high wavenumbers. This point needs to be explicitly addressed; otherwise, I remain unconvinced by the interpretation of the high-wavenumber strain spectra.
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Although the editor’s comments are mostly based on my comments above, I believe it would have been preferable for the authors to provide direct responses to each reviewer comment individually, rather than addressing them only indirectly through responses to the editor. Such a format would facilitate a clearer scientific dialogue and make it easier to assess how each concern has been resolved.

That said, I find that the authors have carefully responded to the editor's comments, and I would not object to publication of the manuscript in Ocean Science.

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ED: Publish subject to minor revisions (review by editor) (09 Jun 2026) by Katsuro Katsumata

Thank you for revising the manuscript.

I agree with Reviewer #1 that the physical consistency of the manuscript has improved. I also agree that directly replying to the four major comments raised by the Reviewer in previous correspondence but not addressed would improve the discussion when the manuscript is published. Please provide point-by-point reponses to the four comments.

Thank you for the supplementary material, but I find it difficult to follow. Some of the questions I have are listed below.

There are a couple of inconsistent places in the main text that should be fixed before publication.

L.441, If the symbols with asterisk are to be used, this should be applied to Eq.(6), too. The statement is also inconsistent with what is written in L.428-431 "from which we estimate a local value of 𝜔 in the water-column, given 𝑁(𝑧) and the local 𝑓, that we assume representative of a certain regional extent in the horizontal. From 𝜔 we can estimate 𝛽 perpendicular to 𝛼. The relation between 𝑅𝜔, 𝜔 and 𝛽 will be exploited later in our study to associate the beam angle with 𝑅𝜔 value and compare it with the bathymetrical slope to infer propagation insights."

L.511-, Please doublecheck the panel for Fig.3 in this paragraph. E.g. Figure 3b (L.514) → Figure 3c

L.554, "Values for 𝑅ω∗ are necessary in the finescale parameterization" The value of unstarred 𝑅ω are necessary but use of 𝑅ω∗ should be avoided (Polzin et al., 2014, P.1398).

Supplementary material

Figure S1ab, The confidence interval for the bootstrap is not found -- 68%? 99%?

Figure S1ab, left panels, significant wave numbers are found for both B>A and A>B in one spectrum, sometimes in a neighbouring wavenumbers. It is unclear how to interpret these.

Table S1, S2, "large scales 640-80m", "intermediate scales 160-80 m" -- why overlap?

L.321, "the bottommost 640m" while the 1st line of Section 2 in the supplement materila says "the bottom [0-960 m] layer". I guess you have one spectrum for a 640 m bin i.e. bin i=1 at 0-640m (from the bottom), bin i=2 at 10-650 m, bin i=3 at 20-660m, ..., bin i=33 at 320-960m. Is this correct?

Each spectrum is actually a group of 9 spectra shown in Table S3. Then you take a pair from the group, say, REF and SAME_redux. You have 33 spectra (bin i=1..33) for REF and 33 spectra (bin i=1..33) for SAME_redux. Then you calculate the spearman rank correlation for the pair. Or did you treat all spectra from all stations? Since on Figure S3, the index i runs upto about 1900. The caption says "Median of R ratio across spectral subsets" -- but which subset? Each i indicates station number or depth or both?

Table S4, Do you really need 7 significant digits? How different is 0.541860 from 0.541861? I see a blue raw for Sh_redux2. What does this mean? I also see the same numbers in diagonal positions. This is consistent but is it necessary? I believe most interesting comparison would be between physically meaningful "SAME_redux,same1,2,3" and the parameter used in this manuscript "REF". The correlation seem smaller (0.47--0.62) than other entries. Would the use of "SAME_redux" change some of the conclusion of the manuscript?
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AR by Federico Falcini on behalf of the Authors (17 Jun 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (23 Jun 2026) by Katsuro Katsumata

AR by Federico Falcini on behalf of the Authors (25 Jun 2026) Manuscript

Short summary

The deep Ionian Sea strongly influences how the Mediterranean water masses circulate. By studying how internal waves interact with the seafloor, we found that rougher terrain changes how wave energy is spread out. Energy shifts from large to small scales, affecting deep water mixing. These findings help improve models of Mediterranean circulation by showing how seafloor shape impacts mixing in the deep sea.