the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Oct 2025
Bottom topography effects on abyssal diapycnal mixing in the Eastern Mediterranean Sea
Abstract. The abyssal Ionian Sea is a deep region of interest for the entire ocean circulation of the Mediterranean Sea, since it plays an important role in the ventilation processes of the whole basin. Here we investigate spatial patterns of diapycnal mixing due to internal waves, over the bottom of the Ionian sub-basin. To identify regional features of the internal wave field in terms of vertical shear and strain, we analyze LADCP and CTD profiles, measured across the basin in 2007, covering various seafloor morphologies (shelf, shelf break, and abyssal plain). Our results show that increasing seafloor roughness reduces the variability of the shear-to-strain ratio, a pattern also influenced by correlations between slope and roughness. Roughness appears to constrain waves toward higher frequencies, with high shear-to-strain ratios associated with lower frequencies and flatter propagation angles, and low ratios linked to higher frequencies and steeper beams. Spectral analyses indicate that rougher regions enhance strain variance at small vertical scales while reducing shear variance at larger scales, leading to flatter shear spectra in the low-wavenumber band. Together, these findings suggest that roughness redistributes energy from large-scale toward small-scale, fundamentally altering the balance of internal wave energy across scales. These results expand our insights for 3D ocean circulation models, providing useful knowledge for ad hoc parameterization of mixing that should capture abyssal, internal wave–driven processes in the Mediterranean Sea.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-4762', Anonymous Referee #1, 18 Nov 2025
- AC1: 'Reply on RC1', Federico Falcini, 09 Jan 2026
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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
Peer review completion
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-4762', Anonymous Referee #1, 18 Nov 2025
- AC1: 'Reply on RC1', Federico Falcini, 09 Jan 2026
-
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
Peer review completion
Journal article(s) based on this preprint
Data sets
CTD and LADCP data from the KM3NET cruise, Ionian Sea, July 2007 M. Borghini et al. https://www.seanoe.org/preview/108742?token=NkpdOxO5966RjZ--Rqdw1c0dCZ-6iGSW
Model code and software
Finescale parameterization shear/strain GM F. Kokoszka https://zenodo.org/records/17170422
Interactive computing environment
Finescale parameterization shear/strain GM F. Kokoszka https://zenodo.org/records/17170422
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Florian Kokoszka
Stefania Sparnocchia
Davide Cavaliere
Vincenzo Artale
Mireno Borghini
Beatrice Giambenedetti
Federico Falcini
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2220 KB) - Metadata XML
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Supplement
(224 KB) - BibTeX
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- Final revised paper
Please see attached pdf.