the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Nov 2024
A global summary of seafloor topography influenced by internal-wave induced turbulent water mixing
Abstract. Turbulent water motions are important for the exchange of momentum, heat, nutrients, and suspended matter including sediments in the deep-sea that is generally stably stratified in density. To maintain ocean-density stratification, an irreversible diapycnal turbulent transport is needed. The geological shape and texture of marine topography is important for water mixing as most of deep-sea turbulence is generated via breaking internal waves at sloping seafloors. For example, slopes of semidiurnal internal tidal characteristics can ‘critically’ match the mean seafloor slope. In this paper, the concept of critical slopes is revisited from a global internal wave-turbulence viewpoint using seafloor topography- and moored high-resolution temperature sensor data. Observations suggest that turbulence generation via internal wave breaking at 5±1.5 % of all seafloors is sufficient to maintain ocean-density stratification. However most, >90 %, turbulence contribution is found at supercritical, rather than the more limited critical, slopes measured at 1'-scales that cover about 50 % of seafloors at water depths < 2000 m. Internal tides (~60 %) dominate over near-inertial waves (~40 %), which is confirmed from comparison of NE-Atlantic data with East-Mediterranean data (no tides). Seafloor-elevation spectra show a wavenumber (k) fall-off rate of k-3, which is steeper than previously found. The fall-off rate is even steeper, resulting in less elevation-variance, in a one-order-of-magnitude bandwidth around kT=0.5 cycle-per-km. The corresponding length is equivalent to the internal tidal excursion. The reduction in seafloor-elevation variance seems associated with seafloor-erosion by internal wave breaking. Potential robustness of the seafloor-internal wave interaction is discussed.
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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
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RC1: 'Comment on egusphere-2024-3603', Anonymous Referee #1, 04 Jan 2025
The article reviews several decades of results from the moored thermistor campaigns of Prof. Hans van Haren and addresses the strength of the turbulent dissipation and vertical buoyancy flux as a function of the slope of the sea floor. The authors view their results in terms of time periods of millions of years, during which the shape of the sea floor changes due to the resuspension and lateral movement of sediment. In this regard the paper is quite unusual, in that physical oceanography almost always takes the sea flor topography as an unchangeable given.
The paper stresses the observational evidence that intense mixing tends to occur over sea floor slopes that are slightly supercritical to the breaking of internal gravity waves, and that the intense mixing occurs mostly in stratified water just above any well-mixed bottom boundary layer. These aspects are certainly an improvement over the older papers of Cacchione.
In my opinion the manuscript deserves to be published in Ocean Science.
Citation: https://doi.org/10.5194/egusphere-2024-3603-RC1 -
AC1: 'Reply on RC1', Hans van Haren, 23 Jan 2025
>>>We thank the reviewer for the time to comment our paper.
The article reviews several decades of results from the moored thermistor campaigns of Prof. Hans van Haren and addresses the strength of the turbulent dissipation and vertical buoyancy flux as a function of the slope of the sea floor. The authors view their results in terms of time periods of millions of years, during which the shape of the sea floor changes due to the resuspension and lateral movement of sediment. In this regard the paper is quite unusual, in that physical oceanography almost always takes the sea flor topography as an unchangeable given.
The paper stresses the observational evidence that intense mixing tends to occur over sea floor slopes that are slightly supercritical to the breaking of internal gravity waves, and that the intense mixing occurs mostly in stratified water just above any well-mixed bottom boundary layer. These aspects are certainly an improvement over the older papers of Cacchione.
In my opinion the manuscript deserves to be published in Ocean Science.
>>>Thank you for the appraisal.
Citation: https://doi.org/10.5194/egusphere-2024-3603-AC1
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AC1: 'Reply on RC1', Hans van Haren, 23 Jan 2025
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RC2: 'Comment on egusphere-2024-3603', Anonymous Referee #2, 24 Jan 2025
Review of "A global summary of seafloor topography influenced by internal-wave induced turbulent water mixing" by Hans van Haren and Henk de Haas
In this paper the authors connect near bottom turbulence generated by internal waves (tides and near-inertial) to topographic slopes at various scales. They rely on bulk calculations over global scales, with more detailed exploration at two regional sites to make their arguments. Sections of this paper are well written and clear, but on the whole I found the arguments difficult to follow, with the manuscript lacking enough detail to reproduce many of the calculations. Key variables are not defined, and the reader is left trying to understand them by reverse engineering the results. Oddly, the methods section describes the moorings in detail, yet data from them is hardly (if at all?) used. The methods section hardly includes any information or methods leading to Figures 4, 5 and 6, which are central to the results of this work.
I think this MS is of great interest to the community, and has the potential to be influential in the way that we think about how the shapes of ocean basins relate to internal waves and turbulence. However, it needs a careful and thorough re-read to ensure it meets the standard of reproducibility, in particular relating to the methods section, with a clearer explanations of many of the "simple" bulk calculations.
I have catalogued my confusion below, which I hope will help the authors clarify and improve on this interesting paper.
L 196: Spectral band broadening of what?
L 271: Do you mean two thirds, or 66%, to be consistent with your statements on p4?
L 290: Should comment on the (large) uncertainties in mixing efficiency of 0.2
L 325: I calculate 1/(3.5e-7*250/(1.6*6e-10*3900)) and get 4%
L 341: The range of different SD frequencies would lead to a range in IT slopes, but not with a spring-neap cycle.
L 343: not if you allow for the non traditional approximation, as described earlier
L 346/347: The conflation of vertical averaging and time scales is confusing here.
L 350: I don't follow why you are calculating vertical scales (?) here, and how this relates to excursion lengths at the end of the paragraph.
L 363: editorial
L 474/475 I don't see the black dot or star
L 537: editorial
Fig 3: Why not show East-Med profiles with a continuous line, like the Mt J profiles?
Line 498: Why use 10m in Mt J, and 100m for smoothing in East-Med? Makes it hard to compare...
Line 506: I cannot follow this sentence.
Line 508: "errors"?
Line 511: Mt Jos site is more stratified than Med site well above the bottom, but near the bottom (where the nonlinear wave processes that are discussed in this paper occur), the stratification is similar. I do not understand what point is being made in this paragraph.
L 516: remove parentheses around citation
L 530: Given that these are bulk estimates, the uncertainties on 5% are large, encompassing 4%.
L 537: "what" -> "where"?
Fig 4: At 37N/S, 1.6" = 49m, 0.375" = 11m, 3.75" = 115m, 15" = 463m. It would be more helpful to the reader to use "m" in the caption, rather than seconds, given that the figure uses m. Are these spectra created from averages over the regions presented in Fig 2?
L 559: "with a small"er slope ?
L 561: It took me a long time to read and understand this section wrt Fig 4. Consider splitting Fig 4 to show Mt Jos vs. East Med separately, and highlighting the transition regions to make it easier to follow the arguments in the text.
L 578/9: The text (and figure) suggests k0 is the low wave number cut-off.
L 590: Define "tidal transition wavenumber"?
L 600: As the tides are larger at Mt Jos, the excursion length should be longer, and, if I have followed this argument correctly, k_T should be smaller. Why, then, does the spectrum slump at higher wavenumber at Mt Jos compared to at the Med site?
Fig 5: Define "angle excess occurrence". How does this relate to "ratio slope-occurrence", and anything discussed in the methods section? How did you use eq. 1 and 2 to calculate the green and yellow lines? (I note that there are three green lines, two of which are labeled "mean" and "median").
L 645: remove parentheses around citation
Fig 6: The resolution is so poor I can barely discern the magenta plusses. What kind of averaging does <> mean? Could you provide an explicit expression for the volume-weighted average (e.g. int_z(V*N)/int_z(V)), and explain how this becomes the x-label in this figure. Perhaps in the methods section?
L 716: Perhaps "range" is a better word here than "error".
L 724: Where did this error of 33% come from?
L 774: PE-Pacific -> NE-PacificCitation: https://doi.org/10.5194/egusphere-2024-3603-RC2 -
AC2: 'Reply on RC2', Hans van Haren, 10 Feb 2025
>>>We thank the reviewer for the time to comment our paper. Our replies are behind >>>
Review of "A global summary of seafloor topography influenced by internal-wave induced turbulent water mixing" by Hans van Haren and Henk de Haas
In this paper the authors connect near bottom turbulence generated by internal waves (tides and near-inertial) to topographic slopes at various scales. They rely on bulk calculations over global scales, with more detailed exploration at two regional sites to make their arguments. Sections of this paper are well written and clear, but on the whole I found the arguments difficult to follow, with the manuscript lacking enough detail to reproduce many of the calculations. Key variables are not defined, and the reader is left trying to understand them by reverse engineering the results. Oddly, the methods section describes the moorings in detail, yet data from them is hardly (if at all?) used. The methods section hardly includes any information or methods leading to Figures 4, 5 and 6, which are central to the results of this work.
>>>More of requested information is included now in the Methods section now, new sub-section 2.3.
I think this MS is of great interest to the community, and has the potential to be influential in the way that we think about how the shapes of ocean basins relate to internal waves and turbulence. However, it needs a careful and thorough re-read to ensure it meets the standard of reproducibility, in particular relating to the methods section, with a clearer explanations of many of the "simple" bulk calculations.
I have catalogued my confusion below, which I hope will help the authors clarify and improve on this interesting paper.
>>>Thank you for the criticism and appraisal.
L 196: Spectral band broadening of what?
>>>Apologies for the confusion, this was unclearly written: spectral band-broadening à band with increased spread of topographic height-variance.
L 271: Do you mean two thirds, or 66%, to be consistent with your statements on p4?
>>>Yes, as here the percentage is taken of energy of internal tides, whereas on p4 it was on total of internal waves.
L 290: Should comment on the (large) uncertainties in mixing efficiency of 0.2
>>>Mixing efficiency is indeed highly variable in the ocean as was already noted by the quoted references, but there is considerable consistency in its mean value, after ‘sufficient’ averaging. We added now: ‘over values spread over one order of magnitude’.
L 325: I calculate 1/(3.5e-7*250/(1.6*6e-10*3900)) and get 4%
>>>Yes, correct (4.3%), albeit factor 1.67 makes 4.46%. However, accounting for the errors, the monotonic distribution provides a mean of 4.7% with standard deviation of 1.4 while the random distribution gives 5.0% with standard deviation of 1.7. This is rounded to 5+/-1.5%.
L 341: The range of different SD frequencies would lead to a range in IT slopes, but not with a spring-neap cycle.
>>>Yes, good point, corrected now.
L 343: not if you allow for the non traditional approximation, as described earlier
>>>True, with the notion that: Unlimited (up to |phi| = 90degr) propagation exists for non-TA under N < 2Omega. However, for non-TA poleward free propagation of M2-tides beyond 74.degr is limited under well stratified conditions: to 76.5degr for N = 2f, to 75.0degr for N = 4f, to 74.5degr for N=100f, as indicated now.
L 346/347: The conflation of vertical averaging and time scales is confusing here.
>>>Modified now for clarity.
L 350: I don't follow why you are calculating vertical scales (?) here, and how this relates to excursion lengths at the end of the paragraph.
>>>Indeed vertical scales, as indicated now. The sentence relating to excursion lengths is removed now.
L 363: editorial
>>>The first sentence (without verb) is removed now, as it is somewhat redundant given the title of the sub-section.
L 474/475 I don't see the black dot or star
>>>Correct, apologies for description of previous version with smaller symbols. Dotàcircle, staràtriangle.
L 537: editorial
>>>whatàwhere
Fig 3: Why not show East-Med profiles with a continuous line, like the Mt J profiles?
>>>Because, for clarity, the short-10-m-scale profiles are given by coloured dots where continuous lines would give messy plots, as indicated now.
Line 498: Why use 10m in Mt J, and 100m for smoothing in East-Med? Makes it hard to compare...
>>>The reasoning was to provide some insight in the variability of layering sizes in the deep-sea/ocean. The variability is similar for both regions.
Line 506: I cannot follow this sentence.
>>>We understand, typos. We now modified: but near meanà At
Line 508: "errors"?
>>>’errors and natural’ now removed.
Line 511: Mt Jos site is more stratified than Med site well above the bottom, but near the bottom (where the nonlinear wave processes that are discussed in this paper occur), the stratification is similar. I do not understand what point is being made in this paragraph.
>>>The last sentence now commences with ‘At a given pressure level however’, to contrast with preceding lines.
L 516: remove parentheses around citation
>>>Done
L 530: Given that these are bulk estimates, the uncertainties on 5% are large, encompassing 4%.
>>>Yes, we added now ‘, albeit within one standard deviation from’
L 537: "what" -> "where"?
>>>Yes, fine.
Fig 4: At 37N/S, 1.6" = 49m, 0.375" = 11m, 3.75" = 115m, 15" = 463m. It would be more helpful to the reader to use "m" in the caption, rather than seconds, given that the figure uses m. Are these spectra created from averages over the regions presented in Fig 2?
>>>OK, meters included now. Yes, spectra are averages over data in Fig. 2 as better indicated now.
L 559: "with a small"er slope ?
>>>Yes, better, thank you.
L 561: It took me a long time to read and understand this section wrt Fig 4. Consider splitting Fig 4 to show Mt Jos vs. East Med separately, and highlighting the transition regions to make it easier to follow the arguments in the text.
>>>Fig. 4 is now split as suggested, with the one (green) curve for MntJos in Fig. 5. The steep slope transition regions are highlighted now.
L 578/9: The text (and figure) suggests k0 is the low wave number cut-off.
>>>Thank you for pointing out. The caption was wrong: k_0 should be one line up, high-k roll-off is ‘to noise’, as modified now.
L 590: Define "tidal transition wavenumber"?
>>>As excursion length has been removed above, ‘(tidal)’ has been removed from this sentence.
L 600: As the tides are larger at Mt Jos, the excursion length should be longer, and, if I have followed this argument correctly, k_T should be smaller. Why, then, does the spectrum slump at higher wavenumber at Mt Jos compared to at the Med site?
>>>As indicated a few sentences above, the range around k_T is about one order of magnitude. Tides are indeed larger at MtJos but total IW speed probably not (N is the same).As the excursion length of near-inertial waves is 1.8 times that of SD tides, the slump down at higher wavenumber at MT Josephine is likely explained. This is better indicated now. A sentence is added to indicate the potential variability associated with nonlinear internal waves.
Fig 5: Define "angle excess occurrence". How does this relate to "ratio slope-occurrence", and anything discussed in the methods section? How did you use eq. 1 and 2 to calculate the green and yellow lines? (I note that there are three green lines, two of which are labeled "mean" and "median").
>>> Now Fig. 6. With “angle excess occurrence” we meant percentage of slopes being larger than particular slope angle, as was indicated end of Section 2.2, improved with definition now. Angle excess occurrence --> slope occurrence. “mean” does not exist in this figure: besides “median” the other horizontal line is named ‘5%’. The yellow and green ‘curves’ (now: ‘graphs’) are the internal tidal slope computed as a function of N, and plotted against buoyancy frequency/maximum buoyancy frequency. This is better indicated in the caption now.
L 645: remove parentheses around citation
>>>Done.
Fig 6: The resolution is so poor I can barely discern the magenta plusses. What kind of averaging does <> mean? Could you provide an explicit expression for the volume-weighted average (e.g. int_z(V*N)/int_z(V)), and explain how this becomes the x-label in this figure. Perhaps in the methods section?
>>>Now Fig. 7. Visibility is improved now using larger symbols. <> indicates vertical averaging. The explicit expression is given in sub-section 2.3 now.
L 716: Perhaps "range" is a better word here than "error".
>>>Error-range is used now.
L 724: Where did this error of 33% come from?
>>>Error by a factor of two, as indicated now.
L 774: PE-Pacific -> NE-Pacific>>>Yes, thank you.
Citation: https://doi.org/10.5194/egusphere-2024-3603-AC2
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AC2: 'Reply on RC2', Hans van Haren, 10 Feb 2025
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-3603', Anonymous Referee #1, 04 Jan 2025
The article reviews several decades of results from the moored thermistor campaigns of Prof. Hans van Haren and addresses the strength of the turbulent dissipation and vertical buoyancy flux as a function of the slope of the sea floor. The authors view their results in terms of time periods of millions of years, during which the shape of the sea floor changes due to the resuspension and lateral movement of sediment. In this regard the paper is quite unusual, in that physical oceanography almost always takes the sea flor topography as an unchangeable given.
The paper stresses the observational evidence that intense mixing tends to occur over sea floor slopes that are slightly supercritical to the breaking of internal gravity waves, and that the intense mixing occurs mostly in stratified water just above any well-mixed bottom boundary layer. These aspects are certainly an improvement over the older papers of Cacchione.
In my opinion the manuscript deserves to be published in Ocean Science.
Citation: https://doi.org/10.5194/egusphere-2024-3603-RC1 -
AC1: 'Reply on RC1', Hans van Haren, 23 Jan 2025
>>>We thank the reviewer for the time to comment our paper.
The article reviews several decades of results from the moored thermistor campaigns of Prof. Hans van Haren and addresses the strength of the turbulent dissipation and vertical buoyancy flux as a function of the slope of the sea floor. The authors view their results in terms of time periods of millions of years, during which the shape of the sea floor changes due to the resuspension and lateral movement of sediment. In this regard the paper is quite unusual, in that physical oceanography almost always takes the sea flor topography as an unchangeable given.
The paper stresses the observational evidence that intense mixing tends to occur over sea floor slopes that are slightly supercritical to the breaking of internal gravity waves, and that the intense mixing occurs mostly in stratified water just above any well-mixed bottom boundary layer. These aspects are certainly an improvement over the older papers of Cacchione.
In my opinion the manuscript deserves to be published in Ocean Science.
>>>Thank you for the appraisal.
Citation: https://doi.org/10.5194/egusphere-2024-3603-AC1
-
AC1: 'Reply on RC1', Hans van Haren, 23 Jan 2025
-
RC2: 'Comment on egusphere-2024-3603', Anonymous Referee #2, 24 Jan 2025
Review of "A global summary of seafloor topography influenced by internal-wave induced turbulent water mixing" by Hans van Haren and Henk de Haas
In this paper the authors connect near bottom turbulence generated by internal waves (tides and near-inertial) to topographic slopes at various scales. They rely on bulk calculations over global scales, with more detailed exploration at two regional sites to make their arguments. Sections of this paper are well written and clear, but on the whole I found the arguments difficult to follow, with the manuscript lacking enough detail to reproduce many of the calculations. Key variables are not defined, and the reader is left trying to understand them by reverse engineering the results. Oddly, the methods section describes the moorings in detail, yet data from them is hardly (if at all?) used. The methods section hardly includes any information or methods leading to Figures 4, 5 and 6, which are central to the results of this work.
I think this MS is of great interest to the community, and has the potential to be influential in the way that we think about how the shapes of ocean basins relate to internal waves and turbulence. However, it needs a careful and thorough re-read to ensure it meets the standard of reproducibility, in particular relating to the methods section, with a clearer explanations of many of the "simple" bulk calculations.
I have catalogued my confusion below, which I hope will help the authors clarify and improve on this interesting paper.
L 196: Spectral band broadening of what?
L 271: Do you mean two thirds, or 66%, to be consistent with your statements on p4?
L 290: Should comment on the (large) uncertainties in mixing efficiency of 0.2
L 325: I calculate 1/(3.5e-7*250/(1.6*6e-10*3900)) and get 4%
L 341: The range of different SD frequencies would lead to a range in IT slopes, but not with a spring-neap cycle.
L 343: not if you allow for the non traditional approximation, as described earlier
L 346/347: The conflation of vertical averaging and time scales is confusing here.
L 350: I don't follow why you are calculating vertical scales (?) here, and how this relates to excursion lengths at the end of the paragraph.
L 363: editorial
L 474/475 I don't see the black dot or star
L 537: editorial
Fig 3: Why not show East-Med profiles with a continuous line, like the Mt J profiles?
Line 498: Why use 10m in Mt J, and 100m for smoothing in East-Med? Makes it hard to compare...
Line 506: I cannot follow this sentence.
Line 508: "errors"?
Line 511: Mt Jos site is more stratified than Med site well above the bottom, but near the bottom (where the nonlinear wave processes that are discussed in this paper occur), the stratification is similar. I do not understand what point is being made in this paragraph.
L 516: remove parentheses around citation
L 530: Given that these are bulk estimates, the uncertainties on 5% are large, encompassing 4%.
L 537: "what" -> "where"?
Fig 4: At 37N/S, 1.6" = 49m, 0.375" = 11m, 3.75" = 115m, 15" = 463m. It would be more helpful to the reader to use "m" in the caption, rather than seconds, given that the figure uses m. Are these spectra created from averages over the regions presented in Fig 2?
L 559: "with a small"er slope ?
L 561: It took me a long time to read and understand this section wrt Fig 4. Consider splitting Fig 4 to show Mt Jos vs. East Med separately, and highlighting the transition regions to make it easier to follow the arguments in the text.
L 578/9: The text (and figure) suggests k0 is the low wave number cut-off.
L 590: Define "tidal transition wavenumber"?
L 600: As the tides are larger at Mt Jos, the excursion length should be longer, and, if I have followed this argument correctly, k_T should be smaller. Why, then, does the spectrum slump at higher wavenumber at Mt Jos compared to at the Med site?
Fig 5: Define "angle excess occurrence". How does this relate to "ratio slope-occurrence", and anything discussed in the methods section? How did you use eq. 1 and 2 to calculate the green and yellow lines? (I note that there are three green lines, two of which are labeled "mean" and "median").
L 645: remove parentheses around citation
Fig 6: The resolution is so poor I can barely discern the magenta plusses. What kind of averaging does <> mean? Could you provide an explicit expression for the volume-weighted average (e.g. int_z(V*N)/int_z(V)), and explain how this becomes the x-label in this figure. Perhaps in the methods section?
L 716: Perhaps "range" is a better word here than "error".
L 724: Where did this error of 33% come from?
L 774: PE-Pacific -> NE-PacificCitation: https://doi.org/10.5194/egusphere-2024-3603-RC2 -
AC2: 'Reply on RC2', Hans van Haren, 10 Feb 2025
>>>We thank the reviewer for the time to comment our paper. Our replies are behind >>>
Review of "A global summary of seafloor topography influenced by internal-wave induced turbulent water mixing" by Hans van Haren and Henk de Haas
In this paper the authors connect near bottom turbulence generated by internal waves (tides and near-inertial) to topographic slopes at various scales. They rely on bulk calculations over global scales, with more detailed exploration at two regional sites to make their arguments. Sections of this paper are well written and clear, but on the whole I found the arguments difficult to follow, with the manuscript lacking enough detail to reproduce many of the calculations. Key variables are not defined, and the reader is left trying to understand them by reverse engineering the results. Oddly, the methods section describes the moorings in detail, yet data from them is hardly (if at all?) used. The methods section hardly includes any information or methods leading to Figures 4, 5 and 6, which are central to the results of this work.
>>>More of requested information is included now in the Methods section now, new sub-section 2.3.
I think this MS is of great interest to the community, and has the potential to be influential in the way that we think about how the shapes of ocean basins relate to internal waves and turbulence. However, it needs a careful and thorough re-read to ensure it meets the standard of reproducibility, in particular relating to the methods section, with a clearer explanations of many of the "simple" bulk calculations.
I have catalogued my confusion below, which I hope will help the authors clarify and improve on this interesting paper.
>>>Thank you for the criticism and appraisal.
L 196: Spectral band broadening of what?
>>>Apologies for the confusion, this was unclearly written: spectral band-broadening à band with increased spread of topographic height-variance.
L 271: Do you mean two thirds, or 66%, to be consistent with your statements on p4?
>>>Yes, as here the percentage is taken of energy of internal tides, whereas on p4 it was on total of internal waves.
L 290: Should comment on the (large) uncertainties in mixing efficiency of 0.2
>>>Mixing efficiency is indeed highly variable in the ocean as was already noted by the quoted references, but there is considerable consistency in its mean value, after ‘sufficient’ averaging. We added now: ‘over values spread over one order of magnitude’.
L 325: I calculate 1/(3.5e-7*250/(1.6*6e-10*3900)) and get 4%
>>>Yes, correct (4.3%), albeit factor 1.67 makes 4.46%. However, accounting for the errors, the monotonic distribution provides a mean of 4.7% with standard deviation of 1.4 while the random distribution gives 5.0% with standard deviation of 1.7. This is rounded to 5+/-1.5%.
L 341: The range of different SD frequencies would lead to a range in IT slopes, but not with a spring-neap cycle.
>>>Yes, good point, corrected now.
L 343: not if you allow for the non traditional approximation, as described earlier
>>>True, with the notion that: Unlimited (up to |phi| = 90degr) propagation exists for non-TA under N < 2Omega. However, for non-TA poleward free propagation of M2-tides beyond 74.degr is limited under well stratified conditions: to 76.5degr for N = 2f, to 75.0degr for N = 4f, to 74.5degr for N=100f, as indicated now.
L 346/347: The conflation of vertical averaging and time scales is confusing here.
>>>Modified now for clarity.
L 350: I don't follow why you are calculating vertical scales (?) here, and how this relates to excursion lengths at the end of the paragraph.
>>>Indeed vertical scales, as indicated now. The sentence relating to excursion lengths is removed now.
L 363: editorial
>>>The first sentence (without verb) is removed now, as it is somewhat redundant given the title of the sub-section.
L 474/475 I don't see the black dot or star
>>>Correct, apologies for description of previous version with smaller symbols. Dotàcircle, staràtriangle.
L 537: editorial
>>>whatàwhere
Fig 3: Why not show East-Med profiles with a continuous line, like the Mt J profiles?
>>>Because, for clarity, the short-10-m-scale profiles are given by coloured dots where continuous lines would give messy plots, as indicated now.
Line 498: Why use 10m in Mt J, and 100m for smoothing in East-Med? Makes it hard to compare...
>>>The reasoning was to provide some insight in the variability of layering sizes in the deep-sea/ocean. The variability is similar for both regions.
Line 506: I cannot follow this sentence.
>>>We understand, typos. We now modified: but near meanà At
Line 508: "errors"?
>>>’errors and natural’ now removed.
Line 511: Mt Jos site is more stratified than Med site well above the bottom, but near the bottom (where the nonlinear wave processes that are discussed in this paper occur), the stratification is similar. I do not understand what point is being made in this paragraph.
>>>The last sentence now commences with ‘At a given pressure level however’, to contrast with preceding lines.
L 516: remove parentheses around citation
>>>Done
L 530: Given that these are bulk estimates, the uncertainties on 5% are large, encompassing 4%.
>>>Yes, we added now ‘, albeit within one standard deviation from’
L 537: "what" -> "where"?
>>>Yes, fine.
Fig 4: At 37N/S, 1.6" = 49m, 0.375" = 11m, 3.75" = 115m, 15" = 463m. It would be more helpful to the reader to use "m" in the caption, rather than seconds, given that the figure uses m. Are these spectra created from averages over the regions presented in Fig 2?
>>>OK, meters included now. Yes, spectra are averages over data in Fig. 2 as better indicated now.
L 559: "with a small"er slope ?
>>>Yes, better, thank you.
L 561: It took me a long time to read and understand this section wrt Fig 4. Consider splitting Fig 4 to show Mt Jos vs. East Med separately, and highlighting the transition regions to make it easier to follow the arguments in the text.
>>>Fig. 4 is now split as suggested, with the one (green) curve for MntJos in Fig. 5. The steep slope transition regions are highlighted now.
L 578/9: The text (and figure) suggests k0 is the low wave number cut-off.
>>>Thank you for pointing out. The caption was wrong: k_0 should be one line up, high-k roll-off is ‘to noise’, as modified now.
L 590: Define "tidal transition wavenumber"?
>>>As excursion length has been removed above, ‘(tidal)’ has been removed from this sentence.
L 600: As the tides are larger at Mt Jos, the excursion length should be longer, and, if I have followed this argument correctly, k_T should be smaller. Why, then, does the spectrum slump at higher wavenumber at Mt Jos compared to at the Med site?
>>>As indicated a few sentences above, the range around k_T is about one order of magnitude. Tides are indeed larger at MtJos but total IW speed probably not (N is the same).As the excursion length of near-inertial waves is 1.8 times that of SD tides, the slump down at higher wavenumber at MT Josephine is likely explained. This is better indicated now. A sentence is added to indicate the potential variability associated with nonlinear internal waves.
Fig 5: Define "angle excess occurrence". How does this relate to "ratio slope-occurrence", and anything discussed in the methods section? How did you use eq. 1 and 2 to calculate the green and yellow lines? (I note that there are three green lines, two of which are labeled "mean" and "median").
>>> Now Fig. 6. With “angle excess occurrence” we meant percentage of slopes being larger than particular slope angle, as was indicated end of Section 2.2, improved with definition now. Angle excess occurrence --> slope occurrence. “mean” does not exist in this figure: besides “median” the other horizontal line is named ‘5%’. The yellow and green ‘curves’ (now: ‘graphs’) are the internal tidal slope computed as a function of N, and plotted against buoyancy frequency/maximum buoyancy frequency. This is better indicated in the caption now.
L 645: remove parentheses around citation
>>>Done.
Fig 6: The resolution is so poor I can barely discern the magenta plusses. What kind of averaging does <> mean? Could you provide an explicit expression for the volume-weighted average (e.g. int_z(V*N)/int_z(V)), and explain how this becomes the x-label in this figure. Perhaps in the methods section?
>>>Now Fig. 7. Visibility is improved now using larger symbols. <> indicates vertical averaging. The explicit expression is given in sub-section 2.3 now.
L 716: Perhaps "range" is a better word here than "error".
>>>Error-range is used now.
L 724: Where did this error of 33% come from?
>>>Error by a factor of two, as indicated now.
L 774: PE-Pacific -> NE-Pacific>>>Yes, thank you.
Citation: https://doi.org/10.5194/egusphere-2024-3603-AC2
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AC2: 'Reply on RC2', Hans van Haren, 10 Feb 2025
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Hans van Haren
Henk de Haas
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