Internal tides off the Amazon shelf during two contrasted seasons: Interactions with background circulation and SSH imprints
 LEGOS, Université de Toulouse, CNES, CNRS, IRD, UPS, Toulouse, France
 LEGOS, Université de Toulouse, CNES, CNRS, IRD, UPS, Toulouse, France
Abstract. The Amazon shelf break is a key region for internal tides (IT) generation. The region also shows a large seasonal variation of circulation and associated stratification. The objective of this study is to document how these variations will impact IT generation and propagation properties. A highresolution regional model (1/36° horizontal resolution), explicitly resolving IT is analyzed to investigate their interactions with the background circulation and stratification, over two seasons: first MAMJJ (March to July), with weaker mesoscale currents, shallower and stronger pycnocline, and second ASOND (August to December) with stronger mesoscale currents, deeper and weaker pycnocline. IT are generated on the shelf break between the 100 and 1800 m isobaths, with a maximum on average at about 10 km offshore. South of 2° N, the conversion from barotropic to baroclinic tide is more efficient in MAMJJ than in ASOND. At the eight main IT generations sites, the local dissipation is higher in MAMJJ (30 %) than in ASOND (22 %). The remaining fraction propagates away from the generation sites and mainly dissipates locally every 90–120 km. The remote dissipation increases slightly during ASOND and the coherent M2 fluxes seem blocked between 4°–6° N west of 47° W. Further analysis of 25 hours mean snapshots of the baroclinic flux shows deviation and branching of the IT when interacting with strong mesoscale and stratification. We evaluated sea surface height (SSH) frequency and wavenumber spectra for subtidal (f < 1/28h^{−1}), tidal (1/28h^{−1} < f < 1/11h^{−1}) and super tidal (f > 1/11h^{−1}) frequencies. Tidal frequencies explain most of the SSH variability for wavelengths between 300 km and 70 km. Below 70 km, the SSH is mainly incoherent and supertidal. The length scale at which the SSH becomes dominated by unbalanced IT was estimated to be around 250 km. Our results highlight the complexity of correctly predicting IT SSH in order to better observe mesoscale and submesoscale from existing and upcoming altmetrics missions, notably the Surface Water Ocean Topography (SWOT) mission.
Michel Tchilibou et al.
Status: closed

RC1: 'Comment on os2021114', Anonymous Referee #1, 16 Jan 2022
Great work by the authors. Some suggestions and possible corrections in the attached files.
Thank you.

AC1: 'Reply on RC1', Tchilibou Michel Lionel, 15 Apr 2022
We thank the reviewer for taking the time to review our manuscript. We particularly appreciate the recommended publications on the internal tide regime. We are glad that the reviewer finds the article publishable after minor revisions. Please find the reviewers’ comments and our responses in the attached file

AC1: 'Reply on RC1', Tchilibou Michel Lionel, 15 Apr 2022

RC2: 'Comment on os2021114', Anonymous Referee #2, 31 Jan 2022
Review of “Internal tides off the Amazon shelf during two contrasted seasons: Interactions with background circulation and SSH imprints”
This paper presents an internal tide energy budget and wavenumber frequency spectra analysis for two seasons for the Amazon internal tide hot spot using nested high resolution model simulations. It is good to see that the model captures the nonlinear aspect of the internal tides near the Amazon (higher harmonics in Figure 9f), an aspect that most global and regional studies have not focused on much.
The paper’s English is generally good with small grammatical errors here and there and the figures are pretty and clear (although the spectral line plot is quite dense). However, I noticed more grammatical errors in the discussion section, which seemed to be less well polished. The paper is quite long, dense, and in some places descriptive. To make sure the reader stays captivated, I suggest shortening the paper and make it more focused. The title suggests the theme is about seasonal internal tide variability (very interesting topic), but it seems to be that for the variables considered it is not very strong and/or not well communicated in the paper. The authors could go more in depth in either the energy analysis or the SSH frequency wavenumber analysis (I think you could make two standalone papers on these topics).
Regarding the energy analysis, why do the authors consider the energetics of the coherent surface and internal tides but not the incoherent internal tides? To describe the incoherent internal tides the authors use SSH in sections 3.4 and 3.5. Similar to Pickering et al (2015) and Buijsman et al (2017), the authors could have computed incoherent signals as the tidal bandpassed minus the harmonically fitted time series. This allows for a better discussion on what fraction is scattered to the incoherent internal tide and what fraction is “truly” dissipated.
Quite a bit of text is focuses on 8 separate generation sites. I suggest the authors focus mainly on site A as that is the largest generation site and its beam is best captured by the high resolution model. On a site note, to better investigate the energetics of this beam a bigger model domain would be better. This could also be discussed in the discussion section.
The authors show there are significant seasonal differences in mesoscale currents and stratification, suggesting that this may be important for the energetics and beam orientation. However, they show this does not have a strong impact on the conversion. I am not completely surprised because conversion generally happens between 100 and 1000 m, where N does not change much. How does this seasonality affect the propagation of the modes for example (e.g. in their energy fluxes)? The authors could do some ray tracing to entangle the mechanisms behind the refraction?
The discussion section reads like a long summary section of the results. I suggest the authors write a shorter and more focused discussion section and also a standalone conclusion section. It would be nice to see a discussion section that discusses the paper’s findings in light of the literature and any deficiencies the model and or analysis may have (e.g., the spectral bump at 20 km).
L35. Also cite Shriver et al (2012) here.
L41. Some more references would be justified here. Zaron and Egbert (2014), Shriver et al (2014), Buijsman et al, (2017), Ponte et al (2015), etc etc
L52. I believe Zaron et al and Muller et al also wrote some papers on the seasonal variability of the internal tide. Maybe include some more references here?
Figure 1. Instead of contours use curves.
L105. 45 and 30 degrees are relative to what (east, north)?
L114. Please define “(un)balanced motions”.
L116. I do not understand “before calculating geostrophic currents”.
L125. Here you suggest you look into the total dissipation, but the paper discusses only the energetics of the coherent internal tide.
L108131. The paper raises questions that are not discussed in the same order in the manuscript.
L174. It is not clear what definitions you mean precisely.
L176. What is a nonzero mode? After depth integration?
L177. Can you comment how much the improvement is (1%, 10%)? This is useful information for future studies.
L180. Can you provide some more information on your steps here? Do you solve for the eigenfunctions using spatially varying stratification? Then you fit the U eigen modes to the harmonic constants of the 3D velocity and pressure fields? This yields the modal amplitudes that you then use in the energy analysis? Or do you only use barotropic and baroclinic SSH? You can compute baroclinic SSH from the sum of the rigid lid modal surface pressures (or is this what you do)? How many modes do you fit (this is most likely limited by frequency and by vertical and horizontal resolution; see Buijsman et al, 2020)?
L207. Figure 2c should be Figure 1b?
L208. “differences” Note that the altimetry is based on 20+ years of data while your model is only based on 9 months. The longer the period over which the harmonic analysis is performed the smaller the coherent amplitude (see Ansong et al, 2015 and the appendix of Buijsman et al, 2020). Hence, your comparison may not be quite an applestoapples comparison. In the model far field there is clearly some coherent energy that is not present in the altimetry, possibly due to time series duration?
L233. There is no Coriolis balanced flow near/at the equator. How does that affect AVISO and your comparison?
Figure 3. Why do you not show the currents in the Aviso data?
Figure 4. Can you explain negative N in the figure? Maybe correct for that (set N=0)?
L258. “expected” since you do a modal analysis do you have the answer?
L260. “barrier” for the total or the coherent internal tide? This causes reflections?
L265. What are the reasons you ignore these terms?
Equations 1 and 2 and table 3. I am confused here. Why is BT dissipation positive and BC dissipation negative? Both should be positive. See Kang and Fringer (2012).
Eq3. Z=H not z=H+eta?
L357378. The authors discuss the dissipation of the coherent internal tide in these sections. It is generally known from Zaron and Buijsman studies that the coherent dissipation includes energy loss to the incoherent internal tide and higher harmonics. However, the authors do not clearly a priori state that. Hence, it sometimes seems if they are discussion the total dissipation. The authors could focus more on determining what fraction of the coherent dissipation scatters to the nonstationary internal tides.
Section 3.4 and 3.5. Instead of focusing on the SSH, the authors could focus on the total internal tide energetics and compare that to the coherent energetics?
Section 3.4. This is very dense description of Figure 8. I wonder if this can be either shortened or made more quantitative (e.g. include ray tracing)?
Eqs 89. You assume that the higher harmonics are always incoherent. Is this really true? Can you do a harmonic analysis and fit for M4, M6, etc and see what variance fraction they comprise of the total higher harmonic variance?
L493. “justifying the incoherence ratio of more than 0.5 noted by Zaron (2017, its Figure 8)”
I am not sure if this is correct. Zaron looks at the primary frequencies, while you also include the higher harmonics. Hence this is not an apples to apples comparison.L499. “components” what components precisely?
Figure 11. Add period [hours] to the right axis of right subplot.
Figure 12. This is a nice figure, but the colored lines are hard to distinguish. You could add more clarity by increasing the thickness for some lines and making the panels wider?
L559. “However, defining the transition scale from the super tidal is delicate” It is not directly clear to what the super tidal scale transitions to (supersuper tidal?). Why is it relevant to discuss this transition scale?
L567. What are meridian spatial scales?
L665. Refer to a Figure here?
L677. The MAR radiates southward waves.

AC2: 'Reply on RC2', Tchilibou Michel Lionel, 15 Apr 2022
We thank the reviewer for taking the time to review our manuscript. We thank the reviewer for taking the time to review our manuscript. We found the comments extremely helpful in correcting some inconsistencies and improving the writing of the paper.
Please find the reviewers’ comments and our answers in the attached file

AC2: 'Reply on RC2', Tchilibou Michel Lionel, 15 Apr 2022
Status: closed

RC1: 'Comment on os2021114', Anonymous Referee #1, 16 Jan 2022
Great work by the authors. Some suggestions and possible corrections in the attached files.
Thank you.

AC1: 'Reply on RC1', Tchilibou Michel Lionel, 15 Apr 2022
We thank the reviewer for taking the time to review our manuscript. We particularly appreciate the recommended publications on the internal tide regime. We are glad that the reviewer finds the article publishable after minor revisions. Please find the reviewers’ comments and our responses in the attached file

AC1: 'Reply on RC1', Tchilibou Michel Lionel, 15 Apr 2022

RC2: 'Comment on os2021114', Anonymous Referee #2, 31 Jan 2022
Review of “Internal tides off the Amazon shelf during two contrasted seasons: Interactions with background circulation and SSH imprints”
This paper presents an internal tide energy budget and wavenumber frequency spectra analysis for two seasons for the Amazon internal tide hot spot using nested high resolution model simulations. It is good to see that the model captures the nonlinear aspect of the internal tides near the Amazon (higher harmonics in Figure 9f), an aspect that most global and regional studies have not focused on much.
The paper’s English is generally good with small grammatical errors here and there and the figures are pretty and clear (although the spectral line plot is quite dense). However, I noticed more grammatical errors in the discussion section, which seemed to be less well polished. The paper is quite long, dense, and in some places descriptive. To make sure the reader stays captivated, I suggest shortening the paper and make it more focused. The title suggests the theme is about seasonal internal tide variability (very interesting topic), but it seems to be that for the variables considered it is not very strong and/or not well communicated in the paper. The authors could go more in depth in either the energy analysis or the SSH frequency wavenumber analysis (I think you could make two standalone papers on these topics).
Regarding the energy analysis, why do the authors consider the energetics of the coherent surface and internal tides but not the incoherent internal tides? To describe the incoherent internal tides the authors use SSH in sections 3.4 and 3.5. Similar to Pickering et al (2015) and Buijsman et al (2017), the authors could have computed incoherent signals as the tidal bandpassed minus the harmonically fitted time series. This allows for a better discussion on what fraction is scattered to the incoherent internal tide and what fraction is “truly” dissipated.
Quite a bit of text is focuses on 8 separate generation sites. I suggest the authors focus mainly on site A as that is the largest generation site and its beam is best captured by the high resolution model. On a site note, to better investigate the energetics of this beam a bigger model domain would be better. This could also be discussed in the discussion section.
The authors show there are significant seasonal differences in mesoscale currents and stratification, suggesting that this may be important for the energetics and beam orientation. However, they show this does not have a strong impact on the conversion. I am not completely surprised because conversion generally happens between 100 and 1000 m, where N does not change much. How does this seasonality affect the propagation of the modes for example (e.g. in their energy fluxes)? The authors could do some ray tracing to entangle the mechanisms behind the refraction?
The discussion section reads like a long summary section of the results. I suggest the authors write a shorter and more focused discussion section and also a standalone conclusion section. It would be nice to see a discussion section that discusses the paper’s findings in light of the literature and any deficiencies the model and or analysis may have (e.g., the spectral bump at 20 km).
L35. Also cite Shriver et al (2012) here.
L41. Some more references would be justified here. Zaron and Egbert (2014), Shriver et al (2014), Buijsman et al, (2017), Ponte et al (2015), etc etc
L52. I believe Zaron et al and Muller et al also wrote some papers on the seasonal variability of the internal tide. Maybe include some more references here?
Figure 1. Instead of contours use curves.
L105. 45 and 30 degrees are relative to what (east, north)?
L114. Please define “(un)balanced motions”.
L116. I do not understand “before calculating geostrophic currents”.
L125. Here you suggest you look into the total dissipation, but the paper discusses only the energetics of the coherent internal tide.
L108131. The paper raises questions that are not discussed in the same order in the manuscript.
L174. It is not clear what definitions you mean precisely.
L176. What is a nonzero mode? After depth integration?
L177. Can you comment how much the improvement is (1%, 10%)? This is useful information for future studies.
L180. Can you provide some more information on your steps here? Do you solve for the eigenfunctions using spatially varying stratification? Then you fit the U eigen modes to the harmonic constants of the 3D velocity and pressure fields? This yields the modal amplitudes that you then use in the energy analysis? Or do you only use barotropic and baroclinic SSH? You can compute baroclinic SSH from the sum of the rigid lid modal surface pressures (or is this what you do)? How many modes do you fit (this is most likely limited by frequency and by vertical and horizontal resolution; see Buijsman et al, 2020)?
L207. Figure 2c should be Figure 1b?
L208. “differences” Note that the altimetry is based on 20+ years of data while your model is only based on 9 months. The longer the period over which the harmonic analysis is performed the smaller the coherent amplitude (see Ansong et al, 2015 and the appendix of Buijsman et al, 2020). Hence, your comparison may not be quite an applestoapples comparison. In the model far field there is clearly some coherent energy that is not present in the altimetry, possibly due to time series duration?
L233. There is no Coriolis balanced flow near/at the equator. How does that affect AVISO and your comparison?
Figure 3. Why do you not show the currents in the Aviso data?
Figure 4. Can you explain negative N in the figure? Maybe correct for that (set N=0)?
L258. “expected” since you do a modal analysis do you have the answer?
L260. “barrier” for the total or the coherent internal tide? This causes reflections?
L265. What are the reasons you ignore these terms?
Equations 1 and 2 and table 3. I am confused here. Why is BT dissipation positive and BC dissipation negative? Both should be positive. See Kang and Fringer (2012).
Eq3. Z=H not z=H+eta?
L357378. The authors discuss the dissipation of the coherent internal tide in these sections. It is generally known from Zaron and Buijsman studies that the coherent dissipation includes energy loss to the incoherent internal tide and higher harmonics. However, the authors do not clearly a priori state that. Hence, it sometimes seems if they are discussion the total dissipation. The authors could focus more on determining what fraction of the coherent dissipation scatters to the nonstationary internal tides.
Section 3.4 and 3.5. Instead of focusing on the SSH, the authors could focus on the total internal tide energetics and compare that to the coherent energetics?
Section 3.4. This is very dense description of Figure 8. I wonder if this can be either shortened or made more quantitative (e.g. include ray tracing)?
Eqs 89. You assume that the higher harmonics are always incoherent. Is this really true? Can you do a harmonic analysis and fit for M4, M6, etc and see what variance fraction they comprise of the total higher harmonic variance?
L493. “justifying the incoherence ratio of more than 0.5 noted by Zaron (2017, its Figure 8)”
I am not sure if this is correct. Zaron looks at the primary frequencies, while you also include the higher harmonics. Hence this is not an apples to apples comparison.L499. “components” what components precisely?
Figure 11. Add period [hours] to the right axis of right subplot.
Figure 12. This is a nice figure, but the colored lines are hard to distinguish. You could add more clarity by increasing the thickness for some lines and making the panels wider?
L559. “However, defining the transition scale from the super tidal is delicate” It is not directly clear to what the super tidal scale transitions to (supersuper tidal?). Why is it relevant to discuss this transition scale?
L567. What are meridian spatial scales?
L665. Refer to a Figure here?
L677. The MAR radiates southward waves.

AC2: 'Reply on RC2', Tchilibou Michel Lionel, 15 Apr 2022
We thank the reviewer for taking the time to review our manuscript. We thank the reviewer for taking the time to review our manuscript. We found the comments extremely helpful in correcting some inconsistencies and improving the writing of the paper.
Please find the reviewers’ comments and our answers in the attached file

AC2: 'Reply on RC2', Tchilibou Michel Lionel, 15 Apr 2022
Michel Tchilibou et al.
Michel Tchilibou et al.
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