the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Mode-1 N2 internal tides observed by satellite altimetry
Abstract. Satellite altimetry provides a unique technique for observing the sea surface height (SSH) signature of internal tides from space. Previous studies have constructed empirical internal tide models for major tidal constituents M2, S2, K1, and O1. Minor tidal constituents are difficult to observe, due to their weak SSH signals. The advances in mapping technique, combined with the accumulation of satellite altimetry data, make it possible to construct empirical models for minor internal tidal constituents. In this paper, the global mode-1 N2 internal tides (the fifth largest oceanic tidal constituent) are observed using 100 satellite-years of SSH data from 1993 through 2019. This paper employs a newly-developed mapping procedure that includes two rounds of plane wave analysis and a two-dimensional bandpass filter in between. Thanks to the large SSH data set and the new mapping procedure, we can observe mode-1 N2 internal tides with O (1 mm) SSH amplitudes. The results are confirmed using independent satellite altimetry data in 2020 and 2021. The satellite observations show that N2 and M2 internal tides have similar spatial patterns, and that the N2 amplitudes are about 20 % of the M2 amplitudes. Both features mimic their barotropic counterparts. The satellite observations also show that N2 and M2 internal tides can propagate hundreds to thousands of kilometers in the open ocean, but at different phase speeds as predicted by theory.
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Notice on discussion status
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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Preprint
(5956 KB)
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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.
- Preprint
(5956 KB) - BibTeX
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- Final revised paper
Journal article(s) based on this preprint
Zhongxiang Zhao
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-1029', Clément Vic, 14 Nov 2022
The manuscript reports on a method that allows to map the global mode-1 N2 internal tides from sea surface height (SSH) measured by satellite altimetry. Results are presented and discussed in light of a similar product for the well-described mode-1 M2 internal tides. The model’s predictive skill is tested vis-aÌ-vis of an independent global time series of SSH, and it proves to be good. The manuscript is clearly written and well presented, and the science looks robust to me. The scientific interest of mapping internal tides is emphasized in the context of the new SWOT satellite mission. I recommend this manuscript for publication after some minor revisions that I hope can help to clarify some points.
Minor comments:
- Line 6 and elsewhere: “1993 through 2019” replace “through” with “to”?
- Line 10: “Both features mimic their barotropic counterparts” is unclear to me. This could be rephrased and developed a bit, including considerations on the energy conversion etc.
- Line 20: the acronym should be expanded first and put into parentheses afterward, i.e., “Surface Water and Ocean Topography (SWOT)”
- Line 20: The SWOT mission has not been designed to strictly study the submesoscales only I think, but to have a wider picture of entangled motions and waves that have a signature in SSH.
- Line 27: remove “(Section 2)” and stick it to where the plan is announced?
- Line 31: I think it would be useful for the reader to be introduced to the semidiurnal tide components in general, before getting into the details of N2 and L2.
- Line 37: insert “see their Figure 4” within the previous parentheses?
- Line 39: “can better parameterize” is not very clear. I think you mean more than just parameterize, i.e., increase our understanding?
- Line 70: why is the fitting window size not varying geographically? I thought it would take into account mode-1 wavelength.
- Line 75: add “horizontal” before “wavenumber”
- Line 98 (and perhaps before): It would be good to stress out that only the coherent internal tides are mapped.
- Line 112: rephrase “they have same generations over rough topography” to be more specific (amplitude, phase, etc.)
- Line 114: add “energy” before “conversion”
- Line 115: “in the causative chain” is unclear. If I understood correctly, you mean that the similar M2 and N2 barotropic tides generate similar baroclinic tides and that the ratio between barotropic tides is also observed in baroclinic tides.
- Line 120: I assume 0 degree is East? It should be mentioned.
- Line 137: typo? “prone to” be?
- Line 146: remove “percentage”
- Line 157: I do not understand the sentence “Thus, ...”
- Figure 4 and line 173: I think it would be good to give globally integrated numbers for all terms, and perhaps the integrated contribution of all negative and positive terms to make sure that the variance is indeed reduced.
- Line 198: add “mode-1”
- Line 201: I do not understand how one can do “parameterizing the temporal variation” with the elements provided. It could be developed.
- Line 208: typo (sub and not sum). And perhaps rephrase into something that reminds the reader on the fast (waves) and slow (balanced motions) manifolds?
- AC1: 'Reply on RC1', Zhongxiang Zhao, 14 Apr 2023
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RC2: 'Comment on egusphere-2022-1029', Anonymous Referee #2, 12 Dec 2022
Review of "Mode-1 N2 internal tides observed by satellite altimetry."
by ZhaoThis paper discusses the author's efforts to map the baroclinic N2 tide from satellite altimeter data collected from 1993 to 2019. The newly-derived maps are used to predict tides for missions in the 2020-2021 time period, and evaluate the quality of the maps. The mapping methodology has been presented in the author's previous papers.
Mapping of baroclinic N2 was previously attempted by Dushaw (2015), and the work in this paper shows that addiitonal data collected since that time, in combination with the author's analysis technique, makes it possible to map the N2 tide with more precision. While the results in this paper may be a step forward, I don't believe that it provides enough new material or insight to justify publication at this time. Although, with some added analysis, the paper could stand on its own and make a worthwhile contribution to the literature.
Major Comments:
(1) The paper's qualitative observations about N2 in relation to M2 are completely plausible and expected, as the author points out. I don't understand the significance of the analysis of wave dispersion (section 3.3), though, since it seems to just verify the properties of the wave fields which are already assumed by the analysis technique. I would be surprised if there is anything of significance to say about the dynamics of N2 in contrast to M2, but maybe the author can convince me otherwise.
(2) At line 48, the author states, "the resulting N2 internal tides still have considerable errors ... and work as a useful internal tide model," but I believe this is unproven. The qualitative discussion of the errors, from lines 170 to 183, may be correct, but there are certainly plenty of locations in Fig 4a where N2 is large-amplitude, but it exhibits negative explained variance (e.g., in the Western Pacific and Philippines Sea). If the discussion of noise or error level of the tide model could be made precise, then it might provide an objective means of deciding where the model can or cannot be a "useful internal tide model." Otherwise, it is just guesswork whether this could be used to provide a useful correction for the SWOT mission.
Minor Comments:
l3: "technique" -> "techniques"
l57-58: Some of these missions have not been used previously for the estimation of N2 tides. What are the alias periods of N2 for the following missions: Cryosat-2, Haiyang-2A/2B, and Sentinel-3A/B? The Copernicus web site mentions that the products used are "tailored for data assimilation". It would be useful to explain what this involves.
l80-81: "orthogonal equation" ? Please use correct terminology
l86: I am curious why this bandwidth was selected and what are the implications?
l137: typo: "beams are prone to affected" Also -- the beams are not affected by the measurement noise; the estimates for these features are affected by the noise.
Section 3.3: I don't really understand the significance of this section. The frequencies of the tides are given, and the wavenumbers are assumed given by the dispersion relation. Thus, the observations of wave dispersion reported here are a consequence of the assumptions of the analysis method, aren't they?
Section 3.4: Figure 4a shows that the proposed model of N2 does explain SLA variance in some regions and not others, as the text states. I think it would be important to provide an error estimate for the N2 tide. How would someone know where the correction should be applied and where it should not be applied? The qualitative discussion in the text mentions the amplitude of N2 in relation to the model error, \sigma_\epsilon, but this quantity is not estimated, even though it appears in mathematical inequalities.
l205: "sum-mesoscale" ?
Figures: I would like to see the figures much larger; I cannot make out much detail in the global maps in the sizes they are presented.
Citation: https://doi.org/10.5194/egusphere-2022-1029-RC2 - AC2: 'Reply on RC2', Zhongxiang Zhao, 14 Apr 2023
- AC3: 'Reply on RC3', Zhongxiang Zhao, 14 Apr 2023
-
RC3: 'Comment on egusphere-2022-1029', Anonymous Referee #3, 19 Dec 2022
This manuscript presents a global map of the sea-surface height (SSH) signals of the N2 internal tides observed by satellite altimetry. The topic is important for mapping the tidal energy available for diapycnal mixing and also for reducing the tidal signals in SSH data in the studies of mesoscale and sub-mesoscale phenomena. Although I do not understand the technical details, the presented maps of the N2 internal tides seem all reasonable.
Minor Comments:
- The explanation about the method for extracting the N2 internal tides (section 2.2) is hard to understand. I would suggest the authors rewrite this part more to the point, or omit it. Right now, the readers who are not very familiar with this method cannot judge whether this method is really suitable for mapping the N2 internal tides.
- A few specific examples of the above comment are:
1. Why are “five” plane-waves needed to fit the N2 internal tides?
2. Is the plane wave fitting applicable when the wavenumber of the internal tide changes rapidly over variable bottom topography?
3. Bandpass filtering in the wavenumber space: The barotropic tides may have horizontal scales comparable to those of the mode-1 internal tides. Does this matter? Also, what happens when the mode-2 and higher mode internal tides have large amplitudes near the generation sites?
4. What happens if the larger-amplitude M2 and S2 internal tides are Doppler-shifted to the N2 tidal frequency by time-varying background fields?
5. Do the results depend on the choice of several arbitrary parameters (such as the size of the fitting window)?
- Although the results presented in the manuscript seem reasonable overall, it is unclear what are the new findings in terms of the internal tide dynamics. Now the manuscript reads more like a progress report.
Citation: https://doi.org/10.5194/egusphere-2022-1029-RC3 - AC3: 'Reply on RC3', Zhongxiang Zhao, 14 Apr 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-1029', Clément Vic, 14 Nov 2022
The manuscript reports on a method that allows to map the global mode-1 N2 internal tides from sea surface height (SSH) measured by satellite altimetry. Results are presented and discussed in light of a similar product for the well-described mode-1 M2 internal tides. The model’s predictive skill is tested vis-aÌ-vis of an independent global time series of SSH, and it proves to be good. The manuscript is clearly written and well presented, and the science looks robust to me. The scientific interest of mapping internal tides is emphasized in the context of the new SWOT satellite mission. I recommend this manuscript for publication after some minor revisions that I hope can help to clarify some points.
Minor comments:
- Line 6 and elsewhere: “1993 through 2019” replace “through” with “to”?
- Line 10: “Both features mimic their barotropic counterparts” is unclear to me. This could be rephrased and developed a bit, including considerations on the energy conversion etc.
- Line 20: the acronym should be expanded first and put into parentheses afterward, i.e., “Surface Water and Ocean Topography (SWOT)”
- Line 20: The SWOT mission has not been designed to strictly study the submesoscales only I think, but to have a wider picture of entangled motions and waves that have a signature in SSH.
- Line 27: remove “(Section 2)” and stick it to where the plan is announced?
- Line 31: I think it would be useful for the reader to be introduced to the semidiurnal tide components in general, before getting into the details of N2 and L2.
- Line 37: insert “see their Figure 4” within the previous parentheses?
- Line 39: “can better parameterize” is not very clear. I think you mean more than just parameterize, i.e., increase our understanding?
- Line 70: why is the fitting window size not varying geographically? I thought it would take into account mode-1 wavelength.
- Line 75: add “horizontal” before “wavenumber”
- Line 98 (and perhaps before): It would be good to stress out that only the coherent internal tides are mapped.
- Line 112: rephrase “they have same generations over rough topography” to be more specific (amplitude, phase, etc.)
- Line 114: add “energy” before “conversion”
- Line 115: “in the causative chain” is unclear. If I understood correctly, you mean that the similar M2 and N2 barotropic tides generate similar baroclinic tides and that the ratio between barotropic tides is also observed in baroclinic tides.
- Line 120: I assume 0 degree is East? It should be mentioned.
- Line 137: typo? “prone to” be?
- Line 146: remove “percentage”
- Line 157: I do not understand the sentence “Thus, ...”
- Figure 4 and line 173: I think it would be good to give globally integrated numbers for all terms, and perhaps the integrated contribution of all negative and positive terms to make sure that the variance is indeed reduced.
- Line 198: add “mode-1”
- Line 201: I do not understand how one can do “parameterizing the temporal variation” with the elements provided. It could be developed.
- Line 208: typo (sub and not sum). And perhaps rephrase into something that reminds the reader on the fast (waves) and slow (balanced motions) manifolds?
- AC1: 'Reply on RC1', Zhongxiang Zhao, 14 Apr 2023
-
RC2: 'Comment on egusphere-2022-1029', Anonymous Referee #2, 12 Dec 2022
Review of "Mode-1 N2 internal tides observed by satellite altimetry."
by ZhaoThis paper discusses the author's efforts to map the baroclinic N2 tide from satellite altimeter data collected from 1993 to 2019. The newly-derived maps are used to predict tides for missions in the 2020-2021 time period, and evaluate the quality of the maps. The mapping methodology has been presented in the author's previous papers.
Mapping of baroclinic N2 was previously attempted by Dushaw (2015), and the work in this paper shows that addiitonal data collected since that time, in combination with the author's analysis technique, makes it possible to map the N2 tide with more precision. While the results in this paper may be a step forward, I don't believe that it provides enough new material or insight to justify publication at this time. Although, with some added analysis, the paper could stand on its own and make a worthwhile contribution to the literature.
Major Comments:
(1) The paper's qualitative observations about N2 in relation to M2 are completely plausible and expected, as the author points out. I don't understand the significance of the analysis of wave dispersion (section 3.3), though, since it seems to just verify the properties of the wave fields which are already assumed by the analysis technique. I would be surprised if there is anything of significance to say about the dynamics of N2 in contrast to M2, but maybe the author can convince me otherwise.
(2) At line 48, the author states, "the resulting N2 internal tides still have considerable errors ... and work as a useful internal tide model," but I believe this is unproven. The qualitative discussion of the errors, from lines 170 to 183, may be correct, but there are certainly plenty of locations in Fig 4a where N2 is large-amplitude, but it exhibits negative explained variance (e.g., in the Western Pacific and Philippines Sea). If the discussion of noise or error level of the tide model could be made precise, then it might provide an objective means of deciding where the model can or cannot be a "useful internal tide model." Otherwise, it is just guesswork whether this could be used to provide a useful correction for the SWOT mission.
Minor Comments:
l3: "technique" -> "techniques"
l57-58: Some of these missions have not been used previously for the estimation of N2 tides. What are the alias periods of N2 for the following missions: Cryosat-2, Haiyang-2A/2B, and Sentinel-3A/B? The Copernicus web site mentions that the products used are "tailored for data assimilation". It would be useful to explain what this involves.
l80-81: "orthogonal equation" ? Please use correct terminology
l86: I am curious why this bandwidth was selected and what are the implications?
l137: typo: "beams are prone to affected" Also -- the beams are not affected by the measurement noise; the estimates for these features are affected by the noise.
Section 3.3: I don't really understand the significance of this section. The frequencies of the tides are given, and the wavenumbers are assumed given by the dispersion relation. Thus, the observations of wave dispersion reported here are a consequence of the assumptions of the analysis method, aren't they?
Section 3.4: Figure 4a shows that the proposed model of N2 does explain SLA variance in some regions and not others, as the text states. I think it would be important to provide an error estimate for the N2 tide. How would someone know where the correction should be applied and where it should not be applied? The qualitative discussion in the text mentions the amplitude of N2 in relation to the model error, \sigma_\epsilon, but this quantity is not estimated, even though it appears in mathematical inequalities.
l205: "sum-mesoscale" ?
Figures: I would like to see the figures much larger; I cannot make out much detail in the global maps in the sizes they are presented.
Citation: https://doi.org/10.5194/egusphere-2022-1029-RC2 - AC2: 'Reply on RC2', Zhongxiang Zhao, 14 Apr 2023
- AC3: 'Reply on RC3', Zhongxiang Zhao, 14 Apr 2023
-
RC3: 'Comment on egusphere-2022-1029', Anonymous Referee #3, 19 Dec 2022
This manuscript presents a global map of the sea-surface height (SSH) signals of the N2 internal tides observed by satellite altimetry. The topic is important for mapping the tidal energy available for diapycnal mixing and also for reducing the tidal signals in SSH data in the studies of mesoscale and sub-mesoscale phenomena. Although I do not understand the technical details, the presented maps of the N2 internal tides seem all reasonable.
Minor Comments:
- The explanation about the method for extracting the N2 internal tides (section 2.2) is hard to understand. I would suggest the authors rewrite this part more to the point, or omit it. Right now, the readers who are not very familiar with this method cannot judge whether this method is really suitable for mapping the N2 internal tides.
- A few specific examples of the above comment are:
1. Why are “five” plane-waves needed to fit the N2 internal tides?
2. Is the plane wave fitting applicable when the wavenumber of the internal tide changes rapidly over variable bottom topography?
3. Bandpass filtering in the wavenumber space: The barotropic tides may have horizontal scales comparable to those of the mode-1 internal tides. Does this matter? Also, what happens when the mode-2 and higher mode internal tides have large amplitudes near the generation sites?
4. What happens if the larger-amplitude M2 and S2 internal tides are Doppler-shifted to the N2 tidal frequency by time-varying background fields?
5. Do the results depend on the choice of several arbitrary parameters (such as the size of the fitting window)?
- Although the results presented in the manuscript seem reasonable overall, it is unclear what are the new findings in terms of the internal tide dynamics. Now the manuscript reads more like a progress report.
Citation: https://doi.org/10.5194/egusphere-2022-1029-RC3 - AC3: 'Reply on RC3', Zhongxiang Zhao, 14 Apr 2023
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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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