Review of "Mode-1 N2 internal tides observed by satellite altimetry."

by Zhao

This 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.

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.