Review of “Regional modeling of internal tide dynamics around New Caledonia: energetics and sea surface height signature”

This paper presents a broad, rather than in depth, analysis of numerical simulations of the semidiurnal internal tide around New Caledonia. The paper presents 1) a validation of the model results for mesoscales and surface and internal tides 2) internal tide energetics and comparison with analytical models, 3) nonstationary internal tides and the causes of the nonstationarity, and 4) transition scales computed from wavenumber spectra. It is worthy to publish on the strong internal tides around New Caledonia, but I think the paper needs to be improved in several aspects before it can be published. The most interesting and relevant result is presented in Figure 12c.

First, the paper is long and detailed, and it has many story lines (see above): the paper has 8 pages of references (~120 citations), 835 lines of text (~15,500 words), and 15 figures. To make the paper more digestible, I suggest shortening it to 500-600 lines (30-40% reduction) by omitting text from the introduction, focusing on only information that is relevant to the story line, and focusing on fewer story lines (and go more in depth; maybe (4) can be omitted if the paper focuses on the nonstationarity?).

2) It is difficult to learn what the objectives are from the introduction. The introduction needs to clearly state, preferably in the same paragraph, the main objectives of this paper.

3) The diagnostics section 2.2 is not well organized. Why are modes discussed in section 2.2.1 on coherent internal tides? I suggest the authors present the energy balances for undecomposed internal tides and modal energy balances and then discuss how these terms are computed with either bandpassing or harmonic analysis (see Buijsman et al (2020) and the Kelly papers referenced therein).

I am confused about the explanation on how the authors compute the total, coherent, and incoh. internal tides near line 247. As in Nash, Pickering, and Buijsman papers the total internal tide signal is the tidally band-passed signal (e.g. 10-14 hours), the coh. signal is computed with a harmonic analysis of the band-passed fields, and the incoh. signal is taken as the difference. Your method differs from this. Can you explain why? It seems you add the coh. and incoh. signals to get the total D2 signal, which should be better emphasized.

4) For section 2.3.6 you need to explain first that you compare the simulated IT conversion rates to these analytical models. The purpose of this section was not clear to me. This section can be shortened too. It is mostly about why these models break down, which is well-known.

5)  For section 4, you use the harmonically analyzed fields over 1 year. That means that your dissipation estimates contain the scattering to the incoherent internal tide (possibly a significant fraction). This may be a reason that your q values are too high (L744)? I suggest you redo this analysis and compute the dissipation rates for the band-passed fields.

6) Can you explain to the reader how precisely the ‘transition scale’ is computed?  This transition scale should always occur for scales larger than the mode 1 internal tide? On line 797 you write “Correcting our model for the coherent internal tide, we were able to improve SWOT observability (here measured by the transition scale between subinertial and superinertial motions) in winter from 160 km to 50-80 km” How is that possible? You still have the incoherent internal tide in your model?

7) I suggest the authors redo their comparison with the analytical models (section 4.3) and compute conversion rates below 700 m for all models as in Buijsman et al (2020). This may yield a better comparison.

8) In-depth analysis. Figure 12c shows a nice result. I wonder why the authors do not show the correlation between the incoherence in the open ocean away from the ridge with monthly EKE (see also Zaron et al 2014 and Savage, Waterhouse, Kelly 2020 for metrics that may explain the sources of variability (EKE, N, and vorticity)). That correlation does not exist?



Why is conversion not shown instead of the flux divergence? If C does not have that correlated variability, then the variability is in the Dissipation? This is interesting and worthy of further investigations.

It may also be interesting to evaluate the mode-mode coupling term (see Kelly 2019 and Zaron 2022 papers) because the internal tide in this area must be affected by topographic scattering.

The paper has some grammatical errors, inconsistencies, or key points that I circled in the pdf. Note that all mathematical variables should be cursive.

Some minor comments.

L31. For the modes cite Gill here.

L43. Who is ‘they’?

L56. Cite Nelson et al (2019) here.

L57. I do not understand how incoherent internal tides contribute to dissipation.

L75. Formation = generation

L153. Incorrect citation year for Nelson. I think it should be 2020? You may also cite Siyanbola et al (2023; https://doi.org/10.1016/j.ocemod.2022.102154) here.

L547. Low modes are also affected by wave-wave interactions (subharmonic: Ansong et al 2018 and superharmonic: Sutherland (2022)).

L675-676. Please see Xu et al (2022; https://doi.org/10.1029/2022JC018769) in which this difference is illustrated.

L729. It is generally well understood that tall supercritical ridges generated strong mode 1s.

Fig 1b and c. Fontsizes are hard to read. Please make a smaller and b and c larger.

Fig 4. What is the peak at SD in the blue line? Residual tides?

Plot axis in cycles per day to facilitate easier reading of the tides and their higher harmonics.

Fig 5. How many modes are used for (e) and (f)?

Fig 7. Dbt is mentioned twice in legend of (a)

Fig.8 Please better explain the percentage values. What variables are in these ratios?

Fig.9 Blue patches in (b) are because the residual is based on coherent tide only? Nonlinear terms are missing?

Fig 10. I do not see a red box in (c)

Can you indicate the transect line for (d) in (c)?

Fig 15. Text in legend is too small.

This paper investigates the internal tide dynamics around New Caledonia using a dedicated one-year long high-resolution numerical simulation. The results presented are interesting in several aspects: first, it provides an unprecedented, model-based quantification of the internal tide energetics and some aspects of its dynamics (including interaction with the mesoscale fields, albeit to a limited extent) of a region of the ocean. Second, this region is of particular interest for the recently-launched SWOT mission and the imminent in-situ campaign associated with the CalVal phase, but also for several biological aspects. On the downsides, the paper is rather long -- because it aims at treating several, somewhat distincts aspects of the internal tide dynamics. In particular, sections 5 and 6, which address the coherent/incoherent part and the SSH signature of ITs, could justify a separate paper with more thorough investigation. That being said, the results are rather well presented on average (with some noticeable exceptions listed below) and the figures are well designed, clearly displaying the informations. Moreover, I appreciated the effort put into validating the simulation using several external datasets.

Below are my comments: first the remarks and question which must be addressed prior publication, unless the authors justify otherwise; then some minor comments and typos, which I leave up to the other decision whether to take it into account or not.

Remarks / Questions

 - Organisation of section 2.2 is somewhat misleading. You are talking about the vertical mode decomposition in the "coherent tide" subsection. Besides, I think the energy equation should be applied to the full (coherent+incoherent) tidal signal, otherwise there is an additional term representing the loss-of-coherency. If the results in Figs. 7, 8 and 10 are computed using the coherent tide computed from a year-long harmonic analysis, then the high values of the inferred dissipation misleadingly includes loss-of-coherency. I would suggest either doing the diagnostics presented in these figures using the signal over the whole semi-diurnal band (which I presume you can do, given the results presented on the incoherent tide) or modifying the text to explicit this subtlety. 

 - sect. 2.3.6 and around l.505: I was not able to understand whether you used the data available from the literature or did your own computation using the method of Falahat et al 2014 and Vic et al 2019. Could you please specify? In particular, is the same bathymetry dataset used?

 - end of sect. 4.4: regarding the energy dissipation, what about the potential impact of the bottom drag, and other forms of parameterized dissipation? Do you reckon this could constitute a non-negligible contribution? If so, please mention it.

 - l.585 -- 590: it has also been shown that the presence of background currents could impact the generation of ITs (e.g. DLamb & Dunphy (JFM 2018), Shakespeare & Hogg (JPO 2019).

 - l.590-595. I found the procedure a bit puzzling. Using one month averages, you discard variability that occurs over shorter time scale, thereby not taking into account a potentially substantial impact of mesoscale currents. 

Minor comments / typos

 - l.34 "They tend to dissipate locally not far away from the formation sites": this phrase seems a bit clumsy

 - l.55: Although in a one layer RSW context, Ward & Dewar (JFM 2010) showed that this result from standard resonant triads theory between between one low-frequency (horizontal) mode and 2 tidal-frequency modes

 - l.256 "terms which consider to contribute to the incoherent flu.": phrasing seems clumsy

 - l.297 "It is a very significant [...]" and l.308 "Eventually, HRET [...]": I think these comments are not very relevant for the present paper. Given that the article is already quite long, I would suggest removing any comment with this level of significance in the context of the paper.

 - l.353: remove "of waters"

 - l.367: "through" -> "of"

 - l.373: "also computeD"

 - l.379: "this CAN BE attributed"

 - Figure 4: I was surprised by the peak just above the SD frequency in the no-tide run. Also, blue and orange lines are inverted in the caption.

 - l.390: "<f" -> ">f"

 - l. 403: why not using only the mode 1 only, or mode 1 + mode 2, for a better comparison with HRET?

 - l.407: see also Ansong et al (JGR:Oceans 2015), Fig. 8

 - Fig. 6a & l.420: I would suggest adding an inset zooming over the first few hundreds of meters for the stratification profiles.

 - Fig. 7: there are some weird patterns close to the edge of the left panel, which are hopefully plotting or diagnostic computation artefacts.

 - l. 493: "[...] previous conclusions.": meaning in the literature?

 - l. 506: "The modal energy [...]"

 - Fig. 9: is it possible to add the total barotropic-to-baroclinic conversion, thus allowing to estimate the overall discrepancies?

 - end of sect. 4.3: interesting conclusion. 

 - Fig. 12: I don't see the point of displaying the geostrophic velocity + SLA, which overloads the figure (left panel) in my opinion.

 - l. 527: "The M2 barotropic-to-baroclinic energy conversion and BAROCLINIC ENERGY dissipation [...]"

 - l.549: whiy "However"? I don't see the contradiction between the two consecutives sentences.

 - l.571: "energy of the first mode": aren't we looking at the total baroclinic energy flux?

 - l.575: "increasing distance to the generation" -> "increasing distance FROM the generation"

 - l.613: no uppercase after ":"

 - Fig. 15: for the sake of clarity, I would suggest displaying these panels in a 2x2 grid, with the legend in the fourth -- unused -- panel. Font size in the legend is too small, and curves are too steep to clearly distinguish them.

 - l.657: "Superinertial processes dominate OVER subinertial motions"

 - l.665 - 670: this result is interesting, and a bit surprising, as one would think that the IT would be more incoherent in winter because of a more energetic submesoscale eddy field.

 - l.688: Dominance of unbalanced motionS"

 - section 7: I think you could use proper sub-sectioning for this section.

 - l.764: "adovate" -> "advocate"

References

  - Ansong, J.K., Arbic, B.K., Buijsman, M.C., Richman, J.G., Shriver, J.F., Wallcraft, A.J., 2015. Indirect evidence for substantial damping of low‐mode internal tides in the open ocean. JGR Oceans 120, 6057–6071.

 - Lamb, K.G., Dunphy, M., 2018. Internal wave generation by tidal flow over a two-dimensional ridge: energy flux asymmetries induced by a steady surface trapped current. Journal of Fluid Mechanics 836, 192–221. https://doi.org/10.1017/jfm.2017.800

 - Shakespeare, C.J., Hogg, A.McC., 2019. On the Momentum Flux of Internal Tides. J. Phys. Oceanogr. 49, 993–1013. https://doi.org/10.1175/JPO-D-18-0165.1

 - Ward, M.L., Dewar, W.K., 2010. Scattering of gravity waves by potential vorticity in a shallow-water fluid. Journal of Fluid Mechanics 663, 478–506. https://doi.org/10.1017/S0022112010003721