the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 22 May 2024
Coupled estimation of incoherent inertia gravity wave field and turbulent balanced motions via modal decomposition
Abstract. The non-linear interactions between an internal wave field propagating through a balanced turbulent flow make the incoherent propagation of ocean internal tides difficult to understand and to predict. In this paper, we propose a data-driven method that extracts the structures of a wave field correlated with the fluctuations of the background flow, exploiting the fact that the scattering of the wave results from a quadratic nonlinearity involving both types of motions. The method consists of applying the extended proper orthogonal decomposition method to the complex wave envelope, extracted by complex demodulation, in order to provide the spatial structures of an incoherent wave contribution correlated to the proper orthogonal decomposition modes of the balanced motion. Using the rotating shallow water as a canonical model for wave / balanced flow interactions, we describe the connection between the variability of the jet and the incoherence of the internal wave, which provides some theoretical foundations to the proposed method. This expected connection is then confirmed by numerical simulations of the rotating shallow water model, and the variability modes of the jet and wave field are analysed. Finally, an algorithm for estimating the jet component and the associated wave field from single snapshots of the sea level height is proposed and tested using outputs from numerical simulations. We show that such algorithm provides a valuable coupled estimate of the two dynamics, especially in configurations where the wave signal is small compared to the jet.
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RC1: 'Comment on egusphere-2024-1483', Aurelien Ponte, 10 Jul 2024
10/07/2024
EGUSsphere-2024-1483 - review 0
Review summary
This manuscript reports on the development and application of data-driven methods for the description of interactions between a turbulent jet and an internal tide and the disentanglement of associated signals in (wide-swath) altimetric like data. Experiments are carried in an idealized configuration. This work is timely in light of the recent launch of the SWOT wide-swath altimeter and associated problematics of the disentanglement of internal tide and lower frequency (balanced) circulation signatures.
The novelty of the paper stems first from the use of original methods to describe the interaction between the jet and the internal and tide and second from the exploitation of systematic correlations between internal propagation pathways and the jet state in order to disentangle associated signatures.
The analysis is thorough with multiple sensitivity experiments to internal tide and jet characteristics and to methods parameters (via the number of modes employed typically) and to the observational setup (via spatial coverage).
I have two major concerns regarding the insufficient level of the manuscript form (language, length) and the insufficient discussion and roadmap for application in more realistic configurations. Once these concerns will be addressed, my opinion is that this manuscript deserves publication.
Major points
1. The form of the manuscript is insufficient at the moment and I fear it will adversely affect the impact this work may have. The manuscript is first of all lengthy and authors should strive to reduce its length. Here are some leads as to how to do that:
- there are numerous repeats in transitions about what is about to be performed which are superfluous. L327-329 for instance is one example. Another example is L331-L334 where we have to wait three sentences before entering into the « meat » of the results, this is too long.
- Some optimization in the number of choice of figures could also help: Figure 5a and 5b are fairly redundant and their overall relevance may be questioned for the sake of conciseness; Figure 9 is barely discussed which should be taken as a sign it does not bring much and may be discarded.
Second, the level of language is low and substantially complicates the prompt understanding of the paper. I suggest resorting to AI (deepL, chatGPT), a professional editing service, or any other solution that may improve the flow of the manuscript.
2. A second major concern is about the insufficient discussion regarding the applicability of the proposed method to more realistic configurations and the steps required to go there. The last paragraph of the conclusion is too light for that purpose. Potential questions I’d have liked to see addressed:
- Is the level of mesoscale activity the sole parameter relevant to identify potential geographical areas of applications?
- Can we anticipate increased/decreased performances in realistic configuration given identified limitations?
- What observations and datasources could be used to evaluate the applicability of the method in realistic/operational configurations ?
- Do we have a grasp as to whether the methods will have to be adapted ? « localisation technique » is mentioned albeit with little detail and no references.
- Or is more work required on the idealized side? And if yes to answer what questions?
A more detailed comparison with similar approaches (Egbert and Erofeeva 2021 for instance) is also missing.
Minor points
Note that I am skipping here language issues on the basis that they are too numerous to be accounted for.
- I suggest adjusting the title according: « Coupled estimation of incoherent internal tide and balanced turbulent motions via statistical modal decomposition ». Modal decomposition is ambiguous with vertical modes used for internal tide descriptions, the method is targeting internal tide and not internal gravity waves in general
- Terminology: the use of « internal tide » instead of « internal wave » seems more appropriate and I would recommend sticking to this choice throughout the manuscript.
- Abstract: mention of the fact that this work is carried in an idealized configuration should come very early; sentences are too long; the first sentence is not necessary.
- L28: « realistic » -> idealized
- L29: « «contribute significantly to » -> enhances
- L73: « the model used to investigate the dynamics » -> the dynamical model used to investigate interactions between …
- L111: « the potentially broaden spectrum » -> typo?
- L112: « the fluctuations » -> anomalies
- L117: « can be performed » -> could have been performed
- L145: can we expect that an inverse of the operator is allways available ? If yes, this should be mentioned
- L145-150: physical implications for this are missing. If the domain was large enough, the impact of jet fluctuations should be delayed at a distance. Can this approach represent such situation? Such element are important to gauge the applicability of the method in other configuration (e.g. more realistic ones)
- L155: I find the presence of the nonlinear correction intriguing, maybe puzzling. Can we expect this correction to be substantial, e.g. shouldn’t the correlation drop?
- L173: « showing that … as expected » : this statement does not follow scientific writing standards.
- L184: the SPOD acronym should be introduced as it is not described in the appendix
- L190: « The algorithm … » serious language issues here
- Eq 17 and elsewhere: it may be useful to retain spatial coordinates dependance at least sometimes. One may loose track about what depends on space and not at times.
- L272 : « alternative method to using the geostrophic balance for BM …» this statement probes the question as to how far are velocity estimates from geostrophy and polarization relationships. You are not answering this in the manuscript which you may want to specify in order for the reader not remain in expectation.
- L282: « To our knowledge, … » … I would strongly disagree, you need to be more specific
- L331-332: need to report on values of alpha, hyperviscosity and all other parameters employed in the numerical simulations
- L310: « a sufficient sampling » I do no understand what you mean - reformulate
- L314: « less than 3 days » you need to specify at what latitude
- L314: « magnitude spectrum » don’t you mean « power spectrum » instead?
- L314: the method employed for spectral estimation needs to be specified
- L320: « scale separation in amplitude » this is an awkward formulation
- L324-325: This paragraph seems out of place
- L327-335: see major comment 1
- L335: « nudging » it would be more straightforward to talk about « wave forcing »
- L339: « almost zero mean » this statement does not follow scientific writing standards.
- L346: « definition » -> « construction »
- L346: « essentially non-zero » awkward formulation
- L349: « slight deviations to a single-mode structure » This needs to be more clearly reformulated.
- L351-L357: see major comment 1
- L372-L373: could you use (19) to compute EPOD modes ? If yes, has the correspondence been verified?
- L381: « time evolution » of … ?
- L389: « stationary wave » Is « stationary » the most adequate term here, I fail to understand its precise meaning here.
- L390: « one third » -> 30%
- L394-395: the second part of the sentence needs clarification
- L405: « an accurate estimate » -> « a visually accurate estimate »
- L406: « a well identified structure » -> vague statement
- L407-410: the description of the « naive » method needs to be improved. It may be also relevant to push this alternative approach towards the end of the section.
- Figure 9 is not particularly useful and may be skipped, color map is not adequate in any caseL
- L412: here or elsewhere you may want to specify that you could also have estimated wave energy fluxes
- L412: « more than 50% of the energy recovered at approximately each point … » this is not an adequate report of performance, you may want to report on an averaged or percentile value instead.
- L416-417: specify that this is as a function of the number of modes
- L422 « The figure … » is this expected?
- L423: « For the wave … » I fail to see how you compute incoherent energy … make sure you explain this somewhere
- Figure 10: x label and legend are missing on my computer
- Table A1: I would bring this table in the core of the manuscript and discuss it properly. The sensitivity to wave and jet properties is interesting. The table needs a bit of work (first lign is useless, make it clearer this is for wave part and/or add jet corresponding metrics)
- L443: « Yet, this frequency … » please double check and specify latitude
- L463: « «of regularisation » you may want to specify « that penalizes higher mode amplitudes »
- L479 « standing wave » is it the same as the earlier « stationary » wave ? If yes you may want to align terminology and make sure it makes sense
- L495-L501: see major comment 2
- L501: « localisation » reference missing
- L504: « SPOD » acronym not specified I believe
- L540: this seems like a different subject from here on, so I would create another appendix section
Citation: https://doi.org/10.5194/egusphere-2024-1483-RC1 - RC2: 'Comment on egusphere-2024-1483', Anonymous Referee #2, 24 Oct 2024
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RC3: 'Comment on egusphere-2024-1483', Anonymous Referee #3, 04 Nov 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1483/egusphere-2024-1483-RC3-supplement.pdf
Data sets
demod.h5 Igor Maingonnat https://gitlab.inria.fr/imaingon/internal-tide-simulation.git
Model code and software
Codes to compute the methods in this article. Igor Maingonnat https://gitlab.inria.fr/imaingon/internal-tide-simulation.git
Interactive computing environment
Notebooks for diagnostics, visualisation and estimates. Igor Maingonnat https://gitlab.inria.fr/imaingon/internal-tide-simulation.git
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