the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Aug 2022
Characteristics of Robust Mesoscale Eddies in the Gulf of Mexico
Abstract. Although numerous studies on mesoscale eddies in the Gulf of Mexico (GoM) have been conducted, a comprehensive study on their temporal and spatial characteristics is still lacking. In this study, we combine three eddy detection algorithms to detect eddies from the 26-year sea surface height record in the GoM and examine their characteristics. We find distinct characteristics between Loop Current Eddies (LCEs), Loop Current Frontal Eddies (LCFEs), and mesoscale eddies that are not directly related to the Loop Current (LC). Seasonal variability appears in both the LCFEs and non-LCFE cyclonic eddies and shows large uncertainties. More specifically, more LCFEs are formed in January to July than in August to December, likely related to the seasonal variation of the northward penetration of the LC. And the formation of non-LCFE cyclonic eddies shows a biannual variability, which could be linked to the position and strength of the background current in the western GoM. Low-frequency (interannual to multidecadal) variability is also detected. In the eastern GoM, the extent of northward penetration of the LC can affect the generation of LCFEs and result in low-frequency variations. In the western GoM, the low-frequency variability of eddy occurrence and amplitude could be related to the surface circulation strength. This study can serve as an up-to-date reference for eddy-related investigations in the GoM.
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RC1: 'Comment on egusphere-2022-789', Anonymous Referee #1, 17 Sep 2022
Eddy activities in the Gulf of Mexico are analyzed by applying a set of three eddy detection algorithms to satellite altimetry product. Characteristics of the eddies are described, and seasonal variations are analyzed. The eddies are discussed in terms of different types: Loop Current Eddies, Loop Current Front Eddies, and non-Loop Current Front Eddies, etc. Huge effort has been made in this study, and the manuscript is very long with a lot of information. The eddy detection results provide some special information to the circulation in the Gulf of Mexico. There are still several places not clear to this Reviewer. Further clarifications may be needed before the manuscript is to be accepted for publication. Specific comments are listed as follows:
- The use of “robust detection algorithm” in Figure 2 caption may not be appropriate. It easily leads to an impression that it is a new eddy detection method in parallel with the other three algorithms. Actually, it is not. It is just a combination of the results from the other three eddy detections. It is not a more robust method than the other three.
- A related issue – the definition of “robust eddy” is confusing and a bit misleading. It is defined as a result of some consensus from the three eddy detection algorithms, not based on some eddy characteristics (which I would prefer), e.g., eddies with certain sizes/amplitudes, etc.
- Some of the eddies shown in Figure 2 are small. I am not sure they should be considered as eddies or not. I would think a consensus from all three eddy detection algorithms, not just two of the three, should be used as the standard to select eddies. According to Figure 2, the three features not considered as eddies are small and should be discarded anyway. Using “all three” seems to be a better criterion.
- Lines 16-17, “Seasonal variability appears in both the LCFEs and non-LCFE cyclonic eddies and shows large uncertainties”. Does this mean the seasonal variations of the eddies are not robust? Please clarify.
- Line 28, abbreviation “GoM” is used, but “Gulf of Mexico” is still found later in the main text. Be consistent throughout the text.
- Line 33, it would be good to add an example of LCE on Deepwater Horizon oil spill transport (Liu et al., 2011).
- Lines 44-45, it would be good to add a relevant publication (Liu et al., 2016b), which summarizes the characteristic patterns of the LC system also using satellite altimetry product.
- The abbreviation of Caribbean Sea to “CS” should be avoided. It does not save much space, but causes unnecessary confusion – readers need to go back to search what “CS” stands for. Actually, later in the manuscript, it is written as “ Caribbean Sea”.
- Lines 52-53, a relevant publication (Meza-Padilla et al., 2019) should be referred here.
- Lines 66-67, it would be good to cite Nickerson et al. (2022) for an example.
- Figure 1(a), it would be good to add an isobath of 200 m (as a dashed line or in a different color) to indicate continental shelf regions in the Gulf of Mexico.
- Lines 282-283, it is claimed that the separation dates of 28 LCES are less than 1 month difference from those reported by Hall and Leben, 2016) as shown in Table 1. But I found Number 7, eddy Creole, the difference is larger than 1 month (10 August – 20 October). Also Number 9, eddy Fourchon, 6 April – 11 February.
- Table 1, the last column should be labeled as “difference”?
- Lines 166-167, Conventional altimetry data are not reliable for coastal regions for various reasons. Thus, previous altimetry applications in the Gulf of Mexico were limited to 100 m and deeper region (e.g., Liu et al., 2016a, 2016b). However, altimetry data very close to the coast (30 km) and in shallow areas are still used in this study as seen from Figure 2. Justifications or proper discussions are needed. If you overlay a 200 m isobath on the panels of Figure 2, you will see the Dry Tortugas eddy contours already span onto the West Florida Shelf. This cannot be true.
References:
Liu, Y., R.H. Weisberg, S. Vignudelli, and G.T. Mitchum (2014), Evaluation of altimetry-derived surface current products using Lagrangian drifter trajectories in the eastern Gulf of Mexico, Journal of Geophysical Research Oceans, 119, 2827-2842, doi:10.1002/2013JC009710.
Liu, Y., R.H. Weisberg, C. Hu, C. Kovach, and R. Riethmüller (2011), Evolution of the Loop Current system during the Deepwater Horizon oil spill event as observed with drifters and satellites, in Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record-Breaking Enterprise, Geophysical Monograph Series, 195, 91-101, doi:10.1029/2011GM001127.
Liu, Y., R.H. Weisberg, J.M. Lenes, L. Zheng, K. Hubbard, and J.J. Walsh (2016a), Offshore forcing on the "pressure point" of the West Florida Shelf: Anomalous upwelling and its influence on harmful algal blooms, J. Geophys. Res. Oceans, 121, 5501-5515, http://dx.doi.org/10.1002/2016JC011938.
Liu, Y., R.H., Weisberg, S. Vignudelli, and G.T. Mitchum (2016b), Patterns of the Loop Current system and regions of sea surface height variability in the eastern Gulf of Mexico revealed by the self-organizing maps, Journal of Geophysical Research Oceans, 121, 2347-2366, doi:10.1002/2015JC011493.
Meza-Padilla, R., Enriquez, C., Liu, Y., Appendini, C. (2019), Ocean circulation in the western Gulf of Mexico using self-organizing maps, Journal of Geophysical Research Oceans, 124, 4152-4167, doi:10.1029/2018JC014377
Nickerson, A.K., Weisberg, R.H., Liu, Y. (2022), On the evolution of the Gulf of Mexico Loop Current through its penetrative, ring shedding and retracted states, Advances in Space Research, 69(11), 4058-4077, doi:10.1016/j.asr.2022.03.039.
Citation: https://doi.org/10.5194/egusphere-2022-789-RC1 -
AC1: 'Reply on RC1', Yingli Zhu, 26 Sep 2022
1. The use of “robust detection algorithm” in Figure 2 caption may not be appropriate. It easily leads to an impression that it is a new eddy detection method in parallel with the other three algorithms. Actually, it is not. It is just a combination of the results from the other three eddy detections. It is not a more robust method than the other three.
We removed the note of “robust” in the revised manuscript and used “eddies were selected by a combination of the three algorithms” in Figure 2 caption.
2. A related issue – the definition of “robust eddy” is confusing and a bit misleading. It is defined as a result of some consensus from the three eddy detection algorithms, not based on some eddy characteristics (which I would prefer), e.g., eddies with certain sizes/amplitudes, etc.We removed the note of “robust” in the revised manuscript. Mesoscale eddies were selected in this way so that we had more confidence in the detected eddies than those given by one algorithm.
3. Some of the eddies shown in Figure 2 are small. I am not sure they should be considered as eddies or not. I would think a consensus from all three eddy detection algorithms, not just two of the three, should be used as the standard to select eddies. According to Figure 2, the three features not considered as eddies are small and should be discarded anyway. Using “all three” seems to be a better criterion.
The detected eddies have a radius larger than 37 km and can be resolved by the gridded SSH product as we discussed in section 2.1 and Figure 1.
We selected the mesoscale eddies in this way so that we had more confidence in the detected eddies than those given by one algorithm, but they were less restrictive than those given by one method. We have tried using mesoscale eddies that can be detected by “all three algorithms”, but the selected eddies are too restrictive by one of the algorithms, the H14 algorithm.
4. Lines 16-17, “Seasonal variability appears in both the LCFEs and non-LCFE cyclonic eddies and shows large uncertainties”. Does this mean the seasonal variations of the eddies are not robust? Please clarify.
We changed the statement to “Seasonal variability appears in both the LCFEs and non-LCFE cyclonic eddies and shows large uncertainties (not significant at the 95% confidence level)”.
5. Line 28, abbreviation “GoM” is used, but “Gulf of Mexico” is still found later in the main text. Be consistent throughout the text.
We used the notion of “GoM” later in the main text.
6. Line 33, it would be good to add an example of LCE on Deepwater Horizon oil spill transport (Liu et al., 2011).
We cited the work by Liu et al., 2011.
7. Lines 44-45, it would be good to add a relevant publication (Liu et al., 2016b), which summarizes the characteristic patterns of the LC system also using satellite altimetry product.
Liu et al., 2016b was cited.
8. The abbreviation of Caribbean Sea to “CS” should be avoided. It does not save much space, but causes unnecessary confusion – readers need to go back to search what “CS” stands for. Actually, later in the manuscript, it is written as “ Caribbean Sea”.
We removed the abbreviation of Caribbean Sea (CS).
9. Lines 52-53, a relevant publication (Meza-Padilla et al., 2019) should be referred here.Meza-Padilla et al., 2019 was cited.
10. Lines 66-67, it would be good to cite Nickerson et al. (2022) for an example.
Nickerson et al. (2022) was cited.
11. Figure 1(a), it would be good to add an isobath of 200 m (as a dashed line or in a different color) to indicate continental shelf regions in the Gulf of Mexico.
We added the 200-m isobath in the revised manuscript.
12. Lines 282-283, it is claimed that the separation dates of 28 LCES are less than 1 month difference from those reported by Hall and Leben, 2016) as shown in Table 1. But I found Number 7, eddy Creole, the difference is larger than 1 month (10 August – 20 October). Also Number 9, eddy Fourchon, 6 April – 11 February.
There are 35 LCEs listed in Table and the separation dates of 28 of the 35 LCEs are less than 1 month difference from those reported by Hall and Leben (2016). We rewrite the statement as “Among the 35 LCEs listed in Table 1, separation dates of 28 LCEs are less than 1 month different from those reported by Hall and Leben (2016).”
13. Table 1, the last column should be labeled as “difference”?
Corrected.
14. Lines 166-167, Conventional altimetry data are not reliable for coastal regions for various reasons. Thus, previous altimetry applications in the Gulf of Mexico were limited to 100 m and deeper region (e.g., Liu et al., 2016a, 2016b). However, altimetry data very close to the coast (30 km) and in shallow areas are still used in this study as seen from Figure 2. Justifications or proper discussions are needed. If you overlay a 200 m isobath on the panels of Figure 2, you will see the Dry Tortugas eddy contours already span onto the West Florida Shelf. This cannot be true.At locations more than 30 km away from the coast, there are less than 30% of missing along-track data used in the mapping of the gridded SSH product (Figure R1). Therefore, we used the gridded data that are more than 30 km away from the coast. We added this justification in the manuscript.
Figure R1. Missing along-track data along track 230 in the northwest GoM (marked by the thick black line in Figure 1).Citation: https://doi.org/10.5194/egusphere-2022-789-AC1 -
RC3: 'Reply on AC1', Anonymous Referee #1, 16 Oct 2022
Most of the responses to my comments are satisfactory. Thanks.
The very last one, 30 km as a cut-off distance for altimetry data in this study may not be the best choice. The main reason is not about the availability of along-track data, rather it is the quality of the altimetry data in shallow area that may be a concern. For example, on the wide West Florida Shelf, 30 km offshore may be aound 30 m isobath. In this shallow area, the global tide model for altimetry data tidal correction may not be reliable in this shallow area. That is why the coastal altimetry product is preferred (and was tested in previous studies, e.g., Liu et al., 2012) for the shallow water area, not the conventional altimetry product. This can be discussed in the paper.
Reference:
Liu, Y., R.H. Weisberg, S. Vignudelli, L. Roblou, and C.R. Merz (2012), Comparison of the X-TRACK altimetry estimated currents with moored ADCP and HF radar observations on the West Florida Shelf, Adv. Space Res., 50, 1085-1098, doi:10.1016/j.asr.2011.09.012.
Citation: https://doi.org/10.5194/egusphere-2022-789-RC3 -
AC4: 'Reply on RC3', Yingli Zhu, 16 Oct 2022
Thanks for your suggestions. We'll add more discussion on the choice of cut-off distance for altimetry data.
Citation: https://doi.org/10.5194/egusphere-2022-789-AC4
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AC4: 'Reply on RC3', Yingli Zhu, 16 Oct 2022
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RC3: 'Reply on AC1', Anonymous Referee #1, 16 Oct 2022
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CC1: 'Comment on egusphere-2022-789', Francisco Beron-Vera, 18 Sep 2022
All of the eddy detection/tracking methods employed are Eulerian, streamline based. Thus conclusions for transport drawn from their application are \emph{observer dependent}. The authors don't seem to be aware of (have intentionally chosen to ignore?) progress made on objective vortex framing during the last decade. Andrade-Canto et al. (2020, Physics of Fluids 32, 116603, https://doi.org/10.1063/5.0030094) reviews the issue with observer-dependent detection of eddies (including the simple minded U/c > 1 condition) with Loop Current rings as the main focus. The authors cite - out of context - Andrade-Canto et al. in a GRL paper of theirs, but they do not do it here while it is clearly relevant (supporting my suspicion above). The notion of flow invariance discussed in Andrade-Canto et al. (and many papers cited therein) may not be familiar to oceanographers, but it is key to unequivocally frame the vortex notion. This ms should not be published.
Citation: https://doi.org/10.5194/egusphere-2022-789-CC1 -
AC2: 'Reply on CC1', Yingli Zhu, 26 Sep 2022
Both Lagrangian and Eulerian methods have been widely used to detect eddies. The selection of the detection method depends on the mesoscale features people are interested in and the definition of eddies also varies with the detection methods. Both methods can provide useful information. It is not fair to claim one is certainly better than others without stating the specific purposes.
In this study, we focused on the mesoscale features with closed SSH contours or streamlines and we called those mesoscale features “mesoscale eddies”, which were clearly stated in the method section and widely used in a large number of publications. These mesoscale eddies identified with the Eulerian methods may change form and exchange material with background fluid, but are still interesting mesoscale features with different temperature, salinity characteristics (e.g., Brokaw et al., 2020). In addition, we did not consider the coherence of eddies based on the condition that the rotational velocity of the eddy exceeds its translational velocity and U/C was only used to characterize the advective nonlinearity in this study. For those who are interested in the mesoscale features with closed streamlines, the characteristics of eddies detected with the Eulerian methods are useful. And the results here are comparable to many studies carried out in other regions of the global ocean that used the Eulerian detection methods. Although Eulerian eddy detection methods are likely not perfect, they have been widely used and greatly advanced our understanding of the dynamics and impacts of mesoscale eddies over the past few decades. The Eulerian methods of detecting eddies are still under development and used in recent studies. For example, one Eulerian method was still used in the eddy trajectory product released by AVISO (Pegliasco et al., 2021a, 2021b; Pegliasco et al., 2022). Based on Eulerian methods, many eddy characteristics in other oceans and the global ocean were reported in recent studies (e.g., Escudier et al., 2016; Schütte et al., 2016; Keppler et al., 2018; Laxenaire et al., 2018; Pessini et al., 2018; Trott et al., 2018; Mason et al., 2019; Martínez‐Moreno et al., 2019; Chen et al., 2022; Atkins et al., 2022; Evans et al., 2022; López-Álzate et a., 2022).
Please note that in this study we did not draw any conclusions on eddy-induced transport, for which Lagrangian detection methods are indeed better choices. In addition, although we are aware of your recent paper (Andrade-Canto et al. 2020) that focused on the coherent Lagrangian vortices with boundaries that withstand stretching or diffusion, because as you said we utilized the Eulerian rather than Lagrangian based methods in this study, we did not cite your paper.
References
Andrade-Canto F., Karrasch D., and Beron-Vera F. J., (2020). Genesis, evolution, and apocalypse of Loop Current rings, Physics of Fluids, 32, 116603, https://doi.org/10.1063/5.0030094
Atkins, J., Andrews, O., & Frenger, I. (2022). Quantifying the contribution of ocean mesoscale eddies to low oxygen extreme events. Geophysical Research Letters, 49, e2022GL098672. https://doi.org/10.1029/2022GL098672
Brokaw, R. J., Subrahmanyam, B., Trott, C. B., & Chaigneau, A., (2020). Eddy surface characteristics and vertical structure in the Gulf of Mexico from satellite observations and model simulations. Journal of Geophysical Research: Oceans, 125(2), e2019JC015538. https://doi.org/10.1029/2019JC015538.
Chen, G., Chen, X., & Cao, C. (2022). Divergence and Dispersion of Global Eddy Propagation from Satellite Altimetry, Journal of Physical Oceanography, 52(4), 705-722
Escudier, R., B. Mourre, M. Juza, and J. Tintore (2016), Subsurface circulation and mesoscale variability in the Algerian subbasin from altimeterderived eddy trajectories, J. Geophys. Res. Oceans, 121, 6310–6322, doi:10.1002/2016JC011760.
Evans, D.G., Frajka-Williams, E. & Naveira Garabato, A.C. Dissipation of mesoscale eddies at a western boundary via a direct energy cascade. Sci Rep 12, 887 (2022). https://doi.org/10.1038/s41598-022-05002-7
Keppler, L., Cravatte, S., Chaigneau, A., Pegliasco, C., Gourdeau, L., & Singh, A. (2018). Observed characteristics and vertical structure of mesoscale eddies in the southwest tropical Pacific. Journal of Geophysical Research: Oceans, 123, 2731–2756. https://doi. org/10.1002/2017JC013712
Laxenaire, R., Speich, S., Blanke, B., Chaigneau, A., Pegliasco, C., & Stegner, A. (2018). Anticyclonic eddies connecting the western boundaries of Indian and Atlantic Oceans. Journal of Geophysical Research: Oceans, 123, 7651–7677. https://doi.org/10.1029/2018JC014270
López-Álzate, M.E., Sayol, JM., Hernández-Carrasco, I. et al. Mesoscale eddy variability in the Caribbean Sea. Ocean Dynamics (2022). https://doi.org/10.1007/s10236-022-01525-9Martínez‐Moreno, J., Hogg, A. M., Kiss, A. E., Constantinou, N. C., & Morrison, A. K. (2019). Kinetic energy of eddy‐like features from sea surface altimetry. Journal of Advances in Modeling Earth Systems, 11, https://doi.org/10.1029/2019MS001769
Mason, E., Ruiz, S., Bourdalle-Badie, R., Reffray, G., García-Sotillo, M., and Pascual, A., 2019. New insight into 3-D mesoscale eddy properties from CMEMS operational models in the western Mediterranean, Ocean Sci., 15, 1111–1131, https://doi.org/10.5194/os-15-1111-2019
Pegliasco, C., Delepoulle, A., Faugère, Y., 2021a. Mesoscale Eddy Trajectories Atlas Delayed-Time all satellites: version META3.1exp DT allsat. https://doi.org/10.24400/527896/A01-2021.001
Pegliasco, C., Delepoulle, A., Faugère, Y., 2021b. Mesoscale Eddy Trajectories Atlas Delayed-Time two satellites: version META3.1exp DT twosat. https://doi.org/10.24400/527896/A01- 2021.002
Pegliasco, C., Delepoulle, A., Mason, E., Morrow, R., Faugère, Y., Dibarboure, G., 2022. META3.1exp: a new global mesoscale eddy trajectory atlas derived from altimetry. Earth Syst. Sci. Data 14, 1087–1107. https://doi.org/10.5194/essd-14-1087-2022
Pessini, F., Olita, A., Cotroneo, Y., and Perilli, A., 2018. Mesoscale eddies in the Algerian Basin: do they differ as a function of their formation site?, Ocean Sci., 14, 669–688, https://doi.org/10.5194/os-14-669-2018.
Schütte, F., Brandt, P., and Karstensen, J., 2016. Occurrence and characteristics of mesoscale eddies in the tropical northeastern Atlantic Ocean, Ocean Sci., 12, 663–685, https://doi.org/10.5194/os-12-663-2016
Trott, C. B., Subrahmanyam, B., Chaigneau, A., & Delcroix, T. (2018). Eddy tracking in the northwestern Indian Ocean during southwest monsoon regimes. Geophysical Research Letters, 45, 6594–6603. https://doi.org/ 10.1029/2018GL078381
Citation: https://doi.org/10.5194/egusphere-2022-789-AC2 -
CC2: 'Reply on AC2', Francisco Beron-Vera, 26 Sep 2022
'The selection of the detection method depends on the mesoscale features people are interested in and the definition of eddies also varies with the detection methods. ' Objective eddy detection lies in the antipode of this type of thinking. The reason is that all users, independent of their viewpoint, should see the same flow-invariant feature(s). This way the dabate over which eddy detection method is to be employed is constrained to be that one or those that do not depend on the obsever assessment. I include the possibility that there can be more than one observer-independet vortex detection method, e.g., design to frame flow-invariant structures with boundaries that extremize relative stretching or diffusion across or as regions that minimally deform under advection, for which there are several measures. The Authors should take the time to read the Introduction to Focus Issue: Objective Detection of Coherent Structures, Chaos 25, 087201 (2015); https://doi.org/10.1063/1.4928894. This paper should be allowed to be published.
Citation: https://doi.org/10.5194/egusphere-2022-789-CC2 -
CC3: 'Reply on CC2', Francisco Beron-Vera, 26 Sep 2022
Correction: This paper should not be published, I meant to say.
Citation: https://doi.org/10.5194/egusphere-2022-789-CC3 -
CC4: 'Reply on CC3', Xinfeng Liang, 26 Sep 2022
Dear Dr. Beron-Vera,
We appreciate your efforts to clarify the concept of eddies in the oceanographic community. And we agree that if oceanic transport or transport-related questions were the objectives, the elegant way shown in many of your papers is the right choice and should be utilized. However, for this study, we don’t think that is the case. The Eulerian, streamline-based methods are at least OK choices, and our findings are still a useful contribution to the literature.
Please allow me to say a bit about the background of this study, which we did not state in the manuscript. This paper was motivated by a previous study Ying Li and I conducted in the GoM (Zhu and Liang, 2020), in which we explored the connections between surface mesoscale features and deep ocean circulation. The data we used were mainly deep ocean moorings (Eulerian measurements) and satellite data. And we found that mesoscale features (the Eulerian view) could be important in some regions of the GoM in connecting the upper and bottom layers. Note that those mesoscale features could be lagrangian coherent eddies or even large-scale waves. And because of our objectives, which were certainly not transport related, there was no need for us to separate them in that study. And during that study, we found that a compressive study of the characteristics of those mesoscale features in the GoM, like many studies conducted in the open ocean and other regional seas, was lacking. So this following-up study is to fill in the gap about the spatial and temporal patterns of those mesoscale features in the GoM.
Again, if you feel calling those features eddies is misleading (although a large number of studies did that), we could modify the text to make it clearer that we were not talking about lagrangian coherent eddies. We can also explicitly remind the readers that if transport-related topics are what they care about, they should refer to Andrade-Canto et al. (2020) to learn and use the more appropriate methods.
Regards,
Xinfeng Liang
Zhu, Y., & Liang, X. (2020). Coupling of the surface and near-bottom currents in the Gulf of Mexico. Journal of Geophysical Research: Oceans, 125, e2020JC016488. https://doi.org/10.1029/2020JC016488
Citation: https://doi.org/10.5194/egusphere-2022-789-CC4 -
CC5: 'Reply on CC4', Francisco Beron-Vera, 27 Sep 2022
Dear Xinfeng,
You might consider okay that other authors call ''eddy'' a flow region instantaneously filled with closed streamlines of the SSH field such that U/c > 1. But the problem is that when they do that, they are immediately implying consequences for transport. In fact, the U/c > 1 criterion was included by Chelton in an attempt to distinguish between flow-invariant structures of the elliptic type (not in these words, clearly) and anything else (call this linear waves, if you like). You yourself by invoking the U/c > 1 criterion are doing just that. However, as colleagues and I have shown many times over the last decade, U/c > 1is a simple-minded heuristics that in general fails to isolate elliptic Lagrangian coherent structures. In Andrade-Canto et al. (2020) we show, for the case of LCRs, clearly relevant to your work, that Eulerian, streamline-based vortex detection is incapable of distinguishing conception from birth of LCRs. Moreover, they also tend to track past their decease dates vortex-like features unrelated to the LCRs in question. In other cases, material initially inside SSH eddies simply disperse rather quickly after a week or so - cf. references in Andrade-Canto et al. (2020). There you go! You can call your Eulerian coherent structures SSH eddies and omit any reference to advection, or transport, or material, and then the reader will understand the scope of your work or what to expect from it.
Best,
Francisco
Citation: https://doi.org/10.5194/egusphere-2022-789-CC5 -
CC6: 'Reply on CC5', Xinfeng Liang, 27 Sep 2022
Dear Francisco,
Thank you very much for the further clarification and constructive suggestions. We agree it is critically important for us to revise the text to make sure that the readers understand the scope of this study and won’t make incorrect inferences about oceanic transport. We will follow your suggestions to explicitly name those structures described in this paper SSH eddies and to remove references to advection, transport, or materials. Some discussions about the differences between the mesoscale features presented in this study and the Lagrangian coherent structures will be added in the last part of the study as well. We hope this revision plan sounds reasonable to you.
Again, we appreciate your efforts in helping us improve this paper. And we invite you to provide more critical feedback on a revised version of this manuscript in the near future if that becomes possible.
Best,
Xinfeng
Citation: https://doi.org/10.5194/egusphere-2022-789-CC6
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CC6: 'Reply on CC5', Xinfeng Liang, 27 Sep 2022
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CC5: 'Reply on CC4', Francisco Beron-Vera, 27 Sep 2022
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CC4: 'Reply on CC3', Xinfeng Liang, 26 Sep 2022
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CC3: 'Reply on CC2', Francisco Beron-Vera, 26 Sep 2022
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CC2: 'Reply on AC2', Francisco Beron-Vera, 26 Sep 2022
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AC2: 'Reply on CC1', Yingli Zhu, 26 Sep 2022
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RC2: 'Comment on egusphere-2022-789', Anonymous Referee #2, 21 Sep 2022
The manuscript analyzes eddy activity in the Gulf of Mexico by applying three eddy detection algorithms to satellite altimetry data. The authors analyze the characteristics of the eddies, such as dimension, location and date of birth/death, trajectory and temporal variability.
The authors make an effort to provide detailed information between circulation and eddy characteristics. However the methodology used to detect and track eddies I do not believe is adequate. Neither calling their identified eddies as robust.
The reason is because the authors use detection/tracking techniques based on Eulerian algorithms (instantaneous velocities) that are observer-dependent and not on the geometrical properties of the flow. There are papers that show a large discrepancy between Eulerian and Lagrangian detected eddies. For example, the work of Andrade-Canto et. Al, 2020 (https://doi.org/10.1063/5.0030094), where they analyze the birth, evolution and death of loop current eddies by coherent Lagrangian vortex detection. They also show that Eulerian techniques are unable to accurately distinguish the birth, evolution and death of the eddies in question, because they are based on instantaneous velocity fields which makes the detection of an eddy between one time and the subsequent one not in complete agreement.
Furthermore, their criterion for determining which eddies are coherent is based on the condition that the rotational velocity of the eddy exceeds its translational velocity (U/c > 1), a criterion that has been shown to be invalid for defining an eddy as coherent. The work of Beron-Vera et. Al, 2013 (https://doi.org/10.1175/JPO-D-12-0171.1) showed that the Lagrangian evolution of closed SSH contours (all with U/c>1 for at least 90 days) stretch and fold rapidly, exhibiting leakage and filamentation, that discualifies them as coherent eddy boundaries.
In my opinion the manuscript does not present relevant results, much of what the authors present only confirms what has already been said in other studies about eddies in the Gulf of Mexico, simply that the authors use a larger database.
The method that the authors propose as "robust" is not a new method, it is simply the combination of three similar methods.
Therefore, this reviewer recommends not to publish this manuscript.
Citation: https://doi.org/10.5194/egusphere-2022-789-RC2 -
AC3: 'Reply on RC2', Yingli Zhu, 26 Sep 2022
We removed the notion of “robust” in the revised manuscript to eliminate the confusion. Mesoscale eddies were selected by combining three previous eddy detection algorithms so that we had more confidence in the selected eddies than those given just by one algorithm.
As to your concern about the Eulerian method of detecting mesoscale eddies, we give the following explanations. First, the definition of mesoscale eddy in this study is different from coherent Lagrangian vortices, and our focus is not on the coherent Lagrangian vortices. We considered the mesoscale eddies detected with Eulerian methods that may change form and exchange material with background fluid. In addition, we did not consider the coherence of eddies based on the condition that the rotational velocity of the eddy exceeds its translational velocity and U/C was only used to characterize the advective nonlinearity in this study. For those who are interested in the mesoscale features with closed streamlines, the characteristics of eddies detected with the Eulerian methods are still useful. For example, a recent study has used one Eulerian method to examine the eddy surface characteristics and vertical structure in the Gulf of Mexico from 2016-2018 and found distinct mesoscale features in the eddies with closed sea surface height contours (Brokaw et al., 2020).
In addition, we are fully aware of the limitations of different Eulerian eddy detection methods, which we clearly stated in the text. In fact, mitigating those limitations is one of the major motivations of this study and that is why we put a lot of effort to combine different eddy detection algorithms to select eddies. In addition, although eddy detection methods are likely not perfect, they have been widely used and greatly advanced our understanding of the dynamics and impacts of mesoscale eddies over the past few decades. The Eulerian methods of detecting eddies are still under development and used in recent studies. For example, one Eulerian method was still used in the eddy trajectory product released by AVISO (Pegliasco et al., 2021a, 2021b; Pegliasco et al., 2022). Based on Eulerian methods, many eddy characteristics in other oceans and the global ocean were reported in recent studies (e.g., Escudier et al., 2016; Schütte et al., 2016; Keppler et al., 2018; Laxenaire et al., 2018; Pessini et al., 2018; Trott et al., 2018; Mason et al., 2019; Martínez‐Moreno et al., 2019; Chen et al., 2022; Atkins et al., 2022; Evans et al., 2022; López-Álzate et a., 2022). Last but not the least, some of our findings being consistent with previous studies, which you considered as a negative point, actually indicate that our approach works just fine.
Regarding the novelty, we would like to argue that there are two open and important questions examined in this study. The first question is that most previous studies only focus on the Loop Current Eddies (LCEs) and Loop Current Frontal Eddies (LCFEs), while characteristics of other types of mesoscale eddies in the Gulf of Mexico (GoM) have not been comprehensively described. The second question is that the seasonal and low-frequency variability of eddy number and amplitude of all types of eddies in the GoM have not been fully reported. Our study provides useful results to address those two questions.References
Atkins, J., Andrews, O., & Frenger, I. (2022). Quantifying the contribution of ocean mesoscale eddies to low oxygen extreme events. Geophysical Research Letters, 49, e2022GL098672. https://doi.org/10.1029/2022GL098672Brokaw, R. J., Subrahmanyam, B., Trott, C. B., & Chaigneau, A., (2020). Eddy surface characteristics and vertical structure in the Gulf of Mexico from satellite observations and model simulations. Journal of Geophysical Research: Oceans, 125(2), e2019JC015538. https://doi.org/10.1029/2019JC015538.
Chen, G., Chen, X., & Cao, C. (2022). Divergence and Dispersion of Global Eddy Propagation from Satellite Altimetry, Journal of Physical Oceanography, 52(4), 705-722
Escudier, R., B. Mourre, M. Juza, and J. Tintore (2016), Subsurface circulation and mesoscale variability in the Algerian subbasin from altimeterderived eddy trajectories, J. Geophys. Res. Oceans, 121, 6310–6322, doi:10.1002/2016JC011760.
Evans, D.G., Frajka-Williams, E. & Naveira Garabato, A.C. Dissipation of mesoscale eddies at a western boundary via a direct energy cascade. Sci Rep 12, 887 (2022). https://doi.org/10.1038/s41598-022-05002-7
Keppler, L., Cravatte, S., Chaigneau, A., Pegliasco, C., Gourdeau, L., & Singh, A. (2018). Observed characteristics and vertical structure of mesoscale eddies in the southwest tropical Pacific. Journal of Geophysical Research: Oceans, 123, 2731–2756. https://doi. org/10.1002/2017JC013712
Laxenaire, R., Speich, S., Blanke, B., Chaigneau, A., Pegliasco, C., & Stegner, A. (2018). Anticyclonic eddies connecting the western boundaries of Indian and Atlantic Oceans. Journal of Geophysical Research: Oceans, 123, 7651–7677. https://doi.org/10.1029/2018JC014270
López-Álzate, M.E., Sayol, JM., Hernández-Carrasco, I. et al. Mesoscale eddy variability in the Caribbean Sea. Ocean Dynamics (2022). https://doi.org/10.1007/s10236-022-01525-9Martínez‐Moreno, J., Hogg, A. M., Kiss, A. E., Constantinou, N. C., & Morrison, A. K. (2019). Kinetic energy of eddy‐like features from sea surface altimetry. Journal of Advances in Modeling Earth Systems, 11, https://doi.org/10.1029/2019MS001769
Mason, E., Ruiz, S., Bourdalle-Badie, R., Reffray, G., García-Sotillo, M., and Pascual, A., 2019. New insight into 3-D mesoscale eddy properties from CMEMS operational models in the western Mediterranean, Ocean Sci., 15, 1111–1131, https://doi.org/10.5194/os-15-1111-2019
Pegliasco, C., Delepoulle, A., Faugère, Y., 2021a. Mesoscale Eddy Trajectories Atlas Delayed-Time all satellites: version META3.1exp DT allsat. https://doi.org/10.24400/527896/A01-2021.001
Pegliasco, C., Delepoulle, A., Faugère, Y., 2021b. Mesoscale Eddy Trajectories Atlas Delayed-Time two satellites: version META3.1exp DT twosat. https://doi.org/10.24400/527896/A01- 2021.002
Pegliasco, C., Delepoulle, A., Mason, E., Morrow, R., Faugère, Y., Dibarboure, G., 2022. META3.1exp: a new global mesoscale eddy trajectory atlas derived from altimetry. Earth Syst. Sci. Data 14, 1087–1107. https://doi.org/10.5194/essd-14-1087-2022
Pessini, F., Olita, A., Cotroneo, Y., and Perilli, A., 2018. Mesoscale eddies in the Algerian Basin: do they differ as a function of their formation site?, Ocean Sci., 14, 669–688, https://doi.org/10.5194/os-14-669-2018.
Schütte, F., Brandt, P., and Karstensen, J., 2016. Occurrence and characteristics of mesoscale eddies in the tropical northeastern Atlantic Ocean, Ocean Sci., 12, 663–685, https://doi.org/10.5194/os-12-663-2016
Trott, C. B., Subrahmanyam, B., Chaigneau, A., & Delcroix, T. (2018). Eddy tracking in the northwestern Indian Ocean during southwest monsoon regimes. Geophysical Research Letters, 45, 6594–6603. https://doi.org/ 10.1029/2018GL078381
Citation: https://doi.org/10.5194/egusphere-2022-789-AC3 -
CC7: 'Reply on RC2', Xinfeng Liang, 17 Oct 2022
Thank you for your critical comments, particularly on the definition of eddies. As suggested by Dr. Francisco Beron-Vera, which you can find in our exchanges above, we are planning to use a different notation “SSH eddies” in the revised manuscript to distinguish our detected eddies from the Lagrangian coherent eddies. We will also remove references to advection, transport, or materials. By doing so, the readers can better understand the scope of this study and won’t likely make incorrect inferences. In addition, discussions about the differences between the mesoscale features presented in this study and the Lagrangian coherent eddies will be added in the last part of the study. We hope this revision plan can address the concerns you raised and sounds reasonable to you.
Citation: https://doi.org/10.5194/egusphere-2022-789-CC7 -
RC4: 'Reply on CC7', Anonymous Referee #2, 19 Oct 2022
Detecting eddies with Eulerian methods is fine from an Eulerian perspective (assuming that the focus of the work was changed). However, the most interesting part of the work could be the trajectory, birth and death of the eddies, but the nature of the detection method, which is Eulerian, does not guarantee that the new eddy detected is the same one detected an instant before,
and also gives different results in reference frames that move or rotate with respect to each other, as shown in the work of Haller 2005. This leads to determine trajectories with significant uncertainty. Therefore, it is important to re-emphasize Lagrangian methodologies, with which it is possible to objectively determine the trajectory, birth and death of eddies, as shown in the works of Andrade-Canto et. al. 2021, Andrade-Canto et. al. 2022a and Andrade-Canto et. al. 2022b.
Andrade-Canto et. al. 2022b show that the eddy trajectory together with a material ring stretching value indicating the loss of coherence. In the supplementary material an example is presented showing that within the closed SSH contour a hyperbolic point is found together with two elliptic points (or two eddy centers). This indicates that the eddy will separate. Which of the two centers should be followed from the Eulerian perspective?
I consider what underpins some of the main work to be rather weak, especially when it is presented as novel and informative work on eddy life in the Gulf of Mexico. The work of Bello-Fuentes et. al. 2021, previous to this work and that has not been considered, makes a Lagrangian census of the eddies, determining radii, retention times, as well as the preferred regions for cyclones and anticyclones.
In spite of the above, I consider that the information from the Eulerian perspective is important, so this work should not be wasted. The analysis of the seasonality and low frequency variability associated with the increase in vorticity associated with instantaneous eddies is very important information that can be used as a framework for the validation of numerical models, for example. So I strongly suggest that at least this perspective be taken into account.
On the other hand, it seems inappropriate to me that in order for the work to be accepted, a change of approach of such magnitude is required, at least that is the impression suggested in the responses to other comments. However, I appreciate your willingness, although this does not imply that I am willing to accept a second revision. I recognize that it was a hard work with useful information, but I think you should consider the arguments mentioned above, rewrite the paper and resubmit it as another paper.
Bibliography:
Andrade-Canto, F., Karrasch, D., & Beron-Vera, F. J. (2020). Genesis, evolution, and apocalypse of Loop Current rings. Physics of Fluids, 32(11), 116603.
Andrade-Canto, F., Beron-Vera, F. J., Goni, G. J., Karrasch, D., Olascoaga, M. J., & Triñanes, J. (2022). Carriers of Sargassum and mechanism for coastal inundation in the Caribbean Sea. Physics of Fluids, 34(1), 016602.
Andrade‐Canto, F., & Beron‐Vera, F. J. (2022). Do eddies connect the tropical Atlantic Ocean and the Gulf of Mexico?. Geophysical Research Letters, e2022GL099637.
José Bello-Fuentes, F., García-Nava, H., Andrade-Canto, F., Durazo, R., Castro, R., & Yarbuh, I. (2021). Retention time and transport potential of eddies in the northwestern Gulf of Mexico. Ciencias Marinas, 47(2).
Haller, G. (2005). An objective definition of a vortex. Journal of fluid mechanics, 525, 1-26.
Citation: https://doi.org/10.5194/egusphere-2022-789-RC4 -
CC8: 'Reply on RC4', Xinfeng Liang, 20 Oct 2022
Thank you very much for the prompt and helpful comments. We agree that the trajectory, birth, and death of the eddies presented in this study will likely differ from the results based on the Lagrangian approaches. In other words, unlike the Lagrangian coherent eddies, the Eulerian eddies are not likely the same eddies from birth to death but a series of perturbations that are related. Clearly, the meaning of our results depends on the interpretation of those "eddies." In this study, as mentioned above, we interpret the "SSH/Eulerian eddies" as perturbations or "waves", which reflect the generation, propagation, and dissipation of those related signals rather than coherent mass. We would like to state explicitly in the paper the differences between Eulerian eddies and Lagrangian coherent eddies. This can actually serve as a good opportunity to remind the oceanography community of the issues of Eulerian methods, such as what they are good for, and what they are not.
As you kindly pointed out, there is much useful information in this paper. And we aim to present that information in a more accurate way in a revised manuscript. A similar study based on the Lagrangian approaches presented in Andrade-Canto et. al. 2021, Andrade-Canto et. al. 2022a and Andrade-Canto et. al. 2022b is certainly important and could be done. But due to the tremendous effects needed for that, we prefer to conduct that as a follow-up study in the near future. And the comparison between Eulerian and Lagrangian results could be interesting.
Citation: https://doi.org/10.5194/egusphere-2022-789-CC8 -
AC5: 'Reply on RC4', Yingli Zhu, 27 Oct 2022
Thank you very much for the prompt and helpful comments. We agree that the trajectory, birth, and death of the eddies presented in this study will likely differ from the results based on the Lagrangian approaches. In other words, unlike the Lagrangian coherent eddies, the Eulerian eddies are not likely the same eddies from birth to death but a series of perturbations that are related. Clearly, the meaning of our results depends on the interpretation of those "eddies." In this study, as mentioned above, we interpret the "SSH/Eulerian eddies" as perturbations or "waves", which reflect the generation, propagation, and dissipation of those related signals rather than coherent mass. We would like to state explicitly in the paper the differences between Eulerian eddies and Lagrangian coherent eddies. This can actually serve as a good opportunity to remind the oceanography community of the issues of Eulerian methods, such as what they are good for, and what they are not.
As you kindly pointed out, there is much useful information in this paper. And we aim to present that information in a more accurate way in a revised manuscript. A similar study based on the Lagrangian approaches presented in Andrade-Canto et. al. 2021, Andrade-Canto et. al. 2022a and Andrade-Canto et. al. 2022b is certainly important and could be done. But due to the tremendous effects needed for that, we prefer to conduct that as a follow-up study in the near future. And the comparison between Eulerian and Lagrangian results could be interesting.
Citation: https://doi.org/10.5194/egusphere-2022-789-AC5
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CC8: 'Reply on RC4', Xinfeng Liang, 20 Oct 2022
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RC4: 'Reply on CC7', Anonymous Referee #2, 19 Oct 2022
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AC3: 'Reply on RC2', Yingli Zhu, 26 Sep 2022
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-789', Anonymous Referee #1, 17 Sep 2022
Eddy activities in the Gulf of Mexico are analyzed by applying a set of three eddy detection algorithms to satellite altimetry product. Characteristics of the eddies are described, and seasonal variations are analyzed. The eddies are discussed in terms of different types: Loop Current Eddies, Loop Current Front Eddies, and non-Loop Current Front Eddies, etc. Huge effort has been made in this study, and the manuscript is very long with a lot of information. The eddy detection results provide some special information to the circulation in the Gulf of Mexico. There are still several places not clear to this Reviewer. Further clarifications may be needed before the manuscript is to be accepted for publication. Specific comments are listed as follows:
- The use of “robust detection algorithm” in Figure 2 caption may not be appropriate. It easily leads to an impression that it is a new eddy detection method in parallel with the other three algorithms. Actually, it is not. It is just a combination of the results from the other three eddy detections. It is not a more robust method than the other three.
- A related issue – the definition of “robust eddy” is confusing and a bit misleading. It is defined as a result of some consensus from the three eddy detection algorithms, not based on some eddy characteristics (which I would prefer), e.g., eddies with certain sizes/amplitudes, etc.
- Some of the eddies shown in Figure 2 are small. I am not sure they should be considered as eddies or not. I would think a consensus from all three eddy detection algorithms, not just two of the three, should be used as the standard to select eddies. According to Figure 2, the three features not considered as eddies are small and should be discarded anyway. Using “all three” seems to be a better criterion.
- Lines 16-17, “Seasonal variability appears in both the LCFEs and non-LCFE cyclonic eddies and shows large uncertainties”. Does this mean the seasonal variations of the eddies are not robust? Please clarify.
- Line 28, abbreviation “GoM” is used, but “Gulf of Mexico” is still found later in the main text. Be consistent throughout the text.
- Line 33, it would be good to add an example of LCE on Deepwater Horizon oil spill transport (Liu et al., 2011).
- Lines 44-45, it would be good to add a relevant publication (Liu et al., 2016b), which summarizes the characteristic patterns of the LC system also using satellite altimetry product.
- The abbreviation of Caribbean Sea to “CS” should be avoided. It does not save much space, but causes unnecessary confusion – readers need to go back to search what “CS” stands for. Actually, later in the manuscript, it is written as “ Caribbean Sea”.
- Lines 52-53, a relevant publication (Meza-Padilla et al., 2019) should be referred here.
- Lines 66-67, it would be good to cite Nickerson et al. (2022) for an example.
- Figure 1(a), it would be good to add an isobath of 200 m (as a dashed line or in a different color) to indicate continental shelf regions in the Gulf of Mexico.
- Lines 282-283, it is claimed that the separation dates of 28 LCES are less than 1 month difference from those reported by Hall and Leben, 2016) as shown in Table 1. But I found Number 7, eddy Creole, the difference is larger than 1 month (10 August – 20 October). Also Number 9, eddy Fourchon, 6 April – 11 February.
- Table 1, the last column should be labeled as “difference”?
- Lines 166-167, Conventional altimetry data are not reliable for coastal regions for various reasons. Thus, previous altimetry applications in the Gulf of Mexico were limited to 100 m and deeper region (e.g., Liu et al., 2016a, 2016b). However, altimetry data very close to the coast (30 km) and in shallow areas are still used in this study as seen from Figure 2. Justifications or proper discussions are needed. If you overlay a 200 m isobath on the panels of Figure 2, you will see the Dry Tortugas eddy contours already span onto the West Florida Shelf. This cannot be true.
References:
Liu, Y., R.H. Weisberg, S. Vignudelli, and G.T. Mitchum (2014), Evaluation of altimetry-derived surface current products using Lagrangian drifter trajectories in the eastern Gulf of Mexico, Journal of Geophysical Research Oceans, 119, 2827-2842, doi:10.1002/2013JC009710.
Liu, Y., R.H. Weisberg, C. Hu, C. Kovach, and R. Riethmüller (2011), Evolution of the Loop Current system during the Deepwater Horizon oil spill event as observed with drifters and satellites, in Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record-Breaking Enterprise, Geophysical Monograph Series, 195, 91-101, doi:10.1029/2011GM001127.
Liu, Y., R.H. Weisberg, J.M. Lenes, L. Zheng, K. Hubbard, and J.J. Walsh (2016a), Offshore forcing on the "pressure point" of the West Florida Shelf: Anomalous upwelling and its influence on harmful algal blooms, J. Geophys. Res. Oceans, 121, 5501-5515, http://dx.doi.org/10.1002/2016JC011938.
Liu, Y., R.H., Weisberg, S. Vignudelli, and G.T. Mitchum (2016b), Patterns of the Loop Current system and regions of sea surface height variability in the eastern Gulf of Mexico revealed by the self-organizing maps, Journal of Geophysical Research Oceans, 121, 2347-2366, doi:10.1002/2015JC011493.
Meza-Padilla, R., Enriquez, C., Liu, Y., Appendini, C. (2019), Ocean circulation in the western Gulf of Mexico using self-organizing maps, Journal of Geophysical Research Oceans, 124, 4152-4167, doi:10.1029/2018JC014377
Nickerson, A.K., Weisberg, R.H., Liu, Y. (2022), On the evolution of the Gulf of Mexico Loop Current through its penetrative, ring shedding and retracted states, Advances in Space Research, 69(11), 4058-4077, doi:10.1016/j.asr.2022.03.039.
Citation: https://doi.org/10.5194/egusphere-2022-789-RC1 -
AC1: 'Reply on RC1', Yingli Zhu, 26 Sep 2022
1. The use of “robust detection algorithm” in Figure 2 caption may not be appropriate. It easily leads to an impression that it is a new eddy detection method in parallel with the other three algorithms. Actually, it is not. It is just a combination of the results from the other three eddy detections. It is not a more robust method than the other three.
We removed the note of “robust” in the revised manuscript and used “eddies were selected by a combination of the three algorithms” in Figure 2 caption.
2. A related issue – the definition of “robust eddy” is confusing and a bit misleading. It is defined as a result of some consensus from the three eddy detection algorithms, not based on some eddy characteristics (which I would prefer), e.g., eddies with certain sizes/amplitudes, etc.We removed the note of “robust” in the revised manuscript. Mesoscale eddies were selected in this way so that we had more confidence in the detected eddies than those given by one algorithm.
3. Some of the eddies shown in Figure 2 are small. I am not sure they should be considered as eddies or not. I would think a consensus from all three eddy detection algorithms, not just two of the three, should be used as the standard to select eddies. According to Figure 2, the three features not considered as eddies are small and should be discarded anyway. Using “all three” seems to be a better criterion.
The detected eddies have a radius larger than 37 km and can be resolved by the gridded SSH product as we discussed in section 2.1 and Figure 1.
We selected the mesoscale eddies in this way so that we had more confidence in the detected eddies than those given by one algorithm, but they were less restrictive than those given by one method. We have tried using mesoscale eddies that can be detected by “all three algorithms”, but the selected eddies are too restrictive by one of the algorithms, the H14 algorithm.
4. Lines 16-17, “Seasonal variability appears in both the LCFEs and non-LCFE cyclonic eddies and shows large uncertainties”. Does this mean the seasonal variations of the eddies are not robust? Please clarify.
We changed the statement to “Seasonal variability appears in both the LCFEs and non-LCFE cyclonic eddies and shows large uncertainties (not significant at the 95% confidence level)”.
5. Line 28, abbreviation “GoM” is used, but “Gulf of Mexico” is still found later in the main text. Be consistent throughout the text.
We used the notion of “GoM” later in the main text.
6. Line 33, it would be good to add an example of LCE on Deepwater Horizon oil spill transport (Liu et al., 2011).
We cited the work by Liu et al., 2011.
7. Lines 44-45, it would be good to add a relevant publication (Liu et al., 2016b), which summarizes the characteristic patterns of the LC system also using satellite altimetry product.
Liu et al., 2016b was cited.
8. The abbreviation of Caribbean Sea to “CS” should be avoided. It does not save much space, but causes unnecessary confusion – readers need to go back to search what “CS” stands for. Actually, later in the manuscript, it is written as “ Caribbean Sea”.
We removed the abbreviation of Caribbean Sea (CS).
9. Lines 52-53, a relevant publication (Meza-Padilla et al., 2019) should be referred here.Meza-Padilla et al., 2019 was cited.
10. Lines 66-67, it would be good to cite Nickerson et al. (2022) for an example.
Nickerson et al. (2022) was cited.
11. Figure 1(a), it would be good to add an isobath of 200 m (as a dashed line or in a different color) to indicate continental shelf regions in the Gulf of Mexico.
We added the 200-m isobath in the revised manuscript.
12. Lines 282-283, it is claimed that the separation dates of 28 LCES are less than 1 month difference from those reported by Hall and Leben, 2016) as shown in Table 1. But I found Number 7, eddy Creole, the difference is larger than 1 month (10 August – 20 October). Also Number 9, eddy Fourchon, 6 April – 11 February.
There are 35 LCEs listed in Table and the separation dates of 28 of the 35 LCEs are less than 1 month difference from those reported by Hall and Leben (2016). We rewrite the statement as “Among the 35 LCEs listed in Table 1, separation dates of 28 LCEs are less than 1 month different from those reported by Hall and Leben (2016).”
13. Table 1, the last column should be labeled as “difference”?
Corrected.
14. Lines 166-167, Conventional altimetry data are not reliable for coastal regions for various reasons. Thus, previous altimetry applications in the Gulf of Mexico were limited to 100 m and deeper region (e.g., Liu et al., 2016a, 2016b). However, altimetry data very close to the coast (30 km) and in shallow areas are still used in this study as seen from Figure 2. Justifications or proper discussions are needed. If you overlay a 200 m isobath on the panels of Figure 2, you will see the Dry Tortugas eddy contours already span onto the West Florida Shelf. This cannot be true.At locations more than 30 km away from the coast, there are less than 30% of missing along-track data used in the mapping of the gridded SSH product (Figure R1). Therefore, we used the gridded data that are more than 30 km away from the coast. We added this justification in the manuscript.
Figure R1. Missing along-track data along track 230 in the northwest GoM (marked by the thick black line in Figure 1).Citation: https://doi.org/10.5194/egusphere-2022-789-AC1 -
RC3: 'Reply on AC1', Anonymous Referee #1, 16 Oct 2022
Most of the responses to my comments are satisfactory. Thanks.
The very last one, 30 km as a cut-off distance for altimetry data in this study may not be the best choice. The main reason is not about the availability of along-track data, rather it is the quality of the altimetry data in shallow area that may be a concern. For example, on the wide West Florida Shelf, 30 km offshore may be aound 30 m isobath. In this shallow area, the global tide model for altimetry data tidal correction may not be reliable in this shallow area. That is why the coastal altimetry product is preferred (and was tested in previous studies, e.g., Liu et al., 2012) for the shallow water area, not the conventional altimetry product. This can be discussed in the paper.
Reference:
Liu, Y., R.H. Weisberg, S. Vignudelli, L. Roblou, and C.R. Merz (2012), Comparison of the X-TRACK altimetry estimated currents with moored ADCP and HF radar observations on the West Florida Shelf, Adv. Space Res., 50, 1085-1098, doi:10.1016/j.asr.2011.09.012.
Citation: https://doi.org/10.5194/egusphere-2022-789-RC3 -
AC4: 'Reply on RC3', Yingli Zhu, 16 Oct 2022
Thanks for your suggestions. We'll add more discussion on the choice of cut-off distance for altimetry data.
Citation: https://doi.org/10.5194/egusphere-2022-789-AC4
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AC4: 'Reply on RC3', Yingli Zhu, 16 Oct 2022
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RC3: 'Reply on AC1', Anonymous Referee #1, 16 Oct 2022
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CC1: 'Comment on egusphere-2022-789', Francisco Beron-Vera, 18 Sep 2022
All of the eddy detection/tracking methods employed are Eulerian, streamline based. Thus conclusions for transport drawn from their application are \emph{observer dependent}. The authors don't seem to be aware of (have intentionally chosen to ignore?) progress made on objective vortex framing during the last decade. Andrade-Canto et al. (2020, Physics of Fluids 32, 116603, https://doi.org/10.1063/5.0030094) reviews the issue with observer-dependent detection of eddies (including the simple minded U/c > 1 condition) with Loop Current rings as the main focus. The authors cite - out of context - Andrade-Canto et al. in a GRL paper of theirs, but they do not do it here while it is clearly relevant (supporting my suspicion above). The notion of flow invariance discussed in Andrade-Canto et al. (and many papers cited therein) may not be familiar to oceanographers, but it is key to unequivocally frame the vortex notion. This ms should not be published.
Citation: https://doi.org/10.5194/egusphere-2022-789-CC1 -
AC2: 'Reply on CC1', Yingli Zhu, 26 Sep 2022
Both Lagrangian and Eulerian methods have been widely used to detect eddies. The selection of the detection method depends on the mesoscale features people are interested in and the definition of eddies also varies with the detection methods. Both methods can provide useful information. It is not fair to claim one is certainly better than others without stating the specific purposes.
In this study, we focused on the mesoscale features with closed SSH contours or streamlines and we called those mesoscale features “mesoscale eddies”, which were clearly stated in the method section and widely used in a large number of publications. These mesoscale eddies identified with the Eulerian methods may change form and exchange material with background fluid, but are still interesting mesoscale features with different temperature, salinity characteristics (e.g., Brokaw et al., 2020). In addition, we did not consider the coherence of eddies based on the condition that the rotational velocity of the eddy exceeds its translational velocity and U/C was only used to characterize the advective nonlinearity in this study. For those who are interested in the mesoscale features with closed streamlines, the characteristics of eddies detected with the Eulerian methods are useful. And the results here are comparable to many studies carried out in other regions of the global ocean that used the Eulerian detection methods. Although Eulerian eddy detection methods are likely not perfect, they have been widely used and greatly advanced our understanding of the dynamics and impacts of mesoscale eddies over the past few decades. The Eulerian methods of detecting eddies are still under development and used in recent studies. For example, one Eulerian method was still used in the eddy trajectory product released by AVISO (Pegliasco et al., 2021a, 2021b; Pegliasco et al., 2022). Based on Eulerian methods, many eddy characteristics in other oceans and the global ocean were reported in recent studies (e.g., Escudier et al., 2016; Schütte et al., 2016; Keppler et al., 2018; Laxenaire et al., 2018; Pessini et al., 2018; Trott et al., 2018; Mason et al., 2019; Martínez‐Moreno et al., 2019; Chen et al., 2022; Atkins et al., 2022; Evans et al., 2022; López-Álzate et a., 2022).
Please note that in this study we did not draw any conclusions on eddy-induced transport, for which Lagrangian detection methods are indeed better choices. In addition, although we are aware of your recent paper (Andrade-Canto et al. 2020) that focused on the coherent Lagrangian vortices with boundaries that withstand stretching or diffusion, because as you said we utilized the Eulerian rather than Lagrangian based methods in this study, we did not cite your paper.
References
Andrade-Canto F., Karrasch D., and Beron-Vera F. J., (2020). Genesis, evolution, and apocalypse of Loop Current rings, Physics of Fluids, 32, 116603, https://doi.org/10.1063/5.0030094
Atkins, J., Andrews, O., & Frenger, I. (2022). Quantifying the contribution of ocean mesoscale eddies to low oxygen extreme events. Geophysical Research Letters, 49, e2022GL098672. https://doi.org/10.1029/2022GL098672
Brokaw, R. J., Subrahmanyam, B., Trott, C. B., & Chaigneau, A., (2020). Eddy surface characteristics and vertical structure in the Gulf of Mexico from satellite observations and model simulations. Journal of Geophysical Research: Oceans, 125(2), e2019JC015538. https://doi.org/10.1029/2019JC015538.
Chen, G., Chen, X., & Cao, C. (2022). Divergence and Dispersion of Global Eddy Propagation from Satellite Altimetry, Journal of Physical Oceanography, 52(4), 705-722
Escudier, R., B. Mourre, M. Juza, and J. Tintore (2016), Subsurface circulation and mesoscale variability in the Algerian subbasin from altimeterderived eddy trajectories, J. Geophys. Res. Oceans, 121, 6310–6322, doi:10.1002/2016JC011760.
Evans, D.G., Frajka-Williams, E. & Naveira Garabato, A.C. Dissipation of mesoscale eddies at a western boundary via a direct energy cascade. Sci Rep 12, 887 (2022). https://doi.org/10.1038/s41598-022-05002-7
Keppler, L., Cravatte, S., Chaigneau, A., Pegliasco, C., Gourdeau, L., & Singh, A. (2018). Observed characteristics and vertical structure of mesoscale eddies in the southwest tropical Pacific. Journal of Geophysical Research: Oceans, 123, 2731–2756. https://doi. org/10.1002/2017JC013712
Laxenaire, R., Speich, S., Blanke, B., Chaigneau, A., Pegliasco, C., & Stegner, A. (2018). Anticyclonic eddies connecting the western boundaries of Indian and Atlantic Oceans. Journal of Geophysical Research: Oceans, 123, 7651–7677. https://doi.org/10.1029/2018JC014270
López-Álzate, M.E., Sayol, JM., Hernández-Carrasco, I. et al. Mesoscale eddy variability in the Caribbean Sea. Ocean Dynamics (2022). https://doi.org/10.1007/s10236-022-01525-9Martínez‐Moreno, J., Hogg, A. M., Kiss, A. E., Constantinou, N. C., & Morrison, A. K. (2019). Kinetic energy of eddy‐like features from sea surface altimetry. Journal of Advances in Modeling Earth Systems, 11, https://doi.org/10.1029/2019MS001769
Mason, E., Ruiz, S., Bourdalle-Badie, R., Reffray, G., García-Sotillo, M., and Pascual, A., 2019. New insight into 3-D mesoscale eddy properties from CMEMS operational models in the western Mediterranean, Ocean Sci., 15, 1111–1131, https://doi.org/10.5194/os-15-1111-2019
Pegliasco, C., Delepoulle, A., Faugère, Y., 2021a. Mesoscale Eddy Trajectories Atlas Delayed-Time all satellites: version META3.1exp DT allsat. https://doi.org/10.24400/527896/A01-2021.001
Pegliasco, C., Delepoulle, A., Faugère, Y., 2021b. Mesoscale Eddy Trajectories Atlas Delayed-Time two satellites: version META3.1exp DT twosat. https://doi.org/10.24400/527896/A01- 2021.002
Pegliasco, C., Delepoulle, A., Mason, E., Morrow, R., Faugère, Y., Dibarboure, G., 2022. META3.1exp: a new global mesoscale eddy trajectory atlas derived from altimetry. Earth Syst. Sci. Data 14, 1087–1107. https://doi.org/10.5194/essd-14-1087-2022
Pessini, F., Olita, A., Cotroneo, Y., and Perilli, A., 2018. Mesoscale eddies in the Algerian Basin: do they differ as a function of their formation site?, Ocean Sci., 14, 669–688, https://doi.org/10.5194/os-14-669-2018.
Schütte, F., Brandt, P., and Karstensen, J., 2016. Occurrence and characteristics of mesoscale eddies in the tropical northeastern Atlantic Ocean, Ocean Sci., 12, 663–685, https://doi.org/10.5194/os-12-663-2016
Trott, C. B., Subrahmanyam, B., Chaigneau, A., & Delcroix, T. (2018). Eddy tracking in the northwestern Indian Ocean during southwest monsoon regimes. Geophysical Research Letters, 45, 6594–6603. https://doi.org/ 10.1029/2018GL078381
Citation: https://doi.org/10.5194/egusphere-2022-789-AC2 -
CC2: 'Reply on AC2', Francisco Beron-Vera, 26 Sep 2022
'The selection of the detection method depends on the mesoscale features people are interested in and the definition of eddies also varies with the detection methods. ' Objective eddy detection lies in the antipode of this type of thinking. The reason is that all users, independent of their viewpoint, should see the same flow-invariant feature(s). This way the dabate over which eddy detection method is to be employed is constrained to be that one or those that do not depend on the obsever assessment. I include the possibility that there can be more than one observer-independet vortex detection method, e.g., design to frame flow-invariant structures with boundaries that extremize relative stretching or diffusion across or as regions that minimally deform under advection, for which there are several measures. The Authors should take the time to read the Introduction to Focus Issue: Objective Detection of Coherent Structures, Chaos 25, 087201 (2015); https://doi.org/10.1063/1.4928894. This paper should be allowed to be published.
Citation: https://doi.org/10.5194/egusphere-2022-789-CC2 -
CC3: 'Reply on CC2', Francisco Beron-Vera, 26 Sep 2022
Correction: This paper should not be published, I meant to say.
Citation: https://doi.org/10.5194/egusphere-2022-789-CC3 -
CC4: 'Reply on CC3', Xinfeng Liang, 26 Sep 2022
Dear Dr. Beron-Vera,
We appreciate your efforts to clarify the concept of eddies in the oceanographic community. And we agree that if oceanic transport or transport-related questions were the objectives, the elegant way shown in many of your papers is the right choice and should be utilized. However, for this study, we don’t think that is the case. The Eulerian, streamline-based methods are at least OK choices, and our findings are still a useful contribution to the literature.
Please allow me to say a bit about the background of this study, which we did not state in the manuscript. This paper was motivated by a previous study Ying Li and I conducted in the GoM (Zhu and Liang, 2020), in which we explored the connections between surface mesoscale features and deep ocean circulation. The data we used were mainly deep ocean moorings (Eulerian measurements) and satellite data. And we found that mesoscale features (the Eulerian view) could be important in some regions of the GoM in connecting the upper and bottom layers. Note that those mesoscale features could be lagrangian coherent eddies or even large-scale waves. And because of our objectives, which were certainly not transport related, there was no need for us to separate them in that study. And during that study, we found that a compressive study of the characteristics of those mesoscale features in the GoM, like many studies conducted in the open ocean and other regional seas, was lacking. So this following-up study is to fill in the gap about the spatial and temporal patterns of those mesoscale features in the GoM.
Again, if you feel calling those features eddies is misleading (although a large number of studies did that), we could modify the text to make it clearer that we were not talking about lagrangian coherent eddies. We can also explicitly remind the readers that if transport-related topics are what they care about, they should refer to Andrade-Canto et al. (2020) to learn and use the more appropriate methods.
Regards,
Xinfeng Liang
Zhu, Y., & Liang, X. (2020). Coupling of the surface and near-bottom currents in the Gulf of Mexico. Journal of Geophysical Research: Oceans, 125, e2020JC016488. https://doi.org/10.1029/2020JC016488
Citation: https://doi.org/10.5194/egusphere-2022-789-CC4 -
CC5: 'Reply on CC4', Francisco Beron-Vera, 27 Sep 2022
Dear Xinfeng,
You might consider okay that other authors call ''eddy'' a flow region instantaneously filled with closed streamlines of the SSH field such that U/c > 1. But the problem is that when they do that, they are immediately implying consequences for transport. In fact, the U/c > 1 criterion was included by Chelton in an attempt to distinguish between flow-invariant structures of the elliptic type (not in these words, clearly) and anything else (call this linear waves, if you like). You yourself by invoking the U/c > 1 criterion are doing just that. However, as colleagues and I have shown many times over the last decade, U/c > 1is a simple-minded heuristics that in general fails to isolate elliptic Lagrangian coherent structures. In Andrade-Canto et al. (2020) we show, for the case of LCRs, clearly relevant to your work, that Eulerian, streamline-based vortex detection is incapable of distinguishing conception from birth of LCRs. Moreover, they also tend to track past their decease dates vortex-like features unrelated to the LCRs in question. In other cases, material initially inside SSH eddies simply disperse rather quickly after a week or so - cf. references in Andrade-Canto et al. (2020). There you go! You can call your Eulerian coherent structures SSH eddies and omit any reference to advection, or transport, or material, and then the reader will understand the scope of your work or what to expect from it.
Best,
Francisco
Citation: https://doi.org/10.5194/egusphere-2022-789-CC5 -
CC6: 'Reply on CC5', Xinfeng Liang, 27 Sep 2022
Dear Francisco,
Thank you very much for the further clarification and constructive suggestions. We agree it is critically important for us to revise the text to make sure that the readers understand the scope of this study and won’t make incorrect inferences about oceanic transport. We will follow your suggestions to explicitly name those structures described in this paper SSH eddies and to remove references to advection, transport, or materials. Some discussions about the differences between the mesoscale features presented in this study and the Lagrangian coherent structures will be added in the last part of the study as well. We hope this revision plan sounds reasonable to you.
Again, we appreciate your efforts in helping us improve this paper. And we invite you to provide more critical feedback on a revised version of this manuscript in the near future if that becomes possible.
Best,
Xinfeng
Citation: https://doi.org/10.5194/egusphere-2022-789-CC6
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CC6: 'Reply on CC5', Xinfeng Liang, 27 Sep 2022
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CC5: 'Reply on CC4', Francisco Beron-Vera, 27 Sep 2022
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CC4: 'Reply on CC3', Xinfeng Liang, 26 Sep 2022
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CC3: 'Reply on CC2', Francisco Beron-Vera, 26 Sep 2022
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CC2: 'Reply on AC2', Francisco Beron-Vera, 26 Sep 2022
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AC2: 'Reply on CC1', Yingli Zhu, 26 Sep 2022
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RC2: 'Comment on egusphere-2022-789', Anonymous Referee #2, 21 Sep 2022
The manuscript analyzes eddy activity in the Gulf of Mexico by applying three eddy detection algorithms to satellite altimetry data. The authors analyze the characteristics of the eddies, such as dimension, location and date of birth/death, trajectory and temporal variability.
The authors make an effort to provide detailed information between circulation and eddy characteristics. However the methodology used to detect and track eddies I do not believe is adequate. Neither calling their identified eddies as robust.
The reason is because the authors use detection/tracking techniques based on Eulerian algorithms (instantaneous velocities) that are observer-dependent and not on the geometrical properties of the flow. There are papers that show a large discrepancy between Eulerian and Lagrangian detected eddies. For example, the work of Andrade-Canto et. Al, 2020 (https://doi.org/10.1063/5.0030094), where they analyze the birth, evolution and death of loop current eddies by coherent Lagrangian vortex detection. They also show that Eulerian techniques are unable to accurately distinguish the birth, evolution and death of the eddies in question, because they are based on instantaneous velocity fields which makes the detection of an eddy between one time and the subsequent one not in complete agreement.
Furthermore, their criterion for determining which eddies are coherent is based on the condition that the rotational velocity of the eddy exceeds its translational velocity (U/c > 1), a criterion that has been shown to be invalid for defining an eddy as coherent. The work of Beron-Vera et. Al, 2013 (https://doi.org/10.1175/JPO-D-12-0171.1) showed that the Lagrangian evolution of closed SSH contours (all with U/c>1 for at least 90 days) stretch and fold rapidly, exhibiting leakage and filamentation, that discualifies them as coherent eddy boundaries.
In my opinion the manuscript does not present relevant results, much of what the authors present only confirms what has already been said in other studies about eddies in the Gulf of Mexico, simply that the authors use a larger database.
The method that the authors propose as "robust" is not a new method, it is simply the combination of three similar methods.
Therefore, this reviewer recommends not to publish this manuscript.
Citation: https://doi.org/10.5194/egusphere-2022-789-RC2 -
AC3: 'Reply on RC2', Yingli Zhu, 26 Sep 2022
We removed the notion of “robust” in the revised manuscript to eliminate the confusion. Mesoscale eddies were selected by combining three previous eddy detection algorithms so that we had more confidence in the selected eddies than those given just by one algorithm.
As to your concern about the Eulerian method of detecting mesoscale eddies, we give the following explanations. First, the definition of mesoscale eddy in this study is different from coherent Lagrangian vortices, and our focus is not on the coherent Lagrangian vortices. We considered the mesoscale eddies detected with Eulerian methods that may change form and exchange material with background fluid. In addition, we did not consider the coherence of eddies based on the condition that the rotational velocity of the eddy exceeds its translational velocity and U/C was only used to characterize the advective nonlinearity in this study. For those who are interested in the mesoscale features with closed streamlines, the characteristics of eddies detected with the Eulerian methods are still useful. For example, a recent study has used one Eulerian method to examine the eddy surface characteristics and vertical structure in the Gulf of Mexico from 2016-2018 and found distinct mesoscale features in the eddies with closed sea surface height contours (Brokaw et al., 2020).
In addition, we are fully aware of the limitations of different Eulerian eddy detection methods, which we clearly stated in the text. In fact, mitigating those limitations is one of the major motivations of this study and that is why we put a lot of effort to combine different eddy detection algorithms to select eddies. In addition, although eddy detection methods are likely not perfect, they have been widely used and greatly advanced our understanding of the dynamics and impacts of mesoscale eddies over the past few decades. The Eulerian methods of detecting eddies are still under development and used in recent studies. For example, one Eulerian method was still used in the eddy trajectory product released by AVISO (Pegliasco et al., 2021a, 2021b; Pegliasco et al., 2022). Based on Eulerian methods, many eddy characteristics in other oceans and the global ocean were reported in recent studies (e.g., Escudier et al., 2016; Schütte et al., 2016; Keppler et al., 2018; Laxenaire et al., 2018; Pessini et al., 2018; Trott et al., 2018; Mason et al., 2019; Martínez‐Moreno et al., 2019; Chen et al., 2022; Atkins et al., 2022; Evans et al., 2022; López-Álzate et a., 2022). Last but not the least, some of our findings being consistent with previous studies, which you considered as a negative point, actually indicate that our approach works just fine.
Regarding the novelty, we would like to argue that there are two open and important questions examined in this study. The first question is that most previous studies only focus on the Loop Current Eddies (LCEs) and Loop Current Frontal Eddies (LCFEs), while characteristics of other types of mesoscale eddies in the Gulf of Mexico (GoM) have not been comprehensively described. The second question is that the seasonal and low-frequency variability of eddy number and amplitude of all types of eddies in the GoM have not been fully reported. Our study provides useful results to address those two questions.References
Atkins, J., Andrews, O., & Frenger, I. (2022). Quantifying the contribution of ocean mesoscale eddies to low oxygen extreme events. Geophysical Research Letters, 49, e2022GL098672. https://doi.org/10.1029/2022GL098672Brokaw, R. J., Subrahmanyam, B., Trott, C. B., & Chaigneau, A., (2020). Eddy surface characteristics and vertical structure in the Gulf of Mexico from satellite observations and model simulations. Journal of Geophysical Research: Oceans, 125(2), e2019JC015538. https://doi.org/10.1029/2019JC015538.
Chen, G., Chen, X., & Cao, C. (2022). Divergence and Dispersion of Global Eddy Propagation from Satellite Altimetry, Journal of Physical Oceanography, 52(4), 705-722
Escudier, R., B. Mourre, M. Juza, and J. Tintore (2016), Subsurface circulation and mesoscale variability in the Algerian subbasin from altimeterderived eddy trajectories, J. Geophys. Res. Oceans, 121, 6310–6322, doi:10.1002/2016JC011760.
Evans, D.G., Frajka-Williams, E. & Naveira Garabato, A.C. Dissipation of mesoscale eddies at a western boundary via a direct energy cascade. Sci Rep 12, 887 (2022). https://doi.org/10.1038/s41598-022-05002-7
Keppler, L., Cravatte, S., Chaigneau, A., Pegliasco, C., Gourdeau, L., & Singh, A. (2018). Observed characteristics and vertical structure of mesoscale eddies in the southwest tropical Pacific. Journal of Geophysical Research: Oceans, 123, 2731–2756. https://doi. org/10.1002/2017JC013712
Laxenaire, R., Speich, S., Blanke, B., Chaigneau, A., Pegliasco, C., & Stegner, A. (2018). Anticyclonic eddies connecting the western boundaries of Indian and Atlantic Oceans. Journal of Geophysical Research: Oceans, 123, 7651–7677. https://doi.org/10.1029/2018JC014270
López-Álzate, M.E., Sayol, JM., Hernández-Carrasco, I. et al. Mesoscale eddy variability in the Caribbean Sea. Ocean Dynamics (2022). https://doi.org/10.1007/s10236-022-01525-9Martínez‐Moreno, J., Hogg, A. M., Kiss, A. E., Constantinou, N. C., & Morrison, A. K. (2019). Kinetic energy of eddy‐like features from sea surface altimetry. Journal of Advances in Modeling Earth Systems, 11, https://doi.org/10.1029/2019MS001769
Mason, E., Ruiz, S., Bourdalle-Badie, R., Reffray, G., García-Sotillo, M., and Pascual, A., 2019. New insight into 3-D mesoscale eddy properties from CMEMS operational models in the western Mediterranean, Ocean Sci., 15, 1111–1131, https://doi.org/10.5194/os-15-1111-2019
Pegliasco, C., Delepoulle, A., Faugère, Y., 2021a. Mesoscale Eddy Trajectories Atlas Delayed-Time all satellites: version META3.1exp DT allsat. https://doi.org/10.24400/527896/A01-2021.001
Pegliasco, C., Delepoulle, A., Faugère, Y., 2021b. Mesoscale Eddy Trajectories Atlas Delayed-Time two satellites: version META3.1exp DT twosat. https://doi.org/10.24400/527896/A01- 2021.002
Pegliasco, C., Delepoulle, A., Mason, E., Morrow, R., Faugère, Y., Dibarboure, G., 2022. META3.1exp: a new global mesoscale eddy trajectory atlas derived from altimetry. Earth Syst. Sci. Data 14, 1087–1107. https://doi.org/10.5194/essd-14-1087-2022
Pessini, F., Olita, A., Cotroneo, Y., and Perilli, A., 2018. Mesoscale eddies in the Algerian Basin: do they differ as a function of their formation site?, Ocean Sci., 14, 669–688, https://doi.org/10.5194/os-14-669-2018.
Schütte, F., Brandt, P., and Karstensen, J., 2016. Occurrence and characteristics of mesoscale eddies in the tropical northeastern Atlantic Ocean, Ocean Sci., 12, 663–685, https://doi.org/10.5194/os-12-663-2016
Trott, C. B., Subrahmanyam, B., Chaigneau, A., & Delcroix, T. (2018). Eddy tracking in the northwestern Indian Ocean during southwest monsoon regimes. Geophysical Research Letters, 45, 6594–6603. https://doi.org/ 10.1029/2018GL078381
Citation: https://doi.org/10.5194/egusphere-2022-789-AC3 -
CC7: 'Reply on RC2', Xinfeng Liang, 17 Oct 2022
Thank you for your critical comments, particularly on the definition of eddies. As suggested by Dr. Francisco Beron-Vera, which you can find in our exchanges above, we are planning to use a different notation “SSH eddies” in the revised manuscript to distinguish our detected eddies from the Lagrangian coherent eddies. We will also remove references to advection, transport, or materials. By doing so, the readers can better understand the scope of this study and won’t likely make incorrect inferences. In addition, discussions about the differences between the mesoscale features presented in this study and the Lagrangian coherent eddies will be added in the last part of the study. We hope this revision plan can address the concerns you raised and sounds reasonable to you.
Citation: https://doi.org/10.5194/egusphere-2022-789-CC7 -
RC4: 'Reply on CC7', Anonymous Referee #2, 19 Oct 2022
Detecting eddies with Eulerian methods is fine from an Eulerian perspective (assuming that the focus of the work was changed). However, the most interesting part of the work could be the trajectory, birth and death of the eddies, but the nature of the detection method, which is Eulerian, does not guarantee that the new eddy detected is the same one detected an instant before,
and also gives different results in reference frames that move or rotate with respect to each other, as shown in the work of Haller 2005. This leads to determine trajectories with significant uncertainty. Therefore, it is important to re-emphasize Lagrangian methodologies, with which it is possible to objectively determine the trajectory, birth and death of eddies, as shown in the works of Andrade-Canto et. al. 2021, Andrade-Canto et. al. 2022a and Andrade-Canto et. al. 2022b.
Andrade-Canto et. al. 2022b show that the eddy trajectory together with a material ring stretching value indicating the loss of coherence. In the supplementary material an example is presented showing that within the closed SSH contour a hyperbolic point is found together with two elliptic points (or two eddy centers). This indicates that the eddy will separate. Which of the two centers should be followed from the Eulerian perspective?
I consider what underpins some of the main work to be rather weak, especially when it is presented as novel and informative work on eddy life in the Gulf of Mexico. The work of Bello-Fuentes et. al. 2021, previous to this work and that has not been considered, makes a Lagrangian census of the eddies, determining radii, retention times, as well as the preferred regions for cyclones and anticyclones.
In spite of the above, I consider that the information from the Eulerian perspective is important, so this work should not be wasted. The analysis of the seasonality and low frequency variability associated with the increase in vorticity associated with instantaneous eddies is very important information that can be used as a framework for the validation of numerical models, for example. So I strongly suggest that at least this perspective be taken into account.
On the other hand, it seems inappropriate to me that in order for the work to be accepted, a change of approach of such magnitude is required, at least that is the impression suggested in the responses to other comments. However, I appreciate your willingness, although this does not imply that I am willing to accept a second revision. I recognize that it was a hard work with useful information, but I think you should consider the arguments mentioned above, rewrite the paper and resubmit it as another paper.
Bibliography:
Andrade-Canto, F., Karrasch, D., & Beron-Vera, F. J. (2020). Genesis, evolution, and apocalypse of Loop Current rings. Physics of Fluids, 32(11), 116603.
Andrade-Canto, F., Beron-Vera, F. J., Goni, G. J., Karrasch, D., Olascoaga, M. J., & Triñanes, J. (2022). Carriers of Sargassum and mechanism for coastal inundation in the Caribbean Sea. Physics of Fluids, 34(1), 016602.
Andrade‐Canto, F., & Beron‐Vera, F. J. (2022). Do eddies connect the tropical Atlantic Ocean and the Gulf of Mexico?. Geophysical Research Letters, e2022GL099637.
José Bello-Fuentes, F., García-Nava, H., Andrade-Canto, F., Durazo, R., Castro, R., & Yarbuh, I. (2021). Retention time and transport potential of eddies in the northwestern Gulf of Mexico. Ciencias Marinas, 47(2).
Haller, G. (2005). An objective definition of a vortex. Journal of fluid mechanics, 525, 1-26.
Citation: https://doi.org/10.5194/egusphere-2022-789-RC4 -
CC8: 'Reply on RC4', Xinfeng Liang, 20 Oct 2022
Thank you very much for the prompt and helpful comments. We agree that the trajectory, birth, and death of the eddies presented in this study will likely differ from the results based on the Lagrangian approaches. In other words, unlike the Lagrangian coherent eddies, the Eulerian eddies are not likely the same eddies from birth to death but a series of perturbations that are related. Clearly, the meaning of our results depends on the interpretation of those "eddies." In this study, as mentioned above, we interpret the "SSH/Eulerian eddies" as perturbations or "waves", which reflect the generation, propagation, and dissipation of those related signals rather than coherent mass. We would like to state explicitly in the paper the differences between Eulerian eddies and Lagrangian coherent eddies. This can actually serve as a good opportunity to remind the oceanography community of the issues of Eulerian methods, such as what they are good for, and what they are not.
As you kindly pointed out, there is much useful information in this paper. And we aim to present that information in a more accurate way in a revised manuscript. A similar study based on the Lagrangian approaches presented in Andrade-Canto et. al. 2021, Andrade-Canto et. al. 2022a and Andrade-Canto et. al. 2022b is certainly important and could be done. But due to the tremendous effects needed for that, we prefer to conduct that as a follow-up study in the near future. And the comparison between Eulerian and Lagrangian results could be interesting.
Citation: https://doi.org/10.5194/egusphere-2022-789-CC8 -
AC5: 'Reply on RC4', Yingli Zhu, 27 Oct 2022
Thank you very much for the prompt and helpful comments. We agree that the trajectory, birth, and death of the eddies presented in this study will likely differ from the results based on the Lagrangian approaches. In other words, unlike the Lagrangian coherent eddies, the Eulerian eddies are not likely the same eddies from birth to death but a series of perturbations that are related. Clearly, the meaning of our results depends on the interpretation of those "eddies." In this study, as mentioned above, we interpret the "SSH/Eulerian eddies" as perturbations or "waves", which reflect the generation, propagation, and dissipation of those related signals rather than coherent mass. We would like to state explicitly in the paper the differences between Eulerian eddies and Lagrangian coherent eddies. This can actually serve as a good opportunity to remind the oceanography community of the issues of Eulerian methods, such as what they are good for, and what they are not.
As you kindly pointed out, there is much useful information in this paper. And we aim to present that information in a more accurate way in a revised manuscript. A similar study based on the Lagrangian approaches presented in Andrade-Canto et. al. 2021, Andrade-Canto et. al. 2022a and Andrade-Canto et. al. 2022b is certainly important and could be done. But due to the tremendous effects needed for that, we prefer to conduct that as a follow-up study in the near future. And the comparison between Eulerian and Lagrangian results could be interesting.
Citation: https://doi.org/10.5194/egusphere-2022-789-AC5
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CC8: 'Reply on RC4', Xinfeng Liang, 20 Oct 2022
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RC4: 'Reply on CC7', Anonymous Referee #2, 19 Oct 2022
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AC3: 'Reply on RC2', Yingli Zhu, 26 Sep 2022
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