Summary

Using a newly developed wave flux diagnostic as a tool, the authors examine the genesis of the eastern equatorial Atlantic warming in 2019. The model allows analyzing the contributions of individual baroclinic modes, and the authors examine the first four of those. They find that the 3rd and 4th modes have substantial contributions to the warming and that these modes are locally forced. Prior those higher modes, there is a 2nd mode Rossby wave that appears to be excited in the off-equatorial region and reflected into a Kelvin wave at the western boundary. The authors suggest that this 2nd mode Kelvin wave helped to precondition the event.

The authors show some interesting results and I believe the diagnostic tool could be useful for obtaining a deeper understanding of equatorial Atlantic variability. It is less clear, however, how useful this diagnostic tool is for prediction purposes and for quantifying individual contributions. Furthermore, the English in the manuscript could use some editing. Detailed comments follow.

Major Comments

1) Figure 8 shows some good evidence for Kelvin wave propagation. For the Rossby waves, however, there is little agreement with the theoretical phase speed and, in fact, the data shows little evidence for any westward propagation. Does this mean that the Kelvin waves are mostly transmitted into coastally trapped waves at the eastern boundary? Do you have a way of quantifying the relative amounts of reflected and transmitted energy?

2) How well do the Kelvin waves correspond to the surface wind stress forcing in terms of location and timing? Is there a proportionality between the strength of the equatorial wind stress anomalies and the excited wave energy? This could also help to further clarify the relative contributions from off-equatorial and equatorial waves.

3) The 3rd and 4th modes seem to make a strong contribution to the equatorial Atlantic warm event. Since these waves seems to be excited locally, they offer very little predictive potential. Does this diminish the prospect of predicting similar events? Can you estimate the relative contributions from the 2nd (reflected) mode and the 3rd and 4th modes?

4) The potential negative interference of baroclinic modes is an interesting argument. It would be interesting to examine this in more detail and to show how important this effect is and if it is a systematic feature. Previous studies have shown that similar (average) equatorial Atlantic wind forcing can have different outcomes in terms of the ATL3 SST (Richter et al. 2013; Martin-Rey et al. 2019). Could this be explained by wave interference? This also connects to the inconsistent influence of ENSO on the equatorial Atlantic (Chang et al. 2006).

5) How do your results compare with those of Richter et al. (2022) who specifically examined the genesis of the 2019 event?

6) In Fig. 9, modes 3 and 4 seem to be maximum at the 0-meridian in late fall/early winter. This is the eastern edge of the ATL3 region and so it is not clear how important these two modes are for the equatorial warm event. Does the strong amplitude at this longitude indicate that the waves pass through to the eastern boundary? Is there evidence that they are transmitted into coastally trapped waves?

7) In Fig. 9b, the authors stress the S1 peak in September and how it is followed by an opposite signed peak in S2. This, however, is only a secondary peak. A much stronger peak occurs in late June. How do they authors explain that this peak is not followed by a peak in S2?

Minor Comments

1) l. 14: Please provide some references for the Atlantic Niño phenomenon.

2) ll. 16-19: I believe Rodriguez-Fonseca et al. (2009) is an important paper for the influence of the Atlantic Niño on ENSO and should be referenced here.

3) Do you use realistic bottom topography to obtain Hb (depth of ocean bottom)?

4) In the methods section you say that you use long-term climatological temperature and salinity distributions to calculate the modes. Would your results change much if you used the actual temperature and salinity from 2019?

5) There are many places were editing the English would improve the readability of the manuscript. A few examples are listed below:

1. a) l. 41: “in addition to involve in-situ and altimetric data”

The meaning is not clear. Maybe “in addition to including in-situ and altimetric data” was meant?

1. b) ll. 41-42: “The implementation of ocean linear model in those proposals are necessary”

Maybe “This will require the use of linear ocean models” was meant?

1. c) l. 97: “Then though Eq. (5)” -. Then, through Eq. (5),”
2. d) ll. 97-98: “pressure flux is redirected to the direction of the group velocity”

I am not quite sure I follow this. Please rephrase.

1. e) l. 99: “are hence able to be detected” -> “can therefore be detected”
2. f) ll. 126-127: “It may suggest that mixed RWs in the nature of cross equatorial meridional velocity are raised by subseasonal forcing.”

“in the nature of”: perhaps “in the form of” was meant?

“raised by” -> “excited by”

References

Chang, P., Fang, Y., Saravanan, R. et al. The cause of the fragile relationship between the Pacific El Niño and the Atlantic Niño. Nature 443, 324–328 (2006). https://doi.org/10.1038/nature05053

Martín-Rey, M., Polo, I., Rodríguez-Fonseca, B., Lazar, A., & Losada, T. (2019). Ocean dynamics shapes the structure and timing of Atlantic Equatorial Modes. Journal of Geophysical Research: Oceans, 124, 7529– 7544. https://doi.org/10.1029/2019JC015030

Richter, I., Behera, S. K., Masumoto, Y., Taguchi, B., Sasaki, H., & Yamagata, T. (2013). Multiple causes of interannual sea surface temperature variability in the equatorial Atlantic Ocean. Nature Geoscience, 6, 43– 47.

Rodríguez-Fonseca, B., Polo, I., García-Serrano, J., Losada, T., Mohino, E., Mechoso, C. R., and Kucharski, F. (2009), Are Atlantic Niños enhancing Pacific ENSO events in recent decades? Geophys. Res. Lett., 36, L20705, doi:10.1029/2009GL040048.

 General comments:

In their study „Equatorial wave diagnosis for the Atlantic Nino in 2019 with an ocean reanalysis“, the authors use output from the CMEMS GLORYS12V1 reanalysis product to which they apply a wave energy flux scheme to study equatorial wave propagation during the 2019 Atlantic Nino event. The authors find that both equatorial Kelvin waves (locally forced) and off-equatorial Rossby waves (reflecting into equatorial Kelvin waves at the western boundary) contributed to triggering the Atlantic Nino in late 2019. Their diagnostic tool allows for modal decomposition showing that third and fourth baroclinic mode Kelvin waves are locally forced, while the second baroclinic mode Kelvin wave was remotely forced by off-equatorial Rossby waves. The authors suggest to apply this wave energy flux scheme to real-time data in order to better predict Atlantic Nino events.

This study examines an important research topic and advocate (rightfully) that a more skillful prediction of extreme events like the 2019 Atlantic Ninos is needed. The results are interesting and potentially helpful for a better understanding of which waves are at play during Atlantic Nino. However, several questions remain. Most importantly, the study is missing a validation of the reanalysis product with observations. Further, even though the authors motivate their study with the need for a better prediction of Atlantic Nino, it remains unclear how the presented study might be helpful in doing so. Lastly, a more thorough discussion with recent studies would be helpful to highlight the new findings of this study.

I am listing my comments and suggestions below. Based on these, I recommend major revisions of the manuscript before publication.

Major comments:

• A potential weakness of the presented analysis is the use of reanalysis data on the equator without providing any validation with observations. Most ocean reanalysis products have been found to underestimate observed velocity variability on the equator (see e.g., Tuchen et al., 2022a). How is GLORYS12V1 handling this issue? A comparison of equatorial velocity from GLORYS12V1 with observations from PIRATA buoys would be a meaningful assessment of the reanalysis’ capability of reproducing realistic velocity signals in the tropical Atlantic Ocean. Potential data sets of velocity are provided at 0°, 23°W (Tuchen et al., 2022b), at 0°, 10°W (Brandt et al., 2021) or at 4°N, 23°W (Perez et al., 2019). Additional, but possibly shorter, timeseries are available at other PIRATA sites: https://www.pmel.noaa.gov/tao/drupal/disdel/.
• Lines 153-165: The comparison between theoretical Kelvin wave and Rossby wave propagation with the observed AGC flux (Fig. 8) is not very convincing. There is hardly any westward propagation visible in all four modes that would fit to theoretical Rossby wave propagation. There is better evidence for Kelvin wave propagation, but I think the authors have to clearly address and discuss this shortcoming which is not done in this paragraph.
• The authors motivate their study by mentioning an “early warning system” that is needed for a better prediction of such extreme warm events. It would be meaningful if the authors pick up this motivation and further evaluate and discuss how their study is helping to achieve this goal. What is the potential on more skillful predictability of Atlantic Nino events when using the AGC scheme and real-time data or reanalysis output?

Minor points:

• Analogously to velocity (major comment 1), how do estimates of vertical N profiles compare to observations? Errors in N would directly propagate into errors of gravity wave speed and y(n).
• Several sentences are hard to follow and require revision and rephrasing. Some of these sentences are mentioned in the specific comments, but I encourage the authors to carefully go through the manuscript again and to clarify those statements.
• A number of important statements and sentences are missing references. For some of these statements the authors provide no references at all, while some require additional references or the correct references (see below for more detailed comments). This will help to better outline the new insights from this study by clarifying which statements are based on previous studies and which are based on the authors’ new results.
• Figure 6b: I find this a nice figure. It nicely shows where off-equatorial Rossby waves are excited that will then reflect at the western boundary into equatorial Kelvin waves. However, I am wondering if these figures would look different if considering seasonally averaged anomalies instead of annually averaged climatologies (Fig. 6) and anomalies (Fig. 7)? This could potentially better highlight the dynamics of the 2019 Atlantic Nino event in Fig. 7.
• Figure 9: If there is local forcing of the third and fourth mode between 20°W and 0° in the ATL3 region, it would be interesting to examine where exactly these modes are excited. Could the authors examine the spatial origin of these modes and discuss what is forcing them?

Technical corrections and minor comments:

• Line 3: “grid point” instead of “grid”.
• Line 9: “locally” instead of “local”.
• Lines 13-14: Atlantic Nino is associated with positive SST anomalies, while Atlantic Nina is associated with negative SST anomalies. Here, it should be made clear that only positive SST anomalies are referred to Atlantic Nino events (as part of the Atlantic zonal mode with its negative and positive phases).
• Lines 14-16: There are several mechanisms that can trigger Atlantic Nino events (Luebbecke et al., 2018; Valles-Casanova et al., 2020) with the Bjerknes feedback being of one them.
• Line 15: “eastern” instead of “east”.
• Line 20: I believe Prigent et al. (2020) is the correct reference here, instead of Crespo et al. (2022), for showing the reduction of interannual SST variability since 2000. The study of Crespo et al. (2022) focuses on projected changes of Atlantic Nino variability in CMIP6 models.
• Line 27: What exactly do the authors mean by “warning system”?
• Line 30: Remove “in” before “(Richter et al., 2022)”.
• Lines 31-32: Please add a reference for this statement.
• Lines 37-38: What do the authors mean with vertical wave energy transfer that takes one month to reach the surface? Wind-forced KWs/RWs are excited at the surface and would transfer energy downward. Are the authors implying a wave forcing mechanism in the deep ocean?
• Line 39: “an” instead of “a”.
• Line 44: “scheme” instead of “schemes”.
• Line 45: “is” instead of “are”.
• Line 80: Following the authors’ notation, would it not be consequent to also denote the sea level anomaly with a prime? h’ instead of h?
• Line 81: “sides” instead of “side”.
• Line 94: “an offset term” instead of “a offset term”.
• Line 97: Do the authors mean “through” instead of “though”?
• Lines 101-103: A reference like Cane & Moore (1981) or Brandt et al. (2016) is needed here.
• Lines 103-105: This sentence is hard to understand and needs rephrasing.
• Line 109: “includes” instead of “include”.
• Line 109: What is meant here with instability waves?
• Lines 109-121: The results on climatological geopotential in Figure 3 are hardly described at all in this paragraph. A more detailed description of the results would be helpful.
• Lines 113-115, lines 118-121: Again, these sentences are hard to follow. Please rephrase.
• Line 122: What is meant here with “features”? It would help to be more precise and to avoid such terms.
• Line 123: “are” instead of “is”.
• Line 124: Better “deepening” than “drop”.
• Lines 124-127, lines 133-134: Meridional velocity seems very noisy and at very low levels (0.8 cm/s). I don’t understand how the authors see/conclude sign-alternating behavior along the equator? The conclusion of mixed Rossby-Gravity waves in this discussion is rather speculative and not really based on the presented results. Either the authors should provide clearer evidence or consider removing this part.
• Line 127: Gravity waves instead of inertial waves on the equator?
• Line 129: Add a bracket after “see Figure 5”.
• Line 141: Please be more precise. Where do the authors see strong eastward energy flux in Fig. 6a? It is north and south of the equator in the western basin and to a lesser degree on the equator in the eastern basin.
• Line 161: Remove one “the”.
• Lines 161-162: “likely eliminates” instead of “is likely eliminate”.
• Line 162: “occurrence” instead of “occur”.
• Line 176: “locally” instead of “local”.
• Lines 180-181: I don’t understand why the authors say that the westward energy flux at S1 for the second mode peaks in September? Figure 9b shows maximum westward energy flux at S1 in January, February and June?
• Line 186: “recently” instead of “recent”.
• Lines 188-190: Figure 4 shows that BCM4 is fairly low and close to zero during the 2019 Atlantic Nino event?
• Line 192: “propagation” instead of “travelling”.
• Line 195: Figure 6a does not show such a pronounced westward energy flux as Figure 6b. How do the authors conclude that both modes are affecting westward Rossby waves?
• Line 199: “demonstrate” instead of “demonstrated”.
• Lines 199-202: Another sentence that is very hard to follow. Please rephrase.
• Line 202: “research” instead of “researches”.
• Line 213: This statement requires a reference. Which study concludes that equatorial waves provide great potential to predict Atlantic Ninos?
• Figure 2 caption: Remove one “by” in the second line.
• Figure 4: Please add a label to the y axis. 

References

• Brandt, P., Claus, M., Greatbatch, R. J., Kopte, R., Toole, J. M., Johns, W. E., & Böning, C. W. (2016), Annual and Semiannual Cycle of Equatorial Atlantic Circulation Associated with Basin-Mode Resonance. Journal of Physical Oceanography, 46, 3011-3029, https://doi.org/10.1175/JPO-D-15-0248.1
• Brandt, P., Hahn, J., Schmidtko, S., Tuchen, F. P., Kopte, R., Kiko, R., Bourlès, B., Czeschel, R., & Dengler, M. (2021), Atlantic Equatorial Undercurrent intensification counteracts warming-induced deoxygenation. Nature Geoscience, 14, 278-282, https://doi.org/10.1038/s41561-021-00716-1
• Cane, M. A., and D. W. Moore (1981), A Note on Low-Frequency Equatorial Basin Modes. Journal of Physical Oceanography, 11, 1578-1584, https://doi.org/10.1175/1520-0485(1981)011,1578:ANOLFE.2.0.CO;2
• Lübbecke, J. F., Rodríguez-Fonseca, B., Richter, I., Martín-Rey, M., Losada, T., Polo, I., & Keenlyside, N. S. (2018), Equatorial Atlantic variability – modes, mechanisms, and global teleconnections. WIREs Climate Change, 9:e527. https://doi.org/10.1002/wcc.527
• Perez, R. C., Foltz, G. R., Lumpkin, R., & Schmid, C. (2019), Direct Measurements of Upper Ocean Horizontal Velocity and Vertical Shear in the Tropical North Atlantic at 4°N, 23°W. Journal of Geophysical Research: Oceans, 124, 4133-4151. https://doi.org/10.1029/2019JC015064
• Prigent, A., Lübbecke, J., Bayr, T., Latif, M. & Wengel, C. (2020), Weakened SST variability in the tropical Atlantic Ocean since 2000. Climate Dynamics, 54, 2731–2744. https://doi.org/10.1007/s00382-020-05138-0
• Tuchen, F. P., Perez, R. C., Foltz, G. R., Brandt, P., & Lumpkin, R. (2022a), Multidecadal Intensification of Atlantic Tropical Instability Waves. Geophysical Research Letters, 49, e2022GL101073. https://doi.org/10.1029/2022GL101073
• Tuchen, F. P., Brandt, P., Hahn, J., Hummels, R., Krahmann, G., Bourlès, B., & Coauthors (2022b), Two Decades of Full-Depth Current Velocity Observations From a Moored Observatory in the Central Equatorial Atlantic at 0°N, 23°W. Frontiers in Marine Science, 9:910979. https://doi.org/10.3389/fmars.2022.910979
• Vallès-Casanova, I., Lee, S.-K., Foltz, G. R., & Pelegrí, J. L. (2020), On the spatiotemporal diversity of Atlantic Niño and associated rainfall variability over West Africa and South America. Geophysical Research Letters, 47, e2020GL087108. https://doi.org/10.1029/2020GL087108