Review of “Seasonality of meridional overturning in the subpolar North Atlantic: implications for relying on the streamfunction maximum as a metric of AMOC slowdown” by Fox et al.

The manuscript presents an interesting analysis of the relationships between different metrics of the meridional overturning circulation at seasonal timescale, and discusses their drivers using diverse decompositions of the overturning streamfunctions. The main conclusion of the manuscript is that each metric responds to different physical processes, with the maximum of the overturning streamfunction (MOC) being dominated by Ekman transports and surface density. As such, it would be valuable to routinely use the other metrics (i.e., density, heat and freshwater fluxes) in addition to the MOC when studying the overturning variability at this timescale.

The study provides a valuable evaluation of the different metrics that have been used to study the overturning variability. It is well-written, and the results are interesting and timely. However, it currently suffers from shortcomings that cast doubt on some of the results obtained, as indicated in the main comments below. I hope the authors find my comments and suggestions useful when revising the manuscript. 

Major Comments

1) I find the discussion of the processes involved in each metric a bit hasty. I agree that the decomposition of the overturning streamfunction support the main conclusions of the study, but the authors repeatedly associate these processes to specific mechanisms and locations over the subpolar gyre without providing figures or references to support these statements. For example, lines 230-236, it is not clear how the dipole shown in Figure 6d can be interpreted as an underestimation of seasonal cycles in the North Atlantic Current and Labrador Current outflow? Again, lines 254-255, it is not clear how Figure 7 shows that the temperature-driven MOC anomalies are dominated by variability in the southward western boundaries rather than at another location along the section (e.g., interior pathways?). The comment applies to the seasonal cycle of the metrics at OSNAP East and OSNAP West individually (e.g., lines 261-262, lines 279-282 or lines 350-353).

The authors should develop these arguments and walk the reader through these interpretations of the results or show convincing figures to support these results (e.g., similar to Figure 14).

2) One of the conclusions of the paper (line 506, also in the title) is misleading and should be rephrased: an AMOC slowdown would be identified on longer timescales than seasonal, so it is not clear to me how the MOC or any other metrics at seasonal timescale could miss or help to detect an overturning slowdown.

3) Can the authors comment on the significance of the relationships shown between the metrics? It can shed light on the differences noted between the 6-year and 20-year simulated timeseries.  

Specific Comments

Lines 25-29: In addition to theoretical models, ocean models and state estimates, the use of coupled models also helped to better understand feedback mechanisms between ocean and atmosphere. I encourage the author to discuss Swingedouw et al. (2007) for an overview of the AMOC feedback mechanisms.

Line 53: What is meant by “In a wider, ocean conveyor belt, sense”? We moved from this view of the overturning circulation from Lozier et al. (2010), can you clarify?

Lines 67-71: The introduction of density flux needs a little more explanation to discuss its differences with the MOC metric. Related to this comment, can the authors justify more clearly in the introduction why looking at these specific metrics to represent the AMOC in density space instead of other ones that are also commonly used to measure the North Atlantic Ocean (e.g., NAO, subpolar gyre index, surface forced water mass transformation)?

Lines 80-87: I encourage the authors to better introduce the data used in the study. The horizontal and vertical resolutions of the data are a minimum. They should also indicate the forcings used at the boundary for the model, whether they are using monthly outputs, and comment on the representation of the simulated North Atlantic subpolar gyre as compared to observations.

Lines 85-86: I also encourage the authors to add a map showing the locations of the OSNAP East and OSNAP West sections in the observations and/or the extracted sections in the model.

Equations (9) and (13): As I understand it, these 2 metrics are not used in the study and can be removed.

Line 136: The “maximum” should be replaced by “extrema” considering that MOC_S is estimated as a minimum of the overturning streamfunction in salinity space.

Line 140: The equations in this section are clearly explained but I would recommend clarifying with a sentence at the beginning of section 2.3 what are main goals by looking at these decompositions of the overturning streamfunction.

Line 142: There is a missing “following” before “Mercier et al. (2024)”.

Line 152: Please indicate in the text that the RHS are “velocity” integrals.

Line 162: Can the authors indicate the time period over which the mean of salinity and temperature are estimated? In particular, is it the same climatology used when discussing the 20-year or 6-year model results?

Lines 245-246: If I am correct, the salinity-driven anomalies are expressed in MOC because its peak in density is close to sigma_moc. I suggest the author to comment on this aspect for clarity.

Line 192: There is a missing “difference” after “most noticeable”.

Line 334: Consider indicating that the competition is won by the southward flow “in spring”.

Line 336: I am confused by this statement. It is not clear to me why the seasonal cycle of sigma_moc depth is related to MOC at seasonal timescale, or where it was shown in the study. Please justify whether these 2 timeseries co-vary in the model at this timescale. Considering the importance of Ekman forcing on the MOC variability, would you say that the sigma_moc variability is also mainly driven by this surface forcing?

Line 345: I think it is Fig. 15 instead of Fig. 13.

Line 372: There is an extra “is” in “the property variability term also plays a role”.

Lines 375-378: Related to my first main comment, I am not sure to understand the argument here. Can the authors justify why “the largest seasonal salinity variability is confined to the southward flow at the western boundaries”?

Line 398: I am not sure that “simple” is the right term to use here. It is not more difficult to estimate the MOC, both MOC and density flux being based on overturning streamfunction.

Lines 401-404: I am not sure to understand why the NAC would be included in the density flux but not in the MOC metric? Please clarify.

Lines 423-425: The sentence doesn’t read well, please rephrase.

Lines 459-462: Related to my main comment above, it would be interesting to see a map of the sigma_moc location over the Irminger Sea and its variability to support this statement.

Lines 486-487: Can the author comment on how the barotropic compensation transport is applied “crudely” in the observations? It would be interesting to discuss what can be done to improve it.

References

Swingedouw, D., Braconnot, P., Delecluse, P. et al. Quantifying the AMOC feedbacks during a 2×CO2 stabilization experiment with land-ice melting. Clim Dyn 29, 521–534 (2007). https://doi.org/10.1007/s00382-007-0250-0

M. Susan Lozier. Deconstructing the Conveyor Belt. Science, 328 (2010). DOI: 10.1126/science.1189250

This is a very well written paper that will be of great interest to those working on the Atlantic overturning circulation.  Research on Atlantic circulation has a strong focus on the MOC metric, that has enabled major advances in our understanding and capability to measure the overturning circulation and meridional transports, but this paper is a timely and important reminder of the importance of other metrics. 

There is a lot of information in the paper and many of the 17 figures have multiple panels.  Whilst I do not recommend shortening or removing any of the figures, I would discourage lengthening or adding figures during revision.

I have only a few minor comments:

1. Following equation 5, I think it is correct to ignore the first term, but I am not sure the sentence following the equation explains why (numerically the first term is large, the net transport is small, but sigma_max is large compared to sigma_max minus sigma_min). Observational estimates of the overturning circulation usually impose that the net volume transport is zero, this is partly pragmatic (it would be very difficult to measure) but also because the net transport has little impact on the divergence of heat and freshwater (atleast on long timescales).  Maybe it would be better just to remove the net transport from the model the same way it is done with observations?
2. Does equation 1 give the correct sign for the MOC? dz/dsigma is negative, and for densities between sigma_min and sigma_moc the meridional velocity, v, is positive and so integrating up form sigma_min (i.e. dsigma positive) would make the MOC negative.   Perhaps the limits on the second integral need to be swapped (similarly for equation 11)
3. In equation (15), and elsewhere, z_sigma(0) looks odd because sigma is never 0. Would it not be better to replace "z_sigma(0)" with "0"?