Bold text show the authors comments on this review.

The authors would like to thank Tim Smith for their second detailed and helpful review of this manuscript. Advice from all comments has been incorporated into the updated manuscript.

Main summary and recommendation

This study uses the MITgcm and its adjoint modeling capabilities to study the processes that lead to mode water formation in the South Pacific. The authors use adjoint-based sensitivities together with surface flux anomalies to isolate and quantify the impact on mode water formation resulting from surface heat, wind stress, and freshwater flux sources. It is shown that heat fluxes dominate, followed by zonal wind stresses, where impacts typically follow forcing at <1 and ~1.5 year lead times, corroborating previous work. Notably, the work relies on a density based objective function which allows the model to more accurately track mode water pools than previous depth based approaches. Nonlinear forward model perturbation experiments are used to further probe the evolution of heating and cooling.

The paper is well organized and while I have more of a background relevant to the modeling aspects of this paper rather than one relevant to the South Pacific mode water conclusions, I think the study is well motivated and provides useful conclusions to the community. Additionally, I want to additionally congratulate the authors on contributing the density objective function capabilities to the MITgcm code base - this is a highly technical effort which will help to advance the community.

I have reviewed a prior version of this work, and most of my major comments during that review have been addressed. I am therefore recommending minor revisions at this point, given that I only have 1-2 substantive comments at this point.

-Tim Smith 

Conceptual Comments

• Section 3.1: I totally agree that it is useful to use “impacts” as a way to quantify the sources of variability in SAMW mode water formation (or any other quantity of interest). However, I’m not used to looking at these quantities, so it’s hard for me to understand the scales of each of these impact plots (e.g. Figure 3). For example, within the first year local surface heat fluxes generate ~4x10^12 m^3 of SAMW mode water formation. Is this a lot? How does this compare to the seasonal cycle or recent amplitudes of interannual variability? If it’s possible to provide any context for these numbers, that would be very helpful. – Extra information has been added on how to interpret these impacts in the first 3 paragraphs of Section 3.1. The interannual and seasonal variability of both pools are of the same order of magnitude as the impacts, showing that heat flux is very important in the formation of each mode water pool.
• Figure 4: I’m still not totally following the interpretation of these plots. Are these generated by accumulating in time from lead_time to 0? Or by simply looking at the “snapshot” of (sensitivity_at_lead_time) * (anomaly_at_lead_time)? Some clarification (or pointing me to the description, in case I missed it) would be very helpful here. – Line 267, winter 14-day snapshot of impact.

Small grammatical comments – All these grammatical changes have been completed, thank you.

• Line 34: At this point in the text there has been no mention of or build up to the use of adjoints, so it feels like it comes out of nowhere. I would recommend moving it to line 65
• Line 163: fromt he -> from the
• Line 164: aand -> and
• Line 272: “both regions local and upstream regions” -> “both local and upstream region

Bold text show the authors comments on this review.

The authors would like to the thank David Marshall for their insightful and helpful review of the manuscript. All comments have been considered and the manuscript has been updated to reflect them.

I enjoyed reading this manuscript. The authors present a series of adjoint sensitivity calculations with the MITgcm to reveal how the volume of Subantarctic mode water is sensitive to remote buoyancy forcing. The surprising conclusion is that the optimal conditions for Subantarctic mode water formation consist of a cooling-heating dipole pattern. This is an interesting result that should be of wide interest. The manuscript is mostly well written and presented, and I therefore happy to recommend it for publication after relatively minor revisions. 

Specific points: 

1. Advection of anomalies: In a number of places it is suggested that density anomalies are "advected" (e.g., line 9 of the abstract). While I suspect that advection is dominating the propagation, I am less sure that this has been firmly established and certainly the language should be tightened. In general, density anomalies propagate at the relevant wave speed, which may or may not be dominated by advection. In contrast, the propagation of water mass properties (T-S anomalies on the density surface) and potential vorticity (closely related to the layer thickness in practice) should be dominated by advection. My advice is to carefully check the manuscript to ensure that what is written is accurate when discussing advection, i.e, take care to focus on potential vorticity/layer thickness anomalies rather than density anomalies. – Text has been edited in multiple places to reflect this helpful comment. Now layer thickness is mentioned with reference to advection rather than density.
2. Review of the adjoint method: I was surprised to find the only references in section 2.1 are to papers written by the authors of the present study. While they have made a valuable contribution through the inclusion of a density following feature in the MITgcm adjoint, they are nevertheless building on the shoulders of others who have developed the adjoint machinery within the MITgcm over the past three decades - I think it is fitting and appropriate to give proper acknowledgment to these efforts here. The authors are well aware of this literature. – Thank you for this comment, there has been more information added on the development of adjoint machinery with lots of updated references in the Introduction.
3. Definition of density surfaces: I missed any statement of the definition of the density surfaces following equation (3) and indeed throughout most of the manuscript (an exception being the caption to Figure 6). The authors need to state whether they are using neutral density, potential density (referenced to which depth), or something else. – We are using neutral density. The text has been updated in multiple places to reflect this.

Minor points: 

• Line 374: "The adjoint sensitivities are linear due to how the partial derivatives are calculated in the model."  This doesn't really make sense - the sensitivities are linear because you have only retained the first derivatives, not because of the way in which the partial derivatives have been calculated. – The text has been changed to reflect this.
• Figure 1: The sub-panels are fine to interpret when zoomed in on the screen, but extremely small when viewed at A4 size. I wonder if it you might remove the x- and y-axis labels on all but one of the panels, enabling each panel to be enlarged? Also the labels are in a smaller font than in the remainder of the figures and could be enlarged to help the reader. 
• Figure 2: The blue and magenta contour labels are overlapping.  It might be better to turn these off the labels for one of the contours since the perturbations are modest. – This has been corrected, the labels are now only shown for one line colour.

Typographical issues: 

• In the caption to Figure 1, Antarctic Circumpolar Current should be capitalised (and there is a space missing in the third line of the caption). I also noticed that the full name is used three times in the Introduction before the acronym ACC is introduced (and there is a further space missing in line 24). – ACC acronym has been better defined and used now.
• General comment: I spotted a small number of minor mis-spellings, so it would be wise to subject the manuscript to a careful spell check. – Spell check has been completed.

Bold text show the authors comments on this review.

The authors would like to thank the editor for their thorough review of the manuscript. All the suggested text changes have been completed.

In light of the other two referees comments and my reading, I would suggest the authors make a revision incorporating all the comments (mine are given below but I most focused on the writing; some of it overlaps with some referee comments). Given the nature of the comments I think I can make the call on the paper when the revision comes through. 

A few extra comments are given here in reference to a few more detailed comments:

* line 34-35: floating sentence? Adjoint hasn't been introduced and reads out of place in my opinion. Probably fits better down near line 65, and brings it closer to the outline, supports that sentence content a bit more. – moved to appropriate section, as in Tim Smith review.

* somewhere in 2.1 to raise it now, and/or in the conclusion for comparison/outlook: might want to talk about why SOSE was not used (and add related references), presumably because then the non-local contributions would be defined differently (but similar calculations can in principle be performed with SOSE right?) – paragraph added to discussion section

* line 436: "Lines 2 and 3 of the code checkS if..." – I have rewritten parts of this appendix to be more consistent and follow this advice.

* bibliography: the Campin et al references have non-standard author names in them, please consider fixing (it's referencing the github usernames, not sure how to fix that automatically though...) – This is the only way that zenodo outputs this reference. I checked the github accounts associated with the non-standard names and they do not list their full name anywhere, so it is too hard to determine who definitely owns the specific github accounts. Therefore, I have left the MITgcm version references to be the same as the previous submission.

* do acknowledge the referees comments etc. if the authors feel they were helpful – Reviewers are now thanked in the acknowledgements section.