This manuscript aims to explore historical variability of Labrador Sea Water volume and the processes that drive that variability. The authors use the ECCO state estimate and its adjoint, in combination with an objective function to reconstruct and attribute variability. Although in the discussion the authors indicate the study has multiple limitations based around the assumption their approach makes, the authors show that the volume of LSW accumulated in the Labrador Sea exhibits a delayed response to surface wind stress and buoyancy forcing outside the convective interior of the Labrador Sea (e.g. the NAC). They use this response to predict a fraction of the LSW variability a year in advance. They also suggest that all of wind stress, freshwater fluxes, and heat fluxes make contributions of comparable magnitude to LSW volume anomalies, rather than wintertime cooling being the dominant driver.

Given the importance of the Labrador Sea and its deep water formation, looking at drivers of its variability is important. The new results, if robust, will help us understand past changes in the Labrador Sea, as well as its future evolution. The paper is also generally well written, with good quality figures. Thus, the work is eventually worth publishing. Before then, I do have some concerns about the authors approaches and assumption that need to be addressed before it can be published. I also think the background literature needs to be improved and the work better sited in what we already know about the Labrador Sea. Thus. I would recommend major revisions.

The introduction feels short and underwhelming for such a full length manuscript. There is less than a page of general material before the authors begin to delve into their own approach and plans for the manuscript. I would like to see more background on the Labrador Sea and LSW formation. What do we know about the processes that drive its formation and variability to help put the author’s work in context. Especially important is a well-developed literature over the past ~20 years looking at processes that drive LSW formation, from idealized models, to water mass transformation approaches, to numerical models. Many of these studies have looked at the role of winds, the buoyancy forcing (including separating the two components – the heat and freshwater forcing) – yet I don’t see a single reference to any such studies. And although the authors focus is on air-sea forcing, lateral exchange from the boundary currents to the interior are also important in balancing the air-sea forcing, yet I don’t see any discussion of these processes and their potential relevance. Also, later on the authors bring in the role of forcing in regions like the EGC, the NAC, but yet there really isn’t a discussion of the sub-polar gyre circulation and how all these pieces are linked. To truly understand the significance of the authors work and what is now, a reader needs that missing background.

The authors use the ECCO state estimate for their analysis. I feel the authors assume the reader is very familiar with this product. Which is likely not always the case. More background is needed, especially discussion of the quality of its representation of the SPG and the Labrador Sea, so give the reader confidence in its being the authors underlying tool. Also, what years were ECCO run over? I understand it limits how far back the authors can go. But why does their study stop in 2012. The latest version of ECCO goes to 2017 I believe. And given the strong convection in the Labrador Sea (and its shift to the east) in 2012, and 2015-2018, it seems to be a major loss to ignore those recent years.

Another important question is the authors definition of LSW. How was the range 27.7-27.84 arrived at? It doesn’t seem to fit any common definition I’ve seen in the literature. Many studies break it down into upper LSW and classical LSW, but those ranges are typically 27.68-27.74 and 27.74-27.8. The various Yashayaev papers argue there are various ‘vintages’ of LSW and one can’t use a fixed density range through time (Feucher et al show how much difference that can make in a model that include salinity drift). Other works (especially models) define a higher upper bound because of those drift (i.e. a model LSW). Do the authors pick their LSW range based on ECCO’s behavior? If so, that is fine, but the choices must be explained and justified, with discussion of why the range differs from other studies. I’d also like to see some sensitivity analysis related to that range. And then discussion of how such a range may impact the results (in the discussion section).

I also wonder about the choices of the time period of the winter objective function and the two winter functions. Firstly, today, is it really not possible to broadly compute the functions for all years and seasons. Yes, it would take longer but I would have thought the authors could have gotten some supercomputer access to do so.  But if it is not possible to go beyond these 3 periods, I am still wondering about their choice. 2006, 2007 and 2011 are all towards the end of the ECCO timeseries used. And although ECCO has significant LSW formation in 2006, I don’t believe that year is shown to have high LSW in the observations, such as some of the Yashayaev papers. March 2008 would have been a better strong LSW formation winter.

My next major questions resolves around the forcing functions that the authors look at – wind, heat and freshwater. It looks like the authors are comparing each term to the LSW formation. But for example, sensible heat fluxes depend significantly on the wind. How is that taken into account and attributed? At the very least, this needs to be discussed to help the reader understand what the authors mean by wind or heat forcing, for example. Beyond this, the authors show a breakdown based on these 3 forcing mechanisms but there is little text and discussion. Figure 2 has lots of interesting signals that get a superficial discussion at best. Also, the heat and freshwater spatial flux plots are shown using different units – maybe convert them both to buoyancy flux components, so the reader can more easily compare the magnitude and significance of the terms.

Why rescale to a perturbation order of 10^-8? Why not to order 1, to make the numbers simpler?

The authors define their sensitivity pattern as a “Traffic Controller”. I assume they are hoping this will make the concept easier for the readers to understand. But honestly, I had trouble seeing that acronym and got confused during that discussion. More discussion and a focus to make the definition clear for all readers is needed. Also in the applied perturbation experiments, over exactly what region were the patterns applied?

Given the salinification along the Greenland shelf, is there a link to Fram Strait and Arctic outflow/processes?

I also feel there is too much material in the Appendices – too many times the reader is referred to a figure in the appendices, which has relevant material for understanding the main text. For example, the definitions of the regions. I think such information could be included on other figures.

Review of “Surface Factors Controlling the Volume of Accumulated Labrador Sea Water” by Kostov, Messias, Mercier, Marshall, and Johnson

The manuscript reconstructs accumulation and variability of the Labrador Sea Water (LSW) using the ECCO state estimate. Specifically, it examines contributions of local and remote surface momentum and buoyancy fluxes to the LSW variability. In general, the present findings are very similar to those reported in several previous studies. Presumably, the novelty is in the use of the linear adjoint technique for this topic, noting that the adjoint had been used similarly for other applications. Overall, I feel somewhat on the fence about this manuscript. It keeps jumping from one point to another with quite a few figure panels, not all of which are discussed in detail. There are many small spatial scale features in the figures and their interpretations are not usually prvided. I worry about the caveats listed on l.463-473, especially the robustness of the findings – though they are similar to the ones found in other studies. There seem to be larger NAO events (Fig. B1) in 1995, 1996, and 2000. Why weren’t those chosen? Can additional runs, including for the summertime, be included, increasing the ensemble size? I think the robustness / fidelity of the “traffic controller” pattern should be quantified. Also, what is the reason for using freshwater fluxes for the forward experiment? Would use of momentum and heat fluxes from Fig. 4 produce similar results?

Other comments and suggestions:

l.19-20: This sentence is stronger than what is said in the text on l.409-411.

l.23: Rephrase the last part of this sentence.

Fig. 1 caption: Indicate what “R” is both here and elsewhere.

l.89-91: Include spatial resolution information.

l.106: Delete the comma after “Lozier”.

l.116: “in Appendix A”, that is delete “the”.

l.121: Use larger parentheses for the most outside ones.

l.127: “Figs.”

l.132-135: I am not following what is said here. How does a simple scaling reduce noise? Also, despite what is said here, the units of 10^14 m^3 seem to be in use throughout the manuscript.

l.137: “measure” -> “compute”.

l.140-141: How do these seasonal objective functions relate to monthly LSW calculations, say, as plotted in Fig. 1b?

l.144: Please refer to much earlier works on this topic.

l.154: Subscripts “N” and “E” do not appear to refer to “zonal” and “meridional”. Please clarify.

l.179-181: How does this impact the adjoint optimization? Does it mean that the surface fluxes are not being adjusted?

Figs. 2 & 3: They can be combined to a single 6-panel figure.

l.271: Both here and elsewhere, specify what is meant by “short lead times”.

l.280: “3c” -> “2c”.

l.299: Use “NAO” as it was introduced earlier.

l.307: What does “themselves” refer to?

l.317: Why is this particular scaling used? Also, why such a small perturbation? Is it because the adjoint has to be linear and it cannot accommodate a larger perturbation?

l.317-318: What is the reason for imposing only one-month perturbation and only in January 2000?

l.320-321: This adjustment is unclear. Why are the poles adjusted, rather than considering an area-average adjustment?

l.322-323: I cannot see this “deceleration”.

l.328: delete “water”.

Fig. 6 caption: “cm” -> “m”. Also, “SSS” has not been defined yet.

l.355 & 357: Both here and elsewhere, no need to repeat “at each model grid point”.

l.358 & 359: Fig. 8 is for January, so winter is shown, correct?

l.361: Please update the date for Petit et al. citation, both here and elsewhere.

l.362: “ …. Surface buoyancy flux …. ”.

Fig. 9 caption: To be precise, Fig. 4g is for 61 months, not 5 years.

l.386-387: What does “short characteristic lead time” mean?

l.391: “drive even more delayed response” why?

l.392: Figure 10 panels have large magnitude differences. Please discuss implications. Are all regions equally important?

Fig. 10: Panel titles do not seem to match what these plots are. They are supposed to be contributions of the surface flux components into these regions. Not the other way around. Also, l.401: “panel b” -> “panel c”.

l.405-406: What is the reason for the “1 year” choice?

Fig. 11: Panel title does not match what is shown.... 1 year into the future, not longer than 1 year.

l.425-426: I am not sure if this sentence is correct. The traditional view concerns (multi-)decadal time scales. The present work does not really cover that time horizon.

l.427: “significant” statistically?

l.430: Delete parentheses for Pillar et al.’s year.

l.439: Delete “be”.

l.456: “plays a key role” -> “contributes”.

l.469” “on” -> “in”.

Fig. A1 caption: “in a” -> “is” ?

l.503: What does “This” refer to?

l.526: No need to repeat the figure information again.

l.549: Again, why this citation? There are many seminal ones on this topic.

l.580: Why does the skill peak around 2.5 years? Why is it rather low early on? Also, the decline of skill is rather small. So, does not really justify the cutoff at 6.5 years.

l.581: “for all points on” -> “in”.

Appendix D: Is this Appendix really needed?

l.604: “Irminger”.

Fig. F1: Why not just use one panel only with different colors for regions? In the caption: “Labrador”.

Fig. F2 caption: Same comments as for Fig. 10 caption above.

l.665: “the helpful” -> “helpful”.

l.678: Delete the first sentence.

l.682: Is this language still acceptable for the journal?