General comments

Your revisions address all the comments by reviewers of your original manuscript. However, in the process your manuscript has become less accessible due to the amount of detail and - at times convoluted - discussion of additional simulations. Reviewer 1 provides some comments in this regard. While I find the additional material to be relevant, your paper would gain substantially by tightening the presentation of results in Section 3 somewhat. The additional hind cast simulations do seem to complicate the discussion and some of this can be addressed by revising the text as outlined by Reviewer 1 and a few comments below. However, you may also want to consider to include some of the presentation of results for additional hind cast simulations in the Supplemental Materials section (which currently only consists of a single figure). Parts of sections 3.2 and 3.3 could hence be moved into the Supplement with a more succinct and less confusing summary of findings for some of the additional simulations presented in the main body of the paper.

While I leave it up to you to decide which path you want to take in addressing the reviewer’s and my concerns, there are a few additional points that need to be addressed in revising the manuscript.

First, one aspect of the paper that I found confusing and that would benefit from clarification (unless I’m just confused by the presentation, in which case some revisions and an brief explanation in a message directly to me will suffice) concerns your presentation of heat content and salinity variations and their impact on ice concentration and extent.

In discussing your results with respect to ocean heat content (ll. 311ff., Fig. 4) I did not see a specific explanation of the reference state that these heat contents have been calculated against. Is that the local freezing point or a constant (potential?) temperature? Since the freezing point will shift with salinity changes for the freshwater perturbation experiments, interpretation of the heat content variations is not straightforward and I’m not sure I fully follow your line of reasoning in ll. 314ff, and l. 376ff. since any freshening of the surface layer would by default increase ocean heat content if the latter is measured against the local freezing point. In fact, I was surprised to see what appear to be very small variations in upper ocean heat content. It would be very helpful to the reader to see these numbers discussed in terms of actual temperature anomalies (from what I can gather they amount to something on the order of a mK or less?).

Along the same lines, how large are the precipitation rate increases discussed on p.10, in terms of surface freshwater flux per unit area? The same point applies to the salinity anomalies. Thus, it may help to specify what the magnitude of the ocean heat content and salt content anomalies shown in Fig. 4 is in terms of the heat content and upper ocean salinity per unit area of ocean surface (i.e., per m2). In your discussion you imply (l. 318ff.) that the covariation of salinity and temperature are in response to external forcing, but it’s not clear whether the response is fully coupled and coherent (i.e., constrained mostly by the salinity-dependence of the freezing point and its impact on the annual temperature cycle) or whether the two variables are responding independently. Addressing these points may also help further clarify how the ice mass budget is responding to changes in freshwater input.

Second, in revising the paper, please include a clear statement in the first half of the paper (i.e., introduction or methodology sections) in regards to the magnitude of freshwater flux variations imposed by your autoregressive model relative to observed variations in freshwater input through glacial ice melt. For somebody not familiar with the details of this debate, it is difficult to pull together the different references that you currently have spread throughout the text as to what the freshwater flux (in Sv) compares to in terms of ice sheet mass balance and loss through melt (in Gt/yr). Stating this clearly upfront will help readers better understand the figures and text before you start to touch on this in a bit more detail on p. 15ff.

Third, your conclusions (Section 4) are very helpful in identifying the key findings from your study. In fact, the conclusions section may help guide the revisions to the sections 3.2 and 3.3 outlined above in helping you focus on the relevant findings. However, at the same time the text in the conclusions section is convoluted and at times difficult to follow. While I have suggested some editorial improvements below, I would encourage you to go through this section carefully and clarify the text, e.g., by breaking up long sentences into shorter statements.


Specific comments
(below, if no additional explanation is provided, the text in quotation marks indicates how to modify the original wording to correct errors or clarify statements)

l. 6: “with data assimilation, the inclusion of an additional freshwater flux”
l. 10: “or some compensations”
l. 12: “that is in agreement with satellite observations”
l. 15: “it does not seem to be required”
l. 22ff.: “The present work thus provides encouraging results … Southern Ocean, as in our simulation the positive trend”
l. 63: “but for future projections this requires”
l. 83: “the present study aims to identify a procedure”
l. 91: “associated, for instance, with the Antarctic ice”
l. 93: “requires a large ensemble”
l. 140: “differ amongst each other in the additional”
l. 235ff: “A detailed investigation of the impact of different spatial distributions on the additional freshwater input … but is outside the scope of”
l. 249: “the fraction of a grid cell”
l. 252ff: “otherwise, have been derived from … through version 2 of the Bootstrap algorithm”
l. 302: Referring to “melting of sea ice [that] occurs everywhere in the Southern Ocean” is incorrect. The trends shown in Fig 3 refer to reductions or increases in ice concentrations over time and should be discussed as such. The reductions cannot solely be explained as a result of melt (unless the model provides evidence not discussed presently in the paper). In addition, seasonal ice melt and basal melt of the ice cover may occur over much larger areas and may not be associated with a trend towards reduced ice concentration which further complicates the issue. Simply referring to ice reduction instead of melt may be sufficient to address this point, unless further details from the model results are discussed.
l. 332: “no observations”
l. 431: “in detail”
l. 575: “this finding suggests”
l. 578: “in this configuration, i.e., the one obtained in NODA”
l. 582: “ this encouraging result provided by HINDCAST_3.1 needs to be viewed in the context of model drift that produces”
l. 611: “is in good agreement”
l. 623: “an appropriate freshwater input”
l. 642: “in our simulations”
l. 658ff.: “data assimilation identify several factors that can help increase the model skill for predictions of Southern Ocean sea ice concentration trends for coming decades. Specifically, we highlight three findings. ”
l. 681: “may help to correctly reproduce a positive”

Figures:
Many of the figures contain axis labels, legends and other information that is much too small to be seen clearly. Please be sure to enlarge the font or find other ways to illustrate this information. These problems apply to the following figures (but include others not mentioned explicitly below):
Fig. 2 & 7 (legends)
Fig. 4 & 5 (axis labels)
Fig. 3 & 8 (different types of shading/colors/hatchmarks are difficult to make out)
Figure 1, caption: Please explain what is shown in green/blue and in grey in the figure. Also, is there any significance to the fine lines shown in white over the grey areas? If not, please remove or otherwise explain and show more clearly.

Dear Dr. Zunz,

Thank you for your thorough revisions of your manuscript on the influence of freshwater input on decadal scale sea ice forecast skills in the Southern Ocean. With much of the additional material now moved into the supplements section the manuscript is much more accessible and less convoluted.

Other than a few minor corrections listed below, the paper is now ready for publication.

With best regards,

Hajo Eicken.

Minor corrections (line numbers refer to clean version of revised text without annotations):

(i) Main manuscript
l. 382: Change to “Note that correlation between” or “Keep in mind that correlation between”
l. 405: Remove duplicate period at end of sentence
l. 412: Here “Remind that” also needs to be replaced by “Note that” or “Keep in mind that”.
l. 490: Cut “for brevity” or reword to “for brevity’s sake”
l. 504: “Anyway” is a colloquialism, either remove or replace by something like: “In conclusion”.

Figure caption for Fig. 4, last line: Change to “against absolute zero” or against O K”

(ii) Supplemental materials
l. 12: change to “imply a larger”
l. 19/20: “fits the observations relatively well”
l. 27: “towards lower values”

Figure caption for Figure S4: Change to “against absolute zero” or against O K”