Dear Amy,

Thank you for the revisions which helped improve the manuscript substantially. The present coverage of observations and the large inter-model spread do not allow you to reach solid conclusions as a new science contribution. In contrast, an updated *review* on freshwater in the Arctic Ocean is a welcome contribution. Your review aims to increase awareness on a few processes previously ignored and updates a previous review by including new data in the analysis. However, the review overlooks important previous work, and possibly observations, and must be improved. The observation coverage (both in situ and remote sensing) does not do justice to available data. There are also shortcomings in the discussion which require a major revision. Reviewers provide detailed comments which will help improve the review.

Please also consider the following minor comments from me.

Thank you,
Ilker Fer


(Line numbers from manus version 3)
In general there is a mix of selected isohaline for vertical integration (34.8 vs. 34) and units of FWC (km^3 vs m). Could you be more consistent in a review (perhaps reproduce figures consistently)?
Li 35: do we have enhanced mixing in the ocean? Does Timmermans and Marshall 2020 cover this? I think this claim is overreaching. Perhaps supported in the eastern EB (Fig 11 of Polyakov et al. JClim 2020).
In line 40 you could cite Carmack et al. BAMS paper.
Li 43-44: it is a bold statement that ocean stratification determines sea ice growth.
Li 45: I cannot follow how the part after “;” connects to the previous sentence. Perhaps a separate sentence could help.
Li 46-51: AO freshwater balance somewhat ignored the vertical mixing.
Li 55-95: Discussion around freshwater. I am disappointed that you join many others and follow the flawed traditional approach instead of taking a step in the right direction in a review in 2021. Fine. But as you end this section (page 3) please also mention what the alternative is (e.g., ocean salinity and salinity flux divergence analyses).
Li 58: “the concept of” instead of “the existence of such a concept as”.
Li 60: remove prime after freshwater-
Li 99: Here OK to mention the two different contributions from GIS but could also mention its relatively small contribution in the Arctic freshwater budget and comment on the location and rapid export through Fram Strait.
Li 102-106: “Halocline” (or ‘cline) concept in ocean does not only apply to the depth range there is a gradient between only two water masses. This statement from Rudels is misleading. Halocline is a depth range with strong salinity gradient (no matter how many water masses are involved). Please remove such comparisons with the “rest of the ocean”. To call the halocline “a cold and freshwater mass” is not accurate- please reword.
Fig 1 caption: Please also spell out VS and SZ.
Fig 2A y-axis label is missing. Fig 2C, please mark the BG region as defined.
Fig 3B. Please mark BG. Unit of FWC anomaly is in km^3. Fig 2c in m.
Satellite observations: It seems like you cut across the Arctic Ocean along 60E. There must be more data on the “other hemisphere”, particularly important for the freshwater budget.
Table 2. It would help to show the time and space distribution of the new data in a figure. Table could include total number of profiles. Where is NABOS data?
Li 240: require[s]
Li 261: delete “and changes in”
Li 274: increasing rain as climate warms- any citation on this for the Arctic Ocean?
Li 290: instead of “up to 50%” please give a range from ORAs.
Li 300: You mean “New” sea ice in the Arctic forms on shelves?
Li 308: comment why faster TD matters, by exporting more FW?
Li 327: in response to storms vertical mixing can also bring up oceanic heat and melt sea ice. There are several observations in the literature. Do you want to also include this in the “sea ice” section? [and/or in the vertical redistribution discussion?]
Page 18: if so important, please mark the mentioned glaciers in Fig 1 so the reader sees where they are relative to the Arctic Ocean.
Li 380-395: around here, more comments are needed on the location of Greenland in the large Arctic Ocean freshwater landscape and eventually to tone down its contribution. So, how much km^3 of FWC is actually going into the Arctic Ocean freshwater balance?
Li 404: define mSv
Li 436-437: an entire sentence is repeated.
Section 3 is not well structured. It is a mixture of different processes and regions and their role in redistribution (lateral and vertical). There is also some overlooked literature and processes.
------ Thank you -----

Dear Dr. Solomon,

Thank you for your diligence in carefully and thoroughly revising the manuscript. I reviewed your response and the revised version, and do not see the need to send the manuscript to referees for a further review. You have responded satisfactorily to the reviewers’ comments, and the manuscript has improved substantially.

I do not need to see the manuscript again, hence accept subject to technical corrections. I trust you will make the necessary corrections as needed where I noted below. Once submitted, the manuscript will move on to the production stage.

Thank you,
Ilker

Page and line numbers of the clean manuscript, version 4 (apparently the first digit of 3 digit line numbers are cut, and may lead to some confusion):

p2, li59: delta is missing in S = S-Sref

p4, li41-47: 2010-2017 mean is used (most runs except 2 extend to 2019). If you chose the 2010-2017 period because this is the common period for all ORAs, please mention so.

Table 1 is full of acronyms. Some are defined throughout the manuscript. Please make sure to define the most relevant in the Table caption (e.g. L50, L75) and cross-reference for others as needed. Define all in Table 1, if you prefer so.

p10, li13, unit, kg m^{-3}, missing for \rho. Also typeset subscript, _1, _2.

p11, li3, 2012 [are] given

p18-last few lines to p19 end of first parag.: I cannot follow and miss some transitions in the narrative between mass loss, net ice loss and total freshwater flux Is mass loss equivalent to ice loss? Please improve the write up here. How can a “net ice loss” can be loss if it is “balanced”?

p21, li78 (78 is 8 if counting from top). Linking Polyakov 2020 findings to "there appears to be no trend in volume fluxes at boundaries...." is over reaching.

p21, li 94: sea ice [retreat] may

Sect. 3.2. Please provide a statement on how the last part (mixing of AW with deep water) links to the «competing processes in the BG»

p24, li 71: has been shown [to be of] importance (or a similar edit)

Sect. 3.4. Please consider to change the title to “Dense water cascading and tidal mixing” (or similar). As is, the second paragraph does not belong here. Can you conclude this section with a statement that the contribution of these processes to the freshwater budget of the Arctic Ocean remains unquantified and unknown (or similar)?

P34. Li80 (in summary): Because most of these results are based on existing literature, please explicitly mention: “Inferred from the published literature, the most notable differences…” (or similar).
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