The authors present an analysis of coupled GCM simulations of the aftermath of a snowball Earth event, with an emphasis on the ocean response including the consequences of the melting of continental ice sheets and sea ice/glaciers and the resulting fresh water layer that is expected to develop over the ocean. This seems to be the first GCM study of the process, the problem is very interesting, the analysis very well done, and the writing is especially clear, including of the model description, analysis, and the implications of the results. Some minor comments are suggested below, and I recommend the paper for acceptance after a minor revision.

Specifics:

The motivation in terms of cap carbonate formation, effects on ocean life, comparison with previous estimates of the de-stratification timescale of the fresh water layer is very helpful and well written.

The model description is especially helpful. The authors seem to have identified all weaknesses in their experiment design, anticipated all possible caveats/criticisms and addressed them very well. As part of this they discuss the coarse atmospheric and oceanic resolution, flat ocean topography, the unavoidable arbitrariness of the vertical mixing scheme that is addressed by sensitivity experiments, inability of the model to simulate full-thickness ice layer that is addressed via a readjustment of the salinity stratification upon melting of sea-ice to 35% area extent, the inability of the model to represent sea ice/glacier dynamics for a thick ice cover (sea ice dynamics is appropriately turned off then, leaving only the thermodynamics active), our incomplete knowledge of CO2 after snowball events that is addressed via 3 different sensitivity scenarios, and more.

Figure 2: perhaps show also the overturning for the fully glaciated state (and the temperature and salinity for both states), so that it can be compared with the following simulated times shown later.

Figure 3: may want to show sea ice instead/also in units of thickness/equivalent sea level, volume seems less easily interpreted here.

I agree with the authors that their circumpolar current is a weak point, and that this is a result of the flat topography. A mid-ocean ridge across the circumpolar opening would indeed have helped. It seems to me that the authors address this deficiency reasonably well in their analysis and discussion.

The thick snowball sea ice cover is sometimes referred to as sea glaciers, to distinguish it from the very different present-day sea ice. I don't know that this terminology is necessarily better than sea ice, admittedly.

Lines 240-245: Interesting finding of distinct MOC cells in the freshwater and salty layers.

Figure 5: given the focus on stratification/re-stratification, it would make sense to show the temperature and density too. Perhaps another column of panels for temperature, with density contours over both temperature and salinity.

Around line 255: the density is not shown, but sloping and then vertical circumpolar salinity contours suggest that the circumpolar current is initially baroclinic and then mostly barotropic once adjusted, likely a result/artifact of the flat bottom as the authors mention. Is it? The relevance of this baroclinicity is mentioned below.

Section 6: nice analysis of the overall warmth of climate and a useful comparison to previous studies.

Lines around 320 and 395: a very important and helpful discussion of the de-stratification timescale, and its causes, and a useful contrast with previous 1D vertical model results. This seems one of the highlights of this work. A comment on this: the important part is not the strength of the circumpolar current but its baroclinicity, given the thermal wind balance: drho/dy~du/dz. The sloping iso-halines shown at some stage of the deglaciation suggests a baroclinic current and later barotropic. The sloping lines should help the de-stratification process. Would be interesting to compare the top-to-bottom vertical shear in the circumpolar current simulated here vs in present-day and thus the implications on the sloping isolines of salinity and their contribution to the destruction of the fresh water layer.

Review for COP

Title: Climate and Ocean Circulation in the Aftermath of a Marinoan Snowball Earth

Authors: L. Ramme and J. Marotzke

In this paper, the question of the ocean destratification is addressed using an Earth System Model (ICON-ESM). Based on extended set of simulations, this study demonstrates that the post-melting stratification cannot length more than a few kyrs, so one order of magnitude shorter than expected (Yang et al. 2017).

Scientific interest

The paper is very well written and considerable care has been taken to the modeling approach. Moreover, the authors have clearly identified the fundamental processes hidden behind the “fast” freshwater stratification break-up (section 7.3), a tendency enhanced by the super-greenhouse climate (section 6). If some minor points require clarification, this manuscript deserves to be published.

Here are some minor recommendations that the authors may consider to improve the paper (ranked by order of importance)

1) The conclusion is a bit weird compared to the findings highlighted in the core of the MS. Statements presented here are speculative or not enough constrained. I encourage the authors to rewrite this section.

           lines 436-440: this statement seems to be very speculative. My main concern regards the assumption made for the post-snowball sea surface temperature. Indeed by using 15 000ppmv as a melting threshold, the authors probably underestimate the pCO₂ at the end of the snowball earth event, so the Earth’s climate is not drastic enough (the used CO₂ threshold is more in agreement with the water belt solution (Abbot et al. 2011)).

          lines 441: In addition to underestimate the pCO₂, this study also assumed an instantaneous ice sheets melting, so this paragraph needs to be rephrased. (we could speculate that this melting occurs on a very short period of time, 2 kyrs as defended by Hyde et al, 2000 but this behavior seems to be inconsistent with Benn et al. 2015, ice sheet-climate simulations suggesting a decreasing of the ice sheet volume with the rising of the CO₂ above 0,02bar).

2) lines 360-374: Here the authors try to infer the time scale and environment for cap dolostone using their results about the ocean destratification. This approach is interesting but suffers a major flaw caused by the use of a uniform ocean depth (and held constant to 3500m) as a boundary condition. In my view the surface salinity simulated in the vicinity of continents (fig.7) cannot be considered as representative of coastal areas where cap dolostones were formed.

        - Abstract (lines 14): without an accurate bathymetry, results of this study are not robust enough to support this conclusion.  

          - line 364 - I don’t understand why the authors used Allen and Hoffman, 2005 here. This paper is explicitly focused on giant ripples recorded in cap dolostones. This paper is related to the topic but seems to be more appropriated to explore wind speeds during the sea level rise.

3) lines 422-425: According to my understanding, the main reason of the circumpolar existence seems to be the singularity of the Marinoan paleogeography, the northern hemisphere being characterized by the absence of continents above 50° of latitudes (fig.1).

Minor points

- table 2. TSI → Total Solar Irradiance reduced by …

- what’s difference between aureal and austral winter?

- fig. 6a “global MOC” is misleading and could be replaced by MOC at 30°S (to be consistent with the caption). fig 6b, c, d global values or zonally averaged ? (if yes you need to precise the location)