A “waterbelt” is a band of open water centered on the equator, of width 20 degrees or so, which is stable in some climate models of Snowball Earth. This new paper by Hörner and Voigt (HV) is important, showing how the maintenance of an equatorial waterbelt on an otherwise ice-covered ocean can be the artifact of a model defect, namely inadequate vertical resolution in the sea ice.  I have a few comments

Major comment.  On the modern Earth, snow and ice occur mostly in the polar regions, where the Sun is low, or in midlatitudes in winter, when the days are short, so snow and ice do not get exposed to much solar energy. The exact values of snow and ice albedo become much more important to global climate when ice advances into low latitudes (Snowball Earth), but many snowball modelers have been using inappropriate albedos. On line 66, the albedo for cold snow should be 0.83, not 0.79. Warm (melting) snow has albedo 0.76 if it is clean, not 0.66 (these values are in Table 2 of Webster and Warren, 2022; WW22), but the value 0.66 used by HV could be appropriate if the snow contains dust. Bare cold thick sea ice has albedo 0.47-0.49, slightly higher than HV’s 0.45 (Table 1 of Warren et al., 2002). Melting Arctic sea ice develops a granular surface scattering layer (SSL), resulting in a relatively high albedo of 0.60 (WW22), i.e. higher than that of bare cold thick sea ice. In depressions on the melting Arctic sea ice, little ponds form, with albedo 0.2 (WW22). So on line 67, the albedo 0.38 used by HV for warm ice implies that the areal fraction of ponds on melting ice is ~55%, which is far more than is now found on the Arctic Ocean in summer (Table 1 of WW22).

     In summary, the albedos used by HV are lower than observed. Ideally HV would rerun their models with more-appropriate albedos. If they choose not to make this revision, their paper is still a useful test of their hypothesis, since they are using the same values in both models. But the authors should acknowledge that the albedos they used are too low. This acknowledgment will strengthen their conclusion, because using higher, more-realistic, albedos for snow and ice in models will make the waterbelt even less accessible.

Minor comments.

Line 22. Change “decreasing” to “increasing”.

Line 31. “Thanks to heat convergence by the ocean circulation to ocean heat transport” is awkwardly worded. Maybe the last four words can be deleted.

Line 35. Change “evaporation” to “sublimation/evaporation”.

Line 63. Change “45 vertical levels” to “45 atmospheric vertical levels”. Otherwise the reader may think you have 45 levels in the sea ice.

Figure 1a. I’m glad you’re showing the time scale of the transition to global glaciation, and also on Figure 5. This is interesting. If you had an interactive deep ocean, I assume the time required to reach the snowball state would be much longer.

Line 84. Change “the upper model boundary” to “the upper boundary of the model’s atmosphere”.

Line 86. Change Semnter to Semtner.

Line 99. Change “550 0ppmv” to “5500 ppmv”.

Figure 2 is confusing. The caption says “Gray boxes indicate the region where stable states are found”. Since the orange Winton curves do not avoid the gray box labelled “Waterbelt state”, it seems to show that a stable waterbelt is accessible with the Winton model, in conflict with the message of the paper. Some changes to the figure and/or the caption are needed to clear up this confusion. Maybe the figure is showing the non-equilibrium time-dependent path of transition into a snowball, rather than the equilibrium stable state?

Line 106. “a higher value of CO2 than the tipping point of Snowball Earth initiation”. What is the CO2 value for the tipping point?

Figure 3. In the labels at the top of parts a and c, change Semter to Semtner.

Line 123. Change “siulations” to simulations

Line 130. Change “beyond 30” to “below 30”

Figure 4a. Why does TOAnet not go to zero in the snowball state (ice-margin latitude zero)?

Figure 4 caption line 1. Change “the ice-margin latitude” to “the transient ice-margin latitude” because TOAnet ≠ 0 means we’re not in equilibrium.

Figure 5. In the labels at the tops of parts a and c, change Semter to Semtner.

Line 299. Change Marnoun to Marinoan.

References

Warren, S.G, R.E. Brandt, T.C. Grenfell, and C.P. McKay, 2002:  Snowball Earth:  Ice thickness on the tropical ocean.  J. Geophys. Res. (Oceans), 107, C10, 3167, doi:10.1029/2001JC001123.

Webster, M.A., and S.G. Warren, 2022: Regional geoengineering using tiny glass bubbles would accelerate the loss of Arctic sea ice. Earth’s Future,10, doi:10.1029/2022EF002815.

Jormungand state, in which the sea ice edge can reach deep tropics without triggering the ice-albedo runaway feedback, was first obtained by Abbot et al. (2011) in a slab-ocean model and postulated to provide a solution for the survival of life during the Neoproterozoic global glaciations. The key mechanism for the formation of such a state is the formation of a wide bare sea-ice region in the low latitudes. However, the existence of such solution has only been possible in climate models of reduced complexity, for example, removal of ocean dynamics (i.e. slab ocean); in fully coupled atmosphere-ocean general circulation models, the waterbelt solution obtained was very different from a Jormungand state in that the former did not have a hysteresis associated with it (i.e. it melts back easily when CO₂ is increased). Even in simplified models, the existence of a Jormungand state is dependent on some particular settings, e.g. cloud parameterization. This study further tests the robustness of Jormungand solution against the sophistication of sea ice model.

Specifically, the authors test two thermodynamic sea-ice model (Semtner-0L and Winton-3L). They find that the Jormungand mechanism is greatly weakend in the more sophisticated energy conserving sea ice module, Winton-3L. This study is another demonstration that the Jormungand solution is achievable only under strict conditions, and is thus a useful addition to the field. The manuscript is well organized and written. I have few comments as listed below and can be delt with easily.

Major Comments: the paper spends considerable time discussing the response of bare sea-ice region at the ice margin on Semtner-0L and Winton-3L. However, the discussion on the net evaporation due to the Hadley cell in 10°-20°N/S is missing. Is the net evaporation the same in that region in both sea ice configurations? The statement in Line 189-191 needs a support from some energy budget analysis to estimate the influence of the ice heat capacity more quantitatively.

Minor Comments: in Line25-33, a previous study showed that the surface topography could facilitate the formation of waterbelt solution by reducing the snow coverage over continental interior when climate became cooler and cooler (Liu et al., 2018; DOI: 10.1175/JCLI-D-17-0821.1).