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According to the snowball Earth theory, all of Earth froze over at least once (possibly twice) in the far past. However, Wikipedia says that there are opponents of the theory who state that tropical portions of the oceans were not entirely covered. These responses have been motivated both by sedimentary deposits (also used by proponents of the theory) and by computer simulations.

Is there any consensus as to whether or not the surface of Earth's oceans froze over entirely during either of the two main snowball Earth periods (~ 650 million years ago and ~2.1 billion years ago)?

To be clear, my question is about surface ice, not underwater freezing.

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    $\begingroup$ Possible duplicate of Why deep ocean didn't freeze during snowball Earth? $\endgroup$ – arkaia Oct 14 '15 at 15:37
  • $\begingroup$ @aretxabaleta Doesn't that ask about subsurface ice, while my question asks about surface ice? I clarified, by the way. $\endgroup$ – HDE 226868 Oct 14 '15 at 15:41
  • $\begingroup$ I see your edit at the end, but could you edit the entire question to clarify this? $\endgroup$ – arkaia Oct 14 '15 at 15:49
  • $\begingroup$ @aretxabaleta Sure. $\endgroup$ – HDE 226868 Oct 14 '15 at 15:49
  • $\begingroup$ It would be hard to know, would the evidence from one completely covered year in a given century be the same as for all years. You would need a set of varve deposits. Also the sedimentary evidence is based on a replenishing gacier margin so a complete cover could look different - less sheet movement?. $\endgroup$ – Ralph_CCL Oct 15 '15 at 15:20
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By looking at the recent literature on the question, I see neither a consensus or a definitive answer on the extent of the snowball earth.

Since the Neoproterozoic Snowball Earth event is more recent, there seem to be more evidences available and therefore more relevant research on this event than the 2.1 BY one - and will consider in the following only the latest event.

This paper suggest that the ice cover was likely global but some open water would have persisted in equatorial regions where complex life would have been able to survive during the glaciation.

This other paper suggest that glaciogenic sequences (sedimentary rocks containing sediments deposited by glacier actions, for modern analog non-consolidated examples see till or moraine) in high latitudes (North) contains fragments of carbonates which was likely formed near the equatorial zone and somewhat transported by glacier action.

This yet another paper modeled how glaciation likely reach the equator, where this paper suggest that open sea must exists.

Other papers suggested that once a significant part of the Earth was covered by glaciers, albedo effect significantly cooled the planet until some kind of massive volcanic eruption interrupted the cycle.

The only consensus I figure is that it most likely happened (a late Proterozoic Snowball Earth Event) but it still remain to be seen if a thick cover of ice 'a la Encalade' covered the Earth at one time or another, or not.

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There is no consensus, but educated opinions. I tend to think that they did not freeze over. Some interesting arguments are given by Dorian Abbot in his paper where he first published about the Jormungand model. I tend to think it's sensible to assume that since photosynthetic bacteria survived, there must have been some open water.

In fact, I have a recent paper where we show that under many generalization to Abbot's theory about the near-equator albedo (i.e. near the equator you have lower albedo to account for the lack of snow cover due to Hadley cells and other effects) you tend to get areas of open water, i.e. Jormungand models. Thus to me it seems that Snowball Earth is a good first approximation, while when one begins to add some details you tend to get at least some open water near the equator.

Of course, more studies will need to be done to get anywhere near certainty.

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