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When we have full insolation, that net energy received massively exceeds heat loss out of the atmosphere, permitting significant melt at 2m SSTs as low as -10c.
Cloud cover will reduce the exchange out of the atmosphere, but replaces direct insolation with what is primarily down-welling IR, which doesn’t come close to what is applied to the surface directly. It can be warmer, but unless heat is available, you won’t get melt.
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All this is entirely true, but I was getting at something different about the dynamics of melt pond formation. Several times in previous melt seasons, we've had periods of arctic overcast, When the overcast clears, we see a surprising extent of melt pond formation. I think there's a physical explanation for this pattern.
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Yes, the melt ponds have a lower albedo than snow or ice. However, clouds have a higher albedo than melt ponds, but lower than snow or ice. Hence, once melt ponds have formed, cloudy days have a higher albedo, resulting in less deposition of radiation at the surface.
"As the surface changes during the melt period from snow-covered sea ice to partially snow- melt pond-covered sea ice to totally open water, the albedo of this heterogenous surface will decrease. Because the cloud albedo lies between the albedo of snow and the albedo of dark open water, an increase in cloud cover due to loss of sea ice coverage is expected to partly compensate for the associated albedo decrease and tend to restore the TOA albedo during the sea ice melt period to the pre-melt value. The planetary albedo is determined by reflection from both the surface and the atmosphere."
https://www.nature.com/articles/s41598-019-44155-w#:~:text=As%20the%20sea%20ice%20melts%20and%20ponds%20form%2C,absorbed%20energy%20will%20enhance%20the%20sea%20ice%20melt.
@jdallen seems to be talking about early meltpond formation which can happen at surprisingly cold temperatures, while @SteveMDFP is talking about the phenomenon that we have actually witnessed, when cloud cover disperses and seems to leave meltponds in its wake, although I think this has only happened a lot later in the melt season, when surface temperatures have been above freezing.
@The Walrus, the paper you quote is interesting but does not state that "once melt ponds have formed, cloudy days have a higher albedo" - meltponds have a much lower albedo than open waters, and "cloudy days" can mean a lot of different things!
The paper does however point out that, during insolation over open water, TOA anomalies are higher in clear weather than in cloudy weather, while the opposite is true over ice. Or in other words, over open water, direct insolation is the most effective heat transfer, while over ice, some cloud cover strengthens heat transfer. This is not a new conclusion, we have seen similar in other scientific papers in the past.
Ice albedo, and meltpond albedo, varies quite a lot depending on circumstances, as described in
Arctic sea ice albedo: Spectral composition, spatial heterogeneity, and temporal evolution observed during the MOSAiC drift - see image below.
Standard sea ice (once snow has melted) has an albedo of 0.6-0.7, and thin ice had a measured albedo of 0.55 (presumably this varies with the thickness of the ice - the thinner the ice, the lower the albedo, and probably in an accelerating relationship.
Light melt ponds have an albedo of 0.25-0.32 while the open ocean has 0.06. Which means that melt ponds are closer to ice (at least in the beginning), than to "dark open waters".
All in all, the evidence seem to support what @SteveMDFP says, and which we believe we have observed, but this probably only applies later in the year and not during early melt onset, where direct insolation is probably the main thing as @jdallen points out.