Not true. The paper you cite is basing its conclusion over a period from June 15th - September 15th. It's certainly true that in late August and in September, clouds have a net warming effect. However, in June and July, they have a net cooling effect as is clearly seen by comparison on June and July SLP to temperature patterns and also the fact that high pressure tends to lead to faster PIOMAS volume drops in May and June.
So we still expect clear skies to accelerate the melting process at this time of year and cloudy skies to slow it down, as we saw in 2013.
I won't claim to have all the answers and I am sure there is more to be said on the subject. But I do cite more than one paper. Have you any papers to prove your last statement and that disproves mine? That would lead to an interesting discussion.
Note that I don’t suggest that clear skies actually cause net cooling in summer months, but what I was pointing out is that there is less summer warming in clear skies over ice with high albedo in the Arctic than there is under cloudy skies.
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I don't get the impression that the paradox does not apply in certain months. Although, as I have allready noted, open water, melt ponds, thin ice etc will reduce albedo and then the effect does not apply.
insolation - albedo - re-radiation + direct thermal transfer via import = net regional enthalpy change.
It's pretty straight forward. The fiddly bits are figuring out exactly what does what to whom. For amusement, let's consider the mechanism at a qualitative level as a thought experiment.
Clouds to present a serious barrier to re-radiation, and tend to put a lid on what energy does get through them - they are a bi-directional barrier. Whether they are net positive or negative influence *is* directly tied to two things - incidence angle and length of day. The shorter the day, the greater they would tend to be a positive influence. To that end, this would imply that large scale import of moisture and cloud from lower latitudes in winter is a huge threat to the ice, even as they dump snow onto the ice. I think we would find there is an almost absolute correlation between increased cloudiness and the astonishingly high positive temperature anomalies we saw last fall and winter. While we had more open water in the fall, which favors rapid loss of heat captured during the melt season, add clouds and a skin of ice, and that heat now has a much "smaller" aperture to escape through.
The higher the incidence angle the greater they tend to be a negative influence. Here I think a big factor is the concentration under the cloud. The lower the concentration, the more clouds will increase regional albedo.
Contrary wise,
if concentration is high (fewer smaller leads), or there is significant snow cover on the ice, or both, even with complete cloud cover, your net energy balance will be better than it would be with clear skies. The mechanic here ties back to the a number of factors. First, clouds present a non-uniform, amorphous surface - you've got no (reasonably) well defined planes to reflect light. You have much more random diffraction, and the redirection will have a higher potential of redirecting light into rather than out of the system. Second, the clouds present a much greater barrier to escaping energy than clear skies, for exactly the same reasons they reduce solar input. Energy has no direct path back out of the atmosphere. There are others as well, but with them we start drilling into quantitative analysis and my lack of depth on the subject would become more telling
Similarly, these mechanics high albedo ice during periods of low solar incidence angle would capture more energy as well.
So, I think conclusions follow...
Even during periods of high insolation, clouds can be a net positive factor over areas of ice with high concentration and high albedo.
Clouds influence as a positive feedback to melt diminishes geometrically with decreasing concentration and decreasing surface albedo
Clouds as a positive feedback increase geometrically both with decreasing insolation and lower solar incidence angles
