First, even if there was a full melt out of the arctic (sub 1,000,000KM2 of ice at minimum), the refreeze in fall would recover completely, and will continue to do so for decades to come. It will be the best part of a century before we have a year round ice free Arctic, at the least.
I don't think an ice free September would mean an ice free winter, of course, but...
Second, ice, even relatively thin ice (sub 2 meters) embodies a huge amount of thermal lag during the melt season. Exposure to bursts of energy, even very significant atmospheric heat (think 5C+) won't dent it seriously. It requires fairly continuous exposure to energy before it will start coming apart.
The same applies to open water in the reverse, which is my concern. The freezing season, if started over substantially open water would need time to cool that water to 0 C first - that huge amount of thermal lag. Getting that ball rolling a couple weeks late would mean less ice freezes.
I can't see how a substantially ice free arctic loses heat better than any previous year to allow a "complete" recovery. In fact, I don't see a mechanism for it to freeze as much as it has in previous years, especially with CO2/methane.
Don't get me wrong. I'm not saying it won't recover. I just don't think it'll be complete. Maybe it'll be 80% of usual, but that is a tipping point with albedo effects considered. And less freeze has all sorts of knock on effects that I've mentioned.
Basically I argue once you reach the ice free point, the planet has to spend more time ventilating heat from open water before it can get to freezing that water, and that means less freezing.
Third, conductive atmospheric transfer of heat from atmosphere is a very small component of the heat that goes into melting. The melt season "Heavy Lifting" is done by sunlight - either captured by open ocean or melt ponds. Put this way, a layer of water at +1C can deliver approximately 15 times the energy to the ice than atmosphere at +5C.
So, the major story of what's coming up in the Chukchi will be the sunlight. Atmospheric heat will be a thin bonus, perhaps helping start melt ponding, which will amplify the effect of the sunshine.
Pity the Beaufort, then. In the other thread where we looked at albedo impacts... as best I can tell they are significant. (Also per that thread, atmosphere matters a lot; rivers and currents not as much. Go check it out, I'm not 100% confident in those results).
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Even with that, there is a fixed amount of energy per day that the sun dumps into the high Arctic this time of year - most areas will look at between 12-14KWH/day/M2 equivalent. Albedo if low - .25 or lower - will capture 75% of that, of which we might generously see half applied to the ice. That's only enough to tear through 5-8CM of ice per day. So even with near continuous conditions like what's coming up, it would take a solid month of this weather to burn through even "average" ice of about 1.8M thickness.
Peak arctic insolation at north pole is 520 W/M^2... so yeah, 12-14kwh/day/m^2. Heat of fusion for water is 333.55 J/g... pretending everything is freshwater that gives me 12 cm - close enough. That means an average thickness of 1.8M would last 15 days. More like 30 in your scenario. Summer is longer than that, of course.
Incidentally, on the darkest days of the long polar night, what kind of black body radiation loss to space does it have? We could come up with the same kind of numbers for how fast freezing goes in ideal terms. I'm more concerned with the "delay in refreeze" impacts than I am on the ice melting, because of thermohaline impacts.
Now, this doesn't include latent heat already in place at depth in the Arctic oceans. If we get wind and movement, that would accelerate things. That would also spread the ice out, which would provide additional exposure to heat.
So, my conclusion is... the weather is very alarming. If it continues it will be crushing. However, it will still take considerable time for the damage being done to become clearly visible.
And there's the heat absorbed by anomalous open water (hi, Beaufort!), which I assume gets shuttled to the ice interface somehow. Albedo anomaly now counts a lot more for heat accumulation than September (and 2012) anomaly.
We agree that it's alarming. I don't know about crushing. Depending who you ask, it's already very clearly visible; if you look at any extent graph you know something is wrong.
But worldwide impacts? I think that's where we disagree. I think this may be the year, especially this winter.
Of course there's a very good chance we don't lose anything like all of the ice this year, but if we're on a downhill slope where the winter we just had is not anomalous, and we aren't freezing like we used to (e.g., post-2012 recovery), we'll get there soon enough.