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I meant not strong but clear of clouds. When beautiful weather comes, if so, so to speak.
It is 30° above horizon midday but it starts to get very close to horizon at 'midnight', right? Temperatures drop. Sun radiation no sufficient anymore.
Temperatures plummet during those cold hours. I observed that last year from sat data. But you know better than me for sure living at higher latitude. 
(you live in Russia?). I am at less than 40N (NH).
What is clear is that storms are not helping the loose ice pack at all. Floe breaking, dispersing, mixing. Weak storms. Probably clouds reradiating heat back to ice and avoiding temps plummet during coldest hours of the day.
So when ' here comes the sun' , the frost too.
Moscow region, Russia, yes.
Up there in Barrow, Sun gets below horizon for a few hours every day already. For ~12 hours every day, though, it's not "very low" - but quite a bit higher than that.
As for temperature drop during night hours, it's nothing as dramatic as (it seems that) you think it is. In
one of my recent posts, i was giving a link to a
bouy in Bering strait, complete with both surface air and surface water temperatures, very nicely graphed in several daily cycles real-time. As you can see from it, short night does not allow temperatures to drop down more than for ~2°C below daily average, at best. Usually even less than that. Sunny day can warm up surface water more than that for a few hours, up to by ~5°C or so, and that temperature "bump" would quickly be lost (in a few hours), but the daily minimums of _water_ surface temperature - SST, - from day to day are remarkably stable, no matter if it's sunny or cloudy; even not-so-large surface air fluctuations are barely noticeable in SST graph during night hours, as you can see. This would remain to be the case, i believe, as long any small part of mixable column of water - for any deep sea that's ~150m meters deep, - would remain significantly above freezing point (~-1.8°C for sea water), because as right-at-the-surface water cools, it gets more dense and sinks (mixing helping - and _sea_ water does not have density peak at ~4°C as fresh water does), being replaced by still-warmer water "from just below", and the cycle continues pretty much until all the water in mixable layer is rather close to freezing point.
All the above is as true for Bering strait as for most of Beaufort sea, i believe - at this point of the melt season.
The key thing here is to realize that water is quite opaque to IR radiation, which means that heat "inside" mixable layer - anything few dozens centimeters deeper than very surface water and down to ~150m deep, - is quite trapped in there; it can't be directly radiated "out". Another key thing to remember is huge thermal capacity of water. And yet another key thing to keep in mind is significant transparency of water to visible radiation - which most of sunlight is.
So this is what typically happens to ice-free sea/ocean during (sunny) day cycle, in my humble opinion: Sun goes up, (much of) sunlight penetrates into the water (especially when there are any significant waves, which is - most of the time), and travels through water column dozens (some photons - hundreds) meters trajectories (not equal "dozens or hundreds meters downwards" unless we talk close to equator, when entry angle is close to vertical). Beaufort sea, this - still significant now and for several more weeks, - insolation heats few dozens meters of upper sea water, being absorbed by water. Water then re-radiates part of absorbed energy as (mostly) IR radiation, but it can't easily go out as mentioned above, and so every sunny day simply adds more energy into the sea, but temperature rises very gradually - due to above mentioned water thermal capacity. But the energy stored by the end of summer - is quite huge.
When it's cloudy days, very little visible light makes it to the surface, most scattered, quite negligible; so then surface air temperatures, amount and features of precipitation (if present), cloud IR reflection and re-radiation, winds and other factors together form the SST direction, which may be upwards sometimes, but usually (and on average for cloudy days) is gradual cooling, i believe - much slower than open skies cooling, yes. That's how it sort of compensates: a full 24 clear sky (sunny) cycle in Beaufort right now would involve ~12 hours of still powerful sunlight, plus few more hours of "low sun" sunlight, plus some hours of near-darkness (Sun not much below horizon), with relatively fast cooling of the surface - i.e. "not much a change" in terms of net surface temperature change "after full 24h have passed"; while full 24 cloudy sky cycle in Beaufort now would be defined by temperature and features of clouds and airmass in general - and if it's a warmer airmass, may even be gradual warming (this time of the year, quite lots of warm air comes into Arctic, in general), but it as well might be gradual cooling - or even "no change". But in any case one midnight SST minimum would differ from both previous (24h earlier) and next (24h later) by few .decimals of a single degree celcius (except special, unfrequent occasions), - which is what we see the Buoy reporting indeed (i believe we got two sunny days last week on that bouy in Bering Strait, rest ~5 days being quite cloudy, moderate winds, today intensifying significantly if wave size reported is any indication).
As nights get longer and sun keeps going lower and for shorter times every day, amount of incoming solar radiation decreases, but the amount stored in the water is many times higher than any given "summer's day" worth of sunlight - a result of summer months and all the 24/7 summer sunlight of all clear-sky days. Convection of warmer waters to the surface is relatively slow process when we speak thick columns of sea water (50+ meters) and few degrees, if not few .decimals of degrees C, differencies. Storms can accelerate the process. Ocean (water) currents can affect any given location, replacing warmer mixable layer of water with colder (mechanically), or vice-versa. Surface air temperatures, if very low, can further accelerate loss of heat. But still it'd take few weeks for some well-mixed 3+°C sea to cool down enough for any good ice to appear, i think - not a single night or two, no matter what weather would be there, except some rather rare extremities, like extremely intense and very cold snowfall happening without any wind. And so there is still quite long road to re-freeze in non-CAB in general and in much of Beaufort sea in particular, for all parts with night SSTs (ok, morning SSTs if to be more precise) any higher than ~3°C. As demonstrated in one of graphs recently given in this topic, non-CAB refreeze in 2012 didn't start in any noticeable in terms of whole Arctic amount till quite much into October - i believe, exactly because extra ~2 weeks were needed for significantly warmer-than-freezing-point non-CAB seas to lose accumulated heat even in their _cooler_ regions.
The warmer your august seas are, the longer (more weeks) it'd take for them to do so. And right now, much of Beaufort is already noticeably above freezing point, iirc.
I hope this clarifies, if a bit, my ongoing confusion about those "frost comes" words.
Please do correct me - this is a request to everyone - if something in my understanding above is flawed. I am willing to learn.P.S. Quite a storm there in Bering Strait now, it seems? Up to 3m waves - i wouldn'a go fishin' in there for sure... It will mix quite some more heat into deeper layers, me thinks.
