i'd say we can safely settle on very approximate range of ~180...300 W/m2 absorbed at the surface under clear skies (high pressure systems) for late July / early August
So about 5-9 cm of ice per day might be melting under the clear skies of the big high pressure system soon to arrive in the CAB.
Reason: it takes about 35 W/m^2 to melt each centimeter of ice per day:
Energy flux to melt 1 cm thickness of ice per day [in units of W/m^2] = 1 cm x (10^4 cm^2/m^2) x (334 J/g latent heat of melt) x (0.9 g/cm^3 density) / ( 3600x24 seconds/day)
= 35 W/m^2
(Uses the definition W = J/s)
DISCUSSION POINT
Doesn't that seem a bit high?
...
Understandable confusion. What you miss in the basic picture of the process - is basics about how absorption works. You assume that all 180...300 W/m2 goes into melting the ice. In reality it does not: like already mentioned above, some of that energy is lost via evaporation (mostly from liquid water at the surface, but even dry ice actually evaporates slowly).
Further, whenever there is any noticeable open water - most of those 180...300 W/m2 gets absorbed at significant depth of downwards water column, since you know, water is a transparent thing. Noticeable amounts of light are present even at ~200 meters depth if my memory serves, - that's basically how deep significant fraction of absorption happens.
Same effect also happens to a lesser degree through the ice itself whenever there is no snow cover on it, increasingly so when the ice getting thinner: much sunlight simply goes through it and into water column below it, since ice is often significantly transparent, itself.
With water density being the highest at +4 Celcius iirc, a layer of colder melt water often remains near remaining ice, with warmer water sinking down as it's a bit heavier (though this much depends on water column mixing factors present at the location), which is another "sink" for some absorbed heat. "Sink" if we talk immediate insolation effects on ice thickness, of course - but in the same time, often it's also "delayed bottom melt" if we look further into melt season, as quite often large masses of warmer water from below end up getting near the surface and doing said bottom melt to still-remaining ice at a later date. This effect gets really nasty whenever some layers of water end up much warmer then 4C, thus losing density and starting to go up "themselves", without any water current forcing.
Yet one more heat sink which "steals" much of absorbed energy - is IR re-radiation. We know that in the absense of sunlight, Arctic ocean under clear skies cools down quickly and freezes into thick ice, during polar night. Why? Because it loses its surface heat, much via IR radiation right up into near-Earth space. Well, if you'd think about it, then you'd realize that this process is STILL happening summer-time, continuously, removing significant fraction of absorbed energy from the surface in short order. The intensity of this heat loss is not anyhow dependant on insolation, it's merely a function of surface temperature and emissivity of surface matherial. It's just that insolation brings in significantly more energy per second than amount lost via IR emissivity of the surface.
So, if you start to crunch 'em numbers of cm/day of ice lost, you can't neglect this and other heat loss mechanisms, if you want to arrive to anyhow realistic figures. Sadly, this kind of calculations takes more than a single small napkin. But one can try, of course. It's just that this topic is not quite the place to delve deeper into this, i suspect.
P.S. Neven, if you're going to snip this post, i'll understand... But IMHO it's better to achieve understanding about this among gentlemen here, which all the above helps to do in pretty short form, given relative complexity of described processes.
