Rob, your comment is demonstrating the dangers of thinking you can get to grips with heat transfer without "overanalysing". Unless you have just expressed your thoughts poorly, I get the impression you don't know what radiation balance is. Could you provide a link for Screen et al?
I'm sorry, Andreas, re-reading my own comment I can see that indeed I was sloppy with my words.
Let me rephrase.
All I wanted to do was to come up with a ballpark number for how much bottom melt is happening in the Beaufort, and how much goes to warming the water.
Making some simple assumptions (20 meter mixing layer, 280 W/m^2 SW insolation, 3 C warming of the Beaufort since it opened up) I concluded that some 17% goes to warming the water, and thus that more than 80% must have gone to bottom melt.
I am perfectly open to adjustments to these assumptions, but only with supporting evidence.
Now somebody said that I should subtract 40 W/m^2 because of surface LW imbalance.
There I mentioned two issues :
1) If we are going to bring in LW imbalance, then we should also bring in regular atmospheric heat transfer. After all, if there is a significant LW radiative imbalance, then even the surface temperature of "white" (reflecting SW) areas like these floes that are drifting in the Beaufort should cool down. But since these floes are now also top-melting suggests that any LW imbalance is compensated by plain old atmospheric heating.
2) I questioned that 40 W/m^2 LW loss. Just seems quite a lot.
There I found fig 3 in the Screen et al 2010 paper ""The central role of diminishing sea ice in recent Arctic temperature amplification" in your "Radiative balance in the Arctic" thread :
https://farm3.staticflickr.com/2936/14234219758_372564238c_o.pngwhich suggests that indeed in spring there is a radiative imbalance of some -40 W/m^2 while in summer there is a surplus (atmosphere radiatively warming the surface) of something like +30 W/m^2. I figured that are the transition time between spring and summer (over the past month) there would not be much or LW radiative imbalance.
However, I now realize that this Screen 2010 figure is total net surface radiation (SW plus LW) over all latitudes in general. That means the figure is not very useful for determining LW imbalance for specific surfaces in specific locations.
Your CERES figures are more useful there, although it is very hard to determine the LW imbalance over open water, the last CERES graphs your posted show something very useful :
The very interesting part there is the "Surface Net Total Flux", specifically over the open water areas in June 2015 (which was the Bering Strait). There CERES reports about 200 W/m^2, which is a very useful adjustment to my 280 W/m^2 insolation number.
But if we go there, we should really try to determine heat input from lower latitudes (my point (1)) too. After all, the land areas are much above 0 C and thus the winds blowing over ocean have quite a bit of heat that WILL warm the water too.