The picture of the complete cloudless arctic is quite dramatic. However, as the ice is some months from minimum, the albedo is higher than it would be mid September. OTOH, there would be less insolation in September . Perhaps there is a 'maximum melt date' for given insolation. Has anybody
done a study on this ?
I have no idea, but I think it is a good question, and no-one has responded yet. Very probably someone already has the answer, and I bow humbly to them. But I like thinking aloud, so here goes. From my limited perspective, I think if you assumed clear skies, and went for calculating average watts absorbed per square meter by the ice, and divided that by average albedo values, it could be done.
To fluff this out a bit: We already know the insolation received per square meter of a theoretical flat surface in clear conditions at a given latitude at a given time. That is largely a geometric question. If we chopped the year up into, say, numbered weeks, and were able to access good data on the average albedo of the arctic ice during each week in the melting season, then we could take the average watts per square meter received for that week at that location and divide it by the average ice albedo value for that week. I think the units would still be W/m^2 actually (but from an absorption and not an insolation perspective), since albedo is expressed as a pure ratio with no units. I seem to recall there is a measure of albedo for the Arctic ice out there somewhere. (Choose your unit of time, multiply by that and you have energy absorbed if you want that too.)
So then we would know which week or weeks were likely to result in the absorption of the most solar radiation by a given area of ice at a given latitude, which I think is what you are asking for. One would have to take albedo data from a considerable number of years to accomplish this, and so the results would be historically weighted towards the past, but if there were a trend you could factor that in. And if it were this simple, someone has already done it. Or perhaps there isn't enough meaningful data on albedo to do this or perhaps I have missed something above. So... yeah... maybe I should just shuffle off stage now...