After I wrote that message I realized that this would bring us back to our discussion at the start of the season; What adds more energy to system? Storms, or insolation? So it's good you wrote that.
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It's all about adding energy to the system, and so we're back to our debate from old; What adds more energy to the system? A storm, or the sun?
I'm stubborn thinking it must be insolation, but I understand your argument now that storms add a lot of energy to the system as well. And storms do open up the ocean so that the heat from the sun can more easily be added to the system...
Indeed, it is a rehashing of an old haggis. And I seem to remember that both of us, and with Oren weighing in as well, came to the shared conclusion that insolation is the main cause of heat entering the system during peak insolation.
And we both agree that a storm causes mixing and thus brings heat from the ocean to bear on the ice.
But what seems to be missing from your reasoning is the fact that a typical storm is also a bringer and conveyor of warmth in and of itself. This is something that is obvious to those living in coastal areas in along the North Atlantic, Scotland, Iceland and Norway.
Outside of the short months of summer, a storm always has higher air temperatures than before or after. A typical late autumn or early spring storm in Iceland is easily 10 degrees centigrade, with heavy rain. I've even experienced storms like that in the middle of winter. And there are periods where the storms come one after another, three or four in a week. And it is always colder between storms than during a storm except during high summer.
So back to the Arctic - I'd suggest that during June and July, storms would bring less energy to bear on the ice than insolation. During August, September and even further into the Autum, cyclones coming in from open water will transfer quite a lot of energy to the ice, while insolation is rapidly dropping down to nothing. During late spring, before insolation picks up, the same shold apply.
But we must not forget the third vector of energy infusion - ocean heat. And I would suggest that it is dwarves the others - but is at the same time inefficient in a melting contexts, since most of the heat does not reach the ice.
So can we rank these vectors and their interplay when it comes to melting ice? Even if Insolation would seem to be the favorite, we must remember that it still accounts for only around half the melt (simply because so much of a melting season happens outside of peak insolation).
Most of the rest I suppose is caused by ocean heat. And this is where storms kick in - they act both to give mechanical force to the system, mixing waters and moving the ice, and thus enabling the ocean heat to interact more efficiently with the ice. And secondly, the increased air temperatures and moisture that a storm carries in over the ice has it's origins in that same ocean heat.
So I'd suggest that insolation and ocean heat are the two main drivers of melt each year, with storms playing an important part in bringing the latter to bear on the ice, thus increasing melt at all times other than the during peak insolation.
And that storms can inhibit melt only during peak insolation, but will enhance melt during all other times.