The comparison between a PIOMAS model run without the cyclone shows that the cyclone caused an additional 450,000 km2 of melt by the 21st of August. However after this date the model run without the cyclone gains ground, quickly at first, and then slowly right until minimum. A large amount of ice is separated from the main pack, and melts rapidly during and immediately after the cyclone. It is about the 21st that the melt of the separated portion is complete. A large part of the extra melt is found in the model to be due to mixing of ocean heat from the near surface maximum temperature layer. This results in a significant reduction in the amount of heat available in the near surface maximum layer. I am guessing that the large gains made by the no-cyclone case after the 21st are due to the fact that the detached portion of ice is still melting out. By the time this process is complete slow gains continue to be made, and my guess is that this due to the large amounts of heat available in the near surface layer.
The rapid melt due to the GAC 2012 was largely due to a rapid melting of the detached area of weak ice, and due to a rapid mixing of heat from the near surface maximum layer. If this cyclone had not occured the detached area of ice would have melted regardless , and a lot of the near surface maximum temperature layer heat would have reached the ice anyway. A lot of the impact of the GAC 2012 was to speed up melt that was going to happen anyway.
Some interesting reading on the
near surface temperature maximum layer. It is roughly 10-20 meters down, is not throughout the Arctic, but is particularly prevalent in the Beuafort Gyre and Candian Basin. It is formed by heat absorbed from above during summer. Research in 1995 found that the layer disappeared by about October, however current research finds that thinning of the Beaufort Gyre, increased downwelling of water and stratification have allowed some of this layer to survive through winter.