I really wish we had more information about what is going on below the ice, and the state of submerged ice.
Like Wayne has showed there is an active melt-refreeze zone of porous ice. The more porous the ice is, the higher the effective area vs. volume is. And the higher the effective area vs. volume heat is allowed to work on, the faster the melt will be. If the ice is thin enough this porous zone will also contribute through decreased albedo.
From this laymans perspective the low quality of the 2012 ice could be a significant part of the explanation behind the rapid and extensive reduction last season.
If the quality of the ice is worse than last season 2013 might prove to be even more of a surprise than last year, especially if you just consider volume and area, without considering the quality of the ice itself.
If some of that warm atlantic water upwelled during the winter (and it probably did in Chukchi at least) we could have huge areas of porous low-quality ice, primed for accelerated melt when insolation starts doing it's thing.
I know most of this is pure speculation, but I just can't get past the similarities between the way a high alpine lake behaves at ice-off and the way the Arctic sea ice has behaved the last 5 years.
I just skimmed
Ice Tank Experiments Highlight Changes in Sea Ice Types. Does anyone know if a similar experiment has been done in reverse?