NeilT, it is exactly that: double average melt rates and it'll be Blue Arctic, but 150% of average melt rates from now till early September - would not be exactly enough. I know that. But to me, that's not an argument against what i said above. Here's why.
Thing is, it seems you and Bill are both missing one most simple fact of ice melting process: it accelerates much (with everything else being the same) when ice concentration drops below 50%. Weather can both delay and accelerate "remaining melt" dramatatically at any given time and location, of course, even reverse it to freezing sometimes; but with "everything else the same", low-concentration areas will melt times faster than solid pack ice at near 100% concentration, which is why so many here are concerned about state of the ASI this season.
The most simple and obvious evidence comes from simple observation: a piece of ice allowed to melt while placed into non-changing melting environment. Here's a of the process. As you can easily see, after 15 seconds of the video, the piece still keeps its form, and its "area" is still more than a half of the area of the initial size, and its "extent" is pretty much 100% of the initial extent (assuming the piece is less in size than 1 satellite grid cell). Then the melt starts to accelerate visibly, bit by bit. 0:20 mark of the video, - is nearly where we're now in terms of this season, if i might add. Still, by 0:20, the piece still has its distinct shape and still occupies much of its initial size area and especially extent (still more than the "standard" 15%, so in NSIDC terms, that piece is still a part of 100% extent ice, eh). But the melt accelerates further, and by 0:25, much more than a half of remaining by-0:20 ice is gone, and all of it melts away by 0:29 mark of the video.
This means, you can't expect linear melt rates to be the case all the way to "0.0 thicknes / extent" situation. There is a point which can be designated as "less than a half than normal amount of ice left", after which melt rates will increase massively.
In 2012, we had, in my opinion, the 1st case when large parts of ASI went beyond this point; the GAC did so much damage exactly because there was little enough ice in its path for this natyural mechanic to kick in and help the GAC to melt lots of ice. Fortunately, 2012's melt season happened to end very soon after the GAC, plus 2012 had much of ASI still being relatively strong in other areas, wouldn't melt so easy.
This season, though, it's much worse. Which is why GAC(s), if they happen late in the season, are likely to clear much more ice than some people anticipate they would.
The above is the 1st mechanic (higher melt rate when "too little" ice is remaining), but not the only. The other big one "in the room" is that melt season, depending on weather, may last significantly longer than it usually does. The overall ASI _melt_ week some time during November 2016 is an excellent indication that this is possible, given weather which assists with it. If the melt season lasts till the beginning of October this year, for example, - then your "150%" rate will be quite sufficient to see Blue Arctic event at the minimum.
Overall, apart from the GAC of 2012 demonstrating _substantial_ effect of described mechanism in practice, the Arctic and especially the CAB has so far never demonstrated to us how quick "finishing touches" before the Blue Arctic event may happen. However, field scientists who see how ice melts in practice daily for many years of their life - they know this is real at least intuitively, but also often very consiously, too. This is why you so often hear field collegues reporting all kinds of "fear" that seemingly abrupt, sudden change may happen: they've seen this kind of "big acceleration near the end" in all sorts of melting processes, on mighty different scales, with their very eyes. Much like we see that ice cube accelerating its melt in the video above.
P.S. The above video with the ice cube is simplest, but not the best explanation for the acceleration of melt rates at "final" stages of ASI meltdown towards Blue Arctic. The better one -
is this: the more thin and more fractured ASI gets, the bigger total surface of ice-water boundary relative to remaining ice volume forms up. Due to always present imperfections in ice and fluctuations of salt content, ongoing melt creates "canals" and "complex surfaces" within remaining ice, which further increases said ice-water border surface (again, relative to remaining volume) total. This increasing ratio affects direct heat exchange intensity between remaining ice and water, plus leads to higher percentage of remaining ice volume to be penetrated by any given same level of IR radiation, which both lead to faster melt rate for remaining ice. This is why there is ever-present acceleration of melt rates "with everything else being the same" - a positive feedback very "built-in" into very process of melting ice.