Update: I stumbled across a source for the albedo feedback of a Blue Arctic event. See footnote .
We haven’t had a good algorasm here in a while, so let’s break out our calculators and do some plug-and-chug math regarding a critical topic: the consequences of a Blue Arctic.
I define “Blue Arctic” as the Arctic Ocean being largely ice free for at least a few days. I say “largely ice free” because even once Blue Arctic events become regular features of late Northern summers there will certainly still be considerable ice around the northern or northwestern coast of Greenland, for example. I’m sure scientists will come up with some metric for declaring the Arctic to be “virtually ice free”, such as total sea ice extent or area below a magic number, or perhaps everything north of a certain latitude being open water. The point is, it’s going to happen and we’ll know it when we see it.
Right now, we’re on a trend of losing roughly 300 billion tons of ice per year from the Arctic ice cap, as seen in the PIOMAS graph we all know, love, and lose sleep over. Once we reach the point of regular Blue Arctic events, we won’t be able to lose that much ice, net, in a given year; unless you make the wildly implausible assumption that the Arctic volume will suddenly begin to rebound by 300 billion tons/year every winter, even as it experiences much greater levels of warming due to albedo flip, or the summer melt is suddenly much decreased, the rate of yearly ice volume loss simply has to slow down. For the sake of this calculation, let’s assume that the Arctic in a given year has a net ice loss of “only” 200 billion tons. Ignoring the albedo flip issue for the moment and all the additional heat that will be absorbed by open ocean instead of being reflected back into space by white snow and ice, how much extra heat are we talking about being absorbed by the ocean simply because we’re not melting ice the full 300 billion tons of ice?
Melting 200 billion tons means that we’re not melting 100 billion tons. That heat has to go somewhere, and the open ocean will surely get the vast majority of it, as over 90% of global warming currently winds up in the oceans.
100 billion tons of ice is 1.0 x 1011 tons, which is
Result 1: 1.0 x 1017 grams of ice
The energy needed to melt ice, that is, to convert it from ice at 0°C to water at 0°C, or its heat of fusion, is 334 Joules per gram of water.
Therefore, the amount of heat that would have gone into melting that 100 billion tons of ice is:
Result 2: 3.34 x 1019 Joules
(Note that I’m ignoring the heat that would have been absorbed by raising ice from below 0°C to 0°C, as well as the heat to warm the resulting water above 0°C.)
If you used all that newly-available heat to warm liquid water, you can find the amount of water you could raise by 1°C by dividing by the specific heat of water, 4.18 Joule / gram ° C, which gives us:
Result 3: 8.0 x 1018 grams of water
That’s a lot of water. The amount of water in Lake Ontario, for example, is about 1,640 km3, or the same number of billions of tons. Converting that to grams gives us:
Result 4: 1.64 x 1018 grams
Dumping all that heat from our non-melting of Arctic ice into Lake Ontario would therefore raise the temperature of the entire lake by (Result 3) divided by (Result 4), or
4.87°C, roughly 8.8°F
Once we transition into this new state, where we experience yearly Blue Arctic events, we would see additional heat accumulation every year, with the amount starting smaller than I’ve calculated above but rising as the amount of ice in the Arctic continues to decline, allowing less yearly net melt out each year.
Speaking as someone who lives very close to Lake Ontario, up here on the “Fourth Coast” of the US, as some people like to refer to it, and has driven around it a few times, I can tell you with utmost certainty that this result is terrifying.
And let me stress again that this calculation does not include albedo flip — all that additional open ocean every summer on top of the world will lead to much more heat absorbed by the environment.
It seems we’re just beginning to appreciate how rapidly the environment can flip. As I’ve pointed out several times, if you simply look at maps of the Arctic and Antarctic regions and think in terms of ice, permafrost, and hydrate deposits, you couldn’t ask for two more different geographies and what they imply in a warming climate. Antarctica, with its central land mass and very little surrounding land, is conducive to stability: Slower ice dynamics because so much of the ice is on land, no major albedo flip component, and little to no permafrost and hydrates in the area. The Arctic is just the opposite: A huge area of sea ice that can melt quickly and then create the albedo flip feedback, surrounded by massive permafrost and hydrate deposits primed to accelerate the whole process.
In fact, I don’t see how one can escape the conclusion that the saw-tooth pattern that arises in temperature reconstructions (note the rapid rise of the black line, most obvious in the sections highlighted in yellow):
(Source: NOAA Paleoclimatology Program)
is a direct function of geography. During warm periods, biological carbon builds up in the northern latitudes, dropping atmospheric CO2 levels and slowly cooling the environment. Eventually, those areas freeze into permafrost, locking away huge stores of carbon (currently about 1.7 trillion tons), and more hydrates form due to cooler ocean temperatures, until something comes along and jostles the system, whether that’s an orbital perturbation or human beings burning every bit of fossil fuel we can get our hands on. That little bit of warming is the first domino to fall; it then pushes albedo flip and permafrost and hydrates, resulting in a relatively quick liberation of at least some of that locked-away carbon, and the result is a temperature spike.
Without realizing it, we’ve been living on a razor’s edge since the beginning of the Holocene, and we’re ending it very abruptly with our emissions.
For all the “it’s worse/happening quicker than we thought” discoveries of the last decade, I fear that we’re set up for one of the worst epiphanies possible when Arctic change builds some momentum and starts liberating even a tiny portion of the 1.7 trillion tons of carbon in the permafrost. There’s endless discussion about climate sensitivity — how much warming you get, pre-feedback, from a doubling of atmospheric CO2 — and I’m increasingly convinced that this is a misguided view of our precarious situation. The question is not how big is that first domino, but how much larger are the next few it sets in motion once disturbed.
 At least those of us not at the mercy of irrational financial or ideological leanings who will somehow refuse to see it at all.
 Anyone here have a handle on how to convert sea ice area converted from ice to open ocean to heat absorbed? I’ve seen a number quoted that the ice loss already realized is equivalent to a forcing of 0.3 W/square meter over the entire Earth’s surface, but I’m not comfortable trying to extrapolate that to new ice loss and the Blue Arctic events addressed in this post.
Estimating the global radiative impact of the sea ice–albedo feedback in the Arctic
Abstract [emphasis added]:
A simple method for estimating the global radiative forcing caused by the sea ice–albedo feedback in the Arctic is presented. It is based on observations of cloud cover, sea ice concentration, and top-of-atmosphere broadband albedo. The method does not rely on any sort of climate model, making the assumptions and approximations clearly visible and understandable and allowing them to be easily changed. Results show that the globally and annually averaged radiative forcing caused by the observed loss of sea ice in the Arctic between 1979 and 2007 is approximately 0.1 W m−2; a complete removal of Arctic sea ice results in a forcing of about 0.7 W m−2, while a more realistic ice-free summer scenario (no ice for 1 month and decreased ice at all other times of the year) results in a forcing of about 0.3 W m−2, similar to present-day anthropogenic forcing caused by halocarbons. The potential for changes in cloud cover as a result of the changes in sea ice makes the evaluation of the actual forcing that may be realized quite uncertain since such changes could overwhelm the forcing caused by the sea ice loss itself, if the cloudiness increases in the summertime.
Looks like my vague recollection mentioned in  was in the ballpark but not right — the magic number for a Blue Arctic event is 0.3 W m-2, and I thought that was the number for the loss already realized.