The 3.66 x 10[SUP]23[/SUP] joules is just the
heat of fusion. That is the energy required to melt that much ice. Just what percentage of the earth energy imbalance do you think would be available for that result?
Why are you making this a scavenger hunt?
If you want a genuine answer to a genuine question, then you need to ask the entire question, with all the relevant parameters.
we are speaking real world, not hypothetical. I did not move the goalpost.
If we are speaking of the real world, then we know that global temperatures are already warming enough (in the atmosphere and oceans) to cause the melting of global ice, both at the poles and in various glaciers around the world.
Since I am not (and do not claim to be) a trained climatologist, and if you want actual accurate answers based on projections informed by empirical observations, I'd have to find some academic research which provides the answers you want. Or am I supposed to ignore empirical evidence, and continue your mathematical scavenger hunt instead?
It takes an amazing amount of heat.
I have absolutely no doubt that is the case.
However, it takes an amazing amount of extra heat trapped in the atmosphere to increase global temperatures by 0.85° C. And that is what's happened since 1880.
We should also note that sea levels have risen by 8" since 1880. That's a lot less than 3700 years, no...?
3.66 x 1023 joules of heat
Uh huh
So, more napkin (restaurant?) math. Roughly speaking, it takes 417 kJ to increase the temperature of 1 kg (1 liter) of ice from 0° C to 20° C. Let's use this as a high estimate.
All of the ice in Greenland is estimated at 2.85E18 kg; if it all melted, sea levels would rise an estimated 23 feet (276"). To increase sea levels by 10", we need to melt 1.03260869565214E17 kg of ice.
That requires 4.30597826086942E22 joules.
Let's take my previous figures as a benchmark. Reducing radiation to space by 0.1% adds 1.49472E19 joules per day. That amount of energy would take 2,880 days, or a mere 7 years, to trap that much extra heat.
As you noted, that's not all going to go directly and exclusively to glaciers that will melt directly into the oceans. However, if 10% of it reaches those glaciers, then we've got 10" of sea level increase in 70 years.
Obviously, this is a vast oversimplification. For example, land-based glaciers that flow into the ocean do not need to melt to raise ocean levels -- even if they remain frozen, a large enough glacier would displace ocean water, and raise ocean levels long before it actually melts.
Anyway... I'm sure that the radiation and polar absorption figures are not correct, so it's probably just a coincidence that I'm in the right neighborhood. However, it does at least show that the "amazing" amounts of energy required
can be conceivably trapped in the Earth's atmosphere.
More importantly, though, is that it
has happened. We know sea levels have risen 8" since 1880. We know global temperatures, in the atmosphere and oceans, are rising. We know this is producing feedback effects, and we are already seeing them. Rising global temperatures are almost certainly responsible for the crack in the Larsen C ice shelf, which is thousands of years old... and the topic of this thread.
Even as I type this, the crack is accelerating;
there are only 8 miles left, and it could calve any day.. It's not clear if this will destabilize the entire shelf, as happened with Larsen B. If it does, then the land-based glaciers will likely be able to flow into the ocean, and this will accelerate the rate of sea level rise.
So yes, I'm confident that 10" of sea level rise is
much closer to 70 years, than 3700 years.