My understanding is that only the West Antarctic is vulnerable to
disintegrating over a century and that most of the base of Greenland
is above sea level, which it sort of has to be, or it would have
disintegrated already. East Antarctica will not go anywhere for a very
long while.

> I have been doing some back of the envelope calculations, like to melt
> 70 metres of water by mixing it with sea water would require cooling
> around 600 metres of water by 10C, or something of the order of three
> decades worth of the complete insolation the Earth receives. Or, at
> 200 W per m2 just for Antarctica alone (say around 10 million square
> kilometres) it would take of the order of a thousand years to melt the
> ice.
>
> What sort of scenario do you need to get the ice sheets to melt
> completely in less than 100 years?

The west Antarctic ice sheet will not melt. It will fail mechanically
and will float away in bits. Sea level can consequently increase by
meters in a century, and has done so in prior failures of West
Antarctica. "The rise of sea level during meltwater pulse 1A was as
much as 16 meters within 300 years (14.6 to 14.3 thousand years ago)."

http://initforthegold.blogspot.com/2007/08/4-meter-sea-level-rise-precedent.html

Some people seem to believe that some sort of mechanical
disintegration is possible in Greenland, abetted by moulins.

As for your calculations:

If Greenland and WAIS were to melt completely, sea level would rise 12
m. Ocean area is 3.6e14 m^2 http://en.wikipedia.org/wiki/Ocean so the
volume of ice at issue is 4.3e15m^3 or 4.3e15 tons.

Watt-hours to melt a ton of ice:
latent heat of melting = 334 kJ/kg = 3.34e8J/ton = 92778 watt-hour/ton
Total energy to melt the vulnerable ice sheets = 9.28e4 * 4.3e15 =
3.99e20; call it 4e20 watt-hours.

Solar energy at top of atmosphere per meter, average =  330 W /m^2
Total energy impinging on earth = earth area * top of atmosphere solar
constant = 5.1e14m^2 *3.3e2W = 1.6e17 W

Number of hours to melt all ice if the sun did no other work:
4e20/1.6e17 = 2500, or 104 days.

Suppose we only use the excess energy at the surface due to CO2
doubling (feedbacks included), believed to be around 4 W/m^2. Then the
time is multiplied by 330/4 = 206250 hours = 23.5 years.

So it would take about a quarter of the excess energy due to 2xCO2
over a century to melt Greenland and the WAIS. As you point out, some
of the energy will come from thermal energy banked in the ocean rather
than directly from the sun.

But I am not getting numbers comparable to yours. To go from my 12 m
to your 70 requires a factor of only 6, meaning it would require the
complete solar input for 624 days.

While I agree you could not in practice melt the main Antarctic ice
mass in a century, we are in disagreement by a factor of 15 if I
understand you correctly.

mt

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