Melting the Antarctic ice sheet
How long might this take, in the worst case?
The Antarctic ice sheet has a volume of about , according to Bedmap2^{1}. This is of ice. The density of ice is about (about a tonne per cubic metre, which is approximately the same as water of course), so this is about of ice. The enthalpy of fusion of water is about so, if we assume that the ice is all at freezing point^{2}, then we require to melt it all.
Let’s assume we use the Sun to do this. The solar constant is about : this is the amount of power per square meter that the Sun provides at the top of the atmosphere. So, imagine we use all of the power that the Earth intercepts from the Sun to do this^{3}. Well, the Earth’s radius is about so the total power available is about , or about .
So to melt the Antarctic ice cap, using all of the power from the Sun that reaches the top of the atmosphere would take
Well, there are about seconds in a year, so this is about 1.5 years.
Of course we can’t use all the Sun’s power: even if we had the technology to do this (which we are not anywhere near doing!), doing this would cause an inconceivable catastophe for the rest of the planet: this would be a winter night which lasted for a year and a half. Everyone would die.
A plausible figure might be a tenth of one percent^{4}: in this case the Antarctic ice sheet would melt in about years.

The ice is, of course, far below freezing so the actual energy required will be much greater. ↩

This is enormously more than the amount of power that we could plausibly use: see later. ↩

This is just a number I have pulled out of thin air: one percent seems too high, so perhaps a tenth of one percent is plausible. ↩