Given the current hullabaloo about Al Gore winning the Nobel Peace Prize, I thought that I'd publish a little analysis that I did regarding the Greenland ice sheet. As you may have heard, the Greenland ice sheet is in peril- note, for instance, this 2006 study suggesting that climate change could melt the ice sheet in as little as 500 years. Since this is a worst-case-scenario (even most climatologists aren't this pessimistic), we'll probably have to wait much longer for the darned thing to melt. The problem is that the ice sheet has a mind-boggling amount of thermal inertia. Wikipedia describes the Greenland ice sheet as containing 2.85 km^3 of ice. Now, a km^3 is a billion m^3, and each m^3 of ice weighs about one metric ton (I know the density is off, but it makes the math easier.) The heat of fusion for water is 334 J/g, so melting each m^3 of ice requires 334 x 10^11 joules of energy, presuming it's already at o degrees centigrade. Since the primary sources of heat for melting the ice sheet is the dim arctic sun, it will take centuries for the ice sheet to melt.
(334 x 10^11) x 1,000,000,000 x 2.85= 9.519 x 10^20 joules
(This is the amount of energy 7,268 billion gallons of gasoline.)
Perhaps this isn't soon enough for you. Maybe you're a supervillain or someone suffering from an ice phobia. You want that ice sheet gone, by, say, next month.
Fortunately, technology has an answer.
One megaton is 4.184 x 10^15 Joules, so the amount of energy needed to melt the ice sheet is 227, 509.56 MT.
This is a very large amount of megatonnage, far more than existed even at the very height of the Cold War- but far from beyond the scale that could be built, as we will see.
The first nuclear weapon, the Mk-1 dropped on Hiroshima in 1945, had a yield of approximately 15 kT. Therefore, it would take 15,167,304 Hiroshimas to melt the ice sheet. This is an imposing number, and would require far too much enriched uranium to be practical. Large thermonuclear weapons make this far more practical. The largest nuclear weapon ever built, the Soviet Tsar Bomba, had a predicted yield of 100 MT. (It tested at 56 MT because the U-238 tamper was replaced with lead to reduce fallout.) It would take 2,275 of these bombs to melt the ice sheet. The largest nuclear weapon ever mass-produced, the American B-41, had a maximum yield of 26 MT. It would take 8,751 B-41s to melt the ice sheet. As 400-500 of the B-41 were built during the early 1960s, large thermonuclear bombs can almost certainly be built in the quantity required. The primary problem would be sourcing enough tritium and Li-6 to build the bombs (or maybe deuterium, as the bombs don't need to be deliverable.) In any case, it is definitely possible to melt the ice sheet on a short-term basis if need be.