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I'm thinking biggest in volume, regarding which area of the planet will contribute more to a raising in sea level - were the ice in those regions to melt.
I can basically think of two candidates, namely Greenland and Antarctica. So maybe some comparison between the contributions of the two would be great.
Antarctica is the ice sheet (cap) that will contribute most IF it would melt completely. The 2013 IPCC report (Ch. 4, the Cryosphere) provides an estimate of 58.3 m of sea level equivalent (sle). Greenland would if completely wasted away provide 7.36 m sle. Remaining glaciers provide an additional 0.41 m sle. The likelihood of Antarctica completely wasting away seems unlikely with our current understanding although the so-called West Antarctic Ice sheet (closes to the Antarctic Penninsula is sitting with its base deep below the current sea level) is far more likely to be lost than the East Antarctic Ice Sheet. Hence the contribution from Antarctica is likely less than the maximum number. Greenland on the other hand is thought to have a "point of no return" beyond which it will irreversibly be lost given the current or warmer climate. Since Greenland is mostly land-based, much of the mass loss will be by surface melting while West-Antarctica can lose much of its mass by ice berg calving which is likely a much faster loss mechanism. Estimates on the scenarios are emerging but there are still uncertainties and there may also be feedbacks that we either do not fully understand or have not yet seen that can change these scenarios (particularly for West-Antarctica). This Science article published online May 12 2014 is a good example of emerging research on the stability issues of West Antarctica.
