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The great ice sheets covering Antarctica and Greenland have enough frozen water locked in them to raise the global sea level by some 70 metres. The West Antarctic Ice Sheet may be inherently unstable and if it collapses the universal belief is that it would raise sea levels by 5–6 metres globally. But that estimate is wrong. What happens to sea levels when an ice sheet melts is complex and surprising. In some places, even, levels can go down. Jonathan Bamber explains.