Scientists have solved the enigma of the Antarctic apparently getting cooler, while the rest of the world heats up.

New research shows that while some parts of the frozen continent have been getting slightly colder over the last few decades, the average temperature across the continent has been rising for at least the last 50 years.

In the remote and inaccessible West Antarctic region the new research, based on ground measurements and satellite data, show that the region has warmed rapidly, by 0.17C each decade since 1957. "We had no idea what was happening there," said Professor Eric Steig, at the University of Washington, Seattle, and who led the research published in Nature.

This outweighs the cooling seen in East Antarctica, so that, overall, the continent has warmed by 0.12C each decade over the same period. This matches the warming of the southern hemisphere as a whole and removes the apparent contradiction.

The issue, which had been highlighted by global warming sceptics, was an annoyance, said Steig, despite the science having been reasonably well understood. "But it has now been killed off," he said.

Gareth Marshall, climatologist at British Antarctic Survey, commented: "This work allows us to look at the continent as a whole, which we have not been able to do before with confidence. It fills a big hole in the data in West Antarctica – it is the final piece in the jigsaw."

The rapid warming now revealed in the west concerns some scientists. The new analysis suggests the West Antarctic ice sheet, like that in Greenland, is precariously balanced, said Professor Barry Brook at the University of Adelaide. "Even losing a fraction of both would cause a few metres of sea level rise this century, with disastrous consequences," he said.

It was well known that a small part of Antarctic was warming – the peninsula that protrudes northwards towards South America and is the site of many research stations. But researchers knew that East Antarctica had cooled a little in recent decades and thought that might be the case across the continent's great mountain range in West Antarctica.

Temperature records have been taken on the ground since the first weather stations were built in 1957. But all but two of the 42 are very close to the coast and therefore give no information on the vast interior of the continent. Satellite data, in contrast, can take the temperature of the entire region by measuring the intensity of the infrared radiation reflected from the snow pack and has been available since 1980.

Steig's team found the mathematical relationships between the weather station data and satellite data, tested them, and then used them to go back in time to estimate temperatures across the continent back to 1957. Their statistical model has now been validated by an ice core drilled into the Rutford ice stream in West Antarctica by the British Antarctic Survey, from which temperature records can be measured. That independent work also came up with a warming of 0.17C a decade for the region, and stretched the trend back to at least 1930.

The cooling seen in East Antarctica is caused in part by the ozone hole that opens each year in the atmosphere. The ozone hole causes an increase in westerly winds which, by a complex interaction of wind, sea and ice, results in lower temperatures in the east. Emissions of ozone-destroying gases have now almost been eliminated and the hole is expected to recover by mid-century. When that happens, there will be a rapid catch up of temperatures, says Marshall.

The 2007 report from the UN's Intergovernmental Panel on Climate Change said that the impact of greenhouse gas emissions could be seen on every continent bar Antarctica. The new work, along with another recent study, now clearly shows that the rising temperature of the continent cannot be explained by natural climate variation alone.