He has skimmed across it on sledges, flown over it in planes and even sailed under it in a submarine, using instruments to measure the ice's thickness.

Wadhams, 65, has predicted for years that a long-term shrinking of the ice cap will culminate in disaster. He believes the ice will melt entirely, accelerating a change in climate, and stranding the region's most famous inhabitant, the polar bear.

Last year, it seemed the prediction might be coming true. A huge late-summer storm ripped across the 2m square miles of ice. By the time it was over, a quarter of the ice cap had disappeared.

This year, Wadhams wondered if the same thing might happen again, leaving the Arctic partly free of ice. It would have provided a powerful symbol of the threat from climate change - but it was not to be.

Instead, as Wadhams and his colleagues monitored their satellite images and other data, there was another surprise in store. They saw that the ice cap had grown back during the winter. Not only that, but it then held its own during the summer. Last week, when it was probably at its smallest size for the year, it had been restored to its 2m square mile expanse.

The climate sceptics - those who see global warming as a myth or an exaggeration - claimed vindication. "Now it's global cooling" screamed one headline.

Wadhams said the picture was a little more complex than that. "It is true that the ice has grown in extent compared to last year," he said. "But what was not reported is that it is also much thinner. If you look at the total volume there may be a little more ice there than last year, but not much. What's more, it is still far below the long-term average and the overall trend is downwards."

Benny Peiser, the director of the Global Warming Policy Foundation, a London-based think tank that challenges many aspects of climate science, saw it differently. He seized on reports of the Arctic ice cap's recovery, circulating them to ministers, MPs and other policymakers.

"The science is going nowhere," he said. "Even if you accept the idea that CO2 [carbon dioxide] and other greenhouse gases will warm the world, science cannot tell us by how much or what the effects are. The climate models have failed."

Doubters like Peiser believe the phenomenon of the refrozen north has exposed another flaw in the calculations of climate scientists - especially those of the Intergovernmental Panel on Climate Change (IPCC), whose latest assessment is due out this week.

The IPCC's scientific project is one of the most ambitious ever attempted. Its aim is to collate the findings of thousands of researchers around the world and turn their work into a practical guide to climate change in the hope that politicians and the public will act on it.

With big ambitions have come big mistakes, however. Perhaps the worst was in 2010 when the IPCC had to retract one of its most apocalyptic warnings, that climate change could melt most Himalayan glaciers by 2035.

That claim, in the IPCC's 2007 report, was accompanied by the suggestion that rain-fed crops in north Africa could be hit by a 50 per cent decline in yields by 2020. This has also been judged untenable and dropped.

Climate science is now facing a broader challenge since it emerged that global warming has virtually stopped. In the years from 1998 to 2012, the Met Office recorded a rise in surface temperatures of just 0.051C, far below what had been expected.

No wonder a study by the UK Energy Research Centre last week found that the proportion of people who do not believe in climate change has more than quadrupled since 2005: 19 per cent say it is not happening and another 9 per cent are uncertain.

A YouGov poll for The Sunday Times today shows that 39 per cent think the risk has been exaggerated. Only 56 per cent now think the climate is changing as a result of human activity.

The scientists seem baffled that public confidence in their findings is melting faster than a Himalayan glacier, just as they are getting more certain of their ground.

The IPCC's new report, to be released this Friday, will say humanity's emissions have already warmed the Earth by around 0.7C - and could push temperatures up by between 2.6C and 4.8C by 2100 if the emissions keep rising, with 3.7C the most likely figure.

Today about 500 scientists and civil servants from all over the world are flying into Stockholm to put the final touches to the "fifth assessment report", an account of how greenhouse gases are affecting the Earth.

The meeting, in a former brewery, will also generate a sober 30-page document advising politicians on how to respond.

A leaked draft says climate change has been having significant impacts since 1950. "The atmosphere and ocean have warmed; the extent and volume of snow and ice have diminished; and sea level has risen," says the draft.

On temperature, it points out that "each of the last three decades has been warmer than all preceding decades since 1850, and the first decade of the 21st century was the warmest".

What is more, it warns that warming is likely to accelerate. Since 1951 global temperatures have increased by 0.13C a decade. If CO2 emissions keep going up, it says, temperatures could eventually rise around twice as fast.

The report says sea levels are rising by 3mm a year, a rate that is also likely to accelerate as the world warms.

Myles Allen, professor of geosystem science at Oxford and a lead author for the IPCC, said the report would present solutions as well as problems.

"If we want to limit average global temperature rises to 2C or less, then we have to limit the total carbon dumped in the atmosphere to about one trillion tonnes," he said.

"Since 1700 we have released about half a trillion tonnes, but we are burning fossil fuels so fast that we are on course to release the trillionth tonne in 2040. We would need to start cutting emissions by an average of 2.5 per cent a year from now to keep below that limit. But instead emissions are actually rising at around 2-3 per cent."

Some argue that Britain need not worry too much. Studies suggest there may be some benefits in the short term from warmer weather, not least a boost for tourism and cuts in the cost of heating homes in winter.

Professor Stephen Belcher, head of the Met Office's Hadley Centre for Climate Prediction and Research, disagrees. He warns that climate change is already raising the risk of extreme weather events such as the European heatwave in 2003, when the hottest summer for at least 500 years was said to have caused 70,000 premature deaths.

"Such events are now about twice as likely because of greenhouse gas emissions," Belcher said.

Claims of this kind are greeted more and more warily by policymakers and the public, however. Some are put off because climate change has been exploited to further the agenda of anti-capitalist greens opposed to economic growth.

In America that perception has seen opposition to climate science crystallising in the Republican party.

In Australia, the recent election propelled Tony Abbott's Liberal party to power after a campaign in which he expressed scepticism about climate change and opposition to Labor taxes on carbon emissions.

In Britain, by contrast, climate change policies have had cross-party support so far. But there are many who want that to change, especially among Conservatives, where senior figures such as Lord Lawson, the former chancellor, have questioned climate science. Owen Paterson, the environment secretary, and George Osborne, the chancellor, have expressed scepticism about measures to counter warming.

Such tensions mean an interesting time ahead for Sir Mark Walport, the government's chief scientist, who, over the coming weeks and months, will be briefing David Cameron and his ministers on the IPCC's findings and how to respond.

"There are some uncertainties about the future, but what's clear is that if we continue to emit greenhouse gases then we are heading for trouble," Walport said.

Lord Stern, president of the British Academy and professor of economics at the London School of Economics, has put forward radical plans.

"If temperatures rose 3C it would produce mass migration around the world. Areas like southern Europe could become uninhabitable," he said. "Our current economic models need to be changed to take account of the cost of this. In Britain, for example, it means decarbonising all our electricity and transport within 20 years."

The idea is to convert the nation's electricity generation to low carbon sources such as nuclear, wind and solar - and then use that power to run our cars (which will be largely electric by then) and our homes.

Geoengineering is another solution discussed by the IPCC - but without much optimism. It looks at the idea of launching giant mirrors into space to deflect sunlight and acknowledges that this would have the "potential to substantially offset a global temperature rise".

Such an approach would be technologically highly challenging, warns the report, and would "modify the global water cycle", meaning it would alter weather systems. What is more, if the mirror were damaged, for example by a meteor, the planet would experience a sudden surge in temperature.

Another approach is to try to strip CO2 from the atmosphere, for example by using minerals or chemicals that react with it as air passes over them. Some scientists have proposed building forests of artificial trees treated with CO2-absorbing chemicals. But the IPCC report warns that this too is beset with problems, not least the cost.

What seems clear is that whatever our response to climate change, whether it is geoengineering or replacing fossil-fuelled electricity generation with low-carbon power stations and wind farms, the bills are likely to be astronomical. As long as public confidence in climate science is falling, it would take a brave political leader to sanction spending on that scale.