It is calving season in the Arctic. A flotilla of icebergs, some as jagged as fairytale castles and others as smooth as dinosaur eggs, calve from the ice sheet that smothers Greenland and sail down the fjords. The journey of these sculptures of ice from glaciers to ocean is eerily beautiful and utterly terrifying.

The wall of ice that rises behind Sermilik fjord stretches for 1,500 miles (2,400km) from north to south and smothers 80% of this country. It has been frozen for 3m years. Now it is melting, far faster than the climate models predicted and far more decisively than any political action to combat our changing climate. If the Greenland ice sheet disappeared sea levels around the world would rise by seven metres, as 10% of the world's fresh water is currently frozen here.

This is also the season for science in Greenland. Glaciologists, seismologists and climatologists from around the world are landing on the ice sheet in helicopters, taking ice-breakers up its inaccessible coastline and measuring glaciers in a race against time to discover why the ice in Greenland is vanishing so much faster than expected.

Gordon Hamilton, a Scottish-born glaciologist from the University of Maine's Climate Change Institute, is packing up equipment at his base camp in Tasiilaq, a tiny, remote east coast settlement only accessible by helicopter and where huskies howl all night.

With his spiky hair and ripped T-shirt, Hamilton could be a rugged glaciologist straight from central casting. Four years ago he hit upon the daring idea of landing on a moving glacier in a helicopter to measure its speed.

The glaciers of Greenland are the fat, restless fingers of its vast ice sheet, constantly moving, stretching down into fjords and pushing ice from the sheet into the ocean, in the form of melt water and icebergs.

Before their first expedition, Hamilton and his colleague Leigh Stearns, from the University of Kansas, used satellite data to plan exactly where they would land on a glacier.

"When we arrived there was no glacier to be seen. It was way up the fjord," he says. "We thought we'd made some stupid goof with the co-ordinates, but we were where we were supposed to be." It was the glacier that was in the wrong place. A vast expanse had melted away.

When Hamilton and Stearns processed their first measurements of the glacier's speed, they thought they had made another mistake. They found it was marching forwards at a greater pace than a glacier had ever been observed to flow before. "We were blown away because we realised that the glaciers had accelerated not just by a little bit but by a lot," he says. The three glaciers they studied had abruptly increased the speed by which they were transmitting ice from the ice sheet into the ocean.

Raw power

Standing before a glacier in Greenland as it calves icebergs into the dark waters of a cavernous fjord is to witness the raw power of a natural process we have accelerated but will now struggle to control.

Greenland's glaciers make those in the Alps look like toys. Grubby white and blue crystal towers, cliffs and crevasses soar up from the water, dispatching millenniums of compacted snow in the shape of seals, water lilies and bishops' mitres.

I take a small boat to see the calving with Dines Mikaelsen, an Inuit guide, who in the winter will cross the ice sheet in his five-metre sled pulled by 16 huskies.

It is not freezing but even in summer the wind is bitingly cold and we can smell the bad breath of a humpback whale as it groans past our bows on Sermilik Fjord. Above its heavy breathing, all you can hear in this wilderness is the drip-drip of melting ice and a crash as icebergs cleave into even smaller lumps, called growlers.

Mikaelsen stops his boat beside Hann glacier and points out how it was twice as wide and stretched 300 metres further into the fjord just 10 years ago. He also shows off a spectacular electric blue iceberg.

Locals have nicknamed it "blue diamond"; its colour comes from being cleaved from centuries-old compressed ice at the ancient heart of the glacier. Bobbing in warming waters, this ancient ice fossil will be gone in a couple of weeks.

The blue diamond is one vivid pointer to the antiquity of the Greenland ice sheet. A relic of the last Ice Age, this is one of three great ice sheets in the world. Up to two miles thick, the other two lie in Antarctica.

While similar melting effects are being measured in the southern hemisphere, the Greenland sheet may be uniquely vulnerable, lying much further from the chill of the pole than Antarctica's sheets. The southern end of the Greenland sheet is almost on the same latitude as the Shetlands and stroked by the warm waters of the Gulf Stream.

Driven by the loss of ice, Arctic temperatures are warming more quickly than other parts of the world: last autumn air temperatures in the Arctic stood at a record 5C above normal. For centuries, the ice sheets maintained an equilibrium: glaciers calved off icebergs and sent melt water into the oceans every summer; in winter, the ice sheet was then replenished with more frozen snow. Scientists believe the world's great ice sheets will not completely disappear for many more centuries, but the Greenland ice sheet is now shedding more ice than it is accumulating.

The melting has been recorded since 1979; scientists put the annual net loss of ice and water from the ice sheet at 300-400 gigatonnes, which could hasten a sea level rise of catastrophic proportions.

As Hamilton has found, Greenland's glaciers have increased the speed at which they shift ice from the sheet into the ocean. Helheim, an enormous tower of ice that calves into Sermilik Fjord, used to move at 7km (4.4 miles) a year. In 2005, in less than a year, it speeded up to nearly 12km a year. Kangerdlugssuaq, another glacier that Hamilton measured, tripled its speed between 1988 and 2005. Its movement – an inch every minute – could be seen with the naked eye.

The three glaciers that Hamilton and Stearns measured account for about a fifth of the discharge from the entire Greenland ice sheet. The implications of their acceleration are profound: "If they all start to speed up, you could have quite a large rise in sea level in the near term, much larger than the official estimate by the Intergovernmental Panel on Climate Change (IPCC) would project," says Hamilton.

The scientific labours in the chill winds and high seas of the Arctic summer seem wrapped in an unusual sense of urgency this year. The scientists working in Greenland are keen to communicate their new, emerging understanding of the dynamics of the declining ice sheet to the wider world. Several point out that any international agreement forged at the UN climate change conference in Copenhagen in December will be based on the IPCC's fourth assessment report from 2007. Its estimates of climate change and sea-level rise were based on scientific research submitted up to 2005; the scientists say this is already significantly out of date.

The 2007 report predicted a sea level rise of 30cm-60cm by 2100, but did not account for the impact of glaciers breaking into the sea from areas such as the Greenland ice sheet. Most scientists working at the poles predict a one metre rise by 2100. The US Geological Survey has predicted a 1.5 metre rise. As Hamilton points out: "It is only the first metre that matters".

Record temperatures

A one metre rise – with the risk of higher storm surges – would require new defences for New York, London, Mumbai and Shanghai, and imperil swaths of low-lying land from Bangladesh to Florida. Vulnerable areas accommodate 10%of the world's population – 600 million.

The Greenland ice sheet is not merely being melted from above by warmer air temperatures. As the oceans of the Arctic waters reach record high temperatures, the role of warmer water lapping against these great glaciers is one of several factors shaping the loss of the ice sheet that has been overlooked until recently.

Fiamma Straneo, an Italian-born oceanographer, is laboriously winding recording equipment the size of a fire extinguisher from the deck of a small Greenpeace icebreaker caught in huge swells at the mouth of Sermilik fjord.

In previous decades the Arctic Sunrise has been used in taking direct action against whalers; now it offers itself as a floating research station for independent scientists to reach remote parts of the ice sheet. It is tough work for the multinational crew of 30 in this rough-and-ready little boat, prettified below deck with posters of orang-utans and sunflowers painted in the toilets.

Before I succumb to vomiting below deck – another journalist is so seasick they are airlifted off the boat – I examine the navigational charts used by the captain, Pete Willcox, a survivor of the sinking of the Rainbow Warrior in 1985. He shows how they are dotted with measurements showing the depth of the ocean but here, close to the east coast of Greenland, the map is blank: this part of the North Atlantic was once covered by sea ice for so much of the year that its waters are still uncharted.

Earlier in the expedition, the crew believe, they became the first boat to travel through the Nares Strait west of Greenland to the Arctic Ocean in June, once impassable because of sea ice at that time of year. The predicted year when summers in the Arctic would be free of sea ice has fallen from 2100 to 2050 to 2030 in a couple of years.

Jay Zwally, a Nasa scientist, recently suggested it could be virtually ice-free by late summer 2012. Between 2004 and 2008 the area of "multiyear" Arctic sea ice (ice that has formed over more than one winter and survived the summer melt) shrank by 595,000 sq miles, an area larger than France, Germany and the United Kingdom combined.

Undaunted by the sickening swell of the ocean and wrapped up against the chilly wind, Straneo, of Woods Hole Oceanographic Institution, one of the world's leading oceanographic research centres, continues to take measurements from the waters as the long Arctic dusk falls.

According to Straneo, the rapid changes to the ice sheet have taken glaciologists by surprise. "One of the possible mechanisms which we think may have triggered these changes is melting driven by changing ocean temperatures and currents at the margins of the ice sheet."

She has been surprised by early results measuring sea water close to the melting glaciers: one probe recovered from last year recorded a relatively balmy 2C at 60 metres in the fjord in the middle of winter. Straneo said: "This warm and salty water is of subtropical origin – it's carried by the Gulf Stream. In recent years a lot more of this warm water has been found around the coastal region of Greenland. We think this is one of the mechanisms that has caused these glaciers to accelerate and shed more ice."

Straneo's research is looking at what scientists call the "dynamic effects" of the Greenland ice sheet. It is not simply that the ice sheet is melting steadily as global temperatures rise. Rather, the melting triggers dynamic new effects, which in turn accelerate the melt.

"It's quite likely that these dynamic effects are more important in generating a near-term rapid rise in sea level than the traditional melt," says Hamilton. Another example of these dynamic effects is when the ice sheet melts to expose dirty layers of old snow laced with black carbon from forest fires and even cosmic dust. These dark particles absorb more heat and so further speed up the melt.

After Straneo gathers her final measurements, the Arctic Sunrise heads for the tranquillity of the sole berth at Tasiilaq, which has a population of fewer than 3,000 but is still the largest settlement on Greenland's vast east coast. Here another scientist is gathering her final provisions before taking her team camping on a remote glacier.

Invisible earthquakes

Several years ago Meredith Nettles, a seismologist from Colombia University, and two colleagues made a remarkable discovery: they identified a new kind of earthquake. These quakes were substantial – measuring magnitude five – but had been invisible because they did not show up on seismographs. (While orthodox tremors registered for a couple of seconds, these occurred rather more slowly, over a minute.)

The new earthquakes were traced almost exclusively to Greenland, where they were found to be specifically associated with large, fast-flowing outlet glaciers. There have been 200 of them in the last dozen years; in 2005 there were six times as many as in 1993.

Nettles nimbly explains the science as she heaves bags of equipment on to a helicopter, which will fly her to study Kangerdlugssuaq glacier. "It's quite a dramatic increase, and that increase happened at the same time as we were seeing dramatic retreats in the location of the calving fronts of the glaciers, and an increase in their flow speed," she says. "The earthquakes are very closely associated with large-scale ice loss events."

In other words, the huge chunks of ice breaking off from the glaciers and entering the oceans are large enough to generate a seismic signal that is sent through the Earth. They are happening more regularly and, when they occur, it appears that the glacier speeds up even more.

The scientists rightly wrap their latest observations in caution. Their studies are still in their infancy. Some of the effects they are observing may be short-term.

The Greenland ice sheet has survived natural warmer periods in history, the last about 120,000 years ago, although it was much smaller then than it is now. Those still sceptical of the scientific consensus over climate change should perhaps listen to the voices of those who could not be accused of having anything to gain from talking up climate change.

Inuit warnings

Arne Sorensen, a specialist ice navigator on Arctic Sunrise, began sailing the Arctic in the 1970s. Journeys around Greenland's coast that would take three weeks in the 1970s because of sea ice now take a day. He pays heed to the observations of the Inuit. "If you talk to people who live close to nature and they tell you this is unusual and this is not something they have noticed before, then I really put emphasis on that," he says. Paakkanna Ignatiussen, 52, has been hunting seals since he was 13. His grandparents travelled less than a mile to hunt; he must go more than 60 miles because the sea ice disappears earlier – and with it the seals. "It's hard to see the ice go back. In the old days when we got ice it was only ice. Today it is more like slush," he says. "In 10 years there will be no traditional hunting. The weather is the reason."

The stench of rotting seal flesh wafts from a bag in the porch of his house in Tasiilaq as Ignatiussen's wife, Ane, remarks that, "the seasons are upside down".

Local people are acutely aware of how the weather is changing animal behaviour. Browsing the guns for sale in the supermarket in Tasiilaq (you don't need a licence for a gun here), Axel Hansen says more hungry polar bears prowl around the town these days. Like the hunters, the bears can't find seals when there is so little sea ice. And the fjords are filled with so many icebergs that local people find it hard to hunt whales there.

Westerners may shrug at the decline of traditional hunting but, in a sense, we all live on the Greenland ice sheet now. Its fate is our fate. The scientists swarming over this ancient mass of ice, trying to understand how it will be transformed in a warming world, and how it will transform us, are wary of making political comments about how our leaders should plan for one metre of sea level rise, and what drastic steps must be taken to cut carbon emissions. But some scientists are so astounded by the changes they are recording that they are moved to speak out.

What, I ask Hamilton, would he say to Barack Obama if he could spend 10 minutes with the US president standing on Helheim glacier?

"Without knowing anything about what is going on, you just have to look at the glacier to know something huge is happening here," says the glaciologist. "We can't as a scientific community keep up with the pace of changes, let alone explain why they are happening.

"If I was, God forbid, the leader of the free world, I would implement some changes to deal with the maximum risk that we might reasonably expect to encounter, rather than always planning for the minimum. We won't know the consequences of not doing that until it's way too late. Even as a politician on a four-year elected cycle, you can't morally leave someone with that problem."

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• This article was amended on Tuesday 1 September 2009. The words in brackets were removed from this sentence: "The melting has been recorded since 1979; scientists put the annual net loss of ice and water from the ice sheet at 300-400 gigatonnes (equivalent to a billion elephants being dropped in the ocean), which could hasten a sea level rise of catastrophic proportions." It was not a good comparison: a gigatonne is 1 billion tonnes and elephants do not weigh 300-400 tonnes.