In the early summer of 1901, the steamship Lavelle Young - having travelled 1,500km up the Yukon and Tanana rivers into the wild interior of Alaska - hit shallow water and began to scrape the riverbed. On board was an ambitious trader, ET Barnette, who hoped to establish the "Chicago of Alaska" 300km further upriver, from where rumours of rich gold and copper strikes were quickly spreading.

But Barnette never got to his destination. Having failed to persuade the Lavelle Young's captain to press on further, the young trader found himself dumped unceremoniously on the riverbank. As his wife sat crying, and the steamship pulled away from the shore, Barnette had little choice but to pick up his axe and begin building a stockade. He had initially been aiming to leave as soon as another ship passed by, perhaps in as little as a year. But his luck was about to change. A few months later, a ragged and hungry mining prospector, having seen the smoke from Barnette's cabin, pounded on the door and announced that he'd just found gold. Barnette decided to stay put and operate a trading post. And within two years his accidental settlement had become the largest log-cabin town in the world, with four hotels, two stores, a newspaper, a row of waterfront saloon bars and a thriving red-light district. Fairbanks had been born.

Today, the city still retains a frontier feel. Although the old log cabins now rub shoulders with fast-food outlets, moose still graze beside the busy dual carriageways and bears roam the spruce forests that surround the city. Fairbanks has always been a boom-and-bust town. In 1920, at the end of the gold rush, the town's population dwindled to 1,000 - after a high of nearly 20,000 a decade before. Another boom came during the second world war, when several military bases were established to counter the Japanese threat. The army and air force stayed on during the cold war, and Fairbanks began to prosper as a military town. But the biggest boom of all has proved to be oil. The Trans-Alaska Pipeline runs right past Fairbanks, and the town was the centre of pipeline construction in the mid-1970s. Much of the state's economy revolves around the oil industry.

However, Alaska's current prosperity has come at a high price. Although few in the state care to recognise it, Alaskan oil - of which more than one million barrels a day are exported to the mainland US - has rebounded heavily on the state through global climate change. And, whatever their views on global warming, almost every resident will admit one thing: Alaska's weather has gone crazy.

I arrived in Fairbanks late one evening following a 12-hour train journey north from Anchorage. My companions and I bundled our gear into a taxi and found a cheap backstreet hostel. The proprietor, a young hunting enthusiast called Dale Curtis, watched us unpack. "You guys tourists or something?" He adjusted his baseball cap uneasily. "No, we're journalists. We're investigating climate change." He looked blank. "Global warming," I continued. "Asking people how the weather has changed and that sort of thing." He looked intrigued. "Well, the weather sure has got strange. It don't get cold enough fast like it used to, and then it warms up real quick."

I encouraged him to continue. "What really struck me was watching ducks swimming on the river all winter. It was Christmas time, January even, and they were still swimming around. They're not supposed to be here at that time, they're supposed to be south already." He shook his head in amazement. "And the bears come out too early. They don't know whether to go into hibernation or to wake up. Folks round here are real worried about it. A couple of years ago at Christmas it rained and melted all the snow away. That just ain't right, you know?"

Just 150km shy of the Arctic circle, Fairbanks in mid-December has only three hours of daylight. The sun doesn't really come up at all - it just skirts along the horizon, as if entangled in the icy peaks of the Alaska Range, before plunging back down south and leaving Fairbanks in frigid night. Temperatures regularly plummet to -40C.

Or at least they used to. In recent winters, temperatures have reached -30C for only a couple of days, Curtis told me, while in previous decades they had remained at -40C for months at a time. And similar stories come from all over the state. The reason is simple: Alaska is baking. Temperatures in the state - as in much of the Arctic - are rising 10 times faster than in the rest of the world. And the effects are so dramatic that entire ecosystems are beginning to unravel, as are the lifestyles of the people who depend on them. In many ways, Alaska is the canary in the coal mine, showing the rest of the world what lies ahead as global warming accelerates.

The man who has done more than perhaps any other to highlight this is a quietly spoken scientist based at the University of Alaska in Fairbanks, Professor Gunter Weller. I met him on a warm May morning, and the season's first mosquitoes were descending from the trees as we walked through patches of thawing snow behind Weller's Centre for Global Change and Arctic Systems Research. "This year we had extreme high temperatures," Weller was saying in his soft German accent, "in fact, it's been the second warmest year on record."

When he first arrived in the state, the weather had been quite different - sometimes reaching -50C. "In fact, I remember my first New Year's Eve here in 1968. I was invited next door to a party and I put a shot of very good scotch in an ice-cube tray outside, and it was frozen within half an hour. You wouldn't see that now, no way."

Alaskan wintertime temperatures have risen by an average of 6C, Weller told me. "This is an absolutely enormous signal," he emphasised, "bigger than anything the computer models have predicted." Summer temperatures were rising, too: Fairbanks now regularly sees summertime highs of 25C.

One of the best temperature records comes not from scientists but from gamblers. Each year, the people of Nenana, a small town south-west of Fairbanks, place bets on the exact minute when the ice on the river will begin to break up for the spring thaw. The contest began when Alaska Railroad engineers put down an $800 wager in 1917; by 2000, the jackpot had grown to $335,000, and thousands of people across the state compete. The high financial stakes ensure constant vigilance by the locals - and the record shows that the first day of spring has advanced by more than a week since the 1920s.

So was this global warming, I asked Weller. His answer was unequivocal. "I think it's clearly understood and clearly accepted by the scientific community that this is in part due to the human-induced global greenhouse effect." This greenhouse effect, he explained, was amplified at high latitudes by a positive feedback: once snow and ice begin to melt, the reflectivity of the earth's surface decreases, allowing more of the sun's heat to be absorbed. This in turn melts more ice and snow, further reducing the planet's albedo (reflective power), allowing still more warming, and so on. In Fairbanks, the rising temperatures were having a dramatic impact. Much of the area is underlain by permafrost - permanently frozen ground - that now, for the first time in thousands of years, is beginning to thaw. As a result, houses are sagging, roads are collapsing and entire buildings are being swallowed up by holes in the ground.

Weller gave us a lift to one of the worst-affected neighbourhoods, the aptly named Madcap Lane, where most of the wooden one-storey properties were distorted. On the righthand side one house was tilting sideways, the guttering at one end about one foot further from the roof than at the other. The wonky front steps barely fitted into the porch. I climbed them carefully and knocked on the door. "I work nights, and I've just gone to bed," complained the woman who opened it, Vicki Heiker, but she invited us in anyway. Her daughter Jessica smiled at us: "Here, look at this." She placed a pencil at one end of the kitchen table. It quickly rolled off the other end on to the floor. Her mother laughed. "When you spill something, it's like you don't have much of a chance. You've got to clean it up fast otherwise it'll get away from you."

"Do you get used to it?" I asked.

"Well, it helps build up your calf muscles since you're always walking uphill."

I wandered into the kitchen, and through the window I could see the house across the street also tilting - in the opposite direction. The whole place was like a badly built Toyland. Roads all around Fairbanks are affected by thawing permafrost: driving over the gentle undulations is like being at sea in a gentle swell. In some places the damage is more dramatic - crash barriers have bent into weird contortions, and wide cracks fracture the dark Tarmac. Permafrost damage now costs a total of $35m every year, mostly spent on road repairs. Some areas of once-flat land look like bomb sites, pockmarked with craters where permafrost ice underneath them has melted and drained away. These uneven landscapes cause "drunken forests" right across Alaska. In one spot near Fairbanks, a long gash had been torn through the tall spruce trees, leaving them toppling over towards each other.

Permafrost degradation is one of the clearest signals that something unprecedented is happening in the far north. In Siberian cities, hundreds of tall buildings have begun to subside and crack. In Alaska, whole sections of coastline are breaking off and falling into the sea, as the ice, which has kept cliffs solid for centuries, begins to melt. More than half a kilometre has eroded from some stretches of coastline over the past few decades. This may not matter too much when nobody lives there - but many of these coastal areas have been inhabited by indigenous peoples for centuries. And in Shishmaref, on the west coast of Alaska, the Native Americans who have made their home there now live in daily terror of the sea.

Shishmaref is about as far west as you can get on the entire North American landmass. The village sits on a long narrow island at the tip of the Seward Peninsula, barely 100km from the eastern edge of Russian Siberia. The two landmasses are so near that their peoples are closely related, too. Almost all Shishmaref's residents are Inupiat Eskimos, who share a close language and ancestry with their Siberian Eskimo relatives. (Unlike in Canada and Greenland, the name "Inuit" never caught on in Alaska, and the terms "Eskimo" and "Indian" are still universally used to describe the two culturally distinct Native Alaskan first peoples.) Indeed, Alaskan Eskimo hunters, cut off from home by open-water leads appearing behind them in the sea ice, would sometimes accidentally spend entire summers in Siberia. A lost hunter's family would never give up hope until the following winter, when men who had survived would return over the newly frozen ice.

Until comparatively recently, all Shishmaref's food and clothing supply came from the surrounding environment: polar bears, seals, fish, walrus and caribou. Though dog sleds and bone arrows have now been exchanged for snow machines and guns, and Eskimo kayaks replaced by wooden or fibreglass boats, "subsistence" living remains a crucial part of people's culture and livelihood. Bits of hunted animal - a frozen caribou leg or part of a seal - were propped up around almost every doorstep, and polar bear skins and dried fish hung on racks behind the houses. A few decades ago, people lived in "sod houses", turf-roofed dwellings dug out of the ground; today, everyone lives in wooden or prefabricated modern homes, scattered in rows all around the island. Nine houses had to be moved during the most recent big storm, Robert Iyatunguk, Shishmaref's "erosion coordinator", told me. As 90mph winds whipped around them, and sections of thawed cliff tumbled into the raging sea, the whole community had mobilised to save the dwellings closest to the edge - dangerous work. "We lost 50ft of ground in one night with that storm. We're in panic mode now because of how much ground we're losing."

We crunched down a shallow slope where sandbags were protruding through the snow: the remnants of Shishmaref's last battle with the sea. All the sea walls had failed, Iyatunguk went on. The water just undercut or washed over them.

Now the talk was of relocation - something that would have to be agreed by all 600 residents through a community ballot. It would cost $50m, and there was no sign of the state authorities coming up with the cash. But the worst-case scenario was no longer that of having to move the village, Iyatunguk said, but of another big storm while they were still living in the danger zone. Time is running out, he emphasised. "The wind is getting stronger, the water is getting higher, and it's noticeable to everybody in town." We stood together under the crumbling cliffs. Up above us an abandoned house hung precariously over the edge, at least a third of its foundation protruding into thin air. The house next door had toppled over and been reduced to matchwood by the waves.

I spent that evening with Clifford Weyiouanna, a 58-year-old Shishmaref elder, who sat polishing his gun as we spoke. It was true, he told me, that the permafrost underlying the village was melting, but another factor was just as important: the gradual disappearance of the sea ice. The sea ice used to lock up the shore for six months of every year, he explained, and so for half the year the eroding power of the waves was banished. Storms could rage all they wanted, but the sandy cliffs would stand. Now that had begun to change. "The currents have changed, the ice conditions have changed, and the freeze-up of the Chukchi Sea out here has really changed, too. We used to freeze up in the last part of October. This year, we didn't freeze up until Christmas time."

"So, how different is it when you're out on the ice?"

"It's not as stable. We used to get icebergs from the north many years ago - turquoise blue icebergs. Not any more - it's all young ice now. Thin stuff, only about a foot thick. Right now, the ice on that ocean out there should be, under normal conditions, four foot thick."

The animal behaviour was changing, too. "I think they're migrating a lot earlier than they used to because of the warming of the ocean. They migrate north in the spring to stay in the cooler waters. That's the polar bears, the walrus, the spotted seal, the bearded seal, the belugas and the bowhead whales." He leaned forward to emphasise the point: "Last summer, we covered thousands of miles by boat trying to get walrus - there was nothing, except for one boat that found one walrus."

Shishmaref would go on, both Weyiouanna and Iyatunguk assured me. If not here, then someplace else further up the coast. But whatever happened, the community would stay together. It was the traditional way.