"Good morning. Here is the shipping forecast for midday, June 21 2020. Seas will be calm, and visibility will range from good to excellent for the next 24 hours. The sea lanes from Bergen to Tokyo via the north-east passage will largely be free of ice, but occasional small floes may drift near the Siberian coast. The north-west passage from Europe to Fairbanks, Alaska, and Vancouver will also be clear, although iceberg hazards cannot be ruled out between Greenland and Ellesmere Island. The Bering Strait was, for the fourth time in the past decade, free of ice for the entire winter and will remain open for the rest of the summer."

That's just the Arctic. By the summer of 2020, global warming will have had such devastating effect on the northern icecap that European ships may routinely cross the high latitudes to take the short routes to Asia and the Pacific. The Arctic Ocean, once frozen solid all winter and choked with hazardous floes for most of the summer, could be one of the friendlier seas. The perilous shortcuts that defied the heroic attempts of the Englishman Martin Frobisher and the Dutchman Willem Barents more than 400 years ago may soon become not just plain sailing, but the standard summer sea route from Europe to the Pacific.

Cruise tourists and shipping magnates might wish to thank global warming. But the chances are they will not. That is because one of the Arctic's great spectacles, the polar bear, will have taken a dive: they need the sea ice to survive. For them, the ice is the way to a diet of seals, walruses and small whales. When the floes go, ursus maritimus will be on the road to extinction.

The polar bear's base of operations has been shrinking inexorably as the planet warms. Over the past 40 years, the sheath of ice that covered the Arctic Ocean has thinned by 40%. The area covered by ice has also shrunk by more than 25%. Although much climate science is necessarily based on indirect evidence, the state of the Arctic Ocean has been monitored directly by people whose lives depend on the accuracy of their measurements. US, Russian and British nuclear submarines began charting the thickness of Arctic ice at the height of the cold war, and satellite cameras have been recording seasonal changes in ice cover for more than three decades. The conclusions are beyond dispute and the process is unstoppable. By 2020, according to the US Office of Naval Research, the north-east and north-west passages should be navigable. By 2050, according to the UK Hadley Centre for Climate Prediction, the Arctic Ocean could be free of ice in summer.

That will happen because although the planet as a whole is warming perceptibly, the Arctic is warming eight times faster - largely because of a phenomenon called the albedo effect.

Put simply, white reflects light, but dark absorbs it. So the sunlight crashing on to the Arctic and Antarctic ice sheets, the Alpine and tropical glaciers, and the snows of the great mountain chains bounces back into space. In effect, ice is its own insulator: glaciers tend to keep themselves glacial even in the summer.

But once ice starts to melt, dark ocean or rock is exposed. That absorbs the heat, and begins to accelerate the melting process. As long as the average temperatures stay low, there is a natural brake: in high summer, snow evaporates but falls again in winter, to replace the melting ice and to keep conditions more or less stable. The problem is that things have begun to change. Glaciers in Alaska and the mountains of tropical Africa are in retreat, and climate scientists have predicted that by 2020 the snows of Kilimanjaro and Mount Kenya will have vanished.

In Europe, Alpine economies built on skiing and other mountain sports will have begun to fail. In south Asia, for at least part of the year, snow melt is the only source of water for millions of farmers.

Adventure tourists will lose their holidays. Others stand to lose rather more. On the Indian subcontinent, half a billion people depend on the Indus and Ganges rivers, whose sources lie among melting snows of the the Hindu Kush, the Karakoram and the western Himalaya. But these great snowfields, too, are disappearing.

All this is on the basis of an annual global average temperature rise of 0.1C a decade up to now. But it wouldn't take much to make things change faster, and those changes would be irreversible. If global average temperatures rise by more than 2.7C, according to calculations published in Nature in April, then the great sheet of ice that covers Greenland will start to melt faster than it can be replaced. The Geological Survey of Greenland and Denmark warned this summer that the ice sheet, which covers 772,000 square miles and is up to two miles thick, is melting 10 times quicker than previously thought. The sheet is thinning at 10 metres per year, not one metre. It could take 1,000 years for the sheet to completely disappear, but as it does so, sea levels will begin to rise by about 7mm a year. Once all the ice has gone, the world's oceans will have risen by around seven metres.

This will happen, because global temperatures seem likely to rise by far more than 2.7C. Ten years ago, the UN's Intercontinental Panel on Climate Change (IPCC) set up to study global warming proposed a maximum temperature rise of about 3C by 2100. Three years ago, IPCC revised that prediction. The maximum temperature rise during the present century is set at almost 6C. And the predicted maximum temperature rise for Greenland is put at up to 8C.

That is not the only danger posed by the thawing of the world's cold places. The Arctic regions are rimmed by permafrost: regions of tundra that enjoy an urgent spring, a brief, brilliant summer and then a long, hostile winter. These landscapes hold stores of ancient carbon and methane in the form of decaying vegetation imprisoned for 10,000 years or more. Once the permafrost starts to melt, awesome quantities of carbon dioxide and methane - two potent greenhouse gases - will be released from thawing peat bogs to accelerate the warming process yet further. This climate phenomenon is known as "positive feedback".

By 2020, then, the Arctic will have begun to change for ever. The adventure tales of the past will be distant history: stories of explorers fighting their way by sled across the perilous frozen seas will be science fiction to young readers and nostalgic yearnings for a lost world to their parents.

"Here is the long-term weather forecast for the tropical and temperate zones at midday, June 21 2020. After a series of increasingly wet winters, northern Europe could once again be at risk of a lethal heat wave. Forest fires are raging in the Iberian Peninsula, southern France and the Balkans. Water rationing has once again been imposed in California. Relief agencies have warned that late rains raise the spectre of widespread hunger in the Sahel and southern Africa. Bangladesh, however, is once more preparing for catastrophic floods."

It's a matter of simple physics: a warmer world means a rising sea level. Warm water is less dense than cold, so some of the sea level rise will happen just because the water already in the oceans has begun to expand. But sea levels have begun to rise still further with the melting of continental ice and the retreat of the glaciers. The effects of the rise will only slowly become apparent - even the most pessimistic predictions suggest that by 2100 the sea level will only be a metre higher - but even at that slow rate many millions of people will be imperilled. Sea level rise is a threat to anybody who lives at or a fraction above sea level, and especially to citizens of those countries classed as developing. That, of course, means poor.

For such people, the future looks very bleak. There are 54 members of the Commonwealth. Only six of these are classed as developed nations. Around 93% of the Commonwealth lives in the other 48. Some of these countries may have no future at all. "If the scientific forecasts prove correct, then by the end of the century membership of the Commonwealth will have declined because two or three nations will have disappeared," warned Clive Hamilton, director of the Australian Institute, in September 2003. Two Commonwealth states - the Maldives and Tuvalu - are at risk of complete submersion by 2080. Two other groups of islands - Kiribati and the Bahamas - will be in a bad way, because almost all their territories lie below the four-metre mark.

Each of those states will already be facing periodic devastation and permanent crisis by 2020. The bedrock of many of the islands is coral limestone. Coral is a living thing, so if sea levels were to rise slowly enough - over 1,000 rather than 100 years - then coral could grow to keep up with the water levels. But coral is extremely sensitive to rising temperatures: the corals that make up most reefs and atolls are already at the limits of their temperature tolerance. Those reefs near human settlements are choked by man-made pollutants, and their ecologies have been permanently altered by intensive fishing.

Any increase in ocean temperatures means death by bleaching - the corals turn white and die. This has happened a number of times in the Caribbean, the Indian Ocean and the Great Barrier Reef near Australia, with cyclical rises in water temperatures. Those rises have been followed by cyclical falls, so the corals have had the chance to recover. But global warming means permanent heating, and the living corals that support life - both human and non-human - in the Pacific and Indian Oceans are expected to perish on a massive scale.

The coral won't be the only thing to suffer. The oceans will seep into the bedrock, polluting the subterranean fresh water. Agriculture will become impossible, supplies of drinking water will be minimal and as the waters rise the islands will start to drown in seawater.

Island dwellers, of course, will not be the only ones at risk. Hundreds of millions of people in densely populated countries with low-lying coastal plains or vast estuaries will come under threat from rising sea levels. According to Sir John Houghton, a former director of the UK Met Office and author of Global Warming: The Complete Briefing, a sea level rise of half a metre could sweep away or make uninhabitable about 10% of the habitable land of Bangladesh. That land is currently home to at least six million people. Sea levels will not need to rise by half a metre worldwide to make this happen: the delta region of Bangladesh is subsiding, partly because groundwater is being abstracted for agriculture to feed the nation's 140 million citizens.

By 2050, waters could have risen by a metre, claiming 20% of Bangladesh and displacing 15 million people. By 2100, the ocean may have encroached up the rivers almost as far as Dhaka, one of the world's fastest growing cities, and across the Indian border to the edge of Calcutta.

A glance around the world shows the same pattern being repeated again and again. In Egypt, a metre rise in the Mediterranean will mean the fertile lands of the Nile delta will disappear beneath the sea, claiming 12% of the country's arable land and displacing seven million people. A sea level rise of half a metre would also cause havoc in the Netherlands and in the Mississippi delta. But the difference between those two regions and those in the developing world is that the Dutch and the Americans already spend money on sea defences and can afford more. In China, a half-metre rise in the sea level could inundate the alluvial plains of the eastern coast, covering an area of land the size of the Netherlands, leaving 30 million homeless.

And if the sea doesn't get you, the storms will. Hurricanes and cyclones are freak events whose existence is controlled by sea temperatures. If the surface temperature of the ocean is below 26.5C, typhoons, tropical cyclones and hurricanes hardly happen. But with each rise of the mercury beyond that point they become more frequent and more ferocious. Savage storms, and the sea surges they bring, will pose huge threats to small island states and could scour low-lying land completely clear.

Twenty years ago, climate scientists warned that in a greenhouse world, the kind of fierce storms that had been once-a-century occurrences would come around every decade. The fatal combination of very high tide and tropical cyclone has hit Bangladesh and the Bengal coast of India many times. In 1991, one such storm surge claimed an estimated 139,000 lives. In 1970, another killed 300,000 people. UN researchers warned in June that an estimated one billion people live in the path of the kind of flood that used to occur every 100 years: by 2050, the number of potential victims could reach two billion.

If two billion people are at risk of dramatic inundation in 2020, around 2.3 billion others living in the world's water-poor nations could face an even more wretched future. They will see increasingly parched landscapes, empty wells, polluted lakes and rivers that run dry. UN experts calculated that in 2000, people in 30 nations faced water shortages. By 2020, they predict, that number will have risen to 50 nations.

As temperatures rise, more water will evaporate, but rainfall will remain capricious. Countries in the monsoon belt will face more severe droughts in the dry season but could also have to deal with more catastrophic flooding. Other regions - the southern Mediterranean, north Africa, southern Africa and the Sahel - could become even more arid, with olive groves succumbing to desertification. The great plains of North America, the breadbasket for the planet, could turn again into a dustbowl, delivering less and less grain to a world that acquires an extra 240,000 mouths to feed every single day.

The pattern of falling crop yields will be seen all over the planet. They are expected to decline by at least 10% in most African Commonwealth countries, and by even more in Mozambique, Tanzania, Botswana and Namibia. There could also be dramatic falls in food production in India, Pakistan and Bangladesh, although harvests could increase by 10% in Brunei, Malaysia, Singapore and Papua New Guinea. Canada and New Zealand could also see dramatic increases in crop yields but Australia, already largely arid, will be one of the economic losers.

And forget the glib remarks about the one good side-effect of global warming being decent summers. In 2003, more than 20,000 people died in northern Europe because of a heat wave that saw Germany roasting in its hottest temperatures for 450 years. Climate scientists believe that if atmospheric warming continues unchecked, such heat waves can be expected every 20 years or so - so expect summer 2020 to be every bit as oppressive as last year.

"The summer of 2003 was a summer of the future," said Gerhard Berz, head of natural risks research at Munich Re, one of the insurance giants that has to calculate hazard and pick up the bill for floods, heat waves, ice storms, hurricanes, forest fires and droughts.

Global warming is expected to bring good news for some. But right now it looks like it will be delivering bad news to most people by 2020. The IPCC, the international consortium of climate scientists that has delivered increasingly urgent warnings since it was established in 1988, is that rare thing: a group of scientists who would love to be proved wrong. Their predictions have been made in the hope that governments will take action, and in doing so direct the planet towards a less fearful future. There is evidence that governments have been listening.

Action, however, has been slow. Acting now would be too late to avert the challenges of 2020. We are starting to see the effects of carbon emissions of a few decades ago: your fuel-efficient small car is an investment in the future, because we're currently paying for that great gas guzzler your family was driving in the 70s. Every cook who knows a bit about science understands a concept called thermal inertia: the gas is on full, but the kettle takes a few minutes to boil, and though the gas is off, it takes a while to cool down. We're still waiting for the earth to start simmering, but by 2020 the bubbles will be appearing, whatever we do today.

· Tim Radford is the Guardian's science editor

Can we predict the weather?

As Sam Goldwyn said, prediction is always difficult, especially of the future. There are huge uncertainties in climate forecasting. The planet is a complicated place: its climate is influenced by the interplay of sunlight, atmosphere, dust, ocean currents and rainfall; by the temperature gradient between the tropics and the poles; by the topography of continents; by the balance of forests, wetlands, deserts, savannahs and oceans, as well as by the chemistry and biochemistry of the seas.

To grasp the patterns of the future, climate scientists have to know the pattern of climate change in the past. That means they have to examine the indirect evidence provided by ice cores, tree rings, coral growths, and mud samples from oceans and lakes in order to estimate greenhouse gas levels and average temperatures in the distant past. Then they must monitor the oceans, the upper and lower atmosphere, and weather patterns around the whole planet to understand the mechanics of climate now. Only then can they start composing computer models of what might happen the day after tomorrow. So when politicians - and, sometimes, other scientists - make accusations of uncertainty, speculation and possible error, they have a point. There is no doubt the planet is warming, but how much of that is caused by some natural cycle nobody yet understands? And how much is the result of human interference? And what will humans do in the future that might make conditions better or worse?

Atmospheric chemists say they understand the principal greenhouse gas, carbon dioxide, quite well. But methane, though shorter-lived, is an even more potent greenhouse gas: what role could it play in the future? Water vapour, too, is a greenhouse gas: a warmer world means more water vapour in the atmosphere. Will it make the world an even hotter place? Or will it mean greater cloud cover, which might then act as a brake on global warming by cutting out more sunlight? Those questions are unanswered and the debate goes on.

Through 15 years of intensive climate study, however, the broad message from the scientists has remained much the same. They are now convinced that indiscriminate burning of fossil fuels is steadily increasing the global average atmospheric temperature. And the only way to halt or at least slow global warming would be to make dramatic cuts in carbon emissions. Which leads to the other great unanswered question: can we meet that challenge? TR

Earth blows hot and cold

Earth's climate has always been subject to ups and downs, and there is nothing novel about a warm Arctic. Ninety million years ago, during the Cretaceous era, deciduous forests stretched into the Arctic circle, and carnivorous dinosaurs roamed Antarctica. Five years ago, palaeontologists uncovered the bones of an eight-foot champosaur, a reptile with a crocodile-like snout and razor-sharp teeth, under the Alaskan snows. Such a creature could only have survived in a warmer world, and experts calculate that the average annual temperature in Alaska must have been 14C. That is, it may never have frozen, even in the coldest winters.

The globe can blow both hot and cold: much earlier, glaciers reached almost to the equator. Some climate scientists have hypothesised a "snowball Earth" - a completely frozen world - for at least four spells between 750m years ago and 580m years ago, before things warmed up again.

Human civilisation is generally adapted to a cooler world. Around 21,000 years ago, during the height of the last ice age, sea levels were 135 metres lower than they are today, and the continents were covered by an extra 52 million cubic kilometres of ice. The interglacial thaw that took place 11,000 years ago gave agriculture, metalwork and urban civilisation its kickstart.

For a while back in the 1970s some climate scientists wondered about the possibility of an imminent return of the ice age. And earlier this year, European scientists drilling in the Antarctic settled an answer to that question. The evidence from the ice cores suggests that, even if carbon dioxide levels were normal, there could still be another 15,000 years before the glaciers return to southern England.

But carbon dioxide levels are not normal. They're rising and they're rising fast. The evidence from the same ice cores confirms that both temperatures and carbon dioxide levels are now higher than at any time in the last 400,000 years. The evidence from fossil plankton drilled from the seabed tells an even more ominous story: carbon dioxide levels are higher than at any time in the last 20m years. And they are expected to double in the coming century. That means higher temperatures, for longer - and it means that any existing forecasts of a new ice age are likely to be way off course. TR