But they used a methodology that even their sternest critics believed could be improved until it delivered the right results: the cuts just needed to be raised and accelerated.

Three papers released earlier this year changed all that. The first, published in ‘Proceedings of the National Academy of Sciences’ in February, showed that the climate change we cause today will be “largely irreversible for 1,000 years after emissions stop”. About 40 per cent of the carbon dioxide produced by humans this century will remain in the atmosphere until at least the year 3000. Moreover, thanks to the peculiar ways in which the oceans absorb heat from the atmosphere, global average temperatures are likely to “remain approximately constant … until the end of the millennium despite zero further emissions”.

In other words, governments’ hopes about the trajectory of temperature change are ill-founded. Most, including the UK’s, are working on the assumption that we can overshoot the desired targets for temperature and atmospheric concentrations of CO2, then watch them settle back later. What this paper shows is that, wherever temperatures peak, that is more or less where they will stay. There is no going back.

The other two papers were published by ‘Nature’ in April. While governments and the United Nations set targets for cuts by a certain date, these papers measured something quite different: the total volume of carbon dioxide we can produce and still stand a good chance of avoiding more than 2C of warming. One paper, from a team led by Myles Allen, shows that preventing more than 2C means producing a maximum of half a trillion tonnes of carbon (1,830bn tonnes of CO2) between now and 2500 — and probably much less. The other paper, written by a team led by Malte Meinshausen, proposes that producing 1,000bn tonnes of CO2 between 2000 and 2050 would give a 25 per cent chance of exceeding 2C of warming.

If you want an idea of what this means, take a look at the global carbon clock at www.know-the-number.com. The level of greenhouse gases in the atmosphere is rising at the rate of 2bn tonnes a month (CO2 equivalent). The Allen paper suggests that the world can produce only the equivalent of between 63 and 75 years of current emissions between now and 2500 if we want to avoid more than 2C of warming.

Writing elsewhere, the two teams gave us an idea of what this means. At current rates of use, we will burn the ration that Allen set aside for the next 500 years in four decades. Meinshausen’s carbon budget between now and 2050 will have been exhausted before 2030.

The World Energy Council (WEC) publishes figures for global reserves of fossil fuels - the minerals that have been identified and quantified, and which it is cost-effective to exploit. The WEC says 848bn tonnes of coal, 1,77,000bn cubic metres of natural gas and 162bn tonnes of crude oil are good to go. We know roughly how much carbon a tonne of coal, a cubic metre of gas and a barrel of oil contain. The calculations and references are on my website: the result suggests that official reserves of coal, gas and oil amount to 818bn tonnes of carbon.

Unaccounted but huge

The molecular weight of carbon dioxide is 3.667 times that of carbon. This means that current reserves of fossil fuel, even when we ignore unconventional sources such as tar sands and oil shale, would produce 3,000bn tonnes of carbon dioxide if they were burnt. So, in order not to exceed 2C of global warming, we can burn, according to Allen’s paper, a maximum of 60 per cent of current fossil fuel reserves by 2500. Meinshausen says we’ve already used one-third of his 2050 budget since 2000, which suggests that we can afford to burn only 22 per cent of current reserves between now and 2050. If you counted unconventional sources, the proportion would be even smaller.

There are some obvious conclusions from these three papers. The trajectory of cuts is more important than the final destination. An 80 per cent cut by 2050, for instance, could produce very different outcomes. If most of the cut were made towards the beginning of the period, the total emissions entering the atmosphere would be much smaller than if it were made at the end of the period. The peak atmospheric concentration must be as low as possible and come as soon as possible, which means making most of the reductions right now. Ensuring that we don’t exceed the cumulative emissions discussed in the ‘Nature’ papers means setting an absolute limit on the amount of fossil fuel we can burn, which, as my rough sums show, is likely to be much smaller than the reserves already identified. It means a global moratorium on prospecting and developing new fields.

None of this is on the table. The targets and methodology being used by governments and the UN — which will form the basis of their negotiations at Copenhagen — are irrelevant. Unless there is a radical change of plan between now and December, world leaders will not only be discussing the alignment of deckchairs on the Titanic, but disputing whose deckchairs they really are and who is responsible for moving them. Fascinating as this argument may be, it does nothing to alter the course of the liner.

But someone, at least, has a radical new plan. This afternoon the team that made the film ‘The Age of Stupid’ is launching the 10:10 campaign, which aims for a 10 per cent cut in the UK’s greenhouse gas emissions during 2010. This seems to be roughly the trajectory needed to deliver a good chance of averting 2C of warming. By encouraging people and businesses and institutions to sign up, the campaign hopes to shame the UK government into adopting this as its national target. This would give the government the moral leverage to demand immediate sharp cuts from other nations, based on current science rather than political convenience.

I don’t agree with everything the campaign proposes. It allows businesses to claim reductions in carbon intensity as if they were real cuts: in other words, they can measure their reductions relative to turnover rather than in absolute terms. There’s an uncomfortable precedent for this: cutting carbon intensity was George Bush's proposal for tackling climate change. As economic growth is the major cause of rising emissions, this looks like a cop-out. The cuts will not be independently audited, which might undermine their credibility with the government. But these are quibbles. 10:10 is the best shot we have left. It may not be enough, it may not work, but at least it’s relevant.