Since the 1990s the prevailing scientific view has been that we must limit global warming to no more than 2°C above pre-industrial levels to avoid dangerous climate change - although there is increasing evidence of serious potential effects in many parts of the world even at 2°C degrees.

The well-documented physics of the greenhouse effect alongside data on the long-term relationship between temperature and the concentration of CO2 and other greenhouse gases (GHGs) have led to a paradigm in considering the future warming potential in terms of both carbon dioxide equivalent (CO2e) concentrations and temperature limits.

The accepted wisdom has been that we should avoid exceeding 450 parts per million of CO2e (many scientists now suggest lower concentrations).

This scientific paradigm has long underpinned international negotiations on climate change, translating into emissions-reductions targets focused on annual emission rates.

The Intergovernmental Panel on Climate Change, however, began discussing “cumulative emissions” in 2001. A flood of more recent analyses has resulted in a shift in emphasis from annual emissions to cumulative emissions as summarised in January in a special volume of the Philosophical Transactions of the Royal Society.

The rationale is: oceans and terrestrial vegetation can only take up CO2 slowly, so a significant fraction accumulates in the atmosphere for centuries or longer.

Analyses indicate that it is the cumulative amount of CO2 that determines maximum temperature the most, rather than any particular emissions pathway.

This has led to a reframing of mitigation science in terms of “cumulative carbon budgets”.

It follows, then, that we can calculate near enough a specific amount of carbon – about a quarter the mass of CO2 – that is the maximum we can emit in order to avoid exceeding 2°C average warming.

Dr Myles Allen from Oxford University and his colleagues estimate the limit to be about one trillion tonnes.

The fact that about half of this has already been produced puts real constraints on the options for staying under budget. Data provided by Oxford’s department of physics suggest that the trillionth tonne may be released in 2044 if emissions trends of the last 20 years are simply extrapolated forwards.

But if rates were to fall from now by a cumulative 2.3% a year we could stay within this trillion tonne limit.

Ninety-five per cent confidence intervals around 2°C, ranging from 1.3–3.9°C, however, beg the question:

“How confident do we want to be of this outcome?”

The Oxford data suggest that we can increase our confidence to a 75% likelihood of not exceeding 2°C if the world were only to emit 75 billion tonnes, but emissions would need to fall by 4.85% a year, starting now.

The Avoid programme – a collaboration between the Met Office, Walker Institute, Tyndall Centre, and Grantham Institute – takes similar approach, concluding that an emissions peak in 2016 would require at least a 4% annual emissions reduction, and a peak in 2020 would require at least a 5% annual reduction.

This is unlikely without significant global political will and a price on carbon, as well as an evolution in energy technology and use, including behaviour change.

The cumulative carbon budget approach is a much more accessible take on global warming – an analogy would be a slightly leaky bath with many taps flowing into it (different CO2 sources), with policy options on which taps to close at which rates in order to avoid exceeding the volume limit.

It implies also that temperatures will not drop soon after “peak emissions”, since the cumulative CO2 volume will either still be increasing (the taps are still running), or, at best, will be relatively static.

A reduction in CO2 emissions will thus only reduce global average temperature in the very long term.

Another implication is that the later the peak of emissions, the greater the rate of emissions reductions required to limit the total volume – that is, if the bath is nearly full, you need to turn off the taps pretty quickly.

Professor Robert Watson (chief scientific adviser, Defra) and Dr Rupert Lewis (deputy director/head of evidence, Defra)