Emissions of carbon dioxide since 1750 comprise just over half a trillion tonnes of carbon, and are estimated to have caused just under 1 °C of global warming. Emitting a further half trillion tonnes will commit us to a most likely warming of around 2 °C, widely regarded as the threshold for the most serious global impacts of climate change.
The trillionth tonne could be released in less than 40 years time, or, if we take the measures necessary to avoid dangerous climate change, it could never be released.
The fate of this tonne of carbon sums up the climate challenge.
Why limit warming to less than 2 °C?
A sustained 2 °C warming would already be well outside the range of temperature fluctuations experienced since the last ice age, and many vulnerable ecosystems and societies are expected to suffer under this level of climate change.
Many are calling for global warming to be limited to 1.5 °C if possible. But there is a large body of evidence that the risk of dangerous climate change rises if we fail to limit warming to 2 °C above pre-industrial temperatures, and many of the world's governments have now adopted this limit as their goal.
The need to limit cumulative emissions of carbon dioxide applies even more forcibly if we are to limit warming to a lower temperature.
Don't other things matter for climate as well?
They certainly do. Other greenhouse gases also cause warming, while other forms of pollution cause cooling. So far, these effects very approximately cancel out, but this is unlikely to remain so.
Natural factors also play a role, but human influence is already dominant.
Carbon dioxide emissions are the single most important factor in the future and, under all current scenarios, the net effect of other emissions is to add to the warming caused by carbon dioxide. So to limit total global warming caused by human activity to less than 2 °C, we clearly have to limit the warming caused by carbon dioxide to less than 2 °C.
Why do we need to limit cumulative emissions of carbon dioxide?
A certain fraction of the carbon dioxide we release accumulates in the atmosphere, in effect, indefinitely because of the way it interacts with ocean chemistry. So it is the total amount that we emit that matters in the long term, not the rate we emit it in any given year or the average rate of emission over a limited period.
Both peak temperatures and peak carbon dioxide concentrations, which matter for impacts like ocean acidification, are primarily determined by cumulative carbon dioxide emissions.
How does this link up with "Target 350"?
Very simply: 350.org is a campaign to limit long-term carbon dioxide levels to 350 parts per million. To achieve this, we will need to limit cumulative carbon dioxide emissions to less than one trillion tonnes of carbon.
But the case for limiting cumulative emissions to less than one trillion tonnes of carbon is even more immediate: to avoid temperatures more than 2 °C above pre-industrial in the next century, we have to keep cumulative emissions below a trillion tonnes regardless of the long-term concentration of carbon dioxide we aim for thereafter.
Why does this matter in practice?
The fact that we will need to limit cumulative emissions of carbon dioxide to avoid dangerous climate change matters because there are several trillion tonnes of carbon available in fossil fuel reserves.
To be effective in the long term, climate policies must address the question of what is to be done with the carbon that will never be safely released. Measures to reduce emissions will help in the short term, but not all of them will lock carbon away forever.
What can I do?
Clearly, reducing your carbon footprint helps - key "carbon footprint" into any search engine. Emitting carbon slower buys time, which we will certainly need.
But to solve the problem in the long term, we need to reduce net emissions to almost zero. You can't do this on your own, no matter how heroic a consumer you are.
So the most important thing you can do is make sure your government recognises the importance of cumulative carbon dioxide emissions in climate policy. Not all measures to reduce greenhouse gas emissions in the short term will necessarily help reduce cumulative carbon dioxide emissions overall.
What should my government do?
In June 2009, the lead authors of several of the key scientific papers in this area presented an open letter to the UNFCCC negotiators in Bonn urging them to acknowledge the need to limit cumulative carbon dioxide emissions as one element of their long-term vision to avoid dangerous climate change.
The scientists did not call for a specific target: the "budget" depends on the warming we decide we can tolerate and the risk we are prepared to accept of exceeding it. These are not purely scientific questions. But the need in principle to limit cumulative carbon dioxide emissions applies regardless, and has practical implications for the best ways to reduce emissions in the short and medium term.
How do you come up with these numbers?
The figure for current emissions is derived from carbon dioxide emissions data published on the CDIAC web-site for fossil fuels and land use change, assuming land-use emissions in 1750 were 75% of land-use emissions in 1850 and interpolating, and assuming 0.1 GtC per year of land-use change emissions were already in quasi-equilibrium with the natural carbon cycle.
The first version of this website assumed separate emissions in its algorithm, but in this new version data on both land use change and fossil fuel emissions are combined.
Average percent-per-year rate of increase over the last 23 or so years for which accurate data are available (1987-2009 in 2012) is computed using an exponential fit of combined data of both fossil and land-use-change emissions and applied to the most recent year's emissions to give the current cumulative total and predicted date and time on which cumulative emissions exceed one trillion tonnes. The corresponding rate is computed for a 22 year period shifted one year earlier (1986-2009 in 2012) to estimate the current rate of change of the date at which the threshold is crossed. Note that this is purely an extrapolation of recent trends, not an explicit emissions scenario.
The required rate of decrease to avoid releasing the trillionth tonne is computed directly from ratio of current emissions to remaining atmospheric capacity before the trillionth tonne is emitted and assuming an exponential decline (constant percent-per-year decrease).
We stress that none of these figures are known to anything like this level of precision, but we are giving them in full to illustrate how they are changing over time. They will be updated as new data on emissions become available. Current data and calculations are contained in the spread-sheet.
The background to these informal calculations is contained in a series of scientific papers: