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:
- Allen, M. R. et al (2009) Warming caused by cumulative carbon emissions towards the trillionth tonne, Nature, 458:1163-1166, which argues that a one trillion tonne release of carbon gives a most likely warming of 2 °C, with a likely (one-sigma) uncertainty range of 1.6-2.6 °C.
- Meinshausen, M. et al (2009) Greenhouse gas emission targets for limiting global warming to 2 °C, Nature, 458:1158-1162, which argues that a total release of 0.9 (0.71) trillion tonnes of carbon gives a 50% (25%) risk of temperatures exceeding 2 °C.
- Allen, M. R. et al (2009) The Exit Strategy, Nature Reports Climate Change, 3:56-58, which provides a commentary on the implications of the above papers for non-specialists.
- Matthews, H. D., et al. (2009) The proportionality of global warming to cumulative carbon emissions. Nature, 459:829-832