A new yardstick is proposed by Damon Matthews, a professor in Concordia University’s Department of Geography, Planning and the Environment. With colleagues from Victoria and the U.K., Matthews used a combination of global climate models and historical climate data to derive a simple linear relationship between total cumulative emissions and global temperature change.
As complex as the climate change is, a new metric is always possible to relate to it in a better manner. What could you come up with if you compared various climate modeling experiments? Some observations were noted, for example, in the global temperature response to increasing atmospheric CO2:
(1) the warming per unit CO2 emitted does not depend on the background CO2 concentration;
(2) the total allowable emissions for climate stabilization do not depend on the timing of those emissions and;
(3) the temperature response to a pulse of CO2 is approximately constant on timescales of decades to centuries.
In Nature, Matthews et al. published how they generalize these results and show that the carbon–climate response, defined as the ratio of temperature change to cumulative carbon emissions, is approximately independent of both the atmospheric CO2 concentration and its rate of change on these timescales. Their Fig. 1 is a schematic representation of the progression from CO2 emissions to climate change. Here, in words are the figure's relationships:
CO2 emission + Carbon sensitivity = CO2 concentration
CO2 concentration + Climate sensitivity = Climate change
Climate sensitivity + Climate-carbon feedbacks = Carbon sensitivity
CO2 emission + Carbon-climate response = Climate change
where carbon sensitivity is the increase in atmospheric CO2 concentrations that results from CO2 emissions, as determined by the strength of natural carbon sinks.
Climate sensitivity is a general characterization of the temperature response to atmospheric CO2 changes.
Feedbacks between climate change and the strength of carbon sinks are defined as the climate–carbon feedbacks.
Thus the carbon–climate response (CCR) "aggregates the climate and carbon sensitivities (including climate–carbon feedbacks) into a single metric representing the net temperature change per unit carbon emitted."
Furthermore, CCR represents the product of the temperature change per unit atmospheric carbon increase and the airborne fraction of cumulative carbon emissions. The team estimated "CCR to be in the range 1.0–2.1 °C per trillion tonnes of carbon (Tt C) emitted (5th to 95th percentiles), consistent with twenty-first-century CCR values simulated by climate–carbon models."
The models used in the study were these eleven: BERN-CC, CSM-1, CLIMBER2-LPJ, FRCGC, HADCM3LC, IPSL-CM2C, IPSL-CM4-LOOP, LLNL, MPI, UMD, and UVIC-2.7. "Both the airborne fraction of cumulative emissions and the temperature change per unit atmospheric carbon increase are dependent on the atmospheric CO2 concentration and its rate of increase; however, the CCR (as the product of the two) showed a remarkable constancy with time."
Their Fig. 4 shows an estimate of CCR for 1990–99 of 1.0–2.1 °C per Tt C (5 to 95% confidence interval), with a best estimate of 1.5 °C per Tt C.
In summary, independent of the timing of emissions or the atmospheric concentration of carbon dioxide, each tonne in carbon emissions means -- as a best estimate --0.0000000000015 degrees of global temperature increase.
To restrict global warming to no more than 2 °C, we must simply restrict the total carbon emissions from now until forever to about half a trillion tonnes of carbon, which is about as much as we have emitted since the beginning of the industrial revolution.
(1) LETTER: The proportionality of global warming to cumulative carbon emissions by H. Damon Matthews, Nathan P. Gillett, Peter A. Stott&Kirsten Zickfeld. Nature 459, 829-832 (11 June 2009) | doi :10.1038/nature08047; Received 4 December 2008; Accepted 14 April 2009.
(2) 1 teratonne of carbon, 1 Tt C, is equivalent to 3.7 trillion tonnes of CO2.