Assuming an equilibrium climate sensitivity of 3°C from doubling atmospheric CO2, and 90% of the equilibrium warming at the time of the CO2 peak from the Climber model, and also neglecting other anthropogenic greenhouse gases, it would take an atmospheric pCO2 of about 490 ppm to keep the global warming below the 2°C danger limit. This corresponds to about 400 Gton C of anthropogenic carbon in the atmosphere. If we divide 400 Gton C by a maximum airborne fraction of 55%, we calculate a maximum allowable total emission of about 700 Gton C, of which 300 Gton C has already been released, if we are to avoid dangerous climate change at any time in the future.
This is a more restrictive estimate than we would get if we limited our scope to the year 2100 and earlier, because the Earth takes several centuries to warm. As CO2 rises, the warming lags behind, largely because of the thermal inertia of the ocean. The warming we have experienced so far today is only about 60% of the equilibrium warming expected at today’s atmospheric CO2 value (Hansen et al. 2005). A 40% warming lag will also exist in the year 2100. Limiting our concern to what happens between now and the year 2100, neglecting what comes after, results in a substantial increase of the calculated allowable emissions, to about 1,050 Gton C. This calculation seems rather callous, given the inevitability of the eventual warming once the CO2 is released, but it is the perhaps unintended consequence of limiting the scope of consideration to the year 2100.