Journal of Climate | MacDougall et al. 
An emergent property of most Earth system models is a near linear relationship between cumulative emission of CO2 and change in global near surface temperature. This relationship, which has been named the transient climate response to cumulative CO2 emissions (TCRE), implies a finite budget of fossil fuel carbon that can be burnt over all time consistent with a chosen temperature change target. Carbon budgets are inversely proportional to the value of TCRE and are therefore sensitive to the uncertainty in TCRE. Here we have used a perturbed physics approach with an Earth system model of intermediate complexity to assess the uncertainty in the TCRE that arises from uncertainty in the rate of transient temperature change and the effect of this uncertainty on carbon cycle feedbacks. The experiments are conducted using an idealized 1% per year increase in CO2 concentration. Additionally we have emulated the temperature output of 23 Climate Model Intercomparison Project Phase Five (CMIP5) models. The experiment yields a mean value for TCRE of 1.72 K EgC−1 with a 5th to 95th percentile range of 0.88 to 2.52 K EgC−1. This range of uncertainty is consistent with the likely range from the fifth assessment report of the Intergovernmental Panel on Climate Change (0.8 to 2.5 K EgC−1) but by construction underestimates the total uncertainty range of TCRE, as our experiments cannot account for the uncertainty from our models imperfect representation of the global carbon cycle. Transient temperature change uncertainty induces a 5th to 95th percentile range in the airborne fraction at the time of doubled atmospheric CO2 of 0.50 to 0.58. Overall the uncertainty in the value of TCRE remains considerable.
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