Quantifying the probability distribution function of the transient climate response to cumulative CO2 emissions

The Transient Climate Response to Cumulative CO2 Emissions (TCRE) is the proportionality between global temperature change and cumulative CO2 emissions. The TCRE implies a finite quantity of CO2 emissions, or carbon budget, consistent with a given temperature change limit. The uncertainty of the TCRE is often assumed be normally distributed, but this assumption has yet to be validated. We calculated the TCRE using a zero-dimensional ocean diffusive model and a Monte-Carlo error propagation (n = 10 000 000) randomly drawing from probability density functions of the climate feedback parameter, the land-borne fraction of carbon, radiative forcing from an e-fold increase in CO2 concentration, effective ocean diffusivity, and the ratio of sea to global surface temperature change. The calculated TCRE has a positively skewed distribution, ranging from 1.1 to 2.9 K EgC(-1) (5%-95% confidence), with a mean and median value of 1.9 and 1.8 K EgC(-1). The calculated distribution of the TCRE is well described by a log-normal distribution. The CO2-only carbon budget compatible with 2 degrees C warming is 1100 PgC, ranging from 700 to 1800 PgC (5%-95% confidence) estimated using a simplified model of ocean dynamics. Climate sensitivity is the most influential Earth System parameter on the TCRE, followed by the land-borne fraction of carbon, radiative forcing from an e-fold increase in CO2, effective ocean diffusivity, and the ratio of sea to global surface temperature change. While the uncertainty of the TCRE is considerable, the use of a log-normal distribution may improve estimations of the TCRE and associated carbon budgets.