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 °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. (letter)