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, effective ocean diffusivity, radiative forcing from an e-fold increase in atmospheric CO₂ concentration, and the ratio of sea to global surface temperature change. The calculated TCRE has a positively skewed distribution, ranging from 1.1-2.9 K EgC^-1 (5-95% confidence), with a mean and median value of 1.9 K EgC^-1 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 1 100 PgC, ranging from 700-1 800 PgC (5-95% confidence) estimated using a simplified model of ocean dynamics. Climate sensitivity (climate feedback) 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.