Revisiting carbon budgets of IPCC 1.5-degree report by taking into account correlation with non-CO2 warming and TCRE

The discovery of a nearly linear relationship between cumulative CO₂ emissions and global mean surface temperature increase has given rise to intensive scientific research to assess the maximum allowable CO₂ emissions compatible with some temperature threshold such as the goals of the Paris Agreement. The recent IPCC Special Report on Global warming of 1.5 °C (SR15) used a novel method to calculate remaining carbon budget for the 1.5 °C warming. The first step was to estimate non-CO₂ warming contribution based on a perturbed parameter ensemble of two simple models to get the allowable CO₂-caused warming. The second step was to use a probability density distribution for Transient Climate Response to cumulative CO₂ emissions (TCRE) to calculate the carbon budget from the CO₂-caused warming. One shortcoming of this method is that it ignores potential correlation between non-CO₂ warming contribution and TCRE. A significant part of the non-CO₂ warming comes from decreasing aerosol forcing, and the present-day aerosol forcing linked with TCRE.

Here, we revisit the carbon budgets presented in SR15 by taking correlation into account. We analysed the FaIR model simulations used in SR15 individually and found a linear relationship between TCRE and non-CO₂ warming for a given temperature increase. After a slight rescaling to get the revised carbon budget (for 0.5 °C additional warming)  match with SR15 budget (600 Gt CO₂) for the 50th-percentile TCRE value of 0.45 K/1000 Gt CO₂, the 33th-67^th percentile revised range was 380-960 Gt CO₂, whereas SR15 gave narrower range of 440-850 Gt CO₂. The wider range was expected as high TCRE is likely associated with high present-day aerosol forcing and hence with high non-CO₂ contribution in future warming when aerosol forcing is decreasing. We analysed only results of FaIR model, and final SR15 numbers are an average of results based on FaIR and MAGICC. Therefore, this analysis should be repeated also for the MAGICC runs. As a conclusion, our results show that TCRE and non-CO₂ warming contribution should not be considered independent variables when assessing remaining carbon budgets.