On the proportionality between global temperature change and cumulative CO 2 emissions during periods of net negative CO 2 emissions

Recent research has demonstrated that global mean surface air warming is approximately proportional to cumulative CO2 emissions. This proportional relationship has received considerable attention, as it allows one to calculate the cumulative CO2 emissions ('carbon budget') compatible with temperature targets and is a useful measure for model inter-comparison. Here we use an Earth system model to explore whether this relationship persists during periods of net negative CO2 emissions. Negative CO2 emissions are required in the majority of emissions scenarios limiting global warming to 2 °C above pre-industrial, with emissions becoming net negative in the second half of this century in several scenarios. We find that for model simulations with a symmetric 1% per year increase and decrease in atmospheric CO2, the temperature change (ΔT) versus cumulative CO2 emissions (CE) relationship is nonlinear during periods of net negative emissions, owing to the lagged response of the deep ocean to previously increasing atmospheric CO2. When corrected for this lagged response, or if the CO2 decline is applied after the system has equilibrated with the previous CO2 increase, the ΔT versus CE relationship is close to linear during periods of net negative CO2 emissions. A proportionality constant—the transient climate response to cumulative carbon emissions (TCRE)− can therefore be calculated for both positive and net negative CO2 emission periods. We find that in simulations with a symmetric 1% per year increase and decrease in atmospheric CO2 the TCRE is larger on the upward than on the downward CO2 trajectory, suggesting that positive CO2 emissions are more effective at warming than negative emissions are at subsequently cooling. We also find that the cooling effectiveness of negative CO2 emissions decreases if applied at higher atmospheric CO2 concentrations.