Extending the relationship between global warming and cumulative carbon emissions to multi-millennial timescales

The transient climate response to cumulative carbon emissions (TCRE) is a highly policy-relevant quantity in climate science. The TCRE suggests that peak warming is linearly proportional to cumulative carbon emissions and nearly independent of the emissions scenario. Here, we use simulations of the Earth System Model (ESM) from the Geophysical Fluid Dynamics Laboratory (GFDL) to show that global mean surface temperature may increase by 0.5 degrees C after carbon emissions are stopped at 2 degrees C global warming, implying an increase in the coefficient relating global warming to cumulative carbon emissions on multi-centennial timescales. The simulations also suggest a 20% lower quota on cumulative carbon emissions allowed to achieve a policy-driven limit on global warming. ESM estimates from the Coupled Model Intercomparison Project Phase 5 (CMIP5-ESMs) qualitatively agree on this result, whereas Earth System Models of Intermediate Complexity (EMICs) simulations, used in the IPCC 5th assessment report to assess the robustness of TCRE on multi-centennial timescales, suggest a post-emissions decrease in temperature. The reason for this discrepancy lies in the smaller simulated realized warming fraction in CMIP5-ESMs, including GFDL ESM2M, than in EMICs when carbon emissions increase. The temperature response to cumulative carbon emissions can be characterized by three different phases and the linear TCRE framework is only valid during the first phase when carbon emissions increase. For longer timescales, when emissions tape off, two new metrics are introduced that better characterize the time-dependent temperature response to cumulative carbon emissions: the equilibrium climate response to cumulative carbon emissions and the multi-millennial climate response to cumulative carbon emissions.