Path independence of climate and carbon cycle response over a broad range of cumulative carbon emissions

Abstract. Recent studies have identified an approximately proportional relationship between global warming and cumulative carbon emissions, yet the robustness of this relationship has not been tested over a broad range of cumulative emissions and emission rates. This study explores the path dependence of the climate and carbon cycle response using an Earth system model of intermediate complexity forced with 24 idealized emissions scenarios across five cumulative emission groups (1275–5275 Gt C) with varying rates of emission. We find the century-scale climate and carbon cycle response after cessation of emissions to be approximately independent of emission pathway for all cumulative emission levels considered. The ratio of global mean temperature change to cumulative emissions – referred to as the transient climate response to cumulative carbon emissions (TCRE) – is found to be constant for cumulative emissions lower than ∼1500 Gt C but to decline with higher cumulative emissions. The TCRE is also found to decrease with increasing emission rate. The response of Arctic sea ice is found to be approximately proportional to cumulative emissions, while the response of the Atlantic Meridional Overturning Circulation does not scale linearly with cumulative emissions, as its peak response is strongly dependent on emission rate. Ocean carbon uptake weakens with increasing cumulative emissions, while land carbon uptake displays non-monotonic behavior, increasing up to a cumulative emission threshold of ∼2000 Gt C and then declining.