Do the TCRE and ZEC metrics work under net negative CO2 emissions?

Two key metrics of the coupled carbon-climate system are used to inform the remaining carbon budget for climate stabilization: the transient climate response to cumulative CO₂ emissions (TCRE) and the zero emissions commitment (ZEC), which govern the global temperature response to positive and zero emissions, respectively. We ask whether and how these two metrics describe global temperatures under net negative CO₂ emissions, using an idealized scenario defined by a gradual and symmetric reversal from positive to negative emissions. Using a full Earth system model and an ensemble of simple climate model simulations, we show that the two metrics do capture the global temperature dynamics even under large amounts of negative emissions, with ZEC predicting the deviation from symmetric TCRE proportionality under negative emissions. Further, we show that because ZEC begins to influence global temperatures even before reaching net zero, it can be better thought of as a measure of the deviation from the path-independence of the TCRE relationship than as a measure of the committed warming after reaching net zero.