What does Net Zero mean for reactive gases?

The decrease in carbon dioxide concentrations following a zeroing of emissions leads to a cooling that approximately balances the hidden warming from past emissions, due to the similarity of the timescales of climate response and carbon cycle response. But what are the climate implications of zero emissions of chemically-reactive gases such as nitrous oxide, halocarbons and methane with response timescales that don’t align with those of the climate system? In this work we invert the analytical formulae used by the IPCC to represent the evolution of climate, to derive the time evolution of radiative forcing needed to stabilise temperatures. We find that stabilising the warming attributable to any gas requires decreases in radiative forcing that depend on the past history of that gas (more rapid historical ramp-up requires stronger future mitigation). We show that for reactive gases the analytically-derived radiative forcing decreases are most closely matched by step-like cuts in emissions, but that even for long-lived gasses such as nitrous oxide the emissions cuts do not need to be 100%. N2O emission cuts of 60-80% are sufficient to stabilise its temperature contribution - depending on the previous emission history. It has been suggested that a more ambitious goal is to mitigate reactive gases sufficiently that their contribution to temperatures reduces rather than stabilises. We show that the above methodology can equally be applied to a declining temperature profile and so were are able to quantify the cuts in reactive gas emissions consistent with achieving desired cooling goals.