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We find that the slow climate feedbacks counteract the reduction of the hydroxyl radical in the troposphere, which is caused by the strongly enhanced CH₄ mixing ratios. Thereby also the resulting prolongation of the tropospheric CH₄ lifetime is weakened compared to the quasi-instantaneous response considered previously.

Changes in the stratospheric circulation evolve clearly with the warming of the troposphere. The Brewer-Dobson circulation strengthens, affecting the response of trace gases, such as ozone, water vapour and CH₄ in the stratosphere, and also causing stratospheric temperature changes. In the middle and upper stratosphere, the increase of stratospheric water vapour is reduced with respect to the quasi-instantaneous response. Weaker increases of the hydroxyl radical cause the chemical depletion of CH₄ to be less strongly enhanced and thus the in situ source of stratospheric water vapour as well. However, in the lower stratosphere water vapour increases more strongly when tropospheric warming is accounted for enlarging its overall radiative impact. The response of the stratospheric adjusted temperatures driven by slow climate feedbacks is dominated by these increases of stratospheric water vapour, as well as strongly decreased ozone mixing ratios above the tropical tropopause, which result from enhanced tropical upwelling.

While rapid radiative adjustments from ozone and stratospheric water vapour make an essential contribution to the effective CH₄ radiative forcing, the radiative impact of the respective slow feedbacks is rather moderate. In line with this, the climate sensitivity from CH₄ changes in this chemistry-climate model setup is not significantly different from the climate sensitivity in carbon dioxide-driven simulations, provided that the CH₄ effective radiative forcing includes the rapid adjustments from ozone and stratospheric water vapour changes.