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The role of stratospheric water vapor (SWV) changes, in response to increasing CO 2, as a feedback component of quantitative significance for climate sensitivity has remained controversial. Here, we calculate the SWV climate feedback under abrupt CO 2 quadrupling in the CMIP5 ensemble of models. All models robustly show a moistening of the stratosphere, causing a global mean net stratosphere adjusted radiative perturbation of 0.89 +/- 0.27Wm -2 at the reference tropopause. The stratospheric temperature adjustment is a crucial component of this radiative perturbation. The associated climate feedback is 0.17 +/- 0.05Wm -2 K -1, with a considerable inter-model range of 0.12-0.28 Wm -2 K -1. Taking into account the rise in tropopause height under 4 x CO 2 slightly reduces the feedback to 0.15 +/- 0.04Wm -2 K -1, with a range of 0.10-0.26Wm -2 K -1. The SWV radiative perturbation peaks in the midlatitudes and not the tropics: this is due primarily to increases in SWV in the extratropical lowermost stratosphere, which cause the majority (over three quarters) of the global mean feedback. Based on these results, we suggest an increased focus on understanding drivers of water vapor trends in the extratropical lowermost stratosphere. We conclude that the SWV feedback is important, being on the same order of magnitude as the global mean surface albedo and cloud feedbacks in the multi-model mean.