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The dominant pattern of Northern Hemisphere extratropical climate variability is the Northern Annular Mode (NAM), which in wintertime represents the coupling of the stratospheric and tropospheric circulations. The internal variability associated with the NAM has been shown to give rise to substantial uncertainty in climate projections of regional surface air temperatures (SATs), but it's unclear how much of this variability arises from stratosphere‐troposphere coupling processes. Here, using three large‐ensemble coupled climate model simulations from 1850 to 2100 with varying fidelity of stratosphere‐troposphere coupling processes, we demonstrate that regional SAT variability across timescales is amplified when the tropospheric NAM is coupled to the stratospheric NAM. Moreover, models that lack adequate simulation of stratosphere‐troposphere coupling processes may not capture the magnitude of uncertainty in near‐term SAT projections associated with this coupling. Plain Language Summary: Large‐scale atmospheric circulation variability drives substantial variation in regional surface air temperatures (SATs), so that even on 30–40 year timescales local cooling trends are possible even as global‐mean temperatures increase. We provide evidence that when the stratospheric mean flow is coupled to the tropospheric mean flow, the decadal variability of SATs is amplified in some regions. Some models do not represent well the observed coupling of the stratosphere to the troposphere, and these models may underestimate decadal variability associated with this coupling. Key Points: The Northern Annular Mode (NAM) exhibits decadal variability that can accelerate or slow the rate of anthropogenic regional surface warmingAmplified decadal variability of extratropical surface temperatures occurs when the NAM is coupled from the stratosphere to the troposphereModels that fail to adequately capture vertical coupling may underestimate the magnitude of decadal variations in surface air temperatures [ABSTRACT FROM AUTHOR]