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The effect of future Arctic amplification (AA) on the extratropical atmospheric circulation remains unclear in modeling studies. Using a collection of coordinated atmospheric and coupled global climate model perturbation experiments, we find an emergent relationship between the high‐latitude 1,000–500 hPa thickness response and an enhancement of the Siberian High in winter. This wave number‐1‐like sea level pressure anomaly pattern is linked to an equatorward shift of the eddy‐driven jet and a dynamical cooling response in eastern Asia. Additional simulations, where AA is imposed directly into the model domain by nudging, demonstrate how the sea ice forcing is insufficient by itself to capture the vertical extent of the warming and by extension the amplitude of the response in the Siberian High. This study demonstrates the importance of the vertical extent of the tropospheric warming over the polar cap in revealing the "warm Arctic, cold Siberia" anomaly pattern in future projections. Plain Language Summary: Surface air temperature averaged within the Arctic Circle is rising more than twice as fast as the rate of the globally averaged temperature. This is known as "Arctic amplification" and is the result of numerous feedbacks in the Earth system. This warming is not restricted to the surface, as the temperature is also increasing at least to the middle troposphere in the Arctic. The effects of this warming on weather patterns in the midlatitudes remain uncertain in observations and model simulations. In this study, we conduct a series of climate model experiments to better understand how the vertical extent of warming in the Arctic atmosphere connects to a strengthening of the Siberian High in boreal winter. This high‐pressure response leads to colder air temperatures in eastern Asia through advection. We find that climate models prescribed with only Arctic sea ice loss do not fully capture the vertical extent of warming in the atmosphere, and thus underestimate the linkage between projected Arctic amplification and Eurasian climate. Key Points: Climate models forced only by sea ice anomalies do not capture the vertical extent of Arctic warming during winterIncrease in thickness of the winter 1,000–500 hPa layer is linked to a strengthening of the Siberian High and cold anomalies in eastern AsiaRole of the stratosphere is unclear due to large internal variability at future global warming of 2° C above preindustrial levels [ABSTRACT FROM AUTHOR]

We assess the reliability of an indirect method of inferring the atmospheric response to projected Arctic sea ice loss from CMIP5 simulations, by comparing the response inferred from the indirect method to that explicitly simulated in sea ice perturbation experiments. We find that the indirect approach works well in winter, but has limited utility in the other seasons. We then apply a modified version of the indirect method to 11 CMIP5 models to reveal the robust and non‐robust aspects of the wintertime atmospheric response to projected Arctic sea ice loss. Despite limitations of the indirect method, we identify a robust enhancement of the Siberian High, weakening of the Icelandic Low, weakening of the westerly wind on the poleward flank of the eddy‐driven jet, strengthening of the subtropical jet, and weakening of the stratospheric polar vortex. The surface air temperature response to projected Arctic sea ice loss over mid‐latitude continents is non‐robust across the models. Plain Language Summary: The continued melt of Arctic sea ice will likely affect weather and climate in places far from the Arctic. To better understand the far‐flung implications of sea ice loss, scientists can perform bespoke climate model experiments in which sea ice is reduced, but all other climate drivers are fixed. In our paper, we test the reliability of an indirect method to infer the atmospheric response to sea ice loss, which makes use of a large set of climate model experiments originally performed for other purposes. We find that the indirect approach works well in winter, but not so well in other seasons. We then apply the indirect method to 11 climate models to reveal the robust and non‐robust aspects of the wintertime atmospheric response to projected Arctic sea ice loss—the largest such comparison to date. We found that the models agreed on quite a few aspects of the response, including warming over the Arctic, regional surface pressure changes over Siberia and Iceland, and a slowing of the mid‐latitude jet stream. On the other hand, the models disagreed on whether surface air temperatures over Europe, North America, and East Asia will warm or cool in response to future Arctic sea ice loss. Key Points: Wintertime atmospheric response to projected Arctic sea‐ice loss can be well‐estimated indirectly from CMIP5 simulationsRobust changes across models including stronger Siberian High, weaker Icelandic Low, slower eddy‐driven jet and faster subtropical jetNon‐robust changes in surface air temperature over mid‐latitude continents and sea level pressure over the North Pacific [ABSTRACT FROM AUTHOR]