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This paper compares surface signatures of the zonally symmetric and asymmetric modes of stratospheric variability, which describe the strength of the polar vortex and a planetary wave‐1 pattern, respectively. Unlike a weak polar vortex followed by negative Arctic Oscillation–like anomalies, strong stratospheric wave activity features a polar vortex displacement with a deep planetary wave‐1 structure, resulting in positive North Atlantic Oscillation–like North American cooling in about 10 days. Moreover, the linkage between the stratosphere and surface is examined in two reanalyzes and four models of different configurations, which show more robust North American cooling following the displacement of the polar vortex due to strong stratospheric wave activity than the zonally symmetric weakening of the polar vortex. This suggests strong stratospheric wave activity acts as a better predictor for cold spells in the northern U.S. and Canada compared with a weak polar vortex. Plain Language Summary: A weak polar vortex in the winter stratosphere is likely associated with cold spells at the surface, yet there are large uncertainties in predicting surface cold events based on stratospheric signals. This study introduces a new method to separate stratospheric variability into the leading modes of zonally symmetric and asymmetric circulations. The zonally symmetric mode describes the strength of the polar vortex. A weak polar vortex is followed by cooling over northern Eurasia and midlatitude North America. In contrast, the zonally asymmetric mode characterizes a displacement of the polar vortex or a planetary wave‐1 pattern, with the positive phase featuring a high anomaly over North America and a low anomaly over Eurasia. This stratospheric wave pattern extends down to the surface, resulting in North American cooling and Eurasian warming in about 10 days. While both stratospheric modes are associated with surface cooling over North America, the linkage is more robust for the displacement than the zonally symmetric weakening of the polar vortex, based on analyses of several reanalyzes and models. This indicates that strong stratospheric wave activity serves as a better predictor for cold air outbreaks in the northern U.S. and Canada than the commonly used weak polar vortex events. Key Points: Distinct North American cooling signatures follow zonally symmetric and asymmetric modes of the stratosphereStrong stratospheric wave activity precedes positive North Atlantic Oscillation like North American coolingThe linkage between the stratospheric wave activity and the surface is robust in reanalyzes and models [ABSTRACT FROM AUTHOR]