A diagnostic of Northern-Hemisphere winter extratropical stratosphere-troposphere interactions is presented to facilitate the study of stratosphere-troposphere coupling and to examine what might influence these interactions. The diagnostic is a multivariate EOF combining lower-stratospheric planetary wave activity flux in December with sea-level pressure in January. This EOF analysis captures a strong linkage between the vertical component of lower stratospheric wave activity over Eurasia and subsequent development of hemispheric-wide surface circulation anomalies, which are strongly related to the Arctic Oscillation. Wintertime stratosphere-troposphere events picked out by this diagnostic often have a precursor in autumn: years with large October snow extent over Eurasia feature strong wintertime upward-propagating planetary wave pulses, a weaker wintertime polar vortex, and high geopotential heights in the wintertime polar troposphere. This provides further evidence for predictability of wintertime circulation based on autumnal snow extent over Eurasia.