A strong link exists between stratospheric variability and anomalous weather patterns at the Earth's surface. Specifically, during extreme variability of the Arctic polar vortex termed a "weak vortex event", anomalies can descend from the upper stratosphere to the surface on timescales of weeks. Subsequently the outbreak of cold-air events have been noted in high Northern Latitudes, as well as a quadrapole pattern in surface temperature over the Atlantic and western European sectors. It is currently not understood why certain events descend to the surface while others do not, although this may be associated with the scale of vertically propagating Rossby waves which cause the initial vortex perturbation. In this study we demonstrate that the subdivision of weak vortex events into vortex displacements and vortex splits has important implications for tropospheric weather patterns on weekly-monthly timescales. Using reanalysis data we find that vortex splitting events play a highly significant role on surface weather with positive temperature anomalies over eastern North-America of more than 1.5K, and negative anomalies over Eurasia of up to -3K. Associated with this is an increase in tropospheric blocking over the Pacific basin and a decrease over the Atlantic/European sector. The corresponding signals are far weaker during displacement events, although ultimately they prove to be the cause of cold-air outbreaks over North America. Owing to the predictability and importance of stratosphere-troposphere coupling for medium-range weather forecasts, our findings suggest the need for such forecasting systems to correctly identify the type of stratospheric variability, otherwise surface responses cannot be accurately reproduced.