This study compares and contrasts the impacts of single versus multiple (i.e., a series of anomalously strong vertically propagating waves entering the polar stratosphere) events in both ERA-Interim and hindcasts of operational subseasonal models in the S2S Prediction Project Database. First, we construct a catalogue of single and multiple wave pulse events in the recent past (1979-2018) from a specific set of criteria based on the vertical structure and duration of vertically propagating waves. These event dates are analyzed via lag compositing to investigate the difference between the two events in both the extratropical stratosphere and troposphere. Precursors found to multiple pulse events include anomalous ridging over Northern Eurasia and the North Atlantic, co-located with vertical wave activity flux anomalies leading up to the events. Single pulse events, by contrast, are found to be relatively short-lived and weaker compared to multiple pulse events. As a result, the vortex is much weaker following multiple pulse events than single pulse events. The 3-D structure of these wave pulses along with their primary forcing mechanisms (e.g., synoptic-scale vs. planetary scale) are also studied to resolve why some events are single or multiple pulse events. Results from reanalysis are then contrasted with the same criteria applied to the S2S models to identify potential biases. Applications of these wave pulse events to predicting surface weather patterns on the subseasonal timescale are also discussed.