\subsection{Temporal characteristics}

Consistent with previous studies \citep[e.g.][]{vanLoon1984,Mo1985}, the composite mean 500 hPa streamfunction zonal anomaly pattern for days (with 30-day running mean applied) where the PWI exceeds its 90th percentile (Figure \ref{fig:pwi_spatial_summary}) migrates zonally by approximately 15$^{\circ}$ from its most easterly location during summer to its most westerly during winter (notwithstanding the fact that the pattern breaks down from around 240-330$^{\circ}$E during summer). It has a slightly larger amplitude during the winter months and the frequency of strong planetary wave activity was also far more pronounced at that time of the year (Figure \ref{fig:annual_distribution}a). The seasonal counts of the number of days exceeding the PWI 90th percentile (Figure \ref{fig:annual_distribution}b) show that 1980 was associated with a particularly high frequency of planetary wave activity, however there were no statistically significant linear trends in these counts for timeseries including or excluding (i.e. 1981-2014) the year 1980.  

While our focus is on the monthly (30-day running mean) timescale, it is interesting to consider whether similar behavior is observed at other timescales. It can be seen from Figure \ref{fig:periodograms}b that wavenumber three dominates the average periodogram when the running mean applied to the daily 500 hPa meridional wind is greater than 10 days, with wavenumber one becoming progressively more influential as the smoothing increases. When the same process is repeated using the 500 hPa geopotential height (not shown), the results are very different. The ZW1 dominates at all timescales and except for a slight upswing from wavenumber two to three, the variance explained monotonically decreases for subsequent wavenumbers. This is an important result because \citet{vanLoon1972} analyzed geopotential height data and concluded that ZW1 explains (by an appreciable margin) the largest fraction of the spatial variance in the 500hPa SH circulation (a finding that has been quoted in many subsequent papers). In light of the results presented here and the previous discussion about the fact that $v_k \propto k Z_k$ in Fourier space and that the meridional wind may be a more appropriate quantity to analyze in this context, it is clear that ZW3 plays a greater role than previously thought, particularly when there is a strong meridional component to the hemispheric flow. 

    