\subsection{SAM and ENSO}

Composite analysis was also used to assess the relationship between the PWI and the major modes of SH climate variability. SAM events were defined according to the 75th and 25th percentiles of the AOI, while positive (El Ni\~{n}o) and negative (La Ni\~{n}a) ENSO events were defined as a Ni\~{n}o 3.4 above 0.5$^{\circ}$C and below -0.5$^{\circ}$C respectively. Composites for each phase of SAM and ENSO were then calculated by taking the average across all data times for which the PWI exceeded its 90th percentile \textit{and} the AOI or Ni\~{n}o 3.4 was greater or less than the relevant threshold. 

The SAM composites show that the phase of the planetary wave pattern moves east during positive SAM events and west during negative events (Figure \ref{fig:sam_composite}). Planetary wave activity was also more common when the SAM was negative: of the 1312 data times where the PWI exceeded its 90th percentile, 510 (39\%) had an AOI that was less than the 25th percentile as compared to only 166 (13\%) with an AOI greater than the 75th percentile. Consistent with this finding, the aforementioned outlying year for planetary wave activity (1980; see Figure \ref{fig:annual_distribution}b) was associated with a large negative SAM.

The association between ENSO and planetary wave activity was far less pronounced. Besides a subtle east (La Ni\~{n}a) / west (El Ni\~{n}o) movement of the anticyclone over the south-east Pacific, no appreciable changes were seen in the phase of the planetary wave pattern (not shown) and planetary wave activity was only slightly more common during El Ni\~{n}o conditions (282 data times to 176).      