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\noindent where $s_y^2$ is the sample variance and $n$ the length of the data series. This rescaling is particularly useful as it shows the proportion of variance in the original data series accounted for by each harmonic \citep{Wilks2011}.  \subsubsection{Climate indices}  Two of the major modes of SH climate variability are the SAM and ENSO. In order to assess their relationship with the PSA pattern, the Antarctic Oscillation Index \citep{Gong1999} and Ni\~{n}o 3.4 index \citep{Trenberth2001} were calculated from 30-day running mean data (i.e. the same timescale that was used for the PSA pattern analysis). The former represents the normalized difference of zonal mean sea level pressure between 40$^{\circ}$S and 65$^{\circ}$S, while the latter is the sea surface temperature anomaly for the region in the central tropical Pacific Ocean bounded by 5$^{\circ}$S-5$^{\circ}$N 5$^{\circ}$S--5$^{\circ}$N  and 190-240$^{\circ}$E. 190--240$^{\circ}$E.