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\subsubsection{EOF analysis}  \subsubsection{Periodograms}  The characteristics of data series that have been Fourier-transformed are often summarized using a plot known as a periodogram or Fourier line spectrum \citep{Wilks2011}. These plots are also referred to as a power or density spectrum, and most commonly display the squared amplitudes ($C_k^2$) of the Fourier transform coefficients as a function of their corresponding frequencies ($\omega_k$). As an alternative to the squared amplitude, we have chosen to rescale the vertical axis and instead use the $R^2$ statistic commonly computed in regression analysis. The $R^2$ for the $k$th harmonic is,  \begin{equation}\label{eq:variance_explained}  R_k^2 = \frac{(n/2)C_k^2}{(n-1)s_y^2}  \end{equation}  \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 Southern Annular Mode (SAM) and El Ni\~{n}o Southern Oscillation (ENSO). In order to assess their relationship with the PWI, the Antarctic Oscillation Index \citep[AOI;][]{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 to calculate the PWI). 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 and 190-240$^{\circ}$E.