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In order to align the new equator with the approximate path of the PSA pattern, a global 0.75$^{\circ}$ latitude by 0.75$^{\circ}$ longitude grid was defined (i.e. the same resolution as the original ERA-Interim data) with the north pole located at 20$^{\circ}$N, 260$^{\circ}$E. The 500 hPa zonal and meridional wind data were used to re-calculate the meridional wind relative to the new north, and then the temporal anomaly of this new meridional wind was linearly interpolated to the rotated grid for use in the Fourier transform (e.g. Figure \ref{fig:rotation}). It should be noted that existing zonal wave studies \citep[e.g.][]{IrvingSimmonds2015} tend to skip this final step of calculating the anomaly, because in the case of zonal waves the temporal mean of the meridional wind is typically close to zero (and hence waveforms defined by the meridional wind already oscillate about zero).   On this rotated grid, the search region of interest was defined as the area bounded by 10$^{\circ}$S to 10$^{\circ}$N and 115$^{\circ}$E to 235$^{\circ}$E (this approximate area is referred to as the PSA-sector at times throughout the paper). This region was selected via visual comparison with existing definitions of the PSA pattern (e.g. Figure \ref{fig_eof}), \ref{fig:eof}),  however the final results were not sensitive to small changes in pole location or search region bounds. \subsubsection{Fourier transform}