\section{Discussion}

A novel methodology has been presented for objectively identifying the PSA pattern. By rotating the global coordinate system such that the equator (a great circle path) traces the approximate path of the PSA pattern, the method was able to utilize Fourier analysis to quantify the phase and amplitude of wave-like variability in the PSA sector. In reconciling the results of this Fourier analysis with existing EOF-based definitions of the PSA pattern, a strong resemblance was found between the existing PSA-1 mode and the spatial pattern corresponding to the bimodal phase peaks of wavenumber 5--6 dominant variability in the PSA sector. The lack of a higher-order, multi-modal phase distribution questions the physical reality of the existing PSA-2 mode, and may explain the difficulty that researchers have had in identifying a tropical driver for that mode.     

These bimodal phase peaks were used as a means to define the positive and negative phase of the PSA pattern. The climatology arising from this definition revealed that the PSA pattern is most active during winter and spring, often persisting for months at a time. It propagates to the east on average, but a substantial number of events remain relatively stationary or even propagate to the west. The pattern was also shown to have a strong influence on regional temperature, precipitation and sea ice variability. With respect to the former, our results confirm existing relationships established between pattern and station temperatures over the Antarctic Peninsula \citep[e.g.][]{Schneider2012,Yu2012}, extending the regional picture to highlight equally strong temperature anomalies (of opposite sign) over West Antarctica. Large precipitation anomalies were also identified along the coast of West Antarctica and the Antarctic Peninsula, as well as over South America. These South American anomalies show a more complex spatial pattern than previous analyses (perhaps due to the higher resolution data), but are otherwise broadly consistent with the results of \citet{Mo2001}, who found the positive phase of the PSA pattern to be associated with anomalously wet conditions over southern South America and anomalously dry conditions further north. Previous studies also indicate that the PSA pattern plays an important role in sea ice variability in the Amundsen and Bellingshausen Seas \citep{Raphael2014}. Our results suggest that this role is not uniform across that region, with composites of the positive phase of the PSA pattern simultaneously displaying positive sea ice anomalies in the Bellingshausen Sea and negative in the Amundsen Sea.  

With respect to trends in the PSA pattern over the period 1979--2014, a trend towards the negative phase was identified on an annual basis and also during summer, autumn and winter. This autumn trend (and the high latitude temperature and sea ice anomalies associated with the negative phase of the PSA pattern) is consistent with the work of \citet{Ding2013}, who found that autumn warming over the Antarctic Peninsula and associated sea ice declines over the Bellingshausen Sea are associated with an atmospheric circulation resembling the negative phase of the PSA pattern. While this explanation makes sense on the eastern flank of the central circulation anomaly associated with that pattern, the negative phase of the PSA pattern is also associated with strong cooling over West Antarctica. Autumn temperature declines have not been observed in that region, and thus our results suggest that the PSA-related cooling must have been offset by other factors. 

In contrast to the autumn warming over the Antarctic Peninsula, winter warming over West Antarctica has been associated with an atmospheric circulation resembling the positive phase of the PSA pattern \citep{Ding2011}. Our climatology revealed a (albeit non-significant) trend towards the negative phase of the PSA pattern during winter, which raises the question: how is it that winter temperature trends over West Antarctica are associated with an atmospheric circulation resembling the positive phase of the PSA pattern, but a climatology of PSA pattern activity reveals a trend that directly opposes that finding? One possible answer to this question comes from \citet{Li2015a}. They analyzed Rossby wave trains associated with observed SST trends in the tropical Atlantic, tropical Indian, west Pacific and east Pacific regions and found that all four have a center of action over the Amundsen Sea. While none of these individual wave trains resembled the PSA pattern, a linear combination of the four of them did (with the tropical Atlantic and west Pacific identified as most influential). In other words, the integrated influence of tropical SST trends on the atmospheric circulation resembles the positive phase of the PSA pattern, but the waves underpinning that teleconnection do not. This result is consistent with an earlier study that identified the tropical Atlantic as a driver of recent winter trends in West Antarctica \citep{Li2014}. Another possible answer comes from \citet{Fogt2015}, who suggest that radiative forcing has played a role in Amundsen Sea Low trends that are consistent with winter warming in West Antarctica. The absence of any springtime trend in the PSA pattern suggests that it has also not played a role in high latitude warming during that season. Similar to winter, the Atlantic has been linked to warming in West Antarctica during spring \citep{Simpkins2014}, while others point to a more meridionally oriented wave train associated with the Pacific Decadal Oscillation \citep[PDO;][]{Clem2015,Clem2015a}. 

This idea that radiatively forced Amundsen Sea Low variability and/or wave trains associated with the Atlantic or PDO might be responsible for a teleconnection resembling the PSA pattern (i.e. as opposed to changes in actual PSA pattern activity) goes to the heart of the reversibility argument made at the beginning of this paper. For a proposed teleconnection to be robust, it must be evident when looking through the lens of both the variable and mechanism of interest. However, even if these alternative explanations do reconcile the discrepancy between our climatology and winter warming over West Antarctica, the associated circulation anomaly would bring cooler conditions and wind-driven increases in sea ice along the western Antarctic Peninsula, contrary to the observed warming and sea ice declines \citep{Clem2015}. One possible explanation is that the negative autumn sea ice anomalies persist into winter \citep{Ding2013}, however it is clear that there is still work to be done to fully understand recent winter temperature and sea ice changes in the region.

One topic not addressed here is variability in the east/west location of the PSA pattern. In response to the emergence of central Pacific ENSO events in recent years \citep[e.g.][]{Ashok2007}, some authors have suggested that the PSA pattern moves east/west depending on the precise location of the associated tropical SST anomalies \citep[e.g.][]{Sun2013,Wilson2014,Ciasto2015}. Others suggest that the pattern is relatively stationary \citep[e.g.][]{Liu2007,Ding2012}, however either way the broad region (10$^{\circ}$N to 10$^{\circ}$S in the rotated coordinate system) used by our identification algorithm renders it insensitive to subtle east/west movements. Given that the PSA pattern did not show a strong association with the Ni\~{n}o 3.4 index (an index that is sensitive to both central and eastern Pacific ENSO events), it would be fair to say that even if the location of tropical SSTs does cause the pattern to move slightly, this would represent only a small fraction of all PSA pattern activity. 

This weak association with ENSO challenges our fundamental understanding of the PSA pattern. The most commonly held view to date is that the pattern is primarily a response to ENSO forcing \citep[e.g.][]{Mo2001}, whereby anomalous ENSO-related SST anomalies modify tropical convection, leading to atmospheric vorticity gradients conducive to Rossby wave generation \citep{Sardeshmukh1988}. A more comprehensive analysis of the relationship between the pattern and tropical convection would be required to confirm this (e.g. lagged correlations with SSTs and other indicators of tropical convection like the outgoing longwave radiation), but our results suggest that the PSA pattern might actually be better conceptualized as a preferred regional atmospheric response to various internal and external forcings (i.e. with ENSO being just one of many players). Tropical convection is almost certainly an important factor, but its role is likely more complicated than can be captured by a broad-scale ENSO index like the Ni\~{n}o 3.4. This complex relationship between tropical SSTs, convection and the PSA pattern has been the focus of a small number of studies \citep[e.g.][]{Harangozo2004,LachlanCope2006} and is a topic that warrants much more attention. The relationship between the PSA pattern and ENSO has also traditionally been thought to be moderated by the state of the `atmospheric bridge' \citep{Liu2007}. In particular, the pattern is thought to be most active when ENSO and the SAM are in phase \citep{Fogt2006}. Rather than casting the SAM in a facilitating/bridging role, the strong association identified here is more consistent with the idea that the PSA pattern is an integral part of the zonally asymmetric structure of the SAM \citep[e.g.][]{Ding2012,Fogt2012}. 

In addition to a more detailed analysis of the relationship between the PSA pattern, tropical convection and the SAM, our new methodology could also be adapted for use in future studies of other quasi-stationary waveforms. The most obvious candidate is the Pacific-North American (PNA) pattern \citep{Wallace1981}, which plays an important role in winter climate variability over the North Pacific and North America \citep[e.g.][]{Notaro2006}. Like its SH counterpart, the PNA pattern follows an approximate great circle path, has traditionally been analyzed via EOF analysis and has been implicated in recent mid-to-high latitude trends \citep[e.g.][]{Ding2014,Liu2015}. Other non-zonal waveforms that do not follow an approximate great circle path would be more challenging, however methods have been developed for applying Fourier analysis to synoptic-scale, non-zonal waveforms \citep{Zimin2006,Souders2014} and may represent a starting point for future research. 
