1. Introduction
Many mechanisms have been invoked to explain the modulation of persistent circulation patterns in the South Pacific. These include direct processes, such as tropical convection and Rossby wave sources associated with El Niño–Southern Oscillation (ENSO) (Karoly 1989; Renwick and Revell 1999; Cai et al. 2011) and the Madden–Julian oscillation (MJO) (Mo and Paegle 2001; Hirata and Grimm 2016), to more indirect modulation of the subtropical and polar jets in response to changes in the Hadley circulation (Hu and Fu 2007; Freitas and Ambrizzi 2012; Nguyen et al. 2013; Freitas et al. 2016) or by the thermal winds (Reid and Gage 1984; Dickey and Marcus 1992; Mo et al. 1997). Alternately, local drivers such as the resonant interaction between Rossby waves, flow instabilities, and the internal dynamics of the jets have been invoked [see O’Kane et al. (2016b) and references therein]. While undoubtedly multiple processes play a role, even a cursory reading of the literature indicates there is a considerable degree of disagreement as to the relative importance of each, particularly on time scales from intraseasonal to interannual.
The now standard interpretation of an empirical orthogonal function (EOF)/principal component (PC) analysis (Lorenz 1956; Hannachi et al. 2007) of Southern Hemisphere (SH) 500-hPa geopotential height anomalies (
On time scales from a few days to about a month, it has for some time now been posited that atmospheric blocking events over the South Pacific could also be strongly modulated by the ENSO cycle, particularly during austral spring and summer. Renwick and Revell (1999) examined 30-day low-pass-filtered 
In a broader sense, dynamical mode theory produces classes of intermediate scale and period modes—on the intraseasonal time scale—which, apart from the tropical signal of the MJO, have been little studied based on observations. Frederiksen and Lin (2013) describe how these intermediate scale and period modes have extratropical structures quite similar to the major Pacific–North American (PNA) and North Atlantic Oscillation (NAO) teleconnection patterns (i.e., dipolar patterns of low-frequency tropospheric height variability manifesting in the North Pacific and North Atlantic sectors of the Northern Hemisphere). In the case of the PSA, the leading dynamical mode is an instability that has an intraseasonal period (22 days) (Frederiksen and Frederiksen 1993), which is consistent with the earlier findings of Lau et al. (1994).
O’Kane et al. (2013) investigated systematic changes (secular trends) and regime behavior (frequency of occurrence and persistence) in the SH tropospheric circulation in terms of blocking, planetary wavenumber-3, and the respective phases of the SAM via application of data driven nonparametric cluster analysis. O’Kane et al. (2016b) extended this approach to reveal the secular behavior of the PSA pattern and blocking modes over recent decades. They found the PSA exhibited significant variations on interannual-to-decadal time scales. However, consistent with the study of South Pacific winter blocking by Oliveira et al. (2014), no large systematic linear trends were identified in the region upstream of South America. The studies of O’Kane et al. (2013, 2016b) found resonant interactions between local disturbances and local stationary Rossby wave sources within the SH midlatitude subtropical and polar jets to be the dominant mechanism by which coherent structures, such as blocking and the PSA, form (i.e., extratropical internal dynamics on synoptic-to-intraseasonal time scales).
The alternative interpretation to the instability paradigm is one in terms of stationary Rossby waves in a stable background flow generated via a sustained source (up to 16 days), usually tropical SST anomalies of several degrees (Hoskins and Karoly 1981; Karoly 1983; Branstator 1983; Hoskins and Ambrizzi 1993; Renwick and Revell 1999). Based on Wentzel–Kramers–Brillouin (WKB) and ray tracing theory, Hoskins and coworkers (Hoskins and Ambrizzi 1993; Ambrizzi et al. 1995; Jin and Hoskins 1995; Ambrizzi and Hoskins 1997) articulated the role of the subtropical and polar jet streams as waveguides for stationary Rossby wave activity. These studies, and in particular the one of Karoly (1983), were highly influential on later studies of the PSA such as the one by Mo and Paegle (2001) where the low-frequency variability of the PSA1 is attributed to stationary Rossby waves generated via large-amplitude tropical SST anomalies (SSTAs) in response to ENSO. On synoptic time scales, Renwick and Revell (1999) hypothesized that the divergence associated with tropical outgoing longwave radiation anomalies forces an extratropical wave response resulting in enhanced blocking over the southeast Pacific. They argue that linear Rossby wave propagation provides the link between anomalous convection in the tropics and the occurrence of blocking over the southeast Pacific Ocean.
Many recent studies, of which the one of Cai et al. (2011) is characteristic, have continued to invoke the aforementioned early examinations of stationary Rossby wave propagation to explain the influence of tropical forcing on midlatitude dynamics, often without sufficient regard for the seasonally dependent barriers to stationary Rossby wave propagation of the type identified by Ambrizzi et al. (1995) and more recently reexamined by Li et al. (2015). In particular, it is well known from ray tracing theory that, coincident with the establishment of the subtropical jet in the austral winter, Rossby wave propagation from the tropics to the midlatitudes in the South Pacific is largely blocked by the establishment of a reflecting surface poleward of the subtropical jet east of 60°E and west of 120°W (Hoskins and Karoly 1981; Hoskins and Ambrizzi 1993; Ambrizzi et al. 1995; Ambrizzi and Hoskins 1997; Li et al. 2015). This surface occurs where the total wavenumber is imaginary due to a negative meridional gradient of vorticity (see schematic in Fig. 1). This barrier represents a major problem for studies that invoke the excitation of equivalent barotropic Rossby wave trains propagating from the tropics into the extratropics, initiated by diabatic heating anomalies in the tropical equatorial Pacific during the austral autumn, winter, and or spring, as an explanation for the establishment of the PSA pattern and even blocking in the southeast Pacific (Karoly 1989). That said, Jin and Hoskins (1995) showed that, during the austral summer (December–February), anomalous divergence over the Maritime Continent imposed on the background state could lead to the excitation of stationary Rossby wave trains that propagate into the SH in the absence of the subtropical jet. The schematic in Fig. 9 of Cai et al. (2011) is the canonical representation of much current thinking about the role of tropical–extratropical wave trains associated with the PSA, largely based on the ENSO mechanism of Karoly (1989).
Climatological Rossby wave source values (contours) and the leading EOF pattern of Rossby wave source (shaded) calculated from daily anomalies w.r.t. the climatological mean for (a) winter and (b) summer. The range of values is indicated in the top right of each panel with contours uppermost and shaded below. Approximate regions where Rossby wave breaking occurs (O’Kane et al. 2016b) in the tropics are indicated by the white ellipses, whereas the region where a reflective barrier to Rossby wave propagation forms, with maximum extent in the austral winter, is indicated by the gray ellipse. The colors and intervals of the color bar are scaled to min–max values indicated by their corresponding absolute value in the top right hand of each panel (contour absolute value at top, shading below).
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
There is a growing body of literature regarding the influence of both ENSO and global warming on the zonal mean Hadley circulation. In particular global warming has been shown to lead to a general expansion of the tropical circulation (Lu et al. 2007; Vecchi and Soden 2007; Lu et al. 2009), whereas it has been argued that during strong El Niño events there is a corresponding contraction of the Hadley circulation (Hu and Fu 2007; Freitas and Ambrizzi 2012; Nguyen et al. 2013; Freitas et al. 2016).
The role of the stationary Rossby waves and the internal dynamics of the subtropical and polar jets on the frequency and duration of persistent patterns in SH has been the subject of detailed studies by O’Kane et al. [2013, 2016a (manuscript submitted to Climate Dyn.), 2016b]. Here we focus on midlatitude SH tropospheric variability with a particular focus on that part of the variability that is highly correlated with ENSO. To this end, we consider 
Here we are interested to see how changes in the tropical circulation might modulate persistent circulation patterns in the extratropical Pacific via changes in the Hadley circulation (Freitas and Ambrizzi 2012). We also investigate the influence of the thermal winds on the South Pacific tropospheric circulation via coherent interannual fluctuations in atmospheric angular momentum associated with the ENSO cycle (Reid and Gage 1984; Dickey and Marcus 1992; Mo et al. 1997). Correlation with the multivariate ENSO index (MEI) is employed to indicate tropical Pacific influences. We are particularly motivated to ascertain what fraction of variance described by the SSA-reconstructed components is highly correlated with ENSO in each of the respective PSA modes.
Identifying the mechanisms by which the PSA occurs has important consequences for understanding its effect on the high latitudes of the South Pacific. Recent studies of temperature and precipitation variability over West Antarctica and the Antarctic Peninsula (Ding et al. 2011; Schneider et al. 2012; Steig et al. 2012; Ding and Steig 2013; Clem and Fogt 2015) and on sea ice variability in the adjacent Amundsen, Bellingshausen, and Weddell Seas [Matear et al. (2015) and references therein] have been linked to the low-frequency circulation variations due to PSA variability and modulated by anomalous tropical Pacific sea surface temperatures due to ENSO. It is noticeable that in the recent study of ERA-Interim data by Irving and Simmonds (2016), while confirming that the PSA pattern does indeed have a strong influence on observed warming over the Antarctic Peninsula during the austral autumn, they find only a very weak relationship between PSA variability and ENSO.
The data and diagnostics are described in section 2. Section 3 contains results of the EOF/PC analysis and multiscale spectral analysis of geopotential height, the Hadley circulation, as well as air temperature and thermal wind anomalies. Section 4 contains the conclusions. Details of the SSA are presented in the appendix.
2. Data and diagnostics
To examine the dynamics of the troposphere, we consider geopotential height on the 
In the sections to follow we undertake a systematic examination of atmospheric variability in the region (90°S–0°, 120°–300°E). We perform an initial EOF/PC analysis of the SH troposphere, appropriately cosine of the latitude weighted, considering covariances of 
3. Multiscale spectral analysis of the PSA
We first apply EOF/PC analysis to reduce the dimensionality of the data and to verify that the JRA-55 can reproduce the now familiar patterns and variability associated with SAM and the PSA modes. Here, and for convenience, we apply the usual interpretations of the leading EOF patterns of 
The SAM is well represented as the EOF1 mode in Fig. 2. The PSA modes are generally regarded as the low-frequency component of EOFs 2 and 3, here displayed in Fig. 2 in terms of the 360-day SSA-filtered PCs 2 and 3. From the PCs of the leading five modes we can already see that the low-frequency component of the annular mode (EOF1), accounts for a significantly greater percentage of the variability than occurs for the PSA modes (EOFs 2 and 3). To determine statistical significance we calculated the power spectra of an AR(1) and AR(2) process (1000 realizations) fit to the PC time series of the leading six empirical modes. We found that an AR(2) process was required to fit the tail of the spectra, shown in Fig. 3 with the corresponding 5th, 50th, and 95th percentile ranges. This analysis reveals a statistically significant peak in power on the 2–7-yr time scale for PCs 2 and 4. In every case—PCs 1 to 6—the spectra reflect multiscale features. Correlation between 
The leading five EOF patterns and their corresponding PCs calculated from combined 300-, 500-, and 700-hPa 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
Log–log plots of power spectra in decibels (db) of an AR(2) process fit to the PCs (blue lines) of the leading six empirical 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
Correlation of the multivariate ENSO index (MEI) and 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
Many studies of the PSA modes prefilter the data (low pass), typically removing variability on time scales less than 120–360 days (Mo 2000). Subsequent analysis of the leading invariant EOF patterns and their relevance to physical mechanisms can only be meaningful where those patterns account for a significant fraction of the total variance, not the fraction of the variance retained after the data has been filtered. In the following we are interested to quantify the fraction of total variance described by the various frequency components of the multiscale PCs and to ascertain whether these components [SSA reconstruction component 
a. Geopotential height
To identify any likely ENSO influence on the low-frequency components of the leading EOF/PC modes, we apply SSA to the leading five 
Time series of the three least oscillating reconstruction components [slowest 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
Thus far we have confirmed significant correlation of the PSA1 with ENSO and identified PC4 as another higher-order mode influenced by tropical Pacific interannual variability. On synoptic-to-intraseasonal time scales, O’Kane et al. (2016b) identified quasi-stationary regime states in the South Pacific, associated with blocking, with the same patterns as the PSA modes. This raises the question as to whether the PSA should more accurately be characterized, not simply in terms of the low-frequency component of EOF/PCA 2 and 3, but as multiscale regimes manifesting on a hierarchy of time scales? If the answer is yes, then what fraction of the variability arises purely due to dynamics internal to the waveguide relative to that due to tropical influences, and what are the mechanisms by which each occurs? O’Kane et al. (2016b) examined internal waveguide dynamics, blocking, and persistent patterns of the SH troposphere, including Rossby wave sources, velocity potential, wave activity flux, and potential vorticity. On synoptic time scales, they found little evidence of sustained tropical sources, rather that local sources within the waveguide were the primary mechanism for the generation of stationary Rossby waves. We will confine the rest of our analysis to quantifying the role of the tropics on multiscale PSA variability.
We identify the patterns associated with the SSA 
Winter (JJA) spatial pattern of the least oscillating SSA reconstruction component 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
The PSA1 pattern also manifests at all embeddings (from daily to interannual) but weakens as the time scale increases and progressively less of the variance is explained. At the 30-day embedding, the pattern depicting the correlation between PC2 and the least oscillating SSA reconstruction component (R30) (Fig. 6) reflects the tendency for very long-lived persistent blocks to form in the South Pacific. At 120- and 480-days embedding, the PC2 R120 and PC2 R480 patterns highlighted (bold outlines Fig. 6) in the Pacific are composed of a residual PSA1 signal and an emerging ENSO signal in the tropics. This feature is commonly misrepresented as a Rossby wave train (Cai et al. 2011) when there is little evidence of any sustained equatorial Rossby wave source at this time scale. From Fig. 1, we see Rossby wave sources in the SH largely located in the subtropical (JJA) and polar (DJF) jets. The SSA pattern for PC3 reveals the PSA2 mode to be largely expressed at short time scales, an indication that internal waveguide processes are dominant. For PC4, where we find significant correlation with ENSO at time bands greater than 120 days, we largely observe the correlation patterns of 
b. Temperature
To further examine the source of variance at given time bands, we consider the fractional in-band variance of surface air temperature (
Fractional in-band variance of surface air temperature (
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
At 500 hPa (Fig. 8), the SH fractional in-band variance on 1–2 days, is again largest in the Indian Ocean (SH) and downstream of the Rockies and Himalayas (NH). On 2–5 days, the SH variance spans the midlatitudes, contracting to the subtropical jet at 5–10 days. At 15–90 days, the Maritime Continent has by far the largest variance signal, presumably due to the Walker circulation and the Madden–Julian oscillation. As for 
As in Fig. 7, but for temperature at 500 hPa (i.e., 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
c. Thermal wind
We next consider the role of the thermal wind 
The leading two EOF patterns and PC time series of the (a) meridional (υ) and (b) zonal (u) components of the thermal wind 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
Correlation of the zonal component of the thermal wind with ENSO (MEI) by season and over the entire period 1958–2013.
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
The role of ENSO in modulating the low-frequency variability of the zonal component of the thermal wind is confirmed by correlations of 0.936 and 0.559 for the least oscillating SSA reconstruction component of the leading two zonal 
Time series of the three least oscillating SSA reconstruction components [slowest (blue), next slowest (magenta), and fastest (mustard)] of the leading five PCs of the zonal component of 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
Power spectra of an AR(2) fit to the leading six PCs of the empirical zonal 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
Annual spatial pattern of the correlation of the least oscillating reconstruction component of the zonal component of the leading five 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
d. Hadley circulation
Many studies have focused on the expansion of the Hadley circulation in response to global warming (Hu and Fu 2007; Lu et al. 2007), and in response to El Niño (Oort and Yienger 1996; Lu et al. 2008; Nguyen et al. 2013; Freitas et al. 2016). For example, Lu et al. (2008) found large-amplitude El Niño events could produce a contraction and strengthening of the Hadley circulation. Recent modeling studies by Tandon et al. (2013) and Freitas et al. (2016) found that thermal forcing applied to the equatorial Pacific in a narrow band (between 5°S–5°N) could stimulate an El Niño–like Hadley circulation contraction and concomitant poleward shift of the jets. These modeling studies show that small changes to the meridional structure of the thermal forcing have the potential to significantly modulate the circulation response. However, the aforementioned studies largely consider differences between periods or, composites of a few strong El Niño and La Niña events. Here we apply SSA to examine the variability of the Hadley circulation, its correlation to ENSO, and the response of the midlatitude troposphere.
The seasonal climatological 
The seasonal time mean (shaded) meridional streamfunction 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
Correlation of 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
The leading six EOFs calculated from 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
On shorter time scales, in-band variances as a fraction of the total 
Fractional in-band variance of 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
In Fig. 18, we examine the correlation of the least oscillating SSA reconstruction component of the leading six 
Correlation of the least oscillating SSA reconstruction component for the leading six 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
To ascertain what proportion of the variance is associated with the interannual ENSO signal, we calculate SSA for an embedding dimension of 360 days (Fig. 19). Here we plot the three least oscillating reconstruction components [slowest (blue), next slowest (magenta), and fastest (mustard)] of the leading six 
Time series of the three least oscillating SSA modes [slowest (blue), next slowest (magenta), and fastest (mustard)] of the leading six 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0291.1
e. Discussion
The results described in the previous section highlight the dangers of prefiltering or averaging of data, as forewarned by Lau et al. (1994). Specifically, prefiltering the data via application of a low-pass or running average will remove all variability on time scales shorter than the filtering scale. Subsequent application of EOF/PCA to the low-pass-filtered data means that the retained variance explained by the invariant patterns represents only a fraction of the total variance of the unfiltered data. This is problematic where there is substantive energy at high wavenumbers or where the power in the spectra occurs at short time scales. The general point we make is that the correlation of any low-frequency component of a given EOF/PCA mode with a known physical mode, is only significant when that component accounts for a large percentage of the total variance. We have shown that this is not the case for the slow reconstruction component of PSA1, where the correlation with ENSO resides. We further identified PC4 of 
Correlations of the leading SSA reconstruction components with 
Further evidence of the role of internal waveguide dynamics in determining the variance on time scales from 1 to 10 days, can be seen in the fractional in-band variances of temperature at the surface and at 500 hPa (Figs. 7 and 8). On time scales between 10 and 60 days at 500 hPa, the subtropics and Indian subcontinent contain the majority of the variance (Fig. 8), presumably associated with the monsoon and MJO. The central and eastern equatorial Pacific is the major source of variance from 91 to 180 days as ENSO variability manifests at the surface (Fig. 7).
The leading modes of the meridional component of 
Another potential source of tropical variability in the midlatitude troposphere is the Hadley circulation. We considered Pacific 
In this study we have focused on the mechanisms by which the low-frequency ENSO variability is communicated to the SH extratropical Pacific and in particular the role of stationary Rossby waves, the HC, and the thermal wind. A more general question concerns the role of stochastic forcing due to fast tropical convection as a cause of extratropical variability on slower time scales. Franzke (2009) applied empirical mode decomposition, in many respects comparable to SSA, to examine the relative fraction of interannual and longer time scale variability to climate noise of the SAM, NAO, and North Pacific climate teleconnection indices. While our results indicate that a very large fraction of PSA variability manifests on intraseasonal time scales, it remains unclear what fraction of the low-frequency variability of the PSA manifests in part due to fast stochastic physical processes. This is a question we will examine in a future study.
4. Conclusions
In the climate community, the PSA modes have traditionally been defined as the low-frequency variability of EOF/PCA modes 2 and 3 of the SH midtropospheric circulation (Mo 2000), manifesting largely in response to the influence of ENSO communicated via stationary Rossby waves (Karoly 1989; Cai et al. 2011). However, because of the presence of reflecting and breaking barriers in all seasons, apart from the austral summer, the perceived role of stationary Rossby waves in determining the PSA modes is in fact inconsistent with the ray tracing theory (Ambrizzi et al. 1995; Li et al. 2015). Calculation of Rossby wave source shows the subtropical and polar jets to be the major source regions for the generation of stationary Rossby waves, with little evidence for sustained equatorial tropical sources influencing the South Pacific. Rather, we see that the source of the low-frequency ENSO signal on the PSA modes arises due to meridional temperature gradients and modulation of the SH midlatitude jets by the thermal winds. These results are consistent with dynamical mode theory (Frederiksen and Frederiksen 1993), the early SSA study of Lau et al. (1994), and the more recent cluster analysis of O’Kane et al. (2016b) that the PSA modes arise largely as intraseasonal oscillations associated with eastward-propagating wave trains and resonant interactions with local disturbances, independent of tropical forcing.
Analysis of higher-order modes (PCs 4 and 5), explaining a significant fraction of the total variance (5.3% and 5.0%, respectively), reveal similar characteristics to the PSA modes. Both are indicative of an eastward-propagating wave train where a similarly strong correlation occurs between ENSO and the low-frequency component of the leading mode (PC4), as is found for the PSA1 mode.
Whereas the mean South Pacific Hadley circulation is most highly correlated with ENSO during the summer and spring, most of the variability, as determined by spectral analysis of the airmass transport across meridians, occurs in the midlatitudes within the polar and subtropical jets. EOF/PCA of Hadley circulation variability shows that the correlation of the slowly varying component of the Hadley circulation modes with ENSO is very low, and that the fraction of the total variance described by these modes is small. The patterns associated with the PSA modes were found to manifest at all time scales with the largest fraction of total variance occurring on synoptic time scales. These results, on short time scales, agree with the prior study of blocking in the South Pacific by O’Kane et al. (2016b).
To summarize we find that the PSA is a multiscale nonlinear dynamical mode manifesting on time scales from synoptic to interannual. The major percentage of PSA variability occurs on time scales from synoptic to intraseasonal, is largely independent of persistent coherent tropical processes, and manifests via internal waveguide instabilities and dynamics. The small fraction of the total variability with a tropical signal arises entirely due to modulation of the SH midlatitude jets, via the zonal component of the thermal wind. Finally, we identify a higher-order mode, in terms of the slow components of PCs 4 and 5 of tropospheric geopotential height, with similar characteristics to the PSA, most notably a high correlation of the leading mode (PC4) with ENSO, again arising largely due to the influence of the zonal component of the thermal wind. This observational study provides a basis for a unified theory for persistent patterns in the South Pacific that is able to reconcile apparent inconsistencies between earlier ray tracing, dynamical mode, and observational studies.
Acknowledgments
TJO acknowledges funding support of an Australian Research Council Future Fellow (Grant FT120100008). DPM was supported by the Australian Climate Change Science Program. JSR was supported by the Grains Research Development Corporation.
APPENDIX
Singular Spectral Analysis
The general method [Eqs. (A1)–(A4)] described below is the same as employed in Monselesan et al. (2015), and the following paragraph of text is derived from there with only minor modifications. We include it here for completeness.
The variance explained 
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