1 Introduction

The Southern Annular Mode (SAM) is the main mode of variability in the Southern Hemisphere extratropical circulation (Rogers and van Loon 1982) on daily, monthly, and decadal timescales (Mark P. Baldwin 2001; Fogt and Bromwich 2006) and exerts an important influence on temperature and precipitation anomalies, and sea ice concentration (e.g. Fogt and Marshall 2020). Its positive phase is usually described as anomalously low pressures over Antarctica surrounded by a ring of anomalous high pressures in middle-to-high latitudes.

Most authors describe the SAM as a zonally symmetric pattern, a fact that is reflected not only in its name, but also in the various methods used to characterise it. Of the several different indices presented in the literature, many of them are based on zonal means of sea level pressure or geopotential height (Ho, Kiem, and Verdon-Kidd 2012). Gong and Wang (1999) defined the SAM index as the zonal mean sea level pressure difference between 40S and 65S, which is also the definition used by the station-based index in Marshall (2003). Mark P. Baldwin and Thompson (2009) proposed defining the Northern and Southern Annular modes as the leading EOF of the zonally averaged geopotential height at each level.

Even though these indices are based on zonal averages, their associated geopotential height spatial anomalies contain noticeable deviations from zonal symmetry, particularly in the Pacific Ocean region. The zonal asymmetries have not been widely studied, but previous work suggests that they strongly modulate the regional impacts of the SAM (Fan 2007; Silvestri and Vera 2009; Fogt, Jones, and Renwick 2012; Rosso et al. 2018). The fact that the SAM is not entirely zonally symmetric hinders our ability to reconstruct its historical variability prior to the availability of dense observations in the Southern Hemisphere (J. M. Jones et al. 2009).

Some of the variability associated with the zonal asymmetries of the SAM seems to be forced by the tropics. ENSO-like variability affects the Southern Hemisphere extratopics through the Rossby wave trains (Mo and Ghil 1987; Kidson 1988; Karoly 1989) which project strongly onto the zonal anomalies associated with the SAM in the Pacific sector. Moreover, tropical influences on the SAM have been observed (Fan 2007; Fogt, Bromwich, and Hines 2011; Clem and Fogt 2013). Fan (2007) computed SAM indices of the Western and the Eastern Hemispheres separately and found that they were much more correlated to each other if the (linear) signal of the ENSO was removed.

Positive trends in the SAM have been documented by various researchers using different indices, mostly in austral summer and autumn (e.g. Fogt and Marshall 2020 and references therein). It is thought that these trends are driven primarily by stratospheric ozone depletion and the increase in greenhouse gases, and understood in the context of zonal mean variables (Marshall et al. 2004; N. P. Gillett, Allan, and Ansell 2005; Arblaster and Meehl 2006; Nathan P. Gillett, Fyfe, and Parker 2013). However, it’s not clear yet how or if the asymmetric SAM component responds to these forcings, or how its variability alters the observed trends.

The impact of the zonally asymmetric component of the SAM at regional scales has not been studied in detail yet. The positive phase of the SAM is associated with colder-than-normal temperatures over Antarctica and warmer-than-normal temperatures at lower latitudes (M. E. Jones et al. 2019) (and vice versa for negative SAM). But there are significant deviations from this zonal mean response, notably in the Antarctic Peninsula and the south Atlantic (Fogt, Jones, and Renwick 2012). The SAM-related signal on precipitation anomalies behaves similarly, although with even greater deviation from zonal symmetry (Lim et al. 2016). The SAM-precipitation relationship in Southeastern South America can be explained by the Pacific-South American (PSA)-like zonally asymmetric circulation associated with the SAM (Silvestri and Vera 2009; Rosso et al. 2018). Fan (2007) also found that precipitation in East Asia was impacted by the variability of only the Western Hemisphere part of the SAM.

The study of the temporal variability of the asymmetric component of the SAM has not received much attention except for Fogt, Jones, and Renwick (2012). This study provides evidences for the relevance of the SAM’s asymmetric component. However, their conclusions are based on composites of positive and negative SAM events including a small number of cases unevenly distributed among years with and without satellite information. The latter is particularly important due to the inhomogeneities in reanalysis products prior to the satellite era and the possible change in the asymmetric structure of the SAM (Silvestri and Vera 2009). Moreover, Fogt, Jones, and Renwick (2012) studied the zonal asymmetric component of the SAM only in sea level pressure. Zonal asymmetries in the SAM spatial pattern are fairly barotropic throughout the troposphere, but they change dramatically in the stratosphere (Mark P. Baldwin and Thompson 2009).

In summary, previous research strongly suggests that the zonally asymmetric component of the SAM can potentially be very different from the zonally symmetric component. It might have different sources of variability, impacts and long-term response to radiative forcing. A single SAM index that mixes the zonally symmetric and zonally asymmetric variability is only able to capture the combined effect of these two potentially distinct modes.

Our objective is, then, to describe the zonally asymmetric and symmetric components of the SAM variability. We first propose a methodology that provides for each level, two indices which aim to capture independently the variability of the symmetric and asymmetric SAM component respectively. Their vertical structure and coherence, temporal variability and trends are consequently assessed. We then study the spatial patterns described by the variability exclusive to each index focusing on 50 hPa as representing the stratosphere and 700 hPa as representing the troposphere. Finally, the relationships of the SAM at 700 hPa with temperature and precipitation anomalies are investigated.

In Section 2 we describe the methods. In Section 3.1 we describe the temporal variability and vertical coherence of the indices. In Section 3.2, we analyse the spatial patterns of geopotential height associated with them. In Section 3.3, we study their relationship with surface-level temperature and precipitation.

2 Methods

2.1 Data

We used monthly geopotential height at 2.5 longitude by 2.5 latitude of horizontal resolution and 37 vertical isobaric levels as well as 2 metre temperature from ERA5 (Hersbach et al. 2020) for the period 1979 to 2018. We restrict our analysis to the post-satellite era to avoid any confounding factors arising from the incorporation of satellite observations.

For precipitation data we used monthly data from the CPC Merged Analysis of Precipitation (P. Xie and Arkin 1997), with a 2.5 resolution in latitude and longitude. This rainfall gridded dataset is based on information from different sources such as rain gauge observations, satellite inferred estimations and the NCEP-NCAR reanalysis, and it is available since 1979 to present.

2.2 Definition of indices

Traditionally, the SAM is defined as the leading empirical orthogonal mode (EOF) of sea-level pressure or geopotential height anomalies at low levels (Ho, Kiem, and Verdon-Kidd 2012). Following Mark P. Baldwin and Dunkerton (2001), we extend that definition vertically and use the term SAM to refer to the leading EOF of the monthly anomalies of geopotential height south of 20S at each level. We performed EOFs by computing the Singular Value Decomposition of the data matrix consisting in 480 rows and 4176 columns (144 points of longitude and 29 points of latitude). We weighted the values by the square root of the cosine of latitude to account for the non-equal area of each gridpoint (Chung and Nigam 1999). We consider in the EOF analysis all months together without dividing by seasons.

To separate the zonally symmetric and asymmetric components of the SAM, we computed the zonal mean and anomalies of the full SAM spatial pattern, as shown in Figure 2.1 at 700 hPa. The full spatial signal (\(\mathrm{EOF_1}(\lambda, \phi)\)) is the sum of the zonally asymmetric (\(\mathrm{EOF_1^*}(\lambda, \phi)\)) and symmetric (\([\mathrm{EOF_1}](\lambda, \phi)\)) components. We then compute the SAM index, Asymmetric SAM index (A-SAM) and Symmetric SAM (S-SAM) indices as the coefficients of the regression of each monthly geopotential height field on the respective patterns (weighting by the cosine of latitude). The three indices are then normalized by dividing them by the standard deviation of the SAM index at each level. As a result, the magnitudes between indices are comparable. However, only SAM index has unit standard deviation per definition. The explained variance of each pattern is used as an indicator of the degree of zonally symmetry or asymmetry of each monthly field. To quantify the coherence between temporal series corresponding to different indices or the same index at different levels, we computed the temporal correlation between them.

Spatial patterns of the first EOF of 700 hPa geopotential height for 1979 – 2018 period. (a) Full field, (b) zonally asymmetric component and (c) zonally symmetric component. Arbitrary units; positive values in blue and negative values in red.

Figure 2.1: Spatial patterns of the first EOF of 700 hPa geopotential height for 1979 – 2018 period. (a) Full field, (b) zonally asymmetric component and (c) zonally symmetric component. Arbitrary units; positive values in blue and negative values in red.

The method assumes linearity in the asymmetric component of the SAM. That means that zonal asymmetries associated with positive SAM phase (SAM+) are almost opposite in sign and of the same magnitude to the ones associated with negative SAM phase (SAM-). Fogt, Jones, and Renwick (2012)’s composites (their Figure 4) suggest that this might not be entirely valid, although much of that apparent non-linearity could be due to the heterogeneous nature of the selected years for constructing the composites. To test this assumption, we computed seasonal composites of zonal anomalies of geopotential height for SAM+ and SAM- (defined as months in which the SAM index is greater than 1 standard deviation and lower than minus 1 standard deviation, respectively) for the period from 1979 to 2018 at the 700 hPa and 50 hPa levels (Figures 5.1 and 5.2). In all seasons and both levels, SAM+ composites are similar to SAM- in structure but with the opposite sign. Spatial correlations between composites for each season are high. The method considered in this study seems then a reasonable approximation of the phenomenon.

By performing the EOF analysis using data for all months we are assuming that the zonally asymmetric structure of the SAM is the same at all seasons. The latter was assessed by computing geopotential height zonal anomalies by projecting the first EOF of each season independently. The following seasons were considered – December to February (DJF), March to May (MAM), June to August (JJA) and September to November (SON). Results are very similar to each other in the troposphere (Figure 5.3, row 2) and show spatial correlations between 0.65 (DJF with JJA) and 0.9 (MAM with SON). In the stratosphere (Figure 5.3, row 1), patterns are similar for all seasons except DJF, when the wave-1 zonal anomalies are rotated 90 in comparison with the rest of the year. Spatial correlations in the stratosphere are between -0.24 (DJF with SON) and 0.95 (MAM with JJA). Therefore, the results confirm that the zonal asymmetric structure of the SAM is very similar throughout most of the year. The DJF trimester shows much lower correlations with the other seasons at both levels and the weakest zonal anomalies (Figure 5.1), which is consistent with Fogt and Marshall (2020). Therefore, we would expect that, even though the analysis is performed including all months, it represents more accurately the rest of the seasons.

The method also assumes that the zonally asymmetric pattern of the SAM remains stationary along the period considered. Silvestri and Vera (2009) suggest that this might not be the case between 1958 and 2004. Zonal asymmetric patterns of SAM were computed for the two halves of the period (1979 to 1998 and 1999 to 2018) respectively. The differences between the two periods appear to be relatively small in both the troposphere and stratosphere (Figure 5.4).

2.3 Regressions

We performed linear regressions to quantify the association between the SAM indices and other variables. Moreover, we apply multiple linear regression analysis to describe the combined influence of both A-SAM and S-SAM. To obtain the linear coefficients of a variable \(X\) (geopotential, temperature, precipitation, etc…) with A-SAM and S-SAM we fit the equation

\[ X(\lambda, \phi, t) = \alpha(\lambda, \phi) \operatorname{A-SAM} + \beta(\lambda, \phi) \operatorname{S-SAM} + X_0(\lambda, \phi) + \epsilon(\lambda, \phi, t) \]

where \(\lambda\) and \(\phi\) are the longitude and latitude, \(t\) is the time, \(\alpha\) and \(\beta\) are the linear regression coefficients, \(X_0\) and \(\epsilon\) are the constant and error terms. From this equation, \(\alpha\) represents the (linear) association of \(X\) with the variability of A-SAM that is not explained by the variability of S-SAM; i.e. it is proportional to the partial correlation of \(X\) and A-SAM, controlling for the effect of S-SAM, and vice versa for \(\beta\). When performing a separate regression for each trimester (DJF, MAM, JJA, SON), we averaged the relevant variables seasonally for each year and trimester before computing the regression.

Statistical significance for regression fields were evaluated adjusting p-values by controlling for the False Discovery Rate (Benjamini and Hochberg 1995; Wilks 2016) to avoid misleading results from the high number of regressions (Walker 1914; Katz and Brown 1991).

Linear trends were computed by Ordinary Least Squares and the 95% confidence interval was computed assuming a t-distribution with the appropriate residual degrees of freedom. To the amplitude of the zonal waves is defined through computing the Fourier transform of the spatial field at each latitude circle.

We computed density probability estimates using a Gaussian kernel of optimal bin width according to Sheather and Jones (1991).

2.4 Computation procedures

We performed all analysis in this paper using the R programming language (R Core Team 2020), using the data.table package (Dowle et al. 2020) and the metR package (Campitelli 2020). All graphics are made using ggplot2 (Wickham 2009). We downloaded data from reanalysis using the ecmwfr package (Hufkens, Stauffer, and Campitelli 2020) and indices of the ENSO with the rsoi package (Albers and Campitelli 2020). The paper was rendered using knitr and rmarkdown (Y. Xie 2015; Allaire et al. 2019).

3 Results

3.1 Temporal evolution

Time series for A\nobreakdash-SAM and S\nobreakdash-SAM at (a) 50~hPa and (b) 700~hPa. To the right, probability density estimate of each index. Series are standardised by the standard deviation of the SAM at each level.

Figure 3.1: Time series for A-SAM and S-SAM at (a) 50~hPa and (b) 700~hPa. To the right, probability density estimate of each index. Series are standardised by the standard deviation of the SAM at each level.

We first asses the temporal evolution of A-SAM and S-SAM. Figure 3.1 shows the corresponding time series for 700 hPa and 50 hPa and their corresponding density estimates. We selected these two levels as representative of the tropospheric and stratospheric variability respectively. As it is shown below, the variabilities of both indices are highly coherent within each atmospheric layer, therefore is reasonable to take one level as representative of each layer.

Month-to-month variability is evident for both indices, with noisy variations in the low frequencies. At first glance the series can be distinguished by their distributions. Compared to the tropospheric indices, the stratospheric indices are much more long-tailed; that is, extreme values (both negative and positive) abound. The A-SAM series have both more variability in the higher frequencies than the S-SAM series.

The stratospheric S-SAM varies strongly with a period between 15 and 30 months (the maximum spectrum is located at 20 months), which can be seen by spectral analysis (Figure 5.6). A local peak at a similar frequency range is discernible in the periodogram of the tropospheric S-SAM, although it’s not statistically significant. This period band is around the range of periodicity of the Quasi-Biennial Oscillation (M. P. Baldwin et al. 2001) and is consistent with (Vasconcellos, Gava, and Sansigolo 2020), who found that the SAM and the QBO share significant common high power around the 2-year band. The fact that this periodicity is not evident on the A-SAM index, is also consistent with their composites of geopotential height anomalies during easterly and westerly QBO, which show a rather symmetric monopole over Antarctica. In the troposphere the most significant peak of variability is found in A-SAM at around 3.6 months.

From a visual inspection, the A-SAM and S-SAM time series appear to be correlated. Moreover, looking at the extremes in the stratosphere, the S-SAM series appears to lag the A-SAM series (see, for example, the positive events on late 1987). Figure 3.2 shows these correlations along all levels considered, for zero and -1 lags. Values of zero-lag correlations between A-SAM and S-SAM are relatively constant throughout the troposphere, fluctuating between 0.39 and 0.45. One-month-lag correlations are similarly constant but significantly reduced to around 0.17. In the stratosphere, zero-lag correlations drop to a minimum of 0.21 at 20 hPa and then increase again monotonically with height up to the uppermost level of the reanalysis (although results near the top of the models are to be interpreted with care). At the same time, one-month-lag correlations increase with height. Therefore, stratospheric A-SAM index tends to precede the S-SAM index. (Correlations at lags -5 to 5 are shown in Figure 5.5.)

Correlation between S\nobreakdash-SAM and A\nobreakdash-SAM at each level for lag zero and lag -1 (A\nobreakdash-SAM leads S\nobreakdash-SAM) for the 1979 -- 2018 period.

Figure 3.2: Correlation between S-SAM and A-SAM at each level for lag zero and lag -1 (A-SAM leads S-SAM) for the 1979 – 2018 period.

Cross correlation between levels for the (a) SAM, (b) A\nobreakdash-SAM, and (c) S\nobreakdash-SAM for the 1979 -- 2018 period.

Figure 3.3: Cross correlation between levels for the (a) SAM, (b) A-SAM, and (c) S-SAM for the 1979 – 2018 period.

Figure 3.3 shows (zero-lag) cross-correlation across levels for the SAM, A-SAM and S-SAM indices. For the SAM (Figure 3.3a), high values below 100 hPa reflect the vertical (zero-lag) coherency throughout the troposphere. Above 100 hPa, correlation between levels falls off more rapidly, indicating less coherent (zero-lag) variability. But correlations between tropospheric and lower-to-middle stratospheric levels are still relatively high (e.g. greater than 0.4 between tropospheric levels and levels below 30 hPa). A-SAM and S-SAM (Figure 3.3b and c, respectively) share similar high level of coherency in the troposphere but they differ in their stratospheric behaviour. Stratospheric coherency is stronger for the A-SAM than the S-SAM. The stratospheric S-SAM seems to connect more strongly to the troposphere than the stratospheric A-SAM.

Linear trends (in standard deviations per decade) at each level for annual (row 1) and seasonal values (rows 2 to 5) for the period 1979 -- 2018 and for the (column a) SAM index, (column b) A\nobreakdash-SAM index, and (column c) S\nobreakdash-SAM index. Shading indicates the 95\% confidence interval from a t-distribution.

Figure 3.4: Linear trends (in standard deviations per decade) at each level for annual (row 1) and seasonal values (rows 2 to 5) for the period 1979 – 2018 and for the (column a) SAM index, (column b) A-SAM index, and (column c) S-SAM index. Shading indicates the 95% confidence interval from a t-distribution.

The linear trends for each of the indices (SAM, S-SAM and A-SAM) were evaluated for the complete period 1979 – 2018 at each level for the whole year and separated by trimesters (Figure 3.4). The SAM index presents a statistically positive significant trend (Figure 3.4a.1) that extends throughout the troposphere up to about 50 hPa and reaches its maximum value at 100 hPa. The seasonal trends (rest of Figure 3.4 column a) indicate that positive trends are present in autumn and particularly in summer, where the 100 hPa maximum is much more defined. In winter and spring, we detect no statistically significant trend. This is consistent with the results of previous studies, which find large positive trends in summer, smaller in autumn and no trends in the other seasons (e.g. Fogt and Marshall 2020 and references therein) using indices of the SAM based on surface or near-surface circulation.

By separating the SAM signal in its asymmetric and symmetric parts, not only we can see that these trends are almost entirely due to the symmetric component (column b vs. column c in Figure 3.4), but in some cases the trends become clearer. In summer, A-SAM has a statistically non significant negative trend in the middle troposphere that obscures the trend in the SAM index; as a result, trends computed using only the Symmetric component are stronger (compare the shading region in Figure 3.4a.2 and c.2). In autumn, the S-SAM index reveals a statistically significant positive trend in the stratosphere that is not significant using the SAM index.

A positive trend in the S-SAM index and no trend in the A-SAM index might at first suggest a trend towards a more symmetric SAM. However, a very negative S-SAM trending towards a less negative S-SAM would be translated into a positive S-SAM trend but a more asymmetric SAM.

Linear trends (in percent per decade) of the variance explained by A\nobreakdash-SAM and S\nobreakdash-SAM at each level and for each trimester for the period 1979 -- 2018. Shading indicates the 95\% confidence interval.

Figure 3.5: Linear trends (in percent per decade) of the variance explained by A-SAM and S-SAM at each level and for each trimester for the period 1979 – 2018. Shading indicates the 95% confidence interval.

To study the question of whether the SAM is becoming more or less asymmetric, we show trends for the explained variance of each index for each trimester in Figure 3.5. In the troposphere the only significant trend is in DJF, in which the A-SAM has a positive trend of about 2% per decade, suggesting that the DJF SAM has become more asymmetric in the period from 1979 to 2018. Fogt, Jones, and Renwick (2012) observed a change from a more asymmetrical SAM before 1980 to a more symmetrical SAM after 1980, but our study period (1979 – 2018) prevents us from detecting that change. However due to the atypical nature of the asymmetric component of the SAM during DJF (Section 2.2) this should be taken only as preliminary evidence. The other significant trend is in the stratosphere during SON, where there is a positive trend in the variance explained by the S-SAM of about 4% per decade. This change could be the result of the forcing from ozone depletion.

3.2 Spatial patterns