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.