2 Introduction
The large-scale extratropical circulation in the Southern Hemisphere (SH) is much more zonally symmetric than that of the Northern Hemisphere, but departures from the zonal mean are associated with regional impacts (e.g. Hoskins and Hodges 2005). They strongly modulate weather systems and regional climate through promoting longitudinally varying meridional transport of heat, humidity, and momentum (K. E. Trenberth 1980; M. N. Raphael 2007) and could even be related to the occurrence of high-impact climate extremes (Pezza, Rashid, and Simmonds 2012).
The zonally asymmetric circulation is typically described by the amplitude and phase of zonal waves obtained by Fourier decomposition of geopotential height or sea-level pressure at each latitude (e.g. van Loon and Jenne 1972; K. E. Trenberth 1980; Turner et al. 2017). This approach suggests that zonal waves 1 and 3 explain almost 99% of the total variance in the annual mean 500 hPa geopotential height zonal anomalies at 50ºS (van Loon and Jenne 1972). K. F. Trenberth and Mo (1985) concluded that wave 3 plays a role in the development of blocking events. In addition, previous works have identified wave-like patterns with dominant wavenumbers 3-4 at extratropical and subpolar latitudes with distinctive regional impacts. M. N. Raphael (2007) showed that variability in the planetary wave 3 projected onto its climatological location is associated with anomalies in the Antarctic sea-ice concentration.
Fourier decomposition relies on the assumption that the circulation can be meaningfully described in terms of zonal waves of constant amplitude along a latitude circle. However, this is not valid for meridionally propagating waves or zonal waves with localised amplitudes. Addressing this limitation, the Fourier technique can be generalized to integrate all planetary wave amplitude regardless of wave number by computing the wave envelope (Irving and Simmonds 2015). The wave envelope can represent planetary waves with different amplitude at different longitudes, but lacks information about phase and wave number. Using this method, Irving and Simmonds (2015) showed that planetary wave amplitude in general is associated with Antarctic sea-ice concentration and temperature, as well as to precipitation anomalies in regions of significant topography in SH mid-latitudes and Antarctica.
Another extensively-used approach to characterise the SH tropospheric circulation anomalies, is computing Empirical Orthogonal Functions (EOF, also known as Principal Component Analysis). Within the EOF framework, the Southern Annular Mode (SAM) appears as the leading mode of variability of the SH circulation (Fogt and Marshall 2020). Spatially, the SAM is characterised by a centre of geopotential anomalies over Antarctica surrounded by anomalies of the opposite sign at middle latitudes. Embedded in this zonally symmetric structure is a wave 3 pattern that is more prominent in the Pacific sector. The 2nd and 3rd EOFs, usually known as Pacific–South American Patterns (PSA) 1 and PSA2 patterns, respectively, describe meridionally propagating wave trains that originate in the eastern equatorial Pacific and Australian-Indian Ocean sector, and travel towards the South Atlantic following a great-circle arch along the Antarctic coast (Mo and Paegle 2001). These patterns influence precipitation anomalies in South America (Mo and Paegle 2001). Although these patterns are usually derived by applying EOF to temporal anomalies, M. Raphael (2003) also applied EOF methods specifically to zonal anomalies. Irving and Simmonds (2016) proposed a novel methodology for objectively identifying the PSA pattern using Fourier decomposition. More recently Goyal et al. (2022) created an index of amplitude and phase of zonal wave 3-like variability by combining the two leading EOFs of meridional wind anomalies.
Some of the zonally asymmetric patterns of the SH circulation variability described previously appear to have experienced secular changes. For instance, M. Raphael (2003) suggests that the amplitude of the zonal wave 1 experienced a large increase and that the zonal wave 3 experienced changes in its annual cycle between 1958 and 1996. However, little is known yet about variability and trends of these patterns.
Patterns resulting from EOF analysis are more flexible than Fourier decomposition-derived modes in that they can capture oscillation patterns that cannot be characterised by purely sinusoidal waves with constant amplitude. Nonetheless, they are restricted to standing oscillation modes and cannot properly represent propagating or phase-varying features such as zonal waves. A single EOF can also represent a mixture of two or more physical modes.
A third methodology commonly used to describe circulation anomalies consists on identifying particular features of interest and creating indices using simple methods such as averages and differences. Examples of this methodology are the SAM Index of Gong and Wang (1999), the SH wave 3 activity index defined by M. N. Raphael (2004) and the SH zonally asymmetric circulation index from Hobbs and Raphael (2010). These derived methods are grounded on other methods such as Fourier decomposition or EOF to identify the centres of action for the described phenomena and can be useful to characterise features that are not readily apparent with these methods. These kinds of indices are generally easy to compute, but they usually do not capture non-stationary patterns.
An alternative methodology that has been proposed to study travelling and standing waves is complex Empirical Orthogonal Functions (cEOF; Horel (1984)). This method extends EOF analysis to capture oscillations with varying amplitude and phase and has been applied to the time domain. For instance, Krokhin and Luxemburg (2007) applied cEOF to station-based monthly precipitation anomalies and monthly temperature anomalies in the Eastern Siberia and the Far East region to characterise the main modes of variability and their relationship with teleconnection indices. Similarly, Gelbrecht, Boers, and Kurths (2018) applied cEOF to daily precipitation from reanalysis to study the propagating characteristics of the South American Monsoon. To our knowledge, cEOF analysis has not been applied in the spatial domain to capture the phase-varying nature of planetary waves in the atmosphere.
The general goal of this study is to improve the description and understanding of the zonally asymmetric extratropical SH circulation using cEOF, which can describe phase varying planetary waves with variable amplitude along a latitude circle. In addition, we try to expand the knowledge of the simultaneous behaviour of SH asymmetric circulation in the troposphere and the stratosphere.
We restrict this work to the September-October-November (SON) trimester. During this season the tropical teleconnections over South America are maximised (Cazes-Boezio, Robertson, and Mechoso 2003), and the SH zonal winds associated with the stratospheric polar vortex increase to peak in October and extend downward after that (Lim, Hendon, and Thompson 2018).
In Section 3 we describe the methods. In Section 4.1 we analyse the spatial patterns of each complex EOF. In Section 4.2 we study the spatial regressions with geopotential height, temperature, and ozone anomalies. In Section 4.3 and 4.4 we analyse the relationship between cEOF2, the PSA and SAM modes. In Section 4.5 we study tropical forcings that explain the variability of each cEOF. In Section 4.6 we show the relationship between these modes of variability and precipitation and surface temperature anomalies in South America and Oceania. In Section 5 we compare our results with previous studies and discuss the benefits of our methodology.