Asymmetry of the Antarctic Oscillation in Austral Autumn

The annular structure of Antarctic oscillation (AAO) is a research hotpot, but its asymmetry receives less attention. In this paper, the self‐organizing map method is employed to cluster the AAO patterns into symmetric and asymmetric modes in austral autumn. The asymmetry is mainly reflected in the Pacific‐Atlantic sector, and the AAO evolves toward asymmetric positive polarity, with the most pronounced asymmetry in May. Originating from near Australia, the asymmetry indicates a zonal wave train in the Pacific‐Atlantic sector. Both modeled and observed results demonstrate that the sea surface temperature anomaly in the equatorial western Pacific stimulates a local meridional circulation anomaly and induces anomalous Rossby wave sources near Australia subsequently. An anomalous wave train propagating toward the Antarctic Peninsula is formed, and the associated geopotential anomaly enhances the asymmetry of AAO. Asymmetric AAO is conducive to the Antarctic dipole, which modulates the air temperature and sea ice anomalies around Antarctica.

• Via a cluster method, we obtained the zonal asymmetric Antarctic oscillation (AAO) mode, and analyzed its trend and preferred month • The source of its asymmetry is from the sea surface temperature anomaly in the tropical western Pacific • The asymmetric AAO mode has a vital influence on the Antarctic dipole Supporting Information: Supporting Information may be found in the online version of this article. 10.1029/2023GL105678 2 of 11 climate near the Antarctic Peninsula by triggering wave trains propagating into southeastward (Chen et al., 2022;Clem et al., 2022).The relationship between the ENSO and AAO has been reflected in earlier studies (H.Ding et al., 2015;Gong et al., 2013;L'Heureux & Thompson, 2006).However, when the influence of tropical ENSO is removed, tropical SST can still explain the AAO variability to a considerable extent (H.Ding et al., 2014).Subsequently, the important role of tropical signals on the zonal wave in Southern Hemisphere is also emphasized (Goyal et al., 2021).The tropical signals in the above studies mostly affect the divergence anomaly in the subtropical region via Hadley circulations to excite wave trains propagating toward Antarctica, although the tropical signal can directly influence the polar region via the meridional circulations (Yuan & Martinson, 2001).
Teleconnections between tropics and Antarctica established by Rossby wave trains provide reasonable explanations for Antarctic climate and the AAO variability.
Despite being named as the annular mode, the AAO still has the non-negligible zonal asymmetry.The effects of this asymmetry have been demonstrated in previous studies (Campitelli et al., 2022;Q. Ding et al., 2012;Fan, 2007;Fogt et al., 2012).This asymmetry has a clear seasonal dependence and is most pronounced in the Pacific and Atlantic sectors, which shows a zonal wave number 3 pattern (Campitelli et al., 2022;Fogt et al., 2012).Some studies have attempted explain the reason for this asymmetry, with emphasis on tropical signals (Campitelli et al., 2022;Q. Ding et al., 2012;Fan, 2007) and the subtropical jet (Song et al., 2011).Here, we select the austral autumn (March-April-May) with the strongest asymmetry of the AAO as the example, and aim to explain the source of the AAO's asymmetry (Figure S1 in Supporting Information S1).

Data, Diagnosis Methods and Model
The European Centre for Medium-Range Weather Forecasts fifth-generation reanalysis product (ERA5) data is utilized, with a horizontal resolution of 1° × 1° (Hersbach et al., 2020).The monthly ERA5 data is used from 1950 to 2019.Moreover, extended reconstructed SST monthly data is employed from 1950 to 2019, with a resolution of 2° × 2° (Huang et al., 2017a).Previous study has confirmed that the ERA5 data provides a good homogeneous representation of the AAO before and in the Satellite Era (Marshall et al., 2022).The seasonal cycle is removed in all data to obtain the anomalous variables.
To examine the pathway of Rossby wave trains, the wave activity flux (WAF) is defined by previous study (Takaya & Nakamura, 2001).The available potential energy conversion (CP) and kinetic energy conversion (CK) are used to determine the energy source of the wave train (Kosaka & Nakamura, 2006;Kosaka et al., 2009).The linear Rossby wave source (RWS) is employed to determine the RWS (Sardeshmukh & Hoskins, 1988).
We employed the Benjamini-Hochberg p-value adjusting via controlling for the False Discovery Rate to decrease the false positive error and obtain the high confidence test results (Benjamini & Hochberg, 1995;Wilks, 2016).The atmospheric general circulation model is used with the "F_2000_CAM5" component.We use the f19_g16 configuration with the horizontal resolution of 1.9° × 2.5° and 30 hybrid vertical layers.We run 35 model years and use the last 30 model years for analysis, which is defined as the CTL experiments.We add the anomalous positive (negative) SST forcing to the climatic austral autumn SST for the each of the 30 cases, and then run continuously 3 model months (March-April-May) as the positive (negative) experiments, abbreviated as POS (NEG).To obtain clear results, the strength of SST forcing in CESM is twice of the strength of the composite SST anomaly.

Self-Organizing Map
As an unsupervised neural network method, self-organizing map (SOM) can map high-dimensional samples to two-dimensional nodes (Kohonen et al., 2001).This dimensionality reduction can also be called clustering.The SOM method has been widely used in meteorology (Wang et al., 2022;Zhang et al., 2022).The process of SOM can be summarized as: SOM randomly initializes the weights of the two-dimensional nodes, and calculates the Euclidean distance between each sample and the two-dimensional nodes, and selects the two-dimensional nodes 10.1029/2023GL105678 3 of 11 with the smallest distance as the winner node, and then update the weights and related neighborhoods of this node, which will move closer to the sample.The above operations are repeated so that each sample is classified.Unlike other neural networks based on the gradient descent training, SOM uses a competitive learning strategy to gradually optimize the network by the competition between neurons, and use the neighborhood function to maintain the topological structure of the input.Therefore, it is suitable for the high-dimensional data of climatology and has strong generalization ability.In this paper the SOM is implemented by the python library named "miniSOM" (Vettigli, 2022).
To obtain an appropriate structure of the SOM nodes, we employ the quantitation error and the topographic error to measure the ability of SOM to distinguish raw data and SOM training state (Kiviluoto, 1996;Kohonen et al., 2001).The hyperparameter of SOM includes the learning rate (0.1), neighborhood function (Gaussian), neighborhood range (0.5), initialization (random), topology (rectangular), and random seed (10).The training epoch is 2,500.The 4 × 2 and 3 × 3 structure with both low quantitation and topographic errors are employed to cluster the AAO patterns (Figure S2 in Supporting Information S1).However, the clustering results of the two structures are quite similar, except for one more non-AAO mode, so we focus on the 4 × 2 nodes, which is sufficient to distinct the AAO patterns.

Clustering for the AAO Mode
Different from decomposing the atmospheric modes directly by statistical methods (Campitelli et al., 2022), we employ the SOM method to cluster the extratropical sea level pressure anomaly (90°-20°S) in Southern Hemisphere, and get eight patterns (Figure S3 in Supporting Information S1).Four of the eight patterns are associated with Pacific-South America (PSA) mode, and the other four are the AAO modes.The distribution of the SOM patterns is consistent with the fact that the explained variance of the AAO in empirical orthogonal function is comparable to that of the sum of the two PSA modes (Echevarria et al., 2020).Additionally, consistent with previous studies (Fogt & Marshall, 2020;Schroeter et al., 2022), our results indicate the AAO's feature of maximum signals over Amundsen Sea in Figures 1b and 1d.In this paper, we focus on the AAO mode, and do not describe too much about PSA. Figure 1 shows four AAO modes derived from SOM.The pressure anomalies at the mid-latitude and high latitude indicate a quasi-symmetric seesaw mode in Figures 1a and 1c, and the zonal symmetry axis is located at 60°S, corresponding to the positive and negative phases of the AAO, respectively (noted as psAAO and nsAAO).Different from Figures 1a and 1c, Figures 1b and 1d show seesaw anomalies in the middle and high latitudes of the Southern Hemisphere, however, they present zonal asymmetric structures, especially in the Pacific and Atlantic sectors.The polar pressure anomaly extends to low latitudes, which destroys the zonal symmetric structure of the AAO, and these two modes are corresponding to the positive and negative phases of zonally asymmetric AAO, respectively (noted as paAAO and naAAO).
According to previous studies, the asymmetry of AAO is mainly reflected in the pressure anomaly over the Amundsen and Bellingshausen Sea (ABS; Campitelli et al., 2022;Q. Ding et al., 2012;Fogt et al., 2012).Therefore, we measure the symmetry and asymmetry of the AAO mode by calculating the averaged sea level pressure anomaly over the ABS (120°-90°W) on the zonal symmetry axis (60°S).Moreover, the results are not sensitive to the longitude range.The results show that the ABS indices of psAAO and nsAAO modes are located below the tenth of all AAO ABS indices, while the ABS indices of paAAO and naAAO modes are located at about 60th of all AAO ABS indices, considering that the composite paAAO and naAAO are the averaged results, we believe that the SOM separates the symmetric and asymmetric AAO modes to some extent.This asymmetry agrees with previous studies, which confirms the strongest zonal asymmetry of the AAO existing over the Pacific and Atlantic sectors (Campitelli et al., 2022;Fogt et al., 2012).
Concentrating on the occurrence frequency of different types of the AAO, the psAAO shows no obvious time dependence, while the frequency of the nsAAO decreases with time (slope = −0.6; Figure 2a).With the evolution of time, the number of occurrences of the paAAO increases with a strongest trend (slope = 0.75), and the number of occurrences is the most in the period of 2010-2019 (Figure 2b).On the contrary, the naAAO appears most frequently in 1950-1959, and shows a decreasing trend (slope = −0.75; Figure 2d).The positive trend of the paAAO and the negative trends of the nsAAO and naAAO are consistent with the fact that the AAO is shifting toward a positive polarity (Campitelli et al., 2022;Marshall, 2003), and furthermore indicates that the AAO is developing toward a more asymmetric mode (Campitelli et al., 2022;Schroeter et al., 2022).By analyzing the frequency of occurrence months of different AAO modes, the symmetric AAO modes (psAAO and nsAAO) have no pronounced preference for months, but the frequency of nsAAO in May is lower than that in March and April (Figure 2e).The asymmetric AAO modes (paAAO and naAAO) obviously tend to appear in May, scilicet, the AAO mode in May is more likely to be an asymmetric mode.In addition, previous researchers preferred to employ the influence of the AAO in May to represent the influence of the AAO in austral autumn, which indirectly indicates that the influences of asymmetric AAO have been indirectly reflected in other studies (Dou & Wu, 2018;Liu et al., 2018;Tang et al., 2022).In view of the fact that previous studies basically believed that the AAO is a zonally symmetric mode and is maintained by the wave-mean flow interaction, here we focus on the zonal asymmetry of the AAO (paAAO and naAAO).So, what causes the asymmetry of the AAO?

Source of the Asymmetric AAO
In order to clearly reflect the asymmetry, we computed the eddy geopotential anomaly (departures from the zonal mean) for analysis.In Figures 3a and 3b, the geopotential and WAF anomalies indicate a Rossby wave train over the Pacific and Atlantic sectors, and this wave train is quasi-barotropic (figures not shown).The wave train propagates from Australia and to Weddell Sea along the westerly jet, and splits into two branches over the Drake Passage, propagating toward east and northeast, respectively.The geopotential anomalies corresponding to the paAAO are co-located with the anomalies corresponding to the naAAO but with the opposite sign, which further indicates the rationality of asymmetric AAO clustering via SOM.Moreover, there is a cross-equatorial wave train over central Pacific in Figure 3a, which is consistent with previous study (Song et al., 2009), and demonstrates that the AAO-related anomalies can influence the climate in Northern Hemisphere, via a cross-equatorial Rossby wave.To better understanding the energy source of this wave train, we calculate the CK and CP related to the anomalous circulation (Figures 3c and 3d).This wave train mainly exchanges CP from the basic flow, while the CK anomalies are limited over the sea near Antarctica, showing weak intensity.The wave energy diagnosis is conducive to anchoring the location of the Rossby wave, which confirms that this wave train originates from near Australia (Kosaka et al., 2009).Existing studies have suggested that the tropical signals can trigger Rossby wave trains via the divergence anomaly in upper level associated with the local Hadley circulation anomaly, and the wave trains can propagate southeastward to affect the climate near the Antarctic Peninsula (Q.Ding et al., 2012;Fogt & Clem, 2020;X. Li et al., 2015).Thus, we calculate the RWS around Australia in Figure S4 in Supporting Information S1.The RWS results show that there are clear RWS signals over eastern Australia, and this is also in the sinking branch of climatic Hadley cell, which indicates that the wave train, originating from here, is closely related to the tropical effects.Previous studies have confirmed that a tropical SST forcing can enhance the vertical motion, associated with the planetary-scale divergence anomaly, which interacts with the background flow in the flanks of the subtropical jet and induces a Rossby wave train (Hoskins & Karoly, 1981;Jin & Hoskins, 1995;Sardeshmukh & Hoskins, 1988).Thus, we focus the tropical SST anomaly.Figures 3e and 3f indicates that there exists a significant SST anomaly in the equatorial western Pacific, and the sign of the SST anomaly is consistent with the phase of the AAO.Different from previous studies, there is no significant SST signal in the tropical central and eastern Pacific, so we believe that such an anomalous Rossby wave train is related to the SST in the  Ding et al., 2012;Gong et al., 2013;L'Heureux & Thompson, 2006).Similar results for psAAO and nsAAO are shown in Figure S5 in Supporting Information S1, and the Rossby wave train is mainly located over the middle and high latitude rather than from the subtropics (Figures S5a-S5d in Supporting Information S1).The significant SST anomalies in eastern Indian Ocean are not accompanied with a clear WAF from the composite analysis of nsAAO, which only indicates the statistical rather than dynamical connections (Figure S5f in Supporting Information S1).
The SST anomalies in the red boxes of Figures 3e and 3f are selected as the SST forcing for CESM experiments (details in Section 2.1).There are the meridional circulation and geopotential responses of model experiments in Figure 4.The SST anomaly in tropical western Pacific is conducive to strengthening the ascending branch of local Hadley cell associated with convergence anomaly over 30°S (Figure 4a).The anomalous convergence, combined with subtropical westerly jet can induce the RWS anomaly around Australia (Figures 3a and 3b, Figure S4 in Supporting Information S1).Due to far from the equator, the disturbance can develop and propagate along the westerly jet, toward Antarctic Peninsula and Weddell Sea (Figure 4b).The wave train in Figure 4b is highly consistent with that in Figures 3a and 3b, which indicates that the anomalous Rossby wave train results from the tropical western Pacific SST anomaly.The experimental results show that the SST anomaly in the equatorial western Pacific can trigger anomalous Rossby waves propagating southeastward, superimposed on the zonal symmetry mode of the AAO, resulting in the enhancement of the zonal asymmetry of the AAO over Pacific and Atlantic sectors.

Influence of the Asymmetric AAO
We further explore the influence of the asymmetric AAO. Figure 5a shows the 925 hPa air temperature anomaly around Antarctica related to asymmetric AAO.Because the AAO asymmetry is mainly reflected in the Pacific and Atlantic sectors, the related air temperature anomaly is also strongest in the Pacific and Atlantic sectors, and the strongest air temperature signal presents a dipole mode, which shows a warm anomaly over Bellingshausen and Weddell Sea, and a cold anomaly over Amundsen Sea, which is consistent with previous study (Campitelli et al., 2022).This temperature dipole anomaly is mainly induced by the temperature advection, and the vital role of temperature advection over western Antarctic coastal seas has been confirmed in previous studies (X.Li et al., 2014;Nuncio & Yuan, 2015).Due to the dipole geopotential anomaly near Drake Passage in Figures 3a  and 3b, the meridional wind and circulation anomalies affect the temperature anomaly near western Antarctica via the temperature advection, which can also be reproduced in the model results (Figure 5b).The air temperature dipole mode associated with the asymmetric AAO is highly consistent with the Antarctic dipole mode defined by previous researchers (Yuan & Martinson, 2000, 2001).Therefore, we believe that the asymmetric AAO mode can affect the Antarctic dipole through the atmospheric circulation and modulate the air temperature and sea ice anomalies near the western Antarctica, which contributes to our further understanding of the physical importance of asymmetric AAO.

Conclusions and Discussion
We employ the SOM method to classify the AAO modes in austral autumn, and divide them into two zonal symmetric modes and two asymmetric modes.The asymmetry of the AAO is mainly reflected in the Pacific and Atlantic sectors.The AAO modes generally show a trend of transition to the positive phase, which is most obvious in the asymmetric AAO modes, and indicate that the AAO would develop toward an asymmetric positive mode.In addition, the asymmetric AAO mode prefers to appear in May.The geopotential anomaly associated with the asymmetric AAO presents a zonal wave train anomaly in the Pacific and Atlantic sectors, and is mainly maintained by extracting baroclinic energy from the basic flow.Composite SST anomalies indicate that the tropical western Pacific SST anomaly is closely related to this wave train.The SST sensitivity experiments from an atmospheric general circulation model show that the tropical western Pacific SST anomaly can affect the convergence anomaly over Australia via a local meridional circulation, and cooperate with the subtropical westerly jet to trigger a wave train.This result agrees well with the asymmetric AAO-related Rossby wave train, which propagate to southeastward, along the westerly jet.Therefore, the enhancement of the asymmetric AAO is from the wave train anomaly excited by the SST in tropical western Pacific.Due to the anomalous circulation and temperature advection, the asymmetric AAO mode is conducive to the Antarctic temperature dipole over Amundsen Sea, Bellingshausen Sea and Weddell Sea, which further indicates the dynamic influences of asymmetric AAO.
Although there are significant SST signals in the tropical Atlantic, we consider that the tropical Atlantic SST is more likely to be affected by the wave train due to its downstream location rather than a wave source (Figure S6 in Supporting Information S1).Significant SST anomaly in tropical Indian Ocean is related to the naAAO.However, when we consider both the tropical Indian Ocean and the western Pacific SST anomaly in the forcing experiment, we cannot obtain the observed wave train anomaly.Thus, the SST anomaly in the Indian Ocean is also affected by the AAO rather than affecting the AAO, which is consistent with previous results (Dou & Wu, 2018;Nan et al., 2009;Tang et al., 2022).
The model we used is an atmospheric model, and it lacks the air-sea/air-sea ice feedback processes which underestimates the responses.Previous studies also pointed out the model bias in polar regions (G.Li & Xie, 2014;Park et al., 2014).However, the model can still reproduce the atmospheric circulation and temperature in response to a tropical SST forcing, which gives us reason to believe the dynamical analysis is correct.

Figure 1 .
Figure 1.The composite ERA5 sea level pressure anomaly (unit: hPa) associated with four clusters of self-organizing map; psAAO and paAAO indicate the positive phase of symmetric and asymmetric AAO modes (a and b), and nsAAO and naAAO indicate the negative phase of symmetric and asymmetric AAO modes (c and d); the upper right number of each figure indicates the mode ratio; the frequencies of psAAO, paAAO, nsAAO, and naAAO are 21, 29, 24, and 24; the pink and red dots indicate the areas with p-value less than 0.1 and 0.05.AAO, Antarctic oscillation.

Figure 2 .
Figure 2. The time distribution for psAAO, paAAO, nsAAO and naAAO (a-d), and each slope and p-value are shown in the upper right corner; month distributions of four clustering AAO modes of self-organizing map (b); the orange, pink, blue and cyan bars indicate the frequencies of the psAAO, paAAO, nsAAO, and naAAO patterns.AAO, Antarctic oscillation.

Figure 3 .
Figure 3.The composite ERA5 eddy geopotential anomaly (unit: m 2 /s 2 ) and wave activity flux associated with the paAAO (a) and naAAO (b) in 200 hPa; The black contours indicate the climatic zonal wind in 200 hPa (unit: m/s), and the minimum value is 25 m/s and the interval is 5 m/s; (c and d) is the same as (a and b), except for the kinetic energy conversion (CK) (shading; unit: W/m 2 ) and potential energy conversion (CP) (contour; unit: W/m 2 ) anomalies, integrated from 100 to 1,000 hPa, and the blue, white and orange lines indicate the negative, zero and positive values, and the interval is 0.15 W/m 2 ; panels (e and f) is the same as panels (a and b), except for the sea surface temperature anomalies (unit: K), and the red boxes indicate the region in 20°S-20°N, 120°-170°E; the pink and red dots indicate the areas with p-value less than 0.1 and 0.05.AAO, Antarctic oscillation.

Figure 4 .
Figure 4.The meridional circulation (vector; units: m/s, −10 −2 Pa/s) and vertical velocity (shading; unit: −10 −2 Pa/s) anomalies in response to the POS minus NEG experimental results (a); panel (b) is the same as panel (a), except for the geopotential (unit: m 2 /s 2 ) response in 200 hPa; the pink and red dots/vectors indicate the areas with p-value less than 0.1 and 0.05.

Figure 5 .
Figure 5.The composite ERA5 temperature advection (contour; unit: K/s) and temperature (shading; unit: K) in 925 hPa associated with the paAAO and naAAO (paAAO minus naAAO) (a); the temperature response in 925 hPa related to the difference of POS and NEG experiments (b); the blue, white and orange lines indicate the negative, zero and positive values; the pink and red dots represent the areas with p-value less than 0.1 and 0.05.