Introduction

The El Niño-Southern Oscillation (ENSO) significantly impacts South America, with effects linked to the Walker circulation's descending branch in the tropics (e.g., Kousky et al. 1984;Cai et al. 2020) and Rossby wave trains via the Pacific-South American (PSA) pattern in the extratropics (e.g., Karoly 1989;Mo 2000;Mo and Paegle 2001). The PSA modes are most commonly analyzed using two empirical orthogonal function (EOF) modes, referred to as the PSA-1 and PSA-2, (Mo and Higgins 1998;Mo 2000;Mo and Paegle 2001), though recent studies have introduced new methods for their representation (Irving and Simmonds 2016;Risbey et al. 2021;Goyal et al. 2022;Campitelli et al. 2023). The PSA depicts a zonal wavenumber 3 feature with centers from the central Pacific via the Southern Ocean towards the Atlantic, significantly impacting Southern Hemisphere climate variability (e.g., Mo and Paegle 2001;Müller and Ambrizzi 2007;Irving and Simmonds 2016;Lou et al. 2021;Reboita et al. 2021). Specifically, South American rainfall variability is found to be influenced by Rossby wave trains associated with the PSA (e.g., Mo and Paegle 2001;Hirata and Grimm 2016;Junquas et al. 2016;Gelbrecht et al. 2018;Wang 2019). However, whether such rainfall variability can influence the PSA and extend it to the Northern Hemisphere has not been investigated previously. Studying the impact of South American rainfall on the PSA can enhance the understanding of teleconnections between the Pacific and Atlantic Oceans and those between the Northern and Southern Hemispheres.

During the austral summer (December-February, DJF), rainfall anomalies over southeastern South America (SESA), the La Plata Basin, are found to be associated with the South American rainfall dipole, which characterizes the intraseasonal rainfall variability of the South American monsoon system (SAMS) (e.g., Boers et al. 2014;Cherchi et al. 2014;Vera et al. 2018;Díaz et al. 2020). Recently, Zhao et al. (2023) demonstrated that SESA rainfall anomalies can induce cross-equatorial propagation of Rossby waves (CEPRW) along a great circle path in the southwest-northeast direction and influence weather patterns over the tropical Atlantic, northwestern Africa and western Europe over a period of 4 days. The influence of SESA rainfall and associated CEPRW are confirmed by equatorward propagating EP-flux anomalies (Edmon et al. 1980) and barotropic model simulations (Ting 1996). The CEPRW arises due to three main factors: (1) the upper-tropospheric westerly wind over tropical regions, which allows Rossby waves to travel between two hemispheres (Dickinson 1968;Webster and Holton 1982;Hsu and Lin 1992;Thomas and Webster 1994), (2) the meridional background flow, locally opening up a tunnel for the one-way propagation of stationary waves across the easterlies (Schneider and Watterson 1984;Li et al. 2015bLi et al. , 2019;;Zhao et al. 2015Zhao et al. , 2019)), and (3) the diabatic heating associated with convection in the source region, which triggers Rossby wave trains that propagate downstream and potentially cross the equator (Yang and Webster 1990;Ambrizzi and Hoskins 1997;Gong et al. 2020). In particular, diabatic heating is often estimated as the residual of the thermodynamic energy equation, commonly referred to as the apparent heat source Q 1 (e.g., Yanai et al. 1973;Ling and Zhang 2013;Zermeño-Diaz and Zhang 2013;Tseng et al. 2020).

As demonstrated by Mo and Paegle (2001), the relationship between the PSA and South American rainfall has been identified by analyzing cases with extreme PSA amplitudes. For instance, the PSA corresponds to a north-south dipole pattern of rainfall anomalies, with positive rainfall anomalies particularly over the southern part of South America. In our study, we will delve deeper into how positive rainfall anomalies over SESA can, in turn, influence the PSA on intraseasonal time scales. Given that the PSA is generally confined to the mid-to-high latitudes of the Southern Hemisphere, this raises an intriguing question: Can the PSA be extended to the Northern Hemisphere by SESA rainfall through CEPRW?

We will first identify events linked to the daily PSA index, distinguishing those associated with the daily SESA rainfall index from those that are not. This will allow us to categorize events into two groups: those influenced by SESA rainfall and those that are not. Given that the PSA represents the Southern Hemisphere's response to tropical convections such as those linked to the ENSO, Madden-Julian oscillation, and Quasi-biennial Oscillation (Mo and Higgins 1998;Renwick and Revell 1999;Mo and Paegle 2001;Li et al. 2015a), we will use an intermediate atmospheric model, the linear baroclinic model (LBM; Watanabe and Kimoto 2000), to investigate how atmospheric circulation responds to tropical convection alone versus tropical convection combined with SESA rainfall forcing. We will utilize observed heat sources (the diabatic heating) associated with identified events. The LBM, has been successfully used to diagnose wave train pattern response to diabatic heating (e.g., Yasui and Watanabe 2010;Zhao et al. 2015Zhao et al. , 2019;;Hayashi and Watanabe 2017;Tseng et al. 2019Tseng et al. , 2020)). In this study, we utilize the LBM because, unlike other complicated atmospheric models, it focuses solely on linear processes and is linearized about observed climatology, eliminating basic state biases. This is crucial, as the Rossby wave pathway is highly dependent on the background flow (Hoskins and Karoly 1981;Hoskins and Ambrizzi 1993;Li et al. 2015b;Zhao et al. 2015), enabling a more accurate representation of atmospheric circulation anomalies in response to diabatic heating.

The rest of the paper is structured as follows. Section 2 describes the data and methodology. Section 3.1 presents the PSA modes and SESA rainfall. Section 3.2 discusses the observational evidence of the extension of the PSA by SESA rainfall. In Sect. 3.3, the LBM simulations are conducted to further confirm the observed findings. Section 4 provides a summary and further discussion of the results.

Data and methodology

Data

The daily precipitation is from National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center (CPC) Global Unified Gauge-Based Analysis of Daily Precipitation with a spatial resolution of 0.5° (Chen et al. 2008). The daily mean near-surface temperature (2 m), near-surface (10 m) zonal and meridional winds, and multilevel zonal and meridional winds, vertical velocity, air temperature, and geopotential height are from the European Centre for Medium-Range Weather Forecasts fifth-generation reanalysis (ERA5) (Hersbach et al. 2020). The spatial resolution of the near-surface temperature is 1.0° and that of other fields is 2.5°. The analysis period for this study is from 1979 to 2021. Given the focus on the characteristics of composite events, adding or removing a few years from the dataset will not significantly impact the results.

Identifying events associated with the PSA and/ or SESA rainfall indices

An EOF analysis via a covariance matrix is applied to the monthly 500 hPa geopotential anomalies over the entire Southern Hemisphere with all seasons pooled together following Mo and Paegle (2001). The second (EOF-2) and third EOF (EOF-3) modes represent the PSA-1 and PSA-2, respectively, but these two modes are unable to be separated according to the North test (North et al. 1982). Then, the Kaiser varimax rotation is applied to the EOF modes to obtain rotated EOF (REOF) modes (Richman 1986). The third REOF (REOF-3) mode represents the combined PSA-1 and PSA-2 and will be used in this study. For simplicity, we refer to this combined PSA mode as the PSA.

The daily 500 hPa geopotential height anomalies are projected onto REOF-3 to derive the associated principal component (PC) of the PSA. The PC of the PSA is referred to as the PSA index on daily time scales. In addition, daily precipitation anomalies averaged over SESA (20ºS-40ºS, 50ºW-65ºW) is referred to as the SESA rainfall index, [ Pr] SESA . Both the PSA and SESA rainfall indices are standardized. In this study, we will identify several groups of events with different thresholds of the daily PSA and [ Pr] SESA . For each group, when consecutive days satisfy associated requirements, only the first day is used as Day 0 for the composite (e.g., Bowerman et al. 2017). Day -1, Day + 1, …, Day + 5 represents one day before the first day of the composite, one day after the first day of the composite, …, and five days after the first day of the composite, respectively.

Heating source

We estimate total diabatic heating as the apparent heat source (Q 1 ) using the approach of Yanai et al. (1973). Following Ling and Zhang (2013), Q 1 is calculated as:

where T, , �� ⃗ V , and are three-dimensional air temperature, potential temperature, horizonal winds, and vertical velocity, respectively. = T(p 0 ∕p) R∕C p , where p 0 , p, R, and C p are surface pressure, pressure, specific gas constant of dry air, and specific heat capacity of dry air, respectively.

The linear baroclinic model

The LBM developed by Watanabe and Kimoto (2000) is employed in this study. We use a dry version of the LBM (1)

which consists of primitive equations linearized about an observed three-dimensional DJF climatology based on ERA5 reanalysis data from 1979 to 2021. The model adopts a T42 horizontal resolution and 20 vertical levels using the sigma coordinate system, and includes horizontal and vertical diffusion, Rayleigh friction, and Newtonian damping.

The horizontal diffusion has a damping time scale of 2 h for the smallest wave, and the Rayleigh friction and Newtonian damping have a time scale of (0.5 day) -1 in the lowest three levels and the top level, (5 day) -1 in the fourth level, and (30 day) -1 in the remaining levels. Details of the model formulation are given in Watanabe and Kimoto (2000). To obtain the linear atmospheric response to diabatic forcing, we integrate the model up to 30 days and use averaged results from days 26-30 as the steady response. The circulation response generally approaches a steady state at around day 20.

Results

The PSA modes and SESA rainfall

Figure 1 shows the leading EOF modes of the monthly mean 500 hPa geopotential height anomalies with all seasons pooled together following Mo and Paegle (2001). EOF-1, accounting for approximately 20% of the total variance, exhibits a zonally symmetric pattern with a phase reversal between high-and mid-latitudes (Fig. 1a). EOF-2 and EOF-3, representing the PSA-1 and PSA-2 respectively and accounting for approximately 10% of the total variance, are characterized by a zonally oriented wave train with a zonal wavenumber 3 feature (Fig. 1b-c). However, these two EOF modes cannot be separated according to the North test. Thus, we rotate the EOF modes and obtain REOF modes. The pattern of REOF-1 resembles that of EOF-1 (Fig. 1d). REOF-2 shares similarity with EOF-2, with a dipole pattern over the Pacific and Southern Ocean, but the zonal wave structure and wave center over the Atlantic are not well shown (Fig. 1e). REOF-3 shows a zonally oriented wave train with a zonal wavenumber 3 feature and confines over mid-to-high latitudes, generally within the widely considered PSA sector (the domain within the green lines; Irving and Simmonds 2016) (Fig. 1f). There is a phase shift of approximately 15º of the REOF-3 compared to the PSA-1 and PSA-2.

Given the significant SAMS-related rainfall anomalies over SESA (e.g., Boers et al. 2014;Cherchi et al. 2014;Vera et al. 2018;Díaz et al. 2020) and the increased likelihood of CEPRW occurring over the Atlantic sector (e.g., Li et al. 2015bLi et al. , 2019) ) during the austral summer (DJF), our study focuses on this season. Figure 2 shows the interannual variability of the PSA-1, PSA-2, and REOF-3 in austral summer. The correlation between the PSA-1 and REOF-3 is 0.49 and that between the PSA-2 and REOF-3 is 0.70, both significant at 99% confidence level according to the Student's t-test. However, the correlation between the PSA-1 and REOF-2 is 0.46 and that between the PSA-2 and REOF-2 is only -0.27, significantly lower than the correlations between REOF-3 and PSA-1/PSA-2. Since REOF-3 pattern is generally within the PSA sector (the domain within the green lines in Fig. 1) and shows high correlations with PSA-1 and PSA-2, REOF-3 is referred to as the combined PSA mode, or simply as the PSA in this study.

On interannual time scales, the PSA is significantly correlated with the Oceanic Niño Index (ONI) at the 95% confidence level, with a correlation coefficient of 0.39. This finding aligns with previous studies (e.g., Karoly 1989;Mo 2000;Mo and Paegle 2001) that suggest the PSA is a response to tropical convection associated with the ENSO. To investigate the relationship between the PSA and South American rainfall on seasonal time scales, we calculate the correlation between the DJF mean PSA index and rainfall anomalies. Figure 3a shows a dipole rainfall structure with positive rainfall anomalies over SESA and negative anomalies to the north, representing the pattern of the South American rainfall dipole identified in previous studies (Nogués-Paegle and Mo 1997;Cherchi et al. 2014;Vera et al. 2018). In addition, the DJF mean PSA is positively correlated with streamfunction anomalies over the southeastern Pacific and northern South America (Fig. 3a).

Due to significant variances in the PSA on intraseasonal time scales (Kiladis and Mo 1998;Mo and Paegle 2001), we identify anomalous events occurring in DJF using the daily index. Following the method in Sect. 2.2, we create the daily PSA index using the daily PC associated with REOF-3 and daily [ Pr] SESA using domain averaged precipitation (within the gray box in Fig. 3a). Figure 3b shows that daily PSA and [ Pr] SESA have no significant correlation during DJF (represented by gray dots), indicating that a strong PSA does not necessarily lead to strong SESA rainfall, nor does strong SESA rainfall lead to a strong PSA. The correlation between the DJF mean PSA index and SESA rainfall anomalies is significant, but it weakens at intraseasonal (daily) time scales. This is primarily because, on daily time scales, SESA rainfall exhibits larger fluctuations, while the PSA shows lower variability with consistent phases lasting from a few days to several weeks (Fig. S1). These large daily fluctuations in SESA rainfall tend to cancel out over a seasonal time scale, leading to a stronger correlation with the PSA. Although the statistical correlation between the two daily indices is insignificant, we will focus on some anomalous events and aim to understand whether strong SESA rainfall produces a different PSA pattern compared to weak SESA rainfall. In this study, we will specifically examine whether strong We focus on daily events where the positive phase of PSA (PSA ≥ 1) coincides with strong SESA rainfall ( [ Pr] SESA ≥ 1) (pink dots in Fig. 3b). A total of 100 anomalous events with daily PSA ≥ 1 and [ Pr] SESA ≥ 1 can be captured in DJF during 1979-2021. We calculate the duration (i.e., the total number of consecutive days meeting the criterion mentioned above) and 68% of the events are short-lasting events and 8% of the events last 3 days or more. Next, we explore the connection between lower-frequency variability and higherfrequency variability. Figure 3c shows the number (orange bars) of events with daily PSA ≥ 1 and [ Pr] SESA ≥ 1 in each year. The interannual variability of the number is quite large, ranging from zero to six events per year. We also compute seasonal mean index by averaging the daily index in DJF for each year and then identify anomalous years with DJF mean PSA ≥ 0.5 and [ Pr] SESA ≥ 0.5. We use 0.5 as threshold to allow more years to be captured. A total of six anomalous years (red triangle markers) are identified, including four years with a relatively large number of anomalous events (1992, 1998, 2007, and 2016). This suggests that the intraseasonal variability indicated by these events is also reflected on interannual time scales.

Observational evidence of the extension of the PSA by SESA rainfall

In this section, we examine atmospheric circulation patterns associated with the events with strong or weak [ Pr] SESA . To understand the role of [ Pr] SESA , we identify another group of events without strong [ Pr] SESA , defined as daily PSA ≥ 1 and -0.25 < [ Pr] SESA < 0.25, and a total of 107 events are identified. We set this threshold to represent weak [ Pr] SESA , ensuring a comparable number of events between the strong (100 events) and weak (107 events) groups. To obtain a better representation in the tropics, we will utilize standardized atmospheric circulation patterns as suggested by Bowerman et al. (2017) and Zhao et al. (2023). Figure 4 compares the evolution map of 200 hPa streamfunction and near-surface winds between the PSA events with weak [ Pr] SESA (upper row) and strong [ Pr] SESA (bottom row). Note that the sign of streamfunction anomalies over the Southern Hemisphere is opposite to that of geopotential height anomalies shown in REOF-3 (Fig. 1f). The bootstrap significance test is applied to determine if anomalous fields are significant at the 95% confidence level (Efron and Tibshirani 1994).

For PSA events with weak [ Pr] SESA , negative and posi- tive streamfunction anomalies at 60ºS slightly increase in magnitude from Day -1 to Day + 1 and weaken from Day + 3 to Day + 5 (Fig. 4a-d), but the locations of these anomalous centers change very slowly, indicating the presence of quasi-stationary Rossby waves. This slow-moving structure is consistent with the characteristics of the PSA, which predominantly occurs within an intraseasonal (10-90 day) band (Mo and Paegle 2001). In addition to this zonally oriented wave train at 60ºS, negative streamfunction anomalies appear over SESA from Day -1 (Fig. 4a). The negative streamfunction anomalies over SESA may be triggered by positive streamfunction anomalies associated with the zonal wave train at 60ºS (i.e., the rightmost positive anomalies), suggesting that the PSA has the potential to excite equatorward-propagating circulation anomalies on intraseasonal time scales. However, when [ Pr] SESA is weak, there is no clear evidence that the negative streamfunction anomalies over SESA can further excite cross-equatorial waves or lead to significant growth of circulation anomalies in the tropics. This suggests that the dominant activities of the PSA are confined to the Southern Hemisphere when rainfall anomalies over SESA are weak.

For PSA events with strong [ Pr] SESA , a stronger easterly low-level (represented by near-surface winds) flow from the Atlantic turns southward upon reaching the Andes Mountains, bringing more moisture and intensifying [ Pr] SESA (Fig. 4e). The strong rainfall anomalies can act as a source of diabatic heating, generate a Rossby wave train through baroclinic processes (e.g., Danard 1964;Emanuel et al. 1987;Lapeyre and Held 2004;Zhao et al. 2018), and further amplify the negative streamfunction anomalies over SESA from Day -1 to Day + 1 (Fig. 4e-f). Compared to PSA events with weak [ Pr] SESA (Fig. 4b), the negative stream- function anomalies over SESA with strong [ Pr] SESA are larger in magnitudes (Fig. 4f) and provide a more favorable condition for exciting cross-equatorial waves. From Day + 1, the northeastward propagating quasi-stationary wave train becomes clearer, following a great circle path (the magenta curve) in a southwest-northeast direction (Fig. 4f). Circulation anomalies over the tropical Atlantic, southern Europe and northern Africa are amplified and peak in Day + 3 (Fig. 4g), indicating the observational evidence of CEPRW. CEPRW originated from SESA or surrounding region has been identified in previous studies (e.g., Li et al. 2019;Zhao et al. 2023). The northeastward propagating wave train and the zonally oriented wave train at higher latitudes together indicate the cross-equatorial extension of the PSA. The connection between these two wave trains is the negative streamfunction anomalies over SESA, which are significantly amplified by strong SESA rainfall anomalies and extend the PSA further north. On Day + 5, CEPRW weakens as SESA rainfall anomalies decrease (Fig. 4h). [ Pr] SESA in DJF (gray dots). The pink dots indicate the events with daily PSA ≥ 1 and [ Pr] SESA ≥ 1. c The total number (orange bars) of events with daily PSA ≥ 1 and [ Pr] SESA ≥ 1 for each year of 1979-2021 in DJF. The red triangle markers denote the years with seasonal mean (DJF mean) PSA ≥ 0.5 and [ Pr] SESA ≥ 0.5

To further investigate the factors influencing the strength of the cross-equatorial wave train, we conduct a series of observational sensitivity tests. We define a CEPRW index

where sf () indicates streamfunction anomalies at each loca- tion on the great circle path (the magenta curve in Fig. 4).

We first examine how [ Pr] SESA magnitudes influence the CEPRW index. When [ Pr] SESA becomes stronger (Fig. 5b), the PSA index does not necessarily become stronger in Only wind vectors significant at the 95% level are shown. The region of the SESA is shown within the black box (20ºS-40ºS, 50ºW-65ºW). e-h Same as a-d, but for selected events with daily PSA ≥ 1 and [ Pr] SESA ≥ 1. The magenta curve indicates the pathway of the cross-equatorial wave train Fig. 5 The evolution of the daily a PSA index, b [ Pr] SESA , and c CEPRW index averaged for selected events with daily PSA ≥ 1 and different thresholds of [ Pr] SESA (shown as different colors of lines). d-f Same as a-c, but for selected events with -0.25 < [ Pr] SESA < 0.25 and different thresholds of the PSA index

magnitudes (Fig. 5a), consistent with the insignificant statistical correlation between the PSA and [ Pr] SESA (Fig. 3b).

The CEPRW index clearly becomes stronger from Day 0 when [ Pr] SESA peaks and the influence of stronger [ Pr] SESA can last for three days (from Day 0 to Day + 2) (Fig. 5c).

Next, we examine how PSA magnitudes influence the CEPRW index. A stronger PSA (Fig. 5d) can only slightly increase [ Pr] SESA at Day + 1 (Fig. 5e), but such increase is insignificant at the 95% confidence level according to the bootstrap test, suggesting that the strong [ Pr] SESA seen in Fig. 4e-h is not mainly triggered by the PSA but may instead be related to SAMS (e.g., Boers et al. 2014;Cherchi et al. 2014;Vera et al. 2018;Díaz et al. 2020). Figure 5f shows that increasing PSA magnitudes does not lead to a stronger CEPRW index. This suggests that the strength of the CEPRW is primarily driven by the magnitude of SESA rainfall rather than the PSA. The results above provide observational evidence that zonally oriented PSA at higher latitudes can be extended to the tropics and even the Northern Hemisphere when strong rainfall anomalies appear over SESA.

We move a step further to show how cross-equatorial wave influences weather patterns in the Northern Hemisphere. Figure 6 shows the change in precipitation and near-surface temperature over the Eurasia-Africa sector after the peak of SESA rainfall. Before the influence of the CEPRW reaches the extratropical Northern Hemisphere, positive temperature anomalies (red contours) emerge over western and southern Europe, accompanied by positive precipitation anomalies, particularly over the Iberian Peninsula (Fig. 6a). As the influence of the CEPRW intensifies, positive precipitation anomalies propagate eastward across Europe, accompanied by a decrease in surface temperature (Fig. 6b-c). The change of precipitation and surface temperature anomalies is associated with the formation of cyclonic circulations over Europe, as shown by 850 hPa winds. Once the precipitation anomalies move through, surface temperature rises again over western Europe (Fig. 6d). This suggests that the CEPRW can lead to cooler, wetter weather conditions over western and southern Europe.

Fig. 6 a-d Composite anomalies of precipitation (shading; mm day -1 ), near-surface temperature (contours; ºC), and 850 hPa winds (vectors; m s -1 ) from Day + 1 to Day + 4 for selected events with daily PSA ≥ 1 and [ Pr] SESA ≥ 1. Red and blue lines represent the positive (0.5 and 0.8 ºC) and negative (-0.5 and -0.8 ºC) values, respectively. Stippling indicates precipitation anomalies significant at the 95% level according to the bootstrap test. Contours and vectors shown are significant at the 95% level

The LBM model simulations

To further explore the role of SESA rainfall, we use the LBM (Watanabe and Kimoto 2000) forced by observed Q 1 over the Pacific and SESA, respectively. Since the PSA is response to tropical convection (e.g., Karoly 1989;Mo 2000;Mo and Paegle 2001), we examine Q 1 for the events on Day 0 with daily PSA ≥ 1. Figure 7a shows the composite of 1000-100 hPa vertically integrated Q 1 for the PSA events (i.e., PSA ≥ 1) over the Pacific derived from ERA5 reanalysis data, revealing that the largest Q 1 value appears over the central Pacific in the Southern Hemisphere. Figure 7b shows the same field for the PSA events with strong [ Pr] SESA (i.e., PSA ≥ 1 and [ Pr] SESA ≥ 1) over South Amer- ica. As expected, the largest Q 1 value appears over SESA. Sensitivity tests suggest that very similar results are obtained when using the composite Q 1 for the strong [ Pr] SESA events without constraint of the PSA.

Next, we average Q 1 over the selected domain over the Pacific and SESA (within the green boxes in Fig. 7), respectively. The vertical profiles of Q 1 for the two domains share some similarities, showing an increase from the surface to 400 hPa, followed by a decrease toward the upper troposphere (Fig. 8). The difference between the two profiles is that Q 1 at 400 hPa over SESA is larger, attributable to the convective activity associated with strong rainfall anomalies in this region. The heating source of the two domains is obtained by multiplying the observed Q 1 pattern (within the green box of Fig. 7) by associated vertical profile for each domain (Fig. 8). Since we focus on the heating source, the negative values of Q 1 are excluded.

Using heating source over the Pacific, we run the LBM following the method in Sect. 2.4. The Pacific heating source (indicated by the green contour) induces 200 hPa Fig. 7 a Composite of 1000-100 hPa vertically integrated Q 1 (K day -1 ; derived from ERA5) on Day 0 for selected events with daily PSA ≥ 1 over the Pacific. b Same as a, but for selected events with daily PSA ≥ 1 and [ Pr] SESA ≥ 1 over SESA. The regions of diabatic heating source for the model simulations are shown within the green boxes Fig. 8 a The mean Q 1 (K day -1 ; derived from ERA5; thick red curve) from 1000 to 100 hPa averaged for the selected events (Day 0) with daily PSA ≥ 1 averaged in the green box (15ºS-5ºS, 170ºE-160ºW) of Fig. 7a. Shading represents the spread of the minimum and maximum values of the domain averaged Q 1 among selected events. b Same as a, but for selected events with daily PSA ≥ 1 and [ Pr] SESA ≥ 1 averaged in the green box (35ºS-20ºS, 60ºW-50ºW) of Fig. 7b streamfunction anomalies with negative anomalies to the west and positive anomalies to the east over the southern hemispheric Pacific (Fig. 9a). The model successfully simulates the positive anomalies to the west of South America, aligning well with the observed streamfunction anomalies in Fig. 3a. However, the observed negative anomalies over high latitudes around 60ºS are simulated further west and with smaller magnitudes. The discrepancies between the observed and simulated PSA patterns may be due to the idealized experiment design, which prescribes only the tropical heating source over the selected area. Over the Atlantic sector, a series of streamfunction anomalies can be seen, though they may not represent the PSA extending from the Pacific.

When incorporating the heating source over SESA (indicated by the green contour) into the model, a Rossby wave train emerges, extending from the central Pacific via southern South America towards the Atlantic and Africa along a great circle path (shown by the magenta curve) in Fig. 9b. This wave train pattern bears some similarities to the observed pattern in Fig. 4f, particularly over the Atlantic sector, suggesting a possible northeastward extension of the PSA due to SESA rainfall forcing. The circulation pattern resulting from both Pacific and SESA forcings reflects a linear combination of the Pacific forcing and SESA forcing responses. Moreover, streamfunction anomalies along this wave train path are intensified and extended compared to the experiment with only the Pacific heating source prescribed, as seen in the positive anomalies over the South Pacific near 50ºS, 90ºW and those over the Atlantic and African sector (Fig. 9b vs 9a). Sensitivity tests have been conducted, including selecting a larger domain for the forcing, but the results remain largely consistent with those shown in Fig. 9. The LBM experiments corroborate the observational evidence, demonstrating that rainfall anomalies over SESA can extend the PSA to the Northern Hemisphere.

Summary and discussion

This study examines the impact of SESA rainfall anomalies on the PSA during the austral summer. The PSA is identified as REOF-3, characterized by a zonal wavenumber 3 feature, with centers of significant magnitude extending from the central Pacific, across the Southern Ocean, and towards the Atlantic-encompassing the widely recognized PSA sector. REOF-3 better represents both PSA-1 and PSA-2 modes compared to REOF-2. Daily index of the PSA is created based on REOF-3. Following Zhao et al. (2023), we focus on rainfall anomalies over SESA and develop a daily rainfall index, denoted as [ Pr] SESA . A total of 100 events for the positive phase of PSA associated with strong [ Pr] SESA are identified in DJF during 1979-2021. The intraseasonal variability indicated by these events is also reflected on interannual time scales, indicated by anomalous years with positive PSA phase and strong [ Pr] SESA . When rainfall anomalies over SESA are weak, the dominant activities of the PSA are confined to higher latitudes of the Southern Hemisphere, with no clear evidence of the CEPRW. However, when strong [ Pr] SESA is present, a quasi-stationary Rossby wave train can be generated from the higher latitudes where the PSA is most significant. This wave train propagates downstream along a southwest-northeast great circle path and crosses the equator, representing a cross-equatorial extension of the PSA. As [ Pr] SESA reaches its peak, atmospheric circulation anomalies along this path intensify, inducing a wet and cool weather condition over western and southern Europe. Additional analyses show that the strength of the CEPRW is primarily driven by the magnitude of SESA rainfall rather than the PSA.

To further investigate the influence of [ Pr] SESA , we prescribed the observed heat source (Q 1 ) associated with the PSA alone and with both the PSA and [ Pr] SESA in the LBM. When incorporating the heat source over SESA into the model, atmospheric circulation anomalies triggered by the central Pacific forcing are extended and amplified, forming a wave train along a great circle path from the central Pacific to northern Africa. The LBM simulations confirm the significant role of [ Pr] SESA in extending the PSA.

In this study, we use the dry version of the LBM, which excludes both moisture and eddy feedback. While moisture feedback may amplify the wave response in certain regions and eddy feedback in the mid-latitudes may also have an impact, these factors are secondary in importance compared to the core dynamics of the LBM.

The main conclusions of this study are: (1) the PSA and SESA rainfall are two independent variables, and strong SESA rainfall does not amplify the magnitudes of the PSA index or vice versa; (2) SESA rainfall is the main cause for the CEPRW; and (3) such CEPRW can be regarded as the equatorward extension of the PSA pattern (though the magnitude of the PSA index is unaffected) because negative streamfunction anomalies over SESA connect the zonally oriented wave train (explained by the PSA index) and northeastward propagating wave train (explained by the CEPRW index). It is worth noting that our conclusion-that SESA rainfall can extend the PSA pattern-is not limited to the specific pattern of REOF-3. Similar analyses conducted for PSA-1, PSA-2, and REOF-2 yield comparable results (not shown). Therefore, we expect that applying other methods to identify the PSA pattern would lead to similar conclusions.

This study builds upon the findings of Zhao et al. (2023), further exploring the influence of rainfall variability over SESA on adjacent oceans and continents. To our knowledge, the influence of South American rainfall on adjacent oceans, such as the tropical Atlantic, has not been widely studied. Most previous research has focused on the oceanto-land direction (e.g., Yoon and Zeng 2010), while the reverse-land-to-ocean-has been largely overlooked. The cross-equatorial pathway of Rossby waves over the Atlantic sector has been identified in earlier studies through numerical model simulations (e.g., Ambrizzi and Hoskins 1997) or diagnostic tools like wave ray tracing (e.g., Li et al. 2019). However, only Zhao et al. (2023) and the present study have linked the CEPRW to South American rainfall and explored the potential impact of SESA rainfall on Northern Hemisphere weather patterns, including Europe. Compared to Zhao et al. (2023), this study takes a further step by connecting SESA rainfall with a well-known atmospheric mode, the PSA.

Our results underscore the crucial role of the South American continent as a land bridge, linking the Pacific and Atlantic Oceans and connecting the Southern and Northern Hemispheres. The knowledge of this study will enhance our understanding of teleconnections between the two ocean basins and interhemispheric relationships through hydroclimate variability over South America. Moreover, this study provides valuable insights for evaluating the likelihood of temperature and precipitation extremes over Europe based on upstream precursory circulation anomalies, as well as for introducing initial condition perturbations in ensemble predictions (e.g., et al. 2020). For example, strong PSA events linked to strong SESA rainfall can alert official forecast centers to potential weather extremes in Europe, ultimately enhancing the accuracy of weather extremes predictions on subseasonal time scales.