The tropical Atlantic as a negative feedback on ENSO

The influence of the tropical Atlantic on El Niño-Southern Oscillation (ENSO) is examined using dedicated climate model experiments with sea-surface temperature (SST) restoring. Partial SST restoring to climatology in the tropical Atlantic leads to slower decay of ENSO events and to a shift of the power spectrum to longer periods. Perfect model hindcast experiments with and without restoring tropical Atlantic SST to climatology indicate that both the northern tropical and equatorial Atlantic have a very small influence on ENSO development. During decaying ENSO events, on the other hand, northern tropical Atlantic SST anomalies strongly accelerate the decay. Key to the Atlantic influence on ENSO decay are Atlantic SST anomalies just north of the equator (~ 5°N). These lead to local convection anomalies that change the Walker circulation so as to accelerate ENSO decay. Importantly, anomalous events in either the northern tropical or equatorial Atlantic fail to develop in the hindcast ensemble mean, when tropical Pacific SSTs are restored to climatology. This indicates that anomalous tropical Atlantic events in boreal spring and summer are strongly dependent on preceding ENSO events in boreal winter. Thus, the role of the tropical Atlantic is to mediate a negative feedback of ENSO on itself. Despite this passive role of the tropical Atlantic in the Pacific-Atlantic interaction, accurate simulation of the Atlantic feedback should play some role in ENSO prediction. Further model experiments will be required to evaluate model dependence of these findings and to quantify the impact of the Atlantic on ENSO prediction skill.


Introduction
Interactions between the tropical Atlantic and Pacific have attracted much attention in the scientific community. Early studies focused on the influence of El Niño-Southern Oscillation (ENSO) on the tropical Atlantic. Enfield and Mayer (1997) highlighted the robust influence of ENSO on the northern tropical Atlantic (NTA), in which an El Niño event in boreal winter leads to a warming in the NTA in spring, and vice versa for La Niña events. Mechanisms for this influence include stationary atmospheric Rossby waves extending from the tropical Pacific to the North Atlantic (Wallace and Gutzler 1981), the so-called Pacific North America (PNA) pattern; widespread warming of the upper troposphere that suppresses convection over the tropical Atlantic (Chiang and Sobel 2002) and weakens the trade winds that feed into these convection centers; and changes in the Walker Circulation leading to anomalous subsidence over the equatorial Atlantic and a subsequent weakening of the Atlantic Hadley cell and associated trade winds (Saravanan and Chang 2000). The influence of ENSO on equatorial Atlantic sea-surface temperatures (SSTs) is less apparent, with the correlation of equatorial Pacific SST in boreal winter and equatorial Atlantic SST in the following summer close to zero (Supplementary Fig. 1; Chang et al. 2006), although the strength of this correlation is subject to interdecadal modulation (Martin-Rey et al. 2014). Chang et al. (2006) attribute this weak relationship to the opposing dynamic and thermodynamic ENSO influences on the equatorial Atlantic. For an El Niño event, for example, the dynamic influence consists of changes in the Walker circulation that lead to a strengthening of the equatorial Atlantic trade winds, which in turn strengthens upwelling and leads to SST cooling in the following months. The thermodynamic influence, on the other hand, lies in the stabilization of the tropical Atlantic troposphere suppressing convection, which leads to a build-up of moisture in the atmospheric boundary layer, reduced latent heat flux and SST warming. Lübbecke and McPhaden (2012), on the other hand, emphasize the opposing dynamical influences of ENSO on the equatorial Atlantic and the NTA, where an El Niño event induces easterly anomalies over the former region but westerly anomalies over the latter. The resulting wind stress curl induces downwelling oceanic Rossby waves north of the equator that are reflected into downwelling equatorial Kelvin waves at the western boundary and eventually lead to warming that opposes the influence from the local wind stress anomalies (Richter et al. 2013).
More recently, the tropical Atlantic influence on ENSO has received increasing attention. Rodriguez-Fonseca et al. (2009) suggested that equatorial Atlantic warm events can influence the Walker circulation to induce anomalous subsidence over the equatorial Pacific, leading to easterly wind stress anomalies and subsequent cooling. SST variability in the equatorial Atlantic is sometimes referred to as the Atlantic Niño but we will refer to it as the Atlantic zonal mode (AZM; see Lübbecke et al. 2018; for reviews). AZM events primarily peak in summer, when ENSO tends to be weak, which may allow the equatorial Atlantic to exert a relatively strong influence on the equatorial Pacific.
The NTA has also been suggested to influence ENSO. Variability in this region has been associated with the Atlantic meridional mode (AMM; Hastenrath and Heller 1977;Xie 1996;Chang et al. 1997;Amaya et al. 2017), which tends to be most pronounced in spring. Ham et al. (2013a, b) suggest that a warm AMM event in spring excites atmospheric Rossby waves that induce cyclonic circulation anomalies over the northeastern subtropical Pacific, with cool SST anomalies on its western flank. These cool SST anomalies gradually propagate southwestward toward the equator and lead to a La Niña event in the following winter. This pathway from the Atlantic to the Pacific has attracted further scrutiny. A follow-up study by Jiang et al. (2022), while agreeing with the basic premise of AMM events eliciting opposite-signed ENSO events, could not confirm the mechanism outlined by Ham et al. (2013a, b), and also suggested that boreal summer may be more important than spring for the NTA influence.  suggest that both the AZM and AMM influences on ENSO are relatively weak, while Zhang et al. (2021) suggest that the AMM influence on ENSO could just be a statistical artifact brought about by the ENSO influence on the NTA and the tendency of ENSO events to reverse sign in the following year.
If a consistent influence of the tropical Atlantic on ENSO does exist, then it may also help to increase the skill of ENSO predictions. Accordingly, skillful prediction of the AMM in spring and of the AZM in summer should increase the skill for predicting ENSO in the following winter and help overcome the spring predictability barrier. Some studies have suggested that such benefits indeed exist (Jansen et al. 2009;Frauen and Dommenget 2012;Keenlyside et al. 2013;Martin-Rey et al. 2015;Exarchou et al. 2021). The usefulness of the tropical Atlantic in ENSO prediction hinges on two conditions: (1) variability in the tropical Atlantic is, at least to some extent, independent of ENSO (Ding et al. 2012); (2) models are able to skillfully predict tropical Atlantic variability several months ahead. Prediction of tropical Atlantic variability remains a challenge ) and may be limited by inherent predictability (Richter et al. 2020), though it seems that some recent models have made progress in extending the lead time of skillful predictions in the equatorial Atlantic (Exarchou et al. 2021).
In the present study we aim to clarify the potential benefit of the tropical Atlantic to ENSO prediction skill using perfect model hindcasts with selective SST restoring in either the tropical Atlantic or tropical Pacific, and in pre-industrial coupled simulations with and without SST restoring in the tropical Atlantic. The general circulation model (GCM) and the experiment design used in this study are described in Sect. 2. The pacemaker experiments are examined in Sect. 3, while the perfect model hindcasts are examined in Sect. 4. In Sect. 5, we examine the ability of a linear inverse model (LIM) to emulate the behavior of the GCM. This is followed by a summary and discussion in Sect. 6.

Methods
The GCM used in this study is the Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model version 2.1 (CM2.1; Delworth et al. 2006), which consists of the GFDL AM2.1 atmospheric component (GFDL Global Atmospheric Model Development Team 2004) coupled to the MOM4 ocean component (Griffies et al. 2005). The model represents reasonably well ENSO variability with spectral peaks similar as in observations. There are, however, a few shortcomings, including weak seasonal phase locking and excessive variability ( Supplementary Fig. 2a). The latter deficit also applies to variability in the equatorial Atlantic ( Supplementary Fig. 2a). See Wittenberg et al. (2006) for a detailed evaluation of CM2.1 performance. We note that weak seasonal phase locking is a common problem in GCMs (Supplementary Fig. 2c;Liao et al. 2021). Furthermore, even though the phase locking in CM2.1 is weak, the events that do peak in boreal winter compare relatively well with observations (see composite shown in Fig. 1a).
The control experiment (CTRL0), which is the reference for the Atlantic SST restoring experiment (noTATL0) and the basis for the perfect model hindcasts, is a 1000 year fully coupled integration of CM2.1 with radiative forcing fixed at 1860 levels (Zhang et al. 2022). The use of steady radiative forcing facilitates the interpretation of the model results because it removes extraneous influences such as global warming trends and volcanic eruptions. In noTATL0, tropical Atlantic SSTs are restored to the daily mean climatology of CTRL0 between 30°S and 30°N through overriding the surface sensible heat flux into the ocean, with an e-folding time of 10 days for the top 50 m. This restoring coefficient is linearly tapered off over 10-degree zonal bands poleward of 30°S and 30°N over the Atlantic. Outside of the restoring region, the ocean and atmosphere are fully coupled. Due to limited computational resources, noTATL0 was only integrated for 300 years.
The perfect model hindcasts are initialized on January 1 from selected years of CTRL0 (13 cases; Supplementary  Fig. 3), with predictions extending up to December 31 of each year. Each hindcast experiment consists of a 20-member ensemble, with ensemble members generated by random perturbations of the atmospheric initial conditions. The original selection of the hindcast years was based on either an AMM or an AZM event preceding ENSO, with the two types of events identified by SST anomalies in the NTA (40-10°W, 8-20°N) and ATL3 (20°W-0, 3°S-3°N) regions, respectively. Not all hindcasts were successful, however, in the sense that the control prediction without SST intervention (CTRL) did not reproduce the ENSO event in CTRL0 ( Supplementary  Fig. 3). This is partly because we selected extreme ENSO events, which, by definition, are rare and therefore have a low probability of recurrence, even if the initial conditions are very similar. In addition, the spring predictability barrier may also play a role in the failed predictions. Regardless of Fig. 1 a SST anomalies (K) composited on 1 standard deviation of the Niño3.4 index in CTRL0 and noTATL0. The individual lines show the Niño3.4 in CTRL0 (green), the Niño3.4 in noTATL0 (blue), the ATL3 in CTRL0 (orange), and ATL3 in noTATL0 (brown). The black and grey lines show composites from the ERA5 for the Niño 3.4 and ATL3, respectively. Filled circles indicate where differences with CTRL0 are significant at the 95% level based on a Student's t test. b Similar to a, but for the NTA SST (K). c Similar to a, but for zonal 10 m wind (m/s) and with the Niño3.4 and ATL3 replaced by the Niño4 and ATL4, respectively. d Similar to c, but for the NTA zonal wind (m/s) the cause, even the predictions that fail to reproduce CTRL0 can serve as a reference for our intervention experiments. The unexpected outcome from some of the perfect model hindcasts, however, prompted us to recategorize scenarios into developing and decaying ENSO events. In CTRL0, on the other hand, all but two events are developing even though they differ in their tropical Atlantic SST patterns (AMM vs. AZM). Twelve of the cases are El Niño events, while one case is a La Niña event (year 126).
In the first of the intervention experiments, noTATL, SSTs in the tropical Atlantic are restored to climatology, with the restoring region and tapering the same as in noTATL0, but the restoring strength in the top 50 m gradually ramped up from January 1 through March 1, after which it is held constant at an e-folding time of 1 day. The purpose of this experiment is to evaluate the impact of tropical Atlantic SST anomalies on ENSO evolution and to quantify the impact of the tropical Atlantic on ENSO prediction skill.
In the second intervention experiment, noTPAC, we examine how ENSO affects the evolution of tropical Atlantic variability by restoring SSTs to climatology in the tropical Pacific (coast-to-coast, 30°S-30°N with tapering as in the Atlantic). Like in noTATL, the restoring strength gradually increases from January 1 to March 1. All hindcast years feature either an AMM or an AZM event in boreal spring or summer, and so it is of interest to what extent these events depend on preceding ENSO events, which relates to the question of the independence of tropical Atlantic variability raised in the introduction.
In two additional experiments, noEqAtl and noNTA, SST restoring toward climatology is limited, respectively, to the equatorial Atlantic (10°S-3°N, with 5-degree tapering zones north and south) and the NTA (8-30°N, with 10-degree and 5-degree tapering zones north and south, respectively), with other settings as in noTATL. Only one case is considered in these experiments.
A study by  indicates that linear inverse models (LIMs) can serve as a GCM surrogate. LIMs are empirical statistical models that, in the context of climate science, are typically constructed from observations. , however, showed that, when constructed from GCM output, the seasonal prediction skill of these LIMs relates to that of the underlying GCM when run in forecast mode. This idea is further explored in Sect. 5, where we construct a LIM from CTRL0 and modify the SST initial conditions in the tropical Atlantic and Pacific to mimic the setup of noTATL and noTPAC, respectively. A similar approach has also been used by Kido et al. (2022), where the reader can also find more details on the LIM methodology, as well as in Penland and Sardeshmukh (1995) and Newman et al. (2009). The goal of this analysis is to test the feasibility of LIMs as a surrogate for GCM pacemaker and hindcast intervention experiments. If successful, this would allow using existing simulations to construct LIMs and run pacemaker experiments at a fraction of the computational cost of GCM pacemaker experiments. It would also allow tapping into the Coupled Model Intercomparison (CMIP) database to examine the model dependence of pacemaker experiments.
The reference data for SST and near-surface winds are from the European Centre for Medium Range Weather Forecasting (ECMWF) Reanalysis version 5 (ERA-5; Hersbach et al. 2020). Additionally, we use the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis version 1 in the Supplementary Information (Kalnay et al. 1996). For our intermodel comparison we use experiment piControl from the CMIP phase 6 (CMIP6; Eyring et al. 2016). For this experiment, models were integrated with full ocean-atmosphere coupling under steady radiative forcing representative of the pre-industrial period. The models used in this study are listed in Supplementary Table 1.

Statistical analysis of the CTRL0 and noTATL0 experiments
Here we analyze the pacemaker experiment with SST restoring in the tropical Atlantic (noTATL0) and compare it to the free-running control simulation (CTRL0). Composite El Niño events (based on DJF averages of SST anomalies in the Niño 3.4 region [170-120°W, 5°S-5°N] exceeding 1 standard deviation) show that CTRL0 reproduces the basic behavior seen in the ERA-5 reanalysis, with SST anomalies developing in the spring of year 0, peaking in December, and decaying in the spring of year 1 (Fig. 1a). Relative to the observations, however, the SST anomalies in CTRL0 develop earlier and decay later, and have a stronger amplitude. This is reflected in the standard deviation of Niño 3.4 SST anomalies ( Supplementary Fig. 2a), which shows the weak phase locking of events in CTRL0. Observed SST anomalies in the equatorial Atlantic ATL3 region are close to zero during the entire period of the composite. In April and May following the peak of the El Niño event, observed ATL3 SSTs show a slight dip but return to neutral afterward ( Fig. 1a). In CTRL0, on the other hand, the drop in ATL3 SST occurs later (in June) and develops into a strong negative event. This indicates that the influence of El Niño on the equatorial Atlantic is much stronger in CTRL0 than in observations. For the NTA region ( Fig. 1b), on the other hand, CTRL0 shows weaker SST anomalies than the observations in the spring of year 1. Winds in the Niño 4 region (160°E-150°W, 5°S-5°N; Fig. 1c) are consistent with the evolution of the El Niño event, with westerly anomalies strengthening until November (observations) or December (CTRL0), one to two months before the peak of the SST anomalies. For the winds, too, CTRL0 displays a tendency for longer persistence but the difference is less striking than for the SST.
The observed winds averaged over the ATL4 region (45°W-20°W, 3°S-3°N) show a strengthening of the trades (negative anomaly) in April following the El Niño peak, which indicates that the influence of ENSO on the tropical Atlantic is more apparent in the surface winds than in the SST, as pointed out by Münnich and Neelin (2005). We note that even though the Niño 3.4 declines from winter to spring the trade wind strengthening is only pronounced in April and May. This strong seasonality of the Pacific influence on the Atlantic may be related to the phase locking of ATL4 wind variability (Richter et al. 2017) and the seasonal migration of the ITCZs in both basins (Tokinaga et al. 2019). The trade wind strengthening is consistent with the dynamic forcing of El Niño (Chang et al. 2006). Supplementary Fig. 1b underscores that the correlation between Niño 3.4 SST and ATL4 near-surface zonal winds in MAM is quite robust across models, more so than the corresponding correlations of Niño 3.4 SST with ATL3 SST in MAM ( Supplementary  Fig. 1c). The westerly wind anomalies over the NTA region during winter of year 1 (Fig. 1d) are pronounced in both the observations and CTRL0, in support of the robust ENSO influence on the northern tropical Atlantic.
The tropical Atlantic pacemaker experiment (noTATL0) produces stronger and more persistent El Niño events ( Fig. 1a) with consistent wind anomalies in the western equatorial Pacific (Fig. 1b). There are ATL3 SST anomalies with an amplitude of up to 0.4 K, which indicates that the SST restoring does not eliminate tropical Atlantic SST variability completely. The cool SST anomalies in June and July are consistent with the easterly wind anomalies in the western equatorial Atlantic from April through June (Fig. 1b). We note that the ATL4 wind anomalies in noTATL0 are stronger than those in CTRL0. This is puzzling as numerous studies have indicated that the Bjerknes feedback (Bjerknes 1969) is active in the equatorial Atlantic to some extent (Zebiak 1993;Keenlyside and Latif 2007;Richter et al. 2014b;Dippe et al. 2018Dippe et al. , 2019. Accordingly, the cold SST anomalies in the ATL3 region should contribute to a strengthening of the easterly wind anomalies. In noTATL0, however, the opposite seems to be the case: easterly wind anomalies become stronger when the cold SST anomalies are reduced. A similar observation holds true for the NTA: westerly wind anomalies become stronger when SSTs in the region are restored to climatology. We will revisit this point in Sect. 4.5. Some studies have attempted to estimate the Atlantic influence on the tropical Pacific using partial regressions (Ham et al. 2013b;, in which the ENSO signal is regressed out first. It is instructive to place the behavior of the GFDL CM2.1 in the context of these previous studies. Partial regression on the negative NTA index (an indicator of the AMM) in CTRL0 (Fig. 2a) yields patterns that are quite comparable to those obtained from observations and other GCMs their Fig. 5). Cold NTA SST anomalies in MAM are associated with a strengthening of the local trades that extends into the eastern and central equatorial Pacific (Fig. 2a; see also Supplementary Fig. 4a, which shows all values, regardless of statistical significance), while in the western equatorial Pacific there are westerly anomalies. Consistently with the equatorial Pacific wind anomalies, there are slightly warm and cold SST anomalies in the western and eastern equatorial Pacific, respectively. We note that the cool NTA anomalies are accompanied by a southward shift of the ITCZ and a weakening of the equatorial trades over the Atlantic, which is qualitatively consistent with observations and other models ) but more pronounced.
Partial regressions on the ATL3 (an indicator of the AZM) in JJA (Fig. 2b) also show similarities with previous work. Warm SST anomalies in the eastern equatorial Atlantic are accompanied by a weakening of the trades both on and to the north of the equator, while the ITCZ is shifted southward. The westerly wind anomalies over the northeastern tropical Pacific are also consistent with previous work. A discrepancy is found in the western equatorial Pacific, where CTRL0 fails to reproduce the pronounced easterly anomalies seen in observations and many models.
We have seen that the removal of tropical Atlantic SST anomalies in noTATL0 leads to more persistent ENSO events. In addition, previous studies have indicated that ENSO shifts to lower frequencies under such conditions (Dommenget et al. 2006). Spectral analysis of SST anomalies in the Niño 3.4 region (Fig. 3) shows roughly consistent results: while CTRL0 has only one peak at 5 years, noTATL0 has two at 4 and 6.5 years. Also, overall, noTATL0 has more power at periods of 6-15 years.

Developing vs. decaying El Niño years
We first show the composites for the free-running control simulation (CTRL0). Here the developing years are 358,614,755,763,902,917,139,165, 547 and 661. The average over these years (Fig. 4a) shows SST anomalies in the Niño 3.4 region starting from about 1 K in January of year 0 and peaking at about 3.5 K by November. SST anomalies in the NTA region start from 0 K in January of year 0 and gradually increase to 1 K by March of year 1. SST anomalies in the ATL3 region drop from 0 K in May to − 2 K in June, and peak 1 month later in July. Note the extreme amplitudes of both the El Niño and the negative AZM event. This is due partly to the model's excessive variability and partly to the fact that we selected the most extreme events from the 1000 year time series.
For the decaying El Niño years (651 and 711; Fig. 4b), Niño 3.4 SST anomalies start out at approximately 3 K in January of year 0. SST anomalies rapidly decline from late boreal spring and reach 0 K in July, followed by the development of a La Niña event. The NTA SST anomalies in the spring of year 0 are more pronounced than for the developing events and peak at 1.5 K in May, consistent with the stronger SST anomalies in the equatorial Pacific. SST anomalies in the ATL3 region are weaker, on the other hand, consistent with the fact that the El Niño event is decaying in Fig. 3 Spectral power as a function of period (years) for the Niño3.4 index in CTRL0 (green line) and noTATL0 (blue line). Note that the y-axis is logarithmic. The dashed green and blue lines show the 95% confidence intervals for CTRL0 and noTATL0, respectively. These are estimated based on a Markov red noise spectrum  Fig. 3) summer. We note that for both developing and decaying El Niño years, the tropical Atlantic SST anomalies develop in opposite ways in the NTA and ATL3, with warm anomalies in the former and cold anomalies in the latter. This reflects the opposite sign of the wind anomalies that are forced by ENSO in the two regions (see Sect. 1), but may also be partly due to interaction between the two variability modes. The anticorrelation between NTA and ATL3 SST anomalies is also seen in observations and other model simulations (not shown) but is less pronounced there. This again indicates that CM2.1 exaggerates the remote effects of ENSO on the tropical Atlantic. The later-than-observed peak of the NTA (Fig. 4b) and its unrealistic persistence (Fig. 1b) likely contribute to this behavior.

Perfect model hindcasts in CTRL, noTATL, and noTPAC
For all selected years, predictions are initialized on January 1 and integrated until December 31 (Fig. 5). The CTRL prediction ( Fig. 5a and b), without model interference, qualitatively reproduces the behavior of CTRL0 (Fig. 4), i.e., the perfect model prediction is successful. However, the amplitude of both the El Niño and negative AZM events is weaker than in CTRL0. This is expected because we selected extreme events from CTRL0 and because, for a given prediction year, CTRL0 is a single realization while CTRL is the average over a 20-member ensemble.
In the noTATL intervention experiment, the Niño 3.4 index evolves very similarly to CTRL but is slightly weaker (Fig. 5c). Averaged from October through December (OND) the difference is 0.05 K, which is not significant at the 95% level. In the tropical Atlantic, the strong SST restoring of noTATL leaves almost no anomalies, as can be seen from the ATL3 index (Fig. 5c). We note that for the developing La Niña case (year 126) the difference between CTRL and noTATL is also very small ( Supplementary Fig. S3).
For the decaying El Niño years, on the other hand, the impact of the tropical Atlantic on ENSO evolution is pronounced (Fig. 5d). The El Niño event decays more slowly in noTATL, leading to a difference of 1.55 K in the Niño 3.4 index during OND. The results suggest an important role of the tropical Atlantic in accelerating ENSO decay. This is consistent with some previous studies (Dommenget et al. 2006;Wang et al. 2017;. We note that the signs are opposite to what we found for the developing El Niño years: the presence of the NTA warming (though weak) and ATL3 cooling weakens the El Niño (Figs. 5 and 6). The latter contrasts with previous studies of the Atlantic influence on ENSO (Rodriguez-Fonseca et al. 2009), but is consistent with the regression analysis in Sect. 3. In the following we will mostly focus on the years with decaying El Niño events since they show a robust influence of the tropical Atlantic on the Pacific.
The noTPAC predictions ( Fig. 5e and f) underscore the strong influence that ENSO has on the tropical Atlantic in the model (see Sect. 3): without the tropical Pacific influence, SST and wind anomalies in the equatorial Atlantic are essentially zero (Fig. 5e and f) and the same holds true for the NTA region (not shown). Individual ensemble members still feature considerable anomalies (inferable from Fig. 11a) but those are random and cancel each other out in the ensemble mean. Thus, while there is a strong influence of the AZM and AMM on El Niño decay, the tropical Atlantic anomalies are themselves strongly influenced by the preceding El Niño event. In other words, the tropical Atlantic mediates a negative feedback of ENSO on itself.

Changes in the Walker circulation
Analysis of the Walker circulation indicates that there are no important circulation changes during the first three months of the prediction (Fig. 7b), even though there are already warm SST anomalies in the tropical Atlantic during that time (Fig. 6b). In the following season (April-May-June or AMJ), there are upward anomalies over the eastern equatorial Atlantic (Fig. 7d). Latitude-pressure sections averaged between 30°W and 0°W ( Supplementary Fig. 6) indicate that the upward anomalies are most pronounced between 5 and 10°N. Along the equator (Fig. 7), the upward anomalies appear to be part of an anomalous weakening of the Atlantic Walker cell, with westerly anomalies in the lower troposphere (Fig. 7d). This clearly shows that, in AMJ, the changes in the Walker circulation are dominated by the response to the northern tropical Atlantic SST anomalies. Remote impacts over the eastern tropical Pacific are marked by anomalous subsidence and strengthening of easterlies in the lower troposphere. While these differences are not statistically significant at the 95% level, they are consistent with the influence of the northern tropical Atlantic on ENSO (Ham et al. 2013a, b) but not with that of the equatorial Atlantic (Rodriguez-Fonseca et al. 2009). This highlights that the northern tropical Atlantic dominates the far-field response. It is interesting to note that, in CM2.1, the NTA and equatorial Atlantic have competing impacts on the tropical Pacific, because they are anticorrelated with each other.
During the JAS season, the cold SST anomalies in the equatorial Atlantic strengthen in CTRL (Fig. 6e) but the geopotential height anomalies are weaker than in AMJ, indicating an overall weakening of the atmospheric response. This can be explained by the climatological northward shift of the ITCZ (inferable from the northward shift of the precipitation anomalies in Fig. 6c-f), which limits the impact of SST anomalies on convection (Richter et al. 2017). There are anomalous subsidence and m/s). The three rows show CTRL, noTATL, and noTPAC. The filled circles in (c) and (d) indicate where noTATL is significantly different from CTRL at the 95% level. Significance is not shown for noTPAC as the lines are bunched too closely easterlies over the eastern equatorial Atlantic (Fig. 7f), indicative of a strengthened Atlantic Walker cell, but the upper-level response over the western equatorial Atlantic is still consistent with a weakened Atlantic Walker cell, as is the remote response in the eastern tropical Pacific.

Additional experiments for separating NTA and equatorial Atlantic influences
We attempt to isolate the influences from the NTA and equatorial Atlantic in two additional experiments (experiments noNTA and noEqAtl). These experiments only use year 651, which features a decaying El Niño with a pronounced negative AZM event in JJA. The evolution of SST and zonal wind anomalies in CTRL and noTATL ( Fig. 8a and b) is very similar to the corresponding means over all decaying El Niño years ( Fig. 5b and d).
In no EqAtl (Fig. 8c), the El Niño event decays slightly faster and the easterly wind anomalies in the ATL4 become more pronounced than in CTRL (Fig. 8a). Put differently, the experiment suggests that the equatorial Atlantic SST anomalies slightly slow the decay of El Niño and considerably weaken the ATL4 wind anomalies. Since the experiment extends to 3°N, with an additional 10-degree tapering zone, this result is consistent with the notion that SST anomalies directly north of the equator interfere with the local atmospheric response to equatorial Atlantic SST anomalies. This result is also qualitatively consistent with Rodriguez-Fonseca et al. (2009) because the equatorial Atlantic elicits an opposite-signed response in the Pacific.
In noNTA (Fig. 8d), El Niño anomalies decay much more slowly than in CTRL, while the ATL4 winds are approximately unchanged. Put differently, the experiment suggests that the NTA SST anomalies substantially accelerate the decay of El Niño but do not affect the ATL4 winds. This is roughly consistent with the results shown in Figs. 6 and 7, where the northern tropical Atlantic SST anomalies dominate the far-field response. The results are also qualitatively consistent with the findings of Ham et al. (2013a, b), who suggest that NTA SST anomalies lead to an oppositesigned response in the tropical Pacific.

The Bjerknes conundrum
As in the pacemaker experiments (Sect. 3), we find that the easterly wind anomalies over the equatorial Atlantic ATL4 region are stronger when the tropical Atlantic SST anomalies are suppressed (Figs. 5 and 6). This seems to suggest that SST anomalies in the equatorial Atlantic counteract the ATL4 wind anomalies, which would be in conflict with the Bjerknes feedback. The apparent conundrum can be resolved by considering that, on the whole, the tropical Atlantic anomalies tend to counteract those in the Pacific, which is apparent in Fig. 7, where the free tropospheric circulation anomalies over both the Atlantic and Pacific are stronger in the absence of tropical Atlantic SST anomalies. Thus, the absence of tropical Atlantic SST anomalies allows the Pacific to fully exert its influence on equatorial Atlantic surface winds, which is to strengthen the easterlies.
The role of the northern tropical Atlantic becomes apparent in the SST difference between CTRL and noTATL (Fig. 6d). While there is anomalous cooling in the eastern equatorial Atlantic during AMJ, consistent with the development of the negative AZM event in Fig. 6 Horizontal maps of anomalous SST (shading; K), 10 m wind (vectors; reference 2 m/s and 1 m/s for the left and right columns, respectively), and precipitation (contours; negative contours dashed, zero-contour omitted; mm/day), averaged over perfect-model hindcast years in which El Niño is decaying, for (a, b, e) CTRL, and (b, d, f) the difference CTRL minus noTATL. The fields are seasonally averaged over January-February- March  (a, b), April-May-June (c, d), and July-August-September (e, f). For the difference CTRL-noTATL, only values significant at the 95% level are shown Decaying El Niño years: SST (shading), 10m wind (vectors), precip (contours) CTRL, this is overshadowed by intense warm anomalies to the north. Consistent with the warmer SSTs, there is anomalous precipitation off the West African coast, at around 5°N. The differences in near-surface winds indicate anomalous southwesterly flow from the western equatorial Atlantic into this convection center (Fig. 6d). This suggests that the SST and precipitation anomalies north of the equator promote equatorial wind anomalies that undermine the Bjerknes feedback. In the following season (July-August-September or JAS; Fig. 6f), on the other hand, the Bjerknes feedback is able to assert itself. SST and precipitation differences shift further north and weaken, while at the same time the colder SST anomalies in CTRL strengthen, which allows them to control equatorial surface winds in accordance with the Bjerknes feedback. Consistently, the easterly anomalies are stronger in CTRL than in noTATL.

Prediction skill
The 13 initialization years can be used to calculate skill metrics of the hindcasts. Due to the limited sample size and the selection criteria, the skills obtained in this way may not be entirely representative of the actual skill of the model. Since we are mostly interested in the relative differences between experiments, this is not a major issue.
The anomaly correlation coefficient (ACC) for CTRL in the Niño 3.4 is high, with a value of 0.75 at lead time 11.5 months (Fig. 9a). Thus the model successfully overcomes the spring predictability barrier. As stated above, Fig. 7 Longitude-pressure sections, averaged between 5 S and 5 N, for anomalous geopotential height (shading; m), and pressure velocity and divergent zonal wind (vectors; pressure velocity in hPa/day*0.1, zonal wind in m/s), averaged over perfect-model hindcast years in which El Niño is decaying, for (a, c, e) CTRL, and (b, d, f) the difference CTRL minus noTATL. The fields are seasonally averaged over January- February-March (a, b), April-May-June (c, d), and July-August-September (e, f). For the difference CTRL-noTATL, values significant at the 95% level are shown by shading (geopotential height) and black vectors (pressure velocity and zonal wind), while values that are not significant are shown by contour lines and grey vectors. The zero contour line is thickened these skills may be overly optimistic because the prediction years include many decaying events, which should be easier to predict, and because we selected extreme events, which are easy to predict in terms of their sign, though not their amplitude. Indeed, while the ACC is relatively high, the amplitude of the predictions tends to be too low (Supplementary Fig. 3), which also shows in the corresponding root-mean-square error (RMSE) metric (Fig. 10a).
For the ATL3 region, the ACC declines rapidly after initialization but is still much higher than persistence in March and April. Starting from June, skill rebounds but remains close to persistence. The skill for the NTA region is similar to that for the ATL3 region but slightly lower.
Near-surface zonal winds in the Niño 4 and ATL4 regions are predicted relatively well (Fig. 9b), with higher skill in the former consistent with the high skill for Niño 3.4 SST anomalies (Fig. 9a). The ACC is substantially lower in the NTA region.
We compare the skills in CTRL to those in noTATL (Figs. 9c and d; skills for the ATL3 and NTA in noTATL are included for completeness). Contrary to expectations, the ACC for the Niño 3.4 region is better when the tropical Atlantic SST anomalies are eliminated (green line in Figs. 9a and c), and the same holds true for the RMSE (Fig. 10a and c). While these differences are not statistically significant, the outcome is unexpected as previous studies have suggested that tropical Atlantic SST anomalies should increase skill in the Pacific (see Sect. 1). Our results may not necessarily contradict those studies, because the higher skill in noTATL seems to be due to "error" compensation. As we have noted, CTRL tends to underpredict the extreme El Niño events we have selected from CTRL0. On the other hand, the removal of tropical Atlantic SST anomalies leads to increased amplitude and persistence of El Niño (Fig. 2). These two effects partially cancel each other out, leading to increased skill in noTATL.
ACCs for ATL4 zonal wind are very similar in CTRL and noTATL from January through July. In August and September, the ACC is lower in noTATL, presumably due to the maturing AZM event exerting an important influence on the equatorial Atlantic winds. In other months, it appears that most skill comes from the remote tropical Pacific influence, consistent with the results of Richter and Doi (2019). This is also supported by the strongly reduced ATL4 skill in noTPAC (Fig. 9f). Since both the ensemble mean Niño 3.4 and ATL3 SST indices are close to zero in noTPAC (Fig. 5) their skills (Fig. 9e) are not further discussed here, though there are some interesting features, such as the pronounced negative Niño 3.4 skill in April.

Analysis of the ensemble spread
So far, we have focused on the ensemble means in our analysis. Even for the same experiment and initialization year, however, there is substantial spread across members, with large differences in the regions of our interest. This can be used to obtain a robust estimate of the statistical relations between the regions. In addition, each initialization year presents a different configuration of SST anomalies, adding spread. We therefore examine statistical relations in scatter plots, where each point represents one initialization year and ensemble member for a given experiment. Since there are 13 initializations and 20 perturbed ensemble members, this results in a total of 260 data points for each scatter plot (Fig. 11).
We first examine to what extent JJA ATL3 SST anomalies influence JJA Niño 4 surface winds in the absence of tropical Pacific SST anomalies ( Fig. 11a; experiment noTPAC). The correlation is weak (R = 0.25) but statistically significant at the 95% level. The regression coefficient is 0.11 m/s/K, Fig. 9 Anomaly correlation coefficients (ACCs), relative to CTRL0, for the perfect-model hindcasts in CTRL (a, b), noTATL (c, d), and noTPAC (e, f). The left column shows ACC for the following SST indices: Niño 3.4 (green), ATL3 (blue), and NTA (orange). The right column shows ACC for the following 10 m zonal wind indices: Niño4 (brown), ATL4 (red), and NTA (dark blue). The x-axis indicates the lead time, with all forecasts initialized on January 1. The ACC is calculated using the ensemble means of all 13 hindcast years, and thus the ACC for each lead month is based on 13 values. Filled circles indicate where values are significantly different from CTRL at the 95% level. The dashed lines in a and b indicate persistence suggesting that an ATL3 anomaly of + 1 K leads to a westerly wind anomaly of 0.11 m/s in the Niño 4. This indicates a weak influence on the Pacific that is opposite in sign to what previous studies have suggested but consistent with the partial regression analysis of CTRL0 (Fig. 2) and the comparison of the CTRL and noTATL hindcasts (Fig. 5).
The influence of the equatorial Pacific SST on the equatorial Atlantic wind anomalies is examined in scatter plots of AMJ ATL4 zonal wind anomalies against AMJ Niño 3.4 SST anomalies in the noTATL experiment (Fig. 11b). Consistent with our previous results, we find a strong correlation (R = − 0.86) and a regression coefficient of − 0.99 m/s/K. This is much stronger than what observations suggest.
Equatorial Atlantic SST anomalies typically peak 1-2 months after the peak of the equatorial zonal wind anomalies, both in observations and models (Richter et al. 2014a;Illig et al. 2020). This suggests an important role of the zonal wind anomalies in forcing AZM events. Through the Bjerknes feedback, these wind anomalies are themselves influenced by equatorial Atlantic SST anomalies, leading to a coupled feedback loop. The following analysis, however, focuses on the role of wind anomalies in forcing SST anomalies and how this is represented in the CM2.1 experiments. We examine how the ATL4 zonal wind forcing in AMJ affects ATL3 SST two months later, in JJA. In experiment noTPAC (Fig. 11c) the correlation and regression coefficients are 0.75 and 0.77 K/m/s, respectively. In CTRL, on the other hand, the corresponding values are 0.89 and 0.68 K/m/s (Fig. 11d). The higher correlation in CTRL is likely due to the larger spread reducing the effect of noise. The larger regression coefficient in noTPAC may reflect the absence of destructive interference from the tropical Pacific (Chang et al. 2006;Lübbecke and McPhaden 2012).  Fig. 9, but for the root-mean-square error (RMSE) instead of ACC 1 3

LIM experiments
Here we examine to what extent LIMs built from CTRL0 can emulate the behavior of the GCM hindcast experiments in Sect. 4. Figure 12 shows the results from these LIM experiments and should be compared with Fig. 5. Note that the LIM is constructed from SST only and thus there are no wind fields to show. As for the GCM hindcasts, we also show all individual years for the Niño 3.4 predictions (Supplementary Fig. 5).
LIM CTRL struggles to reproduce the developing El Niño event (Fig. 12a). It is important to note that the underlying dynamics of the LIM are those of a damped oscillator (Penland and Sardeshmukh 1995). Constructive interference between modes as well as stochastic forcing can allow temporary growth of anomalies but it seems that in LIM CTRL the built-in tendency for decay dominates, resulting in persistent weak El Niño conditions. While the El Niño is weak, it seems to be able to excite a negative AZM event that becomes apparent in July and matures in August and September. This is quite similar to the GCM CTRL.
For the decaying El Niño years, LIM CTRL seems to be more successful at reproducing the amplitude of the Niño 3.4 anomalies (Fig. 12b) and also captures the decay very well. Also consistent with the GCM CTRL experiment is the relatively pronounced negative AZM event that forms in late summer (Fig. 12b).
The behavior in LIM noTATL (Figs. 12c and d) mimics that of GCM noTATL: for the developing El Niño years the changes are small (though of the opposite sign as in GCM noTATL), and, for the decaying El Niño years, the event becomes much more persistent. Also consistent with the GCM experiments is the fact that the AZM events fail to develop in the absence of tropical Pacific variability (Figs. 12e and f). This is also documented by the prediction skill of LIM noT-PAC ( Supplementary Fig. 7e), where the skill for the ATL3 is lower than in LIM CTRL.
Overall, the LIM experiments are moderately successful in reproducing the qualitative behavior seen in the GCM experiments. While these results are encouraging, some refinement of the method is desirable. This could be achieved, for example, by including additional variables, such as winds and sea-surface height, into the construction of the LIM (e.g. Newman et al. 2009).

Summary
We have investigated the two-way interaction between the tropical Atlantic and ENSO using pacemaker experiments Overall, the results indicate that, in this particular GCM, the tropical Atlantic mostly acts as a negative feedback to ENSO by accelerating the decay of events. It has little impact on the development of ENSO events.
The pacemaker experiments indicate that tropical Atlantic SST anomalies slightly weaken ENSO events and shorten their duration. Consistent with the latter result, we find that, in the absence of tropical Atlantic SST anomalies, the power spectrum of ENSO shifts to longer periods, which confirms previous results (Dommenget et al. 2006).
The perfect model hindcasts with SST restoring document a clear difference between developing and decaying ENSO years. For the developing ENSO years, the Atlantic influence is very weak, undermining the notion that the tropical Atlantic can excite ENSO events. The tropical Atlantic does seem to play an important role, however, in the acceleration of ENSO decay. Additional sensitivity tests show that the influence on ENSO decay mostly comes from the northern tropical rather than the equatorial Atlantic. Specifically, warm SST anomalies over the northeastern tropical Atlantic, which grow during the peak and early decaying phase of El Niño, contribute to convection over the region and subsequent subsidence over the eastern tropical Pacific. This is overall consistent with previous results by Ham et al. (2013a, b), and in particular with Jiang and Li (2021), who stress the importance of the northern tropical Atlantic influence in late spring and early summer.
An important finding of the present study is that, without tropical Pacific SST anomalies, there are no AMM or AZM events in the ensemble mean. This further underlines the notion that the tropical Atlantic cannot act as an initiator of ENSO. As a result, the potential contribution of the tropical Atlantic state to ENSO prediction skill may be limited but correct simulation of tropical Atlantic SST should still be important for the prediction of ENSO decay.
While not our initial motivation, we also made a few interesting discoveries regarding the influence of ENSO on the tropical Atlantic, as simulated by the CM2.1 GCM. Recall that, while the observed influence of ENSO on equatorial Atlantic SST is inconsistent, the influence on surface winds over the equatorial Atlantic is more robust. Perplexingly, the easterly anomalies that El Niño excites over the equatorial Atlantic become more pronounced when tropical Atlantic SST anomalies are removed. Our results show that this is mainly due to northern tropical Atlantic SST anomalies counteracting the ENSO influence.

Caveats
The GFDL CM2.1 differs from observations and many other models in two regards. First, it features stronger than observed variability both in the equatorial Pacific and Atlantic. Second, the correlation between ENSO and the equatorial Atlantic is stronger than in observations, and also stronger than in most CMIP6 GCMs. Both these factors suggest that the ENSO influence on the tropical Atlantic is unrealistically strong in the model. In nature, the equatorial Atlantic is likely less dependent on preceding ENSO events and may therefore have some potential to initiate ENSO events.
The seasonal evolution of tropical Pacific and tropical Atlantic events in CM2.1 differs from observations in some respects. NTA warming in CM2.1 persists longer than in observations, which may enhance its influence on ENSO. Furthermore, the decaying El Niño events in CTRL (Fig. 5b) persist longer than typically observed (although multi-year events are sometimes observed; Tokinaga et al. 2019). This may alter the Atlantic-Pacific interaction. We note, however, that for year 711, which does feature rapid ENSO phase transition ( Supplementary Fig. 3), the estimated Atlantic influence is quite consistent with other years.
Our estimate of the Atlantic influence on ENSO prediction skill in perfect model hindcasts is uncertain because we used only 13 years, of which 12 featured strong El Niño events. A more comprehensive hindcast with a representative sample of prediction years (La Niña, neutral, El Niño) would have to be performed but would require substantial computational resources.
In the selection of the hindcast years, we have focused on El Niño events, although there is one developing La Niña year (year 126), which, consistently with the developing El Niño years, indicates a very weak Atlantic influence. Future studies should also examine La Niña events in detail.

Reconciliation with previous studies
Several studies have reported gains in prediction skill from precise knowledge of tropical Atlantic SST, either in a perfect model setting (Frauen and Dommenget 2012) or in the prediction of observations (Keenlyside et al. 2013;Exarchou et al. 2021). How do these results compare to ours and can the differences be reconciled? Exarchou et al. (2021) find a modest increase in the prediction skill for the Niño 3 index when observed tropical Atlantic SSTs are specified in their model. For predictions initialized in June, the ACC for the following winter increases by about 0.05. Keenlyside et al. (2013) find a more pronounced increase in skill for predictions initialized in February, with ACCs in the following winter increasing by about 0.2 when observed tropical Atlantic SSTs are specified. Our limited prediction experiments do not allow a reliable quantitative comparison but even the higher skill gain of 0.2 is not necessarily inconsistent with our results. As we have seen, ENSO decay is substantially influenced by the tropical Atlantic. Even if the Atlantic were just a negative feedback of ENSO on itself, as our results suggest, representation of this feedback relies on properly predicting the tropical Atlantic response to ENSO. Models that fail to simulate this Atlantic response should benefit substantially from prescribing tropical Atlantic SSTs. One should also note that our experiments, using a perfect model setting, only consider the skill that can be gained by knowledge of tropical Atlantic SST anomalies, while the experiments by Keenlyside et al. (2013) and Exarchou et al. (2021) also consider the skill that can be gained from correcting imperfect models in the tropical Atlantic.
The study by Frauen and Dommengent (2012) uses a similar perfect model setting as our study and finds a decrease in Niño 3 ACC of more than 0.1 when the tropical Atlantic is initialized with climatological values. It should be noted, however, that their ocean component is a simple recharge oscillator in the Pacific and a slab ocean in the Atlantic and Indian Oceans. Comparison with their results is therefore not straightforward and would require evaluation of how the model represents two-way interaction between the Atlantic and Pacific.

Outlook
While CM2.1 has some unrealistic features and exaggerates Pacific dominance, we believe the present study to be an important step toward quantifying the strength of the Pacific-Atlantic linkage. Future studies should assess the model dependence of these results. Such studies could utilize the experimental framework developed here that may be termed "perfect model hindcast intervention". These experiments offer several advantages, including the absence of an initialization shock and limited intervention in the model physics. This allows addressing the issue of interbasin interaction and its impact on prediction skill without having to deal with involved initialization procedures such as data assimilation. In addition, the LIM framework developed here could be a useful tool for assessing basin interactions and their model dependence without the need for any GCM sensitivity tests. Some improvements may be required though to make this approach a viable alternative.