1 Introduction

Tropical sea surface temperature (SST) variation plays an important role in regulating atmospheric general circulation to generate global climatic, ecological, and socioeconomic impacts (Saji and Yamagata 2002; McPhaden et al. 2006; Xie and Carton 2004; Yadav et al. 2018; Wang 2019). Skillful seasonal climate predictions primarily originate from atmospheric responses to those slow varying oceanic boundary thermal forcing (Tippett et al. 2004). Therefore, issuing timely and accurate predictions for several major ocean–atmosphere coupled modes, such as the El Niño–Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD), are major goals of operational short-term climate prediction, and could provide many beneficial implications for various uses, from climate disaster management to the energy sector. At present, current climate models can provide effective predictions of ENSO and IOD events at 6–24 months (Chen et al. 2004; Barnston et al. 2012; Luo et al. 2016; Tang et al. 2018; Ren et al. 2019; Ham et al. 2019; Liu et al. 2022a,b; Sun et al. 2023; Zhou and Zhang 2023) and 3–7 months (Luo et al. 2005; Zhao and Hendon 2010; Zhu et al. 2015; Liu et al. 2017; Wu and Tang 2019; Zhao et al. 2019, 2020; Liu et al. 2021; Song et al. 2022a, b, c), respectively. Moreover, a series of ENSO and IOD predictability studies have been well conducted, focusing on prediction error growth dynamics, predictability variation on multiple time scales, intrinsic limit of predictability, etc. (Duan and Mu 2006; Mu et al. 2007; Hou et al. 2018; Feng et al. 2017; Feng and Duan 2019; Hou et al. 2019; Hu et al. 2019; Zhou et al. 2020; Xu et al. 2021; Liu et al. 2022a, b, c; Song et al. 2022a, b). These predictability studies have greatly enhanced our understanding of the predictability of ENSO and IOD and promoted the development of seasonal climate prediction.

In contrast to the Pacific and Indian Oceans, prediction and predictability studies of ocean–atmosphere coupled modes in the Atlantic Ocean began to come to light later. Until the 1970s, the influence of the Atlantic Ocean on climate variability received increasing attention (Xie and Carton 2004). The SST variability in the Atlantic Ocean not only impacts the weather and climate over the surrounding continents (Giannini et al. 2003; Sutton and Hodson 2005; O’Reilly et al. 2016) but also has the potential to regulate the climate over the Pacific Ocean (Rodriguez et al. 2009; Ham et al. 2013; Exarchou et al. 2021; Ruprich et al. 2021; Zhang et al. 2021; Wang et al. 2024), Indian Ocean (Barimalala et al. 2012; Wang 2019) and Asia (Kucharsk and Joshi 2017; Sun et al. 2017, 2019; Yadav et al. 2018). Therefore, skillful prediction of the Atlantic SST variability is crucial for climate prediction in the surrounding regions, which has profound socioeconomic implications. However, relatively little attention has been given to investigating seasonal predictability specifically in the Atlantic Ocean over the past decades. The prediction of the Atlantic climate has only recently emerged as a high-profile activity (Hurrell et al. 2006). A number of statistical and dynamic models have been employed for SST prediction in the Atlantic sector (Chang et al. 1998; Collins et al. 2006; Stockdale et al. 2006; Hu and Huang 2007; Wang and Chang 2008; Hu et al. 2013; Lee et al. 2016; Li et al. 2020; Wang et al. 2021).

However, previous studies have mainly demonstrated the actual prediction skill of SST in the Atlantic Ocean, while the potential predictability has seldom been considered, and mainly concentrated on the decadal scale (Collins et al. 2006; Msadek et al. 2010). When we speak of predictability, two concepts should be kept in mind. One is practical predictability, and the other is intrinsic predictability. The former is often referred to as the actual prediction skill, which quantifies the accuracy of current predictions by the best-known model against actual observations and can be measured with either deterministic or probabilistic metrics. The latter is also referred to as potential predictability, which indicates the upper limit of the prediction skill if the optimal procedure were used (Lorenz 1996; Tang et al. 2018). Perfect model experiment (Collins et al. 2006; Msadek et al. 2010) is always employed to quantify the potential predictability, in which the prediction and the corresponding “observation” are both from the model integration. Therefore, ensemble retrospective/hindcast forecasts based on state-of-the-art coupled models are powerful tools for promoting our understanding of predictability both from practical and intrinsic perspectives. Current predictability studies focused on the Atlantic sector are mainly based on hindcast forecasts over the past few decades only (Chang et al. 1998; Collins et al. 2006; Stockdale et al. 2006; Hu and Huang 2007; Wang and Chang 2008; Hu et al. 2013; Lee et al. 2016; Li et al. 2020; Wang et al. 2021). Such relatively limited data available may be problematic for reliably measuring the predictability and can potentially lead to precluding statistically robust conclusions. Recently, we performed a long-term retrospective prediction with the Community Earth System Model (CESM; Liu et al. 2022a), which provides a unique opportunity to explore a wide range of predictability problems regarding the Atlantic climate, especially for the potential predictability. In this study, we employed this retrospective ensemble forecast covering the 1880–2017 period to comprehensively investigate the Atlantic SST predictability. The remainder of this paper is organized as follows: in Sect. 2, we present a detailed description of the retrospective forecasts and measurement metrics used. In Sects. 3 and 4, practical and intrinsic predictability traits, respectively, are described. Finally, we provide a summary and in-depth discussion of the findings in Sect. 5.

2 Data and methodology

2.1 Data

The retrospective forecasts analyzed in this study were extracted from our recently developed ensemble prediction system based on the CESM (Liu et al. 2022a). The long-term hindcast retrospective forecasts lasting 12 months were initialized each January 1st, April 1st, July 1st, and October 1st from 1880–2017 by assimilating the sea temperature at depths above 500 m and wind at heights below 500 hPa with nudging simulation coupled CESM (Song et al. 2022c). Regarding oceanic data, we employed the monthly Simple Ocean Data Assimilation version 2.2.4 (SODA 2.2.4; Carton and Giese 2008) and the Global Ocean Data Assimilation System (GODAS; Behringer and Xue 2004) datasets before and after 1983, respectively. The nudging coefficient for the sea temperature varies from about 10 days at the surface to about 140 days at 500 m. Regarding atmospheric data, six hourly ERA-20C reanalysis (Stickler et al. 2014) and ERA-interim reanalysis data points (Berrisford et al. 2011) were used before and after 1983, respectively. The nudging coefficients for the wind are uniformly (6 h) below 500 hPa and 0 above 500 hPa. In a given start month, 20 ensemble members generated by the climatically relevant singular vector (Kleeman et al. 2003) were produced to represent the influence of the uncertainty in the subsurface ocean temperature on the SST forecasts. More details of our nudging scheme and ensemble construction can be found in Song et al. (2022c) and Liu et al. (2022a).

To eliminate the influence of the decadal variation of the climatology states, the prediction and observation anomalies were defined as the departure from the climatology of the corresponding running 20-year period. In this study, “one month lead forecast” denotes the monthly mean forecast conducted from the initial conditions at the first day of one month to the current month itself. For example, the one month lead forecast for January 1st initial conditions is the monthly mean forecast for January. We also employed the partial correlation to exclude the influence of the ENSO signal and used the effective number of degrees of freedom to test the statistical significance of the correlation coefficients between two high auto-correlate variables, such as SST in this study. The merged monthly SSTs from the SODA and GODAS datasets before and after 1983 were utilized to evaluate the actual prediction skill.

2.2 Methodology

2.2.1 Deterministic prediction metrics

We employed the anomaly correlation coefficient (ACC) and root mean square error (RMSE) to measure the deterministic prediction skill. These are defined as:

$$ACC(t)=\frac{\sum \limits_{i=1}^{N}{x}_{p}(i,t){x}_{o}(i,t)}{\sum \limits_{i=1}^{N}{x}_{p}{(i,t)}^{2}\sum \limits_{i=1}^{N}{x}_{o}{(i,t)}^{2}}$$
(1)
$$RMSE(t)=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}{[{x}_{p}(i,t)-{x}_{o}(i,t)]}^{2}}$$
(2)

where \(x\) is the variable of interest. \(p\) and \(o\) denote the anomalous ensemble mean prediction and observation, \(i\) and \(t\) indicate the initial condition and lead month, and \(N\) is the total number of predictions.

2.2.2 Probabilistic prediction metrics

To evaluate the probabilistic skill, we employed the commonly used Brier skill score (BSS; Wilks 2011) and ranked probability skill score (RPSS, Epstein 1969). Following previous studies (Yang et al. 2016, 2018; Liu et al. 2018; 2022b), we split the probability density distribution of the data from 1880 to 2017 to define above-normal (upper 1/3 tercile), neutral (middle 1/3 tercile), and below-normal (lower 1/3 tercile) events. BSS here measures the performance of the probabilistic prediction for each category event, and RPSS represents the weighted average of the BSS for all event categories (Bradley and Schwartz 2011). These are defined based on Brier score (BS, Wilks 2011) and ranked probability score (RPS, Epstein 1969):

$$BS=\frac{\frac{1}{N}\sum \limits_{k=1}^{10}{N}_{k}{({\overline{p} }_{k}-{\overline{o} }_{k})}^{2}}{B{S}_{REL}}-\frac{\frac{1}{N}\sum_{k=1}^{10}{N}_{k}{({\overline{o} }_{k}-\overline{o })}^{2}}{B{S}_{RES}}+\frac{\overline{o }(1-\overline{o })}{B{S}_{UNC}}$$
(3)

where \(N\) denotes the total number of initial conditions. \({N}_{k}\), \({\overline{p} }_{k}\) and \({\overline{o} }_{k}\) are number, the average forecast probability and corresponding observed frequency at \(k\) th probability bin, which divided from 0.1 to 1.0 with intervals of 0.1, respectively. \(\overline{o }\) is the climatological probability of an event.

$$RPS(i,t)={\sum_{m=1}^{3}\left[\sum_{j=1}^{m}{p}_{j}(i,t)-\sum_{j=1}^{m}{o}_{j}(i,t)\right]}^{2}$$
(4)

where \({p}_{j}(i,t)\) and \({o}_{j}(i,t)\) are the forecast probability and observed frequency of the \(j\) th category event for the \(i\) th initial condition at lead time of \(t\).

Based on the BS and RPS, and taking the climatology as the reference forecast, BSS and RPSS can be defined as:

$$BSS=1-\frac{BS}{B{S}_{REF}}=\frac{B{S}_{RES}}{B{S}_{REF}}-\frac{B{S}_{RES}}{B{S}_{REF}}=BS{S}_{RES}-BS{S}_{REF}$$
(5)
$$RPSS=1-\frac{\overline{RPS} }{\overline{RP{S }_{REF}}}$$
(6)

Positive BSS and RPSS mean better prediction than climatology. BSS consists of two terms, the resolution (\(BS{S}_{RES}\)) and the reliability (\(BS{S}_{REL}\)). The former measures the extra information captured by the forecast system when the occurrence of the event is different from the climate state. The latter quantifies the ability of forecast probability to represent the corresponding observed frequency.

Regarding the potential predictability, we used an information-based measure, namely, the relative entropy (RE), which quantifies the additional information from the predicted distributions over the climatological distribution (Kleeman 2002). As the above two distributions of seasonal variables (including SST) are approximately Gaussian, RE may be expressed as:

$$RE(i)=1/2\left[\frac{{\frac{({\mu }_{P}-{\mu }_{c})}{{\sigma }_{c}^{2}}}^{2}}{SC}+\frac{ln(\frac{{\sigma }_{c}^{2}}{{\sigma }_{p}^{2}})+\frac{{\sigma }_{p}^{2}}{{\sigma }_{c}^{2}}-1}{DC}\right]$$
(7)

where \({\sigma }_{p}^{2}\), \({\sigma }_{c}^{2}\), \({\mu }_{p}\) and \({\mu }_{c}\) are the ensemble variance, climatological variance, ensemble mean, and climatological mean, respectively. RE can be divided into the signal component (SC, the first term of Eq. 7) and dispersion component (DC, the last three terms of Eq. 7). SC measures the additional information between the climatological and prediction means, while DC indicates a reduction in the climatological uncertainty from the prediction.

3 Practical predictability

3.1 Overall performance

Figure 1 shows the AAC of SST in the Atlantic Ocean against the corresponding observations with the lead time. Obviously, the ACC skill varies with the region and lead time. For the 1-month lead prediction, the ACC skills are generally higher than 0.5 in the whole basin. Beyond a 3-month lead, the ACC skills rapidly deteriorated in most regions of the domain, except for some areas in the northern tropical Atlantic (NTA). This indicates that the most predictable region is located in the NTA within the Atlantic sector on the seasonal scale. Therefore, the following discussion focuses on the NTA unless otherwise specified. To further explore the predictability in this region, we defined the regionally averaged (5–20°N, 20–80°W) SST anomalies over the NTA as the NTA SST index (NTASI) to quantify the SST variability in this region. Figure 2 shows the evolution of the ACC and RMSE of the NTASI with the lead time. For all lead times, the predictions notably exceeded the persistence forecasts in terms of both the ACC and RMSE, and high ACC corresponds to low RMSE. These superiorities enlarge with increasing lead time. This indicates that our ensemble prediction system performed reasonably well and could yield skillful SST predictions in the NTA at least 6 months ahead when 0.5 is chosen as a criterion to determine the effectiveness of the ACC. Figure 3 shows the predicted time series of the NTASI at different lead times (blue line) with the corresponding observations (red line). At first glance, the model generally captured the prominent warm and cold events in the NTA and yielded skillful predictions at a 6-month lead. At a 2-month lead, the predictions were quite consistent with the observations. With increasing lead time, however, there was a substantial deterioration in the agreement between the ensemble mean predictions and observations with a tendency to underestimate the amplitude of the SST variability in the NTA.

Fig. 1
figure 1

ACC of SST at (a)-(f) 1–6 lead months from 1880 to 2017. The green box indicates the NTA region

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Fig. 2
figure 2

(a) ACC and (b) RMSE of the NTASI against the observations as a function of the lead time from 1880 to 2017. The black and red lines indicate the ACC of ensemble mean and persistence, respectively

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Fig. 3
figure 3

Time series of the forecasted NTASI at (a) 2-month, (b) 4-month, and (c) 6-month lags and the corresponding observations. The red and blue lines are the observations and ensemble means, respectively, while the gray shading denotes the prediction spread

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Except for the deterministic skill, we also assessed the probabilistic predictions of the NTASI. Figure 4a shows that the BSS skill for below-normal, neutral and above-normal events varied with the lead time. A positive BSS indicates a skillful probabilistic prediction, while a negative BSS suggests that the model prediction is inferior to the climatological forecast. A larger BSS value represents a greater improvement in model probabilistic predictions with respect to the climatological forecasts, which benefits from the contributions of the high resolution (Fig. 4b) component and low reliability (Fig. 4c) term. Overall, our ensemble system attained a better performance for below- and above-normal events, especially for the latter. It could provide skillful probabilistic predictions for below- and above-normal events 6 and 8 months ahead, respectively. Regarding below- and above-normal events, the resolution component sharply decreased with increasing lead time, while there was little fluctuation in the reliability component month to month. This suggests that the variation in the resolution component dominates the decrease in the probabilistic prediction ability. However, the BSS of neutral events was negative for all lead times, indicating that the probabilistic prediction is inferior to the climatological forecast. This suggests that the predictive information may primarily originate from below- and above-normal events, which can provide a large predictable signal. This is further examined in the next section.

Fig. 4
figure 4

(a) BSS, (b) resolution and (c) reliability of the ensemble NTASI as a function of the lead time from 1880 to 2017. The blue, green and red lines indicate below-normal, neutral and above-normal events, respectively

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3.2 Seasonal variation

The SST variability over the NTA exhibited the characteristics of phase locking. The standard deviation of the observed NTASI varied month to month, with a maximum amplitude in March–April-May (Fig. 5a). Figure 5b shows the ACC of the NTASI as a function of the target month and lead time. It is noticeable that the ACCs are still larger than 0.5 even at a 7-month lead in the target month of April, while they are smaller at a 4 or 5-month lead in the other target months. A similar feature was also observed in the RPSS skill of the NTASI (Fig. 5c). Skillful probabilistic predictions (RPSS > 0) could be made at least 10 months ahead in the target month of April over the shorter lead times in the other target months. The seasonal variation in the deterministic and probabilistic skills is further consistent with the phase locking of the SST variability over the NTA rather than the seasonality of corresponding persistence skill (Fig. 5d). This indicated that the predictability of the NTA SST is not only originate from the persistence of local SST and may be related to the lagged influence of ENSO and its seasonality. Generally, ENSO reaches its peak phase in winter and has the potential to regulate the SST variability over the NTA, with the maximum influence at a lag of approximately one season and corresponding to the peak amplitude of the SST variation in this region (Carton and Huang 1994; Enfield and Mayer 1997; Latif and Grötzner 2000; Chiang and Sobel 2002; Wang 2002; Chang et al. 2003; Huang 2004; Tourre and White 2005; Hu and Huang 2007; Ding and Li 2011; Hu et al. 2013; Chen et al. 2021). This will be further examined in the next section.

Fig. 5
figure 5

(a) The standard deviation (SD) of the observed NTASI as a function of the month. (b) ACC, (c) RPSS and (d) Persistence of the NTASI with the lead and target months

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4 Intrinsic predictability

4.1 Overall performance

The actual prediction skill quantifies the ability of the current model to predict the future evolution of the system against corresponding observations, which can be influenced by a combination of errors due to the initial conditions and model formulation. The estimation of potential predictability metrics does not make use of observations, which assume model to be perfect and eliminate consideration of the errors resulting from model formulation. Therefore, the potential predictability is considered to be a useful indicator for the actual prediction skill (Tang et al. 2008; Liu et al. 2018). The potential predictability of SST over the NTA was measured via information-based framework metrics and is determined by a combination of SC and DC. Figure 6 shows the variations in RE, SC and DC as a function of the initial condition and lead time. It is apparent that RE and SC significantly varied among the different initial conditions and decreased with increasing lead time, while DC exhibited a relatively smooth variation among initial conditions and sharply decreased after 2 lead months. Generally, the large SC generally depended on a few events with large amplitudes, as shown in Fig. 2, suggesting that such events could provide strong initial signals for the corresponding predictions and often provide a large RE and high predictability. Figure 7 further reveals that SC was significantly correlated with RE (Fig. 7a), with a correlation coefficient of 0.89. In contrast to the favorable relationship between SC and RE, however, DC was much less related to RE (Fig. 7b). This indicates that strong events associated with abundant initial predictable signals contain much additional information that resides in each prediction. Accordingly, these events typically correspond to a large SC and dominate the interannual variation in RE.

Fig. 6
figure 6

(a) RE, (b) SC, and (c) DC for the ensemble NTASI with the initial condition and lead time from 1880 to 2017

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Fig. 7
figure 7

Scatter plots of (a) SC and (b) DC vs. RE at 1–12 lead months for the ensemble NTASI from 1880 to 2017

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4.2 Seasonal variation

As shown in Fig. 8, the potential predictability also exhibited significant seasonality. However, the seasonality in SC obviously differs from that of DC. Compared to that in the other target months, SC gradually declined in the target month of April. In contrast, significant phase locking of DC occurred around early autumn. It is straightforward to understand the above discrepancy. Both SC and DC can contribute to the predictability. SC represents the additional information of the initial signal of the prediction system compared with the climatological mean. The SST variance over the NTA reaches its peak time around April, which corresponds to a maximum amplitude of initial signal and SC. Therefore, SC plays a dominant role during the SST variance at its peak time. DC captures the reduction in the uncertainty in ensemble predictions compared with the climatology prediction, which works more effectively when the initial signal is relatively low. In the NTA, SST variance reach its valley time around October, which can and provide limited predictive signal and the mainly predictability is rooted in the reduction of the predictive uncertainty. Comparing Figs. 5 and 8, it can reveal that the phase locking of the actual prediction skill around April is determined by SC, while the seasonality in DC contributes to the second peak of the actual prediction skill around early autumn. This seasonality is radically different from that of the ENSO (Liu et al. 2022a) and IOD (Song et al. 2022a), which are dominant by SC.

Fig. 8
figure 8

(a) SC and (b) DC of the NTASI with the lead and target months

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4.3 Source of predictability

One emphasis of predictability studies is the exploration of the possible source of predictability. The following question naturally arises: what accounts for the predictability of SST over the NTA? As described based on the above results and previous literature (Kleeman 2002; Yang et al. 2012; Saha et al. 2016; Pillai et al. 2018), the inherent signals in the initial conditions can provide predictability of slow-varying climatic modes. Here, we first focus on the relationship between the potential predictability (RE) of SST over the NTA and the SST signal in the initial conditions. According to Eq. (7) and the results in Figs. 6 and 7, the RE is dominated by the SC, which is related to the square of the ensemble mean and independent of the sign of the ensemble prediction mean (Tang et al. 2007; Yang et al. 2012; Song et al. 2022a, b). So we employ the square of SSTA instead of the SSTA itself to address the strength of the SST signal.

Firstly, we investigate the correlation between the observed SSTA at 1, 4, 7, and 10 lead months (Fig. 9a-d) with NTASI targeted at April. In the observation, the local and the remote forcing from the tropical Pacific and Indian Oceans are all significantly correlated with the peak phase of SST variation over the NTA. However, the significant effect of the Indian Oceans has almost disappeared and the local forcing over the NTA is still maintained after excluding the ENSO signal in each lead month (Figs. 9e-h). This indicates that the influence of the Indian Ocean mainly originated from the effect of ENSO (Song et al. 2022a, b) and the local forcing in the NTA is partly independent of ENSO. Therefore, we further explore correlations of the observed preceding NTASI and Niño 3.4 index with the NTASI of April, respectively (Fig. 10a). Before April, ENSO always reaches its peak phase in the preceding winter, and its lagged influence on the flowing April SST variation over NTA lasts in its whole development phase via two possible ways: the PNA pattern or the Walker and Hadley circulations. Both have the potential to regulate the Atlantic subtropical high, and the associated anomalous northeast trade winds resulting in the NTA SST anomalies by affecting the latent heat flux (Wang 2002; Xie and Carton 2004). Although the influence of preceding ENSO on the SST variation in April always exists, the influence of the local signal suppresses the contribution of ENSO in the short lead months. Figure 11 shows the correlation between the SST signal in the initial conditions and RE of SST over the NTA targeted at April, when the SST variation over the NTA reaches its peak phase. Consistent with the relative contributions of the ENSO and the local forcing in the observation, the predictability of SST over the NTA mainly depends on the local signal over the NTA at 1-month lead. As the lead time increases, the local influence of the NTA declines, and the effects from the tropical Pacific Ocean gradually emerge. Beyond a 7-month lead, the main predictability of SST over the NTA in April was mainly determined by the preceding ENSO signal. This further indicated that the high predictability of SST over the NTA in April was due to the combined influences of the local signal and the preceding remote forcing from the tropical Pacific Ocean. Regarding the prediction at long lead times, the predictability of SST over the NTA targeted at April mainly benefited from the contribution of the preceding ENSO forcing.

Fig. 9
figure 9

Correlation between observed NTASI in April and the SSTA in in (a) April, (b) January, (c) October and (d) July. (e)-(f) same as (a)-(d), but the partial correlation after removing the ENSO Signal in each month. The dotted area indicates the values that pass the 99% confidence level

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Fig. 10
figure 10

Lead correlation between observed NTASI in (a) April and (b) October with the preceding NTASI (blue) and Niño 3.4 index (red)

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Fig. 11
figure 11

ACC between RE of the NTA region in April and the square of SSTA in the initial conditions in (a) April, (b) January, (c) October and (d) July. The dotted area indicates the values that pass the 99% confidence level

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We also assess the predictability source of the SST variation over the NTA targeted at October, when the SST variation over the NTA reaches its minimum value. Due to the weak variance of ENSO in its transition phase, the influence of the ENSO on the flowing October SST variation in NTA is limited (Figs. Figure 10b and 12). In addition, the persistence of the local signal of NTA before October is higher than that before April (Fig. 10b). Therefore, local signal makes more contribution to the SST variation in October over NTA than ENSO at all lead months in the observation. Correspondingly, the local signal was notable at 1, 4 and 7 lead months in the correlation maps between the SST signal in the initial conditions and the RE targeted at October (Fig. 13), which provide the main predictability source of SST in October over the NTA. Compared with the results of April, there were weak initial signals to provide the additional information for SST prediction in October over the NTA as the lead time was increased. The aforementioned results revealed that the predictability of SST over the NTA is jointly influenced by the local signal and preceding remote forcing from the tropical Pacific Ocean. The seasonality in the lagged influences of the tropical Pacific Ocean on the SST variation over the NTA leads to a high predictability targeted at April.

Fig. 12
figure 12

Correlation between observed NTASI in October and the SSTA in (a) October, (b) July, (c) April and (d) January. (e)-(f) same as (a)-(d), but the partial correlation after removing the ENSO Signal in each month. The dotted area indicates the values that pass the 99% confidence level

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Fig. 13
figure 13

ACC between RE in October and the square of SSTA in the initial conditions in (a) October, (b) July, (c) April and (d) January. The dotted area indicates the values that pass the 99% confidence level

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5 Summary and discussion

The SST variation over the Atlantic Ocean has the potential to regulate the weather and climate worldwide (Xie and Carton 2004; Hurrell et al. 2006). Therefore, skillful prediction of SST over the Atlantic Ocean has tremendous social and economic implications. However, our knowledge of the predictability of the Atlantic SST and the related dynamic mechanism is limited relative to the Pacific and Indian Oceans. Based on long-term retrospective forecasts with the CESM, we comprehensively and thoroughly investigated the seasonal predictability of the Atlantic SST from both practical and intrinsic predictability perspectives. From the perspective of potential predictability, we focused in depth on two problems that have rarely been mentioned in the previous research. One is what is the dominant factor that controlling the seasonal variation of predictability over the NTA. The other is to identify the seasonality difference of the predictability source between peak and trough periods of the SST variation over NTA.

Overall, the most predictable region was located in the NTA within the Atlantic sector on the seasonal to interannual scales. Our ensemble prediction system could reasonably capture the prominent warm and cold events in the NTA and yield skillful deterministic predictions at least 6 months ahead. It could provide better probabilistic predictions for below- and above-normal events than for neutral events. This occurs because below- and above-normal events generally exhibit high intensities, which provide immense additional predictive information. Naturally, these events are typically associated with a large SC that dominates the variation in RE and corresponds to a high actual prediction skill.

In addition, there was a remarkable seasonality in the predictability of the SST variation over the NTA. Interestingly, this seasonal variation in predictability is not well consistent with the seasonality of the corresponding persistence skill, indicating that the predictability of NTA SST is not only contributed by the persistence of local SST. The phase locking of the SST variation over the NTA corresponded to the significant seasonality in SC, which led to the high predictability targeted at April regardless of the lead time. Taking this a step further, the high predictability in April was jointly influenced by the local signal over the NTA and preceding remote forcing from the tropical Pacific Ocean. The local signal was notable at a short lead time, while the preceding remote forcing from the tropical Pacific Ocean was more prominent at a long lead time. This coincides with the previous result that the predictability of IOD beyond persistence at long lead times is mostly controlled by ENSO predictability and the signal-to-noise ratio of the Indo-Pacific climate system (Zhao et al. 2019, 2020). In contrast, the predictability targeted at October was mainly dominated by the local influence over the NTA and stemmed from the contribution of DC, which was higher given a relatively low initial signal. Notably, the difference in the lagged influences of the tropical Pacific Ocean on the SST variation over the NTA between April and October led to the phase locking of the SST variation and its predictability.

Increasing attention has been focused on the prediction and predictability of climate modes over the Atlantic sector. A number of climate centers have adopted this problem as a high-profile activity and begun routinely issuing seasonal predictions of the Atlantic climate. However, despite only moderate success, it is encouraging that there exists much room for improvement in current prediction of SST over the NTA. Further scientific advances regarding this problem crucially depend on our ability to fully realize the potential of seasonal Atlantic predictions. Potential efforts for three aspects can be expected. One is the design of a sustained observation system that can provide the key state variables and effectively use these data via intelligent assimilation methods. The other is the reduction in the model bias and improvement in the model performance by considering the interactions among ocean basins. In addition, the booming method of machine learning has achieved remarkable success in the seasonal prediction of the SST in the Indo-Pacific Ocean (Ham et al. 2019; Liu et al. 2021; Sun et al. 2023; Zhou et al. 2023). Therefore, the application of machine learning is expected to greatly enhance the accuracy of seasonal prediction of SST in the NTA. Beyond the issues outlined above, another overarching challenge facing the climate community is that SST over the Atlantic sector also exhibits obvious variability on the decadal scale (Karspeck et al. 2015; Yeager and Robson 2017; Yeager et al. 2018; Buckley et al. 2019; Yeager 2020). It is of primary importance to advance our understanding of the predictability of the Atlantic sector on a decadal scale. In terms of this issue, an in-depth systematic investigation is underway.