Analyzing the Influence of the North Atlantic Ocean Variability on the Atlantic Meridional Mode on Decadal Time Scales

Important features of the Atlantic meridional mode (AMM) are not fully understood. We still do not know what determines its dominant decadal variability or the complex physical processes that sustain it. Using reanalysis datasets, we investigated the influence of the North Atlantic Ocean variability on the dominant decadal periodicity that characterizes the AMM. Statistical analyses demonstrated that the correlation between the sea surface temperature decadal variability in the Atlantic Ocean and the AMM time series characterizes the Atlantic multidecadal oscillation (AMO). This corroborates previous studies that demonstrated that the AMO precedes the AMM. A causal inference with a newly developed rigorous and quantitative causality analysis indicates that the AMO causes the AMM. To further understand the influence of the subsurface ocean on the AMM, the relationship between the ocean heat content (0–300 m) decadal variability and AMM was analyzed. The results show that although there is a significant zero-lag correlation between the ocean heat content in some regions of the North Atlantic (south of Greenland and in the eastern part of the North Atlantic) and the AMM, their cause-effect relationship on decadal time scales is unlikely. By correlating the AMO with the ocean heat content (0–300 m) decadal variability, the former precedes the latter; however, the causality analysis shows that the ocean heat content variability drives the AMO, corroborating several studies that point out the dominant role of the ocean heat transport convergence on AMO.


Introduction
The last four decades of climate research have revealed the influence of the ocean-atmosphere coupled system variability within the tropical Atlantic basin on the observed climate conditions in the adjacent continental regions [1][2][3][4][5][6]. Recent studies have also shown that atmospheric perturbations generated in this region by the ocean-atmosphere coupled variability act as forcing conditions on the El Niño-Southern oscillation (ENSO) [7][8][9][10], Pacific meridional mode [11], North Atlantic oscillation (NAO) [10,12], and Indian monsoon [13,14]. Therefore, a more accurate understanding of the tropical Atlantic variability could improve climate prediction over the adjacent regions, benefiting their populations, and, from a broader perspective, deepen our understanding of the interactions between the tropical Atlantic variability and diverse large-scale phenomena.
Tropical Atlantic ocean-atmosphere coupled variability is characterized by the Atlantic zonal mode (AZM) [15] and the Atlantic meridional mode (AMM) [4,16]. The former presents an interannual periodicity and impacts the precipitation regime in the West African region [15][16][17], whereas the latter presents interannual and decadal periodicities that impact the precipitation regimes in northeastern Brazil [1,4,18] and West Africa [2,3]. The AMM manifests as an interhemispheric sea surface temperature anomaly (SSTA) gradient that is coupled to anomalous cross-equatorial low-level winds that modulate the intertropical convergence zone (ITCZ) towards the positive lobe of the SSTA gradient [4,16,[19][20][21]. The physical mechanism that initiates and sustains the AMM is known as wind-evaporation-SST positive feedback (WES feedback) [19,20,22], a thermodynamic coupling between the low-level wind speed, the sea surface evaporation induced by the wind stress, and the SSTA. Several studies have shown that external forcing excites the AMM. The ENSO impacts the tropical North Atlantic (TNA) SSTAs by inducing anomalous surface latent heat flux, particularly via the Pacific-North America teleconnection pattern [4,23], as well as via changes in the Walker and Hadley tropical circulation cells [24,25]. These TNA SSTAs can propagate equatorward via the WES feedback, potentially generating an AMM in the tropical Atlantic [26][27][28][29]. The ENSO influence dominates on interannual time scales [30][31][32][33]. During similar physical processes, the NAO can excite the AMM via its southern lobe (the Azores high) [16,31,[34][35][36]. Although the AMM is characterized by interannual and decadal time scale periodicities, the decadal periodicity, with a spectral peak at ~11-13 years, is the dominant temporal pattern [37,38]. Despite significant advances in our understanding of the AMM features, the basis for its dominant decadal variability remains to be explained [39].
The multidecadal variability of the SSTAs in the North Atlantic, known as the Atlantic multidecadal oscillation (AMO), is also statistically linked to the AMM on decadal time scales. Based on a lead-lag correlation analysis of their low-pass filtered time series, Vimont and Kossin [40] found that the AMO is maximally correlated with the AMM when the former leads by roughly a year, suggesting that the AMO can excite the AMM on decadal time scales. A lead-lag relationship between the Atlantic high-latitude SSTAs and the AMM has also been highlighted [41,42], although Vimont [42] points out that the mechanism underlying this link is unclear. Since a lead-lag statistical relationship is not solid proof of causality between two phenomena, we can propose hypotheses based on two scenarios: that the AMO induces mechanisms that modulate the AMM on decadal time scales or that a third variability excites both the AMO and AMM on decadal time scales. The ocean dynamics in the North Atlantic exhibit a complex behavior that is most strongly influenced by the dominant imprint of the different components of the Atlantic Meridional Overturning Circulation (AMOC), as the thermohaline circulation (THC) and wind-driven circulations, which includes the subtropical, subpolar gyres and Ekman transport [43]. The upper limb of the AMOC is responsible for the poleward heat transport in the Atlantic Ocean that impacts the SSTAs variability in the North Atlantic [44], manifested as the AMO [45,46] and the ocean heat content variability in the upper layers on decadal to multidecadal time scales [47][48][49]. In this paper, the relationship between the SSTAs over the Atlantic Ocean and the AMM on decadal time scales is investigated using the traditional lead-lag correlation analysis and a newly developed causality analysis that is capable of inferring the causal relationship between two time series in a rigorous and quantitative sense [50,51]. Next, the same methodologies are used to analyze the relationships between the AMM and the ocean heat content in the upper 300 m (OHC300) and the SSTAs and OHC300 on decadal time scales to investigate whether the OHC300 variability over the North Atlantic modulates both phenomena or not.

Data
For these analyses, the SST data are taken from the extended reconstructed sea surface temperature version 4 (ERSSTv4) [52], which has a 2° × 2° horizontal global resolution covering 1854 to the present. The wind components at 10 m are taken from the 20th century reanalysis dataset version 2 (20CRv2) [53], which has a global horizontal resolution of 2° × 2° covering 1871 to 2012. The OHC300 has been obtained from the Centro Euro-Mediterraneo sui cambiamenti climatici (CMCC) historical pcean reanalysis (CHOR_RL) [54], which covers the period 1900-2010. Since the original OHC300 dataset is not in a regular grid resolution, the data has been interpolated into a 1° × 1° grid resolution. The CHOR_RL reanalysis assimilates vertical profile data by being nudged to monthly Hadley Centre global sea ice coverage and SST (HadISST) reconstructed fields, while the atmospheric forcings are from the 20CRv2 reanalysis [54].

Methodology
In all of the analyses, we used a detrended monthly anomalies dataset covering the period 1900-2010. The anomalies were obtained by removing the annual cycle via subtraction of the climatological monthly means from the respective individual months. The detrended datasets were obtained by removing the linear trend based on a least-squares regression. To compute the AMM, we followed the methodology proposed by Chiang and Vimont [16] and Amaya et al. [55]. The AMM was obtained by performing a maximum covariance analysis (MCA) [56] using the SST and 10-m wind components over the tropical Atlantic region (30° S-30° N). The MCA consisted of applying singular value decomposition on the cross-covariance matrix between anomalies in the SST and 10-m wind components, which yielded a two time series (known as expansion coefficients) (Figure 1b) related to the SST (AMM-SST) and 10-m wind components (AMM-Wind). We obtained the regression map by projecting the original SST and 10-m wind anomaly components at each grid point onto the AMM-SST expansion coefficient (Figure 1a), which in this case represents the leading zero-lag coupled variability between SST and 10-m wind. Figure 1c shows the predominant decadal timescale variability (11-13 years) of the AMM determined via a power spectral analysis of the AMM-SST time series; a similar result was observed using AMM-Wind time series (not shown). Detailed discussions of the features that characterize the AMM are presented in Chiang and Vimont [16] and Amaya et al. [55]. Although the datasets and period analyzed differ from those used in these references, the results are similar, with a correlation of 0.90 between the AMM-SST computed here and that computed by Chiang and Vimont [16] over the period 1948-2010. Before applying the MCA, the datasets were processed in several ways. First, the 10-m wind components were interpolated into SST grid resolution, and the SST and 10-m wind components were smoothed via a three-month running mean at each grid point. Second, the linear ENSO influence was removed by removing the cold tongue index (CTI; SSTAs averaged over the Pacific regions from 6° S-6° N to 180°-90° W) at each grid point based on a least-squares regression. Finally, each field was normalized to its corresponding longterm standard deviation at each grid point. Since we are interested in understanding the decadal variability relationship between the AMM and other variables, all of the analyses are performed using low-pass filtered datasets. Following Zhang et al. [57] and Vimont [58], to filter the high-frequencies, 25-and 37-month running means were successively applied to the AMM-SST expansion coefficient and to each grid point of the OHC300 and SST fields. Figure 1 of Vimont [58] shows the filter amplitude response function of such a low-pass filter. Throughout this paper, the AMM-SST expansion coefficient was used to characterize the AMM temporal variability.
The analyses performed in this paper are mainly based on the statistical relationship between the variabilities reflected by correlation spatial patterns and time series lead-lag correlations. Since these methods do not prove causality between the analyzed variabilities, a more rigorous method has been applied to reinforce the conclusions. In a newly developed method, the causality analysis between two time series is measured as the rate of information flowing from one time series to the other computed via the following equation: in which ( , = 1,2) is the sample covariance between two time series ( and ) and is the sample covariance between and ̇= , +1 − , ∆ , with ∆ being the time step size. The units are natural unit of information (nats) per unit time. Ideally, if | 2→1 | ≠ 0, then 2 is causal to 1 , otherwise it is noncausal. In practice, statistical significance must be tested. To assess whether the results are different from zero, significance test were carried out at the 95% confidence level. Equation (1) is the maximum likelihood estimator of a rigorously derived physical formula from first principles. A negative value of 2→1 means that 2 makes 1 more uncertain, while a negative value means that 2 makes 1 more stable. A detailed description of the method and its theoretical basis can be found in Liang [50,51]. As example of climate variability application, Liang [50] tested the Equation (1) to analyze the causality relationship between the El Niño/La Niña and the Indian ocean dipole (IOD) over the period 1958-2010. The results showed that the flow of information from El Niño to IOD was → = −6 × 10 −3 nats/month, while the flow of information from IOD to El Niño was → = 13 × 10 −3 nats/month. This means that both phenomena are mutually causal, in which El Niño tends to stabilize IOD and IOD tends to make El Niño more uncertain. Stips et al. [59] used this technique to investigate the relationship between the global CO2 radiative forcing and the global mean surface temperature anomalies (GMTA) over the period 1850-2005. The authors show that 2→ = 0.316 ± 0.108 nats/year, while 2→ = 0.003 ± 0.003 nats/year. Here, the values 0.108 and 0.003 represent the confidence interval significant at the 95% level. Therefore, based on this new technique, such one-way causality between the CO2 and GMTA adds more evidence supporting anthropogenic climate change in the last decades. This technique has been used to study climatological change patterns over Southeast Asia [60,61].
Two-tailed Student's t-tests with an effective number of degrees of freedom N eff given by the approximation: in which N is the sample size and ( ) and ( ) are the autocorrelations of two sampled time series X and Y at time lag j were used to assess the statistical significance of correlations between two autocorrelated time series, as are present in the low-pass filtered datasets [62][63][64]. Correlation coefficients were considered significant at the 95% confidence level.

Relationship between the AMM and SSTAs
Vimont and Kossin [40] found a strong correlation between the AMM and AMO for the period 1950-2005, with a maximum of ~0.82 when the AMO led the AMM by one year (using low passfiltered yearly data). Here, by analyzing the correlation between the AMM-SST and the SSTA variability at each grid point over the Atlantic basin, we identified a significant positive spatial correlation pattern in the south of Greenland where the AMO peaks (black box, Figure 2a). Since the SSTAs over the south of Greenland resembles an AMO-like variability, as defined by Goldenberg et al. [65], we will use the term AMO for simplicity.
Moreover, when taking the entire Atlantic basin into consideration, the pattern resembles the pan-Atlantic pattern [34], with significant positive correlations in the tropical North Atlantic (TNA), significant negative correlations in the center of the tropical South Atlantic (TSA), and significant positive correlations in the western part of the subtropical South Atlantic. Nevertheless, it should be noted that the significant correlations in the TNA and TSA are expected since the AMM-SST index was taken from this region. To analyze the relationship between the AMM and the SSTAs over the south of Greenland, an index was defined based on the spatially averaged SSTAs for the region to the south of Greenland (10°-50° W; 50°-65° N; black box). The unfiltered and low-pass filtered time series of the AMM-SST and AMO are shown in Figure 2b. The relationship reported by Vimont and Kossin [40] is corroborated by the lead-lag correlation between the AMM-SST and AMO on a decadal time scale, in which the AMO leads by two to three months with clear persistence (Figure 2c). Nevertheless, a maximum correlation of only 0.55 was observed for the period 1900-2010, while the correlation for the period 1950-2010 increased to 0.77.
The difference between the correlations of the two periods is likely related to the lack of quality of the dataset prior 1950. For instance, the reconstruction of the monthly ERSSTv4 SST is based on measurements from in situ buoy and ship observations from 1875 to present and then processed by a sophisticated statistical analysis (empirical orthogonal teleconnections) [52]. Therefore, due to sparser observations prior 1950, it is likely that the accuracy of the SST dataset was affected. This lead-lag relationship is not proof of cause-effect relationship. Thus, the causality analysis (Equation (1)) was applied to both time series.
The rate of information flow from the AMO to the AMM-SST ( → ) was 0.003 ± 0.001 nats/month, which indicates a cause-effect relationship between the two variabilities. The rate of information flow from the AMM-SST to the AMO ( → ) was not significantly different from zero at a 95% confidence level, with a value of 0.0004 ± 0.001 nats/month, which indicates no causation, as expected from the correlation analysis. Based on this result, the AMO appears to be part of a mechanism that potentially forces the AMM on decadal time scales. The study of such mechanism would not be explored here, but we should highlight that several studies have pointed out the NAO as an external forcing of the AMM [16,31,[34][35][36], hence the connection between AMO and NAO is a potential candidate for the mechanism. Nevertheless, the connection between AMO and NAO is highly complex and remain to be fully understood.
Based on observational datasets, Guan and Nigam [66] reports that the two modes have different temporal variability and they are essentially uncorrelated. On the contrary, recent study have reported their connection, in which the AMO positive phase leads to a negative phase of the NAO in winter [67]. In a multi-model study, Ba et al. [68] shows that the AMOC is the main driver of the AMO but found no linear link on decadal time scales between AMOC and NAO. However, there are modeling studies that find a link between the SSTAs and NAO based on feedback processes between atmosphere and ocean [69][70][71], which implies that the results are model dependent. For instance, Wen et al. [72] used a climate model and found that there is a coupled variability of AMOC and NAO in decadal time scale. This coupling is more effective when compared with the simulations produced by the same with lower resolution.  Figure 2a; 10°-50° W; 50°-65° N). All series were normalized by their respective long-term standard deviations. (c) Lead-lag correlation of the AMM-SST and AMO filtered time series. The gray line represents statistical significance at the 95% confidence level value for the zero-lag correlation. It should be noted that the 95% confidence level values changed for each lag correlation performed. However, as the changes in the values were negligible, we chose to display only the 95% confidence level value for the zero-lag correlation.

Relationship between the AMM and OHC300
As shown in the previous section, the SSTAs variability in the subpolar North Atlantic leads the AMM on a decadal time scale, while the causality analysis is supported by the cause-effect relationship. Nonetheless, we can hypothesize that the ocean subsurface variability in the North Atlantic also exerts influence on the AMM on decadal time scales. A rich body of studies has linked the AMO to the strength of the AMOC, in which the northward transport of warm waters in the upper layers driven by the AMOC impacts the SSTs in the North Atlantic and, together with air-sea heat flux processes, imprints its multidecadal variability [45,[73][74][75]. A stronger AMOC leads to warmer SSTs (AMO positive phase) and a weaker AMOC leads to cooler SSTs (AMO negative phase) in the North Atlantic [73]. In general, SSTs are influenced by the ocean-atmosphere interactions on shorter time scales and by large-scale oceanic circulation on longer time scales [76]. Here, our hypothesis assumes that the AMOC can also be an external forcing of the AMM, as it is on the AMO. However, this analysis focuses on the decadal variability of the northward heat transport in the upper layers of the ocean driven by the AMOC over the entire Atlantic basin and not on the strength of the AMOC defined by the latitude/depth plane [77]. The decadal OHC300 is assumed to be an indicator of the decadal variability of the northward heat transport in the upper layers of the ocean. Seidov et al. [48] shows that the decadal OHC is correlated with decadal AMO in the North Atlantic. Nevertheless, the AMOC variability may differentially affect the OHC300 in various North Atlantic regions [48,49]. Zhang [49] shows that the AMO is positively correlated with higher ocean subsurface temperatures in subpolar regions and negatively correlated with ocean subsurface temperatures in the Gulf Stream pathway. The OHC is the integrated ocean temperature at depth, and its anomalies can persist for long periods (from months to years) and potentially imprint an influence on the overlying ocean surface on lower frequencies [78].
To investigate the link between the AMM and Atlantic OHC300 variability on a decadal time scale, we performed an analysis of the zero-lag correlation between low-pass filtered AMM-SST and OHC300 data at each grid point over the Atlantic basin. The spatial correlation pattern is illustrated in Figure 3a. The most extensive areas showing a significant correlation between the AMM-SST and OHC300 lay to the south of Greenland (50°-60° N), extending zonally, and in the subtropical to midlatitudes in the eastern Atlantic region (5°-35° W; 30°-45° N). In both cases, significant positive correlations indicated that the AMM positive phase correlated with increases in the OHC300 in these regions on a decadal time scale. To further understand the nature of these correlations, two indices were defined based on the spatially averaged OHC300 data for each region, i.e., to the south of Greenland (10°-50° W; 50°-65° N; black box) and in the eastern North Atlantic (10°-30° W; 30°-40° N; purple box), which are called the OHC300-SG and OHC300-ENA indices, respectively. The unfiltered and low-pass filtered time series of the AMM-SST with OHC300-SG and OHC300-ENA are shown in Figure 3b,d, respectively. The lead-lag correlation between the AMM-SST and OHC300-SG shows a slightly antisymmetric structure in which the AMM-SST leads by five to six months (Figure 3c). This result suggests that the OHC300 variability to the south of Greenland does not exert any influence on the AMM variability on a decadal time scale. Concerning the OHC300-ENA, the lead-lag correlation with the AMM-SST shows a symmetric structure around zero lag, suggesting that it was unlikely that the OHC300 variability in the eastern North Atlantic was an AMM forcing ( Figure 3e). The same analysis was performed using unfiltered data showed similar results (not shown). Nevertheless, despite the symmetric structure, Figure 3e shows a higher persistence associated with the OHC300 leading. If the OHC300 variability over this region preconditions the AMM phases, it would likely occur via the OHC300 influence on the SSTAs persistence that ultimately affect lower atmosphere, potentially generating conditions to trigger the WES feedback process. Hasanean [79] shows that SSTAs over the tropical North Atlantic influence the sea level pressure of the subtropical high, which leads to trade wind variations that can then influence the SSTAs over the same region. Therefore, to reinforce our conclusion, the causality analysis was applied to the AMM-SST and OHC300-ENA time series. The rate of information flow from the OHC300-ENA to the AMM-SST ( 300→ ) was −0.0011 ± 0.0017 nats/month, a value that is not significantly different from zero at 95% confidence level, indicating no cause-effect relationship between the two variabilities. The information flow rate from the AMM-SST to the OHC300-ENA ( → 300 ) also implied no cause-effect relationship, with a value of 0.0002 ± 0.0013 nats/month (not significantly different from zero at 95% confidence level). This result suggests that the AMM decadal variability was not influenced by the decadal variability of the OHC300 in the Atlantic basin. Figure 3. (a) Zero-lag spatial correlation pattern between the OHC300 at each grid point and the AMM-SST time series. A low-pass filter was applied to the AMM-SST and OHC300 data at each grid point to retain the decadal variability. Dotted areas are statistically significant at the 95% confidence level. The black boxes represent regions where the OHC300-SG (south of Greenland, 10°-50° W; 50°-65°) and OHC300-ENA (eastern North Atlantic, 10°-30° W; 30°-40° N) indices were computed. (b) AMM-SST filtered (thick black line) and unfiltered (thin black line) time series and OHC300-SG filtered (thick red line) and unfiltered (thin red line) time series. The OHC300-SG indices were computed by spatially averaging the OHC300 in the region to the south of Greenland (black box). All series are normalized by their respective long-term standard deviations. (c) Lead-lag correlation of the AMM-SST and OHC300-SG filtered time series. The gray line represents statistical significance at the 95% confidence level value for the zero-lag correlation. (d) AMM-SST filtered (thick black line) and unfiltered (thin black line) time series and OHC300-ENA filtered (thick red line) and unfiltered (thin red line) time series. The OHC300-ENA indices were computed by spatially averaging the OHC300 in the eastern North Atlantic region (purple box). All series were normalized by their respective long-term standard deviations. (e) Lead-lag correlation of the AMM-SST and OHC300-ENA filtered time series. The gray line represents statistical significance at the 95% confidence level value for the zero-lag correlation. For (c) and (e) the 95% confidence level values changed for each lag correlation performed. However, as the changes in the values were negligible, we chose to display only the 95% confidence level value for the zero-lag correlation.
From Figure 2a and Figure 3a, we observed that both SSTAs and OHC300 variabilities to the south of Greenland significantly correlated with AMM-SST. To analyze the SSTAs and OHC300 relationship, the zero-lag correlation between the OHC300 and the SSTA at each grid point over the Atlantic basin was performed (Figure 4a). For this analysis, the OHC300 dataset was interpolated into the resolution of the SST grid points. The OHC300 was strongly correlated with the SSTAs in the North Atlantic and subpolar eastern North Atlantic. There was also a large area with significant correlations in the western mid-latitudes of the South Atlantic. The unfiltered and low-pass filtered time series for the SSTA (AMO) and OHC300-SG calculated based on the same index region to the south of Greenland are shown in Figure 4b; the respective lead-lag correlations on a decadal time scale are shown in Figure 4c. The SSTA led the OHC300 by roughly 12-15 months. A similar result was reported by Hazeleger et al. [80]. This result suggests that the OHC300 does not lead the SSTAs variability in the region. However, a deeper understanding of their relationship was provided by the causality analysis. The information flow rate from the SSTA to the OHC300 ( → 300 ) was 0.0083 ± 0.0011 nats/month (significantly different from zero at 95% confidence level) and, on the opposite direction, the information flow rate from the OHC300 to the SSTA ( 300→ ) was −0.0064 ± 0.0013 nats/month (significantly different from zero at 95% confidence level). The asymmetric causality relationship suggests that the OHC300 stabilized the SSTAs over the subpolar North Atlantic, therefore enhancing the AMO persistence, while the SSTAs variability made the OHC300 variability more uncertain. The result suggests that the OHC300 stabilizes the AMO is in accordance with several studies that reported the dominant role of the ocean heat transport convergence on the AMO [81][82][83]. However, ocean-atmosphere interaction may also play an important role, since dynamic coupling between atmospheric and oceanic circulation patterns appears to be key component modulating the complex processes underlying the North Atlantic SSTAs variability, as recent studies have indicated [84]. The OHC300 datasets were interpolated into the resolution of the SST grid point. A low-pass filter was applied to the data at each grid point to retain the decadal variability. Dotted areas are statistically significant at the 95% confidence level. (b) AMO filtered (thick black line) and unfiltered (thin black line) time series and OHC300-SG filtered (thick red line) and unfiltered (thin red line) time series. Both indices were computed by spatially averaging the data to the south of Greenland region (black box of Figure 4a; 10°-50° W; 50°-65° N). All series are normalized by their respective long-term standard deviation. (c) Lead-lag correlation of AMO and OHC300-SG filtered time series. The gray line represents statistical significance at the 95% confidence level value for the zero lag correlation. It should be noted that the 95% confidence level values changed for each lag correlation performed. However, as the changes in the values were negligible, we chose to display only the 95% confidence level value for the zero-lag correlation.

Conclusions
This article reexamines the link between the AMO and AMM on decadal time scales. The spatial correlation between the variability in the SSTA over the Atlantic basin and the AMM on decadal time scales are more significantly correlated in the region in which the AMO exhibits highest variability (south of Greenland). The SSTA variability over this region leads the AMM by two to three months. These results corroborate the conclusions of Vimont and Kossin [40]. However, such a relationship could indicate that either the AMO modulates the AMM on decadal time scales or that both variabilities are influenced by a third phenomenon. Based on a newly developed causality analysis method, we showed indications that the AMO has causal influence on the AMM on decadal time scales.
We also investigated whether the variability in the ocean heat content in the upper 300 m (OHC300) over the North Atlantic could impact both variabilities. The results showed that there are significant zero-lag statistical correlations between the AMM and OHC300 to the south of Greenland and in the eastern North Atlantic mid-latitudes. Nevertheless, the lead-lag correlations show that the AMM leads the OHC300 in the northern Atlantic region and that there is a symmetrical structure around the zero-lag correlation between the AMM and the OHC300 in the eastern North Atlantic. Moreover, we determined via the causality analysis that there is no causal relationship between the OHC300 variability in the eastern North Atlantic mid-latitudes and the AMM on decadal time scales. Concerning the SSTA variability and the OHC300 variability over the North Atlantic, the lead-lag correlation shows that the SSTA leads the OHC300 on decadal time scales. However, based on the causality analysis result, it is found that the OHC300 drives the SSTAs over the subpolar North Atlantic region, and, therefore, influences the AMO on decadal time scales. cmcc.it/index/index-3.html?sec=2. We are thankful for the support of Dr. Chunxue Yang for access to the CHOR_RL Historical reanalysis datasets. We also thank Dr. X. San Liang for his guidance on the interpretations of the causality analysis results, and for reading and commenting the manuscript, which helped to improve it. We thank the editor and two anonymous reviewers whose comments led to significant improvements of the paper.

Conflicts of Interest:
The authors declare no conflict of interest.