The relationship between the North and South Atlantic bidecadal sea level (SL) oscillations during the twentieth century is investigated for the first time using Simple Ocean Data Assimilation reanalysis. Complex empirical orthogonal function analysis of the bidecadal band gives two dominant modes: the first dominating from 1915 to 1965 and the second from 1970 onward. The long-term time-dependent change of mode dominance suggests a structural-type regime shift. The first mode is characterized by states with North and South Atlantic subtropical gyres in phase, while tropical and subpolar regions are in opposite phase relative to them. The second mode is characterized by the subpolar gyre and North subtropical gyre almost in quadrature, with North and South subtropical gyres out of phase. Thermal Rossby waves are very clear only in the second mode. These waves seem to be influenced by bottom topography. Known Atlantic meridional overturning circulation (AMOC) sea level fingerprints and AMOC strength indices are discussed in the bidecadal oscillations context.
 Interest in disentangling anthropogenically forced from natural climate variability has been an important driver for studies at interdecadal time scales [see, e.g., Solomon et al., 2011, and references therein]. In the present paper, interdecadal refers to climate variability on time scales from 10 to 100 years. At these scales, several studies have shown that the bidecadal band (20–30 years) is prominent in several oceanic and atmospheric variables [e.g., Venegas et al., 1998; Danabasoglu, 2008; Frankcombe and Dijkstra, 2009; Chylek et al., 2011, and references therein].
 In the North Atlantic Ocean, Frankcombe and Dijkstra , based on long-term tide gauge (TG) data and modeling, suggest that the bidecadal sea level (SL) signal in this region is linked to the variability of the upper layer ocean temperatures [see Dijkstra, 2013, and references therein]. Chylek et al.  analyzed the Arctic air temperature variability reconstructed from Greenland ice cores and presented robust evidence that the North Atlantic interdecadal variability is dominated by oscillations with a period of about 20 years. In the South Atlantic, Venegas et al.  also found that the interdecadal spectral power of sea surface temperature (SST) and sea level pressure is concentrated in an 18–25 year band. Vianna and Menezes  analyzed long-term tide gauge data from the southwestern Atlantic and found SL oscillations around 21 years.
 Different physical processes have been proposed to explain the North Atlantic bidecadal oscillations [Huck and Vallis, 2001; Von der Heydt and Dijkstra, 2007; Danabasoglu, 2008; Frankcombe et al., 2010; Dijkstra, 2013; Sevellec and Fedorov, 2013]. Idealized models and numerical simulations with heat and freshwater flux forcing suggest that these oscillations are mostly explained by internal ocean dynamics related to the Atlantic Meridional Overturning Circulation (AMOC). In Sevellec and Fedorov , the basic bidecadal oscillation mechanism involves the east-west density contrasts and westward propagating thermal Rossby waves. The phase speed of these waves is dominated by geostrophic self-advection of temperature anomalies relative to the mean meridional density gradient. The oscillations caused by these waves are shown to be in quadrature with AMOC oscillations. These processes are similar to those described by Huck and Vallis  and Dijkstra and collaborators [te Raa and Dijkstra, 2002; Von der Heydt and Dijkstra, 2007; Frankcombe et al., 2009, 2010].
 The above cited studies on the North and the South Atlantic Oceans are collectively quite provocative in the following sense: How do the bidecadal SL oscillations in the North Atlantic relate to those in the South Atlantic? Are there regional similarities between known AMOC SL fingerprints and bidecadal SL signatures?
 In the present paper, we investigate the SL bidecadal variability in both South and North Atlantic Oceans using the Simple Ocean Data Assimilation (SODA) reanalysis for the twentieth century [Giese and Ray, 2011]. In recent years, several papers [e.g., Carton et al., 2005; Giese and Ray, 2011, and references therein] have shown that SODA reproduces reasonably well the SL variability in longer time scales and constitutes a good tool to study these time scales in the lack of long-term and well-distributed observations. Our study is complemented by the analysis of long-term tide gauge (TG) data.
 The monthly mean SL and meridional velocity data belongs to version 2.2.4 of SODA reanalysis, which assimilates only hydrography and SST observations [Giese and Ray, 2011]. These data sets span from 1908 to 2008 and have grid resolution of 0.5°×0.5°. SODA SL includes influences of mass redistributions and steric components.
 We also analyzed 102 monthly mean SL time series from TGs provided by the Permanent Service for Mean Sea Level (PSMSL) [Woodworth and Player, 2003]. These TGs have records of at least 50 years with 75% or more of good data reduced to a common datum by the PSMSL, the RLR (Revised Local Reference) data set. Good data refer to data that passed by all quality control checks applied by the PSMSL. The missing data were interpolated as in Vianna and Menezes . SLs were corrected for the glacial isostatic adjustment [Peltier, 2004] and for inverted barometer effects using the Hadley Centre Sea Level Pressure data set [Allan and Ansell, 2006].
3 Bidecadal Signals, AMOC Indices, and Analysis
 Bidecadal SL signal extraction was done using the method described in Vianna and Menezes . The method consists in projecting the original SL data into subjectively chosen nonoverlapping period bands by using Singular Spectrum Analysis (SSA) and Maximum Entropy Method (MEM) [Ghil et al., 2002], as described in the supporting information. In the present work, we focus on the bidecadal band. The supporting information also contains a brief discussion on the constraints of the SSA-based method, mainly related to TGs, for readers interested in this issue.
 The propagating space-time structures of the SODA bidecadal band were analyzed using Complex Hilbert Empirical Orthogonal Functions (CEOF) [see, e.g., Venegas et al., 1998]. Prior to the CEOF, the SL bidecadal data set was averaged into annual mean fields. To help the interpretation of the CEOF modes, three auxiliary bidecadal indices were calculated: (i) the subpolar gyre index (SPG), defined as the SL averaged over the region 55°W–30°W and 50°N–65°N, (ii) the North subtropical gyre index (NSG) over the region 65°W–40°W; 25°N–40°N, and (iii) the South subtropical gyre index (SSG) over the region 40° W–15°W; 35°S–20°S.
 Additionally, we calculated two AMOC strength indices (AMOC-N and AMOC-S) from the SODA meridional volume transport stream function given by , where v is the meridional velocity, zb is the bottom depth, x, y, z, and t are longitude, latitude, depth, and time, respectively. Note that the Mediterranean Sea has been excluded from the ψ calculation. The AMOC-N (AMOC-S) was defined as the ψ(y,z,t) averaged between 30°N–45° N (25°S–10°S) and 500–1800 m depth. Since we are interested in the interdecadal variability, we linearly detrended both indices and smoothed them with a 5 year running mean. We also extracted the bidecadal oscillations using SSA from the original detrended indices.
4 Bidecadal Oscillations in SODA and TGs
 In SODA, the SL bidecadal band accounts for 19.5% of the signal variance. From 102 TGs analyzed here, 75 stations have spectral power in the bidecadal band (variance >5% of their interdecadal signals) (Figure S1, supporting information). Typical amplitudes of bidecadal oscillations are of order 3–6 cm in both TG and SODA data sets as shown in Figure S1c. No remarkable differences can be seen between the bidecadal amplitudes from TGs (circles) and the amplitudes illustrated in the background map from SODA, except for TG station located at 25°S;48°W. To determine the dominant periods within the bidecadal band, MEM analyses were performed for those TGs with varbidec>10%. We found that most of the TGs have spectral peaks between 21 and 24 years (45 TGs), while 22 TGs have spectral peaks around 28 years, but without any noticeable spatial distribution. The CEOF analysis of the SODA bidecadal band shows dominance of 22–24 year periods (see next section).
 Although SL from SODA and TGs are not exactly equivalent in their definitions, as explained by Carton et al. , and SODA has limitations on coastal regions, the amplitudes of the bidecadal signals and spectral peaks from both data sets are quite consistent in the Atlantic Ocean.
4.1 Space-Time Structure of SODA Bidecal Oscillations
 The first two CEOF modes, denoted here as M1 and M2, explain 70% of the total bidecadal variance, with M1 accounting for 40.1% and M2 for 29.9%, respectively. Figure 1 shows the temporal characteristics (amplitudes and phase angles) of M1 and M2 modes. The usual sawtooth graph for the phase angles gives cycle periods between 22 and 24 years. The M1 mode has dominant amplitudes between 1915 and 1965, and M2 dominates from the mid-1960s onward. Zero amplitudes for the M1 mode are found in 1910 and 1988, while M2 has near zero amplitude in 1930 (Figure 1b).
 The M1 mode is characterized by North and South subtropical gyres in phase and the tropical (off-equatorial) and subpolar regions in opposite phase relative to the subtropical gyres (Figures 1 and 3a).
 The sequence of M1 reconstructed snapshots in Figure 1 starts in 1931, when the North and South subtropical gyres are in their SL maximum positive anomalies, while the subpolar gyre and the high latitudes in South Atlantic (south of 40°S) present negative SL anomalies (see also Figure 3a). Notice the absence of a SL zonal gradient over the Equator. In 1936, the SL signatures are still negative in the South Atlantic high latitudes and in the subpolar gyre. The signatures are also negative in the shelf and continental slope of eastern North America, suggesting a displacement of the Gulf Stream axis to the south. This is the onset of the so-called subpolar gyre-Gulf Stream path dipole, corresponding to a known SL AMOC maximum fingerprint [Zhang, 2008, and references therein]. This AMOC SL fingerprint corresponds to a strong (near maximum) AMOC strength state (Figure S2b). In this epoch, the AMOC-S index is also positive, though smaller than the AMOC-N (Figure S2c). In the 1936 snapshot, notice the onset of an equatorial tongue with positive SL anomalies in the Gulf of Guinea embedded in a region (10°N–10°S) with negative anomalies. In 1941, the SL anomalies are positive in the subpolar gyre and in the South Atlantic high latitudes and negative in the North and South subtropical gyres. The snapshot of 1946 shows an opposite phase to that of 1936, with the onset of an equatorial negative SL signature in the Gulf of Guinea. The opposite dipole SL AMOC fingerprint indicates the onset of a weak AMOC state, which agrees with the AMOC-N strength index (Figure S2b, grey shading). The transition state in 1951 shows an opposite phase to the 1941. In 1956, the M1 structure returned to the initial 1931 state, again with zero equatorial zonal gradient in the Gulf of Guinea.
 A comparison between the M2 (Figure S3) and M1 snapshots reveals remarkable differences between these modes. The M2 mode presents different large-scale symmetries as compared to M1. The in-phase symmetries of the North and South subtropical gyres observed in the M1 mode no longer occur in M2 (Figure 3b). Moreover, the subtropical gyres are not in opposite phase relative to the subpolar regions. The small amplitudes of the NSG index reflect the meridional (dipolar) asymmetry between the northern (30–40°N) and the southern (20–30°N) regions of the North subtropical gyre, which when averaged gives a low amplitude NSG index.
 In the M2 snapshots, the subpolar gyre circulation has been somewhat quiescent during the 1980s and 1990s, with no clear signature of the Zhang  dipole AMOC fingerprint, in contrast to M1. The absence of dipole-type fingerprints in the M2 snapshots agrees with the M2 SL indices shown in Figure 3b, at which the subpolar gyre and the North subtropical gyre indices are now in quadrature, although the AMOC-N index (Figure S2d) shows a relatively strong signature in the 1980s. These facts suggest that the dipole-type fingerprint for the AMOC strength may be associated to processes influencing the M1 mode, which are different from M2 as described in section 4.2.
 The NSG, SSG, and SPG indices for the bidecadal band, which include the M1 and M2 modes, are shown in Figure 3c. Between 1930 and 1970, when the M1 mode is dominant, the subtropical gyres are almost in phase, and the subpolar gyre is in opposite phase relative to them. Before 1930 and after 1970, when the M2 mode is dominant, this symmetry does not occur. The indices in Figure 3c suggest that the bidecadal oscillations of the SSG are quite regular. In contrast, in the Northern Hemisphere, the SPG and NSG indices present abnormal small amplitudes and weak bidecadal signatures around 1984–1994, a fact also apparent in the M1 indices.
 The bidecadal band in the AMOC indices explains 30.4% (AMOC-N) and 32.2% (AMOC-S) of the interdecadal variance. The AMOC bidecadal indices are almost in phase and have similar amplitude before 1970 when M1 is dominant (Figure S2d). After 1970, while the AMOC-N bidecadal amplitude is weakly decaying, the AMOC-S amplitude is weakly growing. Notice that the AMOC-N 5 year running mean index also shows a damping in the AMOC strength variability after 1970. In SODA, the AMOC bidecadal signal in the South Atlantic precedes the North Atlantic signal by an increasing number of years, clearly visible after 1970 when the M2 mode dominates.
4.2 Rossby-Like Westward Propagation
 Several Hovmoeller diagrams from different latitudes (and average latitudes) in both North and South Atlantic were analyzed to determine whether SODA SL bidecadal band and CEOF reconstructed modes show signatures of westward propagating waves. Only the M2 mode has distinguishable westward propagation signatures, but not M1 (e.g., Figure 4, at 42°N and 40°S). The M2 diagram at 42°N shows a westward propagating positive signal between 1970 and 1980, which is very similar to that shown by Frankcombe et al. . The diagram also shows westward propagating positive signals in 1940–1950 and 1990–2000.
 Local propagation discontinuities appear in the Hovmoeller diagrams at longitudes corresponding to the presence of abrupt bottom topography, as ridges and shelf slopes. For example, at 42°N, westward propagation is seen only in the M2 mode to the west of 30°W, the longitude of the Mid-Atlantic Ridge (MAR). The M1 diagram at 42°N is dominated by standing waves between three bottom topographic features (the Canadian coast, the western shelf slope at 50°W, and the MAR). In this diagram, an eastward weak signal propagation is observed east of the MAR, which is also seen in the M2 and bidecadal band (Figures 4b and 4c). At 40°S, the MAR is located at 10°W and the Argentinian shelf slope is at 50°W. In M1, the signal propagation is eastward between the shelf slope and the MAR, but to the east of the MAR, the signal is westward (Figure 4d). In M2, the propagation is westward between the MAR and the Argentinian shelf slope.
 The analyses of the Hovmoeller diagrams suggest that bottom topography strongly scatters extratropical thermal bidecadal Rossby waves. The scattering of dynamic β-induced Rossby waves from mid-ocean ridges has been studied by few authors [e.g., see Owen et al., 2005, and references therein]. They found that if the density variation is confined to a thin thermocline, a large amount of incident Rossby wave energy is efficiently reflected by small-amplitude ridges. However, the influence of bottom topography on the bidecadal Rossby waves is outside of the scope of the present paper.
5 Summary and Conclusions
 CEOF analysis of the SODA bidecadal band gave two basic modes M1 and M2, with M1 dominating in 1915–1965 and M2 from mid-1960s onward. The long-term time-dependent change of mode dominance in bidecadal SL can be interpreted as a structural-type regime shift which seems to be different from the known types (see Overland et al.  for concepts and definitions). The onset of a regime shift in the bidecadal oscillations has been detected around 1970, when the M1 amplitudes are smaller and M2 is starting to dominate. The changes in the bidecadal oscillations between 1970 and 1990 occur at the same epoch of a regime shift in European climate [Sutton and Dong, 2012; Zhang, 2008]. Perhaps not coincidentally, a remarkable regime shift in 1990 has also been recorded in the southern Benguela shelf, as described in detail by Blamey et al. . This regime shift caused drastic changes in the rock lobster fishery of South Africa with great ecological and socioeconomic impacts.
 The M1 mode is characterized by states with the North and South subtropical gyres in phase while the tropical, the South Atlantic in high latitudes, and the subpolar gyre are in opposite phase relative to the subtropical gyres. In contrast, the M2 mode is characterized by the subpolar gyre and the North subtropical gyre almost in quadrature, with North and South subtropical gyres out of phase. The M2 mode also presents clear thermal Rossby waves, which seem to be influenced by bottom topography. Structures resembling known AMOC SL fingerprints in the North Atlantic [e.g., Zhang, 2008] are found only in the M1. The fingerprints are in agreement in timing with the maximum/minimum amplitudes of the SODA AMOC strength indices. The times of onset of an eastern equatorial anomaly perturbations might be a useful equatorial SL fingerprint for the AMOC bidecadal oscillations.
 Thanks to PSMSL and the SODA teams for the data made available on the web. We thank the two anonymous reviewers for their constructive comments and suggestions, which significantly contributed to improve the quality of the paper. We also thank Helen Phillips (UTAS) for her criticism and Petr Chylek (Los Alamos) for inviting one of us (M.L.V.) to present a talk on this theme on the Third Sta. Fe Conference on Global and Regional Climate Change (31 October to 4 November 2011) based on which this Letter was written.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.