On the basis of the multidecadal component of a Fram Strait sea ice export reconstruction and on a sea surface temperature proxy for changes in the ocean circulation, a bifurcation diagram for two cycles of the Atlantic Ocean multidecadal oscillation is constructed. It suggests a hysteresis behavior that is consistent with nonlinear convective adjustment to changes in deep-water formation in the North Atlantic and with the meridional overturning circulation bistability associated with two distinct configurations of the North Atlantic subpolar gyre, simulated in response to idealized carbon dioxide increase. The nonlinear dynamics of the Atlantic Ocean circulation emphasized here on the basis of observational data adds to the hysteresis behavior shown in theoretical and numerical studies.
The large-scale ocean circulation largely driven by freshwater and heat fluxes is known as the thermohaline circulation (THC). Through its meridional overturning circulation (MOC), the ocean transports a large amount of heat (∼1 PW) from low to high latitudes in the Atlantic Ocean basin (Ganachaud and Wunsch 2000). There is mounting evidence from paleodata that MOC was involved in past abrupt climate changes (e.g., Broecker 1966, 1997; Barber et al. 1999; McManus et al. 2004). On the basis of theoretical concepts (e.g., Stommel 1961) and complex models (Bryan 1986; Manabe and Stouffer 1988), it was shown that THC exhibits nonlinear behavior. Its nonlinearity results from three properties: it possesses multiple equilibria, it has two distinct states that correspond to the same forcing, and it can suffer transitions between them. All three features can be synthetically represented in the stability/bifurcation diagram, which is a graphical representation of the equilibrium response of the MOC to slowly varying forcing. Thermohaline hysteresis was reproduced in various coupled circulation models, with the forcing being represented by freshwater (e.g., Stocker and Wright 1991; Rahmstorf et al. 2005), temperature (Knorr and Lohmann 2007), or wind (Ashkenazy and Tziperman 2007).
Rahmstorf (1995a) emphasized the distinction between the advective-related and convective-related hysteresis. The former is generated by the salt positive feedback, in which a strong MOC advects more saline waters toward the deep-water formation regions in the North Atlantic. This further enhances the meridional circulation (Stommel 1961). The convective-related hysteresis is due to the accumulation of freshwater near the surface when convection stops and leads to multiple equilibria with different convection patterns (Lenderink and Haarsma 1994). It was recently argued that the hysteresis behavior, which is not detected in full dynamical models, could be an artifact of models of intermediate complexity (Liu et al. 2009). Although the bistability of the ocean circulation was emphasized in models of different complexity (Stommel 1961; Rahmstorf et al. 2005), evidence for such dynamics in the real world has not yet been presented.
To investigate the THC hysteresis behavior in observational data, one has to know the forcing and the ocean response over at least a complete cycle of its variation. Various numerical experiments have shown that the MOC is sensitive to North Atlantic freshwater forcing (e.g., Stouffer et al. 2006). An important source of freshwater for the North Atlantic sector is represented by the sea ice export from the Arctic Ocean through Fram Strait, which can have a significant influence on MOC variations (Häkkinen 1999).
The interdecadal variability in the Northern Atlantic sector is dominated by the Atlantic multidecadal oscillation (AMO; Kerr 2000), which was first identified in the global sea surface temperature (SST) fields (Folland et al. 1986; Schlesinger and Ramankutty 1995). Numerical integrations have shown that its specific uniform North Atlantic SST structure reflects changes in the MOC (Knight et al. 2005), in a linear way (Latif et al. 2004). On the basis of observational data and previous numerical integrations, a physical mechanism based on ocean–atmosphere–sea ice interactions was proposed to explain the oscillatory nature of the AMO (Dima and Lohmann 2007). In this mechanism uniform North Atlantic SSTs induce a hemispheric dipolar structure in the atmosphere that affects the sea ice export through Fram Strait. The sea ice export influence on MOC represents a key link in this mechanism. The main idea of this investigation is to use information, derived from reconstructed and observational data, about the multidecadal Fram Strait sea ice export (FSSIE) and MOC changes, to construct a bifurcation diagram.
2. Data and methods
Two datasets are used in this study. Annual values of FSSIE for the 1820–2000 period were reconstructed on the basis of historical observations of multiyear sea ice southwest of Greenland (Schmith and Hansen 2003). The 181-yr record allows the identification of multidecadal variability through singular spectrum analysis (SSA; Vautard et al. 1992). This method is designed to extract information from short and noisy time series by providing data-adaptive filters that help to separate the record into statistically independent and narrow band components such as trends, oscillatory signals, and noise (Allen and Smith 1997).
Annual SST fields from the extended reconstructed SST, version 3, (ERSSTv3) dataset (Smith et al. 2008), extending over the 1854–2008 period, are used to derive a proxy index for MOC variations. These fields are used because they include an improved representation of multidecadal variability. The SST mode related to MOC changes is identified through the empirical orthogonal function (EOF) method (Lorenz 1956). The analysis was performed on global SST fields because a larger amount of data allows a better separation of distinct climate modes (Dima and Lohmann 2010). Before the analysis the globally uniform warming trend was removed by subtracting the mean of each global map from its grid points. Note that two complete AMO cycles are resolved by the instrumental SSTs over 155 yr.
A hysteresis diagram can be constructed only if the forcing extends over at least one cycle. If it would include information related to several time scales (e.g., a superposition of several periodicities), then the one-to-one-relation forcing-response of each cycle, which is the definitory element for a hysteresis diagram, is masked by the other time scales, and therefore this kind of behavior would not be visible in the phase-space representation.
Therefore, the first goal is to identify and separate the multidecadal component, presumably corresponding to AMO, in the FSSIE reconstruction. This record includes interannual to centennial variations (Fig. 1a; thin line), but no abrupt transitions between distinct regimes are visible. To increase the signal-to-noise ratio, two preliminary operations are performed on the data. First, a 7-yr running-mean filter is applied to the record (Fig. 1a; thick line) to remove the interannual variations. Second, an intercentennial component is identified through SSA. The eigenvalue spectrum is obtained by applying this method using an 80-yr window (Fig. 1b). The dominant pair of eigenvalues is associated with an intercentennial time series (Fig. 1c). Because of the dominance of this secular component in this analysis, a multidecadal component associated with the third eigenvalue plays a secondary role in explaining the variance in the record. However, it is of specific importance for this study. To emphasize the multidecadal component, a new time series is derived by subtracting the intercentennial signal (Fig. 1c) from the initial 7-yr running-mean-filtered reconstruction (Fig. 1a). Therefore, the residual record contains only decadal to multidecadal variability. Note that the results presented here do not depend on these preliminary operations.
A new SSA is performed on the residual record (Fig. 2a) using an 80-yr window. The first pair of eigenvalues in the spectrum (Fig. 2b) and the corresponding time EOFs, which show constant phase shift (Fig. 2d), are associated with a robust multidecadal signal, which explains 29% of variance in the time series. It shows maxima around 1835, 1900, and 1970 and minima around 1868, 1934, and 2000 (Fig. 1c; solid line). A very similar time component is obtained by applying a Fourier filter that retains periodic signals in the 60–80-yr band to the annual values of the FSSIE time series (Fig. 1c; dashed line). Note that, unlike Fourier analysis, SSA is efficient in identifying quasi-periodic signals with variable amplitude and phase.
The centennial component identified in the first SSA has only two extreme phases during the FSSIE period (1820–2000): the maximum before 1890 and the minimum after 1940 (Fig. 1c). During the rest of this period, the secular signal is in transition phases. Both of these extremes are quasi simultaneous (within one decade) with the corresponding extreme phases of the multidecadal component: the maximum before 1900 and the minimum before 1940 (Fig. 2c). Therefore, the most important part of the potential influence of the centennial component on the Atlantic meridional overturning circulation (AMOC), associated with its two extremes, appears to be masked by the corresponding phases of the multidecadal signal.
On the basis of numerical experiments that show that MOC is sensitive to sea ice export from the Arctic (Häkkinen 1999) and on observational studies emphasizing multidecadal coherent variations of freshwater and MOC (Dima and Lohmann 2007), the multidecadal component of the FSSIE record is considered as forcing for ocean circulation changes.
The second goal is to isolate the multidecadal time component associated with AMO, which is considered to be a proxy for MOC changes. For this reason, an EOF analysis is performed on the annual SST fields. The first EOF, explaining 18% of variance, is associated with ENSO, whereas the time component associated with the second EOF, explaining 11% of variance, is characterized by a trend starting in the first half of the twentieth century. The third EOF (Fig. 3b), explaining 7% of variance, is of specific importance here. Note that if a 15-yr running-mean filter is applied to the data before the analysis, then this EOF becomes the second dominant mode in the SST field. However, here we present only the EOF derived on the basis of annual SST fields, because the rapid transitions of interannual time scales are more pronounced in the associated time component. EOF3 has the typical AMO structure (Enfield and Mestas-Nuñez 1999), which includes quasi-uniform SST values in the North Atlantic and anomalies of opposite signs in the Southern Hemisphere (Fig. 3b). The associated time series, principal component 3 (PC3; Fig. 3a; solid black line), shows pronounced multidecadal variations superimposed on interannual and decadal fluctuations. It includes maxima during the 1880s, 1930s, and 2000 and minima during the 1910s and 1970s that correspond to the AMO extremes (Sutton and Hodson 2005). Note that, unlike the annual FSSIE time series (Fig. 1a), assimilated with the forcing, PC3 (Fig. 3a), as an MOC proxy, includes abrupt transitions.
Unlike FSSIE, which extends only in time, the SST data have both temporal and spatial dimensions, and therefore EOF analysis can be applied. This method acts as a spatial filter that separates the global pattern and the corresponding time series associated with multidecadal variability. The advantage of this specific filtering results from the properties of PC3 (Fig. 3a). It shows rapid transitions that extend over just several years but that are separated by several decades. The preservation of this mixture of time scales in PC3 was possible because of the spatial filtering performed by the EOF method. On the basis of the association between AMO and meridional overturning fluctuations emphasized in numerical experiments (Knight et al. 2005), PC3 is further used as a proxy for MOC changes. From this perspective, the presence of different time scales in PC3 represents a key aspect for the identification of nonlinear behavior of the Atlantic Ocean circulation.
c. Bifurcation diagram
To infer the MOC response time to freshwater forcing, the cross-correlation function between the multidecadal signal obtained from FSSIE (Fig. 2c) and PC3 (Fig. 3a) is calculated. This analysis emphasizes a significant correlation of −0.73 when FSSIE leads by 6 yr (Fig. 4). To test if this lagged relation is influenced by the trapezoidal shape of PC3, a new cross correlation was performed between the multidecadal component of FSSIE and the multidecadal component identified through SSA on the PC3. Note that this last component has a harmonic-like shape. A significant negative correlation of −0.96 is observed when the FSSIE multidecadal signal leads by 4 yr (Fig. 4).
Previous studies have shown that the North Atlantic SSTs represent a 2–3-yr lagged response to MOC changes (Latif et al. 2004), which are induced by the multidecadal component of FSSIE (Dima and Lohmann 2007). It was also shown that the MOC can respond quickly, in just 2–3 yr, to convective instabilities generated by freshwater forcing in the North Atlantic (Rahmstorf 1995a; Getzlaff et al. 2005). The observed Iceland sea ice extent anomaly, a proxy for the freshwater forcing from the Arctic, leads the changes in the Labrador Sea by 3 yr (Zhang and Vallis 2006), indicating the approximate propagation time scale of the salinity anomaly from the east Greenland coast to the Labrador Sea. On the basis of these studies, we assume that the North Atlantic SSTs describe the quasi-equilibrium MOC response to FSSIE recorded 4–8 yr before.
In view of these considerations, we show PC3 (as a proxy for MOC changes), for the 1873–2004 period, as a function of the multidecadal component of FSSIE (as a proxy for freshwater forcing), for the 1869–2000 time interval (Fig. 5). Therefore, a 4-yr lag between forcing and response is considered. For any lag in the 4–8-yr interval the results are similar, but for lead–lag relations of longer than 8 yr, the shape of the diagram starts to degenerate. To investigate how the filtering of PC3 affects its shape, three running-mean filters (of 5-, 11-, and 15-yr lengths) are alternatively applied to PC3.
In the diagram corresponding to the 5-yr running-mean filter (Fig. 5a), two stability curves associated with two AMO cycles are completed. The 1873–98 and 1925–65 periods correspond to the positive AMO phases, marked in Fig. 3a by straight blue lines. They are followed by rapid transitions during the intervals 1898–1904 and 1965–72 (Fig. 5a), which are marked by red straight lines in Fig. 3a. These rapid changes are leading to negative AMO phases extending over the 1904–12 and 1972–94 time intervals, which are further followed by positive AMO states. Overall, the diagram emphasizes two distinct states separated by rapid transitions. The positive AMO phase corresponds to relatively strong MOC, and the negative one is associated with weak overturning circulation.
These features of the representation are reproduced also when an 11-yr running-mean filter is applied to PC3 (Fig. 5b). The transitions are less abrupt, but the steady states are more clearly represented. A smoothed version of the diagram is obtained when a 15-yr running-mean filter is applied to PC3. It is clear from this representation that the second loop is shifted toward lower MOC values.
The three diagrams emphasize typical hysteresis properties: two distinct values of the overturning corresponding to the same forcing and quasi-equilibrium states linked by curves of relatively large slopes. It is important to observe that these properties are translated in the hysteresis diagram from PC3, which shows rapid decreases and slower increases in amplitude, separated by several decades-long quasi-steady states (Fig. 3b). Note the trapezoidal shape of PC3, which is typical for the time evolution of Dansgaar–Oeschger events in the North Atlantic (Dansgaard et al. 1993).
4. Discussion and conclusions
Two specific properties are observed in PC3 and in the diagrams representations. First, the quasi-stable states present slopes toward the other quasi-equilibrium states (Figs. 3a and 5). These features are shown in numerical experiments simulating rapid transitions of the overturning circulation under modern boundary conditions (e.g., Schulz et al. 2007) and hysteresis behavior of the Atlantic thermohaline circulation in response to freshwater input (Rahmstorf 1995a). Second, the transitions from the positive to the negative phase are faster than from weak to strong MOC states. Such asymmetry of the transitions is reproduced by models of various complexities (Stouffer et al. 2006).
Numerical experiments have shown that a uniform North Atlantic SST structure can be generated by variations in the MOC, which are induced in just several years by changes in the Labrador Sea deep-water formation (Rahmstorf 1995a; Getzlaff et al. 2005). This is supported also by observational studies that show changes in the Labrador convection that are consistent with the AMO evolution (Dickson et al. 1996; Yang 1999). This relatively short MOC adjustment time to convective changes is determined by the waves’ propagation time (Döscher et al. 1994). Such an MOC response was characterized by convectively induced hysteresis behavior, distinct from the advectively generated loop, which is typical for much longer time scales. Unlike the case of an advectively generated hysteresis, which includes an off state of the overturning, the convectively generated hysteresis includes states of relatively strong and weak MOC. Note that changes in the convection are sensitive mainly to local forcing and therefore can be induced by relatively small freshwater fluxes. Two separate states of the MOC, associated with two distinct configurations of the North Atlantic subpolar gyre, were also simulated in response to idealized carbon dioxide increase (Marzeion et al. 2010). It is interesting to observe that the AMO pattern shows maximum loadings in the North Atlantic subpolar gyre (Fig. 3b).
The distinction between the 1873–98 and 1925–65 states in the two hysteresis curves (Fig. 5a) is consistent with the multiple equilibria of the ocean (Lenderink and Haarsma 1994), which are linked to changes in the convection pattern in the North Atlantic (Rahmstorf 1995b). In numerical experiments, such changes are generated by shutdowns of the Labrador deep-water (LDW) formation (Rahmstorf 1995a). It was shown that the MOC can suffer rapid changes generated by jumps between on and off states of LDW formation (Schulz et al. 2007). Of interest is that, if the freshwater forcing is increased, the MOC spends more time in the off mode. This is also observed in the AMO time series (Fig. 3a), which shows a longer weak MOC state observed during the 1972–94 period than during the 1904–12 time interval (Fig. 3a). In correspondence, the most recent hysteresis curve is shifted toward weaker MOC states. This can be due to a slight change in the climate background conditions during the last century. The nonlinear dynamics of the Atlantic Ocean circulation emphasized here on the basis of observational data adds to the hysteresis behavior shown in theoretical and numerical studies.
We thank one reviewer for constructive comments that contributed to the improvement of the manuscript. The work has been supported by the Humboldt Foundation and the Alfred Wegener Institute for Polar and Marine Research through the PACES program. Mihai Dima was partially supported by CNCSIS/UEFISCSU, IDEI 31/2010 project, regarding part of the data analyses.
Corresponding author address: Mihai Dima, Faculty of Physics, University of Bucharest, Str. Atomistilor 405, CP MG-11, Bucharest-Măgurele, RO-76900, Bucharest, Romania. Email: firstname.lastname@example.org