Abstract

Multidecadal SST variability is studied in idealized one- and two-ocean-basin configurations, using simulations with the Modular Ocean Model. The authors demonstrate that the multidecadal variability on the global “conveyor type” circulation is localized in the North Atlantic Ocean. Interbasin exchange processes determine the locations where regions of deep-water formation occur and induce a localization of SST multidecadal anomalies in the Atlantic. The physics of this localization is subsequently investigated by considering more equatorially symmetric background flows in two-basin and one-basin configurations. A cross-equatorial flow in the Atlantic induces the localization of the multidecadal variability in the North Atlantic. By using the mechanism of multidecadal variability as proposed in 2002 by Te Raa and Dijkstra in a single-hemispheric configuration, the physics of these localization processes can be explained.

1. Introduction

It has now been about a decade since it was demonstrated that spontaneous multidecadal variability can appear in simple ocean-only models (Greatbatch and Zhang 1995; Chen and Ghil 1995). In the calculations in these papers, an ocean in a single-hemispheric three-dimensional basin was first forced by a time-independent meridional temperature gradient under restoring conditions, and the equilibrium flow state was determined. Next, the heat flux of this state was diagnosed and used to force the flow in a subsequent integration. In the latter simulation, multidecadal variability, for example, in the meridional overturning circulation (MOC) and in the temperature field, appeared spontaneously.

Over the last few years, the physical mechanism causing this multidecadal variability in these idealized models has been clarified. The oscillation appears because the large-scale equilibrium flow obtained under restoring conditions is unstable under prescribed heat flux conditions. In this case, an internal mode of variability, referred to as the multidecadal mode (MM), grows on the equilibrium flow. The MM is therefore an eigensolution of the linear stability problem of the equilibrium state and has a particular time scale and spatial pattern that are set by the parameters in the problem. An analysis of the interaction of this internal mode and the equilibrium state (on which it grows) has lead to a description of the propagation features in the pattern of the MM and of the mechanism why the MM can obtain a positive growth factor (Colin de Verdière and Huck 1999; Huck and Vallis 2001; Te Raa and Dijkstra 2002).

In case of only temperature forcing, the propagation mechanism of temperature anomalies associated with the MM can be described as follows. A warm anomaly in the north-central part of the basin causes a positive meridional perturbation temperature gradient, which induces—via the thermal wind balance—a westward zonal surface flow (Fig. 1a). The anomalous anticyclonic circulation around the warm anomaly causes southward (northward) advection of cold (warm) water to the east (west) of the anomaly, resulting in westward propagation of the warm anomaly. Owing to this westward propagation, the zonal perturbation temperature gradient becomes negative, inducing a negative surface meridional flow (Fig. 1b). The resulting upwelling (downwelling) perturbations along the northern (southern) boundary cause a negative meridional perturbation temperature gradient, inducing an eastward zonal surface flow, and the second half of the oscillation starts. The crucial elements in this oscillation mechanism are the phase difference between the zonal and meridional surface flow perturbations and the westward propagation of the temperature anomalies (Te Raa and Dijkstra 2002). The growth of this pattern occurs through a positive correlation of temperature anomalies causing the flow variations and the flow-induced temperature perturbations (Colin de Verdière and Huck 1999). Note that this physical mechanism appears quite robust. One crucial aspect is the propagation of a temperature anomaly in a background potential vorticity field set only by the meridional temperature gradient of the equilibrium flow. Another is the response of the large-scale circulation to the temperature changes in the basin. Although lateral boundaries and vertical and horizontal mixing processes influence this response, the major balances controlling it are geostropic and hydrostatic. The suggested mechanism is also in agreement with the many sensitivity results in Huck et al. (1999), where it is, for example, shown that the β effect and convective mixing (adjustment) are not central for the multidecadal variability to occur.

Fig. 1.

Schematic diagram of the oscillation mechanism associated with the multidecadal mode. The phase difference between (a) and (b) is about π/2. See text and Te Raa and Dijkstra (2002) for further explanation.

Fig. 1.

Schematic diagram of the oscillation mechanism associated with the multidecadal mode. The phase difference between (a) and (b) is about π/2. See text and Te Raa and Dijkstra (2002) for further explanation.

Subsequent studies have tried to link the multidecadal variability in these idealized ocean-only models to the multidecadal variability as found in general circulation models (Delworth et al. 1993; Delworth and Mann 2000; Cheng et al. 2004; Kravtsov and Ghil 2004; Dong and Sutton 2005). One approach has been to trace the multidecadal variability through a hierarchy of ocean models, that is, by including continental boundaries, bottom topography, salinity, and wind forcing (Te Raa et al. 2004). To decide whether the physical mechanism associated with the MM is causing the multidecadal variability, the phase difference between the anomalies in the meridional overturning streamfunction (ΨM) and the zonal overturning streamfunction (ΨZ) has been used. It was shown (Dijkstra et al. 2006) that the North Atlantic Ocean continental boundaries deform the sea surface temperature pattern of the MM to a pattern qualitatively very similar to that seen in GCMs (Delworth et al. 1993) and in observations (Kushnir 1994). This pattern of variability is often referred to as the Atlantic Multidecadal Oscillation (AMO).

One of the problems connecting the physics of the MM with that in GCMs and observations, however, is the limited spatial domain of the single-hemispheric models. In reality, there is a cross-equatorial flow, and complete upwelling does not occur in the North Atlantic. This cross-equatorial flow may strongly affect the response of the meridional overturning circulation to temperature (or more general, density) anomalies in the northern part of the basin. In addition, the Atlantic is also coupled to the Pacific Ocean through the Southern Ocean, and this connection may affect the spatial pattern of the multidecadal variability in the North Atlantic.

In this paper, we systematically investigate the effect of cross-equatorial flow and interbasin exchange on the multidecadal variability in the Atlantic and show that, under the present asymmetry of the meridional overturning circulation, where deep-water formation occurs in the North Atlantic (and not in the North Pacific), the multidecadal variability becomes localized in the North Atlantic. We use the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model (MOM) in idealized single-basin and two-basin double-hemispheric configurations to simulate the multidecadal variability. We use an ocean-only model, in order to study the mechanism of the oceanic multidecadal variability. We expect that in a coupled atmosphere–ocean model the same oscillations would occur. The SST anomalies would then be damped by the atmosphere, which would lead to smaller amplitudes of the variability. This is, indeed, observed in most GCM studies Delworth et al. (1993). Here, we are interested in relations between qualitative properties of the mean state and its multidecadal variability, and therefore, the approach using an ocean-only model is justified.

In section 2, results are presented for an idealized two-basin (Atlantic and Pacific) configuration. The impact of cross-equatorial flow and interbasin exchange on the spatial pattern and time scales of the multidecadal variability are analyzed in section 3 with the help of different forcings and additional geometrical configurations. The results are summarized and discussed in section 4.

2. The two-basin configuration

We will focus in this section on wind- and buoyancy-driven ocean flows in a double-basin Atlantic–Pacific configuration (Fig. 2) similar to that used in Marotzke and Willebrand (1991).

Fig. 2.

Schematic view of the two-basin configuration.

Fig. 2.

Schematic view of the two-basin configuration.

The meridional extent of each basin is 64° from pole to equator; the zonal extent of each basin is 60°. The continental barrier between the basins is 15° wide and extends to 48°S; periodic lateral boundary conditions are prescribed south of this latitude. In the southern channel there are two sills: in the middle a sill with a height of 2100 m and at the boundary of the domain a sill with a height 1100 m; otherwise the depth of each basin is a constant 4500 m. The zonal extent of the sill in the middle is 15° (of which 7.5° is 2100 m high) and the zonal extend of the sill at the domain boundary is 7.5°.

a. Model

All computations in this study have been done with version 3.1 of the GFDL Modular Ocean Model. An extensive description of the equations, their discretization, and the solution methods in this model is given in Pacanowski and Griffies (1999). We use the rigid-lid version of the model, in which the vertical velocity is exactly zero at the ocean–atmosphere boundary. No-slip conditions for the velocity are imposed at the continental boundary, while slip conditions are assumed at the bottom boundary. At the continental boundaries and at the bottom, heat and salt fluxes are zero. The model domain (Fig. 2) is discretized into an equidistant horizontal grid with a resolution of 3.75° in longitude and 4° in latitude. In the vertical we use a nonequidistant grid with resolutions varying from 50 m at the surface to 550 m at the bottom. In total, there are 15 vertical layers.

The wind stress forcing (Pa) is prescribed as in Bryan (1987):

 
formula
 
formula

where ϕ and θ are the longitudinal and latitudinal coordinates, respectively, and τ0 is the amplitude of the wind forcing.

We will use several different surface boundary conditions for temperature and salinity: Spinup of the model runs will be done under restoring boundary conditions, different equilibira of the meridional overturning circulation will be determined under mixed boundary conditions, and finally, the multidecadal variability will be studied under flux boundary conditions.

In the case of restoring conditions, the sea surface temperature and sea surface salinity are restored (with time scales τT and τS) to prescribed profiles TS and SS, defined as

 
formula
 
formula

where T0 = 15°C is a reference temperature, S0 = 34.7 psu a reference salinity, (ΔT, ΔS) are typical equator-to-pole temperature and salinity differences, and θn = 64°N is the northern boundary of the domain. The restoring time scale is taken as 30 days for both temperature and salinity. Note that restoring the sea surface temperature and salinity with such a short time constant, in practice, means that we approximately prescribe the sea surface temperature and salinity itself.

In the case of mixed boundary conditions, the surface freshwater flux, as diagnosed from an earlier simulation with restoring boundary conditions is prescribed, while the temperature is again restored to the profile TS. Last, in the case of prescribed flux boundary conditions, also the surface heat flux is diagnosed from an earlier simulation and both surface fluxes are prescribed.

We use two different values for the equator-to-pole temperature and salinity differences: In case S (the “strong circulation case”) we use ΔT = 20°C and ΔS = 2 psu, while in case W (the “weak circulation case”) we use ΔT = 10°C and ΔS = 1 psu. We have chosen these two cases (W and S) to get an impression on the dependence of the period and pattern of the multidecadal variability on the strength of the background flow.

In MOM the density is calculated by fitting a third-order polynomial to the United Nations Educational, Scientific, and Cultural Organization equation of state (Gill 1982) at each vertical level. We use constant coefficients for the horizontal (KH) and vertical (KV) mixing of heat and salt, and for horizontal (AH) and vertical (AV) mixing of momentum. The parameters for the standard case in the MOM are listed in Table 1. Since convection is not resolved by the hydrostatic model, an implicit mixing scheme is used as a variant of convective adjustment. This means that, in unstably stratified regions, the vertical mixing coefficient KV is increased. As we are only interested in the qualitative feature of the localization of patterns of multidecadal variability, a more detailed representation of mixing processes is not needed.

Table 1.

Standard values of parameters used in the numerical calculations. Here Ω is the rotation rate of the earth, r0 is the earth’s radius, D is the maximum depth of the ocean basin, ρ0 is the reference density of seawater, τT and τS are the restoring time scales in the case of prescribed surface temperature and salinity, AV and AH are the vertical and horizontal momentum mixing coefficients, KV and KH are the vertical and horizontal tracer mixing coefficients, Cp is the heat capacity of water, g is the gravitational acceleration, T0 and S0 are the seawater reference temperature and salinity, Hm is the thickness of the surface ocean layer, and τ0 is the amplitude of the wind stress forcing.

Standard values of parameters used in the numerical calculations. Here Ω is the rotation rate of the earth, r0 is the earth’s radius, D is the maximum depth of the ocean basin, ρ0 is the reference density of seawater, τT and τS are the restoring time scales in the case of prescribed surface temperature and salinity, AV and AH are the vertical and horizontal momentum mixing coefficients, KV and KH are the vertical and horizontal tracer mixing coefficients, Cp is the heat capacity of water, g is the gravitational acceleration, T0 and S0 are the seawater reference temperature and salinity, Hm is the thickness of the surface ocean layer, and τ0 is the amplitude of the wind stress forcing.
Standard values of parameters used in the numerical calculations. Here Ω is the rotation rate of the earth, r0 is the earth’s radius, D is the maximum depth of the ocean basin, ρ0 is the reference density of seawater, τT and τS are the restoring time scales in the case of prescribed surface temperature and salinity, AV and AH are the vertical and horizontal momentum mixing coefficients, KV and KH are the vertical and horizontal tracer mixing coefficients, Cp is the heat capacity of water, g is the gravitational acceleration, T0 and S0 are the seawater reference temperature and salinity, Hm is the thickness of the surface ocean layer, and τ0 is the amplitude of the wind stress forcing.

To analyze the solutions we calculate the meridional overturning streamfunctions for each basin separately, that is, the Atlantic meridional overturning (AMOC) streamfunction, referred to as ΨA, and the Pacific meridional overturning (PMOC) streamfunction, ΨP. Furthermore, sea surface temperatures are diagnosed for all simulations.

b. Results: Multidecadal variability

Just as in Marotzke and Willebrand (1991), we specify ΔT, ΔS, and τ0 and integrate the model to equilibrium under restoring conditions. The model reaches an equilibrium flow state after 3500 years of integration for case W (ΔT = 10°C, ΔS = 1), and after 4000 years for case S (ΔT = 20°C, ΔS = 2). We assume an equilibrium to be reached when the surface heat flux, averaged over the whole domain, becomes smaller than 5 × 10−4 W m−2. While the short restoring time scales limit the spinup time substantially, the surface fluxes are relatively large, and therefore we get relatively strong overturning circulations.

From the equilibrium solution under restoring boundary conditions, we diagnose the freshwater flux and continue the integration under mixed boundary conditions. By perturbing the freshwater flux slightly in the first 500 years of this integration and integrating for another 1500 years with the unperturbed freshwater flux, we are able to obtain four different flow solutions (conveyor, northern sinking, southern sinking, and inverse conveyor) as equilibrium solutions under mixed boundary conditions as they were found in Marotzke and Willebrand (1991). The patterns of the meridional overturning streamfunction ψM in the Atlantic and Pacific of the conveyor state are plotted in Fig. 3 for both cases W and S.

Fig. 3.

Equilibrium patterns of the meridional overturning streamfunction (for the conveyor circulation) under mixed boundary conditions of (a) ψA and (b) ψP for case W (ΔT = 10, ΔS = 1.0 psu) and (c) ψA and (d) ψP for case S (ΔT = 20, ΔS = 2.0 psu). These patterns are determined from the average over the last 500 years of integration under mixed boundary conditions.

Fig. 3.

Equilibrium patterns of the meridional overturning streamfunction (for the conveyor circulation) under mixed boundary conditions of (a) ψA and (b) ψP for case W (ΔT = 10, ΔS = 1.0 psu) and (c) ψA and (d) ψP for case S (ΔT = 20, ΔS = 2.0 psu). These patterns are determined from the average over the last 500 years of integration under mixed boundary conditions.

The strength of the Atlantic MOC for case W is about 30 Sv (Sv ≡ 106 m3 s−1) and that of the Pacific about −25 Sv (Figs. 3a–b). In this simple configuration, there is no Antarctic Bottom Water formation in the Atlantic and hence the northern sinking cell exists over the whole basin. Because of the larger buoyancy forcing in case S (Figs. 3c–d), the strength of both meridional overturning in the Atlantic and Pacific is larger, but the spatial patterns hardly change compared to those of case W.

From the “conveyor” equilibrium state we next diagnose the surface heat flux and integrate the model further in time for 1500 years, prescribing both the diagnosed surface heat and freshwater fluxes. The time series in Figs. 4a–b demonstrate that the flow becomes oscillatory with a period that depends on the strength of the buoyancy forcing.

Fig. 4.

(a) Time series of the maximum values of ψA (dotted) and |ψP| (solid) for (a) the weak conveyor state (case W) and (b) the strong conveyor state (case S). Difference pattern of SST between the positive and negative phase of the oscillation in the Atlantic overturning streamfunction for (c) the weak conveyor state (case W), contour interval: 0.2°C, and (d) for the strong conveyor state (case S), contour interval: 0.4°C.

Fig. 4.

(a) Time series of the maximum values of ψA (dotted) and |ψP| (solid) for (a) the weak conveyor state (case W) and (b) the strong conveyor state (case S). Difference pattern of SST between the positive and negative phase of the oscillation in the Atlantic overturning streamfunction for (c) the weak conveyor state (case W), contour interval: 0.2°C, and (d) for the strong conveyor state (case S), contour interval: 0.4°C.

For the weaker buoyancy forcing (case W), an oscillation with a period of about 45 yr develops with a peak-to-peak variability in ψA of about 28 Sv. The variability in ψP is much smaller (about 4 Sv) and there is a phase difference between the AMOC and PMOC of about 12 yr, with the AMOC leading the PMOC (Fig. 4a). The peak-to-peak variability in both basins slightly increases with increasing buoyancy forcing (Fig. 4b) and the period of the oscillation decreases to about 28 yr. The SST difference pattern between year 6940 (positive peak AMOC in Fig. 4a) and year 6965 (negative peak AMOC in Fig. 4a) indicates (Fig. 4c) that the largest anomalies are present in the North Atlantic. A similar pattern (Fig. 4d) appears for the stronger conveyor state (case S).

As the SST anomaly pattern appears localized in the North Atlantic, we study the propagation of SST anomalies through Hovmöller plots along 42°N (Fig. 5). Note that the contour interval differs in each of the panels. As time is increasing upward along the vertical axis, there is clear westward propagation of the SST anomalies visible in the Atlantic under the weaker buoyancy forcing (Fig. 5a). For case S, the amplitude is larger, the period is smaller, and the pattern is more stationary; the westward propagation is restricted to the most western part of the basin (Fig. 5b). Contrary to the Atlantic, there is eastward propagation in the Pacific (Figs. 5c–d), with the largest propagation speed in the middle of the basin. Note, however, that the size of the anomalies in the North Pacific is much smaller than in the North Atlantic. The anomalies are smaller in strength for case W than for case S, although the mean state and the variability of the overturning in the Pacific hardly change (cf. Fig. 3). As in the Atlantic, the period becomes shorter and the pattern slightly more stationary under the stronger buoyancy forcing (Fig. 5d).

Fig. 5.

Hovmöller plot of SST anomalies along 42°N in the Atlantic (a) for the weak conveyor state (case W) and (b) for the strong conveyor state (case S). Contour intervals are 0.2°C. Hovmöller plot of SST anomalies along 40°N in the Pacific (c) for the weak conveyor state and (d) for the strong conveyor state. Contour intervals are 0.01°C. The vertical axis in all panels shows time in years.

Fig. 5.

Hovmöller plot of SST anomalies along 42°N in the Atlantic (a) for the weak conveyor state (case W) and (b) for the strong conveyor state (case S). Contour intervals are 0.2°C. Hovmöller plot of SST anomalies along 40°N in the Pacific (c) for the weak conveyor state and (d) for the strong conveyor state. Contour intervals are 0.01°C. The vertical axis in all panels shows time in years.

3. Localization of multidecadal variability

From the results in the previous section, it appears that the largest amplitudes of the multidecadal SST anomalies are located in the region of sinking of the equilibrium flow obtained under mixed boundary conditions, that is, in the North Atlantic. In this section, we explore the connection between the asymmetries of the background flow and the localization of multidecadal variability in more detail by considering different buoyancy forcing distributions and basin geometries.

a. The near-asymmetric two-basin configuration

To approach this connection systematically, we first investigate the impact of the asymmetry of the meridional overturning in the Pacific and Atlantic. Thereto we use the solution obtained by the spinup in the simulation for case S (ΔT = 20°C, ΔS = 2) under restoring boundary conditions. In this near-equatorially symmetric equilibrium state, the MOC is almost identical in the Atlantic and Pacific. From this spinup state we diagnose the heat and freshwater fluxes and continue the integration for 1500 years. The mean overturning circulation remains about the same as the spinup state, and the solutions ψA and ψP are plotted in Figs. 6a–b. The MOC in each basin is similar with the northern cell stronger than the southern one. The latter is caused by the absence of a zonal pressure gradient in the unblocked part of the zonal southern channel, which inhibits any geostrophic southward flow—the so-called Drake Passage effect (Toggweiler and Samuels 1995).

Fig. 6.

Meridional overturning streamfunction for the near-equatorially symmetric circulation case (case S). The streamfunctions are averaged over the last 500 years of the simulation under flux boundary conditions, with (a) ψA and (b) ψP. In (a) and (b) the contour interval is 5 Sv. (c) Time series of the maximum values of ψA (dotted) and ψP (solid). (d) Difference pattern of SST between the positive and negative phase of the oscillation (as set by the overturning oscillation in the Atlantic basin); contour intervals: 0.4°C.

Fig. 6.

Meridional overturning streamfunction for the near-equatorially symmetric circulation case (case S). The streamfunctions are averaged over the last 500 years of the simulation under flux boundary conditions, with (a) ψA and (b) ψP. In (a) and (b) the contour interval is 5 Sv. (c) Time series of the maximum values of ψA (dotted) and ψP (solid). (d) Difference pattern of SST between the positive and negative phase of the oscillation (as set by the overturning oscillation in the Atlantic basin); contour intervals: 0.4°C.

The times series of maximum values of ψA and ψP indicate that, again, multidecadal variability occurs (Figs. 6c–d). The peak-to-peak amplitudes of the oscillations are now about equal for the two basins (12 Sv). The period of the oscillation is about 50 yr, and the phase difference between the Atlantic and the Pacific is such that the Pacific is leading the Atlantic by about 1/4 of the period (or the Atlantic is leading the Pacific by about 3/4 of the period). The SST difference pattern between year 5460 (positive peak ψA in Fig. 6c) and year 5491 (negative peak ψA in Fig. 6c) indicates (Fig. 6d) that equal size and amplitude anomalies are present in both the Atlantic and Pacific.

Again, we study the propagation of SST anomalies through Hovmöller plots along 42°N (Fig. 7). Note that, contrary to Fig. 5, the contour values are now the same in each panel of Fig. 7. Both in the Pacific and Atlantic, the propagation of the SST anomalies is westward and the zonal extend of the patterns is similar. From the results of this near-symmetric configuration, we see that the localization of patters of the multidecadal variability is closely linked to the regions of deep-water formation. With a strong northern overturning cell in both basins, similar multidecadal variability develops in both basins. The role of the interbasin exchange in the conveyor solution is therefore to localize the multidecadal variability in the Atlantic.

Fig. 7.

(a) Hovmöller plot of SST anomalies along 42°N (a) in the Atlantic and (b) in the Pacific basin for the near-equatorially symmetric circulation state (case S). The vertical axis in both panels shows time in years; contour interval: 0.2°C.

Fig. 7.

(a) Hovmöller plot of SST anomalies along 42°N (a) in the Atlantic and (b) in the Pacific basin for the near-equatorially symmetric circulation state (case S). The vertical axis in both panels shows time in years; contour interval: 0.2°C.

b. The single-basin configuration

The multidecadal variability in the near-symmetric case of the previous section is not that different in each of the basins and it suggests determining the physics of the localization of the variability in a single-basin configuration. We therefore consider next a configuration of only one 60° wide basin extending from 64°S to 64°N. The spinup with the same restoring surface boundary conditions as for the double-basin flow yields an equatorially symmetric flow state usually referred to as the TH state (Thual and McWilliams 1992) with sinking at both poles; we use case S only (ΔT = 20°C and ΔS = 2 psu).

From this symmetric state, the freshwater flux is diagnosed and a northern sinking pole-to-pole solution (usually referred to as an NPP state; Thual and McWilliams 1992) is determined under mixed boundary conditions. Again, this is done by perturbing the freshwater flux for 500 years and then continuing the integration for another 1500 years with the unperturbed freshwater flux. From this NPP solution, the heat flux is diagnosed and the integration is continued over 1500 years under both prescribed heat and freshwater fluxes. The mean strength of the MOC is strongly asymmetric with only sinking in the north and has a strength of about 35 Sv (Fig. 8a). The strength of the MOC oscillates in time, now with a period of about 24 yr (Fig. 8b). The spatial pattern of the temperature anomalies associated with the oscillation is again localized in the northern part of the basin where the sinking takes place, even though the basin is fully equatorially symmetric (Fig. 8c). There is slight westward propagation of the SST anomalies (Fig. 8d), but otherwise the oscillation appears fairly stationary in the western part of the basin.

Fig. 8.

Analysis of multidecadal variability on the NPP state in the single-basin configuration. (a) Mean meridional overturning streamfunction ψ, averaged over the last 500 years of simulation under prescribed flux conditions. (b) Time series of the maximum value of ψ. (c) Difference pattern of SST anomalies between the positive and negative phase of the oscillation in ψ; contour interval is 0.5°C. (d) Hovmöller diagram of SST anomalies along 42°N. The contour interval is 0.5°C; the vertical axis shows time in years.

Fig. 8.

Analysis of multidecadal variability on the NPP state in the single-basin configuration. (a) Mean meridional overturning streamfunction ψ, averaged over the last 500 years of simulation under prescribed flux conditions. (b) Time series of the maximum value of ψ. (c) Difference pattern of SST anomalies between the positive and negative phase of the oscillation in ψ; contour interval is 0.5°C. (d) Hovmöller diagram of SST anomalies along 42°N. The contour interval is 0.5°C; the vertical axis shows time in years.

To investigate the role of the location of deep-water formation, we finally look at the variability on an equatorially symmetric background state. This situation is obtained in the single-basin configuration by diagnosing both surface heat and freshwater fluxes from the spinup (TH) state and continuing the integration for 1500 years from this flow state under prescribed flux conditions. In this symmetric case, the strength of the mean meridional overturning ψ is about 20 Sv (Fig. 9a). Note that in this case there is deep-water formation at both northern and southern high latitudes. The time series of the maximum value of ψ indicates that an oscillatory flow appears under prescribed flux conditions with a period of about 50 yr (Fig. 9b). This oscillation occurs simultaneously in both overturning cells. The associated pattern of SST anomalies is equatorially symmetric with strong anomalies in the western part of the basin at both northern and southern high latitudes (Fig. 9c). Again, the characteristic westward propagation of the SST anomalies is seen in the Hovmöller plot (Fig. 9d) along 42°N. In the Southern Hemisphere, the anomalies propagate westward as well (not shown). This equatorially symmetric case can be considered as a superposition of two single-hemispheric basins with both a symmetric mean SST state (with an antisymmetric MOC without cross-equatorial transport) and a symmetric SST pattern of multidecadal variability. Hereby it connects to the single-hemispheric configuration, which has been studied in detail (Te Raa and Dijkstra 2002).

Fig. 9.

As in Fig. 8 but on the TH state in the single-basin configuration; contour interval is 0.2°C in (c) and 0.1°C in (d).

Fig. 9.

As in Fig. 8 but on the TH state in the single-basin configuration; contour interval is 0.2°C in (c) and 0.1°C in (d).

Comparing the results for the multidecadal variability around the TH state with that around the NPP state, it follows that the role of the cross-equatorial transport in the Atlantic MOC is to localize the multidecadal variability in the North Atlantic.

4. Summary and discussion

Using simulations with a low-resolution version of MOM, we have investigated the relationship between the asymmetries of the meridional overturning and the spatial pattern of multidecadal oscillations. In our simulations, these oscillations occur when an ocean-only model is forced by prescribed surface momentum, heat, and freshwater fluxes. The multidecadal oscillations are visible in a temporal variation of the strength of the meridional overturning circulation. Associated with the strengthening and weakening of this circulation is a sea surface temperature pattern that in all cases consists of propagating midlatitude SST anomalies. Note that due to the prescribed flux conditions, we underestimate the atmospheric damping of SST anomalies and therefore overestimate the amplitude of the multidecadal oscillations in each simulation. In a coupled ocean–atmosphere model, one would never expect such large peak-to-peak amplitudes and, indeed, in most GCMs the amplitudes are much smaller (Delworth et al. 1993). As in this study, we are interested in relations between qualitative properties of the mean state and its multidecadal variability; the approach using prescribed flux conditions is justified. We have used a relatively high value of the horizontal viscosity in the ocean model. The sensitivity of the temperature oscillations to horizontal viscosity has been studied within the same model in Te Raa et al. (2004). It turned out that the existence of the temperature modes is not changed significantly with different horizontal viscosity.

The different configurations studied in this paper are summarized in Table 2. In the equatorially symmetric single-basin configuration, there is a unique solution for the background meridional overturning circulation with sinking at both poles and upwelling at the equator (Fig. 9). The SST anomaly pattern associated with the multidecadal variability is equatorially symmetric and the anomalies propagate westward in both hemispheres.

Table 2.

Summary of the different configurations studied in this paper. The last column indicates the sections in this paper (I) and the companion paper (Dijkstra and von der Heydt 2007) (II) in which the configurations are discussed.

Summary of the different configurations studied in this paper. The last column indicates the sections in this paper (I) and the companion paper (Dijkstra and von der Heydt 2007) (II) in which the configurations are discussed.
Summary of the different configurations studied in this paper. The last column indicates the sections in this paper (I) and the companion paper (Dijkstra and von der Heydt 2007) (II) in which the configurations are discussed.

The westward propagation of the SST anomalies has been explained for a Northern Hemisphere (NH) single-basin configuration by Te Raa and Dijkstra (2002) and the mechanism was described in the introduction (Fig. 1). In the Southern Hemisphere (SH), the propagation of SST anomalies is also westward according to this mechanism. In dimensional quantities and local Cartesian coordinates x, y, and z the thermal wind balance becomes

 
formula
 
formula

where f is the local Coriolis parameter, αT the thermal compressibility, and ũ, υ̃, and , the zonal and meridional velocity and temperature anomalies, respectively. In the Southern Hemisphere, the background meridional temperature gradient is positive. A positive SST anomaly in the south induces a southward perturbation meridional velocity anomaly (υ̃ > 0) to the west of the anomaly (∂/∂x > 0) according to the thermal wind balance (with f < 0). Similarly, it induces a northward meridional velocity anomaly east of the temperature anomaly. The velocity anomalies then advect warm (cold) water southward (northward) to the west (east) of the anomaly, and hence the temperature anomaly propagates westward (Fig. 10).

Fig. 10.

Schematic diagram of the oscillation mechanism associated with the multidecadal mode in the Southern Hemisphere. The phase difference between (a) and (b) is about π/2. See text for further explanation.

Fig. 10.

Schematic diagram of the oscillation mechanism associated with the multidecadal mode in the Southern Hemisphere. The phase difference between (a) and (b) is about π/2. See text for further explanation.

With the help of the local phase speed of temperature anomalies we can again see why the temperature anomalies propagate westward also in the Southern Hemisphere. The local phase speed c of the temperature anomalies (which is positive when westward) was estimated in Te Raa and Dijkstra (2002) to depend on the background state according to

 
formula

where u is the background zonal velocity (which is positive when eastward), T is the background SST, and α̂ is a constant depending on the vertical background stratification. For the background state, u is positive in both hemispheres. In the NH, the second term in parentheses is negative because ∂T/∂θ is negative and the Coriolis term sinθ is positive. In Te Raa and Dijkstra (2002) it has been shown that the second term is larger than the first term, and therefore c is positive. In the SH ∂T/∂θ is positive, but the Coriolis term is negative, and therefore the propagation direction is the same as in the NH.

Owing to the westward propagation, as explained for the NH, the zonal perturbation temperature gradient becomes negative and, because of the negative Coriolis parameter in the SH, it induces a positive surface meridional flow [Eq. (3a); Fig. 10b]. If the situation is the same as on the NH, that is, if there is mean downwelling at southern high latitudes, the mean meridional flow is opposite to the flow in the NH, and therefore the effect of the perturbation meridional flow on the mean flow is the same as in the NH and the second half of the oscillation begins.

Under mixed boundary conditions for the background state, the salt advection feedback can be responsible for asymmetric solutions due to symmetry breaking. Therefore, in the single-basin configuration, also an asymmetric overturning circulation (the NPP state) is possible. This background flow has sinking in the northern high latitudes, cross-equatorial transport, and upwelling in the southern high latitudes (Fig. 8). For such an asymmetric background state, the pattern of the multidecadal mode is strongly asymmetric with the largest SST anomalies in the sinking region of the background flow. This asks for a physical explanation why SST anomalies remain small in upwelling regions of the background flow, that is, the southern high latitudes.

By considering the potential energy budget along an oscillation cycle, it was found in Te Raa and Dijkstra (2002) that buoyancy work changes play a crucial role in sustaining the oscillation. With infinitesimal perturbations on the background state, the evolution of the volume-integrated potential energy of the perturbations Ũ = 〈− zT〉 (which is proportional to the potential energy of the perturbations) can be written as

 
formula

where angle brackets indicate volume-integrated quantities. Here, only the dominant terms are taken into account and, for example, vertical mixing is neglected. In a situation of mean downwelling (w < 0), −〈w〉 is positive for a warm SST anomaly as relatively warm water is transported downward, which increases the potential energy of the flow. As analyzed in Te Raa and Dijkstra (2002), the signs of 〈w〉 and 〈T〉 should be opposite to sustain the oscillation. Note that T is determined up to a constant T0 under prescribed flux conditions, but this plays no role as is also determined up to the same constant. We choose T0 = 15°C and refer to temperature anomalies with respect to T0.

Consider now a situation in which > 0 in either Northern or Southern Hemisphere; here T < 0 and is determined through ũ, υ̃ and the thermal wind balance. As the perturbation flow is anticyclonic, < 0 and hence 〈T〉 > 0. To obtain a sustained oscillation, we should have 〈w〉 < 0, which is the case when there is mean downwelling; that is, w < 0. On the other hand, when there is mean upwelling, that is, w > 0, an oscillation cannot be sustained because both advection mechanisms have the same effect on the potential energy. In conclusion, independent of whether it is in the Northern or in the Southern Hemisphere, the oscillation is sustained if the background flow has mean downwelling, and the oscillation is inhibited when there is mean upwelling. This explains the localization of the SST anomaly pattern in the northern part of the basin in the case of the NPP background flow. The northward cross-equatorial surface flow associated with this state induces a preference for localization of the multidecadal variablity in the Northern Hemisphere.

These considerations now also explain why in the near-symmetric two-basin configuration (Fig. 6), where the MOC is almost the same in both basins, we find similar multidecadal oscillations with SST patterns localized in the Northern Hemisphere of both basins. In this two-basin configuration, there is a weak interbasin exchange and weaker downwelling in the Southern Hemisphere than in the Northern Hemisphere. Hence, based on the locations and strength of downwelling, we expect the largest SST anomalies in the Northern Hemisphere.

Last, when interbasin exchange appears in a background flow of “conveyor type,” the SST anomalies in the Pacific become much smaller than in the Atlantic. In the Atlantic basin there is deep-water formation in the Northern Hemisphere and therefore the strongest signal of variability is located there. The Pacific basin has a southern sinking solution in this case, and from the considerations above we would expect the multidecadal variability to be located in the Southern Hemisphere. However, because of the zonal flow through the southern channel meridional flow anomalies are very small because of the Drake Passage effect and hence the propagation of anomalies will be inhibited.

The description of these physical mechanisms of the localization of multidecadal variability is one of the main contributions of this study. The results are far too idealized configurations to be directly compared to results of fully coupled GCMs or observations. In both GCMs and observations, many more physical processes and scales (here neglected) are involved in the variability, in particular the influence of the atmospheric variability. Our results, however, provide further support for the view of physics of the Atlantic Multidecadal Oscillation as suggested in Dijkstra et al. (2006). One of the weaknesses there was the absence of the cross-equatorial flow in the background state such that all upwelling occurred north of the equator. The results here have shown that, with cross-equatorial flow, the SST anomaly pattern becomes localized in the North Atlantic anyway, so it does not matter (for multidecadal variability) where the upwelling occurs in the mean flow. The results here also indicate that the Pacific “decadal oscillation” (PDO) cannot be explained by the same physical mechanism as the AMO. Because of the lack of northern sinking in the North Pacific, no (or only weak) multidecadal variability is expected to occur.

Acknowledgments

This project was funded in part by NSF Grant OCE-0425484 (HD). The first author acknowledges personal support through a VENI grant by the Netherlands Organisation for Scientific Research (NWO).

REFERENCES

REFERENCES
Bryan
,
F.
,
1987
:
Parameter sensivity of primitive equation ocean general circulation models.
J. Phys. Oceanogr.
,
17
,
970
985
.
Chen
,
F.
, and
M.
Ghil
,
1995
:
Interdecadal variability of the thermohaline circulation and high-latitude surface fluxes.
J. Phys. Oceanogr.
,
25
,
2547
2568
.
Cheng
,
W.
,
R.
Bleck
, and
C.
Rooth
,
2004
:
Multidecadal thermohaline variability in an ocean-atmosphere general circulation model.
Climate Dyn.
,
22
,
573
590
.
Colin de Verdière
,
A.
, and
T.
Huck
,
1999
:
Baroclinic instability: An oceanic wavemaker for interdecadal variability.
J. Phys. Oceanogr.
,
29
,
893
910
.
Delworth
,
T. L.
, and
M. E.
Mann
,
2000
:
Observed and simulated multidecadal variability in the Northern Hemisphere.
Climate Dyn.
,
16
,
661
676
.
Delworth
,
T. L.
,
S.
Manabe
, and
R. J.
Stouffer
,
1993
:
Interdecadal variations of the thermohaline circulation in a coupled ocean–atmosphere model.
J. Climate
,
6
,
1993
2011
.
Dijkstra
,
H.
, and
A.
von der Heydt
,
2007
:
Localization of multidecadal variability. Part II: Spectral origin of multidecadal modes.
J. Phys. Oceanogr.
,
37
,
2415
2428
.
Dijkstra
,
H.
,
L.
Te Raa
,
M.
Schmeits
, and
J.
Gerrits
,
2006
:
On the physics of the Atlantic Multidecadal Oscillation.
Ocean Dyn.
,
56
,
36
50
.
Dong
,
B.
, and
R. T.
Sutton
,
2005
:
Mechanism of interdecadal thermohaline circulation variability in a coupled ocean–atmosphere GCM.
J. Climate
,
18
,
1117
1135
.
Gill
,
A. E.
,
1982
:
Atmosphere–Ocean Dynamics.
Academic Press, 662 pp
.
Greatbatch
,
R. J.
, and
S.
Zhang
,
1995
:
An interdecadal oscillation in an idealized ocean basin forced by constant heat flux.
J. Climate
,
8
,
82
91
.
Huck
,
T.
, and
G.
Vallis
,
2001
:
Linear stability analysis of the three-dimensional thermally-driven ocean circulation: Application to interdecadal oscillations.
Tellus
,
53A
,
526
545
.
Huck
,
T.
,
A.
Colin de Verdiére
, and
A. J.
Weaver
,
1999
:
Interdecadal variability of the thermohaline circulation in box-ocean models forced by fixed surface fluxes.
J. Phys. Oceanogr.
,
29
,
865
892
.
Kravtsov
,
S.
, and
M.
Ghil
,
2004
:
Interdecadal variability in a hybrid coupled ocean–atmosphere–sea ice model.
J. Phys. Oceanogr.
,
34
,
1756
1775
.
Kushnir
,
Y.
,
1994
:
Interdecadal variations in North Atlantic sea surface temperature and associated atmospheric conditions.
J. Climate
,
7
,
141
157
.
Marotzke
,
J.
, and
P.
Willebrand
,
1991
:
Multiple equilibria of the global thermohaline circulation.
J. Phys. Oceanogr.
,
21
,
1372
1385
.
Pacanowski
,
R. C.
, and
S. M.
Griffies
,
1999
:
The MOM3 manual. NOAA/GFDL Ocean Group Tech. Rep. 4, 680 pp
.
Te Raa
,
L. A.
, and
H. A.
Dijkstra
,
2002
:
Instability of the thermohaline ocean circulation on interdecadal time scales.
J. Phys. Oceanogr.
,
32
,
138
160
.
Te Raa
,
L. A.
,
J.
Gerrits
, and
H. A.
Dijkstra
,
2004
:
Identification of the mechanism of interdecadal variability in the North Atlantic Ocean.
J. Phys. Oceanogr.
,
34
,
2792
2807
.
Thual
,
O.
, and
J. C.
McWilliams
,
1992
:
The catastrophe structure of thermohaline convection in a two-dimensional fluid model and a comparison with low-order box models.
Geophys. Astrophys. Fluid Dyn.
,
64
,
67
95
.
Toggweiler
,
J. R.
, and
B.
Samuels
,
1995
:
Effect of Drake Passage on the global thermohaline circulation.
Deep-Sea Res.
,
42
,
477
500
.

Footnotes

Corresponding author address: Anna von der Heydt, Institute for Marine and Atmospheric Research Utrecht, Department of Physics and Astronomy, Utrecht University, 3584CC Utrecht, Netherlands. Email: a.s.vonderheydt@phys.uu.nl