Abstract

The response of an idealized Atlantic Ocean to wind and thermohaline forcing associated with the North Atlantic Oscillation (NAO) is investigated both analytically and numerically in the framework of a reduced-gravity model. The NAO-related wind forcing is found to drive a time-dependent “leaky” gyre circulation that integrates basinwide stochastic wind Ekman pumping and initiates low-frequency variability along the western boundary. This is subsequently communicated, together with the stochastic variability induced by thermohaline forcing at high latitudes, to the remainder of the Atlantic via boundary and Rossby waves. At low frequencies, the basinwide ocean heat content changes owing to NAO wind forcing and thermohaline forcing are found to oppose each other. The model further suggests that the recently reported opposing changes of the meridional overturning circulation in the Atlantic subtropical and subpolar gyres between 1950–70 and 1980–2000 may be a generic feature caused by interplay between the NAO wind and thermohaline forcing.

1. Introduction

The North Atlantic Oscillation (NAO) is the dominant mode of atmospheric variability in the North Atlantic sector (e.g., Hurrell 1995) and has a significant impact on the North Atlantic Ocean’s circulation and hydrographic properties through its modulation of air–sea momentum, heat, and freshwater fluxes. During the last 50 years, the NAO has exhibited large interannual and decadal variability, switching from its negative phase in the 1960s to strong positive phase in the late 1980s and early 1990s.

Hindcast simulations using ocean general circulation models (OGCMs) have been widely used to study the oceanic response to changes of the NAO (e.g., Häkkinen 1999; Eden and Willebrand 2001; Eden and Jung 2001; Eden and Greatbatch 2003; Dong and Sutton 2005; Böning et al. 2006; Lozier et al. 2008; Deshayes and Frankignoul 2008; Robson et al. 2012; Zhai and Sheldon 2012). During positive NAO years, the anomalous wind stress is generally found to spin up the subtropical and subpolar gyre circulation, whereas the enhanced heat loss at high latitudes, particularly in the Labrador Sea, leads to a strengthening of the meridional overturning circulation (MOC; see Visbeck et al. 2003 for a review). Although significant progress has been made over the last decade, detailed adjustment mechanisms remain unclear due, in part, to the complex nature of the OGCMs as well as to the lack of observations.

In a theoretical study, Marshall et al. (2001) argued that the meridional shift in the jet stream associated with the NAO, through anomalous wind stress curl, drives an anomalous “intergyre gyre” at midlatitudes between the climatological subtropical and subpolar gyres. The anomalous wind forcing of this intergyre gyre is coherent in space but stochastic in time,1 which initiates upper-ocean buoyancy anomalies that propagate westward as baroclinic Rossby waves. As a result, the strength of the intergyre gyre fluctuates in time, albeit at much lower frequencies than that of the imposed forcing. However, it is not clear what happens to these buoyancy anomalies when they arrive at the western boundary. It is possible that boundary waves may be excited that propagate southward along the western boundary, and after that communicate the buoyancy anomalies into the ocean interior in a similar fashion as described by Johnson and Marshall (2002a) for the upper-ocean adjustment to thermohaline forcing.

Zhai et al. (2011) studied the Atlantic heat content and sea level change in response to stochastic deep-water formation at high latitudes in the framework of a reduced-gravity model. They identified the “Rossby buffer” effect: high-frequency basinwide anomalies in heat content are confined to low latitudes whereas low-frequency anomalies extend to mid- and high latitudes in both hemispheres. However, the ocean heat content change in response to the wind forcing was left unexplored. There are a number of theoretical investigations on oceanic adjustment to idealized wind forcing (e.g., Frankignoul et al. 1997; Cessi and Louazel 2001; Primeau 2002; Cessi and Otheguy 2003; Sirven et al. 2007), but the focus has been on the thermocline variability, with little attention being paid to the response of the MOC and ocean heat content, in particular to the wind forcing associated with the NAO. Furthermore, there is the issue of the interplay between the NAO wind forcing and thermohaline forcing in determining the ocean heat content and transport variability.

The present study aims to investigate the response of an idealized Atlantic Ocean to wind and thermohaline forcing associated with the NAO in the context of a reduced-gravity model. The paper is organized as follows. In section 2, a quantitative theory is developed for the ocean response to NAO-related wind forcing. In section 3, the reduced-gravity model experiments and results are described. In section 4, we use the theory to explore the possible mechanism behind the recently reported opposing changes of the MOC in the Atlantic subtropical and subpolar gyres. Finally, in section 5, we summarize our key findings.

2. Theory

In this section we focus on providing a simple linear theory of the ocean response to the NAO-related wind and high-latitude thermohaline forcing in the framework of a reduced-gravity model. Readers are referred to Johnson and Marshall (2002a) and Zhai et al. (2011) for related theory of ocean heat content and MOC variability induced purely by high-latitude thermohaline forcing.

We consider a semienclosed rectangular domain that is open to the south, with 0 < x < Lx in the zonal direction and 0 < y < Ly in the meridional direction (Fig. 1). As the NAO wind forcing is dominated by the zonal wind stress anomaly that is largely uniform in the zonal direction over the North Atlantic, we hereafter consider only the zonally averaged zonal wind stress anomaly2, τx(y, t), and we further assume τx(y, t) vanishes approaching the northern and southern boundaries. Ekman pumping associated with this simplified NAO wind forcing is thus uniform in space in the zonal direction but stochastic in time.

Fig. 1.

Schematic of the rectangular model domain employed in section 2. The wind-forced Ekman upwelling, wEk, varies with the meridional coordinate, y. A thermohaline-forced outflow, TN, is prescribed at the northern edge of the domain. The model is not solved in the shaded deep-water formation region. The dotted lines indicate the western boundary region and equator, and the dashed line indicates the southern edge of the domain (where the basin connects to the Southern Ocean). A similar rectangular domain, except with spherical coordinates, is employed in section 3. See the main text for further details.

Fig. 1.

Schematic of the rectangular model domain employed in section 2. The wind-forced Ekman upwelling, wEk, varies with the meridional coordinate, y. A thermohaline-forced outflow, TN, is prescribed at the northern edge of the domain. The model is not solved in the shaded deep-water formation region. The dotted lines indicate the western boundary region and equator, and the dashed line indicates the southern edge of the domain (where the basin connects to the Southern Ocean). A similar rectangular domain, except with spherical coordinates, is employed in section 3. See the main text for further details.

Outside the western boundary layer, the linear dynamics are described by the momentum and continuity equations:

 
formula
 
formula
 
formula

Here u and υ are the zonal and meridional velocities, respectively, h is the anomaly in the layer thickness from its initial value H, f(y) is the Coriolis parameter, g′ is the reduced gravity, and ρ0 is a reference density.

Although presented in Cartesian coordinates and a rectangular basin for pedagogical simplicity, the theory is easily generalized to spherical geometry and realistic basin geometries. The solutions presented in section 3 are obtained in a basin bounded by latitude and longitude lines on the sphere, and in section 4 in a realistic Atlantic basin geometry.

a. Volume budget

Substituting for u and υ in (3) using (1) and (2) gives the forced long Rossby wave equation:

 
formula

where

 
formula

is the Ekman upwelling velocity,

 
formula

is the long Rossby wave speed, and β(y) = df(y)/dy is the meridional gradient of the Coriolis parameter.

The solution to (4) is obtained by integrating westward along the Rossby wave characteristics (e.g., Frankignoul et al. 1997; Cessi and Louazel 2001):

 
formula

where x = Lx is the longitude of the eastern boundary. In (7) we assume that the upper layer thickness anomaly along the eastern boundary, he(t), is uniform because of fast boundary wave propagation (Johnson and Marshall 2002a; Marshall and Johnson 2013).

Following Johnson and Marshall (2002a) and zonally integrating (4) from just outside the western boundary current region, x = δ, to the eastern boundary, we obtain

 
formula

where

 
formula

is the upper layer thickness anomaly just outside the western boundary current and Lx/c(y) is the Rossby wave basin-crossing time. Physically (8) indicates that the change of zonally integrated layer thickness at any given latitude is caused by wind Ekman pumping integrated across the basin as well as the difference between the thickness anomalies propagated by Rossby waves from the eastern boundary into the ocean interior, and propagated from the ocean interior into the western boundary current.

A further relation for the rate of change of layer thickness integrated across the basin is obtained by zonally integrating (3):

 
formula

where

 
formula

is the net northward volume transport.

Now combining (8) and (10), and neglecting the volume anomaly of the narrow western boundary region, gives

 
formula

Note that T(y, t) in (12) includes the meridional transport in both the western boundary current and the basin interior. Integrating (12) over the latitudinal extent of the domain gives

 
formula

where TN is the prescribed northward transport anomaly at the northern boundary associated with thermohaline forcing,

 
formula

is the northward transport anomaly across the southern boundary, fs = f(0) is the Coriolis parameter at the southern boundary, and we have used

 
formula

since τx vanishes at y = 0, Ly. In (14), we have assumed that the layer thickness anomaly in the southwestern corner of the domain vanishes, which is justified on the time scales considered in this paper due to the long adjustment time scales of the Pacific and Indian Ocean basins (Johnson and Marshall 2004).

Finally, combining (13) and (14), rewriting in terms of he, and then using (9) to substitute for hb, we obtain an equation for the eastern boundary layer thickness that represents the generalization of (14) in Johnson and Marshall (2002a) to include wind forcing:

 
formula

where

 
formula

The Rossby wave speed,

 
formula

is capped at the equatorial Rossby wave speed to prevent the integrals from diverging in (16).3 The terms on the right-hand side of (16) represent radiation of Rossby waves from the eastern boundary providing the memory of past wind and thermohaline forcing, basinwide wind-forced Ekman pumping, and outflow associated with thermohaline forcing at high latitudes, respectively. Notwithstanding the simplicity of the reduced-gravity model, (16) can be used to explore the relative importance of, and interplay between, wind and thermohaline forcing associated with the NAO in driving MOC and heat content anomalies, as detailed in the following sections.

b. MOC anomaly

Integrating (12) southward from the northern boundary gives the meridional transport as a function of latitude and time:

 
formula

Note that (17) includes the meridional transport in both the western boundary current and the basin interior.

Furthermore, since the wind stress is assumed to vanish at the northern boundary, the final term on the right-hand side of (17) is equivalent to the Ekman transport:

 
formula

Hence the geostrophic northward transport, Tg(y, t) = T(y, t) − TEk(y, t), is given by

 
formula

Substituting for hb from (9), we obtain the expression for the northward geostrophic transport across any latitude:

 
formula

Having determined the geostrophic northward transport in (20), we can, in turn, infer the western boundary layer thickness anomaly through

 
formula

similar to Cessi and Louazel (2001), but independent of the details of the momentum balance in the narrow frictional western boundary layer.

Note that the wind forcing influences MOC variability both directly, through the Ekman transport, TEk, and indirectly by modifying the layer thickness anomaly communicated by Rossby waves into the western boundary current in (20). Also note that the geostrophic transport, Tg(y, t), at any given latitude depends on the entire history of the wind forcing integrated over the whole model domain through the dependence of he on this basinwide forcing in (16). In particular, Tg(y, t) depends strongly on the history of wind Ekman pumping integrated over the whole area poleward of the latitude under consideration.4 As such, the wind-induced geostrophic transport variability at any given latitude cannot be diagnosed from a linear Rossby wave model driven by wind forcing at that single latitude alone. The same is also true for the thermocline depth on the western boundary [see (21)]. Physically, it is the boundary wave propagation along the western boundary that integrates the layer thickness anomalies arriving at the western boundary at latitudes farther to the north, thereby coupling wind forcing at these latitudes.

Furthermore, since the sea level anomaly is proportional to the upper layer thickness anomaly in the reduced-gravity model, (21) shows that the sea level variability along the east coast of the United States and Canada depends on the history of wind forcing over the whole ocean basin at higher latitudes to the north and, thus, cannot be predicted using models driven by wind forcing at a single local latitude such as Sturges and Hong (1995) and Frankignoul et al. (1997).

There are two geographic regimes associated with (17): regions under direct NAO wind forcing and regions to the south. At latitudes under direct influence of stochastic NAO wind forcing, the Ekman contribution, TEk, is also stochastic at any given latitude, and vanishes at the latitude where τx = 0, forming opposing meridional transport anomalies north and south of that latitude. The geostrophic transport anomaly, Tg, at any given latitude, on the other hand, depends on the time integral of stochastic Ekman pumping over the whole area farther to the north and thus varies at much lower frequencies.

In regions to the south of the NAO wind forcing, the ocean feels only the low-frequency hw that integrates stochastic Ekman pumping along Rossby and boundary wave characteristics over the whole area under wind forcing. The low-frequency hw then propagates equatorward along the western boundary, eastward along the equator and poleward along the eastern boundary, followed by the slow radiation of Rossby waves off the eastern boundary. This pattern is in contrast to the ocean’s response to stochastic deep-water formation at high latitudes, where the upper layer thickness anomaly along the western boundary exhibits both high-frequency and low-frequency variability, both of which spread into the interior of the model domain through boundary and Rossby wave adjustment processes (Zhai et al. 2011). Consequently, the MOC in the thermohaline-forced case varies at all frequencies, although the high-frequency component tends to be confined in the hemisphere in which it is generated (Johnson and Marshall 2002b).

c. Ocean heat content anomaly

In the reduced-gravity model, the ocean heat content change at each latitude, is proportional to the zonally integrated layer thickness anomaly,

 
formula

where ΔΘ is the conservative temperature difference between the abyssal and surface layer and is a constant close to the specific heat capacity at the sea surface of the present ocean (McDougall 2003). Substituting (7) into (22) gives

 
formula

For further discussion, in the limit of no wind forcing, the reader is referred to Zhai et al. (2011). It is worth pointing out that the spectrum of in (23) is a function of latitude, which may provide an explanation for the observed strong interannual variability of the subtropical property changes that stand in sharp contrast to the nearly decadal variability of the subpolar gyre recently reported by Lozier et al. (2010).

3. The reduced-gravity model experiment

We now examine the anomalies in the MOC and ocean heat content in response to recent NAO-related wind and thermohaline forcing in the idealized reduced-gravity sector model.

a. Numerical model description

The nonlinear, numerical reduced-gravity model used in this study is similar to that described in Johnson and Marshall (2002a) and Zhai et al. (2010). The governing equations for the model are the following:

 
formula
 
formula

Here u(u, υ) is the horizontal vector velocity, ξ = ∂υ/∂x − ∂u/∂y is the relative vorticity, B = gh + (u2 + υ2)/2 is the Bernoulli potential, k is a unit vertical vector, and Kh is the lateral viscosity coefficient. The model domain is an idealized sector ocean 40° wide and stretching from 45°S to 75°N, with vertical sidewalls and a resolution of 0.25°. The background model layer thickness is 750 m, with a reduced gravity of 0.02 m s−2 and lateral viscosity of 103 m2 s−1. No-slip and no-normal flow boundary conditions are applied. Sponges are applied at the northernmost and southernmost regions of the model domain to damp out any waves approaching these boundaries. In particular, the northern sponge layer prevents any communication of thickness anomalies from the east to the west along the northern boundary. With the parameters chosen, it takes the Rossby waves roughly 7 years to cross the basin at latitudes just south of the northern sponge layer.

b. Experiment design

1) NAO wind forcing

In the first experiment, the reduced-gravity model is forced solely by the wind stress anomaly associated with the NAO. The wind stress anomaly is obtained in a similar way as in Eden and Jung (2001). First, the spatial pattern of the wind stress associated with the NAO is estimated by regressing the monthly National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis wind stress (Kalnay et al. 1996) on the NAO index (Hurrell 1995) for the period 1950–2010. The regressed wind stress is concentrated in the North Atlantic Ocean and reveals an anticyclonic wind stress curl situated at the gyre boundary that drives an intergyre gyre (not shown; Marshall et al. 2001). The regressed zonal wind stress in the Atlantic Ocean is then zonally averaged (Fig. 2a) and multiplied by the monthly NAO index from 1950 to 2010 to drive the reduced-gravity model. In other words, the reduced-gravity model is forced by the zonal-mean intergyre gyre wind stress anomaly that pulses in time with the NAO index.

Fig. 2.

(a) Zonal-mean zonal wind stress regressed on the NAO index in the Atlantic Ocean. (b) TN prescribed at the northern boundary of the model in the experiments with thermohaline forcing.

Fig. 2.

(a) Zonal-mean zonal wind stress regressed on the NAO index in the Atlantic Ocean. (b) TN prescribed at the northern boundary of the model in the experiments with thermohaline forcing.

2) NAO thermohaline forcing

In the second experiment, the NAO thermohaline forcing is simply prescribed as a northward transport anomaly, TN, at the northern boundary of the model, following Johnson and Marshall (2002a), representing the deep-water formation process at high latitudes (outside the model domain).5 The intensity of deep ocean convection at high latitudes in the North Atlantic and associated dense water renewals have been found to be closely linked to the phase of the NAO (e.g., Dickson et al. 1996; Curry et al. 1998; Marshall and Schott 1999). During positive NAO years, cold and dry air outbreaks from the nearby continent to the Labrador Sea in late winter tend to be more frequent and more severe, which can lead to enhanced convective activity and deep-water formation, while the opposite is true during negative NAO years. This signal has often been traced downstream to the subtropics along the North Atlantic Deep Western Boundary Current (e.g., Talley and McCartney 1982; Fine and Molinari 1988; Curry et al. 1998), strongly suggesting that variability of deep convection in the Labrador Sea can influence the strength of the Atlantic MOC.6 In the present process study, TN is, for simplicity, assumed to vary linearly with the NAO index for the period 1950–2010, with a standard deviation of ~2 Sv (1 Sv ≡ 106 m3 s−1; Fig. 2b; Josey et al. 2009; Wunsch and Heimbach 2013). Although the choice of TN here is highly idealized, the exact magnitude of TN is only of quantitative importance in the proposed framework for understanding the dynamical ocean response to the NAO forcing.

3) NAO wind and thermohaline forcing

In the final experiment, the reduced-gravity model is forced by both NAO wind and thermohaline forcing in order to investigate the interplay between the two.

c. Results

1) NAO wind forcing

Figure 3 shows the time evolution of the upper layer thickness anomaly during years of negative NAO (1956, 1962, and 1972) and positive NAO (1992, 1994, and 1996) in the experiment with only NAO wind forcing. The anomalous positive wind stress curl associated with the negative phase of the NAO before 1956 reduces the upper layer thickness between 35° and 55°N, creating an anomalous cyclonic gyre circulation there. There is also indication of a weaker anticyclonic gyre circulation farther to the south owing to the relatively weak negative wind stress curl there before 1956. The negative layer thickness anomaly generated by the “intergyre” wind forcing in the 1950s is shown to leak equatorward along the western boundary, eastward along the equator, and then poleward along the eastern boundary, followed by the slow radiation of Rossby waves into the ocean interior. Over the following two decades of negative NAO, the leakage of negative anomalies from the cyclonic gyre intensifies, and eventually fills the whole model domain by the year 1972. During the late 1980s and early 1990s when the NAO is switched to its strong positive phase, the anomalous negative wind stress curl deepens the upper layer between 35° and 55°N and drives an anomalous anticyclonic gyre there. The positive layer thickness anomaly, again, leaks equatorward and eventually spreads over the whole model domain by the year 1996. Our results thus suggest that the NAO wind stress forces a basinwide upper layer thickness/ocean heat content change via a time-dependent “leaky” gyre circulation.

Fig. 3.

Time evolution of the upper layer thickness anomaly (m) during years of (top row) negative NAO (1956, 1962, and 1972) and (bottom row) positive NAO (1992, 1994, and 1996) in the experiment with only NAO wind forcing. The color scale is saturated in regions north of 35°N, where the thickness anomalies can reach ±40 m.

Fig. 3.

Time evolution of the upper layer thickness anomaly (m) during years of (top row) negative NAO (1956, 1962, and 1972) and (bottom row) positive NAO (1992, 1994, and 1996) in the experiment with only NAO wind forcing. The color scale is saturated in regions north of 35°N, where the thickness anomalies can reach ±40 m.

The zonally averaged layer thickness at latitudes under direct influence of wind forcing varies at both high and low frequencies, but is dominated by the large negative anomalies before the early 1970s and positive anomalies in the late 1980s and early 1990s (Fig. 4a). In contrast, in regions south of about 15°N where there is almost no direct wind forcing, only a multidecadal signal emerges. This multidecadal signal has a phase lag that varies with latitude, owing to the decrease in Rossby wave speed with increasing latitude (Zhai et al. 2011). There is a noticeable amount of layer thickness variability in the tropics (Figs. 3 and 4), suggesting that the low-frequency ocean variability generated by the NAO wind forcing in the extratropics can, via oceanic teleconnections, modulate the thermocline depth and thereby potentially exert an influence on sea surface temperature in the tropics where the atmosphere is particularly sensitive to small sea surface temperature anomalies. Figure 4b shows the zonally averaged layer thickness predicted from the theory using (16) and (23), which broadly agrees with that in the numerical model experiment.

Fig. 4.

Time evolution of the zonal-mean layer thickness anomaly (m) at different latitudes from the case with only NAO wind forcing: (a) numerical model experiment and (b) theory.

Fig. 4.

Time evolution of the zonal-mean layer thickness anomaly (m) at different latitudes from the case with only NAO wind forcing: (a) numerical model experiment and (b) theory.

The meridional transport anomaly, T, reveals a complex pattern with high-frequency variability in the North Atlantic, especially at latitudes under direct wind forcing, and low-frequency variability in the South Atlantic (Fig. 5a). Furthermore, T appears somewhat disconnected at about 42°N. To understand the mechanism behind these features, T is decomposed into its Ekman component, TEk, and its geostrophic component, Tg. The Ekman component, existing only in the North Atlantic, varies at high frequencies with a distinct discontinuity at 42°N (Fig. 4b). This pattern is consistent with the discussion in section 2b: TEk varies stochastically in response to stochastic NAO wind forcing, and vanishes at the latitude where τx = 0, forming opposing meridional transport anomalies to the north and south of this latitude. The geostrophic component, taken as the residual (i.e., TTEk), predominantly shows the multidecadal variability that spreads from the North Atlantic into the South Atlantic (Fig. 4c), and agrees well with that calculated using boundary layer thickness anomalies through geostrophy [Tg = gH(hehw)/f; Fig. 5d], providing justifications for the linear approximation used in deriving (14) and (16) in section 2.

Fig. 5.

Time evolution of (a) T(y, t), (b) , (c) T(y, t) − TEk(y, t), and (d) Tg(y, t) = gH(hehw)/f in the experiment with only NAO wind forcing (Sv).

Fig. 5.

Time evolution of (a) T(y, t), (b) , (c) T(y, t) − TEk(y, t), and (d) Tg(y, t) = gH(hehw)/f in the experiment with only NAO wind forcing (Sv).

It is instructive to further investigate the boundary layer thickness anomalies that balance the geostrophic MOC anomalies. At latitudes under direct influence of stochastic wind forcing, hw, integrating the high-frequency forcing to the east and north along Rossby and boundary wave characteristics, shows mostly multidecadal variability, while he has a more pronounced high-frequency component on top of a weaker background multidecadal variability (Fig. 6). At latitudes to the south of the wind forcing, the ocean basin, including the lateral boundaries, feels predominately the multidecadal signal of hw. Note again that the strong tilting of hw southward with latitude is associated with the slow Rossby wave propagation in the zonal direction, rather than the fast boundary wave adjustment in the meridional direction. It is clear from Fig. 6b that he is uniform along the eastern boundary apart from latitudes under direct wind forcing.

Fig. 6.

Time evolution of (a) hw and (b) he (m) in the model experiment with only NAO wind forcing. Note the different color scales.

Fig. 6.

Time evolution of (a) hw and (b) he (m) in the model experiment with only NAO wind forcing. Note the different color scales.

Figure 7a compares the eastern boundary layer thickness anomalies, he, predicted using (16) from the linear theory and simulated in the numerical model experiment. The two curves broadly agree with each other, particularly well at low frequencies where he predicted from the theory captures the negative eastern boundary thickness anomalies before the late 1980s and positive anomalies thereafter. The theory seems to overestimate the magnitude of the interannual variability of he, which could be due to numerical damping and the sponge layers that exist in the reduced-gravity model but not in the theory. Generally speaking, the theoretically predicted hb, hw, and Tg from (9), (21), and (20) also agree well with those simulated in the numerical model experiment (Figs. 7b–d).

Fig. 7.

Time evolutions of (a) he (m), (b) hb at 40°N (m), (c) hw at 40°N (m), and (d) Tg at 40°N (Sv) in the calculations with only NAO wind forcing. The solid curves are predictions from the theory and the dashed curves are numerical model results.

Fig. 7.

Time evolutions of (a) he (m), (b) hb at 40°N (m), (c) hw at 40°N (m), and (d) Tg at 40°N (Sv) in the calculations with only NAO wind forcing. The solid curves are predictions from the theory and the dashed curves are numerical model results.

Note that the magnitude of the layer thickness anomalies on the western boundary (Fig. 7c) are roughly half those just outside the western boundary current (Fig. 7b). A significant reduction in variability is observed adjacent to the western boundary of the Atlantic, as discussed in Kanzow et al. (2009) and physically interpreted in terms of linear Rossby wave theory. Here, however, the reduction is less dramatic since the NAO-induced layer thickness anomalies occur on large scales, also consistent with the analysis of Cessi and Otheguy (2003).

Finally we note that the magnitude of the layer thickness anomalies in the basin interior are smaller than those inferred from observations (~40 m) by Leadbetter et al. (2007). A possible explanation is that the present calculations are forced only by Ekman upwelling anomalies associated with the NAO, and the NAO only accounts for a fraction of the surface wind stress variability in the North Atlantic (e.g., Hurrell 1995).

2) NAO thermohaline forcing

The response of the reduced-gravity model to thermohaline forcing, TN, at high latitudes has been studied previously (e.g., Johnson and Marshall 2002a, 2004; Deshayes and Frankignoul 2005; Zhai et al. 2011). Here we focus on ocean heat content and MOC variability when TN covaries with the NAO index (Fig. 2b). Figure 8 shows the time evolution of the upper layer thickness anomaly during the same years as in Fig. 3. There are two noticeable differences. First, the basinwide layer thickness/heat content is anomalously positive during negative NAO years and anomalously negative during positive NAO years in the experiment with NAO thermohaline forcing, in the opposite sense to what happens in the experiment with NAO wind forcing. This difference arises due to the fact that during positive NAO years, stronger outflow TN at the northern boundary acts to suck water out of the model, the influence of which gradually spreads to the ocean interior through boundary wave and Rossby wave adjustment processes. The same argument works in reverse for negative NAO years. Second, the stochastic variability excited along the western boundary by NAO thermohaline forcing gradually propagates into the interior of the ocean. As a result, the layer thickness anomaly at any given longitude and latitude is also largely stochastic, manifested by the positive and negative stripes of layer thickness anomalies in the interior of the model domain. In contrast, the layer thickness anomaly at any given longitude and latitude away from the direct influence of wind forcing in the experiment with NAO wind forcing varies predominately on multidecadal time scales.

Fig. 8.

As in Fig. 3, but for the experiment with only NAO thermohaline forcing.

Fig. 8.

As in Fig. 3, but for the experiment with only NAO thermohaline forcing.

Consistent with Zhai et al. (2011), the high-frequency zonal-mean layer thickness/heat content variability in the experiment with NAO thermohaline forcing is confined to low latitudes while the low-frequency variability extends to mid and high latitudes due to the Rossby buffer effect when the model is forced by a stochastic TN (Fig. 9a). The MOC anomaly in this experiment exhibits large variability throughout the Northern Hemisphere of the basin, but its high-frequency component is significantly reduced south of the equator (Fig. 9b), consistent with the prediction of Johnson and Marshall (2002a). The boundary layer thickness anomalies (Fig. 10) also show a very different behavior from those in the experiment with NAO wind forcing: the high-frequency variability at the western boundary is greatly reduced upon arriving at the eastern boundary such that it is now easy to detect the multidecadal variability of he.

Fig. 9.

As in Figs. 4a and 5a, but for the experiment with only NAO thermohaline forcing: (a) zonal-mean layer thickness anomaly (m) and (b) T(y, t) (Sv).

Fig. 9.

As in Figs. 4a and 5a, but for the experiment with only NAO thermohaline forcing: (a) zonal-mean layer thickness anomaly (m) and (b) T(y, t) (Sv).

Fig. 10.

Time evolution of (a) hw and (b) he (m) in the experiment with only NAO thermohaline forcing. Note the different color scale from Fig. 6.

Fig. 10.

Time evolution of (a) hw and (b) he (m) in the experiment with only NAO thermohaline forcing. Note the different color scale from Fig. 6.

3) NAO wind and thermohaline forcing

The results from the experiment with both NAO wind and thermohaline forcing largely represent the linear combination of those from individual experiments with only NAO wind forcing and only NAO thermohaline forcing. Similar behavior has also been reported from studies using OGCMs (e.g., Biastoch et al. 2008).

Figure 11 shows time evolution of the upper layer thickness anomaly in the experiment with both NAO wind and thermohaline forcing. During negative NAO years, the reduced outflow at the northern boundary tends to deepen the upper layer of the ocean, which is counteracted in regions under the positive wind stress curl anomaly that reduces the upper layer thickness and drives an anomalous cyclonic gyre. The thermohaline forcing appears to play a more important role in regions to the south of the cyclonic gyre in the beginning of the negative NAO decade, while the wind forcing becomes more dominant toward the end of it. The same reasoning applies to the positive NAO decade. This phase difference between the wind-forced and thermohaline-forced low-frequency variability is readily seen in Figs. 4a and 9a, and can be explained largely by the time it takes the Rossby waves to cross the basin at midlatitudes, integrating thickness anomalies induced by stochastic NAO wind forcing. In contrast, thickness anomalies induced by the NAO thermohaline forcing originate directly on the western boundary. One consequence of this phase difference is that the zonal-mean layer thickness/heat content anomaly appears to vary at somewhat higher frequency south of the latitudes of the direct NAO wind forcing (south of ~35°N) in the experiment with both NAO wind and thermohaline forcing than in the experiments with either NAO wind or thermohaline forcing alone (Fig. 12a). It is interesting to note that the low-frequency wind-forced and thermohaline-forced layer thickness anomalies nearly cancel each other out in the subtropics in 1962, leaving the model ocean that is not under the NAO wind forcing with only the high-frequency anomalies generated by stochastic thermohaline forcing (Fig. 11). With the addition of thermohaline forcing, the latitude at which the MOC variability appears disconnected is shifted northward from the experiment with wind forcing alone (Fig. 12b) because the thermohaline-forced MOC anomaly is in phase with the wind-driven Ekman transport anomaly south of 42°N, but out of phase north of 42°N.

Fig. 11.

As in Fig. 3, but for the experiment with both NAO wind and thermohaline forcing.

Fig. 11.

As in Fig. 3, but for the experiment with both NAO wind and thermohaline forcing.

Fig. 12.

As in Fig. 9, but for the experiment with both NAO wind and thermohaline forcing.

Fig. 12.

As in Fig. 9, but for the experiment with both NAO wind and thermohaline forcing.

Averaged over the whole Atlantic basin (excluding the sponges), the layer thickness and heat content anomalies in all three experiments exhibit pronounced multidecadal variability, with wind-forced anomalies largely opposing thermohaline-forced anomalies, especially at low frequencies (Fig. 13). While the basinwide heat content anomaly generated by the wind forcing dominates in our experiments, the extent to which the wind- and thermohaline-forced anomalies compensate for each other depends on the parameters chosen (e.g., TN).

Fig. 13.

(a) The NAO index provided by the Climate Analysis Section, NCAR (Hurrell 1995). (b) The basin-averaged layer thickness anomaly (excluding the sponges) in the experiment with only NAO wind forcing (solid thin line), only NAO thermohaline forcing (dashed line), and both NAO wind and thermohaline forcing (solid thick line).

Fig. 13.

(a) The NAO index provided by the Climate Analysis Section, NCAR (Hurrell 1995). (b) The basin-averaged layer thickness anomaly (excluding the sponges) in the experiment with only NAO wind forcing (solid thin line), only NAO thermohaline forcing (dashed line), and both NAO wind and thermohaline forcing (solid thick line).

4. Opposing changes of the MOC in the Atlantic

The meridional overturning circulation in the Atlantic Ocean plays an important role in our climate system through its transport of heat to high latitudes and transfer of atmospheric carbon dioxide to the deep ocean. The traditional view of the Atlantic MOC as a single coherent overturning cell has been called into question by recent modeling studies that have produced gyre-specific decadal and multidecadal MOC changes (e.g., Bingham et al. 2007; Biastoch et al. 2008; Lozier et al. 2010). For example, Lozier et al. (2010) recently reported that the overturning circulation weakened by 1.5 ± 1 Sv in the subtropical gyre between 1950–70 and 1980–2000, but strengthened by 0.8 ± 0.5 Sv in the subpolar gyre over the same period. Furthermore, changes in geostrophic transport associated with changes in the east–west density contrast appear to be responsible for these gyre-specific overturning changes.

Here we examine the changes of the geostrophic transport Tg between 1950–70 and 1980–2000 based on the theory presented in section 2, while taking into account the realistic geometry of the Atlantic Ocean [i.e., Lx = Lx(ϕ) where ϕ is latitude; Fig. 14]. Figure 15a shows Tg diagnosed using (20) with the NAO wind forcing and then averaged over each 20-yr period. The anomalous cyclonic wind stress curl at midlatitudes during 1950–70 is found to result in an overall increase in Tg (blue curve), or equivalently a strengthening of the MOC, that extends from about 50°N all the way into the South Atlantic, whereas the anomalous anticyclonic wind stress curl during 1980–2000 results in an overall weakening of the MOC (red curve). There are opposing changes of Tg north of 50°N, roughly where the anomalous wind stress curl changes sign, but the magnitude is much smaller in comparison. Therefore, with the NAO wind forcing alone, our analytical model predicts an overall reduction of the overturning circulation in the Atlantic Ocean by about 1 Sv from 1950–70 to 1980–2000 (black curve).

Fig. 14.

Schematic of the realistic Atlantic model domain employed in section 4. The wind-forced Ekman upwelling wEk and basin width Lx are each specified as functions of latitude ϕ. A thermohaline-forced outflow TN is prescribed into the shaded deep-water formation region.

Fig. 14.

Schematic of the realistic Atlantic model domain employed in section 4. The wind-forced Ekman upwelling wEk and basin width Lx are each specified as functions of latitude ϕ. A thermohaline-forced outflow TN is prescribed into the shaded deep-water formation region.

Fig. 15.

Variation of the geostrophic meridional volume transport Tg with latitude calculated using the theory with (a) only NAO wind forcing, (b) only NAO thermohaline forcing, and (c) both NAO wind and thermohaline forcing. In each panel, curves represent data averaged over the period 1950–70 (blue), 1980–2000 (red), and the difference (black).

Fig. 15.

Variation of the geostrophic meridional volume transport Tg with latitude calculated using the theory with (a) only NAO wind forcing, (b) only NAO thermohaline forcing, and (c) both NAO wind and thermohaline forcing. In each panel, curves represent data averaged over the period 1950–70 (blue), 1980–2000 (red), and the difference (black).

Figure 15b shows that the thermohaline forcing at high latitudes during 1950–70 results in a southward transport anomaly over the whole Atlantic basin, albeit with amplitude decreasing slightly toward the south. A northward transport anomaly with a similar spatial pattern is found during 1980–2000. Therefore, with the NAO thermohaline forcing alone, the theory predicts an overall strengthening of the overturning circulation in the Atlantic Ocean by about 0.4 Sv from 1950–70 to 1980–2000.

With both the NAO wind and thermohaline forcing, opposing changes of the meridional transport (or MOC) emerge, not unlike what has been reported by Lozier et al. (2010): weakening of the overturning in the subtropical gyre by about 0.3 Sv and strengthening of the overturning in the subpolar gyre by about 0.5 Sv from 1950–70 to 1980–2000 (Fig. 15c). Note that the latitude where Tg changes sign has now shifted southward to about 42°N. Our simple analytical model thus suggests that it is the interplay between the MOC anomalies induced by the NAO-related wind forcing and thermohaline forcing that results in the opposing changes of the MOC in the subtropical and subpolar gyres. However, the magnitude of these gyre-specific overturning changes and the latitude at which these changes switch sign depend on the precise time periods chosen, the choices of model parameters (e.g., g′ and H), and our assumption about the magnitude of the thermohaline forcing associated with the NAO.

5. Conclusions

The response of the Atlantic to NAO-related wind and thermohaline forcing has been studied in the framework of a reduced-gravity ocean model. A quantitative theory has been developed, the results of which compare favorably with those obtained from numerical model calculations.

Our main conclusions are as follows:

  • NAO-related wind forcing is found to drive a time-dependent “leaky gyre” that integrates stochastic wind forcing and spreads low-frequency ocean heat content and MOC variability to the rest of the ocean basin, whereas NAO-related thermohaline forcing excites stochastic variability along the western boundary that is subsequently communicated into the ocean interior via boundary and Rossby waves.

  • Basinwide ocean heat content changes owing to NAO-related wind forcing and NAO-related thermohaline forcing are found to oppose each other, especially at low frequencies.

  • The interplay between the MOCs generated by NAO-related wind forcing and thermohaline forcing appears to cause the opposing changes of the MOC in the subtropical and subpolar gyres found between 1950–70 and 1980–2000.

There are, of course, limitations with our simple reduced-gravity model approach. For example, no mean flow advection has been taken into account, and the model assumes vertical sidewalls and neglects all topographic influences. The need to use a constant background g′ and H limits the model’s ability to represent the differences between the subtropical and subpolar gyres. Furthermore, the NAO-related thermohaline forcing outside of the deep convection region is not included in our model, nor are coupled air–sea interactions that can influence decadal variability in the Atlantic Ocean. Notwithstanding these limitations, the simple model used in this study does have the advantage of providing traceable analytical solutions to the problem at hand, and many of its qualitative features, we believe, are likely to carry over to the ocean.

Acknowledgments

Financial support from the School of Environmental Sciences, University of East Anglia (UEA), is gratefully acknowledged. HLJ thanks the Royal Society for a university research fellowship. DPM acknowledges additional support from the Oxford Martin School. We thank three anonymous reviewers for their constructive and insightful comments that led to significant improvements in the manuscript.

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Footnotes

1

We hereafter describe the NAO as a stochastic forcing, although the spectrum of the NAO index is slightly red (e.g., Wunsch 1999).

2

Anomalies hereafter refer to deviations from time means.

3
As in Johnson and Marshall (2002a), the solution is insensitive to the precise value at which c is capped. To understand this result, note that when c(y) becomes large, performing a Taylor expansion on hb in (9) gives that the integrand on the left-hand side of (13) is approximately 
formula
independent of c(y). Thus, the solution of (13) is unaffected by replacing c(y) by , even though the individual contributions associated with he(t) and hb(y, t) in the integrand both diverge unless c(y) is capped.
4

Here by integration we mean integrating over time along wave characteristics in space, rather than integrating over space at a constant time.

5

Here we do not attempt to model the deep-water formation process itself.

6

Note that convective activities in the Greenland Sea tend to occur in antiphase with those in the Labrador Sea (e.g., Dickson et al. 1996; Marsh 2000). However, the connection between the intensity of deep convection in the Greenland Sea and the strength of the Atlantic MOC remains unclear (e.g., Dickson and Brown 1994).