Generated using version 3.2 of the o!cial AMS LATEX template

A Simple Model of the Response of the Atlantic to the North1

Atlantic Oscillation2

Xiaoming Zhai !

School of Environmental Sciences, University of East Anglia, Norwich, United Kingdom

3

Helen L. Johnson

Department of Earth Sciences, University of Oxford, Oxford, United Kingdom

4

David P. Marshall

Department of Physics, University of Oxford, Oxford, United Kingdom

5

!Corresponding author address: Xiaoming Zhai, School of Environmental Sciences, University of East

Anglia, Norwich NR4 7TJ, United Kingdom.

E-mail: Xiaoming.Zhai@uea.ac.uk

1

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ABSTRACT6

The response of an idealised Atlantic ocean to wind and thermohaline forcing associated7

with the North Atlantic Oscillation (NAO) is investigated both analytically and numerically8

in the framework of a reduced-gravity model. The NAO-related wind forcing is found to9

drive a time-dependent “leaky” gyre circulation that integrates basin-wide stochastic wind10

Ekman pumping and initiates low-frequency variability along the western boundary. This11

is subsequently communicated, together with the stochastic variability induced by thermo-12

haline forcing at high latitudes, to the remainder of the Atlantic via boundary and Rossby13

waves. At low frequencies, the basin-wide ocean heat content changes owing to NAO wind14

forcing and thermohaline forcing are found to oppose each other. The model further suggests15

that the recently reported opposing changes of the meridional overturning circulation in the16

Atlantic subtropical and subpolar gyres between 1950-1970 and 1980-2000 may be a generic17

feature caused by an interplay between the NAO wind and thermohaline forcing.18

1

1. Introduction19

The North Atlantic Oscillation (NAO) is the dominant mode of atmospheric variability20

in the North Atlantic sector (e.g. Hurrell 1995), and has a significant impact on the North21

Atlantic ocean circulation and hydrographic properties through its modulation of air-sea22

momentum, heat and freshwater fluxes. During the last 50 years, the NAO has exhibited23

large interannual and decadal variability, switching from its negative phase in the 1960s to24

strong positive phase in the late 1980s and early 1990s.25

Hindcast simulations using ocean general circulation models (OGCMs) have been widely26

used to study the oceanic response to changes of the NAO (e.g. Hakkinen 1999; Eden and27

Willebrand 2001; Eden and Jung 2001; Eden and Greatbatch 2003; Dong and Sutton 2005;28

Boning et al. 2006; Lozier et al. 2008; Deshayes and Frankignoul 2008; Robson et al. 2012;29

Zhai and Sheldon 2012). During positive NAO years, the anomalous wind stress is generally30

found to spin up the subtropical and subpolar gyre circulation, whereas the enhanced heat31

loss at high latitudes, particularly in the Labrador Sea, leads to a strengthening of the32

meridional overturning circulation (MOC) (see Visbeck et al. 2003, for a review). Although33

significant progress has been made over the last decade, detailed adjustment mechanisms34

remain unclear due, in part, to the complex nature of the OGCMs as well as to the lack of35

observations.36

In a theoretical study, Marshall et al. (2001) argued that the meridional shift in the jet37

stream associated with the NAO, through anomalous wind stress curl, drives an anomalous38

“intergyre gyre” at midlatitudes between the climatological subtropical and subpolar gyres.39

The anomalous wind forcing of this intergyre gyre is coherent in space but stochastic in40

time1, which initiates upper ocean buoyancy anomalies that propagate westward as baroclinic41

Rossby waves. As a result, the strength of the intergyre gyre fluctuates in time, albeit at much42

lower frequencies than that of the imposed forcing. However, it is not clear what happens43

1We hereafter describe the NAO as a stochastic forcing, although the spectrum of the NAO index is

slightly red (e.g. Wunsch 1999).

2

to these buoyancy anomalies when they arrive at the western boundary. It is possible that44

boundary waves may be excited that propagate southward along the western boundary, and45

after that communicate the buoyancy anomalies into the ocean interior in a similar fashion as46

described by Johnson and Marshall (2002a) for the upper ocean adjustment to thermohaline47

forcing.48

Zhai et al. (2011) studied the Atlantic heat content and sea level change in response49

to stochastic deep-water formation at high latitudes in the framework of a reduced-gravity50

model. They identified the “Rossby bu!er” e!ect: high-frequency basin-wide anomalies in51

heat content are confined to low latitudes whereas low-frequency anomalies extend to mid52

and high latitudes in both hemispheres. However, the ocean heat content change in response53

to the wind forcing was left unexplored. There are a number of theoretical investigations on54

oceanic adjustment to idealised wind forcing (e.g. Frankignoul et al. 1997; Cessi and Louazel55

2001; Primeau 2002; Cessi and Otheguy 2003; Sirven et al. 2007), but the focus has been on56

the thermocline variability, with little attention being paid to the response of the MOC and57

ocean heat content, in particular to the wind forcing associated with the NAO. Furthermore,58

there is the issue of the interplay between the NAO wind forcing and thermohaline forcing59

in determining the ocean heat content and transport variability.60

The present study aims to investigate the response of an idealised Atlantic ocean to61

wind and thermohaline forcing associated with the NAO in the context of a reduced-gravity62

model. The paper is organised as follows. In Section 2, a quantitative theory is developed63

for the ocean response to NAO-related wind forcing. In Section 3, the reduced-gravity64

model experiments and results are described. In Section 4, we use the theory to explore65

the possible mechanism behind the recently-reported opposing changes of the MOC in the66

Atlantic subtropical and subpolar gyres. Finally, in Section 5, we summarize our key findings.67

3

2. Theory68

In this section we focus on providing a simple linear theory of the ocean response to the69

NAO-related wind and high-latitude thermohaline forcing in the framework of a reduced-70

gravity model. Readers are referred to Johnson and Marshall (2002a) and Zhai et al. (2011)71

for related theory of ocean heat content and MOC variability induced purely by high-latitude72

thermohaline forcing.73

We consider a semi-enclosed rectangular domain that is open to the south, with 0 <74

x < Lx in the zonal direction and 0 < y < Ly in the meridional direction (Fig. 1). As the75

NAO wind forcing is dominated by the zonal wind stress anomaly that is largely uniform in76

the zonal direction over the North Atlantic, we hereafter consider only the zonally-averaged77

zonal wind stress anomaly2, !x(y, t), and we further assume !x(y, t) vanishes approaching the78

northern and southern boundaries. Ekman pumping associated with this simplified NAO79

wind forcing is thus uniform in space in the zonal direction but stochastic in time.80

Outside the western boundary layer, the linear dynamics are described by the momentum81

and continuity equations:82

"fv + g!"h

"x=

!x#0H

, (1)

fu+ g!"h

"y= 0, (2)

"h

"t+H

!"u

"x+

"v

"y

"

= 0. (3)

Here u and v are the zonal and meridional velocities, h is the anomaly in the layer thickness83

from its initial value H , f(y) is the Coriolis parameter, g! is the reduced gravity and #0 is a84

reference density.85

Although presented in Cartesian coordinates and a rectangular basin for pedagogical sim-86

plicity, the theory is easily generalized to spherical geometry and realistic basin geometries.87

The solutions presented in Section 3 are obtained in a rectangular basin on the sphere, and88

in Section 4 in a realistic Atlantic basin geometry.89

2Anomalies hereafter refer to deviations from time-means.

4

a. Volume budget90

Substituting for u and v in (3) using (1) and (2) gives the forced long Rossby wave91

equation:92

"h

"t" c(y)

"h

"x= "wE(y, t), (4)

where93

wE(y, t) = ""

"y

!!x(y, t)

#0f

"

(5)

is the Ekman upwelling velocity,94

c(y) =$(y)g!H

f(y)2= "

"

"y

!

g!H

f(y)

"

(6)

is the long Rossby wave speed, and $(y) = df(y)/dy is the meridional gradient in the Coriolis95

parameter.96

The solution to (4) is obtained by integrating westward along the Rossby wave charac-97

teristics (e.g. Frankignoul et al. 1997; Cessi and Louazel 2001):98

h(x, y, t) = he

!

t"Lx " x

c(y)

"

"

t#

t"Lx"xc(y)

wE(y, t!) dt!, (7)

where x = Lx is the longitude of the eastern boundary. In (7) we assume that the upper99

layer thickness anomaly along the eastern boundary, he(t), is uniform due to fast boundary100

wave propagation (Johnson and Marshall 2002a; Marshall and Johnson 2013).101

Following Johnson and Marshall (2002a) and zonally-integrating (4) from just outside102

the western boundary current region, x = %, to the eastern boundary, we obtain103

"

"t

Lx#

!

h dx = c(y) [he(t)" hb(y, t)]" wE(y, t)Lx, (8)

where104

hb(y, t) = he

!

t"Lx

c(y)

"

"

t#

t"Lx

c(y)

wE(y, t!) dt!, (9)

5

is the upper layer thickness anomaly just outside the western boundary current and Lx/c(y)105

is the Rossby wave basin-crossing time. Physically (8) indicates that the change of zonally-106

integrated layer thickness at any given latitude is caused by wind Ekman pumping integrated107

across the basin as well as the di!erence between the thickness anomalies propagated by108

Rossby waves from the eastern boundary into the ocean interior, and propagated from the109

ocean interior into the western boundary current.110

A further relation for the rate of change of layer thickness integrated across the basin is111

obtained by zonally integrating (3):112

"

"t

Lx#

0

h dx = ""T (y, t)

"y, (10)

where113

T (y, t) =

Lx#

0

vH dx (11)

is the net northward volume transport.114

Now combining (8) and (10), and neglecting the volume anomaly of the narrow western115

boundary region, gives:116

"T (y, t)

"y= "c(y) [he(t)" hb(y, t)] + wE(y, t)Lx. (12)

Integrating (12) over the latitudinal extent of the domain gives:117

Ly#

0

c(y) [he(t)" hb(y, t)] dy = TS(t)" TN (t), (13)

where TN is the prescribed northward transport anomaly at the northern boundary associ-118

ated with thermohaline forcing,119

TS(t) =g!H

fshe(t) (14)

is the northward transport anomaly across the southern boundary, fs = f(0) is the Coriolis120

parameter at the southern boundary and we have used that121

Ly#

0

wE(y, t) dy = 0 (15)

6

since !x vanishes at y = 0, Ly. In deriving (13), we have assumed that the layer thickness122

anomaly in the southwestern corner of the domain vanishes, which is justified on the time123

scales considered in this paper due to the long adjustment time scales of the Pacific and124

Indian basins (Johnson and Marshall 2004).125

Finally, combining (9), (13) and (14), we obtain an equation for the eastern boundary126

layer thickness that represents the generalization of equation (14) in Johnson and Marshall127

(2002a) to include wind forcing:128

he(t) =1

&

Ly#

0

c(y) he

!

t"Lx

c(y)

"

dy

$ %& '

previous time history

+1

&

Ly#

0

c(y)

t#

t"Lx

c(y)

wE(y, t!) dt! dy

$ %& '

wind forcing

"1

&TN

$ %& '

high-latitudethermohaline

forcing

, (16)

where129

& =

Ly#

0

c(y) dy "g!H

fs.

The Rossby wave speed,130

c(y) = min

!

c(y),

#g!H

3

"

is capped at the equatorial Rossby wave speed to prevent the integrals from diverging in131

(16).3 The terms on the right hand side of (16) represent radiation of Rossby waves from132

the eastern boundary providing the memory of past wind and thermohaline forcing, basin-133

wide wind-forced Ekman pumping, and outflow associated with thermohaline forcing at134

3As 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, the integrand on the left-hand side of (13) is

7

high latitudes, respectively. Notwithstanding the simplicity of the reduced-gravity model,135

(16) can be used to explore the relative importance of, and interplay between, wind and136

thermohaline forcing associated with the NAO in driving MOC and heat content anomalies,137

as detailed in the following sections.138

b. MOC anomaly139

The northward transport can be decomposed into Ekman and geostrophic components,140

T (y, t) = TEk(y, t) + Tg(y, t)

=!x(y, t)Lx

#0f(y)+

g!H

f(y)[he(t)" hw(y, t)]. (17)

Integrating (12) southward from the northern boundary, the geostrophic northward transport141

is given by142

Tg(y, t) = TN (t) +

Ly#

Ly"y

c(y!) [he(t)" hb(y!, t)] dy!. (18)

The MOC variability at any latitude can thus be determined from the basin-wide wind143

forcing, high-latitude thermohaline forcing, and the history of the eastern boundary layer144

thickness anomaly. Notice that the wind forcing influences the MOC transport through both145

modifying the layer thickness anomaly communicated by Rossby waves into the western146

boundary current and directly driving an Ekman transport. Substituting for hb, we obtain147

approximately

c(y) [he(t)" hb(y, t)] = c(y)

(!!he(t)

!t+ wE(y, t)

"Lx

c(y)+ · · ·

)

=

!!he(t)

!t+ wE(y, t)

"

Lx + · · · ,

independent of c(y). Thus, the solution of (13) is una"ected by replacing c(y) by c(y), even though the

individual contributions associated with he(t) and hb(y, t) in the integrand both diverge unless c(y) is capped.

8

the expressions for the northward geostrophic transport across any latitude,148

Tg(y, t) = TN(t) +

Ly#

Ly"y

c(y!)

(

he(t)" he

!

t"Lx

c(y!)

"

+

t#

t"Lx

c(y!)

wE(y!, t!)dt!

)

dy!, (19)

and the western boundary thickness anomaly,149

hw(y, t) = he(t)"f(y)Tg(y, t)

g!H. (20)

Here we have derived a similar expression for hw to Cessi and Louazel (2001), but independent150

of the details of the momentum balance in the narrow frictional western boundary layer.151

It is worth pointing out that Equation (19) shows that the geostrophic transport, Tg(y, t),152

at any given latitude depends on the entire history of the wind forcing integrated over the153

whole model domain through the dependence of he on this basin-wide forcing in (16). In154

particular, Tg(y, t) depends strongly on the history of wind Ekman pumping integrated over155

the whole area poleward of the latitude under consideration. As such, the wind-induced156

geostrophic transport variability at any given latitude cannot be diagnosed from a linear157

Rossby wave model driven by wind forcing at that single latitude alone. The same is true158

for the thermocline depth on the western boundary.159

Furthermore, since the sea level anomaly is proportional to the upper layer thickness160

anomaly in the reduced-gravity model, (20) shows that the sea level variability along the161

east coast of the United States and Canada depends on the history of wind forcing integrated162

over the whole ocean basin at higher latitudes to the north and thus cannot be predicted163

using models driven by wind forcing at a single local latitude such as Sturges and Hong164

(1995) and Frankignoul et al. (1997).165

There are two geographic regimes associated with (17): regions under direct NAO wind166

forcing and regions to the south. At latitudes under direct influence of stochastic NAO wind167

forcing, the Ekman contribution in (17) is also stochastic at any given latitude, and vanishes168

9

at the latitude where !x = 0, forming opposing meridional transport anomalies north and169

south of that latitude. The geostrophic transport anomaly, Tg, at any given latitude, on the170

other hand, depends on stochastic Ekman pumping integrated over the whole area further171

to the north and thus varies at much lower frequencies.172

In regions to the south of the NAO wind forcing, the ocean feels only the low-frequency173

hw that integrates stochastic Ekman pumping over the whole intergyre gyre area. The174

low-frequency hw then propagates equatorward along the western boundary, eastward along175

the equator and poleward along the eastern boundary, followed by the slow radiation of the176

Rossby waves o! the eastern boundary. This pattern is in contrast to the ocean’s response to177

stochastic deep-water formation at high latitudes, where the upper layer thickness anomaly178

along the western boundary exhibits both high-frequency and low-frequency variability, both179

of which spread into the interior of the model domain through boundary and Rossby wave180

adjustment (Zhai et al. 2011). Consequently, the MOC in the thermohaline-forced case181

varies at all frequencies, although the high-frequency component tends to be confined in the182

hemisphere in which it is generated (Johnson and Marshall 2002b).183

c. Ocean heat content anomaly184

In the reduced-gravity model, the ocean heat content change at each latitude, H, is185

proportional to the zonally-integrated layer thickness anomaly,186

H(y, t) = #0c0p "#

Lx#

0

h(x, y, t) dx, (21)

where "# is the Conservative Temperature di!erence between the abyssal and surface layer187

and c0p is a constant close to the specific heat capacity at the sea surface of the present ocean188

10

(McDougall 2003). Substituting (7) into (21) gives189

H(y, t) = #0c0p"#

t#

t"Lx

c(y)

he(t!) dt!

"#0c0p "#

Lx

c(y)#

0

t#

t"t!!

wE(y, t!)

c(y)dt! dt!! (22)

For further discussion, in the limit of no wind forcing, the reader is referred to Zhai et al.190

(2011).191

3. The reduced-gravity model experiment192

We now examine the anomalies in the MOC and ocean heat content in response to recent193

NAO-related wind and thermohaline forcing in the idealized reduced-gravity sector model.194

a. Numerical model description195

The nonlinear, numerical reduced-gravity model used in this study is similar to that196

described in Johnson and Marshall (2002a) and Zhai et al. (2011). The model domain is197

an idealised sector ocean 40# wide and stretching from 45#S to 75#N, with vertical sidewalls198

and a resolution of 0.25#. The background model layer thickness is 750 m, with a reduced199

gravity of 0.02 m s"2. No-slip and no-normal flow boundary conditions are applied. Sponges200

are applied at the northernmost and southernmost regions of the model domain to damp201

out any waves approaching these boundaries.202

11

b. Experiment design203

1) NAO wind forcing204

In the first experiment, the reduced-gravity model is forced solely by the wind stress205

anomaly associated with the NAO. The wind stress anomaly is obtained in a similar way as206

in Eden and Jung (2001). First, the spatial pattern of the wind stress associated with the207

NAO is estimated by regressing the monthly NCEP reanalysis wind stress (Kalnay et al.208

1996) on the NAO index (Hurrell 1995) for the period 1950-2010. The regressed wind stress209

is concentrated in the North Atlantic Ocean and reveals an anticyclonic wind stress curl210

situated at the gyre boundary that drives an “intergyre gyre” (not shown; Marshall et al.211

2001). The regressed zonal wind stress in the Atlantic Ocean is then zonally-averaged (Fig.212

2a) and multiplied by the monthly NAO index from 1950 to 2010 to drive the reduced-gravity213

model. In other words, the reduced-gravity model is forced by the zonal-mean “intergyre214

gyre” wind stress anomaly that pulses in time with the NAO index.215

2) NAO thermohaline forcing216

In the second experiment, the NAO thermohaline forcing is simply prescribed as a north-217

ward transport anomaly, TN , at the northern boundary of the model, following Johnson and218

Marshall (2002a), representing the deep-water formation process at high latitudes (outside219

the model domain). The intensity of deep ocean convection at high latitudes in the North220

Atlantic and associated dense water renewals have been found to be closely linked to the221

phase of the NAO (e.g. Dickson et al. 1996; Curry et al. 1998; Marshall and Schott 1999).222

During positive NAO years, cold and dry air outbreaks from the nearby continent to the223

Labrador Sea in late winter tend to be more frequent and more severe, which can lead to224

enhanced convective activity and deep-water formation, while the opposite is true during225

negative NAO years. In the present process study, TN is, for simplicity, assumed to vary226

linearly with the NAO index for the period 1950-2010, with a standard deviation of $ 2 Sv227

12

(Fig. 2b). However, it should be noted that convective activities and associated deep-water228

formation in the Greenland Sea are often observed to occur in anti phase with those in the229

Labrador Sea (e.g. Dickson et al. 1996; Marsh 2000).230

3) NAO wind and thermohaline forcing231

In the final experiment, the reduced-gravity model is forced by both NAO wind and232

thermohaline forcing in order to investigate the interplay between the two.233

c. Results234

1) NAO wind forcing235

Fig. 3 shows the time evolution of the upper layer thickness anomaly during years236

of negative NAO (1956, 1962 and 1972) and positive NAO (1992, 1994 and 1996) in the237

experiment with only NAO wind forcing. The anomalous positive wind stress curl associated238

with the negative phase of the NAO before 1956 reduces the upper layer thickness between239

35#N and 55#N, creating an anomalous cyclonic intergyre gyre circulation there. There is also240

indication of a weak anticyclonic gyre circulation to the south of the intergyre gyre owing to241

the relatively weak negative wind stress curl there before 1956. The negative layer thickness242

anomaly generated in the intergyre gyre area in the 1950s is shown to leak equatorward243

along the western boundary, eastward along the equator and then poleward along the eastern244

boundary, followed by the slow radiation of Rossby waves into the ocean interior. Over the245

following two decades of negative NAO, the leakage of negative anomalies from the intergyre246

gyre intensifies, and eventually fills the whole model domain by the year 1972. During247

the late 1980s and early 1990s when the NAO is switched to its strong positive phase,248

the anomalous negative wind stress curl deepens the upper layer and drives an anomalous249

anticyclonic intergyre gyre. The positive layer thickness anomaly, again, leaks equatorward250

and eventually spread over the whole model domain by the year 1996. Our results thus251

13

suggest that the NAO wind stress forces a basin-wide upper layer thickness/ocean heat252

content change via a time-dependent “leaky” intergyre gyre circulation.253

The zonally-averaged layer thickness at latitudes under direct influence of the intergyre254

wind forcing varies at both high and low frequencies, but is dominated by the large negative255

anomalies before the early 1970s and positive anomalies in the late 1980s and early 1990s256

(Fig. 4a). In contrast, in regions south of about 15#N where there is almost no direct257

wind forcing, only a multidecadal signal emerges. This multidecadal signal has a phase258

lag that varies with latitude, owing to the decrease in Rossby wave speed with increasing259

latitude (Zhai et al. 2011). There is a noticeable amount of layer thickness variability in260

the tropics (Figs. 3 and 4), suggesting that the low-frequency ocean variability generated261

by the intergyre gyre NAO wind forcing in the extra-tropics can potentially, via oceanic262

teleconnections, modulate the thermocline depth and sea surface temperature in the tropics263

where the atmosphere is particularly sensitive to small sea surface temperature anomalies.264

Fig. 4b shows the zonally-averaged layer thickness predicted from the theory using (16) and265

(22), which broadly agrees with that in the numerical model experiment.266

The meridional transport anomaly, T , reveals a complex pattern with high-frequency267

variability in the North Atlantic, especially at latitudes under direct wind forcing, and low-268

frequency variability in the South Atlantic (Fig. 5a). Furthermore, T appears somewhat269

disconnected at about 42#N. In order to understand the mechanism behind these features,270

T is decomposed into its Ekman component, TEk, and its geostrophic component, Tg. The271

Ekman component, existing only in the North Atlantic, varies at high frequencies with a272

distinct discontinuity at 42#N (Fig. 4b). This pattern is consistent with the discussion in273

Section 2b: TEk varies stochastically in response to stochastic NAO wind forcing, and van-274

ishes at the latitude where !x = 0, forming opposing meridional transport anomalies to the275

north and south of this latitude. The geostrophic component, taken as the residual, i.e.,276

T " TEk, shows predominantly the multidecadal variability that spreads from the North At-277

lantic into the South Atlantic (Fig. 4c), and agrees well with that calculated using boundary278

14

layer thickness anomalies through geostrophy (Tg = g!H(he " hw)/f ; Fig. 5d), providing279

justifications for the linear approximation used in deriving (14) and (16) in Section 2.280

It is instructive to further investigate the boundary layer thickness anomalies that balance281

the geostrophic MOC anomalies. At latitudes under direct influence of stochastic wind282

forcing, hw, integrating the high-frequency forcing to the east and north, shows mostly283

multidecadal variability, while he has a more pronounced high-frequency component on top284

of the background multidecadal variability (Fig. 6). At latitudes to the south of the wind285

forcing, the ocean basin, including the lateral boundaries, feels only the multidecadal signal286

of hw. Note again that the strong tilting of hw southward with latitude is associated with287

the slow Rossby wave propagation in the zonal direction, rather than the fast boundary wave288

adjustment in the meridional direction. It is clear from Fig. 6b that he is uniform along the289

eastern boundary.290

Fig. 7a compares the eastern boundary layer thickness anomalies, he, predicted using291

(16) from the linear theory and simulated in the numerical model experiment. The two292

curves broadly agree with each other, particularly well at low frequencies where he predicted293

from the theory captures the negative eastern boundary thickness anomalies before the late294

1980s and positive anomalies thereafter. The theory seems to overestimate the magnitude of295

the interannual variability of he, which could be due to numerical damping and the sponge296

layers that exist in the reduced-gravity model but not in the theory. Generally speaking,297

the theoretically-predicted hb, hw and Tg from (9), (20) and (19) also agree reasonably well298

with those simulated in the numerical model experiment (Figs. 7b, c and d).299

Note that the magnitude of the layer thickness anomalies on the western boundary (Fig.300

7c) are roughly half those just outside the western boundary current (Fig. 7b) . A significant301

reduction in variability is observed adjacent to the western boundary of the Atlantic, as302

discussed in Kanzow et al. (2009) and physically interpreted in terms of linear Rossby wave303

theory. Here, however, the reduction is less dramatic since the NAO-induced layer thickness304

anomalies occur on large scales, also consistent with the analysis of Cessi and Otheguy305

15

(2003).306

Finally we note that the magnitude of the layer thickness anomalies in the basin interior307

are smaller than those inferred from observations by Leadbetter et al. (2007). A possible308

explanation is that the present calculations are forced only the fraction of the Ekman up-309

welling anomaly associated with the NAO whereas Leadbetter et al. (2007) used the full310

wind stress anomaly.311

2) NAO thermohaline forcing312

The response of the reduced-gravity model to thermohaline forcing, TN , at high latitudes313

has been studied previously (e.g. Johnson and Marshall 2002a, 2004; Deshayes and Frankig-314

noul 2005; Zhai et al. 2011). Here we focus on ocean heat content and MOC variability315

when TN co-varies with the NAO index (Fig. 2b). Fig. 8 shows the time evolution of the316

upper layer thickness anomaly during the same years as in Fig. 3. There are two noticeable317

di!erences. First, the basin-wide layer thickness/heat content is anomalously positive during318

negative NAO years and anomalously negative during positive NAO years in the experiment319

with NAO thermohaline forcing, in the opposite sense to what happens in the experiment320

with NAO wind forcing. This di!erence arises due to the fact that during positive NAO321

years, stronger outflow, TN , at the northern boundary acts to suck water out of the model,322

the influence of which gradually spreads to the ocean interior through boundary wave and323

Rossby wave adjustment processes. The same argument works in reverse for negative NAO324

years. Second, the stochastic variability excited along the western boundary with NAO ther-325

mohaline forcing gradually propagates into the interior of the ocean. As a result, the layer326

thickness anomaly at any given longitude and latitude is also largely stochastic, manifested327

by the positive and negative stripes of layer thickness anomalies in the interior of the model328

domain. In contrast, the layer thickness anomaly at any given longitude and latitude away329

from the direct influence of the intergyre wind forcing in the case with NAO wind forcing330

varies only on multidecadal time scales.331

16

Consistent with Zhai et al. (2011), the high-frequency zonal-mean layer thickness/heat332

content variability in the experiment with NAO thermohaline forcing is confined to low333

latitudes while the low-frequency variability extends to mid- and high latitudes due to the334

“Rossby bu!er” e!ect when the model is forced by a stochastic TN (Fig. 8a). The MOC335

anomaly in this experiment exhibits large variability throughout the northern hemisphere336

of the basin, but its high-frequency component is significantly reduced south of the equator337

(Fig. 8b), consistent with the prediction of Johnson and Marshall (2002a). The boundary338

layer thickness anomalies (Fig. 10) also show a very di!erent behaviour from those in the339

experiment with NAO wind forcing: the high-frequency variability at the western boundary340

is greatly reduced upon arriving at the eastern boundary such that it is now easy to detect341

the multidecadal variability of he.342

3) NAO wind and thermohaline forcing343

The results from the experiment with both NAO wind and thermohaline forcing largely344

represent the linear combination of those from individual experiments with only NAO wind345

forcing and only NAO thermohaline forcing. Similar behaviour has also been reported from346

studies using OGCMs (e.g. Biastoch et al. 2008).347

Fig. 11 shows time evolution of the upper layer thickness anomaly in the experiment348

with both NAO wind and thermohaline forcing. During negative NAO years, the reduced349

outflow at the northern boundary tends to deepen the upper layer of the ocean, which is350

counteracted by the positive wind stress curl anomaly that reduces the upper layer thickness351

and drives an anomalous cyclonic intergyre gyre. The thermohaline forcing appears to play352

a more important role in regions to the south of the intergyre gyre in the beginning of the353

negative NAO decade, while the wind forcing becomes more dominant towards the end of it.354

The same reasoning applies to the positive NAO decade. This phase di!erence between the355

wind-forced and thermohaline-forced low-frequency variability is readily seen in Figs. 4a and356

9a, and can be explained largely by the time it takes the Rossby waves to cross the basin at357

17

mid-latitudes, integrating thickness anomalies induced by stochastic NAO wind forcing. In358

contrast, thickness anomalies induced by the NAO thermohaline forcing originate directly on359

the western boundary. One consequence of this phase di!erence is that the zonal-mean layer360

thickness/heat content anomaly appears to vary at somewhat higher-frequency south of the361

intergyre gyre (south of $ 35#N) in the experiment with both NAO wind and thermohaline362

forcing than in the experiments with either NAO wind or thermohaline forcing alone (Fig.363

12a). It is interesting to note that the low-frequency wind-forced and thermohaline-forced364

layer thickness anomalies nearly cancel each other out in the subtropics in 1962, leaving the365

ocean to the south of the intergyre gyre with only the high-frequency anomalies generated366

by stochastic thermohaline forcing (Fig. 11). With the addition of thermohaline forcing,367

the latitude at which the MOC variability appears disconnected is shifted northward from368

the experiment with wind forcing alone (Fig. 12b) because the thermohaline-forced MOC369

anomaly is in phase with the wind-driven Ekman transport anomaly south of 42#N, but out370

of phase north of 42#N.371

Averaged over the whole Atlantic basin (excluding the sponges), the layer thickness and372

heat content anomalies in all three experiments exhibit pronounced multidecadal variability,373

with wind-forced anomalies largely opposing thermohaline-forced anomalies, especially at low374

frequencies (Fig. 13). While the basin-wide heat content anomaly generated by the wind375

forcing dominates in our experiments, the extent to which the wind- and thermohaline-forced376

anomalies compensate for each other depends on the parameters chosen.377

4. Opposing changes of the MOC in the Atlantic378

The meridional overturning circulation in the Atlantic Ocean plays an important role in379

our climate system through its transport of heat to high latitudes and transfer of atmospheric380

carbon dioxide to the deep ocean. The traditional view of the Atlantic MOC as a single381

coherent overturning cell has been called into question by recent modelling studies that have382

18

produced gyre-specific decadal and multidecadal MOC changes (e.g. Bingham et al. 2007;383

Biastoch et al. 2008; Lozier et al. 2010). For example, Lozier et al. (2010) recently reported384

that the overturning circulation weakened by 1.5 ± 1 Sv in the subtropical gyre between385

1950-1970 and 1980-2000, but strengthened by 0.8 ± 0.5 Sv in the subpolar gyre over the386

same period. Furthermore, changes in geostrophic transport associated with changes in387

the east-west density contrast appear to be responsible for these gyre-specific overturning388

changes.389

Here we examine the changes of the geostrophic transport, Tg, between 1950-1970 and390

1980-2000 based on the theory presented in Section 2, while taking into account of the re-391

alistic geometry of the Atlantic Ocean, i.e., Lx = Lx(') where ' is latitude (see Fig. 14).392

Fig. 15a shows Tg diagnosed using (19) with the NAO wind forcing and then averaged over393

each 20 year period. The anomalous cyclonic intergyre wind stress curl during 1950-1970 is394

found to result in an overall increase in Tg (blue curve), or equivalently a strengthening of395

the MOC, that extends from about 55#N all the way into the South Atlantic, whereas the396

anomalous anticyclonic wind stress curl during 1980-2000 results in an overall weakening of397

the MOC (red curve). There are opposing changes of Tg north of 55#N, roughly where the398

anomalous wind stress curl changes sign, but the magnitude is much smaller in comparison.399

Therefore, with the NAO wind forcing alone, our analytical model predicts an overall reduc-400

tion of the overturning circulation in the Atlantic Ocean by about 1 Sv from 1950-1970 to401

1980-2000 (black curve).402

Fig. 15b shows that the thermohaline forcing at high latitudes during 1950-1970 results403

in a southward transport anomaly over the whole Atlantic basin, albeit with amplitude404

decreasing slightly towards the south. A northward transport anomaly with a similar spatial405

pattern is found during 1980-2000. Therefore, with the NAO thermohaline forcing alone,406

the theory predicts an overall strengthening of the overturning circulation in the Atlantic407

Ocean by about 0.4 Sv from 1950-1970 to 1980-2000.408

With both the NAO wind and thermohaline forcing, opposing changes of the meridional409

19

transport (or MOC) emerge, not unlike what has been reported by Lozier et al. (2010):410

weakening of the overturning in the subtropical gyre by about 0.7 Sv and strengthening of411

the overturning in the subpolar gyre by about 0.5 Sv from 1950-1970 to 1980-2000 (Fig. 15c).412

Note that the latitude where Tg changes sign has now shifted southward to about 45oN. Our413

simple analytical model thus suggests that it is the interplay between the MOC induced414

by the NAO-related wind forcing and the MOC induced by the NAO-related thermohaline415

forcing that results in the opposing changes of the MOC in the subtropical and subpolar416

gyres. However, the magnitude of these gyre-specific overturning changes and the latitude417

at which these changes switch sign depend on the precise time periods chosen, and on our418

assumption about the magnitude of the thermohaline forcing associated with the NAO.419

5. Conclusions420

The response of the Atlantic to NAO-related wind and thermohaline forcing has been421

studied in the framework of a reduced-gravity ocean model. A quantitative theory has been422

developed, the results of which compare favorably with those obtained from numerical model423

calculations.424

Our main conclusions are:425

• NAO-related wind forcing is found to drive a time-dependent “leaky intergyre gyre”426

that integrates stochastic wind forcing and spreads low-frequency ocean heat content427

and MOC variability to the rest of the ocean basin, whereas NAO-related thermohaline428

forcing excites stochastic variability along the western boundary that is subsequently429

communicated into the ocean interior via boundary and Rossby waves.430

• Basin-wide ocean heat content changes owing to NAO-related wind forcing and NAO-431

related thermohaline forcing are found to oppose each other, especially at low frequen-432

cies.433

20

• The interplay between the MOCs generated by NAO-related wind forcing and thermo-434

haline forcing appears to cause the opposing changes of the MOC in the subtropical435

and subpolar gyres found between 1950-1970 and 1980-2000.436

There are, of course, limitations with our simple reduced-gravity model approach. For437

example, no mean flow advection has been taken into account, and the model assumes438

vertical sidewalls and neglects all topographic influences. Nevertheless, the simple model439

used in this study does have the advantage of providing traceable analytical solutions to the440

problem at hand, and many of its qualitative features, we believe, are likely to carry over to441

the ocean.442

Acknowledgments.443

Financial support from the School of Environmental Sciences, UEA is gratefully ac-444

knowledged. HLJ thanks the Royal Society for a University Research Fellowship. DPM445

acknowledges additional support from the Oxford Martin School.446

21

447

REFERENCES448

Biastoch, A., C. W. Boning, J. Getzla!, J. M. Molines, and G. Madec, 2008: Causes of inter449

annual-decadal variability in the meridional overturning circulation for the midlatitude450

North Atlantic Osean. J. Climate, 21, 6599–6615.451

Bingham, R. J., C. W. Hughes, V. Roussenov, and R. G. Williams, 2007: Meridional co-452

herence of the North Atlantic meridional overturning circulation. Geophys. Res. Lett., 34,453

doi:10.1029/2007GL031731.454

Boning, C. W., M. Scheinert, J. Dengg, A. Biastoch, and A. Funk, 2006: Decadal variabil-455

ity of subpolar gyre transport and its reverberation in the North Atlantic overturning.456

Geophys. Res. Lett., 33, L21S01, doi:10.1029/2006GL026906.457

Cessi, P. and S. Louazel, 2001: Decadal oceanic response to stochastic wind forcing. J. Phys.458

Oceanogr., 31, 3020–3029.459

Cessi, P. and P. Otheguy, 2003: Oceanic teleconnections: Remote response to decadal wind460

forcing. J. Phys. Oceanogr., 33, 1604–1617.461

Curry, R. G., M. S. McCartney, and T. M. Joyce, 1998: Oceanic transport of subpolar462

climate signals to mid-depth subtropical waters. Nature, 391, 575–577.463

Deshayes, J. and C. Frankignoul, 2005: Spectral characteristics of the response of the merid-464

ional overturning circulation to deep-water formation. J. Phys. Oceanogr., 35, 1813–1825.465

Deshayes, J. and C. Frankignoul, 2008: Simulated variability of the circulation in the North466

Atlanic from 1953 to 2003. J. Climate, 21, 4919–4933.467

Dickson, R. R., J. Lazier, J. Meincke, P. Rhines, and J. Swift, 1996: Long-term co-ordinated468

changes in the convective activity in the North Atlantic. Prog. Oceanogr., 38, 241–295.469

22

Dong, B. and R. T. Sutton, 2005: Mechanism of interdecadal thermohaline circulation vari-470

ability in a coupled ocean-atmosphere GCM. J. Climate, 18, 1117–1135.471

Eden, C. and R. J. Greatbatch, 2003: A damped oscillation in the North Atlantic climate472

system. J. Climate, 16, 4043–4060.473

Eden, C. and T. Jung, 2001: North Atlantic interdecadal variability: Oceanic respose to the474

North Atlantic Oscillation (1865-1997). J. Climate, 14, 676–691.475

Eden, C. and J. Willebrand, 2001: Mechanism of interannual to decadal variability of the476

North Atlantic circulation. J. Climate, 14, 2266–2280.477

Frankignoul, C., P. Muller, and E. Zorita, 1997: A simple model of the decadal response of478

the ocean to stochastic wind forcing. J. Phys. Oceanogr., 27, 1533–1546.479

Hakkinen, S., 1999: Variability of the simulated meridional heat transport in the North480

Atlanic for the period 1951-1993. J. Geophys. Res., 104, 10 991–11 007.481

Hurrell, J. W., 1995: Decadal trends in the North Atlantic Oscillation and relationships to482

regional temperatures and precipitation. Science, 269, 676–679.483

Johnson, H. L. and D. P. Marshall, 2002a: A theory for the surface Atlantic response to484

thermohaline variability. J. Phys. Oceanogr., 32, 1121–1132.485

Johnson, H. L. and D. P. Marshall, 2002b: Localization of abrupt change in the North486

Atlantic thermohaline circulation. Geophys. Res. Lett., 29, doi:10.1029/2001GL014140.487

Johnson, H. L. and D. P. Marshall, 2004: Global teleconnections of meridional overturning488

circulation anomalies. J. Phys. Oceanogr., 34, 1702–1722.489

Kalnay, E. et al., 1996: The NCEP/NCAR 40-year reanalysis project. Bull. Amer. Meteor.490

Soc., 77, 437–471.491

23

Kanzow, T., H. L. Johnson, D. P. Marshall, S. A. Cunningham, J. J.-M. Hirschi, A. Mujahid,492

H. L. Bryden, and W. E. Johns, 2009: Observing basin-wide integrated volume transports493

in an eddy-filled ocean. J. Phys. Oceangor., in press.494

Leadbetter, S. J., R. G. Williams, E. L. McDonagh, and B. A. King, 2007: A twenty year495

reversal in water mass trends in the subtropical North Atlantic. Geophys. Res. Lett., 34,496

L12 608, doi:10.1029/2007GL029 957.497

Lozier, M. S., V. R. an M. S. C. Reed, and R. G. Williams, 2010: Opposing decadal changes498

for the North Atlantic meridional overturning circulation. Nature Geo., 3, 728–734.499

Lozier, M. S., S. Leadbetter, R. G. Williams, V. Roussenov, M. S. C. Reed, and N. J. Moore,500

2008: The spatial pattern and mechanisms of heat-content change in the North Atlantic.501

Science, 319, 800–803.502

Marsh, R., 2000: Recent variability of the North Atlantic thermohaline circulation inferred503

from surface heat and freshwater fluxes. J. Climate, 13, 3239–3260.504

Marshall, D. P. and H. L. Johnson, 2013: Propagation of meridional circulation anomalies505

along western and eastern boundaries. J. Phys. Oceanogr., to be submitted.506

Marshall, J., H. L. Johnson, and J. Goodman, 2001: A study of the interaction of the North507

Atlantic Oscillation with the ocean circulation. J. Phys. Oceanogr., 14, 1399–1421.508

Marshall, J. and F. Schott, 1999: Open ocean deep convection: observations, models and509

theory. Rev. Geophys., 37, 1–64.510

McDougall, T. J., 2003: Potential enthalpy: a conservative oceanic variable for evaluating511

heat content and heat fluxes. J. Phys. Oceanogr., 33, 945–963.512

Primeau, F., 2002: Long Rossby wave basin-crossing time and the resonance of low-frequency513

basin modes. J. Phys. Oceanogr., 32, 2652–2665.514

24

Robson, J., R. Sutton, K. Lohmann, D. Smith, and M. D. Palmer, 2012: Causes of the rapid515

warming of the North Atlantic Ocean in the mid-1990s. J. Climate, 25, 4116–4134.516

Sirven, J., C. Herbaut, J. Deshayes, and C. Frankignoul, 2007: Origin of the annual to517

decadal peaks of variability in the response of simple ocean models to stochastic forcing.518

J. Phys. Oceanogr., 37, 2146–2157.519

Sturges, W. and B. G. Hong, 1995: Wind forcing of the Atlantic thermocline along 32#N at520

low frequencies. J. Phys. Oceanogr., 25, 1706–1715.521

Visbeck, M., E. P. Chassignet, R. G. Curry, T. L. Delworth, R. R. Dickson, and G. Krah-522

mann, 2003: The ocean’s response to North Atlantic Oscillation variability. The North523

Atlantic Oscillation: Climatic Significance and Environmental Impact, J. W. Hurrell,524

Y. Kushnir, G. Ottersen, and M. Visbeck, Eds., American Geophysical Union, Geophysical525

Monograph, Vol. 134, 113–146.526

Wunsch, C., 1999: The interpretation of short climate records, with comments on the North527

Atlantic and Southern Oscillations. Bull. Amer. Meteor. Soc., 80, 245–255.528

Zhai, X., H. L. Johnson, and D. P. Marshall, 2011: A model of Atlantic heat content and529

sea level change in response to thermohaline forcing. J. Climate, 24, 5619–5632.530

Zhai, X. and L. Sheldon, 2012: On the North Atlantic ocean heat content change between531

1955-70 and 1980-95. J. Climate, 25, 3619–3628.532

25

List of Figures533

1 Schematic of the rectangular model domain employed in Section 2. The wind-534

forced Ekman upwelling, wEk, varies with the meridional coordinate, y. A535

thermohaline-forced outflow, TN , is prescribed at the northern edge of the536

domain. The model is not solved in the shaded deep-water formation region.537

The dotted lines indicate the western boundary region and equator, and the538

dashed line the southern edge of the domain (where the basin connects to539

the Southern Ocean). A similar rectangular domain, except with spherical540

coordinates, is employed in Section 3. See the main text for further details. 29541

2 (a) Zonal-mean zonal wind stress regressed on the NAO index in the Atlantic542

Ocean. (b) TN prescribed at the northern boundary of the model in the543

experiments with thermohaline forcing. 30544

3 Time evolution of the upper layer thickness anomaly (m) during years of545

negative NAO (1956,1962 and 1972) and positive NAO (1992, 1994 and 1996)546

in the experiment with only NAO wind forcing. The color scale is saturated547

in the “intergyre gyre” region, where the thickness anomalies can reach ±40 m. 31548

4 Time evolution of the zonal-mean layer thickness anomaly (m) at di!erent549

latitudes from the case with only NAO wind forcing: (a) numerical model550

experiment; (b) theory. 32551

5 Time evolution of (a) T (y, t), (b) TEk(y, t) =* Lx

0 !x/(#0f)dx, (c) T (y, t) "552

TEk(y, t) and (d) Tg(y, t) = g!H(he " hw)/f in the experiment with only NAO553

wind forcing (units: Sv) . 33554

6 Time evolution of (a) hw and (b) he (m) in the model experiment with only555

NAO wind forcing. Note the di!erent colour scales. 34556

26

7 Time evolutions of (a) he (m), (b) hb at 40#N (m), (b) hw at 40#N (m) and (c)557

Tg at 40#N (Sv) in the calculations with only NAO wind forcing. The solid558

curves are predictions from the theory and the dashed curves are numerical559

model results. 35560

8 The same as Fig. 3 except for the experiment with only NAO thermohaline561

forcing. 36562

9 The same as Figs. 4a and 5a except for the experiment with only NAO563

thermohaline forcing. (a) Zonal-mean layer thickness anomaly (m). (b) T (y, t)564

(Sv). 37565

10 Time evolution of (a) hw and (b) he in meter in the experiment with only566

NAO thermohaline forcing.. Note the di!erent colour scale from Fig. 6. 38567

11 The same as Fig. 3 except for the experiment with both NAO wind and568

thermohaline forcing. 39569

12 The same as Fig. 9 except for the experiment with both NAO wind and570

thermohaline forcing. 40571

13 (a) The NAO index provided by the Climate Analysis Section, NCAR (Hur-572

rell 1995). (b) The basin-averaged layer thickness anomaly (excluding the573

sponges) in the experiment with only NAO wind forcing (solid thin line), only574

NAO thermohaline focing (dashed line), and both NAO wind and thermoha-575

line forcing (solid thick line). 41576

14 Schematic of the realistic Atlantic model domain employed in Section 4. The577

wind-forced Ekman upwelling, wEk, and basin width, Lx, are each specified578

as a functions of latitude, '. A thermohaline-forced outflow, TN , is prescribed579

into the shaded deep water formation region. 42580

27

15 Variation of the geostrophic meridional volume transport, Tg, with latitude581

from the theory with: (a) only NAO wind forcing; (b) only NAO thermohaline582

forcing; (c) both NAO wind and thermohaline forcing. In each panel, curves583

represent data averaged over the period 1950–1970 (blue), 1980–2000 (red),584

and the di!erence (black). 43585

28

TN

wE(y)

Fig. 1. Schematic of the rectangular model domain employed in Section 2. The wind-forcedEkman upwelling, wE, varies with the meridional coordinate, y. A thermohaline-forcedoutflow, TN , is prescribed at the northern edge of the domain. The model is not solved inthe shaded deep-water formation region. The dotted lines indicate the western boundaryregion and equator, and the dashed line the southern edge of the domain (where the basinconnects to the Southern Ocean). A similar rectangular domain, except with sphericalcoordinates, is employed in Section 3. See the main text for further details.

29

−0.02 0 0.02 0.04 0.06−40

−20

0

20

40

60

τ (N/m2)

latit

ude

(a)

1950 1960 1970 1980 1990 2000 2010−5

0

5

year

T N (S

v)

(b)

Fig. 2. (a) Zonal-mean zonal wind stress regressed on the NAO index in the AtlanticOcean. (b) TN prescribed at the northern boundary of the model in the experiments withthermohaline forcing.

30

Fig. 3. Time evolution of the upper layer thickness anomaly (m) during years of negativeNAO (1956,1962 and 1972) and positive NAO (1992, 1994 and 1996) in the experiment withonly NAO wind forcing. The color scale is saturated in the “intergyre gyre” region, wherethe thickness anomalies can reach ±40 m.

31

Fig. 4. Time evolution of the zonal-mean layer thickness anomaly (m) at di!erent latitudesfrom the case with only NAO wind forcing: (a) numerical model experiment; (b) theory.

32

Fig. 5. Time evolution of (a) T (y, t), (b) TEk(y, t) =* Lx

0 !x/(#0f)dx, (c) T (y, t)" TEk(y, t)and (d) Tg(y, t) = g!H(he"hw)/f in the experiment with only NAO wind forcing (units: Sv).

33

Fig. 6. Time evolution of (a) hw and (b) he (m) in the model experiment with only NAOwind forcing. Note the di!erent colour scales.

34

1950 1960 1970 1980 1990 2000 2010−2

−1

0

1

2m

(a) he

1950 1960 1970 1980 1990 2000 2010−20

−10

0

10

20

m

(b) hb at 40N

1950 1960 1970 1980 1990 2000 2010

−5

0

5

m

(c) hw at 40N

year1950 1960 1970 1980 1990 2000 2010−1

−0.5

0

0.5

1

Sv

(d) Tg at 40N

year

Fig. 7. Time evolutions of (a) he (m), (b) hb at 40#N (m), (b) hw at 40#N (m) and (c) Tg at40#N (Sv) in the calculations with only NAO wind forcing. The solid curves are predictionsfrom the theory and the dashed curves are numerical model results.

35

Fig. 8. The same as Fig. 3 except for the experiment with only NAO thermohaline forcing.

36

Fig. 9. The same as Figs. 4a and 5a except for the experiment with only NAO thermohalineforcing. (a) Zonal-mean layer thickness anomaly (m). (b) T (y, t) (Sv).

37

Fig. 10. Time evolution of (a) hw and (b) he (m) in the experiment with only NAOthermohaline forcing. Note the di!erent colour scale from Fig. 6.

38

Fig. 11. The same as Fig. 3 except for the experiment with both NAO wind and thermo-haline forcing.

39

Fig. 12. The same as Fig. 9 except for the experiment with both NAO wind and thermo-haline forcing.

40

1950 1960 1970 1980 1990 2000 2010

−2

0

2

NAO

inde

x

(a)

1950 1960 1970 1980 1990 2000 2010−4

−3

−2

−1

0

1

2

3

4

year

basi

n−w

ide

h an

omal

y (m

)

(b)Wind

ThermohalineBoth

Fig. 13. (a) The NAO index provided by the Climate Analysis Section, NCAR (Hurrell1995). (b) The basin-averaged layer thickness anomaly (excluding the sponges) in the exper-iment with only NAO wind forcing (solid thin line), only NAO thermohaline focing (dashedline), and both NAO wind and thermohaline forcing (solid thick line).

41

Lx(!)

TN

wE(!)

Fig. 14. Schematic of the realistic Atlantic model domain employed in Section 4. Thewind-forced Ekman upwelling, wE, and basin width, Lx, are each specified as a functionsof latitude, '. A thermohaline-forced outflow, TN , is prescribed into the shaded deep waterformation region.

42

−1

−0.5

0

0.5

1

Sv

(a)

−1

−0.5

0

0.5

1

Sv

(b)

−20 0 20 40 60−1

−0.5

0

0.5

1

Sv

latitude

(c)

50−7080−00diff

Fig. 15. Variation of the geostrophic meridional volume transport, Tg, with latitude fromthe theory with: (a) only NAO wind forcing; (b) only NAO thermohaline forcing; (c) bothNAO wind and thermohaline forcing. In each panel, curves represent data averaged over theperiod 1950–1970 (blue), 1980–2000 (red), and the di!erence (black).

43