The eects of mesoscale ocean-atmosphere coupling on the large-scale ocean circulation

The e!ects of mesoscale ocean-atmospherecoupling on the large-scale ocean circulation

Andrew McC. Hogg!

Australian National University, Canberra, Australia

William K. DewarFlorida State University, USA

Pavel Berlo!Woods Hole Oceanographic Institution, USA

Cambridge University, UK

Sergey KravtsovUniversity of Wisconsin, Milwaukee

David K. HutchinsonAustralian National University, Canberra, Australia

November 25, 2008

ABSTRACT

Small-scale variation in wind stress due to ocean-atmosphere interaction withinthe atmospheric boundary layer alters the temporal and spatial scale of Ekmanpumping driving the double gyre circulation of the ocean. A high resolution QGocean model, coupled to a dynamic atmospheric mixed layer, is used to demon-strate that, despite the small spatial scale of the Ekman pumping anomalies, thisphenomena significantly modifies the large-scale ocean circulation. The primarye!ect is to decrease the strength of the nonlinear component of the gyre circula-tion by approximately 30–40%. This result is due to the highest transient Ekmanpumping anomalies destabilising the flow in a dynamically sensitive region close tothe western boundary current separation. The instability of the jet produces a fluxof potential vorticity between the two gyres which acts to weaken both gyres.

1. IntroductionRecent satellite observations have shown that the stress on the surface of the ocean varies

on the relatively fine spatial scales governed by oceanic mesoscale dynamics. This spatialvariability can be attributed primarily to a combination of the dependence of stress upon oceanvelocity (Chelton et al. 2004; Park et al. 2006) and patterns of sea surface temperature (SST)

!Corresponding author address: Andrew McC. Hogg, Research School of Earth Sciences, The AustralianNational University, Canberra ACT 0200, AustraliaE-mail: [email protected]

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variations (Nonaka and Xie 2003; Chelton et al. 2004; Xie 2004). In this paper we focus uponthe latter of these two e!ects, and in particular whether mesoscale coupling of SST and windstress can alter the large-scale (that is, basin-scale) ocean circulation.

SST variations are greatest in regions of strong fronts, or where eddies cause rapid changesin SST in the along wind direction (Spall 2007b). Prime candidate areas for strong mesoscalecoupling include regions close to the equator where tropical instability waves occur and nearwestern boundary current separation regions where eddies and fronts are most active. Theseregions are analysed in a recent review article (Small et al. 2008) which summarises the knownprocesses contributing to mesoscale wind stress variability. The dynamics leading to correlationsbetween the spatial variability of wind stress and SST is subtle, and there are a number ofpossible contributing factors including vertical mixing of momentum, changes in the planetaryboundary layer depth, a secondary atmospheric response due to pressure gradients within theboundary layer, and changes in cloud cover across the fronts.

When the sea surface is warmer than the atmospheric boundary layer, excessive convectivemixing will magnify vertical eddy momentum flux and hence enhance stress close to the seasurface (Sweet et al. 1981). Samelson et al. (2006) argue, with support from analytical models,that the convective mixing mechanism will result in enhanced wind stress over warmer water;but that the reverse situation requires an aphysical “upward unmixing”. They imply that theprimary e!ect on stress is therefore due to e!ect of convective mixing upon the depth of theatmospheric boundary layer. Spall (2007b) use an idealised model to confirm the role of theboundary layer thickness in governing stress for the case of equilibrium winds (that is, far fromfronts where gradients of SST are large), but point out that the linear relationship betweenthe boundary layer thickness and stress breaks down in the immediate vicinity of the front.The horizontal momentum balance in these model simulations emphasises the role of turbulentvertical mixing as the rapid response mechanism to SST gradients.

An alternative hypothesis to explain mesoscale variations in wind stress is that of pressuregradients induced by the SST patterns (Lindzen and Nigam 1987). This hypothesis has beenconfirmed using recent observations (Cronin et al. 2003) and numerical simulations (Small et al.2003, 2005) in the tropical Pacific, although the possibility of vertical mixing contributing tothe momentum balance in those cases has not been ruled out. In addition, the drag coe"cientitself can vary with temperature, although this e!ect is expected to be second order (Spall2007b).

In their review article, Small et al. (2008) point out that a single, universally acknowledgedmechanism for small-scale wind stress variations does not exist. Instead, it appears that a com-bination of di!erent processes contribute. For example, if strong winds cross a sharp front, theair temperature does not have time to respond to SST and thus vertical mixing of momentumdominates over pressure gradients (Spall 2007b). Conversely, if winds are weak then the airtemperature has time to equilibrate to SST, and the air pressure response may dominate. Fur-thermore, the role of vertical turbulent mixing is di!erent for the case of a warm-to-cold front,implying that either the Coriolis e!ect (Spall 2007b) or the boundary layer height reduction(Samelson et al. 2006) is responsible for the reduction in stress near the front.

Thus it appears likely that di!erent mechanisms operate in di!erent regions, depending uponthe strength of the front, and the strength and direction of the large scale winds. It is thereforesurprising that satellite observations yield a simple statistical relationship between wind stressand SST: namely that wind stress divergence is linearly proportional to the downwind SSTgradient, while wind stress curl is proportional to the cross-wind SST gradient (Chelton et al.2004). This relationship was initially observed in the eastern tropical Pacific (Chelton et al.2001), but also applies in the Southern Ocean (O’Neill et al. 2003, 2005), as well as the Kuroshioand Gulf Stream (Chelton et al. 2004). While the constant of proportionality varies in eachcase (presumably due to variations in the operating mechanisms), a universal pattern is that

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the constant is approximately twice as large for the divergence as for the curl. This covariationsuggests that a relatively simple parameterisation may be able to capture the essential dynamicsof this process.

The dependence of wind stress curl upon cross-wind temperature gradients means thatlarge values of transient, small-scale Ekman pumping are expected. Ekman pumping plays afirst order role in driving ocean currents, and mesoscale coupling is therefore likely to havean e!ect on local flow, raising the prospect of further feedback onto ocean circulation. Forexample, it was established by Dewar and Flierl (1987) that variations in Ekman pumping mayhave small-scale local e!ects on steering and dissipating Gulf Stream rings. Modelling of theNorth Atlantic gyre system showed that high frequency perturbations to the wind stress curlenhanced both the mean and eddy kinetic energy in the eastern part of the gyre (Milli! et al.1996). Spall (2007a) proposes that feedback between fronts and the atmospheric boundarylayer will enhance the growth rates of baroclinic instability on those fronts, thereby a!ectingthe ocean circulation. The possibility for dynamic feedback with the ocean was demonstratedusing a high resolution regional coupled model of the tropical Pacific (Seo et al. 2007). Here,the growth rate of Tropical Instability Waves was damped by this feedback process.

The results of Milli! et al. (1996) and Seo et al. (2007) indicate that mesoscale coupling mayfeed back on the ocean circulation to produce e!ects which are not merely local. However, Milli!et al. (1996) used a forcing which represented the wind stress variations statistically, rather thandynamically, while Seo et al. (2007) concentrated on the tropical ocean dynamics. In this paperwe ask the question: can mesoscale coupled feedback act to modify the large-scale midlatitudeocean gyre circulation? To answer this question we use an idealised coupled ocean-atmospheremodel which resolves ocean eddies. The model (described in section 2 below) includes a simple,first order parameterisation for mesoscale coupling. We firstly test this parameterisation todetermine whether it produces correlations between mesoscale wind stress patterns and SSTthat are consistent with satellite observations. We then conduct numerical experiments todetermine the nature and cause of the large scale oceanic response to mesoscale coupling; anddemonstrate the operating dynamics with a conceptual low order model for interaction.

2. ModelWe use Q-GCM (Hogg et al. 2003b), which is designed to model the ocean at eddy resolving

scales in a coupled setting. Q-GCM is an idealised model with three quasigeostrophic oceanlayers – the reduced layer representation allows the model to be run e"ciently at very highresolution, thereby permitting a number of experiments over a wide range of governing param-eters. Version 1.4! of the model is used, with some key modifications. In this model version,instead of the full coupling, we prescribe the geostrophic wind field to be purely zonal. Themodel has a dynamic atmospheric mixed layer which enables us to calculate the evolution ofthe atmospheric mixed layer temperature (AMLT) and wind stress, as well as a dynamic oceanmixed layer embedded within the first QG ocean layer where sea surface temperature (SST)evolution is calculated. These layers are shown schematically in Figure 1. In this version of themodel we use 10 km resolution in both ocean and atmosphere to capture the dynamic e!ect ofmesoscale eddies and the role of coupling on this scale. The model equations are summarisedbelow; for a full description of the model see (Hogg et al. 2003a).

a. Ocean dynamical core

The QG equations describing the dynamics in all parts of the three-layer ocean domain(except for the boundaries) are

q1t =1

f0J(q1, p1)"

A4

f0#6

Hp1 +f0wek

H1, (1)

3

q2t =1

f0J(q2, p2)"

A4

f0#6

Hp2, (2)

q3t =1

f0J(q3, p3)"

A4

f0#6

Hp3 ""ek

2H3#2

Hp3, (3)

where pk is the layer pressure and qk layer potential vorticity. Mean layer thickness is denotedHk, while A4 is a coe"cient for biharmonic viscosity, f0 the mean Coriolis parameter, wek theEkman pumping velocity imposed by the wind stress forcing and "ek the Ekman layer thicknessat the bottom of layer 3. Pressure is determined at each timestep from the potential vorticityby inverting

f0qk = #2Hpk + f0!(y " y0) +

f 20

Hk(#k " #k!1), for k = 1, 3, (4)

where ! is the latitudinal gradient of the Coriolis parameter and we define interface heightperturbations as

#k = "pk " pk+1

g"k, for k = 1, 2, (5)

#0 = #3 = 0.

Here, g"k is the reduced gravity between layers k and k + 1.Pressure on the boundaries is determined using boundary conditions

pk = fk(t), (6)

where the function fk(t) is determined by mass conservation, and is constant around the bound-ary. Boundary conditions are also required for the derivatives of pressure on all solid bound-aries, and we use a mixed condition, applied to the normal derivatives, following Haidvogelet al. (1992),

pknn = "$bc

#xpkn, (7)

pk4n = "$bc

#xpk3n, (8)

where the nondimensional coe"cient $bc is zero for free slip and infinite for no-slip boundaryconditions (although, in practice, $bc > 2 is a good approximation to no-slip), #x is thehorizontal grid spacing and subscript n denotes the outward normal derivative.

b. Mixed layer evolution

The evolution of the oceanic mixed layer temperature (relative to the mean temperature)oTm, is determined using

oTmt = "(oumoTm)x " (ovm

oTm)y + oK2#2H

oTm " oK4#4H

oTm " F0 + F "S

o%oCpoHm

(9)

where

(oum, ovm) =1

f0("p1y, p1x) +

1

f0oHm

(o& y,"o&x) (10)

is the mixed layer velocity and (o&x, o& y) the dynamic stress at the ocean surface. Note the useof both Laplacian and biharmonic di!usion with coe"cients oK2 and oK4 respectively. Fluxesof heat at the surface include a steady insolation, F "

S, and a time-dependent ocean-atmosphereheat flux, F0, which is calculated using a linearised radiation and heat flux scheme. The heatfluxes are described in detail by Hogg et al. (2003a), but are based primarily on the sensible andlatent heat flux, '(oTm" aTm), due to the ocean-atmosphere temperature di!erence. Boundary

4

0 3840

0

-4

Z (k

m)

Y (km)

OCEAN LAYER 1OCEAN MIXED LAYER

OCEAN LAYER 2

ATMOSPHEREMIXED LAYER

INCOMING SOLARRADIATION

HEAT DISTRIBUTED INTERNALLY BYRADIATION ANDENTRAINMENT

WIND STRESSLEADS TO EKMAN

PUMPING

EKMAN PUMPING

QUASIGEOSTROPHICDYNAMICS

ENTRAINMENT

OCEAN LAYER 3

PRESCRIBEDWINDS

10

Fig. 1. North-south transect through model domain showing 3 QG ocean layers, embeddedmixed layers in both ocean and atmosphere, prescribed (steady) winds in the atmosphere andprocesses included in the model.

conditions are zero flux on all boundaries, except for the southern boundary where temperatureis specified as a proxy for advection of warm tropical water into that region.

The temperature evolution the atmospheric mixed layer is given by

aTmt = "(aumaTm)x " (avm

aTm)y + aK2#2H

aTm " aK4#4H

aTm +"Fm + F0a%aCp

ahm, (11)

where

(aum, avm) =1

f0("ap1y,

ap1x) +1

f0aHm

("a& y, a&x). (12)

Here, Fm is the outgoing radiative flux (derived in full by Hogg et al. 2003a) and other parame-ters are atmospheric equivalents of the parameters in (9). North and south boundary conditionson atmospheric temperature are zero flux, while east-west boundaries are periodic.

c. Wind stress

The standard bulk formulation for calculating wind stress in Q-GCM is

(a&x, a& y) = CD|aum|(aum, avm)

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Parameters Value DescriptionX, Y 3840 km Square domain size#x 10 km Horizontal grid spacing|F "

s| 90 W/m2 Amp. of variable incoming radiationf0 1$ 10!4 s!1 Mean Coriolis parameter! 2$ 10!11 (ms)!1 Coriolis parameter gradient' 35 W/m2/K Sensible and latent heat flux coe"cient

#ot 30 min Ocean TimestepoHk (300, 1100, 2600) m Ocean layer heightsoHm 100 m Ocean mixed layer height

o% 1000 kg/m3 Ocean densityoCp 4000 J/kg/K Ocean specific heat capacityg"k (0.05, 0.025) m/s2 Reduced gravityA4 2.0$ 1010 m4/s Biharmonic horizontal viscosity coe"cient$bc 0.5 Mixed BC coe"cient"ek 1 m Bottom Ekman layer thickness

oK2, oK4 380 m2/s, 4$ 1010 m4/s Ocean di!usion coe"cientsordk (51, 32) km Ocean baroclinic Rossby radii (derived)#at 1 min Atmosphere TimestepaHm 1000 m Atmosphere mixed layer height

a% 1 kg/m3 Atmosphere densityaCp 1000 J/kg/K Atmosphere specific heat capacityCD 1.3$ 10!3 Drag coe"cient

aK2, aK4 2.7$ 104 m2/s, 3$ 1014 m4/s Atmosphere di!usion coe"cients

Table 1. Standard parameters for simulations, divided into global, ocean and atmosphere compo-nents.

which represents the quadratic e!ect of wind speed on drag using a constant drag coe"cientCD (Pedlosky 1987). In this study we investigate the role of small-scale ocean-atmospherecoupling by allowing the wind stress to depend upon the temperature di!erence between oceanand atmosphere. This e!ect is parameterised in a crude way, by writing

(a&x, a& y) = CD(1 + $#T )|aum|(aum, avm) (13)

where #T = oTm " aTm is the atmosphere-ocean temperature di!erence. In this manuscriptwe refer to this scheme as a temperature-dependent wind stress. We then calculate ocean stressfrom o& = a%a& /o%. Ocean Ekman pumping velocity is calculated from ocean stress using

wek =1

f0(o& y

x " o&xy ), (14)

which is the forcing term in (1).

d. Calibration and comparison with observations

The proposed parameterisation for temperature-dependent wind stress (Eq. 13) is designedto emulate the role of convective instability driving the vertical mixing of momentum withinthe atmospheric boundary layer (Sweet et al. 1981; Spall 2007b). However, it is clear that morethan one mechanism contributes to mesoscale wind stress variations (Samelson et al. 2006;Small et al. 2008): atmospheric boundary layer thickness and secondary pressure gradients

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may also play a major role. The present study is concerned not with the mechanism of stressvariation, but with the e!ect that it has on the ocean circulation. For this reason, we aim toconfirm that the simple parameterisation, Eq. (13), gives similar results to observations.

The most complete and robust observations of mesoscale wind stress variability come fromsatellite scatterometer measurements. A number of studies have shown a linear correlationbetween downwind (crosswind) SST gradients and wind stress divergence (curl) (Chelton et al.2001; O’Neill et al. 2003; Chelton et al. 2004; O’Neill et al. 2005). These data provide a solidmetric to test whether the present model can reproduce observations.

The procedure we use is to spin the model up to steady state (this takes 20 model years)using $ = 0.1 and then run 24 consecutive 90 day simulations. The mean wind stress from each90 day simulation has a large-scale component which has to be filtered out; this is achievedeasily for these simulations by subtracting the known large-scale imposed stress field (that is,from the case with $ = 0). This leaves just the small-scale contributions to wind stress whichwe denote & ". The mean SST from each case also has a large-scale component, but this is weakcompared to local gradients and the results are insensitive to whether or not the SST datais spatially filtered. Thus, from each simulation we can calculate the wind stress divergence(#·& ") and curl (#$& "), as well as the SST gradients in the downwind (#oTm ·&) and crosswind(#oTm $ &) directions. Then, following the procedure established by Chelton et al. (2001) weuse the downwind (crosswind) temperature gradient at each data point to divide the wind stressdivergence (curl) into bins, and find the average within each bin. The same procedure appliesto each 90 day segment, after which the mean and standard deviation of the 24 segments canbe found. These results are shown in Fig. 2.

There are a number of striking similarities between the results shown in Fig. 2 and thesatellite observations of the Kuroshio and Gulf Stream region (see Fig. 4 of Chelton et al. 2004).First, there is a roughly linear trend between divergence and the downwind SST gradient, andbetween the curl and the crosswind SST gradient. Second, the magnitude of slope (calculatedfrom a least squares fit, and plotted by the dashed line) is similar to observations – for example,the slope of the divergence plot is 0.57, compared to 0.96 for the Kuroshio and 1.09 for the GulfStream (Chelton et al. 2004). Third, there is approximately a factor of 2 di!erence between theslope of the wind stress divergence and curl correlations, matching a ubiquitous feature of theobservations. Finally, the error bars (an indicator of variability between the 90 day segments)are similar to observations. The one feature which di!ers from observations is the large biasin the calculation of crosswind SST gradient and wind stress curl. This result stems from thesteady zonal geostrophic wind field imposed in this model, meaning that there are relatively fewsamples with a negative crosswind SST gradient. For this reason we only use positive values ofthe crosswind gradient in calculating the least squares fit.

The magnitude of the correlations discussed above are half the observed values, implyingthat the coupling coe"cient ($) is too low. For example, Fig. 3 shows that the correlationsincrease almost linearly with the coupling coe"cient, so that a value of $ % 0.2 may givethe closest match to observations. However, there are a number of other factors in the modelwhich can a!ect this relationship, including the strength of the zonal winds, the SST di!usion,model resolution and the parameterisation of ocean-atmosphere heat flux. Furthermore, thereis su"cient regional variability in the strength of wind stress correlations to indicate that anexact match with data should not be expected.

Thus we contend that, while the simple parameterisation used in the present model is notdesigned to represent all possible processes contributing to mescoscale wind stress variations,the statistical e!ect upon the ocean surface is su"ciently close to observations to justify itsuse.

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−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1−1

−0.5

0

0.5

1x 10−6

Downwind SST Gradient (°C/km)

Dive

rgen

ce (m

2 /s2 /k

m)

(a)

slope = 0.54

−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1−2

−1

0

1

2

3x 10−7

Crosswind SST Gradient (°C/km)

Curl

(m2 /s

2 /km

)

(b)

slope = 0.21

Fig. 2. Correlation between the local SST gradients and small-scale wind stress gradients forthe case with $ = 0.1. (a) Downwind SST gradient vs wind stress divergence; (b) CrosswindSST gradient vs wind stress curl. Error bars show the standard deviation of the 24 simulations,and the slope has been converted to units of N/m2/#C and multiplied by 100 to enable directcomparison with Chelton et al. (2004).

e. Experiments

The model described above is used for a series of numerical experiments designed to isolatethe e!ect of ocean-atmosphere coupling on the large-scale circulation through mesoscale varia-tion of wind stress. The standard parameter set for all simulations is shown in Table 1. Eachsimulation was given a 20 year spinup period, and then mean fields are accumulated over an80 year model run.

Initial experiments involve forcing by steady atmospheric winds, and varying the strengthof the wind stress feedback parameter, $. In this study we allow $ to vary between 0 and 0.15to model the range of relevant parameters of the system. The results of these experiments aredescribed in the following section.

3. Resultsa. Temperature-independent wind stress forcing case ($ = 0)

The model is forced by prescribed atmospheric velocity, which is a function of y only, asshown in Fig. 4(a). The velocity field is designed to be slightly asymmetric so that the maximumvelocity occurs about 200km south of the centre of the domain (to avoid the artificial symmetry

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160

0.2

0.4

0.6

0.8

α

slope

Fig. 3. Slopes from Fig. 2 as a function of the coupling coe"cient $.

0 2 4 6

500

1000

1500

2000

2500

3000

3500

(a)

u (m/s)

Y (k

m)

0 0.02 0.040

500

1000

1500

2000

2500

3000

3500

(b)

τx (m2/s2)

Y (k

m)

−4 −2 0 2 4x 10−7

0

500

1000

1500

2000

2500

3000

3500

(c)

wek (m/s)

Y (k

m)

Fig. 4. Forcing as a function of latitude for case with temperature-independent forcing ($ = 0).(a) Prescribed atmospheric wind field au1; (b) Zonal component of stress in the atmosphericmixed layer; (c) Ocean Ekman pumping velocity.

of the QG equations; see Berlo! and McWilliams 1999). For this case, with $ = 0, wind stressand Ekman pumping velocity are also simple functions of y, and are shown in Fig. 4 (b,c)respectively.

The time mean SST and circulation in the upper layer of the ocean resulting from this steady

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(a)

Y (k

m)

1000 2000 3000

500

1000

1500

2000

2500

3000

3500

(b)

0 1000 2000 30000

1000

2000

3000

(c)

X (km)

Y (k

m)

1000 2000 3000

500

1000

1500

2000

2500

3000

3500

(d)

X (km)0 1000 2000 3000

0

1000

2000

3000

Fig. 5. Results for experiment with temperature-independent wind stress forcing. (a) MeanSST field (relative to domain averaged temperature; Contour Interval 2#C); (b) Mean upperlayer streamfunction (CI 2 Sv); (c) Instantaneous SST field at year 20; (d) Instantaneousstreamfunction at year 20. Negative contours are shown with a dashed line, zero contour witha bold line.

forcing is shown in Fig. 5(a,b). These figures describe a turbulent double gyre circulation whichhas been well characterised in the literature (e.g. Holland 1978): the western boundary current,inertial recirculations and a strong eastward jet separating the two gyres are superimposed ona Sverdrupian background circulation. The jet has a very strong SST gradient, which plays nodynamical role in this experiment (as $ = 0), but has the potential to alter the forcing at finite$. The slight asymmetry in the forcing field is responsible for a shift in the jet to the south ofthe zero wind stress curl line, and some weak meanders in the jet.

The instantaneous fields (Fig. 5c,d) show the strong mesoscale activity in this parameterregime. The mean flow is strongly overprinted by geostrophic turbulence which plays a keyrole in controlling both the mean state and low frequency variability of the system (Hogg et al.2005; Berlo! et al. 2007a). This mesoscale activity is also reflected in the SST field, producinga very intense front across the jet, and additional small fronts in the interior of the flow. It isreasonable to expect that these fronts will play a role in determining the mean circulation atfinite $.

b. Temperature-dependent wind stress forcing (nonzero $)

We now conduct simulations with the same prescribed atmospheric winds, but with theinclusion of temperature-dependent wind stress. We show results from three simulations using

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(a) α = 0.05

Y (k

m)

0 1000 2000 30000

1000

2000

3000

(b) α = 0.1

0 1000 2000 30000

1000

2000

3000

(c) α = 0.15

X (km)

Y (k

m)

0 1000 2000 30000

1000

2000

3000

0 1000 2000 30000

0.2

0.4

0.6

X (km)

u (m

/s)

(d)

00.050.10.15

Fig. 6. Mean upper layer streamfunction (CI 2 Sv) for (a) $ = 0.05; (b) $ = 0.1; (c) $ = 0.15.(d) Maximum zonal velocity as a function of x along the jet core for varying $.

$ = 0.05, 0.10, 0.15 in Fig. 6. The structure of the large scale double gyre circulation in thesesimulations show clear di!erences from that in Fig. 5(b). The temperature-dependent windstress acts to substantially shorten the mean length of the jet dividing the two gyres, while alsoenhancing meanders in the jet and reducing the strength of the inertial recirculations.

Fig. 6(d) shows the variation of jet strength as a function of $. Here the maximum zonalvelocity in the jet is plotted as a function of x in each case. The e!ect of increasing $ is shownto clearly and systematically reduce the maximum jet velocity and to shorten the jet. Thecombination of these two e!ects provide a simple metric to allow comparison between di!erentexperiments in the following sections.

This result leads to the obvious question: what elements of the temperature-dependentwind stress scheme are responsible for the gross changes in behaviour of the double gyre cir-culation? We now analyse this question in the context of several di!erent hypotheses to showthat the time-dependent small-scale forcing in the western boundary current separation regionis responsible for the primary changes to the circulation.

In this model, $ a!ects the ocean circulation through modifications to the wind stress andocean Ekman pumping velocity (see eqs 13–14). The time mean of both components of windstress and the Ekman pumping for the case with $ = 0.1 are plotted in Fig. 7(a,b,c). The zonalwind stress (Fig. 7a) is enhanced over the western boundary of the subtropical gyre, and reducedover the corresponding region of the subpolar gyre. In addition, there are changes to wind stressin the ocean interior, primarily along the core of the jet where SST fronts are common. Themeridional wind stress (Fig. 7b) is due to atmospheric Ekman transport within the atmospheric

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(a)

Y (k

m)

0 500 1000 15001000

1500

2000

2500(b)

0 500 1000 15001000

1500

2000

2500

(c)

X (km)

Y (k

m)

0 500 1000 15001000

1500

2000

2500(d)

X (km)0 500 1000 1500

1000

1500

2000

2500

Fig. 7. Forcing fields for the temperature-dependent forcing case ($ = 0.1) concentrating on asmall region of interest around the ocean jet. (a) Mean zonal wind stress field (CI 0.01 m2/s2);(b) time mean meridional wind stress field (CI 0.001 m2/s2); (c) time mean Ekman pumpingvelocity (CI 4$ 10!7 m/s); and (d) standard deviation of ocean Ekman pumping velocity (CI1$ 10!6 m/s).

mixed layer (see eq. 12 for the generation of meridional velocity within the atmospheric mixedlayer), and thus is directly proportional to zonal stress and O(0.1&x) in magnitude. The stresschanges near the western boundary produces strongly positive Ekman pumping anomalies overwestern edge of the subtropical/subpolar gyre (Fig. 7c). In the interior, gradients in wind stressalong the eastward jet generate maxima in Ekman pumping anomalies along the core of thejet; these maxima are an order of magnitude larger than the background Ekman pumping, butare confined to a small region. Finally, we also show the standard deviation in Ekman pumpingvelocity (Fig. 7d). This shows that the standard deviation (with a maximum of 10!5m/s) isa factor of 20 greater than the background maximum Ekman pumping for the temperatureindependent stress case (see Fig. 4c), indicating that extremely large instantaneous values ofEkman pumping occur in this simulation.

The simplest explanation for the large scale impact of temperature-dependent wind stresswould be the role of changes to the time mean forcing. However, the turbulent double gyrecirculation is a nonlinear flow in which interaction between small-scale eddies and the large-scaleflow controls the circulation. For example, eddies alter the mean flow either by mixing quantities(such as potential vorticity, or PV) between the gyres; or alternatively act to sharpen gradientsin PV between the gyres through upgradient PV flux (see Berlo! et al. 2007a). Furthermore,eddies are a product of instabilities of the mean circulation. This eddy–mean flow interaction

12

0 500 1000 15000

2

4

6

8

x 104

X (km)

Mea

n KE

(J/m

2 )

(a) Mean KE along the jet

0 500 1000 15000

1

2

3

4x 104

X (km)

Eddy

KE

(J/m

2 )

(b) Eddy KE along the jet

0.00.050.10.15

Fig. 8. (a) Mean kinetic energy, and (b) eddy kinetic energy averaged across a band 200kmeither side of the jet as a function of zonal position.

implies that careful investigation of both the eddy field and the mean flow is needed to determinethe controlling dynamics of this flow.

The spatial variation of the eddy field as a function of $ is shown in Fig. 8. Here we comparethe zonal spatial variation of mean kinetic energy along the jet, with eddy kinetic energy inthe jet region. The mean kinetic energy in the jet monotonically reduces with $, consistentwith the data shown above. However, eddy kinetic energy increases with $ near the westernboundary current separation region, with a much faster decay in the zonal direction. In otherwords, very high eddy kinetic energy is induced by the temperature dependent wind stress, butthis is confined the the western boundary region.

The dynamical role of eddies in reducing the circulation strength with $ can be investigatedusing the gyre-wide budget of PV. These are evaluated as an average over the closed (mean)streamlines of the subtropical gyre, following Berlo! et al. (2007a), and yield the relative fluxof PV into and out of the gyre from wind stress curl, eddy fluxes and di!usive flux. Here wedo not discriminate between di!usive flux of PV through the boundary and di!usive intergyreflux, but Berlo! et al. (2007a) have shown that boundary fluxes dominate the di!usive flux inthis turbulent parameter regime.

The PV budgets for the $ = 0 and $ = 0.1 cases are shown in Table 2. (Here our signconvention is such that a positive PV flux equates to an input of PV into the subtropical gyre.)Introduction of the temperature-dependent wind stress both reduces the amplitude of the windstress curl (a positive PV input) and increases the eddy flux between the gyres. Both of thesee!ects act to weaken the gyre. The change in wind forcing is due to a combination of a change

13

$ = 0 $ = 0.1Wind Forcing -7160 -7010Eddy Intergyre Flux 770 1170Di!usive Flux 6390 5840

Table 2. Mean potential vorticity forcing of the subtropical gyre ($ 104 m2/s2).

0 0.5 1 1.5 2 2.5 3 3.5 4x 106

−1000

0

1000

2000

3000

4000

5000

6000

7000

8000

X (km)

PV F

lux

(× 1

04 m2 /s

2 )

α=0α=0.1

Fig. 9. Cumulative eddy PV flux as a function of zonal position along the intergyre boundaryof the mean field. Positive flux near the western boundary represents a downgradient exchangeof PV between the gyres, while the negative slope in the jet region represents an upgradientflux.

in gyre shape, and local Ekman pumping. The di!usive PV flux reduces correspondingly,presumably due to a weaker western boundary current which leads to smaller PV gradientsclose to the western wall (data not shown).

The cumulative eddy flux of PV between the subtropical and subpolar gyres can be mappedas a function of longitude, as shown in figure 9 . It is interesting to note that, despite theenhanced EKE near the western boundary in the finite $ cases, the flux of PV in that regionis not significantly altered. Instead, the primary di!erence between the two simulations shownis that at small or zero alpha, the longer jet provides a larger barrier to the transport of PVbetween the gyres. In this region, PV flux is upgradient (negative), and the small $ casestherefore result in weaker PV flux between the gyres.

This result demonstrates the subtleties involved in modelling the turbulent double gyrecirculation. The strong dependence of the mean circulation upon the parameter $ can bepartially ascribed to the PV forcing, but this result does not uniquely determine the dynamical

14

cause. The gyre dynamics is also governed by transport of PV between the gyres by eddies,which are themselves closely coupled to the strength of the circulation. For this reason, it’snot clear from the above diagnosis whether the mean forcing is of su"cient magnitude toproduce the observed changes. Instead, we frame two possible hypotheses to explain the e!ectof temperature-dependent wind stress. These hypotheses can then be explicitly tested withadditional simulations.

Hypothesis 1 – That the mean circulation is controlled by time mean PV input. Thus,changes in Ekman pumping act to modify the total PV input to, and dynamics of, bothgyres. The Ekman pumping may be dominated by broad scale changes a!ecting thegyre-wide budget. Alternatively, large values of Ekman pumping very close to the jetmay act to modify the jet dynamics so that both inertial recirculations and the jet areweakened. Under this scenario the changes in eddy activity are assumed to be a dynamicalconsequence of changing the mean PV balance of the gyres.

Hypothesis 2 – That it is the time-dependent variability of the Ekman pumping which mod-ifies the circulation structure. This may occur via several mechanisms, namely: (a)variable Ekman pumping acts as a random forcing of large-scale circulation, either di-rectly by adding to the mesoscale-eddy random forcing (Berlo! 2005a,b), or indirectly bydestabilizing the flow (Spall 2007a) and thus enhancing mesoscale eddy forcing variance;or (b) the essential part of Ekman-pumping variability is due to its correlation with theposition of the variable oceanic jet. Under this scenario, it is the mean circulation whichalters in response to Ekman-driven changes in the eddy field.

Both of these hypotheses are plausible; but also independently testable using the model formu-lated here.

4. Additional experimentsa. Mean forcing experiments

We now perform a number of additional simulations to investigate the primary cause ofchanges to the double gyre circulation caused by the inclusion of temperature-dependent windstress. Firstly, we test Hypothesis 1: that changes in the mean forcing control the large scaleresponse of the system. We achieve this by defining the time mean atmospheric wind stressfrom the case with $ = 0.1, and denote this &&!=0.1'. We then force the ocean componentof the model with this field replacing a& . Simulations are integrated for 80 model years, andcompared with the $ = 0 and $ = 0.1 cases (Figs 5b and 6b respectively).

The ocean state (Fig. 10a) shows a double gyre circulation which resembles the temperature-independent forcing case (Fig. 5b). The zonal velocity profile of the jet (solid line in Fig. 10e)is 200km shorter and 15% slower than the temperature-independent case, but these changes aresmall when compared with the full temperature-dependent case (grey dashed line in Fig. 10e).We conclude that the mean wind stress curl cannot be responsible for the primary circulationchanges induced by the temperature-dependent wind stress scheme, implying that Hypothesis1 above does not account for the first order e!ect of temperature-dependent wind stress onthe system. Nonetheless, there is a quantifiable di!erence between the present simulationsand the temperature-independent case, which deserves some attention. In particular, we raisethe question of whether interior or western boundary forcing dominates the response to meanforcing changes.

The role of interior and western boundary forcing are separated by isolating two spa-tial modes of the forcing. We do this by defining the di!erence in wind stress between the

15

(a)

Y (k

m)

0 1000 2000 30000

1000

2000

3000

(b)

0 1000 2000 30000

1000

2000

3000

(c)

X (km)

Y (k

m)

0 1000 2000 30000

1000

2000

3000

(d)

X (km)0 1000 2000 3000

0

1000

2000

3000

0 500 1000 1500 2000 2500 3000 35000

0.2

0.4

0.6

X (km)

u (m

/s)

(e)

α=0α=0.1<τ

α=0.1><τ

α=0.1WBC >

<τα=0.1INT >

τVAR

Fig. 10. Mean upper layer streamfunction (CI 2 Sv) for (a) case forced with &&!=0.1'; (b)case forced with

!&WBC!=0.1

"; (c) case forced with

!& INT!=0.1

"; and (d) case forced with &V AR. (e)

Maximum zonal velocity as a function of x along the jet core for these four experiments.

temperature-dependent and the temperature-independent cases,

#& = &&!=0.1' " &&!=0.0' . (15)

We then write the western boundary component of this forcing di!erence as a separable function,#&WBC = #&(x = 0) $ e!x/L, where L is chosen to maximise the fit with the pattern of #&near the western boundary. This allows us to define two new mean forcing fields;

!&WBC!=0.1

"=

&&!=0.0' + #&WBC for the western boundary forcing, and!& INT!=0.1

"= &&!=0.1' " #&WBC which

represents only changes to forcing in the ocean interior. These fields are used to drive twoadditional simulations, with results shown in Figs 10(b,c) respectively.

16

These two cases highlight the nonlinearity of the turbulent double-gyre circulation. Nei-ther simulation shows a measurable reduction in maximum velocity from the temperature-independent forcing case, and the jet length for the

!&WBC!=0.1

"case slightly exceeds the original.

However, there is a reduction in the jet length of about 100 km in the!& INT!=0.1

"case, implying

that the pattern of Ekman pumping either side of the jet plays some role in shortening the jet,while the western boundary contribution to forcing has very little e!ect on its own. The two ef-fects combine nonlinearly to slightly weaken the jet, but that e!ect is minor compared with thetemperature-dependent wind stress cases. This result implies that it is primarily the variabilityof Ekman pumping anomalies (Hypothesis 2 above) that dominates the system response, andwe now proceed to conduct numerical experiments to confirm this assertion.

b. Variable forcing experiments

Hypothesis 2 focusses not on the spatial pattern of mean forcing but on the variability ofthe transient component of the forcing. We now aim to establish the exact role of forcingvariability by separating the variability from the mean. This is achieved by synthesising a newforcing field based on averages from the previous simulations. Specifically, we calculate windstress forcing (for non-zero $) through Eq. (13), and then modify the forcing through

&V AR = & "#& (16)

where #& is the di!erence in mean forcing from the two references cases as described above.In this case, the mean wind stress of the forcing,

!&V AR

", approaches the stress for the

temperature-independent case &&!=0.0', but the temporal and spatial variance of the forcingfrom the temperature-dependent case is retained.

The resulting time mean circulation is shown in Fig. 10(d). The shortened jet and largemeanders of this simulation are very similar to the temperature-dependent wind stress case(Fig. 6b). In addition, the zonal velocity profile (dashed black line in Fig. 10e) shows markedlyweaker velocities than the mean forcing simulations, and is only a few percent greater than thefull temperature-dependent case.

Fig. 10(e) summarises the results from each of the experiments described above, and showsclearly that the primary e!ect of the temperature-dependent wind stress scheme on the jetlength and velocity is unambiguously due to changes in the forcing variability, rather than themean forcing. Applying the mean forcing from the $ = 0.1 case shortens the jet by about200 km (compared with the $ = 0 case). Separating this into a WBC and interior componentdemonstrates the nonlinearity of the system, in that neither of these experiments nor theiraverage equals the mean forcing case, but that it is most likely that the interior forcing ismore e!ective than the boundary forcing. However, these changes are small compared tothe temperature-dependent case and the variable forcing case, where the jet is shortened byapproximately 1000 km (nearly half its original length) and is 35% weaker. Given that the timemean wind stress of the variable forcing case is almost identical to the temperature-independentforcing case, this result provides strong support for Hypothesis 2: that the variability in windstress curl forcing is responsible for the primary mesoscale coupling e!ect of the temperature-dependent wind stress scheme.

c. Variance-modified experiments

The role of eddy forcing variance in these simulations is now modified to test which char-acteristics of the variance are essential to controlling the flow. In particular, Berlo! (2005b)shows that the space-time correlations of random forcing is important to the overall e!ect, andwe now proceed to investigate this in the current model. In this context we ask the question:

17

(a)

X (km)

Y (k

m)

0 1000 2000 30000

1000

2000

3000

0 1000 2000 30000

0.2

0.4

0.6

X (km)

u (m

/s)

(b)

α=0α=0.1uncorrelated

Fig. 11. Mean upper layer streamfunction (CI 2 Sv) for (a) uncorrelated forcing, without thecorrelation between ocean state and forcing variance; and (b) Maximum zonal velocity as afunction of x along the jet core for the uncorrelated case, compared with the two referencecases.

is the correlation between jet position and forcing required? In other words, does it matterwhether an SST front causes forcing variance locally, or at another location?

We address this question with a numerical experiment where forcing is specified, rather thancalculated from the coupled fields. The specified forcing comes from the forcing history of a 10year segment of the temperature-dependent case ($ = 0.1), where ocean Ekman pumping hasbeen saved at daily intervals. This forcing field is used for an 80 year simulation using a di!erentinitial state. In this experiment, the position of strong forcing will be spatially uncorrelatedwith the ocean fronts, but the statistics (mean and variance) of the forcing are identical to theoriginal run. We call this simulation the “uncorrelated” case.

The results from the uncorrelated simulation are shown in Fig. 11, again in the form ofthe mean double gyre circulation. The time mean state shows a long, straight jet, only slightlyweaker than the temperature-independent case. This simulation demonstrates that not only isthe variability of the forcing important; but that the correlation between variable forcing andthe flow state plays a role in the e!ect of the temperature-dependent wind stress. It remainsto discern the relevant nature of those correlations, determine why they alter the flow state sosignificantly and whether this dynamical e!ect is likely to play a role in determining the realocean circulation.

An additional test on this system is to examine whether the role of Ekman pumping anoma-lies is local or gyre-wide. For example, one could argue that the integrated PV input to thetime-dependent gyre is more relevant to the flow state than the PV input to the time mean gyre.We test this idea by running two further simulations. In the first simulation the component offorcing due to the temperature-dependent stress e!ect is averaged over the instantaneous time-dependent subtropical gyre, and distributed evenly over the gyre. In general this representsa weakening of the forcing, and may result in a weakening of the circulation. A complemen-tary test is one in which the gyre-wide forcing anomalies are compensated for by a uniformadditional value, but the localised time-dependent forcing near the jet is retained. These twosimulations are called the “redistributed” and “local” tests respectively in Fig. 12. The resultsin this case are again unambiguous. It is the localised time-dependent forcing near the ocean jetwhich acts to weaken the circulation. Thus we conclude that localised correlations between thetime-dependent forcing and flow state are of critical importance to the e!ects observed here.

18

(a) Redistributed forcing

X (km)

Y (k

m)

0 1000 2000 30000

1000

2000

3000

(b) Local forcing

X (km)

Y (k

m)

0 1000 2000 30000

1000

2000

3000

0 500 1000 1500 2000 2500 3000 35000

0.2

0.4

0.6

X (km)

u (m

/s)

(c) velocity profiles along jet

α=0α=0.1redistlocal

Fig. 12. Mean upper layer streamfunction (CI 2 Sv) for (a) redistributed forcing case, wherePV forcing anomalies are distributed across the entire time-dependent gyre; (b) local forcing,where redistribution is used to ensure that the gyre-wide PV input is equal to the time meanPV forcing, and (c) Maximum zonal velocity as a function of x along the jet core for theredistributed and local cases, compared with the two reference cases.

d. Low order model

The role of mesoscale wind stress variability is now clarified using a low order model forthe temperature-dependent stress parameterisation. The goal is to represent the wind stressvariability using ocean flow variables only. To do this we note that the wind stress curl (thedriving term in Eq. 1) depends linearly on the crosswind temperature gradients in both thenumerical experiments (Fig. 2b) and observations. Furthermore, SST is negatively correlatedwith PV (and relative vorticity) in the WBC separation region. Thus we propose that thedynamical e!ect of temperature-dependent wind stress forcing in this model may be capturedby a simple parameterisation scheme which assumes a linear relationship between the meridionalvorticity gradient and Ekman pumping anomalies. We choose a parameterisation based on therelative vorticity gradient (rather than the PV gradient), under the assumption that relativevorticity dominates PV on smaller scales (and has the advantage that it eliminates the ! e!ect).Thus we write

wek = wek + ()

)y

##2

Hp1

$(17)

where wek is the wind stress curl calculated from (14) with $ = 0 and ( is an empirical factortuned using the $ = 0.1 case to match the Ekman pumping forcing there (we use ( = 8$107m2s,yielding maximum Ekman pumping velocities of 2 $ 10!5m/s). Equation (17) is applied over

19

(a)

X (km)

Y (k

m)

0 1000 2000 30000

1000

2000

3000

0 1000 2000 30000

0.2

0.4

0.6

X (km)

u (m

/s)

(b)

α=0α=0.1param

Fig. 13. (a) Mean upper layer streamfunction (CI 2 Sv); and (b) maximum zonal velocity asa function of x along the jet core for the simulation using the parameterisation described by(17).

all points except those within 3 grid points of the boundary (where high relative vorticity isdue to boundary friction rather than fronts in the ocean interior) for a simulation without adynamic mixed layer or explicit temperature-dependent stress.

The results for this simulation are shown in Fig. 13. The time mean flow is faster thanthe $ = 0.1 case in the inertial part of the jet core, but jet length matches the temperature-dependent wind stress case to a surprising degree. The higher velocities in the jet core are mostlikely due to di!erences in the boundary Ekman pumping which alters the PV distribution closeto the western boundary current. However, the primary result of this simulation is that theparameterisation described by (17) curtails the jet length in the same way as the temperature-dependent wind stress scheme, implying that the primary e!ect of the wind stress scheme onthe mean circulation is due to small scale correlations between forcing and the ocean flow state.

5. DiscussionThe numerical experiments described here are designed to determine the e!ect of temperature-

dependent wind stress upon the large scale ocean circulation in an eddy-resolving model.Temperature-dependence causes elevated wind stress in regions where strong fronts in SST(and PV) produce large gradients in the stress, and hence large values of wind stress curl. Inthis model, where we have restricted the atmospheric winds to be time-independent and purelyzonal, and most fronts are oriented in the zonal direction, the dominant term is the ageostrophicnorthward Ekman transport in the atmospheric mixed layer which brings warm air across thefront. The result is a strong atmosphere-ocean temperature di!erence north of the front which,according to the parameterised temperature-dependence of stress, produces strong wind stresscurl from both components of the wind stress.

The above simulations show that the changes in wind stress due to temperature-dependencecan have a very strong e!ect on the circulation of the ocean in this eddy-resolving model. Thee!ect is produced not by changes to the mean wind stress, but is instead due to the temporalvariations of stress. Moreover, we have shown that the correlation between the instantaneousflow state and the time-dependent stress is crucial in altering the circulation. This was demon-strated by comparing runs with the same forcing variability, but one of which had forcingprescribed from a previous simulation, rather than part of the coupled calculation. As a result,a simple empirical parameterisation of the flow state can replace the full coupled equation withsome success.

20

The exact mechanism by which small-scale forcing terms near the jet modify the gyre-widecirculation is not entirely clear from this study, because of the coupled nature of the eddyforcing and the mean circulation. However, some clarification is provided by Table 2 and Fig. 9with reference to the results of Berlo! et al. (2007b). This data shows that the simulation withtemperature-dependent stress included has both a smaller PV forcing from the wind field, and astronger eddy intergyre flux. The stronger intergyre flux is due to a weakening of the intergyrePV barrier, implying that the jet dividing the two gyres is destabilised by the small-scale windforcing in this region. Enhanced baroclinic instability was predicted by Spall (2007a) for thecase of poleward air flow over a front, however the mechanisms proposed by Spall do not appearto be active in this flow.

We have used a suite of experiments to eliminate a number of plausible hypotheses for thesystem behaviour. The final result is that we know that the small-scale forcing near the oceanjet is critical. This forcing can be parameterised as a linear function of the gradient of relativevorticity, acting to produce intense positive Ekman pumping over regions of strong fronts. Theprimary e!ect of positive Ekman pumping is to attract fronts, including the primary jet dividingthe two gyres, to the south. We propose that this southward movement acts to destabilise thejet either by tilting the jet in a south-easterly direction or by creating a large meander nearthe western boundary separation point (which is controlled independently). The e!ect on thesystem is thus high EKE near the western boundary (Fig. 8), and a shorter jet which resultsin a weaker PV barrier between the gyres, and thus a weaker circulation in total.

The results in this study pertain to a particular, idealised, numerical model of the ocean.It remains to determine whether or not such an e!ect will be equally significant in the realocean. We do not directly answer this question in the present paper, but instead make thecase that the e!ect seen here is a potentially important part of the ocean-atmosphere system,and that it deserves additional attention. In particular, we used scatterometer observations todemonstrate that the temperature-dependent wind stress scheme produced realistic e!ects, butthere are significant uncertainties in the estimate of the best value of the coupling coe"cientto use. Thus, process modelling and observations of the ocean and atmospheric boundary layerare needed to better constraint the magnitude of wind stress forcing changes. Futhermore,the present simulations used a purely zonal geostrophic wind field; simulations using a modelwith time-dependent winds, including synoptic events, may result in significantly greater e!ectsdue to non-zonal geostrophic wind over SST fronts. The present study is idealised in manyrespects; simulations with large scale, high resolution ocean-climate models are needed to gaugethe overall e!ect of temperature-dependent wind stress on the ocean.

Scatterometer studies also show the emergence of small-scale stress variability due to di!er-ences between oceanic and atmospheric velocity (Chelton et al. 2004; Park et al. 2006). Thise!ect was not included in the present simulations. Additional tests (not shown here) indicatethat this component of small-scale stress does not alter the mean circulation significantly forthe double gyre case, but can do in the case of a channel ocean (mimicking the AntarcticCircumpolar Current). This is the subject of ongoing work.

The results shown here also have implications for the forcing of eddy-resolving ocean models.The importance of small-scale wind stress curl may lead one to assume that realistic forcing(for example, directly importing QuikSCAT wind stress data) will produce a mean circulationcloser to observations. However, unless the model is a perfect representation of reality, sucha forcing strategy will miss the mesoscale e!ects seen here because the correlation betweenflow states and forcing anomalies will be absent (Seo et al. 2007). Therefore, we propose thateddy resolving models require forcing by large scale winds, with an additional high resolutiondynamic mixed layer (or parameterisation) to represent the mesoscale coupling e!ect.

The existence of temperature-dependent wind stress has been noted by several previousstudies. However, the e!ect is small-scale, and perhaps assumed by many to be local. This

21

study has demonstrated the opposite – that small-scale forcing of the ocean can produce large-scale e!ects. The implication is that the next generation of eddy-resolving ocean-climate modelswill either need to parameterise, or else directly simulate, the e!ects of mesoscale coupling dueto ocean-atmosphere interactions on the scale of the oceanic Rossby radius.

6. Conclusions1. Including a temperature-dependent wind stress scheme with realistic magnitude in an

eddy-resolving ocean model substantially changes the time mean circulation.

2. The primary e!ect in this model is due to ageostrophic meridional Ekman transport ofatmospheric mixed layer temperature, which acts to produce a local intense wind stresscurl close to fronts.

3. We propose that this local forcing enhances turbulence in the region of the jet separationby destabilising the flow, and reduces the up-gradient eddy flux further downstream. Theresulting mean circulation consists of weaker gyres and a weaker jet.

AcknowledgementsAH and WD were supported by an ARC Linkage International Grant (LX0668781). WD was

also supported by NSF grants OCE 0424227 and OCE 0550139. Funding for PB was providedby NSF grants OCE 0344094, OCE 0725796 and by the research grant from the Newton Trustof the University of Cambridge. SK was supported by US DOE grant DE-FG02-02ER63413and NASA grant NNG-06-AG66G-1. Numerical computations were supported by an awardunder the Merit Allocation Scheme on the National Facility of the Australian Partnership forAdvanced Computing.

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