17
Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific* KELVIN J. RICHARDS AND SHANG-PING XIE International Pacific Research Center, University of Hawaii at Manoa, Honolulu, Hawaii TORU MIYAMA Frontier Research Center for Global Change, Yokohama, Japan (Manuscript received 30 June 2008, in final form 26 November 2008) ABSTRACT The zonal and meridional asymmetries in the eastern tropical Pacific (the eastern equatorial cold tongue and the northern intertropical convergence zone) are key aspects of the region that are strongly influenced by ocean–atmosphere interactions. Here the authors investigate the impact of vertical mixing in the ocean on these asymmetries, employing a coupled ocean–atmosphere regional model. Results highlight the need to study the impact of processes such as vertical mixing in the context of the coupled system. Changes to the vertical mixing in the ocean are found to produce large changes in the state of the system, which include changes to the surface properties of the ocean, the ocean currents, the surface wind field, and clouds and precipitation in the atmosphere. Much of the strength of the impact is through interactions between the ocean and atmosphere. Increasing ocean mixing has an opposite effect on the zonal and meridional asymmetries. The zonal asymmetry is increased (i.e., a colder eastern equatorial cold tongue and increased easterly winds), whereas the meridional asymmetry is decreased (a reduced north–south temperature difference and reduced southerlies), with the impact being enhanced by the Bjerknes and wind–evaporation–sea surface temperature feedbacks. Water mass transformations are analyzed by consideration of the diapynic fluxes. Although the general character of the diapycnic transport remains relatively unchanged with a change in ocean mixing, there are changes to the magnitude and location of the transport in density space. Oceanic vertical mixing impacts the balance of terms contributing to the heating of the ocean surface mixed layer. With reduced mixing the advection of heat plays an increased role in areas such as the far eastern tropical Pacific and under the intertropical convergence zone. 1. Introduction In assessing the impact of a particular physical process in the ocean–atmosphere system it is important that the assessment is done in the proper context. Vertical mixing in the equatorial ocean is a good example. A number of studies have shown that the magnitude and time evolution of El Nin ˜ o–Southern Oscillation events depends very much on the state of the ocean (see, e.g., Neelin 1991; Jin and Neelin 1993; Timmermann et al. 1999; Meehl et al. 2001). For instance, Meehl et al. (2001) find an increase in the amplitude of ENSO ac- tivity in a coupled numerical model when the vertical mixing is reduced (resulting in a sharpening of the thermocline). Recognizing the importance of the ocean state, nu- merous studies have focused on improving the perfor- mance of ocean general circulation models (OGCMs) in the tropics by testing and refining the parameterization of vertical mixing in such models. A list of studies, which is by no means all inclusive, includes Pacanowski and Philander (1981), Rosati and Miyakoda (1988), Blanke and Delecluse (1993), Chen et al. (1994), Yu and Schopf (1997), Li et al. (2001), and Noh et al. (2005). All of the cited works describe experiments in which an ocean * International Pacific Research Center Publication Number 560 and School of Ocean and Earth Science and Technology Publication Number 7586. Corresponding author address: Kelvin Richards, International Pacific Research Center, University of Hawaii at Manoa, 1680 East-West Rd., Honolulu, HI 96822. E-mail: [email protected] 1JULY 2009 RICHARDS ET AL. 3703 DOI: 10.1175/2009JCLI2702.1 Ó 2009 American Meteorological Society

Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific*

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Page 1: Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific*

Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–AtmosphereSystem in the Eastern Tropical Pacific*

KELVIN J. RICHARDS AND SHANG-PING XIE

International Pacific Research Center, University of Hawaii at Manoa, Honolulu, Hawaii

TORU MIYAMA

Frontier Research Center for Global Change, Yokohama, Japan

(Manuscript received 30 June 2008, in final form 26 November 2008)

ABSTRACT

The zonal and meridional asymmetries in the eastern tropical Pacific (the eastern equatorial cold tongue

and the northern intertropical convergence zone) are key aspects of the region that are strongly influenced by

ocean–atmosphere interactions. Here the authors investigate the impact of vertical mixing in the ocean on

these asymmetries, employing a coupled ocean–atmosphere regional model. Results highlight the need to

study the impact of processes such as vertical mixing in the context of the coupled system.

Changes to the vertical mixing in the ocean are found to produce large changes in the state of the system,

which include changes to the surface properties of the ocean, the ocean currents, the surface wind field, and

clouds and precipitation in the atmosphere. Much of the strength of the impact is through interactions

between the ocean and atmosphere. Increasing ocean mixing has an opposite effect on the zonal and

meridional asymmetries. The zonal asymmetry is increased (i.e., a colder eastern equatorial cold tongue

and increased easterly winds), whereas the meridional asymmetry is decreased (a reduced north–south

temperature difference and reduced southerlies), with the impact being enhanced by the Bjerknes and

wind–evaporation–sea surface temperature feedbacks.

Water mass transformations are analyzed by consideration of the diapynic fluxes. Although the general

character of the diapycnic transport remains relatively unchanged with a change in ocean mixing, there are

changes to the magnitude and location of the transport in density space. Oceanic vertical mixing impacts

the balance of terms contributing to the heating of the ocean surface mixed layer. With reduced mixing the

advection of heat plays an increased role in areas such as the far eastern tropical Pacific and under the

intertropical convergence zone.

1. Introduction

In assessing the impact of a particular physical process

in the ocean–atmosphere system it is important that

the assessment is done in the proper context. Vertical

mixing in the equatorial ocean is a good example. A

number of studies have shown that the magnitude and

time evolution of El Nino–Southern Oscillation events

depends very much on the state of the ocean (see, e.g.,

Neelin 1991; Jin and Neelin 1993; Timmermann et al.

1999; Meehl et al. 2001). For instance, Meehl et al.

(2001) find an increase in the amplitude of ENSO ac-

tivity in a coupled numerical model when the vertical

mixing is reduced (resulting in a sharpening of the

thermocline).

Recognizing the importance of the ocean state, nu-

merous studies have focused on improving the perfor-

mance of ocean general circulation models (OGCMs) in

the tropics by testing and refining the parameterization

of vertical mixing in such models. A list of studies, which

is by no means all inclusive, includes Pacanowski and

Philander (1981), Rosati and Miyakoda (1988), Blanke

and Delecluse (1993), Chen et al. (1994), Yu and Schopf

(1997), Li et al. (2001), and Noh et al. (2005). All of the

cited works describe experiments in which an ocean

* International Pacific Research Center Publication Number 560

and School of Ocean and Earth Science and Technology Publication

Number 7586.

Corresponding author address: Kelvin Richards, International

Pacific Research Center, University of Hawaii at Manoa, 1680

East-West Rd., Honolulu, HI 96822.

E-mail: [email protected]

1 JULY 2009 R I C H A R D S E T A L . 3703

DOI: 10.1175/2009JCLI2702.1

� 2009 American Meteorological Society

Page 2: Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific*

model is forced with a prescribed atmospheric forcing.

What this numerical experimentation strategy does not

allow for is a feedback from a changed ocean, caused by

a change in the ocean physics, to the atmosphere. The

result is a possible inconsistency across the ocean–

atmopshere interface. The limitations of experiments

using ocean-only models as opposed to fully coupled

models to study ocean processes has been known for

some time (see, e.g., Guilyardi and Madec 1997). A

prime example is the Bjerknes feedback [Bjerknes

(1969): a colder SST in the eastern Pacific, possibly

brought about by increased mixing, drives stronger

easterlies, which in turn produce stronger upwelling and

cooling]. Choosing between parameterization schemes

on the basis of a ‘‘better’’ SST field therefore may be

misleading. Another factor that should not be forgotten,

although not explored here, is the interplay between

processes. For instance, Maes et al. (1997) find the rate

of vertical mixing in their model changes as the level of

lateral mixing is changed.

The focus of the present study is on the eastern tropical

Pacific. Mitchell and Wallace (1992) and Kessler (2006)

describe the features of the atmospheric climatology

and ocean circulation, respectively. The coupled dy-

namics of the region are reviewed by Xie (2004).

The region plays an important role in ENSO dynamics

through, in particular, the state of the eastern cold tongue

and the Bjerknes feedback described above. The pur-

pose of the present paper is twofold. The first is to

identify where and at what rate diapycnic fluxes are

occurring. The utility of estimating water mass trans-

formations by considering the flux across density sur-

faces dates back to Walin (1982); see also Marshall et al.

(1999) and references therein. These studies have con-

centrated on the transformations in the surface mixed

layer and seasonal thermocline. Sun and Bleck (2006)

extend the analysis to the deep ocean. Here we employ

the technique presented by Sun and Bleck, which pro-

jects model variables onto discrete density layers and

calculates the implied fluxes between layers. This pro-

duces a different, and we argue more correct, picture

than that produced by simply calculating the Eulerian

averaged vertical velocity field, which can be misleading

(see Hazeleger et al. 2001). The second and main pur-

pose is to investigate the sensitivity of the coupled sys-

tem to changes in the prescribed vertical mixing. Our

intent is not to choose between vertical mixing schemes

(in fact, we use a relatively simple parameterization

scheme) but to highlight the inherently coupled nature

of the response of the system to changes in the mixing.

As we will see, changing the level of ocean mixing in a

coupled model produces significantly larger changes to

SST than those produced in ocean-only experiments.

The coupling also produces substantial changes to the

ocean currents that can radically alter the balance of

terms affecting the heat content of the ocean mixed layer.

The tool used in this study is a regional coupled

ocean–atmosphere model configured for the eastern

tropical Pacific (Xie et al. 2007). Advantages of using a

regional coupled model are that the local processes are

isolated and the coupling ensures consistency between

the oceanic and atmospheric components. In our par-

ticular case, we use a moderately high horizontal reso-

lution (0.58 in both the atmosphere and ocean), which

for the atmospheric component means that the model

atmosphere is able to resolve and respond to relatively

small horizontal scale changes in SST.

The rest of the paper is structured as follows: Details

of the regional coupled model are briefly described in

section 2. The methodology and results of the analysis of

diapycnic fluxes are described in section 3. The impact

of changing the level of vertical mixing in the coupled

model is investigated in section 4. An analysis of the

balance of terms affecting the heat content of the ocean

mixed layer is presented in section 5. Section 6 provides

some concluding remarks.

2. Regional coupled model

The model we use is the International Pacific Research

Center (IPRC) Regional Ocean Atmosphere Model

(IROAM) configured for the eastern tropical Pacific.

The atmospheric component is the IPRC Regional

Atmospheric Model (RAM) (Wang et al. 2003) con-

figured for the region from 358S to 358N, 1508 to 308W.

The oceanic component is the Geophysical Fluid Dy-

namics Laboratory Modular Ocean Model version 2

(MOM2) (Pacanowski 1995) configured for the Pacific

basin from 358S to 358N. The oceanic and atmospheric

components each have a horizontal resolution of 0.58 3

0.58. The vertical discretization is 28 sigma levels in the

atmosphere and 30 z levels in the ocean with enhanced

resolution close to the lower and upper boundary,

respectively. The two components are coupled from

1508W to the American coast and from 308S to 308N.

Outside this domain, over the western part of the Pacific

Ocean, the oceanic component is forced by prescribed

surface fields from the daily National Centers for

Environmental Prediction–National Center for Atmo-

spheric Research (NCEP–NCAR) reanalysis (Kistler

et al. 2001) with turbulent fluxes computed using the

bulk formula of Fairall et al. (2003). The temperature

and salinity at the closed northern and southern bound-

aries of the ocean are relaxed back to the Levitus (1982)

climatology. For the atmospheric component the SST

over the Atlantic sector is prescribed by the weekly SST

3704 J O U R N A L O F C L I M A T E VOLUME 22

Page 3: Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific*

product of Reynolds et al. (2002). The lateral bound-

aries of the RAM are nudged toward the NCEP–NCAR

reanalysis. Full details of the model can be found in Xie

et al. (2007).

Lateral mixing in the ocean is prescribed as horizontal

Laplacian diffusion with a constant coefficient of 200

m2 s21. Pezzi and Richards (2003) find the results of ex-

periments with an ocean model configured for an ide-

alized tropical ocean basin are little changed by the

form of lateral mixing (isopycnic versus horizontal), or

grid resolution, provided a small value is used for the

lateral diffusion coefficient (their small value was 400

m2 s21). The contribution by lateral mixing to the heat

balance of the mixed layer in our experiments is found

to be negligible (see section 5). We therefore do not

expect our results to be unduly affected by the level or

form of lateral mixing. Vertical diffusion of tracers, on

the other hand, is found to be very influential on the

model solution. Vertical mixing is prescribed by

the Richardson number–dependent Pacanowski and Phi-

lander (1981) parameterization scheme. The minimum

(background) value for viscosity is set to 1024 m2 s21 to

avoid numerical stability issues and is kept the same for

all experiments. The background value of the diffusion

coefficient of tracers is set to 1026 m2 s21 for our control

experiment (also referred to as experiment LOW—the

effect of changing this value is investigated in section 4).

The low value for the background diffusion coefficient is

chosen in part because of the observation of low values

at low latitudes (Gregg et al. 2003) and in part by nu-

merical experiments that demonstrate that a low value

gives an improved zonal current structure in the tropics

(R. Furue 2007, personal communication).

In all experiments the ocean component, MOM2,

is initialized by setting the tracer fields to Levitus

(1982) climatology for January and the velocity to zero.

The oceanic component is spun up for five years with

NCEP–NCAR reanalysis fluxes across the whole do-

main, starting in January 1991. The oceanic and atmo-

spheric components are then coupled in January 1996

and the coupled model is run an additional eight years.

In terms of the Nino-3 SST, the model tracks both the

annual and interannual observed variability very well

(Xie et al. 2007). Here we present results averaged over

years 2000–03 to avoid the 1997–98 El Nino–La Nina,

and we will refer to the average as the annual average.

To assess the degree to which the ocean had adjusted to

the specified vertical mixing, the stratification in the

thermocline was examined in individual yearly averages

over the period used in the analysis. No discernable

change was detected, except for the change associated

with a weaker undercurrent in 2002.

Additional ocean-only experiments were performed.

Here the ocean component (MOM2) is forced by the

NCEP–NCAR reanalysis over the whole of the tropical

Pacific basin.

To demonstrate the fidelity of the model we present

the IROAM annual average surface wind field, SST,

and precipitation in Fig. 1. Realistic features of the

model include the northward displaced intertropical

convergence zone (ITCZ), the strength and westward

extension of the equatorial cold tongue, and the

southeasterly winds over the southeast Pacific. A more

thorough comparison of the model’s annual mean and

seasonal cycle with observations is presented in Xie

et al. (2007); de Szoeke and Xie (2008) evaluate the

model performance in comparison with state-of-the-art

coupled GCMs. The zonal component of velocity as a

function of latitude and depth along 1258W from ob-

servations (Johnson et al. 2002) and the control run is

shown in the top and middle panels of Fig. 2. The ob-

served structure of the currents is well reproduced

by the model. The shape of the model Equatorial Un-

dercurrent (EUC) is good, although its maximum

(1.26 m s21) is approximately 20% greater than that ob-

served and the thermocline is too diffuse. The subsurface

FIG. 1. The annual mean precipitation (mm day21) (gray shading), surface wind field (arrows),

and SST (8C) (contours) for the control run: LOW.

1 JULY 2009 R I C H A R D S E T A L . 3705

Page 4: Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific*

countercurrents (SSCCs) centered at 58S and 48N are

well placed but somewhat too weak, particularly the

southern SSCC. The model North Equatorial Counter-

current (NECC) has a maximum of 0.34 m s21, which is

somewhat greater than that observed (0.26 m s21) and is

displaced approximately 18 to the south of the observed

maximum.

3. Diapycnic fluxes

We start by considering the meridional overturning

circulation. As noted by Hazeleger et al. (2001), calcu-

lating the meridional overturning streamfunction by

averaging the flow at constant depth, denoted by cz

(shown in Fig. 3a for the control case), produces a

misleading result in terms of the ventilation character-

istics of the tropics. The streamfunction cz exhibits

strong so-called tropical cells that would imply a

downward, diapycnic flux between 38 and 58 north and

south of the equator. This misleading, or spurious, result

arises from a combination of averaging across the east–

west sloping density surfaces and the highly variable

flow caused by the tropical instability waves (TIWs)

(Hazeleger et al. 2001). Instead, we choose to view

the overturning circulation in density space. The stream-

function cs (Fig. 3b), where s denotes potential density,

is calculated by first projecting daily averages of the

horizontal velocity field (u, y) onto discrete density

layers to obtain the isopycnic volume transport uhs 5

(uhs, yhs), where u and y are the eastward and north-

ward components of velocity, respectively, and hs 5

h(x, y, s, t) denotes the thickness of a given density

layer. Here we discretize density by increments of Ds 5

0.02 kg m23. The time-averaged meridional component

of the isopycnic mass transport, yhs, is then integrated

zonally to produce cs.

The circulation in density space (Fig. 3b) is dominated

by the two subtropical cells (STCs) north and south of

the equator (cf. McCreary and Lu 1994). The transport

of the northern and southern cells, based on the maxi-

mum and minimum value of cs, is 18 and 16 Sv (Sv [

106 m3 s21), respectively, with the center of the northern

cell at a somewhat lighter density than the southern.

Note that the majority of the transport occurs between

308S and 308N. There is, however, a modest amount

of water mass transformation occurring in the relaxa-

tion regions applied to MOM2 poleward of 308 latitude.

In the southern cell water is advected south in the

FIG. 2. The annual-mean zonal component of velocity (m s21) along 1258W (color). Also shown is the potential

density (contour interval 0.25 g m23). The black contours indicate s 5 23 and 23.8 (kg m23), the bottom surface of the

two layers examined in Fig. 4. (top) Observations (Johnson et al. 2002), (middle) LOW, and (bottom) HIGH.

3706 J O U R N A L O F C L I M A T E VOLUME 22

Page 5: Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific*

surface layer, becoming progressively denser. Subduc-

tion occurs around 208S followed by an approximately

adiabatic flow to the equator. A strong diapycnic flux

ensues in the vicinity of the equator with this flux being

somewhat off the equator for lighter layers. The situa-

tion in the northern cell has two important differences.

First, there is a significant diapycnic flux from approxi-

mately 158N as water is moved to the equator along the

lower (denser) branch of the cell. Second, there is a

counterrotating cell centered at 38N and s 5 23 such

that the upwelling is pushed well off the equator. Note

that the diapycnic flux (from dense to light) is in the

opposite direction, in terms of density, to that implied

by the tropical cells found in cz (Fig. 3a).

The spatial distribution of the diapynic flux can be

determined by calculating the diapycnic velocity ws from

the lateral divergence of the isopycnic volume transport,

w1s � w�s 5 �$s(hsu) (1)

in which w1s and w�s refer to the diapycnic velocity at

the top and bottom of a given layer, respectively, and we

have assumed the tendency term for layer thickness is

negligible (which is the case here). The diapycnic ve-

locity across a given interface between layers can be

found by taking ws 5 0 at the top and bottom of the

water column. Sun and Bleck (2006) use the same

method to calculate the geographic distribution of the

diapycnic component of the thermohaline circulation in

a number of climate models.

The diapycnic velocity, ws, at the bottom of two

density layers is shown in Fig. 4. A positive ws indicates

a diapycnic flow in the direction of decreasing density

(i.e., an upward flow, on the whole). Also shown in

Fig. 4 is the depth of the layer and the isopycnic mass

flux. The layers have been chosen so that they cut

through the centers of the southern STC (bottom panel,

s 5 23.7) and the secondary circulation in the northern

STC (top panel, s 5 22.9), respectively (see Fig. 3b). On

the denser s 5 23.7 layer (bottom panel in Fig. 4), as

expected, we see a region of positive ws on the top of

the eastward-flowing EUC where there is high shear

and, hence, mixing. We also see, however, regions of

positive ws as the flow peels off and retroflects to join

the northern and, in particular, the southern branches of

the South Equatorial Current (SEC). This positive flux

is consistent with the warming of the SEC as it flows

westward. The region of positive ws in the SEC moves

westward as s decreases. The circulation is closed by the

regions of negative ws as water is cooled while it moves

southward in the surface layer. On s 5 23.7 this is oc-

curring along 128S, whereas it is just starting to appear at

208N. The regions of negative ws move equatorward as

s decreases. The isopycnic layer s 5 23.7 is domed

along 108N under the model’s ITCZ and farther east as

the Costa Rica Dome. The positive ws in these regions

contributes to the diapycnic flux inferred from the lower

limb of a Lagrangian meridional streamfunction

(Fig. 3b). It is interesting to note the additional doming

of water centered on 78N, 828W.

On s 5 22.9 (top panel in Fig. 4) the near-equator

vertical flux is dramatically different from that below.

The vertical flux is now dominated by bands of negative

and positive ws centered on approximately 28 and 58N,

respectively. The sense of the diapycnic flux is consis-

tent with that required to close the residual circulation

induced by the TIWs, as indicated in Fig. 3b, and is such

as to recirculate and mix water in the mixed layer be-

tween the southern flank of the eastward flowing NECC

and the westward flowing water in the northern branch

of the SEC. To reemphasize the importance of aver-

aging flow fields in an appropriate way, the vertical

FIG. 3. The meridional streamfunctions (a) cz and (b) cs for the control run, contour interval 2 Sv.

Gray shading indicates negative values.

1 JULY 2009 R I C H A R D S E T A L . 3707

Page 6: Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific*

component of velocity associated with the northern

tropical cell, obtained by averaging fields at a constant

depth, is downward along 58N with a minimum value of

around 24 3 1025 m s21, which is of opposite sense, in

terms of the flux across density surfaces, and a factor of 4

greater in amplitude compared to ws at this latitude (see

Fig. 3b).

The diapycnic transport integrated over the area 88S–

88N, 1008–1408W is shown in Fig. 5. The transport peaks

at 18 Sv at around s 5 23.5. The region captures most of

the diapycnic transport at this range of latitude with the

maximum transport being 70% of that obtained by in-

tegrating over the entire width of the basin. The con-

tributions from regions of positive and negative values

of ws, respectively, are also shown. The peak in

the contribution from negative ws at s 5 22.8 is asso-

ciated with the TIWs. It is noteworthy, however, that

the contribution from negative ws is significant over the

density range shown and indicates that there is appre-

ciably more transformation of water masses than in-

ferred from the net transport alone.

4. Impact of vertical mixing

To assess the impact of vertical mixing in the ocean on

the coupled system we consider the effect of changing the

vertical diffusivity in the ocean component of the model.

The vertical mixing schemes for momentum and trac-

ers in the ocean model are based on Pacanowski and

Philander (1981); that is, the vertical viscosity, v, and

diffusion coefficient, kz, are given by

n 5n0

(1 1 aRi)n 1 n0 (2)

and

FIG. 4. Diapycnic velocity ws (m s21) across the bottom of the given density layer (color); the

isopycnic volume transport, uhs (vectors, scale arrow indicates 10 m2 s21); and depth of the

density layer for the control run (top) s 5 22.9 and (bottom) s 5 23.7 (kg m23).

3708 J O U R N A L O F C L I M A T E VOLUME 22

Page 7: Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific*

kz 5n

(1 1 aRi)1 k0, (3)

where Ri is the gradient Richardson number and v0 and

k0 are the background viscosity and diffusion coeffi-

cient, respectively. The constants a and n are set to 5

and 2, respectively (as in Pacanowski and Philander

1981), and the background viscosity, v0, to 1024 m2 s21

in all experiments. We consider a change to the back-

ground diffusion coefficient alone and take two cases: k0 5

1026 m2 s21 (the control run) and k0 5 50 3 1026 m2 s21.

The two model runs are labeled LOW and HIGH, re-

spectively. It should be noted from (3) that changes to k0

can influence the magnitude of kz through changes to

the Richardson number. Indeed, with a weaker strati-

fication and lower Richardson number kz is increased

in the thermocline with the maximum value of kz (at the

top of the EUC) in HIGH (8 3 1023 m2 s21) being

approximately twice that found in LOW.

a. Changes in diapycnic fluxes

The general character of the diapycnic fluxes changes

little with the change in the background diffusivity. The

integrated diapycnic transport of HIGH is compared to

that of LOW in Fig. 5. The shape of the transport with

respect to density is similar in the two experiments.

There are changes, however, to the magnitude and lo-

cation of the transport in density space. The maximum

diapycnic flux in HIGH is 20% greater than that in

LOW (22.2 Sv compared to 19.6 Sv, respectively, con-

sistent with the stronger easterlies in HIGH; see later)

with the peak being narrower but with the tail reaching

to somewhat higher densities. The maxima in the up-

ward and downward diapycnic transports are shifted to

lower densities in HIGH compared to LOW. The peak

in the net downward transport associated with the TIWs

is increased by 60% (21.9 Sv at s 5 22.8 for HIGH

compared to 21.2 Sv at s 5 22.6 for LOW).

b. Changes in surface properties

To characterize the changes to the system brought

about by a change in the ocean vertical diffusivity

we first consider the change in two surface properties.

Figure 6 shows the difference in surface temperature

and near-surface wind field between the HIGH and

LOW runs for the April and October climatologies (top

and bottom panels, respectively). Also shown in Fig. 6

are the results using the ocean-only model (right col-

umn), that is, the ocean model forced with NCEP–

NCAR reanalysis over the entire domain. For the

ocean-only case, the change in SST brought about by

increasing k0 is greatest where and when the mixed-

layer depth is shallow. In April the change in SST rea-

ches 21.48C toward the eastern end of the region,

whereas in October the change is much smaller. In the

coupled system we find the change in SST is consider-

ably more than in the ocean-only case. In April it rea-

ches 24.08C in the far east with the signal spreading into

the Gulf of Panama. The signal also spreads farther

toward the west than in the ocean-only case. Associated

also with the cooler SST along the equator is a reduction

FIG. 5. Diapycnic mass transport as a function of potential density averaged over the area

88S–88N, 1408–808W: total transport (thick solid line), averaged over positive ws only (thin

solid line), and averaged over negative ws only (dashed line) for the (left) LOW and (right)

HIGH runs.

1 JULY 2009 R I C H A R D S E T A L . 3709

Page 8: Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific*

in the southeasterly winds in the south Pacific, particu-

larly along the South American coast, and a reduction in

the gap winds in the Gulfs of Panama and Papagayo (the

latter seen in the October climatology). This decrease in

the strength of the gap winds is a consequence of the

increase in sea level pressure on the Pacific side caused

by the cooler SST. In October there is a substantial

warming off the coast of South America south of 58S

and a substantial cooling over the eastern side of the

South American continent.

The annual variation in the difference in SST and

surface wind between HIGH and LOW, averaged be-

tween 28S and 28N, is shown in Fig. 7 as a function of

longitude. An increase in vertical mixing in the ocean

causes a reduction in the southerly component of the

surface wind throughout the year in the far east, peaking

in December–February in the central and western parts

of the region. This reduction of the southerly wind at the

equator is caused by the meridional asymmetry in the

change in SST (Fig. 8), which itself is a consequence of

the stronger stratification of the ocean north of the

equator compared to that to the south. In the central

and western equatorial parts of the region the cooling

peaks in April (in excess of 1.58C) with a strong easterly

anomaly in the surface wind. This strong cooling occurs

at a time when the equatorial ocean is at its warmest and

most strongly stratified. The net effect of increased

ocean mixing is to reduce the range of the annual cycle in

the equatorial SST by as much as 1.58C. As the equatorial

annual cycle arises from the meridional asymmetry

in mean climate (Xie 1994), the reduction in the latter

causes the former to weaken. The annual cycle affects

FIG. 6. Differences in surface properties between the HIGH and LOW runs: surface tem-

perature (color; contour interval of 0.58C) and near-surface winds (vectors) for (top) March

and (bottom) October climatologies in the (left) fully coupled and the (right) ocean-only

experiments.

FIG. 7. Differences in the annual cycle of surface properties

between the HIGH and LOW runs, averaged between 28S and

28N, as a function of longitude: surface temperature (gray shading,

contour interval 0.58C) and near-surface winds (vectors).

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ENSO both in phase and amplitude (e.g., Guilyardi 2006;

Timmermann et al. 2007).

Increasing the vertical mixing in the ocean is found

to increase the zonal asymmetry (a colder cold tongue

and stronger easterlies) while reducing the meridional

asymmetry (reduced north–south temperature differ-

ence and southerly wind). These asymmmetries are key

aspects of the eastern tropical Pacific. The sense of the

surface wind anomalies shown in Figs. 7 and 8

is indicative of an amplification of the impact of mix-

ing on the zonal and meridional asymmetries of the

eastern tropical Pacific through ocean–atmosphere

interactions—the Bjerknes feedback (Bjerknes 1969)

and the wind–evaporation–SST (WES) feedback (Xie

2004), respectively. In the case of the zonal asymmetry,

colder surface water in the east of the equatorial Pacific,

brought about by increased vertical mixing, increases

the sea level pressure. The increased surface pressure

drives stronger easterlies that increases upwelling, lead-

ing to a further cooling of the surface ocean. In the case

of the meridional asymmetry, the eastward and west-

ward turning of the southerly wind north and south of

the equator, respectively, caused by the Coriolis force,

means that the reduced southerlies at the equator as

ocean mixing is increased is accompanied by an increase

(decrease) in the easterly wind north (south) of the

equator. This tendency is seen in the annual mean of

the change in surface winds (Fig. 8), particularly to the

south of the equator. The increased easterlies to the

north of the equator tend to increase the latent heat

flux and cool the ocean. The opposite occurs south of

the equator, leading to a warming of the ocean. The

net result is a reduction in the meridional gradient

in SST.

The changes to the annual mean latent, QLA, and

shortwave, QSW, surface heat fluxes (the two main con-

tributors to the net heat flux) are shown in Fig. 8. A

positive flux indicates a tendency to warm the underlying

surface. The change in QLA over the ocean broadly

reflects the change in SST (latent cooling is reduced

over colder SSTs). The exception is 58–108S, where the

positive change in QLA (decreased cooling) is consistent

with the WES feedback described above. Changes to

the shortwave radiation are directly related to changes

to the model’s low-level cloud (as measured by the total

liquid water content below 700 mb), as evidenced by the

very similar patterns in the changes to the two quantities

(the latter quantity is not shown). The shortwave radi-

ation, and low-level clouds, are increased and decreased

off the coast of South America and in the Gulf of

FIG. 8. Differences in the (top left) annual mean precipitation (mm day21), (top right) surface

shortwave radiation QSW (W m22), (lower left) surface latent heat flux QLA (W m22), and

(lower right) surface temperature (8C) and surface wind (scale arrow over South America

indicates 2 m2 s21) between the HIGH and LOW runs. The gray boxes on the surface tem-

perature plot indicate the regions over which the heat budget is calculated.

1 JULY 2009 R I C H A R D S E T A L . 3711

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Panama, respectively. Both changes are brought about

by the positive feedback between the SST and low-level

stratus clouds (see Norris and Leovy 1994; de Szoeke

et al. 2006). Off South America the reduction in

southwesterly winds reduces upwelling and produces a

warming of SST. This warming tends to destabilize the

atmospheric boundary layer, reducing the stratus cloud,

which amplifies the warming of SST. In the Gulf of

Panama the reverse is happening, with the increased

stratus cloud contributing to the cooling of SST in

the region. In the ITCZ and Gulf of Panama the SST

cooling, induced by increased ocean mixing, reduces

deep convection (increased OLR) and the resultant

precipitation [the pattern of changes in model OLR (not

shown) and precipitation are very similar but of oppo-

site sign]. In the ITCZ the increase in ocean mixing has

led to a 25% reduction in the level of precipitation. The

precipitation in the Gulf of Panama is almost com-

pletely suppressed.

There is a markedly different relationship between

changes in latent heat flux and surface temperature over

land compared to the ocean. Over the South American

continent there is an increase in precipitation. This is a

result of an eastward shift of the edge of the precipita-

tion over the central continent. The reason for the shift

is not totally clear but is presumably associated with the

reduced pressure gradient across the continent caused

by the decreased equatorial SST in the Pacific and the

resultant decrease in cross-continent winds. The change

in precipitation does have a large effect on the surface

temperature through an increase in cooling caused by

the increased latent heat release from the moister land

surface.

c. Changes in ocean currents

In the coupled system changing the vertical diffusivity

can impact ocean currents in two ways: (i) a change

in vertical viscosity brought about by a change in the

stratification and (ii) a change in the surface wind

forcing caused by changes in SST. To highlight the need

to study the coupled system in assessing the sensitivity

of the system to changes in model parameters, we note

that the maximum speed of the EUC remains essentially

unchanged with an increase in the diffusivity (1.26 m s21

in LOW and 1.27 m s21 in HIGH), suggesting a balance

between the effects of the increase in surface stress

caused by the Bjerknes effect (mechanism ii) and the

retardation by the increased viscosity (mechanism i).

This is in sharp contrast to the 15% decrease in the

maximum speed of the EUC in the equivalent twin

ocean-only experiments with the same increase in ver-

tical diffusivity and fixed wind forcing (mechanism i

alone).

As shown in Fig. 2, there is a reduction in the speed of

the NECC from LOW to HIGH. The eddy kinetic

energy of the tropical instability waves (the eddy com-

ponent of the flow is defined here as motions with

temporal scales less than 45 days) is reduced by 15%,

associated with the reduced shear between the SEC and

the NECC and a reduced barotropic conversion of en-

ergy (cf. Masina et al. 1999) (not shown). The NECC is a

result of the meridional asymmetry in the eastern

tropical Pacific, with its strength related to the zonal

integral of the meridional gradient of curl t, as discussed

below. Changing the meridional asymmetry changes the

strength of the NECC.

The annual mean surface wind stress curl, curl t, for

LOW and HIGH is shown in Fig. 9. There are two no-

table differences between the two cases that impinge on

the surface current field. The first is the deeper mini-

mum and greater meridional gradient, from 1208 to

858W, of the zonally oriented minimum in curl t cen-

tered on 48N in LOW compared to HIGH. The second

is the greater positive curl associated with the gap winds

in the Gulf of Papagayo and, less prominently, in the

Gulf of Panama in LOW compared to HIGH. For ref-

erence, the wind stress curl calculated from Quick

Scatterometer (QuikSCAT) data is also shown in Fig. 9.

The general pattern of the observed wind stress curl is

captured by the model. The observed positive curl as-

sociated with the Papagayo wind jet and the meridional

gradient of the curl in this area is better represented in

LOW than in HIGH. There are, however, some distinct

differences in both model runs to observations: most

notably, the stronger than observed positive curl asso-

ciated with the Tehuantepec wind jet and the linear

feature in negative curl along 2.58N, associated with the

anticylonic turning of the southeasterlies north of the

equator, which is less distinct in the observations.

The Sverdrup (1947) estimate of the depth-integrated

zonal transport is given by

MS 51

rb

ðxe

x

›/›y(curlt) dx, (4)

where r is the density of seawater, b 5 ›f/›y ( f is the

Coriolis parameter), and x and y are eastward and

northward coordinates, respectively. Yu et al. (2000)

find that MS is a good approximation for the total zonal

transport in the region of the NECC using results from a

numerical model forced with different wind fields. (They

also find that the structure of the NECC is also dependent

on the near-equatorial zonal component of the wind

stress.) Figure 10 compares the depth-integrated zonal

transport, M, and the Sverdrup estimate, MS, averaged

between 48N and 108N. For LOW, from the South

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FIG. 9. The annual-mean surface wind stress curl (N m22) for (top)–(bottom) LOW, HIGH,

and QuikSCAT.

FIG. 10. The depth-integrated zonal transport, M, averaged between 48N and 108N (black

lines) and the Sverdrup estimate, MS, (gray lines) as a function of longitude for expts LOW

(solid lines) and HIGH (dashed lines).

1 JULY 2009 R I C H A R D S E T A L . 3713

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American coast to around 958W, the westward increase

in transport in MS is somewhat greater than that of M.

Westward of 1008W, however, the two track each other

very well. Between 1058 and 1408W, the transport, M, in

HIGH is reduced compared to that in LOW; a similar,

but larger, reduction is seen in MS. Although not con-

clusive, the results are suggestive that the change in the

depth-integrated zonal transport in the model, brought

about by the increase in the ocean diffusivity, is through

the change in the wind stress curl. The caveat to this

result is that the model wind stress curl toward the

southern limit of the latitude range considered is some-

what different in amplitude to that observed.

As noted by Kessler (2002), east of approximately

1108W the zonal flow, centered on 68N, is not a direct

continuation of the NECC but is a consequence of the

existence of the Costa Rica Dome. This is evident in the

depth of isopycnic layers shown in Fig. 4. The flow av-

eraged over the upper 30 m for LOW and HIGH in the

far eastern tropical Pacific, superimposed on SST, is

shown in Fig. 11. The effect of the stronger positive wind

stress curl associated with the Papagayo and Panama

wind jets in LOW, compared to HIGH (see Fig. 9), is to

produce a stronger doming of water in the Costa Rica

Dome and the secondary dome in the Gulf of Panama.

This stronger doming produces considerably stronger sur-

face currents in LOW as compared to HIGH. (The cy-

clonic circulation associated with the doming in the

Gulf of Panama is seen in surface drift data, although

the circulation in the model is displaced farther to the

west than in observations; see Fig. 4 of Kessler 2002) The

northern edge of the northern branch of the SEC is dis-

placed somewhat farther south in LOW than in HIGH.

The SST in the region is considerably warmer in LOW

than in HIGH. The effect of the change of surface cur-

rents on the heat balance is examined in the next section.

5. Mixed-layer heat balance

The impact of the changes to the system on the near-

surface ocean temperature can be assessed by exami-

nation of the terms producing a change in the heat

content of the surface mixed layer. Here we average the

equation for temperature over the depth of the mixed

layer and a 4-yr period. The result is

where angled brackets denote an average over the mixed

layer depth, h, and an overbar denotes a time average

over the specific period (cf. Vialard and Delecluse 1998;

Menkes et al. 2006). The temperature T and the three

velocity components, u, y, and w, have been divided into

a high-frequency (eddy) component, denoted by a prime

and a low-frequency (LF) component, denoted by m.

Here we define high frequency as variations with a period

shorter than 45 days (increasing this to 90 days does not

change the results unduly). The lateral mixing term is

h�um›xTm � ym›yTm � wm›zTmi|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}A

1 h�u9›xT9� y9›yT9� w9›zT9i|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}B

11

h(kz›zT)z5h|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}

C

1 hDl(T)i|fflfflfflffl{zfflfflfflffl}D

1Q* 1 Qs(1� f (z 5 h))

roCph|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}E

’ 0, (5)

FIG. 11. The velocity averaged over the upper 30 m (arrows) in the eastern tropical Pacific for

the (left) LOW and (right) HIGH runs. Also shown is the SST (contour interval 0.58C).

3714 J O U R N A L O F C L I M A T E VOLUME 22

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represented by Dl. The total heating rate by the atmos-

phere, Q, is written as the penetrative solar shortwave

flux [the difference in the surface shortwave flux, Qs, and

that penetrating through the base of the mixed layer,

Qsf(h)] and the nonpenetrative flux, Q*. The mixed layer

depth is taken to be the depth at which the difference in

density from that at the surface is 0.125 kg m23. This

threshold is somewhat greater than used by Menkes et al.

(2006). Reducing the threshold does not significantly

change the mixed layer depth, and we do not expect the

results of the analysis to be unduly sensitive to its value

(cf. Menkes et al. 2006).

The various terms in Eq. (5) represent the heating rate

of the mixed layer by A: advection by low-frequency

currents, B: advection by high-frequency currents, C:

vertical diffusion, D: lateral diffusion, and E: the atmo-

sphere. The tendency term over the averaging period is

negligible. The terms have been calculated from 1-day

averages of the variables. As such, the calculation is not

exact. The error (determined by the residual in the sum-

mation of all terms), however, is small, except in one case

considered below. We have chosen not to further sub-

divide the advection term into zonal, meridional, and

vertical components. As noted by Lee et al. (2004),

caution needs to be exercised in the interpretation of

the relative importance of the components since the

result is dependent on both the form used for the ad-

vection term and the reference temperature and the

results can be misleading.

We consider three regions (see Fig. 8). The first is a

region affected by the TIWs. The heat balance terms

are averaged over the area 08–48N, 908–1408W. The

northern boundary was chosen to cut through the center

of TIW activity. Relatively modest changes to the spec-

ification of the region do not change the results signifi-

cantly. The results for low (LOW) and high (HIGH)

diffusion experiments are tabulated in Table 1 (region 1).

The total diffusion (terms C 1 D) is dominated by

vertical diffusion, lateral diffusion being approximately

1% of the total. We find that the atmospheric heating

(term E) is almost balanced by vertical diffusion (term

C). Although the low- and high-frequency advection

terms are relatively large, they almost balance each

other. A number of authors have analyzed the mixed

layer heat budget in the Pacific in the TIW region (e.g.,

Kessler et al. 1998; Vialard et al. 2001; Menkes et al.

2006; Jochum and Murtugudde 2006) and, on the whole,

found similar results as shown here in regard to the

relative importance of terms and the balancing of the

heat flux by low- and high-frequency advection. Only

Menkes et al. (2006) present the total advection of heat.

In their case, the total advection produces a net warm-

ing of the region, although the balance is still dominated

by the atmospheric flux and vertical diffusion.

Increasing the background diffusivity (HIGH) in-

creases the magnitude of both atmospheric heating (E)

and vertical diffusion (C) but not the overall balance. In

both LOW and HIGH the total advection plays a minor

role in the heat balance, although the low- and high-

frequency terms are themselves relatively large; the

cooling by the low-frequency currents (term A) is more

or less balanced by the warming by the high-frequency

TIWs (term B), with the magnitude of each little

changed between LOW and HIGH (interestingly, al-

though the TIWs of HIGH have a lower eddy kinetic

energy than in LOW, the eddy advective heat flux is

slightly higher). The residual in the balance of terms is

satisfyingly small in both experiments.

The second region considered is 58–158N, 1108–1408W

(Table 1, region 2), situated under the ITCZ. Increasing

TABLE 1. Terms contributing to the heating rate of the ocean surface mixed layer (8C month21) for the LOW and HIGH runs. Eddy

is defined as processes that have temporal scales less than 45 days; low frequency (LF) is defined as the remainder. Region 1: 08–48N,

908–1408W; region 2: 58–158N, 1108–1408W; and region 3: 08–108N, 1008W to the American coast.

Low diffusion (LOW) High diffusion (HIGH)

Region Heat source Total LF Eddy Total LF Eddy

1 Atmosphere 0.94 1.50

Total diff 20.85 21.41

Total advection 20.08 20.81 0.74 20.00 20.83 0.83

Residual 0.01 0.09

2 Atmosphere 20.23 0.05

Total diff 20.15 20.30

Total advection 0.34 0.41 20.07 0.26 0.31 20.05

Residual 0.05 0.01

3 Atmosphere 0.40 1.17

Total diff 20.25 21.17

Total advection 20.29 20.22 20.07 20.01 20.01 20.0

Residual 20.14 20.03

1 JULY 2009 R I C H A R D S E T A L . 3715

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the vertical diffusion from LOW to HIGH results in a

doubling of the cooling caused by the vertical diffusion

of heat. The cooling is enhanced by a decrease (23%) in

the advection term in HIGH, as compared to LOW,

brought about by the weaker surface currents in HIGH,

in particular the NECC (see Fig. 2). This combined ef-

fect of vertical diffusion and advection in LOW is

enough to support a net warming of the atmosphere

(term E is negative; see Table 1), leading to enhanced

convection and resultant precipitation (compared to

HIGH in which E is positive). For the equivalent region

centered on 108S the increased cooling brought about by

increasing the vertical mixing is approximately a third of

that to the north (the mixed layer and thermocline are

considerably shallower in region 2, as compared to the

equivalent region to the south). The preferential cooling

north of the equator leads to a reduced meridional

asymmetry as discussed above.

The third region considered is in the far eastern Pa-

cific from the equator to 108N and 1008W to the

American coast (Table 1, region 3): the southerly half of

the area shown in Fig. 11. Now we see a dramatic change

in the balance of terms in the heat equation between

experiments LOW and HIGH. For HIGH the situa-

tion is as in the TIW region; that is, the major balance

is between atmospheric heating and vertical entrain-

ment, although now the magnitude of the low- and high-

frequency advection terms is relatively much smaller.

For LOW a substantially stronger surface circulation

increases the net effect of advection in the heat balance.

Because of the higher SST the flux from the atmosphere

is decreased through an increase in the latent cooling

(relative to that in HIGH). There is a marked increase

in the total advection term (principally in the low-

frequency term), however, so that now its magnitude is

approximately 75% of that of the atmospheric term and

such that advection is contributing significantly to the

heat balance.

Unfortunately, the residual in the sum of the calcu-

lated heat balance terms for region 3 of LOW has be-

come uncomfortably large relative to the individual

terms; it is approximately 50% of the total advection

term. The size of the residual, however, is not large

enough, we suggest, to cast too much doubt on our

conclusion that advection plays an important role in the

heat balance in region 3 when the vertical diffusivity is

set to a small value. We note that the 3–4-day-period

easterly waves in the atmosphere are enhanced more in

IROAM compared to those in the NCEP reanalysis.

These waves induce strong vertical velocities in the

oceanic component of IROAM that are not properly

sampled by the 1-day averages used in the calculation of

the heat balance terms.

6. Concluding remarks

The regional coupled model has proved to be a

valuable tool in investigating the impact of ocean ver-

tical mixing on the ocean–atmosphere system in the

eastern tropical Pacific. The results highlight the need to

consider the coupled system when assessing the role of

physical processes in such a strongly interacting envi-

ronment. Here, we find increasing the background tracer

diffusion coefficient in the ocean has a marked effect on

the surface properties of the ocean, the ocean currents,

the surface wind field, and the clouds and precipitation in

the atmosphere. Much of the strength of the impact is

through interactions between the ocean and atmosphere

that tend to amplify the changes to the system brought

about by changes to the ocean mixing.

We find that increasing ocean mixing has an opposite

effect on the zonal and meridional asymmetries in the

eastern tropical Pacific. Increased mixing cools the east-

ern equatorial ocean. This cooling is further enhanced

through the Bjerknes feedback, leading to an increased

east–west temperature gradient. Because of the meridi-

onal asymmetry the stratification to the north of the re-

gion is greater than that to the south. Increasing ocean

mixing leads to a preferential cooling to the north, re-

ducing the north–south temperature gradient, convection

in the ITCZ, and the meridional asymmetry. Ocean–

atmosphere interaction again enhances the impact of the

change in ocean mixing, with the wind–evaporation–sea

surface temperature (WES) effect tending to reduce the

meridional asymmetry still further. A number of studies

point to a dominant role of the atmospheric component

of coupled models in producing tropical biases (e.g.,

Schneider 2002; Guilyardi et al. 2004; de Szoeke and Xie

2008). An implication from this work, however, is that

the biases relating to the too strong zonal and too weak

meridional asymmetries found in many climate models

may be improved by consideration of the level of vertical

mixing in the ocean.

In the TIW region, the balance of terms in the heat

budget for the ocean mixed layer remains relatively

unaltered as the background ocean diffusion is changed.

The cooler SST in HIGH increases the atmospheric

heating by 50% over that in LOW, but this increase is

met (at least in the balanced state) by an increased

cooling by vertical diffusion. As remarked before, there

is little change in the low- and high-frequency advective

components. In the far eastern Pacific, on the other

hand, the situation is very different. Here the changes

in the strength of the surface circulation in the ocean

(brought about by a change in the surface wind field)

radically alter the balance of heat such that advection is

a significant player in the budget for LOW. One may

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speculate that the response to low-frequency (externally

forced) changes may be different in the two systems

(LOW and HIGH).

The above puts into question the suitability of seeking

‘‘improvements’’ in ocean-only or atmosphere-only sim-

ulations by numerical experimentation if the feedbacks

to the other medium are not considered. The schemes

used here for the vertical mixing of momentum and

tracers in the oceanic component of the model are rel-

atively simple. The use of more sophisticated schemes

will undoubtedly change the sensitivity of the system to

changes in the background ocean diffusivity through the

way that mixing is changed in the thermocline and

mixed layer. We suggest, however, that the basic nature

of the changes to the ocean–atmosphere interactions

will not be changed. Such an assertion, of course, needs

to be tested. Equally, convection in the model atmos-

phere is very susceptible to subtleties in atmospheric

convection schemes. Of course, there are issues with

regard to the necessary resolution in the horizontal and

vertical in both oceanic and atmospheric components of

the model required to capture the relevant physics and

interactions. Additional numerical experimentation

is required, but the impact of changes to the system

can only be fully assessed in the context of the coupled

system.

The results from IROAM have revealed a strong

oceanic response to easterly waves in the model atmos-

phere. Recent observations have shown the existence

of an oceanic response to such waves in the atmosphere

(J. Mickett 2007, personal communication). One impact

of the higher horizontal resolution in RAM compared to

the NCEP–NCAR reanalysis is that the relative vorticity

field associated with easterly waves is more intense in the

former than the latter. This vorticity drives a strong

vertical circulation in the surface layers of MOM2. A

detailed analysis of the easterly waves and their impact

on the ocean dynamics and thermodynamics is beyond

the scope of the present study and warrants a better

ocean mixing scheme and probably better resolution

than utilized here.

Calculating the diapycnic model fluxes has proved to

be illuminating in terms of determining the spatial dis-

tribution of the flux and in providing a quantitative

measure of water mass transformation. We find that

increasing the vertical diffusivity changes the portrait of

diapycnic mass transport in density space. In terms of

the water mass properties, changing the vertical diffu-

sion in the ocean component of the model, therefore,

not only changes the thickness of the thermocline but

also the water mass transformations. The diapycnic

transport is an integral part of the overturning circula-

tion of the subtropical cells. The changes to the dia-

pycnic transport found here are modest. It is unclear

how large an impact these changes make by themselves;

however, it is an aspect that needs to be taken into ac-

count when comparing different vertical mixing schemes

or other parameterizations in ocean models.

We encourage the use of the diapycnic flux as a useful

diagnostic in modeling studies and as a target for ob-

servational programs. In terms of the model, the cal-

culated diapycnic flux is the total diapycnic flux and

therefore includes not only the flux due to the explicit

vertical mixing in the model but also from the flux due

to horizontal mixing across sloping density surfaces (the

‘‘Veronis effect’’; Veronis 1975). Estimating the mag-

nitude of this effect is difficult. Employing a numerical

scheme that approximates isoneutral diffusion (Griffies

et al. 1998) will minimize spurious mixing but not totally

remove it.

Finally, there is often an interplay between physical

processes. Maes et al. (1997) note the interplay between

lateral and vertical mixing: when the former is reduced,

the latter is enhanced in their OGCM. Unresolved

processes such as interleaving (Richards and Edwards

2003), which can produce significant lateral and vertical

mixing and also depends on the large-scale flow, may

feed back to the large-scale flow itself. The interplay

between processes in the coupled environment is yet to

be fully explored.

Acknowledgments. We wish to thank Pierre Dutrieux

and Simon de Szoeke for help with the coding of the

diagnostic analysis of the model output; K. Horuichi,

Sharon DeCarlo, and Y. Shen for maintaining the data

servers in Yokohama and the IPRC, which hold the

model output; and Shan Sun for discussions on dia-

pycnic fluxes. The computation was carried out on the

Earth Simulator, Yokohama, Japan. This work was

supported by the Ministry of Education, Culture, Sci-

ence and Technology (Project Kyosei-7 RR2002), the

Japan Agency for Marine–Earth Science and Technol-

ogy, and the U.S. National Oceanic and Atmospheric

Administration.

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