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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
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
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
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
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
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
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
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).
3710 J O U R N A L O F C L I M A T E VOLUME 22
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
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
3712 J O U R N A L O F C L I M A T E VOLUME 22
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
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
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
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
3716 J O U R N A L O F C L I M A T E VOLUME 22
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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