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Changes in mixed layer depth under climate change projectionsin two CGCMs
Sang-Wook Yeh Bo Young Yim Yign Noh
Boris Dewitte
Received: 10 February 2008/ Accepted: 20 January 2009/ Published online: 12 February 2009
Springer-Verlag 2009
Abstract Two coupled general circulation models, i.e.,
the Meteorological Research Institute (MRI) and Geo-physical Fluid Dynamics Laboratory (GFDL) models, were
chosen to examine changes in mixed layer depth (MLD) in
the equatorial tropical Pacific and its relationship with
ENSO under climate change projections. The control
experiment used pre-industrial greenhouse gas concentra-
tions whereas the 2 9 CO2 experiment used doubled CO2levels. In the control experiment, the MLD simulated in the
MRI model was shallower than that in the GFDL model.
This resulted in the tropical Pacifics mean sea surface
temperature (SST) increasing at different rates under global
warming in the two models. The deeper the mean MLD
simulated in the control simulation, the lesser the warming
rate of the mean SST simulated in the 2 9 CO2 experi-
ment. This demonstrates that the MLD is a key parameter
for regulating the response of tropical mean SST to global
warming. In particular, in the MRI model, increased
stratification associated with global warming amplified
wind-driven advection within the mixed layer, leading to
greater ENSO variability. On the other hand, in the GFDL
model, wind-driven currents were weak, which resulted in
mixed-layer dynamics being less sensitive to global
warming. The relationship between MLD and ENSO was
also examined. Results indicated that the non-linearitybetween the MLD and ENSO is enhanced from the control
run to the 2 9 CO2 run in the MRI model, in contrast, the
linear relationship between the MLD index and ENSO is
unchanged despite an increase in CO2 concentrations in the
GFDL model.
Keywords Mixed layer depth Climate change projections CGCM Sea surface temperature ENSO
1 Introduction
The mixed layer is the ocean surface zone that responds
most quickly and directly to atmospheric fluxes, and it is
through the mixed layer that heat and momentum fluxes are
transmitted to the deeper ocean and generate longer time-
scales of variability. Therefore, the oceans mixed layer
depth (hereafter referred to as MLD) is one of the most
important quantities in the upper ocean, and is closely
associated with physical, chemical and biological systems
(Sutton et al. 1993; Chen et al. 1994; Fasham 1995; Kara
et al. 2003).
MLD variability dominates on several short-term time-
scales, i.e., diurnal, intra-seasonal, and seasonal (McCreary
et al. 2001). However, recent studies of long-term obser-
vation records have suggested that the MLD undergoes
low-frequency changes in the North Pacific and Atlantic
Oceans (Timlin et al. 2002; Deser et al. 2003; Carton et al.
2008). In addition, a number of studies have reported a
long-term trend in MLD (Chepurin and Carton 2002;
Polovina et al. 1995; Michaels and Knap 1996; Freeland
et al. 1997; Carton et al. 2008). Such low-frequency
S.-W. Yeh (&)
Korea Ocean Research and Development Institute, Ansan,
South Korea
e-mail: [email protected]
B. Y. Yim Y. NohDepartment of Atmospheric Sciences/Global Environmental
Laboratory, Yonsei University, Seoul, South Korea
B. Dewitte
Laboratoire dEtude en Geophysique et Oceanographie Spatiale,
Toulouse, France
123
Clim Dyn (2009) 33:199213
DOI 10.1007/s00382-009-0530-y
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variability and the shallowing or deepening trend in MLD
over the past few decades have raised the question of
whether and how human-induced greenhouse warming
impacts MLD variability. The variability of the MLD under
global warming would determine a physical environment
in the upper ocean which could affect oceanatmosphere
interactions, ocean physics and upper ocean productivity
(Pierce 2004). In particular, as the site of significant cli-mate variability, the MLD closely links the dynamics and
thermodynamics of the upper layers in the tropical Pacific
and as such, is likely to be a key parameter for under-
standing the response of the tropical Pacific climate system
to global warming.
In spite of a large number of studies on the influence of
climate change using coupled general circulation models
(CGCMs) (see http://www-pcmdi.llnl.gov/ipcc/subproject_
publications.php), there has been little investigation of
changes in MLD under climate change projections. The
intent of this paper is to examine changes in MLD under
atmospheric CO2 doubling in two different CGCMs, focus-ing on changes in MLD in the tropical Pacific. Furthermore,
we examine changes in the relationship between the MLD
and El ENSO under increased greenhouse gases. Indeed, the
variability associated with heat storage or release in the
mixed layer is quite diverse due to competition between
the equatorial waves and the direct heat flux forcing in the
tropical Pacific. This balance is likely to be sensitive to the
environmental conditions in a way that depends on MLD
characteristics. More generally, since the MLD determines
the heat capacity of the ocean, it has a strong impact on air
sea exchanges, and therefore on ENSO, which includes its
teleconnections (Sui et al. 2005). For these reasons it is
worthwhile examining changes in the MLDENSO rela-
tionship under increased CO2 concentrations.
In order to analyze changes in the MLD under atmo-
spheric CO2 doubling we examined a control simulation
using pre-industrial greenhouse gas concentrations and a
simulation with doubled CO2 levels in two different
CGCMs. Detailed descriptions of the CGCMs and the
reasons for selecting these models are given in Sect. 2. In
the doubled CO2 (2 9 CO2) experiment, CO2 increased at
a rate of 1% per year to a level twice that of the present
climate. After the 70-year period to CO2 doubling, the
CGCMs were integrated for an additional 150-year period
to examine the climate systems long-term response. In the
control experiment, there was no anthropogenic or natural
forcing for the entire simulation period.
The paper is organized as follows: the descriptions of
the model experiments and methodology are described in
Sect. 2. Changes in MLD under atmospheric CO2 doublingin two different CGCMs are analyzed in Sect. 3. Section 4
is devoted to a description of the MLDmean SST rela-
tionship, and the relationship between the MLD and ENSO
is examined in Sect. 5. The results are summarized in Sect.
6.
2 Model and methodology
We used selected CGCM simulations, namely,
MRI_CGCM2_3_2a and GFDL_CM2_0 (hereafter refer-
red to as MRI and GFDL; see Table 1 for referencesand additional model details). The CGCM simulations
were made available by the Program for Climate Model
Diagnosis and Intercomparison (PCMDI) on the website
http://www-pcmdi.llnl.gov/ipcc/about_ipcc.php. Table 1
summarizes the description of the pre-industrial control
experiment and the 1%/year 2 9 CO2 experiment using the
two CGCMs. Detailed documentation and validation of
these models can be found on the PCMDI website at
http://esg.llnl.gov/portal. It is noteworthy that the MRI
model uses monthly climatological flux adjustment for the
heat, water and momentum between 12N and 12S only
in order to keep the model climatology close to the
observed one (see http://www-pcmdi.llnl.gov/ipcc/model/
documentation/MRI-GCGM2.3.2.htm). Such procedure,
however, should not prevent the model from developing
wind anomalies on various time scales of climate vari-
ability as suggested by a study using similar methodology
with another model (Kirtman et al. 2002). Therefore, there
is little problem to directly compare with the mean state
simulated by the two CGCMs.
There were several reasons behind the selection of the
MRI model and the GFDL model for this study. First of all,
Table 1 CGCM experiments used in this study
Model name
(Center)
Global ocean resolution
(longitude 9 latitude)
Simulation period References
Pre-industrial
control exp.
1%/year CO2 increase
(to doubling)
MRI_CGCM2_3_2a (MRI/Japana) 144 9 111 350 years 220 years Yukimoto et al. (2001)
GFDL_CM2_0 (NOAA GFDLb) 144 9 90 500 years 280 years Delworth et al. (2006)
a Meteorological Research Institute (MRI)/Japanb NOAA Geophysical Fluid Dynamics Laboratory (GFDL)
200 S.-W. Yeh et al.: Changes in mixed layer depth under climate change projections in two CGCMs
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http://www-pcmdi.llnl.gov/ipcc/subproject_publications.phphttp://www-pcmdi.llnl.gov/ipcc/subproject_publications.phphttp://www-pcmdi.llnl.gov/ipcc/about_ipcc.phphttp://esg.llnl.gov/portalhttp://www-pcmdi.llnl.gov/ipcc/model/documentation/MRI-GCGM2.3.2.htmhttp://www-pcmdi.llnl.gov/ipcc/model/documentation/MRI-GCGM2.3.2.htmhttp://www-pcmdi.llnl.gov/ipcc/model/documentation/MRI-GCGM2.3.2.htmhttp://www-pcmdi.llnl.gov/ipcc/model/documentation/MRI-GCGM2.3.2.htmhttp://esg.llnl.gov/portalhttp://www-pcmdi.llnl.gov/ipcc/about_ipcc.phphttp://www-pcmdi.llnl.gov/ipcc/subproject_publications.phphttp://www-pcmdi.llnl.gov/ipcc/subproject_publications.php7/29/2019 Yeh Et Al Changes in Mixed Layer Depth Under Climate Change Projections in 2 CGCMs (1)
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the two CGCMs have been extensively documented in
recent studies based on the present climate simulation and
the climate change simulation (van Oldenborgh et al. 2005;
Yeh et al. 2006; Guilyardi 2006; Capatondi et al. 2006;
Yeh and Kirtman 2007) which provides background
material for interpreting the results presented in this study.
Second, both the MRI and GFDL models are reasonably
capable of simulating ENSO variability in the controlexperiment, although they presented different characteris-
tics in terms of decadal variability and thermocline
structure (Capatondi et al. 2006; Lin 2007). In addition,
these two CGCMs exhibit robust ENSO-monsoon con-
temporaneous teleconnections in the twentieth century
integrations (Annamalai et al. 2007), indicating that the
characteristics of the oceanatmosphere interactions are
fairly good. Despite their relatively good performance in
simulating ENSO, interestingly, there was a comparative
difference between the MRI model and the GFDL model
with respect to the sensitivity of ENSO statistics and
change in tropical Pacific mean state to increased atmo-spheric CO2 concentrations (Collins et al. 2005; Yeh et al.
2006; Yeh and Kirtman 2007). For instance, Yeh et al.
(2006) showed that the ENSO amplitude increased in
response to a transient rise in atmospheric CO2 in the MRI
model, but found no significant sensitivity in the GFDL
model. Because there is no consensus so far on the changes
in ENSO statistics due to increased greenhouse gases, it is
therefore useful to examine changes in MLD under
anthropogenic climate change by directly comparing two
CGCMs which have different sensitivity in the tropical
Pacific.
In this study the MLD was obtained from Monterey and
Levitus (1997) and Suga et al. (2004) based on the depth
where the density differs from the surface density by
0.125 kg m-3. We choose a density difference criterion
because salinity also contributes to the density variation
significantly in the tropical Pacific. Note that small change
of the surface density criteria leads to slight differences in
the estimation of MLD but the overall results of this paper
are unchanged. The terms control experiment and
2 9 CO2 experiment refer to data from the last
100 years for the control experiment and the 2 9 CO2experiment, respectively.
3 Analysis of the MLD
3.1 MLD in the control experiment
Prior to showing the MLD simulated in the CGCMs we
begin by showing the climatological annual mean MLD in
observations. Figure 1a shows the climatological mean
MLD in the tropical Pacific calculated from the Levitus
data (Levitus 1982). Mean MLD ranges from 20 to 80 m in
the tropical Pacific. A shallow MLD is found in the eastern
tropical Pacific, which is associated with a shallow ther-
mocline depth in the same region (Yu and McPhaden 1999;
Wang and McPhaden 2000). In the central equatorial
Pacific the spatial structure of the mean MLD is charac-
terized by a pair of deep MLDs off the equator in both
hemispheres, which is similar to the results obtained byKara et al. (2003) and de Boyer Montegut et al. (2004) in
spite of different definitions of MLD. Using the data from
the World Ocean Database 2005 archive for the period
19602004, Carton et al. (2008) showed that the climato-
logical maximum MLD may exceed 75 m in the central
tropical Pacific basin, decreasing to less than 40 m in the
east, which is also generally consistent with Fig. 1a. A
deep MLD in the central equatorial Pacific could be asso-
ciated with significant vertical turbulent kinetic energy due
to strong zonal wind stress over this zone (Garwood et al.
1985). On the other hand, upwelling at the equator drags up
the thermocline, and thus causing the decrease of MLDcompared to the off-equatorial region, although it is not
clearly observed in the climatological data of low resolu-
tion (Noh et al. 2005). The MLD pattern is also associated
with equatorial wave dynamics. Strong zonal wind stress in
the central equatorial Pacific (Wittenberg 2004) produces
strong upwelling off the equator in both hemispheres. This
is mainly due to an Ekman pumping by wind stress curl off
the equator in both hemispheres (Kessler 2006), resulting
in a deep MLD through active mixing process as seen in
Fig. 1a. On the other hand, an Ekman pumping continu-
ously forces a Rossby wave propagating to the west (Qu
et al. 2008), therefore, the variability of MLD is closely
associated with equatorial wave dynamics in the central
equatorial Pacific from the forcing region, in particular the
annual equatorial Rossby wave in which its maximum
center is located off the equator (Kessler and McCreary
1993) or the tropical instability wave activity that can also
rectify the background state (Perez and Kessler 2008).
Figure 1b, c are the same as Fig. 1a but relate to the
control experiments in the MRI model and the GFDL
model, respectively. The spatial structure of the mean
MLD simulated in both the MRI model and the GFDL
model is dominated by a pair of deep MLDs which are at a
maximum off the equator in the western and central
equatorial Pacific, which is in agreement with the obser-
vations. However, the pattern is much more symmetric
towards the equator, suggesting that equatorial Rossby
waves have a greater impact on MLD variability in the
CGCMs than in the observations. In addition, the mean
MLD simulated in the MRI model is shallow, below 50 m,
along the equator in the central tropical Pacific compared
to the observations, which may be largely due to strong
upwelling along the equator. Meridional sections of
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climatological annual mean temperature (not shown)
indeed indicate a sharp rise in the isotherms at the equator
in the MRI model. In the GFDL model, on the other hand,
the MLD peaks at 100 m near the date line which is 20
30 m greater than in the observations and the MRI model.
Note also that the location of the maximum MLD is sig-
nificantly shifted to the west in the GFDL model as
compared to the observations and the MRI model. These
model biases may be associated with deficiencies in the
mixed-layer physics used.1 For instance, Halpern et al.
(1995) have shown that the use of a different mixing
scheme results in a variety of CGCM behavior in the
tropical Pacific Ocean in terms of the upper ocean
structure.
3.2 MLD in the 2 9 CO2 experiment
The mean MLD under the increased greenhouse gases
scenario in the two CGCMs is presented in Fig. 2a, b. The
figures can be compared to Fig. 1b, c (i.e., the control
experiments). There is similarity in the spatial pattern of
the mean MLD between the two experiments for both
CGCMs, namely a pair of deep MLDs which are at a
maximum off the equator in the western and central
equatorial Pacific, and a shallow MLD in the eastern
tropical Pacific. In the tropical Pacific, the mean MLD
ranges from 20 to 50 m in the MRI model and from 20 to
80 m in the GFDL model. The greatest differences in mean
MLD between the two experiments in the MRI and GFDL
(c)
(b)
(a)Fig. 1 Climatological meanmixed layer depth (MLD) in the
tropical Pacific based on the
Levitus data (Levitus 1982).
Contour interval is 10 m and
shading indicates values above
50 m. Climatological annual
mean MLD simulated in the
control experiment for the MRI
model (b) and the GFDL model
(c). The analyzed period is the
last 100 years for the control
experiment. Contour interval is
10 m
1 The mixed-layer treatment used in the MRI model was a turbulent
closure level 2 (Mellor and Yamada 1974, Mellor and Durbin 1975).
On the other hand, that in the GFDL model was a K-profile
parameterization (KPP) scheme (Large et al. 1994).
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models are found in the central and western equatorial
Pacific, respectively, consisting in a shallowing of 530 m.
The maximum difference of mean MLD between the
control and the 2 9 CO2 experiments (not shown) is
observed in the region of the deepest simulated MLD in the
control experiment in both models, that is, off the equator
(i.e., 23N and 23S) around the central equatorial
Pacific (180E150W) in the MRI model and in the
western equatorial Pacific (150E180E) in the GFDL
model. For more details we have also provided the ratio of
mean MLD between the control experiment and the
2 9 CO2 experiment in the MRI (Fig. 2c) and GFDL
(Fig. 2d) models. This ratio is less than one over most of
the basin for both models (the exceptions are a region
around the northeastern tropical Pacific for the MRI model,
and in the south-central tropical Pacific for the GFDL
model), indicative of shallowing of the MLD under global
warming. Interestingly, the ratios of MLD changes are not
homogeneous in the MRI model, unlike the GFDL model
which exhibits a more uniform pattern. The MLD changes
in the MRI model are projected to be large in the central
equatorial Pacific with an off-equatorial maximum in both
(a)
(b)
(c)
(d)
Fig. 2 a and b are the same as
in Fig. 1b, c except for the
2 9 CO2 experiment. Contour
interval is 10 m. c and d show
the ratios of MLD changes from
the control experiment to the
2 9 CO2 experiment in the MRI
model and the GFDL model,
respectively. Contour interval is
0.1, shading indicates below 1.0
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hemispheres (Fig. 2c). In contrast, the MLD changes are
small in the eastern equatorial Pacific, where the ratio
values are around 0.80.9. On the other hand, the ratio
values for MLD changes in the GFDL model are nearly
uniform in the equatorial Pacific, where they are around
0.80.9 over most of the basin. These results indicate first,
that changes in the MLD due to climate warming does not
respond linearly in the equatorial Pacific (cf. the MRImodel, which exhibits very distinct patterns of MLD in
both experiments) and second, that there is great uncer-
tainty about the MLD changes under climate change
projections, considering the above-mentioned differences
between both models.
4 Relationship between the MLD and mean SST
4.1 Thermodynamic processes
The fact that the GFDL model simulates a deeper MLDthan the MRI model in the control experiment (i.e., Fig. 1b,
c) may influence the response of the tropical Pacific mean
SST to global warming in the two CGCMs. By definition,
the mixed layer is the quasi-homogenous region of the
upper ocean in terms of physical quantities like tempera-
ture and salinity. Therefore, a deep or shallow MLD may
influence changes in mean SST through the homogenous
distribution of heat flux forcing induced by global
warming.
Changes in mean SST from the control experiment to
the 2 9 CO2 experiment (i.e., 2 9 CO2 minus the control)
in the MRI and GFDL models are shown in Fig. 3a, b,
respectively. The two models exhibit El Nino-like warming
trends under the doubled CO2 concentrations that have
quite different characteristics. Whereas in the MRI model
(Fig. 3a), the warming is projected to be considerable over
a large portion of the central and eastern tropical Pacific,
the warming in the GFDL model (Fig. 3b) is centered
along the equator in the central and far eastern Pacific. In
addition, the tropical Pacific mean SST increases by about
2.63.6C i n t h e 2 9 experiment for the MRI model,
which is almost double the increase in the GFDL model
(i.e., 1.61.8C). This indicates that the climate sensitivity
(the equilibrium mean temperature change following a
doubling of the atmospheric CO2 concentration) is different
in the two CGCMs. Our results suggest that the deeper the
mean MLD simulated in the control simulation, the lesser
the warming rate of mean SST simulated in the 2 9 CO2experiment (cf. Figs. 2, 3). In order to examine the possi-
bility that the heat flux differences between the two
CGCMs can make a contribution to mean SST changes in
the 2 9 CO2 experiment, we display the differences of the
heat fluxes in the two CGCMs (i.e., the MRI model minus
the GFDL model) in the control experiment and the
2 9 CO2 experiment, respectively (Fig. 4a, b). If the heat
flux differences between the two CGCMs are comparable
in the two experiments one may conclude that the differ-
ences in MLD can be considered responsible for the
different warming in the two CGCMs. Figure 4a, b indicate
that the net heat flux in the MRI model is smaller than that
in the GFDL model in most of the equatorial Pacific for
both the control experiment and the 2 9 CO2 experiment,
which means that the ocean absorbs more heat flux from
the atmosphere in the GFDL model than in the MRI model
in both experiments. Furthermore, the net heat flux dif-
ferences in the two CGCMs are comparable in the
equatorial Pacific between the control experiment (Fig. 4a)
and the 2 9 CO2 experiment (Fig. 4b), supporting that the
heat flux differences between the two CGCMs makes a
small contribution to mean SST changes from the control
experiment to the 2 9 CO2 experiment.
In a warmer climate, a shallowing of the MLD is
expected in association with a more stratified ocean.
Indeed, when the climate warms, the oceans surface
becomes warmer and the water column tends to stabilize.
This suggests that different ratios of MLD shallowing
under global warming in the MRI and GFDL models are
related to different SST warming rates (Fig. 3a, b). The
shallowing of the MLD is greater in the MRI model than in
the GFDL model, and this is associated with greater
(a)
(b)
Fig. 3 Difference in annual mean SST simulated in the MRI model
(a) and the GFDL model (b) between the control experiment and the
2 9 CO2 experiment. Contour interval is 0.2C
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warming of mean SST in the MRI model than in the GFDL
model. As we argue above, the deeper the mean MLD
simulated in the control simulation, the lesser the warming
rate of mean SST simulated in the 2 9 CO2 experiment.
The reduced warming rate of mean SST then results in alesser shallowing of the MLD simulated in the 2 9 CO2experiment. These results illustrate the feedback process of
the MLDSST changes from the control experiment to the
2 9 experiment. For instance, a shallow MLD in the
control experiment is associated with relatively large SST
warming through more global-warming-induced heat flux
trapped around the near surface layer in the 2 9 CO2experiment. This leads to a more stratified ocean. A large
change in stability is associated with a significant MLD
shallowing rate, which in turn feeds back on the tendency
of SST to increase under heat flux induced by global
warming. Such processes are reversed for a deeper MLD inthe control experiment. Figure 5 displays a schematic of
such a feedback process in the MLDSST changes. We
argue here that the MLD is a key parameter for regulating
the response of tropical Pacific mean SST due to increasing
greenhouse gases in a CGCM. On the other hand, equa-
torial wave dynamics also enables us to understand the
variation of the tropical Pacific on interannual and longer
times scales as well as the mean state, therefore, in the next
subsection we will examine the impact of climate change
associated with the MLD variability on some aspects of the
oceanic dynamical processes.
4.2 Dynamical processes
Changes in the tropical Pacific mean state, which are
related to changes in MLD, are likely to be associated with
changes in equatorial wave dynamics. The MLD is influ-enced by advection process which is a major process
controlling the rate of SST change in the equatorial Pacific.
Whereas anomalous vertical advection is to a large extent
controlled by thermocline depth fluctuations, anomalous
horizontal advection within the mixed layer has a signifi-
cant contribution from the wind-driven Ekman currents.
Both processes are linked to the equatorial wave dynamics,
which can be quantified through the estimation of the
baroclinic mode contribution.
In order to assess the impact of a change in mean state
on the equatorial wave dynamics of the models, the pro-
jection coefficients of the wind forcing (in the linear sense)according to the gravest baroclinic modes, i.e., [Pn]n = 1,3,
2
were first estimated from the results of a vertical mode
decomposition of the mean stratification along the equator
for both CGCMs. The [Pn]n = 1,3 quantify the amount of
momentum flux that projects on a particular baroclinic
mode (Philander 1978). In that sense they characterize the
thermocline structure and brings information on how the
ocean has to respond (in the linear sense) to wind stress
forcing. The coefficients [Pn]n = 1,3 quantify subtle chan-
ges of the thermocline depth. Whereas P1 is mostly
associated with change in mean thermocline depth, P2 and
P3 accounts for the change in the vertical density gradient
within the thermocline. The reader is invited to refer to
Dewitte et al. (2007) for more details on the value of such
parameters to measure the change in the thermocline
structure. The methodology for deriving the vertical modes
was similar to Dewitte et al. (1999). Consistently with Yeh
et al. (2008), the results indicate that the MRI model
exhibits changes in the Pn, with P1 decreasing by 8.3%
from the control experiment to the 2 9 CO2 experiment
and P2 (P3) increasing by 38.4% (37.5%) at the equator
(0N, 180E). On the other hand, the GFDL model exhibits
lesser change in the Pn, with P1 decreasing by 4.6% from
the control experiment to the 2 9 CO2 experiment and P2(P3) increasing by 22.4% (25%) at the equator. This result
indicates that the impact of climate change is more influ-
ential on the equatorial wave dynamics in the MRI model
than in the GFDL model. This is consistent with the largest
(a)
(b)
Fig. 4 The differences of the net heat fluxes in the two CGCMs (i.e.,
the MRI model minus the GFDL model) in the control experiment (a)
and the 2 9 CO2 experiment. Contour interval is 20 W/m2 and
dashed line denotes below zero
2
Pn
RzHmixz0
Fnzdz
Hmix
,Rz0zH F
2nzdz; where n indicates the order of
baroclinic mode and Hmix is the MLD. H is the depth of the ocean
bottom and Fn(z) the vertical mode structure.
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change in MLD due to climate change observed in the MRI
model compared to the GFDL model.In order to highlight the impact of such change in the
density structure on the mixed-layer dynamics, we consider
the surface currents which are a combination of baroclinic
currents (here, taken into account as the contribution of the
first three baroclinic modes to the current) and wind-driven
currents. Following Blumenthal and Cane (1989), the lat-
ter, which account for the contribution of the higher-order
modes, can be estimated from a frictional equation forced
by s~f s~1
HmixP3
i1 Pi
(Pi being the wind projection
coefficient for the baroclinic mode i and Hmix is the MLD),
which represents the share of the flux momentum that doesnot project on the gravest baroclinic modes (here, the first
three baroclinic modes).
The wind-driven Ekman current (us, vs) are therefore the
solutions of the following system:rsus byvs
sxf
q0
rsvs byus s
y
f
q0
8