yeh et al changes in mixed layer depth under climate change projections in 2 cgcms (1)

7/29/2019 Yeh Et Al Changes in Mixed Layer Depth Under Climate Change Projections in 2 CGCMs (1)

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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

123
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.php


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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

S.-W. Yeh et al.: Changes in mixed layer depth under climate change projections in two CGCMs 201

123


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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

yeh et al changes in mixed layer depth under climate change projections in 2 cgcms (1)

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