15 NOVEMBER 2003 3585W A N G E T A L .

q 2003 American Meteorological Society

A Tropical Ocean Recharge Mechanism for Climate Variability. Part I:Equatorial Heat Content Changes Induced by the Off-Equatorial Wind

XIAOCHUN WANG* AND FEI-FEI JIN

Department of Meteorology, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, Hawaii

YUQING WANG

International Pacific Research Center, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa,Honolulu, Hawaii

(Manuscript received 8 April 2002, in final form 3 May 2003)

ABSTRACT

A reduced-gravity shallow-water model, an oceanic general circulation model for the Pacific region, and theanalytical model of the equatorial b plane bounded in the zonal direction are used to investigate the equatorialthermocline response to tropical and subtropical wind stress forcing. The results show that the wind stress forcingin the tropical and subtropical region can generate a nearly zonal uniform thermocline depth change in theequatorial region. The response timescale is longer when the wind stress is placed farther away from the equator.There exist latitude bands around 108–158N and 108–158S where the forcing can cause a relatively large equatorialresponse. When the forcing is located in the eastern basin, the response timescale is longer and its magnitudeis larger than the case when the forcing is located in the western basin. Thus the eastern tropical to subtropicalregion is a relatively effective area for off-equatorial wind stress to generate an equatorial thermocline response.When the wind stress forcing has a longer period, the response of the equatorial thermocline has a largermagnitude. The results from this study’s numerical experiments and the analytical solution are consistent. Thepresent study has implications for the broad-scale ocean–atmosphere interaction in the tropical region.

1. Introduction

In addition to the well-known ENSO phenomenon onan interannual timescale, the Pacific basin also has cli-mate variability on decadal to interdecadal timescales(e.g., Mantua et al. 1997; Nakamura et al. 1997; Zhanget al. 1997; Chao et al. 2000). This variability is com-monly referred to as the Pacific decadal oscillation(PDO). To some significant extent, the ENSO and thePDO have similar spatial structures in the associatedatmospheric and oceanic fields in the Tropics, such assea level pressure, sea surface temperature (SST), andsurface wind stress. The basic mechanism of ENSO isnow understood (Neelin et al. 1998). However, the phys-ical mechanism of decadal to interdecadal timescale var-iability in the Pacific basin is still elusive [for a recentreview, see Miller and Schneider (2000)].

* Current affiliation: Jet Propulsion Laboratory, California Instituteof Technology, Pasadena, California.

Corresponding author address: Dr. Xiaochun Wang, Jet PropulsionLaboratory, M/S 300-323, California Institute of Technology, 4800Oak Grove Dr., Pasadena, CA 91109.E-mail: xiao@pacific.jpl.nasa.gov

It is generally believed that the timescale of ENSOis controlled by the equatorial oceanic dynamics, whichgovern the equatorial thermocline change. The equa-torial thermocline change could be separated into aneast–west contrast component and a component that hasa zonally uniform feature in the equatorial region. Theeast–west contrast component rapidly responds to thewind stress forcing in the equatorial region. The zonallyuniform component slowly adjusts to the wind stresscurl forcing in the tropical region through meridionalheat content transport between the equatorial region andthe tropical region. The phase change mechanism ofENSO is associated with the zonally uniform equatorialthermocline change (Jin 1997). Following the work byCane and Moore (1981), Jin (2001) noted that in theequatorial region, without coupling to the atmosphere,there exist very-low-frequency (VLF) modes that areeigensolutions for the equatorial b plane bounded inzonal directions. For slow modes that have longer pe-riods, the spatial structure of the equatorial thermoclineis zonally uniform (Fig. 3 in Jin 2001). For the gravestocean basin mode, which has a period about four timesthe Kelvin wave basin-crossing time, the equatorial ther-mocline shows an east–west contrast. It is suggested

3586 VOLUME 16J O U R N A L O F C L I M A T E

that the ocean–atmosphere interaction in the tropicalregion could destabilize these free ocean-only modesand generate ENSO variability (Jin and Neelin 1993;van der Vaart et al. 2000).

On the other hand, numerical experiments by Nonakaet al. (2002) demonstrated that on a decadal to inter-decadal timescale the wind stress in the off-equatorialregion contributes as much as the equatorial wind stressto the equatorial SST variability, which is associatedwith the equatorial thermocline change. So the questionof how the equatorial region responds to the off-equa-torial wind stress forcing is important for the under-standing of both the ENSO and the PDO. The issue waspartly addressed from the perspective of the mainte-nance of the equatorial thermocline and equatorial un-dercurrent (Liu et al. 1994; McCreary and Lu 1994).Both analytical solution and numerical experimentsshowed that the wind stress at the boundary betweenthe subtropical and tropical regions is important for theshallow, meridional subtropical cell, which controls thewater exchange between the subtropical and equatorialregions. Klinger et al. (2002) analyzed the response ofthe equatorial region to off-equatorial wind stress forc-ing by using an intermediate model. The strength changeof the shallow, meridional subtropical cell is their focus.In their model the equatorial SST change could be at-tributed to the westward shift of the equatorial upwellingregion.

The two issues of how the equatorial thermoclineresponds to the off-equatorial wind stress forcing andof its implications for the understanding of both theENSO and the PDO are addressed in this two-part paper(see Wang et al. 2003, hereafter Part II). In the first partof this two-part paper we explore the relationship be-tween the tropical and subtropical wind stress forcingand the equatorial thermocline response from the per-spective of recharge and discharge of the equatorial heatcontent. Our focus is on the response of the equatorialthermocline to wind stress forcing at different latitudes,longitudes, and timescales. Cane and Sarachik (1981)gave an analytical solution for the equatorial ocean re-sponse to periodic forcing by using an equatorial b-plane reduced-gravity shallow-water model. They ex-amined the time-dependent behavior of the equatorialthermocline for two idealized situations: with the windstress being symmetric and antisymmetric about theequator. Our present work is an extension of Cane andSarachik (1981) and Jin (2001). A reduced-gravity shal-low-water model (SWM) is used to conduct numericalsensitivity tests. The major findings in the reduced-grav-ity shallow-water model are also confirmed in an oce-anic general circulation model (OGCM), which is adapt-ed from National Oceanic and Atmospheric Adminis-tration/Geophysical Research Laboratory’s (NOAA/GFDL) Modular Ocean Model version 3.0 (MOM3.0;Pacanowski and Griffies 1998). Shin and Liu (2000)have done similar research to investigate the responseof the equatorial thermocline by using OGCMs but only

to buoyancy forcing. Along the line of the ventilatedthermocline theory (Luyten et al. 1983), Huang and Ped-losky (2000) used a two-moving-layer model to inves-tigate the equatorial thermocline response to extratrop-ical forcing. The results presented here provide furtherinsight into the recharge and discharge of the equatorialheat content. The implications for the understanding ofthe dynamics of the PDO and ENSO will be discussedin Part II.

The paper is organized as follows. The SWM and theOGCM are described in section 2. Section 3 presentsthe analytical solution of the response of the equatorialthermocline to off-equatorial wind stress forcing by us-ing the equatorial b-plane system. The numerical ex-periments using the SWM are analyzed in section 4.Section 5 discusses the numerical experiments by usingan OGCM for the Pacific region. Our findings and fur-ther discussions are summarized in section 6.

2. Models used in numerical experiments

a. Reduced-gravity shallow-water model

A nonlinear reduced-gravity shallow-water model inspherical coordinates is used in our analysis:

]u u ]u y ]u u tanf1 1 2 y 2V sinf 11 2]t a cosf ]l a ]f a

g9 ]h tl5 2 1 1 ADu (1)a cosf ]l rH0

]y u ]y y ]y u tanf1 1 1 u 2V sinf 11 2]t a cosf ]l a ]f a

tg9 ]h f5 2 1 1 ADy (2)

a ]f rH0

]h 1 ]hu 1 ]hy1 1 5 2g(h 2 H ), (3)0]t a cosf ]l a ]f

where H0 is the layer thickness, g9 is the reduced gravity,tl and tf are the wind stress forcing in zonal and me-ridional directions, r is the density of water, and a isthe radius of the earth. The lateral viscosity is repre-sented by terms ADu and ADy, in which A is the vis-cosity coefficient and D is an operator in spherical co-ordinate D 5 (1/a 2 cos 2 f)[] 2 /]l 2 1 cosf (]/]f)(cosf(]/]f)]. The g(h 2 H0) is a very weak re-storing term, which is used to damp the numerical noise.The ocean basin is rectangular (408S–408N, 1208E–1208W) to roughly represent the size of the PacificOcean. The model resolution is 0.58 in both the zonaland meridional directions with the staggered ArakawaC-grid system. The time step is 1.2 hs. Table 1 sum-marizes the standard parameters used in the model.

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TABLE 1. Parameters of the reduced-gravity shallow-water model.

Parameter Value

Reduced gravityLayer thicknessRestoring coefficientLateral viscosityTime stepZonal resolutionMeridional resolutionDomain extent in the zonal direc-

tion

g9H0

gA

0.066 m s22

100 m1.157 3 10211 s21

10 000 m2 s21

1.2 h0.580.581208E–1208W

Domain extent in the meridionaldirection

408S–408N

Radius of the earthAngular velocity of the earthWind stress amplitude

aVA0

6.371 3 106 m7.292 3 1025 s21

0.24 dyn cm22

Meridional scale of the wind stress Df 58Density of water r 1.0 3 103 kg m23

In most of the following numerical experiments anidealized wind stress distribution is used:

22[(f2f )/Df]0t 5 A e for l , l , l , (4)l 0 1 2

t 5 0, (5)f

where A0 is the amplitude of wind stress, f is latitudeand f0 is a central latitude at which the wind stressreaches its maximum A0, l1 and l2 are the western andthe eastern longitudes of wind stress forcing, and Dfis a constant representing the meridional scale of thewind stress forcing. In later discussions, the central lon-gitude of the wind stress forcing is (l1 1 l2)/2. Thelongitude range of the wind stress forcing (l2 2 l1) is308. The wind stress curl associated with the above windstress patch has two centers of opposite sign located tothe north and south of the maximum wind stress (f 5f0). This wind stress patch is applied at different lo-cations and for different timescales to analyze the re-sponse of the equatorial thermocline. The above windstress distribution is chosen because of its simplicity,since it is impossible to have a single wind stress curlcenter without generating wind stress in a much largerdomain.

b. The OGCM

Our OGCM is adapted from MOM3.0 (Pacanowskiand Griffies 1998). The MOM3.0 is based on the pio-neering work of Bryan (1969) and was designed anddeveloped by the researchers at the Geophysical FluidDynamics Laboratory. The MOM3.0 is a three-dimen-sional primitive equation model. The model providesseveral numerical schemes for the parameterization ofsubgrid-scale processes, alternative ways to split baro-tropic and baroclinic components, and also many di-agnostic tools to analyze the integration results.

In the following, the major features of our OGCMare briefly presented, such as the numerical schemes for

subgrid-scale processes and the model’s grid and ge-ometry. For details of the OGCM, we refer to Wang(2001). The OGCM has a variable resolution in the me-ridional direction. Within 108S–108N the meridional res-olution is 0.58. Within 108–208S and 108–208N the mod-el meridional resolution gradually increases from 0.58to 2.08. Beyond 308N(S), the meridional resolution iskept as 28. The zonal resolution is 38. The model coversthe region from 318S to 618N, and from 117.58E to68.58W. There are 20 levels in the vertical, and 10 ofthem are in the top 300 m. Topographic data from theScripps Institutition of Oceanography (Pacanowski andGriffies 1998, p. 15) are used in the model. The ge-ometry of the basin is modified to eliminate small-scalecoastal features. The Japan Sea is removed since ourOGCM has low resolution in the zonal direction.

For horizontal viscosity and diffusivity the Smago-rinsky scheme is used (Pacanowski and Griffies 1998,p. 354):

2A 5 (k /k ) |D| 1 A , (6)m 0 m m0

A 5 A 1 A /Pr, (7)h h0 m

where k0, Am0, and Ah0 are adjustable parameters andkm is the largest resolvable wavenumber local to the gridcell of interest. The Prandtl number Pr is also an ad-justable parameter in the implementation of the scheme.The total deformation rate | D | is , in which2 2ÏD 1 DT S

DT and DS are the horizontal tension and shearing rateof strain and computed as

1 ]u ](y secf)D 5 2 cosf , (8)T a cosf ]l ](af)

1 ]y ](u secf)D 5 1 cosf . (9)S a cosf ]l ](af)

The actual parameters used in the OGCM are k0 5 15,Am0 5 5 3 106 cm2 s21, Ah0 5 5 3 106 cm2 s21, andPr 5 100. In the region of the model western boundarycurrent and its extension (418–498N, 1388–1718E), theparameters used are Am0 5 5 3 107 cm2 s21, Ah0 5 53 107 cm2 s21, and Pr 5 10. The above parameterssatisfy the Munk boundary condition (Munk 1950) andsignificantly reduce the horizontal viscosity and diffu-sivity compared with a model if the constant viscosityand diffusivity were used. As pointed out by Wajsowicz(1986), the horizontal diffusivity and viscosity can sig-nificantly damp the large-scale Rossby waves.

The Pacanowski and Philander scheme (Pacanowskiand Philander 1981) is used for the vertical mixing:

KmaxK 5 1 K , (10)m m02(1 1 5Ri)

KmaxK 5 1 K , (11)h h03(1 1 5Ri)

where Ri is the Richardson number,

3588 VOLUME 16J O U R N A L O F C L I M A T E

]rg

]zRi 5 2 , (12)

2 2]u ]y

11 2 1 2]z ]z

and Km0 and Kh0 are the background vertical viscositycoefficient and diffusivity coefficient. The parametersKmax, Km0, and Kh0 are adjustable parameters, which arechosen as Kmax 5 50, 1, and Kh0 5 0.1 cm2 s21, re-spectively. To account for the effect of high-frequencywind mixing near the surface (which is absent in theclimatological monthly mean wind stress), the mixingcoefficient at the base of level one is not allowed to beless than a prescribed value Wmix, which is taken as 10cm2 s21. So at level one, Km and Kh are calculated as

KmaxK 5 max 1 K , W , (13)m m0 mix2[ ](1 1 5Ri)

KmaxK 5 max 1 K , W . (14)h h0 mix3[ ](1 1 5Ri)

3. Analytical solution

a. Analytical model

We start from the nondimensionalized equatorial b-plane system with a long-wave approximation,

(] 1 e)u 2 yy 1 ] h 5 X, (15)t x

yu 1 ] h 5 Y, (16)y

(] 1 e)h 1 (u 1 y ) 5 0, (17)t x y

and consider the solution of the system in a zonally bound-ed basin. The boundary condition for the system is

`

u dy 5 0 at x 5 0,E2`

u 5 0 at x 5 1. (18)

The following dimensional variables are used to non-dimensionalize the equatorial b-plane system: basinwidth L for the zonal distance, equatorial Rossby de-formation radius (c/b)1/2 for the meridional distance, c5 for the zonal current, c/L(c/b)1/2 for the me-Ïg9H0

ridional current, L/c for time, H0 for the thermoclineanomaly, and rH0c2/L for the wind stress. The relevantparameters used in the analytical model are essentiallythe same as those used in the SWM and are listed inTable 1. A similar problem was treated in Cane andSarachik (1981) but only for wind stress that is zonallyuniform and meridionally either symmetric or antisym-metric with respect to the equator. We consider the windstress that is outside the equator and that has a generalform in the zonal direction. Our analysis is an extensionof Cane and Sarachik (1981).

The traditional method of solving the above systemis to introduce two new variables,

q 5 h 1 u, and (19)

r 5 h 2 u, (20)

and project all the variables in terms of function cm(y):

`

q 5 q (x, t)c (y), (21)O m mm50

`

r 5 r (x, t)c (y), and (22)O m mm50

`

y 5 y (x, t)c (y), (23)O m mm50

where m 5 0, 1, 2, . . . , andmd2 2m 1/2 21/2 y /2 2y mc (y) 5 (2 m!p ) e e (21) .m mdy

The function cm(y) is referred as the Hermite function(Moore and Philander 1977). It is the conventional Her-mite polynomial multiplied by an exponentially decayingterm e and a normalization coefficient (2mm!p1/2)21/2.22y /2

b. Response of equatorial thermocline to wind stressforcing

If we only consider the zonal wind stress and restrictour analysis to the symmetric Rossby waves, the ana-lytical model [Eqs. (15)–(17)] can be written in the fol-lowing form (cf. Battisti 1988; Jin 2001)

] ]1 e q 1 q 5 f , (24)0 0 01 2]t ]x

] ](4m 1 3) 1 e q 2 q 5 f , (25)2m12 2m12 2m121 2]t ]x

1/22m 1 2r 5 q , (26)2m 2m121 22m 1 1

where f 0 and f 2m12 are the projections of the zonal windstress forcing on different Hermite functions and are de-fined later. Equation (24) describes the equatorial Kelvinwave. When m 5 0, 1, 2, . . . , Eq. (25) describes thesymmetric Rossby waves. Assuming the zonal wind stressforcing X is periodic and that the response is also periodic,

ivtˆX 5 Xe , (27)ivtf 5 f (x)e , (28)2m12 2m12

ivtq 5 q (x)e , (29)2m12 2m12

ivtf 5 f (x)e , and (30)0 0

ivtq 5 q (x)e . (31)0 0

Substituting the above equations into Eqs. (24) and (25),we have

15 NOVEMBER 2003 3589W A N G E T A L .

x

2(iv1e)x (iv1e)j 2(iv1e)xq (x) 5 q (0)e 1 f (j)e dj e and (32)0 0 E 0

0

1

2(4m13)(iv1e)(12x) 2(4m13)(iv1e)j (4m13)(iv1e)xq (x) 5 q (1)e 1 f (j)e dj e . (33)2m12 2m12 E 2m12

x

The boundary condition is` d2mq (0) 5 q (0),O0 2m121/2[2(m 1 1)(2m 1 1)]m50

when x 5 0, and (34)

1/22m 1 1q (1) 5 q (1) ,2m12 2m 1 22m 1 2

when x 5 1, (35)

where

1/2[(2m)!]d 5 . (36)2m m2 m!

Using the boundary conditions (34) and (35) in (32)and (33), we can solve

` `

2(iv1e)D F 1 C F eO O2m 2m12 2m 0m50 m50q (0) 5 , (37)0 `

2(iv1e)1 2 C eO 2mm50

in which

d2mD 5 ,2m 1/2[2(m 1 1)(2m 1 1)]

d2mC 52m 1/2[2(m 1 1)(2m 1 1)]1/2

(2m 1 1)!!2(iv1e)(4m13)3 e ,[ ](2m 1 2)!!

1

(iv1e)jF 5 f (j)e dj,0 E 0

0

1

2(iv1e)(4m13)jF 5 f (j)e dj,2m12 E 2m12

0

ˆf (x) 5 Xc (y) dy,0 E 0

ˆf (x) 5 X{(2m 1 1)c2m12 E 2m12

1/22 [(2m 1 1)(2m 1 2)] c } dy.2m

After computing q0(0), the problem is solved by inte-grating (32) and (33) and using the boundary conditions

(34) and (35). The thermocline response is calculatedby

`1h(x, y, t) 5 q (x)c (y)O 2m 2m[2 m50

`

ivt1 r (x)c (y) e , (38)O 2m 2m ]m50

in which r2m(x) is defined in a similar manner as q2m(x).The calculations in the following are evaluated with thetruncation of m as 100.

Figure 1 shows the zonally averaged equatorial ther-mocline response as a function of the central longitudeand central latitude of the wind stress forcing when thedamping rate e is 0.01 (0.005 month21 in dimensionalunits) and the period of the forcing is around 20 yr (v5 0.05). The wind stress forcing is in the form of (4)and (5). It is clear that there is a maximum center inthe eastern basin along 108–128N (upper panel in Fig.1). When the wind stress is placed progressively fromsouth to north and its central longitude is fixed as 1458W,the equatorial thermocline response reaches a maximumwhen the wind stress forcing is located around 108N(middle panel in Fig. 1). On the other hand if the windstress is placed progressively from west to east and itscentral latitude is fixed as 158N, the equatorial ther-mocline response increases steadily (lower panel in Fig.1). The above analytical solutions are for the equilibriumstate. How the system reaches the state and why certainlocations of the wind stress forcing are effective in gen-erating the equatorial thermocline response are analyzedusing numerical experiments in the next two sections.The above solution is not sensitive to the truncation ofthe Hermite functions. When m is as small as 60, thesolution is not changed significantly.

4. Numerical experiments using SWM

a. Standard experiment

The standard experiment is a steady wind stress forc-ing with f0 5 158N, l1 5 1608W, l2 5 1308W, andDf 5 58 in (4) and (5). The time evolution of thethermocline depth anomalies along 188N (north of themaximum wind stress), 128N (south of the maximumwind stress), and the equator shows quite different char-acteristics (Fig. 2). Along 188N (128N) a negative (pos-itive) thermocline depth anomaly develops rapidly inthe forcing region. Rossby waves with a negative (pos-

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FIG. 1. (top) Equatorial thermocline response to the wind stressforcing at different locations (m), (middle) the response with thelongitude range of the wind stress forcing between 1608 and 1308W(with central longitude at 1458W), and (bottom) the response withthe central latitude of the wind stress forcing at 158N. The period ofthe wind stress forcing is 20 yr.

FIG. 2. Time evolution of the thermocline depth anomaly at dif-ferent latitudes for the standard experiment with the wind stress forc-ing located between 1608 and 1308W and having a maximum at f0

5 158N: (top) along 188N, (middle) along 128N, and (bottom) at theequator.

itive) thermocline depth anomaly propagate westward.The propagation speed along 128N is faster than thatalong 188N, which is as expected from the theoreticalfree Rossby wave speed in such a system. The Rossbywave speeds estimated from Fig. 2 are 7.1 3 1022 and1.8 3 1021 m s21 for 188 and 128N, respectively, whichare comparable with those calculated from the formulabc2/ f 2 (7.1 3 1022 m s21 for 188N and 1.6 3 1021 ms21 for 128N, c2 5 g9H0, f 5 2V sinf). For the equa-torial region, the thermocline depth anomaly is nearlyzonally uniform and increases gradually after the freeRossby waves along 128N reach the western boundary.Though a similar phenomenon was noted in numericalexperiments by Schneider et al. (1995), the connectionbetween the off-equatorial wind stress forcing and theequatorial thermocline response has not been analyzedin detail.

After 7 yr of integration the thermocline depth anom-aly in the equatorial region nearly reaches the equilib-rium. Before year 3 a positive thermocline gradient(2]h/]l . 0) develops rapidly in the forcing region(1608–1308W) along 128N. This positive thermoclinegradient is associated with a meridional transport towardthe equatorial region, leading to the recharge of theequatorial heat content. At the end of 6 yr of integration,

the response of the equatorial thermocline is about one-third of the local response along 128N, whereas the ther-mocline anomaly along 188N is about three times asstrong but of opposite sign. It should be mentioned thatthe small-scale structures along the western boundaryat 128N form the feature associated with the model west-ern boundary current and short Rossby waves.

The horizontal distribution of the thermocline depthanomaly at four different stages is shown in Fig. 3. Itshould be pointed out that in order to show the ther-mocline response of different regions (which have quitedifferent magnitudes), the contour interval is not uni-form and only a group of selected contours is shown.A positive and a negative thermocline depth anomalycenter are generated in the forcing region (Fig. 3a) andthey then gradually propagate westward with a fasterspeed at lower latitudes (Figs. 3b–d). The magnitude ofthe thermocline depth anomaly also increases with time.The different magnitudes of the thermocline depthanomalies north and south of 158N are clearly dem-onstrated, especially in Fig. 3d. To the east of the windstress forcing, there is no significant thermocline depthanomaly. In the unforced region the spatial pattern re-sembles the VLF modes (Fig. 3 in Jin 2001) with anearly zonally uniform thermocline depth anomalyalong the equator, and the eastern side of the ocean has

15 NOVEMBER 2003 3591W A N G E T A L .

FIG. 3. Snapshots of the thermocline depth anomaly for the standard experiment: (a) month 6, (b) month 18,(c) month 30, and (d) month 42. Only the following contours are shown: 240, 230, 220, 210, 25, 1, 2, 3,5, 10, and 15 m.

a larger meridional scale. The positive thermoclinedepth anomaly along the eastern boundary is associatedwith the coastal Kelvin waves and its reflection to Ross-by waves.

To further delineate that the thermocline change inthe equatorial region is caused by the meridional trans-port associated with the wind stress forcing, the me-ridional velocity y along 108N for four different stagesin the integration is shown in Fig. 4. The region ofdirect wind stress forcing (1608–1308W) has a south-ward velocity. In other regions, the y is small exceptnear the western boundary. The western boundary cur-rent gradually grows in strength after the thermoclineanomaly in the interior of the ocean reaches the westernboundary (Figs. 4b–d). The meridional transport of thewestern boundary region (integration of y 3 h from1208 to 1308E), the interior region (integration of y 3h from 1308E to 1208W), and the total transport (sumof the above two components) along 108N, 108S, 28N,and 28S are shown in Fig. 5. Since the transport along108S is negligible, the transport along 108N plays adecisive role in the equatorial thermocline response.The interior southward transport is built up by the windstress forcing along 108N through the beginning of theintegration and gradually grows in strength (dashedline in Fig. 5a). The western boundary current transportis negligible in year 1 and starts to grow in strengthin year 2 (solid line). As a result, the total meridional

transport is southward until year 7 (dotted line). As-sociated with the southward meridional transport, theequatorial thermocline (zonally averaged between 28Sand 28N) steadily deepens until year 7 (solid line inFig. 5e) when the interior transport and the westernboundary transport roughly balance each other. Afteryear 7 the equatorial thermocline anomaly changes lit-tle with time. At first glance the meridional transportalong 108N seems irrelevant to the equatorial ther-mocline response. In this idealized experiment, thewind stress forcing exponentially decays from its cen-tral latitude of 158N. In the equatorial region, the windstress forcing is quite small, less than 0.01% of that at158N. The thermocline depth anomaly caused by thenet transport along 108N is just redistributed by theequatorial Rossby and Kelvin waves (Fig. 3). From thetransport along 28N and 28S (Figs. 5c,d), the interiortransport is small. The western boundary transportplays a decisive role. The total southward transportalong 28N is larger than the southward transport along28S. The equatorial region has a convergence of trans-port. Thus the equatorial thermocline gradually deep-ens and shows a positive anomaly. The small windstress anomaly along the equatorial region does notplay a significant role in terms of the equatorial ther-mocline response. Another experiment is conductedwith the following wind stress:

3592 VOLUME 16J O U R N A L O F C L I M A T E

FIG. 4. Snapshots of the meridional velocity along 108N: (a) month 6, (b) month 18, (c) month 30, and (d) month 42. The westernboundary and the ocean interior are shown separately.

f 2 f0t 5 B cos p 1 1 for l , l , l ,l 0 1 21 2[ ]Df1

f 2 Df # f # f 1 Df , (39)0 1 0 1

t 5 0. (40)f

Here Df1 is 108, l1 and l2 are the same as in (4) and(5), and the constant B0 is chosen as Df1 /DfpÏ2exp21/2A0 such that the maximum wind stress curl ofthe above wind stress profile is the same as that givenby (4) and (5). For the above wind stress forcing, boththe wind sress and its curl are zero outside the regionof l1 , l , l2 and f0 2 Df1 # f # f0 1 Df1. Theequatorial thermocline response for the above windstress forcing (dashed line in Fig. 5e) is roughly thesame as the response in the standard experiment, exceptthat the magnitude of the response is larger. This shouldbe related to the difference of the detail spatial featuresof the two wind stress patterns.

If the viscosity (A) is changed by one order of mag-nitude, the result does not change significantly. If therestoring coefficient (g) is set as zero or changed byone order of magnitude, the result is also not changed(figures not shown). If the restoring coefficient is in-creased by several orders of magnitude to 3.21 3 1028

s21, which is equivalent to a damping timescale of 1 yr,the response of the equatorial thermocline is greatlyreduced, from 3.6 to 0.7 m. This reduction could beexplained by the influence of damping on the propa-gation of Rossby waves. Since the viscosity and dif-

fusivity in a shallow-water model can be significantlyreduced compared with those in an OGCM, it will beinteresting to compare the response of an OGCM withthe present SWM.

The equatorial thermocline anomaly reaches a max-imum around year 6 and gradually reaches an equilib-rium state after 20 yr. At equilibrium state, the responseis reduced to 2.7 m compared with the maximum value(3.6 m) reached around year 6. If a second wind stressforcing is placed in the Southern Hemisphere and issymmetric about the equator (with respect to the presentone), the equatorial response is almost doubled.

b. Wind stress forcing at different latitudes

A set of experiments is designed to investigate theresponse of the equatorial thermocline to the wind stressforcing at different latitudes. The longitude of the windstress forcing is fixed between 1608 and 1308W. Theupper panel in Fig. 6 compares the equatorial thermo-cline response to the wind stress forcing at differentlatitudes from 78 to 198N. The indices used are the max-imum response of the equatorial thermocline (zonallyaveraged between 28S and 28N, solid line) and the timeat which the maximum response is reached (dashedline). When the wind stress is close to the equator (78N),the equatorial thermocline response is weak (2.5 m).The time needed to reach the response is slightly lessthan 2 yr. When the wind stress is placed northward,the equatorial thermocline response first increases rap-

15 NOVEMBER 2003 3593W A N G E T A L .

FIG. 5. Time evolution of the western boundary transport (solidline), the interior transport (dashed line), and the total transport (dot-ted line) along (a) 108N, (b) 108S, (c) 28N, and (d) 28S for the standardexperiment. Units are 106 m3 s21. Time evolution of the equatorialthermocline depth anomaly (zonally averaged between 28S and 28N)for the standard experiment [solid line in (e)] and the steady windstress forcing as given in (39) and (40) [dashed line in (e)]. Unitsare m.

FIG. 6. (top) The maximum equatorial thermocline response (zon-ally averaged between 28S and 28N, solid line) to the steady windstress forcing and the time at which the maximum response is reached(dashed line) when the longitude range of the wind stress is fixedbetween 1608 and 1308W with its central latitude (abscissa) beingchanged. (bottom) As in the top panel except that the central latitudeof the wind stress forcing is fixed at 158N and its longitude range ischanged (abscissa).

idly and then decays. The maximum response is reachedwhen the wind stress is located between 108 and 138N.The timescale of the equatorial thermocline response isdetermined by the westward Rossby wave propagationalong the forcing region. Farther away from the equator,the westward propagation speed of Rossby waves de-creases and thus it takes a longer time for Rossby wavesto reach the western boundary and for the westernboundary current to spin up. As shown in Fig. 5, themagnitude of the equatorial thermocline response is con-trolled by the net meridional transport before the west-ern boundary transport balances the interior transportalong the forcing region. When the wind stress is closeto the equator, the Rossby wave speed is fast. The west-ern boundary current is built up rapidly and the netmeridional transport is small, so the equatorial ther-mocline response is small. When the wind stress is far-ther away from the equator, though the Rossby wavespeed is slow and the net meridional transport is pre-sumably large, the equatorial thermocline response isreduced. This is partly due to the fact that the zonallyuniform equatorial thermocline change involves a largermeridional scale when the wind stress forcing is fartheraway from the equator. Note that the 108–138N latitude

band between which the maximum equatorial responseexists is related to the meridional scale of the wind stressforcing. When the meridional scale is reduced to Df 518, the latitude band that has the maximum responsebecomes 88–98N instead of 108–138N. The response isalso reduced to 1.3 m instead of close to 4 m. The timewhen the maximum response is reached is reduced byless than 1 yr. In reality the wind stress anomaly oninterannual and decadal to interdecadal timescales tendsto have a broad meridional structure ($108), so the se-lection of Df 5 58 is reasonable.

c. Wind stress forcing at different longitudes

A set of experiments is conducted to investigate theresponse of the equatorial thermocline to the wind stressforcing at different longitudes (lower panel in Fig. 6).In this set of experiments, the latitude of the wind stressforcing is fixed at f0 5 158N. The longitude range ofthe wind stress forcing [controlled by parameters l1 andl2 in (4) and (5)] is varied from east (1608–1308W, witha central longitude at 1458W) to west (1308–1608E, witha central longitude at 1458E). When the wind stressforcing is located on the eastern side, the equatorialthermocline response has the largest magnitude (3.6 m).When the forcing is placed westward, the equatorialresponse becomes weaker. The time needed for the equa-torial maximum response becomes shorter when theforcing region is placed westward. For the case of the

3594 VOLUME 16J O U R N A L O F C L I M A T E

FIG. 7. The amplitude of the equatorial thermocline response tothe periodic wind stress forcing located between 1608 and 1308Wwith its central latitude at 158N. The abscissa is the period of thewind stress forcing. Solid line, reduced-gravity shallow-water model;dashed line, analytical solution.

forcing longitude at 1608–1308W, the time needed forthe equatorial thermocline to reach the maximum anom-aly is slightly more than 5 yr. For the case of the forcinglongitude located at 1308–1608E, it is only slightly morethan 1 yr. This could still be explained by the propa-gation of Rossby waves. When the forcing region islocated farther east, it takes a longer time for Rossbywaves to reach the western boundary and for the westernboundary current to balance the interior meridionaltransport associated with the wind stress forcing. So fora wind stress forcing located farther east, the responsetime is longer, and the magnitude of the equatorial ther-mocline response is larger.

d. Periodic wind stress forcing of different timescales

Figure 7 compares the equatorial thermocline re-sponse for wind stress forcing with periods of 2, 4, 6,8, 10, 12, 14, and 16 yr. The location of the wind stressforcing is the same as that in the standard experiment(1608–1308W, f0 5 158N). The time integration for theSWM is 100 yr. When the period of the wind stressforcing is 2 yr, the amplitude of the equatorial ther-mocline depth anomaly is small (0.07 m). The amplitudesteadily increases when the forcing period is increased.It is interesting that when the period of the wind stressforcing is longer than 12 yr, the response amplitude doesnot increase significantly with increasing period. Thuswhen the forcing period is longer, the response is larger.There is no specific timescale that is selected by thesystem. The result is consistent with that of the buoy-ancy forcing in Shin and Liu (2000), in the sense thatwhen the period of forcing is longer, the response islarger. When the period of the wind stress forcing islonger, Rossby waves have a longer time to propagatewestward. The net meridional transport becomes largertoo. The analytical solution shows the same tendency(dashed line). When the period of the forcing is longer,the equatorial region tends to have a larger response.The analytical solution and the results of the SWM arecomparable.

5. Numerical experiments using the OGCM

Our OGCM for the Pacific region is used to verifythe major findings from the SWM. The OGCM is firstintegrated for 85 yr using an annual mean wind stressforcing (Hellerman and Rosenstein 1983). The sea sur-face temperature and salinity are restored to Levitus data(Levitus 1982). In the southern and northern boundariesthe temperature and salinity are also restored to Levitusdata. After 85 yr of integration, the model state doesnot change much with time. The experiments describedbelow start from the end of the 85-yr integration. Thediagnosed heat flux and ‘‘salinity flux’’ are then usedto force the model. The surface temperature and salinityare restored to the model climatology for a timescale of300 and 600 days, respectively. The restoration at thenorthern and southern boundaries is also maintained.The wind stress used to force the model is the sum ofthe annual wind stress (Hellerman and Rosenstein 1983)and a perturbation wind stress. The model is integratedfurther with specified perturbation wind stress at dif-ferent spatial locations and with different periods. Theperturbation wind stress is still in the form of (4) and(5). The zonal perturbation wind stress decays expo-nentially both northward and southward away from thecentral latitude, and the meridional wind stress pertur-bation is zero. For most of the results we present belowthe model is integrated for 10 yr. Starting from aroundyear 6 or 7, the model state does not change much withtime. In our first experiment, the wind stress is locatedat 1738–1438W with the central latitude at 158N. Withthe steady wind stress forcing, a pair of isopycnal sur-face depth anomalies are generated and propagate west-ward on the su 5 24.5 surface (Figs. 8a–d). The dif-ference in the propagation speed between 208 and 108Nis clearly seen. For the same wind stress curl forcingthe response along 208N (10–20 m) is about 3 times theresponse along 108N (5 m), which is consistent with theresults from the SWM. In the equatorial region a pos-itive isopycnal surface depth anomaly is gradually builtup with a broad meridional scale in the eastern equa-torial Pacific. At the end of the 10-yr integration, alongthe equatorial thermocline there is a positive tempera-ture anomaly with a magnitude of around 0.18–0.28C(Fig. 9). In the central to eastern equatorial Pacific, thepositive temperature anomaly extends to the surfacewith a magnitude of around 0.18C.

A group of experiments is designed to demonstratethe influence of the central latitude of the wind stressforcing on the equatorial thermocline response. The lon-gitude of the wind stress forcing is fixed between 1738and 1438W, while its central latitude is changed to 98,118, 138, 158, 178, and 198N. In the OGCM the equatorialthermocline response does not have an obvious maxi-mum in its time evolution. The response of the equa-torial thermocline at the end of the 10-yr integration isused instead of the maximum response. When the windstress forcing is placed farther away from the equator,

15 NOVEMBER 2003 3595W A N G E T A L .

FIG. 8. Snapshots of the isopycnal depth anomaly on the su 5 24.5 surface for the steady wind stress forcing locatedbetween 1738 and 1438W with the central latitude at 158N: (a) 12, (b) 24, (c) 36, and (d) 48 month.

FIG. 9. Temperature anomaly (solid line) at the end of the 10-yrintegration with the steady wind stress forcing as in Fig. 8 and themodel climatology (dashed line) along the equator.

the equatorial thermocline response first increases andthen decreases as in the SWM (in Fig. 10 top). It shouldbe noted that in the OGCM the equatorial thermoclineresponse is systematically smaller than that in the SWM.If the central latitude of the wind stress forcing is fixedat 158N, and its longitude range is changed from theeastern Pacific (1608–1308W, with central longitude at1458W) to the western Pacific (1408–1708E, with centrallongitude at 1558E), the equatorial thermocline responseis gradually reduced (lower panel in Fig. 10). If theposition of the wind stress forcing is fixed (1738–1438W,with central latitude at 158N), the period of the windstress forcing is varied at 2, 4, 6, 8, 10, and 12 yr. The

amplitude of the equatorial thermocline response firstincreases and then remains at a steady level (Fig. 11),which is similar to the situation in the SWM and theanalytical solution (Fig. 7). In summary the features ofthese three groups of OGCM experiments are consistentwith those of the SWM. The spatial distribution of theisopycnal surface depth anomaly is more complicatedand the response magnitude is reduced. The systematicreduction in the equatorial response is likely due to thestronger damping in the OGCM than in the SWM.

6. Summary and discussion

The response of the equatorial thermocline to thewind stress forcing in the tropical and subtropical regionis derived using the equatorial b-plane system boundedin the zonal directions. The eastern tropical and sub-tropical region appears to be an effective region for theoff-equatorial wind stress to generate an equatorial ther-mocline response. The equatorial thermocline responseshows the spatial features of the very-low-frequencymodes described in Jin (2001), with a nearly zonallyuniform thermocline change in the equatorial region anda large meridional scale in the eastern basin.

Numerical experiments using a reduced-gravity shal-low-water model and an oceanic general circulationmodel in the Pacific region verify the analytical solu-tions and further reveal the detailed features of the equa-torial thermocline response to the wind stress forcing.

3596 VOLUME 16J O U R N A L O F C L I M A T E

FIG. 10. (top) The response of the equatorial isopycnal depth onthe su 5 24.5 surface at the end of the 10-yr integration to the steadywind stress forcing located between 1738 and 1438W with its centrallatitude (abscissa) being changed. (bottom) As in the top panel exceptthat the central latitude of the wind stress forcing is fixed at 158Nwith its central longitude (abscissa) being changed.

FIG. 11. The amplitude of the equatorial isopycnal depth anomalyon the su 5 24.5 surface for the periodic wind stress forcing locatedbetween 1738 and 1438W with the central latitude at 158N. The ab-scissa is the period of the wind stress forcing.

FIG. 12. The response to a westerly wind stress forcing exponen-tially decaying with latitude and located in the central equatorialregion: (a) thermocline depth anomaly at month 6, (b) thermoclinedepth anomaly at month 42, (c) meridional transport along 28N, (d)meridional transport along 28S, and (e) zonally averaged thermoclinedepth anomaly along the equatorial region (28N–28S).

The response timescale is longer and the magnitude ofthe response first increases and then decreases when thewind stress forcing is placed away from the equator.The subtropical region along 108–158 seems to be aneffective region for subtropical wind stress forcing togenerate equatorial thermocline response. When thewind stress is located in the eastern basin, it takes alonger time for the equatorial thermocline to reach itsmaximum response than the case when the wind stressforcing is located in the western basin. The equatorialthermocline also tends to have a larger response whenthe wind stress is located in the eastern basin. Whenthe wind stress forcing has a longer period, the responseof the equatorial thermocline has a larger amplitude.There is no preferred timescale that is selected by thesystem.

In our analysis only very idealized wind stress forcingpatterns are used. For complicated wind stress patterns,the response of the equatorial thermocline is also com-plicated. Two examples that are relevant to our coupledstudies (Wang et al. 2003, hereafter Part II) are zonalwind stress forcing in the equatorial region and cyclonicwind stress forcing in the subtropical region. The detailsof these wind stress patterns are presented in Part II.Figure 12 shows the response to a westerly wind stressforcing in the central equatorial region (1508E–1508W).The wind stress exponentially decays away from theequator until 108N and 108S. Outside of these two lat-

itudes the wind stress vanishes. For a westerly windstress in the equatorial region, there is a thermoclinedepth anomaly gradient along the equator. To the westof the wind stress forcing, the thermocline depth anom-aly is negative. To the east of the wind stress forcing,the thermocline depth anomaly is positive (Figs. 12a,b).The wind stress curl outside the equator causes a nettransport away from the equator along 28N and 28S(Figs. 12c,d). Along these latitudes, the interior trans-port has an opposite sign from the western boundary

15 NOVEMBER 2003 3597W A N G E T A L .

FIG. 13. The response to the symmetric cyclonic wind stress boringin on the subtropical region: (a) thermocline depth anomaly at month60, (b) thermocline depth anomaly at month 120, (c) meridional trans-port along 28N, (d) meridional transport along 28S, and (e) zonallyaveraged thermocline depth anomaly along the equatorial region(28N–28S).

transport. These two transports tend to balance eachother after 3 yr. The total transport away from the equa-torial region before these two transports balance eachother causes a negative zonally averaged thermoclinedepth anomaly along the equator (Fig. 12e). The equa-torial region is discharged because of the wind stressforcing.

For symmetric cyclonic wind stress forcing in thesubtropical region, the wind stress curl has a triple-center structure. North of the equator in the central re-gion the wind stress curl is positive. To the north andsouth of it, the wind stress curl is negative. Associatedwith the wind stress forcing, one negative and two pos-itive centers of thermocline depth anomaly are gener-ated. These centers propagate westward as time passes(Figs. 13a,b). Its influence on the equatorial region alsoevolves with time. The interior transport and the westernboundary transport along 28N and 28S are out of phasemost of the time (Figs. 13c,d). The total transport beforeyear 4 is toward the equatorial region. Thus the equa-torial region is recharged. The thermocline depth anom-aly along the equator is positive and increases with time.After year 4 the total transport is away from the equa-torial region along 28N and 28S. The equatorial regionis discharged and the thermocline depth anomaly grad-ually decreases to a negative state. After year 10, theequatorial region is recharged again and the equatorial

thermocline depth anomaly increases to a positive value(Fig. 13e). The evolution of the equatorial thermoclineis associated with the complex structure of the windstress forcing.

The response of the equatorial thermocline to thewind stress forcing along the equator is on an interan-nual timescale, whereas its response to the subtropicalwind stress forcing is on a decadal timescale. Consid-ering these differences in ocean memory, a decadaltimescale oscillation may be generated through a broad-scale tropical ocean–atmosphere interaction. Furthercoupled studies will be presented in Part II.

Acknowledgments. The research is supported byATM9615952 and ATM0226141, and NOAA GrantsGC01223 and GC01264. YW is partly supported by theFrontier Research System for Global Change throughthe International Pacific Research Center (IPRC). Wewould like to thank Drs. Peter Muller, Bo Qiu, BinWang, Tim Li, Shang-ping Xie, Julian P. McCreary,Dailin Wang, and Masami Nonaka for insightful dis-cussions; Dr. Ronald C. Pacanowski for his e-mail com-ments about using the MOM3.0; and Ms. Diane Hen-derson for reading the manuscript. The comments fromtwo anonymous reviewers helped us in revising the man-uscript.

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