VOLUME 33 AUGUST 2003J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y

q 2003 American Meteorological Society 1549

Why Are There Rossby Wave Maxima in the Pacific at 108S and 138N?

ANTONIETTA CAPOTONDI AND MICHAEL A. ALEXANDER

NOAA–CIRES Climate Diagnostics Center, Boulder, Colorado

CLARA DESER

National Center for Atmospheric Research, Boulder, Colorado

(Manuscript received 23 January 2002, in final form 4 February 2003)

ABSTRACT

Observations indicate the existence of two bands of maximum thermocline depth variability centered at ;108Sand 138N in the tropical Pacific Ocean. The analysis of a numerical integration performed with the NationalCenter for Atmospheric Research ocean general circulation model (OGCM) forced with observed fluxes ofmomentum, heat, and freshwater over the period from 1958 to 1997 reveals that the tropical centers of thermoclinevariability at 108S and 138N are associated with first-mode baroclinic Rossby waves forced by anomalous Ekmanpumping. In this study the factors that may be responsible for the Rossby wave maxima at 108S and 138N,including the amplitude and spatial coherency of the forcing at those latitudes, are systematically investigated.A simple Rossby wave model is used to interpret the OGCM variability and to help to discriminate betweenthe different factors that may produce the tropical maxima. These results indicate that the dominant factor inproducing the maximum variability at 108S and 138N is the zonal coherency of the Ekman pumping, a char-acteristic of the forcing that becomes increasingly more pronounced at low frequencies, maximizing at timescalesin the decadal range. Local maxima in the amplitude of the forcing, while not explaining the origin of the centersof variability at 108S and 138N, appear to affect the sharpness of the variability maxima at low frequencies.Although the Rossby wave model gives an excellent fit to the OGCM, some discrepancies exist: the amplitudeof the thermocline variance is generally underestimated by the simple model, and the variability along 138N iswestward intensified in the wave model but reaches a maximum in the central part of the basin in the OGCM.Short Rossby waves excited by small-scale Ekman pumping features, or the presence of higher-order Rossbywave modes may be responsible for the differences in the zonal variance distribution along 138N.

1. Introduction

Thermocline processes have recently received con-siderable attention because of their potential role in cli-mate variability at decadal timescales. Thermal anom-alies have been observed to propagate along isopycnalsfrom the surface midlatitudes toward the Tropics (Deseret al. 1996; Schneider et al. 1999) with a transit timeof 7–8 yr. According to a recent theory of decadal cli-mate variability (Gu and Philander 1997), the thermo-cline anomalies may reach the equator, where they havethe potential to alter the upper ocean heat budget andgive rise to equatorial sea surface temperature (SST)anomalies that may affect the atmosphere.

Another mechanism that can produce thermoclinevariability is propagation of baroclinic Rossby waves.Several midlatitude theories of decadal variability relyupon Rossby wave dynamics. Some of the proposedmechanisms (Latif and Barnett 1994, 1996; Robertson

Corresponding author address: Antonietta Capotondi, NOAA–CI-RES Climate Diagnostics Center, 325 Broadway, Boulder, CO 80305.E-mail: mac@cdc.noaa.gov

1996; Jin 1997; Xu et al. 1998; Munnich et al. 1998;Grotzner et al. 1998; Talley 1999; Neelin and Weng1999; Cessi 2000; Watanabe and Kimoto 2000) involvecoupled ocean–atmosphere interactions, where changesin the surface wind stress induce changes in the strengthof the subtropical gyre and in the northward heat trans-port by the western boundary current. These theoriesthen postulate that the resulting sea surface temperature(SST) anomalies may affect the atmospheric circulationand ultimately produce changes in the surface windstress. Since atmospheric processes are relatively fast,it is the slow oceanic adjustment that is responsible forthe decadal timescales.

Although feedbacks of SST anomalies on the atmo-sphere can enhance the decadal signal, stochastic at-mospheric forcing with a coherent basinwide spatialstructure can also give rise to variability at interdecadaltimescales (Jin 1997; Frankignoul et al. 1997; Neelinand Weng 1999). Frankignoul et al. (1997) have shownthat a simple baroclinic Rossby wave model forced bya zonally uniform and temporally stochastic wind stresscurl can produce spectra of the oceanic response thathave enhanced power at low frequencies. The spectra

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FIG. 1. (a) Standard deviation of the depth of the 25.5-su isopycnal diagnosed from a numerical simulation performed withthe NCAR OGCM forced with observed fluxes of momentum, heat, and freshwater over the period 1958–97. Standard deviationsare based upon 3-month averages of monthly anomalies (seasonal cycle removed). Contour interval is 5 m. Values larger than15 m are shaded. (b) Meridional gradients of the depth of the 25.5-su isopycnal. Contour interval is 0.5 3 1024. Values largerthan 1024 are shaded. (c) Standard deviation of thermocline depth computed with the wave model forced by the same Ekmanpumping field used to force the OGCM. Contour interval is 5 m. Values larger than 15 m are shaded. (d) Standard deviationof = 3 t, based on annual values. Contour interval is 1 3 1025 cm s21. Values larger than 2 3 1025 cm s21 are shaded. Thedot–dash line in (a), (b), and (d) is the line where the annual mean = 3 t vanishes.

of the oceanic response predicted by the simple modelvary spatially and at low frequencies become relativelymore energetic in the western side of the basin.

The fundamental role of wind variability in forcingbaroclinic Rossby waves has emerged in several obser-vational and modeling studies (Kessler 1990 and ref-erences therein; Qiu et al. 1997). However, it is stillunclear which aspects of the forcing are the most ef-fective in exciting the oceanic baroclinic Rossby wavefield, and how the influence of the wind forcing variesgeographically. Is a spatially coherent and temporallystochastic forcing, as hypothesized by Frankignoul etal. (1997), sufficient to explain the energy level andspectral characteristics of the Rossby wave field overmost of the ocean, or are additional aspects of the windforcing important for the excitation of oceanic Rossbywaves in some regions?

In the Pacific, thermocline variability is maximizedin five areas, as shown in Fig. 1a. The standard deviationof the depth of the 25.5-su isopycnal, an isopycnal thatlies in the core of the main thermocline, is used as a

proxy for thermocline variability. Figure 1a is computedfrom an ocean general circulation model (OGCM)forced with observed fluxes of momentum, heat, andfreshwater over the period from 1958 to 1997. A similarpattern of variability is found in observations (Lysneand Deser 2002). Two of the five centers of variabilityare found in the northern and southern midlatitudes,extending equatorward from the outcrop line of the25.5-su isopycnal. Some fraction of these signals is like-ly associated with thermal anomalies subducting at thesurface in midlatitudes and propagating equatorwardwithin the main thermocline. A third area of large var-iability is found in the eastern equatorial Pacific and isassociated with the El Nino–Southern Oscillation(ENSO). While the nature of the variability in midlat-itudes and along the eastern equatorial Pacific is rela-tively well understood, the processes contributing to thetwo tropical centers of variability are in need of furtherinvestigation.

The two tropical centers lie approximately along theequatorward edges of the subtropical gyres in both

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hemispheres, as indicated by the contours of zero windstress curl in Fig. 1a. Since the wind stress curl changessign at the gyre boundaries, displacements of the gyrestructure can easily give rise to enhanced wind stresscurl variability in these areas. Lysne and Deser (2002)have indeed found evidence of local maxima in windstress curl variance at approximately 108S and 138N, asshown in Fig. 1d, and have suggested that the largeramplitude of the surface forcing in these areas may bethe cause of the enhanced oceanic response.

Based on the analysis of the OGCM in Fig. 1a, Ca-potondi and Alexander (2001a, hereinafter CAa) haveshown that the thermocline variability at 138N consistsprimarily of first-mode baroclinic Rossby waves forcedby anomalous Ekman pumping, and characterized by alarge fraction of energy at periods longer than ;7 yr.At decadal periods (;7–10 yr), Ekman pumping anom-alies east of the date line appear to propagate westwardwith a phase speed that is close to the phase speed offree Rossby waves, an aspect of the forcing which maybe responsible for a preferred oceanic response at lowfrequencies. However, how relevant the westward prop-agation of Ekman pumping anomalies may be for ex-plaining the center of variability at 138N is still unclear.

The two tropical centers are also characterized bylarge meridional gradients of mean thermocline depth(Fig. 1b), and so meridional displacements of the iso-therms could give rise to large thermal anomalies at afixed latitude. It has long been known from observa-tional studies (Wyrtki 1975; White 1977) that enhancedbaroclinic variance tends to occur in areas of large hor-izontal gradients, with the implication that horizontalmovements of the isotherms may produce local thermalanomalies. To our knowledge, the effectiveness of thisprocess in producing variability maxima has never beenverified. Capotondi and Alexander (2001b, hereinafterCAb) have provided estimates of meridional shifts ofthe isotherms at 138N, and have shown that the dis-placements detected with their method can explain alarge fraction of the temperature and depth variabilityin the thermocline between 108–158N, but it is not clearto what extent the meridional displacements are inde-pendent of the Rossby wave field itself.

In this paper we systematically examine the aspectsof the surface forcing that may give rise to the centersof variability at 108S and 138N, and clarify their relativeroles. Some specific questions are addressed. 1) Can thesurface Ekman pumping produce the two tropical cen-ters of variability? 2) If the answer to question 1 ispositive, which aspect(s) of the forcing are the mostimportant: amplitude, spatial/temporal coherency, orpropagation characteristics? 3) Can the meridional ex-cursions of the thermocline detected by CAb be a man-ifestation of the propagating Rossby waves? To answerthese questions we analyze the OGCM simulation con-sidered by CAa and CAb. A simple wave equation isalso used to help interpret the OGCM results and dis-

criminate between the different factors that may be re-sponsible for the two tropical centers of variability.

The presentation of this study is organized as follows.In section 2 we describe the OGCM and the wave model.In section 3 the wave model is used to assess whichaspects of the surface Ekman pumping are the mostimportant in producing the large thermocline variabilityat 138N and 108S. In section 4 we discuss the origin ofthe large zonal coherency of the Ekman pumping along108S and 138N, and whether meridional shifts of theisotherms can result from the Rossby wave field itself.We conclude in section 5.

2. The models

a. The OGCM

The OGCM used for this study is the National Centerfor Atmospheric Research (NCAR) ocean model(NCOM) that has been described in detail in Large etal. (1997, 2001) and Gent et al. (1998). In this sectionwe only provide a brief summary of the basic modelcharacteristics and information about the surface forcingused for the numerical simulation analyzed here.

NCOM is derived from the Geophysical Fluid Dy-namics Laboratory (GFDL) Modular Ocean Model withthe addition of a mesoscale eddy flux parameterizationalong isopycnal surfaces (Gent and McWilliams 1990)and a nonlocal planetary boundary layer parameteri-zation (Large et al. 1994). The model is global, with ahorizontal resolution of 2.48 in longitude and varyingresolution in latitude ranging from 0.68 near the equatorto 1.28 at high latitudes. The model version used forthis study includes an anisotropic viscosity parameter-ization (Large et al. 2001) with enhanced viscosity closeto ocean boundaries and much weaker viscosity in theocean interior.

The surface forcing includes momentum, heat, andfreshwater fluxes for the period from 1958 to 1997. Thewind stress is computed from the reanalyses fields pro-duced at the National Centers for Environmental Pre-diction (NCEP; Kalnay et al. 1996) using bulk formulas.The sensible and latent heat fluxes are computed fromthe NCEP winds and relative humidity and the model’sSSTs using standard air–sea transfer equations (Largeand Pond 1982; Large et al. 1997). Sensible and latentheat fluxes depend on the difference between SST andsurface air temperature. Since SST and air temperatureclosely track each other, when observed air temperaturesare used in the bulk formulas, as in the present modelsimulation, the model’s SST is relaxed toward obser-vations (Haney 1971). The relaxation timescale is rel-atively short (30–60 days for typical mixed layerdepths), and so the SST in the model can be expectedto be strongly constrained by the surface forcing ratherthan by the interior ocean dynamics.

The numerical simulation is started from an initialcondition obtained from a preliminary climatological

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integration so that the initial model state is not too dif-ferent from the mean state characteristic of the 40-yrexperiment. Then the model was run for two 40-yr cy-cles, the second cycle starting from the conditionsachieved at the end of the first 40-yr segment. The mis-match between the model state and the forcing at thebeginning of the second cycle did not seem to produceany long-term transient. Here we analyze the output forthe second 40-yr period using monthly and annual meanvalues. Some residual drift in temperature and salinityappears to be confined to depths larger than approxi-mately 500 m (Doney et al. 2003).

b. The wave model

To interpret the OGCM results we consider a 1½-layer, reduced-gravity system, in which the upper oceanof density r1 overlies an infinitely deep, motionless bot-tom layer of density r2. Under the low-frequency, qua-sigeostrophic assumptions, and in the long wave limit,the equation for the upper-layer thickness h can be writ-ten in the form (Qiu et al. 1997):

]h ]h2 c 5 2W (x, t) 2 Rh, (1)r E]t ]x

where cr 5 bl2 is the phase speed of the long, freebaroclinic Rossby waves, b is the meridional gradientof the Coriolis parameter, f , l 5 c/ f is the baroclinicRossby radius, c 5 is the long gravity wave phaseÏg9Hspeed, g9 5 g(r2 2 r1)/ro the reduced gravity, g theacceleration of gravity, ro the mean ocean density, Hthe mean upper-layer depth, WE the Ekman pumpingdefined as

tW 5 = 3 , (2)E 1 2r fo

t is the wind stress, and 2Rh is a Rayleigh friction term.The Rayleigh frictional timescale, 1/R, has been chosento be 2 yr, based on a sensitivity analysis described byCAb. The Rossby radii of deformation have been esti-mated by CAa for the given model stratification usingthe Wentzel–Kramers–Brillouin (WKB) approximation(Morse and Feshbach 1953). Equation (1) describes thegeostrophic motion below the surface Ekman layer,where the meridional transport Vg is dictated by the sur-face Ekman pumping:

fV 5 W . (3)g Eb

Thus, Eq. (1) differs from the full Sverdrup model,which includes both geostrophic and Ekman transports,and where the total transport V is given by

= 3 tV 5 . (4)

b

Equation (1) is solved at each latitude along Rossbywave characteristics:

2Rteh(x, t) 5 h(x , t 2 t )ee e

x W (j, t 2 t )E j 2Rtj1 e dj, (5)E c (j)rxe

where the solution at each point x and time t is obtainedas the superposition of the Rossby waves generated eastof point x at previous times. The first term on the righthand side (rhs) of Eq. (5) is the contribution of the wavesgenerated at the eastern boundary xe and reaching pointx at time t with a transit time

x djt 5 .e E c (j)rxe

The second term on the rhs of Eq. (5) is the contributionof the waves generated by the Ekman pumping east ofthe target point x, with

x d§t 5 .j E c (§)rj

Both boundary and wind-forced terms decay while prop-agating westward with the frictional timescales 1/R. CAahave shown that variations of thermocline depth at theboundary influence the interior solution only within 108–208 from the boundary, while the largest signals awayfrom the eastern boundary are due to the wind forcing,in agreement with observational studies (Kessler 1990).Thus, in seeking a solution to Eq. (1) we neglect theboundary contribution and focus upon the wind-drivencomponent. As seen from Eq. (5), this component de-pends not only upon the magnitude of the integrand (WE/cr), but also upon the way the signals generated at dif-ferent longitudes superimpose, which, in turn, may berelated to the longitudinal coherency of the forcing. Insection 3 we will examine the influence of these differentaspects of the forcing in controlling the amplitude of thethermocline variability.

3. Wind forcing

As a first step, we assess how well the Rossby waveequation [Eq. (1)] can explain the thermocline vari-ability in the Tropics. The wave equation is solved inthe latitude band 258S–258N, with the exclusion of thearea 58S–58N, and is forced with monthly anomalies ofEkman pumping from the NCEP–NCAR reanalyses, thesame forcing used for the OGCM. The standard devi-ation of thermocline depth computed from the waveequation is shown in Fig. 1c. The two tropical centersof variability are present in the wave equation solutionat approximately the same location and with comparableamplitude as in the OGCM. The detailed longitudinalstructure of the variability at 138N is somewhat differentin the OGCM (Fig. 1a) as compared with the wavemodel (Fig. 1c) in that the variability in the wave modelis westward intensified, while in the OGCM maximumamplitudes are found around 1608W.

The local temporal correlations between the solution

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FIG. 2. Correlations between the thermocline depth variations computed from Eq. (1) forcedwith the observed WE (Fig. 1c), and the depth variation of the 25.5-su isopycnal from the OGCM(Fig. 1a). Light shading indicates correlations larger than 0.7, while dark shading is used forcorrelations larger than 0.9.

FIG. 3. Ratio of the zonally averaged standard deviation of WE andthe zonally averaged Rossby wave phase speed cr as a function oflatitude. The dashed line is obtained using monthly anomalies of theWE field, the thick solid line is computed from 1-yr low-pass filteredvalues, the dot–dash line is from 3-yr low-pass filtered values, andthe dot line is from 6-yr low-pass filtered values. The WE values havebeen multiplied by 105. The thin solid line is obtained using the 1-yr low-pass filtered WE field, where the local maxima of fWE areremoved.

of Eq. (1) and the variations of the 25.5-su isopycnalin the OGCM (Fig. 2) are larger than 0.7 between 188Sand 188N, and west of approximately 1208W, with val-ues larger than 0.9 around 108S and 138N, indicatingthat Eq. (1) is an excellent framework to describe theOGCM variability in the Tropics. The presence of thecenters of variability around 108S and 138N in the so-lution to Eq. (1), as seen in the OGCM, is an indicationthat some aspects of the Ekman pumping can give riseto enhanced variability in those areas. In the followingsections we examine which aspects of the forcing arethe most relevant.

a. Amplitude of the forcing

We first examine whether the latitudinal dependenceof the amplitude of the Ekman pumping can explain thepresence of the two tropical maxima of thermocline var-iability. Lysne and Deser (2002) found local maxima inwind stress curl variability in those areas based on an-nual values (the standard deviation of the wind stresscurl computed from monthly anomalies does not showany pronounced local maxima in the same regions).However, since we are interested only in the interiorgeostrophic flow, Ekman pumping [Eq. (2)], rather thanwind stress curl (= 3 t) is the actual forcing term ofthe wave model Eq. (1). The integrand of the charac-teristics solution Eq. (5) is WE/cr 5 Vgf /c2, indicatingthat meridional motions are a fundamental part of Ross-by waves and that the latitudinal variations of the in-tegrand depends not only upon the meridional variationsof the Ekman pumping but also upon the variation ofthe phase speed with latitude.

Figure 3 shows the latitudinal dependence of the stan-dard deviation of WE, zonally averaged across the basin,divided by the zonally averaged phase speed. Monthlyanomalies of WE are considered, as well as 1-, 3-, and6-yr low-pass filtered anomalies. The latitudinal varia-tion of WE/cr depends upon the timescales of the Ekmanpumping. When monthly anomalies are used, WE/cr in-creases monotonically with latitude, while small localmaxima (or inflection points) are found at ;118–128Sand 138–158N when timescales shorter than 1 yr arefiltered out. The presence of these local maxima be-comes relatively more pronounced at longer timescales,due to the decreased variance of the filtered WE fields,but no absolute maximum of WE/cr is found in the Trop-ics.

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FIG. 4. (a) Comparison of the zonally averaged standard deviation of thermocline depth variations forced by the monthly anomalies ofthe observed WE (thick line) and zonally averaged standard deviation forced by the corresponding WE field (thin line). (b) As in (a) but for1-yr low-pass filtered WE. (c) As in (a) but for a 3-yr low-pass filtered WE. (d) As in (a) but for 6-yr low-pass filtered WE.

The variance of WE increases as 1/ f with decreasinglatitude [Eq. (2)], while the phase speed varies as 1/ f 2

so that WE/cr varies approximately as f . Thus, the lat-itudinal variation of the integrand in Eq. (5) can explainthe decreasing amplitude of the solution equatorward of108S and 138N, but it cannot explain the presence ofthe two maxima and the poleward decrease seen in Fig.1c. The phase speed also varies with latitude becauseof changes in stratification, but this latter factor is foundto be secondary to the f dependence of cr (not shown).

To clarify the role of the local maxima of WE/cr attimescales of 1 yr and longer we solve Eq. (1) withmodified WE fields, WE. Since poleward of ;108 WE isvery close to = 3 t / f and the local maxima in WE/cr

are likely associated with the maxima in = 3 t (seeFig. 1d), the WE fields have been obtained by first nor-malizing the time series of fWE at each grid point tounit standard deviation, and then multiplying it by theaverage standard deviation of fWE over the areas (68–258N, 1408E–1308W) and (208–68S, 1608E–958W) in theNorthern and Southern Hemispheres, respectively.Thus, the standard deviation of f WE is spatially uniform,but close to the average standard deviation of fWE, andWE varies with latitude as 1/ f . As an example, the lat-

itudinal variation of WE/cr for the 1-yr low-pass filteredanomalies is shown in Fig. 3 as a thin solid line. Itcaptures the average variation of the annual WE/cr butits latitudinal dependence is purely monotonic.

In Fig. 4 the zonally averaged standard deviation ofthermocline depth variations from the wave modelforced with monthly, 1-, 3-, and 6-yr low-passed filteredWE fields is compared with the h standard deviationobtained with the corresponding WE fields. At yearlyand longer timescales (Figs. 4b–d), the WE fields pro-duce tropical centers of variability that are broader andweaker than those obtained with WE, characteristics thatbecome progressively more pronounced at lower fre-quencies. These results indicate that the local maximain WE/cr do affect the sharpness of the tropical centersof variability, but not their existence. Thus, the ampli-tude of the integrand in Eq. (5) cannot explain the pres-ence of the maxima and, in particular, the amplitudedecrease poleward of 108S and 138N. Figure 4 alsoshows that, despite the dramatic decrease of WE/cr whenthe Ekman pumping is low-pass filtered, the maximumthermocline variability at 108S and 138N remains quitelarge, indicating that the ocean model responds pref-erentially to the low frequencies of the forcing.

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FIG. 5. (a) Zonally averaged coherencies of Ekman pumping anom-alies based on monthly values (thin solid line), 1-yr low-pass filteredvalues (thick solid line), 3-yr low-pass filtered values (dot–dash line),and 6-yr low-pass filtered values (dot line). Instantaneous correlationsare used. (b) Zonally averaged coherencies of 1-yr low-pass filteredEkman pumping anomalies based on lag correlations (solid line) andinstantaneous correlations (dot–dash line).

FIG. 6. Comparison between the zonally averaged coherency of WE

(thick solid line, left axis) based on instantaneous correlations of the6-yr low-pass filtered values and the zonally averaged standard de-viation of thermocline depth from the wave model (dot–dash line,right axis).

b. Spatial coherency

If the integrand in the second term of the Rossbywave solution in Eq. (5) cannot explain the maxima at108S and 138N in Fig. 1c, then the zonal coherency ofthe forcing may be important. If, for example, the Ek-man pumping time series at each longitude were com-pletely uncorrelated in time, the resulting wave fieldwould also be spatially incoherent. If, on the other hand,the Ekman pumping were coherent over a large distance,the waves generated at different points may superimposeconstructively and give rise to a larger amplitude re-sponse. To test this hypothesis we compute zonal de-correlation length scales for the Ekman pumping. Ateach latitude, we consider the correlations between WE

at each grid point x and WE at other points x9 along thesame latitude circle. Eastward and westward directionsare considered independently. For each direction the de-correlation length is computed as the minimum distanceat which correlations decrease to values lower than 0.5.Since we are interested in assessing maximum distancesover which the forcing is coherent, the maximum of theeastward and westward values is chosen as the decor-relation length scale for WE at the given point x. Because

of the strong timescale dependence exhibited by WE/cr

in section 3a, zonal coherencies are computed formonthly anomalies, as well as for 1-, 3-, and 6-yr low-pass filtered WE fields.

At all timescales the zonal coherency of WE is a max-imum along 108S and 138N, where WE is coherent acrossthe eastern two-thirds of the basin (not shown). SinceWE is not defined close to the equator, the equatorialband has been excluded from the coherency computa-tion. The tropical coherency maxima increase at longertimescales. When monthly WE anomalies are considered,the maxima at 108S and 138N in Fig. 5a are barelynoticeable but become more pronounced as the time-scale increases. In particular, the zonal coherencies at108S and 138N for the 6-yr low-pass filtered values are;40% larger than the coherencies obtained with the 1-yr low-pass filtered field.

The zonal coherencies in Fig. 5a are based on in-stantaneous correlations. If lag correlations are insteadused to estimate the zonal coherency of WE, the max-imum coherencies along 108S and 138N increase, whenlags between 23 and 3 yr are considered (Fig. 5b). At108S and 138N zonal coherencies are ;30% larger whenlag correlations are used. The lag dependence of thezonal coherency at 108S and 138N indicates that thereare zonal phase variations of the Ekman pumping alongthose latitudes. At 138N phase variations can be attrib-uted to the westward propagation of Ekman pumpinganomalies described by CAa, who suggested that west-ward propagation may be responsible for a particularlyefficient excitation of the Rossby wave field. The influ-ence of the zonal phase variations upon the amplitudeof the response along 138N will be examined at the endof section 3c.

In Fig. 6 the zonal average of the decorrelation lengthbased on instantaneous correlations of 6-yr low-passfiltered values is compared with the zonal average ofthe thermocline depth standard deviation computedfrom the simple wave model, as a function of latitude.The maxima in Rossby wave amplitude (thick dot–dashline) are closely aligned with the maxima in decorre-

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FIG. 7. (a) Comparison between the zonally averaged coherencyof WE (solid line), based on 6-yr low-pass filtered values, and theensemble mean of the zonally averaged coherency of (dash–dotSCW E

line). The ensemble contains 99 realizations of . Each fieldSC SCW WE E

is obtained by randomly scrambling the monthly time series of WE

at each grid point. Decorrelation lengths were then calculated fromthe annually averaged scrambled time series. The dark shading in-dicates values of decorrelation lengths within 1 std dev from theensemble mean, while the light shading shows values within 2 stddev from the ensemble mean. (b) Comparison between the zonallyaverage standard deviation of thermocline depth obtained from thewave model forced by WE and the ensemble mean of the zonallyaveraged standard deviation obtained with the fields. Values ofSCW E

thermocline depth standard deviation within 1 and 2 std dev fromthe ensemble mean are indicated by dark and light shading, respec-tively. The dot line in (b) shows the zonally averaged standard de-viation of thermocline depth obtained with the modified forcing

between 58 and 258N.symW E

lation length (thick solid line), supporting the hypothesisthat the spatial coherency of the forcing is a key elementin determining the amplitude of the resulting Rossbywave field.

c. Temporal coherency

The results of section 3b indicate that zonally co-herent Ekman pumping anomalies may be central forthe existence of the variability maxima along 108S and138N. What about temporal coherency? Of course thetwo are not independent. In particular, we can expectthat longer length scales are associated with longer time-scales. Figure 5a confirms this hypothesis, by showingthat spatial coherencies increase with decreasing fre-quencies, and in particular they are larger at timescaleslonger than the interannual ENSO timescales.

In section 3b we have also seen that there are zonalphase variations in the Ekman pumping field and thatthe inclusion of these phase differences can lead to larg-er decorrelation lengths. How important are these phasedifferences? At 138N Ekman pumping anomalies arecoherent approximately between 1808 and 1208W. With-in this longitudinal band, the Ekman pumping at theeastern edge of the coherent region appears to lead theEkman pumping farther west. Lags tend to progressivelyincrease westward (CAa), suggesting a westward prop-agation of the Ekman pumping anomalies. Using co-spectral analysis, CAa have shown that the propagationis especially consistent at decadal timescales, and haveestimated a westward phase speed for the decadal Ek-man pumping anomalies of ;9 cm s21, a value that iscomparable to the phase speed of the first mode baro-clinic Rossby waves (;15 cm s21), and have suggestedthat this ‘‘quasi resonance’’ may play an important rolein exciting a vigorous Rossby wave field. At 108S, how-ever, no indication of westward propagation is found(not shown). On the contrary, Ekman pumping in theeastern basin appears to lag the forcing farther west,consistent with eastward propagation, if any.

To clarify the role of temporal coherency and zonalphase variations, we randomly scramble the time seriesof the monthly Ekman pumping anomalies and createa new field . A sequence of random numbers is cre-scW E

ated using a ‘‘Mersenne Twister’’ algorithm (Matsumotoand Nishimura 1998) and that sequence is used at eachgrid point to alter the time series of monthly Ekmanpumping anomalies. The same sequence of randomnumbers is used at each grid point so that time seriesat different locations are altered in a similar fashion.Thus, this procedure not only preserves the variance ofthe time series at each location, but instantaneous cor-relations between time series at different points are alsopreserved. However, lag correlations may be altered.Also, as we apply the scrambling procedure to monthlyanomalies, the resulting fields can be expected to havea reduced low-frequency content, and increased energyat high frequencies. To increase the statistical signifi-

cance of the results, an ensemble of 99 fields hasscW E

been considered.Figure 7a compares the zonally averaged coherency

of WE, based on 6-yr low-pass filtered values, with thezonally averaged ensemble mean coherency of the

fields, respectively. Values of zonal coherencysc scW WE E

within one and two standard deviations from the en-semble mean are also shown by the shaded areas. Al-though the zonal coherencies of still show maximascW E

at 108S and 138N, their values are largely reduced. Theensemble averages at the location of the two tropicalmaxima are more than 50% smaller than the corre-sponding maxima of the original WE field. The ensembleaverage coherency for the fields is very similar toscW E

the coherency obtained with monthly anomalies using

AUGUST 2003 1557C A P O T O N D I E T A L .

instantaneous correlations (Fig. 5a). As a consequenceof the decreased zonal coherency, the amplitude of thethermocline variability excited by the fields is muchscW E

smaller, as seen in Fig. 7b, where the zonally averagedthermocline depth standard deviation produced by the

fields (in an ensemble average sense) is comparedscW E

with the zonally averaged standard deviation forced bythe original WE field. When are used, the tropicalscW E

maxima at 108S and 138N are much weaker, with am-plitude reductions of the order of 50%, and a much lesspronounced poleward decrease in amplitude.

The effect of the time scrambling procedure is two-fold: first, phase relationships between the forcing atdifferent points are altered at timescales greater than 1month, and so any propagation feature can be expectedto be severely distorted; and second, low-frequency en-ergy is reduced and high-frequency energy increased,thus emphasizing smaller spatial scales.

To understand which of these two effects is the mostimportant in producing the drastic reduction in ther-mocline variability observed with (Fig. 7b), we per-scW E

form an additional experiment by forcing the wave mod-el with another modified Ekman pumping field. In thiscase, the WE values between 1508 and 1208W are sym-metrically exchanged with the values between 1508Wand 1808. This procedure is applied north of 7.58N sinceclearer indications of propagation were found at 138N.The Ekman pumping is coherent approximately betweenthe date line and 1208W, and in the same latitude bandindications of westward propagation were found byCAa. By mirroring the values in the 1508W–1808 lon-gitude band with the values in the 1508–1208W band,spatial coherencies are left unaffected, but westwardpropagation becomes eastward propagation. The ther-mocline variability found with the new WE field ( )symW E

is very similar in amplitude to the variability found withthe original WE field (Fig. 7b), indicating that the west-ward propagation of the forcing and its quasi-resonancewith the free Rossby waves at this latitude is not crucialfor the existence of the center of variability along 138N,as hypothesized by CAa. This result may seem some-what surprising at first. Westward propagation of Ekmanpumping anomalies has been detected by CAa at decadaltimescales, and this feature of the forcing may mainlyaffect the low-frequency components of the Rossbywave field. One may think that, because of the 2-yrfrictional timescale used in Eq. (1), the decadal Rossbywaves may be severely damped and the residual fieldmay be only marginally influenced by the westwardpropagation of the forcing. However, even if a frictionaltimescale of 20 yr is used in Eq. (1), the solutions pro-duced by the WE and fields differ very little insymW E

amplitude, confirming that thermocline variability israther insensitive to the propagation characteristics ofthe forcing.

The explanation of the above result lies in the factthat at decadal timescales the wavelength of the oceanicsignals is much larger than the longitude band over

which WE is coherent so that phase variations over thislongitude band are very small irrespective of the direc-tion of propagation of the forcing. This can be illustratedby considering the simple case in which the Ekmanpumping oscillates at a frequency vf and propagateswestward with a phase speed cf within the zonal bandxf # x # 0:

iv (t1x /c )f fW e x # x # 0o fW 5 (6)E 50 elsewhere,

where x 5 0 corresponds to the eastern edge of theforced area, and not necessarily to the eastern boundaryof the basin. We only consider zonal propagation, so noy dependency is explicitly included here, and for sim-plicity frictional processes are neglected.

Within the forcing band, the solution is the super-position of two traveling waves, one propagating at cf

and the other propagating at the speed of the free Rossbywaves cr:

Wo iv (t1x /c ) iv (t1x /c )f f f rh 5 2 [e 2 e ]. (7)iv (1 2 c /c )f r f

The two traveling wave components have the sameamplitude but opposite signs to satisfy the boundarycondition at x 5 0. Equation (7) can be rewritten in theform

2W ao iv [t1x /(2c)]fh 5 e sin x , (8)1 2c a 2r

where

v c c cf r r fa 5 1 2 and c 5 . (9)1 2c c c 1 cr f r f

The propagation of the forcing versus that of the freewaves affects the amplitude of the resulting Rossbywave field through the factor a. If, for example, cr ;cf , a tends to zero, and Eq. (8) becomes

Wo iv [t1x /(2c)]fh 5 2 |x|e . (10)cr

However, if the wavelength l 5 2pcr/v f is muchlarger than | xf | , the maximum value of | x | (a/2) canbe very small independently of the ratio cr/cf . For vf

5 10 yr, cr 5 16 cm s21, the wavelength is l ; 50 000km. The ‘‘forcing area,’’ where WE is coherent, extendsapproximately between the date line and 1208W so that| xf | ; 5000 km and (2p/l) | xf | ; 0.6.

Thus, because of the long wavelength of the Rossbywaves as compared with the width of the forcing area,the amplitude of the response is not very sensitive tothe westward propagation of the forcing. On the otherhand, the presence in the forcing of long timescales andassociated long spatial scales appears to be crucial forthe existence of the centers of variability at 138N and108S.

1558 VOLUME 33J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y

d. Are the tropical centers of variability consistentwith stochastic forcing?

Frankignoul et al. (1997) have examined how muchof the decadal variability in the extratropical ocean canbe explained by a passive oceanic response to stochasticwind forcing. They have described the characteristicsof the spectra of the first-mode baroclinic Rossby wavesexcited by an Ekman pumping field that is zonally uni-form and white in frequency domain and have shownthat the geographical variations of the spectra are ingood agreement with those diagnosed from the Ham-burg climate model. By taking the Fourier transform ofEq. (5) without the boundary forcing term (first termon the right-hand side) and neglecting friction (R 5 0),the power spectrum of thermocline depth produced bya zonally uniform and temporally stochastic Ekmanpumping is given by

2ˆ2|W |E2|h(x, v)| 5 (1 2 cosvDt), (11)2v

where v is the frequency, and WE are the Fourierhtransforms of h and WE, respectively, and Dt is the wavetransit time from the eastern boundary to point x:

|x 2 x |eDt 5 . (12)cr

Here | WE | 2 is assumed to be independent of space andfrequency (white noise forcing). As described by Fran-kignoul et al. (1997), at frequencies higher than v*(x)5 2p/Dt the spectrum exhibits a v22 behavior with amodulation (1 2 cosvDt), while for frequencies lowerthan v* the spectrum tends to flatten toward a level

2(x 2 x )e2 2ˆ|h | 5 |W | for v K v*. (13)E 2cr

Thus, the shape of the spectrum has a strong longitudinaldependence: the frequency v* decreases westward, andthe low-frequency level increases quadratically with thedistance from the eastern boundary. According to Fran-kignoul et al. (1997) the high-frequency modulation ofthe spectrum is likely due to the neglect of friction intheir simple model and would disappear if some degreeof dissipation were included.

To what extent are the Rossby wave fields from thesimple model and the OGCM consistent with Frankig-noul et al.’s (1997) theory of a stochastically forcedocean? The ensemble averaged spectra of at dif-SCW E

ferent locations (not shown) have similar energy levelsat all frequencies, within the 95% confidence interval,as expected for a stochastic process white in frequencydomain. The ensemble average spectra of the Rossbywave field produced by at 1408W, 13.68N, and 1808,SCW E

13.68N are shown in Figs. 8a and 8c, respectively. Twodifferent longitudes are considered to illustrate the xdependence of the spectra. The spectra predicted by thetheory of Frankignoul et al. (1997) at the same locations,assuming the eastern boundary of the forcing region to

be at ;1158W, are also shown for comparison. Noticethat the spectra from the simple model in Figs. 8a and8c are based on seasonal anomalies, while the theoreticalspectra are computed for a larger frequency range. Thespectrum of the Rossby wave field excited by atSCW E

1408W is in excellent agreement with the theoreticalspectrum. The agreement tends to deteriorate fartherwest, where the low-frequency energy level of the ther-mocline depth spectra forced by does not increaseSCW E

as rapidly as predicted by the theory of Frankignoul etal. (1997). At 1808 (Fig. 8c) the spectral power at pe-riods longer than ;3 yr is lower than the power of thetheoretical spectrum. The reason for the discrepancymay be associated with an energy decrease of withSCW E

decreasing longitude. Also, the presence of frictionalprocesses in the wave model may damp the amplitudeof the westward propagating Rossby waves and lead toa smaller amplitude signal away from the eastern bound-ary than expected from the inviscid theory of Frankig-noul et al. (1997).

We will refer to the spectra of thermocline displace-ment produced by as the ‘‘stochastic spectra.’’ InSCW E

Figs. 8b and 8d the stochastic spectra are compared withthe spectra of thermocline displacement from the simplemodel forced by WE, and from the OGCM, at the samelocations considered in Figs. 8a and 8c. The spectra ofthermocline variability excited by WE, in both theOGCM and the simple model, are characterized by high-er energy levels at low frequencies with respect to thestochastic spectra, the differences being significant atthe 95% level. Thus, the results from spectral analysisare consistent with those inferred from the analysis ofspatial coherencies in sections 3b and 3c, indicating thatthe variability in the two tropical centers cannot be sim-ply explained in terms of a ‘‘white’’ Ekman pumpingforcing. The presence of a large fraction of energy atlow frequencies and long spatial scales in the forcingappears to play a very crucial role for the origin of thecenters of variability at 108S and 138N.

4. Discussion

In section 3 we have seen that a simple first-modeRossby wave model driven by the observed forcing canreproduce the basic characteristics of the variability ex-hibited by the OGCM around 108S and 138N. This resultneeds to be reconciled with the findings of CAb, whohave shown that meridional excursions of the thermo-cline can account for a large part of the variabilityaround 138N. Figure 9 shows the meridional section ofmean temperature at 1748W from the OGCM. Polewardof ;58S and 108N the thermocline deepens, with max-imum slopes at approximately 108S and 138N. At 138N,for example, a southward displacement of the thermo-cline would result in a deepening of the 158C isotherm,which may be used as a proxy for thermocline depth,and vice versa at 108S. Following CAb, meridional dis-placements of the isotherms may be quantified by mon-

AUGUST 2003 1559C A P O T O N D I E T A L .

FIG. 8. (a) Ensemble average spectrum of thermocline depth variations obtained with the wave model forced by SCW E

at 13.68N, 1408W (solid line), and theoretical spectrum expected from the inviscid, first-mode baroclinic Rossby waveequation forced by a stochastic Ekman pumping white in frequency domain (dot–dash line; Frankignoul et al. 1997).(b) Comparison between the ensemble average spectrum of thermocline depth variations in (a) (solid line), the spectrumof thermocline depth variations produced by the wave equation forced with the observed WE (dash–dot line), and thespectrum of the thermocline depth from the OGCM (dashed line) at 13.68N, 1408W. (c) As in (a) but at 13.68N, 1808.(d) As in (b) but at 13.68N, 1808. The spectra from the OGCM and simple model are based on seasonal values. The 95%confidence intervals are indicated. The spectra computed as ensemble averages (with 99 elements) have a larger numberof degrees of freedom.

FIG. 9. Meridional section of mean temperature at 1748W. Contourinterval is 2.58C. Notice the deepening of the thermocline polewardof ;58S and 108N.

itoring the position of the maximum meridional slopearound 138N in the OGCM. The product of the merid-ional displacements around a given latitude and theslope of the thermocline at that latitude provides anestimate of the depth changes that can be expected atthat location as a result of this process. The depth var-iations estimated with this method at 13.68N, 1868E arecompared in Fig. 10a with the depth variations diag-nosed from the OGCM at the same location. The cor-relation coefficient between the two time series is 0.96and the regression coefficient is 0.85. Thus, the merid-ional displacements detected with the above diagnosticsappear to account for most of the depth changes at thislocation, as shown by CAb.

Rossby waves are associated with an anomalous me-ridional velocity y9 given by

g9 ]hy9 5 . (14)

f ]x

Thus, the Rossby wave meridional velocity is pro-portional to the second term in Eq. (1), the radiation

1560 VOLUME 33J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y

FIG. 10. (a) Comparison between the thermocline depth variationsin the OGCM at 13.68N, 1748W (solid line, m), and the thermoclinedepth changes inferred from the meridional excursions of the ther-mocline multiplied by the mean slope of the 158C isotherm (dot–dashline). The correlation coefficient between the two time series is 0.96,and the regression coefficient is 0.85. (b) Comparison between thetime evolution of the latitude at which the zonal component of theeasterlies, averaged between 1728E and 1408W, achieves its maximum(solid line) and the latitudinal position of the maximum meridionalslope of the thermocline around 13.68N, 1748W (dotted line). Bothestimates are based upon annually averaged data. The dotted line hasbeen smoothed using a 3-point binomial filter.

term. In areas where the meridional slope of the meanthermocline is large, one may think that the presenceof a meridional velocity field can give rise to anomalousadvection of mean thermocline depth, y9(dH/dy). How-ever, in a 1½-layer, shallow-water model, like the onewe are considering here, anomalous advection of meanthermocline depth is exactly cancelled by the mean zon-al advection of anomalous depth, U(]h/]x), where

g9 dHU 5 2 (15)

f dy

is the mean zonal velocity. Thus, within the dynamicalframework of a 1½-layer reduced-gravity model no me-ridional displacement of the thermocline can be inducedby the Rossby wave anomalous velocity field. Can thethermocline displacements in Fig. 10a be due to thenature of the surface forcing?

The trade winds achieve their maximum strengthclose to 108S and 138N, and since they are characterizedby a large zonal scale, variations in the strength and/orposition of the trade winds can plausibly be responsiblefor the large zonal coherency of the Ekman pumpinganomalies along those latitudes. We concentrate on theNorthern Hemisphere, where the maximum amplitude

of the zonal wind is achieved along ;138N, approxi-mately between 1608E and 1308W, and focus on thezonal component of the winds. To check the possibilityof meridional displacements of the trade wind systemwe monitor the latitude of the maximum zonal wind,averaged between 1738E and 1408W. As shown in Fig.10b, the position of the maximum zonally averaged zon-al wind does experience latitudinal variations, and thesevariations are largely correlated with the meridional dis-placements of the thermocline (diagnosed as the positionof the maximum slope). The maximum correlations areachieved when the zonally averaged wind excursionslead the thermocline excursions by a lag that increasesprogressively westward, due to the westward propaga-tion of the thermocline signals. At 1748W (Fig. 10b),the maximum correlation (0.94), and maximum regres-sion (1.14) between the two time series are achievedwhen the zonally averaged zonal wind leads the ther-mocline displacement by ;1 yr. Thus, it is conceivablethat the large-scale Ekman pumping anomalies along138N originate primarily from meridional shifts of thetrade wind system.

To understand what changes in the ocean thermalstructure can be induced by this type of wind variabilitywe consider the idealized case of a purely zonal windstress that is independent of x and varies sinusoidallywith latitude over a rectangular domain with 0 , y ,Ly as the latitudinal coordinate and 0 , x , Lx as thezonal coordinate. We further assume that the wind stressundergoes meridional excursions with amplitude a andfrequency v f :

2pt 5 t cos [y 2 y (t)] , (16)0 05 6Ly

where y0(t) 5 a cosvf t and a K Ly. Using trigonometricformulas and given that the amplitude a of the merid-ional excursions is much smaller than the latitudinaldimension of the domain, Eq. (16) can be rewritten inthe form

2p 2pt ù t cos y 1 t sin y cosv t, (17)0 1 f1 2 1 2L Ly y

where t1 5 2pt0(a/Ly). Thus, the resulting wind stresscan be expressed as the sum of a time-independent term( ) and a time-dependent component (t9), that alsotvaries with latitude. The maximum mean easterlies, asexpressed by , are achieved at y 5 Ly/2. For the analogytwith the OGCM we are mainly interested in the vari-ability around this latitude, and for simplicity we ap-proximate the Ekman pumping as WE 5 ty/(r0 f ). Wefurther assume a zonally uniform phase speed and ne-glect friction. The solution of Eq. (1) with the forcingEq. (17) is also the superposition of a time-independentcomponent forced by and a time-dependent com-h tponent h9 forced by t9:

AUGUST 2003 1561C A P O T O N D I E T A L .

FIG. 11. Results from the idealized case of a shallow-water modelforced by a zonal wind stress that undergoes meridional excursionswith a frequency vf 5 2p/10 yr. (a) Variations of thermocline depthat 178N, 1808 (latitude of the mean maximum slope) computed fromEq. (20) (solid line) and estimated by multiplying the meridionaldisplacements of the maximum thermocline slope by the mean slopeat 178N, 1808 (dot–dash line). (b) Meridional excursions of the zonalwind stress (solid line) and evolution of the latitude of the maximumthermocline slope at 1808 (dotted line).

h(x, y, t) 5 h(x, y) 1 h9(x, y, t), (18)

where

2pt 2p0h(x, y) 5 H 2 (L 2 x) sin y (19)e x 1 2r fc L L0 r y y

is the Sverdrup solution, He being the mean thermoclinedepth at the eastern boundary and

2pt 2p1h9(x, y, t) 5 cos y1 2r f v L L0 f y y

x3 sinv t 2 sin v t 2 . (20)f f5 1 2 6[ ]cr

In order to satisfy the boundary condition of no-nor-mal flow at the eastern boundary, He must be indepen-dent of y and h9 must vanish at the eastern boundary:h9 is the superposition of a standing wave component,which oscillates at the frequency of the forcing, and atraveling wave component with the same frequency,which propagates westward at the phase speed cr of thefree Rossby waves.

Solutions are evaluated for the domain extendingfrom 1208E to 1108W, and spanning the latitude rangebetween the equator and 308N, with a 5 1.28, t0 5 0.4dyn cm22, He 5 100 m, and vf 5 2p/10 yr. If we applythe same diagnostics used for the OGCM, by monitoringthe position of the maximum slope as a function of time,we find that depth changes estimated by using the po-sition of the maximum slope can explain most of thedepth anomalies at a given point (Fig. 11a). Also, as inthe OGCM, the meridional displacements of the ther-mocline lag the position of maximum easterlies (Fig.11b) with a lag that increases westward (not shown).

This simple example illustrates how meridional shiftsof the thermal structure, as seen in the OGCM, can resultfrom the propagating Rossby wave field, depending onthe characteristics of the forcing. Independent processes(i.e., mean or anomalous advection) are not necessarilyneeded to justify the occurrence of the meridional shiftsof the isotherms. Also, in the analytical example above,depth anomalies only depend upon the anomalous com-ponent of the Ekman pumping, as indicated by Eq. (18)and (20), showing that the presence of the mean me-ridional slope does not have an enhancing effect on thethermocline variability, as may have been anticipated.

Discrepancies exist between the solution of the simplemodel in Eq. (1) and the OGCM. Specifically, the simplemodel generally underestimate the amplitude of the var-iability, and along 138N thermocline variability fromthe simple model shows a westward intensified struc-ture, while maximum standard deviation is found be-tween approximately 1408E and 1408W in the OGCM(Figs. 1a, c). In particular, local maxima in thermoclinevariability in the OGCM, such as the one centered at;138N, 1608W, coincide with Ekman pumping maxima.Shorter waves not modeled by Eq. (1), which is based

on the long-wave approximation, may be excited bysmall-scale WE features and they may play some rolein modifying the zonal structure of the variability along138N. Using an adjoint approach, Galanti and Tziper-man (2003) have shown that low-frequency, short zonalscale baroclinic Rossby waves may be amplified alonglatitudes very close to the ones considered here (;128Sand 158N) by baroclinic instability processes associatedwith the large climatological meridional temperaturegradients. Thus, low-frequency short waves may playan important role in explaining the fraction of variance(and its zonal distribution) not accounted for by thewave model considered here. There is also the possi-bility that higher-mode Rossby waves are present, andmay give rise to anomalous advection of mean ther-mocline depth, so that the presence of a sloping ther-mocline could influence the zonal distribution of vari-ance. Further analyses are needed to elucidate this point.

5. Summary

In this paper we have systematically examined therelative influence of surface wind forcing and mean ther-mocline topography in producing centers of thermoclinevariability at ;108S and 138N. We have found that thesurface Ekman pumping alone can excite centers of var-

1562 VOLUME 33J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y

iability around 108S and 138N. The aspect of the surfaceforcing that appears to play the dominant role in pro-ducing enhanced Rossby wave amplitudes is the spatialcoherency of the Ekman pumping at those latitudes.Along each latitude, the Rossby wave field generatedat any given longitude is the superposition of the west-ward propagating signals generated by the forcing tothe east of that longitude. A surface forcing that is co-herent over a large distance may excite signals that su-perimpose constructively, thus resulting in a larger am-plitude thermocline response. Spatial coherencies in-crease at low frequencies, indicating that larger spatialscales are associated with longer timescales. As a result,the low-frequency components of the forcing appear tobe the most effective in exciting Rossby waves at 108Sand 138N. Despite the large decrease in the variance ofthe forcing when timescales shorter than 6 yr are filteredout, the maxima in thermocline variability at those lat-itudes remain relatively large.

The spatiotemporal structure of the Ekman pumpingthat emerges from the present analysis differs from thathypothesized in the theory of Frankignoul et al. (1997),where the Ekman pumping is assumed to be uniformacross the basin independently of frequency. Since theocean responds preferentially to those components ofthe forcing with larger spatial scales, the association oflarger zonal coherencies with low-frequencies results ina ‘‘dynamical low-pass filtering’’ of the forcing. As aresult, the spectra of thermocline depth at 108S and 138Ndiffer from the theoretical spectra computed by Fran-kignoul et al. (1997) and show a systematically largerenergy level at low frequencies.

The large spatial coherency of the forcing along 108Sand 138N appears to be the fundamental factor respon-sible for the centers of thermocline variability alongthose latitudes. Local maxima in the amplitude of theforcing cannot explain the origin of the variability max-ima along 108S and 138N but can affect their amplitudeand sharpness, especially at lower frequencies.

Along 138N Ekman pumping anomalies exhibit awestward propagation with a phase speed comparableto the phase speed of the free waves, and Capotondiand Alexander (2001a) suggested that this quasi-reso-nance could be responsible for the large thermoclinevariability around 138N. By forcing the wave modelwith an Ekman pumping field with modified propagationcharacteristics we find that quasi-resonance does notsignificantly influence the amplitude of the thermoclinevariability. Because of the long wavelength of the wavesin comparison with the longitude range of the propa-gating Ekman pumping anomalies, the phase variationsof the forcing are too small to significantly affect thewaves.

Along 108S and 138N the mean thermocline deepenspoleward, with large meridional gradients of thermo-cline depth, and so one may speculate that meridionalexcursions of the thermocline, associated with anoma-lous advection of mean thermocline depth, may be re-

sponsible for a large fraction of thermocline variabilityalong those latitudes. Capotondi and Alexander (2001b)show that the location of the maximum meridional gra-dients of thermocline depth around 138N does exhibitmeridional excursions whose magnitude could accountfor most of the thermocline variability along 138N.However, advection of mean thermocline topography bythe anomalous meridional velocities associated with thewave field is exactly cancelled by the zonal advectionof thermocline depth anomalies by the mean flow. Me-ridional shifts of the trade wind system may be respon-sible for the large zonal coherency of the Ekman pump-ing along 108S and 138N. Using an idealized example,in which a purely zonal wind stress undergoes small-amplitude meridional excursions, we illustrated how thistype of wind variability may produce meridional dis-placements of the thermocline similar to those seen inthe NCAR OGCM as a result of the propagating Rossbywave field, without the inclusion of advection processes.

It is not clear whether the wind variability along 108Sand 138N results from the atmospheric response to seasurface temperature anomalies in the equatorial band orin midlatitudes or is due to internal atmospheric pro-cesses. Another open question concerns the existenceof possible atmospheric feedbacks to sea surface tem-perature anomalies associated with the Rossby wavefield. These issues cannot be properly addressed in thecontext of a hindcast simulation as the one analyzedhere, but need to be examined using observations orcoupled model simulations.

Acknowledgments. We thank the NCAR Oceanogra-phy Section for making the model output available tous, and for useful discussions. We also thank the twoanonymous reviewers, who have provided very insight-ful and constructive comments. This work was sup-ported by NOAA-GOALS Grant GC98-139, and by anomnibus grant from the NOAA Office of Global Pro-grams to the Climate Diagnostics Center.

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