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Tropical Zonal Momentum Balance in the NCEP Reanalyses

IOANA M. DIMA, JOHN M. WALLACE, AND IAN KRAUCUNAS

Department of Atmospheric Sciences, University of Washington, Seattle, Washington

(Manuscript received 15 April 2004, in final form 8 December 2004)

ABSTRACT

The seasonal cycle of the zonal-mean zonal momentum balance in the Tropics is investigated using NCEPreanalysis data. It is found that the climatological stationary waves in the tropical upper troposphere, whichare dominated by the equatorial Rossby wave response to tropical heating, produce an equatorward eddyflux of westerly momentum in the equatorial belt. The resulting westerly acceleration in the tropical uppertroposphere is balanced by the advection of easterly momentum associated with the cross-equatorial meanmeridional circulation. The eddy momentum fluxes and the cross-equatorial flow both tend to be strongestduring the monsoon seasons, when the maximum diabatic heating is off the equator, and weakest duringApril–May, the season of strongest equatorial symmetry of the heating. The upper-level Rossby wavepattern exhibits a surprising degree of equatorial symmetry and follows a similar seasonal progression.Solutions of the nonlinear shallow water wave equation also show a predominantly equatorially symmetricresponse to a heat source centered off the equator.

1. Introduction

The angular momentum balance of the atmosphere isdominated by the poleward flux of westerly momentumassociated with high-frequency baroclinic waves andlow-frequency quasi-stationary eddy circulations in thesubtropical and midlatitude upper troposphere (Starr1948; Peixoto and Oort 1992). However, at low lati-tudes the eddy momentum flux is directed toward theequator (Starr et al. 1970; Rosen and Salstein 1980),which implies an equatorial source of wave activity anda convergence of westerly momentum in the equatorialbelt. Since easterly winds are prevalent in the equato-rial region, some other aspect of the tropical circulationmust provide a mean easterly acceleration in order tobalance the convergence of eddy momentum fluxes.

Lindzen and Hou (1988) noted that the mean meridi-onal circulation (MMC) on Earth almost always exhib-its some amount of equatorial asymmetry, and foundthat the equatorward transport of low angular momen-tum air by a Hadley cell straddling the equator pro-duces a strong easterly acceleration over the equator inan axisymmetric model. Lee (1999) showed that the

seasonal cycle of the MMC at 200 hPa induces a mo-mentum flux divergence in the equatorial belt that off-sets the momentum flux convergence associated withthe eddies. Also Kraucunas and Hartmann (2005, here-after KH) demonstrated that eddy forcing at low lati-tudes in an idealized general circulation model (GCM)leads to persistent equatorial superrotation under equa-torially symmetric boundary conditions, but not undersolstitial boundary conditions. These results imply thatthe equatorial asymmetry of the MMC is crucial formaintaining the deep easterly flow at the equator in thepresence of the westerly acceleration induced by tropi-cal eddies.

In this study, we analyze the tropical angular momen-tum balance in further detail, making use of the Na-tional Centers for Environmental Prediction (NCEP)reanalyses at all available levels. We consider both thezonally averaged flow, as in previous analyses ofLindzen and Hou (1988), Lee (1999), Kraucunas andHartmann (2005), and the horizontal structure of sta-tionary waves in the equatorial waveguide that are re-sponsible for most of the forcing. The interrelationshipbetween the cross-equatorial MMC and the distinctivecharacteristics of the equatorial waves in the upper tro-posphere has not been emphasized in previous studies.We also investigate the degree of hemispheric symme-try of the equatorial stationary waves as a function ofseason and relate this to the solutions of a simple non-

Corresponding author address: Dr. Ioana M. Dima, Dept. ofAtmospheric Sciences, 408 ATG Bldg., Box 351640, University ofWashington, Seattle, WA 98195.E-mail: [email protected]

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© 2005 American Meteorological Society

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linear shallow water wave equation model. Section 2describes the dataset used and analysis techniques, sec-tion 3 presents the results, and the final section dis-cusses their dynamical implications.

2. Data and analysis techniques

This study is based on daily zonal and meridionalwind, vertical pressure velocity (omega) and geopoten-tial height from the NCEP–National Center for Atmo-spheric Research (NCAR) reanalyses over the 1979–2001 period of record (Kalnay et al. 1996). The data aremapped on a 2.5° � 2.5° global latitude � longitudegrid and are available on 17 levels corresponding to the1000, 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, 100,70, 50, 30, 20, and 10 hPa pressure surfaces. The domainof this analysis extends up to 50 hPa.

The Stokes streamfunction field �, which we use todefine the MMC, is calculated by performing a down-ward integration of the meridional wind at all availablelevels and then applying a small, uniform correction ateach level to ensure that � � 0 at the lower boundary.For some figures we also make use of the ClimatePrediction Center Merged Analysis of Precipitation(CMAP) described by Xie and Arkin (1997).

The daily data are first averaged over each of the 73pentads (i.e., 1–5 January, 6–10 January, etc.) of thecalendar year, then the means from each individualpentad (including covariance quantities) are averagedover the 23-yr period of record to obtain 73 long-term(or climatological) pentad-mean values for each vari-able. Finally, the long-term pentad-mean data are av-eraged over individual months, seasons, and the entireyear to obtain monthly, seasonal, and annual-mean val-ues for each variable, respectively.

Means of six consecutive pentads within January–February (JF) and July–August (JA), when the strong-est mean meridional circulations occur, are used to rep-resent what we will refer to as the monsoon seasons,and intervals of comparable length within April–May(AM) and October–November (ON), when the Hadleycirculations in the Northern and Southern Hemispheresare of comparable intensity, are used to represent thetransition seasons (Table 1). The features emphasizedin this study are robust with respect to the definition ofthe monsoon and transition seasons. For example, simi-lar results are obtained when the seasons JF, AM, JA,and ON are defined on the basis of calendar months.

In formulas, the subscript d indicates an individualdaily value, “an” indicates the long-term annual mean,c indicates a climatological (23 yr) pentad-mean value,and variables without subscripts indicate means for in-dividual pentads. Hence, the zonal wind for a particular

location and day may be written ud � uan � u�c � u� �u�d, where u�c � uc � uan represents the deviation fromthe annual mean associated with the climatological sea-sonal cycle, u� � u � uc indicates low-frequency non-seasonal (i.e., interannual and intra-annual) variability,and u�d � ud � u reflects high-frequency (intrapentad)variability. This temporal separation of the terms al-lows for a clearer definition of the relative importanceof eddies with different time scales in the equatorialmomentum budget.

In section 3, the angular momentum balance is diag-nosed using the zonally averaged zonal wind equationin the advective form, which may be written as

��u�

�t≅ ��f �

1cos�

��u� cos�

�y � � ��u�

�p

�1

cos2�

��u*�*� cos2�

�y�

��u*�*�

�p� �Fx�. 1

The notation here is standard, with brackets denotingzonal averages, and asterisks denoting deviations fromthe zonal mean. For seasonal or annual averages, thezonal wind tendency is negligible and the individualterms on the rhs of (1) are simply averaged over allyears and over the indicated seasons. In this expression,the first term on the right-hand side may be recognizedas being equivalent to [�]( f � [�]) where [�] is the rela-tive vorticity and ( f � [�]) the absolute vorticity of thezonally symmetric component of the flow.

We also make use of the following temporal decom-position:

�u*�*�an � �u*an�*an� � �u�*c ��*c �an � �u�*��*�an � �u�d��d�an.

2

Here [u*an�*an] indicates the momentum flux associatedwith the long-term (23 yr) annual-mean stationarywaves, [u�*c ��*c ]an denotes the annual-mean flux of mo-mentum by the climatological seasonally varying sta-tionary waves, [u�*��*]an represents the contributionfrom interannual and intra-annual transient eddies, and[u�d��d]an denotes the momentum flux by the high-frequency transients. This latter term includes a smallcontribution from the intrapentad correlation between

TABLE 1. Seasons as defined in this study.

Season Pentads Dates

JF 4–9 16 Jan–14 FebAM 21–26 11 Apr–10 MayJA 40–45 15 Jul–13 AugON 58–63 13 Oct–11 Nov

2500 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 62

the zonally averaged zonal and meridional wind com-ponents ([u]�d[�]�d), but this distinction will be ignoredsince the intrapentad momentum fluxes are found to besmall in the Tropics.

The long-term annual-mean advection of zonal mo-mentum by the MMC [i.e., the 23-yr annual mean of thefirst term on the rhs of (1)] may also be temporallydecomposed in the form:

��f �1

cos�

��u� cos�

�y ��an

≅ ��can�f �1

cos�

��u�c cos�

�y �an

I

� ��c�f �1

cos�

��u�c cos�

�y ��an

II

. 3

Term I represents the advection of zonal momentumassociated with the long-term annual-mean meridionalwind acting on the long-term mean shear; while term II,which we will subsequently refer to as the seasonallyvarying MMC advection, reflects the temporal correla-tions between [�]c and ( [u]c/ y) over the course of theyear. This term is somewhat different from the transientMMC momentum term calculated by Lee (1999), whobased her analysis on the mean zonal wind equation influx form. The cross correlations between [�] and ( [u]/ y) on other time scales were evaluated and found to besmall, so they are neglected in (3).

3. Annual and seasonal mean fields

a. The annual mean

Figure 1 shows the long-term annual-mean zonallyaveraged zonal wind and MMC. The dominant featuresin the zonal wind field (Fig. 1a) are the midlatitudewesterly jets. Easterlies prevail in the Tropics, with low-level maxima in the trade wind belts and an isolatedmaximum in the upper troposphere centered a few de-grees north of the equator. The long-term annual-meanMMC (Fig. 1b) is dominated by a pair of Hadley cellsstraddling a belt of ascent centered at �5°N, the meanlatitude of the ITCZ. The southern cell is wider and�25% stronger than the northern cell, with cross-equatorial flow evident at both upper and lower levels.

Figure 2 shows the long-term annual-mean meridi-onal and vertical fluxes of westerly angular momentumby the eddies. Sandwiched between the belts of pole-

ward fluxes in midlatitudes are weaker equatorwardfluxes with maxima centered near 10°S and 10°N at the150-hPa level (Fig. 2a). The northward fluxes are some-what stronger than their Northern Hemisphere coun-terparts, and (like the MMC in Fig. 1b) extend slightlyacross the equator. The vertical transport of momen-tum by the eddies (Fig. 2b) is downward in the tropicalupper troposphere, and strongest directly below themaximum meridional flux convergence. In contrast tothe numerical simulations of KH, we find that the ver-tical fluxes in the NCEP reanalyses play only a minorrole in the angular momentum balance and thus weneglect them in our analysis.

To document the contributions from eddies at differ-ent time scales to the momentum fluxes in Fig. 2a, theannual-mean meridional transport of angular momen-tum by eddies was decomposed into the componentsdefined in (2). Figure 3 shows cross sections of thesefour components. In the extratropics eddies at all fourtime scales contribute to the poleward eddy momentumflux, consistent with results of Peixoto and Oort (1992).In contrast, within the tropical belt the equatorwardeddy momentum transport is dominated by the station-ary wave contribution (Fig. 3a), while the seasonallyvarying component (Fig. 3b) and the nonseasonal termresolved by pentad data (Fig. 3c) make a secondary

FIG. 1. Vertical cross sections of annual-mean (a) zonal wind[u]an and (b) MMC [�]an. Solid contours are positive, dashedcontours are negative, and the zero line (apparent only for [u]an)is thicker. For the zonal wind, the contour interval is 5 for posi-tive values and 2 m s�1 for negative values (. . . �4, �2, 0, 5,10, . . .). For the MMC the contour interval is 2 � 1010 kg s�1

(. . . �3, �1, 1, . . .).

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contribution. Lee (1999) obtained similar results, al-though her analysis focused on the characteristics of theinter- and intra-annual eddies in the frequency domainand did not emphasize the singular importance of thestanding eddies in the zonal momentum balance.

Figure 4 shows the annual-mean 150-hPa geopoten-tial height and horizontal wind fields superimposed onthe annual-mean precipitation field, which may beviewed as a proxy for tropical diabatic heating. It isinteresting to note that the main features observed inthe NCEP data are reproduced in theoretical represen-tations of the circulatory response to tropical heatingvariations. The flow pattern over the western Pacific

and Indian oceans resembles the linear planetary waveresponse to an isolated equatorial mass source (Mat-suno 1966) or a midtropospheric heat source (Gill 1980)on an equatorial � plane. The pattern is characterizedby an equatorial Kelvin wave to the east of the maxi-mum latent heating and a pair of anticyclonic Rossbygyres at, and to the west of, the eddy forcing. Thesefeatures bear an even stronger qualitative resemblanceto the nonlinear solutions to the shallow water waveequation [see, e.g., Van Tuyl (1986) for the full set ofthese equations] forced by an isolated heat source onthe equator (Fig. 5). The observed (Fig. 4) and, to alesser extent, the modeled (Fig. 5) wind vectors near

FIG. 3. Vertical cross sections of annual-mean components of the meridional eddy flux: (a) annual-mean sta-tionary waves [u*an�*an] cos�, (b) seasonally varying component of the climatological mean stationary waves[u*�c �*�c ]an cos�, (c) nonseasonal transient eddies resolved by pentad-mean data [u*��*�]an cos�, and (d) high-frequency transients within individual pentads [u*�d �*�d ]an cos�. Solid contours are positive and dashed contours arenegative. The contour interval is 1.5 (. . . �2.25, �0.75, 0.75, . . .) m2 s�2.

FIG. 2. Vertical cross sections of total annual mean (a) meridional [u*�*]an cos� and (b) vertical [u*�*]an cos�eddy fluxes. Solid contours are positive and dashed contours are negative. For the meridional fluxes the contourinterval is 5 m2 s�2 (. . . �7.5, �2.5, 2.5, . . .) and for the vertical fluxes it is 3 � 10�2 m � Pa s�2 (. . . �4.5, �1.5,1.5, . . .). A horizontal dashed line at 200 hPa has been drawn for reference.


the equator both exhibit a predominantly northwest–southeast tilt in the Northern Hemisphere and a south-west–northeast tilt in the Southern Hemisphere, withdiffluent easterly flow over the Indian Ocean and con-fluent westerly flow over the central Pacific. This tilt isresponsible for the equatorward eddy flux of westerlymomentum noted in Figs. 2a and 3a.

The leading terms in the annual-mean zonal momen-tum balance (1) are shown in Fig. 6. In the free tropo-

sphere there exists a strong compensation between theMMC term (Fig. 6a) and the eddy momentum flux con-vergence (Fig. 6b). The contribution from the verticaleddy flux and mean vertical advection (not shown) are�3 to 4 times smaller than the leading terms; includingthese terms does not significantly alter the appearanceof the residual in Fig. 6c. The most significant imbal-ances (Fig. 6c) occur outside of the region of interest inthis study: in the boreal stratosphere, where gravity

FIG. 5. Nonlinear solution of the shallow water wave equation forced by an equatorial heatsource. The geopotential height field is contoured, the wind field is represented by arrows, andthe heat source is shown in gray shades. The response bears a strong qualitative resemblanceto the observed zonal variations in the geopotential height and wind fields.

FIG. 4. The 150-hPa annual-mean geopotential height (contours) and wind (arrows); super-imposed (color) is the tropical annual-mean precipitation (mm day�1). The contour intervalfor the geopotential height is 100 m (gray lines); additional contours (black) at 10 m areinserted in the tropical belt. The contour succession is (. . . 14 100, 14 200, 14 210, 14 220, . . .)m, with the first black contour at the separation between gray and black contours representingthe 14 210-m line. The wind arrows are plotted only up to 23° in both hemispheres.

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wave drag is an important factor, and in the planetaryboundary layer where frictional drag is a significantterm in the momentum balance.

Figure 7 shows the annual-mean acceleration in-duced by the MMC (Fig. 6a) decomposed into annual-mean and seasonally varying components, in accor-dance with (3). The upper tropospheric advection ofmomentum by the annual-mean meridional winds (Fig.7a) induces a weak easterly acceleration near the equa-tor by virtue of the small equatorial asymmetries in theannual-mean MMC and zonal-mean zonal winds (Figs.1a,b), but this acceleration is clearly not sufficient tobalance the annual-mean eddy momentum flux conver-gence over the equator (Fig. 6b). The seasonally vary-ing MMC advection (Fig. 7b), on the other hand, in-duces an easterly acceleration throughout the tropicalupper troposphere by virtue of a strong positive tem-poral correlation between the climatological seasonallyvarying mean meridional wind ([�]c) and the mean

zonal wind gradient ( [u]c/ y) over the course of theyear. This relationship is examined in more detailbelow.

b. The monsoon seasons

The zonally averaged zonal wind, MMC, and eddymomentum fluxes during the monsoon seasons Janu-ary–February and July–August are shown in Fig. 8.During both seasons, strong easterly flow is present inthe tropical upper troposphere of the summer hemi-sphere (Figs. 8a,d); note also the resemblance betweenthe location of maximum equatorial summer easterlies(Fig. 8d) and that in the annual mean (Fig. 1a). Also,during those seasons, the MMC is dominated by asingle cell straddling the equator (Figs. 8b,e). In theupper troposphere over the equator, [u]/ y is positiveduring JF and negative during JA, while [�] is of op-posing sign. Hence, the meridional advection of zonalmomentum by the MMC induces strong easterly accel-erations in the tropical upper troposphere during bothmonsoon seasons, and accounts for much of the sea-sonally varying MMC advection in the annual-meanzonal momentum balance (Fig. 7b).

The eddy momentum fluxes in the equatorial belt,previously pointed out by Newell et al. (1972) and Wal-lace (1983), are also much stronger during the monsoon

FIG. 7. Vertical cross sections of MMC momentum flux [Eq.(3)]: (a) the product of annual means [�]an{ f � (1/cos�)( [u] cos�/ y)}an and (b) the annual mean of the seasonal transient product([�]�c{ f � (1/cos�)( [u] cos�/ y)}�c)an. Solid contours are positiveand dashed contours are negative. The contour interval is 0.5 �10�5 m s�2 (. . . �0.75, �0.25, 0.25, . . .) (half of that used inFig. 6a).

FIG. 6. Vertical cross sections of the leading terms in the annual-mean momentum budget: (a) MMC associated fluxes ([�]{ f �(1/cos�)( [u] cos�/ y})an, (b) eddy fluxes {(1/cos2�)( [u*�*]cos2�/ y)}an, and (c) sum of the two contributions in (a) and (b).Solid contours are positive and dashed contours are negative. Thecontour interval is 1 � 10�5 m s�2 (. . . �1.5, �0.5, 0.5, . . .).


seasons than in the annual mean, and are offset fromthe equator by �5° latitude into the winter hemisphere(Figs. 8c,f). The eddy momentum fluxes coincide withthe strongest mean meridional winds aloft (indicated bythe vertical gradient of � in Figs. 8b,e), and are in theopposite direction. This relationship between [�] and[u*�*] is also apparent in Figs. 10 and 11 of KH.

Figure 9 shows the climatological mean geopotentialheight and horizontal winds at the 150-hPa level duringJF and JA, along with the corresponding precipitationfields. As in the annual-mean patterns (Fig. 4), the lon-gitudinal variations over the Maritime Continent re-semble the stationary wave response to an idealizedmidtropospheric heat source. The JF pattern in Fig. 9resembles the annual mean (Fig. 4), with a slight en-hancement of the Southern Hemisphere geopotentialheight features, while the JA circulation is dominatedby the Tibetan anticyclone associated with the Asiansummer monsoon. Cross-equatorial flow from the sum-

mer hemisphere into the winter hemisphere is clearlyevident in the sectors dominated by the monsoon cir-culations. The easterly component of the air flowingacross the equator gives rise to the eddy fluxes of west-erly momentum from the winter hemisphere into thesummer hemisphere in Figs. 8c and 8f.

Many of the features of the geopotential height andwind patterns in the Tropics are qualitatively replicatedin the nonlinear solution to the shallow water waveequation forced with a heat source centered �8° off theequator, shown in Fig. 10. As in the observations, thestationary wave pattern is most intense and most of thecross-equatorial flow takes place near and just to thewest of the heating and the maximum values of geopo-tential height.

As in the annual mean, the zonal momentum balancefor the monsoon seasons (Fig. 11) is marked by a can-cellation between the easterly acceleration associatedwith the cross-equatorial flow in the upper branch of

FIG. 8. Vertical cross sections of seasonal mean zonal wind, MMC, and meridional eddy fluxes of zonal mo-mentum for (a)–(c) JF and (d)–(f) JA. Solid contours are positive and dashed contours are negative. For the zonalwind, the contour interval is 5 m s�1 for the positive values and 2 m s�1 for the negative values; the zero line isthicker. For the MMC the contour interval is 2 � 1010 kg s�1 (. . . �3, �1, 1, . . .). For the eddy fluxes the contourinterval is 5 m2 s�2 (. . . �7.5, �2.5, 2.5, . . .).

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the MMC (Figs. 11a,c) and the westerly accelerationassociated with the convergence of the eddy momen-tum fluxes in the equatorial belt (Figs. 11b,d). Boththese terms are substantially stronger than the corre-

sponding annual-mean fields shown in Fig. 6. It is ob-vious why the MMC term should be stronger, but it isnotable that the eddy momentum flux convergence isstronger as well.

FIG. 10. As in Fig. 5 but for a heat source centered off the equator.

FIG. 9. As in Fig. 4 but for the (a) JF and (b) JA seasons.


c. The transition seasons

In this subsection we examine the mean circulationduring the transition seasons, when the monsoons arerelatively weak and the MMC is more equatorially sym-metric. Figure 12 shows the mean zonal wind, MMC,and eddy momentum fluxes during April–May and Oc-tober–November. The sections for AM exhibit a highdegree of equatorial symmetry, with westerly jets cen-tered at �30° latitude in both hemispheres, very weakcross-equatorial flow, and virtually nonexistent eddymomentum fluxes in the deep Tropics.

In contrast to AM, the zonally averaged circulationstatistics for ON exhibit a substantial amount of equa-torial asymmetry. The Southern Hemisphere MMC cell(Fig. 12e) extends �7° latitude into the NorthernHemisphere, and the belt of easterly surface winds (Fig.12d) is also shifted north of the equator. The tropicaleddy momentum fluxes (Fig. 12f) are much strongerduring ON than during AM and, as in the monsoonseasons, are directed opposite to upper level [�]. Thedifferences between the AM and ON zonal wind andMMC fields are highlighted in Fig. 13. In agreementwith results of Fleming et al. (1987), the NorthernHemisphere westerly jet stream is shifted northward inON relative to AM. Both the Ferrel cell and the Hadleycell are shifted northward relative to their AM posi-tions in the Northern Hemisphere.

Figure 14 shows the horizontal wind and geopotentialheight fields at the 150-hPa level during the transition

seasons. Vestiges of the Asian summer monsoon circu-lation are still apparent during ON, with northeasterlyflow over the Maritime Continent and the IndianOcean. In contrast, the AM stationary waves are weakand the circulation is essentially symmetric about theequator. Although it is not immediately apparent fromFig. 14a, it is interesting to note that the zonally aver-aged geopotential height over the equator belt is higherduring AM than during any other season.

d. Seasonal variations in the zonally symmetricflow

Figure 15 shows the annual cycle of the climatologi-cal monthly mean zonally averaged zonal wind, meridi-onal wind, and eddy momentum fluxes at the 150-hPalevel, and Fig. 16 shows the annual cycle of the domi-nant terms in the zonal momentum balance [Eq. (1)] atthat level. The zonally averaged and root-mean-squareprecipitation fields {rms(precip) � [precip*2]1/2} are in-dicated by shading in Figs. 15b and 15c, respectively.All three of the contoured fields in Fig. 15 exhibit astrong, quasi-sinusoidal annual cycle (Dima and Wal-lace 2003), with opposing extrema in the monsoon sea-sons and weaker, more equatorially symmetric latitudi-nal profiles during the transition seasons. The meanmeridional wind and flux of eddy momentum both ex-hibit a pronounced seasonal reversal, which accountsfor the relatively weak annual-mean MMC and eddymomentum fluxes in Figs. 1b and 2a. The positive cor-

FIG. 11. Vertical cross sections of the leading terms in the seasonal mean momentum budget: (a), (c) MMCassociated fluxes, (b), (d) eddy fluxes; (a), (b) JF and (c), (d) JA. Solid contours are positive and dashed contoursare negative. The contour interval is 1 � 10�5 m s�2 (. . . �1.5, �0.5, 0.5, . . .).

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relation between [�]c and [u]c / y over the course of theyear, which leads to the easterly accelerations in Figs.7b and 16a, is also apparent. The meridional winds inFig. 15b emanate from the belts of heavy zonally aver-aged precipitation, and the eddy fluxes of westerly mo-mentum in the deep Tropics (Fig. 15c) are directedtoward the belts of high rms precipitation, which pre-sumably represent the regions with the strongest eddyforcing. It is also apparent from Fig. 16 that the strongcompensation between the mean meridional advectionterm and the eddy momentum flux convergence notedduring individual seasons (Fig. 11) is present through-out the year at that level.

Several other features of the annual cycle in Fig. 15relate to the distinctions between the AM and ON tran-sition seasons. The Northern Hemisphere westerliesare located farther poleward during ON than duringAM, and the zero wind line that separates the midlati-tude westerlies from the tropical easterlies shifts north-ward abruptly during late spring and returns moregradually in autumn, consistent with results of Fleminget al. (1987). The tropical rain belt is also located far-ther northward during ON than during AM.

Upon close inspection of Fig. 15a, it is evident that

FIG. 12. As in Fig. 8 but for the AM and ON seasons.

FIG. 13. Seasonal differences AM–ON for zonal wind andMMC. For the zonal wind, the contour interval is 5 m s�1; the zeroline is thicker. For the MMC the contour interval is 2 � 1010

kg s�1 (. . . �3, �1, 1, . . .). Solid contours are positive and dashedcontours are negative.


the zonal winds exhibit a weak semiannual cycle withpeak easterlies in the monsoon seasons and a changetoward westerlies in the transition seasons. This featureshows up more clearly in the latitude–time section ofequatorially symmetric zonal wind {[u]sym � ([u]N �[u]S)/2, where the subscripts N and S refer to the North-ern and Southern Hemisphere values} shown in Fig. 17.The semiannual character of the zonal wind is not re-stricted to the equatorial belt, but extends into middlelatitudes. We will consider the semiannual variability ofthe tropical circulation in further detail in the next sec-tion.

e. Seasonal variations in the eddies

The equatorially asymmetric, seasonally reversingcomponent of the stationary waves near the equatoraccounts for the eddy flux of westerly momentumacross the equator from the winter hemisphere into thesummer hemisphere, as documented in Fig. 8. How-

ever, the equatorially symmetric part of the tropicalstationary waves accounts for roughly 3/4 of the eddykinetic energy at the 150-hPa level equatorward of 30°of latitude and exhibits a pronounced semiannual cycle,with maximum amplitude during the monsoon seasons(Fig. 18).

The equatorially symmetric component of the upper-level flow pattern in JF, AM, JA, and ON is shown inFig. 19. A Rossby wave couplet is evident throughoutthe year over the Indo-Pacific sector. This equatoriallysymmetric wave pattern is strongest during JF and JAand weakest during AM. The center of the gyres shiftsin longitude from �160°E in JF to �80°E in JA. Thiseast–west shift in the stationary wave pattern is accom-panied by a subtle shift in the relative prominence ofthe rainfall maxima that lie just to the east and to thewest of the marine continent. Equatorial easterlies areevident year-round in the zone of east–west geopoten-tial height gradient within and to the west of the Rossby-wave couplet. The tropical easterly jet across the equato-

FIG. 14. As in Fig. 4 but for the (a) AM and (b) ON seasons.

JULY 2005 D I M A E T A L . 2509

rial Indian Ocean during JA is a manifestation of thisfeature. Only during JF, when the geopotential heightgradients along the equator are particularly strong, do thewesterlies in the Kelvin-wave signature, to the east of thecouplet, make a significant contribution to the Tropics-wide rms eddy kinetic energy.

4. Discussion and conclusions

In this study, fields derived from the NCEP reanaly-ses have been used to investigate the seasonal evolution

of the zonally averaged circulation, the climatological-mean stationary waves, and the zonal momentum bal-ance in the tropical upper troposphere. The zonally av-eraged component of tropical diabatic heating forces aseasonally reversing, thermally direct MMC cell, withstrong cross-equatorial flow at the 150-hPa level during

FIG. 17. Time–latitude section of the equatorially symmetriccomponent of the 150-hPa zonal wind ([u]sym). Solid contours arepositive and dashed contours are negative; the zero line is thicker.The contour interval is 2 m s�1, as in Fig. 15a.

FIG. 15. Time–latitude sections for 150 hPa (a) zonally averagedzonal wind [u]c (contour interval 2 m s�1), (b) zonally averagedmeridional wind [�]c (contour interval 0.5 m s�1) and precipitation(gray shading), and (c) zonally averaged meridional eddy fluxes[u*�*]c (contour interval 5 m2 s�2) and rms precipitation (grayshading). Solid contours are positive and dashed contours arenegative; the zero line is thicker. The first five months of thecalendar year are repeated. Gray shading bar as in Fig. 14.

FIG. 16. Time–latitude sections for the leading terms in Eq. (1):(a) the MMC term (first term on the rhs) and (b) the horizontaleddy term (third term on the rhs) in the momentum budget. Solidcontours are positive and dashed contours are negative; the zeroline is thicker. The contour interval is 10�5 m s�2. The first fivemonths of the calendar year are repeated.


the monsoon seasons. The advection of momentum bythis cross-equatorial flow induces an easterly accelera-tion of the upper tropospheric zonal flow, which is bal-anced by the convergence of westerly momentum bythe stationary waves. This balance prevails in both theannual-mean and individual seasons. The strength ofthe tropical eddy momentum fluxes varies in concertwith the strength of the mean meridional flow acrossthe equator, so that the net acceleration experienced bythe zonal flow in the tropical upper troposphere re-mains nearly zero year-round. A similar balance wasobtained by KH using an idealized GCM forced with atropical eddy heat source and solstitial boundary con-ditions.

Presumably, stronger easterlies would be observed inthe equatorial upper troposphere during the monsoonseasons were it not for the convergence of westerlymomentum into the equatorial belt by the stationarywaves. Eddy fluxes are not taken into account in theaxisymmetric models such as Lindzen and Hou (1988)and Fang and Tung (1999), and thus such models tendto produce unrealistically strong easterly winds over theequator. Conversely, were it not for the easterly accel-eration induced by the MMC, the equatorward flux ofmomentum associated with tropical stationary waveswould lead to the buildup of westerly flow over theequator, as demonstrated by KH.

Observations indicate a strong tendency for the massflux in the upper branch of the Hadley circulations andthe flux of westerly momentum by the stationary eddiesin the tropical upper troposphere to be in opposite di-rections. This tendency for opposition may reflect thepreference for the zonally averaged tropical rain beltsto occur at the same latitudes as the eddy forcing, so

that upper tropospheric mass flux divergence coincideswith the eddy flux convergence.

Watterson and Schneider (1987) found that the me-ridional propagation of wave energy is enhanced whencross-equatorial mean flow is present, though they didnot examine the fluxes of momentum associated withthese waves. In view of their results, the observed cor-respondence between the strength of the MMC and thestrength of the eddy momentum flux convergence overthe course of the year suggests that perhaps strongmean meridional flow aloft may be necessary in orderto obtain a strong stationary wave response to the zonalasymmetries in the heating. This relationship needs tobe further examined for a better clarification of causal-ity.

The upper tropospheric stationary waves, which arestrongest near the 150-hPa level, are dominated by ananticyclonic Rossby wave couplet centered near or justto the west of the heating and an equatorial Kelvin-wave signature to the east. Diffluent easterly flowaround the western flank of the Rossby wave couplet,in combination with confluent westerly flow to the eastof the heating, induces the equatorward eddy flux ofwesterly momentum.

A notable result is also the surprising amount ofhemispheric symmetry present in the tropical stationarywave pattern throughout the year. Contrary to whatmight be expected on the basis of simple inferencesbased on the distribution of diabatic heating, this pat-tern is strongest not during the transition seasons, whenthe heating is most symmetric about the equator, butduring the monsoon seasons, when the eddy forcing islocated in the summer hemisphere.

Many of the features in the observations can be rep-licated with a simple model of the nonlinear solution tothe shallow water wave equation forced with a tropicalheat source. As observed, eddy heating on or near theequator leads to a Rossby wave response with an equa-torward eddy momentum flux and the solution retains ahigh degree of equatorially symmetric component evenwhen the heating is moved off the equator.

Another intriguing aspect of the seasonality of thetropical general circulation is the marked distinctionbetween the April–May (AM) and October–November(ON) transition seasons. It is shown that AM is theseason of strongest equatorial symmetry in the distri-butions of rainfall and MMC, and weakest stationarywaves and eddy momentum fluxes. In ON the tropicalrain belt remains centered north of the equator, result-ing in a northward displacement of the Northern Hemi-sphere Hadley cell and subtropical jet streams relativeto their AM positions. The reasons for these asymme-tries have yet to be elucidated.

FIG. 18. Equatorially symmetric (solid line) and asymmetriccomponents (dash–dot line) of the mean eddy kinetic energy ofthe 150-hPa wind field for the 30°N–30°S belt.

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FIG. 19. Horizontal maps of the symmetric component of 150-hPa geopotential height (m),wind (m s�1), and precipitation (gray shading; mm day�1). The contour interval for the geo-potential height is 100 m (gray lines); additional contours (black) at 10 m were inserted in thetropical region. The contour range is similar to that in Fig. 4.


Acknowledgments. The calculations based on thenonlinear shallow water wave equation model were car-ried on in collaboration with James R. Holton. Holtonhad already performed different runs with this modeland had noticed the dominance of the equatorially sym-metric component of the solutions. The work of I. M.Dima and J. M. Wallace was supported by the NationalScience Foundation under Grant ATM 0318675. I.Kraucunas was supported by the NSF Grant ATM9873691.

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