Feedback of Tropical Instability-Wave-Induced Atmospheric ... · Introduction Tropical instability waves (TIWs) are generated from instabilities of equatorial zonal currents and are

Feedback of Tropical Instability-Wave-Induced Atmospheric Variabilityonto the Ocean

HYODAE SEO

Scripps Institution of Oceanography, La Jolla, California

MARKUS JOCHUM

National Center for Atmospheric Research, Boulder, Colorado

RAGHU MURTUGUDDE

ESSIC/DAOS, University of Maryland, College Park, College Park, Maryland

ARTHUR J. MILLER AND JOHN O. ROADS

Scripps Institution of Oceanography, La Jolla, California

(Manuscript received 27 September 2006, in final form 10 April 2007)

ABSTRACT

The effects of atmospheric feedbacks on tropical instability waves (TIWs) in the equatorial AtlanticOcean are examined using a regional high-resolution coupled climate model. The analysis from a 6-yrhindcast from 1999 to 2004 reveals a negative correlation between TIW-induced wind perturbations andTIW-induced ocean currents, which implies damping of the TIWs. On the other hand, the feedback effectfrom the modification of Ekman pumping velocity by TIWs is small compared to the contribution to TIWgrowth by baroclinic instability. Overall, the atmosphere reduces the growth of TIWs by adjusting its windresponse to the evolving TIWs. The analysis also shows that including ocean current (mean � TIWs) in thewind stress parameterization reduces the surface stress estimate by 15%–20% over the region of the SouthEquatorial Current. Moreover, TIW-induced perturbation ocean currents can significantly alter surfacestress estimations from scatterometers, especially at TIW frequencies. Finally, the rectification effect fromthe atmospheric response to TIWs on latent heat flux is small compared to the mean latent heat flux.

1. Introduction

Tropical instability waves (TIWs) are generated frominstabilities of equatorial zonal currents and are a com-mon feature in both the tropical Atlantic (Düing et al.1975) and Pacific Oceans (Legeckis 1977; Legeckis etal. 1983). Observations reveal TIWs as westward propa-gating wavelike oscillations of the sea surface tempera-ture (SST) near the equator with a typical wavelengthof �10° longitude and a phase speed of �0.5 m s�1

(Weisberg and Weingartner 1988; Qiao and Weisberg1995, and references therein). A detailed study of TIWs

is necessary because they are an important element inthe momentum balance (Weisberg 1984) and equatorialocean heat budget (Hansen and Paul 1984; Brydenand Brady 1989; Baturin and Niiler 1997; Jochum andMurtugudde 2006).

Numerous studies have discussed the generationmechanisms and energetics of TIWs. Analytical studiesby Philander (1976, 1978) showed that meridional shearof the zonal currents leads to a barotropic conversion ofmean kinetic energy to eddy kinetic energy (EKE),which supports the growth of waves with wavelengthsand periods similar to those of the observed TIWs. Cox(1980) showed that baroclinic instability, though lessimportant, is also a source of the EKE that is drawnfrom the mean potential energy. In addition, frontalinstability (Yu et al. 1995) and Kelvin–Helmholtz insta-bility (Proehl 1996) were shown to be important EKE

Corresponding author address: Hyodae Seo, Climate ResearchDivision, Scripps Institution of Oceanography, 9500 Gilman Dr.,Mail Code 0224, La Jolla, CA 92093.E-mail: [email protected]

5842 J O U R N A L O F C L I M A T E VOLUME 20

DOI:10.1175/2007JCLI1700.1

JCLI4330

sources for the TIWs. A more comprehensive numeri-cal study of the generation and the energetics of PacificTIWs has shown that the northern temperature front isbaroclincally unstable, while shear of the zonal currentscauses barotropic instability at the equator (Masina etal. 1999, hereafter MPB). These two different instabili-ties are phase locked and are both important energysources for TIWs. On the other hand, Jochum et al.(2004, hereafter JMB) found that barotropic instabilityin the Atlantic was dominant in their energy budget andthe baroclinic term was less important.

Chelton et al. (2004) and Xie (2004) demonstratedthat ocean–atmosphere interactions involving the oce-anic mesoscale occur throughout the World Ocean.SST on this scale induces wind response in the atmo-spheric boundary layer through modification of the ver-tical turbulent mixing (Wallace et al. 1989; Hayes et al.1989). Air over the warm water is destabilized, andincreased turbulent mixing of momentum acceleratesnear-surface winds. Conversely, cold SST suppressesthe momentum mixing, decouples the near-surfacewind from wind aloft, and hence decreases the near-surface wind. Small et al. (2003) and Cronin et al.(2003) reported that the pressure gradient mechanismof Lindzen and Nigam (1987) is likely to be an impor-tant mechanism as well. Furthermore, Chelton et al.(2001) showed that undulating SST fronts by TIWs fur-ther affect the perturbation wind stress derivatives inthe atmosphere, suggesting a possible feedback fromthe atmosphere to the TIWs through Ekman dynamics.The lack of simultaneous measurements of ocean cur-rents and wind stresses on the TIW scale makes it dif-ficult to quantify in great detail the feedbacks from theperturbation wind field on the TIWs.

Pezzi et al. (2004) modeled this SST–wind couplingand showed that it reduces variability of TIWs. Theirsimple coupling parameterization included the effect ofTIW-induced SST variations directly on the wind fieldsand through the modification in wind stress derivatives.Seo et al. (2007) used a full-physics high-resolution re-gional coupled model to explore several aspects of thetropical Pacific TIWs, reproducing the observed cou-pling strength as a function of SST gradient.

Recent findings on this close coupling between theocean and the atmosphere at the oceanic mesoscaleraise new questions that have been largely unexploredin the aforementioned studies. What is the role of thewind response in the energy budget of TIWs? How dothe atmospheric feedbacks amplify or dampen theTIWs? What is the rectification effect on the mean sur-face heat flux from the atmospheric response to theTIWs? These questions will be addressed in the presentstudy, which is among the first of its kind using a re-

gional coupled ocean–atmosphere model at eddy-resolving resolution.

In the present study, the regionally coupled high-resolution model of Seo et al. (2007) is used to quantifythe contribution of tropical Atlantic ocean–atmospherecovariability to the energetics of the TIWs. It is shownthat the direct response of winds to the TIW-inducedSST imposes a negative feedback on the growth ofTIWs. It is also shown that perturbation Ekman pump-ing due to TIWs (Chelton et al. 2001) is a very smallforcing effect compared to baroclinic instability in theequatorial ocean.

It is also argued that ocean currents (mean � TIWs)substantially reduce the surface stress estimation by15%–20% over the large area of the South EquatorialCurrent. Moreover, TIW-induced perturbation oceancurrents can significantly alter the local surface stressestimate during the active TIW season. This suggeststhat numerical studies of TIWs will suffer from a con-sistency problem when the model is forced with theobserved winds such as scatterometer wind stresses.

Last, perturbation latent heat flux generated at thesea surface by evolving TIW–SST is small compared tothe contribution from the mean component, indicatingonly a weak rectification effect on the ocean from thesehigh-frequency perturbations.

In section 2, the model and experiment designed forthis study are explained. In section 3, the main results ofthe study are discussed, followed by the conclusionsand summary in section 4.

2. Model and experiment

The coupled model used for the present study is theScripps Coupled Ocean–Atmospheric Regional(SCOAR) model (Seo et al. 2007). It combines twowell-known, state-of-the-art regional atmosphere andocean models using a flux–SST coupling strategy. Theatmospheric model is the Experimental Climate Predic-tion Center (ECPC) Regional Spectral Model (RSM)and the ocean model is the Regional Ocean ModelingSystem (ROMS).

The RSM, originally developed at the National Cen-ters for Environmental Prediction (NCEP) is describedin Juang and Kanamitsu (1994) and Juang et al. (1997).The code was later updated with greater flexibility andmuch higher efficiency (Kanamitsu et al. 2005; Kana-maru and Kanamitsu 2007). Briefly, it is a limited-areaprimitive equation atmospheric model with a perturba-tion method in spectral computation, and utilizes a ter-rain-following sigma coordinate system (28 levels). Themodel physics are the same as for the NCEP globalseasonal forecast model (Kanamitsu et al. 2002a) and

1 DECEMBER 2007 S E O E T A L . 5843

NCEP–National Center for Atmospheric Research(NCAR) reanalysis model (Kalnay et al. 1996) exceptfor the parameterization of convection and radiativeprocesses.

The ROMS solves the incompressible and hydro-static primitive equations with a free surface on hori-zontal curvilinear coordinates and utilizes stretchedgeneralized sigma coordinates in order to enhance ver-tical resolution near the sea surface and bathymetry.The details of the model can be found in Haidvogel etal. (2000) and Shchepetkin and McWilliams (2005).

A flux–SST coupler bridges the atmospheric (RSM)and ocean (ROMS) models. The coupler works in asequential fashion; the RSM and ROMS take turns in-tegrating while exchanging forcing every 24 h. The in-teracting boundary layer between RSM and ROMS isbased on the bulk formula for surface fluxes of momen-tum and sensible and latent heat adapted from the al-gorithm of Fairall et al. (1996).

Although the drag coefficient is generally a functionof both wind speed and atmospheric boundary layerstability, Liu et al. (1979) showed that, for the typicalenvironmental conditions in the Tropics, with near-surface wind speeds of �7 m s�1, the bulk transfer co-efficients are only marginally sensitive to the typicalchanges in the stability induced by �0.5°C changes inair � sea temperature difference. Thus, bulk transfercoefficients for momentum and the moisture remainlargely unchanged by the changes in the atmosphericstability due to TIW–SST changes.

Seo et al. (2006) showed that resolving mesoscalevariability in the equatorial Atlantic Ocean is importantin improving the simulations of large-scale mean SSTand the precipitation. The present study uses the iden-tical model setup as in Seo et al. (2006), except for anenhanced atmospheric resolution of �1⁄4° to match theunderlying ocean grid at �1⁄4°. Comparable high reso-lution in the coupled model allows for synchronous lo-cal feedback of ocean and atmosphere arising in thepresence of ocean mesoscale eddies including TIWs.

The initialization and forcing procedures for bothcases are as follows. The ROMS ocean was first spun upfor 8 years with the Comprehensive Ocean–Atmo-sphere Dataset (COADS) climatological atmosphericforcing (da Silva et al. 1994) and climatological oceanicboundary conditions from the World Ocean Atlas 2001(Conkright et al. 2002). Then the SCOAR coupled runwas launched for 7 years from 1998 to 2004 with low-wavenumber NCEP/Department of Energy (DOE) re-analysis II (Kanamitsu et al. 2002b) atmospheric forc-ing and climatological oceanic boundary conditions.The 6-yr solution from 1999 to 2004 is analyzed in thisstudy.

The model domain covers the whole tropical Atlanticbasin from 30°S to 30°N, 70°W to 20°E includingeastern Brazil and western Africa. Since the focus ofthe present study is the effect of atmospheric feedbackson TIWs, the domain analyzed here is limited to theregion close to the equator where TIW activity is large.Figure 1 shows a snapshot of SST that represents thetypical spatial patterns of TIWs from the model, incomparison to measurements from the Tropical Rain-fall Measuring Mission (TRMM) Microwave Imager(TMI). The simulated TIWs in the model are qualita-tively similar to the observations, with cusps of SSTnorth of the equator along the equatorial front. How-ever, an exact correspondence of the modeled TIWswith the observations at any given time is not expectedbecause TIWs are generated by internal ocean dynam-ics, rather than deterministically forced. On the other

FIG. 1. Three-day-averaged SST and 10-m winds centered on 2Sep 1999 (a) in the model and (b) from the satellite of the TMItropical instability waves and the QuikSCAT scatterometers. TheTIWs are shown as undulations of the SST front near the equator.The TRMM SST and the QuikSCAT wind vectors are regriddedto the model grid in (a). The vectors are shown on every 10 (5)grid points in x (y).


Fig 1 live 4/C

hand, the eddy statistics of the waves are well repre-sented in the SCOAR model (Fig. 2b).

Figure 2 shows an annual-mean zonal current at23°W and the EKE of the near-surface currents. Thecore of the equatorial undercurrent (EUC) reaching�100 cm s�1 is located at a depth of 150 m, and thiscompares well with the observations (e.g., Brandt et al.2006; Schott et al. 2003) and modeling studies (JMB).The maximum EKE, greater than 400 cm2 s�2 is locatedat the equator, which is also consistent with time-meanperturbation kinetic energy estimated from the obser-vations (Weisberg and Weingartner 1988).

Temporal filtering of data is useful to extract thecharacteristics of the TIWs (e.g., Hashizume et al. 2001;JMB). However, temporal bandpass filtering alone(e.g., 10–40 days) does not completely rid the system ofintrinsic higher frequency (3–15 days) synoptic variabil-ity in the atmosphere. A spatial (zonal) filtering in com-

bination with some temporal smoothing is more usefulwhen one aims to highlight covarying patterns of theocean–atmosphere signals arising from fast-movingTIWs (e.g., Chelton et al. 2001; Small et al. 2003). Thus,all the variables analyzed in this study are zonally high-pass filtered to retain the signals of the ocean and theatmosphere less than 10° longitude and also 5-day av-eraged to reduce the fast-changing atmospheric andoceanic variability.

3. Result

a. Impact of wind current covariability on the TIWs

Figure 3 shows a snapshot of TIW–SST overlaid withsurface currents and wind stresses. Anticyclonic oceancurrents are generated north of the equator in associa-tion with TIWs (Fig. 3a), over which large-scale windsare southeasterly, traversing the SST front (Fig. 3b).Figure 4 shows a 3-day-averaged snapshot of SSTanomaly, SST�, overlaid with the perturbation surfacecurrents, u�, and wind stresses, ��, associated with theTIWs. SST� and �� have an in-phase relationship, suchthat warm (cold) SST� enhances (reduces) southeast-

FIG. 2. (a) Six-year model mean (1999–2004) zonal currentalong 23°W. The westward South Equatorial Current is shown bydashed contour lines. Zero values are shown in thick contours.The core of the equatorial undercurrent is located at 150-m depth.Tsuchiya jets are shown as the eastward subsurface currents cen-tered at 5°N and 5°S. (b) Near-surface model EKE computed byEKE�(u�2 � ��2)/2, where u� and �� are zonally high-pass-filteredsurface currents. The maximum EKE is located north of the equa-tor along the core of the TIWs.

FIG. 3. Three-day-averaged model SST fields centered on 26Sep 2000 with vectors of (a) the model surface current (m s�1) and(b) the model wind stress (N m�2). The vectors are shown onevery 5 (2) grid points in x (y).


erly background atmospheric flows. This is a result ofchanges in stratification of the lower atmosphericboundary layer according to the underlying SST�,which in turn leads to the atmospheric adjustment ofvertical turbulent mixing of momentum (Wallace et al.1989; Hayes et al. 1989).

Apparent in Fig. 4 is that �� is generally in the oppo-site direction of u�, particularly for the meridional com-ponents in Fig. 4a. Figure 5 shows a simple schematicrepresentation of such a relationship. Cold, newly up-welled waters from the equator are pushed northwardby TIWs while they drive warm water from the northequatorward (Fig. 3a). The anomalous meridional cur-rents are slowed down by perturbations in meridionalsurface winds, which are generated in response to theTIW–SST. This feedback results in a significant nega-tive correlation north of the equator where TIWs aremost energetic (Fig. 6a). The significant positive corre-lation south of the equator can be understood similarly.

The relationship between the zonal TIW perturba-tion currents and wind stresses is more complicated be-cause of asymmetric responses in the southern andnorthern part of the TIW–SST. In the northern flank of

the eddy (Figs. 4b and 5b), the above explanation istrue, where zonal wind stress and zonal surface currentgenerally oppose each other. This is because warm SSTincreases the easterly background winds where TIWsgenerate eastward currents (Fig. 3a). Near the equator,however, a significant positive correlation indicates thatwinds and currents are aligned together zonally. Thisresults when the warm water pushed by TIWs from thenorth turns westward at the equator to close the anti-cyclonic ocean eddy over which easterly winds are ac-celerated (Figs. 3a and 4b). Figure 6b shows bands ofpositive correlation near the equator and negative cor-relation north of the equator. We now discuss howthese correlation patterns translate into the EKE bud-get of the TIWs.

Here we use a similar technique as used by MPB andJMB, based on the EKE budget. The difference is thatin their equation the eddy component is defined as adeviation from the time-mean flow, whereas here it isdefined as a deviation from the 10° longitude zonalrunning mean averages. In the Pacific Ocean, a longercutoff wavelength could be used in bandpass filtering,while this is not desirable in the tropical Atlantic Ocean

FIG. 4. Three-day-averaged (centered on 22 Oct 2000) and high-pass-filtered model SST (color shaded)overlaid with high-pass-filtered model surface current (green vectors), and model wind stress (black vectors)in the (a) meridional and (b) zonal components.


Fig 4 live 4/C

because the basin is much smaller and this would giverise to more ocean grid points lost from the continentalboundary. It should be noted, however, that the resultsdiscussed here are not significantly altered by thechoice of cutoff wavelength of the zonal filter, so longas the TIW signals are retained.

MPB estimated each term of the EKE budget in thetropical Pacific Ocean using a numerical ocean model.The EKE equation can be written as

U · �Ke � u� · �Ke � �� · �u�p� � g��w�

� �o�u� · �u� · �U�

� �oAhu� · �2u� � �ou� · �A�u�zz

� u�sfc · ��z. �1

The capital letters denote the annual-mean values andthe primes are zonally bandpass-filtered values. HereKe is the EKE; (u, �, w) the ocean velocity vector com-ponents; p the pressure; � the density; g the gravita-tional acceleration; Ah and A� are the horizontal andvertical viscosities, respectively; and � is the surfacewind stress. The terms on the lhs are horizontal andvertical advections of EKE by the mean and eddy cur-rents. The annual-mean local tendency of the EKE isnegligible. The first term on the rhs is the vertical andhorizontal radiation of energy, and the second termrepresents a baroclinic conversion process, wherebymean available potential energy is converted into EKE.The third term is the horizontal deformation work thatrepresents a conversion from mean kinetic energy to

EKE. The fourth and fifth terms designate the horizon-tal and vertical dissipation, respectively, of EKE by theeddies. The last term, which is the focus of the presentstudy, corresponds to the effect of the correlation ofcurrents and wind stresses integrated to the depth atwhich momentum input from wind stress vanishes.

From the estimates of each term of Eq. (1) using theirmodel output, JMB concluded that barotropic conver-sion of the zonal flow, the component, ��o(u��Uy), ofthe full term, �o�u� · (u� · �U)], was the dominantsource for the TIW EKE. Other deformation terms inthe barotropic convergence rate, ��o(u�u�Ux � u��Vx ��Vy), and the baroclinic conversion rate, �g��w�,were argued to be less important.

For the previous studies of the energetics of TIWs,including MPB and JMB, the effect of the correlationbetween ocean surface currents and wind stresses, thelast term of Eq. (1), was zero by construction becausetheir models were forced with climatological wind. Ver-tical averaging of Eq. (1) gives an estimate of the rela-tive importance of this term, u�sfc · ��z, compared with,for example, the barotropic convergent rate of thezonal flow, ��o(u��Uy). Figure 7 shows the 6-yr meanand zonal-mean �o(u��Uy) and u�sfc · ��z averaged from

FIG. 5. Schematic representation of the relationship betweenwind stress and surface current over TIW–SST. Warm (cold)TIW–SST is shown as light yellow (blue) ovals. Black (green)vectors are perturbation wind stress (surface current). Back-ground wind fields are shown as thick gray vectors.

FIG. 6. Map of correlation of 6-yr high-pass-filtered model windstress and surface current over the tropical Atlantic Ocean in the(a) meridional and (b) zonal directions.


Fig 5 live 4/C Fig 6 live 4/C

the surface to 150-m depth. This depth range shouldinclude the maximal effects of both of these terms. Forexample, the center of the EUC is located at 150-mdepth (Fig. 2a) where ��o(u��Uy) is most dominant(JMB). Wind input, in contrast, should be largest nearthe surface and decrease to small values near the centerof the EUC.

The magnitude of the time- and zonal-mean barotro-pic conversion of the zonal flow, ��o(u��Uy), in thepresent model compares well with the estimate of JMB,although there is a secondary peak at 3°N, which wasnot seen in their study. The sign of the energy conver-sion rate estimated in each direction agrees with themap of correlation. Positive correlation of zonal windsand currents (Fig. 6b), for example, results in an EKEsource at the equator (Fig. 7). Overall, the net impact ofthe correlation of u� and �� is largely negative, with itspeak at 2°N. At this particular latitude, the wind con-tribution to the TIW energy budget is large, amountingto roughly 40% of the barotropic convergent rate term.If averaged over TIW region (2°S–5°N), the contribu-tion from wind–current coupling is �10% of the baro-tropic conversion term, which suggests that overallwind–current coupling is a small but significant sink ofEKE of the TIWs. This is one of the main results of thisstudy. This agrees with the observational study byPolito et al. (2001) who showed, based on the analysisof TIW anomaly relationship using the satellite dataand assuming geostrophy, that meridional wind speedsare in quadrature with sea surface heights, and thus inopposition to the phase of meridional TIW currents.This implies that the opposing winds slow down thesurface current associated with the TIWs.

In addition to the feedback arising from a direct re-sponse of winds to TIWs, Chelton et al. (2001) foundthat perturbation wind stress curl generated at the frontby TIWs could be an additional feedback. Spall (2007)discussed how the observed relationship of SST andwind stresses affects the baroclinic instability of theocean through Ekman pumping. Then he applied thismodel to a classic linear, quasigeostrophic stabilityproblem for a uniformly sheared flow originally studiedby Eady (1949). For the case of southerly backgroundwinds blowing from cold to warm waters, his analysisindicates that Ekman pumping and the forced vorticitywould reduce the growth rate and wavelength of themost unstable wave (Fig. 1 of Spall 2007).

In the current model, the effect of Ekman pumpingon the TIWs is estimated by comparing the magnitudesof Ekman pumping velocity, w�e , and perturbation ver-tical velocity, w�, from the model output which entersthe baroclinic conversion term [Eq. (1)]. This w� is com-puted at the base of the mixed layer, which is defined asdepth at which SST decreases by 0.5°C from the seasurface. In Fig. 8, Hovmöller diagrams of w� and w�e at2°N for one particular TIW season (mid-May 2001 toJanuary 2002) illustrate the westward propagating fea-tures of both w� and w�e , although w� exhibits morecoherent spatial structures that resemble TIWs withmuch stronger amplitudes. Time series of w� and w�e at2°N, 30°W confirm that the amplitudes of w� are muchstronger than those of w�e throughout the whole 6-yrperiod.

This suggests that the effect of wind stress curl due tothe zonal SST gradient is a minor contribution to theTIWs compared to the baroclinic energy source intrin-sic to the ocean. However, this result comes with thecaveat that Ekman pumping velocity becomes singularat the equator and the variability in upwelling due todirect wind effects is difficult to quantify.

Hence, the net effect of the two sources of atmo-spheric feedback (i.e., a direct response of wind andEkman pumping) due to TIW–SST weakly damps theTIWs. This is consistent with the results by Pezzi et al.(2004) who parameterized this feedback effect by add-ing an empirical correlation between SST and surfacewind to the forcing fields of their ocean general circu-lation model (OGCM).

b. Impact of surface current on wind stress

The Quick Scatterometer (QuikSCAT) measureswind stresses at the sea surface from the intensity of thebackscatter in the Ku band (Kelly et al. 2001). Thisstress is a function of the ocean surface state, includingroughness, as well as atmospheric background winds(Chelton and Freilich 2005). Kelly et al. showed that

FIG. 7. Zonal average (30°–10°W) of the 6-yr model mean(dashed line) barotropic conversion rate of the zonal flow,��o(u��Uy) averaged over 150 m, i.e., d�1 sfc

d (��ou��Uy) dz,where d is the depth of the center of EUC (150 m). (Solidline) Time- and zonal-mean u�sfc · ��z averaged over 150 m,i.e., d�1 sfc

d (u�sfc · ��z) dz. Zonal (meridional) component ofd�1 sfc

d (u�sfc · ��z) dz is shown by the light solid line with x (o).


the difference of mean winds from the QuikSCAT andthe Tropical Atmosphere–Ocean (TAO) array closelyresembles the mean equatorial surface currents, andthis is attributed to the QuikSCAT measuring the rela-tive motion of air and sea.

Here the effect of TIW-induced surface currents onthe surface wind stress estimation is examined. The sur-face wind stresses are computed for the different sce-narios with the knowledge of the model 10-m winds andthe ocean surface current using bulk formulae. The

wind stress parameterization of QuikSCAT can be writ-ten as

�1 � �Cd|ua � uo|�ua � uo, �2

where � is the air density, Cd is the drag coefficient (1.3� 10�3), ua is the atmospheric wind velocity, and uo isthe ocean surface current velocity. Thus |�1| is an esti-mated surface stress magnitude in the presence of thesurface ocean current (mean currents � TIW currents).

FIG. 8. Hovmöller diagrams of (a) the model perturbation vertical velocity w�, evaluated at the base of themixed layer (�40–50 m), from the baroclinic convergent rate term (�g��w�) and (b) the model Ekmanpumping velocity, w�e , at 2°N from mid-May 2000 to January 2001. (c) Times series of w� (solid) and w�e (linewith o) at 2°N, 30°W. Note the different color scales in (a) and (b). Time axis of (a) and (b) denotes Januaryof the year.


If the ocean surface were motionless, the wind stress,�2, is written as

�2 � �Cd|ua|ua. �3

If the effect of TIW currents on wind stresses is re-moved by a zonal low-pass filter, this wind stress, �3,can then be written as

�3 � �Cd|ua � uo_lowpass|�ua � uo_lowpass, �4

where uo_lowpass is the low-passed surface current veloc-ity to remove the TIW currents. Comparison of |�1| and|�2| gives an estimate of the effect of ocean currents onthe surface wind stresses. Comparison of |�1| and |�3|will show the effect of TIW-induced perturbation oceancurrents on the surface wind stresses. Figure 9a shows atime series of |�1| at 2°N averaged over 20° and 15°W,where the TIW activity is large. The time series of |�1|exhibits a strong intraseasonal variability, in particularduring the second half of the year when TIWs are ac-tive. The annual-mean wind stress over this area isroughly 0.027 N m�2.

Figure 9b shows that |�1| � |�2| is mostly negative,with a larger deficit in |�1| in the second half of eachyear. This indicates that including ocean currents re-duces the wind stress estimate at this latitude (2°N)evidently because the mean South Equatorial Current isin the same direction as the large-scale winds. This is con-sistent with the results of Kelly et al. (2001). Figure 10ashows the map of the annual-mean (|�1| � |�2|)/|�1| .Over the large area across the equator and the coastalregions, the effect of the ocean surface current is toreduce the surface stress by 15%–20% in the currentmodel, consistent with the previous studies (Pac-anowski 1987; Luo et al. 2005; Dawe and Thompson2006). Even larger values found at the coastal oceanssuggest that strong variability of the coastal currentscan significantly alter the estimated surface stressesnear the coast.

Figure 9c shows a 6-yr time series of |�1| � |�3| , whichclosely resembles TIW currents in the ocean (Fig. 9d,with correlation coefficient of �0.8). This shows theimportance of fluctuating ocean currents on the estima-tion of wind stress. Since the annual mean of |�1| � |�3|is close to zero because of the oscillatory cancellation ofthe TIW currents, the annual-mean TIW currents donot significantly affect the annual-mean surface windstress estimates. However, it should be noted that dur-ing the active season of the TIWs, TIW currents sub-stantially modify the estimate of the surface wind stress.Figure 10b shows one example from the 5-day-averagedfields centered on 23 June 2000 in the model. The spa-tial map of (|�1| � |�3| )/|�1|demonstrates the alternat-

ing bands of positive and negative contribution fromthe TIW-induced perturbation currents. During thisparticular period, the effect of TIW currents on thesurface stress can be �25%–30%. Considering the al-ternating phases of the waves, the peak-to-trough dif-ference is perhaps even larger. The higher (|�1| � |�3| )/|�1| ratio (��40%) near the coast suggests that mesos-cale current variability associated with oceanic ringformation in the north Brazil Current (Johns et al.1998) can be of substantial importance to the surfacestress estimation in this region.

A large influence of the perturbation ocean currenton the surface stress estimation implies a potential

FIG. 9. Six-year time series of model surface wind stress mag-nitudes computed for the different scenarios at 2°N averaged over20° and 15°W for (a) �1 � �Cd|ua � uo| (ua � uo), (b) |�1| � |�2|in which �2 � �Cd|ua|ua, and (c) | �1| � |�3|, where �3 � �Cd|ua�uo_lowpass | (ua � uo_lowpass): ua is the atmospheric wind velocity, uo

is the ocean surface current velocity (mean � TIWs), uo_lowpass isthe low-passed surface current velocity. (d) High-pass-filtered(TIW) surface current speed (m s�1). The correlation coefficientof the TIW current speed with | �1| � |�3| in (c) is �0.8. See textfor details.


problem in those numerical ocean modeling studieswhere the QuikSCAT-derived wind stress product isprescribed at the sea surface. In reality and in theSCOAR model, TIWs induce intraseasonal variabilityin the atmospheric wind field, whereas in OGCMsforced with high-frequency wind fields TIWs occur withrandom phases and will, in general, be mismatched withspecified local surface winds. The large alteration ofsurface stress by the TIW currents suggests that, inthese forced models, the estimation of surface stressmay be significantly misestimated, leading to a possiblesource of error associated with this coupled feedback.

c. Implication of TIW-induced latent heat flux onSST

Observational studies have revealed a negative im-pact from the perturbation surface heat flux on theevolving SST of TIWs. Deser et al. (1993) found a cor-relation between SST and stratocumulus cloudinesswhere increased cloudiness over warm SST reduces in-coming solar radiation flux, thus cooling the SST. Nu-merous investigators (e.g., Thum et al. 2002; Liu et al.2000; Zhang and McPhaden 1995) have shown that in-creased latent and sensible heat flux is found over thewarm phase of TIWs due to strong coupling between

SST and winds, which dampens the growth of the TIWs.Here we examine how the perturbation latent heat fluxgenerated by TIWs compares with the zonal-mean la-tent heat flux, that is, the rectifying effect from pertur-bation heat flux to the mean SST.

In the bulk parameterization (Fairall et al. 1996), la-tent heat flux (LH) can be written as

LH � �LCHU��q, �5

where � is the density of air, L the latent heat of va-porization of water, CH the bulk exchange coefficient,U is the wind speed, and �q is the difference betweenthe specific humidity of air and the saturation specifichumidity at the temperature of the ocean surface. ThusLH is proportional to the product of U and �q. Reyn-olds averaging yields

LH̄ � �LCH�U�q � U��q�, �6

where the overbar denotes a 10° longitude runningmean and the primes denote deviations from the zonalrunning mean. Thus, zonally averaged latent heat fluxin the equatorial ocean is determined both from thezonal mean and the deviation of the product of windand humidity differences. Figure 11 shows a 6-yr time

FIG. 10. (a) Map of the ratio (%) of annual-mean(|�1| � |�2| )/|�1| .Negative values denote the reduction of the wind stress estimatedue to the presence of ocean surface currents. (b) The 5-day-averaged (centered on 23 Jun 2000) ratio, (|�1| � |�3| )/| �1| . Nega-tive values are shaded in gray and contoured in dashed lines;contour interval is 5% and the zero contour line is omitted.

FIG. 11. Six-year time series of (a) �LCHU�q and (b)�LCHU��q� at 2°N averaged over 30°–10°W in the model. Similarresults are found for different areas.


series of the mean and deviation component of latentheat flux at the representative region 2°N averagedover 30°–10°W. The time average of the mean latentheat flux at this latitude is roughly �150 W m�2. Thedeviation can reach �1%–2% of the mean, but is gen-erally small compared to the mean. This implies thatrectification from the perturbation latent heat flux ontothe heat budget in the equatorial ocean is close to zero.

Zhang and McPhaden (1995) found that a 1-Kchange in SST due to TIWs creates a latent heat fluxanomaly of �50 W m�2 in the eastern Pacific Ocean.Seo et al. (2007) found comparable values for pertur-bations of latent heat flux [34 W m�2 (1 K SST)�1] intheir eastern Pacific TIW model. The current modelagrees with these estimates in the eastern Pacific andgenerates approximately 25 W m�2 changes in latentheat flux due to the 1 K change in TIW–SST (notshown). Thum et al. (2002) demonstrate from a simplecalculation that this amount of anomaly in latent heatflux would produce �0.5°C cooling of warm water, in-dicating a negative feedback to the TIW–SST. Thepresent analysis of latent heat flux reveals, however,that, if these alternating positive and negative latentheat flux anomalies are averaged over the TIW period,a zonal cancellation makes the net contribution fromthe perturbations small compared to the mean contri-bution.

It should be emphasized that the TIWs do potentiallyrectify lower-frequency coupled variability throughtheir contribution to the large-scale SST gradients (Jo-chum and Murtugudde 2006). Accumulation of smallannual-mean perturbation heat and momentum fluxescould be important for the long-term climatic bias inSSTs and the equatorial current system in the tropicalAtlantic Ocean (JMB). This low-frequency rectificationmust be revisited in much longer coupled simulations,but the focus here is on the rectification by the high-frequency atmospheric response to TIW-induced SST.

4. Summary and discussion

Ocean–atmosphere covariability arising in the pres-ence of tropical instability waves (TIWs) was examinedusing a regionally coupled high-resolution climatemodel in the tropical Atlantic Ocean. One of the goalsof the present study was to study the impact of theatmospheric wind response on the TIWs. Two mecha-nisms by which atmospheric wind fields feed back ontoTIWs are a direct exchange of momentum and througha modification of wind stress curl.

Perturbations in the wind field are generated by un-dulating SST fronts of TIWs, which also produce a per-turbation of surface currents. It was shown that these

wind perturbations and TIW-induced currents arenegatively correlated over the TIW region. Thus, theperturbation surface winds are in the opposite directionto the surface currents, which slows down the TIW cur-rents. In the EKE equation of the TIWs, this effect is asink. At 2°N this energy sink amounts to �40% of thebarotropic conversion rate, which is the most dominantEKE source to the TIWs (JMB). If averaged over theTIW region (2°S–5°N), the wind contribution is roughly10% of the barotropic conversion term.

Perturbations in wind stress curl are generated due tothe TIW-induced SST gradient (Chelton et al. 2001).This wind stress curl generates perturbation Ekmanpumping over the TIWs. Spall (2007) showed that Ek-man pumping damps the baroclinic instability in theocean in the presence of a southerly background wind.However, the present results suggest that in the case ofAtlantic TIW Ekman pumping variability is negligiblecompared to the dynamically induced variability of up-welling. Thus, TIW-induced wind curl variations wouldnot significantly modify baroclinic instability processes.

Furthermore, Ekman currents forced by the TIW-induced wind stress anomalies are many orders of mag-nitude smaller than the TIW currents (not shown).Thus, their impact on temperature will be negligible.This indicates that the variability of SST altered by al-ready negligible TIW-induced Ekman currents is notimportant.

Overall, the atmosphere reduces the growth of TIWsby adjusting its wind variability according to the under-lying TIW–SST field. This result corroborates the pre-vious idealized modeling study by Pezzi et al. (2004),who implicitly includes these two atmospheric feedbackmechanisms in their wind stress parameterization.

In addition, the effect of surface currents on windstress magnitude is discussed. Over the large areaacross the equator in the tropical Atlantic Ocean, theocean currents, including mean and TIWs, reduce sur-face wind stress estimates, with the maximum effects of20% at 2°N, 20°W. This is because the westward SouthEquatorial Current is in the same direction as the large-scale atmospheric easterly flow (Pacanowski 1987).

In the annual mean, TIW currents only marginallyrectify the wind stress estimates due to the oscillatorycancellation. However, at any time during the activeTIW season, they can alter the local wind stressestimate by �25%–30% depending on the phase of thewaves. Alternating phases of waves indicates that thepeak-to-trough difference of surface stress may beeven larger. This implies a potential for not only gen-erating low-frequency rectification but also generatinga mismatch between the TIWs simulated in forcedocean models with prescribed observed QuikSCAT


wind stresses. The inconsistency between these TIWsand the specified wind forcing when they are in thewrong phase may induce a spurious damping orstrengthening of TIWs through the aforementionedcoupling of the ocean current and the wind stress.

In such forced model simulations with the observedlarge-scale QuikSCAT wind forcing, one way to includethe effect of coupling of wind and current would be toadd, in the prescribed large-scale QuikSCAT forcing,spatially (and/or temporally) high-pass-filtered windfields that are regressed on to the model’s SST anoma-lies by TIWs. A test of this method would be to com-pare such forced ocean simulations with fully coupledsimulations (such as with the SCOAR model). The re-sults will provide a quantitative estimation of the po-tential impact of mismatch between the specified windstress forcing and the model’s TIWs.

Finally, the rectification effect of perturbations onthe atmosphere due to TIWs is examined in terms oflatent heat flux. A Reynolds averaging of the latentheat flux equation showed that zonal canceling of per-turbation terms of wind speed and humidity differencesgives rise to only a 1%–2% difference in latent heat fluxcompared to its mean contribution. This implies that,although negative feedback from heat flux responsemay be large at any given phase of SST, when inte-grated over TIW periods the perturbation heat flux willnot significantly feed back on to the zonal-mean heatbudget of the Atlantic Ocean.

Although our results suggest that TIW-induced la-tent heat flux does not rectify the mean SST on theshort time scales, the TIWs still can operate over thelarger-scale SST gradient to modulate the horizontaland vertical temperature advection that involvesocean–atmosphere heat and momentum exchanges (Jo-chum and Murtugudde 2006; Jochum et al. 2007).Moreover, there are studies that suggest a link betweenthe interannual variability of the TIWs and the asym-metry of ENSO (e.g., Yu and Liu 2003). Long-termaccumulation of small annual-mean perturbation heatand momentum fluxes may be important for the longer-term climatic bias in SSTs and currents in the tropicalAtlantic Ocean. The potential low-frequency rectifica-tion of these apparently small feedbacks can be betterquantified in much longer simulations of the coupledhigh-resolution model, which we are currently carryingout and will report elsewhere. This study is the first ofits kind in addressing TIW feedback processes from ahigh-resolution full-physics coupled model.

Acknowledgments. The work was done during HS’svisit to NCAR during summer 2006, which was madepossible through a student fellowship of the Advanced

Study Program. This work forms a part of the Ph.D.dissertation of HS. This research was partially fundedby NOAA Grant “Impact of oceanic mesoscale vari-ability on the coupled climate” (NA17EC1483). Wegratefully acknowledge additional funding supportfrom DOE (DE-FG02-04ER63857) and NOAA(NA17RJ1231 through ECPC). The views expressedherein are those of the authors and do not necessarilyreflect the views of these agencies. (The TMI data canbe obtained from Remote Sensing Systems online athttp://www.ssmi.com.)

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Feedback of Tropical Instability-Wave-Induced Atmospheric ... · Introduction Tropical instability waves (TIWs) are generated from instabilities of equatorial zonal currents and are