The Effects of SST-Induced Surface Wind Speed and Direction Gradients on Midlatitude Surface Vorticity and Divergence

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1 15 JANUARY 2010 O N E I L L E T A L. 255 The Effets of SST-Inue Surfae Win Spee an Diretion Graients on Milatitue Surfae Vortiity an Divergene LARRY W. O NEILL Marine Meteorology Division, Naval Researh Laboratory, Monterey, California DUDLEY B. CHELTON College of Oeani an Atmospheri Sienes, an Cooperative Institute for Oeanographi Satellite Stuies, Oregon State University, Corvallis, Oregon STEVEN K. ESBENSEN College of Oeani an Atmospheri Sienes, Oregon State University, Corvallis, Oregon (Manusript reeive 2 May 2008, in final form 1 June 2009) ABSTRACT The effets of surfae win spee an iretion graients on milatitue surfae vortiity an ivergene fiels assoiate with mesosale sea surfae temperature (SST) variability having spatial sales of km are investigate using vetor win observations from the SeaWins satterometer on the Quik Satterometer (QuikSCAT) satellite an SST from the Avane Mirowave Sanning Raiometer for Earth Observing System (AMSR-E) Aqua satellite. The win SST oupling is analyze over the perio June 2002 August 2008, orresponing to the first 61 years of the AMSR-E mission. Previous stuies have shown that strong win spee graients evelop in response to persistent mesosale SST features assoiate with the Kuroshio Extension, Gulf Stream, South Atlanti, an Agulhas Return Current regions. Milatitue SST fronts also signifiantly moify surfae win iretion; the surfae win spee an iretion responses to typial SST ifferenes of about 28 48C are, on average, about 1 2 m s 21 an 48 88, respetively, over all four regions. Win spee perturbations are positively orrelate an very nearly olloate spatially with the SST perturbations. Win iretion perturbations, however, are isplae meriionally from the SST perturbations, with yloni flow polewar of warm SST an antiyloni flow polewar of ool SST. Previous observational analyses have shown that small-sale perturbations in the surfae vortiity an ivergene fiels are relate linearly to the rosswin an ownwin omponents of the SST graient, respetively. When the vortiity an ivergene fiels are analyze in urvilinear natural oorinates, the win spee ontributions to the SST-inue vortiity an ivergene epen equally on the rosswin an ownwin SST graients, respetively. SST-inue win iretion graients also signifiantly moify the vortiity an ivergene fiels, weakening the vortiity response to rosswin SST graients while enhaning the ivergene response to ownwin SST graients. 1. Introution On spatial sales spanning oean basins, sea surfae temperature (SST) perturbations are foun to be negatively orrelate with surfae win spee perturbations (e.g., Mantua et al. 1997; Okumura et al. 2001; Xie 2004). Over these broa spatial sales, large-sale atmospheri Corresponing author aress: Larry W. O Neill, Naval Researh Laboratory, 7 Grae Hopper Ave., MS2, Monterey, CA larry.oneill@nrlmry.navy.mil irulation patterns hange surfae oean temperatures through moulation of surfae heat fluxes an upper oean mixing (e.g., Cayan 1992). On smaller spatial sales between 100 an 1000 km, however, surfae win spee an SST perturbations have a strong positive orrelation in regions of large SST graients, whih our near meanering oean urrents (see review by Small et al. 2008). Contemporaneous near-global satellite measurements of surfae vetor wins an SST have shown that these small-sale features in the surfae win fiel are partiularly prevalent near large milatitue oean urrents. Previous stuies have only investigate DOI: /2009JCLI Ó 2010 Amerian Meteorologial Soiety

2 256 J O U R N A L O F C L I M A T E VOLUME 23 TABLE 1. Slopes of the linear relationships between the win stress url an rosswin SST graient (a C ) an the win stress ivergene an ownwin SST graient (a D ) liste in previous stuies over various regions in units of N m 22 per 8C. Aronyms use here inlue: National Center for Atmospheri Researh (NCAR) Community Climate System Moel 3.0 (CCSM3.0); Moel for Interisiplinary Researh on Climate 3.2 (MIROC3.2); Sripps Couple Oean Atmosphere Regional (SCOAR) moel; an Naval Researh Laboratory Couple Oean Atmosphere Mesosale Preition System (COAMPS) moel. The ratio a C /a D is shown in the rightmost olumn. Stuy Region Soure a C a D a C /a D Chelton et al. (2001) Tropial Paifi QuikSCAT TMI 38N 18S S 58S O Neill et al. (2003) Southern Oean QuikSCAT Reynols Chelton et al. (2004) Southern Oean QuikSCAT AMSR Tropial Paifi Kuroshio Gulf Stream Chelton (2005) Tropial Paifi QuikSCAT TMI O Neill et al. (2005) Agulhas QuikSCAT AMSR Maloney an Chelton (2006) Agulhas QuikSCAT AMSR ECMWF NCAR CCSM MIROC Kuroshio QuikSCAT AMSR ECMWF NCAR CCSM MIROC Seo et al. (2007) Tropial Paifi SCOAR Coastal California N N Chelton et al. (2007) California urrent system QuikSCAT AMSR Haak et al. (2008) California urrent system QuikSCAT COAMPS SST-inue hanges in win spee aross SST fronts an not win iretion. The main objetives of this stuy are (i) to etermine how small-sale SST perturbations affet both surfae win spee an iretion from 61 years of satellite observations of vetor surfae wins an SST an (ii) to etermine their umulative effets on the surfae url an ivergene fiels over the SST fronts assoiate with four milatitue oean urrents: the Kuroshio Extension in the North Paifi, the Gulf Stream in the North Atlanti, the Brazil Malvinas Confluene in the South Atlanti, an the Agulhas Return Current in the Inian Oean setor of the Southern Oean. Spatial variations in surfae win spee assoiate with small-sale SST variability evelop surfae url an ivergene perturbations with magnitues omparable to the large-sale url an ivergene (Chelton et al. 2004; O Neill et al. 2003, 2005; Chelton et al. 2007). Satellite observations of these url an ivergene perturbations are remarkably well orrelate with smallsale perturbations in the rosswin an ownwin omponents of the SST graient, respetively (Chelton et al. 2001, 2004, 2007; Chelton 2005; O Neill et al. 2003, 2005). The surfae win stress url an ivergene fiels are relate linearly to the rosswin an ownwin SST graients, respetively. These url an ivergene epenenies are simulate to varying egrees in numerial weather preiation an limate moels (Maloney an Chelton 2006; Haak et al. 2008) an in regional mesosale moels (Seo et al. 2007; Spall 2007b). In all past stuies, the url response to rosswin SST graients has been foun to be signifiantly weaker than the ivergene response to ownwin SST graients, as measure by the slopes a C an a D, respetively, of the linear statistial relations (Table 1). The ratio of these slopes a C /a D varies between about 0.4 an Aitionally, satellite observations have shown strong seasonal variability in a C an a D (O Neill et al. 2005; Maloney an Chelton 2006; O Neill et al. 2009, manusript submitte to J. Climate, hereafter OCE) an strong geographial variability between oean basins (Chelton et al. 2004; OCE) an within iniviual regions (O Neill et al. 2005). From a mesosale moeling stuy over the Gulf Stream, Spall (2007b) note that a C has a signifiant quarati epenene on the large-sale geostrophi win spee. This is shown by OCE to result

3 15 JANUARY 2010 O N E I L L E T A L. 257 from the nonlinearity between SST-inue surfae win spee an win stress perturbations. Beyon what is known about the ynamis of the near-surfae win response to small-sale SST perturbations, as isusse in setion 2, little is known about the ynamis unerlying the url an ivergene responses to SST graients. The ifferenes in the url an ivergene responses reveal an opportunity to better unerstan how the marine atmospheri bounary layer (MABL) respons to small-sale SST perturbations. In this stuy, surfae win spee an iretion are obtaine from the SeaWins satterometer onboar the Quik Satterometer (QuikSCAT) satellite an SST is obtaine from the Avane Mirowave Sanning Raiometer for Earth Observing System (EOS) (AMSR-E) Aqua satellite, as isusse in setion 3. The statistial responses of spatially high-pass filtere surfae win spee an iretion as funtions of SST are shown in setion 4. A relatively simple statistial relation is foun between surfae win spee an SST espite the ompliate fore balanes involve in the SST-inue MABL response esribe by previous stuies. In setion 5, the QuikSCAT vortiity an ivergene of the surfae win fiel are shown to epen on the rosswin an ownwin SST graients in a manner analogous to the epenenies of the win stress url an ivergene onsiere in our previous stuies. While the vortiity an ivergene responses to SST graients have been interprete previously in terms of SST effets on surfae win stress magnitue (or win spee), we show that SST also moifies the surfae win iretion, thus also ontributing to SST-inue hanges in the surfae vortiity an ivergene. These SST-inue moifiations of win iretion are shown to be responsible for the iffering vortiity an ivergene responses to SST. We lose in setion 6 with a isussion of the impliations of the results of this stuy for ouple mesosale win SST interations. 2. Dynamial explanations for mesosale win SST oupling Many observational an moeling stuies have now been unertaken to better unerstan the MABL response to SST perturbations over various regions of the Worl Oean. The response of surfae wins to mesosale SST perturbations is the ulmination of ajustment proesses extening throughout the epth of the MABL an appears to be ontrolle mainly by moifiation of the surfae heat fluxes as air flows aross SST fronts. Surfae heat fluxes are enhane or suppresse epening on whether the flow is from ol to warm water or vie versa. Cross-frontal surfae heating perturbations proue hanges in the MABL hyrostati pressure graients an to the vertial turbulent stress ivergene in the MABL as esribe below, ultimately leaing to hanges in near-surfae wins ouple to the mesosale SST perturbations. Aross SST fronts, variations in surfae heating ause ross-frontal pressure graients near the surfae sine a ooler MABL over ooler water forms higher surfae pressures relative to a warmer MABL over warmer water. Thermally inue pressure graients so forme an therefore aelerate near-surfae flow aross SST isotherms from ooler to warmer water an vie versa. Using an analytial moel of the bounary layer, Linzen an Nigam (1987) attribute aeleration of ross-equatorial surfae flow north of the equatorial ol tongue in the eastern tropial Paifi primarily to thermally inue pressure graients assoiate with the ol tongue meriional SST graient. Even though some of the assumptions of their analytial moel are not generally vali (e.g., Battisti et al. 1999; Stevens et al. 2002; Small et al. 2003), SST-inue pressure graients are inee strong ontributors to the SST-inue surfae win response (e.g., Wai an Stage 1989; Warner et al. 1990; Small et al. 2003; Cronin et al. 2003; Mahrt et al. 2004; Bourras et al. 2004; Song et al. 2004; Small et al. 2005b; Song et al. 2006). Using mesosale numerial simulations over the equatorial Paifi, Small et al. (2003) showe that near-surfae pressure perturbations form in response to SST-inue MABL air temperature variations, whih are governe thermoynamially by a balane between horizontal temperature avetion an surfae sensible heat fluxes. From surfae pressure observations over the equatorial Paifi, Cronin et al. (2003) have shown that SST-inue surfae pressure graient perturbations assoiate with the northern equatorial ol tongue are of a magnitue similar to those generate by mesosale moel simulations. Hashizume et al. (2002) have also suggeste that eepening an shoaling of the MABL assoiate with ross-frontal turbulent mixing variations ounterats this thermoynami ontribution to the SST-inue surfae pressure variations in what has been referre to as a bakpressure effet. Finally, while MABL pressure graients ontribute to near-surfae flow aeleration perpeniular to SST isotherms, it is not lear how they ontribute to the generation of near-surfae vortiity as air blows parallel to SST isotherms, a feature generally observe in satterometer win fiels globally. Wallae et al. (1989) an Hayes et al. (1989) argue that vertial turbulent mixing of momentum from aloft to the surfae was more onsistent with the hanges in vertial win shear an the aeleration of surfae wins ourring aross the northern ege of the equatorial

4 258 J O U R N A L O F C L I M A T E VOLUME 23 Paifi ol tongue than with thermally inue pressure graients. Earlier airraft observations over the north wall of the Gulf Stream by Sweet et al. (1981) also showe that turbulent mixing of momentum from aloft to the surfae also playe a signifiant role in near-surfae win spee variations. With this mehanism, SST-inue surfae heating moifies the stati stability of the bounary layer, enhaning the vertial turbulent mixing of momentum as air blows from ool to warm water an reuing it as air blows from warm to ool water. Observations of the near-surfae vertial turbulent momentum flux throughout the worl s oeans have generally shown onsierable variation upon rossing SST fronts an have supporte this hypothesis (Mey an Walker 1990; Freihe et al. 1991; Bon 1992; Jury 1994; Rouault an Lutjeharms 2000; Mahrt et al. 2004; e Szoeke et al. 2005; Tokinaga et al. 2006). Moeling stuies of the surfae win response to mesosale SST perturbations have been less onsistent about the role that the vertial turbulent stress ivergene plays in the SST-inue surfae win response. Some investigators fin a signifiant role (Wai an Stage 1989; e Szoeke an Bretherton 2004; Bourras et al. 2004; Song et al. 2004; Skyllingsta et al. 2006; Thum 2006; Song et al. 2009; O Neill et al. 2010) while others foun less signifiant roles (Small et al. 2003; Bourras et al. 2004; Small et al. 2005a,b; Song et al. 2006; Samelson et al. 2006; Spall 2007b). Aitionally, the ontribution of surfae oean urrents to the surfae stress may play a small but nonnegligible role in the near-surfae vertial turbulent stress ivergene (Song et al. 2006; Liu et al. 2007). Iealize large-ey simulations of the flow aross sharp SST fronts by Skyllingsta et al. (2006) showe that on spatial sales of 1 20 km, whih are somewhat smaller than onsiere here, near-surfae win spee variations are influene preominantly by SST-inue ross-frontal variations in the vertial turbulent mixing of momentum, onsistent with the Wallae et al. (1989) an Hayes et al. (1989) hypotheses. Finally, weak oupling of surfae wins to SST in the European Centre for Meium-Range Weather Foreasts (ECMWF) moel over the Agulhas Return Current (Maloney an Chelton 2006) was shown by Song et al. (2009) to be attributable primarily to a weak response of the parameterize vertial turbulent stress ivergene to SSTinue surfae heating perturbations. Small et al. (2005a) envisione a quite ifferent role of the vertial turbulent stress ivergene in a numerial simulation of the near-surfae win response over the eastern tropial Paifi. There, it was foun that pressure graients aelerate the near-surfae flow aross the ol tongue SST front, an after some istane, the vertial turbulent stress ivergene ate as a fritional rag on this pressure-riven flow. In this pressure-rag mehanism, turbulene ats to reue the surfae wins in an opposite manner to that hypothesize by Wallae et al. (1989) an Hayes et al. (1989). This pressure-rag mehanism was foun to operate in a numerial simulation over the Agulhas Return Current (O Neill et al. 2010), but only above about 150 m from the surfae; below this level, the near-surfae wins were influene by the turbulent mixing of momentum in aorane with the Wallae et al. (1989) an Hayes et al. (1989) mehanism. Samelson et al. (2006) argue that hanges in bounary layer epth somewhat ownwin of the sharpest SST graients, rather than the vertial reistribution of momentum, oul at to hange the surfae stress. This mehanism ats through a balane of a fixe large-sale pressure graient an the vertial turbulent stress ivergene integrate vertially over the epth of the bounary layer suh that the ratio of surfae stress to bounary layer height t/h is equal to a fixe large-sale pressure graient integrate over the epth of the bounary layer. This balane was foun to be onsistent with the ross-frontal hanges in surfae stress an bounary layer height away from the steepest SST graients in the two-imensional moel simulation of Spall (2007b). This balane assumes that the SST-inue responses of the vertial turbulent mixing of momentum, thermally inue pressure graients, an horizontal avetion are not signifiant terms in the MABL momentum buget in regions iretly over the sharpest SST fronts (see etaile isussion in Small et al. 2008). At milatitues, Coriolis aelerations have been shown to be important to the response of the surfae wins to small-sale SST perturbations (e.g., Wai an Stage 1989; Bourras et al. 2004; Thum 2006; Song et al. 2006; Spall 2007b; O Neill et al. 2010). Over a single SST front, Spall (2007b) has foun that SST-inue turbulent mixing perturbations inue Coriolis aelerations analogous to an inertially riven lee wave. O Neill et al. (2010) has foun eviene of a similar mehanism in a simulation over a part of the Southern Oean. The strong large-sale mean win spees typially foun over milatitue oean fronts also lea to signifiant horizontal avetive aelerations that strongly influene the near-surfae momentum buget (Song et al. 2006; Thum 2006; Spall 2007b; O Neill et al. 2010). Some ebate remains as to the physial mehanisms involve in the oupling between surfae wins an mesosale SST perturbations. It is beoming lear, however, that both pressure graients an the turbulent mixing of momentum are involve signifiantly in the response. There are also likely signifiant regional ifferenes in the large-sale atmospheri foring that may alter the fore balane involve in the surfae win

5 15 JANUARY 2010 O N E I L L E T A L. 259 response. We show below that there are omparatively simple statistial relationships between the surfae wins an SST espite the rather ompliate etails of these physial mehanisms. 3. Desription of satellite observations an methos This stuy utilizes monthly-average surfae vetor win observations from the QuikSCAT satterometer an SST from the AMSR-E over the 75-month perio June 2002 August 2008, oiniing with the first 61 years of the AMSR-E geophysial observational ata reor that began 1 June Eah of these atasets is summarize in this setion. a. QuikSCAT win fiels In nonpreipitating onitions, satterometers infer surfae vetor wins over water from mirowave raar measurements of small-sale surfae roughness ause by surfae win stress. For lak of abunant iret surfae stress measurements, satterometer measurements of mirowave raar baksatter are alibrate to buoy anemometer measurements of the so-alle equivalent neutral stability win at 10 m, whih is the 10-m win that woul be uniquely relate to the observe surfae win stress if the atmosphere were neutrally stratifie (Liu an Tang 1996). The relation between the equivalent neutral stability win vetor u an the surfae win stress vetor t is t 5 r 0 C D N Vu, where r 0 is the surfae air ensity, V is the magnitue of u, an C D N is the neutral stability rag oeffiient. The omputations throughout this paper using QuikSCAT wins are base on 10-m equivalent neutral stability wins. On average, anemometer measurements of the 10-m win spee are about 0.2 m s 21 lower than the orresponing neutral-stability win spee at 10 m (Mears et al. 2001; see also Fig. 16 of Chelton an Freilih 2005) beause the atmospheri surfae layer is, on average, slightly unstable over all oeans. Through omparisons with high-quality buoy anemometer measurements, QuikSCAT win spee measurement errors have been estimate to be about 1.7 m s 21 (Chelton an Freilih 2005). The win iretion auray improves with inreasing win spee; for win spees greater than about 5 m s 21, the iretion auray of iniviual win measurements is better than 158 (see Fig. 8 in Chelton an Freilih 2005). Aitionally, there is no eviene of SST-epenent measurement biases in the QuikSCAT win observations (Chelton et al. 2001; Ebuhi et al. 2002). The spatial erivatives of win omponents, win spee, an win iretion analyze in this stuy were ompute in-swath before interpolating to a regular spatial gri. This avois ompliations arising from the estimation of spatial erivatives near swath eges where entere first-ifferene estimates of erivatives are ompute using measurements from neighboring swaths separate in time by several hours or more. The various win an erivative win fiels of interest in this stuy were then onstrute on a latitue by longitue spatial gri by fitting in-swath measurements to a quarati surfae using loally weighte regression ( loess smoothing; Clevelan an Devlin 1988) with a half span of 80 km. Base on the filter transfer funtion of the loess smoother (Shlax et al. 2001; Chelton an Shlax 2003), the resulting grie fiels have a spatial resolution analogous to that of approximately 50-km blok averages. The spatial erivative fiels were foun at eah gri point iretly from the regression oeffiients of the quarati surfae. The win fiels were then average at monthly intervals from the grie swath ata. b. AMSR-E SST fiels The etaile results of this stuy woul not be possible without the near-all-weather mirowave observations of SST over mile- an high-latitue regions provie by the AMSR-E sine June 2002 (Chelton an Wentz 2005). The main avantage of mirowave measurements of SST is the ability to measure SST through nonpreipitating lous, whih are essentially transparent to mirowave raiation. Clou over generally obsures the milatitue oean regions of interest in this stuy more than 70% of the time (Chelton an Wentz 2005). Large regions of missing ata often our in SST fiels onstrute from infrare satellite measurements over the sharpest oean fronts an eies where strong oean atmosphere interations are expete to our (see, e.g., Fig. 6 of Chelton an Wentz 2005). Inee, stratoumulus an umulus lou bans often form over sharp SST fronts as a onsequene of some of the same MABL ajustment proesses affeting MABL wins of interest in this stuy (e.g., Norris an Iaobellis 2005). While SST measurements by the Tropial Rainfall Measuring Mission (TRMM) Mirowave Imager (TMI) have been available sine Deember 1997 an thus enompass the entire QuikSCAT mission, they are only mae equatorwar of 408 latitue, leaving most of the milatitue regions of interest in this analysis unsample. The AMSR-E measures horizontally an vertially polarize brightness temperatures at six mirowave frequenies aross a 1450-km swath.from these 12 mirowave brightness temperatures, SST is estimate over most of the global oeans using a physially base statistial regression algorithm (Wentz an Meissner 2000). The footprint size of AMSR-E measurements of SST is 56 km an the rms auray of iniviual SST measurements is

6 260 J O U R N A L O F C L I M A T E VOLUME 23 about 0.48C (Chelton an Wentz 2005). The SST fiels were grie onto the same gri as the QuikSCAT surfae win fiels an then average at monthly intervals.. Crosswin an ownwin SST graient omputations As isusse in the introution, previous stuies have shown that the win stress url an ivergene fiels are foun to be relate linearly to the rosswin an ownwin omponents of the SST graient, respetively. Crosswin an ownwin graients in this stuy were ompute within eah QuikSCAT measurement swath using urvilinear natural oorinates (s, n), where s an n are loal along-win an rosswin oorinates, respetively (e.g., Haltiner an Martin 1957; Holton 1992). The unit vetor ^s is in the same iretion as u. The positive unit vetor ^n points 908 ounterlokwise relative to ^s. The rosswin an ownwin omponents of the SST fiel T(x, y) in natural oorinates are ompute from Cartesian erivatives by T T T 5 sin 1 os x y T an T T 5 os 1 sin x y, (1) where (x, y) are the zonal an meriional Cartesian oorinates, respetively, an is the ounterlokwise surfae win iretion relative to the x axis. Crosswin an ownwin SST graients were ompute here on a swath-by-swath basis by ombining win measurements from eah QuikSCAT swath with SST graients ompute from grie 3-ay average AMSR-E SST fiels entere on eah ay of the QuikSCAT measurement swath. Swaths of rosswin an ownwin SST graients were then average at monthly intervals. This proeure minimizes unertainties assoiate with omputing the nonlinear rosswin an ownwin SST graients from win an SST measurements that are not olloate spatially an temporally.. Spatial high-pass filtering SST-inue mesosale win variability was isolate by removing large-sale spatial variability using a multiimensional loess smoothing funtion with half-power filter utoffs of 108 latitue longitue (Clevelan an Devlin 1988). This filtering effetively removes the large-sale omponents of the win an SST fiels that are unrelate to the win SST oupling of interest here. Win an SST fiels spatially high-pass filtere in this way are hereafter referre to as perturbation fiels. To isolate the SST influene on surfae wins that is of interest here, the effets of synopti weather variability were mitigate by using monthly-average win an SST fiels. It is note that this spatial filtering was applie on all variables after omputations involving the win an SST fiels were performe, inluing the nonlinear rosswin an ownwin graient omputations. This is preferable to omputing the rosswin an ownwin graient quantities from monthly-average fiels Observations of SST-inue surfae win response a. Surfae win spee response to SST Maps of the QuikSCAT perturbation surfae win spee an the AMSR-E SST fiels salar-average over the 75-month analysis perio are shown in Fig. 1 for eah of the four regions onsiere here. Large horizontal variations in surfae win spee our near meanering SST fronts, with stronger win spees over warmer water an weaker win spees over ooler water. Typially, surfae win spee variations of more than 1 2 m s 21 aompany SST variations of about 28 48C over rossfrontal istanes of O(100 km). This is an appreiable fration of the unfiltere salar-average win spees in these regions (Fig. 2), whih are typially 8 13 m s 21 in these long-term time averages. For the time-average perturbation fiels, the spatial ross-orrelation between the perturbation win spee an the perturbation SST varies between 0.7 over the Kuroshio to 0.85 over the South Atlanti (Table 2). In aition to the quasi-stationary ouple patterns in the perturbation win an SST fiels apparent in these long-term time-average maps, there is also signifiant ouple variability assoiate with transient SST features evient from satellite ata over the Kuroshio (e.g., Nonaka an Xie 2003), the Gulf Stream (e.g., Park an Cornillon 2002; Park et al. 2006), an all four milatitue regions onsiere here (White an Annis 2003). The win SST oupling in the Kuroshio region is muh more apparent uring the boreal wintertime 1 Crosswin an ownwin graients of SST in our previous stuies (Chelton et al. 2001, 2004; O Neill et al. 2003, 2005) were ompute from grie, vetor-average win stress an SST graient omponents rather than being ompute on a swath-byswath basis an then averaging, whih is more aurate beause of the nonlinearity of these quantities. As a result, the SST-inue win response in those stuies was somewhat unerestimate from those obtaine from the more aurately ompute quantities use here. Aitionally, the efinition of the rosswin SST graient use in those stuies ($T 3 ^u) ^k is equal to 2 T/ an the ownwin SST graient $T ^u is equal to T/, where ^u is a unit vetor in the iretion of the surfae win vetor an ^k is a unit vetor in the vertial iretion.

7 15 JANUARY 2010 O N E I L L E T A L. 261 FIG. 1. Maps of the perturbation QuikSCAT win spee (olors) an AMSR-E SST (ontours) salar-average over the perio June 2002 August 2008 for the four regions onsiere in this stuy. The ontour interval for the perturbation SST is 0.58C, an the zero ontour has been omitte for larity. Soli an ashe ontours orrespon to positive an negative values, respetively. The spatial high-pass filter removes spatial variability with wavelengths longer than 208 longitue latitue, as isusse in the text. (e.g., Nonaka an Xie 2003; OCE) an is assoiate with strong seasonality of the SST fronts in this region (e.g., Nonaka an Xie 2003). The mesosale response of the win spee to SST is quantifie statistially by bin-averaging monthly averages of the perturbation QuikSCAT win spee as a funtion of the perturbation AMSR-E SST over the 75-month analysis perio (Fig. 3). Win spee perturbations are relate linearly to, an orrelate positively with, mesosale SST perturbations over all four regions. The relationship between the monthly-average spatially highpass filtere win spee V9 an SST T9 an thus be expresse empirially as V95a y T9, (2) where a y is the least squares estimate of the slope of these linear relations an represents the hange in win spee per unit hange in SST (i.e., a y 5 V9/ T9) an the primes hereafter represent spatially high-pass filtere fiels. Notably, a y varies by nearly a fator of 2 geographially, from 0.27 m s 21 per 8C over the Gulf Stream to 0.49 m s 21 per 8C over the Agulhas Return Current (see Table 2). Aitionally, a y is muh larger in the two Southern Hemisphere regions ompare to those in the Northern Hemisphere. The larger error bars at large perturbation SST magnitues in Fig. 3 are ue to the smaller numbers of samples in these bins. This is partiularly aute over the Kuroshio, where the monthlyaverage SST perturbations ten, on average, to be smaller in magnitue than in the other three regions. The geographial ifferenes in a y between the four regions are likely ue to geographi ifferenes in the vertial struture of the bounary layer an large-sale foring. Seasonality of a y is investigate from 51 years of satellite ata over these four regions (an the eastern tropial Paifi) in OCE. Finally, we note that for SST perturbations warmer than about 1.58, there is a subtle flattening of the binaverage V9 relative to the linear fit, partiularly over the South Atlanti an Agulhas Return Current regions. Interestingly, this flattening oes not our over ool SST perturbations. This ifferene between the binaverage V9 an the linear fit is less than about 0.25 m s 21, an there are very few ata points in these outer bins, as shown by the histograms in Fig. 3. Beause this flattening

8 262 J O U R N A L O F C L I M A T E VOLUME 23 FIG. 2. Maps of the unfiltere QuikSCAT win spee (olors) an AMSR-E SST (ontours) salar-average over the perio June 2002 August The SST ontour interval is 28C. of V9 is relatively small an affets only a very small perentage of the observations, it oes not signifiantly affet the analysis presente here. This observation is urrently the subjet of ongoing analysis. b. Win iretion response to SST The win iretion over these four regions is shown in Fig. 4 by the streamlines of the vetor-average surfae win from QuikSCAT for the 75-month perio onsiere here. The surfae flow in all four regions has a strong westerly omponent, harateristi of typial milatitue surfae flow. The flow immeiately ownstream of the Asian an North Amerian ontinents has a signifiant northerly omponent before graually turning northwar far offshore. Over the Southern Hemisphere regions, the flow is westerly polewar of the large-sale subtropial antiylones loate near S. For quantitative purposes, it is esirable here to onsier win iretion perturbations analogous to the spatially high-pass filtere win spee perturbations investigate in setion 4a. However, salar win iretion annot be spatially high-pass filtere in the same manner as win spee in regions straling absolute jumps in win iretion exeeing 3608 an where the win spee approahes zero, in whih ase the win iretion beomes unefine. Both ases our intermittently in eah of the four regions uner onsieration. To avoi these iffiulties, mesosale win iretion perturbations are efine here as the ounterlokwise angle between the unfiltere u an the spatially low-pass filtere ~u, where the tile represents spatial low-pass filtering. These win iretion perturbations were ompute from vetoraverage win omponents at monthly intervals only at points where the magnitue of the monthly vetoraverage win spee exeee 1 m s 21. Spatial maps of the so-efine mesosale win iretion perturbations salar-average over the 75-month analysis perio are shown in Fig. 5 along with ontours of the TABLE 2. The (left) oupling oeffiient a y an (right) spatial orrelation oeffiient ompute from the monthly-average perturbation QuikSCAT win spee an AMSR-E SST fiels. a y [m s 21 (8C) 21 ] Correlation oeffiient Kuroshio Gulf Stream South Atlanti Agulhas

9 15 JANUARY 2010 O N E I L L E T A L. 263 FIG. 3. Binne satterplots of the spatially high-pass filtere QuikSCAT win spee (V9) as a funtion of the spatially high-pass filtere AMSR-E SST (T9). The bin averages were ompute from monthly-average QuikSCAT win an AMSR-E SST fiels over the 75-month analysis perio using all available ata points in the regions enlose in Figs. 1 an 2. The points an error bars represent the means an stanar eviations within eah bin, respetively, an the ashe lines are linear least squares fits to the means within eah bin. Below eah satterplot, a histogram of the spatially high-pass filtere AMSR-E SST is inlue for referene. AMSR-E perturbation SST. Perhaps the most striking feature of these win iretion perturbations is the pronoune meriional isplaement of the win iretion perturbations relative to those of SST. In the Northern Hemisphere, negative win iretion perturbations are shifte north of warm SST perturbations an positive win iretion perturbations are shifte north of ool SST perturbations. Conversely, in the Southern Hemisphere, positive win iretion perturbations are shifte south of warm SST perturbations an negative win iretion perturbations are shifte south of ool SST perturbations. Meriional isplaements of the win iretion perturbations relative to those of SST that are qualitatively evient in Fig. 5 prelue the use of simple binne averages to statistially quantify the relationship between win iretion an SST suh as was performe with the win spee perturbations in setion 4a (Fig. 3). Statistial relationships between the win iretion an SST perturbations an nonetheless be obtaine here through ross-spetral analysis of the win iretion an SST perturbations in the meriional wavenumber omain. Estimates of ross-spetral statistis (square oherene, transfer funtion, an phase spetra as funtions of meriional wavenumber) were ompute at monthly intervals along ontinuous meriional segments within eah of the four regions an then ensemble average over all 75 months an segments (Fig. 6). The square oherene is largest over the South Atlanti an Agulhas Return Current, where perturbation SST variability aounts for 10% 15% of the meriional variane in the perturbation win iretion. Over the Gulf Stream an Kuroshio, the square oherene is below Win iretion perturbations are therefore less well orrelate with SST ompare with win spee. The transfer funtion represents an estimate of the oupling oeffiient between the perturbation win iretion

10 264 JOURNAL OF CLIMATE VOLUME 23 FIG. 4. Maps of the unfiltere AMSR-E SST (olors) salar-average over the perio June 2002 August 2008 for the four regions onsiere in this stuy. Overlai are selet streamlines of the surfae flow ompute from the 75-month vetor-average QuikSCAT wins, where the arrows iniate flow iretion. an SST as a funtion of meriional wavenumber. From the transfer funtion in Fig. 6, the linear responses of the win iretion perturbations are roughly 28 per egree Celsius hange in perturbation SST over all four regions an vary little with meriional wavenumber. SSTinue win iretion perturbations are thus about for a 28 48C hange in perturbation SST, whih is onsistent with the magnitue of the win iretion perturbations evient in Fig. 5. The meriional phase spetrum is a measure of the meriional phase ifferene as a funtion of meriional wavenumber. Over all four regions, the phase spetra vary approximately linearly with wavenumber, iniative of a onstant meriional isplaement between the win iretion an SST perturbations. The meriional isplaement L0 of the win iretion perturbations relative to the SST perturbations estimate from the slope of the phase spetra in Fig. 6 is polewar about 18 latitue over all four regions, onsistent with the spatial lags evient visually in Fig. 5. The influene of SST on win iretion has been shown qualitatively from previous ase stuies over the Gulf Stream using mesosale atmospheri moels (Song et al. 2006; Spall 2007b) an satterometer observations of Gulf Stream rings (Park et al. 2006) an over the Southern Oean from moel simulations (Thum 2006; O Neill et al. 2010) an airraft observations (e.g., Jury 1994). The results in these stuies are onsistent with the results shown here base on 75 months of QuikSCAT win an AMSR-E SST observations. These observations of the SST-inue win iretion perturbations show that 1) win iretion perturbations are shifte polewar by about 18 latitue relative to the SST perturbations an 2) in the Northern (Southern) Hemisphere, warm SST perturbations inue negative (positive) win iretion perturbations an ool SST perturbations inue positive (negative) win iretion perturbations; the magnitue of these win iretion perturbations is about 28 per egree Celsius hange in perturbation SST over all four regions. The win vetor responses to meaners in SST fronts are summarize shematially in Fig. 7 for eah hemisphere. For illustrative purposes, the meriional isplaement of the win iretion perturbations relative to the SST front are not shown here beause they are small relative to the overall meriional extent of the SST perturbations, whih is typially latitue. Note that for surfae flow from ool to warm SST, the surfae wins turn antiylonially, whereas for surfae flow

11 15 JANUARY O NEILL ET AL. FIG. 5. As in Fig. 1, but for the QuikSCAT perturbation win iretion salar average over the perio June 2002 August As isusse in the text, win iretion perturbations are efine here as the ounterlokwise angle between the unfiltere an spatially low-pass filtere surfae win vetors. from warm to ool SST, the surfae wins turn ylonially.2 Although the oupling between win iretion an SST is weaker than the oupling between win spee an SST, it nonetheless has important onsequenes for the surfae vortiity an ivergene fiels, as will be isusse below. Small hanges in win iretion over short istanes proue relatively large vortiity an ivergene perturbations, as emonstrate below. 5. SST-inue variability in the surfae vortiity an ivergene fiels The separate effets of spatial graients in win spee an iretion on the vortiity an ivergene fiels are asertaine by expressing the vortiity an ivergene in urvilinear natural oorinates (e.g., Haltiner an Martin 1957): V V, (3) $ 3 u9 5 2 Antiyloni rotation is lokwise in the Northern Hemisphere an ounterlokwise in the Southern Hemisphere. Cyloni rotation is the opposite of this. V V, $ u9 5 (4) where (s, n) are the loal ownwin an rosswin oorinates, respetively. Equation (3) partitions the perturbation vortiity fiel3 into the ifferene between the loal rosswin spee graient an a term relate to the loal ownwin graient in flow iretion. Likewise, Eq. (4) partitions the perturbation ivergene fiel into the sum of the ownwin spee graient an a term relate to the rosswin graient in flow iretion. The iretion graient term in the vortiity is relate to the raius of urvature of surfae streamlines, whereas the iretion graient term in the ivergene is relate to spreaing or ontrating of streamlines in the rosswin iretion, whih is often referre to as the iffluent teneny (Haltiner an Martin 1957). Deomposing the vortiity an ivergene in this manner allows investigation of the separate effets of lateral shear an ownwin 3 The horizontal vortiity shoul be expresse formally as ^ The expression $ 3 u is use as shorthan for this to ($ 3 u) k. simplify the mathematial notation throughout the rest of this analysis.

12 266 J O U R N A L O F C L I M A T E VOLUME 23 FIG. 6. Cross-spetral statistis of the perturbation win iretion epenene on the perturbation SST as a funtion of meriional wavenumber: (top) square oherene, (mile) transfer funtion, an (bottom) phase spetra. Only ross-spetral estimates at wavenumbers with square oherenes above the 95% onfiene level are shown. The ashe lines in the phase spetra plots are linear least squares fits of the phase estimates with slopes as iniate. These are use to ompute estimates of the meriional isplaement L 0 between win iretion an SST perturbations, whih are iniate in eah panel; the units of L 0 shown are in egrees latitue. rotation on the vortiity an the separate effets of ownwin aeleration an rosswin rotation on the ivergene. Crosswin an ownwin win spee graients were ompute in-swath using V 9 V V 9 5 sin 1 os an x y V 9 V V 9. 5 os 1 sin x y

13 15 JANUARY 2010 O N E I L L E T A L. 267 FIG. 7. Summary shemati of the vetor win response to meaners along an extratropial SST front, represente here by the soli urves, as eue from the win spee an iretion epenenies on SST. Whereas the win spee response to SST (as represente by the relative length of the vetors) is the same for both hemispheres, the win iretion response to SST (as represente by the relative turning of the vetors) iffers in sign between the Northern an Southern Hemispheres. The rosswin an ownwin iretion graients were ompute from the grie vortiity, ivergene, an spee graient fiels using V 9 V 9 5 $ u an V 9 V 9. 5 $ 3 u 1 a. Spatial graients of perturbation win spee an SST From the linear statistial relationship between V9 an T9 expresse by Eq. (2), it follows that rosswin an ownwin graients of win spee shoul epen, respetively, on the rosswin an ownwin omponents of the SST graient fiel suh that V 9 5 a sp T 9 an (5) V 9 sp T 9, 5 a (6) where a sp an a sp are the oupling oeffiients for the spee graient responses to the SST graients. The QuikSCAT rosswin an ownwin spee graient omponents are inee relate linearly to the rosswin an ownwin SST graient omponents, respetively, for the 75-month perio of interest here (Fig. 8). Moreover, within eah region a sp an a sp are nearly equal to a y from Fig. 3. The salar win spee an spee graient responses to mesosale SST perturbations therefore appear to be manifestations of the same physial mehanisms. This strong oupling between the rosswin an ownwin spee an SST graients is further illustrate in the maps of the perturbation rosswin an ownwin spee an SST graients average over the 75-month perio (Fig. 9). The orresponing rossorrelation oeffiients between these time-average fiels are shown in Table 3; they are omparable to those of the win spee an SST perturbations presente in Table 2 for the Southern Hemisphere, while being somewhat weaker in the Northern Hemisphere. Note that in the ore of the Gulf Stream region near 378N, 708W, there is little signal in the ownwin spee graients even though the ownwin SST graients are strong. This may be ue to the effets of the strong Gulf Stream oean surfae urrents on the satterometer wins, as argue in Fig. 5 of Chelton et al. (2004). The linear relationships between the perturbation win spee an SST fiels an be investigate further by expressing the perturbation rosswin an ownwin omponents of the SST graient as T 9 5 MT sinu9 an T 9 5 MT osu9, (7)

14 268 J O U R N A L O F C L I M A T E VOLUME 23 FIG. 8. As in Fig. 3, but for the QuikSCAT perturbation rosswin spee graient ( V/)9 binne as a funtion of the rosswin SST graient ( T/)9 (blak) an the QuikSCAT perturbation ownwin spee graient ( V/)9 binne as a funtion of the ownwin SST graient ( T/)9 (gray). where the perturbation SST graient magnitue M T an the angle u9 are efine suh that sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T 9 2 M T 5 1 T 9 2 an u95 tan 1 ( T/) 9 ( T/)9. (8) Geometrially, u9 losely approximates the angle between the surfae streamlines of the unfiltere surfae wins an the perturbation SST graient vetor $T9 (justifiation of this physial interpretation of u9 is given in the appenix). From onsieration of the simple linear relationship between the perturbation win spee an SST in Eq. (2), the largest ownwin spee graients shoul our as surfae wins blow aross perturbation SST isotherms suh that the win spee inreases as wins blow from ool to warm water when u9 508, resulting in ( V/)9.0 in aor with Eq. (6), an ereases as wins blow from warm to ool water when u , resulting in ( V/)9,0. Likewise, the largest rosswin spee graients shoul our as the surfae wins blow along perturbation SST isotherms (when u ). The angular epenenies of the perturbation rosswin an ownwin spee graients on u9 are shown in Fig. 10. The rosswin an ownwin spee graients losely follow sine an osine funtions, respetively, of the angle u9, in agreement with the hypothesize epenenies relating the win spee graients to the orientation of the surfae streamlines relative to the perturbation SST isotherms. Close inspetion of Fig. 10 reveals small but onsistent phase shifts from the expete pure osine urves. From these statistial results, we may thus express the rosswin an ownwin spee graients as V 9 5 a sp M T sin(u91f sp ) an (9) V 9 sp 5 a M T os(u91fsp ), (10) where a sp an a sp are the slopes of the spee graient responses to the SST graients shown in Fig. 8 an f sp

15 15 JANUARY 2010 O NEILL ET AL. 269 FIG. 9. (top maps in eah panel) The perturbation rosswin spee graient (olors) overlai with ontours of the rosswin SST graient. (bottom maps in eah panel) The perturbation ownwin spee graient (olors) overlai with ontours of the ownwin SST graient. The ata in eah map were average over the 75-month perio June 2002 August The ontour interval for the perturbation rosswin an ownwin SST graients is 0.28C per 100 km, an the zero ontour has been omitte for larity. Soli an ashe ontours orrespon to positive an negative values of the SST graient, respetively. sp an f are the phase shifts of the sinusoial responses of the spee graients to u9 shown in Fig. 10 (positive for ounterlokwise rotation). The values of the amplitues an phase shifts are shown in Table 4. Within eah sp an a are nearly equal. Note that fsp is region, asp sp essentially 08 over all four regions whereas a is with opposing signs between hemispheres. b. SST-inue spee an iretion graient effets on vortiity an ivergene The perturbation vortiity an ivergene fiels binne as funtions of the perturbation rosswin an ownwin SST graients, respetively, are shown in Fig. 11. The perturbation vortiity an ivergene fiels are highly orrelate with small-sale perturbations in the SST graient fiel, as emonstrate in our previous stuies using the win stress url an ivergene fiels (Chelton et al. 2001, 2004, 2007; O Neill et al. 2003, 2005). To emphasize the ifferene between the vortiity an ivergene responses, an for onsisteny with our previous stuies, the vortiity is binne as a funtion of the negative rosswin SST graient 2( T/)9 in Fig. 11. In agreement with these previous stuies shown in Table 1, the magnitue of the slope of the ivergene response to ownwin SST graients is signifiantly larger than that of the vortiity response to rosswin SST graients. Aitionally, the variability within eah bin, as represente by the stanar eviation within eah bin, is muh smaller for the spee graient omponents in Fig. 8 than for the vortiity an ivergene in Fig. 11. This is eviently beause ontributions of the SST-inue win iretion responses to the vortiity an ivergene are noisier than the win spee responses. Given the results of setion 3a an Eqs. (3) an (4), if the surfae vortiity an ivergene were epenent only on the rosswin an ownwin spee graients, respetively, then the slopes of the straight line fits in Fig. 11 shoul be equal in magnitue but opposite in sign. Eviently, the iretion graient terms in Eqs. (3) an (4) reue the overall vortiity responses to rosswin

16 270 J O U R N A L O F C L I M A T E VOLUME 23 TABLE 3. Cross-orrelation oeffiients between the various perturbation erivative win fiels an the perturbation rosswin an ownwin SST graient omponents as iniate. These orrelation oeffiients were ompute from the erivative win an SST fiels average over the 75-month analysis perio at monthly intervals. Kuroshio Gulf Stream South Atlanti Agulhas $ 3 u9 an T $ u9 an T V 9 T 9 an V 9 T 9 an V 9 T 9 an V 9 T 9 an SST graients an enhane the ivergene responses to ownwin SST graients. This point is aresse in etail in setion 4. Besies these ifferenes, there are signifiant ifferenes in the vortiity an ivergene epenenies on u9 (Fig. 12) from that expete solely from onsieration of SST-inue win spee perturbations. In our previous work, we hypothesize that the surfae url shoul epen on the sine of u9 whereas the ivergene shoul epen on the osine of u9. Inspetion of the vortiity an ivergene epenenies on u9 in Fig. 12, however, reveals that the vortiity an ivergene o not epen exatly on the sine an osine, respetively, of u9 but rather are phase shifte (Fig. 12). The values of the phase shifts are labele on Fig. 12. These phase shifts have absolute magnitues of approximately 258 for the vortiity an 108 for the ivergene in all four regions but with opposite signs in eah hemisphere. As aresse below, these phase shifts an the amplitue ifferenes in Fig. 11 (also evient from the amplitues of the sinusois in Fig. 12) an be relate iretly to the influene of SST on the iretion graient terms in Eqs. (3) an (4). The epenene of the iretion graient terms on SST an be asertaine oneptually from the shemati in Fig. 7. When the surfae flow is from ool to warm SST, the surfae wins turn antiylonially, whereas for surfae flow from warm to ool SST the surfae wins turn ylonially. This observation suggests that the ownwin graient in win iretion V( /) shoul epen on the ownwin SST graient an hene on the osine of u9. Aitionally, rosswin iretion graients V( /) shoul form as the win blows along perturbation SST isotherms in assoiation with the rosswin SST graient an will thus epen on the sine of u9. The time-average maps of the perturbation ownwin iretion an SST graients an the perturbation rosswin iretion an SST graients in Fig. 13 inee show a orrelation between the iretion graient an SST graients onsistent with these hypothesize epenenies. The polewar isplaement of the win iretion perturbations relative to those of SST isusse in setion 4b is also evient in these maps. The orrelations are weakest over the Kuroshio an strongest in the Southern Hemisphere regions, as quantifie by the ross-orrelation oeffiients between the rosswin an ownwin iretion graients an the rosswin an ownwin SST graients, respetively, in Table 3. Aitionally, the magnitues of the orrelation oeffiients between the ownwin iretion graients an the ownwin SST graients are onsistently smaller than those between the rosswin iretion graients an the rosswin SST graients. However, both are muh smaller than the orrelations between the rosswin an ownwin graients of win spee an SST, thus explaining the higher variability of the vortiity an ivergene binne averages in Fig. 11 ompare with the spee-only ontributions to the vortiity an ivergene in Fig. 8. The epenenies of the iretion graient terms on u9 quantifie statistially in Fig. 14 onfirm that the rosswin an ownwin iretion graients vary as the sine an osine of u9, respetively. As expete in all four regions, the ownwin iretion graient response to u9 (gray urve in Fig. 14) shows that the surfae win tens to rotate antiylonially when the large-sale flow is from ool to warm water (i.e., when u9 508) an ylonially when the large-sale flow is from warm to ool water (i.e., when u ). The rosswin iretion graient response to u9 iniates a maximum surfae iffluent teneny as wins blow approximately along perturbation SST isotherms (i.e., when u ). Statistially, the iretion graient terms an thus be represente by V 9 5 a ir M T os(u9 fir ) an (11) V 9 5 a ir M T sin(u91fir ), (12) where a ir an a ir are oupling oeffiients for the ownwin an rosswin iretion graients, respetively, an f ir an f ir are phase shifts (see Table 4). These statistial relations, along with the statistial relations for the spee graients in Eqs. (9) an (10), are use in setion 4 to ai in unerstaning the ifferenes between