1. Introduction
On spatial scales of 100–1000 km, satellite observations have consistently shown positive correlations between surface wind speed and mesoscale sea surface temperature (SST) variations (see reviews by Xie 2004; Chelton et al. 2004; Small et al. 2008). Small-scale features in the surface wind field generated by this ocean–atmosphere interaction are common near large midlatitude and equatorial ocean current systems and may have significant implications for underlying ocean circulations (Milliff et al. 1996; Spall 2007a; Seo et al. 2007; Jin et al. 2009; Hogg et al. 2009). The SST-induced adjustment of the marine atmospheric boundary layer (MABL) leads to surface winds that are stronger over warmer water and weaker over cooler water, a point well observed in satellite wind and SST fields (e.g., Xie et al. 1998; Rouault and Lutjeharms 2000; Liu et al. 2000; Chelton et al. 2001; Hashizume et al. 2001; Park and Cornillon 2002; Nonaka and Xie 2003; O’Neill et al. 2003; White and Annis 2003; Chelton et al. 2004; Vecchi et al. 2004; O’Neill et al. 2005; Tokinaga et al. 2005; Park et al. 2006; Chelton et al. 2007; O’Neill et al. 2010, 2009, manuscript submitted to J. Climate). This observed coupling between near-surface winds and mesoscale SST perturbations shows large geographical variability between the Northern and Southern Hemispheres and between the equatorial Pacific and extratropics. Less emphasized in most past studies is the effect of SST on the surface wind direction. Satellite scatterometer observations over the Gulf Stream have shown the surface winds rotate clockwise in flow from cool to warm water and rotate counterclockwise as winds blow the opposite way from warm to cool water (Park et al. 2006; Song et al. 2006). In O’Neill et al. (2009a), it is shown from Quick Scatterometer (QuikSCAT) surface wind observations that SST-induced wind directions variations are of this sense in the Northern Hemisphere and of the opposite sense in the Southern Hemisphere. Dynamical origins of the surface wind speed response to SST forcing have been investigated through observational, numerical, and analytical studies (as recently summarized in Small et al. 2008 and references therein). Few previous studies, however, have investigated the influence of mesoscale SST perturbations on wind direction.
The dynamical response of the MABL to mesoscale SST perturbations is examined here during July 2002 from a realistic, high-resolution, three-dimensional numerical simulation using the Weather Research and Forecasting (WRF) mesoscale model. This study is the first dynamical analysis of mesoscale wind–SST interactions in the extratropical Southern Ocean. Unique aspects of this region relevant for this simulation include: strong background winds between 10 and 16 m s−1 averaged over the 1-month simulation period; a much larger range of surface sensible heat flux perturbations of 80–100 W m−2 than seen in most previous model simulations; a quasi-periodic and quasi-stationary series of SST perturbations having a spatial scale of O(200 km) rather than a single SST front or ephemeral ocean eddies; a lack of complicating factors such as strong atmospheric stratification or capping inversions at the MABL top; and distance away from continental landmasses. These factors lead ultimately to a dynamical MABL response that differs substantially from previous simulations, as we will show in this analysis.
Two mechanisms have been identified in previous studies as fundamentally important in the MABL and surface wind response to mesoscale SST perturbations: generation of hydrostatic pressure gradients through adjustments of the MABL mass fields (e.g., Lindzen and Nigam 1987; Wai and Stage 1989; Warner et al. 1990; Small et al. 2003; Cronin et al. 2003; Bourras et al. 2004; Song et al. 2006) and stability-dependent modification of turbulent mixing of momentum from aloft to the surface (e.g., Sweet et al. 1981; Jury and Walker 1988; Wallace et al. 1989; Hayes et al. 1989; Wai and Stage 1989; Freihe et al. 1991; Jury 1994; Anderson 2001; Hashizume et al. 2002; de Szoeke and Bretherton 2004; Mahrt et al. 2004; Tokinaga et al. 2006; Skyllingstad et al. 2006). Over midlatitudes, horizontal advection and Coriolis accelerations also play prominent roles in the MABL wind response because of stronger westerly winds (e.g., Warner et al. 1990; Song et al. 2004; Bourras et al. 2004; Thum 2006; Song et al. 2006; Spall 2007b). Through these studies, mesoscale wind–SST coupling can be seen to vary with the spatial scale of the SST perturbations, the strength of the background wind, latitude, the presence of strong lower-tropospheric stratification and capping inversions, and proximity to landmasses.
In the conditions prevalent over the Agulhas Return Current region of interest here, the MABL is not in equilibrium with the mesoscale SST variations, leading to significant horizontal advection accelerations and an SST-induced response of the near-surface momentum budget that differs substantially from that of the vertically averaged momentum budget. Specifically, as expected, we will find that the surface wind stress acts as a drag on the perturbation pressure-driven flow when the MABL is considered as a whole. The model therefore reproduces the collocation of surface wind stress and SST perturbations seen in satellite wind and SST observations. As we will see in this simulation, however, the vertical turbulent redistribution of momentum acts in concert with SST-induced pressure gradients to accelerate or decelerate the near-surface winds. Only in the middle and upper portion of the MABL do the vertical turbulent stress divergence perturbations act as a drag on the SST-induced perturbation flow.
To understand the reason for these differences in the role of turbulent wind stress in the surface and vertically averaged momentum budgets, it is instructive to vertically integrate the turbulent stress divergence over the depth of the boundary layer H, which becomes 
To determine how SST-induced turbulent stress divergence and pressure gradient variations generate wind speed and direction variations within the MABL over this region of the Southern Ocean, we first obtain a high-resolution 1-month simulation using WRF. Details of the model simulation are presented in section 2, including the choice of realistic lateral and SST boundary conditions that allow comparison of the simulated WRF surface winds with satellite surface wind observations from the QuikSCAT scatterometer. In this section, we also describe some unique aspects of the SST and surface sensible heat fluxes relevant to this investigation. An analysis of the simulated MABL momentum budget is presented in section 3. We show that the momentum budget contains several features observed in previous simulations of mesoscale SST–wind coupling in other regions but also contains unique features not before seen. A straightforward dynamical explanation is presented to account for the MABL wind perturbations in this simulation consistent with the boundary layer vertically averaged momentum budgets and the vertical structure of the terms within the momentum budget.
2. Model simulation
a. Model description
The WRF atmospheric mesoscale modeling system (Skamarock et al. 2005) is utilized to simulate the MABL response to mesoscale SST perturbations over the Agulhas Return Current. WRF is the next generation of the widely used fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5). The basic model configuration used for this simulation is briefly described here.
The model simulation was performed using a triple-nested configuration. The horizontal resolution of the outer nest was 75 km, the middle nest 25 km, and the inner nest was 8.3 km. The location of the inner nest is shown in Fig. 1 along with the SST field used in this simulation, which is discussed further below. Only model fields from the inner fine-resolution nest are considered here. Along the lateral boundaries of the outer nest, the model dynamic and thermodynamic variables were updated every 6 h using the National Centers for Environmental Prediction (NCEP) operational analyses. During the 1-month period analyzed here, several large-scale transient weather disturbances that were initiated outside of the domain propagated through the domain. The NCEP time-dependent lateral boundary conditions thus enabled us to make a more realistic simulation for this time period to compare with the QuikSCAT wind observations. The simulation period is 1–31 July 2002, instantaneous model fields were output every 4 h, and only the fields after 2 July were used in this analysis (1-month averages here refer to the period 3–31 July).
The simulation was performed using a stretched vertical grid with 69 vertical levels, including 19 levels below 1000 m. The lowest level extends from the surface to 12-m height and the highest was near 20-km height. We chose a fine vertical resolution in the boundary layer to accurately resolve the vertical turbulent momentum exchange associated with the formation of convectively unstable and stable internal boundary layers.
The boundary layer parameterization implemented for this simulation was developed by Grenier and Bretherton (2001). This scheme is based on a 1.5-level turbulence closure method that includes detailed handling of moist MABL processes. The surface momentum flux was computed using a similarity-based boundary condition that uses a momentum roughness length from Charnock’s relation to compute the surface friction velocity over the ocean. The surface layer scheme provides stability-dependent information for the boundary layer scheme, including surface exchange coefficients for heat, moisture, and momentum, but does not calculate any tendencies.
The ocean surface was assumed stationary for this analysis. Song et al. (2006) has shown that including the 1–2 m s−1 surface ocean current velocities associated with the Gulf Stream in the surface friction velocity computation made small but noticeable differences in the near-surface turbulent stress divergence. In this region of the Southern Ocean, however, surface ocean current velocities are only around 0.5–0.75 m s−1 within a small latitudinal band centered on 45°S latitude (e.g., Gille and Romero 2003; Lumpkin and Pazos 2007). We thus expect that inclusion of ocean current effects in the surface stress computations would lead only to minor differences from the simulation presented here.
The core of the WRF is the Advanced Research WRF (ARW) dynamic solver (Wang et al. 2004). This ARW solver provides the solutions to the fully compressible nonhydrostatic equations on a mass-based terrain-following coordinate system and provides full two-way nesting capabilities, which were used here. Whenever possible, we have chosen options that have performed well in previous studies or are the defaults for the fifth-generation MM5 and NCEP–eta models. Microphysical parameterizations include explicitly resolved water vapor, cloud, and precipitation processes, and the WRF single-moment 3-class (WSM3) scheme was implemented. A modified version of the Kain–Fritsch scheme is used to represent subgrid-scale effects of convection and shallow clouds.
b. SST boundary condition and spatial filtering
For the SST boundary condition, we used a steady, 1-month-averaged SST field for July 2002 derived from SST observations made by the Advanced Microwave Scanning Radiometer on the Earth Observing System (EOS)–Aqua (AMSR-E) satellite (Fig. 1). Song et al. (2009) found that WRF simulations forced with the AMSR-E SST produced more accurate small-scale surface wind fields compared to those with the real-time global (RTG) SST or Reynolds SST analyses since the AMSR-E SST fields contains more realistic high-wavenumber SST variability. The month of July was chosen because the SST-induced surface wind stress response over the Agulhas Return Current is stronger during the austral winter than during the austral summer (O’Neill et al. 2005, 2009, manuscript submitted to J. Climate).
Removal of the large-scale SST field by spatial high-pass filtering reveals a rich array of SST perturbations corresponding to intrusions of water associated with the meandering Agulhas Return Current (Fig. 2b). Spatially high-pass-filtered fields were isolated in this study by removing spatially low-pass-filtered fields using a multidimensional loess smoothing function with half-power cutoff wavelengths of 10° latitude × 20° longitude (Schlax et al. 2001), similar to the smoothing characteristics of a 6° latitude × 12° longitude block-average smoother. Hereafter, fields spatially high-pass filtered in this manner are referred to as perturbation fields. The mesoscale SST perturbations thus obtained have a dynamic range of about ±4°C in the region of interest here (Fig. 2b).
A unique aspect of the SST field in this region is the quasi-periodic series of SST perturbations with wavelengths of roughly 200 km, well away from landmasses. Most previous modeling studies highlighted in the introduction have investigated flow over single SST fronts, such as flow perpendicular to the Gulf Stream or the cold tongue in the eastern equatorial Pacific, and not over such complicated SST features. As shown below, the response of the MABL is much different than in these other studies and may be due to the rapid transitions the MABL undergoes when passing over these series of mesoscale warm and cool SST meanders.
To justify use of a steady SST field for this simulation, we quantified the temporal variability of the SST field over the Agulhas Return Current region using time-lagged autocorrelation functions of the unfiltered and perturbation AMSR-E SST fields. The autocorrelations were computed using 3-day-averaged SST fields at daily intervals centered on 14 July 2002 (Fig. 3a). The unfiltered AMSR-E SST has an autocorrelation function with a nearly constant value of 1 over time lags of ±15 days while the perturbation SST field has an autocorrelation function that falls off to about 0.75 at time lags of ±15 days. Both reveal that the SST field in this region evolves relatively slowly on submonthly time scales. Total SST differences during July 2002 are quantified using time-lagged RMS differences computed over all grid points in the SST field (Fig. 3b). Maximum RMS SST differences are about 1.1° and 0.8°C for the unfiltered and perturbation SST fields, respectively, some of which is due to the 0.4°C measurement uncertainties of individual AMSR-E SST observations (Chelton and Wentz 2005). Because SST features in this portion of the Agulhas Return Current are quasi-stationary during this period, we chose to use a steady 1-month SST field for simplicity in this WRF simulation.
The Kerguelen Plateau borders the southernmost part of the analysis region (Fig. 1). West of here, water enters into the Agulhas Return Current from the Agulhas Current and Agulhas Retroflection south of Africa near 40°S, 20°E. It then flows eastward, retaining its warm temperature and high-salinity characteristics until somewhere around 70°E (Lutjeharms and Ansorge 2001; Lutjeharms 2006), although this position is highly variable and has been observed to span anywhere between 60° and 80°E. Along its journey, water from the Agulhas Return Current slowly recirculates northward into the interior of the subtropical gyre in the southern Indian Ocean. East of the Kerguelen–Amsterdam Passage, the eastward flow loses its Agulhas water mass properties and is then called the South Indian Ocean Current (Belkin and Gordon 1996; Lutjeharms and Ansorge 2001). We will refer to this region as the Agulhas Return Current throughout this analysis despite the uncertainty over the exact location of its end position.
c. Simulated surface wind and pressure fields
The WRF model winds are strong during July 2002, with the 1-month scalar-averaged surface wind speeds increasing from about 10 m s−1 over the western portion of the domain to nearly 16 m s−1 over the southeastern portion (Fig. 2a). Westerly flow in the western portion of the domain progressively becomes more southwesterly toward the east, as evident by the southwest to northeast tilt of streamlines computed from the 1-month vector-averaged WRF surface wind (Fig. 2a). Although difficult to see in these streamlines, the surface winds turn northward downwind of warm SST and southward downwind of cool SST, as evident from the perturbation surface wind vectors shown in Fig. 2b and the perturbation wind direction shown in Fig. 2d. This is quantified statistically by histograms of the perturbation wind direction separated by warm and cool SST perturbations (Fig. 4a). These wind direction perturbations give rise to a turning of the westerly winds in this region and will be discussed further below. Similar SST-induced wind direction changes have been shown to varying degrees in numerical model simulations and observations (e.g., Park et al. 2006; Song et al. 2006; Spall 2007b; O’Neill et al. 2010). Likewise, the surface wind speed perturbations are, on average, positive over warm SST and negative over cool SST (Fig. 4b). The perturbation wind vectors aloft at 501-m height are also shown in Fig. 2b. Note that the perturbation flow aloft is much different than near the surface. The vertical structure of the wind is discussed in greater detail in section 3.
Low pressure perturbations form about 100–200 km downwind of warm SST perturbations while high pressure perturbations form about the same distance downwind of cool SST perturbations (Fig. 2c). The range of these SST-induced surface pressure perturbations is about ±0.25 hPa, which is comparable to, if not somewhat larger than, those found in previous observational and modeling studies (e.g., Wai and Stage 1989; Warner et al. 1990; Cronin et al. 2003; Small et al. 2003, 2005; Song et al. 2006). Perturbations in the model surface pressure field form hydrostatically as a result of a balance between surface heating and boundary layer temperature advection in the thermodynamic energy equation (Small et al. 2003). Consistent with this balance, θυ perturbations vertically integrated between the surface and 1205-m height are located downwind of the SST perturbations (Fig. 6a). As shown by the first term in Eq. (1), surface pressure perturbations are associated closely with these SST-induced perturbations in the vertically integrated θυ field, as evident from Fig. 6b; the cross-correlation coefficient between these surface pressure and vertically integrated θυ fields is −0.87. According to Eq. (1), a vertically integrated θυ perturbation of 600°C·m and θ0 = 285 K yields a surface pressure perturbation of about 0.21 hPa, which agrees well with these surface pressure perturbations.
As pointed out previously, SST-induced surface heating drives modification of the MABL mass and turbulence fields. The WRF surface sensible heat flux perturbations are shown in Fig. 6c and are enhanced by warm SST and reduced by cool SST, consistent with previous studies. The difference between warm and cool SST in this simulation is about 80–100 W m−2, or roughly 15 W m−2 (°C SST)−1 change, which is a range significantly larger than reported in most previous modeling studies over other regions (e.g., Small et al. 2003; Song et al. 2004; Bourras et al. 2004; de Szoeke and Bretherton 2004; Small et al. 2005; Seo et al. 2007) but comparable to the simulation of Wai and Stage (1989). Since there is no significant capping inversion at the MABL top to reduce the surface pressure signal (the back-pressure effect; Hashizume et al. 2002), the larger sensible heat flux perturbations are likely responsible for the stronger surface pressure perturbations seen in this simulation. It is unclear what role ocean dynamics play in maintaining these strong heat fluxes in the real ocean.
We conclude this section by noting that Liu et al. (2007) has suggested that SST-induced surface wind speed perturbations are driven mainly by stability-dependent changes to the logarithmic wind profile in the surface layer (i.e., Stull 1988, p. 377). To test whether this mechanism can account for the surface wind speed perturbations in this simulation, we computed the difference between perturbations of the 10-m stability-dependent wind speed and the 10-m equivalent neutral stability wind speed (Fig. 6d). In unstable conditions over warm SST, the stability-dependent wind speed is about 0.2 m s−1 less than in neutral conditions, as expected, with the opposite occurring in more stable conditions over cool SST. This can only account for less than 15% of the value of the surface wind speed perturbations found in this simulation, however, and thus cannot fully explain the SST-induced surface wind speed response. As shown in the next section, SST-induced surface stress variations in this simulation are due to SST-induced pressure gradients, turbulent momentum redistribution, and horizontal advection rather than to changes in surface layer stability. This is consistent with several previous investigations of surface layer stability effects associated with mesoscale SST perturbations (Wai and Stage 1989; Small et al. 2003; O’Neill et al. 2005; Spall 2007b; Song et al. 2009; O’Neill et al. 2009, manuscript submitted to J. Climate).
3. Momentum budget analysis
a. Surface momentum budget
1) Surface downwind momentum budget
Perturbations in both the downwind turbulent stress divergence and downwind pressure gradient are comparable in magnitude and act in concert to increase the surface wind speed toward warm SST and decrease the surface wind speed toward cool SST (Figs. 7e–g). In this simulation, both turbulent momentum mixing and pressure gradients are thus important in the SST-induced surface wind speed response. Other examples of these two mechanisms acting together over mesoscale SST perturbations are not readily apparent from previous model simulations; one mechanism has usually been shown to dominate over the other. Near the surface, this result may be interpreted as a mixture of the Wallace et al. (1989) and Hayes et al. (1989) turbulent mixing mechanism and the Lindzen and Nigam (1987) and Small et al. (2005) surface pressure gradient forcing mechanism. Note that the surface downwind turbulent stress divergence perturbations are not collocated spatially with the surface stress perturbations (Fig. 2e).
This balance differs from the simulation of Small et al. (2005) for cross-equatorial surface flow over the equatorial Pacific. In that simulation, the surface turbulent stress divergence was seen to act as a drag on the perturbation flow driven by SST-induced surface pressure gradients until they balanced some distance downwind of the northern cold tongue SST front. We show in section 3b that the Small et al. (2005) “pressure–drag” balance does hold above about 150 m in this simulation, but not down to the surface.
Modulation of near-surface winds by SST-induced turbulent mixing has also been seen in simulations by de Szoeke and Bretherton (2004) over the eastern tropical Pacific and Skyllingstad et al. (2006) for an idealized case study of smaller-scale SST fronts with length scales of O(10 km). In both these studies, however, SST-induced surface pressure gradients were found to have much less influence than found here. Effects of SST-induced pressure gradients on the surface winds are consistent with several other modeling studies (Wai and Stage 1989; Warner et al. 1990; Small et al. 2003, 2005; Song et al. 2006).
Using an idealized two-dimensional coupled simulation characteristic of a midlatitude SST front, Spall (2007b) found that cross-frontal surface wind changes away from the frontal region were consistent with the one-dimensional balance proposed by Samelson et al. (2006), where changes in surface drag, compensating for cross-frontal changes in boundary layer height, caused a change in cross-frontal wind strength at the expense of the along-frontal winds via the Coriolis force. SST-induced pressure gradients and turbulent mixing were insufficient to account for the cross-frontal wind changes, which differ on both accounts from this simulation.
2) Surface crosswind momentum budget
In addition to the waxing and waning of surface wind speed as air flows over these mesoscale SST perturbations, surface winds turn counterclockwise in flow toward warm SST and clockwise in flow toward cool SST, as shown by the perturbation wind direction in Fig. 2d and the crosswind advection perturbations in Fig. 7a. Coriolis force and crosswind pressure gradient perturbations are the largest terms in the surface crosswind momentum budget (Figs. 7c,d), although the crosswind turbulent stress divergence is a significant contributor (Fig. 7b). The imbalance between these three forces results in significant curvature perturbations over the strongest downwind SST gradients.
Coriolis force perturbations result from SST-induced wind speed perturbations (Fig. 7d) and are thus highly correlated with the SST perturbations and are significant even on the small scale of these SST perturbations. The length scale over which the Coriolis term can change the wind direction in inertial flow is Vf −1, and for V = 12 m s−1 this implies a radius of curvature of 120 km, which is smaller than the ∼200-km length scale of the SST perturbations in this region. Note, however, that pure inertial flow is not achieved here on the mesoscale in this simulation since the SST-induced crosswind pressure gradients and crosswind turbulent stress divergence perturbations are large. Additionally, the crosswind pressure gradient and turbulent stress divergence perturbations are not collocated with the Coriolis force perturbations. The crosswind pressure gradient and Coriolis force perturbations are of the same sign on the southeastern (northwestern) flanks of warm (cool) SST and of opposite sign on the northwestern (southeastern) flanks of warm (cool) SST. Crosswind turbulent stress divergence perturbations tend to form in regions where the downwind SST gradients are strongest and contribute to a turning of the winds that are anticyclonic in flow from cool to warm SST and cyclonic in flow from warm to cool SST. This behavior does not appear to be noted in other simulations. As discussed in the next section, SST-induced crosswind turbulent stress perturbations are consistent with a thermal wind adjustment of the crosswind vertical wind shear.
Significant Coriolis accelerations were also found in the simulations of Song et al. (2006) and Spall (2007b). The model simulations used by Wai and Stage (1989) and Spall (2007b) had fixed along-frontal pressure gradients and therefore SST-induced crosswind pressure gradients could not develop. In the Song et al. (2006) simulation, crosswind pressure gradients did partially balance the Coriolis force, consistent with this simulation. The near-equatorial simulations by Small et al. (2003, 2005) had little influence from the Coriolis force, and it appears that the pressure gradient and turbulent stress divergence in the crosswind direction opposed each other analogous to the downwind balance.
b. Response of the MABL vertical structure to mesoscale SST perturbations
1) Analysis method
EOFs are conventionally computed with the mean removed at each grid point to express vertical variability with respect to the vertical mean. For this analysis, the vertical variability associated with the vertical mean is of particular interest, and thus the vertical mean is not removed before computing the EOFs. As a result, instead of explaining vertical variance as in the case when the vertical mean is removed, the EOFs here explain the vertical “mean product.” For all perturbation terms considered, the first two modes explain better than 80% of each terms’ total vertical mean product; we therefore only consider the first two modes of each term.
To evaluate this EOF representation of the 1-month average forcing terms, we compare vertical profiles of the terms in the downwind momentum budget (excluding vertical advection) and the Coriolis force with the sum of the first two EOF modes for each term (Fig. 8). Three locations are chosen to represent different flow regimes: one where flow is from cool to warm SST (44.5°S, 61°E), one where flow is from warm to cool SST (42.2°S, 68°E), and one at a perturbation SST minimum (44°S, 65°E). Except for some minor differences, the EOFs capture most of the important vertical structure of these forcing terms. As we shall see next, these EOFs prove powerful for isolating the physical processes determining the vertical structure of the perturbation forcing terms.
2) Wind speed and the downwind momentum budget
The first horizontal spatial mode of the perturbation wind speed 
The first EOF of the downwind turbulent stress divergence has minimal effect at the surface (Fig. 10). Its second EOF shows strong intensification below 150-m height and has a spatial mode 
The first EOFs of the downwind turbulent stress divergence and downwind pressure gradient, on the other hand, show just the opposite above 150-m height: the 
Below 150 m, the SST-induced downwind pressure gradient does not drive the downwind turbulent stress divergence since the first EOFs of the turbulent stress divergence weaken substantially relative to the pressure gradient (Fig. 10). This imbalance is consistent with the intensification of the first EOF of the downwind horizontal advection below 150-m height, as is evident from 
The vertical structure of the second EOF mode of the downwind pressure gradient 
We have thus identified physical mechanisms associated with the first two EOF modes of the downwind turbulent stress divergence and the downwind pressure gradient. It is our contention that these two variables explain the horizontal and vertical variability in the first mode EOF of the downwind horizontal advection. This can be tested quantitatively by computing bin averages of 
3) Wind direction and the crosswind momentum budget
The first EOF of the perturbation wind direction ψ′ (Fig. 9) shows that the wind rotates clockwise with height downwind of warm SST perturbations and counterclockwise with height downwind of cool SST perturbations, as is evident qualitatively from Fig. 2b. These wind direction perturbations are largest at the surface and diminish with height. The 
EOFs of the crosswind horizontal advection, crosswind turbulent stress divergence, crosswind pressure gradient, Coriolis force, and crosswind vertical advection are shown in Fig. 12. The first EOF of the crosswind pressure gradient explains 97.7% of the vertical variance, diminishes uniformly with height, and has a 
Crosswind turbulent stress divergence perturbations contribute to streamline curvature perturbations that are anticyclonic upwind of warm SST and cyclonic upwind of cool SST, as evident from 
Two physical mechanisms have thus been identified in the crosswind momentum budget. The first is a balance between the first modes of horizontal advection, pressure gradient, turbulent stress divergence, and the Coriolis force. Quantitative intercomparison of these EOFs is accomplished by bin averaging the first mode crosswind advection 
The crosswind vertical shear is to a good approximation in thermal wind balance with the SST-induced air temperature gradients. Qualitatively, cold air advection (i.e., perturbation flow from cool to warm SST) should lead to the perturbation winds turning clockwise with height in the Southern Hemisphere, with the opposite occurring in warm air advection. This can be seen qualitatively in Fig. 2b. This is shown more directly here from comparison of the first and second EOFs of the crosswind vertical wind shear perturbations (V∂ψ/∂z)′ and the thermal wind shear components rotated into the crosswind direction, that is, [(1/ρ f )(∂/∂s)(∂p/∂z)]′, which is shown in Fig. 13. These correspond closely, as evident quantitatively from the cross correlation between the first-mode spatial EOFs of the perturbation crosswind vertical wind shear and thermal wind shear components of 0.87. SST-induced baroclinic pressure gradient perturbations thus give rise via the Coriolis force to a vertically sheared turning of the winds. The crosswind turbulent stress component is related to the crosswind vertical shear, and hence the EOF spatial modes of the crosswind turbulent stress are highly correlated with the spatial modes of the crosswind vertical shear (Fig. 13). While the horizontal structures agree very well, the vertical structure differs for two reasons: first, the crosswind turbulent stress component is defined to be zero at the surface in the surface stress boundary condition, and second, the vertical profile of the crosswind turbulent stress also depends on the vertical structure of the eddy viscosity KM, which tends to be several times larger in the middle of the MABL than near the surface or top (not shown). Crosswind turbulent stress divergence perturbations are therefore consistent with an SST-induced baroclinic modification of the crosswind vertical wind shear.
c. Vertically averaged momentum budgets
From the vertical structure of the downwind turbulent stress divergence in this simulation, it was seen that turbulence redistributes momentum from aloft toward the surface in response to SST-induced surface heating perturbations (Wallace et al. 1989; Hayes et al. 1989) below 150 m while also acting as a drag that balances the SST-induced downwind pressure gradients above 150 m (Small et al. 2005). As discussed briefly in the introduction, there is some question about the relationship between the turbulent stress divergence and the surface stress and how the surface stress relates to the other terms in the MABL momentum budget. Part of this concern also involves the relationship between the vertical structure of the forcing terms shown above to the vertically averaged MABL momentum budget.
Downwind surface stress perturbations correlate very well with the SST perturbations, with a cross-correlation coefficient of −0.89; enhanced stress occurs over warm SST and reduced stress occurs over cool SST (Fig. 14g). These SST-induced surface stress perturbations are opposed largely by the vertically averaged downwind pressure gradient perturbations (Fig. 14h); the correlation coefficient between these fields is −0.76. Differences between the surface stress and vertically averaged downwind pressure gradient give rise to perturbations in the vertically averaged horizontal advection (Fig. 14f).
The vertically averaged downwind momentum budget is much different than the surface downwind momentum budget (Figs. 7e–g). At the surface, downwind turbulent stress divergence and pressure gradient perturbations are collocated with the downwind SST gradients rather than with the SST perturbations themselves as is approximately the case in the vertically averaged downwind stress divergence and downwind pressure gradient. At the surface, the downwind pressure gradient and downwind turbulent stress divergence act together to accelerate the flow, while the surface stress opposes the vertically averaged downwind pressure gradient. This differs from the Small et al. (2005) simulation in which the depth-averaged and surface budgets were comparable in horizontal structure. In this simulation, the vertical structure of the terms in the MABL momentum budget are thus pivotal in describing the complete SST-induced MABL dynamic response in this region; consideration of the vertically averaged MABL momentum budget alone does not adequately describe the surface wind response to mesoscale SST perturbations.
We note that the downwind pressure gradient perturbations at the surface (Fig. 7g) are not collocated with those vertically averaged (Fig. 14h). This is due to the change in sign of the downwind pressure gradient with height seen in the
The vertically averaged crosswind turbulent stress divergence is nearly zero, which is expected since the surface crosswind stress is zero by definition in the surface stress boundary condition. Perturbations in the vertically averaged crosswind pressure gradient and Coriolis forces are in an approximate balance (Figs. 14c,d); the correlation coefficient between these two fields is −0.77. The small difference between these two forces is balanced mainly by the perturbation crosswind horizontal advection (Fig. 14a) analogous to a vertically averaged gradient wind balance. Vertical advection is small but nonnegligible here, but it does not appear related to SST in any clear manner (Fig. 14e).
4. Discussion and conclusions
This study provides the first dynamical analysis of mesoscale wind–SST interactions over the open ocean in the extratropical Southern Hemisphere. We have shown that the high-resolution three-dimensional WRF simulation during the wintertime 1-month period of July 2002 with the Grenier and Bretherton (2001) boundary layer parameterization provides a realistic simulation of the MABL as measured by detailed quantitative comparisons with the QuikSCAT scatterometer surface wind observations.
Several factors contribute to the unique aspects of this simulation. Instead of a single SST front, the meandering Agulhas Return Current produces a quasi-periodic and quasi-stationary series of mesoscale SST perturbations with a spatial scale of ∼200 km. This, in addition to the strong surface wind speeds in this region of 10–16 m s−1, results in large surface heat flux differences between warm and cool SST perturbations of 80–100 W m−2. Other characteristics of this simulation include near-neutral stratification of the lower troposphere, the lack of a strong inversion capping the MABL, and little direct influence from landmasses.
Accordingly, the response of the MABL momentum budget to mesoscale SST perturbations in this simulation is found to be distinct from previous numerical simulations in other regions and conditions. Near the surface, the SST-induced downwind pressure gradients and the vertical turbulent momentum redistribution act together to accelerate the surface flow toward warmer water and decelerate the flow toward cooler water. This simulation is the first example of SST-induced surface pressure gradients and turbulent mixing perturbations acting in concert to force surface wind speed perturbations. We may interpret this result as a mixture of the Wallace et al. (1989) and Hayes et al. (1989) turbulent mixing mechanism and the Lindzen and Nigam (1987) and Small et al. (2005) surface pressure gradient forcing mechanism. At the same time, this simulation reproduces the observed result that perturbation surface wind stress maxima are found over warmer water and minima over cooler water. This leads to the counterintuitive result that surface wind stress perturbations and anomalous downwind accelerations of the surface wind due to the turbulent mixing of momentum are not collocated spatially. By vertically averaging the turbulent stress divergence, however, it is shown that the turbulent exchange of horizontal momentum between the lower and upper portions of the MABL driven by SST-induced surface heating perturbations does not make a significant contribution to the surface wind stress in the transition region between warm and cool SST even though it has a significant effect on the surface wind speed.
The SST-induced turbulent stress divergence perturbations thus accomplish two relatively independent tasks in the downwind momentum budget at the mesoscale. The first is exchanging momentum between the lower and upper portions of the MABL, which alters the wind shear in the layer and accelerates or decelerates the surface wind in the transition regions between warm and cool SST but is not collocated with the surface wind stress perturbations. The second is exerting an anomalous surface drag in the vertically averaged downwind momentum budget, which is being driven by anomalous pressure gradient forcing centered over the warm and cool SST perturbations, consistent with the pressure–drag mechanism of Small et al. (2005). As we have noted, the relatively small spatial scale of the SST perturbations and large surface heat flux perturbations in this simulation prevent the MABL from reaching an equilibrium state in which the turbulent wind stress acts as a drag on the SST-induced pressure-driven perturbation flow. Under the nonequilibrium conditions encountered in this simulation, the perturbation surface momentum budget will not necessarily be in qualitative agreement with the vertically averaged momentum budget.
In the crosswind momentum budget, two force balances were identified that lead to wind direction variations associated with the mesoscale SST perturbations. First, crosswind advective accelerations were caused by the imbalance between the SST-induced crosswind pressure gradients, crosswind turbulent stress divergence perturbations, and Coriolis accelerations. Second, a balance between the Coriolis acceleration, crosswind turbulent stress divergence, and crosswind advective accelerations occurred that is analogous to an inertial lee wave driven by modification of the turbulent stress divergence (Spall 2007b). We also showed that the crosswind turbulent stress perturbations were modified by the adjustment of the crosswind vertical wind shear toward a thermal wind balance. The governing crosswind balance is not simply in an inertial flow balance in which the SST-induced wind speed perturbations cause wind direction perturbations via the Coriolis force. Finally, these SST-induced wind direction changes generate significant surface vorticity and divergence perturbations through changes in surface streamline curvature and diffluence in addition to the effects of horizontal wind speed gradients (O’Neill et al. 2010).
Acknowledgments
We thank Chris Bretherton, Qingtao Song, and Eric Skyllingstad for helpful discussions throughout the course of this analysis and Jim McCaa for providing a preliminary version of the code implementing the Grenier–Bretherton boundary layer parameterization scheme in WRF. We thank Dr. Justin Small and one anonymous reviewer for providing thorough and insightful comments that significantly clarified many of the results and discussion presented here. The AMSR-E SST fields were obtained from the Remote Sensing Systems and are sponsored by the NASA Earth Science MEaSUREs DISCOVER Project and the AMSR-E Science Team. QuikSCAT swath data were also obtained from the Remote Sensing Systems and are sponsored by the NASA Ocean Vector Winds Science Team. This research was supported by NASA Grant NAS5-32965 and Contract 1283973 from the NASA Jet Propulsion Laboratory for funding of Ocean Vector Winds Science Team activities. Part of this research was performed while the lead author held a National Research Council Research Associateship Award at the Naval Research Laboratory in Monterey, California.
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Map of the AMSR-E SST over the Indian Ocean sector of the Southern Ocean averaged over July 2002. The area enclosed in the box is the location of the inner nest subject to the analysis in this paper. The thin black curve traces the 12°C SST isotherm. Gray contours mark the 3000-m isobath.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
Maps of 1-month-averaged (a) WRF unfiltered scalar-averaged surface wind speed (colors) overlaid with streamlines of the WRF vector-averaged surface wind; (b) AMSR-E perturbation SST (colors) overlaid with vectors of the WRF vector-averaged perturbation surface wind (black) and wind at 501-m height (gray; for clarity, only every fourth vector is plotted); (c) WRF perturbation surface pressure (colors); (d) WRF perturbation surface wind direction (colors); (e) WRF perturbation surface wind stress magnitude (colors). The contours overlaid in (c)–(e) are of the AMSR-E perturbation SST having a contour interval (CI) of 0.5°C with solid and dashed contours corresponding to positive and negative values, respectively, and the zero contour has been omitted for clarity. A reference vector key is located below the color bar in (b).
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
(a) Time-lagged autocorrelation functions for the AMSR-E unfiltered SST (solid line) and spatially high-pass-filtered SST (dashed line) computed for 14 Jul 2002. (b) Time-lagged RMS differences between the AMSR-E SST field on 1 Jul 2002 and the SST fields lagged in time afterward. The statistics in both panels were computed from 3-day-averaged AMSR-E SST fields at daily intervals over the region 50°–40°S, 50°–80°E.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
Histograms of the WRF 1-month scalar-averaged perturbation (a) surface wind speed and (b) surface wind direction separated between positive (solid curves) and negative (dashed curves) perturbation SSTs.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
(left) Maps of 1-month scalar-averaged perturbation 10-m equivalent neutral stability wind speed (colors) from (a) QuikSCAT and (b) WRF during July 2002. The solid and dashed contours correspond to positive and negative AMSR-E SST perturbations, respectively, with a CI of 0.5°C; the zero contour has been omitted for clarity. (right) Binned scatterplots of 1-month-averaged perturbations of the scalar 10-m equivalent neutral stability wind speed as a function of the AMSR-E SST for (c) QuikSCAT and (d) WRF. The regression lines in (c) and (d) are linear least squares fits of the points having a slope as indicated at the lower right, and the error bars represent ±1 std dev of the perturbation wind speeds within each bin.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
Maps averaged over the 1-month period of the WRF simulation: (a) perturbation vertically integrated virtual potential temperature; (b) perturbation vertically integrated virtual potential temperature overlaid with contours of perturbation surface pressure; (c) perturbation surface sensible heat flux; (d) perturbation 10-m equivalent neutral stability wind speed minus the perturbation 10-m stability-dependent wind speed, both from WRF. Contours in (a),(c), and (d) are of the AMSR-E perturbation SST shown earlier.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
Maps of the 1-month-averaged perturbation terms of the WRF surface momentum budget: horizontal advection in the (a) crosswind and (e) downwind directions; turbulent stress divergence in the (b) crosswind and (f) downwind directions; pressure gradient in the (c) crosswind and (g) downwind directions; (d) Coriolis force. The dashed and solid contours in each panel correspond to negative and positive AMSR-E SST perturbations, respectively, with a CI of 0.5°C. The zero contour has been omitted for clarity.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
Vertical profiles of select 1-month-averaged forcing terms in the WRF momentum budget at three different points (dashed) along with the EOF representation of these terms computed from the first two modes (solid). Four terms are chosen: (a) downwind turbulent stress divergence (F · ŝ)′ (b) downwind horizontal advection (V∂V/∂s)′ (c) downwind pressure gradient [−(1/ρ)(∂p/∂s)]′ (d) Coriolis force (−f V)′. The three locations chosen are 44°S, 61°E (crosses; cool to warm); 44.5°S, 65°E (circles; SST minimum); and 42.2°S, 68°E (squares; warm to cool).
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
The first two dominant vertical EOFs of the WRF perturbation (top row) wind speed V ′ and (bottom row) wind direction ψ′. (left column) The first dominant mode; (right column) the second dominant mode. Within each column, the amplitude vertical profiles are shown at left and maps of the horizontal spatial modes are shown at right. The contours in the maps are of the perturbation AMSR-E SST fields, as shown previously. The percentage of vertical mean product explained by each mode is shown above the maps.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
The first two dominant EOFs of the perturbation terms in the 1-month-averaged WRF downwind momentum budget: (top row) horizontal advection, (second row) turbulent stress divergence, (third row) pressure gradient, and (bottom row) vertical advection. (left column) The first dominant modes; (right column) the second dominant modes. Within each column, the amplitude vertical profiles are shown at left and maps of the horizontal spatial modes are shown at right. The contours in the maps are of the perturbation AMSR-E SST fields, as shown previously. The percentage of vertical mean product explained by each mode is shown above the maps.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
Binned scatterplots of the dominant balances found from the EOFs in the 1-month-averaged WRF downwind and crosswind momentum budget: (a) downwind balance of 
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
The first two dominant EOFs of the perturbation terms in the 1-month-averaged WRF crosswind momentum budget: (top row) horizontal advection, (second row) turbulent stress divergence, (third row) pressure gradient, (fourth row) Coriolis force, and (bottom row) vertical advection. (left column) The first dominant modes; (right column) the second dominant modes. Within each column, the amplitude vertical profiles are shown at left and maps of the horizontal spatial modes are shown at right. The contours in the maps are of the perturbation AMSR-E SST fields, as shown previously. The percentage of vertical mean product explained by each mode is shown above the maps.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
The first two dominant EOFs of the perturbation terms in the 1-month-averaged WRF (top row) crosswind vertical wind shear (V∂ψ/∂z)′, (middle row) crosswind thermal wind shear [(1/ρ f )(∂/∂s)(∂p/∂z)]′, and (bottom row) the crosswind turbulent stress τ · n̂. (left column) The first dominant mode; (right column) the second dominant mode. Within each column, the amplitude vertical profiles are shown at left and maps of the horizontal spatial mode is shown at right. The contours in the maps are of the 1-month-averaged perturbation AMSR-E SST, as shown previously. The percentage of vertical mean product explained by each mode is shown above the maps.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
Maps of the terms in the 1-month-averaged WRF perturbation vertically averaged (a)–(e) crosswind momentum budget and (f)–(i) downwind momentum budget. Overlaid in each panel are contours of the perturbation AMSR-E SST, as shown earlier. The vertical averages are mass weighted, as discussed in the text.
Citation: Journal of Climate 23, 3; 10.1175/2009JCLI2662.1
