1. Introduction
To illustrate the SST effect on the wind stress, suppose the total W and SST (T) are the sum of a background part b that is driven only by large-scale processes and an eddy part e that relates the W response to Te, such that Ttot = Tb + Te and Wtot = Wb + We. The correspondence of We to Te has been widely studied since Wallace et al. (1989) and Hayes et al. (1989), with the increase (decrease) in wind speed (stress) over the warmer (cold) side of the front and eddies via the change in turbulent heat flux, stability of the MABL, and downward turbulent momentum transfer. The coherent wind response to mesoscale SST has been broadly observed in the global oceans (e.g., Park and Cornillon 2002; Xie 2004; Chelton and Xie 2010; O’Neill et al. 2010, 2012; Frenger et al. 2013; among many others).
Using this positive correlation between Te and We, Chelton et al. (2004) developed an empirical relation that the spatial derivative of wind (vorticity or divergence) is linearly proportional to the SST gradient. This linear proportionality has been the standard metric to measure air–sea coupling on oceanic mesoscales (e.g., Maloney and Chelton 2006; Small et al. 2008; Song et al. 2009). In the California Current System (CCS), considerable SST anomalies and their gradients are found in the vicinity of the upwelling fronts, eddies, and filaments (e.g., Strub and James 2000; Castelao et al. 2006). In such regions, the wind stress curl and divergence fields are linearly proportional to the crosswind and downwind SST gradients, respectively (Chelton et al. 2007; Seo et al. 2007b; Haack et al. 2008; Boé et al. 2011). The SST-driven wind stress curl then leads to a perturbation Ekman pumping velocity (Chelton et al. 2001), which according to a recent survey of satellite observations by Gaube et al. (2015) produces a dipolar structure of Ekman pumping over an eddy. This perturbation Ekman pumping is known to influence the evolution and propagation of an eddy (Dewar and Flierl 1987). In the CCS, Chelton et al. (2007) estimated from satellite observations the summertime SST-induced Ekman pumping velocities to be O(0.15) m day−1. The perturbation Ekman pumping velocities have a greater range of variability than that driven by the large-scale wind stress, suggesting the important role by the eddy-induced SST–wind coupling in the upwelling and the CCS circulation system.
Jin et al. (2009) applied this observed empirical SST–wind stress relationship to an idealized upwelling problem for an eastern boundary current system. The result shows that the SST–wind stress interaction weakens the coastal upwelling largely because the upwelling-favorable nearshore wind stress is weakened in the nearshore zone because of the cold upwelled SSTs. The resulting increase in wind stress curl broadens and amplifies the poleward undercurrent as would be expected from the Sverdrup balance. Cyclonic eddies featuring relatively stronger SST gradients are found to be more strongly damped by the SST–wind stress coupling, resulting in a relative abundance of anticyclonic eddies in the equilibrium state. The overall impact of SST–wind interaction is to reduce eddy kinetic energy (EKE) by 25%. Note, however, that the SST fields used to modify the wind stress contain both the background condition (cold nearshore and warm offshore) as well as the eddies and fronts; hence, a question remains about the true effect of the “small-scale eddies.”
Now suppose the ocean current U is the sum of the background Ub and the eddy-induced surface current Ue. Both components can affect the wind stress through (1). Pacanowski (1987) examined the large-scale effect of the relative motion in the wind stress formulation for the tropical Atlantic Ocean from an ocean general circulation model (OGCM). The inclusion of surface currents, again without distinction between background and eddies, reduces the effective wind stress imparted to the ocean and thus slows the surface currents by 30%. Luo et al. (2005) tested this effect in a coupled general circulation model (CGCM), showing that the prevailing easterly wind stress in the equatorial Pacific is reduced, resulting in slower currents and the reduced equatorial upwelling. This alleviates the cold bias in their model. Similar results have been obtained from numerous ocean modeling studies taking into account the surface current in the wind stress parameterization (e.g., Duhaut and Straub 2006; Hughes and Wilson 2008; Hutchinson et al. 2010; Zhai and Greatbatch 2007; Anderson et al. 2011). Kelly et al. (2001) and Cornillon and Park (2001) demonstrate from the scatterometer measurements of wind stress that the Ue of an eddy can be inferred from the wind stress based on the fact that the scatterometer estimates the wind velocity relative to the ocean surface velocity. An OGCM simulation by Eden and Dietze (2009) shows that the EKE is weakened by 10% in the North Atlantic and by as much as 50% in the tropics when the current–wind interaction is included. This reduction was ascribed to the enhanced surface drag by the ocean eddies, while the reduction in barotropic instability due to the reduced lateral shear of the mean currents was of secondary importance. Again, none of these studies attempted to separate the effect of Ub and Ue.
Eddy-induced SST Te and surface current Ue both affect the Ekman pumping velocities but in different ways. Gaube et al. (2015) considered three mechanisms by which the ocean eddies affect the Ekman pumping, that is, 1) the eddy-induced SST, 2) the relative motion between wind and current, and 3) the gradient of relative vorticity (Stern 1965; McGillicuddy et al. 2007). The first process was already discussed in terms of the SST–wind coupling, while the last two arise from Ue. Gaube et al. (2015) show that these two Ue induced Ekman-pumping velocities are greater than that due to Te for both the cyclonic and anticyclonic eddies. The current-driven Ekman pumping velocities are of the opposite sign to the surface vorticity of the eddy, resulting in divergence (convergence) of the surface current and consequent upwelling (downwelling) at the center of an anticyclone (cyclone). The net impact is to weaken the amplitude of the eddies (Martin and Richards 2001; McGillicuddy et al. 2007; Ledwell et al. 2008; McGillicuddy 2015). Dewar and Flierl (1987) demonstrated that the momentum transfer to the oceans affected by Te and Ue exerts distinctive feedback effects on the evolution and intensity of the eddy; the Ue leads to decay of the eddy via enhanced top-drag (Bye 1986), while the Te, via change in drag coefficients and wind stress, affects the propagation of the eddy.
Some earlier studies suggest that Te and Ue effects are not independent. For example, a regional coupled modeling study for the tropical Atlantic by Seo et al. (2007a) showed that the cold (warm) anomalies associated with the tropical instability waves (TIWs) are accompanied by an anomalous northward (southward) surface current concurrent with anomalous southward (northward) surface wind. The former is driven by the instability of the equatorial ocean leading to an anomalous eddy surface current, while the latter is driven by the wind response to the eddy-induced SST anomalies; therefore, the current–wind coupling is initiated by the SST–wind coupling. The resultant negative correlation between wind (stress) and the surface currents on the TIW spatiotemporal scales weakly damps the EKE. Small et al. (2009) found this understress effect that damps the wave energetics to be even stronger than the original estimate by Seo et al. (2007a) and to be comparable to the energy conversion process during baroclinic instability, the primary energy source of the waves.
These studies suggest consistent results; the inclusion of surface current or SST reduces the energetics of mesoscale eddies and currents via enhanced drags and the modified Ekman pumping. However, ocean-only simulations or coarse-resolution global coupled models used in the earlier studies do not properly capture the simultaneous and mutually dependent effects of the eddy-driven SST and surface currents on the wind speed, the stress, and their rectified effect on the energetics of the ocean. There has been no explicit attempt yet to separate the coupling effects on small-scale versus background scale. This study uses a high-resolution fully coupled ocean–atmosphere model with a novel scale-selective coupling strategy in an attempt to address these issues.
The paper is organized as follows: Section 2 describes the regional coupled model and the experimental configuration. Section 3 examines the mean state changes. Section 4 discusses the mechanism for change in EKE, and section 5 examines the Ekman pumping velocities. Section 6 is a summary and discussion of implications.
2. Model, experiments, and data
a. Model description
We utilize the Scripps Coupled Ocean–Atmosphere Regional (SCOAR) model (Seo et al. 2007b, 2014). SCOAR currently couples one of two weather models, the Weather Research and Forecasting (WRF) Model (Skamarock et al. 2008) or the Regional Spectral Model (RSM; Juang and Kanamitsu 1994), to the Regional Ocean Modeling System (ROMS; Haidvogel et al. 2000; Shchepetkin and McWilliams 2005). This study uses the WRF–ROMS version of SCOAR (Seo et al. 2014). The interacting boundary layer between WRF and ROMS is based on bulk aerodynamic formulae (Fairall et al. 1996, 2003) that calculate surface fluxes of momentum, turbulent and radiative heat, and freshwater based on the near-surface meteorological variables provided by WRF. ROMS is driven by these surface fluxes and, in turn, feeds back to WRF via the SST and surface current. The SCOAR model has been used in a wide range of coupled dynamics studies in the Indian Ocean (Seo et al. 2008b, 2009, 2014), the Pacific Ocean (Seo et al. 2007b; Putrasahan et al. 2013a,b), and the Atlantic Ocean (Seo et al. 2006, 2007a, 2008a; Seo and Xie 2011, 2013).
The SCOAR domain covers the U.S. West Coast (31.1°–46.8°N, 134.5°–116°W; Fig. 1). The horizontal resolutions in WRF and ROMS are identical 7 km with matching grids and land–sea masks. The 7-km resolution in the ocean and atmosphere captures mesoscale processes in the ocean and atmosphere as well as the complex coastline and major headlands that are important for alongshore variation in the near-coast wind (e.g., Koračin et al. 2004; Renault et al. 2016). The use of identical resolution and matching grid not only helps to maximize the effect of air–sea coupling given the simulated finescale SSTs by the ocean model, but it also eliminates the known issue of regridding wind near the steep orography and complex coastlines (e.g., Capet et al. 2004). It also helps to lessen the computing burden associated with regridding. The model coupling is activated every 6 h in order to account for the diurnal cycle. ROMS (WRF) is run with a stretched vertical grid with a total of 30 (29) vertical levels. Approximately 10 layers are allotted in the upper 150-m depth (below 750-m height).
Example of a 500-km lowess filtering applied to the daily snapshot (1 Aug 2008) of the ocean surface fields, (a)–(c) sea surface temperature T, (d)–(f) surface zonal current U, and (g)–(i) surface meridional current V. Left (center) column shows the fields before (after) the smoothing and the right column shows the difference (before minus after), that is, the small-scale fields of interest. The black box in (h) denotes the area to calculate the alongshore average of the EKE budget terms in Figs. 8 and 9.
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
b. Experimental setup
The experiments are designed to separate the Te effect on the wind (and thus the stress) from the Ue effect. The five SCOAR experiments differ only in how the wind stress is calculated in the bulk parameterization equation [(1)] with a different combination of background and eddy parts of T and U (Table 1). In CTL, the full T and U are included, while the effect of Te is suppressed in the noTe experiment, and no effect of Ue is included in noUe. Two additional runs are carried out; noTeUe omits both eddy components of T and U, and the noUtot ignores total (both background and eddy) surface current, and thus it does not consider the relative motion of wind and current. The effect of Te or Ue is then assessed from the statistical differences from the CTL; that is, CTL − noTe (CTL-noTe) [CTL − noUe (CTL-noUe)] reveals the net effect of Te (Ue). Note that since ocean eddies occur spontaneously and randomly in each run, deterministic eddy-phase comparisons between runs are not useful.
Description of the experiments performed in this study. The subscript b (e) denotes background (eddy) field. See section 2b for details.
c. 2D online smoothing
Separating the spatial scales of T and U during the coupled model integration requires an online spatial smoothing. This is done by implementing an online smoothing technique in the SCOAR coupler. Figure 1 shows the examples of the fields before and after the smoothing. This technique was first used for SST fields in Putrasahan et al. (2013a,b); this study extends to surface currents. The online, 2D, spatial, locally weighted scatterplot smoothing (lowess) filter (Chelton and Schlax 1994; Schlax et al. 2001) with the tricubic weighting function of Cleveland (1979) and Cleveland and Devlin (1988) is applied only to the SST and surface currents produced by ROMS that are felt by the atmosphere at each coupling step. Note that the actual SST and surface current in ROMS are left unchanged but evolve instead under the influence of the atmosphere that has seen only the smoothed SST and current fields. Therefore, it allows large-scale coupling effects to be preserved while suppressing the small-scale coupling via Te and/or Ue. To the best of the authors’ knowledge, this sort of modeling approach with both eddy SST and currents has not been attempted in any earlier studies. A loess filter with half-power filter cutoff wavelength of 500 km is used, yielding an effective cutoff wavelength of 300 km. Hence, in this study, processes on a length scale shorter than 300 km are regarded as small scale or eddies. The sensitivity of the result to different cutoff scales has also been assessed, for example, the 250-km lowess filter yielding the cutoff wavelength of 150 km. The results do not vary considerably with the chosen filtering scale as long as key finescale features are filtered.
It is important to note that our interest is to isolate the effect of eddies. In the sensitivity simulations, therefore, the coupling of the wind to the oceanic background SST and surface current is retained in association with the summertime upwelling condition and the CCS, respectively. This is different from Jin et al. (2009) on SST and most of the studies on surface current, where such a distinction is not explicitly made.
Note also that time-scale separation during the coupled integration is not possible. Therefore, the eddies in the online smoothing are defined as the deviation from the spatial mean. The eddies in the subsequent analyses are however treated as the deviation from the time mean. This mismatch between the definitions could affect the interpretation of our results. Nevertheless, the eddies in the CCS are known to have well-defined spatiotemporal scales (e.g., Kurian et al. 2011), so that eddies defined in either way are expected to be equivalent.
d. Experiment details
Prior to the coupled integration, ROMS is spun up for 20 yr with the climatological surface forcing of wind stress, heat, and freshwater flux derived from the Comprehensive Ocean–Atmosphere Dataset (da Silva et al. 1994) and the climatological lateral boundary condition from the Simple Ocean Data Assimilation (SODA) monthly analysis version 2.2.4 (Carton and Giese 2008; Giese and Ray 2011). ROMS in the coupled run is initialized from the end state of the spinup simulation, representing the climatological condition of 1 January from the 20-yr spinup simulation. In the coupled configuration, ROMS is driven by the time-varying monthly T/S/U/V from SODA and the interactive surface forcing from the WRF. The initial and boundary condition for WRF are from the 6-hourly National Centers for Environmental Prediction (NCEP) Operational Global Final Analyses dataset on a 1° × 1° grid (http://rda.ucar.edu/datasets/ds083.2). Initialized from 1 January 2004, CTL is integrated for 7 yr until 31 December 2010. The last 6 yr of the simulations are analyzed, disregarding the first year as a coupled boundary layer spinup process. The sensitivity experiments branch off from the CTL beginning 1 January 2006 (i.e., after the 1 yr of the coupled spinup), from which the wind stress calculation is modified as described above for the following 6 yr.
WRF uses the new Kain–Fritsch cumulus scheme using a mass flux approach (Kain 2004) and the WRF single-moment 3-class scheme for cloud microphysics (Hong et al. 2004). The planetary boundary layer (PBL) is treated with the Yonsei University (YSU) nonlocal PBL scheme (Hong et al. 2006), run with the fifth-generation Pennsylvania State University (PSU)–National Center for Atmospheric Research (NCAR) Mesoscale Model (MM5) surface layer scheme based on Monin–Obukhov similarity theory (e.g., Beljaars 1995). The WRF Model is also run with the Rapid Radiation Transfer Model (RRTM; Mlawer et al. 1997) and the Goddard scheme (Chou and Suarez 1999) for longwave and shortwave radiation transfer through the atmosphere. The Noah land surface model is used for the land surface process (Chen and Dudhia 2001). The mixed layer dynamics of ROMS are parameterized using a K-profile parameterization (KPP) scheme (Large et al. 1994) including penetrative shortwave heating effects (Paulson and Simpson 1977). No explicit horizontal diffusivity is used, although the third-order upstream biased horizontal advection scheme introduces implicit numerical diffusivity (Haidvogel et al. 2000).
e. Datasets
Several observational products are used to validate the model basic states. To calculate the surface geostrophic current, we use the global sea surface height (SSH) anomaly dataset from Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO) produced by Ssalto/Duacs with support from CNES (http://www.aviso.altimetry.fr). For this study, we use the SSH dataset from January 2005 to December 2010 with a weekly interval and a ⅓° × ⅓° spatial resolution. Surface wind and wind stress are obtained from the 3-day-averaged QuikSCAT satellite data on a ¼° × ¼° grid for January 2005 to November 2009, available from the Asia–Pacific Data-Research Center (APDRC) of the University of Hawaii. The NOAA Optimum Interpolation (OI) ¼° daily SST (AVHRR only) is used for SST fields (Reynolds et al. 2007). The surface heat flux fields are obtained from the 1° OAFlux dataset (Yu and Weller 2007). All these observed datasets are linearly interpolated to the model grid.
3. Impact on climatologies
Figure 2 compares the model simulations with the observations for the summertime [July–September (JAS)] climatologies of SST, surface current, latent heat (LH) flux averaged for 2005–10, and wind stress averaged for 2005–09. The observed SST (Fig. 2a, shading) and surface currents (green vectors showing current speed exceeding 10 cm s−1) are taken from the NOAA OI SST and the SODA ocean dataset. Comparison with other datasets for SST and surface currents [e.g., the SODA SST or the Ocean Surface Current Analyses–Real Time (OSCAR) current] reveals similar results (not shown). The observed SSTs and currents are overlaid with the QuikSCAT wind stress (brown vectors showing wind stress magnitude exceeding 0.075 Nm−2) and the latent heat flux from OAFlux (blue contours, negative ocean cooling).
(a) Observed summertime (July–September) SST (shading, °C, from NOAA OI SST), surface current (green vectors, cm s−1, shown only when greater than 10 cm−1, from SODA), latent heat flux (blue contours, W m−2, contour interval (CI) = 20, negative cooling the ocean, from OAFlux), and wind stress vectors (brown vectors, N m−2, shown only when greater than 0.075 N m−2, from QuikSCAT). (b) As in (a), but from CTL. SST, current, and LH are for 2005–10, while wind stress is for 2005–09 to match the QuikSCAT period. Difference fields: (c) CTL − noTe and (d) CTL − noUe. Gray dots denote the area of significant change in SST (p = 0.05) based on a two-sided Student’s t test.
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
The JAS SST fields represent the fully developed summertime upwelling condition, with lower SST along the U.S. West Coast north of Pt. Conception and warmer SSTs offshore. Regions of the nearshore SST minima are found in the lee of major coastal headlands such as Cape Blanco, Cape Mendocino, and Pt. Arena between 37° and 43°N, where the northerly/northwesterly wind stress is high (Koračin et al. 2004). The surface current is southwestward due to the wind-driven Ekman currents in response to the northerly/northwesterly wind. Currents at the deeper depth (e.g., 50 m) reveal the south/southeastward geostrophic California Current (not shown). The zonal extent and the alongshore variation of the nearshore cold SST correspond roughly to that of the offshore current. Latent heat flux reflects the SST pattern, cooling the ocean everywhere in the domain with minimum cooling (<−25 W m−2) in the nearshore upwelling zone and maximum cooling in the southwestern portion of the domain (<−70 W m−2).
CTL reproduces reasonably well the salient features of the summertime climatology in the CCS, although the simulated SST is somewhat too cold in the nearshore upwelling zone and too warm far offshore toward the southwestern portion of the domain, leading to excessive latent cooling there. This strong east–west gradient is accompanied by more vigorous meanders of the CCS in the model than the observations. The simulated wind stress is also stronger than the QuikSCAT and is partly responsible for the stronger upwelling response.
Differences of the surface climatologies between CTL and two sensitivity runs (noTe and noUe) are shown in Figs. 2c and 2d. Recall that the CTL-noTe (CTL-noUe) represents the effect of Te (Ue). Two coupling effects produce different time-mean (rectified) SST response patterns, although in both cases the SST difference fields are characterized as alternating bands of positive and negative values between the coast and 300–500 km offshore. The cold and warm SST anomalies coincide well with the southwestward and northeastward surface current anomalies (green vectors). Latent heat flux and wind stress (magnitude and direction) are in general a response to the change in SST, such that warm (cold) SST is collocated with the anomalous latent cooling (heating) and the southward (northward) wind stress anomalies, the latter being consistent with the MABL response to SSTs. The magnitude of the mean (rectified) SST change is greater from the Ue effect than the Te effect, suggesting that Ue causes a stronger dynamical adjustment process in the CCS.
The ML temperature tendency on the left-hand side of (2) is determined by the terms on the right-hand side. The first two terms are the horizontal advections by depth-averaged current and by the deviation from the mean current. The third and fourth terms are the entrainment and the turbulent heat flux at the ML bottom. The fifth and sixth terms are the heat flux absorbed in the ML and the horizontal heat diffusion.
Results from the summertime (July–September) mixed layer heat budget analysis showing the difference in the budget terms (°C day−1): (top) CTL-noTe and (bottom) CTL-noUe. (a),(e) Mean horizontal advection (Hadvm); (b),(f) eddy horizontal advection (Hadve); (c),(g) net heat flux (Q0); and (d),(h) the residual (R). The red (blue) contours denote the corresponding positive (negative) changes in SST (CI = 0.3°C beginning from ±0.3°C).
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
Overall, the SST–wind and current–wind coupling effects generate different time mean–rectified SST response patterns, which are determined by the differences in advection of the altered wind-driven mean currents and the associated eddies. Since air–sea interaction arises from the altered SST fields brought about by the changes in mean and eddy advection, the following sections investigate the change in eddy energetics and the resultant ocean–atmosphere coupling.
4. Eddy variability
a. Impact on eddy kinetic energy
Figure 4 compares the JAS surface EKE per unit mass: 
(a) The summertime (July–September, 2005–10) surface EKE (cm2 s−2) derived from the altimeter dataset assuming geostrophy. (b)–(f) Simulated surface EKEs. The black box in (b) denotes the area to calculate the mean EKE in Table 2 and Fig. 6 (32°–45°N and 130°–120°W).
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
July–September (JAS) surface EKE averaged over 32°–45°N and 130°–120°W (the black box Fig. 1g). Percent change from CTL is shown in the parentheses.
Figure 5 compares the depth versus cross-shore section of the JAS EKE averaged in the alongshore direction between 30° and 45°N (Fig. 4b). The EKE is surface intensified and exhibits a maximum 50–100 km offshore. The noTe case has essentially the same structure of EKE, while noUe shows a much-enhanced EKE in the upper 50 m and extends deeper (cf. the isopleths of 100 cm2s−2) and farther offshore. The noTeUe case has nearly the same EKE distribution as noUe, and noUtot has slightly stronger EKE due to the additional effect of Ub.
Depth vs cross-shore distribution of the simulated EKE (cm2 s−2). Black curve denotes the isopleth of EKE = 100 cm2 s−2. The dark green contours represent the isotherms of 10°, 12°, and 14°C.
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
Figure 6 shows a year-round time series of the monthly mean surface EKE averaged over 32°–45°N and 130°–120°W (Fig. 4b). The EKE levels have a strong seasonal cycle with the maxima in summer and the minima in winter. The EKE in CTL (red) and noTe (orange) are again similar in both seasons, while the runs without ocean current effects (blue to green curves), whether background or eddy, all display the higher EKE. It is interesting to note that the EKE difference due to the surface current effect is even stronger in winter, while that due to the SST effect remains unimportant. This implies that in winter, while the SST–wind coupling effect ceases to be important because of the lack of upwelling and SST gradients, the current–wind coupling effect continues to affect the energetics of the CCS. A closer examination of the seasonality of the coupling effects is currently underway and will be reported elsewhere; this study focuses solely on the summertime upwelling season.
Monthly time series of the simulated surface EKE (cm2 s−2) averaged over the upwelling zone (32°–45°N, 130°–120°W; Fig. 4b).
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
b. Role of wind forcing and instability on the EKE response
Figure 7 shows the three energy conversion terms from CTL. Strongest near the coast north of San Francisco, P is the dominant source term for EKE. BC is of secondary importance over the shelf. The sum of the effects of barotropic and Kelvin–Helmholtz instabilities (BT) is small, perhaps because the model does not fully resolve the small-scale shear of the currents (Brink 2016; Brink and Seo 2016). Decomposition of P into the zonal 
Energy conversion terms (10−8 m2 s−3) calculated for the summer (July–September) 2005–10 from CTL. (a) BT denotes the sum of two energy conversions: barotropic and Kelvin–Helmholtz instabilities. (b) BC is the baroclinic instability; (c) the P term. (d)–(e) The zonal 
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
The zonal component Px is weak but negative in the upwelling zone, which acts to dissipate the EKE. The negative correlation between u′ and τx′ is explained by the fact that the zonal current at the surface u′ is in part a wind-driven Ekman response to southward τy′ (Fig. 2); that is, when τy′ is negative (upwelling favorable), the portion of u′ that is driven by the Ekman transport is directed offshore. During typical upwelling conditions, τx′ is weakly eastward since the large-scale wind stress is southeastward (Fig. 2). Thus, u′ and τx′ should be in the opposite direction during the upwelling conditions. This is evidenced by the fact that negative Px is strong over the upwelling zone south of Cape Blanco, where the eastward component of the wind stress emerges in the lee of capes and with the southeastward bend of the coastline (Dorman and Koračin 2008). This implies that the inclusion of the surface current effect reflects not only the small-scale eddies (internal variability), but also the linear wind-driven Ekman component that is characteristic of summertime eastern boundary current systems. Therefore, some of the Ue effects discussed in this study might be predictable from the large-scale wind fields, given that the summer wind field is remarkably steady in the CCS (Chelton et al. 2007). However, the wind energy input is dominated by Py.
Since P and BC are the two dominant sources of EKE, the following analysis will focus on these two terms. The subsequent analysis will also focus on CTL, noTe, and noUe only, showing the starkest contrasts. Figure 8 shows EKE, BC, and P as a function of the offshore distance averaged along the coast between 35° and 45°N and over the upper 100-m depth. EKE peaks at 150 km offshore in all three runs, and noUe remains higher much farther offshore with a secondary peak at 300 km. Again EKE in CTL and noTe are nearly the same, and the noUe EKE is greater by about 56% when averaged over the offshore distance. BC peaks at about 50 km offshore in all three runs, coinciding with the location of the summertime upwelling front (Fig. 2). The BC then rapidly decreases offshore out to 450 km. CTL and noTe show similar cross-shore profiles of BC with nearly the same cross-shore average values. On the other hand, noUe has lower BC with the largest reduction in the range between 100 and 200 km. The weaker BC in noUe is, therefore, unlikely to cause the higher EKE. In order for the BC to change significantly, there should be a strong change in alongshore wind stress via the SST–wind coupling relationship. This may occur when the effect of “broader-scale” cold SST in the upwelling zone is removed, as was done in Jin et al. (2009), but not on the oceanic eddy scales. The alongshore wind stress is not so much changed after all (Fig. 2).
Cross-shore distribution of the upper 100-m-averaged (a) EKE (cm2 s−2), (b) BC (10−8 m2 s−3), and (c) P (10−8 m2 s−3) during the summer (July–September) of 2005–10. The cross-shore averaged quantities are shown in the legend of each panel.
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
Changes in eddy–wind interaction clearly explains the difference in the EKE. The P term is strongest near the shore at ~25 km. The P term in noTe is only slightly changed, suggesting that suppressing the Te effect on the wind speed does not affect the wind–energy transfer, consistent with the minimal change in wind stress and BC. On the other hand, there is a strong increase (~24%) in P in noUe over most of the cross-shelf distance; that is, suppressing the Ue effect on wind stress results in more wind energy transfer to the ocean, accounting for the large increase in EKE. Inspection of the zonal and meridional components of the eddy–wind interaction term provides further insights into the cause of this change (Fig. 9). Recall that the Px is negative in the upwelling zone, damping the EKE. This damping effect in CTL is weakened in noUe by about 30%. The noTe case yields some (~11%) increase in the damping effect compared to CTL. The Py shows that the positive wind energy input is increased when Te is suppressed (by ~7%) and when Ue is suppressed (by ~10%), helping to increase further the EKE. Despite the seemingly large difference in percentage changes, the changes in absolute magnitude are comparable between Px and Py; therefore, both terms should be of comparable importance in generating a lower EKE level in CTL.
As in Fig. 8, but showing the (a) zonal and (b) meridional components of the P term.
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
5. Impact on Ekman pumping velocity
The WSST is estimated by calculating the perturbation SST-driven wind stress curl 
Binned scatterplots between perturbation wind stress curls (∇ × τ)′ [N m−2 (104 km)−1] and perturbation crosswind SST gradient 
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
The observations based on the NOAA OI SST and the QuikSCAT wind stress for the period of 2005–09 show a quasi-linear relationship between 
The observed linearity is reasonably well reproduced in CTL, noUe, and noUtot, which contain the eddy SSTs and thus the associated crosswind SST gradients. Note that these runs contain a much wider range of the crosswind SST gradients, as much as ±4°C (100 km)−1, but the linearity in wind stress curl response is well preserved even at the extreme ends of the distribution. In contrast, noTe and noTeUe both feature very weak and insignificant linear regression coefficients with the limited range of the crosswind SST gradients. Using the resulting coupling coefficients, WSST is estimated for each case and compared with two other terms: WLIN and Wζ.
Figure 11 shows the summertime mean Ekman pumping velocities (m day−1) in 2005–09 from the observations and CTL. In both the observations and CTL, WLIN is dominant in WTOTe with magnitudes reaching more than 0.4 m day−1 upwelling near the coastal zone and comparatively weaker downwelling of 0.1–0.2 m day−1 in the broader offshore regions. The term WSST is weakly positive in the upwelling zone near the coast, with typical values of 0.1–0.2 m day−1, while it is negative in the lee of Pt. Conception and into the Southern California Bight. The term Wζ shows noisy spatial structures reflecting the gradients of the vorticity of the eddy-induced surface currents. Large-scale patterns of WTOTe are similar to WLIN, but the detailed structure in WTOTe is determined together by WSST and Wζ, suggesting that small-scale SSTs and surface currents are important in determining the climatological pattern of the Ekman pumping velocity. In noTe (Fig. 12, top), it is not surprising that WSST vanishes; the small-scale structure of the WTOTe climatology is determined by Wζ. Likewise, in noUe (Fig. 12, bottom), Wζ is negligible and WSST becomes important for the small-scale structure of WTOTe.
July–September (2005–09) averaged (a),(e) SST-induced Ekman pumping (WSST); (b),(f) vorticity gradient–induced Ekman pumping Wζ; (c),(g) linear Ekman pumping WLIN; and (d),(h) the estimated total Ekman pumping WTOTe, which is the sum of the first three terms, from (top) observations and (bottom) CTL (units: m day−1).
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
As in Fig. 11, but for (top) noTe and (bottom) noUe.
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
The terms WSST and Wζ have comparable magnitude and range of variability but very different spatial structures. Since WLIN is independent of the eddy fields, it is nearly the same across the experiments. The difference in WTOTe is, therefore, attributed to the difference in eddy fields, either via crosswind SST gradient or surface vorticity. Figure 13 shows the climatological difference in the WTOTe between CTL and noTe (top) and that between CTL and noUe (bottom). The magnitudes of the differences exceed ±0.3 m day−1 in both comparisons. The difference patterns visually correspond well to the differences in SST gradient ∇T in Fig. 13a (overlaid contours) and the surface vorticity ζ in Fig. 13c. The spatiotemporal correspondence is further quantified by constructing binned scatterplots between the difference in WTOTe and the difference in ∇T (Fig. 13b) and ζ (Fig. 13d). Both cases display strong linear relationships with a significant regression coefficient of Sc = 0.05 m day−1 [°C−1 (100 km)−1]−1 for the CTL-noTe case and Sc = −0.25 m day−1 day−1 for the CTL-noUe.
(left) July–September (2005–09) mean difference in the estimated total Ekman pumping velocity WTOTe (shading; m day−1) overlaid with (a) difference in SST gradient [°C (100 km)−1, CI = 1, zero contours suppressed] and (c) surface vorticity (s−1, CI = 0.2, zero contours suppressed). (right) Binned scatterplots between the difference in WTOTe and the difference in (b) SST gradient and (d) surface vorticity. All slopes are statistically significant at p = 0.01.
Citation: Journal of Physical Oceanography 46, 2; 10.1175/JPO-D-15-0086.1
The strong linear relationship in Fig. 13b confirms that the WSST preferentially affects the propagation of the eddy (Dewar and Flierl 1987). For a northerly wind over a cold-core cyclonic eddy, for example, the SST–wind relationship results in upwelling (downwelling) in the western (eastern) part of the eddy, helping it to propagate westward [see results from the idealized eddies or observed composite of the real eddies in Chelton (2013) and Gaube et al. (2015)]. The opposite is true for a warm-core anticyclonic eddy. In contrast, the strong negative relationship between ζ and the Ekman pumping in Fig. 13d suggests that the same cyclonic (anticyclonic) eddies induce anomalous downward (upward) Ekman pumping velocities, acting to weaken the amplitudes of the eddies themselves regardless of the sense of rotation. These two effects are consistent with the result of the spatially averaged EKE difference showing that suppressing Ue produces the stronger eddy activity, while suppressing Te has no significant effect.
6. Summary and discussion
The summertime California Current System (CCS) is characterized by persistent and energetic mesoscale eddies with typical anomalies in SST and cross-shore surface current exceeding 2°C and 0.5 m s−1, respectively. For the first time, this study examines the relative effect of the small-scale eddy SST and surface current on the wind stress and Ekman pumping and the impact on the energetics and dynamic response of the CCS. Our high-resolution (7 km) regional coupled model simulations capture the simultaneous coupling processes due to eddy-induced SST and currents, while the respective effects can be inferred from otherwise identical experiments with either coupling effect suppressed. The online smoothing procedure also allows distinguishing the eddy-driven coupling effect from that due to large-scale coupling.
In general, the results highlight the remarkably strong effect of eddy–wind interaction via surface current. The magnitude of the mean SST change is greater and extends farther offshore when the eddy current is allowed to affect the wind stress. The resulting change in SST is characterized by alternating elongated bands of positive and negative anomalies extending from the coast southwestward. This pattern is closely related to the change in onshore and offshore surface current anomalies. The simplified mixed layer heat budget suggests that the mean horizontal temperature advection between nearshore and offshore are mainly responsible for the emergence of the alternating SST anomaly patterns. The horizontal temperature advection by eddies offsets the mean advection, suggesting an active role of eddies in determining the rectified time-mean SST response. The change in temperature advection by both the mean and eddy currents is greater with the effect of surface current on wind stress than that with SST. Therefore, the eddy current effect on wind stress causes the stronger dynamical response in the CCS.
The subsequent analysis of the EKE and the energy conversion process supports this conclusion. The EKE is considerably reduced when eddy–current interaction is included in the bulk parameterization, whereas eddy–SST interaction shows very little effect. The weakened EKE with the surface current effect is due to the increased surface eddy drag (Eden and Dietze 2009) and the reduced wind energy transfer (Hutchinson et al. 2010). Changes in baroclinic and barotropic conversion processes are comparatively small and hence unlikely to explain the difference in EKE.
Modified wind stress over the CCS eddies produces perturbation wind stress curl and Ekman pumping velocity through the crosswind SST gradient and the surface vorticity gradient. The resultant Ekman pumping velocities are of comparable magnitudes, but their juxtaposition with the SST gradient and the vorticity of the surface current implies different dynamical feedback mechanisms. The eddy current–induced Ekman downwelling (upwelling) are collocated with the cyclonic (anticyclonic) eddies, acting to attenuate the eddy amplitude. In contrast, the SST-induced Ekman upwelling (downwelling) is spatiotemporally well correlated with the positive (negative) SST gradients. Considering the 90° out-of-phase (quadrature) relationship between the SST/SSH and their gradients in typical cold-core cyclonic and warm-core anticyclonic eddies (e.g., Gaube et al. 2014, 2015), this SST-induced Ekman pumping velocity would preferentially influence the propagation of the eddies. The implied feedback effects of the current- and SST-induced Ekman pumping velocity on the eddy activity are consistent with the interpretation of the spatially averaged EKE response. Further eddy-centric analysis is needed to examine the changes in propagation characteristics of the eddies using a Lagrangian eddy-tracking procedure (Jin et al. 2009; Kurian et al. 2011; Gaube et al. 2014; 2015); this also is a topic of a future study.
The results imply that, for the ocean-only model forced with wind products that do not include the ocean current effect (e.g., atmospheric reanalyses), the inclusion of the surface current in the bulk formula for wind stress would help to improve the model simulations in terms of energetics of the ocean circulation and mesoscale eddies (Fig. 4; see also Xu and Scott 2008). However, the same statement may not be true for ocean models forced with scatterometer estimates of the 10-m wind field since the wind estimates are already based on the moving ocean surface. The mismatch between the prescribed (observed) current effects contained in the QuikSCAT and the simulated currents (occurring with random phase) would lead to misrepresentation of the two small-scale processes that require the covariance between the surface current and wind stress, that is, the surface drag and the wind work, as demonstrated in this study. This small-scale error would lead to a possible source of large-scale bias through their effects on surface stress and Ekman pumping. For this reason, the use of “absolute” winds is advised to force the global ocean–sea ice model, which is in agreement with the recommendation from WCRP (2015).
Overall, this study demonstrates the remarkably strong effect of the eddy surface current on the Ekman pumping, the eddy energetics, and the dynamics of the current system in the CCS. Given the persistent and nontrivial amplitude of the rectified response in SST climatology (>±1°C), some ensuing important atmospheric feedback effect is expected by the current–wind coupling in the CCS, for example, on the low-level stratiform cloudiness and the surface radiation budget (e.g., Klein and Hartmann 1993; Norris and Leovy 1994; Schwartz et al. 2014). The effect is likely to be also important in other oceanic regions with strong eddy activities or semipermanent frontal zones such as western boundary currents. In those regions, the eddy current coupling effect exerts continuous influence on wind stress both in summer and winter, while the SST–wind coupling effect might cease to be important in summer without strong SST gradients. The resultant rectified response of low-level baroclinicity and storm track variability in the atmosphere has not been demonstrated or quantified in the literature. To the extent that the eddy current effect is important in the SST, the so-called frontal-scale air–sea interactions, primarily treated as the SST-driven air–sea coupling process, will need to consider the effect of eddy dynamics and oceanic currents as an alternative coupled ocean–atmosphere mechanism that could play an important role in the climate system.
Acknowledgments
We thank NSF for support under Grants OCE-0960770, OCE-1419235, and OCE-1419306. HS is grateful for the WHOI internal support from the Andrew W. Mellon Foundation Awards for Innovative Research and the additional support from the ONR Young Investigator Program (N00014-15-1-2588). Our study of the impact of the smoothing of ocean currents, rather than smoothing of SST alone, was instigated by Dudley Chelton’s presentation at the Workshop on Climate Implications of Frontal Air–Sea Interaction (http://www.cgd.ucar.edu/events/fsasi-workshop) in Boulder in 2013. The online 2D smoothing routine is provided by Dr. Dian Putrasahan. HS thanks Peter Gaube, Ken Brink, and Justin Small for their stimulating discussions. Two anonymous reviewers are thanked for their constructive comments, which helped to substantially improve the manuscript.
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