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Effects of Spatial Scale Modification on the Responses of Surface Wind Stress to the Thermal
Front in the Northern South China Sea
RUI SHI,a,b,c XINYU GUO,d JU CHEN,a LILI ZENG,a,c BO WU,b AND DONGXIAO WANGe
aState Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences,
Guangzhou, Chinab
State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of AtmosphericPhysics, Chinese Academy of Sciences, Beijing, ChinacSouthern Marine Science and Engineering Guangdong Laboratory (Guangzhou), Guangzhou, ChinadCenter for Marine Environmental Studies, Ehime University, Matsuyama, Japane
School of Marine Sciences, Sun Yat-Sen University, Guangzhou, China(Manuscript received 30 June 2021, in final form 7 October 2021)
ABSTRACT: The responses of surface wind stress to the mesoscale sea surface temperature (SST) anomalies associatedwith the SST front in the northern South China Sea (NSCS) are studied using satellite observations and reanalysis data. Bothsatellite and reanalysis data explicitly show the linear relationships between the spatial-high-pass filtered wind stress perturbation derivatives and the underlying SST gradient field. However, the noise in the linear relationships is much smaller inthe reanalysis data than in the satellite observations. This result is rarely reported in other frontal areas. The wavelet analysis
shows that the satellite scatterometer observed numerous high wavenumber perturbations within 100 km in the NSCS, butthese perturbations were absent in the reanalysis data. The linear relationship between the perturbation SST gradient andderivative wind stress fields is not significant at this scale, which enhances the noise in the linear relationship. The spatial
bandpass-filtered perturbation between 100 and 300 km can give reasonable estimates of the coupling coefficients between
the wind stress divergence and downwind SST gradient (ad) and between the wind stress curl and crosswind SST gradient(ac) in the NSCS, with values of 1.33 3 1022 and 0.95 3 1022 N m22 8C21, respectively.
SIGNIFICANCE STATEMENT: We examined the responses of surface wind stress divergence and curl to the sea
surface temperature front in the northern South China Sea (NSCS) using satellite data and reanalysis products. Satellite
observations show significant noise in the linear relationships between surface wind stress derivatives and the sea surface
temperature gradient. This result is rarely reported in the frontal areas. We demonstrated that satellite-observed perturbations with specific high wavenumbers are the primary source of such noise. Appropriate bandpass filtering is
proposed to depress the noise and provide reasonable air–sea coupling features in the NSCS. An accurate calculation of
the coupling features is fundamental for the future study of the interannual variability.
KEYWORDS: Atmosphere; Ocean; Asia; Continental shelf/slope; Sea/ocean surface; Atmosphere-ocean interaction; Fronts;
Mesoscale processes; Sea surface temperature; Wind; Air-sea interaction; Coastal meteorology; Satellite observations

1. Introduction
The thermal front is a mesoscale oceanic phenomenon
identified by a discontinuity in water temperature in the ocean
or at the surface. A sea surface temperature (SST) front is themost commonly observed thermal front in the open ocean andcoastal seas. The SST anomalies associated with a front cansignificantly modify the surface heat fluxes, wind stress, andmarine atmospheric boundary layer (MABL) (Chelton and
Xie 2010; Shao et al. 2019). Many observations and numericalsimulations have identified a positive correlation between
surface wind intensity and SST mesoscale anomalies. The
surface wind intensity is enhanced when passing across a front
from cold to warm water but is reduced when passing from

Denotes content that is immediately available upon publication as open access.
Corresponding author: Rui Shi, shirui@scsio.ac.cn

warm to cold water. The linear fitted relationship between thesurface wind intensity and mesoscale SST variability is defined
as positive SST–wind coupling (Small et al. 2008).
Positive SST–wind coupling is widely confirmed in thefrontal area of the eastern tropical Pacific (Chelton et al. 2001),
the Kuroshio and its extension (Tokinaga et al. 2006), the Gulf
Stream (Minobe et al. 2008), and the Southern Ocean (Byrne
et al. 2015). Additionally, the SST-induced response of thesurface wind leads to a proportional relationship between
the derivative of wind stress and SST gradient components.
The surface wind stress divergence (=  t) and curl (= 3 t)  k
are linearly related to the downwind and crosswind componentsof the SST gradient, respectively. The downwind SST gradientcan be presented by the vector dot product =T  t^ 5 j=Tj cosu,
and the crosswind SST gradient is presented by the vector
cross product =T 3 t^  k 5 j=Tj sinu. Here, T is SST, t^ is a unit
vector in the direction of surface wind stress t, k is the verticalunit vector, and u is the counterclockwise angle from thevector =T to t (Chelton et al. 2001; O’Neill et al. 2010a; Oerder
et al. 2016).

DOI: 10.1175/JCLI-D-21-0498.1
Ó 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright
Policy (www.ametsoc.org/PUBSReuseLicenses).
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FIG. 1. (a) Map of the SCS and surrounding area; shading shows bathymetry. (b) Monthly mean SST gradient(color shading; 8C km21), SST (gray contours; 8C), and sea surface wind (black vectors; m s21) averaged for
December from 2000 to 2019. Three main front systems are marked by the red dashed auxiliary lines.

O’Neill et al. (2010a) clarify that the linear responses of
surface wind stress to mesoscale SST variability are mainly
attributable to a dynamic response of the actual surface wind.
Therefore, the surface wind stress convergence can be directly
related to the mass convergence that modifies the vertical motionof the atmosphere. For example, SST-induced mass convergenceand vertical motion can have a deep atmospheric response in theform of convective systems and rainfall, which shapes the regional climate in strong western boundary current frontal areas(Minobe et al. 2008; Nakamura et al. 2012; Kuwano-Yoshida andMinobe 2017; O’Neill et al. 2017; Skyllingstad et al. 2019) andcoastal front areas (Toy and Johnson 2014; Shi et al. 2019).
Furthermore, the SST–wind coupling feedback also affects thefine structures of ocean fronts through Ekman pumping createdby mesoscale anomalies in the wind stress curl (Spall 2007; Seoet al. 2007; Perlin et al. 2014; Gaube et al. 2015).
As reviewed by Byrne et al. (2015), various hypotheses havebeen proposed to explain the adjustment of the sea surface windfield to the SST gradients associated with oceanic fronts. The
generation of hydrostatic pressure gradients through adjustmentsof the MABL mass fields (Lindzen and Nigam 1987) and thestability-dependent modification of the vertical mixing of momentum from aloft to the surface (Wallace et al. 1989; Hayes et al.
1989) are the two major hypotheses. These two mechanisms havealso been shown to act together (O’Neill et al. 2010b; Koseki and
Watanabe 2010). In addition to these two mechanisms, there areother explanations for the positive SST–wind coupling (Samelson
et al. 2006; Skyllingstad et al. 2007). Building upon these findings,
O’Neill et al. (2010b) concluded that several regional factors
might affect the physical mechanism involved in mesoscale SST–
wind coupling. Therefore, mesoscale ocean–atmosphere coupling
complicates marginal and coastal seas and still needs to be further
studied (Boé et al. 2011; Oerder et al. 2016).
The South China Sea (SCS) is an epicontinental marginal
sea strongly influenced by the East Asian monsoon (Fig. 1a).
The interaction among the monsoon, bathymetry, and tides
generates several kinds of fronts in the coastal sea of thenorthern SCS (NSCS), especially in winter (Wang et al. 2001;
Chu and Wang 2003; Liu et al. 2010; Hu and Wang 2016).
During winter, three unique frontal systems are confirmed in
the NSCS, off western Luzon, and off eastern Vietnam(Fig. 1b). The NSCS front produces the most dramatic SST
gradient among the three frontal systems and has the broadest
coverage area in the SCS. It is the focus of this study.
The responses of the surface wind to the mesoscale SST
anomalies associated with the NSCS front have been investigated in some previous studies (Chow and Liu 2012; Wang et al.
2012; Shi et al. 2015). The main findings of these previous studies
are consistent with the mesoscale SST–wind coupling theory inthe open ocean. However, beyond what is known about the windspeed response to mesoscale SST perturbations, little is known
about the coupling features between the surface wind stress curland divergence and such SST anomalies. Furthermore, different
coupling coefficients between the surface wind speed and mesoscale SST anomalies are obtained from satellite observations
and numerical simulations, and the mechanisms for such differences are still unclear (Shi et al. 2015).
On the other hand, a recent study found that the spatial andpreserving time scales of SST perturbations due to the baroclinic
instability of the front could be extremely small in the NSCS
(Dong and Zhong 2020). These small SST and wind stress perturbations are usually not resolved in the reanalysis data but
rather by scatterometers on satellites. The influence of thesesmall-scale SST perturbations on SST–wind coupling is still
poorly constrained. Therefore, in this paper we will not further
discuss the complicated details of the physical mechanisms but
will focus instead on the statistical characteristics of the relationships between the derivative of surface wind stress and SST
anomalies at different scales in the NSCS.
In this study, two kinds of surface wind stress and SST data
are obtained from satellite observations and ERA5 reanalysis
data, as discussed in section 2. The statistical responses ofspatial-high-pass filtered surface wind stress divergence andvorticity to crosswind and downwind SST gradients are shown

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in section 3. In section 4, the sensitivity experiments show theinterference of specific high-wavenumber perturbations on thelinear relationships between the derivative wind stress fields
and the SST gradient components. An optimal bandpass filter
is given in section 4, and corrected coupling coefficients of theSST–wind coupling are proposed for the NSCS. Section 5gives a brief review of this study.

2. Data and methods
a. Satellite observation and reanalysis data
The sea surface wind data observed by a Quick Scatterometer(QuikSCAT) and Advanced Scatterometer (ASCAT) are usedin this study. QuikSCAT data provide extensive geographicaland temporal coverage (two times in one day) and higher spatial
resolution (0.258) of the ocean vector winds since late 1999. After
QuikSCAT finished its mission in October 2009, ASCAT continued to provide global sea surface wind data. Due to the above
advantages of the long period of operation, these two kinds ofwind data are broadly used to study the mesoscale SST–windcoupling process over the tropical and midlatitude fronts in the
Northern Hemisphere and Southern Ocean (O’Neill et al. 2017).
The Operational SST and Sea Ice Analysis (OSTIA) producedby the U.K. Met Office is used in this study. The OSTIA system
makes extensive use of multiple satellite retrievals and assimilates in situ observations from the Global Telecommunications
System to generate a global daily SST map with 1/208 (;6 km)
resolution back to 1980. It is currently used operationally as themodel input condition for the latest Integrated Forecast System(IFS) of the European Centre for Medium-Range Weather
Forecasts (ECMWF) (Hersbach et al. 2019). OSTIA data havebeen successfully applied to drive a regional atmosphere modeland study the surface wind response to the oceanic front in the
NSCS (Shi et al. 2017).
ERA5 is the latest reanalysis dataset officially released by
ECMWF in 2019. ERA5 is based on 4D-Var data assimilation
using Cycle 41r2 of the IFS operational model at ECMWF in2016 (Hans et al. 2019). It is the successor of the ERA-Interim
reanalysis that started in 2006. Therefore, ERA5 benefits from a
decade of developments in model physics, core dynamics, anddata assimilation relative to its precursor ERA-Interim. In addition to a significantly enhanced horizontal resolution(31-km grid spacing compared to 80 km for ERA-Interim),
ERA5 also features upgraded high-resolution SST data (OSTIA)
and provides remarkable improvements in resolving mesoscale
SST–wind coupling around midlatitude oceanic fronts (Hirahara
et al. 2016). It is expected that ERA5 can also resolve the SST–
wind coupling around the coastal fronts in the NSCS.
In this study, the 10-m equivalent neutral stability wind(ENW) provided by ERA5 was used to calculate the windstress vector directly observed by the satellite scatterometer.
The wind stress vector t and 10-m ENW vector v10n are related
by t 5 ra Cd jv10n j  v10n , where ra is air density (1.29 kg m23) and
Cd is the momentum drag coefficient (1.41 3 1023). Although
the scatterometer data are absorbed in the data assimilation,
the ERA5 surface wind fields still have different statisticalfeatures due to the constraint of the dynamical frame and the

FIG. 2. Monthly average maps in December 2008 of (a) SST(color shading; 8C), sea surface wind (vectors; m s21), and SST
gradient magnitude (contours; 8C km21); (b) SST gradient magnitude (color shading), SST gradient vectors (red), and wind stressvectors (black); (c) wind stress divergence; and (d) wind stress curl.
The contours overlaid in (c) and (d) denote SST, and magenta
contours show the 200-m bathymetries in the northern South
China Sea.

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FIG. 3. Binned scatterplots of the angular dependencies of (a),(b) the number of observations, (c),(d) themagnitude of =jtj, and (e),(f) the magnitude of =T over the three months of data from December 2008 to February
2009. The abscissa is the counterclockwise angle u from the SST gradient vector to the wind stress vector. The solid
circles and vertical bars in (c)–(f) represent the mean and 61 standard deviation of the scatter of points within eachbin. Bins larger than 308 are discarded in (c)–(f) due to the small number of grids shown in (a) and (b). (left) Plots of
QuikSCAT wind and OSTIA SST, and (right) plots of ERA5 wind and SST.

difference in the spatial resolution. Furthermore, qualitatively
similar responses of the surface stress and ENW to the SST are
confirmed in the study of O’Neill et al. (2012). Therefore, SST–
wind coupling is referred to as the wind stress response to the
SST in this study.
The OSTIA SST and ERA5 data are linearly interpolated
to the QuikSCAT grid for the calculation and analysis. It has
been documented that orographic effects create wind stressmesoscale anomalies that are more intense than SST-induced
anomalies in coastal regions (Boé et al. 2011; Renault et al.
2015). Nonetheless, after discarding the grids with an offshore
distance of less than 25 km, QuikSCAT still provides robust
data for the analysis of SST–wind coupling in the coastal seaof the NSCS.
The regridded daily satellite and reanalysis data are low-passfiltered using a 3-day running mean. For the three months ofthe boreal winter [1 December–28 February (DJF)], there are
88 pairs of data at one QuikSCAT grid for quantifying the
responses of surface wind stress to the SST anomalies associated with the front. As shown later, the difference between
satellite data and the reanalysis data for the coupling of wind
and SST can be found in each of the DJFs from 2000 to 2019,indicating that one season of DJF data is sufficient to demonstrate the difference. Because the SST–wind coupling strengthin DJF of 2008 is close to the mean strength of all the DJFs
from 2000 to 2019, we mainly present the analysis results in
DJF of 2008 in this study.

b. Preprocessing for the surface wind stress and SST field
Most previous studies investigating mesoscale SST–windcoupling in the frontal region have applied spatial high-passfiltering to isolate the mesoscale SST influence on surface winds.
The same method is carried out in this study. A rectangular (38 328) moving window is applied to obtain the spatially smoothed(low-pass) SST (T), wind stress (t), and its deriving fields. Then,the mesoscale anomalies of a variable T0 or t0 are obtained by
T 0 5 T 2 T, and t0 5 t 2 t, where the variables with overbars
are the spatially smoothed fields and the dashed variables are theisolated spatial high-wavenumber perturbations.
The perturbation of angle u is not directly calculated using
the spatial-high-pass filter. It is assumed at first that positive
SST–wind coupling is valid for the perturbations induced by
the SST front; then, we should expect =  t0 to vary linearly with(=T  t^)0 and = 3 t0 to vary linearly with (=T 3 t^)0  k. This

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FIG. 4. As in Fig. 3, but for the perturbation wind stress fields and SST, t0 , and T0 . The abscissa is the perturbation
counterclockwise angle u0 defined by Eq. (1).

means that =  t 0 and = 3 t 0 should be proportional to thecosine and sine of u0 defined as
2

3
0
^
(=T
3
t
)

k
5,
u0 5 tan21 4(=T  t^)0(1)since the numerator and denominator in Eq. (1) can be written as(=T  t^)0 5 j=T 0 j cosu0 ,(=T 3 t^)0  k 5 j=T 0 j sinu0 .

andthe zonal scale of these perturbations is less than 100 km.
Therefore, this filter cutoff is long enough to retain most mesoscale perturbations of wind and SST in the frontal area. On theother hand, this filter is short enough to reduce the biases of thespatial smoothing near the boundary due to the absence of data.

3. Response of the surface wind stress field to the SST
front in the NSCS

(2)

a. Mean state of surface wind stress and SST front(3)

A monthly average map of QuikSCAT wind and OSTIA
SST for December 2008 is shown in Fig. 2a. It is a representative period of winter monsoon analyzed in the study area.
During this period, the northeasterly monsoon covered theentire domain, and a southwest–northeast-oriented front was
identified parallel to the coastline. The SST gradient is generally weaker in the western portion of the NSCS than in theeastern area near the Taiwan Strait. Visual examination suggests that coastal fronts mainly occur in three areas in the
NSCS where the magnitude of the SST gradient exceeds 0.018C
km21, and it can be seen clearly that the wind stress is higher
over warm water and lower over cold water. As summarized in
the introduction, the close relationship between SST and windstress magnitude is qualitatively consistent with the positive
SST–wind coupling.

The left sides of Eqs. (2) and (3) are directly calculatedusing the spatial-high-pass filter. Therefore, if the assumed
SST–wind relations are proven, so is the definition of u0(Chelton et al. 2001; O’Neill et al. 2005).
The spatial filter cutoff (38 3 28) applied in this study isnarrower in the meridional direction than in the zonal direction. This is because the coastal front in the NSCS is long but
narrow. The south–north width of the front associated with asignificant SST gradient is less than approximately 220 km in
most areas (Fig. 2b). Therefore, the meridional scale of mostmesoscale SST perturbations should be less than 220 km.
Meanwhile, as evidenced in Liu et al. (2010), there are many
SST perturbations induced by the meandering of the front, andBrought to you by SOUTH CHINA SEAS | Unauthenticated | Downloaded 12/02/21 01:28 AM UTC

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FIG. 5. Binned scatterplots of the relationships between spatial high-pass filtered SST and derived wind stressfield: (a),(b) the perturbation wind stress divergence, =  t0 , plotted as a function of the perturbation downwind SST
gradient (=T  t^)0 ; (c),(d) perturbation wind stress curl, = 3 t 0 , plotted as a function of crosswind SST gradient(=T 3 t^)0 ; and (e),(f) histograms of the number of observations within each bin for (a) and (b). Here =  t 0 and = 3
t0 are separated into 0.18C 1022 km21 bins defined by the perturbation of crosswind or downwind SST gradients.
The solid circles represent the overall mean values within each bin. The associated vertical bars represent the 61
standard deviation of the mean values within each bin, and sL is the averaged standard deviation. The regression
lines represent least squares fits of the binned overall means; ad and ac are defined in the text.

As shown in Fig. 2c, a band of high divergence is overlaid on
the coastal SST front, where the wind stress increases as the
airflow across isotherms moves toward warmer water. Twointense wind stress divergence bands are observed at thewestern NSCS and southwest off Taiwan, where strong SST
gradients are marked by close SST contours. Meanwhile, aconvergence zone is also observed south of the Taiwan Strait,
where the SST contours are close. This convergence is causedby the narrowing effect of the strait, which intensifies thenortheasterly monsoon inside the strait but weakens it out of
the strait. Therefore, the surface winds in this area are strongly
influenced by the topography and are excluded from ouranalysis.
The wind stress curl is negative in areas where the winds
blow almost parallel to the isotherms over the frontal area
(Fig. 2d). This pattern in the wind stress curl field develops
because the winds are weaker over cold water but stronger
over warm water to the south of the wind direction, resulting
in a lateral change in the wind stress and negative wind stresscurl. A dipole pattern of the surface wind stress curl, whose

western boundary is located at approximately 1198E, is observed southwest of Taiwan (Fig. 2d). This feature of thewind stress curl is mainly caused by the influence of mountains on the northeasterly monsoon, which has been documented in other studies (Wang et al. 2008) and will not be
further discussed in this study. Thus, the following analysis iscarried out in the region west of 1198E, where there are 38 3
30 QuikSCAT grids.

b. Response of surface wind stress to the SST front
Figure 3 quantifies the relation between the divergence of
surface wind stress, SST gradient, and angle u in three months
from December 2008 to February 2009 in the NSCS. QuikSCAT
surface wind stress and OSTIA SST are analyzed first, referred
to as satellite observations hereafter. As shown in Fig. 3a, angles
u are not fully sampled from 21808 to 1808. One significant peakin the histogram of u centered near u 5 2608 indicates the observations within the frontal area where the surface wind blows
to the southwest, and the SST gradient is primarily directed tothe south and southeast (Fig. 2b). Meanwhile, there is no

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FIG. 6. Time series of the averaged standard deviation sL in the linear relationship (a) between =  t0 and (=T  t^)0and (b) between = 3 t 0 and (=T 3 t^)0 in all DJF periods from 2000 to 2019.

apparent peak in the histogram of j(=jtj)j, but a peak in themean values of SST gradient =T is observed at u 5 2908.
The composed ERA5 wind and SST results are also shown in
Fig. 3, referred to as the reanalysis data hereafter. Compared tothe satellite observations, there are some small differences in
the histograms of the reanalysis data. For example, the numberof samples seems to be more concentrated in the region fromu 5 21208 to u 5 08 (Fig. 3b). The magnitudes and the standard
deviations of =jtj are smaller in the ERA5 data than in the
QuikSCAT observation. The ERA5 data described the peak of=T in the study area, but the magnitude of =T is smaller thanthat shown by the OSTIA SST.
The asymmetric distributions of u and =T on the abscissa areremoved using the spatial-high-pass filter to isolate the SST
gradient and surface wind stress anomalies. As shown in Fig. 4,
the distributions of u0 , magnitudes of =jt0 j, and =T0 within eachbin are much more nearly uniform than the unfiltered fields
shown in Fig. 3. It is further confirmed that there is good
agreement between the binned mean value of =  t0 and = 3 t 0
and the sine and cosine fitting of u0 , as we expected in the definition of Eq. (1). Therefore, the relationships between the derivative perturbation wind and the underlying perturbation SST
gradient components are quantified in Fig. 5.
As shown in Figs. 5b and 5d, the ERA5 data confirm that thebinned mean values of the perturbation wind stress divergence,=  t 0 , vary linearly with the downwind perturbation SST gradient, (=T  t^)0 , and the binned mean values of the perturbation wind stress curl, = 3 t0 , vary linearly with the crosswind
perturbation SST gradient (=T 3 t^)0  k. The QuikSCAT wind
and OSTIA SST also presented these linear relations in thebinned scatterplots (Figs. 5a,c), but the slopes of the linear
fitting lines were smaller than those of the ERA5 data.
The slope of the linear fitting line is defined as the coupling
coefficient a, indicating the SST–wind coupling strength. The
satellite observations show that the coupling coefficient between=  t0 and (=T  t^)0 , ad, is 0.64 3 1022 N m22 8C21 (Fig. 5a), which
is approximately 2 times larger than the coupling coefficient between = 3 t0  k and (=T 3 t^)0  k, ac (Fig. 5c). Meanwhile, theERA5 data yield a value of 0.93 3 1022 N m22 8C21 for ad and0.73 N m22 8C21 for ac. The coupling strength ac is approximately
30%–50% weaker than ad, consistent with previous studies inother frontal regions at tropical and midlatitudes (O’Neill et al.
2010a). This indicates the different influences of SST gradientcomponents on the derivative wind stress fields.
The satellite observations and reanalysis data confirm the linear
relations between the derivative of t0 and perturbation SST gradient components. However, there are pronounced differences in
the coupling strength and the standard deviations of the binned
scatterplots. It is shown that the coupling coefficients ad and ac areboth smaller in the satellite observations than in the reanalysis
data. Meanwhile, the averaged standard deviations within eachbin, sL, are approximately 2 times larger in the satellite observations than in the reanalysis data. Such apparent differences in
sL between the satellite observation and reanalysis data have notbeen reported in studies at other frontal regions.
Figure 5 shows that the SST–wind coupling strength is more
substantial in the ERA5 data than in the satellite observations.
This is a significant improvement in the ERA5 data since theprevious study reported that the coupling coefficient obtained by
the former ECMWF operational forecast model (T511) is approximately half as large as that of the QuikSCAT observations(Chelton 2005; Maloney and Chelton 2006). However, the noiseof the SST–wind coupling is significant in the satellite observations, which could increase the biases of the coupling coefficients.
Such noise is presented by the averaged standard deviations sL in
the binned scatterplots. The source of this noise and its essential
effect on the linear relations needs to be further clarified.
It is also necessary to examine whether the significant contrast in noise between satellite observations and reanalysis data
in 2008 DJF is not a solitary case. The averaged standard deviations sL in the binned scatterplots are calculated for all the
DJF periods from 2000 to 2019 (Fig. 6). There is no abruptchange in sL from year to year, and the differences between
the sL of the satellite observations and reanalysis data arestable over the past 20 years. The sL of the satellite observations is always approximately 0.5 to 0.6 N m22 per 104 km
larger than the sL of the reanalysis data. Figure 6 suggests thatthe apparent difference in sL between satellite observations

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TABLE 1. Statistical parameters of the linear regressions between (=  t)0 and (=T  t^)0 with different spatially smoothed satellite
observations; sL is the averaged standard deviation; ad is the slope of the linear regression between the wind stress divergence anddownwind SST gradient; r is the correlation coefficient between the regression lines and the overall mean values within each bin; and R2 is
the R-square statistic of the linear regression. The values in parentheses are the results of ERA5 reanalysis data. Asterisks (*) mark thevalues calculated in the region j(=T  t^)0 j , 0:5 3 1022 8C km21 where the total percentage of the sample is more than 95%.
Spatial smoothing window size
sL
ad
r
R2

No smoothing

0.758 3 08

0.758 3 0.758

1.258 3 08

1.258 3 0.758

1.758 3 0.758

1.258 3 1.258

1.758 3 1.758

1.67 (0.72)
0.64 (0.93)
0.98 (0.98)
0.97 (0.97)

1.53
0.89
0.88
0.78

1.29
0.96
0.79
0.62

1.36
0.89
0.87
0.77

1.12
1.07
0.84
0.71

0.96
1.18
0.90
0.81

0.86
1.01
0.70
0.51

0.43*
1.79*
0.99*
0.98*

and reanalysis data in the DJF in 2008 is not a particular casebut a common feature in the NSCS. In the following sections,
our analysis focuses on DJF in 2008, but the results are also
applicable for DJF in other years.

4. Effects of spatial scale modification on SST–windcoupling
a. Influence of smoothed t and SST on the SST–windcoupling
Figures 5 and 6 show that the noise in the linear relations
between the derivative of perturbation wind stress and SST
gradient is relatively large in the satellite observations. This
noise is possibly related to the fine spatial structures of windstress and SST in the satellite observations, although the resolutions of QuikSCAT and ERA5 wind are similar, as introduced in section 2a. Therefore, it is assumed that this noise
should be depressed if presmoothing of the wind and SST fields
is carried out before spatial-high-pass fitting.
Several sensitivity experiments are carried out to examine
this hypothesis. In the sensitivity experiments, the original
QuikSCAT wind and OSTIA SST are spatially smoothed by amoving window that is smaller than a spatial-high-pass filter.
Then, the new spatial-high-pass perturbation fields and theirderivatives are calculated using the smoothed data and applied
to remake the binned scatterplots. Finally, the statisticalcharacteristics of these new binned scatterplots are calculated
and shown in Tables 1 and 2.
Table 1 shows the change in statistical parameters for thebinned scatterplots between =  t0 and (=T  t^)0 . Generally, thenoise in the linear relation is significantly reduced by increasing
the smoothing window size. The averaged standard deviations
sL decreased from 1.67 to 0.86 N m22 per 104 km after theoriginal satellite observations were smoothed by a window of
1.258 3 1.258. Meanwhile, the coupling coefficient ad increases
from 0.64 to 1.01 N m22 8C21. Nevertheless, the change in theconfidence level and correlation coefficient is small. It is also
noticed that the samples of binned scatterplots gradually concentrate in a region where (=T  t^)0 , 0:5 3 1022 8C km21 dueto the depression of extreme values by smoothing.
Table 2 shows the change in statistical parameters for thebinned scatterplots between = 3 t0 and (=T 3 t^)0  k. Similar to
the results shown in Table 1, sL is also reduced by the growth of
the smoothing window size. However, unlike ad, the coupling
coefficient ac and the confidence level of the linear relationshipboth gradually decrease when the smoothing window size increases. Since the meridional length of the smoothing window
gradually approaches the meridional length of the spatial-highpass filter (38 3 28), the perturbation fields are actually collected in a narrow band. Therefore, there is no significant linear
relationship when a smoothing window of 1.758 3 1.758 wasapplied to the original satellite observations.
Tables 1 and 2 show that the spatial smoothing of QuikSCAT
wind and OSTIA SST could significantly reduce the noise andchange the coupling coefficients in the binned scatterplots. Thisis because spatial smoothing not only performs low-pass filtering of t but also depresses some spatial high-wavenumber
perturbations of t 0 and its derivative fields. The depressed
spatial high-wavenumber perturbations of =  t0 and = 3 t0
may be the primary source of noise in the binned scatterplotsof satellite observations. This issue is further discussed in thenext section.

b. The spatial frequency of =  t 0 in one transect
Figure 7 shows the time–longitude distributions of =  t 0
along a zonal transect at 21.3758N. Figures 7a and 7b showrobust perturbations of =  t0 in both QuikSCAT observation

TABLE 2. As in Table 1, but for the linear regressions between (= 3 t)0  k and (=T 3 t^)0  k. A dash (—) means no mathematical values
are obtained.
Spatial smoothing window size
sL
ac
r
R2

No smoothing

0.758 3 08

0.758 3 0.758

1.258 3 08

1.258 3 0.758

1.758 3 0.758

1.258 3 1.258

1.758 3 1.758

1.83 (0.99)
0.34 (0.73)
0.92 (0.88)
0.86 (0.78)

1.71
0.67
0.88
0.78

1.43
0.55
0.71
0.51

1.49
0.57
0.78
0.61

1.19
0.19
0.28
0.08

1.03
0.09
0.17
0.03

1.04
0.09
0.17
0.03

0.27
—
—
0.03

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187

the transect. From Fig. 7a, it can be seen that 1/vs of most
perturbations are approximately 100 km in the QuikSCAT
observations. As a comparison, 1/vs of most perturbations
are longer than 100 km in the ERA5 data (Fig. 7b).
Meanwhile, 1/vs of the 1.258 3 1.258 smoothed QuikSCAT
observation seems longer than 100 km, which is similar to
the ERA5 data (Fig. 7c).
The length scale 1/vs for the perturbations of =  t0 is further
quantified using wavelet analysis in this study. A zonal or
meridional transect of =  t 0 in one day is connected with thesame transect of =  t0 in the day after. Then, a ‘‘time’’ seriesof =  t0 is obtained by connecting the same transect over
88 days. This means that if there were n grids in the transect,
there were n 3 88 points in the ‘‘time’’ series. The abscissa ofthe obtained power spectrum is a composition of space andtime, and the vertical axis is the length scale 1/vs, which is thereciprocal of spatial frequency.
The power spectrum for the perturbations of =  t0 at 21.3758N
is shown in Fig. 8. Two major bands of 1/vs in the QuikSCAT
observations correspond to 1/vs equaling approximately 90 and
190 km (Fig. 8a). Two significant perturbation bands are also
confirmed on the power spectrum of ERA5 data but correspondto 1/vs equaling approximately 75 km and 150 km, respectively(Fig. 8b). Moreover, the QuikSCAT observations show that the
perturbations of =  t0 are also significant in the region where1/vs
is less than 75 km. As a comparison, these perturbations of =  t 0
are confirmed less frequently in the reanalysis data and were alsosignificantly depressed by the spatial smoothing of QuikSCAT
data (Fig. 8c). Figure 8 shows that when 1/vs is less than 75 km,
there are more perturbations of = . t0 in the QuikSCAT observations than in the ERA5 data.
Figure 8 also shows that significant perturbations were notalways observed throughout DJF but were occasionally observed. For example, most perturbations of =  t0 were observedby QuikSCAT in December and January but almost disappeared in February (Fig. 8a). Although some perturbationsof =  t 0 at 1/vs equal to approximately 150 km could still be
confirmed in February from the ERA5 data, the perturbations
at 1/vs equal to 75 km gradually weakened and disappeared(Fig. 8b). On the other hand, the observed lifetime of theperturbations varied with the change in 1/vs. Relatively large
1/vs perturbations could be continuously observed for morethan 5 days, whereas small 1/vs perturbations usually dissipatedin 2 or 3 days. The different preservation times could potentiallychange divergence and curl responses to the SST gradients.

c. Spatial distribution of 1/vs for =  t 0 and = 3 t 0 in
the NSCS

FIG. 7. Time–longitude distribution of =  t0 in the zonal transectof 21.8758N for (a) QuikSCAT observations, (b) ERA5 data, and(c) the 1.258 3 1.258 spatially smoothed QuikSCAT observations.

and reanalysis data. Considering a pair of positive andnegative values as one period for the variation of =  t0 , thehorizontal distance of this pair approximately equals alength scale 1/vs, where vs is the spatial frequency of =  t0 in

Figure 8 is only a snapshot of the spatial frequency of =  t 0
in one transect. The spatial distribution of the different
frequencies needs to be examined across the whole NSCS.
Then, wavelet analysis is applied for =  t0 and = 3 t0 in zonal
and meridional transects with an interval of 0.258 across thewhole study area. For each transect, the power of the perturbations at each length scale 1/vs is summed during thestudy period. The obtained latitude and longitude for the 1/vs
power spectra of =  t0 and = 3 t0 are shown in Figs. 9 and 10,
respectively.

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JOURNAL OF CLIMATEVOLUME 35

FIG. 8. Morlet wavelet power spectrum for the composed time series of =  t0 at 21.8758N for(a) QuikSCAT observations, (b) ERA5 data, and (c) the 1.258 3 1.258 spatially smoothed
QuikSCAT observations. The abscissa is a combination of the same longitude at 21.8758N over
88 days, and the vertical axis marks the length scale 1/vs that is defined in section 4b. The black
contours on the power spectra are at the 95% significance level.

Figure 9 shows an apparent difference between the satellite
observation and reanalysis data for the spatial distribution of
1/vs in =  t0 . In general, the power for the variance of =  t0 is
more energetic in the satellite observation than in the reanalysis
data at the NSCS. Furthermore, the satellite observations show awide range of 1/vs from approximately 70 to 400 km for the zonal
and meridional =  t0 in the NSCS (Figs. 9a,c). However, the short
1/vs perturbations (1/vs , 150 km) of =  t 0 are not significant in
the reanalysis data (Figs. 9b,d). Additionally, changes in significant
1/vs in different areas are observed in the satellite data but are notclearly observed in the reanalysis data. For example, the short 1/vs
perturbations in the satellite observations are mainly confirmed
south of 228N and west of 116.58E, and the long 1/vs perturbations
are much more significant north of 208N and east of 1168E.

Figure 10 examines the spatial distribution of 1/vs for the
perturbation of = 3 t0 . Compared with Fig. 9, Fig. 10 shows apronounced difference in the zonal perturbations of = 3 t0 .
Although the total power of the perturbations is significant insatellite observation and reanalysis data, neither of them passed
the 95% significance test (Figs. 10a,b). The perturbations of = 3
t0 are mainly significant in the meridional direction in the study
area (Figs. 10c,d). Similar to Fig. 9, for the scale of 1/vs less than
100 km, the meridional perturbations are significant in the satellite observations but very weak in the reanalysis data. For thereanalysis data, the meridional perturbations of = 3 t 0 are
mainly concentrated in the region of 1/vs greater than 150 km(Fig. 10d). Nonetheless, both satellite observations and reanalysis data show that the power of long 1/vs perturbations is

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189

FIG. 9. Latitude–1/vs total power spectrum of =  t 0 for (a) QuikSCAT observation and (b) ERA5 reanalysis
data and longitude–1/vs total power spectrum for (c) QuikSCAT observations and (d) ERA5 reanalysis data.
Here, vs is the spatial frequency of =  t 0 . The blank areas are where the obtained 1/vs is longer than the number ofvalid QuikSCAT data grids. White crosses indicate that the power of variance does not pass the test of the 95%
significance level.

much stronger in the eastern area than in the western area of
the NSCS.

d. The influence of different 1/vs perturbations on the
SST–wind coupling
Figures 9 and 10 explicitly demonstrate that for the scale of1/vs less than 100 km, the satellite observations present more
perturbations of =  t 0 and = 3 t0 than the ERA5 reanalysis
data. Moreover, these short 1/vs perturbations could be crucial
in determining the noise and coupling coefficients of the SST–
wind coupling in the NSCS. Therefore, the coupling coefficients and the biases of the linear relationships are examined
for the perturbations withindifferent lengthﬃ scales. The length
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
scale L is defined as L 5 (1/v2sx ) 1 (1/v2sy ), where vsx and vsy
denote the zonal and meridional spatial frequencies of =  t0 or= 3 t 0 , respectively.
Figure 11a presents a pronounced unimodal structure inplotting the change in the coupling coefficients (linear regression slopes) within different L bands. The coupling coefficients ad and ad both increase at first and reach theirmaximum values when L is longer than approximately
200 km but smaller than approximately 300 km. Then, thecoupling coefficients begin to decrease when L is larger than
300 km. This result emphasizes a critical scale range for the
SST–wind coupling over the frontal area, and the linear
relationship is significant in this range but declines outsideof this range.
The coupling coefficient increase is accompanied by an apparent reduction in the noise (sL) in the linear relationship(Fig. 11b). When the length scale L increased from smaller
than 50 km to larger than 100 km, sL was reduced by almost
half by excluding the short L perturbations. In addition, thecurvature showing the change in biases becomes gentle when
the scale of perturbations becomes larger than approximately
200 km. This result proves that short L perturbations are theprimary source of enormous noise in the linear relationships
between SST and wind. In other words, the uncoupling
feature of the SST and wind becomes significant when theperturbations are smaller than approximately 100 km in the
study area.
It is worth noting that the sampling radius of the SST gradient components gradually shrinks when the wavelengths ofthe perturbations increase (Fig. 11c). The sampled maximum
SST gradient perturbation =T0 exceeds 0.9 3 1022 8C km21

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FIG. 10. As in Fig. 9, but for = 3 t0 .

when the length scale of the perturbations is smaller thanapproximately 50 km. The perturbation fields are sampled
within the region where j=T 0 j # 0:3 3 1023 8C km21 when L
is broader than approximately 200 km, while the coupling
coefficient reaches its maximum value. According to theseresults, the optimal wavelength-band filter for investigating
the responses of the derivative wind stress field to the mesoscale SST anomalies can be decided.
Figure 12 shows the binned scatterplots for the bandpass filtered perturbations. The wavelength of the perturbations islonger than approximately 100 km but smaller than approximately 300 km. The noise sL of the linear relation between =  t0
and (=T  t^)0 decreased by approximately 40% from 61.67 in
Fig. 5a to 60.96 N m22 in Fig. 12a, while the coupling coefficient
ad increased from 0.64 3 1022 to 1.33 3 1022 N m22 8C21. The
noise of the linear relation between = 3 t0 and (=T 3 t^)0  kdecreased from 61.83 to 61.06 N m22, and the coupling coefficient ac increased from 0.34 3 1022 to 0.95 3 1022 N m22 8C21.
Bandpass filtering between 100 and 300 km avoids losing too
many perturbations in the frontal area and gives reasonable andgeneral coupling features between the derivative wind stress and
SST gradient components in the NSCS.
A possible explanation is discussed here for the dependence of SST–wind coupling on the spatial frequencies.
According to Small et al. (2008) and Byrne et al. (2015), there
are four length scales whose values help us to determine

which process dominates the response of surface wind to SST
perturbations. The four length scales are the cross-front
length scale (Lf), the length scale on which the Coriolis
term changes (Lc 5 U/f), the length scale over which thepressure gradient changes (Lp 5 Uh2/KT), and the lengthscale responsible for the vertical mixing of momentum (Lm 5
Uh2/Km). Here, U is the wind speed, h is the boundary layerheight, and KT and Km denote the vertical eddy diffusion
coefficient for air temperature and vertical eddy viscosity
coefficient for momentum, respectively.
In this study, the average wind speed U $ 10 m s21 (Fig. 2a),boundary layer height h ’ 1000 m, f ’ 0.5 31024 m s21, andKT ’ Km ’ 50–100 m2 s21. Therefore, Lc has an order of
200 km; Lp and Lm have an order of 100 km, which are all longer
than the length scale of high wavenumber SST perturbations(Lf # 50 km). In this case, when an air column moves over the
SST perturbations, the moving distance is not long enoughfor either the adjustment of the pressure gradient or thevertical diffusion of momentum to change the surface wind.
Consequently, the positive SST–wind coupling is weak, andthe noise in the linear relationship fitting is significant for(Lf , Lp ; Lm).
On the other hand, when the length scale of SST perturbations is larger than 100 km (Lf . 100 km), the moving distanceof the air column is long enough to allow the adjustment of thepressure gradient and the vertical diffusion of momentum to

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191

FIG. 12. Binned scatterplots of the relationships between the
wavelength bandpass filtered field and (a) the perturbation windstress divergence and the perturbation downwind SST gradient and(b) perturbation wind stress curl and crosswind SST gradient;(c) histograms of the number of observations within each bin for(a) and (b). The wavelength band for the spatial perturbations is
100 km # L # 300 km.

FIG. 11. The (a) coupling coefficients a, (b) averaged standard
deviations sL, and (c) maximum SST gradient of the linear relationships between the perturbation fields calculated in different
wavelength bands. The definition of L is given in section 4d. The
subscripts d and c denote the variables obtained from the perturbation wind stress divergence and wind stress curl. The maximum
downwind (=Tdw) and crosswind (=Tcw) SST gradient perturbations in (c) define the region within which the total percentage ofthe sample is more than 95%.

change the surface wind. Therefore, the noise in the linear
relationship fitting weakens, and the positive SST–wind coupling becomes significant (Fig. 11a). When the moving distancebecomes larger than 300 km, the large-scale adjustments of theocean and atmosphere become more significant than the influence of the SST front on the surface wind fields. Then, thepositive SST–wind coupling weakens again (Fig. 11a).

5. Conclusions
The QuikSCAT observations of surface wind stress and
OSTIA SST during the three months from 1 December 2008 to
28 February 2009 are analyzed to study the regional ocean–
atmosphere coupling associated with the SST front in thenorthern South China Sea. The perturbation wind stress

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vorticity and divergence are linearly related to the perturbation crosswind and downwind components of the SST
gradient. However, the satellite observations show significant noise in the linear relationships, as represented by thestandard deviations in the binned scatterplots.
The ERA5 reanalysis data are analyzed and compared withthe satellite observations. The ERA5 reanalysis data gavesatisfactory performance in describing the response of surface wind stress over the frontal area in the NSCS. The linear
relationship between the derivative fields of perturbation
wind stress and SST gradient components is even more substantial in the ERA5 data than in the satellite observations.
Additionally, the noise in the linear relationships, as represented by the standard deviations in the binned scatterplots,
is much smaller in the ERA5 data than in the satellite
observations.
The apparent differences in the noise observed in thesatellite observations and reanalysis data are rarely reported in other frontal areas. The sensitivity experiments
show that spatial smoothing of satellite observations could
significantly reduce the noise and change the coupling coefficients. This indicates that some specific high wavenumber perturbations depressed by spatial smoothing are
crucial in investigating the SST–wind coupling in the NSCS.
Then, a length scale 1/vs (km) is defined to study the influences of perturbations with different wavenumbers (vs) on
the noise in the linear relationships.
The 1/vs length scales for the spatial variation in wind
are obtained using wavelet analysis. The results show thatthe satellite scatterometer observed many perturbations at
the length scale of 1/vs , 100 km in the NSCS. However, theperturbations at this scale were relatively weak in the ERA5
reanalysis data. The robust SST gradient at the length scale of1/vs , 100 km does not lead to the corresponding linear responses in derivative wind stress but contributes to over 40% of
the noise in the linear relations observed by QuikSCAT.
It is further found that the linear relations between surface
vorticity and divergence in the crosswind and downwind SST
gradients are significant when the mesoscale perturbations arelarger than approximately 100 km but smaller than approximately 300 km in the NSCS. Spatial bandpass filtering between
100 and 300 km yields values for the coupling coefficients ad
and ac of 1.33 3 1022 and 0.95 3 1022 N m22 8C21 in 2008 DJF,
respectively. These values are reasonable and confident estimates compared to other frontal areas’ results. Additionally,
the coupling coefficient ac is approximately 30% weaker thanad, which is also consistent with previous studies based on
observations and numerical simulations (O’Neill et al. 2010a).
The evaluation on four dynamical length scales shows that a
distance of 100 km is the shortest distance that allows thepressure gradient and the vertical diffusion of momentum toadjust the surface wind in the NSCS. When the moving distance of an air mass over the front is less than 100 km, theadjustment of the pressure gradient and the vertical diffusionof momentum are insufficient to maintain stable positive SST–
wind coupling. Thus, the noise in the linear relationship fitting
is large. On the other hand, when the moving distance is larger
than 100 km, positive SST–wind coupling is maintained by the

VOLUME 35

combined effect of the pressure gradient and vertical mixing of
momentum.
Distinguishing the dependencies of SST–wind coupling on
spatial scales is the foundation of ongoing work. Although theyear-to-year variability in the noise is small in the observationsof QuikSCAT, there is an apparent change in the couplingstrength. An accurate calculation of the coupling strength isfundamental for this work. On the other hand, as introduced in
the introduction, the feedback of SST-induced mesoscale windstress variability on the ocean is significant. This result may be
used to study the effects of local mesoscale wind stress variability on the fine structure of the coastal front itself.
Acknowledgments. This research was supported by the
Frontier Science Research Project of Chinese Academy of
Sciences (Grant QYZDJ-SSW-DQC022), the Key Special
Project for Introduced Talents Team of Southern Marine
Science and Engineering Guangdong Laboratory (Guangzhou)(GML2019ZD0304), the Science and Technology Planning
Project of Guangzhou City, China (202002030490 and
202102080363, the National Natural Science Foundation ofChina (Grants 41676018, 41521005, 41806035, 42076209,
41776025, and 41876017), and the Ministry of Education,
Culture, Sports, Science and Technology, Japan (MEXT) to a
project on Joint Usage/Research Center-Leading Academia in
Marine and Environment Pollution Research (LaMer), theRising Star Foundation of the South China Sea Institute of
Oceanology (NHXX2019WL0101). The authors thank theHigh-Performance Computing Division of the South China Sea
Institute of Oceanology for the support.
Data availability statement. All data used in this study areavailable at https://www.ecmwf.int/en/forecasts/datasets/
reanalysis-datasets/era5 and https://apps.ecmwf.int/datasets/
data/interim-full-daily/levtype5sfc/ for ERA5 reanalysis data,
https://ghrsst-pp.metoffice.gov.uk/ostia-website/index.html for
OSTIA SST, and http://apdrc.soest.hawaii.edu/data/data.php?
discipline_index53 for QuikSCAT and ASCAT wind.
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