Mesoscale wind stress–SST coupling in the Kuroshio extension and its effect on the ocean

Abstract

Mesoscale perturbations (with a size of 100–1000 km) of wind stress magnitude, divergence and curl in the Kuroshio Extension (KE) are observed to tightly link to those of sea surface temperature (SST), and downwind and crosswind SST gradients, respectively. Based on long-term satellite observational data, their empirical relationships are established, which are further used to represent mesoscale wind stress–SST coupling in an ocean model that is based on the Regional Oceanic Modelling Systems (ROMS). The strength of mesoscale perturbations of wind stress and SST is observed to display a consistent seasonal variability, with the maximum appeared in winter while the minimum appeared in summer. This seasonal variability characteristic is also successfully simulated by ROMS with high resolution. Through comparing two experiments with and without the mesoscale wind stress–SST coupling, it is found that the mesoscale wind stress perturbation (τ _MS) has a negative feedback on SST perturbation (SST_MS). Analyses of sensitivity experiments suggest that the τ _MS acts to inhibit SST_MS mainly by means of surface heat flux. The τ _MS –SST_MS coupling also exerts influences on the ocean mean state and seasonal variability of SST in the KE. The effect of τ _MS on the SST is distinct in autumn and winter when the mesoscale perturbations are most active. Analyses of sensitivity experiments demonstrate that the τ _MS can affect the long term mean SST through either way of surface heat flux or momentum flux.

1 Introduction

Satellite observations have revealed that there are significant mesoscale coupled perturbations between the ocean and atmosphere in the Kuroshio extension (KE) at a spatial scale of about 100–1000 km (e.g., Nonaka and Xie 2003; Xie 2004; Chelton et al. 2004; Maloney and Chelton 2006; Small et al. 2008). The perturbed sea surface temperature (SST) is often accompanied by perturbations in air temperature, cloud fraction, wind stress, and sea level pressure (e.g., Nonaka and Xie 2003; Minobe et al. 2008; Tokinaga et al. 2009; Bryan et al. 2010; Kawai et al. 2014). Positive correlation between SST and wind stress perturbations indicates that these mesoscale air/sea perturbations are driven by the ocean side SST perturbations; otherwise, the increased wind speed would reduce the SST and result in a negative correlation. This fact suggests that the mesoscale air–sea interaction is different from the large scale air–sea interaction (e.g., Small et al. 2008; Bryan et al. 2010). Downward momentum transport and horizontal pressure adjustment are two mechanisms that can explain the wind stress responses to mesoscale perturbed SST (e.g., Lindzen and Nigam 1987; Wallace et al. 1989; Xie 2004; Minobe et al. 2008; Small et al. 2008; Putrasahan et al. 2013), and the former one plays a dominant role as suggested from satellite data analyses (e.g., Frenger et al. 2013; Ma et al. 2015a).

The coupling relationship between wind stress and SST perturbations is most frequently studied from observational data, and then used to test the ability of climate models in simulating this relationship (e.g., Maloney and Chelton 2006; Chelton and Xie 2010; Bryan et al. 2010). It has been demonstrated that the coupling relationship between wind stress perturbations (τ _MS) and SST perturbations (SST_MS) in climate model simulations is weaker than observed. That means the coupling coefficient a in climate models is smaller than that derived from observation, when using the equation τ _MS = a × SST_MS to depict the empirical relationship between them (e.g., Maloney and Chelton 2006; Chelton and Xie 2010; Bryan et al. 2010). Specifically, in case of low spatial resolution climate models, the sign of this coupling coefficient a is simulated opposite to that observed. While the spatial resolution increases, the sign of a can be simulated correctly but the value is still smaller than that observed (e.g., Bryan et al. 2010). That is because capturing mesoscale wind stress responses not only requires high resolution in climate models but also accurate parameterizations of relevant physical processes in the marine atmospheric boundary layer (e.g., Bryan et al. 2010).

The mesoscale wind stress–SST coupling has a significant effect on both atmospheric and oceanic variability. On the one hand, as the SST perturbations directly affect the wind stress divergence and cloud fraction in the atmospheric boundary layer, they are important for precipitation simulations (e.g., Minobe et al. 2008; Putrasahan et al. 2013; Ma et al. 2015b). On the other hand, the induced τ _MS in turn impacts the oceanic variability in the KE by means of momentum flux and heat flux. It is known that the τ _MS can damp the SST_MS by means of surface sensible and latent heat fluxes (e.g., Nonaka and Xie 2003; Xie 2004; Jin et al. 2009), and the wind stress curl perturbations can influence the intensity of local Ekman upwelling and have feedback on the ocean (e.g., Nonaka and Xie 2003; Maloney and Chelton 2006; Gaube et al. 2013; Chelton 2013). Based on these results, the damped mesoscale SST perturbations and affected local Ekman upwelling in the ocean would consequently influence the ocean mean state and low frequency variability in the KE. However, modelling studies of these processes and consequences are relatively insufficient.

Recently, the effect of mesoscale air–sea coupling on the KE is studied using the atmosphere–ocean coupled models (Ma et al. 2016b). The effect is isolated by comparing two experiments with and without the mesoscale SST components before being used to drive the atmosphere model. The advantage of this two-way modelling approach is clear, as all atmospheric responses to SST_MS act to affect the ocean collectively, providing a comprehensive understanding about the effect of mesoscale air–sea coupling (e.g., Small et al. 2008; Ma et al. 2016b). However, effects of τ _MS on the ocean still need to be investigated in a clean way.

In order to understand the feedback of τ _MS in the KE, a modelling study is necessary. Specific questions to be answered include what is the effect of τ _MS on the ocean mesoscale variability and mean state, and what is the mechanism. Two important processes have been identified responsible for the local feedback, i.e., the heat flux response and Ekman pumping induced by τ _MS, but their relative roles remain elusive. This study investigates the coupling relationship between SST_MS and τ _MS by analyzing long-term satellite observations, and then incorporates the coupling relationship between them into an ocean model to study the feedback of τ _MS. Details of the methodology and results follow.

2 Data and method

2.1 Data and highpass filter method to isolate mesoscale perturbations

The data used in this study include monthly wind stress data derived from Quick Scatterometer (QuikSCAT, Version 4) and monthly AMSR-E SST data (Version 7). The QuikSCAT Wind vector is obtained from the SeaWinds scatterometer launched on 19 June 1999 on board the QuikSCAT satellite (Hoffman and Leidner 2005). The monthly data are available from July 1999 to November 2009. The AMSR-E SST data have high precision and wide range of spatial coverage. The monthly data are available from June 2002 to September 2011. Both data are recorded in a spatial resolution of 1/4° × 1/4°. Only the data over their overlapped period from June 2002 to November 2009 are utilized.

In order to extract the mesoscale air/sea variability in the KE, a locally weighted regression (loess) method is utilized (Cleveland and Devlin 1988). Specifically, a smoothed value ($\bar{A}$) of a field ($A$) at a grid point S ₀ is estimated by fitting a regression surface to some local subset data. The subset is determined by a rectangular area that has length of 2 × s _x and 2 × s _y in the zonal and meridional direction, respectively. The regression function is f(x, y) = a ₁ + a ₂ x + a ₃ x ² + a ₄ y +a ₅ y ² + a ₆ xy, where (x, y) denotes the coordinate relative to the grid point S ₀. The weight function is a tri-cubic function. Denote W(u) = (1 − u ³)³ for 0 ≤ u < 1, and W(u) = 0 elsewhere. Let ρ _i be the distance between subset point S _i and grid point S ₀, and $d = \sqrt {s_{x}^{2} + s_{y}^{2} }$, then the weight for each S _i is: w _i  = W(ρ _i /d). The coefficients a _i of the regression function f(x, y) can be determined by minimizing the objective function ∑w _i (g _i –f(x _i , y _i ))², where g _i denotes the data at grid point S _i . By definition, coefficient a ₁ equals the required smoothed value $\bar{A}$.Then, a perturbation field is obtained as $A^{\prime } = A - \bar{A}$. The resultant perturbation field using the loess method depends on the half span parameters s _x and s _y . Generally, the larger s _x and s _y , the smoother $\bar{A}$ field and thus the stronger perturbation field $A'$.

A 10° latitude × 30° longitude loess spatial high-pass filter (corresponding to s _y  = 5° and s _x  = 15°) is employed here in accordance to the work by Maloney and Chelton (2006) and O’Neill et al. (2012). This high-pass spatial filter can well extract mesoscale coupling perturbations of wind stress and SST in the KE as denoted by Maloney and Chelton (2006). Here, an example derived from this filter is shown in Fig. 1. Evidently, the high-pass filtered wind stress amplitude (τ _MS), divergence (div τ)_MS, and curl (curl τ)_MS are tightly linked to the high-pass filtered SST (SST_MS), downwind SST gradients (n∇SST_MS), and the crosswind SST gradients (s∇SST_MS), respectively (Fig. 1). That means the mesoscale perturbations derived from this loess high-pass spatial filter hold well for the inherent coupling relationship between mesoscale wind stress and SST perturbations. The coupling between τ _MS and SST_MS is most significant, and followed by that between (div τ)_MS and n∇SST_MS, and (curl τ)_MS and s∇SST_MS. These results are consistent with previous studies (e.g., Maloney and Chelton 2006).

Fig. 1

Spatially high-pass-filtered a QuikSCAT wind stress magnitude (colors) and AMSRE SST (contours), b wind stress divergence (colors) and downwind SST gradient (contours), and c wind stress curl (colors) and crosswind SST gradient (contours) in January 2003. The SST and its gradient contour intervals are 0.5 and 0.5 °C/100 km, respectively, with the zero contours omitted

2.2 Empirical coupling relations

In order to study the mesoscale wind stress feedback, the empirical relationship between SST_MS and τ _MS is established from satellite observations. Then, the mesoscale perturbed wind stress vector (τ _x , τ _y )_MS is derived from modeled SST, and added onto its climatology part to take its effect into account.

Generally, there are two ways of obtaining (τ _x , τ _y )_MS from SST data. The first method utilizes the observed coupling relationship between (τ _x , τ _y )_MS and SST_MS by using (τ _x , τ _y )_MS = (a _x , a _y ) × SST_MS (Pezzi et al. 2004). The second one utilizes the coupling relationship between their gradients (e.g., Jin et al. 2009), i.e., the observed relationship between (div τ, curl τ)_MS and (n∇SST_MS, s∇SST_MS), where n∇SST_MS, s∇SST_MS indicate the downwind and crosswind SST gradient, respectively. After the (div τ, curl τ)_MS are estimated from (n∇SST_MS, s∇SST_MS), they are then used to calculate the wind stress vector perturbations (τ _x , τ _y )_MS using an inverse technique.

In this study, the way used to obtain the wind stress vector perturbations (τ _x , τ _y )_MS is a little different from previous studies. Note that the wind stress field is determined by its magnitude |τ| and direction θ, the mesoscale perturbation in wind stress magnitude τ _MS is linearly correlated to that in SST (i.e., τ _MS = a × SST_MS, where the a is the regression coefficient and is given in Sect. 3), and wind direction θ response to SST perturbations is small (e.g., O’Neill et al. 2010). Therefore, the effect of mesoscale wind stress perturbations can be taken into account simply by changing the magnitude |τ| into |τ| + τ _MS, without any modification in wind direction θ. The |τ| is always non-negative while τ _MS can be positive or negative, depending on the sign of SST_MS. It is restricted so that the |τ| + τ _MS can still remain non-negative, then the wind stress vector perturbations (τ _x , τ _y )_MS can be easily obtained from τ _MS and θ.

2.3 Ocean model

The Regional Oceanic Modelling Systems (ROMS) is employed to assess the feedback of τ _MS on oceanic variability. The ROMS is a three-dimensional, hydrostatic, free-surface, terrain-following numerical model (Song and Haidvogel 1994; Shchepetkin and McWilliams 2005). It uses the Arakawa “C” gird for horizontal difference (Arakawa and Lamb 1977), and provides several choices on mixing parameterization schemes and discretization schemes. This study takes the harmonic horizontal mixing scheme (Wajsowicz 1993) for horizontal mixing and the K-profile parameterization scheme (Large et al. 1994) for vertical mixing, and the third-order upstream discretization scheme for horizontal advection and the fourth-order centered discretization scheme for vertical advection.

The model domain covers the whole North Pacific (20°S–60°N, 100°E–70°W), although our area of concern is in the KE. In this way, it can eliminate the influence that comes from distortion of strong current at boundaries. In order to simulate both eddies and the Kuroshio Current System adequately, the high resolution ocean model is utilized (e.g., Nakano et al. 2008). Longitude interval is 1/8°, and latitude interval is 1/8° × cos (latitude). There were 50 s-coordinate levels in the vertical direction. The model pre-processing utilizes the package developed by Penven et al. (2008).

The bathymetry is extracted from the Global 2-min Gridded Elevation Data ETOPO2. The maximum and minimum depths are set to 5000 and 75 m, respectively. The initial velocity and sea level elevation are set to zero, and temperature and salinity data are derived from the World Ocean Atlas 2009 (WOA2009) from the National Oceanic and Atmospheric Administration (NOAA). WOA2009 is a set of objectively analyzed (1° grid) climatology hydrographic data recorded in 33 standard depth layers from 0 m at the surface to 5500 m at the bottom.

Boundary conditions are set as follows. The east boundary is treated as a wall and the sea that does not belong to the Pacific is filled as land. The other three (north, south, west) boundaries are open. The temperature, salinity, velocity, and surface elevation at these three open boundaries are prescribed by spatial interpolation of the WOA2009 datasets (velocity and surface elevation are diagnosed from the hydrographic data with a reference level at 1000 m depth). The 3-D velocity, temperature, and salinity are nudged to boundary values at these three open lateral boundaries with a 360-day time scale for outflow and 3-day for inflow. Meanwhile, the logical switches of nudging/relaxation are also turned on to nudge the 2-D momentum and 3-D temperature fields to their climatology in the whole region with a 360-day time scale. By such, the bias in long-term mean ocean temperature can be effectively suppressed. The surface forcing includes monthly mean climatology wind stress, net fresh water flux, net heat flux, surface solar shortwave radiation from the Comprehensive Ocean Atmosphere Data Set (COADS, Diaz et al. 2002).

The time steps are 30 s for the 2-D barotropic equations, and 300 s for the 3-D baroclinic equations. At each time step, the net surface heat flux sensitivity to SST (dQ/dSST) is calculated by bulk formulas, and is used to introduce thermal feedback to correct net surface heat flux (Barnier et al. 1995). The model is run for 20 years to get a quasi-equilibrium state including 3-D velocity, temperature, salinity data, as well as the 2-D sea level elevation. They are used as the initial conditions for experiments carried out for comparison. These experimental settings are given in the following subsection.

2.4 Numerical experiments

In order to assess the feedback of τ _MS, two experiments with and without the τ _MS feedback are carried out. The model variables in January of the 21st year are utilized as initial conditions for these two experiments. In the no-feedback experiment, the model settings are as normal (see Sect. 2.3). In the feedback experiment, mesoscale wind stress–SST coupling is incorporated in the model in the KE. While the τ _MS –SST_MS coupling is considered, an additional wind stress correction term (τ _x , τ _y )_MS is added onto the climatology part (τ _x , τ _y )_clim at each time step, where the (τ _x , τ _y )_MS can be derived from modeled SST. Meanwhile, net heat flux is also modified, accordingly, following the Bulk formulas (e.g., Liu et al. 1979; Fairall et al. 1996). In order to enhance computational speed, mesoscale wind perturbations induced in momentum flux and heat flux corrections are updated daily instead of instantly. Both experiments are run for 10 years with monthly history output and monthly averaged output for investigating the effect on long-term ocean mean state.

In order to understand the way by which mesoscale wind stress perturbations impact the ocean, three additional experiments are carried out. They are the half-feedback experiment (which uses a half strength of τ _MS), the HF-feedback experiment (which considers only the influence of τ _MS on surface heat flux), and the MF-feedback experiment (which considers only the influence of τ _MS on surface momentum flux). These three experiments are all run for 10 years with similar output as for the above two experiments.

3 Observed mesoscale wind stress–SST variability in the KE

After the mesoscale wind stress and SST perturbations are isolated from satellite observations using the loess method, their variability characteristics are analyzed. The standard deviation (SD) of the SST_MS and τ _MS are calculated and presented in Fig. 2. It is clear that the energetic mesoscale variability occurs in the region east of Japan. The largest SD of SST_MS exceeds 2 °C while that of the τ _MS exceeds 0.02 N/m².

Fig. 2

Standard deviations of the spatially high-pass-filtered AMSRE SST (a) and QuikSCAT wind stress (b)

The temporal variability of the strength of mesoscale wind and SST perturbations was investigated. To approach it, an index that can characterize the strength of SST_MS/τ _MS (e.g., Fig. 1a) was defined. The strength of a perturbed field can be defined by its range (i.e., largest value minus smallest value). However, in such a way, the strength of the perturbed field would be sensitive to some extreme values. Instead, the strength of a perturbed field is defined by its interquartile range (IQR). The IQR is defined by the difference between the upper and lower quartiles, i.e., IQR = q _0.75 − q _0.25, so that it specifies the range of the central 50% of data, and is robust to the extreme values. Here, IQRs of SST_MS and τ _MS in the region (32°N–45°N, 145°E–175°E) in each month were calculated and are shown in Fig. 3. It is clear that the τ _MS and SST_MS exhibit a consistent seasonal variability, with the maximum appeared in winter while the minimum appeared in summer, consistent with previous studies. The significant ocean mesoscale activity in winter feeds on the submesoscale kinetic energy via an efficient inverse energy cascade (e.g., Sasaki et al. 2014), and exerts influences on the atmosphere with significant seasonality (e.g., Ma et al. 2016a).

Fig. 3

Time series of the interquartile ranges of the spatially high-pass filtered QuikSCAT wind stress (green) and AMSRE SST (red) in the region (32°N–45°N) × (145°E–175°E)

Now, the coupling relationships between the mesoscale perturbations of wind stress and SST are analyzed. Figure 4a shows the scatterplots of τ _MS binned by the values of SST_MS in the domain (32°N–45°N, 145°E–175°E). An empirical relationship between τ _MS and SST_MS can be derived from regression analysis:

$$\tau_{\text{MS}} \left[ {{\text{N m}}^{ - 2} } \right] = 0.0 1\times {\text{SST}}_{\text{MS}} \left[ {^\circ {\text{C}}} \right].$$

(1)

Fig. 4

Scatterplots showing the spatially high-pass filtered QuikSCAT wind stress binned by values of AMSRE SST perturbations within the domain (32°N–45°N) × (145°E–175°E). The black dots and vertical bars indicate the medians and interquartile ranges in each bin

Similarly, the (div τ)_MS and (curl τ)_MS (in unit: Nm⁻²/10 000 km) can be estimated such as:

$$\left( {{\text{div }}\tau ,{\text{ curl }}\tau } \right)_{\text{MS}} = \, \left( { 1. 1 5, \, 0. 8 2} \right)_{{}} \times \, (n\nabla {\text{SST}}_{\text{MS}} ,{\text{ }s}\nabla {\text{SST}}_{\text{MS}} ),$$

(2)

where n∇SST_MS and s∇SST_MS are in the unit: °C/100 km (Fig. 4b, c). These relationships suggest that the mesoscale wind stress perturbations can be approximated from the perturbations in SST.

In order to assess effectiveness of using SST to get wind stress perturbations, τ _MS, (div τ, curl τ)_MS approximated from SST_MS and (n∇SST_MS, s∇SST_MS) are compared with that derived from observation. Figure 5a–c show the time-longitude cross-sections of the τ _MS, (div τ)_MS, and (curl τ)_MS derived from observation (color) and these approximated from SST (contours) at 42°N. The observed τ _MS are nearly spatially collocated with that approximated from SST_MS (Fig. 5a). Moreover, there is significant seasonal variability in mesoscale perturbations of wind stress and SST (Fig. 5a), with strong perturbations appearing in winter while weak perturbations appearing in summer, which agrees with that reflected in Fig. 3. The (div τ, curl τ)_MS approximated from (n∇SST_MS, s∇SST_MS) also match those observed, but the coincidence between them is not as high as that between τ _MS and SST_MS. This is because the pressure adjustment and downward momentum transport mechanisms have different effects on the SST gradients, although they both can explain τ _MS response to SST_MS (e.g., Frenger et al. 2013). Specifically, corresponding to a monopole pattern in divergence of SST gradient, a monopole pattern in wind stress divergence is induced when the pressure adjustment mechanism dominates, while a dipole pattern is induced when the downward momentum transport mechanism dominates (e.g., Frenger et al. 2013). Coexistence of these two mechanisms leads to a little complex relationship between (div τ, curl τ)_MS and (n∇SST_MS, s∇SST_MS).

Fig. 5

Time-longitude cross-sections of the spatially high-pass-filtered wind stress amplitude (a), divergence (b) and curl (c) derived from observation (colors) and that are approximated from SST, downwind and crosswind SST gradient (contours) at 42°N. The contour intervals are 0.005 Nm⁻² in a and 0.5 Nm⁻²/10 000 km in b and c with the zero contour omitted

4 Effect on the ocean

The effect of τ _MS –SST_MS coupling on the ocean is examined in this section. The area where the τ _MS –SST_MS coupling is considered is located at the east of Japan (Fig. 6), as the τ _MS and SST_MS are observed to be active there (Fig. 2). The τ _MS is processed to decay exponentially to zero at boundaries (red lines in Fig. 6) to avoid the discontinuity effect. The empirical τ _MS –SST_MS coupling relationship is interactively incorporated into the model to affect the ocean (Fig. 7). The effect of τ _MS is isolated through comparing two experiments with and without the τ _MS feedback.

Fig. 6

The model domain and the area where mesoscale wind perturbations are considered (enclosed by red curves). The ocean is indicated by the green color

Fig. 7

A schematic diagram showing how mesoscale wind stress forcing is explicitly taken into account in the ocean model. The total wind stress used to force the ocean is separated into its climatological part (τ ₀) and mesoscale part (τ _MS), written as: τ = τ ₀ + τ _MS. The former is prescribed from the observed long-term climatology, while the latter can be explicitly approximated from modeled SST data. As such, the mesoscale part can be conveniently switched on and off in the ocean model to isolate its effects in a clean way

4.1 Evolution of SST difference

The incorporation of τ _MS –SST_MS coupling can shortly affect the ocean. For example, Fig. 8 shows the SST differences between two experiments on days 30, 60 and 90 after incorporation of τ _MS –SST_MS coupling. On day 30, the SST difference is still less than 0.5 °C (Fig. 8a); on day 60, a relatively large SST difference emerges (Fig. 8b); while on day 90, the SST difference reaches 4 °C and displays complex patterns. These SST differences arise from the effect of τ _MS and its interaction with oceanic intrinsic variability.

Fig. 8

The SST difference between no-feedback and feedback runs on the day 30 (a), 60 (b), and 90 (c) in the 21st year. The contour interval is 0.5 °C. Red curves denote positive difference while blue curves denote negative difference

The SST difference can be induced by τ _MS via ways of influencing surface momentum flux and heat flux. Figure 9a–c show, respectively, the SST difference (relative to that in no-feedback experiment) in feedback, MF-feedback and HF-feedback experiments, as averaged in the first month after the τ _MS effects are considered. It is seen that SST difference in feedback experiment (Fig. 9a) is generally a sum of the differences in MF-feedback (Fig. 9b) and HF-feedback (Fig. 9c) experiments. In the MF feedback experiment, the SST difference is distinct along the SST front, with alternatively appearing positive and negative values. That is because the gradient of τ is larger along the SST front (e.g., Chelton and Xie 2010), and the Ekman upwelling/downwelling associated with curl τ has large changes there. On the other hand, in the HF-feedback experiment, the SST difference is distinct on the two sides of the SST front, with a positive difference appearing on the cold side, while a negative difference appears on the warm side. That is because the turbulent heat flux is linearly related to τ, whose τ _MS part is linearly related to SST_MS that are large at two sides of the SST front. The surface heat flux and SST may, therefore, have proportional (to SST_MS) changes through HF-feedback, with positive (negative) SST difference in the area of cold (warm) SST_MS. These results suggest that the τ _MS can affect SST through either the way of momentum flux or heat flux.

Fig. 9

The SST difference (relative to that in the no-feedback experiment) in the feedback (a), MF-feedback (b) and HF-feedback (c) experiments, as averaged in the first month after the τ _MS effects are considered. Superimposed green, black, and red curves are the 16, 17 and 18 °C SST contours in the no-feedback experiment

The SST difference can interact with the ocean intrinsic variability and evolve with time. Figure 10 shows the time-latitude cross-sections of the differences of SST, surface horizontal thermal advection, and surface heat flux between no-feedback and feedback experiments from the model year 21–30. As seen from Fig. 10a, the magnitude of SST difference is as large as 2 °C, and it is larger during cold seasons (e.g., winter) while smaller during warm seasons, consistent with the seasonality of mesoscale variability itself (Fig. 3).

Fig. 10

Time-latitude cross-sections of differences of SST (shading colors, unit: °C), surface horizontal thermal advections (right terms in equation $\partial T/\partial t = - u\partial T/\partial x - v\partial T/\partial y$, superposed contours in the left panel with interval 1.0 °C/month), and surface heat flux (downward positive, superposed contours in the right panel with interval 10 W/m²) between no-feedback and feedback experiments at 160°E during the model years 21–30

The difference of surface horizontal thermal advection between two experiments is superposed in Fig. 10a. The difference is distinct south of 40°N, like that of the SST. The change in horizontal thermal advection acts to intensify the SST difference when they are in the same sign. The difference of horizontal thermal advection can reach 5 °C/month, which can contribute to 5 °C SST change after a one month integration. This value exceeds the largest monthly averaged SST difference (2 °C) in fact, and must be offset by other processes.

The SST response in the feedback run can further modulate the heat transfer from the atmosphere to the ocean at the sea surface. For example, accompanied by the negative SST difference, a positive heat flux (downward positive) is seen from the atmosphere to the ocean (Fig. 10b). This indicates that when the ocean surface is cooling, more heat comes into the ocean through the sea surface. The maximum difference in the surface heat flux also appears in winter, which is about 60 Wm⁻² (Fig. 10b). Negative correlation between the SST difference and heat flux difference suggests that the large scale SST difference is inhibited by surface heat flux adjustment.

The results in Fig. 10 illustrate how the SST difference is amplified via horizontal thermal advection while inhibited via surface heat flux adjustment. The monthly differences between two experiments are associated with both the τ _MS –SST_MS coupling and the oceanic intrinsic low-frequency (interannual to decadal) variability. To isolate the effect of τ _MS –SST_MS coupling, results from the 10-year model run are averaged to get rid of the effect from oceanic intrinsic variability. In the following part of this section, we examine the effects of τ _MS on the strength of SST_MS and long-term mean ocean temperature. Sensitivity experiments are also analyzed to understand the way by which τ _MS acts to affect the ocean.

4.2 Effect on SST_MS

In this subsection, the effect of τ _MS on SST_MS is examined. The IQR value of SST_MS is used to characterize its strength, similar to that used in observational data analyses. In order to get rid of the effect from oceanic intrinsic variability, 10-year averaged annual cycles of SST_MS magnitude in the experiments are analyzed (Fig. 11). As seen from Fig. 11a, the strength of the SST_MS in the region (32°N–45°N, 145°E–175°E] is strongest in winter while weakest in summer, consistent with that derived from satellite observation (Fig. 3). Standard deviation indicates the uncertainty of the annual cycle of IQR (SST_MS) in each panel (Fig. 11), and is associated with the influence of oceanic intrinsic variability. The feedback of τ _MS on SST_MS is evident through comparing the temporal variation of the IQR values of SST_MS in the no-feedback and feedback experiments (Fig. 11a). It is seen that the strength of SST_MS is reduced (Fig. 11a) after the τ _MS –SST_MS coupling is taken into account. The strength of SST_MS simulated in the half-feedback experiment (Fig. 11b) generally lies between those simulated in the no-feedback and feedback experiments, suggesting that the effect of τ _MS is sensitive to its strength being prescribed.

Fig. 11

Annual cycles of IQR (SST_MS) in different experiments. The IQR (SST_MS) are derived from monthly history output during the model year 21–30. The red lines in four panels denote the 10-year averaged monthly IQR (SST_MS) in the no-feedback experiment, while blue lines denote the corresponding results in feedback (a), half-feedback (b), MF-feedback (c), and HF-feedback (d) experiments. The light shadings are standard deviation intervals. Note that the IQRs (SST_MS) represent the strength of mesoscale SST perturbations

The mesoscale wind stress perturbations act to impact the ocean by ways of influencing surface momentum flux and heat flux, both of which are taken into account in the feedback run, but are not in the no-feedback run. In order to isolate the roles wind stress perturbations play on the SST_MS through different ways, two additional experiments are performed, which are called HF-feedback and MF-feedback experiments (HF aka heat flux, and MF aka momentum flux). The HF-feedback run only includes the influence of τ _MS on the surface heat flux, while the MF-feedback run only includes the influence of τ _MS on the surface momentum flux. The IQRs of SST_MS simulated in these two experiments are shown in Fig. 11c, d. It is seen that the magnitude of SST_MS in the MF-feedback run (Fig. 11c) is similar to that in no-feedback run, while that in the HF-feedback (Fig. 11d) is similar to that in feedback run. That means the τ _MS acts to dampen the SST_MS mainly by means of surface heat flux. The τ _MS has little effect on the overall strength of SST_MS in the KE region via the way of momentum flux (Fig. 11c), because it mainly affects the SST_MS at the margin (Fig. 9b; i.e., along the SST front) in this way.

4.3 Effect on long-term mean ocean temperature

To isolate the effect of τ _MS on the long term mean ocean state, 10-year monthly mean ocean fields are formed for both no-feedback and feedback runs from the model year 21–30.

The effect of interactively represented τ _MS –SST_MS coupling is isolated through comparing the 10-year averaged model fields. Figure 12a shows the SST difference between no-feedback and feedback experiments as averaged over the model years 21–30. it is seen that there is significant SST difference (at the 0.05 significance level) that reaches 0.2 °C. The difference is not limited in the ocean surface, but also appears in the deep ocean. Figure 12b shows the latitude-depth cross-section of temperature difference between no-feedback and feedback experiments at 160°E as averaged from year 21–30. It is seen that there is a positive difference of about 0.3 °C at 37°N in the subsurface. Moreover, the temperature difference also displays seasonal variability. Figure 12c shows the seasonal cycle of SST difference at 160°E as averaged from model year 21–30. It is seen that the magnitude of SST difference is larger in cold seasons while smaller in warm seasons (Fig. 12c), consistent with that appearing in each specific year (Fig. 10). Although the SST difference in cold seasons is not significant at the 0.05 significance level due to fewer number (only ten) of samples, it is significant at the 0.15 significance level (Fig. 12c).

Fig. 12

The differences of SST (a), temperature (b) and annual cycle of SST (c) at 160°E between no-feedback and feedback experiments as averaged from the model year 21–30. Green dots indicate where the difference is significant at the 0.05 significance level as tested from the two-tailed t test method, while the yellow dots in c indicate the difference that is significant at the 0.15 significance level

Three sensitivity experiments are analyzed to examine the way by which τ _MS act to affect the long term mean SST. Figure 13a shows the 10-year mean SST difference (relative to that in the no-feedback experiment) simulated in the half-feedback experiment. This SST difference has relatively smaller magnitude compared to that simulated in feedback experiment (Fig. 12a), which suggests that the effect of τ _MS is sensitive to its strength being prescribed. The SST differences in both MF-feedback (Fig. 13b) and HF-feedback (Fig. 13c) experiments, however, have the magnitude as large as that in the feedback experiment (Fig. 12a). That means the τ _MS can act to affect the long term mean SST through either surface heat flux or momentum flux. Note that the 10-year mean SST difference in feedback experiment (Fig. 12a) is not equal to the sum of those in MF-feedback and HF-feedback experiment (Fig. 13b, c). For instance, the positive SST difference at 36°N, 158°E in Fig. 13b, c is not seen in Fig. 12a at all. This phenomenon suggests that the long term (10-year) mean SST difference in feedback experiment is not linearly related to the MF and HF feedback, contrary to the phenomenon that the short-term (1-month) mean SST difference is almost equal to the sum of those caused respectively from the MF and HF feedback (Fig. 9).

Fig. 13

The SST changes (relative to that in no-feedback experiment) in half-feedback (a), MF-feedback (b), and HF-feedback (c) experiments as averaged over the model years 21–30

An interesting result is that the τ _MS has substantial effect on the long-term mean SST in the MF-feedback experiment, while it has little effect on the IQR (SST_MS). That is because the τ _MS in the MF-feedback experiment can affect the local SST (although not the magnitude of SST_MS) along the SST front (Fig. 9b), and the induced local SST difference can then interact with the ocean intrinsic variability and evolve with time (Fig. 10a), and finally results in long-term mean SST difference as shown in Fig. 13b.

In summary, the τ _MS has a clear effect on the long-term mean SST field in the KE through either way of heat flux or momentum flux. The effect can reach to the deep ocean and has clear seasonal variability (Fig. 12a, c).

5 Conclusion and discussion

The feedback of mesoscale wind stress perturbations in the KE is investigated by using satellite observation and the high-resolution ocean model. First, satellite observational data are analyzed to derive empirical relationships between mesoscale SST and wind stress perturbations. Then, the perturbed wind stress field is estimated from modeled SST and incorporated into the ocean model to study its effect in a clean way.

By analyzing satellite observations, the spatio-temporal variability characteristics of the mesoscale wind–SST perturbations are obtained. It is found that the strength of the perturbations in wind stress and SST displays consistent seasonal variability, with the peak appearing in winter while the trough appearing in summer, consistent with previous studies. These mesoscale perturbations are distinct in the domain (32°N–45°N, 140°E–170°W) east of Japan (Fig. 2). With the long-term observational data, the empirical relationships are established between τ _MS and SST_MS, (div τ)_MS and n∇SST_MS, and (curl τ)_MS and s∇SST_MS in the KE, like those established in other places (e.g., Chelton and Xie 2010).

Through comparing two experiments with and without the effect of τ _MS, it is demonstrated that the τ _MS has a negative feedback on SST_MS. Further sensitivity analyses reveal that the τ _MS acts to dampen SST_MS mainly by means of surface heat flux. This result agrees with previous studies (e.g., Nonaka and Xie 2003; Xie 2004). The τ _MS has little effect on the strength of SST_MS via the way of momentum flux, because it mainly affects the SST_MS at the margin (i.e., along the SST front; Fig. 9b) in this way.

The effect of τ _MS–SST_MS coupling can interact with the oceanic intrinsic variability to affect the SST evolution in the KE. After 90 days the τ _MS –SST_MS coupling is considered, there is more than 4 °C SST difference that emerges (Fig. 8c). The induced SST difference further affects other ocean processes and is, in turn, affected by them. Specifically, the associated change in the surface horizontal thermal advection (Fig. 10a) can occasionally intensify the SST difference, while the surface heat flux adjustment (Fig. 10b) always inhibits it. It is demonstrated that the incorporation of τ _MS can induce about 1.0 °C SST difference on interannual time scale (Fig. 10) and about 0.2 °C SST difference on a time scale of 10 years (Fig. 12a). The τ _MS induced SST difference is patchy (Fig. 12a), and is distinct in winter and autumn (Fig. 12c). Analyses of sensitivity experiments suggest that the SST difference can be induced by τ _MS through either the way of momentum flux or heat flux, no matter in a short (Fig. 9) or a long (Fig. 13b, c) time scale.

In summary, the effect of τ _MS–SST_MS coupling on the ocean is isolated in a clean way in this study. The way used to isolate the τ _MS feedback is simple and based on the ocean model only. In the future, more sophisticated methods based on the atmosphere–ocean coupled models are expected to provide better depictions about the feedback of τ _MS. Nevertheless, the current study demonstrates that τ _MS has a wide range of impacts on the ocean, from mesoscale SST perturbations to large scale SST difference, and short-term to long-term ocean mean temperature.