Local and remote forcing effects of oceanic eddies in the subtropical front zone on the mid-latitude atmosphere in Winter

Multiple oceanic eddies coexist in the North Pacific subtropical front zone (STFZ) in winter, which can be classified into the isolated single eddies, the combined double isotropic eddies and pairs of anisotropic eddies. The forcings of these eddies on the mid-latitude atmosphere are investigated using Climate Forecast System Reanalysis (CFSR) data from year 1979 to 2009, which are divided into the remote and local effects in this research. In the years with a stronger subtropical front, there are more cyclonic isolated and double eddies to the north, more anticyclonic isolated and double eddies to the south of the STFZ, and more eddy pairs with cold to the north and warm to the south concentrated around the main axis of the STFZ. These eddy distributions enhance the strength of the subtropical front, intensify the propagation of upwards baroclinic waves in the lower atmosphere, and finally enhance the zonal wind at upper atmosphere, which is defined as the remote effects of the eddies. However, distinct from this basin-scale remote forcings, three types of oceanic eddies also have different local forcings on the marine atmospheric boundary layer (MABL) above and on the middle atmosphere as expressed in local precipitation difference. The local effects of the isolated single eddies and combined double isotropic eddies take place near the eddy center, whereas that of the pairs of anisotropic eddies at the boundary of the two eddies.


Introduction
The interaction between the ocean and the atmosphere is the focus of attention in atmospheric dynamics and climate research. It has long been a hot and controversial topic for the air-sea interaction in the mid-latitude, especially for the oceanic forcing on atmosphere (Nakamura et al. 1997;Chelton, 2001;Di Lorenzo et al. 2008;Wang et al. 2019;Bai et al. 2019). In the mid-latitude North Pacific, air-sea interaction events can be divided into macroscale climate variability, such as the Pacific Decadal Oscillation (PDO) events, and mesoscale, e.g., the impact of oceanic fronts and eddies on the atmosphere above. The PDO is one of the most representative events (Mantua et al. 1997;Mantua and Hare 2002) in the mid-latitude Pacific in winter, which exhibits as a large-scale cool (warm) sea temperature anomaly in the North Pacific associated with the enhancement (decrement) of upper westerly jet stream, during the "warm" ("cool") phase of the PDO. Researches have pointed out that it is more like a forcing from mid-latitude westerly wind to the basin-scale abnormal sea temperature via changing the latent heat of sea surface (Namias 1969;Palmer 1985;Deser et al. 1997;Miller and Schneider 2000).
The forcings of oceanic fronts and eddies to the atmosphere are considered as the representative mesoscale air-sea interactions in the North Pacific (Nakamura et al. 1997;Minobe et al. 2008;Wang et al. 2019;Chen et al. 2019a;Bai et al. 2019Bai et al. , 2020. In the mid-latitude region, the difference between the forcing effects of oceanic fronts and eddies on the atmosphere and the specific physical process remain to be clarified. The most notable mesoscale air-sea interaction characteristic is the positive statistical correlation between 1 3 sea surface temperature (SST) and near-surface wind speed anomalies (Chelton et al. 2001;Xie 2004;Small et al. 2005), which was found in global oceanic front regions with large SST gradients and multiple oceanic eddies (the numerous long-lasting coexisted oceanic eddies with various types), including the Kuroshio Extension (KE) (Nonaka and Xie 2003), the Gulf Stream (Minobe et al. 2008;Small et al. 2014), the Antarctic Circumpolar Current (O'Neill et al. 2003) and the Somali Current (Vecchi et al.2004;Mafimbo et al. 2010).
In the North Pacific, Nakamura et al. (1997Nakamura et al. ( , 2004; Nakamura and Yamane 2010) and Wang et al. (2016Wang et al. ( , 2019 stressed the effects of two oceanic fronts on mid-latitude atmosphere, the subtropical front zone (STFZ) and the subarctic front zone (SAFZ). The two oceanic fronts have long been emphasized due to its significant connection with the mid-latitude atmospheric circulation and storm tracks (Nakamura et al. 1997(Nakamura et al. , 2004Nakamura and Yamane 2010). Subsequently, Wang et al. (2016Wang et al. ( , 2019 pointed out that the southern STFZ, which is located between 28° N and 32° N, has the closest relationship with the most significant SST anomaly mode (PDO) in the North Pacific. Their researches revealed that the stronger (weaker) year of the subtropical front intensity was accompanied by the PDO warm (cold) phase sea temperature anomaly with the colder (warmer) north and the warmer (colder) south, which increased (weakens) the baroclinity of the lower atmosphere and might affect the upper atmosphere. Furthermore, Chen et al. (2019bChen et al. ( , 2020 pointed out that the STFZ significantly contributes to the variations of atmospheric storm track and westerly jet intensity in mid-latitude via changing the vertical propagation of baroclinic Rossby wave and the incidence of barotropic Rossby wave breaking events. This process well reflects the forcing of the interannual variation of the subtropical front intensity on the middle and upper atmosphere over the entire North Pacific, also known as remote forcing of the STFZ. However, the mechanism of the front interannual variability is still unclear. The subtropical front is believed to be closely related to the North Pacific subtropical countercurrent (STCC), which is an eastward ocean current near the 20° N south to the STFZ. Due to the warm water carried by this current from western Pacific to the east, the SST gradient increases from the south to the north (Yoshida and Kidokoro 1967;Uda and Hasunuma 1969;Roden 1975). Qiu (1999) suggested that the STCC intensity peaks in late winter and spring, and the intensity change of STCC on the seasonal timescale is mainly due to seasonal surface wind stress forcing. However, it is still unclear whether the variability of STCC could cause the interannual variability of subtropical front intensity. Qiu and Chen (2010) suggested that abundant eddy activities with extreme eddy kinetic energy (EKE) distributed along a latitudinal band in the STCC region. Some works also revealed the significant influences of the oceanic eddies on the marine atmospheric boundary layer (MABL) or the lower atmosphere (Kobashi et al. 2008;Minobe et al. 2008;Tokinaga et al. 2009;Small, 2008;Ma et al. 2015a;Xu et al. 2016). The MABL is the lower part of the atmosphere, and has large amounts of heat, moisture, and momentum exchanges via turbulent transport, which is directly influenced by the ocean (Fairall et al. 1996). Previous studies Ma et al. 2015a;Xu et al. 2016) found that the isolated oceanic eddies in the KE region obviously affect the sea surface wind speed and MABL height locally in winter. Cold (warm) eddy causes surface winds to decelerate (accelerate) and reduces (increase) latent and sensible heat fluxes, cloud liquid water, water vapor content, and rain rate locally (Ma et al. 2015a). The influences of some steady isolated oceanic eddies are found even propagating to the top troposphere, causing variances of local convection and precipitation (Minobe et al. 2008;Ma et al. 2015a;Zhang et al. 2019;Sun et al. 2020). All these researches emphasize the local effects of an isolated steady eddy (cyclone or anticyclone). However, a large number of oceanic eddies were observed with various forms in the STFZ (Chelton et al. 2007(Chelton et al. , 2011Wen et al. 2020). Furthermore, the oceanic eddies are not isolated with each other, which is expressed as more than two oceanic eddies of the same or contrary attributes in a small region (Chelton et al. 2011;Wen et al. 2020). Considering the large number of oceanic eddies in the STFZ, it is natural to wonder what the relation is between these eddy activities and the subtropical front intensity on the interannual time scale. This promising relation may reveal the remote effects of oceanic eddies on mid-latitude upper atmosphere.
Thus, previous studies paid attention to the local forcing of a single oceanic eddy on the lower atmosphere in the STFZ. However, in the STFZ, there are numerous oceanic eddies with different forms (Chelton et al. 2011;Wen et al. 2020), such as the isolated single (ISO) eddies, the combined double isotropic (DBL) eddies and pairs of anisotropic (PAIR) eddies which make up a simple classification method. Then what are their differences in terms of the local effects on the MABL? Taking the interannual variability of the subtropical front intensity as a link, does the spatial distribution of these multiple oceanic eddies have basin-scale remote forcing on the middle and upper atmosphere? To solve above problems, Climate Forecast System Reanalysis (CFSR) dataset was used to analyze the local and remote effects of oceanic eddies in the STFZ on the mid-latitude atmosphere in winter. The rest of the paper is organized as following: Sect. 2 describes data and analysis method. Section 3 reveals the remote forcing of the multiple oceanic eddies in the STFZ on upper atmosphere on the interannual timescale. Section 3.1 shows the observations in the mid-latitude ocean-atmosphere system accompany with interannual variation of the subtropical front; Sect. 3.2 reveals how different types of oceanic eddies in the STFZ result in the remote forcing effect on upper atmosphere in winter. Section 4 compares the differences between the local impacts of isolated and combined oceanic eddies on the middle and lower atmosphere. Section 5 is the discussion and summary.

Data and analysis method
In this study, we used atmosphere and ocean reanalysis outputs of Climate Forecast System Reanalysis (CFSR) data in winter (DJF, i.e. Dec., Jan. and Feb.) from 1979 to 2009. This global, coupled and high-resolution product provided by the National Centers for Environmental Prediction (NCEP) has long been credited for its accurate estimation of the atmosphere and the ocean (Xue et al. 2011;Carvalho et al. 2012;Ma et al. 2015a). The CFSR Selected Hourly Time-Series Products (ds093.0) last 32 years from 1979 to 2010 with the 6-hourly time resolution and the 0.5° × 0.5° spatial horizontal resolution. The CFSR oceanic outputs have 40 levels from 5-m to 4478-m, in which top 20 levels are used in this study covered from ocean surface (5-m) to 205-m. The CFSR atmospheric outputs have multiple vertical coordinates. Surface parameters such as 2-m temperature, 10-m winds, sensible heat flux (SHF), latent heat flux (LHF), MABL height, frictional velocity and precipitation are used in our study. Several specific vertical layers of wind and geopotential height data are selected to investigate higher atmosphere. CFSR 6-hourly earth-system reanalysis outputs with the 0.5° × 0.5° spatial resolution should be enough to detect eddies since the large eddies in this region have a typical mean eddy diameter of 200 km (see Fig. 3c in Chelton et al. 2007). Furthermore, to catch more details of approximate eddy center and moving locus, the spatial horizontal resolution is bilinearly interpolated to 0.25° × 0.25° in this study. All the correlation analysis and eddy composited analysis use daily mean of the 6-hourly outputs.
To quantitatively identify the boundary and stronger or weaker years of the subtropical front, we calculated the subtropical front intensity index (ITS) for each winter, which is defined in Wang et al. (2019). According to the climatological wintertime meridional SST gradient distribution (Fig. 1), a prominent large value and a relatively strong zone of zonal mean gradient locate at 28° N and 41° N respectively. The STFZ is defined as the region in the subtropics where the average temperature gradient is above 0.6 ℃ degree −1 . And then the magnitude of the SST gradient in this box of 24° N-32° N, 140° E-140° W is defined as the intensity of the subtropical front. The ITS are basically calculated by spatially averaging meridional SST gradient in the STFZ, and the formula (Wang et al. 2019) goes that where G i is the value of zonally-averaged SST meridional gradient at the i-th latitudinal grid point within the zone, and N is the number of total grid points within the latitude/longitude box above. The oceanic current EKE is calculated by where u and v represent the zonal and meridional current speed respectively, u ′ represents the perturbation term, u � = u −ū , ū represents time-average of zonal current velocity in winter, ū = 1 N days ∑ u , and superscript of the v is similar to the u. Furthermore, we defined the EKE index by spatial average of 3-7 days bandpass filtered sea surface EKE in the eddy locations, which is defined by masking out those sea areas with no eddy formation of the STFZ (24° N-32° N, 140° E-140° W) each winter. Thus, the formula of EKE index goes that where EKE i is the value of 3-7 days bandpass filtered sea surface EKE at the i-th latitudinal grid point within the zone, and N is the number of total grid points within the latitude/ longitude box above. Similarly, the STCC index is defined by the zonal mean u-component of current at sea surface in 18° N-24° N, 140° E-157° W. To clarify the features of wind speed distribution, we analyzed the scalar wind representing the variance of wind speed including the wind EKE (Bai et al. 2019), which is defined as where u and v represent the zonal and meridional wind speed respectively, the subscript i represents the output data on each moment, − u represents time-average of zonal wind velocity within eddy duration, u ' i represents the perturbation term, u i ' = u i − − u, u ϵi represents the remainder term, and N ts is total number of time steps. Besides, the data interval in daily, so the u ϵi represents the disturbance within 24 h and other remainder components (Bai et al. 2019). The subscript and superscript of the v are similar to the u. Moreover, to verify the vertical mixing and dynamic instability, we calculated the gradient Richardson number (Chan 2008) in this study, which is defined as where v is virtual potential temperature, T v is virtual absolute temperature, z is height, g is gravitational acceleration, and (U, V) are the wind components toward the east and north. The critical Richardson number, Ric, is about 0.25 (although reported values have ranged from roughly 0.2-1.0), and flow is dynamically unstable and turbulent when Ri < Ric. Such turbulence happens either when the wind shear is great enough to overpower any stabilizing buoyant forces (numerator is positive), or when there is static instability (numerator is negative).
To detect eddies in CFSR outputs, we used the geometrybased detection algorithm of velocity vector filed (Nencioli et al. 2010). The minimum velocity is found at approximate center of the eddy and tangential velocity increases linearly away from it till coming to a peak then decreasing, and the distance of increment is considered as eddy radius. Besides, the directions of current should rotate in a consistent orientation or tendency. This can be quantitatively implemented by separate analyzing u and v component of current (the zonal and meridional current speed respectively) and constraining adjoining velocity vectors into same or adjacent quadrants. Locations of eddy centers and each estimated spatial extent can be identified through the six constraints referred to Wen et al. (2020). The grids satisfying the six conditions are automatically determined as the eddy center and the corresponding radius will be given in grid numbers. Considering only one component of u/v in four directions (north, south, west, and east) would make the determined radius smaller than the actual radius, we used the current velocity to determine radii in four directions.
CFSR has been proved as an ideal product for this method with its high spatial and temporal continuity (Wen et al. 2020). Furthermore, Wen et al. (2020) compared the interpolated 0.25° × 0.25° CFSR and the finer 1/6° × 1/6° HYCOM global assimilation data (Global HYbrid Coordinate Ocean Model and the Navy Coupled Ocean Reanalysis Data-GLBv0.08/expt_53.X). The interpolated CFSR data has comparable results with the HYCOM when dealt Attached solid lines are zonal mean of corresponding filtered EKE (X bottom axis, units: 10 -4 ·m 2 s −2 , color: orange) and zonal mean of corresponding meridional temperature gradient from 140° E to 140° W (X top axis, units: ℃ degree −1 ; color: black) with the same eddy detection method. Since the results are presented day by day when using daily average data, we selected those located in the STFZ and lasted for 3 days within a 2° × 2° box, then we filtered top 50% as valid eddies by their strengths. In addition, we defined the absolute value of spatially averaged SST anomaly as the strength of eddy. The valid eddies are incorporated into our eddy dataset to present composite effects of oceanic eddies more clearly, the results from all eddies are similar.

Observations of mid-latitude ocean and atmosphere associated with STFZ interannual variation
The impacts of the artificially separated mesoscale SST anomalies using low-pass filter were often regarded as the forcing effects of multiple oceanic eddies in the numerical experiments (Ma, 2015b(Ma, ,2017Sun et al. 2018;Foussard et al. 2019). Is there an approach to capture them in the observations? The observed oceanic eddies distributed confusedly in the North Pacific, which is manifested as the synchronous coexistence of multiple oceanic eddies (Chelton et al. 2007(Chelton et al. , 2011Wen et al. 2020). Especially in the STFZ, previous works discussed the forcing effects of subtropical front intensity variations on above mid-latitude atmosphere (Wang et al. 2016(Wang et al. , 2019Chen et al. 2019bChen et al. , 2020. However, the causes of the interannual variation in the STFZ are not clear. As mentioned in the introduction, the STCC south to the area, which carries the warm water to the central and eastern Pacific, has close relations to the maintenance of the subtropical front. Meanwhile, the abundant presence of oceanic eddies appears in the sea surface of the STFZ and the region farther north (Fig. 1a). Distinct to sea surface, the subtropical front intensity has comparable strength to the norther subarctic front in the subsurface layer, and its position moves southerly (Fig. 1b). The 3-7 day bandpassfiltered (Duchon 1979;Russell 2006) EKE in Fig. 1b, representing the synoptic-scale oceanic eddy activities, mainly exists near 25° N, which coincides the latitude of the STFZ in the subsurface layer. The above results indicate that the variation of the subtropical front may be affected by multiple synoptic-scale oceanic eddies, besides the influence of the STCC (detailed mechanism in Sect. 3.2). The characterization index of oceanic eddies is introduced in formula (2) to present the interannual variability of the ocean current EKE. And to quantify the correlations, Fig. 2 shows the standardized time series of the ITS, STCC and EKE indexes. The EKE index and STCC index represent the activities of oceanic eddies in STFZ and the STCC latitudinal current strength, respectively. The correlation coefficient between EKE index and ITS reaches to 0.41, which passed 95% t-test significant level. However, the correlation coefficient between STCC index and ITS is only 0.12. These results show that the interannual variability of subtropical front intensity has a close linkage to the oceanic eddies, while the STCC has little effect on it. The subtropical front intensity shows an obvious interannual variability, then what happens in response to its enhancement? Then we composited the differences of several atmospheric fields between the years with a stronger (1980,1985,1986,1995,2002,2005,2009) and weaker (1990,1992,1994,1998,1999,2008) subtropical front, using the 1.0 standard deviation of ITS.
The oceanic front zones (STFZ and SAFZ) with larger SST gradients are the most significant areas among midlatitude air-sea interactions (Nakamura et al. 1997;Minobe et al. 2008). The differences of the SHF, LHF, Eady growth rate at 850 hPa, averaged storm tracks (  . The ITS, EKE index, and U-component of STCC index are the spatial average of the SST gradient in 24° N-32° N and 140° E-140° W, 3-7 days bandpass filtered sea surface EKE in the eddy locations within STFZ, and u-component of current at sea surface in 18° N-24° N and 140° E-157° W, respectively. The reference lines are ± σ. X-axis presents the years; Y-axis presents the standardized indexes anomalous responses, which are caused by the larger SST gradient that even bring intense heat exchange and air-sea humidity differences (Fig. 3a, b). Corresponding air temperature change occurs in the lower atmosphere and brings the positive baroclinity (Eady growth rate) response mainly takes place in the region between the STFZ and SAFZ, while the negative value exists north to the SAFZ (Fig. 3c). Chen et al. (2019b) pointed out that the temperature gradient anomaly in the lower atmosphere could generate upward baroclinic waves and energy transport. As results of this process, the u-component of wind was notably increased at 300 hPa (Fig. 3e) and the storm track had significant positive anomaly at the exit of the westerly jet (Fig. 3d). Therefore, the subtropical front intensity anomaly changes the turbulent heat flux (SHF, LHF) in the air-sea interface, causes the temperature gradients and baroclinity anomalies in the lower atmosphere, leads to the abnormal fluctuations of the upward baroclinic Rossby wave and baroclinic energy transport, finally affects the upper storm track and jet stream. Chen et al. (2020) revealed the similar process using the numerical experiments. As seen from Fig. 2, the responses in upper troposphere closely related to the oceanic EKE variation, which are defined as the remote effects of the oceanic eddies in this work. Since the large value of oceanic EKE usually accompanies with complicated distributions of oceanic eddies, how do the complicated eddies cause the regularly enhancing or decreasing of the subtropical front intensity?

How multiple eddies caused the remote forcing effects by changing the subtropical front strength
In the previous section, we found that the collaborated anomalous SST gradients induced by the multiple oceanic eddies have good correlation with the subtropical front intensity, and exert remote forcing on upper atmosphere by the baroclinic adjustment process in the mid-latitude atmosphere. However, previous studies (Qiu 1999;Qiu and Chen 2010) also emphasized the relationship between subtropical front and STCC on the seasonal timescale. Figure 4 displays SST gradient anomaly, oceanic eddies and mean oceanic current (STCC) in winter of each stronger (a-e) and weaker (f-j) years of the subtropical front intensity. The results show that the numbers and strengths of oceanic eddies are irregular. The zonal mean current velocity of u-component between 140° E and 157° W (solid green lines) shows an interannual variability, but it does not coincide with the subtropical front intensity variance (red or blue lines). For instance, the STCC anomalies do not match the variation of front intensity during the stronger (1999Fig. 4-i2, j2) or weaker (1986, 1995Fig. 4-a2, b2) front years. In other words, the stronger (weaker) subtropical front does not correspond to the specific stronger (weaker) STCC on the interannual time scale. On the other hand, although there is a high correlation between the ITS and EKE values of oceanic eddies, the attributes of oceanic eddies perform stochastic, no matter considering the strength or vorticity of eddies. So how do the oceanic eddies specifically cause the changing of subtropical front? Is it a causal connection?
The forms of eddies in real ocean are complicated, including an isolated cyclonic or anticyclonic eddy and different kinds of combined-eddies. The combined-eddies are defined as two oceanic eddies existing longitudinally within a 5° × 5° box, which include the combined double-cyclones, the combined double-anticyclones, and the combined cyclone-anticyclone (anisotropic) pairs. Here we list three major groups in Table 1.
Since the abnormal subtropical front intensity is defined by the change of SST gradients, we need to display the more detailed local meridional SST gradient caused by each group of oceanic eddies. After masking those regions without steady oceanic eddies in winter, Fig. 5 shows the positions of the isolated single (ISO), double isotropic (DBL) and pair of anisotropic (PAIR) eddies (normal, green and purple) and  (Fig. 5c2). In total, the zonal mean of the meridional SST gradient anomalies over the eddy locations matches better with subtropical front intensity anomalies than the areas without any eddies. As a comparison, the zonal mean SST gradient anomalies in those regions without eddies is nearly zero (see Supplementary Materials Figure  S1). It indicated that the multiple oceanic eddies may lead to the interannual variation of the subtropical front by changing the SST gradient anomalies significantly in the eddy locations with certain spatial distributions. As for the stronger and weaker years of the subtropical front, Fig. 5 also shows that the double isotropic and pair of anisotropic eddies have greater positive anomalous SST gradient than isolated single eddies in the years with a stronger subtropical front, and they have nearly equivalent negative anomalous SST gradient during the weaker years. The three groups of eddies all contribute to the abnormal front intensity in these years. Although the combined eddies (including double isotropic and pair of anisotropic eddies) make up less than 30%, their impact is significant. The anomalous SST gradient with double isotropic eddies has greater variations than the original front, whereas the variation of anomalous gradient in the other region is significantly reduced. Such as in the stronger year 2002 of the subtropical front, it is precisely because of the existence of the double isotropic and pair of anisotropic eddies that the subtropical front intensity increases significantly. If the double isotropic eddies (pairs of anisotropic eddies) were removed, the anomalous front intensity wound decrease 35.4% (30.7%) in this year. (see Supplementary Materials Figure S2-4). Therefore, the oceanic eddies (with different forms) and the interannual variability of the subtropical front are closely related.  Thus, what kind of eddy distributions led to this result? To answer the question, the distributional characteristics of the cyclonic and anticyclonic eddies are presented in Fig. 6 in the stronger, normal and weaker years of the subtropical front intensity. Defining 28° N as the central axis of STFZ, in the stronger front years, more cyclone (anticyclone) eddies locate north (south) of 28° N (Fig. 6a), cooling (warming) the sea area north (south) of 28° N, intensifying the overall SST gradient. In the weaker front years, more cyclone (anticyclone) eddies occur south (north) of 28° N (Fig. 6c), reducing the overall SST gradient. While in the normal front years, the distributions of cyclone and anticyclone eddies are totally stochastic (Fig. 6b), which barely change the SST gradient. Figure 7 further shows the spatial distribution and ratio of each group of eddies (isolated single, double isotropic and pair of anisotropic eddies) in stronger, normal, and weaker years of the subtropical front. Also defining 28° N as the central axis of STFZ, in the stronger front years, more isolated cyclones (anticyclones) locate north (south) of 28° N (Fig. 7a), cool (warm) the sea area north (south) of 28°N, intensifying the overall SST gradient. In the weaker front years, more isolated cyclones (anticyclones) occur south (north) of 28° N (Fig. 7c), reducing the overall SST gradient. The situation is the same for double isotropic eddies ( Fig. 7d-f), although there are fewer eddy cases. However, it is obvious that the difference in the north-south percentage of cyclones and anticyclones caused by double isotropic eddies is more significant than that of isolated single eddies. For the longitudinally combined cyclone-anticyclone pairs (cold to the north and warm to the south, orange markers in Fig. 7g-i) and the reversed anticyclone-cyclone ones (green), they can induce the increasing and decreasing of local temperature gradient, respectively. In the stronger years, the pairs of anisotropic eddies located closer to the central axis of STFZ (Fig. 7g), benefiting the stronger front intensity. However, in the weaker years, the eddy pairs dispersed away from the central axis (Fig. 7i), offering insufficient temperature gradient. The above results can explain that the multiple eddies with divergent patterns can lead to the variability of the subtropical front.
In summary, we found a significant connection between the subtropical front intensity and EKE values of oceanic eddies over North Pacific in winter. Furthermore, considering the upper atmospheric subsequent responses to front intensity change, the subtropical front can be considered as a link between the multiple oceanic eddies and the remote effect on the upper atmosphere in the mid-latitude. The abnormal SST gradient induced by the spatial distributions of three types of eddies provide a firm evidence to the interannual variability of the subtropical front. Therefore, the multiple oceanic eddies in the STFZ will exert remote forcings on upper atmosphere by causing anomalies of the basin-scale SST gradient, the atmospheric baroclinicity and the upward baroclinic waves, which are not happened overnight. The local forcings of the three types of eddies on the MABL and lower atmosphere should be considered as the fundamentals.

Local forcings of the different eddy combinations to the middle and lower atmosphere
In Sect. 3, we have discussed the different distribution types of oceanic eddies in the STFZ. By changing the meridional temperature gradient over the eddy locations, these eddies lead to the remote effect on the upper atmosphere in the mid-latitudes, which should base on the direct local forcing on the MABL firstly. Considering the three main types of the multiple oceanic eddies, the forcings of them on MABL are still unclear. Previous researches have emphasized that a single strong eddy exerts local forcing on the atmospheric boundary layer Ma et al. 2015a;Xu et al. 2016). As mentioned above, the forms of eddies in STFZ are complicated, including the isolated single eddies, the combined double isotropic eddies and pairs of anisotropic eddies. The details of numbers and percentages of these eddy events are listed as Table 2. The impacts of these complex eddy combinations on MABL are distinct obviously. The isolated single cyclone eddies (39.9%), isolated single anticyclone eddies (34.1%) and the total combined eddies including double isotropic and pairs of anisotropic eddies (26%) are of the same magnitude. Since the isolated eddy cases and combined-eddies have been distinguished, we made investigation via composite analysis, considering the diversity and heterogeneity of eddies in the five situations. For isolated single cyclone eddies (ISO_CYC), the negative anomalies of 2-m air temperature and 10-m wind speed appear near SST negative anomaly center (Fig. 8a,  e), revealing that cold oceanic eddies would lead to surface air cooling and wind deceleration. Furthermore, the negative anomaly centers of both SHF and LHF as well as MABL height are in-phase with SST anomaly (Fig. 8b-d). Besides, the surface frictional velocity (Fig. 8f) shows an in-phase negative anomalous center with SST. The above results are consistent with previous studies (Ma et al. 2015a;Sun et al. 2020), indicating that the recognition and effects of oceanic eddies under the CFSR reanalysis outputs are  Fig. 6, and more significant percentage characteristics appear for DBL eddies. For the PAIR eddies, longitudinal cyclone-anticyclone pairs (cold to the north and warm to the south) are presented with orange markers of (g-i) and longitudinal anticyclone-cyclone pairs (warm to the north and cold to the south) are presented with green markers of (g-i) in good agreement with the previous data results. Moreover, we made further investigation on the 10-m scalar wind (Fig. 8h), and the anomalies are greater than average wind speed, which means oceanic eddies exert impact on local wind field mainly through high-frequency disturbance. The Richardson number is overall greater than 0.25 (Fig. 8g, shadings in red), indicating dynamic stability in the MABL. For isolated single anticyclone eddies (ISO_ANT), almost symmetric results are shown in Fig. 9 but with a positive phase and unstable boundary layer. As the classification in Table 2, the predecessors paid less concern to the complex combined oceanic eddies, what are their different effects on MABL? For combined double-cyclone (DBL_CYC) and double-anticyclone (DBL_ANT) eddies, the anomalous centers are also nearly in-phase and the 10-m scalar wind anomalies are also greater than 10-m wind speed, and it is equivalent for double-anticyclones (see Supplementary Materials Figure S5-6). Therefore, we hypothesized the synergistic local effects of combined isotropic eddies are similar with the isolated eddy.
However, the composite results are different for the pairs of anisotropic eddies, as Fig. 10 shows, the 2-m temperature,  The situation is reversed in response to the PAIR_ NW_SC since the meridional temperature gradient anomaly is negative (Fig. 11a-d). Furthermore, the 10-m scalar wind and frictional velocity show insignificant or even repressed responses (Figs. 10 and 11). The results explained that the combined cyclone-anticyclone eddies exert effects on atmosphere mainly through the SST gradient anomalies, and the mean surface wind accelerates because of thermal wind effects instead of the intense high-frequency disturbance.
Overall, oceanic eddies are provided with warm or cool SST anomalies based on their vertical features. The thermal anomalies can heat (cool) near surface air by heat flux (usually directly SHF). The abnormal status of wind speed is the consequence of heat and momentum transporting from oceanic eddies to atmosphere. Meanwhile, this energy can also influence the MABL height. The intensity of energy exchange between anticyclone eddy and air is stronger, developing a more unstable condition for anticyclone as underlying surface, and resulting in enhancement of vertical mixing. On the contrary, the atmosphere above cyclone eddies is more stable. Thus, turbulent heat flux is undermined and MABL height is diminished in this situation. However, considering the oceanic eddies are not isolated in real ocean, the combined anisotropic eddies can also influence the local SST gradient thereby exert forcing on MABL via baroclinicity.
The above-mentioned discoveries of isolated single oceanic eddy within MABL are consistent with previous researches in other sea regions Ma et al. 2015a;Chen et al. 2017), yet oceanic eddies have broader influence on free atmosphere beyond MABL (Ma et al. 2015a;Zhang et al. 2019;Sun et al. 2020). Figure 12 presents geopotential height anomalies passing 95% t-test confidence level from MABL top (refer to Fig. 8d) up to 500 hPa (Fig. 12c), and the vectors represent wind velocity at MABL top. Geopotential height anomalies are positive (negative) east to the warm (cold) positive (negative) SST centers of the isolated single eddies, nearly along the downwind direction at MABL top. For combined double isotropic eddies, the responses are also transported to downstream locations but have greater absolute values. The result of anisotropic eddy pairs indicates that the response of middle atmosphere at this time is not the dipole geopotential height anomaly induced by the dipole eddy existing form. Instead, an anticyclonelike height anomaly is produced in response to PAIR_NC_ SW, i.e., an abnormal high at the downwind location of the dipole SST anomalies, whose strength is weaker than the isolated and the combined anticyclone eddies. The geopotential height anomaly distribution of middle atmosphere is consistent with the lower MABL, which is determined by the drastic SST gradient between the warm and cold eddies. The situation for PAIR_NW_SC is reversed. And, in general, geopotential height anomalies increase faster from lower to upper levels over for anticyclonic eddies than that for cyclonic eddies.
In addition to the geopotential height anomalies of the middle atmosphere caused by various oceanic eddies, we also paid attention to the differences in local convective precipitation under different existing forms of eddies (Fig. 13).
The composited analysis of precipitation shows that the convective precipitation anomalies are significantly decreased above cyclonic isolated and double eddies (Fig. 13a, b), but not increased as much over anticyclonic eddies (Fig. 13d, e). Even with anticyclonic double eddies, the convective precipitation increment does not pass the significant test. Instead, the two ascending motions over double warm eddy centers induce a significant air descending and convective inhibition between the extremums of warm eddies (Fig. 13e). Accompanied atmospheric stability and MABL height decrement (see Supplementary Materials Figure S6) also denote the compensated descending motion. However, the PAIR_NC_SW have distinct impact on convective precipitation (Fig. 13f). The convection is inhibited in the frontal area where the cold and warm eddies converge, and the promoted convection occurs where the MABL height (Fig. 11d) rises and on the warmer side of sea water. In general, oceanic eddies would affect cumulus convection above them to adjust precipitation anomalies. However, in the STFZ, a local cooling of SST caused by cyclone eddies can significantly inhibit convective process locally, but a local warming of the anticyclone eddy has the weaker effects. In summary, the isolated single eddies have distinguished local forcing on MABL and free atmosphere from the combined-eddies (double isotropic and pairs of anisotropic eddies). The sign of the isolated eddy's vorticity determines its local forcing effects. The forcing effects of isolated single eddies with different polarities on the lower atmosphere are spatial unevenly distributed in the stronger and weaker years of the STFZ (cold eddies almost exist to the north in stronger years while to the south in weaker years), eventually resulting in the remote forcing of isolated single eddies on the atmospheric upper level. The local forcing of double isotropic eddy composite on the MABL is of consistent character with that of the isolated eddy composite, but due to its dipole-center structure, the same dipole local forcing effects are caused in the MABL. Furthermore, although the temperature anomaly intensity of the double isotropic eddy composite is similar with the isolated eddy composite, its dipole structure caused the most significant changes in the middle atmosphere and precipitation fields among the three eddy types. This also explains that the double isotropic eddies have remote forcing as important as isolated single eddies despite their relatively fewer cases. Finally, for the anisotropic eddy pair composite, its local forcing on MABL is completely different from the previous two. The changes of each physical quantity in MBAL mainly exist over the boundary of two contrary eddies. But when it comes to the middle atmosphere and precipitation field, the atmospheric responses are advected downstream by the background wind. Based on the local forcing effects, the anisotropic eddy pairs do not force the MABL as significantly when compared to the isolated single eddies. However, due to the special drastic meridional temperature gradient between the two contrary eddies, the anisotropic eddy pair composite has the most significant impact on the baroclinicity of the lower atmosphere. This is also the reason why it can cause significant remote forcing effects on the upper atmosphere in certain specific years, with the least quantity among the three types of eddies.

Conclusion and discussion
In this study, we focused on the forcing effects (Fig. 14) of the multiple oceanic eddies on mid-latitude atmosphere in wintertime North Pacific. We detected and classified the oceanic eddies into the isolated single eddies, the combined double isotropic eddies and pairs of anisotropic eddies types in the STFZ using CFSR dataset from 1979 to 2009 ( Fig. 14a-i, ii, iii). Like previous studies Xu et al. 2016;Ma et al. 2015bMa et al. , 2017Sun et al. 2018), this study specifically divides the forcing effects of oceanic eddies on the atmosphere into the remote effects on the upper atmospheric jet at the entire basin scale and the local forcing on the MABL and the lower atmosphere above. Among the three types of ocean eddies in the STFZ, the isolated single anomalies and g the gradient Richardson number at 950 hPa. Dotted areas have passed 95% t-test significant level eddies account for 74% in total. Cyclonic (anticyclonic) isolated eddy can cause surface winds to decelerate (accelerate) and reduce (increase) latent and sensible heat fluxes, MABL height, boundary stability and disturbance locally. These local forcing effects are even transmitted upwards to the middle atmosphere and local convective precipitation fields, providing an energy basis for causing basin-scale remote forcing effect on upper atmosphere. The isolated single eddies are unevenly distributed in the North Pacific basin. Furthermore, we found that more cyclonic (anticyclonic) isolated oceanic eddies persist to the north of the STFZ, and more anticyclonic (cyclonic) isolated eddies to the south in the years with a stronger (weaker) subtropical front, which lead to the positive (negative) SST gradient, atmospheric baroclinicity and remote forcing on the interannual timescale. The local forcing of combined double isotropic eddies on MABL depends on the numbers and properties of eddy centers. In addition, the double isotropic eddies have more significant local effects than isolated type, with the dipole structure in MABL and the more significant anomalies in the local precipitation field. It is the reason why the combined double isotropic eddies, with fewer cases, have remote forcing equivalent to the isolated ones on the upper atmosphere.
The local effect in the MABL caused by the pairs of anisotropic eddies, unlike the other two types, is located at the boundary of the two contrary eddies. For the MABL and middle atmosphere responses to the eddies, the eddy pair type is weaker than the other two types. However, in the years with a stronger subtropical front, more northcold and south-warm (north-warm and south-cold) types are concentrated (dispersed) on the main axis of the STFZ. The opposite sea temperature anomalies caused by each of the two eddies lead to a significant meridional temperature gradient in the STFZ, and result in the significant remote forcing although with fewer anisotropic eddy pairs. Due to the contribution of stronger (weaker) SST gradient caused by the three types of eddies in the STFZ, the subtropical front intensity variations lead to the increased (decreased) upward baroclinic atmospheric energy, and finally enhance (decrease) the storm track and zonal wind at upper 300 hPa level, which brings a link between multiple oceanic eddies and remote forcing effect on upper atmosphere (Fig. 14b). Some researches (Wang et al. 2016(Wang et al. , 2019Chen et al. 2019bChen et al. , 2020 have discussed the atmospheric internal adjustment considering the subtropical front intensity anomaly in atmospheric simulations. We further revealed the causes of the interannual variation of the subtropical front in this work.
The observed interannual variation of the subtropical front intensity has complex influencing factors, including large-scale sea temperature anomalies, oceanic front intensity changes, air-sea temperature difference and changes of the oceanic eddy distribution, etc. The reanalysis outputs diagnosis in this study gives a possible link and mechanism conjectures of statistically different eddy distribution and interannual variability of the subtropical front. Further research requires a series of sensitivity experiments using numerical models to distinguish the effects of the spatial distribution of numerous oceanic eddies. We have designed a series of numerical experiments to distinguish the effects of oceanic eddies and front in the North Pacific, which will be prepared for further research.
On the whole, the present study mainly focused on the existing forms and distribution features of the oceanic eddies in the STFZ and the corresponding local and remote effects 14 Schematic depiction of the a local and b remote forcing of oceanic eddies on atmosphere in the STFZ during winter. a surface layer presents SST anomaly and heat flux induced by eddies, responding geopotential heights are presented by the bulge of each face, and enhanced/decreased precipitation are given as icons; b a certain kind of eddy distribution overlays climatic SST, strengthening the subtropical front intensity and affecting wind at 300 hPa on mid-latitude atmosphere using CFSR reanalysis outputs. On the next stage, more detailed analyses are needed using an eddy-resolved air-sea coupled numerical model. Besides, the KE also contains abundant eddy activities with extreme EKE along a latitudinal band. Ji, (2018) proposed a possible connection by statistically analyzing the eddy characteristics and mechanism of occurrence in the KE region: for eddies with longer durations (greater than 50 weeks), more cyclones (anticyclones) occur in the south (north) part of the Kuroshio main axis; for eddies with shorter duration (less than 20 weeks), more cyclones (anticyclones) occur in the north (south) part of the Kuroshio main axis. However, their effects on the North Pacific mid-latitude atmosphere need further investigation.