1 Introduction

The Kuroshio Current, one of the strongest western boundary currents in the global ocean, transports large amounts of water and heat from the tropical region northward to the North Pacific. It separates from the east coast of Japan near 35° N and is renamed as the Kuroshio Extension (KE). As an inertial jet, the KE is characterized by strong recirculation gyre, time-varying path, and large meanders (Mizuno and White 1983; Wijffels et al. 1998; Qiu and Chen 2005). Overlaid by intense westerly and active atmospheric storms, the KE has been proved to be a key region of ocean circulation and air-sea interaction in mid-latitudes (Qiu and Kelly 1993; Cornillon and Park 2001; Vivier et al. 2002; Nonaka and Xie 2003; Xu et al. 2010; Ma et al. 2016).

In addition to its large-scale characteristics, the KE is also abundant with energetic mesoscale eddies (Jayne et al. 2009; Scharffenberg and Stammer 2010; Waterman et al. 2011; Nakamura et al. 2015; Yang et al. 2017; Dong et al. 2017). Satellite observations reveal that anticyclonic eddies (AEs) are mainly observed along the northern flank of the KE, while cyclonic eddies (CEs) are more frequently distributed along the southern flank (Itoh and Yasuda 2010; Sasaki and Minobe 2015). After generation, both AEs and CEs propagate westward with a speed close to baroclinic Rossby waves and last for 8–13 weeks on average (Sasaki and Minobe 2015; Meng et al. 2021). Further explorations indicate that eddies in this region are generated through shear instability and meander development of the KE jet (Waterman et al. 2011; Ji et al. 2018; Matsuta and Masumoto 2021) or originate from the central North Pacific Ocean (Deser et al. 1999; Qiu 2003).

With the accumulation of observations over the past 30 years, many studies have focused on the decadal variability of eddy activity, which is associated with the fluctuations of dynamical state of KE (Qiu and Chen 2005, Qiu et al. 2014; Kelly et al. 2010; Sasaki et al. 2013; Jiang et al. 2017; Yang et al. 2018; Wang and Tang 2022). During the stable state, the KE jet has a straighter path and larger transport, and eddy kinetic energy (EKE) in the upstream (downstream) is smaller (larger). The reverse is true for the unstable period. To date, several potential factors associated with this decadal variability, such as the instability of background flow (Wang et al. 2017; Yang et al. 2017, 2018), wind-induced Rossby wave adjustment (Miller et al. 1998; Deser et al. 1999; Seager et al. 2001; Kwon and Deser 2007; Ceballos et al. 2009; Sasaki and Schneider 2011), and the effect of topography (Qiu and Chen 2005) have been extensively discussed.

Besides the decadal variability, the seasonality of EKE in the vicinity of KE has also attracted much attention (Tai and White 1990; Stammer and Wunsch 1999; Ducet and Le Traon 2001; Scharffenberg and Stammer 2010; Zhai 2017; Yang and San Liang 2018; Wang and Pierini 2020). Based on satellite observations, Ji et al. (2018) pointed out that the number of eddies tends to be larger (smaller) and EKE tends to be higher (lower) in summer (winter). Meng et al. (2021) suggested that more eddies are found in June, with larger amplitude and larger radius, than in December. Yang and San Liang (2018) found that the anomaly of EKE relative to the annual mean value is different in summer and winter. In summer (winter), large positive (negative) anomaly of EKE is mainly found in 142° E–155° E, 31° N–39° N. Mechanisms underlying the seasonal-varying eddy field have also been proposed in previous studies. Regulated by the surface buoyancy field (Cronin et al. 2013) and Kuroshio transport south of Japan (Imawaki et al. 2001), the KE jet and available potential energy (APE) stored in the mean stratification depict obvious seasonal variability, which influences eddy generation in the upstream KE (Yang and San Liang 2018; Wang and Pierini 2020). Compared with the upstream, the intensity of EKE in the downstream region is much weaker and two potential energy sources have been suggested. By analyzing local eddy energy generation, Yang and San Liang (2018) emphasized the role of baroclinic instability (BC) in regulating the seasonal variations in eddy fields. Others, however, argue that eddies give energy back to mean flow in this region and imply the importance of advection effect (Berloff and McWilliams 1999; Waterman and Hoskins 2013; Yang et al. 2018).

These previous studies have significantly improved our knowledge on the seasonality of the eddy activity in the KE region; however, some important issues remain unsolved. Firstly, eddy characteristics, such as the EKE power spectral density and eddy shapes, are useful indicators for eddy-mean flow interactions (Qiu et al. 2008; Marshall et al. 2012; Waterman and Hoskins 2013) and are not studied at seasonal timescales. Secondly, the dominant energy source of eddy generation in regulating the EKE seasonal variability, especially in the downstream KE, is still controversial (Yang and San Liang 2018; Yang et al. 2018). Thirdly, previous studies have proved that oceanic response to global warming varies seasonally (Yang and Wu 2012; Huang 2015; Wang et al. 2021). Given that the western boundary currents have experienced the accelerated warming since the 1900s, especially in the past 30 years (Wu et al. 2012; Hu et al. 2020), it is important to confirm whether the seasonality of EKE has changed.

In this study, the abovementioned issues regarding the seasonal variability of EKE in the KE region are examined, on the basis of an eddy-resolving reanalysis product. Based on previous estimations, the upstream and downstream KE depict different features in dynamical state of flow and EKE level evolution (Qiu and Chen 2005; Jiang et al. 2017), eddy generation mechanism (Yang and San Liang 2018; Yang et al. 2018), and eddy-mean flow interaction (Waterman and Hoskins 2013; Yang et al. 2018). Actually, as will be shown later, the seasonal evolution of eddy characteristics and energetics is different in the upstream and downstream KE. Therefore, upstream and downstream region of the KE is also investigated in the following discussions. The rest of the paper is organized as follows: Section 2 gives a brief description of the data used in this study. In Section 3, a detailed study of the eddy characteristics and energetics is presented, followed by their changes during 1993–2013. The paper ends with a summary and further discussion in Section 4.

2 Data

2.1 FORA-WNP30 data

In this study, seasonal variability of eddy activity in the KE region is analyzed using the Four-dimensional variational Ocean Re-Analysis for the Western North Pacific over 30 years (FORA-WNP30) product (http://synthesis.jamstec.go.jp/FORA/e/; Usui et al. 2017). It is based on the western North Pacific version of the Meteorological Research Institute (MRI) Community Ocean Model version 2.4 (MRI.COM-WNP; Tsujino et al. 2006). MRI.COM-WNP solves the primitive equations under the hydrostatic and the Boussinesq approximations in the western North Pacific (117° E–160° W, 15° N–65° N). The horizontal resolution of this model is not constant: it is 1/10° within 117° E–160° E and 1/6° in 160° E–160° W zonally, while 1/10° within 15° N–50° N and 1/6° in 50° N–65° N in the meridional direction. In the vertical direction, there are 54 levels with thickness varying from 1 m at the surface to 600 m near the bottom at a maximum depth of 6300 m. A biharmonic operator is used in the horizontal mixing and friction, while the vertical viscosity and diffusivity are determined in accordance with Noh and Jin Kim (1999). MRI.COM-WNP is driven by the atmospheric forcing derived from the Japanese 55-year Reanalysis (JRA-55; Kobayashi et al. 2015). With the application of the multivariate four-dimensional variational (4DVAR) analysis scheme, namely, the MRI Multivariate Ocean Variational Estimation system (MOVE-4DVAR), the model assimilates several available in situ and satellite observations (e.g., in situ temperature and salinity profiles, sea surface temperature, sea surface height (SSH), and sea ice concentration), which makes this product reliable for process analysis. Because of its good performance, FORA-WNP30 has been used to explore multiscale oceanic dynamics in the North Pacific region (Jing et al. 2019; Wang and Pierini 2020; Long et al. 2021). In this paper, daily mean data in the region (140° E–180° E, 25° N–45° N) during 1993–2013 is used.

2.2 Satellite observation

To validate the FORA-simulated eddy activity, the merged absolute dynamic topography (ADT) product (https://www.aviso.altimetry.fr/) is used in our analysis. Using data from the Jason-3, Sentinel-3A, HY-2A, Saral/AltiKa, Cryosat-2, Jason-2, Jason-1, T/P, ENVISAT, GFO, and ERS1/2 altimeter missions, the data is processed by the DUACS multimission altimeter data processing system and distributed by Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO). The temporal resolution of the dataset is 1 day and the horizontal resolution of the dataset is 0.25°, which is useful to analyze mesoscale eddies. As for the FORA-WNP30 dataset, the SSH data from 1993 to 2013 in the region (140° E–180° E, 25° N–45° N) is used.

2.3 Reanalysis data

To validate the results of wind evolution during 1993–2013, JRA-55 and the European Centre for Medium-Range Weather Forecasts ERA5 reanalysis products (ECMWF ERA5; https://rda.ucar.edu/datasets/ds633.1/; Hersbach et al. 2020) are used.

The first full-observing-system reanalysis product JRA-55 covers the period from 1958, when the global radiosonde observing system was established (Kobayashi et al. 2015). JRA-55 has been transformed from the TL319L60 grid to a regular latitude–longitude Gaussian grid, 320 latitudes by 640 longitudes, nominally 0.5625° in the meridional and zonal directions. According to Harada et al. (2016) and Miao et al. (2020), JRA-55 offers good estimates of wind speed over the Northern Hemisphere. As the most recent (5th generation) global atmospheric reanalysis of the European Centre for Medium-Range Weather Forecasts (ECMWF), ERA5 stands out for its high resolution as well as for a large amount of assimilated observations (Hersbach et al. 2020). ERA5 provides global, hourly estimates of atmospheric variables, at a horizontal resolution of 31 km (0.25°) and 137 vertical levels from the surface to 0.01 hPa. Previous studies pointed out that ERA5 works well for the representation of surface and low-level winds over the ocean (Olauson 2018; Belmonte Rivas and Stoffelen 2019; Kalverla et al. 2019). The assimilation of infrared radiances and winds from GMS/MTSAT/Himawari geostationary satellites along 140° E makes it a reliable choice for the research on large-scale air temperature and wind fields in the KE region. In this study, we will focus on the region (130° E–120° W, 15° N–65° N) during the period from 1993 to 2013.

3 Results

3.1 Seasonal variability of EKE

Before analyzing the seasonal cycle of EKE in the KE region, it is necessary to quantify whether FORA can capture the seasonal cycle of mesoscale eddies as observed by satellite. Here, EKE is defined as

$${\text{EKE}}=\frac{1}{2}(u{^{\prime}}^{2}+v{^{\prime}}^{2}),$$
(1)

where \(u\mathrm{^{\prime}}\) and \(v\mathrm{^{\prime}}\) denote zonal and meridional surface velocity deviation from their 240-day-running-mean values, consistent with previous studies (Itoh and Yasuda 2010; Yang et al. 2017). Changing the cutoff period from 180 to 300 days does not generate a significant difference in the following analysis. It is noted that the resolution of FORA is higher than that of satellite observations. To make a comparison between these two datasets, a two-dimensional interpolation is applied to FORA data. Figure 1a and b reveals that the spatial patterns of SSH and EKE simulated by FORA resemble those of AVISO. Two meanders appear at approximately 145° E and 150° E with a meridional span of 4° from 33° N to 37° N, consistent with Lan et al. (2003). Strong eddy activity is concentrated within the area of 145° E–150° E and 32° N–36° N, with the maximum located around the first trough of KE (146° E–148° E, 34° N–36° N). In addition to the spatial pattern, seasonal variability of EKE in the upstream (142° E–152° E, 31° N–39° N), downstream (152° E–170° E, 31° N–39° N), and entire KE (142° E–170° E, 31° N–39° N) is also successfully simulated by FORA (Stammer and Wunsch 1999; Scharffenberg and Stammer 2010; Yang and San Liang 2018; Fig. 1c and d). In both upstream and downstream regions, high EKE level is found in summer (June–August; JJA) and autumn (September–November; SON), while low eddy activity appears in spring (March–May; MAM) and winter (December-February; DJF). The amplitude of seasonal variability of EKE is about 0.023 (0.015) m s in the upstream (downstream) region, close to observation as well. Overall, FORA reasonably reproduces the seasonal variability of eddy activity in the upstream and downstream KE. Next, we will use it to investigate the eddy dynamics.

Fig. 1
figure 1

a Mean EKE during 1993–2013 based on satellite observation (colored shading; m2/s2). Black contours indicate SSH isolines. Red boxes indicate the upstream and downstream regions, respectively. b Mean EKE during 1993–2013 based on FORA (colored shading; m2/s2). Black contours indicate SSH isolines. Seven overlapping boxes with 64 × 64 grid points (6.4° × 6.4°) are shown. The red meridional lines indicate the west boundaries of the boxes, while the black meridional lines represent the east boundaries of the boxes. Seasonal cycle of EKE averaged in upstream KE, downstream KE, and entire KE region from c satellite observation and d FORA. Error bars indicate the standard errors

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To understand the characteristics of mesoscale eddies, we calculate power spectral density

$$E({k}_{x},{k}_{y},t)=\frac{1}{2}\left({{\widehat{u}}{\prime}{\widehat{u}}{\prime}}^{*}+{{\widehat{v}}{\prime}{\widehat{v}}{\prime}}^{*}\right),$$
(2)

as a function of zonal and meridional wavenumbers, kx and ky. Caret and star denote discrete Fourier transform and corresponding complex conjugate, respectively. Following Qiu et al. (2008), the velocity anomaly data is preprocessed as follows. The velocity anomaly is partitioned into seven overlapping boxes (the boxes in Fig. 1b) with 64 × 64 grid points (6.4° × 6.4°). The average of three boxes is used to evaluate the EKE spectra in the upstream KE, whereas four boxes are used for the downstream KE. The latitude and longitude ranges of seven boxes are shown in Table 1. By fitting a bilinear plane via least squares, the velocity anomaly fields are detrended for each box and each time step. A Hanning window is then applied to the detrended data.

Table 1 The latitude and longitude ranges of 7 boxes (3 boxes in the upstream region and 4 boxes in the downstream region)
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The EKE power spectral density distributions in the upstream and downstream KE regions are shown in Figs. 2 and 3, respectively. In the upstream region, the power spectral density reaches the maximum (minimum) in summer (winter). A higher energy level is found at larger ky than kx ranges all year round, suggesting that eddies in this region are more zonally elongated. Compared to the upstream region, the power spectral density in the downstream region reaches the maximum in autumn. A high energy level is found to appear at larger kx range in the downstream region (Fig. 3), which indicates that eddies tend to be meridionally elongated. The difference of eddy shape between the upstream and the downstream regions is further confirmed by estimating the eddy elongation parameter (Fig. 4)

Fig. 2
figure 2

Normalized EKE power spectral density distributions as a function of kx and ky in the upstream KE region in a spring, b summer, c autumn, and d Winter

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Fig. 3
figure 3

Normalized EKE power spectral density distributions as a function of kx and ky in the downstream KE region in a spring, b summer, c autumn, and d winter

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Fig. 4
figure 4

a Spatial distribution of M (colored shading; 0.01 m2/s2) based on FORA. Contours are state-mean SSH isolines. Red and black boxes indicate the upstream and downstream regions, respectively. b Annual cycle of M averaged in the upstream region (142° E–152° E, 31° N–39° N) and the downstream region (152° E–170°E, 31°N–39° N). Error bars indicate the standard errors

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$$M=\frac{1}{2}\left(u{^{\prime}}^{2}-v{^{\prime}}^{2}\right).$$
(3)

As an element of eddy Reynolds stresses, M is suggested to be a useful indicator to present the interaction between eddies and mean flow (Waterman and Hoskins 2013). When M is negative (positive), eddies are meridionally (zonally) elongated and more energy is confined to large kx (ky) than ky (kx). In the upstream region, M depicts large positive values around the first crest of the meandering KE. In contrast, M is characterized by negative values in the downstream east of 152° E. The distribution of M illustrates that eddies tend to be elongated along (across) the mean jet axis in the upstream region (downstream), consistent with the spectral analysis. According to Waterman and Hoskins (2013), this phenomenon implies that eddies draw energy from mean flow in the upstream region and give energy back to mean flow in the downstream region. In the following section, we will further confirm this based on eddy energy budget analysis.

3.2 Energetics

To clarify the dominant energy sources responsible for the seasonal variability of eddy activity, we estimate the energy obtained by eddies through BC and barotropic instability (BT; von Storch et al. 2012 and Chen et al. 2014):

$${\text{BC}}=-\frac{{g}^{2}}{{\rho }_{0}{N}^{2}}{\rho }^{\prime}{v}_{h}{^\prime}\cdot {\nabla }_{h}\stackrel{-}{\rho ,}$$
(4a)
$${\text{BT}}=-{\rho }_{0}(u{^\prime}{v}_{h}{^\prime}\cdot {\nabla }_{h}\overline{u }+{v}{^\prime}{v}_{h}{^\prime}\cdot {\nabla }_{h}\overline{v }),$$
(4b)

where g is gravitational acceleration, N2 is the square of the buoyancy frequency, and ρ0 is the background density 1025 kg/m3. The symbol vh means horizontal velocity vector, and \({\nabla }_{h}\) represents the horizontal gradient operator. Physically, BC (unit: W/m3) denotes the energy between mean flow and eddy through vertical shear, and BT (unit: W/m3) represents the energy exchange between mean flow and eddy through horizontal shear. Based on previous studies, they are the main local energy sources of mesoscale eddies in the global ocean (Gill et al. 1974; Stammer 1998; Noh et al. 2007; von Storch et al. 2012; Chen et al. 2014; Wang et al. 2017). In addition to local energy exchange, eddy activity can also be regulated by remote regions through non-local effects (Chen et al. 2014; Yang et al. 2018). Physically, this non-local energy exchange (Q; unit: W/m.3) involves the energy flux divergence through eddy-induced advection (Adv) and the work done by eddies on the surrounding environment through eddy-induced pressure (Pre). The equation is as follows:

$$Q=-\nabla\cdot[\underbrace{\frac{1}{2}\rho_0{\mathbf{v}}_h\left(u^{\prime 2}+v^{\prime 2}\right)}_{Adv}+\underbrace{{p^\prime{\mathbf{v}}_h{^\prime}} }_{Pre}]$$
(5)

The symbol p indicates the pressure of the water column above a specific depth.

The seasonal cycle of the volume integral values of EKE, BC, BT, and Q is shown in Fig. 5. To get a better knowledge of energy exchange, their horizontal distributions at the sea surface are presented in Fig. 6. Consistent with the distribution of EKE spectral energy (Fig. 2) and M (Fig. 4), significant BC is detected along the KE jet with the maximum occupying the first crest of meander at 145° E. In the upstream region, negative patches are found near the trough around 146° E–148° E, which may be caused by the vertical velocity anomaly related to cold-core rings in that area (Bishop 2013). According to Fig. 5b and d, BT and Q act as EKE sinks in the upstream region throughout the year. Quantitatively, BC exhibits a much larger magnitude than the other two terms, and the correlation coefficient between BC and EKE reaches 0.92 (Fig. 5a and c), suggesting its predominant role in regulating the seasonal variability of mesoscale eddy activity. To further explore the dynamics underlying seasonal evolution of BC, we respectively estimate background buoyancy frequency (N2) and eddy-induced buoyancy flux in Eq. (6). In particular, the eddy-induced buoyancy flux is divided into two parts (Wang and Pierini 2020):

Fig. 5
figure 5

Seasonal cycle of the volume integral of a EKE, b BT, c BC, and d Q. The volume integral is conducted in the upper 600 m over the upstream KE (142° E–152° E, 31° N–39° N) and downstream KE (152° E–170° E, 31° N–39° N). Error bars indicate the standard errors

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Fig. 6
figure 6

Spatial distribution of a EKE (unit: m2/s2), b BT (unit: W/m3), c BC (unit: W/m3), and d Q (unit: W/m3) at the sea surface based on FORA. Contours are state-mean SSH isolines

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$${T}_{x}=-{\rho }{^\prime}{u}{^\prime}\frac{\partial \overline{\rho }}{\partial x},$$
(6a)
$${T}_{y}=-{\rho }{^\prime}{v}{^\prime}\frac{\partial \overline{\rho }}{\partial y}.$$
(6b)

Here, Tx and Ty represent eddy buoyancy flux down the gradient of density in the zonal and meridional directions, respectively. Figure 7a shows the N2 in four seasons, in which it reaches the maximum in summer and minimum in winter. The evolution favors a smaller BC in summer and a larger BC in winter, which is inconsistent with the BC change. Figure 7b illustrates the seasonal evolution of depth-integrated (upper 600-m depth) Tx, Ty, and (Tx + Ty) averaged over the upstream KE region. Similar to BC, (Tx + Ty) is stronger in summer and weaker in winter. By estimating the correlation coefficient of monthly mean (Tx + Ty) and BC over the period 1993–2013, it is found that the coefficient reaches 0.85 (significant at the 90% level based on the Student t-test), suggesting that eddy buoyancy flux is responsible for the evolution of BC. Both Tx and Ty contribute to the seasonal variability of (Tx + Ty). In spring and summer, Tx is the main component of (Tx + Ty), accounting for 76.3% and 67.9% of (Tx + Ty). In comparison, Ty makes up 71.0% of (Tx + Ty) in autumn. In winter, Tx and Ty are almost equal (50.2% and 49.8%).

Fig. 7
figure 7

a Distribution of N2 in four seasons averaged within the upstream KE region (142° E–152° E, 31° N–39° N) in the upper 600 m. b Seasonal cycle of depth-integrated (upper 600-m depth) Tx, Ty, and (Tx + Ty) averaged over the upstream KE region. Error bars indicate the standard errors

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In addition to the interpretation in terms of energy, the seasonal evolution of baroclinicity of the KE jet can also be understood through its physical state. Figure 8a shows the vertical shear of velocity (\(\frac{\partial \mathrm{V}}{\partial \mathrm{z}}=\frac{\partial \sqrt{({u}^{2}+{v}^{2})}}{\partial \mathrm{z}}\)) in the upstream region. In accordance with BC, the vertical shear of velocity is much stronger in summer and autumn, especially in the upper 300 m. Based on thermal wind balance, the vertical shear is proportional to the horizontal gradient of density (\(\frac{\partial u}{\partial z}=-\frac{ g }{f\rho }\frac{\partial \rho }{\partial y}\), \(\frac{\partial v}{\partial z}=\frac{ g }{f\rho }\frac{\partial \rho }{\partial x}\)). At the depth of 250 m, the density front undergoes a weak annual cycle with a suggestion of stronger gradients in summer, weaker in winter (Fig. 8b). This phenomenon could be attributed to the seasonal evolution of surface buoyancy forcing. In winter, large air-sea temperature difference and strong surface wind induce a significant heat loss and intense mixing in the upper ocean (Kelly et al. 2010), which deepens the mixed layer and favors a downward momentum flux. Correspondingly, a smaller vertical shear of the velocity is detected. By contrast, the weaker surface buoyancy forcing in summer results in a shallower mixed layer and larger vertical shear of the velocity.

Fig. 8
figure 8

a Distribution of vertical shear of horizontal speed (\(\frac{\partial V}{\partial z}=\frac{\partial \sqrt{({u}^{2}+{v}^{2})}}{\partial z}\)) in four seasons averaged over the upstream KE region (142° E–152° E, 31° N–39° N). b Seasonal cycle of horizontal density gradient (\(\nabla \rho =\sqrt{{\left(\frac{\partial \rho }{\partial x}\right)}^{2}+{\left(\frac{\partial \rho }{\partial y}\right)}^{2}}\)) averaged over the upstream KE region at the 250 m. Error bars indicate the standard errors

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As shown in the above discussion, BC plays a dominant role in forming the EKE seasonality in the upstream KE region. From Fig. 5, we know that BC is the main source of EKE in the upstream region, while for the downstream region, the energy source is mainly Q. Q is comprised of the energy flux divergence through eddy-induced advection and the work done through eddy-induced pressure, and the role of advection and pressure work at the boundaries of the downstream KE is shown in Table 2. We do not present the numbers for upstream, because Q is not an important factor in the upstream (Fig. 5). Compared to advection, pressure work is about 10 times larger and its seasonal evolution is almost the same as the downstream EKE. As such, we conclude that Q is dominated by eddy-induced pressure work, especially from the west boundary, consistent with Yang et al. (2018).

Table 2 The role of (a) advection and (b) pressure work at the boundaries (western, eastern, northern, and southern boundary) of the downstream KE (152° E–170° E, 31° N–39° N) in four seasons. The positive/negative value means energy is propagated into/out of the downstream via advection or pressure work. Note that units are different for advection and pressure work
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3.3 EKE trend

In consideration of the accelerated warming in the western boundary currents during the past 30 years (Wu et al. 2012; Hu et al. 2020), it is important to confirm whether the seasonality of EKE has changed in the KE region. Figure 9a shows the trend of surface annual mean EKE, in which the EKE level in the KE region depicts a positive (negative) trend on the northern (southern) flank of the jet. The area-mean EKE depicts no change in the upstream but increases in the downstream (based on 90% confidence level of the Student t-test; Fig. 9b and c). There is no clear difference in the trend for each season. Correlation coefficients between summer, winter, and annual mean EKE for the upstream and downstream are shown in Table 3. The six correlation coefficients are above 0.90 (statistically significant at the 90% level based on the Student t-test), indicating there are high correlations between the summer, winter, and annual-mean EKE. Thus, we will focus on the annual mean change in the following discussion. In addition to the area-mean EKE in the upstream and downstream regions, the trend of area-mean EKE in the entire KE (142° E–170° E, 31° N–39° N) is also estimated and an increasing trend is detected (statistically significant above the 90% confidence level; Fig. 9d).

Fig. 9
figure 9

a Spatial pattern of surface EKE trend (colored shading, m2s−2 year−1). The red box indicates the upstream KE region (142° E–152° E, 31° N–39° N) and blue box indicates the downstream KE region (152° E–170° E, 31° N–39° N). Regions where the trends cannot pass the 90% confidence level are marked as white color. Contours denote mean SSH field during 1993–2013. The black bold line denotes 0.4-m SSH contour, which indicates the KE jet. b The time series (curves) and linear trend (straight lines) of summer, winter, and monthly EKE in the upstream region. c Same as b but for the downstream region. d The time series and linear trend of monthly EKE in the entire KE region (142° E–170° E, 31° N–39° N). To remove mean seasonal cycle, the time series of monthly EKE is processed with 13-point smoothing. The first and last 12 monthly values of EKE are not used for the calculation of the trend. The trends of summer, winter, and monthly EKE in c are statistically insignificant above the 90% confidence level. The trends of summer, winter, and monthly EKE in d are statistically significant above the 90% confidence level based on the Student t-test

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Table 3 Correlation coefficients between summer, winter, and annual mean EKE in the upstream and downstream KE region (statistically significant over the 90% level based on a Student t-test with 17 degrees of freedom)
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To obtain a better understanding of the energy level, the change of surface total kinetic energy (TKE) is estimated (Fig. 10a). In accordance with EKE (Fig. 9a), the trend of TKE is also characterized with positive values north of the jet and negative values south of the jet, whereas the area-mean TKE has increased in the entire KE region (Fig. 10b). This consistency implies that the trend is not only a change in eddy activity but also a reflection of the change in the KE system: the KE has experienced a northward migration and intensification during the 21 years.

Fig. 10
figure 10

a Spatial pattern of surface monthly total kinetic energy (TKE) trend (colored shading, m2s−2 year−1). Regions where the trends cannot pass the 90% confidence level are marked as white color. Contours are as noted in Fig. 9a. b The time series and linear trend of monthly TKE in the entire KE region (142° E–170° E, 31° N–39° N). To remove mean seasonal cycle, the time series of monthly TKE is processed with 13-point smoothing. The first and last 12 monthly values of TKE are not used for the calculation of the trend. The trend is statistically significant above the 90% confidence level based on the Student t-test

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According to previous estimations, the evolution of KE system since the 1990s (Yang et al. 2016; Navarra and Lorenzo 2021) may be associated with the change of wind in the subtropical gyre (Cheon et al. 2012; Zhang et al. 2014) or decadal variability in the North Pacific (Qiu and Chen 2005; Qiu and Chen 2016) regulated by westward-propagating Rossby waves. The trends of zonal-mean wind stress curl from JRA-55 and ERA5 over the region (130° E–120° W, 15° N–65° N) are shown in Fig. 11a and b. Though the wind stress curl depicts a northward movement which favors the poleward shift of KE system, its weakening trend within the subtropical region (20° N–29° N latitude bands) is inconsistent with the intensification of the KE system. Therefore, the change of wind in the subtropical gyre cannot totally explain the change in the KE system. In comparison, we examine the Pacific Decadal Oscillation (PDO) index and the evolution of EKE in the 21 years following Qiu and Chen (2016). When the PDO index is positive, enhanced Ekman flux divergence generates negative local SSH anomalies to the east of the KE region in 170° W–160° W along the zonal band of 32° N–34° N (Fig. 12a and b). As negative SSH anomaly signals propagate westward in terms of Rossby waves into the KE region after a delay of 3–4 years, the KE jet inflow is forced southward and rides over the ridge through a shallow segment (Qiu and Chen 2005), leading to an unstable state of the KE system with an active (low-energy) EKE field in the upstream (downstream). During the negative PDO index phase, on the other hand, positive SSH anomalies are generated through the Ekman flux convergence. After propagating into the KE region, these positive anomalies force the inflow northward, leading to a stable state of the KE system with a low-energy (active) eddy field in the upstream (downstream). From Fig. 12c and d, we learn that surface EKE in the upstream (downstream) depicts a crest during 1999–2002/2005–2010 (2002–2006/2010–2013) and a trough in 2002–2005/2010–2012 (1996–2001/2006–2010), matching the evolution of SSH in Fig. 12b associated with PDO. Therefore, the EKE evolution during 1993–2013 reflects the decadal variability of the KE system.

Fig. 11
figure 11

Mean value (blue solid line) and trend (red solid line) of zonal-average wind stress curl over the region (130° E–120° W, 15° N–65° N) derived from a JRA-55 and b ERA5 during 1993–2013. Following Trenberth et al. (1990), wind stress curl is calculated on the basis of zonal and meridional wind velocity. To remove mean seasonal cycle, the time series of wind stress curl is processed with 13-point smoothing. Shading indicates standard error (blue shading) and the 90% confidence interval of the trend (red shading)

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Fig. 12
figure 12

a Time series of the Pacific Decadal Oscillation (PDO) index from https://www.ncei.noaa.gov/pub/data/cmb/ersst/v5/index/ersst.v5.pdo.dat. b Time-longitude pattern of monthly SSH anomalies (cm) along the zonal band of 32° N–34° N from FORA. The time series of monthly EKE in the c upstream and d downstream KE region

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4 Summary

Based on an eddy-resolving reanalysis product, this study investigates the mechanisms underlying the seasonal modulation of mesoscale eddy activity in the Kuroshio Extension region and explores the change in eddy kinetic energy during 1993–2013. The major results of this study are summarized as follows:

  1. 1.

    In four seasons, a high energy level is found to appear at larger meridional (zonal) wavenumber range in the upstream (downstream) Kuroshio Extension, indicating that eddies are more zonally (meridionally) elongated.

  2. 2.

    In the upstream region, baroclinic instability associated with horizontal buoyancy flux plays a predominant role in regulating the seasonal evolution of eddy kinetic energy. In the downstream region, non-local energy exchange associated with pressure work is the main source of eddy kinetic energy.

  3. 3.

    During 1993–2013, the seasonality of eddy kinetic energy in the Kuroshio Extension remains unchanged. There is no change of eddy kinetic energy in the upstream region, while eddy kinetic energy in the downstream region increases significantly. The evolution is a reflection of the decadal variability of the Kuroshio Extension system associated with the Pacific Decadal Oscillation.

This study has explored the seasonal variability of eddy activity in the Kuroshio Extension, which is likely beneficial to the understanding of ocean dynamics in this region. In addition, it should also be noted that longer data is required to confirm the response of the seasonality of eddy kinetic energy to global warming. Moreover, the process of eddy energy dissipation is not analyzed here, which should be investigated in detail in the future. Besides, the meandering of flow is treated as mesoscale eddy when eddy kinetic energy is calculated based on velocity anomaly. The effect of the meandering will be considered in the future. Furthermore, previous studies have shown that air-sea interaction in the Kuroshio Extension may affect eddy activity (Ma et al. 2016; Yang et al. 2019; Shan et al. 2020). The seasonal variability of eddy-atmosphere interactions and their potential role in oceanic energy balance should be studied based on high-resolution coupled models in the future.