The Copernicus Climate Change (CMEMS C3S) two-satellite gridded merged absolute dynamic topography (ADT) from satellite altimetry (L4) with 1/4° spatial resolution, was used to estimate the spatial patterns of long-term (1993-2020) SLR rates in the EJS and to identify the center and boundary of the UWE. The CMEMS C3S product is characterized by a consistent combination of reference and complementary mission satellite data for each period, minimizing the errors that can arise from orbit adjustments or the introduction of new satellite orbits, making it suitable for the analysis of long-term climate and sea-level variability (CMEMS TAC DUAC products manual). The CMEMS C3S was provided at daily intervals, and specific grid points which is nearest to the Ulleung Island tide gauge (TG) station (130.625°E, 37.625°N; Ulleung Island grid) were selected to compare the long-term variability with sea-level data from Ulleung Island TG station (Figure 1). Sea-level data from the Ulleung Island TG station have been recorded at one-minute intervals since 1983, and data from 1993 to 2020 averaged at one-hour intervals were used for comparison with satellite altimetry data. The sea-level at the TG station was the data applied the inverted-barometer correction to reduce the sea-level variation induced by sea-level pressure.

Ship-based hydrographic data provided by the National Institute of Fisheries Science (NIFS) of the Republic of Korea were used to analyze long-term variations in vertical temperature structures within the UWE (Figure 1). The NIFS data are ship-based observations obtained every two months at 15 standard depths, with the distance between sampling points varying from a minimum of approximately 1.8 km near the coast to a maximum of 28 km in the open sea (Figure 1). Although NIFS data have been collected around the Korean Peninsula since 1961, this study focused on the period from 1993 to 2020, when satellite altimetry data were available. The NIFS dataset provides both salinity and temperature measurements; however, because of the known temporal variability of salinity error variables (Park, 2021), which makes it unsuitable for long-term analysis, only temperature data were used.

The centers, boundaries, and tracks of the UWE were identified using gridded satellite altimetry data. First, the SSH-based method (Chelton et al., 2011) was used to identify the centers and boundaries of the mesoscale eddies using the ADT and geostrophic currents based on the ADT from the CMEMS C3S product. The centers of the warm eddies were identified as the grid points with the maximum ADT among the surrounding 3×3 grids, whereas the boundaries were defined by the ADT contours, along which the average geostrophic current velocity reached its maximum among the contours around the grid selected as the warm eddy center. The Rhines scale ( L R = | u ′ | 2 β 0 ), which represents the maximum physical size at which mesoscale structures can grow, was used to extract appropriate mesoscale eddies at a given latitude from the satellite altimetry data (Eden, 2007; Lee et al., 2019), where, u is the deviations of the geostrophic current velocities from the temporal mean in each grid, and β 0 is the Rossby parameter which denotes the latitudinal differences of the Coriolis parameter. By applying the Rhines scale, mesoscale eddies are defined as having a physically valid size that prevents overestimation without the need for a high-pass filtering process (Lee et al., 2019), and consequently reduces errors in the analysis of long-term variability within Ulleung Warm Eddy (UWE) based on internal temperature profiles. Considering the average migration distance of mesoscale eddies in the EJS (43 km), the detected eddies were tracked, and only those that persisted for more than 35 days were extracted, considering the maximum repeating interval of satellite altimetry orbits (Chelton et al., 2011; Lee et al., 2019). Among the detected and tracked warm eddies in the southwestern part of the EJS, all warm eddies that encompassed Ulleung Island grid at least once during their life cycle (from origin to end) were defined as UWE.

The upper (H_u ) and lower boundaries depth (H_l ) within the UWE were identified based on the NIFS hydrographic data. Considering the characteristics of the intra-thermocline eddy, which has two thermoclines at the top and bottom of the temperature-homogeneous layer (THL) within the eddy, the thermoclines with the maximum temperature gradient were defined as H_u and H_l . The NIFS temperature profiles observed within the eddy were extracted based on the detected UWE boundaries. The extracted temperature profiles were then linearly interpolated at 1 m vertical intervals, and dT/dz was calculated. Considering the known average mixed-layer depth in the southwestern EJS (60–100 m; Lim et al., 2012), the maximum dT/dz depth below 80 m was defined as H_l , whereas the maximum dT/dz depth above 80 m was defined as H_u . To eliminate the impact of the variation in H_l in each temperature profile due to its position within the eddy, the estimated lower boundary depth was adjusted by considering the deepening shape of the lower boundary of the warm eddy towards its center as a Gaussian profile, according to H l   ( d ) = H l   ( 0 ) e − d 2 / 2 R 2 , as if all profiles were located at the eddy center, where d is the radial distance from the eddy center, R is the radius of the eddy, and H l   ( d ) and H l   ( 0 ) are the lower boundary depths of the given location and the center of the eddy, respectively (Bashmachnikov et al., 2023). The H l   ( 0 ) was only used in this study to estimate the long-term variations in the lower boundary of the UWE. It was verified that there was no long-term trend in the distance ratio of d/R, as well as the generation location of the UWE.

Most of the sea-level variations in the vicinity of Ulleung Island are well explained by steric height variations due to the heat content in the upper layer, which can be divided into two parts: increasing the temperature and thickness of the upper layer (Kim et al., 2002; Yoon et al., 2016; Gregory et al., 2019). Similarly, the heat content in the upper layer within the warm eddy can also increase because of both the increase in temperature in the THL and deepening of the lower thermocline, which is due to the thickening of the THL. Their long-term mean and variations, thus, can be expressed as follows, Q ¯ + Q ' ≡ ( H ¯ + H ′ ) ( T ¯ + T ′ ) (Yoon et al., 2016). When expanding the right side of the equation, the long-term variation of the heat content, Q ' is expressed as, H ¯ T ′ + T ¯ H ′ + H ' T ' , where the H ' T ' is negligible compared to the other two terms. Thus, H ¯ T ' can be regarded as the effect of a long-term increase in temperature within the warm eddies, and T ¯ H ' is the effect of the long-term thickening of the THL in the warm eddies.

The linear trends of the SLR around Ulleung Island, as well as the linear trends of both the temperature within the UWE and depth of its upper and lower boundaries, were calculated to estimate the long-term SLR rates and long-term variations in the temperature and vertical extent of the UWE. To estimate the long-term linear trends of the SLR around Ulleung Island, the sea-level data (ADT from satellite altimetry and sea-level records from Ulleung Island TG station) were averaged annually. In addition, the annual averaged time series of the sea-level was calculated from satellite altimetry data at each center of the UWE (Figure 2). The correlations among the annual averaged time series was calculated after removing the linear trend. To assess the long-term trends in temperature within the UWE and the depths of its upper and lower boundaries, the temperature profiles within the UWE and estimated depths of the upper and lower boundaries of the eddies were averaged annually. Linear regression was then applied to all corresponding 28 years of time series data for each trend calculation. Considering the characteristics of the datasets, which have small sample sizes and large interannual variability compared to long-term trends, a 90% confidence interval was applied to all trend calculations to guarantee a robust analysis (Frederikse et al., 2020).

The steric part of the SLR rates due to the long-term variations in the UWE around Ulleung Island was estimated by integrating the steric height rise rate derived from the observed long-term trends in the internal temperature ( S L R e d d y − t e m p ) and vertical extent ( S L R e d d y − t h i c k ) of the UWE (Figures 3A, B). The yearly steric height due to the UWE ( h e d d y ( t ) ) was estimated by applying the observed linear trends in both the temperature and upper and lower boundaries to the mean temperature profile within the UWE to assess the contribution of each factor separately as Equation 1:

where t ,   g and p are the time (inputted as a form of n-th year), gravitational acceleration and pressure, respectively, and the steric height is estimated above 500 dbar. The density ρ at each pressure level was calculated by temperature and salinity profiles from NIFS data using the Gibbs Sea waver Oceanographic Toolbox (McDougall and Barker, 2011). Mean temperature and salinity profile ( T ¯   a n d   S ¯ ) were computed by averaging the temperature and salinity profiles, respectively, observed within the UWE during the entire period (1993–2020). The mean salinity profile was used to calculate density, assuming that the steric height variations are more significantly affected by the temperature, rather than salinity, since the density variations in the EJS are influenced approximately 100 times greater by temperature changes (10^-1 –10¹ °) than by salinity changes (10^-3–10^-1 g/kg). Assuming that the mean temperature profile corresponds to t=0, the steric height rise rates were calculated for 10 years, from -5 to +5 years, based on the observed linear trends in both the temperature and upper and lower boundaries within the UWE (Figures 3C, D).

Apart from the steric effect due to the existence of the warm eddy, the barystatic effect is the other significant factor contributing to sea-level rise on a basin scale (Gregory et al., 2019; Chen et al., 2022). The barystatic effect ( S L R b a r y s t a t i c ) results from the water mass exchange, which varies regionally and is estimated about 2.00 mm/yr in the North Pacific regions during this period, as supported by various research findings (Amin et al., 2020; Camargo et al., 2022; Chen et al., 2022; Royston et al., 2020). Thus, in a specific grid, when warm eddies exist, the SLR rates ( S L R e d d y ) can be expressed as Equation 2 synthetically,

Warm eddies, even when not changing their internal structures over the long-term, can contribute to annual sea-level rise if their duration or frequency increases. To assess the impact of the duration of warm eddies on the annual sea-level rise in a specific grid, the number of days within a year that were part of a warm eddy ( D e d d y ) and the number of non-eddy days ( D n o n − e d d y = 365 − D e d d y ) were calculated separately. The long-term variation in the duration of the UWE was estimated by calculating the yearly trend of D e d d y , termed the Eddy duration increasing rate (ER). To quantify the impact of the UWE duration on SLR rates, D e d d y can be predicted using the ER as Equation 3,

where D e d d y ¯ represents the average days of warm eddies in a certain grid per year, which is 174 days for the Ulleung Island grid.

Considering the variations of the internal structures and the durations of the UWE, and the barystatic effect, the total annual sea-level at the Ulleung Island grid can be calculated as Equation 4,

where, h e d d y ¯ and h n o n − e d d y ¯ denote the average sea-level when the grid is and is not within a warm eddy, with values of 699.05 mm and 575.21 mm, respectively, based on the satellite altimetry at the Ulleung Island grid. S L R n o n − e d d y represents the SLR rates when the grid is not within a warm eddy, calculated based on the satellite altimetry at the Ulleung Island grid as 5.51 ± 2.05 mm/yr (Figure 2, Table 1). Same as to calculate the rising rate of h e d d y , assuming that all mean values correspond to t=0, the rising rates of h t o t a l ( S L R t o t a l ) were calculated for 10-year period, from -5 to +5 years. In addition, we verified the effects of the various interpolation methods (linear, modified akima, and spline) on the temperature profiles, which could affect the vertical extent of the UWE and the S L R e d d y − t h i c k within ±6% differences.

The regional SLR rates during 1993–2020 in the EJS were spatially variable with 1–8 mm yr^-1, and were noticeably higher (> 6 mm yr^-1) around Ulleung Island based on satellite altimetry (Figure 1). There is a notable north-south difference in the spatial distribution of the SLR rates in the EJS, with much higher and more variable rates of 2–7 mm yr^-1 in the south of the subpolar front around 40°N than the north, with less than 4 mm yr^-1 (Figure 1). In the south of 40°N in the EJS, the spatial variability of the SLR rates in the western part of 133°E, is more variable at 1–8 mm yr^-1 compared to 2–6 mm yr^-1 in the eastern part. The spatial distribution pattern of high SLR rates in the southwestern part of the EJS (Figure 1, in the red box) exhibited a concentric distribution of SLR rates above 6 mm yr^-1 surrounding Ulleung Island. Notably, both the satellite altimetry data and TG observations show similarly high SLR rates (7.02 and 6.37 mm yr^-1, respectively) at the Ulleung Island grid, which is more than double the global average SLR rates of 3.1 mm yr^-1 (Figure 2).

The interannual variations and long-term linear trends of the annually averaged sea-level, based on both satellite altimetry and TG data in the vicinity of Ulleung Island, exhibited a strong similarity to those at the center of the UWE (Figure 2). The interannual variations of the annually averaged sea-levels at the center of the UWE during 1993–2020 show correlations of 0.69 both with the sea-level changes at the TG station and the satellite altimetry on Ulleung Island grid. Thus, the interannual variations in sea-level around Ulleung Island were well (> 47%) explained by interannual variations in the UWE. Both SLR rates from satellite altimetry (7.02 mm yr^-1) and the TG station (6.37 mm yr^-1) are similar to those at the center of the UWE (7.16 mm yr^-1). When the sea-level from satellite altimetry is averaged only for the period in which the Ulleung Island grid is not included in the UWE ( D n o n − e d d y ), their correlation with the satellite altimetry for all periods drops to 0.45, and its long-term linear trend ( S L R n o n − e d d y ) reduces to 5.51 mm yr^-1 (Figure 2). These results insist that the long-term variations of the sea-level in the vicinity of Ulleung Island are strongly related to the long-term changes of the UWE.

The temperature increased in the subsurface layers within the UWE, particularly at the highest rate of increase at approximately 200 m (Figures 4A, B, C). The vertical profile of the long-term temperature change within the UWE showed a general warming trend at depths deeper than 50 m, with the maximum warming rate of 0.2°C yr^-1 at approximately 200 m and the warming trend extended up to 400 m in the lower boundary of the eddy. Compared to Figure 4A, which shows the characteristic intra-thermocline eddy features of the UWE, the depths with the highest long-term temperature trend was situated in the temperature homogeneous layer with a temperature of 10–12°. Consequently, the SLR rates within the UWE are driven by a temperature increase in the THL.

The depth of the lower boundary of the UWE showed a significant long-term deepening trend, in contrast to the almost constant upper boundary (Figures 4A, C). While the long-term trend of the UWE’s upper boundary depth showed no significant long-term change (-0.10 ± 0.51 m yr^-1), the depth of the lower boundary showed a meaningful deepening trend at a rate of 3.22 ± 2.00 m yr^-1. As the upper boundary of the UWE remained constant, but the lower boundary deepened significantly, the eddy became vertically thicker, which could contribute to the steric height rise owing to thermal expansion. The increase in the UWE thickness was primarily attributed to the thickening of the THL within the eddy, which expanded from approximately 150 m in 1993 to approximately 250 m in 2020.

The days per year that the Ulleung Island grid is included within the UWE is increasing, with the ER of 3.33 ± 3.64 days/yr (Figure 2). During the period from 1993 to 2020, the average days per year ( D e d d y ¯ ) that the Ulleung Island grid is included within the UWE (174 days) almost matches the known average life time of the UWE (160 days) (Lee et al., 2019). The effect of the UWE on the sea-level at the Ulleung Island grid has been gradually increasing, and in 2015, there was a case where the UWE affected sea-level variations at the Ulleung Island grid throughout the entire year. In addition, variations in D e d d y at the Ulleung Island grid show a high correlation with the sea-level variations based on the satellite altimetry at the Ulleung Island grid (0.83). Consequently, the increase in D e d d y can contribute to the higher SLR rates observed around the Ulleung Island.

Because of the warming temperature within the UWE, the steric height increased at a rate of 2.66 mm yr^-1 ( S L R e d d y − t e m p ; Figures 3A, C, Table 1). According to the mean temperature profile, the temperature at 200 m ( T 200 m ¯ ) in which shows the maximum temperature warming rate is 8.85 ° at t=0, which varies from 7.90 ° to 9.80 ° during -5–+5 years. The increase in steric height was predominantly due to the temperature increase in the THL, because the temperature rather decreased in the surface layer above 50 m within the UWE. The steric height rise rate caused by the temperature increase within the UWE was similar to the global average SLR rate of 3.1 mm yr^-1. Therefore, the steric height rise due to the temperature increase in the THL within the UWE alone was insufficient to explain the observed SLR rates exceeding 6 mm yr^-1 in the vicinity of Ulleung Island and within the UWE itself.

Because of the deepening of the lower boundary of the UWE, the steric height increased at a rate of 2.91 mm yr^-1 ( S L R e d d y − t h i c k ; Figures 3B, D, Table 1). According to the mean temperature profile, the mean upper and lower boundaries of the UWE are 50 and 200 m respectively, and the mean THL thickness ( H ¯ ) is 150 m at t=0. Due to the deepening trend of the lower boundary of the UWE, the thickness of the THL increased from 134.35 m to 165.65 m, from which the steric height rise was derived (Figure 3B). The steric height rise rate due to the deepening of the eddy’s lower boundary was similar to the steric height rise rate caused by the temperature increase.

The S L R t o t a l (7.62 mm yr^-1) calculated based on the steric height rise ( h t o t a l ), taking into account the internal temperature warming, the deepening of the lower boundary, and the annual duration of the UWE, were similar to the observed SLR rates from satellite altimetry at the Ulleung Island grid (7.02 mm yr^-1) and the Ulleung TG station (6.37 mm yr^-1) (Figure 3E, Table 1). The estimated steric height rise rate was also similar to the SLR rate based on the satellite altimetry data at the eddy center (7.16 mm yr^-1). Even when assuming that both S L R n o n − e d d y and S L R e d d y are zeros in Equation 4, the steric height can still rise by 1.13 mm yr^-1 ( S L R d u r a t i o n − o n l y ) due to the increase in the duration of the UWE. The S L R e d d y , which is the linear sum of the SLR rates due to the internal temperature warming, the deepening lower boundary within the UWE, and the barystatic effect, is 7.57 mm yr^-1, which is 1.4 times higher than the S L R n o n − e d d y . Considering only S L R n o n − e d d y and S L R e d d y respectively, and the duration of the UWE remains constant ( D e d d y ( t ) = D e d d y ¯ ), the calculated SLR rate is 6.49 mm yr^-1 ( S L R S L R − o n l y ), lower than the observed SLR rate based on the satellite altimetry at the Ulleung Island grid. In practice, both the temperature and thickness of the THL within the UWE, as well as its duration, have increased in the long-term. Considering that the S L R t o t a l was calculated only for the center of the eddy and that the Ulleung Island grid can be located both on the eddy boundary and non-eddy areas, the slightly lower SLR rates at the Ulleung Island grid (7.02 mm yr^-1) than the S L R t o t a l can be explained. As a result, considering the integrated effect of the long-term changes in the UWE on the S L R t o t a l , the high SLR rates observed around Ulleung Island can be explained quantitatively.