The ocean is full of eddies resulting from the cascading of large-scale kinematic energy through the transfer of heat and momentum. Thus, ocean eddies have been a very important research topic in understanding their roles not only in physical processes but also in biological responses from one place to another. In order to determine the eddy sizes, satellite observations have been used to analyze them in terms of life stages at different latitudes in the global ocean (Chelton et al., 2011). In addition, eddies in the East Sea have been extensively investigated based on Ocean Color (OC) and altimetry (Park et al., 2012; 2016; Lee et al., 2019; Park and Park, 2019; Choi et al., 2019).

Although OC and Sea Surface Temperature (SST) observations show apparent individual eddy features, it is difficult to monitor them continuously due to cloud presence. Thus, satellite altimetry is considered a relatively efficient measurement, although its spatial resolutions are relatively coarse than OC and infrared SST observations. Based on the altimetry, there are four methods to detect eddies. The first method is the Okubo–Weiss (OW) approach (Okubo, 1970; Weiss, 1991), which is the most widely used. The physical parameter is computed from the horizontal velocity field. Applications of the OW method can be found in many literature (Chelton et al., 2007; Xiu et al., 2010). The second approach uses Sea Surface Height Anomaly (SSHA) or Sea Level Anomaly (SLA) for eddy identification, in which a threshold is nevertheless always required to delimit eddy dimensions. Different thresholds are applied to different regions, such as a 6 cm threshold in western South America (Chaigneau and Pizarro, 2005). The third approach to identifying the eddies is based on flow geometry characteristics based on clustering closed or spiral streamlines (Sadarjoen and Post, 2000). Lastly, the method based on the Lagrangian Particle Tracking (LPT) provides simple kinematic properties to define its spatial boundaries (Jo et al., 2017).

Fig. 1 shows the six Level 2 altimetry trajectories on June 3, 2023. Two trajectories are near Ulleung Island. The Level 2 altimetry observations comprise Level 3 altimetry products through interpolation and Level 4 through multiple altimetry satellites. Since the eddies have 50–100 km diameters, depending on latitudes, there might be uncertainties arising when producing grid altimetry data.

Figure 1. The ascending and descending altimetry trajectories (a) and composed altimetry Level 4 Sea Surface Height Anomaly (SSHA) on June 3, 2023 (b).

One of the remaining questions on eddy shape is what the intrinsic shape of eddies derived from satellite altimetry: either symmetric or axially asymmetric morphology, as discussed by Chen et al. (2021). Among the eddies in the world ocean, the Ulleung Warm Eddy (UWE) has very interesting characteristics in terms of almost stagnant rotations compared to propagating eddies. The UWE is confined within the Ulleung Basin. According to Jo et al. (2017), UWE has 60.60±18.45 km for the major axis and 40.90±10.77 km for the minor axis, resulting in its elliptical ratio of 0.71±0.19, suggesting that its intrinsic shape is oval rather than a circle. Thus, this study focuses on how much uncertainties in the estimation of eddy boundary determination from the LPT method using in situ subsurface temperature. Since routine measurements operated by the National Institute of Fisheries Science (NIFS) are available southwest of the East Sea, this study aims to address how to determine the eddy boundary determined from altimetry through validation with subsurface eddy shapes. The main results are as follows: (1) the validation of UWE using subsurface temperature profile data, (2) the analysis of uncertain poor detection cases, and (3) examine potential Surface Water Ocean Topography (SWOT) observations to apply UWE detection.

2.1. Data Sources

Altimeter data: the Level 2 and the gridded Level 4 SSHA data obtained from Copernicus (https://data.marine.copernicus.eu/product/SEALEVEL_GLO_PHY_L4_MY_008_047/services). The products are based on multiple satellites (Jason-2 / Envisat or Jason-1 / Envisat or Topex/Poseidon / European Remote Sensing (ERS)) with the same ground track on a MERCATOR 1/4° grid. The SSHA was made by computing with respect to a seven-year mean for the study of ocean variability. In addition, the SWOT was used to validate the UWE boundaries. The SWOT has been jointly developed by National Aeronautics and Space Administration (NASA) and Centre National D’Etudes Spatiales (CNES) with contributions from the Canadian Space Agency (CSA) and the United Kingdom Space Agency (UKSA). It launched on December 15, 2022, on a SpaceX Falcon 9 rocket. The technical information can be found in the SWOT report (Chen, 2018; Fu et al., 2024). The SWOT mission uses an orbit determination instrument suite very similar to the one that has been used by the Jason altimeter series. SWOT has a KaRIn instrument for measuring high-resolution elevations for SSH and surface water measurements. It consists of a dual-beam Ka-band radar interferometer, each beam providing absolute elevation measurements over a nominal 50 km swath that extends from 10 km to 60 km on either side of the altimeter nadir track.

In situ data: The NIFS has been conducting serial hydrographic cruises around the Korean Peninsula four to six times annually (Fig. 2a). The datasets are collected using each station’s Conductivity-Temperature-Depth (CTD) sensors for specific depths. The observation stations consist of 207 points in 25 lines. Detailed information for the Korea Oceanographic Data Center (KODC) of NIFS can be found in Kim and Kim (2023).

Figure 2. Serial hydrographic observations from the National Institute of the Fisheries Science (NIFS) (a) and altimetry-based spatial boundary of Ulleung Warm Eddy (UWE) determined by Lagrangian Particle Tracking (LPT) on January 16, 2016 (b).

2.2. Methodology

LPT: The method used to determine the spatial surface boundary of UWE in this study is the LPT demonstrated by Jo et al. (2017). This relatively new idea includes the advantages of other methods. The Particle Tracking Experiment (PTE) can be defined as,

Where X and Y are the locations of given time, t. U and V are the zonal and meridional velocities estimated from SSHA, respectively. The t is the time interval to compute the next positions (X_n+1 and Y_n+1) by multiplying the velocities U and V. Based on Eq. (1), we simulated numerical particles to trace how these numerical particles are confined within the boundary of an eddy. The sensitive parameter is the threshold used to determine the eddy boundary, which is examined with an in situ subsurface eddy shape.

As Fig. 2(b) shows, once the eddy’s center was measured, the particles continued to deploy around the center until the particles were concentrated to some degree. Empirically, the boundary was determined at 500 particles, as demonstrated by Jo et al. (2017). In this study, the amplitude was determined by the SSH difference between the center of the eddy and the outside of the eddy boundary, as shown in Fig. 2(b). The arrows represent the velocity fields in the study area, and the color shows the numbers of numerical particles concentrated around the center of the eddy due to anticyclonic rotations, tending to move to the center due to the Coriolis. Then, the initial red curve was fitted as oval based on the second-order polynomial. In order to determine the actual boundaries, the subsurface temperature observations (Fig. 2a) were used.

3.1. Comparisons between Surface and Subsurface UWE Spatial Boundary

For UWE validation, we used altimetry and subsurface temperature profile data from 2015 to 2016 due to the longest UWE maintained compared to other UWE formations. Specifically, first, the spatial boundary of UWE is determined based on LPT, as illustrated in Fig. 2(b) and Fig. 3(a). The smooth red contour is after Gaussian fitting. The eddy shape is elliptical, as it is stretched in the south-to-north direction by influencing mean current fields. The major axis to the minor axis of the ellipses is about 2.5:1. Furthermore, the eddy center is located at the south part of the center, suggesting its mass and central axes are not collocated. The elongated eastern part might be non-uniform subsurface temperature profiles (indicated with a black upward arrow in Fig. 3a). This subsurface thermal effect is discussed in Section 2.2.

Figure 3. The surface UWE boundary was determined from LPT (a) and the subsurface temperature profile with isothermal 10°C (white line). (b) The vertical line is from the junction between 100 m depth and isothermal 10°C on October 24, 2015.

Second, the surface UWE boundary was compared with subsurface temperature profiles (Fig. 3b). The yellow dot indicates the location of the subsurface temperature-based UWE, which is determined by the isothermal 10°C for the eddy outer boundary (shown with white contour) and the vertical white line from 100 m depth, as previously reported (Shin et al., 2019). Since the upper layer is occupied by the warm water, the water within 100 m depth does not show eddy shapes. Thus, the 100 m depth is a good criterion for pointing out the outer boundary of the eddy. Although the overall subsurface eddy boundary by isothermal 10°C reveals the general shape of the eddy, the warmer center is located along about 130.3°E at 100 m depth than the eastern part of the eddy. In general, the subsurface UWE structure matches the surface UWE boundary well.

In addition, we examined other cases to validate the LPT method for defining the UWE boundary. As shown in Fig. 4, all four cases have good agreements. As pointed out before, there are elongated parts in the eastern part (Figs. 4a–c). Fig. 4(d) shows that in the southern part. The mean and standard deviation of the differences between surface UWE (red contour) and subsurface-based UWE (yellow dot) boundaries are 7.70–4.71 km.

Figure 4. UWE comparisons between surface UWE features and subsurface temperature profile (shown with yellow dots) on Oct 23 (a), 24 (b), 29 (c), and Dec 10 (d), 2015. The numbers are differences between the UWE boundary determined by LPT (red contours) and the subsurface temperature profile (yellow dots).

3.2. Uncertainties to Determine Eddy Boundary Based on SSHA

In the previous section, we interpreted the elongated from the eddy boundary determined based on LPT as non-uniform thermal content. Thus, although the LPT-based eddy boundary is at 131.5°E, the actual eddy boundary is located further east, as shown with the arrow in Fig. 5. Since the altimetry contains all thermal and haline steric signals in the whole water column, the signals should be inferred. Thus, the shape does not reflect the eddy boundary if the eddy has a non-uniform asymmetric thermal structure.

Figure 5. The LPT surface spatial boundary determined by LPT is shown with a red elliptical shape and yellow dots determined by subsurface isothermal 10°C with 100 m stretched to the sea surface, as illustrated in Fig. 4. Both Lines 104 and 105 indicate the survey line by NIFS.

We investigated the potential reasons for the unmatched boundary shown with a vertical arrow in Fig. 5. We integrated temperature differences at different depths based on Eq. (2) to achieve thermal steric height.

Where, ηT is thermal steric height, ? is the thermal expansion coefficient, ΔT is the temperature differences between two layers. Along Line 105, the vertical temperature profile with isothermal 10°C is shown in Fig. 6(a), and the corresponding thermal steric height is estimated from 400 m depth to the sea surface (Fig. 6b) and from 300 m depth to the sea surface (Fig. 6c). Both steric heights are very similar along Line 105, which means the thermal structures are uniform. However, along Line 104, the thermal steric height with 400 m depth and 300 m depth differ. While thermal steric height over 400 m has one peak surface height, that over 300 m has two peaks due to the non-thermal structure on both sides of the center. It is worth noting that according to Sun et al. (2018), the vertical profile of temperature and salinity in eddies based on Argo data in the South China Sea (SCS) is not symmetric (Fig. 7). Each warm and cold eddies has an asymmetric vertical profile, suggesting that the heat content interior of eddies is associated with different SLA signals like demonstrated in our study. Thus, we can conclude if the thermal steric height determined from the thermal structure at different depths is similar or different, they are uniform or non-uniform heat content within the cross-section, respectively.

Figure 6. Subsurface temperature of UWE along Line 105 (a), Sea Surface Height (SSH) due to thermal expansion from the surface to 400 m depth (b) and from the surface to 300 m depth (c). Similarly, data from Line 104 in August 2015 are shown in (d)–(f).

Figure 7. Level 4 SSHA (a) and Surface Water Ocean Topography (SWOT) altimetry SSHA (b) on June 24, 2023. Contours show sea level anomalies.

In addition to uncertainties in estimating spatial boundaries as shown in Fig. 4, the vertically tilted conditions might make it difficult to determine the spatial boundary based on LPT. As also demonstrated in Figs. 5 and 6, the non-uniform thermal structure might be related to the tilted eddy axis (Li et al., 2022). This important eddy morphology and tilt axis can be resolved with gridded 3D subsurface temperature profiles.

3.3. Potential Capabilities of SWOT to Determine UWE Boundary

The spatial boundary of UWE was validated with a subsurface temperature profile, and most of the LPT-based determination performs well, as illustrated in the previous section. However, there are also some discrepancies when there is non-uniform heat content within UWE (Fig. 6). Thus, we further validated its boundary with instantons altimetry information observed by SWOT. Compared to gridded altimetry products, SWOT can provide very detailed information. However, the overlapping regions differ, especially in the eastern part along 132 E. While gridded SSHA shows about 0.1 m ranges, SWOT SSHA shows –0.1 m. Although SWOT can provide mesoscale eddy information, it has not been technically calibrated. Thus, SWOT is not ready to be used for quantitative analysis.

As a case study, the spatial boundary of UWE was determined based on LPT using geostrophic current derived from satellite altimetry. Then its boundary was validated using subsurface temperature profile measurements. The surface eddy boundary was well determined by subsurface eddy shape from isothermal 10°C with uniform subsurface thermal distributions. However, if there are uneven thermal contents within the UWE, the LPT method is not performed properly. Furthermore, the spatial boundary was also validated based on SWOT altimetry observations. Although SWOT observation does not include eddy boundaries due to the narrow swath, it shows partial eddy boundaries with better resolutions. In addition, the magnitude of SSHA of two different altimetry is different due to perhaps un-fully calibrated SWOT. In order to overcome the limitations of non-uniform thermal contents to use altimetry, three-dimensional thermal profile data are needed, which can be produced using a deep learning approach.

This work was supported by a 2-Year Research grant from the Pusan National University.

No potential conflict of interest relevant to this article was reported.