The Three-Dimensional Structure of the Mesoscale Eddy in the Kuroshio Extension Region Obtained from Three Datasets

Abstract

The high-resolution observation data from June 2019, Argo data from 1997 to 2019, and the multi-observation ARMOR 3D dataset from 1993 to 2019 were used to study the three-dimensional (3D) structural characteristics of the mesoscale cyclonic eddy (CE) in the Kuroshio Extension region (KER). The observed eddy has a typical 3D structure of the KER CE, which was a longer lifespan eddy in this KER. The maximum anomalies of temperature and salinity were −7.69 °C and −0.71 PSU, which were located at the 350 m depth. In the vertical, the observed and composite eddy had a dipole structure, while ARMOR 3D had a monopole. The study of the velocity fields indicate that ARMOR 3D underestimates the velocity below 500 m. The 3D structures of the CE composite eddy of Argo were comparable to the observations, whereas the temperature and salinity anomalies were weaker than the observation. The surface of the Argo composite eddy shows a positive temperature anomaly within 50 m, which used to be opposite to the observation. This phenomenon was due to the limited Argo data of the composite eddy, and most of them were the observed profiles of winter CE in the weak years of EKE in the KER. We tried using ARMOR 3D to explore the reliability of ARMOR 3D composite eddy and compared the seasonal variations of temperature/salinity anomalies of the cyclonic and anticyclonic eddy. The anomalies of temperature and salinity caused by CE have seasonal variations: the anomalies have been strong in summer and weak in winter. This is consistent with the variant of eddy kinetic energy (EKE), but AE has no seasonal variation.

1. Introduction

Ocean mesoscale eddies are widespread in oceans worldwide and play an important role in the oceanic transfer processes of momentum, heat, mass, etc. [1]. Mesoscale eddies have significant effects on temperature and salinity structure. Cyclonic (anticyclonic) mesoscale eddies correspond to areas of low (high) sea surface height (SSH), which causes the seawater in these regions to diverge (converge). This results in a lower (higher) sea surface temperature (SST), higher (lower) sea surface salinity (SSS), and isotherm/isohaline/isopycnal doming. Therefore, eddy can be categorized as cold eddy and warm eddy, corresponding to cyclonic eddy (CE) and anticyclonic eddy (AE), respectively [2].

The Kuroshio Extension region (KER), from 35° N eastward to the mid-Pacific, has long been considered to be filled with energetic mesoscale eddies. The KER is a hotspot for analyzing the structure and energy of mesoscale eddies [3,4]. Most of the eddies in this region come from the present-day shedding of the Kuroshio and have strong baroclinic properties [5]. The activity of eddy plays an important role in the decadal variation of the circulation of the KE system [6,7]. The variations of the state of the KE system will directly affect the strength of the eddies in this region and have a direct impact on the recirculation circulation in the southern KE [7]. The eddies in the KER represent a necessary element for the generation of subtropical mode water in the North Pacific Ocean [8].

The study of the three-dimensional (3D) structure of mesoscale eddies is the basis for analyzing the dynamic characteristics of eddies [9]. The direct method is to obtain the 3D structure of eddies involves through shipboard observations. Previous researchers used submarine target array observation methods to capture the all-depth structure of an eddy [6], which revealed that the significant tilt and sub-mesoscale processes of the eddy axis represent the principle element in eddy dissipation. Using gliders, the researchers constructed a fine-resolution 3D structure of anticyclonic eddy (AE) in the South China Sea and the results confirm the capability of the gliders network to observe a fine-scaled 3D structure of mesoscale eddies [10]. The characteristics of CE structure in the Northwest Pacific were reconstructed and analyzed by using XCTD and ADCP data from ship-based observations. The Hybrid Coordinate Ocean Model (HYCOM) is able to replicate the location and intensity data of mesoscale eddies observed in situ, while the magnitude and location are derived by deviation [11]. A Slocum glider equipped with biochemical sensors was used to reconstruct the eddy in Algerian Basin, which found that the eddies can transport water mass and change the nutrient distribution [8].

Satellite remote sensing observations can efficiently identify surface features, such as an eddy’s position and radius. When the remote sensing data are fused with observational data, the spatial and temporal process of the eddies 3D structure can be tracked continuously. Mason et al. [12] analyzed the eddies of 14 sub-regions of the Brazil Malvinas Confluence (BMC) using the multi-observation fusion dataset ARMOR 3D. They found that the vertical velocity calculated from the ARMOR 3D had an upwelling/downwelling pattern, and the magnitude and sign of the subregions were different. Maximum values were discovered close to fronts and sharp topographic gradients. Using ARMOR 3D, the structure of the AE near Canary Island was reconstructed, and it was pointed out that the surface geostrophic currents in the ARMOR 3D data had been underestimated [13].

The third method includes the usage of the eddy composite analysis method used by Chaigneau et al. [14]. The steps of the composite eddy method are as follows: (1) Identify the eddies in the region. (2) Ascertain the Argo data of eddies and calculate of temperature and salinity anomalies. (3) Collect Argo data and calculate the relative position of the eddy’s center. (4) Normalize these Argo data according to the relative position and compose these data to an eddy. In the Pacific subtropical countercurrent zone (19°–26° N), Yang et al. used the eddy composite method to find structural variations among different sub-regions [15]. Chen et al. [16] used the method to study the seasonal characteristics of heat and salt transport in mesoscale eddies in the South China Sea. Compared with other seasons, the heat transport of eastern Vietnam and the western Luzon Islands in winter is larger, and the equatorial heat transport in the western Luzon Strait is stronger in winter. Liu et al. [17] used the Argo dataset to composite the CE and AE in KER and analyzed the eddy-induced vertical displacement of the thermocline and the halocline. The average vertical structures of eddies were analyzed in the Atlantic subtropical cyclone zone, and the transport volume of the Gulf Stream was calculated [18]. Zhang et al. [19] further proposed the unified analytical structure of mesoscale eddies with the help of eddy composite methods.

At present, the research of the 3D structures of eddy with different characteristics in different regions can be completed through observation, multi-observations fusion datasets, and eddy composite methods. The direct observation method has timeliness and accuracy, however the higher costs and technical difficulties associated are unavoidable facts, and the current available eddy observation data are scarce. ARMOR 3D integrates satellite remote sensing and in site profiles data to ensure the continuity and richness of data. However. its accuracy is an issue that needs to be considered. The eddy composite method helps researchers to reproduce the 3D eddy structures in most ocean regions. Although the composite eddy exhibits the average state in the region for the period of the Argo data, there are some differences from the real state of the ocean eddy. In addition, the dataset cannot be used to study composite eddy structure in regions where Argo observations are sparse. Therefore, it is essential to combine the advantages of the above different methods in the future study of the 3D structure of mesoscale eddy. Based on the observation data, various datasets are integrated to achieve the purpose of precisely analyzing the 3D structure of mesoscale eddy.

The primary aim of this research is to examine the 3D structure of a mesoscale CE, such as temperature, salinity, and geostrophic flow field, in the Kuroshio Extension region (KER) using high resolution observation obtained in June 2019. We additionally investigated the composite eddy by using ARMOR 3D and conducted a comparison with the Argo composite eddy. In addition to the CE, we also compared the AE structures to explore the reliability of the ARMOR 3D composite eddy.

2. Materials and Methods

2.1. In Situ Observations

The observations used in study were collected during a research cruise in the KER, aboard the R/V Zhangjian and the cruise number was FES-19. During the observation (14–22 June 2019), the center of the eddy moved from 149.69° E and 33.55° N to 149.49° E and 33.70° N, with a short westward moving distance of 25 km, which was much shorter than the length of each section. The diameter (125 km) of the eddy was much longer than the moving distance, and the shape of the eddy’s boundary does not change significantly. It can be approximated that the slight modifications in the center and boundary of the eddy obtained from the observations are not significant and do not have an effect on the consequences of the observation. A total of 140 (eight sections) stations have temperature and salinity profile data and flow velocity data (Figure 1a and Table 1).

During our observation period, the eddy data were sampled using the following instruments:

• Moving vessel profiler (MVP): MVP come from AML Oceanographic Instruments in Victoria, Canada. The temperature, conductivity, and pressure were measured by MVP equipped with Temperature∙Xchange^TM, Conductivity∙Xchange^TM, and Pressure∙Xchange^TM. Hysteresis correction and thermal inertia correction were applied to the raw data to deal with errors caused by response times of the temperature and conductivity sensors and thermal mass of conductivity cells [20]. After that, the data were interpolated to 1-m intervals, and a 7-point median filter was applied to reduce salinity spikes [21]. A total of 140 profile stations were distributed along these sections, with zonal interval of 15′ between stations (Figure 1b). At each station, an MVP probe was deployed to a depth of 800 m for thermohaline measurements.

• Acoustic Doppler profiler (ADCP, RDI 38 kHz and 300 kHz): Underway ADCP measurements were taken to observe the eddy’s flow fields. The structure of the flow field in the upper mixed layer of ocean was measured with a 300 kHz ADCP, which can measure the flow field at depths ranging from 13–209 m, flow field were divided into 50 layers with 4 m intervals between layers. The flow field structure of the eddy’s middle layer was measured with a 38 kHz ADCP, which can measure the flow field at depths ranging from 48 to 984 m, and these were binned into 40 layers with 24-m intervals between layers. The research vessel sailed in a straight line at a constant speed of approximately 10 knots during the observation period of the sections. Ordinarily, the quality control of ADCP data is conducted as follows: quality control parameters and corresponding threshold values are set to detect suspicious data, and a water/bottom track is used to correct for system errors [22]. However, bottom tracking is invalid in the deep oceans. Instead, we selected the first cell as reference layers and used a third-order smoothing low-pass filter to calculate accurate current velocities [23]. The filtering period is 1 h. These data were then interpolated into 50-m depths.

2.2. Argo and AVISO Data

The Argo profile data were provided by the China Argo Real-time Data Center (http://www.argo.org.cn/data/argo_en.php, accessed on 20 August 2022), and Argo data had been already subjected to quality control. In addition, we also performed secondary filtering of the data in accordance to Chaigneau’s method [14] and obtained data that met the following requirements: (1) The minimal pressure in the Argo data must be between the sea surface and 10 dbar, and the deepest data ought to be greater than 1000 dbar. (2) The depth interval between two consecutive data points shall not exceed 10 dbar. (3) Each Argo profile point must have at least 30 valid data points beneath 1000 dbar. Argo was used in this study from 1997 to 2019.

Sea level anomaly data were produced by Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO; https://data.marine.copernicus.eu/products?option=com_csw&task=results, accessed on 20 August 2022) and distributed by Copernicus Marine and Environment Monitor Service (CMEMS; https://data.marine.copernicus.eu/product/MULTIOBS_GLO_PHY_TSUV_3D_MYNRT_015_012/description, accessed on 20 August 2022). The all-satellite-merged series combines the most recent datasets from 1993 to present with up-to-date datasets with up to four satellites at a given time (Topes/Poseidon, ERS-1 and ERS-2, Jason-1 and Jason-2, Saral, Cruosat-2, and Envisat missions). We used the global product projected on a 1/4°-spatial-resolution grid with a daily time interval. AVISO data were used in this study from 1 January 1993 to 30 June 2019.

2.3. ARMOR 3D

ARMOR 3D (https://resources.marine.copernicus.eu, accessed on 20 August 2022) estimation that is based on satellite estimates of the sea level anomaly (SLA), sea surface temperature (SST), mean dynamic altitude (MDT), and in situ temperature (T) and salinity (S) vertical profile measurements. The ARMOR 3D construction process consists of three steps: (1) Project the satellite data (SLA, SST) to the vertical direction through the multiple linear regression method. (2) The global 3D dataset of T/S can be obtained by combining the data from step (1) with the optimum interpolation method and temperature (T) and salinity (S) measured in situ (from Argo profiling floats, bathythermograph profiles, CTD, and mooring measurements) [24]. (3) Using the thermal wind equation referenced at the surface, 3D geostrophic currents and geopotential heights were calculated by combining ARMOR 3D T/S fields with surface altimetric geostrophic currents [25]. The surface altimetric geostrophic currents were computed from SLA and MDT through the geostrophic relation. ARMOR 3D are 1/4° × 1/4° spatial resolution. The vertical depth is divided into 33 unevenly spaced layers with a maximum depth of 5500 m [26].

ARMOR3D 3D weekly datasets with 1/4° resolution which including T, S and velocities from 14 and 22 June in 2019 had been used in this study.

2.4. Climatological Data

The climate conditions of the thermohaline data provided by Australia’s Commonwealth Scientific and Industrial Organization (CSIRO) ATLAS OF REGIONAL SEAS 2009 (CARS09 [27]) material consider all available marine observation data and automation buoy profile data, contain a variety of average marine elements and their seasonal changes, and have undergone quality control at a spatial resolution of 1/2° × 1/2°.

The CARS09 file contains information, such as longitude, latitude, and standard layer depth, as well as the average value (mean), the sine value of the annual cycle (an_sin), the cosine value of the annual cycle (an_cos), the sine value of the semi-annual cycle (sa_sin), and the cosine value (sa_cos) of the semi-annual cycle. By using CARS09 dataset, we can obtain T/S data at a certain depth for any day of the year.

For Example:

To construct the temperature map for mid-February at 200 m depth:

Extract variable “depth” and find that 200 m is at level 25. Extract at level 25, and in the region required: mean, an_cos, an_sin, sa_cos, sa_sin.

Evaluate at day-of-year 45 (mid-February): t = 2 pi × 45/366. The temperature of mid-February is calculated by following formula:

$\mathrm{T}=\mathrm{mean}+\mathrm{an}\_\cos \left(\mathrm{t}\right)\ast \cos \left(\mathrm{t}\right)+\mathrm{an}\_\cos \ast \sin \left(\mathrm{t}\right)+\mathrm{sa}\_\cos \ast \cos \left(2\ast \mathrm{t}\right)+\mathrm{sa}\_\sin \ast \sin \left(2\ast \mathrm{t}\right)$

In our study, the anomalies were obtained by calculating the difference between the temperature, salinity, density, and CARS09 of the three datasets.

2.5. Eddy Tracking Method

Eddy track coordinates and properties were obtained using the Angular Momentum Eddy Detection and Tracking Algorithm (AMEDA) [28]. AMEDA combines a physical parameter [29], the local normalized angular momentum (LNAM), and geometrical features of the streamlines to determine the eddy centers and dynamical features. The eddy tracker used daily SLA data from AVISO. The tracking domain was set to 135°~170° E, 30°~40° N for the period 1 January 1993 to 31 December 2019. Eddy properties were saved in each time step, including position, date, effective radius, speed, and eddy kinetic energy (EKE).

2.6. Eddy Composite Method

Chaigneau’s [14] method was used to composite the eddies. The specific steps are described below:

• Eddy recognition: We use the AMEDA algorithm to identify eddies in the range of 32–35° N and 148–151° E (sea surface coordinates; the altitude data were provided by AVISO and comprise the daily data from 1993 to 2019 with a spatial resolution of 1/4°). The core position, contour boundary, and eddy radius of each eddy were obtained.

• The Argo data were screened, and the temperature and salinity data were extracted after quality control using the Akima [30] method. The CARS09 data of the corresponding regions were subtracted to obtain the geopotential temperature anomalies and salinity anomalies.

On this basis, the eddies closest to all Argo were found. According to the distance between the profiles and the center of the eddy, the profiles were divided into two categories: internal the cyclonic eddies, and outside the eddies. Argo profiles data satisfying one of the following two conditions were used for composite analysis: (1) the profile was positioned in the interior of an eddy; or (2) the profile was positioned outside an eddy, and the distance between the buoy position and the eddy center was less than 1.5 times the eddy radius. Then, the zonal distance (ΔX) and the meridional (ΔY) distance of each profile relative to the center of the eddies were calculated. All temperature anomalies, salinity anomalies, dynamic height anomalies, and potential density anomalies are transformed into the relative coordinate (ΔX, ΔY) and interpolated onto the normalized grid according to the inverse distance weighting method [31].

• 3.. In each standard layer, the quartile detection method was used to eliminate possible unreasonable values, and the optimal interpolation method was used to remove the remaining discrete data points.

The composite eddy from this method was an average of all eddies detected in the region for the whole period of the Argo data. In our study, we also tried to use the ARMOR 3D dataset to composite eddies to investigate the feasibility of ARMOR 3D. Further, in order to be able to comprehensively evaluate the composite eddy of two datasets, in addition to the CEs, AEs were also investigated.

3. Results

3.1. Eddy Characteristics

The development process of the lifespan of the eddy was traced (Figure 1). The eddy is a CE that was born on 9 December 2018 (152.99° E, 36.68° N). The eddy rapidly increased in radius and spread westward over a ten-day period, then moved northward with the Kuroshio current after reaching the western boundary. The ending of the eddy occurred on 16 July 2019 (149.36° E, 33.92° N). The lifespan was 194 days, which was much longer than the average lifespan of KER CEs (9.9 weeks) [32]. The eddy travelled 1160.59 km, and the average velocity (5.73 cm/s) was similar to the phase velocity of the first baroclinic Rossby wave (5–10 cm/s) [33]. Radius (57.32 km) was basically consistent with the average radius of KER CEs (62.12 km) [32].

AMEDA was used with the ARMOR3D data to track the lifespan and geometric characteristics of the eddy (Figure 1a). The trajectory and movement direction of the eddy recorded by the two datasets were roughly the same. The time nodes and amplitudes of the radius, and the increase and decrease in velocity that occurred during the life of the eddy were essentially the same (Figure 1b,c). The ARMOR 3D eddy lifespan (182 days), average radius (53.32 km), and movement speed (5.37 m/s) were all smaller than those of the AVISO eddy.

From 18 to 26 June (marked by dark shading in Figure 1b,c), the radius and speed of the eddy recorded by AVISO decreased and weakened, respectively. However, the process was not recorded by ARMOR3D. From 19 to 21 June, the intensity of the eddy began to weaken, and the radius and velocity of the eddy began to decrease, entering the decay period (Figure 2). In the subsequent 5 days, the eddy continued to move northward after meeting and fusing with another CE. The change process of eddy extinction and refusion was recorded by AVISO. The process (less than seven days) occurred exactly in the ARMOR 3D data recording interval (Figure 3). Therefore, when studying eddy using the ARMOR 3D dataset, it is important to note that information regarding some eddy processes (such as eddy refusion) may not be comprehensive.

3.2. Three-Dimensional Structure Features

In previous studies on the 3D geometric structure of eddy, the vertical arrangement of isosurfaces at different depths generally was used to represent the 3D structure of eddies [34]. However, this method cannot display the 3D structure of eddy in the most intuitive way. We selected the 3D geological image modeling software Voxler (Golden Software Company of the United States of America) to display the 3D structure of the studied eddy (Figure 4). In order to display the image as clearly as possible, some isosurfaces were selected to reflect the geometric structure of the entire eddy.

The temperature anomalies had monopole. However, their geometric structures were different. The observed and composite eddy were “cone-shaped”, while the ARMOR3D eddy was “bowl-shaped”. The salinity anomalies of the observed and the composite results were “dipole”, with a negative salinity anomaly in the upper core and a positive salinity anomaly in the lower core. This structure is similar to the CE’s salinity in the KER region summarized by Dong et al. [32]. The salinity anomalies of ARMOR3D only depicts a “monopole” of positive anomalies core.

3.3. Two-Dimensional Structure

3.3.1. Two-Dimensional Structure: Temperature

The temperature distributions of eddy from three datasets were shown in Figure 5. To exhibit the complete eddy structure, we extended the ARMOR 3D region to 148° E. The observation data had a “cold core” (negative temperature anomaly) with a conical structure. The maximum temperature anomaly in the cold core was −7.69 °C. The maximum negative temperature anomaly of ARMOR 3D eddy was −2.46 °C. The composite eddy structure was closer to the observation result and the maximum negative temperature anomaly value was −6.73 °C. The temperature was consistent among the three datasets. The 20 °C and 18 °C isotherms were uniform at shallow depths. As the depth increased, the isotherms began to show an upward bulge in the eddy region. However, the intensity of the upward bending of the isotherms was different among the different datasets, e.g., for the isotherm of 6 °C, the maximum uplift of the observed data reached 500 m.

Because different sections are located at different positions in the eddy, the sections of the contours of different sections at the same temperature are different. Sections W04 and W05 passed through the eddy center, and the bottom boundary of the cold core (the location of the maximum negative anomaly) was located at 370 m. The bottom boundaries of the other sections were shallow. All datasets confirmed the same characteristics: when the section was located closer to the eddy center, it had stronger negative temperature anomalies.

The horizontal distribution of eddy temperature and temperature anomalies at some specific depth layers were shown in Figure 6. The temperature structures of three datasets show the same characteristics: the central areas were negative anomalies, and the peripheral areas had positive anomalies. From 50 m to 800 m, the isotherms presented CE structure. The central area was a negative anomaly, while the peripheral area was a positive anomaly. From the sea surface to 800 m, the observations and ARMOR3D horizontal temperature structures contained negative anomalies, while the temperature composite eddy showed positive anomalies at the sea surface and beneath 500 m.

3.3.2. Two-Dimensional Structure: Salinity

The sectional distributions of salinity and salinity anomalies were shown in Figure 7. The salinity of the observed eddy and the composite eddy contained obvious uplifts, and the distributions of isohaline were similar. However, the isohaline of the ARMOR3D eddy was different from the others. Taking the 34.6 PSU as an example, with 34.6 isohaline, the observed and composite results were broken at the sea surfaces into sections W02, W03, and W04, but the phenomenon did not exist in ARMOR 3D. In addition, the 34.3 PSU isohaline showed that the closed circular isohalines in sections W02, W03, and W04 were uplift, while the 34.2 PSU isohaline of ARMOR 3D and the composite eddy were flat.

The observed salinity anomalies had “negative-positive” dipole (cone-shaped) in which the negative anomaly core was located in the range of 150–500 m, and the maximum salinity anomaly was −0.71 PSU. The positive core was below the depth of 600 m and the largest anomaly was 0.2 PSU. It seems that the negative salinity anomaly in the upper 500 m was brought about by the upwelling of water from the intermediate salinity minimum and the positive salinity anomaly at 650 m and below was brought about by the upwelling of water underneath whose salinity increased with the depth. The ARMOR 3D eddy was bowl-shaped (200~500 m), with the maximum salinity anomaly of −0.2 PSU. The composite eddy had “negative-positive” dipole structure between 180 m and 500 m, with a maximum salinity anomaly of −0.4 PSU. The intensity of the ARMOR3D salinity anomaly was significantly lower than that of the observed and composite eddy.

The horizontal distribution of salinity anomalies in some specific layers were shown in Figure 8. The observations show that ARMOR 3D and the composite eddy had closed isohalines from 50 m to 500 m. The observation results show that the negative salinity anomalies were maximum at 500 m, while the ARMOR 3D and composite eddy structures reached maximum at 350 m (−0.17 PSU and −0.4 PSU). In addition, the observed and composite eddy had closed isohalines of 34.2 PSU (800 m). However, the ARMOR 3D eddy does not have such structure.

3.3.3. Two-Dimensional Structure: Density

The density and density anomaly distribution of different sections and depths are indicated in Figure 9 and Figure 10. From the sea surface to 800 m, the density of the three datasets ranges from 1025 to 1030 km/m³ and is upwardly curved isopycnal. Sections W04 and W05 near the center of eddy have the maximum density anomalies. The three datasets differ in their upward bending of the isopycnal, and the upward bending of the observation structures were the most obvious. Taking the 1028 km/m³ isopycnal as an example, the observation data can reach the depth of 300 m (W04), while the ARMOR 3D (W04) and composite eddy (W04) was 400 m. At different depths, all three datasets had closed isopycnal, showing the typical structure of CE. The density of the eddy’s center was stronger than other regions, and the density decreased with increasing distance from the eddy center. In addition, positive temperature anomalies of the composite eddy lead to the negative density anomalies at the sea surface (Figure 9, the third column). The structures and location distribution of the three dataset density anomalies were similar to temperature anomalies and are not be described in detail in this section.

3.3.4. Two-Dimensional Structure: Flow Field

The actual flow fields had an asymmetric circulation structure with the weakest velocity at the eddy center (Figure 11). The flow direction changes simultaneously in the zonal and meridional directions and the velocity gradually increases as it moves away from the center and reaches the closest to the eddy boundary (the maximum velocity of the flow was 1.45 m/s). The distribution of the flow velocity was non-uniform: it was faster at the east–west boundary, but slower at the south–north boundary. From the depth of 50–800 m, the velocity gradually decreases, but the cyclone structure continues to be shown in the eddy range.

In order to compare actual flow fields with the geostrophic field, we calculated baroclinic geostrophic flow by the formula [35]:

(1)$v\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{v}_0-\frac{g}{f{\rho }_0}{\displaystyle {\int }_{z_0}^z\frac{\partial \rho }{\partial x}}dz$

where $\rho$ is the potential density, g is the gravitational acceleration, f is the Coriolis parameter, ${\rho }_0$ is the average potential density, and $v_0$ is the velocity on reference plane $z_0$. The 800 m layer was adopted as the reference depth.

The geostrophic flow (blue arrows) within the eddy was cyclonic circulation. The velocities were weakest in the eddy center and accelerated steadily with distance outwards and decreased with depth. The maximum geostrophic velocity at the surface was 1.25 m/s. The velocities were minimal change to the direction of flow. For the layers ranging from 50 m to 800 m (reference layer), geostrophic flows agreed well with the actual flows in both directions. As the depth increases, geostrophic flows corresponded well with the actual flows in directions while the magnitude is visibly weaker due to the adoption of the reference calculation depth.

The distribution of geostrophic velocities of three datasets at some specific depth layers were shown in Figure 12. There are the following differences in the stratigraphic flow fields: The observed and composite eddies had faster flow velocity at east–west boundaries, while their north–south boundaries had slower velocities. The ARMOR 3D data had faster velocity at the northeast and southwest boundary, while the southeast and northwest boundary had slower velocities. From the sea surface to 500 m, the observed magnitude and direction of ARMOR 3D were similar. However, from 500 m to 800 m, the difference of flow velocity gradually increases with depth. The temperature and salinity of the composite structure beneath 500 m were significantly higher than those of the other datasets, leading to stronger deep geostrophic currents in the composite eddy.

3.4. Vertical Profile Comparison

To show the differences among different locations, eight representative temperature-salinity profiles were selected (Figure 13). These stations were located in section W04, and the stations are located at the center, edge, and outside of the eddy.

The temperature and salinity anomaly profiles of the three datasets were mostly negative. The deviations of the temperature and salinity anomaly profiles among the different datasets were mainly associated to the relative distance between the position and the eddy center. The closer to the eddy center, the greater the deviation compared with the observation results. The root-mean-square errors of the temperature and salinity anomalies with observations at eight stations are shown in Table 2. Compared with the observation results, the square root deviation of temperature anomaly in the ARMOR3D data was 1.27~4.20 °C, the square root deviation of salinity was 0.27~0.47 PSU; the square root deviation of the composite temperature was 0.86~3.63 °C, and that of the salinity was 0.08~0.17 PSU.

4. Discussion

4.1. Analysis of Surface Anomalies within the Composite Cyclonic Eddy

In the comparison of the temperature horizontal structure shown in Section 3.3, the negative anomaly was observed for the surface temperature of the eddy and the positive anomaly was found for the 50 m layer of the composite eddy. To explore this phenomenon, the Argo data used in the process of compositing the eddy were statistically analyzed.

Among the 200 Argo profiles used in the composite CE, approximately 113 (77) profiles had positive (negative) temperature anomalies at the sea surface, and the mean value of positive (negative) anomalies from the sea surface to 50 m was 2.44 °C (−1.98 °C). Argo data with SSTA > 0 mainly appeared in winter (November, December, and January), accounting for 84.07%. The profiles with SSTA > 0 did not show up in the four months of February, April, June, or September. Research on the remaining months (March, May, July, and August) found that the profiles of SSTA > 0 had been commonly positioned far from the eddy’s center and the boundary of the eddy, which had little influence on the final result of the composite eddy.

The average value of the interannual eddy kinetic energy (EKE is the average of eddies in the observation region) and the distribution of the quantity of ARGO profiles were shown in Figure 14. Values of EKE much less than 200 cm²s⁻² indicates the weak CEs activity year (2013–2016) [15]. Coincidentally, 95 of the 113 sets of SSTA > 0 profiles used in the composite eddy were observed in winter when the eddy activity was weak (accounting for 84.07% of the total number of SSTA > 0 profiles). Due to the low SST in winter, the vertical upward movement of the water mass caused by the CEs lifts the warmer subsurface seawater to the sea surface in years of weaker EKE, resulting in CEs with SSTA > 0 [15]. Most of the Argo profiles used in the composite eddy were derived from winter CEs in weak EKE years, leading to the phenomenon of positive anomalies measured in the surface temperatures of the composite eddy. This result additionally reflects the main characteristics of the cyclones in the KER.

4.2. ARMOR 3D Composite Eddy Feasibility and Monthly Variation Analysis

The 3D structures of the eddies that appeared in the observation region were counted using ARMOR 3D data from 1993 to 2019. The analysis of the temperature and salinity anomalies in different seasons shows that the intensity of CE is stronger than that of the temperature and salt is stronger in CE than in AE. There are variations in different seasons (Table 3). The temperature and salinity anomalies are weakest in spring and strongest in summer. The temperature and salinity anomalies are monopole and dipole structures, respectively. The depth of boundary was located at 600 m, and the depth of the eddy’s influence was more than 800 m.

ARMOR 3D had higher spatial and temporal resolution than Argo, which can provide abundant data for the eddy composite method. The temperature and salinity anomaly distribution of the eddy composite by Argo and ARMOR 3D were shown in Figure 15. The eddy temperature and salinity anomalies based on the two data products have similar core geometric structures and polar distribution characteristics. Except for the anticyclone eddies salinity anomaly correlation of 0.69, the correlation coefficients of other thermohaline anomalies are above 0.80, respectively.

The number of ARMOR 3D used to composite eddy is 29,512, while the number of ARGO profiles is only 451. Compared with Argo, composite eddy using ARMROR 3D can achieve the objective of analyzing the monthly mean variation of eddies. The eddies temperature and salinity anomalies for different months (monthly data for ARMOR 3D from January 1993 to December 2019 of ARMOR 3D) in the survey region were shown in Figure 16. The monthly CE temperature and salinity anomalies are stronger than that of AE, and the average temperature (salinity) anomaly of the CEs is 44% (45% higher than that of the AE). The salinity anomalies are dipole structures (not shown). The intensity of anomalies induced by CEs varies significantly in different months, which were the strongest in summer (May, June, and July) and the weakest in January in winter. There is no significant change in anomalies caused by AEs. EKE is correlate with the intensity of the temperature and salinity anomalies. Hu et al. found that the monthly average EKE of AE in the KER did not show monthly changes based on years of statistics, which supports the use of ARMOR 3D data to composite the eddy [27].

The above analysis indicates that it is reliable and practical to study the composite eddy structure using the ARMOR 3D data. When studying the average state of eddy in some regions, and the Argo profile of the regions are sparse, ARMOR 3D can also help us to finish the work.

4.3. Analysis of Monopole Structure of ARMOR 3D Salinity Anomaly

The internal parameters of the ocean are dynamically related to the surface parameters, due to the forces on the surface attributed to major changes in the entire ocean [36], and many subsurface processes and phenomena yield surface manifestation, such as internal waves, mixed layer depth, and eddies [37]. These surface–subsurface connections enable the retrieval of subsurface and deep ocean data from the surface information [38].

The temperature and salinity (T/S) field (sea surface to 1500 m) of ARMOR 3D was projected to the vertical direction from satellite data (SLA + SST + SSS) through multiple the linear regression method and covariance derived from historical observations. These synthetic fields can be combined with T/S in situ profiles via an optimal interpolation method. In the study of Fox et al., the dynamic height variability is in the upper 300 m [39]. This method of satellite data projected onto the vertical is reliable for most ocean environments, however not appropriate for some eddies (such as our observation). The structure of each ocean eddy is different, and an eddy can be resolved into different vertical modes [40,41]. The salinity anomaly of ARMOR 3D was a monopole structure, while the observed result was dipole. ARMOR 3D had the upper negative salinity core, without the lower positive salinity core (in Section 3.3.2). ARMOR 3D successfully described the structure of the upper layer of the eddies by combining remote sensing data, such as SLA, SST, and SSS. However, maybe due to the lack of observations of the eddies, the deeper structure cannot be accurately described, leading to the phenomenon of salinity anomaly monopoles in this study.

5. Conclusions

Based on high-resolution observed data obtained using the marine multi-parameter profiling system (MVP), the multi-source observation fusion data ARMOR 3D, and composite method, we study the 3D structure of a mesoscale cold eddy in the KER. The major findings of our study are as follows:

• Observed data of CE (with a horizontal resolution 10.21 km and a vertical resolution of 1 m) revealed the typical 3D structural characteristics of CE. The isotherms at the various layers from the subsurface to 800 m consistently exhibited a distinct cyclonic eddy structure. In the vertical, the temperature and salinity anomalies of the observed eddy were monopole (negative) and dipole (negative-positive) structures, respectively. The actual and geostrophic velocities fields at specific layers exhibited an asymmetric cyclonic circulation structure. Velocities close to the eddy’s center were small and increased with distance outwards. The direction was nearly the same, while the distinction in magnitude will increase as the depth increases.

• ARMOR 3D can display the surface information of eddy (such as lifespan, radius, trajectory, etc.) and be used to composite eddy. However, it has limitations in describing the eddy process (such as eddy refusion in this study) and the vertical structure. The doming structure in the CE interior was demonstrated by the in-situ observations. It is reproduced by the ARMOR3D data, well enough for temperature, although the uplift is weaker, and not so well for salinity. The temperature anomalies had a “bowl-shaped” structure (observed eddy: conical). The ARMOR 3D salinity anomalies had a monopole (negative) structure in the vertical, while the observation was a dipole (negative-positive) structure, and the anomaly maximum (−0.2 PSU) was weaker than the observed (−0.71 PSU).

• The composite eddy is an average of all eddies detected in the observation region for the whole period of the Argo data. Compared with ARMOR 3D, the structure and magnitude of the composite eddy were closer to the observed results. The composite eddy had a positive temperature anomaly at the surface of CE. The statistical analysis of the ARGO data of composite eddy showed that the ARGO profiles were mainly derived from the weak-EKE winter of the studied year. These ARGO data of cold eddies had SSTA > 0, leading to abnormal positive temperatures at the surface of the final composite cold eddy structure. Therefore, it is necessary to pay attention to the influence of the seasonal and interannual EKE of Argo data on the composite structure.

• The feasibility of AROMR 3D data to composite eddy is demonstrated by comparing the 3D structures of ARMOR 3D and composite eddy. Based on the ARMOR 3D data for the composite, it was found that the temperature and salinity anomalies caused by CE were the strongest in July in summer and the weakest in January in winter. There was no significant variability in the anomalies of AE in different months.

Author Contributions

X.C., K.L. and K.M. collected the in situ observational data. P.W. treated and analyzed the data. P.W., X.C. and K.M. interpreted the results. P.W., X.C., K.M. and K.L. discussed the results and wrote the paper. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

Not applicable.

Acknowledgments

The authors thank ARMOR 3D and AVISO for providing satellite remote sensing data for free on their websites, and also thank all the crew members who participated in the ship cruising observation.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. (a) Mesoscale eddy trajectory and distribution of observation stations: (b) Eddy radius; (c) Eddy velocity. Note: (a) The color shading shows the average sea level anomaly distribution in KER during in situ period (14–22 June 2019). The yellow arrows were the geostrophic flow arrow; the light gray shades in (b,c) indicate 14–22 June 2019, and the dark shading indicates 19–26 June.

Figure 2. AVISO sea level anomalies and geostrophic velocities from 18 to 26 June 2019.

Figure 3. ARMOR 3D sea surface heights and geostrophic velocities on 18 June to 26 June 2019.

Figure 4. Three-dimensional structure: (a) observed temperature anomalies (°C); (b) ARMOR3D temperature anomalies (°C); (c) composite temperature anomalies (°C); (d) observed salinity anomalies (PSU); (e) ARMOR3D salinity anomalies (PSU); and (f) composite salinity anomalies (PSU). The color shading illustrate the temperature or salinity anomalies.

Figure 5. Sectional temperature distributions along the eight in situ sections. The horizontal axis is longitude and vertical axis is depth. The first column shows the temperature anomalies measured by MVPs, the second column shows ARMOR temperature anomalies, the third column shows the composite temperature anomalies, the fourth column shows the CARS09 (climatology). The gray lines represent the isotherms, and the color shading illustrates the temperature anomalies.

Figure 6. Horizontal distributions of temperature at some specific depth layers. The horizontal axis is longitude and vertical axis is latitude. Same as Figure 5.

Figure 7. Sectional salinity distributions along the eight in situ sections. The horizontal axis is longitude and vertical axis is depth. The first column shows the salinity anomalies measured by MVPs, the second column shows ARMOR 3D salinity anomalies, and the third column shows the composite density anomalies, the fourth column shows the CARS09 (climatology) density. The gray lines represent the isohalines, and the color shading illustrates the salinity anomalies.

Figure 8. Horizontal salinity distributions along the eight sections in situ. The horizontal axis is longitude and vertical axis is latitude. Same as Figure 7.

Figure 9. Sectional distributions of density at some specific depth layers. The horizontal axis is longitude and vertical axis is depth. The first column shows the density anomalies measured by MVPs, the second column shows ARMOR 3D density anomalies, and the third column shows the composite eddy density anomalies. The gray lines represent the isopycnal, and the color shading illustrates the density anomalies. The fourth column shows the ARS09 (climatology) density. The color shading illustrates the density.

Figure 10. Horizontal distributions of density anomalies at some specific depth layers. The horizontal axis is longitude and vertical axis is latitude. Same as Figure 9.

Figure 11. Actual and geostrophic velocities at some specific depth levels. The blue arrows are geostrophic velocities calculated by the MVP T/S data; the red arrows are the actual velocities measured by the ADCP after data interpolation.

Figure 12. Geostrophic Vector (The blue arrow is observation data; the red arrow is the ARMOR3D data; the green arrow is the composite data).

Figure 13. (a) Station distribution map (the color shading shows the average SLA distribution in KER during in situ period); (b,c) temperature anomaly and salinity anomaly profiles (Blue: observation, Green: ARMOR 3D, Red: ARGO composite eddy).

Figure 14. Composite eddy years with SSTA > 0 obtained from the ARGO and EKE data distributions.

Figure 15. Temperature and salt anomaly distribution of ARMOR 3D and Argo composite eddy in vertical section at ΔX = 0 (First row: ARGO; Second row: ARMOR 3D). The horizontal axis label is the normalized radius at zonal direction, and the vertical axis label is the depth.

Figure 16. ARMOR 3D composite temperature and salinity anomalies in different months.

Table 1

Locations of stations along each section.

Section	Location	Time	Number of Stations
W01	148.41–150.40 E, 33.25 N	14–15 June 2019	13
W02	149.41–150.39 E, 33.39 N	15–16 June 2019	12
W03	148.42–150.40 E, 33.54 N	17 June 2019	13
W04	148.60–150.50 E, 33.70 N	18 June 2019	24
W05	148.70–150.40 E, 33.78 N	19 June 2019	24
W06	148.64–150.54 E, 33.75 N	20 June 2019	26
W07	148.41–150.39 E, 33.39 N	21 June 2019	13
W08	150.39–150.41 E, 34.27 N	22 June 2019	15

Table 2

Root mean square errors of temperature and salinity anomalies.

Position	W04-1	W04-2	W04-3	W04-4	W04-5	W04-6	W04-7	W04-8
Location	Outer Profile	Inner Profile	Inner Profile	Inner Profile	Inner Profile	Inner Profile	Inner Profile	Outer Profile
Temperature Anomaly
ARMOR3D	1.27	2.05	3.71	3.94	4.20	3.96	2.81	1.41
Composite	1.86	1.53	3.23	3.63	3.36	2.79	1.63	1.53
Salinity Anomaly
ARMOR3D	0.170	0.325	0.471	0.473	0.484	0.477	0.364	0.19
Composite	0.203	0.081	0.177	0.130	0.111	0.097	0.137	0.206

(Outer profile means the position is located outside at the eddy boundary; Inner profile indicates that the position is located at inside the eddy).

Table 3

Statistics on the extreme value of ARMOR 3D temperature and salinity anomalies in different seasons.

	Spring (Depth)	Summer (Depth)	Autumn (Depth)	Winter (Depth)
Temperature Anomaly
CE	−7.7 (320 m)	−8.2 (270 m)	−7.8 (280 m)	−7.6 (310 m)
AE	4.7 (520)	5.1 (520)	4.1 (520)	4.5 (520 m)
Salinity Anomaly
CE	0.4 (370 m)	0.7 (350 m)	0.6 (350 m)	0.5 (370 m)
AE	−0.2 (490 m)	−0.4 (490 m)	−0.4 (490 m)	−0.3 (500 m)

References

1. Mcgillicuddy, D.J.; Anderson, L.A.; Bates, N.R.; Bibby, T.; Buesseler, K.O.; Carlson, C.A.; Davis, C.S.; Ewart, C.; Falkowski, P.G.; Goldthwait, S.A. et al. Eddy/wind interactions stimulate extraordinary mid-ocean plankton blooms. Science; 2007; 5827, pp. 1021-1026. [DOI: https://dx.doi.org/10.1126/science.1136256] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/17510363]

2. Mikaelyan, A.S.; Zatsepin, A.G.; Kubryakov, A.A. Effect of Mesoscale Eddy Dynamics on Bioproductivity of the Marine Ecosystems (Review). Phys. Oceanogr.; 2020; 6, pp. 590-618.

3. Shan, X.; Jing, Z.; Sun, B.; Wu, L. Impacts of ocean current–atmosphere interactions on mesoscale eddy energetics in the Kuroshio extension region. Geosci. Lett.; 2020; 1, pp. 1-8. [DOI: https://dx.doi.org/10.1186/s40562-020-00152-w]

4. Ji, J.; Dong, C.; Zhang, B.; Liu, Y.; Zou, B.; King, G.P.; Xu, G.; Chen, D. Oceanic Eddy Characteristics and Generation Mechanisms in the Kuroshio Extension Region. Journal of Geophysical Research. Oceans; 2018; 11, pp. 8548-8567.

5. Joyce, T.M.; Yasuda, I.; Hiroe, Y.; Komatsu, K.; Kawasaki, K.; Bahr, F. Mixing in the meandering Kuroshio Extension and the formation of North Pacific Intermediate Water. J. Geophys. Res. Ocean.; 2001; C3, pp. 4397-4404. [DOI: https://dx.doi.org/10.1029/2000JC000232]

6. Qiu, B.; Chen, S. Eddy-mean flow interaction in the decadally modulating Kuroshio Extension system. Deep Sea Res. Part II Top. Stud. Oceanogr.; 2010; 13–14, pp. 1098-1110. [DOI: https://dx.doi.org/10.1016/j.dsr2.2008.11.036]

7. Qiu, B.; Chen, S. Effect of Decadal Kuroshio Extension Jet and Eddy Variability on the Modification of North Pacific Intermediate Water. J. Phys. Oceanogr.; 2011; 3, pp. 503-515. [DOI: https://dx.doi.org/10.1175/2010JPO4575.1]

8. Qiu, B.; Chen, S.; Hacker, P. Effect of Mesoscale Eddies on Subtropical Mode Water Variability from the Kuroshio Extension System Study (KESS). J. Phys. Oceanogr.; 2007; 4, pp. 982-1000. [DOI: https://dx.doi.org/10.1175/JPO3097.1]

9. Hu, J.; Gan, J.; Sun, Z.; Zhu, J.; Dai, M. Observed three-dimensional structure of a cold eddy in the southwestern South China Sea. J. Geophys. Res. Earth Surf.; 2011; 116, [DOI: https://dx.doi.org/10.1029/2010JC006810]

10. Li, S.; Wang, S.; Zhang, F.; Wang, Y. Constructing the Three-Dimensional Structure of an Anticyclonic Eddy in the South China Sea Using Multiple Underwater Gliders. J. Atmos. Ocean. Technol.; 2019; 36, pp. 2449-2470. [DOI: https://dx.doi.org/10.1175/JTECH-D-19-0006.1]

11. Xi, C.; Dong, H.; Mao, K.; Yan, L. Detailed investigation of the three-dimensional structure of a mesoscale cold eddy in the Kuroshio extension region. J. Oper. Oceanogr.; 2018; 11, pp. 87-99. [DOI: https://dx.doi.org/10.1080/1755876X.2018.1505069]

12. Mason, E.; Pascual, A.; Gaube, P.; Ruiz, S.; Pelegrí, J.L.; Delepoulle, A. Subregional characterization of mesoscale eddies across the Brazil-Malvinas Confluence. J. Geophys. Res. Ocean.; 2017; 122, pp. 3329-3357. [DOI: https://dx.doi.org/10.1002/2016JC012611]

13. Barceló-Llull, B.; Pascual, A.; Mason, E.; Mulet, S. Comparing a multivariate global ocean state estimate with high-resolution in situ data: An anticyclonic intrathermocline eddy near the Canary Islands. Front. Mar. Sci.; 2018; 5, pp. 2296-7745. [DOI: https://dx.doi.org/10.3389/fmars.2018.00066]

14. Chaigneau, A.A.B.C.; Le Texier, M.D.; Eldin, G.C.; Grados, C.B.; Pizarro, O.E. Vertical structure of mesoscale eddies in the eastern South Pacific Ocean: A composite analysis from altimetry and Argo profiling floats. J. Geophys. Res. Ocean.; 2011; 11, pp. C11025-C11040. [DOI: https://dx.doi.org/10.1029/2011JC007134]

15. Yang, G.; Wang, F.; Li, Y.; Lin, P. Mesoscale eddies in the northwestern subtropical Pacific Ocean: Statistical characteristics and three-dimensional structures. J. Geophys. Res. D Atmos.; 2013; 4, pp. 1906-1925. [DOI: https://dx.doi.org/10.1002/jgrc.20164]

16. Chen, G.; Gan, J.; Xie, Q.; Chu, X.; Wang, D.; Hou, Y. Eddy heat and salt transports in the South China Sea and their seasonal modulations. J. Geophys. Res. Ocean.; 2012; 117, 5. [DOI: https://dx.doi.org/10.1029/2011JC007724]

17. Liu, Y.; Dong, C.; Guan, Y.; Chen, D.; Mcwilliams, J.; Nencioli, F. Eddy analysis in the subtropical zonal band of the North Pacific Ocean. Deep Sea Res. Part I Oceanogr. Res. Pap.; 2012; 68, pp. 54-67. (In Chinese) [DOI: https://dx.doi.org/10.1016/j.dsr.2012.06.001]

18. Amores, A.; Melnichenko, O.; Maximenko, N. Coherent mesoscale eddies in the North Atlantic subtropical gyre: 3-D structure and transport with application to the salinity maximum. J. Geophys. Res. Ocean.; 2017; 1, pp. 23-41. [DOI: https://dx.doi.org/10.1002/2016JC012256]

19. Zhang, Z.; Yu, Z.; Wei, W.; Rui, X.H. Universal structure of mesoscale eddies in the ocean. Geophys. Res. Lett.; 2013; 40, pp. 3677-3681. [DOI: https://dx.doi.org/10.1002/grl.50736]

20. Ullman, D.S.; Hebert, D. Processing of Underway CTD Data. J. Atmos. Ocean Technol.; 2014; 4, pp. 984-998. [DOI: https://dx.doi.org/10.1175/JTECH-D-13-00200.1]

21. Liu, Y.; Weisberg, R.H.; Lembke, C. Glider Salinity Correction for Unpumped CTD Sensors across a Sharp Thermocline. Coastal Ocean Observing Systems; Academic Press: Cambridge, MA, USA, 2015; pp. 305-325.

22. Shen, J.Q. Application of CODAS system in ship-mounted ADCP data quality control in Xiamen Bay. J. Appl. Oceanogr.; 2014; 4, pp. 472-480.

23. Wu, Y.; Wu, Z.; Li, Z. Shipborne ADCP Data Processing. Hydrogr. Surv. Charting; 2014; 34, pp. 36-39. (In Chinese)

24. Guinehut, S.; Dhomps, A.L.; Larnicol, G.; Le Traon, P.Y. High resolution 3-D temperature and salinity fields derived from in situ and satellite observations. Ocean Sci. Discuss.; 2012; 9, pp. 1313-1347. [DOI: https://dx.doi.org/10.5194/os-8-845-2012]

25. Verbrugge, N.; Mulet, S.; Guinehut, S.; Buongiornonardelli, B. ARMOR3D: A 3D multi-observations T,S,U,V product of the ocean. Proceedings of the Egu General Assembly Conference; Vienna, Austria, 23–28 April 2017.

26. Cipollone, A.; Masina, S.; Storto, A.; Iovino, D. Benchmarking the mesoscale variability in global ocean eddy-permitting numerical systems. Ocean Dyn.; 2017; 67, pp. 1313-1333. [DOI: https://dx.doi.org/10.1007/s10236-017-1089-5]

27. Ridgway, K.R.; Dunn, J.R.; Wilkin, J.L. Ocean Interpolation by Four-Dimensional Weighted Least Squares—Application to the Waters around Australasia. J. Atmos. Ocean Technol.; 2002; 9, pp. 1357-1375. [DOI: https://dx.doi.org/10.1175/1520-0426(2002)019<1357:OIBFDW>2.0.CO;2]

28. Le Vu, B.; Stegner, A.; Arsouze, T. Angular Momentum Eddy Detection and Tracking Algorithm (AMEDA) and Its Application to Coastal Eddy Formation. J. Atmos. Ocean Technol.; 2018; 35, pp. 739-762. [DOI: https://dx.doi.org/10.1175/JTECH-D-17-0010.1]

29. Mkhinini, N.; Coimbra, A.L.S.; Stegner, A.; Arsouze, T.; Taupier-Letage, I.; Béranger, K. Long-lived mesoscale eddies in the eastern Mediterranean Sea: Analysis of 20 years of AVISO geostrophic velocities. J. Geophys. Res. Ocean.; 2014; 12, pp. 8603-8626. [DOI: https://dx.doi.org/10.1002/2014JC010176]

30. Akima, H. A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures. J. ACM; 1970; 4, pp. 589-602. [DOI: https://dx.doi.org/10.1145/321607.321609]

31. Barnes, S.L. Mesoscale Objective Map Analysis Using Weighted Time-Series Observations; National Oceanic and Atmospheric Administration: Washington, DC, USA, 1973.

32. Dong, H.; Xi, C.; Zhao, Y.; Li, Y.; Mao, K.F.; Jiang, H.F.; Wang, D.L. Statistical characteristics of mesoscale eddies in the two western boundary current extension regions, Hai Yang Xue Bao. Acta Oceanol. Sin.; 2018; 40, pp. 15-28.

33. Chelton, D.B. Geographical variability of the first baroclinic Rossby radius of deformation. J. Clim.; 1998; 28, pp. 433-460. [DOI: https://dx.doi.org/10.1175/1520-0485(1998)028<0433:GVOTFB>2.0.CO;2]

34. Sandalyuk, N.V.; Bosse, A.; Belonenko, T.V. The 3D structure of Mesoscale Eddies in the Lofoten Basin of the Norwegian Sea: A composite analysis from altimetry and in situ data. J. Geophys. Res. Ocean.; 2020; 125, e2020JC016331. [DOI: https://dx.doi.org/10.1029/2020JC016331]

35. Zhou, H.; Nan, F.N.; Shi, M.; Zhou, L.; Guo, P. Characteristics of water exchange in the Luzon Strait during September 2006. Chin. J. Oceanol. Limnol.; 2009; 3, pp. 650-657. [DOI: https://dx.doi.org/10.1007/s00343-009-9175-2]

36. Huang, R. Ocean Circulation: Wind-Driven and Thermohaline Processes: Ocean Circulation: Wind-Driven and Thermohaline Processes; Cambridge University Press: Cambridge, UK, 2012.

37. Yan, X.; Jo, Y.; Liu, W.; He, M. A New Study of the Mediterranean Outflow, Air–Sea Interactions, and Meddies Using Multisensor Data. J. Phys. Oceanogr.; 2006; 4, pp. 691-710. [DOI: https://dx.doi.org/10.1175/JPO2873.1]

38. Meng, L.; Yan, C.; Zhuang, W.; Zhang, W.; Yan, X.H. Reconstruction of Three-Dimensional Temperature and Salinity Fields from Satellite Observations. J. Geophys. Res. Ocean.; 2021; 126, e2021JC017605. [DOI: https://dx.doi.org/10.1029/2021JC017605]

39. Fox, D.N.; Teague, W.J.; Barron, C.N.; Carnes, M.R.; Lee, C.M. The Modular Ocean Data Assimilation System (MODAS). J. Atmos. Ocean Technol.; 2002; 19, pp. 240-252. [DOI: https://dx.doi.org/10.1175/1520-0426(2002)019<0240:TMODAS>2.0.CO;2]

40. Shi, Y.; Yang, D.; He, Y. Numerical study on interaction between eddies and the Kuroshio Current east of Taiwan, China. J. Oceanol. Limnol.; 2021; 2, pp. 388-402. [DOI: https://dx.doi.org/10.1007/s00343-020-0010-0]

41. Shevchenko, I.; Berloff, P. On the roles of baroclinic modes in eddy-resolving midlatitude ocean dynamics. Ocean Model.; 2017; 111, pp. 55-65. [DOI: https://dx.doi.org/10.1016/j.ocemod.2017.02.003]