An inverted echo sounder (IES) equipment with a current sensor (C) and a pressure sensor (P) is called CPIES, which consists of a fishing float, a glass float, an Aanderaa current meter, a 50-m communication cable, a PIES body, and a heavy anchor. The working mode is mainly to measure the sound propagation time from the sea surface to the sea bottom. Since its inception in the 1970s, IES has been widely used in marine research with the help of technological developments and the progress of data processing methods (Meinen et al., 2003; Donohue et al., 2008; Watts et al., 2001).

This has relied heavily on the ground-transfer empirical modal GEM method proposed by Watts et al (2001) for data inversion methods. This method establishes an empirical relationship between sound propagation time (τ) and temperature, salinity, and streamflow functions by integrating all historical measured temperature and salinity profiler for the study area, creating a Lagrangian matrix of scatter points and projecting the existing temperature and salinity data onto this two-dimensional space. Also, an observation array consisting of multiple CPIES can be based on the GEM method to obtain an absolute current profile. A reference layer needs to be chosen to create GEM, and this reference layer requires a depth that can basically cover the depth of baroclinic influence. Considering the weak baroclinic below 1,000 m east of Taiwan, this study takes 1,000 m as the reference layer. As a comparison, the 1,000 m selected by Anders et al. (2017) in this region is used as the reference layer.

From December 2017 to July 2018, a total of 40 CPIES were deployed around the Luzon Strait, and 39 sites were successfully recovered in July 2019. Among them, 12 of the CPIES were deployed in the area east of Taiwan with a 3 × 4 size array. All CPIES observations were then preprocessed, which included being despiked, tidally corrected, and dedrifted, following Kennelly et al. (2007). All the final raw data were low-pass filtered with a 72-h window and a fourth-order Butterworth filter. For further information on the data processing and inversion process, see Zhao et al. (2022) and Zheng et al. (2022).

An Archiving, Validation, and Interpretation of Satellite Data in Oceanography (AVISO) altimetry data (http://marine.copernicus.eu/services-portfolio/access-to-products/) set was used in this study to track the mesoscale eddies. Sea surface height anomaly data are used in the manuscript, the data spatial resolution is 1/4° × 1/4°, and the data set extended from June 2018 to July 2019, which provided satisfactory overlap with the CPIES array data.

In order to establish the relationship between the GEM array inversion temperature, salinity, and current, as well as the acoustic wave propagation time (τ) and the pycnocline, it is necessary to draw on as many existing historical data profiles as possible. Historical hydrographic data from the World Ocean Database (WOD) and Argo were selected from the locations shown in Figure 2 , with longitudes of 121.3–127°E and latitudes of 20–23.8°N. The locations selected were larger than the CPIES deployment sites. The total number of profiles is 3,155, of which 1,367 profiles are less than 1,500 m, 1,660 profiles are between 1,500 and 2,000 m, and 128 profiles are greater than 2,000 m.

Changes in the pycnocline depth have been shown in many studies to be one of the mechanisms of interaction between mesoscale eddies and Kuroshio (Ren et al., 2020). The time series of τ measurement from CPIES station C04 and sea level anomaly (SLA) are shown in Figure 3 , and the result reveals a highly negative correlation between SLA with a coefficient of –0.9. This means that the increase in sea surface height caused by the anticyclonic eddies (cyclonic eddies) can reduce (increase) the sound speed round trip propagation time.

To quantify the variation of the pycnocline at the interaction between eddies and Kuroshio, the measured propagation (τ) time series needs to be converted to the pycnocline variation, and here, we use the depth of the maximum density gradient to represent the pycnocline variation. Pycnocline depth is defined in this paper by the maximum density gradient (dρ/dz) below the seasonal thermocline (Tsai et al., 2015; Jan et al., 2017), calculated for each density profile located in the regions in the red point area from the historical Argo data ( Figure 2 ). Thus, it is necessary to establish the relationship between the propagation time τ and the pycnocline depth. As mentioned before, in order to invert the temperature, salinity, and other data, the measurement time τ by PIES needs to be converted into the reference (τ) which is chosen to be 1,000 m. According to this, a function of the pycnocline depth (d_pyn) and τ _1,000 are established based on historical CTD profile data. The result is plotted against the corresponding τ _1,000  in each profile shown in Figure 4 , the mean pycnocline is σ=25.9 kg m⁻³ and the depth is approximately 300 m at eastern Taiwan. The τ _1,000 and pycnocline depth exhibit a linear relationship with a correlation coefficient of 0.8, which means that pycnocline depth increases (decreases) with the increase (decrease) in τ _1,000. Therefore, we can obtain a simple corresponding function of the pycnocline depth and τ _1,000 by linear fitting, shown by the black line in Figure 3B . Thus, we can invert the time series pycnocline depth at each time through τ _1,000 inverted from τ  measured by CPIES. Combining the relationship between τ _1,000 and SLA and pycnocline depth obtained from Figure 3 , we can conclude that the positive (negative) SLA caused by the anticyclonic eddies (cyclonic eddies), which corresponds to a smaller (larger) τ _1,000 is able to cause a deeper (shallower) pycnocline depth at the same time.

During the observation period, multiple eddies propagating east of Taiwan are successfully captured by our CPIES array shown in Figure 5 , and based on the relationship between the eddies and the pycnocline depth obtained in the previous section, we have the opportunity to directly study the interaction between mesoscale eddies and Kuroshio. At the anticyclonic eddy moment, τ _1,000 forms a closed region of low values corresponding to the eddy. The minimum value of τ _1,000  ithe center of the eddy is 1.316 s, and τ _1,000  ll be larger the closer to the edge of the anticyclonic eddy. Additionally, it can be found that the distribution of τ _1,000  shows obvious east–west differences, and τ _1,000 in the region near the western Kuroshio is larger than that in the region controlled by the anticyclonic eddy, and the maximum value of τ ₁₀₀₀  at the Kuroshio location is close to 1.320 s. The depth of the pycnocline at the center of the anticyclonic eddy is calculated from the linear relationship between τ _1,000  and d _pyn and is determined to be approximately 450 m, while the pycnocline depth at the Kuroshio side is approximately 410 m, while at the cyclonic eddy impinging with Kuroshio, τ _1,000 forms a closed region of high values corresponding to the eddy shown in Figure 4A , with a maximum τ _1,000 value of 1.322 s at the center of the eddy and decreasing toward the edge of the eddy. The distribution of τ _1,000  shows a small east–west difference, with a τ _1,000 value of 1.321 s near the Kuroshio side, but is still smaller than the interior of the eddy. According to the relationship, the depth of the pycnocline in the center of the cyclonic eddy and Kuroshio side is approximately 365 m and 370 m, respectively.

Thus, the pycnocline depth at the anticyclonic eddy is significantly greater than at the cyclonic eddy, and the pycnocline is nearly parallel at the cyclonic eddy moment. Based on the possible variation mechanism proposed by Jan et al. (2015) and our calculations, the interaction between the eddy and the Kuroshio can be revealed by the schematic shown in Figure 6 . Under normal conditions, the pycnocline of the Kuroshio is tilted to the lower right (white line in Figure 6 ) and the Kuroshio flows northward. While in the influence of the anticyclonic eddy ( Figure 6A ), the overall pycnocline becomes significantly deeper and the tilt of the pycnocline increases significantly, exhibiting a “see-saw” effect, thus resulting in an increase in the Kuroshio velocity, a wider Kuroshio width, and a greater Kuroshio thickness, even up to 800–1,000 m, while at the cyclonic eddy influence ( Figure 6B ), the pycnocline rises upward and reduces the tilt of the pycnocline, similar to a see-saw reverting to an intermediate state, corresponding to a decrease in the velocity and width of Kuroshio, as well as reducing the thickness of Kuroshio.

An anticyclonic eddy is captured by the CPIES array shown in Figure 8 , where the temperature and salinity anomalies of the eddies are defined as the measured values at each point minus the average of each layer, and the center of each layer of the eddy is identified by the minimum velocity point, which is located at 123.5°E, 22.35°N. The left front of the anticyclonic eddy is adjacent to the Kuroshio, and the radius of this eddy is estimated to be approximately 70 km. The maximum velocity of the eddy at the surface layer is approximately 0.7 m/s, and the eddy extends to a depth of 1,000 m. Combined with Figure 4A , it can be seen that the Kuroshio velocity west of 122.5°E is 0.7 m/s. Ren et al. (2020) measured the Kuroshio velocities by subsurface mooring and noted that the velocities can reach 1 m/s when interacting with anticyclonic eddies, probably due to the fact that the CPIES array is located on the eastern side of the Kuroshio main axis and thus the velocities are relatively small. Taking a latitudinal section along the center of the eddy at 22.35°N shown in Figure 9 , the temperature and salinity anomalies and velocity clearly show that the variation is completely different between the left and right sides of 122.5°E. The isotherm, isohaline, and pycnocline of the anticyclonic eddy are concave, while those in the Kuroshio side are convex.

The largest positive temperature anomaly is located at the center of the eddy, with two positive temperature anomaly cores located at approximately 200 m and 500 m, with values of approximately 0.6°C and 1.4°C, respectively, which are basically located near the seasonal thermocline and the main thermocline. The salinity anomalies also show two cores below the subsurface layer, which are located at depths of 450 m and 850 m, with a maximum positive salinity anomaly of approximately 0.08 psu at 450 m. The characteristics of the salinity anomaly structure are related to the subsurface high-salinity water and intermediate waters. At the center of the anticyclonic eddy, downward movement of saline water from the subsurface will result in positive salinity anomalies at depths of 400–600 m. The downward transport of low-saline water in the intermediate layer will result in negative salinity anomalies below 600 m.

For the Kuroshio region west of 122.5°E, due to the see-saw like changes in the interaction between the anticyclonic eddy process, the variation of the Kuroshio is the opposite of the variation of the anticyclonic eddy. The Kuroshio side produces an overall negative temperature anomaly, and the salinity anomaly of the Kuroshio shows a negative–positive structure below 200 m. The upward movement of the low-salinity intermediate water at depths of 400–600 m results in a negative salinity anomaly at depths shallower than 600 m, with a maximum value of −0.06 psu at 450 m. Positive salinity anomalies of 0.04 psu are due to the upward movement of highly saline water in the deep sea below 700 m.

Figure 9C shows a velocity profile at the moment of the anticyclonic eddies, which shows in detail the characteristics of the velocity structure distribution inside the Kuroshio and anticyclonic eddies. The velocity at the center of the anticyclonic eddies is almost 0 m/s, with the velocity gradually increasing from the center outward. The left side of the eddy is connected to the Kuroshio, and the larger velocity range in the horizontal direction extends to approximately 122.75°E, thus illustrating the increase in the amplitude of the Kuroshio caused by the anticyclonic eddies.

A cyclonic eddy structure is shown in Figure 10 ; the center of this eddy is located at 123.75°E, 22.35°N, and the radius is estimated to be approximately 60 km from the sea surface height. The maximum velocity of the eddy is approximately 0.7 m/s, and can exceed 0.1 m/s at 1,000 m. Based on the latitudinal section of the eddy center at 22.35°N ( Figure 11 ), the isotherm, isohaline, and pycnocline are found to be nearly horizontal, with a slight upward convexity at the center of the cyclonic eddy. The elevation of the pycnocline is evident; for example, the 26 kg m⁻³ density contour is located between 450 m and 500 m in a downward concave structure at the anticyclonic eddy, while at the cyclonic eddy, it is almost entirely above 400 m and is nearly horizontal. It can also be seen that the negative temperature anomaly has two cores, corresponding to two thermoclines with a maximum value of −0.8°C, located between 100 and 200 m. The cyclonic eddy-induced salinity anomaly shows a negative–positive structure below the subsurface layer. The core of the negative salinity anomaly is located at approximately 350 m with a maximum value of −0.06 psu, while the core of the positive salinity is located at approximately 800 m with a maximum value of 0.04 psu. The salinity anomalies can also be explained as follows: the upward movement of eddy center causes the low saline water between 400-600m to upward lift, resulting in negative salinity anomalies above the intermediate layer, while the salinity anomalies below 600m are positive due to the upward lift of the deeper high saline water.

For the cyclonic eddy impinging on the Kuroshio, the reduction in the tilt of the pycnocline has already been analyzed and the corresponding velocity distribution ( Figure 11 ) clearly depicts this reduction in velocity. The velocity of the Kuroshio decreases to approximately 0.2 m/s and the amplitude of the Kuroshio decreases significantly. This is in contrast to the velocity of the eastern side of the cyclonic eddy, which is approximately 0.4 m/s. When a cyclonic eddy interacts with Kuroshio, it weakens the tilt of the pycnocline, and if the cyclonic eddy is strong enough, it can even induce the depth of the pycnocline on the Kuroshio side to be lower than that on the eddy side, resulting in a reversal of the Kuroshio direction.