1 INTRODUCTION

Mesoscale eddies are characterized by closed circulations, with a time scale of a few days to hundreds of days. Those eddies contain considerable energy that directly affects both the ocean thermohaline structure and the velocity distribution. Thus, mesoscale eddies play an important role in ocean circulation, as well as in heat and mass transport(McWilliams, 2008).

The South China Sea(SCS)is the largest semienclosed marginal sea in the northwestern Pacifi c Ocean, with an average depth greater than 1 000 m. The SCS exchanges water masses with surrounding oceans through the Taiwan Strait, the Luzon Strait, the Mindoro Strait, the Balabac Strait, the Karimata Strait, and the Malacca Strait(Yang et al., 2013). The general circulation pattern of the SCS is a basin-wide cyclonic gyre in the winter and an anticyclonic gyre in the summer, which is dominated by seasonally reversing winds that typically blow strongly from the northeast during the boreal winter and from the southwest during the boreal summer(Hu et al., 2000; Hwang and Chen, 2000). Together with the general circulation, active mesoscale eddies with complex vortex structures contribute to a complicated dynamic system in the SCS.

Studies of mesoscale eddies in the SCS have made considerable progress in the last 20 years, benefi ting from the development of marine satellite remote sensing technology. Multi-source remote sensing data combined with conventional observation data and numerical reanalysis data has been widely applied in research on mesoscale eddies. Xiu et al.(2010)identifi ed eddies based on the Okubo-Weiss(OW)algorithm and conducted an eddy census including eddy number, size, lifetime and tracks in the SCS based on numerical results and satellite data. On average, 32.8±3.4 eddies were observed by satellite each year, and about 53% of them were CEs; they also concluded that more than 70% of eddies have a radius smaller than 100 km. Hwang and Chen(2000)adopted TOPEX/Poseidon altimeter data to compute the temporal and spatial distribution of mesoscale eddies from 1993-1999 in the SCS. They detected 94 cyclonic eddies and 124 anticyclonic eddies with lifetimes longer than 1 month and eddy size larger than 150 km. Chen et al.(2011)detected 7 000 eddies in the SCS in 17 years using satellite altimetry data, and examined the eddy propagation and evolution characteristics. The mean eddy size was 132 km, mean lifetime was 8.8 weeks, and there was no signifi cant difference between the two eddy types. Wang(2003)examined the statistical space-time distribution features of mesoscale eddies in the SCS(58 anticyclonic eddies and 28 cyclonic eddies were identifi ed)using 1993-2000 multi-source remote sensing data and analyzed the mechanisms of mesoscale eddies in some major areas. Previous literature reported inconsistent numbers of mesoscale eddies in the SCS, which might have resulted from different eddy identifi cation algorithms. Hwang and Chen(2000)defi ned the edge of an eddy as the 5-cm contour of the dynamic height. Chen et al.(2011)used the winding angle(WA)method to detect eddies. Wang(2003)applied the SSHA-based method to search the SSHA contours that satisfy certain criteria. These detection methods have been reviewed by Yi et al.(2014) and can be further improved to achieve higher accuracy.

Automated detection methods are essential for the study of mesoscale movements in the ocean. Existing eddy detection schemes can be categorized into three classes:(1)physical parameter based methods, (2)fl ow geometry based methods, and (3)hybrid methods, which involves both physical parameters and fl ow geometry characteristics(Nencioli et al., 2010). The effi ciency of the eddy detection method can be validated generally with two parameters: one is the success of detection rate(SDR) and the other is the excess of detection rate(EDR)(Chaigneau et al., 2008; Yi et al., 2014). Most of the algorithms have a high SDR at the expense of a high EDR. Former studies on mesoscale eddy detection in the SCS mostly used the OW method(Isern-Fontanet et al., 2002; Morrow et al., 2004; Chelton et al., 2007) and the SSHA-based method(Chaigneau et al., 2008; Chen et al., 2012 ; Holte et al., 2013). The OW method can reach a 100% SDR, but the EDR was still relatively high(71.9%)(Yi et al ., 2014). The WA method(Chen et al., 2011)takes the SSHA local extrema as eddy centers, which contributed to a high SDR of up to 93.8% while the EDR was less than 25.1%(Yi et al ., 2014). The SDR and the EDR of the SSHA-based method was 78.1% and 28.1%, respectively(Yi et al ., 2014). In this study, an eddy detection method with both a high SDR and a low EDR(an average SDR of 92.9% and EDR 2.9%), proposed by Nencioli et al.(2010), was adopted to detect mesoscale eddies in the SCS.

The rest of the paper is organized as follows: the data and eddy detection scheme used are described in Section 2; statistical analysis of the eddy dataset is presented in Section 3; Section 4 discusses the impact of monsoons on eddies; and the conclusion is in Section 5.

2 MATERIAL AND METHOD2.1 Data

The sea level anomaly(SLA)data and geostrophic velocity were provided by Archiving Validation and Interpretation of Satellite Data in Oceanography(AVISO), the DUACS 2014 version(V15.0), with a 1/4° spatial resolution and daily temporal intervals. The data was then inserted into a weekly temporal grid for later processing. The SLA data in AVISO was the differences between the observed SSH and a 20- year mean profi le(1993-2012). The data still contain aliases from tides and internal waves over the shelf area(Yuan et al., 2007). Hwang and Chen(2000)found that tidal aliasing had the largest error over the continental shelf and the least error in the deep basin. Thus, we chose our study area in the SCS bordered by the 200-m isobaths(shaded area in Fig. 1). Since some eddies could generate and pass into or out of our study domain, which will lead to bias in the generation and termination statistics, we therefore chose an area larger than our study area for eddy detection, as shown in Fig. 1(106°-122°E, 5°-25°N).

The Cross-Correlated Multi-Platform(CCMP)Ocean Winds dataset produced by NASA was also used in our study. This dataset was derived under the CCMP project and contains a value-added monthly mean ocean surface wind and pseudo stress to approximate a satellite-only climatological data record. The CCMP datasets combine cross-calibrated satellite winds obtained from Remote Sensing Systems(REMSS)using a Variational Analysis Method(VAM)to produce a high-resolution(0.25°)gridded wind analysis. The CCMP dataset included cross-calibrated satellite winds derived from SSM/I, SSMIS, AMSR-E, TRMM TMI, QuikSCAT, SeaWinds, WindSat and other satellite instruments.

2.2 Method

An eddy detection scheme based on velocity vector geometry proposed by Nencioli et al.(2010)was adopted to identify eddies in the SCS. In this method, an eddy is defi ned as a fl ow feature where the relative velocity vectors rotate around a center of minimum speed and the geometry of velocity vectors satisfy the following four constraints:

1. Along an east-west section, v had to reverse in sign across the eddy center, its magnitude had to increase away from it, and its magnitude had to increase a point away in both eastward and westward directions;

2. Along a north-south section, u has to reverse in sign across the eddy center, its magnitude had to increase a point away in both southward and northward directions: the sense of rotation had to be the same as for y ;

3. At the eddy center, velocity magnitude had a local minimum within the region that extended to b grid points around it;

4. Around the eddy center, the directions of the velocity vectors had to change with a constant sense of rotation, and the directions of two neighboring velocity vectors had to lay within the same or two adjacent quadrants(the four quadrants are defi ned by the north-south and west-east axes. The fi rst quadrant encompassed all the directions from east to north; the second from north to west; the third from west to south; and the fourth from south to east).

The points that meet the above conditions were identifi ed as eddy centers(Nencioli et al., 2010). After eddy centers were identifi ed, the boundary of eddies were defi ned by the outermost closed streamline around the eddy center, which is different from the defi nition by Nencioli et al.(2010)who defi ned the closed streamline with maximum current speed around the center as the boundary. Because such streamlines do not always exist and are thus unstable, such as for weak eddies or eddies at their generation or termination stage, we chose the outermost closed streamline around the eddy center to be the eddy boundary.

We found that linearly interpolating the velocity fi eld before analysis signifi cantly improved the SDR of detection. The SDR and EDR were mainly affected by three parameters: a, and b, and the number of grid points after interpolation. Parameter a defi nes how many grid points away from the increases in magnitude of v along the east-west axes, and u along the north-south axes, are checked. Parameter b defi nes the dimension(in grid points)of the area used to defi ne the local minimum of velocity(Nencioli et al., 2010). The SDR can be greatly improved when the data is interpolated into much smaller grids. Although changing the parameters a and b, and the interpolation can also lead to a change in EDR, the change is insignificant.

Result showed that, without interpolation, the maximum SDR of the detection was 40% when a=2 and b=1 and the EDR is 1.6%. Velocity fi elds were linearly interpolated between every element into a 1/8°×1/8° grid and the maximum SDR became 76.7% when a=3, b=1-2 and the EDR is 3.3%. After interpolating recursively twice, the velocity fi eld became a 1/16°×1/16° grid and the maximum SDR was 98.3% when a=3-4 and b=1-3 and the EDR was 5%. From these results, we see that the SDR was mainly dependent on the frequency of interpolation.

Before applying the detection method, AVISO velocity fi elds were linearly interpolated into a 1/16°×1/16° grid and we chose parameters a=4, b=3 to get an averaged SDR of 98.3% and a EDR of 5%. An example of an eddy detected using AVISO data after interpolation is shown in Fig. 2.

We also enhanced the tracking method. In the study of Nencioli et al.(2010), eddy tracks were determined by comparing the centers at successive time steps. The track of a given eddy at time step t was updated by searching for eddy centers of the same type(cyclonic/anticyclonic)at time t+1 within a square search area centered around the eddy location at time t .

The dimensions of the search area were derived from multiplying the average current speed by the dataset sampling period(Nencioli et al., 2010). However, in our case the dataset sampling period was 1 week, which was much longer than the 1 day used in Nencioli et al., (2010). Thus, the search area was too large to reduce the accuracy of the eddy tracking. We used distance D to refl ect the relevance of two eddies(Penven, 2005). The nondimensional distance D was defi ned as

where ΔD is the spatial distance between two eddies, ΔR, Δξ, and ΔEKE are the radius, the vorticity and the EKE variations, respectively. D₀, R₀, ξ₀, and EKE 0 are the characteristic length scale(D₀ =100 km), characteristic radius(R₀ =50 km), characteristic vorticity(ξ₀ =10 - 6 /s) and characteristic EKE(EKE₀ =100 cm² /s²), respectively(Chaigneau et al., 2008). The minimized D reflects the maximum degree of similarity between two eddies. Thus, in our tracking method, we selected the eddy pair with the same rotation sense in successive time steps that minimized D, and considered this pair to be the same eddy that is tracked from t to t +1, within an area centered around the eddy location at time t . We found that when choosing the size of the search area proportional to each eddy size at time t, the tracking accuracy was higher than the method used by Nencioli et al.(2010).

3 RESULT3.1 Eddy size, vorticity and lifetime

The total number of eddies with a radius larger than 50 km detected in the SCS from January 1993 to May 2014 was 20 967, including 10 561 cyclonic eddies and 10 406 anticyclonic eddies. However, this number included repetitions of the same eddy over multiple time steps. If one eddy was detected only once during its existence, the number of tracks, which is equal to the number of eddies, was obtained and stored. Therefore, the total number of individual eddies detected was 3 425: including 1 727 cyclonic eddies and 1 698 anticyclonic eddies. There were approximately 1% more cyclonic eddies than anticyclonic eddies. Eddy size distribution is shown in Fig. 3, with a peak at 60 km for both cyclonic eddies and anticyclonic eddies. The mean size of cyclonic and anticyclonic eddies was 84.8 km and 85.3 km, respectively. Eddy vorticity within an eddy varied from its center(theoretically, the magnitude of the vorticity is maximal at the center)to its boundary. The vorticity of an eddy is defi ned as the maximum vorticity value in the area within the eddy boundary(Nencioli et al., 2010). In Fig. 3, the histogram of normalized eddy vorticity(eddy vorticity comparing with the earth rotation)peaks at 0.032 for both cyclonic eddies and anticyclonic eddies, with mean values of 0.044 for cyclones and -0.041 8 for anticyclones. Cyclonic eddies were a little stronger than anticyclonic eddies. The distribution of eddy lifetime is also shown in Fig. 3. The mean lifetime for cyclonic eddies was 8.3 weeks and 8.5 weeks for anticyclonic eddies. Anticyclonic eddies survived longer than cyclonic eddies.

An eddy’s lifetime can be divided into three stages: the young stage, mature stage and aged stage. Both eddy size and vorticity grow during the fi rst 1/5 of an eddy’s lifetime(young stage)to reach a maximum value and stay stable for the next 3/5 of its lifetime(mature stage), then decay in the last 1/5 of its lifetime(aged stage)(Liu et al., 2012). Figure 4 shows the relationship between the maximum vorticity and size of an eddy in the mature stage and its lifetime. The results show a slight increase in both eddy vorticity and size with lifetime, when eddy lifetime is shorter than 20 weeks. It indicates that eddies with longer lifetimes have a tendency to reach higher vorticities and size. Further, eddies with higher vorticities or size have more opportunity to survive longer, because their EKE is more likely to be higher and need more time to dissipate. In Fig. 4, there were not enough eddies with lifetimes longer than 20 weeks, thus the relationship of eddy vorticity or size with eddy lifetime could not be determined.

When an eddy was at its second stage, at which both vorticity and size reached their maximum values and remained stable, the relationship between the eddy’s vorticity and its size was unknown. Figure 5 shows the distribution of the maximum and mean normalized vorticity against the maximum size of an eddy. Both results show that an eddy’s vorticity was not dependent on its radial distance.

Seasonal distributions of eddy number are shown in Fig. 6. The number of both cyclonic and anticyclonic eddies varied seasonally. Cyclonic and anticyclonic eddies showed an anti-phase seasonal variation. There were 5 031 cyclonic eddies and 5 573 anticyclonic eddies detected in the spring(Mar. to May) and summer(Jun. to Aug.), and 5 530 cyclonic eddies and 4 833 anticyclonic eddies in the autumn(Sep. to Nov.) and winter(Dec. to Feb.). Thus, anticyclonic eddies were more likely to occur in the spring and summer, with more cyclonic eddies in the autumn and winter. This is probably related to seasonal variations in the SCS circulation caused by monsoonal winds, which will be discussed in the next section.

Figures 7 and 8 show seasonal variations of eddy size and normalized eddy vorticity, respectively. In Fig. 7 anticyclones showed an oscillating size distribution with maximum sizes in the spring and autumn, while cyclone size peaked in the autumnwinter. In Fig. 8, eddy vorticity in cyclones was greatest in the autumn, while anticyclones showed lower values in the spring. Moreover, their distributions were more related to the topography of the SCS. Figures 9 and 10 show the spatial distribution of eddy size and normalized vorticity, respectively. At each grid point, the mean size and normalized vorticity of eddies whose centers were once located in the point have been calculated. The grid was 0.625×0.625 degrees. The spatial distribution of eddy size(Fig. 9)shows that eddies were larger in the center of the study area, which may be ascribed to the deep basin. The st and ard deviation of eddy size divided by mean eddy size is shown in Fig. 9. The st and ard deviation was also large in the areas with larger eddy sizes, which suggests a high degree of discretization. In Fig. 10, there is a major peak in eddy vorticity distribution in the area southwest of Luzon. In addition, in the east of Vietnam, the eddy vorticity was higher than in the surrounding areas. This may be caused by the northeast winter monsoon producing high positive and negative wind stress curl in the southwest of Luzon, and the southwest summer monsoon causing a high positive wind stress curl in the east of Vietnam.

3.2 Eddy generation and termination

Determining where and when most eddies were generated and terminated will help us to underst and the mechanisms of eddy formation and dissipation. We defi ned the fi rst(last)record in the time series of each eddy lifetime as the eddy generation(termination). Figure 11 shows the trajectory of eddies with lifetimes equal to or longer than 5 weeks from Jan 1993 to May 2014.

Seasonal variations in eddy generation are shown in Fig. 12. The generation of eddies showed no clear seasonal variation. However, in Fig. 6, more anticyclonic eddies were detected in the spring and summer, and more cyclonic eddies were found in the autumn and winter. The reason for the differences between the seasonal variation in eddy number and eddy generation is that anticyclonic eddies tend to survive longer in the spring and summer, while cyclonic eddies have longer lifetimes in the autumn and winter.

The distributions of eddy generation(termination)with latitude and longitude are plotted in Fig. 13. Eddy generation(termination)is bimodal(trimodal)with longitude. The westward movement of eddies means that the peaks of the termination curve was at a lower longitude than those of the generation curve. The zonal distribution shows two high interval regions of eddy generation and termination for cyclonic and anticyclonic eddies. One of the two peaks of termination was between 18°N and 19°N and the other was located around 13°N. The generation peaks are a little further north than the termination peaks, which can be ascribed to the westward movements of eddies that is more likely to be southward than northward(Fig. 14).

Figure 14 shows the statistical distribution of eddy propagation directions. It was noted that both anticyclonic and cyclonic eddies move westward and slightly southward under the impact of the Beta effect(Cushman-Roisin et al., 1990; Morrow, 2004; Tajima and Nakamura, 2005).

4 DISCUSSION

Previous studies have shown that wind is the driving force of the SCS circulation(Hwang and Chen, 2000). Monsoon surges likely represent a robust forcing mechanism for oceanic eddy formation and propagation in the SCS(Pullen et al., 2008). Wang et al.(2008)concluded that the SCS circulation is largely driven by the East Asian monsoons, and wind stress curls associated with jets through the isl and gaps can spin up cyclonic and anticyclonic eddies on the two sides of each jet. To determine the impact of wind on the SCS, we obtained the wind stress over the SCS from the CCMP wind dataset. Both wind stress and wind stress curl contributed to variations in the SCS circulation, but each had different degrees of contribution at different frequencies. The SCS circulation is largely cyclonic in winter and anticyclonic in summer, because of the monsoons(Hwang and Chen, 2000). Figure 15 shows the 19-year averaged SSHA and the monthly circulations of the SCS from Jan. 1993 to Dec. 2011. The 19-year averaged wind stress vectors from Jan. 1993 to Dec. 2011 are shown in Fig. 16. On average, the northeasterly winter monsoons began in October and ended in March. The southwesterly monsoons began in June and ended in August. April and May were the transition periods in the spring. September was the transition period in the autumn, which is shown in Fig. 16. Figure 17 shows the mean wind stress vectors, the SSHA and the averaged circulation in the summer monsoon period and the winter monsoon period. In Fig. 17, the north of the SCS was cyclonic in the winter and anticyclonic in the summer. The inter-annual and seasonal variations of the SSHA are shown in Fig. 18. The original inter-annual variation was analyzed by a technique called Singular-Spectrum Analysis(SSA), which is a form of principal-component analysis applied to lagcorrelation structures of uni- and multivariate time series. SSA decomposes a time series by dataadaptive fi lters into oscillatory, trending, and noise components, and generates statistical signifi cant information on these components. The signifi cant components of the inter-annual variation of SSHA are shown in Fig. 18a(red line). The seasonal variations were calculated, based on the signifi cant component of inter-annual variation in the SSHA(Fig. 18b). The seasonal variation of SSHA was the lowest in April. It then began to rise during the spring transition period and the summer monsoon months from May to September, reached a peak in October and then declined in the winter monsoon months from November to March. These trends were associated with the seawater fl ow into or out of the SCS caused by the alongshore currents east of Vietnam. Hwang and Chen(2000)concluded that the alongshore currents east of Vietnam were in complete accordance with wind stress, which can be also seen in Figs.15 and 16 in our study. Therefore, we speculated that the alongshore currents east of Vietnam bring sea water into the SCS under the impact of the summer monsoon wind stress and raises the mean SSHA of the SCS; winter monsoon wind stress drives the sea water fl ow out of SCS and the mean SSHA of SCS begins to drop.

5 SUMMARY

A highly accurate, automatic eddy detection method was used to obtain the statistical eddy dataset, which includes spatial and temporal information on eddy generation, termination, propagation, and on a broad range of eddy characteristics parameters in the SCS. The geometry-based eddy detection scheme proposed by Nencioli et al.(2010)was applied to the geostrophic current to locate eddies.

Anticyclonic eddies and cyclonic eddies were equally distributed in the SCS. After removing repeatedly counted eddies, there were 1% more cyclonic eddies than anticyclonic eddies. Cyclonic eddies were found to be a little stronger than anticyclonic eddies, and anticyclonic eddies were larger and survived longer than cyclonic eddies. Both eddy size and vorticity distribution showed no obvious changing regularity with time variation. However, their distribution was more related to the topography of the SCS. The relationship among size, vorticity, and lifetime of eddies was: eddies with longer lifetimes had a tendency to reach a greater vorticity and size; and eddies with greater vorticity or size had more opportunity to survive longer. However, the eddy’s vorticity had no clear dependence on its size. After their generation, both anticyclonic and cyclonic eddies moved westwards under the impact of the Beta effect. Anticyclonic eddies tended to survive longer in the spring and summer, while cyclonic eddies had longer lifetimes in the autumn and winter, which is related to the seasonal circulation caused by monsoons. Anticyclonic circulation in the summer monsoon period favors the sustentation of anticyclonic eddies, while cyclonic circulation in the winter monsoon period helped to maintain cyclonic eddies.

Aside from this statistical analysis of mesoscale eddies in the SCS, detailed dynamic forcing processes of mesoscale eddies remain largely unknown. Future studies should focus on eddy dynamics, such as the three-dimensional dynamic structure of eddies and eddy characteristics in the vertical transfer of energy, physical substance, nutrients and dynamics of eddy development, sustenance, and dissipation.(Hu et al., 2011; Lin et al., 2013).

6 ACKNOWLEDGMENT

Altimeter data was obtained from the AVISO website, and the wind product data were obtained from the Remote Sensing Systems.