2 College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China;
3 PLA Naval Submarine Academy, Qingdao 266199, China
Mesoscale eddies are universal features that widely occur in the ocean, play important roles in ocean circulation, such as heat, salinity, and materials transport, and affect global climate change (Chelton et al., 2007; Johnson and McTaggart, 2010; Chelton et al., 2011; Gruber et al., 2011). The effects of these eddies on the vertical mixing of seawater have implications for marine productivity and biochemical processes (Dong et al., 2014; Zhang et al., 2014; Faghmous et al., 2015).
The Kuroshio Extension (KE) is a zonal band of strong eddy activity caused by the instability of the Kuroshio after the jet leaves the restraining coastal area and flows into the open ocean (Miyazawa et al., 2010; Ma et al., 2015, 2016). Using sea level anomaly (SLA) and sea surface temperature (SST) data, sea surface mesoscale eddies in the KE region are detected, and the results show that anticyclonic (cyclonic) eddies with strong kinetic energy and amplitude dominate the north side (south side) of the Kuroshio path and mainly move westward (Ebuchi and Hanawa, 2001; Qiu and Chen, 2010; Hu et al., 2018).
Over the last decade, mesoscale eddies have been extensively investigated using satellite observation data (Chelton et al., 2007, 2011; Mason et al., 2014; Liu et al., 2016). Several different surface eddy detection schemes have been published, e.g., the Okubo-Weiss (OW) method (Okubo, 1970; Weiss, 1991; Isern-Fontanet et al., 2010; Itoh and Yasuda, 2010), the winding-angle (WA) method (Chaigneau et al., 2008; Chelton et al., 2011), the vector geometry (VG) method (Nencioli et al., 2010), and the sea level anomalies (SLA)-based method (Chelton et al., 2011, Mason et al., 2014; Faghmous et al., 2015; Liu et al., 2016). Compared with OW, WA, and VG methods, SLA-based method presents the best performance and can avoid extra noise and excess eddy detections (Chaigneau et al., 2008; Nencioli et al., 2010), and is widely used to analyze the characteristics of eddies (Xiu et al., 2010; Chelton et al., 2011). There are several eddy tracking methods such as the similarity method (Penven et al, 2005), which is based on the physical properties of eddies; the nearest neighbor method, which finds the closest eddy center (Doglioli et al., 2007; Xiu et al., 2010; Chelton et al., 2011); and the hybrid tracking method, which is based on both the physical and geometric properties of eddies (Sun et al., 2017).
However, due to a lack of observations, our understanding of the structure of mesoscale eddies and their impact on heat and salt transports has been rather limited. Based on measurements in the interior provided by shipboard observations, case studies have preliminarily revealed the structure of some individual three-dimensional (3-D) eddies (Johannessen et al., 1989; Chu and Fan, 2001; Dong et al., 2009; Hu et al., 2011; Zhang et al., 2016). With altimeter and in situ data, composite analyses of subsurface mesoscale structure have been performed in global and regional studies. Zhang et al. (2013) found that mesoscale eddies have a universal 3-D structure in the global oceans. Yang et al. (2013) explored the 3-D eddy structure and showed that it varied with distance from the coast in the Northwestern Subtropical Pacific Ocean. Itoh and Yasuda (2010) and Sun et al. (2017) revealed the vertical structure of eddies in the KE region. By combining underwater glider data and SLA data, Li et al.(2019, 2020) constructed the detailed 3-D structure of an anticyclonic eddy (AE) in the northern South China Sea (SCS) and indicated the effectiveness and optimal configuration of the underwater glider network.
Argo and shipboard observations provide measurements at the subsurface, but they are sparse and have limited depth ranges. However, numerical modeling provides output in high horizontal and vertical resolution and can be a good proxy for obtaining detailed 3-D eddy structures. Using VG and nearest neighbor tracking, Dong et al. (2012) and Lin et al. (2015) constructed the 3-D eddy structure of the Southern California Bight (SCB) and SCS such as bowl, lens, and cone shaped with the high-resolution Regional Ocean Modeling System (ROMS) model output. Xia et al. (2016) used a high-resolution wave-tide-circulation coupled model to identify a warm eddy in winter in the northern SCS and analyzed its 3-D structure. Wang (2017) calculated the 3-D structures of ocean eddies in the Western Tropical Pacific with Ocean General Circulation Model for the Earth Simulator (OFES) data and revealed their typical characteristics and possible dynamic explanations area.
Although several methods have been used to reconstruct the 3-D structure of mesoscale eddies, the trajectory characteristics of 3-D eddies remain unclear. In this study, we proposed a method for identifying and tracking 3-D eddies based on high-resolution numerical products and apply this method to analyze the 3-D eddy tracking trajectory and hydrographic features in the KE region. The rest of paper is organized as follows. Section 2 briefly describes the data and methods used for 3-D eddy identification and tracking. Section 3 first validates the model performance in terms of the 5-year mean temperature/salinity profiles and surface eddy identification result and then shows the preliminary results from the application of the algorithm to Hybrid-Coordinate Ocean Model (HYCOM) Ocean Reanalysis datasets in KE region. Section 4 discusses the 3-D eddy structures and the temperature and salinity anomaly characteristics of four eddies. Section 5 presents a final summary.2 MATERIAL AND METHOD 2.1 Data
HYCOM Ocean Reanalysis data is available every day with a 1/12.5°×1/12.5° resolution and 40 levels in the vertical direction (http://ncss.hycom.org/thredds/catalogs/GLBu0.08/expt_19.1.html). The HYCOM assimilates available satellite altimeter observations and in situ SST as well as available in situ vertical temperature and salinity profiles from expendable bathythermographs (XBTs), Argo floats, moored buoys, and so on (Cummings, 2005; Cummings and Smedstad, 2013). We use the HYCOM data from January 2008 to December 2012 to identify and track 3-D eddies in the KE.
The Copernicus Marine Environment Monitoring Service (CMEMS) provides regular Global Ocean multiple altimeter satellite grid data, a merged product of Jason-3, Sentinel-3A, HY-2A, SARAL-AltiKa, CryoSat-2, Jason-1/2, T/P, Enivsat, GFO, and ERS-1/2 altimeter observations (http://marine.copernicus.eu/). The daily product has a spatial resolution of 1/4°×1/4° used to identify eddies at the surface in the KE region.2.2 Three-dimensional eddy identification and tracking method 2.2.1 Three-dimensional eddy identification method
Step 1: two-dimensional eddy identification
In this paper, eddy identification is based on pressure anomalies, P(x, y, z, t) and P(x, y, z) are calculated based on sea surface height (SSH) and average sea surface height (SSH), respectively (Zhang et al., 2013; Schlax and Chelton, 2016), Pa(x, y, z, t), obtained by the removal of the monthly mean pressure P(x, y, z) from the pressure P(x, y, z, t) at each depth level. Zhang et al. (2013) and Schlax and Chelton (2016) pointed out that subsurface pressure anomalies fields can be used to identify the 3-D eddies and the 3-D structure of ocean eddies can be expressed separately as horizontal and vertical components. In addition, pressure anomalies reflect the comprehensive influence of the three hydrological characteristics (temperature, salinity, and depth).
where g is the gravitational acceleration, ρθ is the ocean potential density and x, y, z (z < 0), t represent longitude, latitude, depth, and time, respectively.
First, to remove unrelated large-scale signals, individual pressure anomaly fields (Pa) at different depths are spatially high-pass filtered with a zonal (meridional) major (minor) radius of 10°(5°) (Chelton et al., 2011). Then, we search for the local maximum and minimum of Pa as centers of possible AEs and cyclonic eddies (CEs) in the study area. Criteria similar to that of Chelton et al. (2011) are used here to further determine whether these eddies are effective, and an eddy is confirmed if there is one center and 36–5 000 interior pixels embedded within the closed contour (Liu et al., 2016). The outermost closed pressure anomaly contour meeting these criteria is the eddy boundary (Ceff). The center location of each identified eddy is defined to be the centroid of Ceff within the outermost closed pressure anomaly contour (Chelton et al., 2011; Mason et al., 2014; Liu et al., 2016). The area, A, is the set of pixels enclosed by Ceff; the radius of the eddy is obtained by R=sqrt(A/π); and the amplitude (amp), is defined by amp |Pab-Pac|, where Pab and Pac are the pressure anomalies at the eddy boundary and eddy center, respectively.
Step 2: three-dimensional eddy construction
We use the algorithm described in Step 1 of Section 2.2.1 to detect eddies at all 35 levels from surface to -1 500-m depth and obtain the eddy's location, type, radius, and occurrence time. The 3-D eddy construction in this paper uses the area overlapping method. Supposing that an eddy has enough overlapping area between the two neighboring levels, we start at the surface and move downward to the next level with the same type and same occurrence time to search for eddies meeting the threshold of overlapping area. If the eddy can be found at the next level, we use this level's eddy information to search the next level until reaching the bottom level (-1 500 m). If the eddy cannot be found at a given level, for example, searching downward from -500 to -550 m, and no eddy is found at -550 m, we continue to search down to find whether there is an eddy that meets the area overlap until it is not found even at the bottom layer, and we conclude that this eddy's maximum depth is -500 m.
As shown in Fig. 1, eddy E1 (area S1) is indicated by a black closed contour in the depth 0 layer, and two eddies, E2 (area S2) and E3 (area S3), are represented by red and green, respectively, in the depth 1 layer. To determine the similarity among E1, E2, and E3, we intersect the domains of depth 0 and depth 1 as depth 0–1 with the overlapping area (blue region) S12. We calculate the following ratios:
By analyzing the 3-D eddy construction results with different critical values, we choose the critical value ratioc of 2/3 to determine whether adjacent depth eddies belong to the same 3-D eddy. According to the study of dynamic eddy tracking model, Li et al. (2016) pointed out that a ratioc that is very small will lead to a risk of jumping from one eddy to another, and a ratioc that is too large will lead to a risk of missing eddies. If ratio1 > ratioc or ratio2 > ratioc, we consider E1 and E2 to be the same 3-D eddy; otherwise, they are not the same. By implementing this algorithm, we can obtain a discrete 3-D eddy dataset including each eddy's type, occurrence time, depth, radius, and location.
Step 3: three-dimensional eddy centroid calculation
We define the 3-D eddy centroid to represent the eddy and use it for 3-D eddy tracking. The centroid of the 3-D eddy is calculated by equating it to multiple circular truncated cones according to its different depths. As shown in Fig. 2, there is a hypothetical eddy E1 extending from the surface layer h1 to the bottom layer h4, which can be equivalent to the three circular truncated cones A, B, and C from top to bottom. Taking A as an example, R1(R2) and C1(C2) are defined as the eddy radius and center of E1 at depth h1(h2), respectively. The centroid coordinate vector of A is expressed as r1=(x, y, z), where x, y, and z are the longitude, latitude, and surface-based depth of r1, respectively. The formula is as follows:
where lonC1 (lonC2) is the longitude of C1(C2) and latC1 (latC2) is the latitude of C1(C2).
We calculate the centroids r2 and r3 of the circular truncated cones B and C in the same way. Then, the centroid rσ of E1 is calculated according to the following formula:
where mi and ri are the mass and centroid of the equivalent circular truncated cone, respectively, and i=1, 2, 3 represent the circular truncated cones A, B, and C, respectively.2.2.2 Three-dimensional eddy tracking method
The nearest neighbor method is used in the paper to track the 3-D eddy. The method is based on the 3-D eddy centroid rσ which is analogous to the method proposed by Doglioli et al. (2007) and Chelton et al. (2011) for sea surface eddies.
Three-dimensional eddy tracks are determined by comparing the centroids at successive time steps, starting from the first day. E(i, t) is the ith eddy detected at time step t with corresponding 3-D centroid (x(i, t), y(i, t), z(i, t)). We search for eddy centroids of the same type (AE or CE) at the next time step t+1 within this spatial horizontal search region S. If no centroids are detected within the region at t+1, the eddy is considered dissipated. If more than one eddy of the same type is detected in the searching region, we choose the eddy whose depth is closest to the depth z(i, t) of E(i, t) as the same eddy. Assuming E(j, t+1) is the same eddy observed on day t+1, the trajectory of E(i, t) is updated to E(j, t+1). In most cases, there is only one eddy in the selected search area. For a few cases where there are multiple eddies, we believe that the depth of eddy centroid will not change too much during its existence-time. The minimum depth difference is used as the nearest neighbor criterion, which may indeed lead to classification errors or omission errors of the eddy tracking trajectory (Doglioli et al., 2007).
We carry out this tracking process for CEs and AEs separately. We define the spatial horizontal search region S as a circle with a radius of 0.5° to reduce the likelihood of jumping from one eddy track to another (Liu et al., 2016).3 RESULT
We apply the 3-D eddy identification and tracking method to the KE region (25°N–45°N, 150°E–165°E), which is shown as the red rectangle in Fig. 3, with the color denoting the SLA after processing with a zonal (meridional) radius of 10°(5°) via high-pass filtering of the HYCOM data on December 1, 2012.
The mean temperature and salinity of the 2008– 2012 HYCOM data in a cross section (lon.=157.52°E and lat.=35°N) passing the study area are shown in Fig. 4. Figure 4a–b show the zonal temperature and salinity profiles, respectively, at 157.52°E. Figure 4c–d show the meridional temperature and salinity profiles, respectively, at 35°N. The results show that the zonal temperature and salinity contour have an obvious trend of a northeast to southwest direction, and the meridional temperature and salinity contour slopes down slightly from east to west. The section of mean temperature and salinity hydrological characteristics in the KE region based on the HYCOM data are similar to the results obtained by Dong et al. (2017) using remote sensing and experimental observation data.
To further confirm the reliability of the HYCOM data, the surface eddies (Fig. 5b) identified on December 1, 2012 via the HYCOM were compared with the results of the CMEMS data (Fig. 5a). Thirtynine eddies were identified based on the CMEMS data, including 17 AEs and 22 CEs, and 58 eddies were identified based on the HYCOM data, with 31 AEs and 27 CEs. Thus, the number of eddies obtained based on the HYCOM data is greater than that obtained using the CMEMS data. In terms of distribution position, most eddies determined according to the two datasets basically correspond to each other, especially those on both sides of the main axis of the Kuroshio current, and certain differences are observed in some small positions. However, the sizes of eddies identified by the HYCOM data at the corresponding position are slightly smaller than the sizes identified using the CMEMS data. The comparison reveals that the surface eddies obtained using the two datasets are generally consistent, further verifying the reliability of the HYCOM data for eddy research.
To demonstrate the performance of the 3-D eddy detection and tracking method, we apply the algorithm to the KE region using the 2008–2012 HYCOM data. Table 1 shows the number of detected and tracked 3-D eddies. The number of detected AEs was greater than that of CEs. In contrast, there were slightly more tracked CEs than AEs. This finding is consistent with the results of the identification and tracking of surface eddies in the KE region by Hu et al. (2018). The 3-D eddies tracked in this paper are relatively short. We define the time when the eddy is in the study area as its existence-time. The longest existence-time of an AE is 110 days, and the longest existence-time of a CE is 74 days. Table 2 shows the number of 3-D eddy trajectories with different existence times. According to the analysis, the eddies with an existence-time of less than 1 week accounted for approximately 82.03% of the total number of eddies, and the number of CE trajectories was slightly greater than the number of AEs. There were more AEs than CEs with an existence-time of longer than 1 week. As the existence-time increased, the number of eddies decreased dramatically.
The reason for the short eddy existence-time in this paper may be that the 3-D eddy tracking process is based on the 3-D eddy centroid, which limits its differences in horizontal position and vertical depth, thereby increasing the likelihood that the eddy trajectory will fracture. In addition, some eddies may come from outside the study area, while some eddies may move outside the study area, so eddies exist in the study area for a relatively short amount of time.
To clarify the 3-D eddy tracking results proposed in this study, we took two eddies as examples. We detected an AE with an existence-time of 69 days from August 24 to October 31, 2008 (Fig. 6). Its tracking trajectory and the variation of maximum depth are shown in Fig. 6a, with the blue-circled purple dot denoting the trajectory starting point. The eddy exhibited a tendency to move westward and slightly toward the equator, and there was a certain jump in depth. During its existence-time, the maximum depth remained unchanged at -1 500 m, and there was also a tendency to move westward, which is consistent with the track characteristics. The structure of the eddy changes with time as shown in Fig. 6b–i. Compared to the generation and development stages, the structure of the eddy becomes weaker and smaller until it disappears. Quantitative analysis shows that the eddy moved approximately 1.697° longitude west and approximately 0.743° latitude south. The trajectory depth changed 158.93 m, from -670.05 m to -828.98 m. The maximum depth trajectory moves about 1.721° to the west and 0.745° to the equator, with the same depth.
Another example is the 3-D CE shown in Fig. 7. Its existence-time was 61 days, from August 25 to October 24, 2010. Similarly, Fig. 7a shows its trajectory and maximum depth trajectory variation, with the red-circled cyan dot denoting trajectory starting point. The 3-D eddy trajectory and maximum depth trajectory generally show a trend of moving westward to southward. Its structure changes over time as shown in Fig. 7b–h. Quantitative analysis shows that the CE moved approximately 1.943° longitude west and approximately 0.449° latitude south. It spanned 301.21 m in depth. The maximum depth trajectory moves 1.930° west and 0.432° south at -1 500 m.4 DISCUSSION
As we all know, eddy has three 3D structures, bowl-shaped, in which the eddy radius is largest size at the surface; cone-shaped, in which the eddy radius is largest size at the bottom, and lens-shaped, in which the eddy radius is largest in the stratification layer (Dong et al., 2012; Lin et al., 2015). We found that there is a cylindrical shaped eddy, in which the eddy radius is consistent at almost all depths. Table 3 shows the numbers of the four types of eddies. Most eddies (71.18%) are lens-shaped, 12.30% are cone-shaped, 5.04% are bowl-shaped, and 11.48% are cylindrical shaped. Examples of the four types of eddy shapes are presented in Fig. 8, and their associated hydrographic (temperature and salinity) and current field variables are plotted in Fig. 9.
The centroid of the bowl-shaped CE was near 164.29°E, 28.93°N at -715.84 m on April 16, 2008. No footprint of the eddy can be seen at the sea surface. It was generated near the bottom -200 m and extended to -1 250 m. At the eddy surface at a depth of -200 m, its maximum radius was 48.23 km. The vertical temperature anomaly profile of this bowl-shaped eddy is shown in Fig. 9a. Negative anomalies were present in the internal temperature of the eddy. From the surface down, the anomaly value increased rapidly, and it gradually decreased after reaching the maximum. The maximum value of negative temperature anomalies in the zonal section was 1.19 ℃ at a depth of approximately -500 m. The temperature anomalies distribution was asymmetric, and the isotherms were shallower on the west than on the east of the eddy. Compared with the more uniform negative temperature anomaly distribution, the salinity anomaly distribution of the eddy shows obvious stratification as shown in Fig. 9b. The interior of this CE exhibited a salinity anomaly distribution with opposite levels of "negative-positive" and the negative and positive transition point of outliers was located at a depth of approximately -800 m. The maximum value of the negative (positive) salinity anomaly in the upper (lower) layer was 0.158 (0.032). Figure 9c shows the meridional current field (v) distribution of the bowl-shaped CE. The velocity on the west and east boundaries of the eddy are positive and negative, respectively, and the internal velocity is mainly negative.
Figure 9d & e show the vertical temperature anomaly and salinity anomaly distributions, respectively, of a cone-shaped AE, the centroid of which was located at 162.21°E, 33.12°N, and -815.47 m on July 25, 2010. Its maximum radius was 65.03 km at -1 500 m. The area with larger positive temperature anomalies in this AE was within the depth range of -100– -500 m. The maximum temperature anomaly was 4.4 ℃. In contrast to the bowl-shaped CE, the salinity anomalies inside this cone-shaped AE showed a "positive-negative" distribution. The conversion depth of positive and negative values was approximately -600 m. The salinity anomaly had a maximum value of 0.380 in the upper layer and a minimum value of -0.133 in the lower layer. As shown in Fig. 9f, the meridional current field distribution of this cone-shaped AE presents positive values in its internal, strong positive values in the western boundary and weak negative values in the east upper boundary part.
The third example is a lens-shaped AE with a centroid located at 153.19°E, 30.91°N, and -675.42 m on December 5, 2012, with a maximum radius of 49.82 km at -125 m. Similar to the cone-shaped AE, this AE also exhibited positive temperature anomalies inside the eddy (Fig. 9g), as well as "positive-negative" opposite salinity anomalies (Fig. 9h), but the negative salinity anomalies were relatively weak. Figure 9i shows its meridional current field distribution where velocities of the western and eastern of the eddy show strongly positive and negative at the depth of shallower than -800 m, respectively, and its internal velocities are mainly positive deeper than -800 m.
The vertical temperature and salinity anomaly distributions of a straight-cylindrical CE are shown in Fig. 9j & k, respectively. The centroid of this CE was located at 155.15°E, 35.57°N, and -749.84 m on October 16, 2011. Its radius at different depths was consistent in overall, and the maximum radius was 62.86 km. This CE showed obvious negative temperature anomalies, and the salinity anomalies were similar to those of the bowl-shaped CE in a "negative-positive" distribution. Figure 9l shows its meridional current field distribution in which its west and east boundaries show a strong negative and positive velocities, and the internal negative velocity is dominant and gradually becomes positive from west to east.
In the KE region, CEs will cause the seawater to lift up as a whole, leading the middle low brine to rise to the position of the subsurface high brine, and forming a negative anomaly of salinity within this depth range. The high salt water in the bottom layer is also elevated to the position of the low salt water in the middle layer, which causes positive salinity. Therefore, the overall distribution of salinity anomalies in the upper and lower layers of the CE is "negative-positive", while the situation of the AE is the opposite. CEs and AEs cause the current field to sink and to rise, respectively.5 CONCLUSION
This paper proposed a 3-D eddy identification and tracking method based on pressure anomalies. We applied our method to high-resolution HYCOM data and succeeded in identifying 3-D eddies and tracking their trajectories in the KE region. A 3-D eddy dataset was constructed with eddy parameters, such as the eddy size, existence-time, location, etc. In total, 1 350 CEs and 1 355 AEs were identified with existence-time greater than or equal to a week, and they accounted for 17.97% of eddies. In general, the 3-D eddies tracked in this paper had a short existence-time. The longest existence-time for cyclones and anticyclones were 74 and 110 days, respectively.
This article provides an example of a 3-D CE trajectory with an existence-time of 61 days and an AE trajectory with an existence-time of 69 days. The results show that the 3-D eddy structure changes at different times. There is a certain jump in the eddy trajectory depth, and both eddies have a tendency to move westward and toward the equator.
In additional to bowl-, cone-, and lens-shaped eddies, we found cylindrical-shaped eddies with almost consistent eddy radii across all layers. CEs (AEs) in the KE region cause significant negative (positive) temperature anomalies. The distribution of the salinity anomalies in the upper and lower layers of the CE and the AE is "negative-positive" and "positive-negative", respectively. The conversion depths of the positive and negative salinity anomalies in different eddies are also different. CEs cause the current field to sink, while AEs cause the flow field to rise. Moreover, the distribution of temperature/ salinity anomalies and the current field in eddy is also related to its 3-D structure.6 DATA AVAILABILITY STATEMENT
The HYCOM data and the altimeter data can be obtained freely from http://ncss.hycom.org/thredds/ catalogs/GLBu0.08/expt_19.1.html and http://marine.copernicus.eu/, respectively. The datasets generated and analyzed in the current study are not publicly available because they are the property of the project but are available from the corresponding author on reasonable request.7 ACKNOWLEDGMENT
The authors thank the anonymous reviewers for their thorough reviews and constructive suggestions on a previous version of this manuscript.
Chaigneau A, Gizolme A, Grados C. 2008. Mesoscale eddies off Peru in altimeter records: identification algorithms and eddy spatio-temporal patterns. Progress in Oceanography, 79(2-4): 106-119. DOI:10.1016/j.pocean.2008.10.013
Chelton D B, Schlax M G, Samelson R M, de Szoeke R A. 2007. Global observations of large oceanic eddies. Geophysical Research Letters, 34(15): L15606.
Chelton D B, Schlax M G, Samelson R M. 2011. Global observations of nonlinear mesoscale eddies. Progress in Oceanography, 91(2): 167-216. DOI:10.1016/j.pocean.2011.01.002
Chu P C, Fan C W. 2001. Low salinity, cool-core cyclonic eddy detected northwest of Luzon during the South China Sea Monsoon Experiment (SCSMEX) in July 1998. Journal of Oceanography, 57(5): 549-563. DOI:10.1023/A:1021251519067
Cummings J A, Smedstad O M. 2013. Variational data assimilation for the global ocean. In: Park S K, Xu L eds. Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. Ⅱ). Springer, Berlin, Heidelberg.
Cummings J A. 2005. Operational multivariate ocean data assimilation. Quarterly Journal of the Royal Meteorological Society, 131(613): 3583-3604. DOI:10.1256/qj.05.105
Doglioli A M, Blanke B, Speich S, Lapeyre G. 2007. Tracking coherent structures in a regional ocean model with wavelet analysis: application to cape basin eddies. Journal of Geophysical Research: Oceans, 112(C): C05043.
Dong C M, Lin X Y, Liu Y, Nencioli F, Chao Y, Guan Y P, Chen D, Dickey T, McWilliams J C. 2012. Three-dimensional oceanic eddy analysis in the Southern California Bight from a numerical product. Journal of Geophysical Research: Oceans, 117(C7): C00H14.
Dong C M, Mavor T, Nencioli F, Jiang S N, Uchiyama Y, McWilliams J C, Dickey T, Ondrusek M, Zhang H C, Clark D K. 2009. An oceanic cyclonic eddy on the lee side of Lanai Island, Hawaii. Journal of Geophysical Research: Oceans, 114(C10): C10008. DOI:10.1029/2009JC005346
Dong C M, McWilliams J C, Liu Y, Chen D. 2014. Global heat and salt transports by eddy movement. Nature Communications, 5: 3294. DOI:10.1038/ncomms4294
Dong D, Brandt P, Chang P, Schütte F, Yang X F, Yan J H, Zeng J S. 2017. Mesoscale eddies in the northwestern Pacific Ocean: three-dimensional eddy structures and heat/salt transports. Journal of Geophysical Research: Oceans, 122(12): 9795-9813. DOI:10.1002/2017JC013303
Ebuchi N, Hanawa K. 2001. Trajectory of mesoscale eddies in the kuroshio recirculation region. Journal of Oceanography, 57(4): 471-480. DOI:10.1023/A:1021293822277
Faghmous J H, Frenger I, Yao Y S, Warmka R, Lindell A, Kumar V. 2015. A daily global mesoscale ocean eddy dataset from satellite altimetry. Scientific Data, 2: 150028. DOI:10.1038/sdata.2015.28
Gruber N, Lachkar Z, Frenzel H, Marchesiello P, Münnich M, McWilliams J C, Nagai T, Plattner G K. 2011. Eddy-induced reduction of biological production in eastern boundary upwelling systems. Nature Geoscience, 4(11): 787-792. DOI:10.1038/ngeo1273
Hu D, Chen X, Mao K F, Teng J, Li Y, Peng X D. 2018. Statistical Characteristics of mesoscale eddies near the Kuroshio extension region. Oceanologia et Limnologia Sinica, 49(3): 497-511. (in Chinese with English abstract)
Hu J Y, Gan J P, Sun Z Y, Zhu J, Dai M H. 2011. Observed three-dimensional structure of a cold eddy in the southwestern South China Sea. Journal of Geophysical Research: Oceans, 116(C5): C05016.
Isern-Fontanet J, García-Ladona E, Font J. 2010. Identification of marine eddies from altimetric maps. Journal of Atmospheric and Oceanic Technology, 20(5): 772-778.
Itoh S, Yasuda I. 2010. Water mass structure of warm and cold anticyclonic eddies in the western boundary region of the Subarctic North Pacific. Journal of Physical Oceanography, 40(12): 2624-2642. DOI:10.1175/2010JPO4475.1
Johannessen J A, Sandven S, Lygre K, Svendsen E, Johannessen O M. 1989. Three-dimensional structure of mesoscale eddies in the Norwegian coastal current. Journal of Physical Oceanography, 19(1): 3-19. DOI:10.1175/1520-0485(1989)019<0003:TDSOME>2.0.CO;2
Johnson G C, McTaggart K E. 2010. Equatorial Pacific 13℃ water eddies in the eastern subtropical South Pacific Ocean. Journal of Physical Oceanography, 40(1): 226-236. DOI:10.1175/2009JPO4287.1
Li Q Y, Sun L, Lin S F. 2016. GEM: a dynamic tracking model for mesoscale eddies in the ocean. Ocean Science, 12(6): 1249-1267. DOI:10.5194/os-12-1249-2016
Li S F, Wang S X, Zhang F M, Wang Y H. 2019. Constructing the three-dimensional structure of an anticyclonic eddy in the South China Sea using multiple underwater gliders. Journal of Atmospheric and Oceanic Technology, 36(12): 2449-2470. DOI:10.1175/JTECH-D-19-0006.1
Li S F, Zhang F M, Wang S X, Wang Y H, Yang S Q. 2020. Constructing the three-dimensional structure of an anticyclonic eddy with the optimal configuration of an underwater glider network. Applied Ocean Research, 95: 101893. DOI:10.1016/j.apor.2019.101893
Lin X Y, Dong C M, Chen D, Liu Y, Yang J S, Zou B, Guan Y P. 2015. Three-dimensional properties of mesoscale eddies in the South China Sea based on eddy-resolving model output. Deep Sea Research Part Ⅰ: Oceanographic Research Papers, 99: 46-64. DOI:10.1016/j.dsr.2015.01.007
Liu Y J, Chen G, Sun M, Liu S, Tian F L. 2016. A parallel SLA-based algorithm for global mesoscale eddy identification. Journal of Atmospheric and Oceanic Technology, 33(12): 2743-2754. DOI:10.1175/JTECH-D-16-0033.1
Ma J, Xu H M, Dong C M, Lin P F, Liu Y. 2015. Atmospheric responses to oceanic eddies in the Kuroshio Extension region. Journal of Geophysical Research: Atmosphere, 120(13): 6313-6330. DOI:10.1002/2014JD022930
Ma X H, Jing Z, Chang P, Liu X, Montuoro R, Small R J, Bryan F O, Greatbatch R J, Brandt P, Wu D X, Lin X P, Wu L X. 2016. Western boundary currents regulated by interaction between ocean eddies and the atmosphere. Nature, 535(7613): 533-537. DOI:10.1038/nature18640
Mason E, Pascual A, McWilliams J C. 2014. A new sea surface height-based code for oceanic mesoscale eddy tracking. Journal of Atmospheric and Oceanic Technology, 31(5): 1181-1188. DOI:10.1175/JTECH-D-14-00019.1
Miyazawa Y, Guo X Y, Yamagata T. 2010. Roles of mesoscale eddies in the Kuroshio paths. Journal of Physical Oceanography, 34(10): 2 203-2 222.
Nencioli F, Dong C M, Dickey T, Washburn L, McWilliams J C. 2010. A vector geometry-based eddy detection algorithm and its application to a high-resolution numerical model product and high-frequency radar surface velocities in the Southern California Bight. Journal of Atmospheric and Oceanic Technology, 27(3): 564-579. DOI:10.1175/2009JTECHO725.1
Okubo A. 1970. Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences. Deep Sea Research and Oceanographic Abstracts, 17(3): 445-454. DOI:10.1016/0011-7471(70)90059-8
Penven P, Echevin V, Pasapera J, Colas F, Tam J. 2005. Average circulation, seasonal cycle, and mesoscale dynamics of the Peru Current System: a modeling approach. Journal of Geophysical Research: Oceans, 110(C10): C10021. DOI:10.1029/2005JC002945
Qiu B, Chen S M. 2010. Eddy-mean flow interaction in the decadally modulating Kuroshio Extension system. Deep Sea Research Part Ⅱ: Topical Studies in Oceanography, 57(13-14): 1098-1110. DOI:10.1016/j.dsr2.2008.11.036
Schlax M G, Chelton D B. 2016. The "growing method" of eddy identification and tracking in two and three dimensions.
Sun M, Tian F L, Liu Y J, Chen G. 2017. An improved automatic algorithm for global eddy tracking using satellite altimeter data. Remote Sensing, 9(3): 206. DOI:10.3390/rs9030206
Wang Q Y. 2017. Three-dimensional structure of mesoscale eddies in the western tropical Pacific as revealed by a high-resolution ocean simulation. Science China Earth Sciences, 60(9): 1719-1731. DOI:10.1007/s11430-016-9072-y
Weiss J. 1991. The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Physica D: Nonlinear Phenomena, 48(2-3): 273-294. DOI:10.1016/0167-2789(91)90088-Q
Xia C S, Jung K T, Wang G S, Yin X Q, Guo J S. 2016. Case study on the three-dimensional structure of meso-scale eddy in the South China Sea based on a high-resolution model. Acta Oceanologica Sinica, 35(2): 29-38. DOI:10.1007/s13131-016-0805-1
Xiu P, Chai F, Shi L, Xue H J, Chao Y. 2010. A census of eddy activities in the South China Sea during 1993-2007. Journal of Geophysical Research: Oceans, 115(C3): C03012.
Yang G, Wang F, Li Y L, Lin P F. 2013. Mesoscale eddies in the northwestern subtropical Pacific Ocean: statistical characteristics and three-dimensional structures. Journal of Geophysical Research: Oceans, 118(4): 1906-1925. DOI:10.1002/jgrc.20164
Zhang Z G, Wang W, Qiu B. 2014. Oceanic mass transport by mesoscale eddies. Science, 345(6194): 322-324. DOI:10.1126/science.1252418
Zhang Z G, Zhang Y, Wang W, Huang R X. 2013. Universal structure of mesoscale eddies in the ocean. Geophysical Research Letters, 40(14): 3677-3681. DOI:10.1002/grl.50736
Zhang Z W, Tian J W, Qiu B, Zhao W, Chang P, Wu D X, Wan X Q. 2016. Observed 3D structure, generation, and dissipation of oceanic mesoscale eddies in the South China Sea. Scientific Reports, 6: 24349. DOI:10.1038/srep24349