This study investigated the statistics of eddy splitting and
merging in the global oceans based on 23 years of altimetry data. Multicore
structures were identified using an improved geometric closed-contour
algorithm of sea surface height. Splitting and merging events were discerned
from continuous time series maps of sea level anomalies. Multicore
structures represent an intermediate stage in the process of eddy evolution,
similar to the generation of multiple nuclei in a cell as a preparatory
phase for cell division. Generally, splitting or merging events can
substantially change (by a factor of 2 or more) the eddy scale, amplitude, and
eddy kinetic energy. Specifically, merging (splitting) generally causes an
increase (decrease) of eddy properties. Multicore eddies were found to tend
to split into two eddies with different intensities. Similarly, eddy merging
is not an interaction of two equal-intensity eddies, and it tends to
manifest as a strong eddy merging with a weaker one. A hybrid tracking
strategy based on the eddy overlap ratio, considering both multicore and
single-core eddies, was used to confirm splitting and merging events
globally. The census revealed that eddy splitting and merging do not always
occur most frequently in eddy-rich regions; e.g., their frequencies of
occurrence in the Antarctic Circumpolar Current and western boundary
currents were found to be greater than in midlatitude regions
(20–35
Mesoscale eddies are large bodies of swirling water, which generally refer to ocean signals with spatial scales of tens to hundreds of kilometers and temporal scales of days to months (Robinson, 2010). Eddies are found nearly everywhere in the global oceans (Chelton et al., 2011; Cheng et al., 2014; Fu, 2009), and they dominate the ocean's kinetic energy (Morrow and Le Traon, 2012). Following recent advances in remote sensing satellites and the abundance of in situ observational data, it has been established that mesoscale eddies transport water, heat, salt, and energy as they propagate in the oceans (Dong et al., 2014; Thompson et al., 2014; Xu et al., 2011). By combining satellite altimetry and Argo profiling float data, Zhang et al. (2014) found that eddy-induced zonal mass transport was comparable in magnitude to that of the large-scale wind- and thermohaline-driven circulation, which suggested mesoscale eddies have a strong impact on global climate change and air–sea interaction. Mesoscale eddies also have an important influence on the local circulation of marginal seas, such as the South China Sea (Zheng et al., 2017), the Bay of Bengal (Cui et al., 2016), or the Mediterranean Sea (Escudier et al., 2016).
In many previous studies, eddies have been treated as independent water bodies without consideration of eddy–eddy interaction. The study on formation and dissipation of the eddies suggested that dynamic activities of the eddies are mainly due to baroclinic instabilities of the mean flow, topography effects, and fluctuating surface winds (Fu et al., 2010; Stammer and Wunsch, 1999). In fact, the eddy dynamics in the ocean are more complicated. Some studies found that an eddy's termination is attributed to many causes, including frictional decay, eddy–mean flow interaction, and coalescence with other eddies (Adcock and Marshall, 2000; Morrow et al., 1994; Trieling et al., 2005; Zheng et al., 2011). Schonten et al. (2000) monitored 20 rings which had lifetimes greater than 5 months and analyzed their traces using TOPEX/Poseidon altimetry. They found that 13 rings were generated by split-off from other rings and three rings split once, one split twice, and two even split four times. Fang and Morrow (2003) investigated characteristics of eddies in the Leeuwin Current; they found that interaction with topography can induce splitting or merging of eddies, which further affects the eddy decay. Eddies from different processes may coalesce and form a single eddy due to complicated eddy–eddy interaction (Dritschel and Waugh, 1992; Griffiths and Hopfinger, 1987; Nan et al., 2011). Zhai et al. (2010) modeled a random sea of eddies which propagate westward in the ocean, and the simulation result showed that the eddies interact with one another and cascade energy to larger scales through the merging of eddies of the same parity and finally dissipate near the western boundary.
Studies show that eddy–eddy interaction is universal within the ocean (Trieling et al., 2005; Prants et al., 2011). A very small number of studies have investigated localized eddy splitting and merging, confirming eddy variation through traditional visual interpretation of sea surface height fields (Fang and Morrow, 2003; Schonten et al., 2000). Matsuoka et al. (2016) proposed a new approach for eddy tracking and detected splitting and merging events of eddies as well as the interaction between eddies and ocean currents. Le Vu et al. (2018) presented an angular momentum eddy detection and tracking algorithm (AMEDA) for detecting and tracking eddies in the Mediterranean Sea; this procedure identified the merging and splitting events and provided a complete dynamical evolution of the detected eddies during their lifetime. Similarly, Laxenaire et al. (2018) proposed an original assessment on Agulhas rings, whose novelty lies in the detection of eddy splitting and merging events, and they found these events are abundant and significantly impact the concept of a trajectory associated with a single eddy. Such studies simply considered an eddy at one moment as a single eddy entity, which was then split into two separate eddies at the next moment, without consideration of eddy–eddy interaction processes. Although such a simplified solution can reveal the dynamic behavior of eddies, the evolutionary process remains obscure. Some studies of eddy–eddy interaction have found abundant multicore eddy structures within the global oceans (Du et al., 2014; Le Vu et al., 2018; Trieling et al., 2005; Yi et al., 2014a). Generally, multicore structures, which have two or more closed eddies of the same polarity within their boundaries, represent an important transitional stage in which the component eddies might experience splitting, merging, or other energy-transferring interactions. In studying eddy–eddy interaction processes, clear identification of multicore eddy structures is necessary.
Over the last 10 years, researchers have achieved eddy identification automatically from large remote sensing datasets and in situ datasets in many ways (Dong et al., 2011; Liu et al., 1997; Matsuoka et al., 2016; Sadarjoen and Post, 2000). Especially eddy identification and tracking from sea surface height fields has already developed maturity and has been applied to actual eddy studies (Chaigneau et al., 2008; Isern-Fontanet et al., 2003; Nencioli et al., 2010). More and more research uses a purely geometric method based on sea level anomaly (SLA) that is more accurate and is becoming more of a mainstream method in recent years (Faghmous et al., 2015; Souza et al., 2011; Sun et al., 2017). The purely geometric method for eddy identification stems from Chelton et al. (2011), and some developments and practical improvements have been made by many researchers (Cui et al., 2016; Mason et al., 2014; Schlax and Chelton, 2016). Chelton et al. (2011) recognized that their original identification algorithm can yield eddies with more than one local extremum of SLA. They attempted to separate these multiple eddies and only found extra undesirable problems in eddy tracking, so they eventually abandoned the separating procedure. Note that such multiple eddies are very common in SLA data (Li et al., 2014; Wang et al., 2015; Yi et al., 2014a); this problem can occur when eddies are physically close together.
To solve the multiple eddy problem, Li et al. (2014) employed the closest angle and the closest distance strategies to split the eddies into individual eddies with only one SLA extremum. Yi et al. (2015) presented a Gaussian-surface-based approach to identify and characterize the multicore structures of eddies from SLA datasets, and results of detecting dual-eddy structures in the South China Sea demonstrate the effectiveness of the identification approach. However, merely identifying the multicore eddy structures is not enough; tracking them based on kinematic properties through time allows us to analyze these multicore eddies as either merging or splitting, how they merge or split, and how eddies interact with each other. We believe that revealing the process of eddy splitting and merging in the ocean will have a positive effect on our knowledge about ocean mesoscale dynamic processes.
Based on SLA data acquired over a 23-year period (January 1993 to December 2015), this study used a threshold closed-contour algorithm to identify mesoscale eddies and multiple eddies within the global oceans. Multiple eddies were confirmed as multicore eddy structures through two-dimensional anisotropic Gaussian surface fitting. Based on the sequential kinematic properties of all eddies, the splitting and merging processes of eddies were analyzed. Moreover, remote sensing sea surface temperature (SST) data were used to validate the eddy–eddy interactions. The remainder of this paper is organized as follows. Section 2 describes the satellite data used, as well as the methods adopted for eddy detection and multicore eddy confirmation. Section 3 provides two examples of eddy splitting and merging, and it describes their evolutionary processes. Section 4 reports global statistics of eddy splitting and merging and highlights the average changes of eddy properties. Finally, a summary and conclusions are presented in Sect. 5.
The presence and positions of mesoscale eddies were determined by analyzing
SLA fields and merged and gridded multimission altimeter products, which are
distributed by Archiving, Validation and Interpretation of Satellite Oceanographic
data (AVISO; AVISO, 2015; Pujol et al., 2016). The daily SLA fields
with spatial resolution of 0.25
Advanced Very High Resolution Radiometer (AVHRR) SST data were adopted to validate eddies identified using the SLA fields. The AVHRR SST data comprised merged and gridded monomission products using optimal interpolation, which were provided by the National Oceanic and Atmospheric Administration (NOAA) with the same temporal and spatial scales as the AVISO gridded products. Here, to identify mesoscale variabilities in the ocean, the SST anomaly (SSTA) was constructed by removing the climatological mean and seasonal cycles.
Oceanic mesoscale eddies can generally be identified as regions enclosed by
SLA contours within which waters of unique characteristics are trapped and
subsequently transported. A purely geometric algorithm for eddy
identification based on the outermost closed contour of an SLA has been
proposed by Chelton et al. (2011). Similar to Chelton et al. (2011), we
defined a closed SLA contour and its internal grid points as an eddy when
the following criteria were satisfied:
The SLA values of all of the internal grid points were above (below)
that of the outmost closed SLA contour for anticyclonic (cyclonic) eddies. The number of internal grid points was There was at least one and at most three local maximum (minimum) points
of SLA for anticyclonic (cyclonic) eddies. The local extremum points were
seen as eddy centers. The amplitude of the eddy was at least 3 cm (Chaigneau et al., 2011; Cui
et al., 2016). The amplitude of an eddy was defined as the absolute value of
the SLA difference between the eddy center and its edge. For multiple eddies
that had more than one center, the amplitude was defined as the maximum SLA difference. The distance between the two furthest-apart internal points was less
than a specified maximum for an eddy. Maximum distance was 600 km for latitudes
below 25 The eddy edge was defined as the closed SLA contour for which rotational
speed
Note that criterion 6 was the largest difference from Chelton et al. (2011).
Chaigneau et al. (2011), Flierl (1981), and Yang et al. (2013)
suggested that the boundary of an eddy core was determined by the ratio of
rotational speed to translation speed, and that an eddy advects the interior
water with itself when the ratio is greater than 1. Although Chelton et al. (2011)
used the outermost contour as the eddy boundary, a comparison of
maximum rotational speed
Besides, for criterion 4, the minimum amplitude of an eddy was increased from the original 1 cm used by Chelton et al. (2011) to 3 cm in this study. The reason for this change was that the accuracy of measuring heights using Jason series altimeters (including TOPEX/Poseidon and Jason-1/2/3), which currently have optimal performance for observing ocean dynamics, is only about 2 cm in the open sea (Dufau et al., 2016). Therefore, even though the AVISO gridded SLA products represent the merging of data from different altimeters, it is difficult to claim that ocean signals under a variance of 2 cm could be captured precisely in the SLA fields, especially for the gaps in altimeter tracks that are interpolated from other observation points. This change avoided large, ameba-like eddy structures effectively because eddies with amplitude less than 3 cm tended to be broad and relatively flat (Cui et al., 2016; Dufau et al., 2016).
Here, the definitions of some properties for an eddy are given. Similar to
Chaigneau et al. (2008), the eddy size is represented by the eddy area
Criterion 3 requires at least one local extremum point of SLA in an eddy interior. Here, we limited the number of extremum points to one to three. Experience from experimentation has indicated that eddies with more than three extremum points are very unstable and short lived; i.e., they exhibit distinct transformation of shape within a few days. Eddies with two to three extremum points generally reflect the period of two or more eddies mixing. Multiple eddies can merge into a single entity through eddy–eddy interactions or a single eddy can split into two separate eddies under the influence of external shear or strain. The identification of multiple eddies is an essential step in studying the splitting and merging processes of eddies. Here, we needed only to identify eddies with one center, which were saved as the single-core eddies in the dataset. Multiple eddies with two to three extremum points required further processing to confirm them as a multicore eddy or as single-core eddies in close proximity.
The method of eddy identification in Sect. 2.2.1 can yield eddies with two to three local extremum points of SLA. Multiple eddies could correspond to multicore eddy structures formed because of eddy–eddy interaction and substantial interior-water exchange; however, they could also represent the misidentification of two single-core eddies because of their close spatial proximity and irregularity of the SLA contours associated with noise in the SLA fields. In the cases of two single-core eddies without substantial interaction or water exchange, the process for considering a multicore eddy is not reasonable or appropriate. Therefore, a multicore eddy structure must be identified from multiple eddies based on a certain distinguishing method.
The structure of an idealized mesoscale eddy on the sea surface can be
considered as a mathematical Gaussian shape, which is a valid and common
method for studying eddy properties and dynamics (Chelton et al., 2011;
Maltrud and McClean, 2005; Wang et al., 2015). In this study, a Gaussian
surface was adopted for fitting the multiple eddy structures to determine if
they constituted real multicore eddy structures or should be considered
separate entities. For a multiple eddy structure
Example of fitting a multicore eddy using an anisotropic two-dimensional
Gaussian kernel in the SLA field. At the bottom, the black line represents the
multicore eddy boundary, black asterisks represent the eddy centers, dots with
color represent the SLA gridded points within the eddy interior (the colors
reflect the value of the SLA), and lines with color represent the SLA contours
with 2 cm intervals. The upper two independent Gaussian surfaces,
For ideal Gaussian eddies, a certain eddy scale
Application of the eddy identification procedure and the determination method for multicore eddy structures typically detects about 2300 single-core eddies and 200 multicore eddies on average in an arbitrary SLA field globally. The number of all eddies, which is about 2500, is a little less than the number of 3000 in Chelton et al. (2011). Considering the use of criteria 4 and 6 in Sect. 2.2.1, the number is reasonable and acceptable.
Many sophisticated algorithms for eddy automated tracking have been widely
applied to determine eddy trajectory (Chaigneau et al., 2008; Henson and
Thomas, 2008). In this study, we used the same procedure as Chaigneau et al. (2008)
to track a single-core eddy. For an eddy in the initial map at time
Generally, oceanic mesoscale processes change slowly. Mesoscale eddies can exist in the global oceans for several months or even years (Chelton et al., 2011). Thus, for multicore eddy structures identified using the process in Sect. 2.2.2, it is important to examine their stability, i.e., their lifetimes. Based on fluid mechanics, a multicore structure does not represent a steady state and it will change obviously over time (Overman and Zabusky, 1982; Melander et al., 1988; Dritschel, 1995). Unsurprisingly, the lifetimes of multicore eddies are expected to be shorter than single-core eddies; however, a transient multicore structure that exists in the ocean for only a few days cannot be considered necessarily as a mesoscale process. Based on experience, in this study, only multicore eddy structures that existed for more than 6 d within a 10 d window were considered real eddy structures. In other cases, the multicore structures were considered transient turbulence signatures within the ocean and they were neglected. Without this step, there could have been a problem with the hybrid eddy tracking including both single-core and multicore eddies. For example, in the early and later stages of some eddy trajectories, the eddies could exhibit a single-core structure, whereas in the central few days (e.g., 3–4 d), the structure could be multicore. It is difficult to determine that multicore structures could have really formed in the ocean for just a few days; instead, they are more likely to correspond to misidentification of multicore eddies. In fact, here, we faced an awkward situation; a multicore eddy often has a short lifetime because of its instability, while a multicore structure persisting for just a few days cannot be seen as a real multicore eddy; i.e., multicore structures with longer lifetimes should be considered. This is why we compromised in the multicore eddy tracking. In this study, multicore eddy tracking was conducted before single-core eddy tracking and hybrid eddy tracking (discussed in the next section). Thus, the dataset of multicore eddy trajectories was obtained first.
Flowchart of the eddy tracking process.
Hybrid eddy tracking refers to single-core eddies that are independent
eddies in the daily results (not trajectories) and multicore eddy
trajectories. To match a single-core eddy and a multicore eddy (trajectory),
the tracking procedure is different and more complicated compared with that
involving just single-core or multicore eddies. The similarity principle is
inappropriate considering the significant differences in the properties
between single-core and multicore eddies, e.g., their scale or amplitude
(Fang and Morrow, 2003). In this study, the spatial attributes of the two
types of eddies were considered for the hybrid tracking, which is similar to
the neighbor enclosed area tracking algorithm used for tracking tropical
cyclones in the upper troposphere (Inatsu and Amada, 2013). If at
time
It should be reemphasized that the multicore eddy trajectories were confirmed first. In fact, in searching for the subsequent stage of a single-core eddy, multicore eddy trajectories were searched first using the hybrid tracking procedure; if no counterparts were found, then single-core eddies were searched. This way, the hybrid eddy dataset (not the eddy trajectory dataset over the entire lifetime, discussed in Sect. 4) that includes both single-core and multicore eddies is generated. Moreover, trajectories that included only single-core eddies were saved in the purely single-core eddy trajectory dataset. A flowchart of the eddy tracking process is shown in Fig. 2.
We defined the event of merging of two eddies as follows. If two single-core
eddies at time
SLA maps of eddy splitting from 1 February to 17 March 2009. Color shading represents the value of the SLA field; arrows represent the surface geostrophic velocity components calculated from the SLA; blue and red lines represent boundaries of cyclonic and anticyclonic eddies, respectively; blue and red dots represent cyclonic and anticyclonic eddy cores, respectively; and black lines represent multicore eddies. For better observing the evolution process, the time interval between two adjacent maps is not the same; in the first row, it is 5 d, the last map is after 6 d, and the other intervals are 3 d. The multicore eddy structure persisted for nearly a month before splitting.
Limited by existing observational data and vortex mixing theory, only eddies with the same polarity were considered in the splitting and merging processes; i.e., we analyzed only the splitting and merging of cyclones, or the splitting and merging of anticyclones. Although a cyclonic eddy could theoretically interact with an anticyclonic eddy (Amores et al., 2017; Chang and Park, 2015), sometimes maybe one would devour/tear apart another; the mixing process is too complex and the observation of such an event too difficult for the current research.
Some previous studies of eddy–eddy interaction have found that multicore eddies exist universally within the global oceans (Li and Sun, 2015; Trieling et al., 2005; Yi et al., 2015). Generally, multicore structures, which have two closed eddies of the same polarity within their boundaries, represent an important transitional stage in their lives during which the component eddies might experience splitting or merging. To elucidate such events and to understand their dynamic processes visually, examples of splitting and merging are examined in this section.
The SLA maps of a case of eddy splitting from 1 February to 17 March 2009 are shown in Fig. 3. At the start time (1 February), a strong cyclonic eddy existed as a single core in the center of the SLA map. This cyclonic eddy evolved into a multicore eddy because of the southward movement of a strong anticyclone to the north. Through interaction of the two strong eddies, the cyclonic eddy became deformed. The multicore eddy structure persisted for nearly a month before finally splitting into two single-core eddies on 28 February. The two single-core eddies had smaller scales compared with the multicore eddy before the split, although they gradually became larger as they moved away from each other. Daughter eddy A was larger and it carried more eddy energy, i.e., about 15 % of that of the mother eddy, while the smaller daughter eddy B carried only about 5 % of the energy. The strong anticyclonic eddy that moved southwestward played an important role in the process of splitting the cyclonic eddy.
SSTA maps of eddy splitting 1 February to 17 March 2009 (corresponding to Fig. 3). Color shading represents the value of the SSTA field.
Generally, a cyclonic (anticyclonic) eddy corresponds to a cold (warm) core
in the SST signature due to upwelling (downwelling) of centric water
(Kubryakov et al., 2018). Consequently, the splitting case based on the SLA
maps can be validated through the corresponding SSTA maps
derived from AVHRR data, as shown in Fig. 4. The climatic SST signal has
been removed such that the SSTA data can be used to study the oceanic
variation corresponding to mesoscale processes. Hence, the local temperature
gradients reveal the presence of coherent mesoscale structures. The
sequential SSTA maps exhibit signatures similar to the surface oceanic
structures in the SLA maps. The four SSTA snapshots of the upper panels in
Fig. 4 show that a strong cyclonic (cold core) eddy evolved into a
multicore eddy. The four snapshots of the middle panels show this eddy was
squeezed and deformed by an anticyclonic eddy, before finally splitting into
two eddies. The four snapshots of the lower panels show the evolutions of
the two single-core eddies as they moved apart. Thus, the dynamic process is
consistent with the SLA results. Note that, unlike standard altimetry
products, the SSTA field includes many small-scale oceanic signals. It is
difficult to remove the unconnected variations in the SST data, especially
diurnal variations that tend to appear as random noise. Diurnal variations
of SST of 1
The variations of eddy properties for the total splitting process are shown
in Fig. 5. From the appearance of the multicore eddy structure, the
distance between the two cores increased almost monotonically from 80 km at
the beginning to almost 200 km at the end (Fig. 5a). When the distance
between the two cores was
Changes of eddy properties with eddy split from 1 February to
17 March 2009:
Once the multicore eddy had split into two single-core eddies, the eddy
properties changed considerably. The eddy scale or radius decreased
substantially from 180 km for the multicore eddy to about 100 km for one
eddy and about 50 km for the other, as is also evident in the SLA maps
(Fig. 3). Although it is difficult to estimate the energy and water
exchange between the two daughter eddies, continuing to consider them as a
superimposed multicore structure is inappropriate based on the
discriminating principle discussed in Sect. 2.2.2. The two daughter eddies
moved away from about 200 km apart to over 300 km apart, and they gradually
evolved into two independent stable eddies without interaction (lower panels
of Fig. 3). The significant reduction of eddy scale after the split caused
corresponding reductions in both eddy amplitude and EKE (Fig. 5c and d).
The amplitude decreased from about 50 cm for the multicore eddy to 22 cm for
daughter eddy A and about 12 cm for daughter eddy B. Concurrently, the EKE
decreased from about
The substantial variations of eddy properties were closely related to the spatial changes in the shape of the eddy. When the multicore eddy split, the spatial scales of the two daughter eddies instantaneously became much smaller, meaning they captured only some of the original signal and energy of the multicore eddy (Saito and Ueda, 2004). In fact, most of signal and energy remained “hidden” in the background field. With the evolution of the two single-core eddies, the hidden signal and energy became captured by the two eddies, as evidenced excellently by the increasing scale, amplitude, and EKE of the two independent eddies. It is also suggested that the two single-core eddies gradually evolved into strong, stable eddies that were close to the intensity of the original multicore eddy; in fact, daughter eddy A eventually attained a greater amplitude. The four panels of Fig. 5 indicate that the evolution of eddy properties from a single-core eddy to a multicore eddy is smooth and continuous, while that of the splitting process from a multicore eddy to two daughter eddies is discontinuous and irregular.
The SLA maps of two anticyclonic eddies merging from 20 January to 19 February 2012 are shown in Fig. 6. Many numerical studies have recognized three stages in the merging of two ideal vortices: they first rotate around each other and deform elliptically; then, they establish a common boundary and develop a band of vorticity exchange, before finally merging into a single entity (Huang, 2005; Masina and Pinardi, 1993). The merging process of the two independent eddies (i.e., eddy A and eddy B) shown in the sequential time series of the SLA maps (Fig. 6) is consistent with these three stages. First, the two eddies approached close enough to each other to instigate obvious eddy–eddy interaction and cause reduction of their spatial scales. Subsequently, eddy A and eddy B merged into a dual-core structure that existed for 10 d during 5–14 February. Finally, the dual-core eddy, which was smoothed by diffusion, evolved into a strong, stable single-core eddy. The corresponding SSTA maps derived from AVHRR data are presented in Fig. 7 as validation of eddy merging. The consecutive SSTA maps exhibit eddy signatures similar to the SLA maps. It should be noted that diurnal variation of the SST signal, as mentioned in Sect. 3.1, is also evident in Fig. 7, which slightly obscures the mesoscale signals.
Same as Fig. 3 but showing two eddies merging from 20 January to 19 February 2012. A merged multicore eddy existed for about 10 d during 5–14 February.
Same as Fig. 4 but showing two eddies merging, corresponding to Fig. 6 from 20 January to 19 February 2012.
Changes of eddy properties with merging of two eddies from 20 January
to 19 February 2012:
The variations of eddy properties for the entire merging process are shown
in Fig. 8. The distance between the two eddies decreased almost linearly
from 360 to 160 km (Fig. 8a). When the distance was
Generally, splitting or merging events can substantially change (by a factor of 2 or more) eddy scale, amplitude, and EKE. In other words, the obvious variation of eddy properties for one full-lifetime eddy could correspond to a splitting or merging event (certainly, maybe also to other events, e.g., eddy–current interaction and topographic influence). Eddy–eddy interactions in the oceans are very complex. For example, merging is not limited to two eddies and it could include interactions between three or more eddies merging into a single entity (Saito and Ueda, 2004; Zhai et al., 2010). Moreover, splitting and merging might occur at the same time; e.g., two or more eddies might interact and merge into a multicore structure before the multicore eddy subsequently splits into two or more eddies. Despite these possibilities, the limitations of the eddy identification method and eddy kinetic theory make it very difficult to study such complicated eddy–eddy interactions. Thus, this study focused only on the classical merging of two eddies into one and splitting of one eddy into two, which are perhaps the most representative eddy–eddy interactions in the oceans. Multicore structures are vital intermediate stages in the processes of eddy splitting and merging. The next section discusses the execution of hybrid tracking of single-core and multicore eddies over the 23-year period from January 1993 to December 2015, and it examines the census of splitting and merging events globally.
Statistical analysis of all multicore eddy trajectories identified by the
automated tracking procedure, without hybrid tracking, over the 23-year
period (January 1993 to December 2015) revealed 83 751 cyclonic and
83 406 anticyclonic multicore eddies with lifetimes
The classification of all multicore eddies (exactly, trajectories) based on hybrid tracking and their numbers.
Hybrid tracking is a complicated process when considering both single-core and multicore eddies throughout their full evolutionary lifetimes. If an eddy splits or merges just once during its lifetime, its evolutionary process could be easily discerned. However, some eddies might merge or split many times during their lifetimes. Schonten et al. (2000) tracked 20 eddy rings with lifetime exceeding 5 months in the Agulhas retroflection and found three of the original 20 split once, one split twice, and two even split four times. Fang and Morrow (2003) studied the evolution and decay of 37 eddies originating in the Leeuwin Current and found one eddy split into two eddies, one of which in turn split into two new eddies. Garreau et al. (2018) monitored a particular anticyclonic eddy from its birth to its death in the Algerian Basin and found that this anticyclone split from an Algerian eddy, in October 2015, interacted with the North Balearic Front, and merged 7 months later, in May 2016, with a similar Algerian eddy. The abovementioned tracking is limited to a finite number of eddies (20 and 37, respectively) that is easy for full-lifetime eddy tracking. Full-lifetime global eddy hybrid tracking involves millions of eddy trajectories and it is almost impossible for current research. Eddy splitting and merging multiple times can cause an increase in complexity of 1 order of magnitude. It is not possible to have an effective global means for describing the evolutions of eddies that might merge or split multiple times during their full lifetimes. To investigate splitting and merging events, this study considered a certain time (at least 10 d) before and after the presence of multicore structures was determined, so that they could be observed clearly in the evolutionary process.
In total, the eddy hybrid tracking procedure, summarized in Sect. 2.2.3, detected 47 312 splitting events and 50 166 merging events for all 167 157 multicore eddies (Table 1). Specifically, there were 24 008 cyclonic and 23 304 anticyclonic multicore eddies that split into two eddies (fewer than 10 split into three eddies), which accounted for 28.3 % of the total. Similarly, there were 25 709 cyclonic and 24 457 anticyclonic multicore eddies that merged into one eddy, which accounted for 30.0 % of the total, i.e., slightly more than the number of splitting events in the global oceans.
It is important to note that there were 46 936 multicore eddies identified as part of the evolution of single-core eddies that did not split or merge (which means the eddies before and after the multicore structures were all single core). These multicore eddies represent intermediate states of single-core eddy evolution. They tend to have shorter lifetimes and greater SLA differences between the two cores, which cause the stronger core to absorb the weaker core directly. Moreover, the change in eddy properties from a single-core eddy to a multicore eddy (or the reverse) is smooth and continuous; there is no abrupt change in properties as in the splitting and merging events discussed in Sect. 3. Furthermore, there were 22 743 multicore eddies with transient eddy-like signatures (Sect. 2.2.3). These 22 743 multicore eddies had an average amplitude of about 5 cm, while that of the multicore eddies involved in splitting and merging events was about 16 cm, indicating considerable difference in eddy intensity. Therefore, these weaker eddies with an average radius of about 115 km exhibited a large-scale relatively flat pattern, and they tended to disappear directly under interaction with the background field.
Census statistics for eddy splitting and merging events for each
1
This study focused on multicore eddies that experienced splitting or
merging. Geographic frequency statistics of the 47 312 splitting events and
50 166 merging events are shown in Fig. 9. The upper and lower panels show
the numbers of splitting and merging events, respectively, which occurred in
1
Average changes of eddy properties for all splitting
Eddy splitting and merging events do not always occur most frequently in
eddy-rich regions. Compared with the geographical distribution of global
eddies (Fig. 5 in Chelton et al., 2011), the midlatitude regions of
20–35
The variations of eddy properties for all splitting and merging events are shown in Fig. 10. The properties of the single-core eddies were normalized with respect to the properties of the multicore eddies. For eddy splitting, there is slight increase in terms of the properties of the multicore eddy stage, probably because the two cores stretch the multicore structure to store energy for eddy splitting. Once the multicore eddy has split into two single-core eddies, the eddy properties are reduced considerably. The radius of each of the two daughter eddies is half that (or even smaller) of the mother eddy, and between them, the eddy amplitude and eddy kinetic energy differ greatly. The amplitude of the larger daughter eddy is almost twice that of the smaller one; moreover, they contain about 30 % and 10 % of the original eddy energy, respectively, and the remaining energy is transferred to the background field. With the evolution of the two single-core eddies, the hidden signal and energy became captured by the two eddies, as evidenced excellently by the increasing scale, amplitude, and EKE of the two independent eddies. It is also suggested that the two single-core eddies gradually evolved into strong and stable eddies.
For eddy merging, two single-core eddies with similar radii but different intensities gradually decrease in terms of radius, amplitude, and EKE as the intervening distance decreases. It shows that the two eddies interact and that some of their energy is hidden in the background field, which causes a reduction in the eddy properties, especially the EKE. When the two eddies merge into a multicore eddy structure, the eddy properties change substantially. The eddy radius is almost doubled, indicating that the eddy area could increase by 3–4 times. The multicore eddy recaptured the hidden signal and energy from background field, resulting in the increases of amplitude and EKE. The two single-core eddies do not differ greatly in spatial scale, but one eddy is much larger than the other in terms of eddy intensity (amplitude and EKE); i.e., the large one is nearly double the smaller one. It shows that eddy merging is not an interaction of two equal-intensity eddies, and that it tends to manifest as a strong eddy merging with a weaker one to form a larger multicore eddy in a process that appears the reverse of splitting. Generally, splitting or merging events can change the eddy scale, amplitude, and EKE substantially. In other words, the obvious variation (twice or more) of eddy properties for one full-lifetime eddy could correspond to a splitting or merging event.
This study examined the global statistics of eddy splitting and merging based on SLA data provided by AVISO from January 1993 to December 2015. Multicore structures were identified using a geometric closed-contour algorithm of SLA, which was improved in terms of certain technical details. Then, a two-dimensional anisotropic Gaussian surface fitting is used to confirm the multicore eddy structure rather than a misidentification of multiple eddies. Finally, a hybrid tracking strategy based on the eddy overlap ratio considering multicore and single-core eddies was used to confirm splitting and merging events.
Based on 23 years of satellite altimetry measurements, the census results
showed 83 751 cyclonic and 83 406 anticyclonic multicore eddies with
lifetimes of
The splitting and merging events were discerned from sequential time series of SLA maps. The process of eddy–eddy interaction is firstly presented visually based on real sea surface height fields. Moreover, remote sensing SST data validated the eddy–eddy interaction. Generally, splitting or merging events can change the eddy scale, amplitude, and EKE substantially. In other words, the obvious variation (twice or more) of eddy properties for one full-lifetime eddy could correspond to a splitting or merging event. Merging events generally caused an increase of eddy properties, whereas splitting generally caused a decrease of eddy properties. Multicore eddies were found to tend to split into two eddies with different intensities, with the larger one being on average almost twice the smaller one in terms of amplitude and EKE. Similarly, it was found that eddy merging tended not to involve the interaction of two equal-intensity eddies. Instead, a strong eddy tended to merge with a weaker one to form a larger multicore eddy in a process that appeared the reverse of the splitting process. In fact, multicore structures represent an intermediate stage in the process of eddy evolution, similar to the generation of multiple nuclei in a cell as a preparatory phase for cell division in biology. For eddy splitting and for eddy merging, it is very important to identify the multicore eddies for studying eddy splitting and merging events and understanding the eddy–eddy interaction progress.
Multicore eddies do not always correspond to splitting or merging. The hybrid tracking both considering multicore and single-core eddies globally detected 47 312 splitting events and 50 166 merging events for all 167 157 multicore eddies. Besides, about 14 % of multicore eddies are transient eddy-like signals which do not match with single-core eddies, and more than one quarter (28 %) of multicore eddies neither split nor merge but are intermediate states of single-core eddy evolution.
Geographic frequency statistics of splitting and merging events showed
eddy–eddy interaction tended to occur in the Antarctic Circumpolar Current
and western boundary currents, where typically about five to seven events per
1
It is interesting and instructive to compare the global ocean to the universe. The oceanic eddies are just like galaxies in the universe: both can spin around their cores, move in one direction, collide, split and merge, and finally disappear in the background field. The variation in temperature and salinity fields caused by eddies in the ocean is similar to the space–time curvature caused by a galaxy in the universe. Haller and Beron-Vera (2013) even found coherent Lagrangian eddies can capture and swallow nearby passively floating debris, which means eddies can be viewed as “black holes” in the ocean like in cosmology.
It is worth noting that Amores et al. (2018) showed the vast majority of the eddy field is missed in altimetry-based sea level gridded products because the available observations do not have enough resolution to resolve the smaller eddies. The common AVISO gridded products used to detect and characterize mesoscale eddies in the global ocean largely underestimate the density of eddies (capture of only between 6 % and 16 % of the total number of eddies is suggested by Amores et al., 2018). That is to say that our statistical results of multicore eddies and eddy–eddy interaction are from a very small fraction of the global ocean eddies, so the number of multicore eddies should be much more than that and much more eddy splitting and merging events are expected in the global oceans. Hybrid tracking considering single-core and multicore eddies for full-lifetime evolution is highly complex, given that some eddies might merge or split multiple times. The description of full-lifetime eddy evolution needs to be addressed in a future study. This work is very important for accurately describing the lifetime evolution of eddies in regions where substantial splitting and merging occur. The eddies in such regions are expected to have longer lifetimes. Limited by the satellite altimetry measurements, surface eddy splitting and merging are analyzed in this study. For subsurface information on eddy interaction, we know nothing. This question is being addressed in ongoing research from the analysis of the altimeter data in combination with subsurface float observations and from the Parallel Ocean Program global ocean circulation model.
The Ssalto/Duacs altimeter products were produced and
distributed by the Copernicus Marine and Environment Monitoring Service (CMEMS)
(
The work was carried out by WC as a PhD candidate under the supervision of WW. WC performed the data analyses and wrote the manuscript. WW, JZ, and JY planned the research and co-wrote the manuscript.
The authors declare that they have no conflict of interest.
This work was supported by the National Natural Science Foundation of China
under contract no. 1576176, the National Key R & D Program of China under
contract no. 2016YFC1401800, and in part by National Programme on Global
Change and Air-Sea Interaction. The altimeter products were produced by
Ssalto/Duacs and distributed by AVISO, with support from CNES
(
This paper was edited by John M. Huthnance and reviewed by Angel Amores and one anonymous referee.