The Genealogical Evolution Model (GEM) presented here is
an efficient logical model used to track dynamic evolution of mesoscale
eddies in the ocean. It can distinguish between different dynamic processes
(e.g., merging and splitting) within a dynamic evolution pattern, which is
difficult to accomplish using other tracking methods. To this end, the GEM
first uses a two-dimensional (2-D) similarity vector (i.e., a pair of ratios
of overlap area between two eddies to the area of each eddy) rather than a
scalar to measure the similarity between eddies, which effectively solves the
“missing eddy” problem (temporarily lost eddy in tracking). Second, for
tracking when an eddy splits, the GEM uses both “parent” (the original
eddy) and “child” (eddy split from parent) and the dynamic processes are
described as the birth and death of different generations. Additionally, a
new look-ahead approach with selection rules effectively simplifies
computation and recording. All of the computational steps are linear and do
not include iteration. Given the pixel number of the target region
Although eddy splitting or merging is ubiquitous in the ocean, they have different geographic distributions in the North Pacific Ocean. Both the merging and splitting rates of the eddies are high, especially at the western boundary, in currents and in “eddy deserts”. The GEM is useful not only for satellite-based observational data, but also for numerical simulation outputs. It is potentially useful for studying dynamic processes in other related fields, e.g., the dynamics of cyclones in meteorology.
Eddies are ubiquitous in the ocean, and they move from one place to another (Chelton and Schlax, 1996; Chelton et al., 2007). Eddies in the ocean can cause large-scale transports of heat, salt, and other tracers (Bennett and White, 1986; Chelton et al., 2011a; Dong et al., 2014; McGillicuddy et al., 2011) by trapping these passive tracers inside the eddies. Such transports may have important impacts on the environment and climate of the ocean (Dong et al., 2014). To address various applications in the studies that use satellite products of sea level anomaly (SLA) data (e.g., Chelton et al., 2011b) and numerical simulation outputs (e.g., Petersen et al., 2013), oceanic eddies should be automatically recorded using these data and outputs (e.g., Yang et al., 2013; Sun et al., 2014; Pegliasco et al., 2015). In general, the recording of oceanic eddies often includes two independent steps: automated eddy identification and automated eddy tracking. The eddies are identified in a sequence of SLA maps using an identification algorithm or identified from velocity fields. An automated tracking procedure is then applied to determine the trajectory of each eddy (Chelton et al., 2011b). Several automated identification and tracking algorithms have been developed for eddies in the ocean (Chelton et al., 2011b; Ienna et al., 2014; Mason et al., 2014; Yi et al., 2015).
The evolutions of amplitudes and areas of eddies from 5 July to 3 August 2006 (after Li et al., 2014), where the background field shows the SLA, and white dots mark eddy centers. Two anticyclonic eddies AC1 and AC2 merged into a single eddy on 31 July 2006, and two cyclonic eddies C1 and C2 merged into a single one on 3 August 2006.
For the eddy tracking stage, according to a recent census (Wang et al., 2015; Yi et al., 2015), approximately 10–30 % of eddies may be found in proximity to a neighboring eddy in any given global SLA map, and they frequently interact. Therefore, an eddy tracking process should have the capability to distinguish between different dynamic processes (e.g., merging and splitting) during its dynamic evolution. Moreover, an eddy tracking process must be accurate and fast enough to handle a huge amount of data, which will be even larger in size if the spatio-temporal resolution of observations and numerical simulations increases.
Implemented automated tracking procedures differ in detail, but they are all
similar in concept because they utilize the nearest neighbor strategy
(Chelton et al., 2011b). For each eddy
However, there is a “missing eddy” problem that must be solved in the eddy
tracking stage (Chelton et al., 2011b). An eddy at time step
Recently, the concept of multiple hypothesis assignment (MHA) was introduced
to solve the missing eddy problem by abandoning the simple closest eddy
strategy and applying a new “look-ahead” procedure (Faghmous et al., 2013).
The MHA method can effectively solve the missing eddy problem in a
straight-line model when the trajectory being followed is a branch without
any splitting, but it is algorithmically and computationally complex. Given
the maximum number of eddies in any time frame
The existing straight-line model can trace the kinematic motion of an eddy.
The dynamic evolutionary processes (e.g., merging and splitting) of the eddy
are, however, ignored by the model. This implies that each eddy
To record the dynamic evolution of eddies, two fundamental algorithms are required. First, the two nearby eddies should be distinguished in the identification stage using a segmentation strategy in which the target region is divided into two corresponding eddies. Otherwise, the merging and splitting processes cannot be determined properly. This problem was recently solved by the use of segmentation strategies, e.g., the close-distance segmentation strategy (Li et al., 2014) and the watershed strategy (Li and Sun, 2015). Because these segmentation strategies can distinguish between closed eddies, they can also potentially reduce the risk of missing an eddy in the identification process.
Second, the merging and splitting processes in the tracking stage should be
described in detail. We use a multi-branch tree model to do so. The eddy
Moreover, the GEM also provides a new way to solve the missing eddy problem.
Instead of the existing closest eddy strategy, a temporal track tree with
In this paper, we introduce the GEM to describe mesoscale eddies in a
tracking process with a total number of time steps
The paper is organized as follows. The data and eddy detection methods used in this study are introduced in Sect. 2. Then the GEM is introduced in Sect. 3, including a similarity vector, a look-ahead approach and the worst-case runtime. Results including eddy tracks and examples of merging and splitting events in a sample area in the North Pacific are shown in Sect. 4. The impacts of data noise and parameter uncertainties on the results are discussed in Sect. 5. Finally, a summary and conclusions are given in Sect. 6.
The input data consist of the original altimetry field, which can come from
satellite observations or numerical simulations. The altimetry field used in
this study is the 20-year (1993–2012) daily SLA data from the merged and
gridded satellite product of Maps of Sea Level Anomaly (MSLA) at
0.25
We used the original SLA data (“DT14”) without any filtering or smoothing to identify eddies in this study. However, this does not imply that data smoothing is not needed for the SLA data in related studies (e.g., eddy detection, eddy tracking). For example, to calculate some eddy parameters (e.g., velocity and vorticity), smoothing may be required, as pointed out by Chelton et al. (2011b). Moreover, the data errors, even if they are very small, might affect the eddy detection (see the discussion in Sect. 5.1).
Top panels: time evolution of two merging eddies revealed by the
mononuclear eddy identification without segmentation. Bottom panels: time
evolution of two merging eddies revealed by the mononuclear eddy
identification with segmentation. The
The eddy identification used in this study is similar to those used before
(Chelton et al., 2011b; Mason et al., 2014) to identify eddies from SLA data.
The eddies may be identified as multinuclear (two or more SLA extremes in one
eddy) or mononuclear (only one SLA extremum in one eddy). The following
mononuclear eddy definition is also similar to what was used by other authors
(Chaigneau et al., 2011; Li et al., 2014; Li and Sun, 2015). We have adopted
the eddy detection step from Li and Sun (2015), which provides us with the
necessary input for the tracking routines, namely eddy areas and boundaries.
Each pixel has eight nearest neighbors. A point within the region is a local
extremum if it has an SLA greater or less than all of its nearest neighbors.
We also use such a definition of an extremum in our following analysis, in
which the extrema are identified by checking each pixel in the map along with
the 8 pixels around it. An eddy is defined as a simply-connected set of
pixels that satisfies the following criteria.
The SLA value of all of the pixels is above (below) a given SLA
threshold. Only The amplitude of the eddy (the max difference of SLA values) is larger
than a critical value (e.g., 1 cm). The area of the eddy must be large enough for estimating eddy parameters
(say > 16 pixels).
Conditions 3–4 provide the lower bounds for eddy size and amplitude. These
conditions automatically reduce the total number of detected eddies.
Condition 1 is the same as the first criterion in Chelton et al. (2011b). It
is used in consideration of the 2–3 cm of background SLA error (Carrere et
al., 2016); so, small fluctuations in SLA field would not be taken as eddies
in this study. Condition 3 was generally used previously (Chaigneau et al.,
2011; Chelton et al., 2011). Condition 4 is more restrictive than the
generally used value of 8 pixels (e.g., Chelton et al., 2011; Li et al.,
2014); so, this condition is an add-on, which is potentially useful when
deriving eddy parameters using a nonlinear optimal fitting method (Wang et
al., 2015; Yi et al., 2015). If the eddy area is too small (only a few
pixels), its parameters (e.g., amplitude, area, radius) are very sensitive to
its area (number of pixels). Besides, we do not put limits on eddy pixel
number maximum (e.g., < 1000) and eddy size (e.g.,
< 400–1200 km), while such limits were generally used previously
(e.g., Chelton et al. 2011; Mason et al., 2014).
The SLA extremum so determined is called the eddy center. The set of pixels belonging to an individual eddy is referred to as the area of the eddy, and the outmost SLA contour is the boundary of the eddy. We use the area and boundary to calculate the similarity of eddies in Sect. 3.2.
Each eddy is identified by the following procedures. First, according to
condition 1, we find a simply-connected region with a given threshold of
SLA <
Figure 2 illustrates the necessity for eddy segmentation based on the merging
process of two eddies. Different mononuclear algorithms are used in the upper
and lower rows. In the top panels of Fig. 2, eddies are identified by the
non-segmentation algorithm. Such mononuclear eddies may be very small. The
time evolutions from
Figure 3 illustrates this eddy segmentation strategy. Figure 3a shows two individual but nearby eddies. The pixels between the two dashed lines are naturally divided by the watershed (For basins, the “watershed” is a ridge between them, while it is a valley for plateaus.) As shown in Fig. 3b, the cross section of the eddy clearly shows that two closely located pixels P1 and P2 on the left and right sides of watershed would slide along the path of steepest descent in the map of SLA data to different eddy centers. The shape of SLA can provide sufficient information to segment the multinuclear eddy into mononuclear ones.
Herein, we use the mononuclear eddy identification (MEI) of the Universal Splitting Technology for Circulations (USTC) with watershed segmentation (Li and Sun, 2015) and include in our code the calculation of eddy parameters, including amplitude, radius, area, and boundary (Fig. 3), which might be potentially used in other studies (Sun et al., 2014).
The output eddy parameters from MEI are then used as input for our novel tracking algorithm GEM. The GEM mainly represents the logical relationship of eddies, which is less dependent on physical parameters which may change greatly because of dynamic evolution (e.g., splitting, merging). To this end, the GEM takes the previously identified eddies by MEI (with area/boundary; see Sect. 2.2) as its input data.
The GEM is a logical model used for tracking the dynamic evolution of mesoscale eddies in the ocean (Fig. 4). The model essentially establishes logical relationships of previously identified eddies. The relationships are determined by two relatively independent steps; i.e., the GEM algorithm consists of two parts (see Fig. 4 for details): first, measuring the “map link” between two time steps, and then connecting all time steps to the “track tree”.
Flowchart of the systems. Mononuclear eddy identification (MEI) uses SLA to identify eddies via the Universal Splitting Technology for Circulations (USTC) method. The GEM, which has the two independent parts of “Map link” and “Track tree”, then uses the previously identified eddies for tracking.
Sketch of eddy overlaps.
Sketch of eddy similarities.
The first part of the GEM is “map link”, which uses as input eddy data
obtained in the prior eddy identification step (area/boundary; see Sect. 2.2)
to establish the link of an eddy from one temporal snapshot to the next,
namely living, missing, death, birth, and the associated dynamical processes
of merging and splitting. In this part of the work flow, we use a 2-D vector
rather than a passive scalar to measure the similarity between eddies E1 and
E2 on 2 neighboring days
(Figs. 5 and 6; see Sect. 3.2.1 for details). We then use a relatively
complex look-ahead procedure to solve the missing eddy problem (Sect. 3.2.2).
This new look-ahead approach has a duration of
The second part is “track tree”, which uses the outputs from “map link”
(i.e., eddy links) as its input (Fig. 4). It connects the eddy links from
branches to a tree with the genealogical model (Fig. 8) using two
sub-procedures: “eddy branch” and “eddy tree”. In the “eddy branch”
part, we use
The logical genealogy of an ocean eddy with six states: birth,
death, living, missing, splitting, and merging.
In short, the GEM uses previously identified eddies and/or their links to
make dynamic tracks via a genealogical tree model. In addition to eddy domain
and boundary, it needs two parameters as input, the critical value of area
ratio
To establish the relationships between the previously identified eddies, the first part of the GEM used evaluates the similarity of these eddies, which is defined here based on the overlap of the domain of an eddy in two consecutive time steps. It begins with defining similarity based on the overlapping area of eddies in consecutive time steps. Subsequently, the overlapping area which is closest to the one of the original eddy is defined to be the successor of the original eddy (if the threshold is met).
At first, the eddy similarity is calculated with an example (Fig. 5a) before proceeding to the mathematical expressions. There were three eddies A1, A2, and B1 detected on 28 March 1997. In Fig. 5b, there were four eddies A1, A2, B1, and B2 on 29 March 1997. We overlapped the eddy domains into a single map (Fig. 5c). Then, we used the intersection of eddy domains on different days to calculate the similarity. For eddies A1 and A2, the intersections were very close to their respective domains on 28 and 29 March. For eddy B1, the intersection was close to the area on the second day, but it was only part of that on the first day. Consequently, eddies A1 and A2 had full similarity on these days, while eddies B1 and B2 only had partial similarity on these days.
To estimate the above similarity, let us describe it in a mathematically
logical way. As shown in Fig. 6a, there is an eddy (E1) that is identified by
the thick contour of Boundary 1 in the rectangular comparison region (not
shown in the figure) on day 0, and there are three eddies (E2, E3, and E4)
that are identified in the same region on day 1. This comparison region,
which is centered at the eddy center of E1, moves in time with the target
eddy (E1). To determine the similarities between E1 on day 0 and E2 to E4 on
day 1, we intersect the domains of day 0 and day 1. For example, to determine
the similarity between E1 and E2, we count the overlap area
Using the vector (
For example, as shown in Fig. 6a, the high similarity between E1 and E2 over
a critical value
In previous eddy tracking studies, simple methods were used for weekly SLA data (delayed-time 2010), e.g., the closest distance between eddies (Chelton et al., 2011b; Yi et al., 2015), the closest angle between eddies (Zhang et al., 2014), and the dimensionless similarity scalar (Chaigneau et al., 2008; Mason et al., 2014). There is always a risk of eddy jumping (from one track to another) in these methods, except for that of Pegliasco et al. (2015), who used intersections of eddy boundaries to find the continuing eddy. Compared to the previous tracking methods, we use a more robust technique to assess the relationship of eddies in subsequent time steps by using the overlap of their areas. In addition, we do not simply assign the continuing eddy using the similarity vector for the two adjacent days; rather, we try to solve the temporary missing eddy problem by looking ahead a few days.
In contrast to the procedure used in Chelton et al. (2011b), we use a
relatively complex look-ahead procedure. Examples of a given eddy are shown
in Fig. 7a. In the upper row, both Ec1 and Ec2 take the same eddy Ec3 as
their subsequent T1 type of eddy, which is a merging event (e.g., eddies C1
and C2 in Fig. 1). Since a T1 (merging) eddy has
This new look-ahead approach with
The two selection rules are (1) the most similar day and (2) the earliest day. Rule 1 has priority. We first choose the most similar eddy as the potential successor of Ed1 according to their types. According to Fig. 6b, a T2 (splitting) type eddy covers only part of the original eddy, while a T1 (merging) eddy covers most of the original eddy. The similarity from low to high is T2 < T1 < T3. For example, if there is only one T3 (living) eddy in these days, we choose it as the potential one. However, if there is more than 1 day with the same type of eddy, we need an additional rule: the earliest day. For example, in the upper row of Fig. 7b, there is one T3 (living) eddy on day 1 and one T3 (living) eddy on day 2, and there are two T2 (splitting) eddies on day 3. In this case, we choose day 1 as the following day and the T3 (living) eddy as the following Ed1. In the middle and lower rows, we choose day 2 and day 3 as the following days and the corresponding T3 (living) eddies as the following Ed2 and Ed3, respectively.
After having determined the next subsequent days and the relationship types
between eddies based on the above process, we can now establish the branches
of an eddy from one day to the next. An eddy branch describes the
relationship between two eddies at two different time steps. To describe the
GEM more precisely, we use
The upper row shows a successor relationship: an eddy P on day 1 has only one
successor (eddy P itself) on day 2. In this case, eddy P is allowed to be
missing during day 1 and day 2. Additionally, eddy P will be recorded as
death (black circle) if no successor eddy is found after
In the middle row, two (or more) eddies merge into one. The first type includes principal and subordinate merging. A principal eddy P1 and a subordinate eddy P2 on day 1 merge into a larger eddy P1 on day 2, whereas P2 is recorded as death. This occurs when a large eddy meets and merges with a small eddy (e.g., C1 and C2 in Fig. 1). The anticyclonic eddies A1 and A2 in Fig. 11 also experience a similar process (see Sect. 2 for details). The second type is coordinated merging. Two (or more) parent eddies P1 and P2 merge to produce a new child eddy C, and all of the parent eddies are recorded as death. This is because the similarity is not sufficiently high for the record of eddy C to be appended to either parent. There might be another choice by keeping parent eddies P1 and P2 alive and appending the record of eddy C to both eddies. This choice artificially increases lifetimes of eddy P1 and P2 and leads to other tracking problems; so, we abandon it.
In the lower row, a parent eddy splits into several child eddies. The first type is principal and subordinate splitting. A parent eddy P splits into a relatively large eddy P (itself; i.e., the similarity type is T3 between the two eddies) and a relatively small child eddy C (i.e., the similarity type between parent eddy P and child eddy C is a splitting relationship T2), which is recorded as birth. The second type is coordinated splitting. Two (or more) child eddies are born from the parent eddy P, which is then recorded as death. This occurs when all the similarity types between child eddies and parent eddy are type 2 (T2).
Finally, the track tree is recorded by connecting the eddy branches (Fig. 8b). The track tree of an eddy records information of all the associated eddies (e.g., living, death, birth, merging and splitting) during its entire life. In this process, the role that an eddy plays in the track tree is considered. The first generation is the parent eddy (e.g., P1), the second generation is the child eddy (e.g., C1), and the third generation is the grandchild eddy (e.g., G1). The track tree uses the above eddy branches (Fig. 8a). We connect the branches from one time to another to obtain the whole eddy track tree.
There are two additional notations. First, an eddy emerging from the same family of eddies (e.g., two siblings C2 and C4) will be recorded as a new family member (e.g., eddy C5). Second, an eddy merging from two different families of eddies (e.g., C1 and P2) will be recorded as a new eddy N1.
Although the model could have several generations, we only recorded two generations, i.e., parent and child in this study due to the complexity of the output data structure and the computer time. However, we can indirectly track other generations using the relationships between them.
To calculate similarity vectors, we need to overlap two small regions around
eddy E1. The total number of pixels in the rectangular comparison region is
For example, both
We first apply the MEI to detect the ocean eddies in the North Pacific Ocean
(NPO) during 1993–2012. The eddy centers (SLA extrema of eddy snapshots) on
each day are counted on each 1
We apply the GEM to these eddies detected by MEI with
Eddy C1 was first detected as an eddy initiated on 14 September 1995, with an
extremum at 163.5
To clarify this, we plot the two SLA fields in Fig. 10d. The SLA field on
30 July 1996 is plotted as contours. The eddy center is marked by a black
cross at 167.5
There may be no associated eddy identified at the next time step for an eddy
at time step
The trajectories provide evidence of dynamic evolution. The time evolution of
a couple of anticyclonic eddies is depicted in Fig. 11a, which implies a
merging process occurring in the red boxes in Fig. 9. As shown in Fig. 11a,
eddy A1 had a westward movement with a speed of 2.6 cm s
The dynamic evolutions of two groups of eddies, which are located in
the red boxes in Fig. 9.
The SLA field shows that an eddy splitting process also occurred in the box
at the same time. The time evolutions of anticyclonic eddies B1, B2, and B3
are depicted in Fig. 11b. At first, eddy B1 had a fast westward speed of
10.4 cm s
It is expected that a pair of cyclonic eddies will have a counter-clockwise rotation in the Northern Hemisphere, known as the Fujiwhara effect for atmospheric cyclones (Fujiwhara, 1921). When two cyclones are close enough, they will begin to orbit cyclonically (counter-clockwise in the Northern Hemisphere). Because the above-mentioned eddies (A1, A2; B1, B2, B3) are anticyclonic, they have opposing directions of rotation, which appear as two point vortices moving in circular paths about the center of vorticity in classical fluid dynamics (Batchelor, 1967).
To illuminate how often the merging and splitting processes occurred, we
counted the total number of merging and splitting events on each
1
The frequencies of dynamic processes per
1
The first type of special region is the western boundary. It is known that the western boundary is a sink of eddy energy caused by the interaction with the bottom and lateral topography (Zhai et al., 2010). It is also known as a “graveyard” for westward-propagating ocean eddies (Zhai et al., 2010; Chelton et al., 2011b). The second type of special region is located in strong currents, including the Kuroshio Current and the NEC (Hu et al., 2015). Among those currents, the eddies in the NEC had the highest frequency of merging and splitting events, which was not noted in previous studies. The third type of special region is located in the northeastern Pacific, which is also known as an “eddy desert” (Chelton et al., 2007). The fourth type of special region is located in enclosed marginal seas, especially the Bering Sea.
By comparing Fig. 12 with Fig. 10, we can see that the regions with high frequencies of merging and splitting events have relatively few eddy tracks, especially in the NEC (blue box in Fig. 9c). Besides, very few eddies were observed in the “eddy desert” (black box in Fig. 9c) in the northeastern Pacific, but the frequency of merging and splitting is relatively large (see Fig. S1 in the Supplement). If eddies exist in this region, the reason for the existence of an “eddy desert” may be that they were too small to be identified or their lifetimes were too short to be tracked (Chelton et al., 2011b). However, Figs. 9 and 12 suggest that merging and splitting events may be an important reason why there is no eddy observed in the “eddy desert”.
We also calculate the average dynamic (merging and splitting) events per eddy as a function of lifetime (Fig. 13). The results are similar regardless of eddy polarizations and dynamic types. The merging and splitting events increase approximately linearly with eddy lifetime. However, merging and splitting events are more frequent for anticyclonic eddies than for cyclonic eddies.
The number of merging/splitting events per eddy as a function of eddy lifetime, where AC and C represent anticyclonic and cyclonic eddies.
Comparison of the non-smoothed
Although AVISO product DT1 is much better than previous products, there are still some notable errors, especially for short temporal scales of less than 2 months (Carrere et al., 2016). It was reported that there are along-track SLA errors of about 2–3 cm globally and of more than 3 cm at high latitudes and in shallow waters.
To reduce the noise in SLA data, one may use the Gaussian structure filter (Chelton et al., 2011b; Mason et al., 2014), Hanning filters (Penven et al., 2005), or Lanczos filters (Chaigneau et al., 2008). As certain parameters need to be chosen in these filters, the filtered results depend much on these parameters (see Fig. A1 in Chelton et al., 2011b). As a sensitivity test we apply a simple five-point quadratic smoothing to the SLA data. The filtered data are then piecewise C2-smoothed by a quadratic function, which satisfies the potential requirements for calculating vorticity (second derivative of SLA) from SLA data.
Figure 14 shows the non-smoothed and smoothed SLA data from 1 to 4 January 1993. The smoothed SLA maps are very close to the non-smoothed SLA maps and the values at the SLA extrema (not shown) are close to their original values. This implies that the noise in the DT14 data is sufficiently small for our purpose.
However, the noise cannot be neglected, even when it is small. It might induce additional SLA extrema (see the definition of an extremum in Sect. 2.2), which eventually affect eddy detection, e.g., the additional extremum on 2 January 1993 in box A and the additional extremum on 3 January 1993 in box B (Fig. 14). These additional extrema existed only for a very short period (1 or 2 days), but they can induce additional merging and splitting events, which may cause eddies to unexpectedly terminate (Chelton et al., 2011b). The ambiguity of the eddy identification procedure, which may be caused by sampling errors and measurement noise in the input SLA data, strongly suggests the application of a look-ahead approach.
To discuss the impact of the GEM critical value
In general, one would like the tracking results to be insensitive to the
choice of these parameters. From Fig. 15, we can observe that
0.5 <
It should be pointed out that the GEM is relatively independent of MEI, but
the ratios
Finally, as noted in Sect. 4.2, there are short-term eddies (lifetime < 30 days), which might experience complex evolution processes. If only long-term eddies (lifetime > 30 days) were saved, the corresponding evolution process might not be recorded properly. This should be noted in further applications on eddy dynamics with satellite altimetry data.
Different identification methods may give different eddy boundaries, although
the eddy center is relatively robust. Eddy area S is sensitive to the eddy
boundary, but it is difficult to compare directly the influence of eddy
boundary differences that result from the identification method choice.
However, the area ratio reduces the sensitivity to the eddy area S because
both the overlap area S12 and the eddy area S change synchronously. Moreover,
our tracking results fortunately are not very sensitive to
The census of long-lived eddies, where “Amp” represents the amplitude threshold used in eddy detection, and “C” and “AC”, respectively, represent cyclonic and anticyclonic eddies.
However, such a sensitive test may only be valid for the comparison of different parameter values used in the same identification method. It cannot simply be extended to the comparison of eddies identified by different methods, since the eddy detection algorithms differ a lot from each other. In general, the automated eddy detection algorithms are categorized into three types: (1) physical parameter-based algorithms, e.g., the Okubo–Weiss (O–W) parameter (Isern-Fontanet et al., 2003; Chaigneau et al., 2008); (2) flow geometry-based algorithms (Chaigneau et al., 2011; Chelton et al., 2011b; Wang et al., 2015); and (3) hybrid methods, which involve physical parameters and flow geometry characteristics (Nencioli et al., 2010; Xiu et al., 2010; Dong et al., 2011; Yi et al., 2015). For example, Yi et al. (2015) used the O–W parameter to identify eddy kernels and SLA contour geometries to identify eddy boundaries. So it is difficult to compare the influences of eddy boundary differences resulting from using different identification and tracking algorithms.
The GEM is a flexible model that can easily work with other relevant programs, e.g., data filtering and smoothing algorithms (Chelton et al., 2011b; Ienna et al., 2014; Wang et al., 2014), other hybrid eddy detection algorithms (e.g., Yi et al., 2015), and O–W parameter detection (e.g., Petersen et al., 2013), because the GEM only requires a flow field and previously identified eddies to accomplish dynamic tracking. In addition, the similarity measurement can be replaced by similar methods (e.g., Pegliasco et al., 2015) when considering more complex conditions.
Eddies identified by using algorithms without watershed segmentation can also be tracked with the GEM. In this case, the strong interaction stage of eddies “in conjunction”, which leads to genesis and termination of eddies, is more likely missed, as pointed out in Sect. 2.3. However, the weak interaction stage of eddies (watershed free) in some far distance could still be recorded, because most merging/splitting records occurred at the interaction of two eddies with a certain distance. This weak interaction still cannot be recorded by a previously interaction-free tracking algorithm, which records only the isolated tracks. Thus the GEM extends the potential applications of previously identified eddies.
The GEM is a complex model. The output data include eddy tracks, relationships, and previously identified eddy characteristics (e.g., amplitude and radius). These eddy characteristics, which were directly obtained from the identification process, are useful for censuses (Chelton et al., 2011b). However, they may not be sufficiently accurate for some applications. For example, eddy area was required in our recent studies on typhoons and oceanic eddy interactions (Sun et al., 2010, 2012, 2014). Besides, some physical quantities (circulation, angular momentum, energy) are required to be accurately calculated in the investigation of eddy dynamics process. A better way to obtain these characteristics might be to use a nonlinear fitting of the flow field (Wang et al., 2015; Yi et al., 2015) with appropriate models (e.g., Sun, 2011; Zhang et al., 2013) rather than simply estimation from identification.
Another future research direction may involve comparing different tracking datasets. Because there are several tracking datasets produced by various methods, it is useful to inter-compare them. This may improve both the tracking methods and the available datasets for further studies.
The GEM can be easily applied to larger datasets, even to 3-D numerical
simulation outputs (Petersen et al., 2013; Woodring et al., 2016), because
its computational time increases only linearly as a function of the size of
the dataset. The computation of the 20-year daily global SLA data only
required a few hours on a personal computer. In a personal computer with a
CPU of i7-6700 k and 4.00 GHz, it takes about 15 min to identify snapshots
of eddies, about 20 min to establish similarity, and about 10 min to track
eddies in the North Pacific Ocean (NPO) with
0.25
The GEM opens a window to investigate eddy dynamics (Wang et al., 2015) and other applications (Sun et al., 2014), e.g., (i) the strong eddy interaction which leads to genesis and termination of eddies, (ii) the weak eddy interaction which is associated with merging/splitting events, and (iii) the weak eddy interaction which modulates the eddy track and motion. As illuminated in Fig. 11, the dynamic evolution of eddies is accompanied by abundant phenomena that might be identified using the GEM. The present study is only the beginning of such applications.
We have introduced the GEM for the tracking of the dynamic evolution of
mesoscale eddies in the ocean. Several novel approaches (e.g., vector
similarity and look-ahead approach) were applied to deal with unsolved
problems in tracking. All of the computational steps in the GEM are linear
and do not require iteration. Given the grid number of the target region
We thank the anonymous referees and John M. Huthnance for their comments and
suggestions. We thank the AVISO for providing the SLA data
(