EddyGraph: The Tracking of Mesoscale Eddy Splitting and Merging Events in the Northwest Pacific Ocean
"> Figure 1
<p>The daily <span class="html-italic">eddytrees</span> detected by our method, including eddies (mononuclear eddies, multicore eddies and eddy seeds) as the leaf nodes, <span class="html-italic">eddygroups</span> (green lines) whose children are all eddies and other <span class="html-italic">eddygroups</span> (black lines). Anticyclonic eddies and cyclonic eddies (except eddy seeds) are represented by red lines and blue lines, respectively, while eddy seeds and the eddy cores of anticyclonic eddies and cyclonic eddies are expressed by red dots and blue dots.</p> "> Figure 2
<p>(<b>a</b>) A diagram of an <span class="html-italic">eddytree</span>; (<b>b</b>) the structure of the <span class="html-italic">eddytree</span> corresponding to (<b>a</b>).</p> "> Figure 3
<p>A diagram illustrating a merging event of counterclockwise-rotating (black solid line with arrow) anticyclonic eddies in the Northern Hemisphere. (<b>a</b>) Eddy1 in <span class="html-italic">eddygroup1</span> and eddy2 in <span class="html-italic">eddygroup2</span> approach each other; (<b>b</b>) eddy1 and eddy2 merge into the common <span class="html-italic">eddygroup3;</span> (<b>c</b>) eddy1 and eddy2 approach each other and eventually merge into eddy3 (a multicore eddy); (<b>d</b>) the local maxima points of eddy3 approach each other, eventually yielding a local maximum point. The eddy cores are represented by black dots.</p> "> Figure 4
<p>The four types of segments considered in this paper, where the eddies on day i and day i + 1 are expressed by the gray and red circles, respectively, while the common <span class="html-italic">eddygroups</span> on day i and day i + 1 are represented by the black dashed line and red dashed line, respectively: (<b>a</b>) live segment consisting of the eddies with live relationships in two adjacent time steps; (<b>b</b>) dead segment consisting of an eddy that is dead in the next time step; (<b>c</b>) split segment consisting of the eddies with split relationships in two adjacent time steps; (<b>d</b>) merged segment consisting of the eddies with merged relationships in two adjacent time steps.</p> "> Figure 5
<p>A diagram of a nonlinear <span class="html-italic">Eddy-DAG</span> consisting of splitting or merging branches with segments as the basic units.</p> "> Figure 6
<p>The workflow of tracking for a daily segment.</p> "> Figure 7
<p>A diagram depicting area overlap ratio, where <span class="html-italic">r</span>2 ≥ 2/3 and <span class="html-italic">r</span>3 ≥ 2/3.</p> "> Figure 8
<p>A diagram of tracking for a branch, where the state of the eddy branch on the last day (dark gray circle) of its life is split, merged or dead.</p> "> Figure 9
<p>A diagram of constructing a nonlinear <span class="html-italic">Eddy-DAG</span>. The branches with a merging relationship are taken as an example, where the merging relationship among eddy branches (branch1, branch2 and branch3) is established by the segment, taking the eddies on the last day of the lives of branch1 and branch2 as the sources and the eddy on the first day of the life of branch3 as the sink.</p> "> Figure 10
<p>A splitting event of a cyclonic eddy detected by our algorithm. Mononuclear eddies/multicore eddies and <span class="html-italic">eddygroups</span> are blue lines and black lines, respectively, while the eddy cores of mononuclear eddies/multicore eddies and eddy seeds are black dots.</p> "> Figure 11
<p>A merging event of anticyclonic eddies detected by our algorithm. Mononuclear eddies/multicore eddies and <span class="html-italic">eddygroups</span> are represented by red lines and black lines, respectively, while the eddy cores of mononuclear eddies/multicore eddies and eddy seeds are expressed by black dots.</p> "> Figure 12
<p>The census statistics of the numbers of typical eddy splitting and merging events in each 1° × 1° region over the 27-year period (January 1993–December 2019) in the Northwest Pacific (105°E–165°W, 0°N–60°N). AM, CM, AS and CS denote the typical merging events and splitting events of anticyclonic eddies and cyclonic eddies.</p> "> Figure 13
<p>The temporal normalization of eddy merging and splitting events: in which (<b>a</b>,<b>b</b>) represent the source eddy/eddies and sink eddy/eddies of a merging event and a splitting event, respectively, being projected into different time periods.</p> "> Figure 14
<p>The spatial normalization of an <span class="html-italic">eddygroup</span> and eddy, where (<b>a</b>,<b>b</b>) are simplified representations of the <span class="html-italic">eddygroup</span> and eddy coordinate systems, respectively. In the <span class="html-italic">eddygroup</span> coordinate system (<b>a</b>), the <span class="html-italic">x</span>-axis is determined by the eddy cores of eddy1 and eddy2 and points eastward. The coordinate center O is the midpoint between p1 and p2, which are the intersections of the boundaries of eddy1 and eddy2 with the <span class="html-italic">x</span>-axis. In the eddy coordinate system (<b>b</b>), the coordinate center O is the eddy core and the positive direction of the <span class="html-italic">y</span>-axis points north. Any point A1 in the coordinate system used for normalization will be found in both the <span class="html-italic">eddygroup</span> and the eddy according to (θ,ρ).</p> "> Figure 15
<p>The SSTA composite averages of anticyclonic eddy during the splitting and merging over the 24-year period (January 1996–December 2019), where (<b>a</b>,<b>b</b>) represent eddy splitting process and eddy merging process, respectively. The top panel and the bottom panel represent the source branch and sink branch of the event, respectively, for both <a href="#remotesensing-13-03435-f015" class="html-fig">Figure 15</a>a,b. Moreover, T is the day of splitting or merging.</p> "> Figure 16
<p>The SSTA composite averages of cyclonic eddy during the splitting and merging over the 24-year period (January 1996–December 2019), where (<b>a</b>,<b>b</b>) present eddy splitting process and eddy merging process, respectively. The top panel and the bottom panel represent the source branch and sink branch of the event, respectively, for both <a href="#remotesensing-13-03435-f016" class="html-fig">Figure 16</a>a,b. Moreover, T is the day of splitting or merging.</p> "> Figure 17
<p>A comparison of the trajectories of a cyclonic eddy merging event detected by our algorithm with the trajectories of loopers in Lagrangian trajectories (<b>a</b>) and drifters (<b>b</b>). The loopers complete at least two drifter orbits in Lagrangian trajectories. Eddy1 (red solid line) and eddy2 (blue solid line) during 20100530–20100927 approach one another and eventually merge into eddy3 (orange solid line) in the event trajectories detected by our algorithm. The trajectories of drifters in (<b>a</b>) are the loopers in Lagrangian trajectories, while the trajectories of drifters in (<b>b</b>) are complete trajectories of drifters during this merging event detected by our algorithm <span class="html-italic">EddyGraph</span>. The black dashed line corresponds to the time period (20100728–20100808) in which the signal of drifter 81801 was lost. To express the changes in the shapes of eddies more clearly, the boundaries of each eddy in the middle of its life are shown here in seven-day intervals.</p> ">
Abstract
:1. Introduction
2. Data and Methods
2.1. Data
2.2. Eddytree: Eddy Identification with Spatial Topological Relationship
2.2.1. Eddytree
2.2.2. Eddygroup
2.2.3. Eddy Identification Criteria
- (i)
- Mononuclear eddy
- (1)
- Only one local SLA maxima/minima point is contained.
- (2)
- There are I pixels (0.25° × 0.25°), where 4 ≤ I < ≤ 2000.
- (3)
- The amplitude A ≥ 0.25 cm, where A = |h1 − h0|, h1 is the SLA value at the local maxima/minima point in the eddy and h0 is the SLA value on the outermost closed SLA contour that defines the eddy perimeter.
- (ii)
- Multicore eddyThe boundaries of multicore eddies should satisfy the following criteria:
- (1)
- Multiple local SLA maxima/minima points are contained.
- (2)
- Multicore eddies are independent of mononuclear eddies: multicore eddies do not contain any mononuclear eddies, which means that any local maxima/minima point within a multicore eddy cannot be identified as a mononuclear eddy.
- (3)
- The amplitude A ≥ 0.25 cm, where A =|hm − h0|, hm is the SLA value at the local maxima/minima point with the largest A among all the local maxima/minima points in the eddy and h0 is the SLA value on the outermost closed SLA contour that defines the eddy perimeter.
- (iii)
- Eddy seed
2.3. EddyGraph: Eddy Splitting and Merging Tracking
2.3.1. Criteria
- (i)
- Segment
- (ii)
- Branch
- (iii)
- Eddy-DAG
2.3.2. Tracking for Eddy Splitting and Merging
- (i)
- Segment
- (1)
- Initialization: First, the eddy sets for day i and day i + 1 are generated from the eddytree data set. Then, the eddy set on day i will be traversed (set this eddy to Ei).
- (2)
- Generating the best candidate eddy of Ei (the best CAEi): If Ei is not dead on day i + 1, the tracking object Ei + 1 of Ei should be within the search circle with a radius of 0.5° [27] and the eddy core of Ei as the center, based on which the set of candidate eddies of Ei (the CAEi set) is retrieved from the eddy set of day i + 1. If the CAEi set is empty, Ei is dead on day i + 1. If the CAEi set is a nonempty set, the best CAEi is selected based on the largest overlapping area principle and the nearest principle. When one of the best CAEi and Ei is an eddy seed and the other is a multicore eddy/mononuclear eddy, the best CAEi is the tracking object Ei + 1 of Ei only if eddy seed is within in the boundary of a multicore eddy/mononuclear eddy. For the other classification of the best CAEi and Ei, the best CAEi is the tracking object Ei + 1 of Ei.
- (3)
- Tracking the relationship between Ei and the best CAEi: If the best CAEi is not the tracking object Ei + 1 of Ei, Ei is dead on day i + 1. Otherwise, based on the common eddygroup, the splitting and merging relationships between Ei and Ei + 1 are tracked by the similarity method with the area overlap ratio as the similarity parameter [31]:
- (4)
- Generating daily segment: Finally, when the traversal of the eddy set of day i terminates, the process of tracking the segments for the eddies on day i is finished.
- (ii)
- Branch
- (iii)
- Eddy-DAG
3. Results
3.1. Statistics of the Tracking Data Set
3.2. Extraction of Typical Events
4. Validation
4.1. Verification with Remote Sensing Observations
4.2. Verification with In Situ Data
5. Discussion and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Anticyclonic Eddy | Cyclonic Eddy | Total | |
---|---|---|---|
Branches | 497,339 | 526,374 | 1,023,713 |
Eddy-DAG | 190,594 | 204,713 | 395,307 |
Nonlinear Eddy-DAG | 490,34 | 541,86 | 103,220 |
Linear Eddy-DAG | 141,560 | 150,527 | 292,087 |
Splitting event | 72,224 | 74,198 | 146,422 |
Merging event | 98,157 | 104,124 | 202,281 |
Anticyclonic Eddy Splitting Event | Anticyclonic Eddy Merging Event | Cyclonic Eddy Splitting Event | Cyclonic Eddy Merging Event |
---|---|---|---|
5500 | 4231 | 4584 | 3945 |
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Tian, F.; Li, Z.; Yuan, Z.; Chen, G. EddyGraph: The Tracking of Mesoscale Eddy Splitting and Merging Events in the Northwest Pacific Ocean. Remote Sens. 2021, 13, 3435. https://doi.org/10.3390/rs13173435
Tian F, Li Z, Yuan Z, Chen G. EddyGraph: The Tracking of Mesoscale Eddy Splitting and Merging Events in the Northwest Pacific Ocean. Remote Sensing. 2021; 13(17):3435. https://doi.org/10.3390/rs13173435
Chicago/Turabian StyleTian, Fenglin, Zhijiao Li, Zhonghao Yuan, and Ge Chen. 2021. "EddyGraph: The Tracking of Mesoscale Eddy Splitting and Merging Events in the Northwest Pacific Ocean" Remote Sensing 13, no. 17: 3435. https://doi.org/10.3390/rs13173435