We employ a recently developed single-trajectory Lagrangian diagnostic tool, the trajectory rotation average (TRA¯), to visualize oceanic vortices (or eddies) from sparse drifter data. We apply the TRA¯ to two drifter data sets that cover various oceanographic scales: the Grand Lagrangian Deployment and the Global Drifter Program. Based on the TRA¯, we develop a general algorithm that extracts approximate eddy boundaries. We find that the TRA¯ outperforms other available single-trajectory-based eddy detection methodologies on sparse drifter data and identifies eddies on scales that are unresolved by satellite-altimetry.

1.
R.
Abernathey
,
C.
Bladwell
,
G.
Froyland
, and
K.
Sakellariou
, “
Deep Lagrangian connectivity in the global ocean inferred from Argo floats
,”
J. Phys. Oceanogr.
52
,
951
963
(
2021
).
2.
F. J.
Beron-Vera
,
M. J.
Olascoaga
,
G.
Haller
,
M.
Farazmand
,
J.
Triñanes
, and
Y.
Wang
, “
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
,”
Chaos
25
,
087412
(
2015
).
3.
G.
Froyland
,
R. M.
Stuart
, and
E.
van Sebille
, “
How well-connected is the surface of the global ocean?
,”
Chaos
24
,
033126
(
2014
).
4.
P.
Miron
,
M. J.
Olascoaga
,
F. J.
Beron-Vera
,
N. F.
Putman
,
J.
Triñanes
,
R.
Lumpkin
, and
G. J.
Goni
, “
Clustering of marine debris and sargassum like drifters explained by inertial particle dynamics
,”
Geophys. Res. Lett.
47
,
e2020GL089874
, https://doi.org/10.1029/2020GL089874 (
2020
).
5.
E.
van Sebille
,
M. H.
England
, and
G.
Froyland
, “
Origin, dynamics and evolution of ocean garbage patches from observed surface drifters
,”
Environ. Res. Lett.
7
,
044040
(
2012
).
6.
G.
Haller
, “
Lagrangian coherent structures
,”
Annu. Rev. Fluid Mech.
47
,
137
162
(
2015
).
7.
R.
Abernathey
and
G.
Haller
, “
Transport by Lagrangian vortices in the eastern Pacific
,”
J. Phys. Oceanogr.
48
(
3
),
667
685
(
2018
).
8.
D. B.
Chelton
,
M. G.
Schlax
,
R. M.
Samelson
, and
R. A.
de Szoeke
, “
Global observations of large oceanic eddies
,”
Geophys. Res. Lett.
34
(15),
L15606
, https://doi.org/10.1029/2007GL030812 (
2007
).
9.
J. H.
Faghmous
,
I.
Frenger
,
Y.
Yao
,
R.
Warmka
,
A.
Lindell
, and
V.
Kumar
, “
A daily global mesoscale ocean eddy dataset from satellite altimetry
,”
Sci. Data
2
,
1
16
(
2015
).
10.
M.
Lévy
,
P. J.
Franks
, and
K. S.
Smith
, “
The role of submesoscale currents in structuring marine ecosystems
,”
Nat. Commun.
9
,
4758
(
2018
).
11.
J. C.
McWilliams
, “
Submesoscale currents in the ocean
,”
Proc. R. Soc. A
472
,
20160117
(
2016
).
12.
R.
Lumpkin
, “
Global characteristics of coherent vortices from surface drifter trajectories
,”
J. Geophys. Res.: Oceans
121
,
1306
1321
, https://doi.org/10.1002/2015JC011435 (
2016
).
13.
A.
Hadjighasem
,
M.
Farazmand
,
D.
Blazevski
,
G.
Froyland
, and
G.
Haller
, “
A critical comparison of Lagrangian methods for coherent structure detection
,”
Chaos
27
(
5
),
053104
(
2017
).
14.
G.
Froyland
and
K.
Padberg-Gehle
, “
A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data
,”
Chaos
25
,
087406
(
2015
).
15.
M.
Filippi
,
I. I.
Rypina
,
A.
Hadjighasem
, and
T.
Peacock
, “
An optimized-parameter spectral clustering approach to coherent structure detection in geophysical flows
,”
Fluids
6
(
1
),
39
(
2021
).
16.
A.
Hadjighasem
,
D.
Karrasch
,
H.
Teramoto
, and
G.
Haller
, “
Spectral-clustering approach to Lagrangian vortex detection
,”
Phys. Rev. E
93
,
063107
(
2016
).
17.
K. L.
Schlueter-Kuck
and
J. O.
Dabiri
, “
Coherent structure colouring: Identification of coherent structures from sparse data using graph theory
,”
J. Fluid Mech.
811
,
468
486
(
2017
).
18.
S.
Mowlavi
,
M.
Serra
,
E.
Maiorino
, and
L.
Mahadevan
, “Detecting Lagrangian coherent structures from sparse and noisy trajectory data,”
J. Fluid Mech.
948
,
A4
(
2022
).
19.
A.
Provenzale
, “
Transport by coherent barotropic vortices
,”
Annu. Rev. Fluid Mech.
31
,
55
93
(
1999
).
20.
A. M.
Mancho
,
S.
Wiggins
,
J.
Curbelo
, and
C.
Mendoza
, “
Lagrangian descriptors: A method for revealing phase space structures of general time dependent dynamical systems
,”
Commun. Nonlinear Sci. Numer. Simul.
18
,
3530
3557
(
2013
).
21.
C.
Mendoza
and
A. M.
Mancho
, “
Hidden geometry of ocean flows
,”
Phys. Rev. Lett.
105
(
3
),
038501
(
2010
).
22.
B. L.
Sawford
, “
Rotation of trajectories in Lagrangian stochastic models of turbulent dispersion
,”
Boundary-Layer Meteorol.
93
,
411
424
(
1999
).
23.
R.
Mundel
,
E.
Fredj
,
H.
Gildor
, and
V.
Rom-Kedar
, “
New Lagrangian diagnostics for characterizing fluid flow mixing
,”
Phys. Fluids
26
,
126602
(
2014
).
24.
I. I.
Rypina
,
S. E.
Scott
,
L. J.
Pratt
, and
M. G.
Brown
, “
Investigating the connection between complexity of isolated trajectories and Lagrangian coherent structures
,”
Nonlinear Processes Geophys.
18
,
977
987
(
2011
).
25.
J. M.
Lilly
and
S. C.
Olhede
, “
Bivariate instantaneous frequency and bandwidth
,”
IEEE Trans. Signal Process.
58
,
591
603
(
2009
).
26.
J. M.
Lilly
and
S. C.
Olhede
, “
On the analytic wavelet transform
,”
IEEE Trans. Inf. Theory
56
(
8
),
4135
4156
(
2010
).
27.
I. I.
Rypina
,
T.
Getscher
,
L. J.
Pratt
, and
T.
Ozgokmen
, “
Applying dynamical systems techniques to real ocean drifters
,”
Nonlinear Processes Geophys.
29
(
4
),
345
361
(
2022
).
28.
C.
Dong
,
Y.
Liu
,
R.
Lumpkin
,
M.
Lankhorst
,
D.
Chen
,
J. C.
McWilliams
, and
Y.
Guan
, “
A scheme to identify loops from trajectories of oceanic surface drifters: An application in the Kuroshio Extension region
,”
J. Atmos. Oceanic Technol.
28
,
1167
1176
(
2011
).
29.
A.
Griffa
,
R.
Lumpkin
, and
M.
Veneziani
, “
Cyclonic and anticyclonic motion in the upper ocean
,”
Geophys. Res. Lett.
35
,
L01608
, https://doi.org/10.1029/2007GL032100 (
2008
).
30.
M.
Veneziani
,
A.
Griffa
,
A. M.
Reynolds
, and
A. J.
Mariano
, “
Oceanic turbulence and stochastic models from subsurface Lagrangian data for the Northwest Atlantic Ocean
,”
J. Phys. Oceanogr.
34
(
8
),
1884
1906
(
2004
).
31.
J. M.
Lilly
and
P.
Pérez-Brunius
, “
Extracting statistically significant eddy signals from large Lagrangian datasets using wavelet ridge analysis, with application to the Gulf of Mexico
,”
Nonlinear Processes Geophys.
,
28
,
181
212
(
2021
).
32.
G.
Haller
,
N. O.
Aksamit
, and
A. P.
Encinas-Bartos
, “
Quasi-objective coherent structure diagnostics from single trajectories
,”
Chaos
31
,
043131
(
2021
).
33.
G.
Haller
,
A.
Hadjighasem
,
M.
Farazmand
, and
F.
Huhn
, “
Defining coherent vortices objectively from the vorticity
,”
J. Fluid Mech.
795
,
136
173
(
2016
).
34.
M. J.
Olascoaga
,
F. J.
Beron-Vera
,
G.
Haller
,
J.
Triñanes
,
M.
Iskandarani
,
E. F.
Coelho
,
B. K.
Haus
,
H. S.
Huntley
,
G.
Jacobs
,
A. D.
Kirwan
, and
B. L.
Lipphardt
, “
Drifter motion in the Gulf of Mexico constrained by altimetric Lagrangian coherent structures
,”
Geophys. Res. Lett.
40
,
6171
6175
, https://doi.org/10.1002/2013GL058624 (
2013
).
35.
M. J.
Olascoaga
and
G.
Haller
, “
Forecasting sudden changes in environmental pollution patterns
,”
Proc. Natl. Acad. Sci.
109
,
4738
4743
(
2012
).
36.
See for “E.U. Copernicus Marine Service Information.”
37.
R. E.
Davis
, “
Drifter observations of coastal surface currents during CODE: The method and descriptive view
,”
J. Geophys. Res.: Oceans
90
,
4741
4755
, https://doi.org/10.1029/JC090iC03p04741 (
1985
).
38.
A. J.
Mariano
,
E. H.
Ryan
,
H. S.
Huntley
,
L. C.
Laurindo
,
E.
Coelho
,
A.
Griffa
, and
M.
Wei
, “
Statistical properties of the surface velocity field in the northern Gulf of Mexico sampled by GLAD drifters
,”
J. Geophys. Res.: Oceans
121
,
5193
5216
, https://doi.org/10.1002/2015JC011569 (
2016
).
39.
A. C.
Poje
,
T. M.
Özgökmen
,
B. L.
Lipphardt
,
B. K.
Haus
,
E. H.
Ryan
,
A. C.
Haza
, and
A. J.
Mariano
, “
Submesoscale dispersion in the vicinity of the deepwater horizon spill
,”
Proc. Natl. Acad. Sci.
111
(
35
),
12693
12698
(
2014
).
40.
R.
Lumpkin
and
M.
Pazos
, “
Measuring surface currents with surface velocity program drifters: The instrument, its data, and some recent results
,”
Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics
39
,
67
(
2007
).
41.
F. J.
Beron-Vera
and
J. H.
LaCasce
, “
Statistics of simulated and observed pair separations in the Gulf of Mexico
,”
J. Phys. Oceanogr.
46
,
2183
2199
(
2016
).
42.
A.
Griffa
, “Applications of stochastic particle models to oceanographic problems,” in Stochastic Modelling in Physical Oceanography (Birkhäuser Boston, 1996), pp. 113–140.”
43.
T.
Rossby
,
M.
Omand
,
J.
Palter
, and
D.
Hebert
, “
On rates of isopycnal dispersion at the submesoscale
,”
Geophys. Res. Lett.
48
,
e2021GL093526
, https://doi.org/10.1029/2021GL093526 (
2021
).
44.
M.
Berta
,
A.
Griffa
,
M. G.
Magaldi
,
T. M.
Özgökmen
,
A. C.
Poje
,
A. C.
Haza
, and
M. J.
Olascoaga
, “
Improved surface velocity and trajectory estimates in the Gulf of Mexico from blended satellite altimetry and drifter data
,”
J. Atmos. Oceanic Technol.
10
,
1880
1901
(
2015
).
45.
N.
Aksamit
,
T.
Sapsis
, and
G.
Haller
, “
Machine-learning mesoscale and submesoscale surface dynamics from Lagrangian ocean drifter trajectories
,”
J. Phys. Oceanogr.
50
,
1179
1196
(
2020
).
46.
G.
Haller
,
N. O.
Aksamit
, and
A. P.
Encinas-Bartos
, “Erratum: `Quasi-objective coherent structure diagnostics from single trajectories' [Chaos 31, 043131 (2021)],”
Chaos
32
(5),
059901
(
2022
).
47.
R.
Lumpkin
,
A. M.
Treguier
, and
K.
Speer
, “
Lagrangian eddy scales in the northern Atlantic Ocean
,”
J. Phys. Oceanogr.
32
(
9
),
2425
2440
(
2002
).
48.
T. G.
Shepherd
,
J. N.
Koshyk
, and
K.
Ngan
, “
On the nature of large-scale mixing in the stratosphere and mesosphere
,”
J. Geophys. Res.: Atmos.
105
(
D10
),
12433
12446
, https://doi.org/10.1029/2000JD900133 (
2000
).
49.
F. J.
Beron-Vera
,
A.
Hadjighasem
,
Q.
Xia
,
M. J.
Olascoaga
, and
G.
Haller
, “
Coherent Lagrangian swirls among submesoscale motions
,”
Proc. Natl. Acad. Sci.
116
,
18251
18256
(
2019
).
50.
G.
Haller
, “
Dynamically consistent rotation and stretch tensors from a dynamic polar decomposition
,”
J. Mech. Phys. Solids
80
,
70
93
(
2016
).
51.
A.
Ruiz-Herrera
, “
Some examples related to the method of Lagrangian descriptors
,”
Chaos
25
(
6
),
063112
(
2015
).
52.
A.
Ruiz-Herrera
, “
Performance of Lagrangian descriptors and their variants in incompressible flows
,”
Chaos
26
(
10
),
103116
(
2016
).
53.
C.
Mendoza
,
A. M.
Mancho
, and
S.
Wiggins
, “
Lagrangian descriptors and the assessment of the predictive capacity of oceanic data sets
,”
Nonlinear Processes Geophys.
21
(
3
),
677
689
(
2014
).
54.
F. J.
Beron-Vera
and
P.
Miron
, “
A minimal Maxey-Riley model for the drift of Sargassum rafts
,”
J. Fluid Mech.
904
,
A8
(
2020
).
55.
R.
Lguensat
,
M.
Sun
,
R.
Fablet
,
P.
Tandeo
,
E.
Mason
, and
G.
Chen
, EddyNet: “A deep neural network for pixel-wise classification of oceanic eddies,” in IGARSS 2018 IEEE International Geoscience and Remote Sensing Symposium (IEEE, 2018), pp. 1764–1767.
56.
M.
Farazmand
and
G.
Haller
, “
Computing Lagrangian coherent structures from their variational theory
,”
Chaos
22
,
013128
(
2012
).
57.
O. R.
Southwick
,
E. R.
Johnson
, and
N. R.
McDonald
, “
A simple model for sheddies: Ocean eddies formed from shed vorticity
,”
J. Phys. Oceanogr.
46
,
2961
2979
(
2016
).
58.
O. R.
Southwick
,
E. R.
Johnson
, and
N. R.
McDonald
, “
Potential vorticity dynamics of coastal outflows
,”
J. Phys. Oceanogr.
47
,
1021
1041
(
2017
).
59.
R.
Lumpkin
and
G. C.
Johnson
, “
Global ocean surface velocities from drifters: Mean, variance, El Niño-Southern Oscillation response, and seasonal cycle
,”
J. Geophys. Res.: Oceans
118
(
6
),
2992
3006
, https://doi.org/10.1002/jgrc.20210 (
2013
).
60.
P. L.
Richardson
, “
Eddy kinetic energy in the North Atlantic from surface drifters
,”
J. Geophys. Res.: Oceans
88
(
C7
),
4355
4367
, https://doi.org/10.1029/JC088iC07p04355 (
1983
).
61.
J.
Martínez-Moreno
,
A. M.
Hogg
,
A. E.
Kiss
,
N. C.
Constantinou
, and
A. K.
Morrison
, “
Kinetic energy of eddy-like features from sea surface altimetry
,”
J. Adv. Model. Earth Syst.
11
(
10
),
3090
3105
(
2019
).
62.
D.
Kang
and
E. N.
Curchitser
, “
Gulf Stream eddy characteristics in a high-resolution ocean model
,”
J. Geophys. Res.: Oceans
118
,
4474
4487
, https://doi.org/10.1002/jgrc.20318 (
2013
).
63.
P. L.
Richardson
,
A. E.
Strong
, and
J. A.
Knauss
, “
Gulf Stream eddies: Recent observations in the western Sargasso Sea
,”
J. Phys. Oceanogr.
3
,
297
301
(
1973
).
64.
C. E.
Binding
,
T. A.
Greenberg
, and
R. P.
Bukata
, “
The MERIS maximum chlorophyll index; its merits and limitations for inland water algal bloom monitoring
,”
J. Great Lakes Res.
39
,
100
107
(
2013
).
65.
N.
Tarshish
,
R.
Abernathey
,
C.
Zhang
,
C. O.
Dufour
,
I.
Frenger
, and
S. M.
Griffies
, “
Identifying Lagrangian coherent vortices in a mesoscale ocean model
,”
Ocean Modell.
130
,
15
28
(
2018
).
66.
R.
Lumpkin
and
L.
Centurioni
, “Global drifter program quality controlled 6-hour interpolated data from ocean surface drifting buoys,” NOAA National Centers for Environmental Information, 2019.
67.
T.
Özgökmen
, GLAD experiment CODE-style drifter trajectories (low-pass filtered, 15 min interval records), northern Gulf of Mexico near DeSoto Canyon, July–October 2012. Distributed by: Gulf of Mexico Research Initiative Information and Data Cooperative (GRIIDC), Harte Research Institute, Texas A&M University-Corpus Christi (2013).
68.
M. O.
Williams
,
I. I.
Rypina
, and
C. W.
Rowley
, “
Identifying finite-time coherent sets from limited quantities of Lagrangian data
,”
Chaos
25
,
087408
(
2015
).
You do not currently have access to this content.