OCS Study

BOEM 2015-006

U.S. Department of the Interior

Bureau of Ocean Energy Management

Gulf of Mexico OCS Region

Observations and Dynamics 

of the Loop Current

Mean

Barotropic

Baroclinic

10 m3s-2 ∫ KE

OCS Study

BOEM 2015-006

Published by

U.S. Department of the Interior

Bureau of Ocean Energy Management

Gulf of Mexico OCS Region

New Orleans, LA

February 2015

Observations and Dynamics 

of the Loop Current

Authors

Peter Hamilton

Kathleen Donohue

Cody Hall

Robert Leben

Hui Quian

Julio Sheinbaum

Randolph Watts

Prepared under BOEM Contract

M08PC20043

by

Leidos, Inc.

615 Oberlin Road, Suite 100

Raleigh, North Carolina 27605

DISCLAIMER 

Study concept, oversight, and funding were provided by the US Department of the Interior, 

Bureau of Ocean Energy Management, Environmental Studies Program, Washington, DC, under 

Contract Number M08PC20043. This report has been technically reviewed by BOEM and it has 

been approved for publication. The views and conclusions contained in this document are those 

of the authors and should not be interpreted as representing the opinions or policies of the US 

Government, nor does mention of trade names or commercial products constitute endorsement or 

recommendation for use. 

REPORT AVAILABILITY 

To download a PDF file of this Gulf of Mexico OCS Region report, go to the US Department of 

the Interior, Bureau of Ocean Energy Management, Environmental Studies Program Information 

System website and search on OCS Study BOEM 2015-006.

The report may also be obtained from the BOEM Gulf of Mexico Regional OCS Office.

US Department of the Interior, Bureau of Ocean Energy Management

Gulf of Mexico OCS Region, Public Information Office (MS GM 355A)

1201 Elmwood Park Boulevard

New Orleans, LA 70123-2394

Phone: (504) 736-2519, 1-800-200-GULF, Fax: (504) 736-2620

CITATION 

Hamilton, P., K. Donohue, C. Hall, R. R. Leben, H. Quian, J. Sheinbaum, and D. R. Watts. 2014. 

Observations and dynamics of the Loop Current. US Dept. of the Interior, Bureau of Ocean 

Energy Management, Gulf of Mexico OCS Region, New Orleans, LA. OCS Study BOEM 2015-

006. 417 pp.

ABOUT THE COVER 

The cover figure shows the topography of the study region (contours every 250 m with the 

addition of 100 m; greenish shades down to 2000 m, blue shades from 2000 m to 3500 m). The 

vertical bars, which extend above the frame, represent depth integrated (whole water column) 

kinetic energy (KE) at each mooring in the US and Mexican arrays. The depth-integrated KE is 

proportioned between that due to mean flow (yellow), barotropic or depth-independent velocity 

fluctuations (blue), and baroclinic or surface intensified (mostly from the surface to about 900 m) 

velocity fluctuations (red). The period for the calculations is June 2009 to June 2011. The purple 

line denotes the mean edge of the Loop Current as defined by the 17-cm sea-surface-height 

contour for the study period. The figure shows the dominance of the depth-independent, whole 

water column velocity fluctuations that are generated after the Loop Current leaves the 

continental slope that borders the Campeche Bank.
ACKNOWLEDGEMENTS 

The enthusiastic and timely support of Dr. Alexis Lugo-Fernández, the BOEM Contract 

Officer’s Technical Representative, is gratefully acknowledged. The suggestions and support 

from the Science Review Group (Dr. John Bane, Dr. Eric Chassignet, Dr. Allan Clarke, Dr. 

William Johns and Dr. Susan Lozier) were positive, constructive and greatly appreciated. Dr. 

Lie-Yauw (Leo) Oey and his colleagues at Princeton University are thanked for their numerical 

modeling and data analysis contributions to the contract that resulted in a number of important 

publications on Loop Current dynamics. Leidos program personnel, Paul Blankinship (Data 

Management) and James Singer (Field Operations and Logistics Manager), were crucial to data 

processing and the excellent data return from field activities. These two also played key roles in 

the deployment, rotation and recovery cruises as cruise leaders, and were involved in instrument

servicing and deck operations. Special thanks are also expressed to Craig Boyd, Scott Sharpe 

(Specialty Devices, Inc.), John Evans (Leidos) and John Morris for their “can do” attitude 

handling mooring recovery and deployment operations, as well as their involvement in servicing 

instruments. Mr. Erran Sousa (URI), with the able assistance of Gary Savoie and Stuart Bishop, 

was responsible for and successfully conducted all aspects of PIES instrument servicing and 

related field operations. Many others were important to the program success, including a number 

of students and technicians and the captains and crews of the R/V Pelican and the R/V 

WeatherBird II. Finally, special thanks are expressed to Chuck Guidry at LUMCON for his 

valuable logistical support over the 2.5-year field effort.
i

Contents

LIST%OF%FIGURES.....................................................................................................................................V

LIST%OF%TABLES ...................................................................................................................................XVII

ABBREVIATIONS%AND%ACRONYMS............................................................................................................XXI

CHAPTER(1:(INTRODUCTION.......................................................................................................... 1

1.1 BACKGROUND .................................................................................................................................1

1.2 GENERAL%PROGRAM%DESCRIPTION ......................................................................................................4

1.3 STUDY%PARTICIPANTS ........................................................................................................................6

1.4 LOOP%CURRENT%EDDY%SHEDDING ........................................................................................................7

1.5 MAJOR%EVENTS..............................................................................................................................10

Eddy$Separations.........................................................................................................................10

Deepwater Horizon Oil$Spill.........................................................................................................10

Hurricanes...................................................................................................................................12

1.6 REPORT%ORGANIZATION ..................................................................................................................12

CHAPTER(2:(EXPERIMENTAL(DESIGN(AND(METHODOLOGY...........................................................13

2.1 MOORED%ARRAYS...........................................................................................................................13

2.1.1$Array$Design .......................................................................................................................13

2.2 EQUIPMENT%AND%INSTRUMENTS .......................................................................................................13

2.2.1$Introduction........................................................................................................................13

2.2.2$Moored$and$PIES$Instruments............................................................................................14

2.2.3$Instrumentation..................................................................................................................14

2.2.4$Instrument$Calibration,$Performance$and$Data$Return .....................................................19

2.3 CTD DATA ....................................................................................................................................29

2.3.1$CTD$Data$Acquisition$Systems............................................................................................29

2.4 CICESE MOORING%DATA ................................................................................................................31

2.4.1$Introduction........................................................................................................................31

2.4.2$Instrumentation..................................................................................................................31

2.5 PIES ............................................................................................................................................34

2.5.1$Gravest$Empirical$Mode$Method .......................................................................................34

2.5.2$Conversion$of$Measured$τ to$τ(150P1000)$=$τindex ..............................................................43

2.5.3$UpperPOcean$Maps ............................................................................................................49

2.5.4$Bottom$Pressure .................................................................................................................49

2.5.5$ReferencePLevel$Maps ........................................................................................................51

2.5.6$Total$Maps .........................................................................................................................51

2.5.7$Mooring$Comparisons........................................................................................................55

2.6 REMOTE%SENSING...........................................................................................................................67

2.6.1$Satellite$Altimetry...............................................................................................................67

2.6.2$Satellite$Radiometry ...........................................................................................................78

2.6.3$Ancillary$Satellite$Altimeter$Datasets.................................................................................79

2.7 PIES AND%ALTIMETRY%EVALUATION%AND%COMPARISON.........................................................................79

2.7.1$Altimetric$Sampling$and$Aliasing .......................................................................................80

2.7.2$SignalPtoPNoise ...................................................................................................................88

2.7.3$SeaPSurfacePHeight$Time$Scales .........................................................................................89

2.7.4$Comparison$of$CCAR$Mesoscale,$AVISO,$and$PIES$Mapped$Absolute$SSH .........................93
ii

2.8 NUMERICAL%MODEL .......................................................................................................................98

2.8.1$Model$Skill$Metrics$for$InPSitu$Measurements .................................................................101

2.9 METHODS...................................................................................................................................101

2.9.1$Vertical$Velocities.............................................................................................................101

2.9.2$Relative$Vorticity ..............................................................................................................104

2.9.3$Potential$Vorticity.............................................................................................................104

2.9.4$Streamlines$and$Velocity$Potentials.................................................................................107

2.9.5$Wavelet$Analysis ..............................................................................................................109

2.9.6$Complex$Demodulation ....................................................................................................109

2.9.7$Notes$on$EOF$Analysis......................................................................................................109

CHAPTER(3:(BASIC(DESCRIPTIONS(AND(STATISTICS .....................................................................111

3.1 INTRODUCTION ............................................................................................................................111

3.2 EDDY%FORMATION%AND%SEPARATION ...............................................................................................117

3.2.1$Ekman...............................................................................................................................117

3.2.2$Franklin.............................................................................................................................119

3.2.3$Hadal ................................................................................................................................126

3.3 NUMERICAL%MODELING%OF%HADAL’S%SEPARATION .............................................................................132

3.3.1$Introduction......................................................................................................................132

3.3.2$Model$Forecast$Skill..........................................................................................................133

3.4 STATISTICS ..................................................................................................................................139

3.4.1$Mean$Flows......................................................................................................................139

3.4.2$Depth$Variability$of$Velocities..........................................................................................142

3.4.3$Horizontal$Variability$in$the$Upper$Layer .........................................................................147

3.4.4$Horizontal$Variability$in$the$Lower$Layer .........................................................................166

CHAPTER(4:(DYNAMICS...............................................................................................................185

4.1 INTRODUCTION ............................................................................................................................185

4.2 RELATIVE%VORTICITY, UPWELLING%AND%LC EDDY%SEPARATIONS ............................................................185

4.3 LOOP%CURRENT%FRONTAL%VARIABILITY .............................................................................................187

4.4 RELATIVE%VORTICITY .....................................................................................................................193

4.5 BAROCLINIC%INSTABILITY%ANALYSIS ..................................................................................................204

4.5.1$Eddy$Potential$Energy ......................................................................................................222

4.6 TOPOGRAPHIC%ROSSBY%WAVES.......................................................................................................232

4.7 NUMERICAL%MODELING ................................................................................................................235

CHAPTER(5:(LONG(TERM AND(SEASONAL(VARIABILITY ...............................................................241

5.1 INTRODUCTION ............................................................................................................................241

5.2 REIANALYSIS%OF%THE%“PREIALTIMETRIC” LOOP%CURRENT%RECORD........................................................244

5.3 COMPARISONS%OF%PREVIOUSLY%PUBLISHED%SEPARATION%DATES%WITH%THE%REIANALYSIS ...........................256

5.4 THE%ALTIMETRIC%LOOP%CURRENT%RECORD ........................................................................................260

5.5 STATISTICAL%ANALYSIS%OF%LOOP%CURRENT%SEASONALITY .....................................................................277

General$Conclusions..................................................................................................................294

5.6 INVESTIGATION%OF%DYNAMICS%CONTRIBUTING%TO%LOOP%CURRENT%SEASONALITY .....................................294

Deepwater$EOF$Analysis............................................................................................................295

Coastal$EOF$Analysis .................................................................................................................316

Conclusions................................................................................................................................325

CHAPTER(6:(INERTIAL(OSCILLATIONS ..........................................................................................327

6.1 INTRODUCTION ............................................................................................................................327
iii

6.2 DATA%AND%METHODS....................................................................................................................328

6.3 DESCRIPTION%OF%INERTIAL%RESPONSE%TO%HURRICANE%IDA....................................................................332

6.4 DISCUSSION ................................................................................................................................338

6.4.1$The$Effect$of$Relative$Vorticity$on$the$Distribution$of$Inertial$Oscillations.......................338

6.4.2$The$Effect$of$the$Loop$Current$on$the$Distribution$of$Inertial$Oscillations.......................338

6.5 LONGITERM%VARIABILITY%OF%INERTIAL%OSCILLATIONS .........................................................................340

6.6 SUMMARY%AND%CONCLUSIONS .......................................................................................................344

CHAPTER(7:(SUMMARY(DISCUSSION(AND(RECOMMENDATIONS ................................................351

7.1 INTRODUCTION ............................................................................................................................351

7.2 LC EDDY%SHEDDING%EVENTS...........................................................................................................352

Ekman........................................................................................................................................353

Franklin......................................................................................................................................353

Hadal .........................................................................................................................................353

7.3 STATISTICS%AND%DYNAMICS ............................................................................................................354

7.4 LC EDDY%SEPARATION%DYNAMICS....................................................................................................356

7.5 LONGITERM%AND%SEASONAL%VARIABILITY .........................................................................................358

7.6 RECOMMENDATIONS ....................................................................................................................359

7.7 DEEPWATER%HORIZON%OIL%SPILL .....................................................................................................363

CHAPTER(8:(REFERENCES ............................................................................................................365

APPENDIX:(BAROTROPIC TIDES...................................................................................................385

v

LIST OF FIGURES

Figure 1.1-1. A high resolution SST image (left panel) and SSH altimeter map (right 

panel) showing an extended LC and a partially detached LC eddy (Hadal) on 

21 April 2011........................................................................................................2

Figure 1.2-1. Locations of moorings and PIES deployed in the U.S. and Mexican sectors 

in the eastern Gulf of Mexico during the study of Loop Current dynamics.........5

Figure 1.2-2. Schedule and relationships of data types collected and used during this 

study. ....................................................................................................................6

Figure 1.5-1. Time series of LC area (green) and LC+eddy area (blue) as delineated by the 

17-cm SSH contour from the altimeter maps. ....................................................11

Figure 2.2-1. Schematic of tall mooring. .................................................................................18

Figure 2.2-2a. Timeline of data return for instruments on tall moorings A1 and A2. ...............23

Figure 2.2-2b. Timeline of data return for instruments on tall moorings A3 and A4. ...............24

Figure 2.2-2c. Timeline of data return for instruments on tall moorings B1 and B2. ...............25

Figure 2.2-2d. Timeline of data return for instruments on tall moorings B3 and C1. ...............26

Figure 2.2-2e. Time lines of data return for tall mooring C2 and short moorings D1, D2, 

D3, D4, D5, D7, and D8.....................................................................................27

Figure 2.4-1a. Time lines of data return from CICESE moorings N3, N4, E1, E2, E3, E4, 

and E5.................................................................................................................32

Figure 2.4-1b. Time lines of data return from CICESE moorings N1, N2, Y1, Y2, Y3, Y4, 

YN, Y5, Y6, and Y7...........................................................................................33

Figure 2.5-1. Time series of tau anomaly in seconds in panels arranged according to 

approximate geographic location. ......................................................................35

Figure 2.5-2. Time series of bottom pressure anomaly in dbar arranged according to 

approximate geographic location. ......................................................................36

Figure 2.5-3. Several views of the current and temperature structure in the region for 5 

May 2009 provided by the PIES and current meter measurements. ..................37

Figure 2.5-4. Spatial and temporal distribution of hydrocasts used to construct the Gravest 

Empirical Mode. .................................................................................................39

Figure 2.5-5. Temperature profiles interpolated every 10 dbar and sorted by τ(150-1000) = 

τindex.....................................................................................................................40

Figure 2.5-6. Scatter plots of temperature versus τindex = τ(150 -1000) for six 

representative pressure levels. ............................................................................41

Figure 2.5-7. Contour plot of the cubic smoothing spline fits for the temperature GEM 

field.....................................................................................................................42

Figure 2.5-8. Scatter plots of temperature versus τ(150-1000) for surface (left) and 50 dbar 

(right) with the cubic spline fit shown as a solid dark line.................................44
vi

Figure 2.5-9. Seasonal temperature correction/amplitude contoured as a function of 

yearday and pressure. .........................................................................................45

Figure 2.5-10. Upper panel: Scatter plots of surface geopotential anomaly referenced to 150 

dbar with the cubic spline fit shown as a solid dark line....................................46

Figure 2.5-11. Time series of τ(150-1000) in seconds, with panels arranged according to 

approximate geographic location. ......................................................................47

Figure 2.5-12. Scatter plots of τ(0 -150) versus τ(150 -1000). ..................................................48

Figure 2.5-13. Correlation coefficient between pairs of PIES τ(150 -1000) records.................50

Figure 2.5-14. All the individual pressure records (thin black) and their array-average (red), 

called the common mode....................................................................................52

Figure 2.5-15. Time series of bottom pressure anomaly (dbar) with the common mode 

removed. .............................................................................................................53

Figure 2.5-16. Correlations between pairs of pressure records..................................................54

Figure 2.5-17. Comparison between the A4 mooring (red) and PIES-derived (blue) 

temperature. ........................................................................................................56

Figure 2.5-18. Summary of the temperature comparisons. ........................................................57

Figure 2.5-19. Observed rms and predicted differences between measured and PIESestimated temperature.........................................................................................58

Figure 2.5-20a. Comparison between the A4 mooring (red) and PIES-derived (blue) zonal 

and meridional velocities at 200 and 400 dbar...................................................60

Figure 2.5-20b. Comparison between the A4 mooring (red) and PIES-derived (blue) zonal 

and meridional velocities at 600 and 900 dbar...................................................61

Figure 2.5-20c. Comparison between the A4 mooring (red) and PIES-derived (blue) zonal 

and meridional velocities at 1300 and 2000 dbar...............................................62

Figure 2.5-21. Summary of the zonal velocity comparisons......................................................63

Figure 2.5-22. Summary of the meridional velocity comparisons.............................................64

Figure 2.5-23. Rms and predicted differences between measured and PIES-estimated zonal 

(left) and meridional (right) velocities. ..............................................................65

Figure 2.5-24. PIES-estimated total SSH anomaly (red) and Jason SSH anomaly (blue) for 

the seven PIES sites along groundtracks. ...........................................................66

Figure 2.5-25. Rms differences between altimeter SSH anomaly and PIES-estimated total 

SSH anomaly as a function of γ. ........................................................................68

Figure 2.5-26. Multiplicative factor, γ, applied to the reference SSH (velocity).......................69

Figure 2.6-1. Satellite altimeter exact repeat groundtrack coverage in study region...............70

Figure 2.6-2. Plot showing daily “actual”, “available”, “windowed”, and “used” data 

from operational altimeter satellites during the study program..........................76
vii

Figure 2.7-1. Maps of PIES barotropic unaliased variance for 10-day, 17-day, and 35-day 

sampling. ............................................................................................................82

Figure 2.7-2. Maps of PIES baroclinic unaliased variance for 10-day, 17-day, and 35-day 

sampling. ............................................................................................................83

Figure 2.7-3. Maps of PIES SSH unaliased variance for 10-day, 17-day, and 35-day 

sampling. ............................................................................................................84

Figure 2.7-4. Maps of PIES SSH signal-to-noise ratio (SNR) for 10-day, 17-day, and 35-

day sampling.......................................................................................................90

Figure 2.7-5. Spatial maps of the half-power period, T0.5, computed from the PIES 

barotropic, baroclinic, and combined SSH anomaly time series........................92

Figure 2.7-6. Spatial map of the temporal correlation between the PIES mapped SSH time 

series and the CCAR Mesoscale SSH and AVISO SSH time series 

coincident with the LC study..............................................................................94

Figure 2.7-7. Spatial map of the temporal correlation between the PIES mapped SSH time 

series and the AVISO SSH time series with and without the seasonal steric 

signal removed....................................................................................................95

Figure 2.7-8. Rms SSHA (standard deviation about the mean) during the program time 

period of the CCAR Mesoscale, AVISO, and PIES mapped datasets. ..............96

Figure 2.7-9. Regression of the daily means of the PIES mapped SSH on to the means of 

the CCAR Mesoscale and AVISO mapped SSH in the study region.................97

Figure 2.7-10. CCAR Mesoscale and AVISO mean SSH maps over the program time 

period with the PIES mean SSH as an inset. ......................................................99

Figure 2.7-11. Comparison of the CCAR Mesoscale and AVISO mean SSH maps over the 

program time period. ........................................................................................100

Figure 2.9-1. Average temperature, salinity and sigma-t profiles for CTD casts taken 

during the LC study. .........................................................................................103

Figure 2.9-2. Mapping array and CICESE transects showing the locations of relative 

vorticity points and their surrounding triangles and rectangles........................105

Figure 2.9-3. Comparison of relative vorticity at two depths for location 82 using the 

triangle E2-E3-EN and the E2-E3 pair to estimate velocity gradients.............106

Figure 2.9-4. Geostrophic velocites from mapped geopotential, and observed 2-day 

averaged 40-HLP currents at 160 m.................................................................108

Figure 3.1-1a. 40-HLP temperature and velocity records from the A2 mooring at the 

indicated depths. ...............................................................................................112

Figure 3.1-1b. 40-HLP temperature and velocity records from the C2 mooring at the 

indicated depths. ...............................................................................................113

Figure 3.1-2a. Surface-layer (~ 100 m) currents on the N2 to C1 transect where up is 

normal to the transect. ......................................................................................115
viii

Figure 3.1-2b. Lower-layer currents at ~1300 and ~2000 m on the N2 to C1 transect where 

up is normal to the transect...............................................................................116

Figure 3.2-1. The growth and detachments of Ekman using the SSH 17-cm contour from 

altimeter maps at 15-day intervals....................................................................118

Figure 3.2-2. Maps of the separation of Ekman for the indicated dates. ...............................120

Figure 3.2-3. Loop Current 17-cm frontal boundaries from SSH altimeter maps for 

Franklin for the indicated dates. .......................................................................121

Figure 3.2-4. Mean surface velocities and standard deviation ellipses from drifter tracks 

(gray lines) for May and June 2010..................................................................123

Figure 3.2-5. The first detachment of Franklin showing the depth of the 6 °C isotherm and 

80 to 100-m velocity vectors from the moorings. ............................................124

Figure 3.2-6. Franklin detachment 1: Upper and lower-layer circulation for indicated 

dates..................................................................................................................125

Figure 3.2-7. Five-day average velocity components for transect E moorings......................127

Figure 3.2-8. Loop Current 17-cm frontal boundaries from SSH altimeter maps for Hadal 

for the indicated dates.......................................................................................128

Figure 3.2-9. Maps of the separation of Hadal for the indicated dates in 2011 showing 

upper and lower-layer circulations. ..................................................................130

Figure 3.2-10. Surface Chlorophyl-A from Modis Aqua overlaid with SSH from altimeter 

maps for 12 August 2011. ................................................................................131

Figure 3.3-1. Daily averaged SSH and surface currents for every 10 days of the forecast 

simulation, starting from 1 July 2011...............................................................134

Figure 3.3-2. Comparison between AVISO and forecast SSHA. ..........................................135

Figure 3.3-3. Full-depth ADCP mooring (A1-A4, B1-B3 and C1-C2) locations from the 

US array superimposed on the July mean model forecast SSH. ......................137

Figure 3.3-4. Vertical profiles of complex correlation Rs and Qs, ratio of model-toobserved standard deviations, skill, ratio of model-to-observed mean speeds, 

and angle of modeled observed mean velocity.................................................138

Figure 3.4-1. Mean 40-HLP currents for all moorings overlayed with mean SSH and mean 

depths of the 6 °C isotherm. .............................................................................140

Figure 3.4-2. Mean near-bottom 40-HLP currents and standard deviation ellipses for the 

indicated interval. .............................................................................................141

Figure 3.4-3. Depth range weighted CEOF modes for mooring A3. .....................................143

Figure 3.4-4. CEOF modes for the 2-year common interval. ................................................145

Figure 3.4-5. Normalized mode amplitudes for CEOFs by mooring for the 2-year interval. 146

Figure 3.4-6. EKE spectra in variance preserving form of selected normalized mode 

amplitudes.........................................................................................................148
ix

Figure 3.4-7. Cummulative depth-integrated KE for mean flow, and the QB and SI CEOF 

modes................................................................................................................149

Figure 3.4-8. 200-m depth mapped and measured mean current vectors (bold) and 

standard deviation ellipses superimposed on the time-mean 200-m depth 

eddy kinetic energy...........................................................................................151

Figure 3.4-9. Standard deviation of baroclinic sea-surface height referenced to the bottom 

as a function of frequency band........................................................................152

Figure 3.4-10. Loop Current area, and array mean baroclinic sea-surface height referenced 

to the bottom.....................................................................................................154

Figure 3.4-11. CCAR SSH determined Loop Current positions during CEOF time periods. .155

Figure 3.4-12. CEOFs determined from band-passed baroclinic sea-surface height 

referenced to the bottom, during the Ekman time period.................................156

Figure 3.4-13. CEOFs determined from band-passed baroclinic sea-surface height 

referenced to the bottom during the Franklin time period................................159

Figure 3.4-14. CEOFs determined from band-passed baroclinic sea-surface height 

referenced to the bottom during the Hadal time period....................................161

Figure 3.4-15. CEOFs determined from band-passed baroclinic sea-surface height 

referenced to the bottom during the Icarus time period....................................163

Figure 3.4-16. Wavenumber versus phase speed. ....................................................................165

Figure 3.4-17. Near-bottom mapped and directly-measured mean currents with standarddeviation ellipses superimposed on the time-mean near-bottom eddy kinetic 

energy. ..............................................................................................................167

Figure 3.4-18. Standard deviation of reference sea-surface height as a function of frequency 

band. .................................................................................................................169

Figure 3.4-19. Loop Current area with array-mean baroclinic sea-surface height referenced 

to the bottom and CCAR sea-surface height ....................................................170

Figure 3.4-20. CCAR SSH-determined Loop Current positions during Ekman_deep CEOF 

time period........................................................................................................171

Figure 3.4-21. CCAR SSH-determined Loop Current positions during Franklin_deep 

CEOF time period.............................................................................................172

Figure 3.4-22. CCAR SSH-determined Loop Current positions during Hadal_deep CEOF 

time period........................................................................................................173

Figure 3.4-23. CEOFs determined from band-passed deep reference sea-surface height 

during the Ekman_deep time period.................................................................174

Figure 3.4-24. CEOFs determined from band-passed deep reference sea-surface height 

during the Franklin_deep time period. .............................................................175

Figure 3.4-25. CEOFs determined from band-passed deep reference sea-surface height 

during the Hadal_deep time period. .................................................................176
x

Figure 3.4-26. Snapshots of 100 to 40 day band-passed deep reference sea-surface height 

for a portion of the Franklin_deep time interval. .............................................178

Figure 3.4-27. Snapshots of 40 to 25 day band-passed deep reference sea-surface height for 

a portion of the Franklin_deep time interval. ...................................................179

Figure 3.4-28. Snapshots of 100 to 40 day band-passed deep reference sea-surface height 

for a portion of the Hadal_deep time interval. .................................................181

Figure 3.4-29. Snapshots of 40 to 25 day band-passed deep reference sea-surface height for 

a portion of the Hadal_deep time interval. .......................................................182

Figure 3.4-30. Snapshots of 25 to 16 day band-passed deep reference sea-surface height for 

a portion of the Hadal_deep time interval. .......................................................183

Figure 4.2-1. Array averaged relative vorticity anomaly, eddy kinetic energy at 200 m and 

100 mab, with area averaged 7-DLP vertical velocities at 900 m....................186

Figure 4.2-2. A schematic illustration of the three stages of the LC cycle. ...........................188

Figure 4.3-1. Depth of the 6 °C isotherm along the N3-C1 transect......................................190

Figure 4.3-2. Velocity components, directed 310°T, at 120 m for moorings along the N1-

C1 transect. .......................................................................................................191

Figure 4.3-3. Along-front velocity vectors for the E and N1-C1 transects for the west and 

east sides, respectively......................................................................................192

Figure 4.3-4. EKE spectra of the along-front interpolated velocities on the N2-C1 and E 

transects. ...........................................................................................................194

Figure 4.4-1. Mean along-front velocities and relative vorticity for the indicated interval 

and sections across the Campeche slope during the LC formation of Hadal. ..195

Figure 4.4-2. Time series of relative vorticity for locations 78, and 82 as a function of 

depth. ................................................................................................................197

Figure 4.4-3. Time series of relative vorticity for location 56 as a function of depth............198

Figure 4.4-4. Frequency domain EOFs of vertical profiles of relative vorticity at locations 

56 and 67. .........................................................................................................199

Figure 4.4-5. Time series of relative vorticity for location 67 as a function of depth............200

Figure 4.4-6. Normalized wavelet power for relative vorticity at 160 m at locations 82 and 

78 using the Morlet wavelet. ............................................................................202

Figure 4.4-7. Cross-wavelet normalized power between 166 and 2000 m at locations 56 

and 67. ..............................................................................................................203

Figure 4.5-1. Near-bottom mapped and directly measured mean currents with standard 

deviation ellipses superimposed on the time-mean near-bottom eddy kinetic 

energy. ..............................................................................................................205

Figure 4.5-2. Schematic representation of the characteristic phase offset between upper 

and lower-layer cyclonic or anticyclonic perturbations that favor baroclinic 

instability. .........................................................................................................206
xi

Figure 4.5-3. Coherence and phase between upper, SSH_bcb, and lower, SSH_ref, 

streamfunction for three frequency bands. .......................................................208

Figure 4.5-4a. Loop Current eddy-shedding event Ekman, 4 May through 18 July 2009, 

shown using maps of baroclinic SSH referenced to the bottom embedded 

within altimetric SSH. ......................................................................................209

Figure 4.5-4b. Loop Current eddy-shedding event Ekman, 4 May through 18 July 2009, 

shown using maps of 100-40 day band-passed baroclinic SSH referenced to 

the bottom embedded within altimetric SSH....................................................210

Figure 4.5-4c. Loop Current eddy-shedding event Ekman, 23 July through 16 September 

2009 (Full frequency band). .............................................................................211

Figure 4.5-4d. Loop Current eddy-shedding event Ekman, 23 July through 16 September 

2009 (100-40 day frequency band)..................................................................212

Figure 4.5-5a. Loop Current eddy-shedding event Franklin, 11 April through 25 June 2010, 

shown using maps of baroclinic SSH referenced to the bottom (SSH_bcb) 

embedded within altimetric SSH......................................................................213

Figure 4.5-5b. Loop Current eddy-shedding event Franklin, 11 April through 25 June 2010, 

shown using maps of 100-40 day band-passed baroclinic SSH referenced to 

the bottom embedded within altimetric SSH....................................................214

Figure 4.5-5c. Loop Current eddy-shedding event Franklin, 30 June through 13 September 

2010 (Full frequency band). .............................................................................215

Figure 4.5-5d. Loop Current eddy-shedding event Franklin, 30 June through 13 September 

2010 (100-40 day frequency band)...................................................................216

Figure 4.5-6a. Loop Current eddy-shedding event Hadal, 9 March through 23 May 2011, 

shown using maps of baroclinic SSH referenced to the bottom embedded 

within altimetric SSH. ......................................................................................218

Figure 4.5-6b. Loop Current eddy-shedding event Hadal, 9 March through 23 May 2011, 

shown using maps of 100-40 day band-passed baroclinic SSH referenced to 

the bottom embedded within altimetric SSH....................................................219

Figure 4.5-6c. Loop Current eddy-shedding event Hadal, 28 May through 11 August 2011

(Full frequency band). ......................................................................................220

Figure 4.5-6d. Loop Current eddy-shedding event Hadal, 28 May through 11 August 2011 

(100-40 day.......................................................................................................221

Figure 4.5-7. A linear relationship (black line) exists between mean ψ_bcb and mean T at 

400 m (grey dots)..............................................................................................224

Figure 4.5-8. Eddy heat flux vectors at 400-m depth for the three LC eddy-shedding 

events superimposed on the 400-m depth temperature variance......................225

Figure 4.5-9. Four terms in the steady eddy potential-energy budget determined for the 

Ekman event, 3 May through 31 August 2009 at 400-m depth........................228
xii

Figure 4.5-10. BC and PKC at 400-m depth determined for the Ekman event. ......................229

Figure 4.5-11. Four terms in the steady eddy potential-energy budget determined for the 

Franklin event, 15 February through 14 September 2010 at 400-m depth.......230

Figure 4.5-12. BC and PKC at 400-m depth determined for the Franklin event. ....................231

Figure 4.5-13. Four terms in the steady eddy potential-energy budget determined for the 

Hadal event, 1 March through 14 September 2011, at 400-m depth................233

Figure 4.5-14. BC and PKC at 400-m depth determined for the Hadal event. ........................234

Figure 4.6-1. Wavenumbers from 100 to 20-day EOFs for the 100-mab currents for 

Franklin where the propagation is compatible with TRWs..............................236

Figure 4.7-1. Schematic illustrations of the dominant flow anomalies in the northwestern 

Caribbean Sea for the indicated months based on monthly composites 

derived from EOF analysis of model SSH. ......................................................239

Figure 5.2-1. Examples of the “best” LC images from CZCS ocean color and AVHRR 

SST in the time period before EddyWatch analyses from Horizon Marine, 

Inc. became available in 1984. .........................................................................246

Figure 5.2-2. Sample HMI EddyWatch map from week of 10-17 January 1986 showing 

frontal analysis of “Fast Eddy”, “Hot Core Eddy”, and the Loop Current. ....247

Figure 5.2-3. LC eddy 1978 as observed by Seasat approximately two weeks after eddy 

separation..........................................................................................................249

Figure 5.2-4. LC eddy separation events with LC retreat latitude following separation 

shown by dashed black lines (February 1980 through August 1982). .............251

Figure 5.2-5. LC eddy separation events with LC retreat latitude following separation 

shown by dashed black lines (March 1983 through January 1986). ................252

Figure 5.2-6. LC eddy separation events with LC retreat latitude following separation 

shown by dashed black lines (Sept. 1986 through Nov. 1991). .......................253

Figure 5.2-7. LC eddy 1992 “Unchained” as observed by ERS-1 on the date of separation, 

10 August 1992.................................................................................................254

Figure 5.4-1. Satellite usage in the CCAR gridded altimeter dataset during the time period 

from 1993 through 2012...................................................................................261

Figure 5.4-2. Monthly histograms of separation and detachment dates determined from the 

CCAR, AVISO, and AVISO-CUPOM SSH datasets. .....................................267

Figure 5.4-3. Daily LC area, volume, anticyclonic circulation, westernmost longitude, and 

northernmost latitude time series and corresponding histograms. ...................268

Figure 5.4-4. Monthly mean plots of LC area, area including detachments, northernmost 

latitude, volume, anticyclonic circulation, and westernmost longitude 

statistics. ...........................................................................................................269

Figure 5.5-1. LC eddy separation dates binned monthly from reanalysis and Vukovich 

(2012) pre-altimetry (1978-1992).....................................................................279
xiii

Figure 5.5-2. Monthly-binned histograms of pre-altimetry, altimetry, and combined LC 

eddy separation date datasets............................................................................281

Figure 5.5-3. LC eddy separation dates binned monthly from CCAR, AVISO, and 

AVISO-CUPOM altimetry (1993-2012)..........................................................282

Figure 5.5-4. LC eddy separation dates binned monthly from combined pre-altimetry 

reanalysis (1978-1992) and CCAR, AVISO, and AVISO-CUPOM altimetry 

(1993-2012). .....................................................................................................286

Figure 5.5-5. LC eddy separation dates binned monthly (1978-2012) from combined 

Vukovich (2012) pre-altimetry (1978-1992) and CCAR, AVISO, and 

AVISO-CUPOM altimetry (1993-2012)..........................................................287

Figure 5.5-6. Pre-altimetry reanalysis LC eddy separation dates from 1978-1992 plotted as 

days-of-year on the unit circle in the complex plane, divided into two 

seasons..............................................................................................................289

Figure 5.5-7. LC eddy separation dates from CCAR, AVISO, and AVISO-CUPOM 

altimetry (1993-2012) plotted as days-of-year on the unit circle in the 

complex plane, and divided into two seasons. .................................................290

Figure 5.5-8. LC eddy separation dates (1978-2012) combining the reanalysis prealtimetry with CCAR, AVISO, and AVISO-CUPOM altimetry dates plotted 

as days-of-year on the unit circle in the complex plane, and divided into two 

seasons..............................................................................................................291

Figure 5.6-1. Deepwater EOF mode 1, and EOF mode 2 loading vectors, derived from 

monthly AVISO SSH with the steric signal removed. .....................................296

Figure 5.6-2. Deepwater EOF mode 3, and EOF mode 4 loading vectors, derived from 

monthly AVISO SSH with the steric signal removed. .....................................298

Figure 5.6-3. Deepwater principal component time series PCTS 1 and PCTS 2, and PCTS 

3 and PCTS 4, derived from monthly AVISO SSH with the steric signal 

removed. ...........................................................................................................299

Figure 5.6-4. CACs generated from deepwater EOF mode PCTS 1 and PCTS 2, and PCTS 

3 and PCTS 4....................................................................................................301

Figure 5.6-5. Sum variance of monthly AVISO maps, and fraction of total variance 

captured by first four deepwater EOF modes including correlated signals at 

depths less than 200 m......................................................................................302

Figure 5.6-6. CAC of Loop Current northern boundary latitude. ..........................................303

Figure 5.6-7. CAC of Loop Current area. ..............................................................................304

Figure 5.6-8. CAC_raw deepwater EOF mode 1, and EOF mode 2......................................306

Figure 5.6-9. CAC_raw deepwater EOF mode 3, and EOF mode 4......................................308

Figure 5.6-10. CAC_raw deepwater PCTS for EOF mode 1 and EOF mode 2, and EOF 

mode 3 and EOF mode 4. .................................................................................309

Figure 5.6-11. CAC1234 deepwater EOF mode 1, and EOF mode 2......................................310
xiv

Figure 5.6-12. CAC1234 deepwater EOF mode 3, and EOF mode 4......................................311

Figure 5.6-13. CAC of Loop Current northern boundary latitude. ..........................................312

Figure 5.6-14. CAC of Loop Current area. ..............................................................................313

Figure 5.6-15. Coastal EOF mode 1 loading vector derived with monthly AVISO data from 

1993 through 2012 with CAC removed, low-pass-filtered, and detrended and 

unfiltered...........................................................................................................318

Figure 5.6-16. Interannual EOF mode 1 from monthly tide gauge SSH data for June 1993 

through October 2001 compared to EOF mode 1 derived from coastal 

AVISO SSH data low-pass filtered with CAC/linear trend removed and 

unfiltered...........................................................................................................319

Figure 5.6-17. Gulf Western Boundary Current ship drift speed anomaly CAC as compared 

to the northward geostrophic speed anomaly derived from CAC_raw. ...........320

Figure 5.6-18. CAC1234 EOF mode 1 loading vector, and CM1 loading vector with 5.07-

cm offset applied. .............................................................................................321

Figure 5.6-19. Sum variance of monthly AVISO maps, and fraction of total variance 

generated by monthly reconstruction of CM1..................................................323

Figure 5.6-20. CAC of Loop Current northern boundary latitude, and CAC of Loop Current 

area. ..................................................................................................................324

Figure 6.1-1. Locations for the mooring array in the Gulf of Mexico, the NDBC buoy and 

the track of Hurricane Ida.................................................................................329

Figure 6.2-1. Six-kilometer Intra-Americas Sea circulation model domain. .........................330

Figure 6.2-2. Time series comparison of east and north wind components between hourly 

42003 buoy observations and the merged 6-hourly product used to drive the 

model in late 2009. ...........................................................................................331

Figure 6.2-3. Winds during the passage of Hurricane Ida over the eastern Gulf from 

merged Hurricane Center and NCEP 10-m data. .............................................333

Figure 6.2-4. Model simulated Sea-Surface Height in early November 2009. Purple line is 

the 17-cm SSH contour. ...................................................................................334

Figure 6.3-1. Time series of high-pass filtered horizontal velocity at various depths from 

450-m ADCP measurements at mooring A4 and from model simulations at 

the same location. .............................................................................................335

Figure 6.3-2. Time series of high-pass filtered horizontal velocity at various depths from 

500-m ADCP measurements at mooring E5. ...................................................336

Figure 6.3-3. Clockwise rotary power spectra for high-pass filtered horizontal velocity at 

moorings for the upper 500 m. .........................................................................337

Figure 6.4-1. Mean normalized relative vorticity plot for 6 November to 6 December 2009 

at 200 m for the LC study moorings, and vertical plot of mean normalized 

relative vorticity at the E-transect moorings for the same period.....................339
xv

Figure 6.4-2. Time series evolution of zonal momentum budget at moorings A4 and E5 

during the Hurricane Ida period. ......................................................................341

Figure 6.5-1. Time series of inertial frequency velocity amplitudes from complex 

demodulation at moorings A4, B2 and C1 for depths of 100 and 300 m, 

respectively.......................................................................................................342

Figure 6.5-2. Time series of high-pass filtered horizontal velocity components at various 

depths from the 450-m ADCP measurements at mooring A4 for two periods, 

November 2009 and January 2011. ..................................................................343

Figure 6.5-3. Time series of atmospheric pressure, atmospheric temperature, and wind 

vectors for two winter periods for NDBC buoy 42003. ...................................345

Figure 6.5-4. Time series of high-pass filtered horizontal velocity components at various 

depths from the 450-m ADCP measurements at mooring B2 for two periods, 

November 2009 and January 2011. ..................................................................346

Figure 6.5-5. Time series of high-pass filtered horizontal velocity components at various 

depths from the 450-m ADCP measurements at mooring B2 for the 2010-

2011 winter.......................................................................................................347

Figure 6.5-6. Time series of atmospheric pressure, atmospheric temperature, and wind 

vectors for the 2010-2011 winter periods for NDBC buoy 42003...................348

Figure 7.3-1. Depth range weighted CEOF modes for LC mooring A3 and Exploratory 

mooring L4. ......................................................................................................355

Figure 7.6-1. PIES/mooring arrays deployed in the eastern Gulf for this and prior 

BOEM/MMS programs. ...................................................................................361

Figure 7.6-2. A possible configuration of PIES and moorings for a LC radiation 

experiment. .......................................................................................................362

Figure A-1. Amplitude and phase of the O1, K1, Q1, and P1 constituents determined 

with the tidal response method from the 25 bottom pressure records..............386

Figure A-2. Amplitude and phase of the M2, K2, N2, and S2 constituents determined 

with the tidal response method from the 25 bottom pressure records..............387

xvii

LIST OF TABLES

Table 2.2-1. Triangulated Mooring Locations and Depths by Deployment for the Loop 

Current Study......................................................................................................15

Table 2.2-2. Mooring Deployment Periods for the Loop Current Study................................16

Table 2.2-3. PIES Deployment Locations and Periods for the Loop Current Study ..............17

Table 2.2-4a. Mooring Locations and Moored Instrument Levels for the Loop Current 

Study (American Sector) with Nominal Instrument Depths (Tall Moorings 

A1, A2, A3 and A4) ...........................................................................................20

Table 2.2-4b. Mooring Locations and Moored Instrument Levels for the Loop Current 

Study (American Sector) with Nominal Instrument Depths (Tall Moorings 

B1, B2 and B3)...................................................................................................21

Table 2.2-4c. Mooring Locations and Moored Instrument Levels for the Loop Current 

Study (American Sector) with Nominal Instrument Depths (Tall Moorings 

C1, C2 and Short Moorings D1, D2, D3, D4, D5, D7 and D8) .........................22

Table 2.2-5. Moored Instrument Data Return (by Good Record Count) during the Loop 

Current Study......................................................................................................28

Table 2.3-1. Listing of CTD Casts made at PIES Sites during the Loop Current Study........30

Table 2.4-1. Mexican Mooring Locations and Deployment Periods during the Loop 

Current Study......................................................................................................31

Table 2.6-1. Satellite Altimeter Missions Active During the LC Study Program ..................71

Table 2.7-1. Satellite Altimeter Mission Exact-Repeat Periods and Periods Associated 

with the Nyquist Sampling Frequency ...............................................................80

Table 2.7-2. Unaliased Variance Statistics for 10-day, 17-day, and 35-day Exact-Repeat 

Sampling of the PIES Barotropic, Baroclinic, and Combined SSH Signals......85

Table 2.7-3. PIES SSH, Baroclinic, and Barotropic Statistics and Percent of Unaliased 

Variance Measured by Satellites in 10-day, 17-day, and 35-day ExactRepeat Orbits......................................................................................................86

Table 2.7-4. Signal-to-Noise Ratio (SNR) Statistics for 10-day, 17-day, and 35-day 

Exact-Repeat Sampling of the PIES Barotropic, Baroclinic and Combined 

SSH Signals........................................................................................................89

Table 2.7-5. Half-Power Period of PIES Barotropic, Baroclinic, and Total SSH Signals .....91

Table 3.3-1. A Summary of Various Skill Metrics Computed Using Currents from the 

Model and ADCP Measurements from Moorings A1 to C2............................139

Table 3.4-1. Percent Variance Accounted for by Depth-Range Weighted CEOF Modes (7 

June 2009 to 1 May 2011)................................................................................144

Table 3.4-2. Average Propagation Speeds Determined from the CEOF Analysis...............166
xviii

Table 5.2-1. Eddy separation events with the corresponding retreat latitudes and 

separation periods from July 1978 through December 1992............................245

Table 5.2-2. Date ranges for LC eddy separation events shown in Figures 5.2-4, 5.2-5 and 

5.2-6..................................................................................................................255

Table 5.3-1. Comparison of re-analysis LC eddy separation dates with those from 

Vukovich (2012)...............................................................................................257

Table 5.4-1. LC eddy separation event dates with the corresponding retreat latitudes and 

separation periods from January 1993 through December 2012, derived from 

CCAR SSH dataset...........................................................................................262

Table 5.4-2. Comparison of LC eddy separation event dates derived from CCAR, 

AVISO, and AVISO-CUPOM SSH datasets from January 1993 through 

December 2012.................................................................................................263

Table 5.4-3. Comparison of LC eddy detachment event dates derived from CCAR, 

AVISO, and AVISO-CUPOM SSH datasets from January 1993 through 

December 2012. The HMI industry name of the LC eddy separation event 

following each date is also listed......................................................................265

Table 5.4-4. Comparison of altimetry record LC eddy separation dates from AVISO reanalysis (from Table 5.4-2), Chang and Oey (2013b), Vukovich (2012), and 

Lindo-Atichati et al. (2013)..............................................................................271

Table 5.4-5. LC eddy separation timing of the 19 events where each source – the AVISO 

re-analysis (from Table 5.4-2), Chang and Oey (2013b), Vukovich (2012), 

and Lindo-Atichati et al. (2013) – reported a separation event, excluding 

events #25 and 34 .............................................................................................272

Table 5.4-6. Comparison of LC eddy separation events.......................................................274

Table 5.5-1. Results of significance testing of various sources of LC eddy separation 

event dates........................................................................................................283

Table 5.5-2. Centers (means) and standard deviations (std.) of Table 5.2-1 and 5.4-2 

separation events analyzed separately and combined, separated into spring 

and fall seasons and presented circularly and linearly .....................................293

Table 5.6-1. Proportion of LC northern latitude and area variance explained by first four 

deepwater EOF modes reconstructed as monthly time series and as CACs 

(CAC1, CAC12, CAC123, and CAC1234) with reference to complete 

monthly time series and CAC of original AVISO data (CAC_raw)................305

Table 5.6-2. Proportion of CAC_Raw and CAC1234 LC northern latitude and area 

variance explained by CACs of reconstructions of first four deepwater EOF 

modes of CAC1234 ..........................................................................................314

Table 5.6-3. Proportion of CAC_Raw and CAC1234 LC northern latitude and area 

variance explained by the monthly reconstruction of CM1 .............................322

Table A-1. Amplitude in CM and Phase in Degrees for Four Major Tidal Constituents 

(O1, K1, Q1, P1)...............................................................................................388
xix

Table A-2. Amplitude in CM and Phase in Degrees for Four Major Tidal Constituents 

(M2, K2, N2, S2)..............................................................................................389

xxi

ABBREVIATIONS AND ACRONYMS

ADCP: Acoustic Doppler Current Profiler

APEX: Autonomous Profiling Explorer

ARGOS: Advanced Research Global Observation Satellite (nolonger an acronym)

AVHRR: Advanced Very High Resolution Radiometer

AVISO: Archiving, Validation and Interpretation of Satellite Oceanography

BC: Baroclinic Conversion

BCB: Baroclinic Referenced to the Bottom

BOEM: Bureau of Ocean Energy Management

BT: Barotropic Streamfunction

CAC: Composite Annual Cycles

CASE/EJIP: Climatology and Simulation of Eddies/Eddy Joint Industry Project

CCAR: Colorado Center for Astrodynamics Research

CCMP: Cross-Calibrated Multi-Platform

CEOF: Complex EOF

CICESE: Centro de Investigacion Cientifica y de Educacion Superior de Ensenada

CLS: Carrere and Lyard (2003) Sea state bias

CM1: Coastal EOF Mode 1

CNES: Centre National d’Etudes Spatiales, France

CPD: Cycles per Day

CPIES: PIES with an attached Doppler current sensor suspended 50 m above the PIES

CT: Conductivity/Temperature

CTD: Conductivity/Temperature/Depth

CTW: Coastal-Trapped Wave

CUPOM: University of Colorado version of the Princeton Ocean Model

CWT: Continuous Wavelet Transform

CZCS: Coastal Zone Color Scanner

DBAR: Decibars

DGPS: Digital Global Positioning System

DLP: Day Low Pass

DOF: Degrees of Freedom

DOY: Days of Year

DT: Delayed Time

DWH: Deepwater Horizon

EAP: Eddy Potential Energy

EEZ: Exclusive Economic Zone

EKE: Eddy Kinetic Energy

EOF: Empirical Orthogonal Function

ERM: Exact Repeat Mission

ERS-2: Earth Resources Satellite – 2

ESA: European Space Agency

FIO: Florida Institute of Oceanography

GEM: Gravest Empirical Mode or Gulf Eddy Model

GEOSAT: Geodetic Satellite
xxii

GERG: Geochemical and Environmental Research Group (TAMU)

GFE: Government Furnished Equipment

GFO: Geosat Follow-On

GFS: Global Forecast System

GHRSST: Group for High Resolution Sea-Surface Temperature

GIM: Global Ionosphere Map

GMT: Greenwich Mean Time or UTC

GOES: Geostationary Operational Environmental Satellite

GOM: Gulf of Mexico

GOMRI: Gulf of Mexico Research Initiative

GPS: Global Positioning System

GS: Gulf Stream

GSFC: Goddard Space Flight Center

GVAR: Global Vector Auto-Regression

HCMM: Heat Capacity Mapping Mission

HHP: Hour High Pass

HLP: Hour Low Pass

HMI: Horizon Marine, Inc.

HRD: Hurricane Research Division

HYCOM: Hybrid Coordinate Ocean Model

IAS: Intra-American Sea

IES: Inverted Echo Sounder

JPL: Jet Propulsion Laboratory

KE: Kinetic Energy

LC: Loop Current

LCFE: Loop Current Frontal Eddy

LCS: Lagrangian Coherent Structures

LCT: Loop Current Toolbox

LH: Left Hand

LSU: Louisiana State University

LUMCON: Louisiana Universities Marine Consortium

MAB: Meters above Bottom

MADT: Maps of Absolute Dynamic Topography

MAP: Mean Advection of Eddy Potential Energy

MCSST: Microwave Instrument for SST

MICOM: Miami Isopycnic Coordinate Ocean Model

MMS: Minerals Management Service

MODIS: Moderate Resolution Imaging Spectroradiometer

MPI: Message Passing Interface

MUR: Multi-Scale Ultra-High Resolution

NAD 83: North American Datum of 1983

NASA: National Aeronautics and Space Administration

NCEP: National Center for Environmental Prediction

NDBC: National Data Buoy Center

NEPA: National Environmental Policy Act

NGDC: National Geophysical Data Center
xxiii

NOAA: National Oceanic and Atmospheric Administration

NODC: National Ocean Data Center

NOS: National Ocean Survey

NRT: Near Real Time

NSF: National Science Foundation

OA: Objective Analysis

OBPG: Ocean Biology Processing Group

PCTS: Principal Component Time Series

PDR: Precision Depth Recorder

PE: Potential Energy

PI: Principal Investigator

PIES: Inverted Echo Sounder with Pressure

PKC: Eddy Potential to Kinetic Energy Conversion

PO: Physical Oceanography

PO.DAAC: Physical Oceanography Distributed Active Archive Center

POM: Princeton Ocean Model

PROFS: Princeton Regional Ocean Forecast System

PSU: Practical Salinity Unit

PV: Potential Vorticity

PVA: Potential Vorticity Anomaly

QB: Quasi-Barotropic

R: Correlation Coefficient

RADS: Radar Altimeter Database System

RAFOS: Ranging and Fixing of Sound (SOFAR spelled backwards)

RDI: RD Instruments

Re: Regression Coefficient

RFP: Request for Proposal

RG: Reduced Gravity

RH: Right Hand

RHS: Right Hand Side

RMS: Root Mean Square

ROMS: Regional Ocean Modeling System

RV: Relative Vorticity

SAIC: Science Applications International Corporation

SAR: Synthetic Aperture Radar

SI: Surface Intensified

SLA: Sea-Level Anomaly

SNR: Signal-to-Noise Ratio

SOFAR: Sound Fixing and Ranging

SSH: Sea Surface Height

SSHA: Sea Surface Height Anomaly

SST: Sea Surface Temperature

SUW: Subtropical Underwater

Sv: Sverdrups

T: Temperature

TAMU: Texas A&M University
xxiv

T/C/P: Temperature/Conductivity/Pressure

TOPEX Ocean Topography Experiment

TOP/POS: TOPEX/Poseidon

TRW: Topographic Rossby Wave

T/S/P: Temperature/Salinity/Pressure (or T/P/S: Temperature/Pressure/Salinity)

UCK: Universal Co-Kriging

URI: University of Rhode Island

USCG: United States Coast Guard

USGS: United States Geological Survey

UTC: Coordinated Universal Time or GMT

USF: University of South Florida

VHRR: Very High Resolution Radiometry

WFS: West Florida Shelf

WGS 84: World Geodetic System of 1984

XBT: Expendable Bathythermograph

XCP: Expendable Current Profiler

XCTD: Expendable CTDs

YC: Yucatan Channel
1

CHAPTER 1: INTRODUCTION 

1.1 BACKGROUND

Over the last decade, the Bureau of Ocean Energy Management (BOEM), formerly the Minerals 

Management Service (MMS), of the U.S. Department of the Interior, has conducted major 

physical oceanographic measurement programs in the deep waters of the Gulf of Mexico. These 

studies provided information on circulation and physical processes for aiding the safe exploration 

for oil and gas in U.S. waters in water depths of 1000 m or more, as well as for assessing 

environmental impacts of such activities. These observational studies included the DeSoto 

Canyon Eddy Intrusion Study (Hamilton et al. 2000; Hamilton and Lee 2005), Deepwater 

Observations in the Northern Gulf of Mexico from In-Situ Current Meters and PIES (Hamilton et 

al. 2003), Exploratory Study of Deepwater Currents in the Gulf of Mexico (Donohue et al. 

2006), Survey of Deepwater Currents in the Northwestern Gulf of Mexico (Donohue et al. 2008), 

and Study of Deepwater Currents in the Eastern Gulf of Mexico (Cox et al. 2010). These 

programs have advanced the state of knowledge of the deep Gulf, and have included the first use 

in the Gulf of pressure-equipped inverted echo sounders (PIES), and deep Lagrangian RAFOS 

floats.

The deep waters of the Gulf, including the lower continental slope and abyssal depths, can be 

characterized as being in two layers. Current variation in the upper layer, from the surface to 

800 – 1200 m, is dominated by mesoscale eddies, both cyclonic and anticyclonic (anti-clockwise 

and clockwise rotations, respectively when viewed from above). Also, the Loop Current (LC), a 

segment of the Gulf Stream system, enters the Gulf through the Yucatan Channel (YC), extends 

northward as a quasi-stationary clockwise turning meander and exits through the Straits of 

Florida. The LC sheds large anticyclonic eddies or rings (200 – 400 km in diameter) at irregular 

intervals of between 4 and 18 months (Sturges and Leben 2000). After the eddy detachment is 

complete, a LC eddy will typically translate westward and southwestward across the basin. 

These large energetic LC eddies dominate the upper-layer circulation and appear to have a major 

role in generating smaller-scale cyclones and anticyclones (diameters 30 – 150 km) that are often 

found over the continental slope and in deep water. Figure 1.1-1 illustrates the LC and a 

partially detached LC eddy along with the mesoscale eddy field using satellite remote sensing of 

sea-surface temperature (SST), and sea-surface-height anomalies (SSHA) derived from 

altimeters. There are a number of examples in the above reports and in the literature of eddyeddy and eddy-topography interactions that make the Gulf upper-layer circulation complex and 

highly dynamic.

Whereas the upper-layer eddy flows are surface intensified with the strongest currents occurring 

in the top 100 m, the lower-layer flows, from ~ 1000 m to the seabed, are either slightly bottom 

intensified or nearly depth independent. These lower-layer motions have been attributed to 

propagating planetary waves (e.g., topographic Rossby waves (TRWs) discussed in Hamilton 

(1990; 2009)), though lower-water-column eddies are not ruled out. Near-bottom currents with 

speeds ~ 90 cm/s have been measured near the base of the Sigsbee escarpment in the northern 

Gulf (Hamilton and Lugo-Fernandez 2001). TRWs have wave periods of between 10 and 100 

days, and length scales ~ 70-200 km and, for the most part, are decoupled from the surface-layer 

eddies where they have been observed. However, because TRWs propagate generally westward
−30 −20 −10 0 10 20 30

SSH (cm)

− 20 c m

−20 cm

−2 0 c m

−20 cm

−10 cm

−10 cm

− 10 cm

−1 0 cm

−10 cm

− 10 cm

−1 0 cm

−10 cm

0 cm

0 c m

0 cm

10 cm

20 cm

3 0 cm

30 cm

40 cm

40 cm

50 cm

5 0 cm

6 0 cm

60cm

60 cm

SSH, April 21, 2011

90 ̊W

90 ̊W

88 ̊W

88 ̊W

86 ̊W

86 ̊W

84 ̊W

84 ̊W

82 ̊W

82 ̊W

80 ̊W

80 ̊W

20 ̊N 20 ̊N

22 ̊N 22 ̊N

24 ̊N 24 ̊N

26 ̊N 26 ̊N

28 ̊N 28 ̊N

30 ̊N 30 ̊N

23 24 25 26 27

°C

MODIS SST, April 21, 2011

90 ̊W

90 ̊W

88 ̊W

88 ̊W

86 ̊W

86 ̊W

84 ̊W

84 ̊W

82 ̊W

82 ̊W

80 ̊W

80 ̊W

20 ̊N 20 ̊N

22 ̊N 22 ̊N

24 ̊N 24 ̊N

26 ̊N 26 ̊N

28 ̊N 28 ̊N

30 ̊N 30 ̊N

Moorings

PIES

April 21, 2011

Contour Interval: 5cm

Loop Current: 17cm

Hadal

Figure 1.1-1. A high resolution SST image (left panel) and SSH altimeter map (right panel) showing an extended LC and a partially 

detached LC eddy (Hadal) on 21 April 2011. The fine white lines are isobath contours at 200, 1500 and 3000 m, and the 

dots are mooring and PIES locations (full depth only on left panel; complete array on right panel).

2 
3

with shallower water on the right-hand-side (RHS) of the direction of propagation, major 

generation sources for these deep energetic flows are expected to be the LC, and secondarily the 

westward propagating LC eddies (Oey and Lee 2002).

The LC is, therefore, of major importance to the circulation in the Gulf of Mexico both as a 

direct and indirect generator of surface-layer eddies, and as a source of deep lower-layer flows. 

Until this study, the LC had surprisingly few in-situ observations commensurate with the time 

scales of the LC eddy-shedding cycle. Much of what is known has come from remote sensing 

studies of surface layer variability (Leben 2005; Leben and Born 1993; Vukovich 1986; 

Vukovich et al. 1979), and numerical modeling studies (Oey et al. 2005). Clockwise circulating, 

frontal propagating frontal cyclones, known as LC frontal eddies (LCFEs), were identified as a 

possible trigger for the pinch-off of a LC eddy by the larger scale meander variability of the LC 

front (Schmitz 2005). However, a number of mechanisms, which may act in combination, have 

been identified as playing roles in the separation of a major LC eddy. These include the large 

scale “momentum paradox” of Pichevin and Nof (1997), to baroclinic instabilities (Hurlburt and 

Thompson 1982), to potential vorticity fluxes through the YC (Candela et al. 2002). Longerterm moored current measurements were not attempted until the early 1980s 

(Science Applications International Corporation 1989) when the energetic and depthindependent nature of flows below 1000 m were established for the east side of the LC. Later, a 

single long-term mooring was deployed for several (not contiguous) years on the west side of the 

LC (Inoue et al. 2008). In order to advance understanding of the LC role in the Gulf, BOEM 

funded the present study and a complementary study in Mexican waters, to deploy a 

comprehensive array of instruments in the eastern Gulf, supplemented by remote sensing and 

numerical modeling. The resulting 2 to 2.5 year long observational database is being used to 

study LC variability, LC eddy shedding, and the controlling dynamics from the basin scale to the 

small LCFE scales. The database will also be invaluable for determining the realism, 

particularly in the lower layer, of numerical model simulations of the Gulf, and will be exploited 

for many years to come.

The overarching goal of this study is to increase knowledge of the dynamics of the LC in the 

eastern Gulf of Mexico through a combined analysis of observations and numerical modeling 

output. Specific objectives are to:

Increase understanding of the causes of the LC incursions into the Gulf, 

1. Describe oceanographic conditions leading up to and during eddy shedding, and 

reattachment and to help understand the dynamics of these processes; 

2. Understand how the LC interacts with and drives the lower-layer circulation;

3. Provide statistics from in situ observations supplemented by numerical modeling 

output that describes the general circulation patterns inferred from remote sensing and 

geostrophic calculations; 

4. Analyze the available data and model output to develop an understanding of 

processes and interactions from the large basin to small eddy scales that control the 

variability of the LC, including the separation of rings; and

5. Provide information for BOEM to fulfill its regulatory mission and to comply with 

data and information needs for National Environmental Policy Act (NEPA) 

requirements.
4

1.2 GENERAL PROGRAM DESCRIPTION

The study design for the in-situ measurements consisted of an array of nine full-depth (or tall) 

moorings, six near-bottom moorings, and 25 PIES deployed in U.S. waters. Instrumentation 

used on the moorings is given in Chapter 2. The location of the array, referred to as the mapping 

array in this report, is given in Figure 1.2-1. The location of the array was determined partly by 

the location of the Exclusive Economic Zone (EEZ) boundary between the U.S. and Mexico, and 

an analysis of 19 eddy separations from the altimeter record. Based on these data, the mapping 

array is centered on the region that has the highest probability of capturing the separation zone 

between a recently detached LC eddy and the LC, as well as encompassing both the northwest 

and east sides of an extended LC. The spacing of moorings and PIES was set to resolve the 

coherence scales of both the upper and lower layers based on previous deepwater studies that 

showed that length scales in the lower layer tend to be shorter than at the surface. The mapping 

array was deployed for 2.5 years beginning in April 2009 with the final retrieval in November 

2011. The moorings were rotated half way through at 15 months into the deployment. The PIES 

were deployed for the whole observational period without rotation, though the first 15 months of 

data were retrieved in July 2010 through uploads via a hydrophone. Two 1500-meter depth CTD 

casts were taken at most of the PIES sites. These were used for calibration of round-trip travel 

times during the deployment period (see Chapter 2 for details).

Because this study was restricted to deploying moorings inside the U.S. EEZ, BOEM funded 

complementary arrays in Mexican waters that were deployed by the CANEK group at the Centro 

de Investigación Científica y Educación Superior de Ensenada (CICESE), Mexico. The 

locations of the CICESE moorings are also given in Figure 1.2-1, where all Mexican moorings 

were full depth. Instrumentation and mooring design, which differs from the mapping array, are 

again given in Chapter 2. The CICESE moorings were deployed in June 2009 and rotated on an 

annual basis, providing a two-year overlap with the mapping array data (see Figure 1.2-2). 

BOEM funded the work associated with transects E and N across the Campeche Bank eastern 

slope. The Yucatan Channel (YC) moorings were part of an already established Mexican funded 

study, and BOEM provided some assistance with instrumentation for this transect. For these 

reasons, the data from transects E and N will be integrated into the analysis, but YC data will 

only be used for some derived products (such as volume transport) that have been supplied by 

our colleagues at CICESE. Many of the CICESE moorings were still deployed (as of June 2013) 

for a third year of measurements that naturally will not be included in the combined datasets.

Monitoring LC variability at the larger scales is important so as to place the in-situ 

measurements in context. Therefore, the study included a remote sensing task using satellite 

altimetry for SSHA, and ocean color and SST for examining features at higher resolution. The 

SSHA altimetric database that resolves mesoscale eddies in the Gulf of Mexico now extends 

over nearly three decades, and is used herein to place the in-situ LC observations in historical 

context, as well as for analysis of longer term and larger space-scale processes such as upstream 

and downstream influences on the eddy separation processes.
100 m

100 m

500 m

1000 m

3000 m

3500 m

2000 m

1000 m

Loop Current Moorings (CICESE/SAIC)

April 2009

- November 2011

June 2009

- June 2011

PIES

SAIC Tall Moorings

SAIC Short Moorings

CICESE Campeche

Moorings

CICESE Yucatan

Moorings

Campeche

Bank

Yucatan Peninsula

Cuba

Florida

West Florida

Shelf

Mississippi Fan

Florida

Straits

Yucatan

Channel

EEZ

5

Figure 1.2-1. Locations of moorings and PIES deployed in the U.S. and Mexican sectors in the eastern 

Gulf of Mexico during the study of Loop Current dynamics.
6

Data Acquisition Intervals

Figure 1.2-2. Schedule and relationships of data types collected and used during this study.

Dashed line represents additional CICESE data collected but not discussed in this report.

A numerical modeling component is included in this study, and was designed to primarily assist 

in the analysis of LC processes by performing experiments on LC growth and eddy-shedding 

processes, and relating them to the observations. Model studies are also used in a similar manner 

to the long time series of altimetric SSHA maps to examine remote influences and basin-scale 

processes in three dimensions.

The general schedule for the measurement programs and data acquisition is shown above. The 

Science Applications International Corporation (SAIC1

) contract was awarded in September 

2008 with mobilization taking place over the first six months. The deployment, rotation and 

recovery cruises for the mapping-array moorings and PIES were complex logistical operations 

requiring several legs because of the amount and weight of the hardware. Subsequently, the 

cruises lasted three to four weeks, with staging at Cododrie, Louisiana (LUMCON), and St.

Petersburg, Florida (FIO), and use of the R/V Pelican (LUMCON) and the R/V Weatherbird II 

(FIO).

1.3 STUDY PARTICIPANTS

Participants in the study included the science team of principal investigators (PIs), support 

personnel, both at SAIC and the home institutions of the science team, and PIs of co-operating 

studies. The science team and their primary areas of responsibility were:

Affiliation Responsibility

Dr. Peter Hamilton Science Applications 

International Corporation 

(SAIC)

Moorings, upper and 

lower; layer circulation; 

inertial currents

Dr. Kathleen Donohue University of Rhode Island PIES; upper- and lowerlayer subtidal circulation

Dr. Randy Watts University of Rhode Island PIES; upper- and lowerlayer subtidal circulation

 1 SAIC was split into two companies on September 27, 2013; the newly-named Leidos Corporation inherited 

the contract. 

Mapping Array

CICESE Array

Remote Sensing

Deployment

Deployment

Rotation

Rotation Rotation

Recovery
7

Affiliation Responsibility

Dr. Robert Leben University of Colorado Remote sensing and 

altimetry

Dr. Leo Oey Princeton University Modeling and data 

synthesis

It is important to note that the complete data set from the U.S. and Mexican sectors was available 

to both the science team and investigators at CICESE. Dr. Julio Sheinbaum was the program 

manager for the CICESE measurements, and he made many contributions through the program 

meetings of this study, and through informal collaborations with SAIC’s team members. 

Collegial interactions within the team and with cooperating studies were an important part of the 

approach to the analysis tasks so that combined expertise was brought to bear on complex 

physical processes.

Ms. Hui Quian worked as an intern under the supervision of Dr. Hamilton and her advisor Dr. 

Ruoying He of North Carolina State University. As part of her dissertation (Ph.D. awarded in 

December 2013), she performed a statistical and model-based analysis of inertial currents 

measured by the array, which contributed to Chapter 6 in this report. Mr. Cody Hall worked as a 

graduate research assistant under the supervision of Dr. Robert Leben at the University of 

Colorado. He was awarded a Ph.D. in Aerospace Engineering Sciences on May 8, 2014 based on 

his dissertation titled “Loop Current Seasonality”, which contributed substantially to Chapter 5 

in this report.

The science team was supported by SAIC Management and Logistic personnel as follows:

Dr. Peter Hamilton, Program Manager

Mr. James Singer, Logistics Manager and Cruise Chief Scientist

Mr. Paul Blankinship, Data Manager

All moored current-meter arrays in the U.S. sector were the responsibility of SAIC. The 

University of Rhode Island was responsible for PIES instrumentation, including preparation, 

deployment, at-sea interrogation, and recovery. The University of Colorado handled satellite 

remote sensing, and Princeton University handled the facilities for numerical modeling. The 

CICESE physical oceanographic group was responsible for moorings in the Mexican sector.

Until he left the company, Dr. Scott McDowell was the program manager for the first year of the 

program. Dr. Nick Shay of the University of Miami was the PI for a cooperative study involving 

aircraft AXBT/AXCTD/AXCP surveys of the LC related to hurricane activity in the eastern Gulf 

of Mexico.

1.4 LOOP CURRENT EDDY SHEDDING

As outlined in Section 1.1, the Loop Current (LC) provides the dominant influence on upperlayer circulations in the Gulf. It can have a wide variety of configurations ranging from turning 

directly eastward from the Yucatan Current to the Straits of Florida along the coast of Cuba (port 
8

to port mode) to extending in a loop far northwards or northwestwards so as to directly impact 

the continental slopes south of Mississippi and Alabama (Huh et al. 1981). The upper-layer 

current is characterized by strong velocity shears laterally and vertically with flow limited to a 

depth of ~ 800 to 1000 m; it carries warmer water and a saline core (>36.5 psu) of subtropical 

underwater (SUW) at about 200 m depth. In this study, the upper layer is defined from the 

surface to the depth of the 6 °C isotherm, and the lower layer from the 6 °C isotherm depth to the 

bottom. The 6 °C surface corresponds to the lowest part of the LC and also corresponds to the 

sill depth (~ 800 m) in the Straits of Florida (Bunge et al. 2002). 

At irregular intervals, as the LC extends northwards or northwestwards towards the Mississippi 

delta, it sheds a warm anticyclonic ring called a Loop Current eddy of diameter ~ 200 to 400 km. 

The separated LC eddies subsequently move into the western Gulf, eventually interacting with 

the topography of the western Mexican slope and dissipating there. Often a recently detached 

LC eddy will reattach to the LC. Detachment and reattachment may happen several times, over 

intervals as long as a few months, before the final detachment, when the eddy separates and 

moves into the western Gulf. In this report, reference to a detachment implies that there may be 

a subsequent reattachment, and only the last detachment is referred to as a separation, i.e., the 

eddy is shed. 

In this report, reference will often to be made to the LC or LC eddy front or boundary. In most 

cases this is defined to be the 17 cm SSH contour, which approximates the position the 

maximum horizontal shear on the cyclonic side of the jet, and is close to the maximum velocity 

of the surface jet. There is also a distinct surface temperature front (Figure 1.1-1) ~ 20 to 50 km 

to the left of the 17 cm SSH contour, looking downstream along the jet (Leben 2005), that is 

often blurred by the advective affects of cyclonic frontal eddies, and has a very small 

temperature contrast in the summer months. This front, and its associated subsurface downward 

sloping pycnocline, separates the warmer LC water mass with its high salinity SUW core, from 

external Gulf waters.

Immediately following LC eddy separation, the northern boundary of the LC itself has generally 

reformed south of 26°N (the retreat latitude), and the northward extension begins again. Leben 

(2005) showed that there is a strong correlation between the retreat latitude and the time to the 

next subsequent eddy shedding that may be explained as a consequence of mass conservation

and vorticity changes between retreated and extended positions (Lugo-Fernandez and Leben

2010). A 54-year free-running HYCOM numerical model of Gulf circulation has been able to 

reproduce this retreat latitude correlation. The mean time interval between eddy sheddings, 

based on the altimeter record, is ~ 9 to 11 months. However, based on a new, longer and 

improved database of eddy sheddings, there is evidence of seasonality in the probability that 

some months have higher incidences of separation events (see Chapter 5). Causes of this 

seasonality in the mean annual cycle may be related to the biannual variation in the strength of 

Caribbean trade winds (Chang and Oey 2013b), or alternatively, sea-level variability along the 

southeastern U.S. Atlantic and Gulf of Mexico continental shelf and slope (Chapter 5).

Eddy-shedding dynamics, including the effects of external influences, have been primarily 

explored using numerical models, where there seem to be as many explanations as there are 

models (see Oey et al. (2005) for a review). At one end of the spectrum, LC eddy separation is 
9

purely an upper-layer phenomenon that occurs once the LC extends northwards due to increases 

in upper-layer volume transport through the YC. Westward translation of the extended LC arises 

from momentum imbalance, analyzed by Pichevin and Nof (1997), that stretches the LC and 

effects a separation, whereupon the LC eddy translates westward at the long Rossby wave speed 

(referred to as β-advection). Separation is often preceded by a reduction in Yucatan Current 

volume transport. On the one hand, for example, Chang and Oey (2013a) suggest that the 

Pichevin-Nof mechanism is the only dynamics necessary for eddy separation. On the other hand, 

the model-based analyses of Chérubin et al. (2005) propose a more complex scenario in which 

instabilities that couple the upper and deepest layers in and under the LC, can develop suddenly, 

with a deepening of an extended LC, and pinch off a ring. Similarly, Le Hénaff et al. (2012) use 

potential vorticity arguments to account for the generation of lower-layer cyclones in their model 

when the upper-layer LC flows across the topography of the Mississippi Fan.

Frontal cyclones or LCFEs are observed, in remote sensing data, translating clockwise along the 

LC front, and have long been thought to play a role in LC eddy separations. The LCFEs are 

assumed to grow along the extended loop and effect a separation by extending from the west 

Florida slope across the neck. They are sometimes assisted by the appearance of a cyclone 

between the western LC front and the Campeche Bank slope that is assumed to propagate 

northwards through the Yucatan Channel (see Schmitz (2005) for further discussion). Model 

results of Chérubin et al. (2006) and Oey (2008) interpret deep lower-layer cyclones as being 

generated by LCFEs through instability processes that Chérubin et al. (2006) analyzed as 

barotropic and baroclinic vortex rim instabilities. In this report, LCFEs, originating along the 

Campeche Bank slope, are distinguished from large amplitude meanders of the north and eastside LC front (Chapter 4). 

The pioneering model studies of Hurlburt and Thompson (1982) showed that the LC is 

inherently unstable and will shed eddies even if Yucatan Channel transports are unvarying. 

Moreover the ring formation process requires an active lower layer for the model to generate 

realistic eddy shedding intervals. The role of the lower layer, which spans two-thirds of the 

water column in the deep eastern basin, has had relatively few observations, most of which are 

summarized by Hamilton (2009). Lower-layer flows in the eastern basin are observed to be 

either depth-independent or slightly bottom intensified, and are quite energetic, and can be 

considered to arise from a mixture of TRWs plus cyclonic and anticyclonic eddies. Their role in 

eddy-shedding dynamics has not been established, as the above discussion of model studies 

indicates. The results of Chapter 4 will show that energetic lower-layer currents are generated by 

intervals of baroclinic instability, and these deep eddy currents directly influence LC eddy 

detachments. 

On longer time scales of LC growth and eddy separation, Bunge et al. (2002) showed that 

observed lower-layer transport in the Yucatan Strait is directly related to change in LC area, 

approximately consistent with mass conservation. Chang and Oey (2011) have a more 

sophisticated view of this connection that involves exchange vertically between upper and lower 

layers and laterally between eastern and western basins (see Chapter 4).

The major thrusts in the present study combining observations and companion modeling 

activities are: (1) To study the variability of LC incursions into the Gulf, on time scales that span 
10

eddy-shedding, interannual, and multi-decadal processes; (2) To describe circulation processes 

that lead to detachments, reattachments, and separations during eddy shedding; (3) To 

understand how the LC interacts with and forces the lower-layer circulation; and (4) To 

incorporate observations from the Mexican sector of the Eastern Gulf into the investigation of 

circulation and dynamics. Many of the scientific topics outlined above, such as baroclinic 

instability, the influence of LCFEs on detachments and deep cyclones, are addressed in 

subsequent chapters, and in some cases the results differ from preceding paradigms.

1.5 MAJOR EVENTS

Eddy Separations

One of the primary aims of the study was to document and analyze LC eddy-shedding processes. 

A brief outline of the formation and eddy-shedding events is given here so as to place in context 

the following analysis and statistics chapters. The measurement program documented the 

formation and separation of three LC eddies: Ekman, Franklin, and Hadal, where the names were 

defined by an oil industry group (Eddy Watch). The study also documented the formation and 

first detachment of Icarus over the last three months of the U.S. observational period. Eddy 

Icarus did not fully separate from the LC until January 2012. Figure 1.5-1 gives an overview of 

the eddy detachments, showing the deepening of the isotherms over the array as the LC extended 

to the north and northwest. Both Ekman and Franklin were large eddies with multi detachments 

and re-attachments over several months, before finally separating, where the detachment points 

were south of the mapping array in the vicinity of transect E. Hadal was almost a canonical LC 

eddy that was preceded by the LC extending far to the northwest in a sequence of growth spurts. 

The eddy separated on its first detachment with the separation point being in the center of the 

mapping array. Eddy Watch also identified eddy Galileo as separating at the end of June 2011 

when the LC was fully extended to the northwest. However, it was not a true LC eddy, but 

rather a small region of anticyclonic circulation that was extruded from the northwest tip of the 

forming Hadal that rapidly dissipated.

Deepwater Horizon Oil Spill

During the first deployment of the mapping array, the Deepwater Horizon (DWH) disaster 

occurred. DWH, situated about 80 km southeast of the Mississippi delta in about 1200-m water 

depth, exploded on 20 April 2010, claiming 11 lives. The subsequent discharge of oil and gas 

continued from the seafloor until the wellhead was capped three months later (Liu et al. 2011a). 

The oil discharge took place during the latter stages of the formation and first detachments of 

Franklin, and concern was expressed that the extensive surface oil would find its way into the 

eddy and be transported south to the Florida Keys and beyond (Maltrud et al. 2010; Weisberg 

2011). This did not occur, however, even though a large quantity of surface oil was present in 

mid-May 2010 in a large cyclone immediately north of the northern part of the LC/Franklin front 

(Walker et al. 2011). To support the national response to the disaster, BOEM funded the taking 

of water samples on the July 2010 rotation cruise for analysis for hydrocarbons by the Texas 

A&M University Geochemical and Environmental Research Group (GERG). No significant 

hydrocarbon concentrations, at any depth, were found south of the LC front implying that 

entrainment of oil-polluted water into Franklin was minimal. Wade et al. (2011) published an 

analysis of these hydrocarbon measurements, and therefore, they are not included in this report.
103 km2 m

 Mean of A2, A3, A4, B2 & B3 6°C Isotherm Depth

LC Area & Area + Eddy

Ekman Franklin Hadal Icarus

200 m

200 m

500 m

1000 m

3000 m

3500 m

2000 m

1000 m

60 cm/s

200 m

200 m

500 m

1000 m

3000 m

3500 m

2000 m

1000 m

60 cm/s

Ekman Franklin

200 m

200 m

500 m

1000 m

3000 m

3500 m

2000 m

1000 m

60 cm/s

Hadal Icarus

5-day Average Velocities

200 m

200 m

500 m

1000 m

3000 m

3500 m

2000 m

1000 m

60 cm/s

 7/6/2009 6/8/2010 8/15/2011 11/8/2011

21 N 21 N

25 N 25 N

27 N 27 N

29 N 29 N 91 W 89 W 87 W 85 W 83 W 91 W 89 W 87 W 85 W 83 W 91 W 89 W 87 W 85 W 83 W 91 W 89 W 87 W 85 W 83 W

23 N 23 N

Figure 1.5-1. Time series of LC area (green) and LC+LCE area (blue) as delineated by the 17-cm SSH contour from the altimeter maps. The 

second panel shows the mean depth of the 6 oC isotherm from the center of the mapping array. The maps show the17-cm contour 

on the day of the first detachment along with the 5-day average currents at 80 to 100 m depth, centered on the detachment date.

11 
12

The circulation of Franklin during the oil spill was also analyzed using in-situ velocity and 

temperature measurements from the mapping array (Hamilton et al. 2011).

Hurricanes

Unlike the summers previous to, and after the deployment of the mapping array, no major 

hurricanes occurred in the eastern Gulf of Mexico during the three summer-hurricane periods 

encompassed by the deployments. The only hurricane/tropical storm that passed close to the 

array was the late season Hurricane Ida (8–10 November 2009) that tracked northwards through 

the Yucatan Channel making landfall close to the Mississippi delta.

1.6 REPORT ORGANIZATION 

The following chapters of the report are organized as follows. Except where noted, all the 

principal PIs contributed to the chapters.

Chapter 2: A description of the experiment and experimental methodology, along with 

the major analysis methods used in the remainder of the report.

Chapter 3: A detailed description of eddy formation, detachments and separation events, 

including a numerical simulation of Hadal’s separation, followed by a statistical analysis 

of the observed flow fields.

Chapter 4: A dynamical analysis of eddy growth and separation, including the role of 

LCFEs and a baroclinic instability analysis of meander growth. Principal authors are Dr. 

Donohue, Dr. Watts and Dr. Hamilton.

Chapter 5: Multi-decadal analysis of the historical record with a newly constructed 

record mainly from remote sensing and altimetry. Principal authors are Dr. Leben and 

Dr. Hall.

Chapter 6: An observational and numerical model analysis of the inertial response 

caused by hurricane Ida. Principal authors are Dr. Quian and Dr. Hamilton.

Chapter 7: Summary discussion of the major results from the study, followed by 

recommendations for further studies to fill knowledge gaps for the Gulf of Mexico. 
13

CHAPTER 2: EXPERIMENTAL DESIGN AND METHODOLOGY 

2.1 MOORED ARRAYS

2.1.1 Array Design

The U.S. component of the moored current-meter array consisted of nine full-depth, tall 

moorings and seven near-bottom, 100-meter-tall, short moorings deployed in the U.S. part of the 

LC region in the eastern Gulf of Mexico (GOM). These were embedded in an array of 25 

inverted echo sounders with pressure (PIES). Further south, in the Mexican sector, ten currentmeter moorings were deployed along two sections north and northeast of the Yucatan Peninsula 

off Campeche Bank, and eight additional moorings extended from the Yucatan Peninsula 

halfway across the Yucatan Channel opposite Cuba. The locations were shown earlier in Figure 

1.2-1. Mooring deployments, rotations, and recoveries were undertaken by separate entities 

(SAIC and CICESE for the U.S. and Mexican sectors, respectively). The initial deployments of 

the Mexican sector moorings occurred 1-2 months after the U.S. sector deployment, and they 

were recovered after 24 months, approximately 5-6 months before the U.S. sector moorings and 

PIES were recovered. 

The U.S. sector full-depth moorings were grouped to both span the major part of the LC and be 

in the most likely locations to capture a LC eddy separation, with the limitation that they had to 

be north of the EEZ. By embedding these moorings in an array of PIES and near-bottom or short 

moorings, this placed the tall mooring measurements in a wider context by mapping fields of 

temperature, salinity, geostrophic velocity, bottom pressure and sea-surface height (SSH). It was 

expected that a comparison of current profiles from the tall moorings with geostrophic velocity 

profiles would allow evaluation of the non-linear ageostrophic components of the dynamics 

expected to be important for peripheral eddies and eddy-separation events. The spacing of the 

PIES array was ~53 km, which was less than that used in both the Exploratory and NW GOM 

programs (~60 km) but a little more than that used for the small PIES array in the Eastern Gulf 

program. The PIES were also laid out along TOPEX/Jason interleaved ground tracks to facilitate 

incorporation of altimetry into the analyses. The inevitable compromise between area covered 

and spatial resolution of the array resulted in the roughly rectangular array in the U.S. sector 

(Figure 1.2-1) with approximately equal north and east spacing of about 53 km. The regular 

spacing of the array also makes the calculation of dynamical quantities involving horizontal 

gradients (e.g., relative vorticity) less error prone. The addition of PIES to the array was 

designed in part to increase the horizontal resolution, because for geostrophic dynamics, fulldepth moorings and PIES can be considered as providing equivalent information.

2.2 EQUIPMENT AND INSTRUMENTS

2.2.1 Introduction

Moored data collection consisted primarily of in-situ moored current, temperature, conductivity 

and pressure measurements at nine full-depth, tall mooring sites and current and temperature 

measurements at seven near-bottom, short mooring sites. In addition, 48 conductivity/ 

temperature/depth (CTD) casts (one, two or three at each PIES site) were made to support 

calibration of inverted echo sounder measurements made at 25 locations during the field effort. 
14

2.2.2 Moored and PIES Instruments 

Moored measurements in the U.S. sector were made from 16 current meter moorings (nine tall 

and seven short) deployed in the eastern Gulf of Mexico, north of 25°00’N to ~27o00’N, and 

west of 85o00’W to ~88o30’W, in waters ranging in depth from 2700 to 3350 meters. Tall

mooring tops were at 60 to 70 meters depth. Measurements at these sites were made 

continuously for 30 + months beginning in late April 2009 and, except for one short mooring, 

were completed in early November 2011. One of the short moorings was not recovered until 

mid-January 2012. The moorings were rotated after ~15.0 months. The locations and 

deployment periods for all 16 moorings are listed in Tables 2.2-1 and 2.2-2, respectively, and the 

locations and deployment periods for the 25 PIES are listed in Table 2.2-3. A map showing the 

mooring and PIES locations was presented earlier in Figure 1.2-1. 

The navigation datum used for mooring placement was the World Geodetic System of 1984 

(WGS 84), which is nearly the same as the North American Datum of 1983 (NAD 83). After 

deployment, mooring locations were triangulated and depth determined based on DGPS fixes, 

precision depth recorder (PDR) readings corrected for the speed of sound, and minimum acoustic 

ranges to the mooring releases. Later, instrument pressure data were evaluated as another check 

on mooring depth. Fallback of each mooring from the anchor-drop site to the final resting place 

on the bottom was also determined. This ranged from a minimum of approximately 130 meters 

to 450 meters for the short moorings, and from approximately 400 meters to 900 meters for the 

tall moorings. Fallback was affected primarily by the magnitude and direction of upper layer 

currents during deployment.

Each tall mooring was equipped to measure near-surface currents with an upward looking 75-

kHz ADCP using 8-meter bins and was deployed at 450 meters depth. Currents were also 

measured at 600, 900, 1300, and 2000 meters depth and 100 meters above bottom (MAB). 

Temperature data were collected at each current-meter level on the tall moorings as well as at 75, 

150, 250, 350, 525, 750, 1100, and 1500 meters depth. Salinity data were collected only at the 

150-meter and 750-meter levels and pressure data were generally collected at 150, 450, 750, 900, 

1300 and 2000 meters depth on each tall mooring. Short moorings measured only current and 

temperature at 100 MAB. A schematic of a tall mooring is shown in Figure 2.2-1. 

2.2.3 Instrumentation

The moorings were instrumented with a number of different type current meters. These included 

Aanderaa RCM-7/8s (rotor type) at 900 and 1300 meters depth on the tall moorings and 100 

MAB on the short moorings; and RCM-11s (Doppler type) at 2000 meters and 100 MAB on 

each tall mooring. In addition, an InterOcean S4 (electromagnetic) current meter was deployed 

at 600 meters depth and an RDI 75-kHz LongRanger ADCP at 450 meters depth on each of the 

tall moorings. A small number of additional current meters were deployed during the second 

deployment period on the B1 and B2 tall moorings and included the following:
15

Table 2.2-1. Triangulated Mooring Locations and Depths by Deployment for the 

Loop Current Study

Mooring

(DD)

Deployment 1

Triang. Location

Triang. 

Depth (M)

Deployment 2

Triang. Location

Triang. 

Depth (M)

Dist.

Between 

A1

(3036 M)

25°57.666’N

88°03.159’W

3035 

[3024]

25°57.658’N

88°03.113’W

3023 

[3025]

0.078 km

A2

(3208 M)

25°49.012’N

87°33.126’W

3200 

[3190]

25°49.029’N

87°32.970’W

3195 

[3190]

0.262 km

A3

(3302 M)

25°40.531’N

87°02.891’W

3293

[3283]

25°40.540’N

87°02.953’W

3295

[3282]

0.105 km

A4

(3270 M)

25°29.164’N

86°33.565’W

3262

[3255]

25°29.152’N

86°33.677’W

3270

[3255]

0.189 km

B1

(3049 M)

26°15.245’N

87°18.998’W

3049

[3031]

26°15.319’N

87°19.069’W

3053

[3032]

0.181 km

B2

(3138 M)

26°06.701’N

86°50.359’W

3132

[3123]

26°06.744’N

86°50.321’W

3146

[3121]

0.102 km

B3

(3160 M)

25°55.617’N

86°21.301’W

3156

[3147]

25°55.663’N

86°21.370’W

3167

[3146]

0.143 km

C1

(3190 M)

26°22.536’N

86°08.597’W

3182

[3161]

26°22.647’N

86°08.497’W

3182

[3166]

0.265 km

C2

(3257 M)

26°10.737’N

85°38.921’W

3250

[3236]

26°10.644’N

85°38.860’W

3254

[3237]

0.200 km

D1

(100 MAB)

26°24.986’N

87°51.007’W

2827 26°24.878’N

87°51.050’W

2832 0.213 km

D2

(100 MAB)

26°41.751’N

87°07.587’W

2885 26°41.614’N

87°07.638’W

2866 0.268 km

D3

(100 MAB)

26°32.949’N

86°37.301’W

3098 26°33.077’N

86°37.200’W

3101 0.291 km

D4 

(100 MAB)

25°17.993’N

86°04.783’W

3259 25°18.144’N

86°04.939’W

3264 0.382 km

D5

(100 MAB)

25°44.336’N

85°51.744’W

3234 25°44.507’N

85°51.765’W

3236 0.319 km

D7

(100 MAB)

25°33.042’N

85°22.986’W

3311 25°32.967’N

85°22.412’W

3293 0.973 km

D8

(100 MAB)

25°59.946’N

85°09.216’W

3309 26°00.014’N

85°09.200’W

3299 0.129 km

Deployment 1: 04/20/2009–07/26/2010 (11/11/2010 end for B1 & B2)

Deployment 2: 07/01/2010–11/28/2011 (01/14/2012 end for D4)

(DD) = Design Depth following adjustments for bathymetric survey at target site. 

[ ] = Mooring Depth calculated from 150 m MicroCat/SeaCat or 450 m ADCP pressure-sensor data, 

whichever produced smaller variation from planned instrument depth.
16

Table 2.2-2. Mooring Deployment Periods for the Loop Current Study

Mooring Deployment

Number

Deployment Periods

(UTC)

A1 1

2

05/05/2009 – 07/19/2010

07/20/2010 – 11/13/2011

A2 1

2

05/04/2009 – 07/17/2010

07/18/2010 – 11/13/2011

A3 1

2

04/30/2009 – 07/10/2010

07/11/2010 – 11/08/2011

A4 1

2

04/30/2009 – 07/08/2010

07/09/2010 – 11/03/2011

B1 1

2

05/14/2009 – 11/09/2010

11/10/2010 – 11/01/2011

B2 1

2

05/11/2009 – 11/11/2010

11/12/2010 – 11/08/2011

B3 1

2

05/10/2009 – 07/02/2010

07/03/2010 – 11/09/2011

C1 1

2

04/20/2009 – 07/12/2010

07/15/2010 – 10/28/2011

C2 1

2

04/22/2009 – 07/04/2010

07/07/2010 – 10/27/2011

D1 1

2

05/15/2009 – 07/19/2010

07/20/2010 – NR

D2 1

2

05/06/2009 – 07/16/2010

07/16/2010 – 11/14/2011

D3 1

2

05/09/2009 – 07/12/2010

07/12/2010 – NR

D4 1

2

04/27/2009 – 07/01/2010

07/02/2010 – 01/14/2012

D5 1

2

04/27/2009 – 06/30/2010

07/01/2010 – 11/02/2011

D7 1

2

04/21/2009 – 07/26/2010

07/26/2010 – 11/02/2011

D8 1

2

04/21/2009 – 07/26/2010

07/26/2010 – 10/27/2011

NR = Not Recovered. Note: There was no D6 Mooring. 
17

Table 2.2-3. PIES Deployment Locations and Periods for the Loop Current Study

PIES Latitude Longitude Water Depth (M) Deployment Period

(UTC)

P51 26°42.845’N 87°59.480’W 2733 04/23/2009 – 11/01/2011

P52 26°16.459’N 88°11.953’W 2823 04/26/2009 – 11/05/2011

P53 25°50.150’N 88°24.455’W 3114 05/01/2009 – 11/05/2011

P54 27°00.635’N 87°16.318’W 2882 04/19/2009 – 10/26/2011

P55 26°34.062’N 87°28.821’W 2833 04/23/2009 – 11/01/2011

P56 26°07.733’N 87°41.468’W 3029 04/26/2009 – 11/01/2011

P57 25°41.472’N 87°53.975’W 3209 05/01/2009 – 11/05/2011

P58 26°51.826’N 86°45.471’W 3065 04/19/2009 – 10/26/2011

P59 26°25.386’N 86°58.320’W 3023 04/23/2009 – 10/29/2011

P60 25°59.034’N 87°11.058’W 3184 04/26/2009 – 11/02/2011

P61 25°32.876’N 87°23.817’W 3332 05/01/2009 – 11/04/2011

P62 26°43.025’N 86°14.809’W 3169 04/19/2009 – 10/27/2011

P63 26°16.683’N 86°27.902’W 3108 04/23/2009 – 10/29/2011

P64 25°50.267’N 86°40.210’W 3247 04/26/2009 – 11/02/2011

P65 25°24.073’N 86°53.477’W 3326 04/30/2009 – 11/04/2011

P66 26°31.902’N 85°45.658’W 3226 04/19/2009 – 10/27/2011

P67 26°05.497’N 85°58.772’W 3240 04/21/2009 – 10/28/2011

P68 25°39.161’N 86°11.594’W 3213 04/27/2009 – 11/02/2011

P69 25°12.893’N 86°24.497’W 3293 04/30/2009 – 11/04/2011

P70 26°18.275’N 85°17.950’W 3298 04/20/2009 – 10/27/2011

P71 25°51.902’N 85°31.001’W 3278 04/21/2009 – 10/28/2011

P72 25°25.562’N 85°43.943’W 3286 04/27/2009 – 11/03/2011

P73 24°59.229’N 85°56.835’W 3325 04/29/2009 – 11/04/2011

P74 25°38.033’N 85°03.289’W 3336 04/21/2009 – 10/28/2011

P75 25°11.899’N 85°16.260’W 3341 04/28/2009 – 11/03/2011

Note: Water depth was calculated from the record mean PIES pressure converted to depth in meters 

using seawater depth with the PIES site latitudes.
Figure 2.2-1. Schematic of tall mooring.

18

1300 m

900 m

600 m

450 m

Star-Oddi T

MicroCat T/S

70 m

150 m

Upper 450 m of Full-Depth Moorings

INSTR. DEPTH

75 m

350 m

890 m

1290 m

1990 m

3260 m

Full-Depth Mooring Schematic

75 kHz ADCP 450 m

INSTR. DEPTH

5 glass 590 m

 IO S4 CM

 Star-Oddi T 1100 m

 AA RCM-7 

 6 glass

Paired Acoustic

Releases

4 glass 3170 m

 AA RCM-11 3180 m (100 MAB)

Hugrun T

7 glass

5 glass

 AA RCM-11 2000 m

3 glass 2490 m

~3280 m

 48" Steel Float

75 kHz ADCP

w/ 40" Syntactic 

 Buoy

 48" Steel Float 140 m

MicroCat T/S 750 m

 7 glass

Star-Oddi T 250 m Star-Oddi T 1500 m

 6 glass 1640 m

Hugrun T 525 m

 AA RCM-7
19

• 300-kHz RDI Sentinel ADCP (at 90 meters depth on the B1 mooring)

• RCM-8 current meter (at 599 meters depth on the B1 mooring)

• S4 current meter (at 90 meters depth on the B2 mooring)

• RCM-11 current meter (at 91 meters depth on the B2 mooring)

The tall moorings also included Hugrún Seamon mini temperature recorders, Sea-Bird MicroCat 

and SeaCat conductivity/temperature recorders, and Star-Oddi Starmon mini temperature 

recorders at the following levels:

• Hugrún recorders (primarily at 250 and 350 meters depth)

• Sea-Bird recorders (at 150 and 750 meters depth)

• Star-Oddi recorders (primarily at 75, 525, 1100 and 1500 meters depth)

Table 2.2-4a–c summarizes the measurement levels for each of the data logging instruments 

deployed on the moorings during the program. All of the tall moorings were equipped with 

paired-Teledyne Benthos 865-A acoustic releases, and the short moorings were equipped with 

various single acoustic releases including Teledyne Benthos 865-A, ORE/EdgeTech 8202 or 

ORE/EdgeTech 8242XS. The PIES instruments (manufactured by the University of Rhode 

Island) were deployed on low profile stands and were mounted about one meter above the 

bottom. 

2.2.4 Instrument Calibration, Performance and Data Return

Except for the Hugrún temperature recorders, all of the moored data logging instruments used in 

the field effort were serviced and calibrated by their respective original manufacturer prior to 

deployment on the Loop Current study moorings. The Hugrún recorders were serviced and 

calibrated by Star-Oddi as the original manufacturer was no longer in business.

Figure 2.2-2a–e presents a timeline of the data return by each mooring instrument level for the 

American Sector moorings deployed by SAIC. Note that not all levels were instrumented on 

each mooring during each deployment period. This is due to the fact that a few extra instruments 

were added to the B1 and B2 moorings during the second deployment period to permit 

instrument comparison or backup. Also, periods where some data were lost are identified as 

having occurred for a variety of reasons including instrument malfunctions, battery failures and 

instrument leaks. 

A total of 272 instrument deployments were made on the moorings over the course of the 30 + 

month field effort, and the total data return from these was approximately 93.8%. This return 

was calculated based on the maximum number of "good" data points expected for the various 

type instruments at their respective settings. However, since an ADCP generally works or does 

not work, the data return for these instruments reflects only that "good data" were obtained for at 

least one level, though anywhere from 20 depth cells on the Sentinel to 51 depth cells on the 

LongRanger may have provided useful data. Table 2.2-5 summarizes the moored instrument 

data return by instrument type.
20

Table 2.2-4a. Mooring Locations and Moored Instrument Levels for the Loop 

Current Study (American Sector) with Nominal Instrument Depths 

(Tall Moorings A1, A2, A3 and A4)

Mooring Location

Water 

Depth (M)

Instrument 

Depth (M)

Instrument Type 

(Serial Number)

A1 25°57.666’N

88°03.159’W

3036

75

150

250

350

450

525

600

750

900

1100

1300

1500

2000

2930 (100 MAB)

TEMP (T1277)

T/S/P (2698)

TEMP (C959)

TEMP (D634)

75 kHz ADCP (4913)

TEMP (T1156)

S4 (08161755) (08161753)

T/S/P (3392) (2702)

RCM-7 (10881)

TEMP (T1160)

RCM-8 (12789)

TEMP (T1162)

RCM-11 (360)

RCM-11 (354)

A2 25°49.012’N

87°33.126’W

3208

75

150

250

350

450

525

600

750

900

1100

1300

1500

2000

3108 (100 MAB)

TEMP (T1276)

T/S/P (2697)

TEMP (C946)

TEMP (C950)

75 kHz ADCP (4856)

TEMP (T1155)

S4 (08161753) (08111779)

T/S/P (3391)

RCM-7 (9949)

TEMP (T2943)

RCM-8 (12788)

TEMP (T2944)

RCM-11 (683)

RCM-11 (353)

A3 25°40.531’N

87°02.891’W

3302

75

150

250

350

450

525

600

750

900

1100

1300

1500

2000

3202 (100 MAB)

TEMP (T1275) (T1278)

T/S/P (2696)

TEMP (C943)

TEMP (C944)

75 kHz ADCP (4817)

TEMP (T1154)

S4 (08111779) (08161757)

T/S/P (3390)

RCM-7 (10350)

TEMP (T2989)

RCM-7 (9950)

TEMP (T2995)

RCM-11 (675)

RCM-11 (351)

A4 25°29.164’N

86°33.565’W

3270

75

150

250

350

450

525

600

750

900

1100

1300

1500

2000

3170 (100 MAB)

TEMP (T1271)

T/S/P (2695)

TEMP (C933)

TEMP (C939)

75 kHz ADCP (4866)

TEMP (T1153)

S4 (07961708) (07961709)

T/S/P (3388)

RCM-7 (11450)

TEMP (T2966)

RCM-7 (9948)

TEMP (T3001)

RCM-11 (362)

RCM-11 (350) 
21

Table 2.2-4b. Mooring Locations and Moored Instrument Levels for the Loop 

Current Study (American Sector) with Nominal Instrument Depths 

(Tall Moorings B1, B2 and B3)

Mooring Location

Water

Depth (M)

Instrument

Depth (M)

Instrument Type

(Serial Number)

B1 26°15.245’N

87°18.998’W

3049 75

90 [2]

150

250

350

450

525

599 [2]

600

750

900

1100

1300

1500

1990

2949 (100 MAB)

TEMP (T1280)

300 kHz ADCP (209)

T/S/P (1341) (2699)

TEMP (D617) (D595)

TEMP (D620)

75 kHz ADCP (4855)

TEMP (T1159)

RCM-8 (7356)

S4 (07801678) (08161755)

T/S/P (3394)

RCM-7/8 (11791) (12804)

TEMP (T3030)

RCM-7/8 (10533) (7582)

TEMP (T3031)

RCM-11 (677)

RCM-11 (357) (349)

B2 26°06.701’N

86°50.359’W

3138 75

90 [2]

91 [2]

150

250

350

450

525

600

750

900

1100

1300

1500

2000

3038 (100 MAB)

TEMP (T1279)

S4 (08111746)

RCM-11 (356)

T/S/P (2700)

TEMP (D597) (T1157)

TEMP (D614) (T3034)

75 kHz ADCP (4888)

TEMP (T1158)

S4 (08291851) (07801678)

T/S/P (3393)

RCM-7 (11389) (11791)

TEMP (T3032)

RCM-8 (7528)

TEMP (T3033)

RCM-11 (682)

RCM-11 (356) (357)

B3 25°55.617’N

86°21.301’W

3160 75

150

250

350

450

525

600

750

900

1100

1300

1500

2000

3060 (100 MAB)

TEMP (T1278) (T1624)

T/S/P (2699) (1342)

TEMP (D591) (D581)

TEMP (D595) (D621)

75 kHz ADCP (4865)

TEMP (T1157) (T1625)

S4 (08161757) (08582010)

T/S/P (2702) (2701)

RCM-7 (11432) (7077)

TEMP (T3034) (T2260)

RCM-8/7 (7582) (11432)

TEMP (T3037) (T3485)

RCM-11 (361) (364)

RCM-11 (355)

MAB = Meters above bottom.

[ ] = Deployed during indicated deployment only.
22

Table 2.2-4c. Mooring Locations and Moored Instrument Levels for the Loop 

Current Study (American Sector) with Nominal Instrument Depths 

(Tall Moorings C1, C2 and Short Moorings D1, D2, D3, D4, D5, D7 

and D8)

Mooring Location

Water

Depth (M)

Instrument 

Depth (M)

Instrument Type 

(Serial Number)

C1 26°22.536’N

86°08.597’W

3190 75

150

250

350

450

525

600

750

900

1100

1300

1500

1995

3090 (100 MAB)

TEMP (T1187)

T/S/P (1719)

TEMP (C919)

TEMP (C926)

75 kHz ADCP (4918)

TEMP (D583)

S4 (08111746) (07961708)

T/S/P (2693)

RCM-7 (6892)

TEMP (T3038)

RCM-7 (6922)

TEMP (T1981)

RCM-11 (358)

RCM-11 (348)

C2 26°10.737’N

85°38.921’W

3257 75

150

250

350

450

525

600

750

900

1100

1300

1500

1990

3157 (100 MAB)

TEMP (T1270)

T/S/P (1720)

TEMP (C932)

TEMP (C929)

75 kHz ADCP (4914)

TEMP (D585)

S4 (07961709) (08161758)

T/S/P (2694)

RCM-7 (9524)

TEMP (T1982)

RCM-7/8 (9525) (9266)

TEMP (T1983)

RCM-11 (349) (361)

RCM-11 (359) 

D1 26°24.986’N

87°51.007’W

2827 2727 (100 MAB) RCM-8 (12806) (12809)

D2 26°41.751’N

87°07.587’W

2885 2785 (100 MAB) RCM-8 (12809) (12810)

D3 26°32.949’N

86°37.301’W

3098 2998 (100 MAB) RCM-8 (12804) (12808)

D4 25°17.993’N

86°04.783’W

3259 3159 (100 MAB) RCM-8 (9266) (12803)

D5 25°44.336’N

85°51.744’W

3234 3134 (100 MAB) RCM-8 (12808) (12805)

D7 25°33.042’N

85°22.986’W

3311 3211 (100 MAB) RCM-8 (7356) (12806)

D8 25°59.946’N

85°09.216’W

3309 3209 (100 MAB) RCM-8 (7355) (12807)
Star-Oddi

MicroCat

MicroCat

Star-Oddi

Star-Oddi

Star-Oddi

S-4

Hugrun

Hugrun

ADCP

RCM7

RCM11

RCM11

RCM8

MicroCat

MicroCat

Star-Oddi

Star-Oddi

Star-Oddi

Star-Oddi

S-4

Hugrun

Hugrun

ADCP

RCM11

RCM11

RCM8

RCM7

T

C/T/P

C/T/P

T

T

T

T/S

T

T

T/P

T/P

T/P

T

T/P

T

T/P

C/T/P

T

T

T

T/S

T

T

T/P

T/P

T/P

T

T/P

No Data, Watchdog Timeout

Cracked Connector, Flooded

No Data

Rotor Stall

23

Figure 2.2-2a. Time lines of data return from moorings A1 and A2. Solid and dashed lines are velocity 

and scalar data, respectively.
T

T/P

C/T/P

T

T

T

T

T

T

T/P

T/P

T

T

T/P

T

C/T/P

C/T/P

T

T

T

T

T

T

T/P

T

T/P

T

T/P

Star-Oddi

MicroCat

MicroCat

Star-Oddi

Star-Oddi

Star-Oddi

S-4

Hugrun

Hugrun

ADCP

RCM7

RCM11

RCM11

RCM8

MicroCat

MicroCat

Star-Oddi

Star-Oddi

Star-Oddi

Star-Oddi

S-4

Hugrun

Hugrun

ADCP

RCM11

RCM11

RCM8

RCM7

No Data, Lost at Recovery

No Data

Power Failure

Rotor Stall

Noisy, Not Concatenated

24

Figure 2.2-2b. Time lines of data return from moorings A3 and A4. Solid and dashed lines are velocity 

and scalar data, respectively.
Star-Oddi

MicroCat

MicroCat

Star-Oddi

Star-Oddi

Star-Oddi

S-4

Hugrun

Hugrun

ADCP

RCM7

RCM11

RCM11

RCM8

MicroCat

MicroCat

Star-Oddi

Star-Oddi

Star-Oddi

Star-Oddi

S-4

Hugrun

Hugrun

ADCP

RCM11

RCM11

RCM8

RCM7

T

C/T/P

C/T

T

T

T

T

T

T

T/P

T

T/P

T

T/P

T

C/T/P

C/T/P

T

T

T

T

T

T

T/P

T/P

T/P

T

T/P

WHADCP T

RCM8 T

RCM11 T

SBE56 T

 No Data, Flooded

No Data, Flooded

 Power Failure

Power Failure

No Data, Recorder Malfunction

Pressure Bad

Some Rotor Binding

 Not Deployed

Not Deployed

Not Deployed

 SBE Experimental Instrument (No Data)

25

Figure 2.2-2c. Time lines of data return from moorings B1 and B2. Solid and dashed lines are velocity 

and scalar data, respectively.
Star-Oddi

MicroCat

MicroCat

Star-Oddi

Star-Oddi

Star-Oddi

S-4

Hugrun

Hugrun

ADCP

RCM7

RCM11

RCM11

RCM8

T

C/T/P

C/T/P

T

T

T

T

T

T

T/P

T

T/P

T

T/P

 No Data, Flooded

 Noisy Currents

Star-Oddi

MicroCat

MicroCat

Star-Oddi

Star-Oddi

Star-Oddi

S-4

Hugrun

Hugrun

ADCP

RCM7

RCM11

RCM11

RCM8

T

C/T/P

C/T/P

T

T

T

T/S

T

T

T/P

T/P

T

T

T/P

 No Data, Watchdog Timeout T only

26

Figure 2.2-2d. Time lines of data return from moorings B3 and C1. Solid and dashed lines are velocity 

and scalar data, respectively.
MicroCat

MicroCat

Star-Oddi

Star-Oddi

Star-Oddi

Star-Oddi

S-4

Hugrun

Hugrun

ADCP

RCM11

RCM11

RCM7

RCM7

T

C/T/P

C/T/P

T

T

T

T

T

T

T/P

T/P

T

T

T No Data, Flooded

Some Rotor Stalls

 Rotor Stalls

Rotor Stalls

RCM8

RCM8

RCM8

RCM8

RCM8

RCM8

RCM8

RCM8

T

T

T

T

T

T

T

T

Mooring Parted, RCM Recovered near Key West No Data, Not Recovered

 No Data, Not Recovered

 Not Deployed

27

Figure 2.2-2e. Time lines of data return for tall mooring C2 and short moorings D1, D2, D3, D4, D5, D7, 

and D8. There was no D6 mooring. Solid lines are velocity and scalar data, respectively.
28

Table 2.2-5. Moored Instrument Data Return (by Good Record Count) during the 

Loop Current Study

Deployment Aanderaa

RCM-7/8 (CUR+T)

Aanderaa

RCM-11 (CUR+T)

Hugrun Seamon

Mini (T)

1 355,719/ 367,781 (25) 198,842/ 198,842 (18) 183,862/ 220,091 (20)

2 305,184/ 360,156 (28) 196,116/ 196,116 (19) 178,324/ 201,543 (18)

TOTALS 660,903/ 727,937 (53) 394,958/ 394,958 (37) 362,186/ 421,634 (38)

Percent 

Good

90.8% 100% 85.9%

Deployment InterOcean

S4 (CUR+T)

RD Instruments

ADCP* (CUR+T)

Sea-Bird

MicroCat (T+S)

1 158,300/ 198,844 (9) 198,844/ 198,844 (9) 334,106/ 355,202 (16)

2 163,661/ 196,113 (10) 196,118/ 196,118 (10) 346,820/ 346,820 (16)

TOTALS 321,961/ 394,957 (19) 394,962/ 394,962 (19) 680,926/ 702,022 (32)

Percent

Good

81.5% 100% 97.0%

Deployment Sea-Bird

SeaCat (T+S)

Star-Oddi Starmon

Mini (T)

GRAND 

TOTAL

1 42,488/ 42,488 (2) 366,006/ 376,458 (34) 1,838,167/ 1,958,550 (133)

2 45,434/ 45,434 (2) 378,314/ 386,844 (36) 1,809,971/ 1,929,144 (139)

TOTALS 87,922/ 87,922 (4) 744,320/ 763,302 (70) 3,648,138/ 3,887,694 (272)

Percent

Good

100% 97.5% 93.8%

* All ADCP bin levels for each instrument counted as one (1) time series record.

(#) = Number of instrument deployments.

A number of instrument types provided 100% data return. These included the Aanderaa RCM11 Doppler current meter, the RD Instruments 75-kHz LongRanger and 300-kHz Sentinel 

ADCPs, and the SeaBird SeaCat conductivity/temperature/pressure recorders. One Sea-Bird 

MicroCat failure out of 32 deployments occurred where the instrument was found to have a 

sheared off I/O connector at recovery. The resultant data return for this instrument type was 

97.0%. Also, one Star-Oddi temperature recorder failed to collect data and a second was lost 

during mooring recovery operations, yet the data return for this type instrument (from 70 

deployments) was 97.5%. 

Four data logging instruments were found to be flooded at recovery. One of these was an 

Aanderaa RCM-7 rotor-type current meter for which the source of the leak was not obvious. 

Three others were Hugrún temperature recorders with plastic housings. In addition to these, two 

other Hugrúns had non-responsive recorders at recovery, so no data were recovered from them, 

as well. The large number of Hugrún failures (only 85.9% data return) is thought to be due to

age-related fatigue of the plastic housing and the instrument electronics. These GFE instruments 

have since been retired. 

Two Aanderaa RCM-8 rotor-type current meters deployed on short moorings were not 

recovered. It is believed that these losses were due to release failures as acoustic release 

problems had been experienced at a number of the short mooring sites. In spite of the loss of two 
29

instruments and the flooding of a third, the data return for the Aanderaa rotor-type current meters 

was 90.8% from 53 instrument deployments. 

Finally, the InterOcean S4 electromechanical current meter had an 81.5% data return from 19 

instrument deployments. Two instruments were affected by firmware mismatches that caused 

them to stop collecting data early or to collect no data at all. Three others experienced power 

failures during the deployment which caused them to also stop collecting data before the 

moorings were recovered. 

2.3 CTD DATA

Forty-eight CTD casts were made with planned profiling depths of 1500 meters at each of the 

PIES deployment sites. Their purpose was to help in creating an appropriate Gravest Empirical 

Mode (GEM) to be used to calibrate the PIES data. These casts are documented in Table 2.3-1.

2.3.1 CTD Data Acquisition Systems

The CTD data acquisition system used on most of the cruises consisted of a Sea-Bird 911 Plus 

system provided and operated by the technical staff onboard the R/V PELICAN, a UNOLS 

vessel operated by Louisiana Universities Marine Consortium (LUMCON) at Cocodrie, 

Louisiana. This particular CTD system was equipped with redundant Sea-Bird CT sensors, a 

Datasonics altimeter and a Sea-Bird Carousel Water Sampler with Niskin water sample bottles. 

A second system used onboard the R/V WEATHERBIRD II in July 2010 consisted of a Sea-Bird 

SBE 25 and a Rosette Water Sampler with Niskin water sample bottles. This latter system was 

provided by Florida Institute of Oceanography (FIO) and operated by one of their technical staff. 

The CTD system sensors were calibrated periodically at the manufacturer’s facilities over the 

course of the study, and bottle salinities were taken at the bottom of each cast as a further check 

on instrument salinity calibration. These were run on a Guildline 8400B Autosal Laboroatory 

Salinometer. No calibration problems were detected during the 30-month study period. Also, 

the lowering speed of the CTD was varied from 15 meters per minute for the first 90 meters of 

descent to 30 meters per minute from 90 to 200 meters depth, and then increased to 60 meters 

per minute once below the 200 meter level. This was to eliminate or reduce the possibility of CT 

sensor mismatch which can cause salinity spiking when passing through a sharp thermocline. 
30

Table 2.3-1. Listing of CTD Casts made at PIES Sites during the Loop Current 

Study

Sta. /CTD Depth (M) Date (UTC) Time (UTC) Cruise

P51 / 1500

P51 / 1500

05/06/2009

07/20/2010

1137 - 1407

0035 - 0138

PE09-34

PE11-01

P52 / 1501

P52 / 1425

05/06/2009

11/09/2010

0150 - 0245

2210 - 2321

PE09-34

PE11-16

P53 / 1500 07/19/2010 0621 - 0723 PE11-01

P54 / 1501

P54 / 1500

07/16/2010

07/16/2011

0502 - 0555

2026 - 2153

PE11-01

PE12-02

P55 / 1501

P55 / 1439

07/16/2010

11/13/2010

2005 - 2124

0735 - 0850

PE11-01

PE11-16

P56 / 1501

P56 / 1500

07/17/2010

11/10/2010

0328 - 0457

0437 - 0521

PE11-01

PE11-16

P57 / 1384

P57 / 1502

P57 / 1500

05/05/2009

07/17/2010

07/19/2011

0255 - 0419

2205 - 2312

2200 - 2301

PE09-34

PE11-01

PE12-02

P58 / 1501

P58 / 1500

07/15/2010

10/26/2011

0537 - 0654

1209 - 1320

PE11-01

PE12-16

P59 / 1500

P59 / 1418

06/28/2010

11/11/2010

2320 - 0043

2006 - 2050

PE11-01

PE11-16

P60 / 1501

P60 / 1501

P60 / 1237

07/03/2010

07/10/2010

11/11/2010

0015 - 0122

2342 - 0040

0420 - 0549

PE11-01

PE11-01

PE11-16

P61 / 1501

P61 / 1499

07/10/2010

11/04/2011

1755 - 1904

2149 - 2248

PE11-01

PE12-16

P62 / 1500

P62 / 1499

06/29/2010

10/26/2011

1455 - 1626

2252 - 0000

PE11-01

PE12-16

P63 / 1501

P63 / 1369

06/29/2010

11/12/2010

0405 - 0510

0200 - 0304

PE11-01

PE11-16

P64 / 1501

P64 / 1500

P64 / 1331

05/11/2009

07/02/2010

11/12/2010

0619 - 0805

1840 - 1957

0652 - 0800

PE09-34

PE11-01

PE11-16

P65 / 1501

P65 / 1500

P65 / 1499

07/10/2010

07/19/2011

11/03/2011

0227 - 0332

1205 - 1314

2238 - 2359

PE11-01

PE12-02

PE12-16

P66 / 1500

P66 / 1500

06/29/2010

07/17/2011

2022 - 2137

1824 - 1920

PE11-01

PE12-02

P67 / 1501

P67 / 1200

06/30/2010

10/28/2011

0154 - 0301

1353 - 1515

PE11-01

PE12-16

P68 / 1502 06/30/2010 1510 - 1630 PE11-01

P69 / 1498 07/28/2010 0635 - 0923 WB10-016

P70 / 1990

P70 / 1500

07/29/2010

07/18/2011

0455 - 0725

2222 - 2322

WB10-016

PE12-02

P71 / 1500

P71 / 1496

07/04/2010

10/28/2011

0600 - 0656

0710 - 0820

PE11-01

PE12-16

P72 / 1498 07/27/2010 1545 - 1902 WB10-016

P73 / 1371 07/27/2010 2218 - 0307 WB10-016

P74 / 1501

P74 / 1500

07/27/2010

07/18/2011

0237 – 0615

1621 - 1719

WB10-016

PE12-02

P75 / 1497 07/27/2010 0910 - 1242 WB10-016
31

2.4 CICESE MOORING DATA

2.4.1 Introduction

In addition to the American sector moorings, current meter data are available from 10 BOEMfunded moorings (N1-N4, E1-E5 and EN in Figure 1.2-1) deployed by CICESE within the 

Mexican EEZ in water depths ranging from 127 m to 3354 m. Also, CICESE deployed eight 

additional moorings extending halfway across the Yucatan Channel (Moorings Y1-Y7 and YN). 

The locations and deployment periods for these moorings are presented in Table 2.4-1 and 

timelines for each instrument level on each mooring are presented in Figure 2.4-1a-b.

2.4.2 Instrumentation

The CICESE moorings were instrumented with a number of different type current meters. These 

included Aanderaa RCM-11 and SeaGuard (Doppler type) current meters, Nortek Aquadopp 

current meters, and RD Instruments 75-kHz LongRanger and 300-kHz WorkHorse ADCPs. 

Teledyne Benthos 865-A acoustic releases were used with each of the current meter moorings. 

In addition to providing a timeline of the data return for each instrument level on each mooring 

during the deployment period, Figure 2.4-1a-b also indicates which type instruments were used 

at each depth on each mooring. 

Table 2.4-1. Mexican Mooring Locations and Deployment Periods during the 

Loop Current Study

Mooring Location Water Depth (M) Deployment

Period

N1 23°45.70’N, 87°55.11’W 130 05/31/2009 - 05/07/2011

N2 24°11.80’N, 87°34.01’W 500 05/31/2009 - 05/07/2011

N3 24°23.90’N, 87°24.68’W 1205 05/31/2009 - 05/07/2011

N4 24°57.47’N, 87°04.95’W 3352 06/01/2009 - 05/06/2011

E1 22°23.01’N, 87°00.43’W 127 06/02/2009 - 05/09/2011

E2 22°49.81’N, 86°38.36’W 501 06/02/2009 - 05/09/2011

E3 23°03.37’N, 86°25.98’W 998 06/02/2009 - 05/08/2011

E4 23°14.48’N, 86°17.58’W 1994 06/02/2009 - 05/08/2011

E5 23°36.17’N, 86°01.37’W 3354 06/01/2009 - 05/08/2011

EN 23°04.09’N, 86°47.01’W 500 06/02/2009 - 04/26/2010

Y1 21°32.42’N, 86°42.00’W 23 04/24/2010 - 04/18/2011

Y2 21°32.44’N, 86°29.74’W 68 06/05/2009 - 05/11/2011

Y3 21°33.46’N, 86°27.00’W 124 06/04/2009 - 05/11/2011

Y4 21°33.96’N, 86°21.30’W 526 06/04/2009 - 04/18/2010 

Y5 21°35.55’N, 86°13.64’W 1206 06/12/2009 - 05/11/2011

Y6 21°38.81’N, 85°59.16’W 1880 06/04/2009 - 05/11/2011

Y7 21°38.37’N, 85°42.97’W 2030 06/03/2009 - 05/10/2011

YN 21°41.65’N, 86°20.50’W 495 06/03/2009 - 08/29/2009

Note: The initial deployments of the Mexican sector moorings occurred 1–2 months after the U.S. sector 

deployments, and were recovered after 24 months, approximately 5–6 months before the U.S. sector moorings were 

recovered. 
LR ADCP T P

T P

T P

T P

T P

T P

T P

T P

T P

T P

T P/T

LR ADCP

LR ADCP

LR ADCP

LR ADCP

LR ADCP

LR ADCP

LR ADCP

LR ADCP

LR ADCP

WH ADCP

T P/T

T P/T

T P/T

T P/T

T P/T

T P/T

T P/T

T P/T

T P/T S

T P/T

T P/T

T P/T

T P/T

T P/T S

T P/T

T P/T

T P/T

T P/T

T P/T

T P T Bad, Range Error

Short Record

 Not Deployed

Short Record

NORTEK/AA SeaGuard

NORTEK/AA SeaGuard

NORTEK/NORTEK

NORTEK/NORTEK

NORTEK/NORTEK

NORTEK/NORTEK

NORTEK/NORTEK

NORTEK/NORTEK

NORTEK/RCM11

NORTEK/RCM11

NORTEK/RCM11

NORTEK/RCM11

NORTEK/RCM11

NORTEK/RCM11

NORTEK/RCM11

NORTEK/RCM11

NORTEK/RCM11

NORTEK/RCM11

NORTEK/RCM11

NORTEK/RCM11

 Short Record

32

Figure 2.4-1a. Time lines of data return from CICESE moorings N3, N4, E1, E2, E3, E4, and E5. Solid 

and dashed lines are velocity and scalar data, respectively.
T P

T P

T P

T P

AQUADOPP T P

T P

T 

T P

T /T P

T /T P

LR ADCP

LR ADCP

LR ADCP

LR ADCP

LR ADCP

LR ADCP

WH ADCP

WH ADCP

WH ADCP

WH ADCP

WH ADCP

WH ADCP

 Not Deployed

 Short Record Not Deployed

 No Data

 Short Record

Not Deployed

 T Bad, Range Error

 Bad Pressure

 Bad Pressure

 Bad T, Range Error

RCM11/RCM11 T

RCM11/NORTEK

RCM11/NORTEK

RCM11/NORTEK

RCM11/NORTEK

RCM11/NORTEK

RCM11/NORTEK

RCM11/NORTEK

RCM11/NORTEK

RCM11/NORTEK

RCM11/NORTEK

RCM11/AA SeaGuard

RCM11/AA SeaGuard

RCM11/AA SeaGuard

RCM11/AA SeaGuard

RCM11/AA SeaGuard

RCM11/RCM11 T 

T 

T 

T 

T 

T 

T 

T 

T 

T 

T 

T 

T 

T P/ T

T P

T S/ T

T S/ T

T / T S

T S No T, Bad Salinity

33

Figure 2.4-1b. Time lines of data return from CICESE moorings N1, N2, Y1, Y2, Y3, Y4, YN, Y5, Y6, and 

Y7. Solid and dashed lines are velocity and scalar data, respectively. 
34

2.5 PIES

A mesoscale-resolving array of twenty-five inverted echo sounders with pressure gauges (PIES) 

was deployed in April 2009 and recovered in October-November 2011 as part of the Loop 

Current study (Figure 1.2-1). The PIES is a bottom-mounted instrument that emits 12 kHz sound 

pulses and measures the round trip travel times, τ (tau), of these pulses from the sea floor to the 

sea surface and back. It is also equipped with a pressure gauge, and measures bottom pressure. 

A detailed description of the instrument and the initial data processing may be found in Hamilton 

et al. (2003) and Donohue et al. (2006). Here, aspects of data processing specific to this data set 

are reported. The data return from the PIES was excellent (Figures 2.5-1 and 2.5-2), and full 

deployment records are available from each of the instruments.

The broad extent of the array of PIES, nominally 89°W to 85°W, and 25°N to 27°N, combined 

with measurements from the tall moorings enabled a quantitative mapping of the regional 

circulation. Knowledge of deep correlation scales from previous Gulf experiments and our 

science objective to map deep relative vorticity, set the nominal 50 km spacing of the PIES and 

current meter moorings. The array placement within the Gulf was guided by historical analysis 

that indicated where eddy separation was most likely to occur. The array size encompassed the 

Loop Current from east to west. The experiment duration of 30 months captured three Loop 

Current Eddy formation events: Ekman, Franklin, and Hadal. Round-trip acoustic travel time 

measured by the inverted echo sounders produced estimates of vertical profiles of temperature, 

salinity, and density, by utilizing empirical relationships established with historical hydrography. 

An exponential-linear drift curve was fitted to the difference between each bottom pressure 

record and the time series of current-meter-derived geostrophic pressure maps, as described in 

Donohue et al. (2010). This methodology de-drifted and leveled the pressure records 

simultaneously. Further details are given in Section 2.5.4. Deep pressure records combined with 

estimated horizontal density gradients yielded referenced geostrophic velocities. With this array, 

4-D maps of temperature, salinity, density, velocity and sea-surface height (SSH) were produced 

(Figure 2.5-3).

2.5.1 Gravest Empirical Mode Method

For this experiment PIES τ measurements were converted into profiles of temperature, salinity, 

and specific volume anomaly through the use of a look-up table. A relationship has been 

established between a τ index and vertical profiles of temperature and salinity using historical 

hydrography. This has been designated the Gravest Empirical Mode (GEM) representation (e.g., 

Meinen and Watts 2000). The procedure consists of two steps. First, the empirical look-up table 

is calculated, and second, the PIES-measured τ is converted to the τindex of the look-up table.

2.5.1.1 Determine τ index

Round-trip travel time between the 150 and 1000 dbar surface, τ(150-1000) was used as the 

τindex. The 150-dbar upper limit of the τ integration avoided the influence of the seasonal cycle 

most evident in this upper layer. Further refinements discussed below detail a seasonal

correction. The 1000-dbar lower limit of the τ integration balanced two needs: extend the

integration below the thermocline and retain as many of the acquired historical hydrocasts as 

possible.
−0.02

−0.01

0

0.01

0.02

sec

 P51

−0.02

−0.01

0

0.01

0.02

sec

 P52

500 1000

−0.02

−0.01

0

0.01

0.02

sec

days 2009

 P53

−0.02

−0.01

0

0.01

0.02

sec

 P54

tau [sec]

 P55

 P56

500 1000

days 2009

 P57

 P58

 P59

 P60

500 1000

days 2009

 P61

 P62

 P63

 P64

500 1000

days 2009

 P65

 P66

 P67

 P68

500 1000

days 2009

 P69

 P70

 P71

 P72

500 1000

days 2009

 P73

 P74

500 1000

days 2009

 P75

Figure 2.5-1. Time series of tau anomaly in seconds in panels arranged according to approximate geographic location. Instrument number is 

noted in the upper left corner of each subplot. 

35 
−0.2

−0.1

0

0.1

0.2

dbar

 P51

−0.2

−0.1

0

0.1

0.2

dbar

 P52

500 1000

−0.2

−0.1

0

0.1

0.2

dbar

days 2009

 P53

−0.2

−0.1

0

0.1

0.2

dbar

 P54

 prs [dbar]

 P55

 P56

500 1000

days 2009

 P57

 P58

 P59

 P60

500 1000

days 2009

 P61

 P62

 P63

 P64

500 1000

days 2009

 P65

 P66

 P67

 P68

500 1000

days 2009

 P69

 P70

 P71

 P72

500 1000

days 2009

 P73

 P74

500 1000

days 2009

 P75

Figure 2.5-2. Time series of bottom pressure anomaly in dbar arranged according to approximate geographic location. Instrument number is 

noted in the upper left corner of each subplot.

36 
100 cms 25 −1 o

N

26o

N

26o

N

26o

N

27o

N

88o

W 87oW 86oW 85oW

Total

100 cms−1

Baroclinic referenced to bottom

220 260 300

20 cms−1

Reference level

−7 −3 1 5

88oW 87oW 86oW 85oW

pressure [dbar]

Temperature

0

500

1000

1500

2000

2500

3000

[

o C]

8

24

0 20 40 60

[cm s−1]

Zonal

−20 0 20

 [cm s−1]

Meridional

Baroclinic

referenced to bottom

Reference level velocity

Total

37

Total and baroclinic referenced to bottom SSH [cm] Reference level SSH [cm]

Figure 2.5-3. Several views of the current and temperature structure in the region for 5 May 2009 

provided by the PIES and current meter measurements. Top panels: Total sea surface 

height in plan view (left), displaying its baroclinic contribution referenced to the bottom, 

φ(z=0)_3000/g (middle), and reference level contribution, p_b/(ρg) (right), both scaled to 

sea surface height. φ(z=0)_3000 is geopotential height at the surface relative to 3000 

dbar, p_b is bottom pressure, ρ is near-bottom density and g is gravity. Anticyclonic 

circulations are shown by reddish hues; cyclonic circulations by bluish hues. Mapped 

current vectors plotted at 20 km spacing. PIES and current meter mooring sites are 

denoted by black filled circles. Bottom left panel: Cross-section of temperature in °C 

along the horizontal black line in the top left panel. Bottom two right panels: Zonal and 

meridional velocity (total: grey, reference level velocity: blue, and baroclinic referenced to 

the bottom: black) at the black square shown in the upper panels.
38

2.5.1.2 Assemble Regional Hydrographic Data Set

The regional hydrographic data set accumulated for the Exploratory Study of Deepwater 

Currents in the Gulf of Mexico (Donohue et al. 2006), consisting of 777 casts, was initially used. 

An additional 359 profiles were added from four sources: hydrocasts taken during the Loop 

Current Study field program (49 casts), NOAA casts taken following the Deepwater Horizon oil 

spill (48 casts), Argo float profiles (27 casts) and historical data from CICESE (235 casts). The 

spatial and temporal distribution of the resulting data set (of 1136 casts) is shown in Figure 2.5-4. 

Hydrocasts represent about 30 years of sampling. The bulk of casts extend between 1000 to 2000 

dbar with relatively few casts below 2000 dbar. 

2.5.1.3 Sort Hydrographic Data by τ index 

Hydrocasts were linearly interpolated to a uniform 10-dbar grid and sorted by τ(150-1000). 

Samples are sparse for the lowest τindex range (<1.122 sec) that would be found in the very center 

of the loop in the Loop Current. It was found that measured τ when converted to τindex (see 

discussion below for the methodology to convert measured τ to τindex) could occasionally extend 

to lower values than the minimum GEM τindex. Therefore, the GEM had to be extended to lower 

τindex values. Synthetic profiles were constructed from temperatures measured by the tall 

moorings to extend the low τindex portion of the GEM. First, a τindex time series was determined 

for each mooring by mapping PIES τindex time series to each mooring site. Second, a time series 

of temperature as a function of pressure was calculated for each temperature record. Recall that 

pressure gauges on each mooring tracked mooring motion. Data were restricted to times when 

the mooring drawdown was relatively small (within ± 15 dbar of nominal level). Third, 

temperature was averaged in 0.5 ms τindex bins from 1.1145 to 1.1222 sec and interpolated onto a 

10 dbar grid from the surface to 1500 dbar. A total of 124 synthetic profiles were added to the 

database (Figure 2.5-5).

To make synthetic salinity profiles, the mean θ/S relationship for τindex < 1.122 sec (41 profiles) 

was created. A salinity profile was then obtained for every synthetic temperature profile by 

interpolating the mean θ/S relationship. 

Every 10 dbar, a cubic smoothing spline was fitted to temperature as a function of τindex = τ(150-

1000) (Figure 2.5-6). Root-mean-square residual, rms, for each curve provides an indication of 

the departure any individual profile might have from the GEM curve. The rms values for 

temperature are small, 0.30°C within the thermocline, decreasing further with increasing depth. 

The curves show that a functional relationship exists between the integrated variable, τ(150-

1000) and vertical profiles of temperature. The two-dimensional GEM fields are shown in

Figure 2.5-7. Note that there is little structure in the fields below 1000 dbar and this reflects the 

uniform deep-water properties in the Gulf of Mexico.
 1136 casts

98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

32°N

1980 1990 2000 2010

0

50

100

150

200

year

number of casts

2 4 6 8 10 12

0

50

100

150

200

month

1000 2000 3000

0

100

200

300

400

500

max pressure [dbar]

39

Figure 2.5-4. Spatial and temporal distribution of hydrocasts used to construct the Gravest Empirical 

Mode. Data provided by the Gulf of Mexico HYDRO Database compiled by TAMU as part 

of the MMS-funded Deepwater Reanalysis and additional stations provided by SAIC, 

NOAA casts taken following the Deepwater Horizon oil spill, historical data from CICESE 

and Argo profiling float hydrocasts. Top panel: Spatial distribution of the hydrocasts with 

bathymetry contoured every 1000 m. Bottom panels: Histograms of the year of hydrocast 

(left), month of hydrocast (middle) and maximum hydrocast pressure (right). 
1.115 1.12 1.125 1.13

0

500

1000

1500

2000

2500

3000

temperature [oC]

pressure [dbar]

tau150−1000 [sec]

4

5

6

8

10

14

18

22

26

30

34

40

Figure 2.5-5. Temperature profiles interpolated every 10 dbar and sorted by τ(150-1000) = τindex. 

Synthetic profiles supplemented the CTDs to the left of the dashed line in the deepestthermocline portion on the warm side of the Loop Current, where we otherwise had only a 

sparse non-representative distribution. The dots along the y-axis (up to 1500 m) show the 

nominal depths at which moored temperatures and pressures gave T(p) profiles to join 

with PIES mapped tau measurements to contribute to the GEM lookup table. We did not 

use the two deepest sensors (2000 and bottom) because of the large vertical sensor 

spacing and small temperature gradient below 1500 m.
10

20

30

o

C

rms = 0.69oC 200 dbar

temperature [o

C]

10

20

o

C

rms = 0.40oC 300 dbar

0

10

20

o

C

rms = 0.32oC 400 dbar

0

10

20

o

C

rms = 0.27oC 500 dbar

5

10

o

C

rms = 0.23oC 750 dbar

1.114 1.116 1.118 1.12 1.122 1.124 1.126 1.128 1.13 1.132

5

10

o

C

rms = 0.20oC 1000 dbar

tau150−1000 [sec]

41

Figure 2.5-6. Scatter plots of temperature versus τindex = τ(150 -1000) for six representative pressure 

levels. At each pressure, temperature versus τ(150 -1000) data were fit by a cubic 

smoothing spline (solid curve).
1.115 1.12 1.125 1.13

0

500

1000

1500

2000

2500

3000

5

5

6

6

8

8

10

10

14

14

18

18

22

26

temperature [oC]

pressure [dbar]

tau150−1000 [sec]

42

Figure 2.5-7. Contour plot of the cubic smoothing spline fits for the temperature GEM field.
43

2.5.1.4 Seasonal Correction

A seasonal depth-dependent temperature model can be added to the upper 150 m of the GEM 

lookup table, generated from the observed monthly-averaged departures of hydrographic profiles 

from the GEM temporal-mean structure. It incorporates seasonal variations in SSH due to 

thermal expansion/contraction. The seasonal model is shown in Figures 2.5-8 and 2.5-9. 

Because the model does not depend on location within the Gulf, it has no effect upon the 

velocities. A seasonal correction for τindex is described later in this section. 

A seasonal depth-dependent model, generated in a manner similar to that described above for 

temperature, was added to the geopotential anomaly calculated from the GEM temperature and 

salinity fields. The model is shown in Figure 2.5-10. Adding the seasonal cycle improved 

agreement between altimetric SSH and PIES-estimated SSH shown later. The peak-to-peak 

range of the seasonal cycle is 1.16 m2s

-2

. 

2.5.2 Conversion of Measured τ to τ(150-1000) = τindex

In order to use the GEM fields with the PIES τ measurements, measured τ was converted to 

τ(150-1000). Advantage was taken of the fact that τ at any deep pressure is linearly related to τ at 

any other deep pressure, τ(150-1000) = A×τp1 + B. Historical hydrography established the slope 

of this relationship and hydrocasts taken during the PIES deployment, current meter turnaround 

and PIES recovery cruises determined B for each time series. The majority of sites had two 

calibration casts. Sites P53, P68, P69, P72, P73 and P75 had only a single calibration cast, while 

three sites, P57, P64 and P65 had three calibration casts. Calibrations at PIES sites with two or 

more hydrocasts generally agreed with each other within 1 millisecond, except where casts were 

taken during periods of rapidly changing τ (sites P57, P58, P64 and P67). The mean pressure of 

each instrument was determined from the record average pressure adjusted for the vertical offset 

between the pressure sensor and the transducer (0.6 dbar) and mean atmospheric pressure (10.16 

dbar). Time series were filtered with a 72-hour 4th order Butterworth filter and subsampled at 

12-hour intervals. The final τ(150-1000) records are shown in Figure 2.5-11.

Before measured τ records were converted to τindex= τ(150-1000), a seasonal τ signal was 

subtracted from the τ records. This seasonal signal was determined from the historical 

hydrography in a manner similar to the seasonal temperature adjustment model described above. 

Here, the influence of the seasonal cycle in τ between the surface and 150 dbar was considered 

since the hydrography showed that there is little seasonal signal below 150 dbar. The scatter plot 

of τ(0-150) versus τ(150-1000) was largely due to the seasonal cycle and it was determined that 

the amplitude of the residual was 0.3147 milliseconds (Figure 2.5-12). The correction was small, 

about 2% of the total range in τ(150-1000).

The error in the time series of τindex= τ(150-1000) was estimated to be near 1.07 ms. The 

methodology to determine the errors in τ follows Donohue et al. (2010). This error derives from 

the measured hourly τ error, 0.05 ms; the residual of the seasonal correction to τ, 0.3 ms; the 

conversion from τ to τindex, 0.25 ms, and a τindex calibration error (from the CTDs at a given site) 

of 1.0 ms.
1.12 1.125 1.13

15

20

25

30

35

 0 dbar

temperature [°C]

1.12 1.125 1.13

−5

0

5

τ

150−1000 [sec]

 0 dbar

residual [°C]

0 100 200 300

−5

0

5

generic yearday

residual [°C]

 0 dbar

1.12 1.125 1.13

 50 dbar

1.12 1.125 1.13

τ

150−1000 [sec]

 50 dbar

0 100 200 300

generic yearday

 50 dbar

44

Figure 2.5-8. Upper panels: Scatter plots of temperature versus τ(150-1000) for surface (left) and 50 

dbar (right) with the cubic spline fit shown as a solid dark line. All samples in all panels 

are color coded by generic yearday transitioning from blue in January to red in December. 

Middle panels: Residual from the cubic spline fit. Lower panels: A clear seasonal signal in 

temperature emerges when the residual is sorted by time of year.
−3.2

−1.6

−1.6

−1.6

0

0

0

0

0

0

1.6

1.6

3.2

temperature [°C]

pressure [dbar]

generic yearday

0 100 200 300

0

20

40

60

80

100

120

140

45

Figure 2.5-9. Seasonal temperature correction/amplitude contoured as a function of yearday and 

pressure. The amplitude of the temperature seasonal correction is about 3°C at the 

surface and decays to less than 0.5°C by 90 dbar. 
1.116 1.118 1.12 1.122 1.124 1.126 1.128 1.13 1.132

2

3

4

5

6

7

8

τ

150−1000 [sec]

Φ [m2 s−2]

0 50 100 150 200 250 300 350

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

yearday (generic year)

residual

Φ [m2 s−2]

46

Figure 2.5-10. Upper panel: Scatter plots of surface geopotential anomaly referenced to 150 dbar with 

the cubic spline fit shown as a solid dark line. All samples in all panels are color coded by 

generic yearday transitioning from blue in January to red in December. Lower panel: A 

clear seasonal signal emerges when the residual is sorted by time of year.
1.115

1.12

1.125

1.13

1.135

sec

 P51

1.115

1.12

1.125

1.13

1.135

sec

 P52

500 1000

1.115

1.12

1.125

1.13

1.135

sec

days 2009

 P53

1.115

1.12

1.125

1.13

1.135

sec

 P54

tau(150−1000) [sec]

 P55

 P56

500 1000

days 2009

 P57

 P58

 P59

 P60

500 1000

days 2009

 P61

 P62

 P63

 P64

500 1000

days 2009

 P65

 P66

 P67

 P68

500 1000

days 2009

 P69

 P70

 P71

 P72

500 1000

days 2009

 P73

 P74

500 1000

days 2009

 P75

Figure 2.5-11. Time series of τ(150-1000) in seconds, with panels arranged according to approximate geographic location. Instrument number is 

noted in the upper left corner of each subplot. 

47 
1.116 1.118 1.12 1.122 1.124 1.126 1.128 1.13 1.132

0.1935

0.194

0.1945

0.195

0.1955

0.196

0.1965

0.197

τ

150−1000 [sec]

τ0−150 [sec]

0 50 100 150 200 250 300 350

−1.5

−1

−0.5

0

0.5

1

yearday (generic year)

residual τ [millisec]

48

Figure 2.5-12. Upper panel: Scatter plots of τ(0 -150) versus τ(150 -1000). Each point is color coded by 

generic yearday transitioning from blue in January to red in December. The scatter about 

the spline fit (solid dark line) is largely due to the seasonal cycle. Lower panel: The 

residual from the cubic spline fit shown in the upper panel sorted by generic yearday 

shows a clear annual signal. 
49

2.5.3 Upper-Ocean Maps

Maps were produced with optimal interpolation techniques adapted from Bretherton et al. (1976) 

and outlined in Watts et al. (1989; 2001). Optimal interpolation requires that the input fields have 

zero mean and uniform variance. In order to meet this requirement a mean field must be 

subtracted from the fields before mapping and then added back to produce maps of the total 

field. The mean has been removed in such a way that the mapped fields behaved well outside 

the measurement sites. Additionally, the cross-correlations among the measurements determined 

the correlation function and length scales utilized in the optimal interpolation to map anomalies. 

A Gaussian correlation function was employed to construct maps. Multivariate optimal 

interpolation mapped geopotential, pressure and velocity. Mapping was constrained to be 

geostrophic.

Maps of τ were calculated by subtracting a 60-day low-passed field mapped with a correlation 

length scale of 160 km. The residual anomaly field was then mapped with a shorter correlation 

length scale of 70 km. Correlation functions of the measurement anomalies determined the 

correlation length scales (Figure 2.5-13). The measurement correlation functions were nearly 

isotropic indicating that the use of an isotropic Gaussian correlation function for the objective 

analysis was appropriate. Maps of τ are used to map temperature at desired depths using the 

GEM look-up tables.

Maps of upper-ocean geopotential and baroclinic velocity relative to 3000 dbar were constructed 

at each desired depth as follows: Time series of geopotential Φ(t) for each PIES site were looked 

up from τindex(t) using the GEM fields. The Φ time series were 60-day low-pass filtered and these 

time series are optimal interpolation mapped (OI-mapped) using a correlation length scale of 160 

km. At each site the residual time series was determined by subtracting the low-passed mapped 

field from the total. The anomaly field was then mapped using a shorter correlation length scale 

of 70 km to create a high-passed field. The low-passed and high-passed fields of geopotential 

and baroclinic velocity were summed to produce the combined best estimate. The suite of depths 

was every 20 dbar from 0 to 1000 dbar; 100 dbar from 1100 to 1500 dbar, and the following 

deep levels: 1750, 2000, 2500, and 3000 dbar. 

2.5.4 Bottom Pressure

Several bottom-pressure processing details are noteworthy. Pressure data were de-tided. Tidal 

response analysis (Munk and Cartwright 1966) determined the eight major tidal constituents for 

each instrument (See Appendix). Tidal amplitudes are generally small. The largest tidal 

amplitudes are near 13 cm for O1 and K1, near 5 cm for P1 and M2, and less than 5 cm for the 

remaining four constituents. Estimated tides and phases vary smoothly across the array. Pressure 

records were de-drifted and leveled simultaneously using the techniques described in Donohue et 

al. (2010). ‘Leveled bottom pressures’ refers to bottom pressures that have been adjusted to the 

same geopotential surface. Mean near-bottom currents and bottom pressures were jointly 

mapped by optimal interpolation to be in geostrophic balance. A linear drift curve was removed 

from 16 of the pressure records, while an exponential-plus-linear drift curve was removed from 

the other nine pressure records. Fifteen instruments have drifts less than 0.1 dbar (equivalent to 

10 cm); seven instruments have drifts between 0.1 and 0.2 dbar; three instruments have drifts

between 0.3 and 0.6 dbar. The final de-drift curves are constrained to yield a slope difference 

between PIES pressures and pressures determined from optimally interpolated current-meter
0 100 200 300 400

−0.5

0

0.5

1 60−day low−pass τ

correlation coefficient

 160 km Gaussian

0 100 200 300 400

−0.5

0

0.5

1 60−day high−pass τ

separation distance [km]

correlation coefficient

70 km Gaussian

50

Figure 2.5-13. Correlation coefficient between pairs of PIES τ(150 -1000) records. Correlation coefficient plotted as a function of separation distance and binned every 10 km (black 

diamonds). Upper panel: Time series have been 60-day low-pass filtered. A 160 km 

Gaussian function is plotted with red line. Lower panel: Time series have been 60-day 

high-pass filtered. A 70 km Gaussian function is plotted with red line.
51

records of ± 1.0 x 10-5 dbar day-1. With this criterion, the residual error resulting from drift is 

less than 0.01 dbar. 

2.5.5 Reference-Level Maps

Lower-ocean mapping paralleled the upper-ocean procedure. In preparation, a common mode or 

array-average pressure was subtracted from the bottom pressures (Figure 2.5-14). The common 

mode in the deep pressures simply adds a time-dependent array-wide constant which has no 

dynamical significance for the mesoscale circulation. The spectrum of the common mode reveals 

three broad spectral peaks near 50, 30 and 18 days as well as a narrow-band spectral peak near 9 

days. A 16-day peak was found in the Exploratory bottom-pressure data set. We hypothesize 

that the low-frequency signals are driven by atmospheric forcing. The 9-day peak is the Mt tide 

(Richard Ray, personal communication). Note that the Mf tide, calculated by the TPXO 7.2 

model, appears as a spectral peak near periods of 13.66 days. TPXO 7.2 is the current version of 

a global model of ocean tides which best fits, in a least-squares sense, the Laplace Tidal 

Equations and along track averaged data from TOPEX/Poseidon and Jason. The methods used 

to compute the model are described in Egbert and Erofeeva (2002). Figure 2.5-15 shows the 

bottom pressure records with the common mode removed. 

Reference level maps were calculated, after removing the common mode pressure, in a similar 

way to those calculated for the upper ocean. First, a 40-day low-passed field mapped with a 

correlation length scale of 70 km was subtracted. Then, an anomaly field with a shorter 

correlation length scale of 65 km was mapped. Correlation functions of the measurement 

anomalies determined the correlation length scales (Figure 2.5-16). Similar to the τ time series, 

the near-bottom-pressure autocorrelations are nearly isotropic (not shown). Streamfunction maps 

were created with inputs from both pressure and current-meter data. The inclusion of the currentmeter data sharpens gradients. The mapped low-passed fields were first calculated, then the 

residual at each site was used as input to map the high-passed fields, and the two maps were 

summed at each time step to produce the combined final fields of reference-level pressures and 

velocities. 

2.5.6 Total Maps

The vector sums of mapped baroclinic velocity profiles plus deep reference velocities give the 

estimated absolute geostrophic velocities at each desired level. Upper-ocean baroclinic 

velocities were created by mapping geopotential referenced to 3000 dbar. This component is 

termed as baroclinic referenced to the bottom (‘bcb’). The 3000 dbar-level (‘ref’) velocities 

mapped with the bottom pressure and current-meter records provided the reference for the upperocean baroclinic velocities to generate absolute velocities throughout the water column. 

Absolute sea-surface heights were also determined. First, 3000-dbar pressures were converted to 

their height equivalent (pressure divided by gravity and density). This component is termed as 

the reference level sea-surface height (ref). Second, surface geopotentials referenced to 3000 

dbar were converted to their height equivalent (geopotential divided by gravity). This component

is termed as the baroclinic SSH referenced to the bottom (bcb). The bcb and the ref 

contributions to sea-surface height are combined to yield absolute sea-surface height. 
200 300 400 500 600 700 800 900 1000

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

days (2009)

pressure [dbar]

all pressure records common mode

Long Period Tide (Mf + Mm) in dbar offset by −0.3

10−2 10−1 0

0.2

0.4

0.6

0.8

1

1.2

1.4

x 10−3

[dbar]2

frequency [cpd]

common mode

common mode − (Mf + Mm tide)

52

Figure 2.5-14. Top panel: All the individual pressure records (thin black) and their array-average (red), 

called the common mode, which was subtracted from each bottom pressure record before 

mapping deep water reference velocities and pressure anomaly fields. Offset from the 

common mode is the time series of the long period tide (Mf + Mm) from the TPXO 7.2 

model. Bottom panel: Spectrum of common mode, (black) before and (red) after removing 

the dominant Mf peak near 14 days and the smaller Mm peak (Spectra calculated on 

window length 355 days). 
−0.2

−0.1

0

0.1

0.2

dbar

 P51

−0.2

−0.1

0

0.1

0.2

dbar

 P52

500 1000

−0.2

−0.1

0

0.1

0.2

dbar

days 2009

 P53

−0.2

−0.1

0

0.1

0.2

dbar

 P54

 prs (common mode removed) [dbar]

 P55

 P56

500 1000

days 2009

 P57

 P58

 P59

 P60

500 1000

days 2009

 P61

 P62

 P63

 P64

500 1000

days 2009

 P65

 P66

 P67

 P68

500 1000

days 2009

 P69

 P70

 P71

 P72

500 1000

days 2009

 P73

 P74

500 1000

days 2009

 P75

Figure 2.5-15. Time series of bottom pressure anomaly (dbar) with the common mode removed. Panels are arranged according to approximate 

geographic location. The instrument number is noted in the upper left corner of each subplot. 

53 
0 100 200 300 400

−0.5

0

0.5

1 40−day low−pass prs 

correlation coefficient

70 km Gaussian

0 100 200 300 400

−0.5

0

0.5

1 40−day high−pass prs

separation distance [km]

correlation coefficient

65 km Gaussian

54

Figure 2.5-16. Correlations between pairs of pressure records. Upper panel: Correlations of 40-day 

low-pass filtered pressures plotted as a function of separation distance (open blue 

triangles) and binned every 10 km (black diamonds). A 70-km Gauss-ian function is 

plotted in red. Lower panel: Correlations of 40-day high-pass filtered pressures plotted as 

a function of separation distance (open blue triangles) and binned every 10 km (black 

diamonds). A 65-km Gaussian function is plotted in red. The common mode has been 

removed from the records in both pannels. 
55

2.5.7 Mooring Comparisons

This section compares mooring measurements of temperature and current to PIES-derived 

estimates. The comparison is not strictly a validation of the PIES methodology because the 

design of the array does not lend itself to strict verification: point measurements differ 

intrinsically from mapped geostrophic estimates. Nine tall moorings embedded in the middle of 

the array provided measurements to evaluate the PIES-derived fields of temperature and 

velocity. 

The comparison of temperatures is most directly done between measured and estimated T(t,p(t)). 

The measurement depth pm(t) varied with time, because the moored temperatures were measured 

as the mooring was drawn deeper by the drag of strong currents. Detailed temperature 

comparisons were conducted at nine nominal depths between 150 and 1100 m. The upper level 

was chosen to be deeper than the influence of the seasonal cycle, and below 1100 m the 

temperature variance is small (standard deviation ~0.14°C). PIES temperatures mapped to the 

mooring locations were vertically interpolated at each time step to the p(t) record for each 

respective moored temperature sensor. Figure 2.5-17 shows the comparison between PIES and 

mooring for four depths at A4 (yellow dot in the right panel; other mooring locations are red, 

PIES locations blue). A summary of temperature comparisons for all nine tall moorings at all 

nine nominal levels is shown in Figure 2.5-18. Correlation coefficients are greater than 0.92 at 

all depths, and are greater than 0.975 at all sites for depths between 250 and 750 m, indicating 

that the PIES capture more than 95% of variance. The rms differences are small compared to the 

signal size as measured by the standard deviations. 

Figure 2.5-19 shows the differences between measured and PIES-estimated temperature 

(squares) as well as predicted differences. Differences derive from instrument errors (both 

mooring and PIES), the GEM parameterization, mapping uncertainty, and uncertainty in the 

absolute pressure of the mooring measurements. The diamonds are the PIES error defined as 

the rms in the GEM table plus the error in the GEM table look-up due to τ uncertainty 

(τ_error*dT/dτ ). τ_error includes both instrument and mapping uncertainty. Mapping 

uncertainty is determined in the same manner as Donohue et al. (2010). The mapping procedure 

(Bertherton et al. 1976) provides a percent variance error. This is dimensionalized by 

multiplying the estimated mapping error by the measured τ(100-1500) variance. Note that the tall 

moorings experienced some vertical motion when ocean currents caused the moorings to blow 

over or draw down. We assumed that the absolute sensor depths are known within 10 m. Our 

inability to determine the absolute pressure of the sensors can lead to discrepancies. For 

example, a themocline temperature gradient of 0.035 °C dbar-1 combined with a 10 dbar 

uncertainty leads to a 0.35° difference between PIES estimated and measured temperature. 

Adding the impact of the uncertainty in absolute mooring sensor pressure (P_error*dT/dp where 

P error = 10 dbar) and an error of 0.1 °C in current meter temperature to the PIES error yields the 

circles in Figure 2.5-19. Observed rms differences agree well with predicted differences.
200 300 400 500 600 700 800 900 1000

10

20

30

Mooring A4

Blue: PIES, Red: Mooring r = 0.99

250 dbar rms difference 0.60 °C

temperature [°C]

200 300 400 500 600 700 800 900 1000

0

10

20

r = 0.99

450 dbar rms difference 0.37 °C

temperature [°C]

200 300 400 500 600 700 800 900 1000

5

10

15

r = 0.99

600 dbar rms difference 0.27 °C

temperature [°C]

200 300 400 500 600 700 800 900 1000

4

6

8

10

r = 0.98

900 dbar rms difference 0.23 °C

temperature [°C]

days [2009]

88W 86W 84W

24N

25N

26N

27N

28N

Figure 2.5-17. Comparison between the A4 mooring (red) and PIES-derived (blue) temperature. The nominal depth is noted in the left-hand 

corner of each panel. The rms difference and the correlation coefficient between PIES and the A4 mooring are noted in the righthand corner of each panel. The right-most panel shows the location of the mooring (yellow). Other mooring locations are red; PIES 

locations blue. Bathymetry contoured every 500 m depth. 

56 
0.6 0.8 1

1200

1000

800

600

400

200

0

correlation coefficient

pressure [dbar]

PIES/Mooring temperature

a1

a2

a3

a4

b1

b2

b3

c1

c2

0 1 2 3 4 5

 [°C]

square: rms difference

circle: standard deviation

57

Figure 2.5-18. Summary of the temperature comparisons. Left panel: Correlation coefficients as a 

function of mooring and pressure level. Right panel: rms differences (squares) and 

standard deviation (circles). Rms differences are less than 1°C (grey vertical line).
0 1 2 3

1200

1000

800

600

400

200

0

 [°C]

pressure [dbar]

PIES/Mooring temperature

square: rms difference

diamond: PIES error

circle: PIES error + CM error

58

Figure 2.5-19. Observed rms and predicted differences between measured and PIES-estimated 

temperature. Squares are the mean rms differences at the nine nominal depths. 

Diamonds show the PIES uncertainty in temperature, including PIES mapping error and 

the error in the GEM table look-up due to τ uncertainty. Circles include the impact of the 

uncertainty in absolute mooring sensor pressure and current meter temperature sensor 

uncertainty.
59

PIES-mapped currents were compared to mooring currents at six nominal depths. Shown here 

are the comparisons for mooring A4 (Figure 2.5-20a through Figure 2.5-20c). The series track 

each other well, with correlation coefficients above 0.89, especially within the thermocline. The 

rms differences are less than 10 cms-1 everywhere and reflect instrument errors (both mooring 

and PIES), errors associated with the GEM parameterization and the intrinsic difference between 

a point measurement and a mapped geostrophic estimate. Ageostrophic motion, such as high 

vertical wavenumber inertial currents, will not be reproduced in the maps of geostrophic 

velocity. The A4 comparisons are representative of all the other moorings. Summaries of 

velocity comparisons for all nine tall moorings are shown in Figures 2.5-21 and 2.5-22. Note 

that the signal (standard deviation) exceeds the noise (rms difference) by a factor of three to ten 

for all comparisons, and for each mooring the correlation coefficients are lowest at mid-depth. 

(The 900 and 1300-m depth current-meter records had prolonged periods of rotor stalls during 

the first deployment, therefore, for these depths, PIES-mooring comparison statistics are 

determined for only the second deployment period.). While it has not been determined as to the 

reason for the poorer comparisons at the A2 and A3 moorings, one cannot discount measurement 

errors in the current-meter measurements or uncertainty in the absolute pressure at the currentmeter mooring. Figure 2.5-23 shows the differences between measured and PIES-estimated 

velocities (squares) as well as predicted differences (diamonds). Mapping uncertainty is 

determined in the same manner as Donohue et al. (2010). The mapping procedure (Bertherton et 

al. 1976) provides a percent variance error, which is dimensionalized by multiplying the 

estimated mapping error by the mapped eddy kinetic energy. The observed rms differences agree 

well with the predicted differences in the upper and lower water column, but are larger than 

predicted in the thermocline. The errors in baroclinic shear estimates contribute the most to 

geostrophic velocity error estimates. 

In the Kuroshio Extension, Bishop et al. (2012) and Park et al. (2012) found that the ref mode 

was better represented by a vertically trapped mode proportional to cosh(z/b), where the vertical 

decay scale b = 8 km to 12 km. The terminology “ref mode” refers to the dominant vertical 

mode structure associated with the reference-level velocity fluctuations. In this experiment, 

frequency domain empirical orthogonal functions calculated from the current meter moorings 

(discussed further in Section 3.4.2) indicate that two modes capture most of the variance in the 

measured velocities: one mode is nearly depth independent and the second mode is a shear mode 

that represents the strong surface-intensified current. Here, the intent was to investigate whether 

or not one could determine a depth-dependent scale function γ(z) that would suit the reference 

velocity mode based on the mooring comparisons and also fit the altimeter-PIES SSH 

comparisons. Specifically, the best fit between measured velocity and scaled mapped PIES 

velocities was determined (e.g., u_pies(x,y,z,t) = u_bcb(x,y,z,t) + γ(z)*u_ref(x,y,t)), as was the 

best fit between along-track altimeter SSH and scaled PIES SSH (e.g., SSH_pies(x,y,t) = 

SSH_bcb(x,y,t) + γ(z=0)*SSH_ref(x,y,t)). 

Altimetric SSH anomaly data from alongtrack Jason-2 data were compared with PIES-derived 

estimates of total SSH anomaly. Just as for mapped SSH, absolute sea-surface heights were 

determined for seven PIES sites (P51-P53 and P70-P73) along Jason-2 groundtracks. The two 

SSH estimates compare well (Figure 2.5-24). The number of passes available for comparison 

varies by location and the number of passes coincident with PIES SSH is listed in the upper left 

of the figure. Rms differences are near 6 cm at all sites and correlation coefficients are 0.98 at
200 300 400 500 600 700 800 900 1000

−100

0

100

velocity [cms−1]

zonal velocity 200 dbar

Mooring A4

Blue: PIES, Red: Mooring

rms difference 9.2 cms−1

r = 0.95

200 300 400 500 600 700 800 900 1000

−100

0

100

velocity [cms−1]

meridional velocity 200 dbar rms difference 6.3 cms−1

r = 0.97

200 300 400 500 600 700 800 900 1000

−100

0

100

velocity [cms−1]

zonal velocity 400 dbar rms difference 7.4 cms−1

r = 0.92

200 300 400 500 600 700 800 900 1000

−100

0

100

days [2009]

velocity [cms−1]

meridional velocity 400 dbar rms difference 5.4 cms−1

r = 0.94

88W 86W 84W

24N

25N

26N

27N

28N

Figure 2.5-20a. Comparison between the A4 mooring (red) and PIES-derived (blue) zonal and meridional velocities. The nominal depths (200 and 

400 dbars) are noted in the left-hand corner of each panel. The rms difference and the correlation coefficient between PIES and 

the A4 mooring are noted in the right-hand corner of each panel. The right-most panel shows the location of the mooring (yellow). 

Other mooring locations are red; PIES locations blue. Bathymetry contoured every 500 m depth. 

60 
Figure 2.5-20b. Comparison between the A4 mooring (red) and PIES-derived (blue) zonal and meridional velocities. The nominal depths (600 and 

900 dbars) are noted in the left-hand corner of each panel. The rms difference and the correlation coefficient between PIES and 

the A4 mooring are noted in the right-hand corner of each panel. The right-most panel shows the location of the mooring (yellow). 

Other mooring locations are red; PIES locations blue. Bathymetry contoured every 500 m depth. 

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 600 dbar

Mooring A4

Blue: PIES, Red: Mooring

rms difference 6.4 cms−1

r = 0.89

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

meridional velocity 600 dbar rms difference 5.9 cms−1

r = 0.89

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 900 dbar rms difference 5.0 cms−1

r = 0.90

200 300 400 500 600 700 800 900 1000

−50

0

50

days [2009]

velocity [cms−1]

meridional velocity 900 dbar rms difference 4.2 cms−1

r = 0.91

88W 86W 84W

24N

25N

26N

27N

28N

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 600 dbar

Mooring A4

Blue: PIES, Red: Mooring

rms difference 6.4 cms−1

r = 0.89

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

meridional velocity 600 dbar rms difference 5.9 cms−1

r = 0.89

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 900 dbar rms difference 5.0 cms−1

r = 0.90

200 300 400 500 600 700 800 900 1000

−50

0

50

days [2009]

velocity [cms−1]

meridional velocity 900 dbar rms difference 4.2 cms−1

r = 0.91

88W 86W 84W

24N

25N

26N

27N

28N

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 600 dbar

Mooring A4

Blue: PIES, Red: Mooring

rms difference 6.4 cms−1

r = 0.89

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

meridional velocity 600 dbar rms difference 5.9 cms−1

r = 0.89

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 900 dbar rms difference 5.0 cms−1

r = 0.90

200 300 400 500 600 700 800 900 1000

−50

0

50

days [2009]

velocity [cms−1]

meridional velocity 900 dbar rms difference 4.2 cms−1

r = 0.91

88W 86W 84W

24N

25N

26N

27N

28N

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 600 dbar

Mooring A4

Blue: PIES, Red: Mooring

rms difference 6.4 cms−1

r = 0.89

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

meridional velocity 600 dbar rms difference 5.9 cms−1

r = 0.89

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 900 dbar rms difference 5.0 cms−1

r = 0.90

200 300 400 500 600 700 800 900 1000

−50

0

50

days [2009]

velocity [cms−1]

meridional velocity 900 dbar rms difference 4.2 cms−1

r = 0.91

88W 86W 84W

24N

25N

26N

27N

28N

61 
200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 1300 dbar

Mooring A4

Blue: PIES, Red: Mooring

rms difference 3.9 cms−1

r = 0.95

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

meridional velocity 1300 dbar rms difference 2.8 cms−1

r = 0.94

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 2000 dbar rms difference 2.3 cms−1

r = 0.98

200 300 400 500 600 700 800 900 1000

−50

0

50

days [2009]

velocity [cms−1]

meridional velocity 2000 dbar rms difference 1.9 cms−1

r = 0.98

88W 86W 84W

24N

25N

26N

27N

28N

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 1300 dbar

Mooring A4

Blue: PIES, Red: Mooring

rms difference 3.9 cms−1

r = 0.95

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

meridional velocity 1300 dbar rms difference 2.8 cms−1

r = 0.94

200 300 400 500 600 700 800 900 1000

−50

0

50

velocity [cms−1]

zonal velocity 2000 dbar rms difference 2.3 cms−1

r = 0.98

200 300 400 500 600 700 800 900 1000

−50

0

50

days [2009]

velocity [cms−1]

meridional velocity 2000 dbar rms difference 1.9 cms−1

r = 0.98

88W 86W 84W

24N

25N

26N

27N

28N

Figure 2.5-20c. Comparison between the A4 mooring (red) and PIES-derived (blue) zonal and meridional velocities. The nominal depths (1300 

and 2000 dbars) are noted in the left-hand corner of each panel. The rms difference and the correlation coefficient between PIES 

and the A4 mooring are noted in the right-hand corner of each panel. The right-most panel shows the location of the mooring 

(yellow). Other mooring locations are red; PIES locations blue. Bathymetry contoured every 500 m depth. 

62 
63

0.6 0.8 1

2000

1800

1600

1400

1200

1000

800

600

400

200

0

correlation coefficient

pressure [dbar]

PIES/Mooring zonal velocity

a1

a2

a3

a4

b1

b2

b3

c1

c2

0 10 20 30 40

 [cms−1]

square: rms difference

circle: standard deviation

Figure 2.5-21. Summary of the zonal velocity comparisons. Correlation coefficients as a function of 

mooring and pressure level are plotted in the left panel. The rms differences (squares) 

and standard deviations (circles) are plotted in the right panel. Note A3 and B3 do not 

include the 600 dbar level. The data from the S-4 current meters at that level during the 

second deployment were noted as noisy during data processing.
64

0.6 0.8 1

2000

1800

1600

1400

1200

1000

800

600

400

200

0

correlation coefficient

pressure [dbar]

PIES/Mooring meridional velocity

a1

a2

a3

a4

b1

b2

b3

c1

c2

0 10 20 30 40

 [cms−1]

square: rms difference

circle: standard deviation

Figure 2.5-22. Summary of the meridional velocity comparisons. Correlation coefficients as a function of 

mooring and pressure level are plotted in the left panel. The rms differences (squares) 

and standard deviations (circles) are plotted in the right panel. Note A3 and B3 do not 

include the 600 dbar level. The data from the S-4 current meters at that level during the 

second deployment were noted as noisy during data processing.
65

0 10 20 30 40

2000

1800

1600

1400

1200

1000

800

600

400

200

0

 [cms−1]

pressure [dbar]

PIES/Mooring zonal velocity

square: rms difference

diamond: PIES error 

0 10 20 30 40

 [cms−1]

PIES/Mooring meridional velocity

Figure 2.5-23. Rms and predicted differences between measured and PIES-estimated zonal (left) and 

meridional (right) velocities. Squares are the mean rms differences at the six nominal 

depths. Diamonds are PIES mapping error. 
200 300 400 500 600 700 800 900 1000

−50

0

50 Number of coincident points 85 out of 91

r = 0.98

rms difference 6.2 cm

P51 Re = 0.85

24−hr filtering, Blue: alongtrack SSH, Red: PIES

200 300 400 500 600 700 800 900 1000

−50

0

50 Number of coincident points 88 out of 91

r = 0.98

rms difference 6.7 cm

P52 Re = 0.85

200 300 400 500 600 700 800 900 1000

−50

0

50 Number of coincident points 87 out of 91

r = 0.98

rms difference 6.6 cm

P53 Re = 0.84

200 300 400 500 600 700 800 900 1000

−50

0

50 Number of coincident points 86 out of 91

r = 0.95

rms difference 6.1 cm

Re = 0.82

sea surface height anomaly [cm]

P70

200 300 400 500 600 700 800 900 1000

−50

0

50 Number of coincident points 88 out of 91

r = 0.98

rms difference 6.0 cm

P71 Re = 0.87

200 300 400 500 600 700 800 900 1000

−50

0

50 Number of coincident points 89 out of 91

r = 0.98

rms difference 6.5 cm

P72 Re = 0.85

200 300 400 500 600 700 800 900 1000

−50

0

50 Number of coincident points 90 out of 91

r = 0.98

rms difference 6.4 cm

Re = 0.87

days [2009]

P73

66

Figure 2.5-24. PIES-estimated total SSH anomaly (red) and Jason SSH anomaly (blue) for the seven 

PIES sites along groundtracks. PIES site is listed in the lower left, rms difference in the 

upper right, and correlation coefficient (r) and regression coefficient (Re) in the lower right. 

PIES data have been interpolated to the Jason-2 measurement times.
67

six of the seven sites. The regression coefficients are all less than one, near 0.85 at all sites, 

indicating that the PIES SSH overestimates altimeter SSH. The correlations are improved by 

applying the above fit with γ<1; the minimum overall rms differences are found for γ = 0.75 

(Figure 2.5-25). 

Figure 2.5-26 shows the estimate of γ(z). γ is near 1.0 at 3000 and 2000-m depth, and decays to 

near 0.85 in the upper 500 meters. The suite of cosh (z/b) curves shown in Figure 2.5-26 

indicate that a vertically trapped structure, with long length scale (b~6000 m) compared to the 

total depth of the ocean, might be appropriate. In subsequent analysis, because the vertical 

structure implies a correction factor γ(z) = (1 - ε(z)) with ε(z) less than 15%, γ(z) has not been 

applied to PIES mapped velocities. Further study would be necessary to fully resolve the vertical 

structure of the ref mode as well as any possible temporal or wavenumber variability in γ(z). 

2.6 REMOTE SENSING

The remote sensing component of the Dynamics of the Loop Current (LC) program acquired 

remotely sensed satellite data in the Gulf of Mexico (GOM), northwest Caribbean and the North 

Atlantic southeast of the U.S. east coast to aid in the interpretation of in-situ data collected in the 

study area. A combination of satellite observing systems has been used. To carry out this task, 

the Colorado Center for Astrodynamics Research (CCAR) collected and processed a 

complementary suite of satellite observations from satellite altimeter and radiometer remote 

sensing systems. This suite incorporates sea-surface-height (SSH) data with high-resolution seasurface-temperature (SST) and ocean-color imagery. Satellite altimetry provides the all-weather 

multi-satellite monitoring capability required to map mesoscale circulation variability of the 

Loop Current in the eastern GOM and to monitor seasonal, annual, and interannual to decadal 

SSH variability in the region. During cloud-free conditions, multi-channel radiometry is used to 

supplement the altimetric sampling by providing high-resolution synoptic SST and ocean-color 

imagery for monitoring the rapidly evolving Loop Current and its associated eddies including 

small-scale frontal features in and around the study region.

2.6.1 Satellite Altimetry

Satellite altimeter data used in the LC Study program is the 20-year record of near real-time and 

archival altimeter data streams available from the ERS-1, TOPEX/Poseidon (TOP/POS), ERS-2, 

Geosat Follow-on (GFO), Jason-1, OSTM/Jason-2, and Envisat satellite missions spanning the 

time period from 1993 through 2012. Processing of the SSH data is based on near real-time 

mesoscale analysis techniques designed to exploit the multi-satellite altimetric sampling (Leben 

et al. 2002). This method has been used to operationally monitor the GOM since November 

1995. 

Altimeter data from a total of three operational satellites were available during the program time 

period from April 2009 through November 2011. Basic information on each of the missions is 

given in Table 2.6-1. The ground-track coverage provided by these satellites in the study region 

is shown in Figure 2.6-1 for the time period until 22 October 2010 when Envisat was in its 

nominal 35-day repeat orbit. Also included is the 17-day repeat ground track for GFO in the plot 
68

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

5.5

6

6.5

7

7.5

8

8.5

9

Blue: western track sites, red: Eastern track sites and black: mean

γ

rms difference [cm]

Minimum rms difference with γ = 0.75

Figure 2.5-25. Rms differences between altimeter SSH anomaly and PIES-estimated total SSH 

anomaly as a function of γ. Thin curves are rms differences at seven PIES sites located 

along the Jason satellite tracks. The minimum value for each curve is denoted by a dot. 

Thick curve is the mean rms difference of the seven PIES sites. The mean rms differences minimum value is γ= 0.75. 
69

0 0.2 0.4 0.6 0.8 1

3000

2500

2000

1500

1000

500

0

pressure [dbar]

γ

 vertical structure

For depths below surface blue: zonal velocity γ, red: meridional velocity γ

cosh(z/b)

b = [4000:500:6000] m

Figure 2.5-26. Multiplicative factor, γ, applied to the reference SSH (velocity) which when added to the 

baroclinic SSH (velocity) referenced to the bottom produces the lowest rms between 

measured and PIES-estimated quantities. Separate values for γ are calculated for zonal 

(blue) and meridional (red) velocities denoted by filled squares for the mean γ. The mean 

γ is computed from all available current meter records at each level. Black curves show y 

= cosh(z/b) for b values ranging from 4000 to 6000 m every 500 m. Note that the vertical 

trapping decreases for increasing values of b.
90 ̊W 88 ̊W 86 ̊W 84 ̊W 82 ̊W 80 ̊W

22 ̊N

24 ̊N

26 ̊N

28 ̊N

30 ̊N

200

200

1000

1000

2000

3000

PaddingMoorings

PaddingMoorings

PaddingMoorings

PIES

Tall Moorings

Short Moorings

GROUND TRACKS

70

 Figure 2.6-1. Satellite altimeter exact repeat groundtrack coverage in study region. Jason-1 (thin red), 

OSTM/Jason-2 (thick red), and Envisat (blue) are shown with a schematic of the instrument array. The 17-day repeat ground track for GFO (green) is also shown. 
71

Table 2.6-1. Satellite Altimeter Missions Active During the LC Study Program

Satellite Launch Date Agency

Repeat

Period

(days)

Cross track Spacing

Degrees of 

Longitude km*

Jason-1 18 Dec 1999 NASA/CNES 10 2.83 278

Envisat 1 Mar 2002 ESA 35 0.72 71

Envisat Extended Mission (started on 02 Nov 

2010)

30 0.84 82

OSTM/Jason-2 20 Jun 2008 NASA/CNES 10 2.83 278

 *at 28°N

OSTM/Jason-2 and Jason-1 Tandem/Interleaved Mission: Jan 2009 to 12 Apr 2012

TOPEX/Poseidon/Jason-1 Interleaved 10 1.42 140

to show the spatial sampling afforded by operational satellites in all four exact-repeat orbits 

occupied historically for mapping of ocean SSH variability. 

Note that during the study program, the OSTM/Jason-2 & Jason-1 satellites were in tandem 

orbits with interleaved ground tracks. NASA/CNES scientists selected this configuration to 

improve the sampling of mesoscale ocean circulation by precision altimeters (Dibarboure et al. 

2011), as was done during the original tandem altimeter mission flown by Jason-1 and TOP/POS 

(Fu et al. 2003). The space/time sampling provided from a single satellite in the original 10-day 

repeat orbit of the TOP/POS satellite, which was selected to map the ocean topography 

associated with large-scale variations in SSH, is not sufficient for monitoring mesoscale 

variability. This is because of the large distance between neighboring ascending or descending 

tracks on the 10-day repeat ground track. In the GOM, this spacing is 2.83° of longitude or about 

278 km at 28°N, which is also the distance between crossover points between ascending and 

descending tracks. Moving a second satellite onto a parallel ground track that is midway between 

two adjacent ground tracks of the original TOP/POS orbit reduced this distance by half to a 

cross-track spacing of 140 km at 28°N. At latitudes midway between intra- and inter-satellite 

crossover points, the ascending/descending ground-track sampling improves by another factor of 

two to a cross-track spacing of just 71 km. Thus, the average cross-track sampling from the 

tandem mission data alone is 70 to 140 km within the study region. 

The addition of Envisat data augments this spatial sampling, but at irregular sampling times. 

During the study program, Envisat was in the nominal 35-day repeat orbit until 22 October 2010, 

when maneuvers were initiated to place the satellite in the drifting 30-day repeat cycle Envisat 

extended mission orbit. A data gap of 35 days occurred between the last cycle of the nominal 

mission and first cycle of the extended. The Envisat 35-day exact repeat orbit (501 orbits per 

cycle) cross track spacing is 0.72° of longitude or about 71 km at 28°N. The Envisat 30-day 

repeat orbit (431 orbits per cycle) cross-track spacing is approximately 0.84° of longitude or 

about 82 km at 28°N.

GFO was not available during the study program, but historically provided cross-track sampling 

along its ground track at a spacing of 1.47° of longitude or about 144 km at 28°N. Tandem 

mission sampling from the OSTM/Jason-2 and Jason-1 orbits was more optimal than the original 
72

TOP/POS since the orbits are interleaved in both space and time. For this second interleaved 

tandem mission, advantage was taken of Jason-1's still healthy propulsion system to put it into a 

much different position than TOP/POS was during the original tandem mission. In that mission 

TOP/POS remained so close to Jason-1 that the two spacecraft were flying almost 

simultaneously over the same region even though the ground tracks were offset by 1.42 degrees 

of longitude. In the OSTM/Jason-2 and Jason-1 tandem mission, Jason-1 was in the interleaved 

orbit, but much further away from OSTM/Jason-2, about five days behind and on the other side 

of Earth. Nevertheless, its ground track still falls mid-way between those of OSTM/Jason-2 in 

the interleaved ground-track sampling pattern with the interleaved Jason-1 track located next to 

Jason-2 with an apparent 5-day shift. There are three advantages to this configuration: 1) it is 

slightly better in terms of global aliasing, but is not the optimal 3.5-day offset tandem mission 

configuration described by Tai (2009), 2) it is slightly westwards propagating, and 3) it is 

slightly more efficient in terms of near-real-time (NRT) observation as measurements from the 

same dates are as far away as possible (Dibarboure et al. 2011).

Intuitively, mapping of SSH should improve if along-track altimeter data from multiple satellites 

are combined using objective analysis. SSH fields produced by combining multi-mission 

altimetry, however, may not be better than those constructed from Jason-1 or Jason-2 data alone, 

if uniform errors and wavelength/frequency resolution satisfying the Nyquist criteria are required 

of the space/time gridded product (Tai 2009), as has been proposed by Greenslade et al. (1997). 

While these constraints may be reasonable for large-scale eddy sampling studies (Chelton et al. 

2011) or mission design, the constraints are too limiting for mesoscale mapping in general. 

Operational multiple-satellite objective mapping of the mesoscale circulation must therefore rely 

on suboptimal smoothing to resolve eddy-scale wavelength, albeit with the commensurate errors 

caused by non-uniform sampling and aliasing. This is true of both formal “optimal” interpolation 

and suboptimal objective analysis schemes. Nevertheless, the efficacy of the interpolated fields 

can be evaluated by comparing the interpolated altimetry with coincident in-situ data to 

quantitatively assess the processing and gridding strategies. PIES data are an ideal in-situ 

measurement type for these comparisons, and instrument sites were selected along altimeter 

ground tracks where possible to allow accurate assessment of not only the space/time gridded 

products, but the along-track data as well. 

2.6.1.1 Along-Track Altimeter Data

Along-track altimeter data were collected from the Radar Altimeter Database System (RADS) 

hosted by the Delft Institute of Earth Observation and Space Systems at the Delft University of 

Technology in the Netherlands. RADS (Naeije et al. 2008; Naeije et al. 2000) is an online 

database that contains validated and verified altimeter data and correction data products for most 

of the historical and operational satellite altimeter missions. Standard corrections from RADS 

were applied to the along-track data including inverted barometer (MOG2D; Carrère and Lyard 

2003), sea state bias (CLS), ionosphere (smoothed dual-frequency correction for Jason-1 and 

OSTM/Jason-2; JPL Global Ionosphere Maps (GIM) for Envisat), wet troposphere (on board 

radiometers) and dry troposphere (ECMWF) corrections. The data were further corrected for 

pole and solid-earth tides and the GOT 4.8 tide model (an update to Ray 1999) was used to 

remove ocean and load tides. Finally, the CNES CLS 2011 Global Mean Sea-Surface height 

(Schaeffer et al. 2012) at the location of each once-per-second sub-satellite point was subtracted 

from the corrected range measurement to produce along-track corrected SSH anomaly (SSHA). 
73

In order to simplify further processing and analysis, collinear along-track SSHA datasets were 

created for each satellite when they were in an exact repeat orbit by interpolating the sub-satellite 

along-track data to reference ground tracks. Each 10-day exact repeat cycle of OSTM/Jason-2 

and Jason-1 along-track SSHA data and each 35-day repeat cycle of Envisat SSHA data were 

linearly interpolated to reference ground tracks based on precision orbit determination 

ephemerides for each satellite at once-per-second along-track spacing. The OSTM/Jason-2 

reference track used the computed ground track for TOP/POS cycle 18. The Jason-1 interleaved 

mission reference ground track was the same ground track with an offset in longitude 

corresponding to the nominal interleaved orbit. The Envisat 35-day reference ground track is 

based on repeat cycle 6 of the ERS-1 Multidisciplinary 1 Mission. Along-track data from the 30-

day Envisat extended-mission orbit was stored and processed as non-repeat data as described for 

ERS-1 Geodetic Mission data in Leben et al. (2002).

Data coverage was very good from all three satellites along the exact-repeat reference ground 

tracks, although a gap of 35 days occurred when the Envisat orbit was changed in late October 

2010. Along-track interpolated 1-Hz SSHA data coverage along the collinear ground-track 

points in water deeper than 200m in the Gulf was 94% for Jason-1 and 88% for OSTM/Jason-2 

during the time period of the study program. Coverage during the Envisat nominal mission was 

92%. We didn’t attempt to calculate a similar statistic for data coverage from the drifting 

Envisat extended-mission orbit, but analysis of the data sampling used by objective mapping to 

be discussed later in this report suggests that the coverage was comparable.

2.6.1.2 Mesoscale Analysis

The processing of the altimeter data is designed to retain mesoscale signals while filtering out 

longer wavelength altimetric errors. This filtering, however, also removes long wavelength 

oceanographic signals. A detailed description of this processing and its implementation and

validation in the GOM can be found in Leben et al. (2002). The procedure incorporates data from 

all of the available satellites, treating each data set in a consistent fashion as follows: 

1. All along-track satellite data are referenced to an independent gridded-mean sea surface by 

subtracting the mean-sea-surface value at the sub-satellite point from each observation. 

2. Along-track loess filtering is used to remove residual orbit and environmental correction 

errors. The loess filter removes a running least-squares fit of a tilt plus bias within a sliding 

window from the along-track data. The window width is approximately 15° of latitude (200 

once-per-second along-track data points). 

3. A multigrid preconditioned Cressman analysis with temporal weighting is used to 

objectively interpolate the along-track data to a 1/4° grid. 

4. A model-mean SSH field is added to the mapped SSH anomaly field to provide an estimate 

of the total SSH in the GOM.

2.6.1.3 Mean-Reference Surface and Model-Mean SSH

All along-track data are referenced to an existing altimetric-mean sea surface. The data are 

treated as non-repeating ground tracks and are referenced directly to the mean sea surface by 

interpolating the mean sea-surface value to the sub-satellite point (the point directly below the 
74

satellite) and subtracting it from the sea- surface height. This applies an implicit cross-track 

geoid gradient correction to the along-track data before interpolation to the reference ground 

tracks. 

The CNES CLS 2011 Global Mean Sea Surface (CLS11MSS) was used as the reference surface 

for the altimetry. The CLS11MSS was calculated from seven satellite missions: TOP/POS, ERS1 GM, ERS-2, Jason-1, TOP/POS interleaved mission, GFO, and Envisat. Jason-2 data were not 

included because the altimetry data set used to determine this mean sea surface was based on 

work done in 2009 using data validated up to and through 2008 (Schaeffer et al. 2012). Although 

the data spans the time period from 1993 to late 2008, the data were processed to obtain a mean 

sea surface referenced to the time period from 1993–1999. This was done by preprocessing the 

altimetry so that the data would be homogeneous in terms of corrections and less contaminated 

by the oceanic seasonal variability. The interannual signals were then removed to obtain a mean 

sea surface referenced to the 7-year time period, 1993 through 1999.

To calculate the synthetic SSH estimates, we used the model-mean sea-surface height computed 

for the time period 1993-1999 from a data assimilation hindcast experiment performed by Drs. 

Lakshmi Kantha and Jei Choi for the MMS Deepwater Physical Oceanography Reanalysis and 

Synthesis Program (Nowlin et al. 2001). The data assimilation experiment used the University of 

Colorado-Princeton Ocean Model (CUPOM) and assimilated along-track TOPEX and ERS-1&2 

sea-surface-height anomalies into CUPOM on a track-by-track basis as subsurface temperature 

anomalies (Kantha et al. 2005). Before adding the model mean to the gridded SSH- anomaly 

fields, we averaged the 1993-1999 SSH-anomaly fields and removed the residual anomalous 

altimetric mean over the time period. This references the SSH-anomaly fields to a mean 

spanning the same time period as determined from the CUPOM hindcast data assimilation 

experiment. The anomalous altimetric mean reflects the difference between the mean circulation 

contained in the CLS11 mean sea surface and the 1993-1999 data-assimilation mean. More 

discussion of these differences is found in Section 2.7.4 of this report.

2.6.1.4 Objective Mapping

Daily analysis maps of height anomaly relative to the mean sea surface were estimated using an 

objective analysis procedure (Cressman 1959) to interpolate the along-track data to a 1/4° spatial 

grid. The method uses an iterative difference-correction scheme to update an initial-guess field 

and converge to a final gridded map. A multigrid procedure provides the initial guess. Five 

iterations were used with radii of influences of 200, 175, 150, 125, and 100 km while employing 

a 100-km spatial decorrelation length scale in the isotropic Cressman weighting function. The 

data were weighted in time using a 12-day decorrelation time scale relative to the analysis date 

using a ±10 day window for the TOP/POS, Jason-1 and OSTM/Jason-2 data and a ±17 day 

window for the ERS-1&2, Envisat, and GFO data. The details of the space and time-weighted 

version of the multigrid preconditioned Cressman analysis is described next and is based on the 

space-weighting-only technique described in Hendricks et al. (1996). 

During the program time period, altimeter data were available from only the OSTM/Jason-2, 

Jason-1 and Envisat satellites. Figure 2.6-2 shows the availability and usage of data from each 

satellite over the time period from April 2009 through November 2011. In the plot, “actual” 

shows the satellites contributing data to the gridded product for any given day. The “available” 
75

plot shows the days when there are valid data for a particular satellite. The “windowed” plot 

shows when there is no valid data on the actual day, but there are data within the window used 

for gridding. The “used” plot shows the days from which satellites could be chosen to be in the 

data product, but does not indicate valid data is available in a specific region. “Actual” is 

computed by forming a logical .AND. operation between “used” and the union of “available” 

and “windowed”. 

2.6.1.5 Objective-Analysis Procedure

An objective-analysis (OA) procedure is used to interpolate the along-track sea-surface-height 

anomalies onto a regularly spaced 1/4° global grid. The OA algorithm is based on the iterative 

difference-correction scheme of Cressman (1959). The initial guess field for the Cressman 

algorithm is supplied by an efficient multigrid procedure.

A rough estimate of the 1/4° field is created by collecting the along-track SSH-anomaly data into 

1/4° grid cells. In grid cells where at least one SSH measurement is available, the average of all 

measurements within the cell is computed. Some of the grid cells may not contain data 

depending on the spacing of ground tracks. The OA procedure is designed to fill in these data 

gaps by creating an SSH-anomaly field that is consistent with the along-track measurements.

The 1/4°-binned data can be used as an initial guess in the Cressman algorithm; however, having 

initial values in the empty grid cells can enhance the efficiency of the iteration procedure. A 

simple multigrid procedure is used to estimate values in cells where no altimeter measurements 

are available. Multigrid methods (Briggs 1987) rapidly solve a set of equations by working at 

several grid resolutions. In this case, if the along-track data are binned into 1° or 2° grid cells, 

there would be fewer or even no empty ocean-grid cells. Using a multigrid interpolation strategy 

to efficiently compute the means, a set of progressively coarser grids (1/2°, 1°, 2°, ...) are 

created from the global 1/4° grid, and the average SSH is computed at all coarser grid resolutions 

in each cell containing data. The mean values are transferred back to the original 1/4° grid from 

the finest-scale grid containing a mean value coincident with that location. Finally, a fast redblack smoothing operator (e.g., see Press et al. 1992) is used on the 1/4° initial guess field to 

smooth high-frequency noise introduced by the multigrid interpolation.

Cressman objective analysis uses an iterative-difference corrections scheme in which a new 

estimate of the SSH value for a given grid cell is equal to the sum of the previously estimated 

SSH at that location and a correction term. The correction term is forced by the difference 

between the estimated heights and the original data values over all grid cells within a specified 

radius of influence. A weight based on the number of original measurements within a grid cell is 

included in the correction term, as is a weight, based on the distance of a grid cell from the point 

being updated.
09 10 11 12

topex

jsn2

jsn1

gfo

geosat

ers2

ers1

envisat

cryosat2

Actual

09 10 11 12

topex

jsn2

jsn1

gfo

geosat

ers2

ers1

envisat

cryosat2

Available

09 10 11 12

topex

jsn2

jsn1

gfo

geosat

ers2

ers1

envisat

cryosat2

Windowed

09 10 11 12

topex

jsn2

jsn1

gfo

geosat

ers2

ers1

envisat

cryosat2

year

Used

76

Figure 2.6-2. Plot showing daily “actual”, “available”, “windowed”, and “used” data from operational 

altimeter satellites during the study program. 
77

The nth iteration for the SSH at grid cell i is computed using:

 

!

hi

n = hin"1 +

wmnm

* hm* " hmn"1

# ( )

wmnm

*

# (2.6.1)

where the sums are taken over all m grid cells within the specified radius of influence R from the 

grid cell i being updated. The variables in (Eq. 1) are defined as:

 

!

hi

n

 nth iteration of SSH at grid cell i;

 hi

n!1

 the (n-1)th iteration of SSH at grid cell i;

 

!

hm

*

 average height at grid cell m based on the original data;

 

!

hm

n"1

 (n-1)th iteration of SSH at grid cell m.

 

!

nm

* number of original measurements within grid cell m.

The weights in the correction term are defined by:

 

!

wm = exp("arm

2 /R2

) for 

!

r " R; (2.6.2) 

!

wm = 0 for 

!

r > R;

where 

!

rm is the distance between grid cell m and the grid cell being updated and R is the 

maximum radius of influence. The parameter a is an adjustable weighting factor that scales the 

exponential spatial weighting of the data.

To incorporate weighting of the data in time, the data and the number of original measurements 

within a grid cell are each scaled by the weighting function: 

 

!

wt = exp("b#tm

2 /T2

) for 

!

"t # T ; (2.6.3)

!

wt = 0 for 

!

"t > T ;

where 

!

"tm is the difference between the measurement time and the time corresponding to the 

analyzed field. The parameter b is the time weighting factor, and T is the maximum time window 

of influence.

The empirical weighting parameters, a and b, are selected to map the mesoscale structure within 

the limitation of the scales resolvable by the cross-track altimeter sampling. The mesoscale 

analysis uses a = 4 and b = 2, which correspond to decorrelation space and time scales of 100 

km and 12 days, respectively, for R = 200 km and T = 17 days. The maximum radius of 

influence, R, is decreased between the Cressman iterations to allow smaller scales to converge 

more quickly and to increase resolution when along-track sampling is available. For this study, R 
78

is decreased from 200 to 100 km over five iterations giving a decorrelation length scale of 50 km 

on the final Cressman iteration. 

2.6.2 Satellite Radiometry

Multi-channel satellite radiometry was used to complement altimeter sampling to provide highresolution synoptic images for monitoring the LC and its associated eddies during cloud-free 

observing conditions. Radiometry from NASA’s Moderate Resolution Imaging 

Spectroradiometer (MODIS) instrument onboard the Aqua satellite was the primary radiometry 

data set acquired and processed by CCAR for use by the project team. Several ancillary SST 

data sets were also acquired for use during the study program and in preparation of this report. 

MODIS Ocean Color and SST 

MODIS ocean color and SST data were downloaded from the Ocean Biology Processing Group 

(OBPG c2012) web and ftp sites at the NASA Goddard Space Flight Center (GSFC). All of the 

MODIS SST and ocean-color data were processed on or before January 19, 2012, and so are 

based on the MODIS data version R2010.0 reprocessing completed in June 2011. All of the 

CCAR processing for this study program used level 2 (L2) swath data.

Ocean-color data were processed by OBPG into chlorophyll-a (CHL-a) concentration using the 

empirical chlorophyll algorithm OC3 (O’Reilly et al. 2000), which uses measured radiances at 

443, 488 and 551 nm to calculate the individual chlorophyll fields from each satellite image. The 

only editing flags applied were the processing flags and masks used by OBPG (Franz 2006). The 

OBPG generates two SST products from MODIS: short-wave (4μm) and long-wave (11μm). The 

L2 long-wave SST product generated from bands 31 and 32 located at 11 and 12 μm, 

respectively, were used. The L2 SST hierarchical data format (HDF) files are generated by the 

Multi-Sensor L1 to L2 processing code (MSL12; OBPG 2010). For SST, the OBPG processing 

generates a quality level flag from a series of quality tests. The level flag ranges from 0 (best) to 

4 (failure). We determined, by visual inspection, that a quality flag of 0 or 1 produced images of 

sufficient quality in the study region and applied that editing criteria to all the L2 SST data 

downloaded. This editing of the data is less stringent than that used by the OBPG in their 

production of L3 image products, where all values where the quality flag is nonzero are flagged. 

The OBPG editing might be preferred for high-accuracy quantitative analysis of SST data; 

however, the less stringent editing provided better coverage and accurate enough data for 

qualitative monitoring in the study region. 

Both the MODIS L2 SST and ocean-color data come as individual HDF files per swath. These 

files contain the derived SST and CHL-a data at 1-km resolution. The geophysical values for 

each pixel are derived from the L1A raw radiance counts by applying the sensor calibration, 

atmospheric corrections, and various retrieval algorithms. Typically the data for one day in the 

GOM are split up across multiple swath files, some of which may overlap. The processing scripts 

read in all of the swaths files covering the GOM for one day, apply any editing masks (none for 

the CHL and only the quality flag for the SST), bin the data into a grid and write the gridded data 

out to a single netCDF file for a given day. The binning process averages data where there is an 

overlap (rare) and forms a grid of approximately 4-km resolution cells. In addition to the 

individual daily images, a moving average of the daily values is used to form 7-day composite 

daily images by averaging all of the valid data points within each 4-km cell. 
79

2.6.3 Ancillary Satellite Altimeter Datasets

A 20-year dataset of Delayed Time (DT) mapped satellite altimeter analyses spanning the time 

period from 1993 through 2012 was downloaded from the Centre National d'Etudes Spatiales 

(CNES) Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) data ftp 

site. The complete weekly DT-mapped time series through December 26, 2012 was released on 

June 4, 2013. This altimeter product was produced by SSALTO/DUACS and distributed by 

AVISO with support from the French Space Agency CNES. The multi-mission mapping of sealevel anomaly (SLA), which is another name for SSHA, is based on an optimal interpolation 

derived from Le Traon et al. 1998, with various improvements (e.g., Ducet et al. 2000, Le Traon 

et al. 2003, Dibarboure et al. 2011). Weekly Maps of Absolute Dynamic Topography (MADT) 

were downloaded on a 1⁄4 degree Cartesian grid based on the sum of the interpolated maps of 

SLA and the Mean Dynamic Topography CNES/CLS 2009 (Rio and Larnicol 2010).

2.6.4 Ancillary SST Datasets

Three fully processed ancillary SST datasets were collected to use in the study program. Dr. Nan 

Walker at the LSU Earth Scan Laboratory provided one of the datasets and the other two were 

downloaded from the NASA/JPL Physical Oceanography Distributed Active Archive Center 

(PO.DAAC). 

Dr. Nan Walker provided Geostationary Operational Environmental Satellite (GOES) Channel 2 

brightness temperatures for the 3-year time period, 2009 through 2011, spanning the study 

program. The GOES GVAR image sensors provide high frequency repeat coverage that 

improves the potential for retrieving ocean temperature information over short time-scales and 

has been used successfully for tracking Loop Current frontal eddies (Walker et al. 2003, Walker 

et al. 2009). 

The datasets downloaded from PO.DAAC were the 24 hour gridded 6-km GOES NRT L3 SST 

(GOES3 c2009) and the daily 0.011° Group for High Resolution Sea-Surface Temperature 

(GHRSST) L4 Multi-scale Ultra-high Resolution (MUR) SST (GHRSST [unknown date]). The 

GOES NRT L3 dataset is provided to PO.DAAC by NOAA/NESDIS. The GHRSST MUR SST 

is produced by the NASA JPL MUR MEaSUREs Project and hosted by PO.DAAC (Chin 

[unknown date]). 

2.7 PIES AND ALTIMETRY EVALUATION AND COMPARISON

PIES and satellite altimetry are complementary data types. Although the two measurement 

systems measure completely different physical quantities, they both yield an estimate of the 

height of the ocean surface relative to some datum, which is commonly referred to as sea-surface 

height (SSH). 

In this section, the altimeter SSH measurement system is evaluated using PIES data as a 

benchmark for theoretical analyses and for comparison of PIES SSH directly to the coincident 

altimeter-derived SSH collected during the Dynamics of the Loop Current program. This is the 

fourth opportunity for these types of analyses and comparisons in the GOM, supplementing the 

results in the central, western, and northeastern GOM reported in the technical reports of the 

Exploratory, Northwestern, and Eastern surveys of deepwater currents (Donohue et al. 2006; 
80

Donohue et al. 2008; Cox et al. 2010). Some of the statistics prepared for those reports will be 

presented again here and will be discussed in light of the results obtained in this program. These 

types of analyses and comparisons have the potential to identify problems in current datasets and 

to develop and test improvements in the altimeter data processing techniques used to produce 

future data products. This will facilitate the synthesis of altimetry data and PIES data from 

current and future arrays deployed in the deepwater GOM, which will improve observing and 

understanding of deepwater circulation patterns and dynamics throughout the water column and 

the Gulf.

2.7.1 Altimetric Sampling and Aliasing

Satellite altimeters provide discrete SSH measurements at sub-satellite points spaced 

approximately 5–7 km along ground tracks with exact repeats approximately every 10 or 35 days 

for the satellites used during the study program (Table 2.7-1). Orbital dynamics determine the 

space/time sampling pattern achieved on orbit, and there is a trade-off between spatial and 

temporal resolution when selecting an orbit during the mission-design phase of a satellite 

program. As an example, see the discussion of the TOP/POS mission in Parke et al. (1987). For 

single satellite sampling, high spatial resolution using a nadir pointing altimeter is achieved only 

at the expense of less frequent sampling of the sea surface in time, and vice versa. 

Table 2.7-1. Satellite Altimeter Mission Exact-Repeat Periods and Periods 

Associated with the Nyquist Sampling Frequency

Satellite

Approximate 

Repeat

Repeat Period

(days)

Nyquist Sampling 

Period (days)

TOPEX/Poseidon 10-day 9.9156 19.8313

ERS-2 35-day 35 70

Geosat Follow-On 17-day 17.0505 34.1010

Jason-1 10-day 9.9156 19.8313

OSTM/Jason-2 10-day 9.9156 19.8313

Envisat 35-day 35 70

Envisat Extended 30-day 30 60

Unlike ground-based instruments, where the sampling rate can be selected to satisfy a specific 

Nyquist criterion, satellite-based measurement systems in non-geosynchronous orbits have a 

temporal sampling rate imposed by the period at which a point on the Earth’s surface is sampled 

from orbit. Increasing the temporal sampling rate for a nadir-pointing altimeter, therefore, 

requires either the placing of the satellite in a shorter-repeat-period orbit, resulting in a loss of 

spatial sampling density, or by the addition of more satellites in the same repeat orbit and 

keeping the same spatial sampling density. Neither option can usually be justified from an 

economic, scientific, or operational perspective. Anecdotally, when additional sampling became 

available from TOP/POS after the commissioning phase of the TOP/POS and Jason-1 tandem 

mission, the decision was made to increase the spatial sampling density (Fu et al. 2003) and, by 

default, accept the existing level of temporal aliasing (i.e., aliasing caused by repeat sampling in 

time of the same spatial points) of the 10-day repeat sampling. A similar decision was made after 

the commissioning phase of OSTM/Jason-2, although the sampling and aliasing characteristics 
81

of the combined measurements of this tandem mission were more optimal (Dibarboure et al. 

2011). A number of studies have addressed spatial/temporal aliasing issues (Schlax and Chelton 

1994, Parke et al. 1998) including assessment of the aliasing of well known periodic signals such 

as tides; however, recently a few theoretrical studies have assessed the SSH variance associated 

with the aliased signal from under-sampled SSH ocean measurements (Tai 2009).

The temporal aliasing of ocean signals by satellite-altimeter sampling can be addressed using the 

high-rate in-situ SSH data provided by PIES measurements. Hendry et al. (2002) performed the 

first study along these lines using PIES data collected within the North Atlantic Current in the 

Newfoundland Basin. They found that the time scales of motion observed in the region are such 

that 86-95% of the subinertial-period SSH variability was not aliased by the approximately 10-

day TOP/POS repeat-period sampling. Gille and Hughes (2001) performed an earlier study of 

sampling using only bottom-pressure records; however, that type of study would not be 

appropriate in the GOM where the time scales associated with the bottom-pressure variability are 

not representative of the time scales of the SSH variability.

Following the methodology of Hendry et al. (2002), assessments were made of the SSH signal in 

the Exploratory, Northwestern, and Eastern Gulf Study regions in the central, northwestern, and 

eastern Gulf, respectively (Donohue et al. 2006, Donohue et al. 2008, Cox et al. 2010), and now 

report similar analyses for the Loop Current study array for the approximately 10-day, 17-day, 

and 35-day exact-repeat-period sampling historically available from the satellite altimeter 

missions. Power spectra were computed for each of the SSH time series – barotropic, baroclinic, 

and combined – and the percentage of cumulative power in the spectra up to each of the Nyquist 

frequencies associated with the 10-day, 17-day, and 35-day repeat sampling periods were 

calculated. The periods corresponding to the Nyquist frequency for each of the altimeter 

satellites are tabulated in Table 2.7-1. Figures 2.7-1, 2.7-2 and 2.7-3 show maps of the unaliased 

variance (i.e., from a signal measured at a sufficiently high sampling rate so that any aliased 

signal is negligible) associated with 10-day, 17-day, and 35-day repeat sampling periods in the 

study region for the current altimeter missions from the barotropic, baroclinic, and combined 

SSH signals, respectively. These study summary statistics are tabulated in Table 2.7-2 along with 

the statistics from the Exploratory, Northwestern, and Eastern Gulf PIES arrays. Tabulated 

values for each of the Loop Current PIES stations are listed in Table 2.7-3.

The aliasing of the barotropic SSH signal is the most severe of the three signals because of the 

shorter time scales associated with that signal in the GOM when compared with the baroclinic 

SSH or total SSH signals. When averaged over the Loop Current PIES array, the mean value of 

the 10-day sampling period unaliased barotropic variance is 81%, much higher than the mean 

values of 59%, 62%, and 63% estimated from the Exploratory Program, Northwestern and 

Eastern Gulf PIES arrays, respectively. The Loop Current array individual station results range 

from a minimum of 57% at PIES 53 to a maximum of 93% at PIES 67, 68, 69 and 73, which is a 

greater range than the 56% to 72% and the 44% to 77% ranges found for the Northwestern Gulf 

and the Exploratory program arrays, respectively. The spatial pattern of aliasing is similar for 17-

day and 35-day sampling, with more aliasing in the northwestern half of the array and the least 

amount in the southeastern half. The mean values of the unaliased variance, however, decreased 

significantly to 66% and 45% for 17-day and 35-day sampling, respectively. This significant
 Barotropic: 10-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 81%

88°W 86°W

25°N

26°N

27°N

60

Unaliased Variance (%)

70

80

90

 Barotropic: 17-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 66%

88°W 86°W

25°N

26°N

27°N

40

Unaliased Variance (%)

50

60

70

80

 Barotropic: 35-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 45%

88°W 86°W

25°N

26°N

27°N

Unaliased Variance (%)

35

40

45

50

55

 82

Figure 2.7-1. Maps of PIES barotropic unaliased variance for 10-day, 17-day, and 35-day sampling. 
 Baroclinic: 10-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 98%

88°W 86°W

25°N

26°N

27°N

96

Unaliased Variance (%)

97

98

99

 Baroclinic: 17-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 95%

88°W 86°W

25°N

26°N

27°N

Unaliased Variance (%)

94

96

98

 Baroclinic: 35-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 86%

88°W 86°W

25°N

26°N

27°N

70

Unaliased Variance (%)

80

90

 83

Figure 2.7-2. Maps of PIES baroclinic unaliased variance for 10-day, 17-day, and 35-day sampling. 
 SSH: 10-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 98%

88°W 86°W

25°N

26°N

27°N

Unaliased Variance (%)

95

96

97

98

99

 SSH: 17-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 94%

88°W 86°W

25°N

26°N

27°N

90

Unaliased Variance (%)

92

94

96

98

 SSH: 35-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 85%

88°W 86°W

25°N

26°N

27°N

Unaliased Variance (%)

70

80

90

 84

Figure 2.7-3. Maps of PIES SSH unaliased variance for 10-day, 17-day, and 35-day sampling.
85

Table 2.7-2. Unaliased Variance Statistics for 10-day, 17-day, and 35-day ExactRepeat Sampling of the PIES Barotropic, Baroclinic, and Combined 

SSH Signals

Stations

Barotropic Signal

Mean (%)

Baroclinic Signal

Mean (%)

Total SSH Signal

Mean (%)

 Repeat: 10-day 17-day 35-day 10-day 17-day 35-day 10-day 17-day 35-day

Loop Current Program

all stations 81 66 45 98 95 86 98 94 85

Eastern Gulf Program

all stations 63 49 35 93 89 76 92 88 75

Northwestern Gulf Program

all stations 62 53 42 97 92 76 94 89 75

Exploratory Program

all stations 59 47 37 97 93 78 95 92 78

above escarpment 56 45 39 96 93 75 94 91 75

below escarpment 61 49 36 97 93 80 96 93 79

Stations

Barotropic Signal

Maximum (%)

Baroclinic Signal

Maximum (%)

Total SSH Signal

Maximum (%)

 Repeat: 10-day 17-day 35-day 10-day 17-day 35-day 10-day 17-day 35-day

Loop Current Program

all stations 93 87 57 100 99 97 99 98 95

Eastern Gulf Program

all stations 70 55 39 97 92 85 97 93 83

Northwestern Gulf Program

all stations 72 64 47 99 97 90 98 95 87

Exploratory Program

all stations 77 60 45 99 98 93 99 98 93

above escarpment 60 50 42 99 98 90 97 96 90

below escarpment 77 60 45 99 98 93 99 98 93

Stations

Barotropic Signal

Minimum (%)

Baroclinic Signal

Minimum (%)

Total SSH Signal

Minimum (%)

 Repeat: 10-day 17-day 35-day 10-day 17-day 35-day 10-day 17-day 35-day

Loop Current Program

all stations 57 38 31 96 92 68 95 90 67

Eastern Gulf Program

all stations 59 44 31 84 79 68 84 80 67

Northwestern Gulf Program

all stations 56 47 36 93 86 52 84 79 53

Exploratory Program

all stations 44 38 29 92 86 54 87 82 54

above escarpment 51 42 36 92 86 54 87 82 54

below escarpment 44 38 29 93 87 56 92 85 56
86

Table 2.7-3. PIES SSH, Baroclinic, and Barotropic Statistics and Percent of 

Unaliased Variance Measured by Satellites in 10-day, 17-day, and 35-

day Exact-Repeat Orbits

PIES

ID# Signal

Length Std T0.5 Unaliased Variance (%)

(days) (cm) (days) 10-day 17-day 35-day

P51

SSH 903.5 22.4 341 96 93 90

Baroclinic 22.0 341 97 94 91

Barotropic 4.2 32 77 59 39

P52

SSH 903.5 25.3 341 98 96 93

Baroclinic 25.2 341 97 95 92

Barotropic 4.0 23 64 48 32

P53

SSH 903.5 25.7 341 97 95 91

Baroclinic 25.6 341 97 95 92

Barotropic 3.3 18 57 43 39

P54

SSH 903.5 18.5 205 96 91 81

Baroclinic 18.1 228 97 92 82

Barotropic 4.6 35 80 60 46

P55

SSH 903.5 23.8 341 97 94 89

Baroclinic 23.4 341 97 94 89

Barotropic 4.5 26 70 50 38

P56

SSH 903.5 26.3 341 98 96 92

Baroclinic 26.8 341 98 96 92

Barotropic 4.0 19 58 38 31

P57

SSH 903.5 26.7 341 98 96 92

Baroclinic 27.4 341 98 96 93

Barotropic 3.6 24 67 52 40

SSH 903.5 19.2 171 95 90 78

P58 Baroclinic 19.4 186 96 93 81

Barotropic 4.5 35 81 60 39

SSH 903.5 25.4 341 98 96 89

P59 Baroclinic 25.3 341 98 97 90

Barotropic 4.5 31 76 53 39

SSH 903.5 28.3 341 99 98 93

P60 Baroclinic 28.6 341 99 98 95

Barotropic 4.5 32 77 54 39

SSH 903.5 28.0 341 99 98 95

P61 Baroclinic 29.0 341 99 98 97

Barotropic 4.7 46 85 69 46

SSH 903.5 19.3 158 96 91 73

P62 Baroclinic 19.3 171 97 94 76

Barotropic 5.2 47 89 70 41
87

Table 2.7-3. (continued)

PIES

ID# Signal

Length Std T0.5 Unaliased Variance (%)

(days) (cm) (days) 10-day 17-day 35-day

P63

SSH 903.5 26.9 293 99 96 88

Baroclinic 26.5 341 99 97 89

Barotropic 5.4 46 89 67 44

P64

SSH 903.5 30.3 341 99 97 91

Baroclinic 30.0 341 99 98 93

Barotropic 5.8 51 90 71 49

P65

SSH 903.5 29.3 341 99 98 95

Baroclinic 30.1 341 100 99 97

Barotropic 5.8 62 92 80 53

P66

SSH 903.5 17.9 137 96 90 68

Baroclinic 17.8 137 97 93 70

Barotropic 4.7 57 90 78 52

P67

SSH 903.5 25.7 293 99 96 85

Baroclinic 25.4 341 99 97 87

Barotropic 5.9 59 93 82 54

P68

SSH 903.5 28.9 341 99 97 90

Baroclinic 28.8 341 99 98 91

Barotropic 6.2 66 93 83 57

P69

SSH 903.5 28.8 341 99 97 92

Baroclinic 29.3 341 99 98 93

Barotropic 5.8 68 93 87 57

SSH 903.5 16.0 89 96 90 67

P70 Baroclinic 16.0 89 97 92 68

Barotropic 3.0 46 80 69 50

SSH 903.5 22.9 256 98 94 80

P71 Baroclinic 23.2 293 98 96 82

Barotropic 4.3 55 89 80 53

SSH 903.5 25.4 341 99 95 83

P72 Baroclinic 25.9 341 99 96 85

Barotropic 4.6 57 90 81 53

SSH 903.5 27.0 341 99 94 81

P73 Baroclinic 26.9 341 99 95 84

Barotropic 5.5 66 93 86 50

SSH 903.5 19.1 108 97 92 74

P74 Baroclinic 19.1 120 98 93 75

Barotropic 2.3 29 69 57 42

SSH 903.5 22.0 114 97 92 70

P75 Baroclinic 21.8 146 98 93 71

Barotropic 3.2 45 81 68 42
88

aliasing of the barotropic signal by the 17-day and 35-day sampling in the northwestern half of 

the Loop Current array is comparable to barotropic signal aliasing seen in the other Gulf study 

programs. The significantly reduced aliasing exhibited by the 10-day sampling of the 

barotropicsignal suggests that the signals with periods less than the 20 days in the Loop Current 

region do not contribute as much to the total barotropic variability as they do in the other study 

regions. One gulf-wide source of aliased barotropic signal is the 16-day common mode that has 

been observed by both the Exploratory and Loop Current PIES arrays.

The unaliased variance of the baroclinic and total SSH signal is much higher than the barotropiconly case because of the longer-period baroclinic signals associated with the Loop Current and 

the dominance of the extremely energetic Loop Current baroclinic signal on the total SSH. Still, 

there are large differences between the 10-day and 35-day patterns, while the 10-day and 17-day 

patterns are more similar. For a 10-day sampling period of the baroclinic signal in the Loop 

Current array, the unaliased-variance-mean value over the array is 98% and ranges from a 

minimum of 96% at PIES 58 to a maximum of nearly 100% at PIES 65. The 35-day sampling 

mean value is only 86% and ranges from a minimum of 68% at PIES 70 to a maximum of 97% 

at PIES 61. The total combined baroclinic and barotropic SSH signal shows similar patterns. The 

SSH 10-day period unaliased-variance-mean value over the array is 98% and ranges from a 

minimum of 95% at PIES 58 to a maximum of 99% at PIES 63, 64 and 65. The 35-day sampling 

mean value decreased to 85% and ranged from a minimum of 67% at PIES 70 to a maximum of 

95% at PIES 61 and 65. These overall averages and ranges are comparable to those found in our 

analyses of the Eastern, NW Gulf and Exploratory PIES, further confirming the similarity of the 

baroclinic and total SSH signals in the GOM deepwater even over separate and distinct 

observational time periods.

In summary, 95% to 98%, 84% to 97%, 84% to 98%, and 87% to 99% of the sub-inertial period 

SSH variability in the Loop Current, Eastern Gulf, Northwestern Gulf, and Exploratory Study 

regions, respectively, are unaliased by the TOP/POS 10-day repeat-period sampling. This is 

comparable to the 86% to 95% estimated from the Newfoundland Basin array by Hendry et al. 

(2002). The results for the 17-day and 35-day repeat sampling show, however, that there can be 

aliasing of GOM SSH signals in satellite altimetry, even with the dominance of the longer-period 

baroclinic signals associated with the LC and LC eddies in the GOM deepwater. The degree to 

which this affects the space/time-interpolated maps of altimetric SSH needs to be investigated in 

more detail. Also, the presence of the ubiquitous common mode needs to be considered when 

processing sea-surface-height data. In most cases, this signal will be removed by standard 

altimetric processing techniques, and the aliasing will be mitigated. However, the signal may be 

retained as more sophisticated processing and higher-frequency corrections are applied to the 

data.

2.7.2 Signal-to-Noise

A useful metric for assessing the accuracy of altimeter-derived estimates of SSH is the ratio of 

the unaliased variance to the aliased variance of the SSH signal, which is an estimate of the 

signal-to-noise ratio (SNR) of a perfect on-orbit measurement system. The amount of aliasing is 

also a function of the repeat-sampling period of the satellite altimeter as can be seen in Figure 

2.7-4. Note that we do not consider the barotropic and baroclinic components separately because 

they cannot be distinguished from on-orbit measurements alone. Also, the “noise” in the 
89

unaliased-to-aliased SNR is colored noise associated with under-sampled geophysical signals 

that are very difficult to remove without excessive smoothing or filtering of the along-track data 

before interpolation. This is the primary reason that the requirement of uniform errors and 

wavelength/frequency resolution satisfying the Nyquist criteria, as proposed by Greenslade et al. 

(1997) for gridded altimeter products, is unrealistic in practice. 

Table 2.7-4 shows a summary of the SNR statistics estimated from the Loop Current, Eastern 

Gulf, NW Gulf, and Exploratory PIES data. In all cases, the Loop Current SNR is equal to or 

higher than the Eastern, NW Gulf, and Exploratory Program statistics for all three sampling 

scenarios. Nevertheless, the SNR in all of the study regions was very good for 10-day and 17-day 

altimetric sampling. The 35-day sampling is more problematic. The 35-day sampling spatial map 

(lower panel of Figure 2.7-4) shows SNR ratios in the low single digits on the outer edge of the 

Loop Current study array, which would make it difficult to distinguish between signal and 

aliased signal at that sampling frequency from a single-point measurement. Similar low SNR was 

found with 35-day repeat sampling of the PIES measurements from the other program arrays.

Table 2.7-4. Signal-to-Noise Ratio (SNR) Statistics for 10-day, 17-day, and 35-day 

Exact-Repeat Sampling of the PIES Barotropic, Baroclinic and 

Combined SSH Signals

Stations Mean SNR Minimum SNR Maximum SNR

 Repeat: 10-day 17-day 35-day 10-day 17-day 35-day 10-day 17-day 35-day

Loop Current Program

all stations 58 22 8 19 9 2 136 49 20

Eastern Gulf Program

all stations 16 8 3 5 4 2 32 13 5

NW Gulf Program

all stations 22 11 4 5 4 1 49 19 7

Exploratory Program

all stations 28 16 5 7 5 1 99 49 13

above escarpment 20 13 4 7 5 1 32 24 9

below escarpment 33 19 5 12 6 1 99 49 13

2.7.3 Sea-Surface-Height Time Scales 

Following the methodology of Hendry et al. (2002), the period corresponding to the frequency at 

which the cumulative power spectrum reaches 50% of the total variance – the half-power period, 

T0.5 – was determined from the spectral analysis of each of the PIES SSH anomaly time series. 

T0.5 is a more robust measure of time scale than the temporal autocorrelation zero crossing, T0, 

and is the preferred scale to be used to define the effective degrees of freedom of a time series 

(Fofonoff and Hendry 1985). This robustness is due, in large part, to the global and integral 

nature of the T0.5 metric, which is less sensitive to competing time scales within the time series. 

In contrast, the calculation of T0 is a less robust measure because the first zero crossing of the 

temporal autocorrelation function is quite sensitive to the presence of multiple time scales and/or 

secular trends in the time series. 
 SNR: 10-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 58

88°W 86°W

25°N

26°N

27°N

Signal-to-Noise Ratio

20

40

60

80

100

120

140

 SNR: 17-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 22

88°W 86°W

25°N

26°N

27°N

10

Signal-to-Noise Ratio

20

30

40

50

 SNR: 35-day Sampling

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 8

88°W 86°W

25°N

26°N

27°N

Signal-to-Noise Ratio

5

10

15

20

 90

Figure 2.7-4. Maps of PIES SSH signal-to-noise ratio (SNR) for 10-day, 17-day, and 35-day sampling. 

SNR is estimated from the ratio of unaliased to aliased variance. 
91

The half-power periods were computed from the 30-month Loop Current PIES barotropic, 

baroclinic, and SSH anomaly time series. Similar values were also computed from the 13-month 

Eastern Gulf, 9-month Northwestern Gulf, and 12-month Exploratory programs. Spatial maps of 

T0.5 in the Loop Current study region for each of the three signals are shown in Figure 2.7-5. No 

effort was made to detrend the time series before calculating the spectra because of the relatively 

short duration of the earlier records. This allows estimation of the longer time scales of 

variability associated with the LC and LC eddies that occur in most of the records. Mean T0.5 

values are listed in Table 2.7-5 for each program, showing the average time scales for each of the 

signals at all PIES stations. The Exploratory Program averages for stations above and below the 

Sigsbee Escarpment are also shown. 

Table 2.7-5. Half-Power Period of PIES Barotropic, Baroclinic, and Total SSH 

Signals

Stations

Barotropic Signal

Half-Power Period

(days)

Baroclinic Signal

Half-Power Period

(days)

Total SSH Signal

Half-Power Period

(days)

mean max min mean max min mean max min

Loop Current Program

all stations 43 68 18 287 341 89 278 341 89

Eastern Gulf Program

all stations 20 25 16 121 158 102 121 158 102

NW Gulf Program

all stations 21 47 14 155 293 66 148 293 66

Exploratory Program

all stations 19 34 12 230 34 12 232 512 60

above escarpment 16 18 14 188 18 14 195 341 64

below escarpment 21 34 12 262 34 12 260 512 60

The mean half-power periods of the barotropic signals are quite similar in all the regions and are 

dominated by the ubiquitous Gulf-wide common mode. The spatial distributions, however, are 

notably different between the east/central and western Gulf. In the Loop Current study region, 

the longer period barotropic signals are located in the southeastern half of the study array in the 

deepest water, as was the case in the Eastern Gulf study array. This pattern in the eastern Gulf is 

similar to the central Gulf where the longer-period signals are in the south-central part of the 

Exploratory array in the deepwater below the Sigsbee Escarpment. In contrast to the eastern and 

central Gulf results, the longer period barotropic signals in the NW Gulf are on the upper slope.

The time scales of the baroclinic and combined-barotropic-and-baroclinic SSH anomaly signals 

are very similar because of the small contribution by the barotropic mode to the total signal. The 

long half-power periods associated with these signals show the dominance of the low frequency 

LC and LC eddy variability observed in all four regions during the observational periods. In the 

Loop Current study, the 300-day and longer periods cover nearly the entire array, reflecting the 

low-frequency variability of the Loop Current that this study array was designed to monitor. The

shortest half-power periods, less than 180 days, are found on the northeastern periphery of the
 Barotropic Signal

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 43

88°W 86°W

25°N

26°N

27°N

Cumulative Half Power

Period (days)

20

30

40

50

60

 Baroclinic Signal

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 287

88°W 86°W

25°N

26°N

27°N

Cumulative Half Power

Period (days)

100

200

300

 SSH Signal

2000

 P51

 P52

 P53

 P54

 P55

 P56

 P57

 P58

 P59

 P60

 P61

 P62

 P63

 P64

 P65

 P66

 P67

 P68

 P69

 P70

 P71

 P72

 P73

 P74

 P75

 mean = 278

88°W 86°W

25°N

26°N

27°N

Cumulative Half Power

Period (days)

100

200

300

 92

Figure 2.7-5. Spatial maps of the half-power period, T0.5, computed from the PIES barotropic, baroclinic, and combined SSH anomaly time series. Mean values over all stations are also 

shown. 
93

array. The higher-frequency signals, contributing these shorter periods, likely arise from the 

high-frequency SSH variability generated by Loop Current frontal meanders or cyclonic eddies 

along the northern and eastern margin of the array. 

2.7.4 Comparison of CCAR Mesoscale, AVISO, and PIES Mapped Absolute SSH 

The CCAR Mesoscale SSH-gridded-altimeter data product that was distributed and used for data 

synthesis activities in this report was evaluated by comparison with the maps of absolute SSH 

derived from the PIES measurements (see section 2.5.6). Comparisons were also made with the 

weekly AVISO maps coincident with the PIES records. Maps of the CCAR Mesoscale versus 

PIES SSH, and the AVISO versus PIES SSH temporal-correlation-coefficient maps are shown in 

Figure 2.7-6. The temporal correlation of the PIES-mapped SSH with the CCAR Mesoscale 

SSH is higher over the entire array than it is with the AVISO SSH; nevertheless, the correlation 

of the PIES-mapped SSH with both altimeter SSH data products is excellent. Differences in the 

correlation maps reflect the filtering and smoothing applied during the data processing and the 

spatial and temporal scales retained by each of the objective-mapping schemes. One difference in 

the data products is the seasonal steric signal, which is only retained by the processing employed 

for the AVISO product. For consistency, the seasonal steric signal was estimated and removed 

from each AVISO SSH map by subtracting the average of the SSH values from that map over all 

points in the Gulf deeper than 200 m, and then the correlation map was recalculated as shown in 

Figure 2.7-7. This improves the correlation of the AVISO product with the PIES data to levels 

nearly as high as those calculated with the CCAR Mesoscale product. The impact of the filtering 

and smoothing of the CCAR Mesoscale SSH processing can be seen by comparing the SSH 

standard deviation computed from each of the data products over the program time period 

(Figure 2.7-8). The SSH standard deviation is comparable between the PIES and AVISOmapped SSH, but attenuated in the CCAR Mesoscale-mapped SSH product primarily because of 

the along-track filtering of the SSHA data before objective mapping. 

The comparison of the CCAR Mesoscale and AVISO-mapped SSH to the PIES-mapped SSH 

shown in Figures 2.7-6, 2.7-7 and 2.7-8 are independent of the mean SSH height added to the

altimeter-derived maps of SSHA to produce an estimate of the total SSH. The 30-month record 

of PIES SSH from the Loop Current study, however, provides the first opportunity to directly 

compare an accurate mean SSH, which spans a large area in the eastern Gulf dominated by the 

presence of the Loop Current, with the mean SSH fields used in the altimeter data products. To 

do this initial comparison, the different reference levels used in each of the mapped SSH datasets 

were accounted for. Then, each of the SSH fields was referenced so that the 17-cm contour 

would be consistent between the three datasets. This was done using the regressions shown in 

Figure 2.7-9. First, the 17-cm tracking contour in the PIES data set was estimated from the 

regression of the PIES daily-mean SSH values on to the CCAR daily-mean SSH values in the 

study region (upper panel of Figure 2.7-9). From this regression, the CCAR 17-cm tracking 

contour was estimated corresponding to the 259.6-cm PIES contour. Then, the 259.6-cm PIES 

contour, corresponding to the 12.1-cm AVISO SSH contour, was estimated using the regression 

of the PIES daily-mean SSH values on to the AVISO daily-mean SSH values in the study region 

using the AVISO weekly 1⁄4 -degree SSH data product (lower panel of Figure 2.7-9). For 

consistency, the seasonal steric signal was removed from each AVISO SSH map as described 
PIES/CCAR Mesoscale

PIES/AVISO

 94

Figure 2.7-6. Spatial map of the temporal correlation between the PIES mapped SSH time series and 

the CCAR Mesoscale SSH (upper panel) and AVISO SSH (lower panel) time series 

coincident with the LC study. 
PIES/AVISO no steric

PIES/AVISO

Figure 2.7-7. Spatial map of the temporal correlation between the PIES mapped SSH time series and 

the AVISO SSH time series with (upper panel) and without (lower panel) the seasonal 

steric signal removed. 

 95
 96

Figure 2.7-8. Rms SSHA (standard deviation about the mean) during the program time period of the 

CCAR Mesoscale (upper panel), AVISO (middle panel), and PIES mapped datasets.
−10 −5 0 5 10 15 20 25 30 35 40

230

240

250

260

270

280

290

CCAR daily means (in region) 

PIES daily means 

slope = 1.2172 cm/cm 

y−intercept = 238.9056 cm 

−10 −5 0 5 10 15 20 25 30 35 40

230

240

250

260

270

280

290

AVISO daily means (in region) 

PIES daily means 

slope = 0.91902 cm/cm 

y−intercept = 248.8417 cm 

 97

Figure 2.7-9. Regression of the daily means of the PIES mapped SSH on to the means of the CCAR 

Mesoscale (upper panel) and AVISO (lower panel) mapped SSH in the study region. Daily 

and weekly sampling were used to derive the CCAR and AVISO regressions, respectively. 
98

previously for the correlation comparisons before making this estimate. Offsets were calculated 

to make the corresponding Loop Current tracking contours in all mean surfaces equal to 17 cm.

This allows direct comparison of each of the altimetric SSH means to the PIES SSH mean during 

the study program, which are shown in the composite maps in Figure 2.7-10. Correspondence 

between the PIES mean SSH is better with the CCAR mean SSH than with the AVISO mean. 

There are significant differences in both the amplitude and spatial structure of the CCAR- and 

AVISO-mean SSH maps in the eastern Gulf, with the largest differences within the Loop Current 

near Cuba (Figure 2.7-11). Uncertainty in the mean SSH in the Gulf remains a significant 

challenge to remote sensing and modeling studies in the region. Fortunately, this is a deficiency 

that can be overcome in the Gulf by PIES SSH measurements of sufficient duration and density 

to directly estimate the mean.

2.8 NUMERICAL MODEL 

The Princeton Regional Ocean Forecast System (PROFS) for the Gulf of Mexico is used for this 

study. This model system is based on the Princeton Ocean Model (POM) and has been 

extensively tested for (i) process studies to understand the Loop Current and eddy-shedding 

dynamics (e.g., Oey et al. 2003a and Chang and Oey 2011); (ii) comparison against observations 

(e.g., Wang et al. 2003, Fan et al. 2004, Oey et al. 2004, Lin et al. 2007); and (iii) hindcasts and 

forecasts (e.g., Oey et al. 2005, Yin and Oey 2007). The present version of the model has 

Message Passing Interface (MPI) directives implemented into POM by Dr. Toni Jordi (Jordi and 

Wang 2012) and achieves good (i.e., linear) scalability. Most of the original PROFS (and POM) 

features are retained. There are 25 terrain-following sigma levels with (logarithmically) finer 

resolutions near the surface and bottom, but a fourth-order pressure gradient scheme (Berntsen 

and Oey 2010) is used to reduce pressure-gradient errors. An orthogonal curvilinear grid is used 

in the horizontal with Δx and Δy ~2-5 km in the Gulf of Mexico. Mellor and Yamada’s (1982) 

turbulence closure scheme is used as modified by Craig and Banner (1994) to include input of 

turbulence energy due to breaking waves near the surface. Also, a Grant and Madsen (1979) 

type bottom-drag scheme is used in the bottom-boundary layer to empirically account for 

increased bottom roughness due to surface gravity waves; this is particularly effective over 

shallow shelves and under strong wind conditions. Finally, Smagorinsky’s (1963) shear and griddependent horizontal viscosity is used with a nondimensional coefficient = 0.1, with the 

corresponding horizontal diffusivity made five times smaller. The sea-surface temperature (SST) 

is relaxed to AVHRR MCSST with an e-folding time constant of 1 day-1 (GCMD [unknown 

date]). However, tests (and previous experience – e.g., Yin and Oey 2007) indicate that the 

effects of SST boundary conditions on Loop Current dynamics are minor.

The model domain includes the northwest Atlantic Ocean west of 55°W and from 5°N to ~55°N. 

The World Ocean Atlas data (i.e., “climatology”) (NODC 2005) is used for boundary conditions 

along the eastern open boundary at 55°W. The topography was set up according to the 

NOAA/NGDC 2-minute Earth topography database (Et opo2) and edited on shelves using NOSdigitized maps. The model is used in both a free mode, forced by external boundary conditions 

and surface forcing, and a data-assimilative mode where sea-surface temperature (SST) and seasurface-height anomalies (SSHAs) are used to infer a three-dimensional analysis field on a daily 

basis. The analysis field was obtained for 19 years from 1993-2011, during which satellite seasurface-height anomaly from AVISO (AVISO+ [date unknown]) is assimilated into the model 

using a statistical surface-to-subsurface projection method (see Yin and Oey 2007 for details and
 99

Figure 2.7-10. CCAR Mesoscale (upper panels) and AVISO (lower panels) mean SSH maps over the 

program time period with the PIES mean SSH inset in the panels on the right. The 17-cm 

LC tracking contour is shown by the thick line. 
 100

Figure 2.7-11. Comparison of the CCAR Mesoscale and AVISO mean SSH maps over the program time 

period. The mean maps of the CCAR Mesoscale (upper panel), AVISO (middle panel), 

and the difference of CCAR minus AVISO (lower panel) are shown. The thick black line is 

the 17-cm LC tracking contour. 
101

references). The model is forced by six-hourly winds (1993-2009: 0.25° x 0.25° cross-calibrated 

multi-platform (CCMP), and 2009-2011: NCEP 0.5° x 0.5° Global Forecast System (GFS)), by 

M2, S2, K1 and O1 tides specified along the open boundary at 55°W, and by daily river 

discharge obtained from the U.S. Geological Survey at 51 locations along the U.S. coastline (34 

rivers in the Gulf and 17 rivers along the eastern coast). 

2.8.1 Model Skill Metrics for In-Situ Measurements

For the LC study, model simulations are compared with currents and temperatures from the nine 

full-depth moorings. Various metrics are used to measure model skill in reproducing in-situ

observations. The complex or vector correlation ‘‘CC’’ between two velocity time series um = 

(um, vm) for model and uo = (uo, vo) for observation, is defined as (Lin et al. 2007, following 

Kundu and Allen 1976):

CC = <wmwo*>/[<wmwm*>1/2. <wowo*>1/2] (2.8.1)

where wn = un + ivn, n = m, o, i = (-1)1/2, the asterisk indicates the complex conjugate, and <.> 

denotes time averaging. Thus CC (= Reiθ) measures how closely the model vector w1 follows 

the observation vector w2 in time. Small complex correlation angle θ (|θ| < 45o, say) and R = 

|CC| ≈ 1 generally indicate good model skill. 

Given model mi and observation oi time series, model skill is defined by Willmott (1981): 

Skill = 1 - <(mi – oi)

2

>/<(|mi - <m>| + |oi - <o>|)2> (2.8.2)

The Skills are computed separately for u and v, and then averaged (=Skilluv). Other metrics 

include computing the ratios of model-to-observed standard deviations (Rstd = stdm/stdo), speeds 

(Rspd = spdm/spdo), and the mean-velocity angles (αm-o = αm-αo).

2.9 METHODS

Prior sections have discussed methods used to process and, in some cases, statistically analyze 

various data types. This section collects together various time-series methodologies that are used 

in the following chapters. Some are small changes to standard methods of time-series analysis, 

such as EOFs, and others were developed for this study, such as calculating vertical velocities 

from mooring data.

2.9.1 Vertical Velocities

In highly energetic regions such as the LC, estimating vertical velocities from velocity and 

temperature observations has to take into account the variability of the depth of the instruments 

caused by mooring motion, which can produce depressions of several hundred meters from 

nominal depths. To accomplish this, the method separates horizontal from vertical 

displacements in the temperature conservation equation:

!!!

!" = 0 = !! !!, !!, !! − !! !! − ∆!, !! = !! − !"#, !! !!

!!!∆! (2.9.1)
102

where the temperature anomaly, TA, at depth z0 is the difference between the observed 

temperature, T and an area averaged mean temperature profile. Thus,

 TA = T (t, x,z) ! Tm (z) (2.9.2)

For the LC study, Tm is the mean of 45 CTD casts taken during the course of the program to 

calibrate the deployed PIES (Figure 2.9-1). The depth of the temperature observation, !!, is also 

a function of t, and is estimated for the instruments by linear interpolation using the pressure 

records. Most of the moorings had pressure recording instruments at nominal depths of 150, 

450, 750, 900, 1300, and 2000 m. 

The basis of the method is to calculate the location of the water particle at time t0 ! "t that is 

advected to location x0 in the horizontal plane z' = z ( 0 ) by the horizontal velocity field u t, x,z ( 0 ). 

The semi-Lagrangian estimation of the horizontal displacement interpolates velocities using 

Kriging (Press et al. 2007) - Section 3.7.4), where each major time step, ∆!, is split into a number 

of smaller increments. Four increments of six hours (the time step of the 40-HLP velocity 

records) were used for each major time step. The advantage of interpolation using Kriging is 

that an array of irregularly spaced observational nodes can be used in an optimal way. To 

estimate the vertical displacement required to satisfy Equation 2.9-1, the temperature anomaly at 

location x ',z ( 0 ) at time t0 ! "t is first estimated from interpolation by Kriging. The nominal 

depth, z0, also varies with time, and the estimated depth z0 t( 0 ! "t, x ')is also calculated by the 

Kriging method from the array of estimated pressure at the nominal depth. The next step is to 

find the depth, z' , where conservation is satisfied by a purely vertical displacement:

!! !! − !! !! !! − ∆!, !! = !! !!, !!, !! − !! !! − ∆!, !!, !! (2.9.3)

The displacements are found by bracketing and bisection, and making use of the monotonically 

decreasing character of !!, from the mean temperature profile, so that z' satisfies Equation 2.9-

3. The use of a mean high-vertical-resolution temperature profile increases the precision over a 

temperature profile from widely vertically-spaced recorders on a mooring. From z' , the vertical 

velocity, w, is obtained by:

 w = z'! z0 t( 0 ! "t, x')

"t (2.9.4)

By using temperature anomalies, and estimating the displacements required to satisfy Lagrangian 

temperature conservation in two separate steps, horizontal and then vertical, where the vertical 

takes into account the varying depths of the observations by interpolating onto a mean profile, a 

reasonably robust estimate of w (positive upwards) is generated at the locations of the tall 

moorings. For this study w was calculated for a nominal depth of 900 m, in the interface 

between upper and lower layers, where temperature and current records were largely complete 

over the observation interval. Estimates were calculated from the 40-HLP records, and then 

subsequently filtered with a 7-DLP Lanzcos kernel to remove high frequency noise.
Average of 45 CTD Casts taken during the LC Study

Figure 2.9-1. Average temperature, salinity and sigma-t profiles for CTD casts taken during the LC study. The RH panels show the standard 

deviations (light solid lines) and extrema (dashed lines) for the profiles. 

103 
104

Estimating errors in w is difficult because it depends on the accuracy of the semi-Lagrangian 

interpolations, which in turn depend on the spacing of the measurements. Also the mean vertical 

temperature gradients may not exactly represent the instantaneous temperature gradients. 

However, the results for 900 m have a reasonable correspondence (not shown) to w estimated 

from the !"/!" where η is the depth of the 6 °C isotherm, which has a mean depth ~ 900 m. A 

very rough estimate of the error is ~ 30% of the magnitude of w.

2.9.2 Relative Vorticity

Because the observational moorings were laid out in an array, higher dynamical quantities can be 

calculated by fitting planes through groups of observations. Minimums of three locations (not 

co-linear) are required to estimate gradients of velocity using:

 u(x, y,t) = u0 + x

!u

!x

+ y

!u

!y

+ (Higher"Order"Terms) (2.9.5)

with a similar equation for the v-component. When there are more than three locations, leastsquare fitting is used where the velocity components are weighted by their standard deviations. 

This is similar to the method given by (Chereskin et al. 2000). After the gradients are obtained, 

relative vorticity is given by:

 ! = !v

!x

" !u

!y

 (2.9.6)

The relative vorticity locations for the array, divided into triangles and rectangles, are given in 

Figure 2.9-2. Because the lower-layer velocities have a larger array, the 100-mab relative 

vorticity locations (yellow dots) differ slightly from higher in the water column (grey dots) 

where only the nine tall moorings were available. Relative vorticity locations have IDs that 

reference the nearest PIES location number.

The CICESE moorings were deployed in transects, and so velocity gradients can only be 

estimated in the along-transect direction. However, for the majority of the time, transects N and 

E are dominated by LC flows along the Campeche slope, and ζ can be approximated by !"/

!", where v is the along-slope velocity component. On transect E, the 2009-2010 deployment 

included mooring EN which formed a triangle so that both gradient terms can be evaluated. A 

comparison of ζ using the triangle, and the two transect moorings is given in Figure 2.9-3, and it 

can be seen that the two calculations give very similar results as regards the fluctuations with 

some underestimation of peak amplitudes at the shallower depth. For the most part, relative 

vorticity is plotted normalized by the local Coriolis parameter.

2.9.3 Potential Vorticity

The Ertel potential vorticity (PV), ( f +! ) hwhere h is the layer depth and the water column is 

divided up into isopycnal layers, is a conserved quantity following streamlines. In Eulerian 

terms, a normalized potential-vorticity anomaly (PVA) is defined as:
100 m

100 m

500 m

1000 m

3000 m

3500 m

2000 m

1000 m

Loop Current Moorings (CICESE/SAIC)

April 2009

- November 2011

June 2009

- June 2011

PIES

SAIC Tall Moorings

SAIC Short Moorings

CICESE Campeche

Moorings

CICESE Yucatan

Moorings

ζ - points

Upper

Lower

 105

Figure 2.9-2. Mapping array and CICESE transects showing the locations of relative vorticity points 

(numbered grey and yellow dots) and their surrounding triangles and rectangles. 
Fractional

f

Fractional

f

Figure 2.9-3. Comparison of relative vorticity at two depths for location 82 using the triangle E2-E3-EN (black line) and the E2-E3 pair (red line) 

to estimate velocity gradients.

106 
107

 PVA = H

f

f +!

h ! f

H

"

#

$ %

&

' = H

h

!

f

"

#

$ %

&

' +

H

h !1 "

#

$ %

&

' (2.9.7)

where H is the mean depth of the layer. The first term on the right-hand-side (RHS) is 

essentially the layer-average relative vorticity and the second term is the layer stretching term, 

sometimes referred to as the Sverdrup PV. For the LC moorings, the depth of the 6 °C isotherm 

is used to divide upper and lower layers, and the mean relative vorticity between the surface and 

6 °C, and 6 °C and the bottom is estimated by averaging the appropriate ! (z,t) f at available 

discrete depth levels (see above).

2.9.4 Streamlines and Velocity Potentials

Analysis often requires that observations be mapped onto a regular grid. For scalar variables, 

standard optimal or statistical interpolation is used with Gaussian autocorrelation functions. For 

the most part, this study uses the method of successive corrections for interpolation as given by 

Pedder (1993), with the length scale given by the average separation of the observations. 

However, for velocity vector data, it is useful to decompose currents into non-divergent 

geostrophic (streamfunction) and divergent (velocity potential) components:

 u = ! 1

f

"!

"y

+

""

"x

;v = 1

f

"!

"x

+

""

"y (2.9.8)

where φ is the geopotential (dynamic height) and also the streamfunction, and ! is the velocity 

potential, which gives the divergent-irrotational component that can be equated to ageostrophic 

flows. The streamfunction and velocity potential can be optimally determined by the universal 

co-Kriging (UCK) method of Pedder (1989), where ! and ! are assumed to be uncorrelated, 

and Gaussian functions are used to model the cross-covariance matrices. Standard least-square 

procedures are used to find the statistically-optimal solutions. Parameters of the method are the 

horizontal length scale for the Gaussian functions, determined by the average spacing of the data; 

fractional-geostrophic variance = 0.9; and thus, fractional-divergence variance = 0.1. The results 

are not particularly sensitive to these parameters. Wang et al. (2003) used the UCK method to 

produce daily maps of rotational and divergent velocity components from current-meter 

observations in the DeSoto canyon (Hamilton and Lee 2005), which were jointly analyzed with 

satellite altimetry and numerical model output.

Figure 2.9-4 shows the results of using the UCK method where the data are two-day averaged 

40-HLP currents at 160 m. The geostrophic velocities align closely with the observations and 

clearly show the closed anticyclonic circulation during the formation of Hadal. The velocitypotential vectors indicate a divergence towards the northeast, and a convergence towards the 

southwest sides of the array, which roughly correspond to the upwelling and downwelling 

regions of vertical velocities at 900 m, respectively. This can be interpreted as illustrating the 

ageostrophic connection between upper and lower layers.
3500 m

2500 m 3000 m

2000 m

1000 m

200 m

200 m

Vertical Velocity (m/d)

25 cm/s

75 cm/s

 108

Figure 2.9-4. Geostrophic velocites from mapped geopotential (gray arrows), and observed 2-day 

averaged 40-HLP currents at 160 m (red arrows); both using the red scale arrow. Blue 

vectors are from the mapped velocity potential (note change in scale). Contours are the 

2-day averaged vertical velocities at 900 m, and the solid purple line is the 17-cm SSH 

contour from satellite altimeter data showing the location of the LC front.
109

2.9.5 Wavelet Analysis

Wavelet analysis decomposes a time series into time and frequency space to determine the 

dominant modes of variability, and how those modes vary in time. This is particularly useful for 

event-dominated regimes such as LC variability, where oscillations can be seen in a clear way. 

For analysis purposes, the continuous wavelet, which is a function localized in time and space 

that scales with time, is more useful than the discrete wavelet. Following Torrence and Compo 

(1998), the Morlet-6 function is used for the transform, where the wavelet time scale is almost 

identical to the Fourier period. The wavelet transform is used to show the variability of the 

power of the input series as a function of time and the Fourier period. Edge effects can be 

significant at longer scales, and it is usual to define a “cone of influence” where such errors are 

negligible. The significance of the peaks can be estimated by determining a background 

spectrum and a significance level. Torrence and Compo (1998) use an autoregressive AR(1) 

process where the lag-1 autocorrelation, α, defines the background red spectrum and the 

significance level, and is determined from the input series (Allen and Smith 1996).

The common power, as a function of time and the Fourier period, between two time series is 

given by the cross-wavelet transform, which is discussed by Torrence and Compo (1998), and 

Grinsted et al. (2004). Local relative phase, represented as an angle between the two series in 

time and frequency space, can be estimated where common power is significant (Grinsted et al. 

2004). There are a number of examples of the continuous-wavelet transform (CWT) and crosswavelet transform (XWT) in the following analysis chapters.

2.9.6 Complex Demodulation

An earlier relative of the CWT is complex demodulation of a scalar time series. It is used when 

the object of the analysis is to find an estimate of the amplitude and phase of a signal with a welldefined period that is imbedded and prominent in the time series. Examples are semi-diurnal and 

diurnal tidal frequencies, and for this study, the inertial frequency f, where f is the Coriolis

parameter. This is the dominant high frequency signal observed in deepwater currents. A time 

series of inertial amplitudes, A, and phases,θ, are obtained from:

! ! !!" ! = !

!

! ! − !!(!) !!!

!!! !!"#!" (2.9.9)

where T is the inertial period (=2π/f), and um is the running mean, i.e., um (! ) = 1

2T

u(t)dt ! !T

! +T

" of 

the variable u. In practice, a 4-day low-pass (4DLP) filter to ensure adequate smoothing of the 

results replaces the integral in 2.9.9. The inertial period for the analysis is chosen to be an 

integral number of time steps to avoid filter edge effects. For highly time variable signals such 

as near inertial internal waves, the resulting amplitudes show when signals are large and how 

they change in time and space (see Chapter 6).

2.9.7 Notes on EOF Analysis

EOF analysis is a standard way of extracting coherent structures from a large number of 

simultaneous time series (Preisendorfer and Mobley 1988). EOF analysis is applied in this study 
110

in both the time and frequency domains. For velocity data, complex EOFs (CEOFs) are used 

where u(x,t) = u + iv , and the eigenmodes are given by:

u(x,t) = An (t) • en (x) n

! (2.9.10)

where all quantities are complex and the mode amplitude, An, is normalized to unit variance (i.e., 

< An

*

An >=1, where < > denotes time average). The record means of U are removed before the 

analysis. The mode amplitudes and eigenvectors, en, are orthogonal and ordered by variance 

explained, but their orientation is relative to an arbitrary reference (Kundu and Allen 1976). The 

usual practice (Merrifield and Winant 1989) is to rotate the spatial eigenvector into the frame of 

the semi-major principal axis of the corresponding amplitude time series.

 

Because EOF analysis maximizes the variance explained by the modes, data with large variations 

in variances by location can produce low numbered modes that are dominated by the high 

variance records, and so de-emphasize significant patterns in the data. For single mooring 

velocity records, the depth range that each velocity record represents is used to weight the record 

variances. Thus, uk t,z ( k )is weighted by 0.5*(zk+1 ! zk!1)where zk is the depth of the record for 

construction of the covariance matrix. The eigenvectors carry the units of the data, and are deweighted before plotting. The de-weighted eigenvectors are also used to construct derived 

quantities such as depth-integrated eddy kinetic energy (Hamilton 2009): 

 EKEH = 1

2 < u*

udz z1

z2

! > (2.9.11) 

Frequency-domain EOFs are similar to time-domain EOFs where record spectra are used to 

construct the cross-spectral matrix for given frequency bands. This allows the analysis of 

propagating signals as phase differences between locations can be found from the eigenvectors.
111

CHAPTER 3: BASIC DESCRIPTIONS AND STATISTICS 

3.1 INTRODUCTION

The purpose of this chapter is to give basic descriptions of the mesoscale variability of the LC, 

including the major detachments and eventual separations of Ekman, Franklin and Hadal, during 

the measurement program. This is followed by a detailed look at the statistics of the

observations of currents, temperature and derived parameters from the PIES mapping array for 

the whole water column, and separately for the upper and lower layers. These discussions will 

serve as the background for a more detailed dynamical analysis in Chapter 4.

An overview of various observations and theories of LC eddy detachment processes is given in 

Section 1.4. To set the scene, Figures 3.1-1a-b shows the 40-HLP time series of velocities and 

temperatures from two moorings: A2 and C2 on the northwest and northeast sides, respectively, 

of the mean LC. The isotherm depths in the upper water column have been corrected for 

drawdown using available pressure records on the mooring, and the intervals for which the 

eddies were part of the LC extending into the Gulf, derived from the SSH maps using the 17-cm 

contour, are indicated by the solid green bar. The large-scale sequences of warm water 

encroaching on the array as the LC front extends to the north are clearly seen at both moorings. 

As the LC front moves across these moorings, velocities increase and decrease in the upper 

layer, generally northward at A2 and southward at C2, corresponding to the clockwise 

anticyclonic flow of this current. The upper-layer fluctuations are markedly different between 

moorings and LC eddies. For Ekman (May 2009) and Franklin (January-March 2010), the initial 

descent of the isotherms at A2 show very rapid, ~10-day fluctuations that correspond to similar 

periodicities in the velocity vectors. The latter do not reverse but have a “haystack” appearance 

that is characteristic of propagating cyclonic frontal eddies (Bane et al. 1981) which, in this 

context, are usually called LC-frontal eddies (LCFEs). For Hadal, these type fluctuations are 

hardly present or have longer periodicities and are short lived. At C2, the rapid fluctuations, 

during the same phase of LC growth, are also only weakly present, but just prior to the first 

detachments of Franklin (May-June 2010) and Hadal, and midway through Hadal’s growth 

(March-May 2011), large cold events intrude on the mooring. It will be shown later that these 

correspond to large-scale meanders (~ 300 km wavelengths) on the east side of an extended LC. 

Crests and troughs of a meander are defined as displacements of the front, defined by the17-cm 

SSH contour, out from and towards the center of the eddy or LC, respectively. The cold events 

correspond to the cyclonic circulations in the troughs of the meanders that have periodicities of ~ 

40 days. The long-wavelength, large-amplitude meanders are not present on the west side of the 

LC. The ~ 40-day periodicities are also present in the isotherm depths during the extensive cool 

intervals after the separations of Ekman and Franklin at both moorings, and this frequency band 

is prominent in the statistical analysis below.

Strong vertical shear characterizes the upper layer with velocity magnitudes decreasing with 

depth. In the lower layer, velocities have weak shears showing only small or no increases in 

magnitude, depending on location, from 1300 m to 2000 m, and then remaining constant to the 

top of the bottom boundary layer. Though the deepest levels, 100 mab, are not shown in Figure 

3.1-1, the 40-HLP records are essentially identical to the 2000-m level. Bottom intensification is
A2 Mooring

16

18

20

22

24

26

14

12

10

8

o

C

Ekman Franklin Hadal Icarus

Figure 3.1-1a. 40-HLP temperature and velocity records from the A2 mooring at the indicated depths. Up is north direction.

112 
C2 Mooring

16

18

20

22

24

26

14

12

10

8

o

C

Ekman Franklin Hadal Icarus

Figure 3.1-1b. 40-HLP temperature and velocity records from the C2 mooring at the indicated depths. Up is north direction.

113 
114

a common characteristic of currents deeper than ~1000 m throughout most of the Gulf (Hamilton 

2009) and has been associated with topographic Rossby waves (TRWs). However, for the LC 

array the lower-layer currents are much more depth independent than for observations made 

further west. Above 900 m, flows are visually coherent, and similarly below 1300 m. The 900-

m level at both moorings shows some characteristics of both layers, with a tendency to look like 

the upper layer when the isotherms deepen, and the lower layer when the isotherms shoal. In 

general, variability in the upper layer is not the same as in the lower layer, though a number of 

events at both moorings seem to be present in both layers, e.g., the strong southward event at 

2000 m ~ 24 June 2010 at A2 could be said to be present through the whole water column 

(Figure 3.1-1a). Lower layer fluctuation amplitudes (and thus eddy kinetic energy – EKE) also 

vary in time with large increases during the detachments and separations of Ekman and Franklin, 

and prior to the separation of Hadal. A mechanism for energy transfer from upper to lower layer 

is given in Chapter 4.

The locations of the CICESE N transect and the U.S. moorings A4, B3 and C1 (Figure 1.2-1) 

allow the definition of a SW to NE section across the LC from the shelf break on the Campeche 

bank to the deep water adjacent to the west Florida escarpment. The section is approximately 

normal to the mean direction at the N transect of the LC front over the Campeche slope, and 

therefore, the coordinate axes for the velocities have been rotated so that the v-component is 

directed 330 °T. The upper- and lower-layer currents for the section are given in Figures 3.1-2ab, which also includes the depths of the 6°C isotherm and the location of the LC front relative to 

the N2 and C1 locations, where the front is defined by the 17-cm SSH contour from the daily 

altimeter maps discussed in Chapter 2.

The LC front over the Campeche slope has relatively little variability in location (the gaps in the 

time series are caused when a detached eddy does not intersect the N2-C1 section). This is 

consistent with the strongest currents being in the vicinity of N2 and N3, and N3 and N4 

isotherm depths having lower variances (Figure 3.1-2a). The N2 mooring is generally on the 

cyclonic side of the front, and during the growth phase of Franklin, and to a lesser extent Hadal, 

the rapid fluctuations characteristic of LCFEs occasionally reverse prevailing LC northwesterly 

flows. These short period LCFE fluctuations are not resolved in the SSH maps. On the 

northeast side of the section, the LC front location has large displacements, and this is reflected 

in the large amplitude long-period fluctuation in the depths of the isotherms at C1 and B3. The 

southeastward flows at C1 and B3 are generally weaker than the equivalent flows at N2 and N3 

even when the fronts are at similar distances from the moorings (e.g., February through April 

2010 in Franklin). Similarly short period fluctuations are much weaker when present at C1 than 

at N2. 

Representative deep currents (> 1000 m) across the section (Figure 3.1-2b) all show only slight 

bottom intensification of the 2000-m versus 1300-m levels. Essentially flows below 1300 m are 

depth independent with amplitudes of the fluctuations having similar magnitudes across the 

section. All locations show a high degree of changes in intensity corresponding to detachment 

events (Ekman and Franklin) or large scale meanders as shown by the C1 isotherm depths 

(Hadal). At some locations (e.g., B3 and A4), the variability resembles decaying wave trains 

triggered by these major upper-layer events.
Ekman Franklin Hadal

100-m 40-HLP Currents on N2-C1 Transect

N2

N1

N3

N4

A4

B3

C1

Location of Front Relative to C1

Location of Front Relative to N2

Depth of 6°C Isotherm

km km cm/s cm/s

m

N3

N4

A4

B3 C1

N

N2

C1

Figure 3.1-2a. Surface-layer (~ 100 m) currents on the N2 to C1 transect where up is normal to the transect (NW direction). The top and bottom 

panels show the distance along the transect of the 17-cm SSH contour from the respective end points, and the center panel 

shows the depths of the 6 °C isotherm at mooring locations.

115 
Location of Front Relative to C1

Location of Front Relative to N2

km km cm/s

N2

C1

N4

A4

B3

C1

N

Ekman Franklin Hadal

Lower Layer 40-HLP Currents on N2-C1 Transect

Depth of 6°C Isotherm

m

N3

N4

A4

B3 C1

Figure 3.1-2b. Lower-layer currents at ~1300 and ~2000 m on the N2 to C1 transect where up is normal to the transect (NW direction). The top 

and bottom panels show the distance along the transect of the 17-cm SSH contour from the respective end points, and the next to 

top panel shows the depths of the 6 °C isotherm at mooring locations, repeated from the previous figure. 

116 
117

The overall view of the variability and the sequencing of the events given here are expanded in 

the following sections where the growth and detachments of Ekman, Franklin and Hadal are 

examined individually. Some common themes emerge, particularly the role of large-scale 

propagating meanders on the east side of an extended LC. However, each eddy separation has 

unique features, and therefore events and their statistics are described on an eddy-by-eddy basis 

in the following sections.

3.2 EDDY FORMATION AND SEPARATION

3.2.1 Ekman

The previous eddy to Ekman separated from the LC on 24 February 2009, two months prior to 

the start of the observational program. The separation point was quite far north (just southeast of 

A2), and the LC did not retreat southwards very far after the eddy departed into the western Gulf. 

The LC grew in area and northward extension in April 2009, and then remained constant in size, 

forming Ekman, until the first detachment on 6 July (see Figure 1.5-1). The detachment point 

was well to the south in the vicinity of E4 and E5. The detached Ekman remained roughly in the 

same place until a lobe of the eddy reconnected to the LC on 20 July. The reattached eddy also 

did not significantly change its area, but the LC bulged to the north, increasing the total area of 

the LC plus eddy. The second detachment took place on 9 August, with the detachment point 

further north than the previous time and the eddy starts to elongate in an east-west direction 

along the north side of the Campeche Bank, with the result that the center of Ekman moves 

slowly westward. Ekman briefly reattached its southeastern side to the LC on 23 August, but at 

this time a large meander trough was developing along the long northern side on the eddy that 

eventually cleaved the eddy in two along 87°W on 29 August, resulting in a larger western 

portion (Ekman) that moved into the western Gulf, and a small eastern anticyclone distinct from, 

but almost attached to, the LC that quickly dissipated.

This sequence is illustrated by the sequence of LC front locations, derived from SSH maps, 

given in Figure 3.2-1, where the interval between the fronts is 15 days. At the beginning of the 

sequence on 25 May the extended LC is regular, showing practically no frontal perturbations. 

The next three contours show a large scale meander (wavelength ~ 300 km) developing on the 

east side that increases in amplitude and also propagates southwards (compare successive 

locations of crests and troughs) such that by the 9 July contour a trough ~ 24°N separates Ekman 

from the LC. The trough then moves northward as the LC pushes into the Gulf even after 

reattachment so that the 9 August detachment takes place a degree further north than the initial 

one on 6 July. It might be expected that the 9 August detachment would be the cause of eddy 

separation. However, the elongation of the LC and eddy towards the west allows the 

development of large scale amplifying meanders on the north side of the extended northwestsoutheast directed front, and it is the developing trough along the ~ 87°W meridian that finally 

separates Ekman and allows the eddy to move into the western Gulf. The Ekman separation 

sequences are the most complex of the three major eddies in the data. Two points should be 

noted: 1) the large amplitude and long wavelength meanders develop on the east or north side of 

an extended LC-eddy system and they occur over, and seem to require, deep water (> 2500 m); 

2) the deepening meander troughs that cause detachment develop from the east or north side of 

the LC, and it is not necessary or even usual for a cyclone to be present on the Campeche slope
1000 m

5/25 6/9 6/24 7/9 7/24 8/8 8/23 9/7 9/22 10/7

Loop Current 17 cm SSH Boundary

3500 m

3000 m

2500 m

2000 m

200 m

200 m

Ekman

-

118

Figure 3.2-1. The growth and detachments of Ekman using the SSH 17-cm contour from altimeter 

maps at 15-day intervals.
119

for a detachment to occur, even though the 17-cm contour may suggest the presence of such a 

feature (e.g., 23 August in Figure 3.2-1). The latter will be discussed more thoroughly below, 

but the presence of an apparent Campeche slope cyclone, despite the presence of shallow water 

and a slope, has been previously advanced as a mechanism for detachment (Schmitz 2005).

Illustration of the upper- and lower-layer flows during Ekman’s final detachment and separation 

are given in Figure 3.2-2. On the 22 August map, the lower-layer geopotential shows highs and 

lows displaced downstream from the crests and trough of the north side meander with both 

upper- and lower-layer currents west of 87°W flowing southwards or southeastwards, and east of 

86.5°W flowing north or northeastward such that the lower-layer flows are reinforcing the 

developing trough along ~ 87°W and the crest at ~ 85.5°W. By 29 August, the lower-layer highs 

and lows have strengthened and become more aligned with the surface layer crest and trough. By 

1 September, the eastern lower-layer high is roughly aligned with the small, detached upperlayer anticyclone, and the low seems to be attached to the east side of the separating Ekman (it 

displaces westward between 29 August and 1 September) such that upper and lower layer flows 

are in a similar south or southwestward direction on the east side of Ekman. Only four days 

later, the small upper-layer eastern anticyclone has weakened, and will dissipate completely in 

another 10 to 15 days, but the lower-layer anticyclonic high remains strong and has translated 

westward with its companion low along with Ekman. On this 5 September map, Ekman is 

apparently contributing to the southward flow on the Campeche slope at N2 and N3, indicating 

that the eddy is interacting with the slope topography. The low SSH centered on the shelf break 

over the Campeche bank in late August is not consistent with the currents on the E and N 

transects. The surface-layer currents at E suggest entrainment from the southeastern Campeche 

shelf and slope into the LC, and a closed cyclonic flow is hard to discern. Except for E5, this is 

one of the few cases where measured upper layer currents are not roughly parallel to SSH 

contours. 

3.2.2 Franklin

After the departure of Ekman, the LC remained south of 24.5°N until the end of November 2009, 

after which there is steady growth to the north through February 2010 (Figure 1.5-1), with the 

northern boundary reaching 26.5°N, and the extended LC having no major frontal perturbations. 

Figure 3.2-3 shows the 17-cm SSH contour at 15-day intervals from March through the middle 

of July. Up to the first detachment on 8 June, Franklin behaved very similarly to Ekman, had a 

similar area and location, with the detachment point being well to the south around section E at ~ 

23°N. Again the eastern boundary develops large-amplitude, long-wavelength meanders that 

increase in amplitude and propagate southwards (compare the crest and trough locations for 

successive fronts beginning 15 April in Figure 3.2-3). The trough between the LC and Franklin 

develops through June as the irregular shaped eddy rotates, developing a strong cyclonic 

“Tortugas” eddy by early July that promotes the southward advection of a southern lobe of 

Franklin to reattach briefly (9 July) to the LC. This southern lobe of Franklin is reabsorbed into 

the LC, reducing the area of the eddy. Franklin moves to the northwest and advects the trough 

cyclone through to the Campeche bank, where it intensifies and promotes the eastern LC front to 

move northwards and reattach to the eddy on 30 July. This next interaction with the LC lasts 

until 18 August, and results in a reduction in the area and maximum SSH of the Franklin portion. 

A third detachment point is ~ 25°N, and even though an elliptical Franklin is clear of the 

northern Campeche bank slope, its small size (~ 150 km diameter) and possibly a blocking
2500 m

200 m

1000 m

200 m

+17

+40

+60

+0

-10

-20

Geopotential Height (cm)

60 cm/s 20 cm/s

2500 m

200 m

1000 m

200 m

60 cm/s 20 cm/s

+17

+40

+60

+0

-10

2500 m

200 m

1000 m

200 m

60 cm/s 20 cm/s

+17

+40

+60

+0

-10

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8/21 to 8/23/2009 8/28 to 8/30/2009

8/31 to 9/2/2009 9/4 to 9/6/2009

 120

Figure 3.2-2. Maps of the separation of Ekman for the indicated dates showing 2-day mean currents at 

~80-100 m (red) and 100 mab (blue), geopotential height for the bottom currents (gray 

shaded), and SSH contours (cm) from altimeter maps.
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3/ 1 3/16 3/31 4/15 4/30 5/15 5/30 6/14 6/29 7/14

Loop Current 17 cm SSH Boundary March - July 2010

7/14 7/29 8/13 8/28 9/12 9/27 10/12

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Loop Current 17 cm SSH Boundary July - October 2010

Figure 3.2-3. Loop Current 17-cm frontal boundaries from SSH altimeter maps for Franklin for the indicated dates.

121 
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anticyclone centered ~ 24°N, 90°W seem to prevent it moving westward. Franklin weakens 

during this 3rd detachment (18 August 18 to 11 September), moves southward along the 

Campeche slope and reattaches for another time. Again, the LC absorbs most of the eddy 

leaving a small area of anticyclonic vorticity, which rapidly dissipates after the final separation 

on 28 September. Though the first detachment of Franklin is very similar to that of Ekman, the 

subsequent reattachments and detachments were very different in that they seem more to be 

chance encounters of lobes of Franklin with a highly variable LC front, mediated by cyclonic 

flows both on the east and west sides of the separation zone. Each encounter reduced the size 

(shown in the July to August sequence of front locations in the right hand panel of Figure 3.2-3) 

and vitality of the eddy until it is speculated that it was small and weak enough not to be able to 

move westward by the β−effect and self-advection (Nof, 1981). 

The Deepwater Horizon (DWH) oil discharge occurred from April through July 2010 while the 

LC was extended to the north, Franklin was forming through the first detachment, and then 

remained in the eastern Gulf south of 27°N (Hamilton et al. 2011). During this interval, a large 

number of satellite-tracked GPS surface drifters were deployed both near the DWH spill site and 

in Franklin by USGS and USF (Liu et al. 2011a). Utilizing the drifters to estimate mean flows 

over the two-month May-June interval for selected 1°x 1° squares (Figure 3.2-4) shows that a 

closed anticyclonic circulation was present even though Franklin did not detach completely until 

8 June according to SSH contours. The drifter means agree well with means from the moorings 

for the same interval and the location of the mean 17-cm SSH frontal contour. The strong 

southwesterly flows in the southern part of Franklin are consistent with the elongating trough at 

~ 24°N as indicated by the tracks of two drifters that leave the eddy and move into the LC. The 

drifter tracks also show a large cyclonic feature, centered at ~27°N, 86°W (Walker et al. 2011)

that produced northward currents over the northern west-Florida slope and outer shelf. Some of 

the drifter tracks also indicate the intrusion of a meander crest over the west-Florida slope 

between 25 and 26°N. Means exceed standard deviations in the southern and western parts of 

Franklin, but are comparable in the north and east where, in some cases, the principal axis of the 

standard deviation ellipses is directed across the front (Figure 3.2-4), indicating that it is the 

movement of a relatively constant current with lateral front displacements that causes variability 

at a fixed location. 

The depth of the 6°C isotherm, calculated from both PIES temperature profiles and mooring 

temperature measurements, on the day (8 June) of the first detachment is given in Figure 3.2-5. 

It closely corresponds to the SSH contours as expected, but shows more clearly the large-scale 

meander troughs and crests along the northern and eastern sides that make the boundary of 

Franklin irregular. The 5-day upper-layer mean flows along transect E in the southwest are 

directed towards the Campeche slope and shelf, indicating that the development of the trough 

between the LC and Franklin should be having a strong influence on this shallow shelf.

The upper- and lower-layer flows just prior to the first detachment through the following 

reattachment are given in Figure 3.2-6. The lower-layer highs and lows are displaced 

downstream from their respective crests and troughs in the SSH, resulting in lower-layer flows 

that are at right angles or opposed to their respective upper-layer currents. The crests and 

troughs for 8 June, are more clearly seen in the 6 °C isotherm surface in Figure 3.2-5 than in 

SSH. Over the six days between the first and second plot, the lower layer high-low pattern is
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Mean Surface Currents by 1°x1° Squares from Drifters

80 m Currents

from Moorings Surface Drifters

 123

Figure 3.2-4. Mean surface velocities and standard deviation ellipses from drifter tracks (gray lines) for 

May and June 2010. The 1°x 1° squares are centered on the nearest one or half latitude 

or longitude degree. The calculated positions (round dots) are the average locations of 

the drifters passing through each square. The 80-m mean velocities and ellipses from the 

moorings (square dots) are given for the same interval. The mean location of the 17-cm 

SSH contour for May and June is given by the thick cyan line, and the location of the 

mean SSH high is given by the purple oval line.
60 cm/s

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+40 cm

+15 cm

+65 cm

m

 124

Figure 3.2-5. The first detachment of Franklin showing the depth of the 6 °C isotherm and 80 to 100-m 

velocity vectors from the moorings (5-day means). Three-day surface drifter tracks from 

USCG and USF with arrow heads every day, and altimeter SSH contours. All means and 

tracks are centered on 8 June 2010.
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+45

-5

Figure 3.2-6. Franklin detachment 1: Upper and lower-layer circulation for indicated dates. Surface layer - SSH (cm) from altimeter with 5-day 

mean 40-HLP velocities (red arrows) at 80 to 120 m. Bottom layer - Geopotential (dynamic height, cm) from 5-day mean 40-HLP 

velocities 100 mab (blue arrows). SSH contour interval is 10 cm from -25 to +25, and 20 cm above +25 cm. Note differing scales 

for upper and lower layer velocities. 

125 
126

displaced eastward. During the reattachment a month later, an intense lower-layer high is 

situated under the east side of Franklin with the result that upper- and lower-layer flows are more 

coincident. The upper-layer circulation appears closed within the eddy, leaving the southern 

lobe, which was the eastern lobe on the 8 June map, to be advected towards the LC (velocities at 

E5 are southwards) by the cyclonic circulation of the Tortugas eddy. Similar to when the trough 

expanded at the first detachment, the E transect shows even stronger flows directly towards the 

Campeche slope and also normal to the SSH contours. This is similar to the first detachment of 

Ekman. The along- and across-isobath velocity components for section E, down to 1000 m, are 

shown for 10 July 2010 in Figure 3.2-7, which shows that the flow is towards the slope at all 

depths inshore of E4. This indicates there is no compensating flow at depth to the onshore 

surface flow so that there is a mean transport, during this detachment, onto the Campeche shelf. 

The along-isobath component shows weak flows at all depths, except at E5 where the flow is 

southward. Flow over shoaling depths should produce an anticyclonic circulation through the 

conservation of potential vorticity. If this exists, it is not resolved by the spacing of the E and N 

transects. 

3.2.3 Hadal

After the final separation and fading away of Franklin in late September 2010, the LC did not 

retreat, and remained moderately extended with the northern boundary at ~ 25°N through 

October and early November. Some long wavelength meanders develop on the east-west 

directed section of the front during late November and December that propagate eastward 

through the Florida Straits. The LC begins to extend northwestward in December, favoring the 

Campeche slope. The LC east-west extent is less than for Franklin and Ekman at a similar stage 

of development (Compare 2 January 2011 front in Figure 3.2-8 with 1 March 2010 (Figure 3.2-

3), and 25 May 2009 (Figure 3.2-1)). The LC extends northwestwards though January and 

February with increasing area (Figure 1.5-1) that plateaus in March 2011. During this phase, 

large amplitude, long wavelength, southward propagating meanders develop on the eastern 

boundary, similar to Ekman and Franklin. The meanders have maximum amplitudes in late 

February and early March, and then begin to decrease so that by early April, the LC has regular, 

fairly straight eastern and western boundaries, and occupies a larger area than at the beginning of 

January (Figure 3.2-8). During the next growth phase in April 2011, the LC again develops large 

meanders on the eastern boundary that also decay when the areal growth again plateaus in MayJune (see Figure 1.5-1). The main difference with the earlier meanders is that the longer length 

of the eastern boundary allows two crests and troughs to develop (see 2 May in Figure 3.2-8), 

instead of one crest and trough. At the end of this sequence in early June, the Hadal part of the 

LC bulges out to the west along 28°N. This western lobe moves northward and becomes the 

northwestern part of developing meanders propagating southeastward along the very long eastern 

boundary of the combined LC and Hadal. This northwestern lobe detaches a very small eddy 

(named Galileo, even though it was not a true LC anticyclone, on 27 June 2011. However, by 

mid to late July a meander trough on the eastern boundary, situated in the middle of the array at 

~ 26°N, 87°W began to amplify and nearly caused a detachment on 26 July when some of the 

cyclonic vorticity was squirted through to the western side of the LC (compare 16 and 31 July 

boundaries in Figure 3.2-8). This event will be discussed in more detail below and resulted in a 

strong cyclone being spun up between the northern side of the Campeche bank and an already 

westward-extended Hadal. This Campeche cyclone further assists the westward movement of 

Hadal, which was large enough and unimpeded by topography for westward translation by β to
 127

Figure 3.2-7. Five-day average velocity components for transect E moorings (E1 to E5). Upper panel: 

cross-isobath component (+ve directed 055°T). Lower panel: along-isobath component 

(+ve directed 325°T).
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1/2 1/17 2/1 2/16 3/3 3/18 4/2

Hadal: January - April 2011

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Hadal: April - June 2011

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6/1 6/16 7/1 7/16 7/31 8/15

Hadal: June to August 2011

Figure 3.2-8. Loop Current 17-cm frontal boundaries from SSH altimeter maps for Hadal for the indicated dates.

128 
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be effective. This results in an eventual final separation on 15 August. The LC remained 

extended and began to increase in size almost immediately after Hadal’s separation, again 

developing meanders on the eastern boundary that led to the first detachment of Icarus on 8 

November 2011 (see Figure 1.5-1) immediately prior to the end of the field program.

The sequence showing the depth of the 6 °C isotherm surface in relation to SSH is shown in the 

top panels of Figure 3.2-9 for late July through 12 August, just prior to the final separation. 

Between 25 and 31 July, the cold-meander trough on the east side of the LC is advected through

to the west side by the south and southwestward flows on the east side of Hadal. This causes the 

17-cm SSH contour on the east side of the LC/Hadal configuration to be deflected 

northeastward, but this apparent developing trough is directly a result of the cold cyclonic 

vorticity being squirted through the neck from the east side of the system. Over the next 15 days, 

the cold cyclone strengthens over the north Campeche slope, and seems to play a role in the 

movement of Hadal westward that stretches the narrow neck in the SSH leading to separation on 

15 August. The lower panels of Figure 3.2-9 show the lower-layer circulation, and on 25 July on 

the west side of the array, there are a high and low displaced southward from the corresponding 

surface-layer high and low (warm and cold, respectively). There is also a lower-layer high on 

the east side of the array that is only slightly displaced from the corresponding warm northern 

lobe of the LC. The two lower-layer highs merge into a ridge that is maintained and increases as 

Hadal and the LC draw apart. On the 12 August map, the lower-layer flows on the west side of 

the ridge are northward, acting as if to further narrow the neck. The southeastward flows on the 

east side of the ridge parallel the LC SSH contours, and thus the similar southeastward surfacelayer flows. These lower-layer circulation patterns are quite different from the meandermediated separation of Ekman (Figure 3.2-2), which occurred in a similar location and was also 

caught by the array.

The surface chlorophyll map for 12 August (Figure 3.2-10) shows the more productive waters 

stretching across the neck in the direction of the flows on the east side of Hadal, in contrast to 

low productivity waters of both the LC and Hadal. The Campeche cyclone, centered at ~25°N, 

88°W, is also clearly advecting low productivity water from the south side of Hadal onto the 

northern part of the Campeche bank. The higher productivity (green color in Figure 3.2-10) that 

intrudes southwards at ~26.5°N on the east side of Hadal originates from the shelf around the 

Mississippi delta, being advected off the shelf by Hadal’s swirl currents. This intrusion is 

consistent with the southward flow at A1, and indicates that circulation is almost closed within 

Hadal event though the 17-cm contour shows a connection.

In summary, the three major LC eddy separations in this dataset are quite different, though there 

are features in common. Common features are:

• The development of long-wavelength, large-amplitude meanders on the eastern 

side of an extended LC that propagate southwards is common to all three 

separations. 

• Detachments occurred when a growing meander trough stretched across the neck 

of the LC.

• Deep cyclones and anticyclones traversed the separation zone in a southwestward 

or westward direction, and seem to play a role in the detachment.
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7/24 to 7/26 7/30 to 8/1 8/11 to 8/13

Figure 3.2-9. Maps of the separation of Hadal for the indicated dates in 2011 showing upper (top row) and lower-layer (bottom row) circulations. 

Parameters are 2-day mean currents at ~80-100 m (gray) and 100 mab (blue), geopotential height for the bottom currents (gray 

shaded), SSH contours (cm) from altimeter maps, and depth of the 6 °C isotherm (color shaded).

130 
200 m

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3500 m

2500 m

3000 m

Chlorophyl-A (ln(mg m-3))

0 cm

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60 cm/s

 131

Figure 3.2-10. Surface Chlorophyl-A from Modis Aqua overlaid with SSH from altimeter maps for 12 

August 2011. Two-day average 40-HLP velocity vectors at 80 to 120 m (thick red arrows) 

are shown for the moorings.
132

Notable differences are:

• Hadal had a greater the extension and hence the length of the eastern boundary with more 

crests and troughs than Ekman or Franklin. This suggests a preferred wavelength. 

• Areal growth of Hadal had plateaus when eastside meanders seem to shutdown. Similar 

plateaus in growth did not apply for Ekman and Franklin. 

• After Franklin’s initial detachment, multiple reattachments with the LC essentially 

drained mass from the eddy, and though a separation was eventually achieved, it rapidly 

dissipated. 

• Hadal’s separation was for an eddy that was well extended into the deep Gulf, and was 

large enough for β-driven westward translation to take over (see next section), though the 

initial partial detachment by the meander trough seemed to be a precondition, and the 

development of the Campeche bank cyclone from this trough also seems to assist the 

westward push of the eddy. 

• Hadal’s lower-layer circulation consisted of a ridge of high pressure linking the LC and 

was quite different from Ekman.

3.3 NUMERICAL MODELING OF HADAL’S SEPARATION

3.3.1 Introduction

One way the shedding of Loop Current eddies can be understood is as a competing imbalance 

between the mass influx through the Yucatan Channel, which grows the Loop, and a westward 

Rossby wave that tends to ‘peel’ an eddy from the Loop; this will be referred to as the PichevinNof mechanism (Nof 2005; Pichevin and Nof 1997). According to Chang and Oey (2013a) and 

Xu et al. (2013b), the Loop Current grows larger and deeper with mass influx from the Yucatan 

Channel. When its Rossby radius, Ro (based on the Loop’s upper-layer depth), reaches a certain 

size, the variation of the Coriolis parameter (f) becomes significant (β effects), and the westward 

eddy’s speed (which is proportional to long Rossby wave velocity ~ βR0

2

) exceeds the LC 

growth rate due to the mass influx. At this point, the Loop Current eddy begins to detach. The 

idea may be extended to the case when the mass influx (i.e., Yucatan channel transport) varies 

slowly in time (longer than 1~2 months), so that eddy shedding may also depend on this 

variation. Oey et al. (2003b) show that models forced by time-dependent winds produce strong 

Yucatan transport fluctuations, of the order of a few Sverdrups (1 Sv = 106 m3s

-1

) and larger, 

which in turn also influence the shedding periods. Chang and Oey (2013a) identify biannual 

preferences of LC eddy shedding in summer and winter by analyzing long-term observational 

data and numerical model results. This will be discussed further in Chapter 5. They found a 

strong dependence of eddy shedding on Yucatan transport. The biannual variation in the trade 

winds forces a corresponding biannual transport through the Yucatan Channel; as a consequence, 

the LC has a tendency to shed eddies as the wind weakens from summer to fall, and also from 

winter to spring. In Chapter 5 and Chang and Oey (2013a), the process is studied in the simplest 

possible setting using a reduced-gravity model forced by idealized, biannually-varying winds. 

The simple model suggests that the biannual signal is produced by vorticity and transport 

fluctuations in the Yucatan Channel due to the piling-up and retreat of warm water in the 

northwestern Caribbean Sea (forced by the trade winds). The LC grows and expands with 

increased northward velocity and cyclonic vorticity of the Yucatan Current, and eddies are shed 

when these are near minima. These findings agree with the prediction based on the Pichevin-Nof 

mechanism and Reid’s (1972) theory. 
133

Chang and Oey (2013a) also suggest that, while other factors such as baroclinic instability and 

upper-lower layer coupling do not determine eddy shedding, they can modify it, by accelerating 

the timing when eddies are shed. Oey (2008) showed that the region north of the Campeche 

Bank is a fertile ground for baroclinic instability, which can generate deep cyclones below 

1000m. In Chapter 4, these baroclinic instabilities will be analyzed using the present study 

observations. These cyclones may accelerate the upper-layer LC eddy shedding. In the initial 

stages of shedding an eddy, the westward-extended LC forces a deep return flow into the eastern 

Gulf where the upper layer then becomes divergent while the lower layer becomes convergent. 

The resulting strong upwelling in the eastern Gulf may also accelerate shedding.

This section uses the free-running version of the model to investigate the separation of Hadal in 

late July 2011. The model is validated against AVISO SSHA fields, and AVISO maps 

determined that the separation occurred on 25 July, which, according to the CCAR analysis that 

is the basis of the observational description above, was a partial but not quite complete 

detachment. The hindcast analysis run (described in Section 2.8), which assimilates AVISO 

SSHA, is used as initial conditions for two free-running experiments to study Hadal’s eddyshedding dynamics. One experiment is initialized from the 1 July 2011 hindcast field (Exp.Jul01) 

and another experiment initialized from the 15 May 2011 hindcast (Exp.May15). The rationale 

for these initialization dates will become clear. For these free-running experiments, neither the 

AVISO SSHA, nor the MCSST data were used; other forcings are the same as in the hindcast 

analysis run. For convenience, these experiments will be called “forecasts” even though, strictlyspeaking, they really are not, since winds (and other forcings) are used. For each experiment, 

daily-averaged fields are used for analyses. The majority of the material in this section was 

originally published in Xu et al. (2013b).

3.3.2 Model Forecast Skill

Exp.Jul01 predicts a LC eddy shedding during the last week of July in agreement with the 

AVISO satellite sea-surface-height (SSH) data (Figure 3.3-1). The hindcast analysis and AVISO 

both show for 1 July (Figure 3.3-1) a northwestward-extended Loop Current, although the 

AVISO zero-SSH contour is some 50 km more extended. Ten days later (on 11 July) the 

forecast LC intrudes northwestward, which compares well with AVISO. On 21 July, both 

AVISO and the model LC developed a thin neck, typical of the situation at incipient eddy 

shedding (Oey 1996; Oey 2008; Schmitz 2005; Schmitz et al. 2005). The forecast shows that a 

large eddy was shed shortly thereafter on July 25 in agreement with AVISO. Exp.May15 

produces an eddy shedding on 8 July, 2-3 weeks earlier than observed with AVISO, and 

predicted by Exp.Jul01. This eddy shedding date is 7-8 weeks into the forecast horizon, which is 

near the limit of modeled LC predictability (Yin and Oey 2007). Exp.May15 will be used in 

Chapter 4 to investigate LC separations as influenced by Yucatan transport, vorticity, and 

Caribbean winds.

Model Skill Assessment Against SSH Observations

To evaluate forecast skill, time series of the spatial correlation coefficient and root-mean-square 

errors between the model and AVISO SSH anomalies are calculated and compared against 

persistence for the open-ocean region of the Gulf: north of 23oN and west of 84oW, in water 

depths deeper than 500m (Figure 3.3-2). The correlation, R, is ≈ 0.8 on 1 July for the initial
 134

Figure 3.3-1. Daily averaged SSH (colors in m) and surface currents (squiggly black lines with scale 

shown) for every 10 days of the forecast simulation, starting from 1 July 2011 (Exp.Jul01). 

Blue vectors are wind stresses with scale shown. White contour indicates the 200-m 

isobath. The magenta line indicates the SSH=0 from AVISO for comparison with the 

model. 
 135

Figure 3.3-2. Comparison between AVISO and forecast (exp Jul01) SSHA. Top: the spatial correlation 

coefficient between the model and AVISO SSHAs in the region north of 23°N and west of 

84°W, over water regions deeper than 500 m in the Gulf of Mexico (for eight weeks from 

1 July to 26 August 2011). Bottom: the corresponding RMS error for the same region. 

Black dotted lines are forecast and grey lines are persistence. 
136

hindcast value. It remains above 0.65 during the first five weeks of the forecast consistent with 

Yin and Oey (2007) who concluded, based on bred-vector analyses, that the LC and eddy 

forecast horizon in the Gulf of Mexico is four to six weeks before the model skill deteriorates. 

At week six, the correlation drops to approximately 0.5 but it remains above this value from 

weeks six to seven before degrading further to about 0.45 at the end of week eight. The RMS 

errors increased from 0.18 to 0.23 over the first eight weeks. For both measures, the model 

forecast beats persistence.

Model Skill Assessment Against In-Situ Observations

Both the model hindcast and forecast skills are calculated for the nine full-depth moorings in the 

U.S. array using the metrics given in Section 2.8.1. Figure 3.3-3a shows the nine mooring 

locations superimposed on the color map of modeled SSH averaged over July 2011, and Figure 

3.3-3b plots the depth-averaged R and |θ| at each mooring. Relatively large errors at moorings 

A1 and A2 are due to the highly variable flow as the main portion of the Loop passed these 

locations during the eddy-shedding process. On the other hand, the relatively large error at 

mooring C2 is caused by the weak altimetry signal there, and data assimilation becomes 

ineffective. At other moorings, the Rs are generally higher than 0.5 and |θ|s are less than 50o. As 

can be expected, the nowcast (i.e., the SSHA data are assimilated through July) is generally more 

accurate than the forecast. These general inferences are also seen from the vertical distributions 

of R, θ and other metrics (Figure 3.3-4). Near the surface, the modeled currents generally agree 

with those observed, with R ≈ 0.7 (forecast) ~ 0.8 (nowcast) and |θ| less than 45o (Figure 3.3-

4a,b). These values degrade in the deep levels (where the model is basically prognostic with no 

assimilation), but the model retains some skills with R > 0.5 for nowcast and ≈ 0.45 for forecast, 

and |θ| < 50o with the forecast |θ| being actually slightly smaller. The model generally 

underestimates the current fluctuations, by as much as 50% near the surface for the forecast (Rstd

≈ 0.5; Figure 3.3-4c), while it overestimates the current fluctuations (Rstd > 1) just above the 

main thermocline at the base of the LC and eddy. This behavior in Rstd also shows up in the 

mean speeds, as indicated by the Rspd plots in Figure 3.3-4e. Thus the modeled currents 

generally have weaker vertical shears in the upper layer (plots not shown). The Skilluv near the 

surface is high, but it degrades substantially to a minimum of about 0.52 (nowcast), and ≈ 0.6 

(forecast) at z ≈ -400 m. The large errors are due to the lower Skill(u) for the zonal velocities at 

most of the moorings in the upper layer. During the comparison period in July 2011, most of the 

moorings were, based on AVISO, to the east of the LC in a region of cyclonic recirculation 

(Figure 3.3-3a) where ADCPs measured generally eastward currents near the surface. In 

contrast, in the model, the cyclonic edge of the Loop was biased southward compared with 

AVISO (Figure 3.3-3a), and the observed moorings were mostly in the region where the modeled 

eastward currents were weak. This apparent slight misalignment of the edge of the LC leads to 

poor Skill(u) in the upper 500-m layer. This large discrepancy near z = -400 m also shows up in 

the mean velocity angles between model and observation, αm-o, in Figure 3.3-4f. On the other 

hand, the directions of the modeled deep currents are quite well simulated.

Table 3.3-1 summarizes the average skill metrics for the model-ADCP comparisons (i.e., above 

500 m). While there can exist large discrepancies due to misalignment of the modeled and 

observed LC fronts during the eddy-shedding event in July 2011, the model possesses some 

skills, as shown by the generally good complex correlations, which indicate that modeled 

currents co-vary reaonably well with those observed. Given the emphasis on east-side meanders
a)

b)

 137

Figure 3.3-3. (a) Full-depth ADCP mooring (a1a4, b1b3 and c1c2) locations from the U.S. array superimposed on the July mean model forecast SSH (color with the zero contour in black, in 

meters). The purple contour is the zero contour of AVISO SSH. (b) Complex correlation 

Rs and |q|s averaged over depths at each of the nine tall moorings (i.e., horizontal 

distribution).
 138

Figure 3.3-4. Vertical profiles (i.e., averaged over all nine moorings at each horizontal level) of: (a) & 

(b) complex correlation Rs and Qs; (c) ratio of model-to-observed standard deviations 

(Rstd); (d) Skill (=[Skill(u)+Skill(v)]/2); (e) ratio of model-to-observed mean speeds (Rspd) 

and (f) angle of modeled observed mean velocity, in degrees, negative if model is clockwise w.r.t observation (αm-o). Black (red) symbols are nowcast (forecast).
139

and their consequences in the observational sections of this report, it is noteworthy that the 

model hindcast underestimates their amplitudes (Figure 3.3-1 and 3.3-3).

Model skills in simulating deep currents are quite high (Figure 3.3-4d), despite the fact that deep 

currents tend to be dominated by highly dispersive topographic Rossby waves (Hamilton 1990; 

Oey and Lee 2002) and are therefore more difficult to model. The magnitudes of the deep 

current fluctuations and means are underestimated and deviation angles are not zero (≈30o; 

Figures 3.3-4c,e,f). However, this represents a major improvement over the earlier, coarserresolution model (Oey et al. 2003a) in which the deep energy was very weak, by almost an order 

of magnitude, when compared with observations.

Table 3.3-1. A Summary of Various Skill Metrics Computed Using Currents from 

the Model and ADCP Measurements from Moorings A1 to C2

Model R θ Skill Mean Std. 

u v Ratio Rspd αm-o Dev Rstd

Hindcast 0.63 28o 0.41 0.88 0.71 20o 0.84

Forecast 0.54 34o 0.55 0.75 0.73 -33o 0.68

3.4 STATISTICS

3.4.1 Mean Flows

Mean velocities are calculated from 40-HLP data for the two-year common interval to both U.S. 

and Mexican field studies. Comparisons with mean velocities from the 2.5-year study show little 

significant differences for the U.S. moorings. The results for all valid measurements are shown 

in a pseudo-3D view in Figure 3.4-1. The largest means occur on the west side along the 

Campeche Bank, reducing somewhat over the deeper water of the north and west side of the LC. 

Upper-layer mean flows are highly sheared, reducing in depth to low values at 750 to 1000 m, 

which is most of the water column in the vicinity of the mean LC front over the Campeche slope. 

Below 1000 m, the mean flows are nearly depth-independent to the lowest level (100 mab). 

Both upper- and lower-layer flows have uniform but generally different directions with a 

transition occurring between ~900 m and 1300 m. Upper-layer currents align with the mean LC 

front (represented by the 15-cm contour in Figure 3.4-1), and the bowl-shaped 6 °C isotherm 

surface matches nicely the area of the mean LC and indicates that the center is between N4, A4 

and A3. It is noted that near-surface flows are slightly divergent on the west side, and slightly 

convergent on the north and east sides of the array. The mean low in SSH north of the LC has 

previously been noted as a quasi-permanent cyclonic flow in the eastern Gulf.

The lower-layer means suggest both anticyclonic and cyclonic flow, with high and low 

geopotential heights, respectively, of flows under the northwestern and northeastern parts of the 

mean LC. This is more evident if the first year (5/2009 to 6/2010) means are used because 

complete near bottom records are available (Figure 3.4-2). The lower-layer mean anticyclonic 

flow, centered on B2, is well defined, but the trailing cyclone to the east is a little more 

ambiguous. An explanation is that as the LC extends into the Gulf it moves over the shoaling 

depths of the Mississippi Fan with the net result that the lower layer will be compressed, and by
3000 m

1000 m

200 m

1000 m

2000 m

2500 m

3500 m

200 m

10 cm/s

+15 cm

+40 cm

-10 cm

Depth of 6°C Isotherm (m)

 140

Figure 3.4-1. Mean 40-HLP currents for all moorings overlayed with mean SSH (contours) and mean 

depths of the 6 °C isotherm (color shaded). Vector depths are color coded: red 0-250 m, 

tan 250-500 m, yellow 500-750 m, cyan 750-1000 m, purple 1000-1500 m, and black > 

1500 m.
3000 m

1000 m

200 m

1000 m

2000 m

2500 m

2500 m

+15 cm

+40 cm

-10 cm

5 cm/s

m 20 cm/s

cm

 141

N4

B2

Figure 3.4-2. Mean near-bottom 40-HLP currents (black scale) and standard deviation ellipses (blue 

scale) for the indicated interval. The mean SSH (cm) contours, and the geopotential 

height (gray shaded; dynamic cm) corresponding to the mean velocities for the same 

interval are also shown. 
142

conservation of potential vorticity generates anticyclonic (negative) relative vorticity anomalies. 

Similarly, because an extended LC tends to move westward, due to the Pichevin-Nof mechanism 

and the β-effect, the lower water column on the northeastern side is stretched as the upper-layer 

shoals, generating cyclonic (positive) relative vorticity anomalies.

The mean flow at the base of the Campeche slope (N4) is to the east in both the one and two-year 

results. This could be consistent with being part of the deep-return current of the basin-wide 

deep-mean cyclonic circulation that runs westward along the Sigsbee escarpment and southward 

along the base of the western Mexican slope (the Perdido escarpment) as observed by 

Lagrangian floats and moorings (Hamilton 2009) and discussed by DeHaan and Sturges (2005).

The variability, as represented by the standard deviation ellipses, is much larger than the mean 

near-bottom currents (Figure 3.4-2) and is quite inhomogeneous. The amplitudes tend to be 

smaller and larger on the southeastern and north and northwestern sides of the array, 

respectively. Lower-layer variances will be explored in more detail in the next section. 

3.4.2 Depth Variability of Velocities 

The mean flow shows that the water column in the deep eastern Gulf may be divided into two 

layers. For much of the analysis, a good analogue of the division between upper and lower water 

columns is the depth of the 6 °C isotherm which represents the lower boundary of the LC (Bunge 

et al. 2002), and roughly corresponds to the bottom depth of the Florida Straits (800 m). 

Analysis of the variability through the water column also shows markedly differing 

characteristics in both space and time of flows above and below the 900 m to 1100 m transition 

between the two layers. To show this, depth-weighted CEOF analysis is performed on the 40-

HLP currents, after means have been removed, for each full-depth mooring separately. Again 

the two-year common interval is used and the results show only minor differences if the full 2.5-

year interval is used for the U.S. moorings alone. In general, over 90% (and often over 95%) of 

the total variability of the currents through the water column at a given mooring can be 

accounted for by two CEOF modes.

Typical depth CEOF modes are given in Figure 3.4-3, and show a relatively depth independent 

dominant mode 1 and a surface intensified mode 2 above 1000 m that has more than twice the 

amplitude of mode 1 at the shallowest depth level. Together, they account for > 97% of the total 

depth range weighted variance of the low-frequency currents in the water column at this location. 

Mode 2 has essentially zero contributions from records below 1000 m, but near-surface flows do 

have a contribution from the nearly depth-independent mode 1, even though its R2 with the 

observed record is low. Flows below 1000 m are almost entirely accounted for by mode 1 that 

shows almost constant amplitudes between 1300 m and 100 mab. Mode 2 is unidirectional, but 

mode 1 has a small change in direction between upper and lower layers. Given these 

characteristics, the nearly depth-independent mode is named “quasi-barotropic” -QB, and mode 

2, though at some locations on the Campeche slope it will be mode 1, is “surface intensified” –

SI. The QB mode implies that some of the surface layer flow is coupled to the lower layer. 

Even though CEOFs are purely statistical constructs, there is a correspondence to barotropic and 

first baroclinic dynamic modes for a stratified water column in a flat-bottomed ocean.
 143

Figure 3.4-3. Depth range weighted CEOF modes for mooring A3.
144

The CEOF modes for all the moorings (Figure 3.4-4) all show similar characteristics. The SI 

mode is roughly aligned with the mean LC front, and is the only mode over the Campeche slope 

where amplitudes are much larger than further downstream. The QB mode shows only weak 

bottom intensification in the lower layer and the principal axis direction is often normal to the SI 

mode, particularly in the vicinity of the mean front. The principal axis directions for the QB 

mode are roughly in the same direction across the deep water U.S. array. The variances 

accounted for by these two modes are given in Table 3.4-1. The QB mode dominates in terms of 

variance explained at locations with water depths > 2000 m, even though amplitudes are less 

than the SI mode. This is because the SI mode decreases rapidly with depth and is only 

significant in the upper 1000 m, whereas the QB mode has significant amplitudes through the 

whole water column which is often > 3000 m deep. In terms of ratios of QB/SI variances, the 

QB mode has lower significance in the northwest (A1 & A2), and most significance in the north 

and center (B2, B3 and A4). The N4 mooring lacked a complete two-year record in the upper 

500 m, and so the results are a little different from the profiles observed at the other deep sites.

Table 3.4-1. Percent Variance Accounted for by Depth-Range Weighted CEOF 

Modes (7 June 2009 to 1 May 2011)

Location QB SI Total Location QB SI Total 

A1 67.7 29.2 96.9 B1 81.8 15.6 97.4

A2 75.5 20.9 96.4 B2 83.8 14.0 97.8

A3 82.7 14.9 97.6 B3 86.8 11.4 98.2

A4 88.8 8.4 97.2 C1 81.0 17.4 98.4

C2 79.7 16.8 96.5

E2 91.7 91.7 N2 8.4 88.6 97.0

E3 9.7 85.1 94.8 N3 90.1 90.1

E4 93.2 93.2 N4 71.5 26.7 98.2

E5 56.3 32.6 88.9

The normalized CEOF-mode amplitude time series for each location (Figure 3.4-5) essentially 

show the complete time history of the velocity field over the 2-year interval. The SI modes show 

the long-term fluctuations through the growth phases of Franklin and Hadal, particularly on the 

LC west side, but also showing the ~ monthly fluctuations on the east side (e.g., C1 & C2), 

associated with large-scale meanders. Rapid, ~ weekly, fluctuations associated with LC frontal 

cyclones are seen at N3, N4, A1 and A2 during the growth phase of Franklin (January - April 

2010), but are largely absent further downstream at C1 and C2. Similar fluctuations are only 

weakly observed along the LC-Campeche slope front for the similar growth phase of Hadal, a 

year later. The most prominent features of the QB-mode fluctuations that dominate the lower 

layer are the marked increases in amplitude during the detachments of Ekman and Franklin, and 

differing periodicities compared with the SI modes that dominate the upper layer. The responses 

are not uniform either in amplitude or timing for the two separation events. For example, the 

Ekman detachment events trigger a strong response resembling a wave train at A1, but for 

Franklin the periodicities are shorter and less intense. These characteristics are reversed for A4 

and N4.
40 cm/s

3000 m

1000 m

200 m

1000 m

2000 m

2500 m

3500 m

200 m

Full Depth CEOF Quasi-Barotropic and

 145

A4

E5

E4

E3

E2

N4

N3

N2

A2

A1

C2

C1

B3

B1

B2

A3

Figure 3.4-4. CEOF modes for the 2-year common interval. Both QB and SI modes are given. Depth 

dependent colors are the same as for Figure 3.4-1. 
Normalized

103 km2

LC Area & Area + Eddy

Ekman Franklin Hadal

N

N

N

N

N

N

N

N

N

N

N

N

N

N

N

N

N

N

N

N

N

B3

B3

C2

C2

C1

C1

B2

B2

B1

B1

A1

A1

A2

A2

A3

A3

A4

A4

N4

N4

N3

QB

SI

QB

SI

SI

Figure 3.4-5. Normalized mode amplitudes for CEOFs by mooring for the 2-year interval. Red and blue vectors correspond to the surfaceintesified and quasi-barotropic modes, respectively. The direction of the principal major axis w.r.t. north for each mode is given on 

the RHS of each ordinate axis. 

146 
147

The EKE spectra of selected normalized amplitude time series are shown in Figure 3.4-6. 

Because the time series are normalized, the apparent differences in power between locations are 

not significant, but the relative variance levels between frequency bands at a single location 

show which periodicities dominate the velocity records. The upper-layer or surface-intensified 

mode shows that long period (> 100-day) fluctuations have the highest variance and are 

associated with the large-scale growth, retreat and eddy shedding of the LC. At shorter periods, 

the variance level changes with location along the mean LC front. Over the Campeche slope (N2 

and N3), there are peaks in EKE at less that 10 days, but at 20 to 40 days there is relatively little 

activity. The A1, the SI mode shows more variance at periodicities longer than 20 days, and also 

peaks at ~15 days and at 10 days or less. On the east side, at C1, the 40-100 day periodicities 

dominate and there is less variance than for the west-side records at short periods. The QB-mode

EKE spectra are quite different and can be considered as characterizing the lower-layer 

fluctuations. For periods > 100 days, variances are small, and the spectra are dominated by 

peaks in the 20- to 100-day band with only A1 showing a secondary peak at ~15 days that 

corresponds to the upper layer at A1. The A4 and C1 EKE have the strongest peak in the 40- to 

100-day band. The spatial variability of the important frequency bands in the upper and lower 

layers is explored in the next two sections using the PIES mapping array data.

The QB and SI CEOFs are used to calculate the depth-integrated total EKE, at each location, as 

outlined in Chapter 2 and also given in Hamilton (2009). Figure 3.4-7 shows the cumulative 

depth-integrated KE from the mean flow and the two CEOF modes. Along the Campeche slope, 

the SI mode dominates, but the mean flow KE is a substantial fraction of the total. The meanflow KE fraction of the total reduces from about a half to a third between E3 and N3, indicating 

that along the front, fluctuations are extracting energy from the mean. Once over deep water, 

both mean flow and SI-KE fractions decrease and the QB-mode EKE is the most important. The 

mean flow KE and the SI-EKE magnitudes, though less than over the Campeche slope, remain 

approximately constant along the path of the mean LC front over the deep basin. The QB EKE, 

however, tends to increase from the NW to the NE side of the LC, implying that transferring 

EKE to the lower layer is occurring all along the northern front after the LC leaves the 

Campeche slope. Total depth-integrated KE is less over deep water than over the slope where 

the totals at E3 and N3 are almost equal. However, the maximum total KE over the deep water 

is at C1 and is about the same as at N3, though the EKE has been transformed from SI to 

strongly QB. Thus, transfer of EKE from SI, and to a lesser extent KE from the mean flow, over 

the Campeche slope to a nearly depth-independent QB mode over deep water, is of major 

importance to the Gulf deepwater circulation processes. It has been observed that deep 

fluctuations that seem to originate from the LC can propagate towards the Sigsbee escarpment 

and the western Gulf in the form of TRWs (Hamilton 2007; Hamilton 2009; Oey and Lee 2002). 

3.4.3 Horizontal Variability in the Upper Layer

The above CEOF analysis of the tall-mooring velocities indicates that most of the variance of the 

mooring velocities can be explained by two modes, one surface-intensified, and the other nearly 

depth-independent. In the following analysis, the statistics of these modes are characterized with 

the two components of PIES-mapped sea surface height (SSH). The surface-intensified (SI) 

mode is represented by the baroclinic SSH referenced to the bottom (SSH_bcb). Recall from 

Chapter 2 that SSH_bcb is surface geopotential referenced to 3000 dbar and converted to a 

height equivalent (geopotential divided by gravity). The nearly depth-independent (QB) mode is
N2

N3

A1

C1

N4

A4

A1

C1

Quasi-Barotropic Mode

EKE Spectra of Normalized Mode Amplitudes

 148

Figure 3.4-6. EKE spectra in variance preserving form of selected normalized mode amplitudes shown 

in Figure 3.4-5. LH and RH panels are for surface-intensified and quasi-barotropic 

modes, respectively.
3000 m

1000 m

200 m

1000 m

2000 m

2500 m

3500 m

200 m

10 m3s

-2

Mean KE

QuasiBarotropic

Surface-

 149

E2

E3

E4

E5

N2

N3

N4

A4

B3

C1

C2

A1

A2

A3

B1

B2

Figure 3.4-7. Cumulative depth-integrated KE for mean flow, and the QB and SI CEOF modes. The 

height of the bars represents the total KE with color coding showing the division between 

the three components.

Cumulative Depth Integrated KE for Mean 

Flows and Full Depth CEOF Modes
150

represented by SSH_ref, which is 3000-dbar pressure converted to a height equivalent (pressure 

divided by gravity and density). 

Loop Current meanders are major contributions to variability at periods shorter than 100 days. 

This section characterizes the statistics of their spatial distribution of energy, frequency, 

wavenumber, and phase speed. 

Figure 3.4-8 shows the near-surface, time-mean velocities and mean EKE over the 30-month 

duration of the U.S. mapping array. Mean near-surface (200-m depth) currents are anticyclonic 

with mean speeds near 15 cm s

-1

, maximum speed near 25 cm s

-1

. This broad-scale circulation 

results from the repeated advance and retreat of the LC during LC eddy shedding events. EKE is

elevated along a swath centered on the mean LC position. Standard-deviation ellipses are 

slightly elongated in the along-path direction in the western portion (moorings A1, A2, and A3),

and they are mainly isotropic elsewhere. EKE is modulated in time, with levels tending to be 

low and increase as the LC moves into the array (Figure 3.4-8b). Elevated EKE levels tend to 

occur during the three LC-eddy-shedding events (Ekman, Franklin, Hadal). Close examination 

indicates that the peak EKE within each individual LC-eddy-separation event can occur just after 

(Ekman), during (Franklin) or prior to (Hadal), a separation. This is likely due to the relative 

positions of the LC and LC eddies within the array, which vary event to event. Multiple time 

scales of variability are present in the EKE time series. For example, there is high-frequency 

variability during February to April 2010, in the buildup prior to Franklin formation that is also 

seen in the individual CEOF vertical modes (Figure 3.4-5). Lower-frequency variability 

dominates from May through September 2010 during and following Franklin detachment and 

separation.

Figure 3.4-9 shows the spatial distribution of SSH_bcb variance where standard deviation, with 

units of cm, is plotted rather than variance. Total SSH_bcb variance is dominated by the LC 

advance and retreat (Figure 3.4-9a), and this is most evident for periods longer than 100 days. To 

investigate spatial patterns of higher frequency signals, SSH_bcb is band passed using four 

frequency bands, 100 to 40 days, 40 to 20 days, 20 to 10 days and 10 to 3 days. The frequency 

range choices were guided by PIES SSH_bcb spectra (not shown, but are similar to the EKE 

velocity spectra given in Figure 3.4-6) that have peaks near 60, 30, and 15 days. The spectrum is 

red: a large fraction, 86% of the total SSH_bcb variance occurs at frequencies greater than 100 

days. Within the 100 to 3-day mesoscale band, variance is distributed as follows: 72% within 

100 to 40 days, 19% within 40 to 20 days, 7% within 20 to 10 days and 2% within 10 to 3 days.

The spatial patterns of variability change systematically with frequency band, as shown in Figure 

3.4-9b-e. As frequency increases, the location of maximum variance transitions from central and 

eastern portions of the array to the northwest corner. Analysis will show that high-frequency 

variability, less than 20 days, occurs along the western side of the array and often occurs well in 

advance of LC eddy shedding. Whether these high-frequency meanders propagate along the full 

length of the LC may depend on the location of the LC front within the eastern Gulf. Low 

frequency variability, 40 to 20 days, propagates clockwise along the LC periphery, intensifying 

either over the Mississippi Fan or in the southeastern portion of the array during LC eddy 

detachments. The lowest frequency variability, 100 to 40 days, peaks during detachment events, 

is confined eastward of the Mississippi Fan, and propagates southwards along the LC front.
24o

N

26o

N

28o

N

89o

W 87 oW 85 oW

10 cms−1

mean Loop Current

(a) 200 m depth eddy kinetic energy [cm 2

 s−2]

0 300 600 900 1200

200

400

600

800

1000

[cm 2 s−2]

namkE nilknarF ladaH

(b) 200 m depth eddy kinetic energy

0

10

20

30

(c) Array−average SSH

[cm]

Jul2009 Jan2010 Jul2010 Jan2011 Jul2011

100

150

200 (d) Loop Current area

[103km2

]

 151

Figure 3.4-8. Upper panel (a): 200-m depth mapped and measured mean current vectors (bold) and 

standard deviation ellipses superimposed on the time-mean 200-m depth eddy kinetic 

energy. Red line denotes the mean Loop Current position defined by the CCAR SSH 

17-cm contour. Bathymetry plotted with gray contours every 500-m depth. Time mean is 

taken over the 30-month experiment duration from 3 May 2009 through 23 October 2011. 

Panel b: Time series of array-averaged 200-m depth eddy kinetic energy. Panel c: Time 

series of array-average SSH. Panel d: Loop Current area.
Total

25o

N

26o

N

27o

N

88o

W 86 oW 84 oW

 a

100 to 40 days

 b

40 to 20 days

 c

20 to 10 days

25o

N

26o

N

27o

N

88o

W 86 oW 84 oW

 d

10 to 3 days

 e

 baroclinic sea surface height referenced to the bottom (SSH bcb) standard deviation [cm]

0 3 5 8 15 20 25 30 35

Figure 3.4-9. Standard deviation of baroclinic sea-surface height referenced to the bottom (SSH_bcb) as a function of frequency band. Upper 

left (a): Total variance. Note all mapped values exceed 10 cm; standard deviation is contoured every 5 cm. Maximum (minimum) 

values are 32 (13) cm. Four right panels (b-e): Standard deviation in four frequency bands noted in the title of each panel. 

Bathymetry contoured in grey every 500-m depth. Note that the contour interval is not uniform. 

152 
153

(Propogation direction and speed associated with each frequency band is determined by complex 

empirical orthogonal analysis presented later in this section.)

To illustrate how SSH_bcb variance compares among LC-eddy detachments, Figure 3.4-10 

shows the time series of SSH_bcb variance as a function of frequency band. To provide a 

broader context, the LC-area index (Figure 3.4-10a), indicating times of detachments and 

reattachments, and the array-mean SSH (Figure 3.4-10b), indicating the presence of the LC 

within the array, are shown. Clearly, variance is elevated during the LC-eddy events while the 

LC is within the array, yet levels and sequencing vary among these events. Hadal appears as the 

strongest, and Ekman as the weakest event. The timing of peak variance within the frequency 

bands varies between eddies: during Ekman and Franklin, peak variance within each band occurs 

at successively later times as frequency decreases. Elevated variance in the 20- to 10-day band is 

a precursor to all three separations. Interestingly, very little variance in the 10- to 3-day band 

appears prior to Hadal formation. Figure 3.4-10 reinforces that each LC-eddy shedding event is 

best treated individually, not only because the basin or regional statistics of each LC-eddy 

shedding event could be different, but also because the array provides a limited spatial window 

into the mesoscale variability associated with each LC eddy.

Ultimately, Figure 3.4-10 is used to identify time intervals for further diagnoses. CEOFs are 

calculated during time intervals that capture enhanced levels of SSH_bcb variance. Interest is in 

the spatial structure of the upper-ocean variability within the mesoscale band with an emphasis 

on amplitude and phase propagation. Four time intervals are analyzed (gray shaded boxes in the 

lower four panels of Figure 3.4-10). We label these time intervals Ekman, Franklin, Hadal and 

Icarus in the following CEOF case studies. In addition, CEOFs are calculated in a broader 

region using the CCAR SSH altimeter data band-passed between 100 and 40 days. The CCAR 

SSH analysis is restricted to the lowest frequency band because for periods 40 days and shorter, 

the altimeter sampling leads to spatial and temporal aliasing. 

Figure 3.4-11 shows the weekly and time-mean position of the LC front during the four time 

intervals. The CCAR SSH analysis provides a basin context for the mesoscale variability. 

CEOF results are shown in Figures 3.4-12 through 3.4-15. The second mode of each CEOF is 

shown only if it explains 30% or more of the total variance with the band. For each individual 

LC-eddy event labeled above, results for the four frequency bands will be discussed. Because in 

each event the high-frequency variance builds up first (as was shown above), followed by 

progressively lower-frequency variance, the CEOF discussions will also proceed from high to 

low frequency. Following that, all the CEOF phase information will be summarized together to 

examine wavenumbers and phase speeds and relate them to previous studies in the Gulf Stream.

Ekman CEOFs

The highest frequency band (10 to 3 days) spatial pattern has its highest amplitudes along the 

western and northern portions of the study area. Mode-1, accounting for 70% of the variance in 

this band, shows phase propagation to the northwest turning in an anticyclonic sense. The mode 

spatial amplitude (left column) remains high to approximately 86.5°W, beyond which it 

decreases rapidly (Figure 3.4-12b). The temporal amplitude peaks in May, about a month before 

the first Ekman separation and earlier than the other frequency bands. 
154

100

150

200

[103km2

]

 Loop Current area

 a

0

20

40

[cm]

 array−mean ssh

 bold−altimeter

 b

50

100

150

200

[cm2

]

 SSHbcb 100−40 day

 variance in frequency bands Ekman Franklin Hadal Icarus

 c

10

20

30

40

50

[cm2

]

 SSHbcb 40−20 day

 d

5

10

15

20

25

[cm2

]

 SSHbcb 20−10 day

 e

2009 2010 2011 2012

5

10

15

[cm2

]

 SSHbcb 10−3 day

 f

Figure 3.4-10. (a) Loop Current area. (b) Array mean baroclinic sea-surface height referenced to the 

bottom, SSH_bcb (CCAR sea-surface height in bold). The mean of the baroclinic seasurface height referenced to the bottom has been adjusted to match the CCAR seasurface height. (c - f) Variance of array-averaged baroclinic sea-surface height referenced to the bottom, SSH_bcb. Frequency band noted in the title of each panel. Gray 

filled boxes in panels c through d correspond to the time period over which complex 

empirical orthogonal functions have been calculated. 
24o

N

25o

N

26o

N

27o

N

28o

N

89o

W 88oW 87oW 86oW 85oW 84oW

 02−May−2009 to 31−Aug−2009 Ekman

24oN

25o

N

26o

N

27o

N

28o

N

89o

W 88oW 87oW 86oW 85oW 84oW

 31−Jan−2010 to 31−Aug−2010 Franklin

24oN

25o

N

26o

N

27o

N

28o

N

89o

W 88oW 87oW 86oW 85oW 84oW

 28−Feb−2011 to 31−Jul−2011 Hadal

24oN

25o

N

26o

N

27o

N

28o

N

89o

W 88oW 87oW 86oW 85oW 84oW

 31−Aug−2011 to 29−Oct−2011 Icarus

 155

Figure 3.4-11. CCAR SSH determined Loop Current positions during CEOF time periods. For each 

panel, the position of the 17-cm contour is plotted every seven days during the interval 

noted in the upper edge of the plot. Location of the PIES represented by open blue 

circles. The mean Loop Current position is shown by the bold red line. Bathymetry 

interval is 500 meters.
Ekman (a)

 156

SSHbcb mode 1: 90%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

100−40 days

phase [degrees]

% variance in 100−40 day modes

 mode 1: 90 mode 2: 9 mode 3: 1 0 120 240 360

05/07 06/26 08/15

0

20

40

[cm]

Loop Current area

2009

80

120

160

200

[103km2

]

SSHbcb mode 1: 63%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

40−20 days

phase [degrees]

0 120 240 360

05/07 06/26 08/15

0

10

20

[cm]

Loop Current area

2009

80

120

160

200

[103km2

]

SSHbcb mode 2: 31%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

40−20 days

phase [degrees]

% variance in 40−20 day modes

 mode 1: 63 mode 2: 31 mode 3: 4 0 120 240 360

05/07 06/26 08/15

0

10

20

[cm]

Loop Current area

2009

80

120

160

200

[103km2

]

Figure 3.4-12a. CEOFs determined from band-passed baroclinic sea-surface height referenced to the 

bottom, SSH_bcb, during the Ekman time period. Two frequency bands are shown: 100 

to 40 days (Mode 1), and 40 to 20 days (Modes 1 and 2). For each CEOF, the left panel 

shows normalized spatial amplitude, the middle panel shows phase in degrees, and the 

right panel shows amplitude time series in cm. In the left panel, the mode number and 

percent explained by the mode is noted in the title. In addition to the mode time series 

(blue), the mean position of the Loop Current (17-cm contour) during the time interval of 

the CEOF is represented by the red line. In the middle panel, the phase is plotted for 

regions where the spatial amplitude exceeds 0.5. Propagation is in the direction of 

increasing phase. Bathymetry is contoured every 1000 m depth. In the right panel, the 

mode time series is blue; Loop Current area is red. 
Ekman (b)

Ekman (c)

 157

SSHbcb mode 1: 49%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

20−10 days

phase [degrees]

% variance in 20−10 day modes

 mode 1: 49 mode 2: 29 mode 3: 12 0 120 240 360

05/07 06/26 08/15

0

10

20

[cm]

Loop Current area

2009

80

120

160

200

[103km2

]

SSHbcb mode 1: 70%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

10−3 days

phase [degrees]

% variance in 10−3 day modes

 mode 1: 70 mode 2: 13 mode 3: 6 0 120 240 360

05/07 06/26 08/15

0

10

20

[cm]

Loop Current area

2009

80

120

160

200

[103km2

]

Altimeter mode 1: 79%

25oN

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

100−40 days

phase [degrees]

% variance in 100−40 day modes

 mode 1: 79 mode 2: 16 mode 3: 4 0 120 240 360

05/07 06/26 08/15

0

20

40

[cm]

Loop Current area

2009

80

120

160

200

[103km2

]

Figure 3.4-12b-c. (b) CEOFs determined from band-passed baroclinic sea-surface height referenced to 

the bottom, SSH_bcb during the Ekman time period. Two frequency bands are shown 

in the upper panels: 20 to 10 days (Mode 1) and 10 to 3 days (Mode 1). (c) CEOFs 

determined from 100 to 40 day band-passed CCAR sea-surface height (cm) during the 

Ekman time period using the same conventions as in Figure 3.4-12a with Envisat 

ground tracks plotted with cyan lines. 
158

The low-frequency CEOF mode for the 100- to 40-day band accounts for 90% of the variance. It 

reaches peak amplitude during Ekman’s first detachment (Figure 3.4-12a). Highest amplitudes 

are found along the eastern side of the array with approximately due-south propagation along the 

LC.

The comparison between the Ekman PIES and CCAR-SSH CEOFs (Figure 3.4-12c) is excellent 

in the 100- to 40-day band. Both show the same spatial pattern, phase propagation and timing 

although the CCAR-SSH phase propagation appears slightly faster.

Franklin CEOFs

Franklin CEOFs (Figures 3.4-13a,b) share several characteristics of the Ekman CEOFs and again 

the LC mean path is well contained by the array during this event. Within the two highfrequency bands (<20 days), mode amplitudes are high only along the northwest portion of the 

array, and phase propagation is anticyclonic (downstream). Their temporal amplitudes grow to a 

peak prior to detachment. 

Within the 40- to 20-day band, the spatial amplitude is largest near the Mississippi Fan, 

propagation is anticyclonic along the LC, and amplitudes peak during Franklin’s first 

detachment. This mode resembles the sum of modes 1 and 2 for Ekman CEOFs in the 40- to 20-

day band, and the phase propagation is downstream along the LC. Relative to eddy detachments, 

the temporal amplitude builds and peaks with very similar timing to Ekman CEOFs.

Within the 100- to 40-day band, the spatial amplitude is largest along the eastern side of the LC, 

propagating south during Franklin’s first detachment. The CCAR-SSH 100- to 40-day CEOF 

(Figure 3.4-13c) demonstrates, for this larger region, that meanders in this frequency band are 

confined east of the Mississippi fan along the southward-flowing portion of the LC. 

Hadal CEOFs

During the Hadal time interval, the mean position of the LC differs from the Ekman and Franklin 

time intervals. It is further west, and the array captures only the eastern side of the LC (Figure 

3.4-11). The CEOF spatial amplitudes are generally highest along this encompassed portion of 

the LC. The mode-1 CEOFs for all four frequency-bands propagate downstream along the LC 

(southeastward and southward) (Figures 3.4-14a,b). An interesting exception is the meander 

mode in the 10- to 3-day band (Figure 3.4-14b), which only partially follows the full length of 

the mean LC and then turn eastwards near 26°N to encounter the Florida shelf break. The 

CCAR-SSH CEOFs (Figure 3.4-14c) in the 100- to 40-day band are remarkably similar to the 

PIES. Like the Ekman and Franklin case studies, they indicate that the 100- to 40-day meanders 

are mainly located east of the Mississippi Fan.

Icarus CEOFs

The LC mean position during the Icarus time interval resembles the Ekman and Franklin time 

intervals. During short interval of the formation of Icarus, variability for periods longer than 20 

days is weak. Consequently CEOF modes are shown only for periods < 20 days (Figures 3.4-

15). Again, the highest frequency band (10 to 3 days) mode is strongest along the western side 

of the array, decaying in amplitude as the mode propagates clockwise along the LC. The 20- to
Franklin (a)

 159

SSHbcb mode 1: 79%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

100−40 days

phase [degrees]

% variance in 100−40 day modes

 mode 1: 79 mode 2: 15 mode 3: 4 0 120 240 360

03/03 04/22 06/11 07/31

0

20

40

[cm]

Loop Current area

2010

80

120

160

200

[103km2

]

SSHbcb mode 1: 58%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

40−20 days

phase [degrees]

% variance in 40−20 day modes

 mode 1: 58 mode 2: 21 mode 3: 11 0 120 240 360

03/03 04/22 06/11 07/31

0

10

20

[cm]

Loop Current area

2010

80

120

160

200

[103km2

]

SSHbcb mode 1: 54%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

20−10 days

phase [degrees]

% variance in 20−10 day modes

 mode 1: 54 mode 2: 21 mode 3: 9 0 120 240 360

03/03 04/22 06/11 07/31

0

10

20

[cm]

Loop Current area

2010

80

120

160

200

[103km2

]

Figure 3.4-13a. CEOFs determined from band-passed baroclinic sea-surface height referenced to the 

bottom, SSH_bcb, during the Franklin time period. Three frequency bands are shown, 

100 to 40 days, 40 to 20 days, and 20 to 10 days. Conventions same as in Figure 

3.4-12a.
Franklin (b)

Franklin (c)

 160

SSHbcb mode 1: 56%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

10−3 days

phase [degrees]

% variance in 10−3 day modes

 mode 1: 56 mode 2: 14 mode 3: 8 0 120 240 360

03/03 04/22 06/11 07/31

0

10

20

[cm]

Loop Current area

2010

80

120

160

200

[103km2

]

Altimeter mode 1: 79%

25oN

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

100−40 days

phase [degrees]

% variance in 100−40 day modes

 mode 1: 79 mode 2: 14 mode 3: 5 0 120 240 360

03/03 04/22 06/11 07/31

0

20

40

[cm]

Loop Current area

2010

80

120

160

200

[103km2

]

Figure 3.4-13b-c. (b) CEOFs determined from band-passed baroclinic sea-surface height referenced to the 

bottom, SSH_bcb during the Franklin time period. One frequency band is shown in the 

upper panel: 10 to 3 days (Mode 1). (c) CEOFs determined from 100 to 40 day bandpassed CCAR sea-surface height (cm) during the Franklin time period using the same 

conventions as in Figure 3-4-12a with Envisat ground tracks plotted with cyan lines. 
Hadal (a)

 161

SSHbcb mode 1: 85%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

100−40 days

phase [degrees]

% variance in 100−40 day modes

 mode 1: 85 mode 2: 12 mode 3: 2 0 120 240 360

04/07 05/27 07/16

0

20

40

[cm]

Loop Current area

2011

80

120

160

200

[103km2

]

SSHbcb mode 1: 66%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

40−20 days

phase [degrees]

% variance in 40−20 day modes

 mode 1: 66 mode 2: 21 mode 3: 8 0 120 240 360

04/07 05/27 07/16

0

10

20

[cm]

Loop Current area

2011

80

120

160

200

[103km2

]

SSHbcb mode 1: 50%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

20−10 days

phase [degrees]

% variance in 20−10 day modes

 mode 1: 50 mode 2: 22 mode 3: 11 0 120 240 360

04/07 05/27 07/16

0

10

20

[cm]

Loop Current area

2011

80

120

160

200

[103km2

]

Figure 3.4-14a. CEOFs determined from band-passed baroclinic sea-surface height referenced to the 

bottom, SSH_bcb, during the Hadal time period. Three frequency bands are shown, 100 

to 40 days, 40 to 20 days, and 20 to 10 days. Conventions same as in Figure 3.4-12a.
Hadal (b)

Hadal (c)

 162

SSHbcb mode 1: 36%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

10−3 days

phase [degrees]

% variance in 10−3 day modes

 mode 1: 36 mode 2: 17 mode 3: 14 0 120 240 360

04/07 05/27 07/16

0

10

20

[cm]

Loop Current area

2011

80

120

160

200

[103km2

]

Altimeter mode 1: 78%

25oN

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

100−40 days

phase [degrees]

% variance in 100−40 day modes

 mode 1: 78 mode 2: 18 mode 3: 3 0 120 240 360

04/07 05/27 07/16

0

20

40

[cm]

Loop Current area

2011

80

120

160

200

[103km2

]

Figure 3.4-14b-c. (b) CEOFs determined from band-passed baroclinic sea-surface height referenced to 

the bottom, SSH_bcb during the Hadal time period. One frequency band is shown in 

the upper panel: 10 to 3 days (Mode 1). (c) CEOFs determined from 100 to 40 day 

band-passed CCAR sea-surface height (cm) during the Hadal time period using the 

same conventions as in Figure 3.4-12a with Envisat ground tracks plotted with cyan 

lines. 
Icarus

 163

SSHbcb mode 1: 80%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

20−10 days

phase [degrees]

% variance in 20−10 day modes

 mode 1: 80 mode 2: 11 mode 3: 8 0 120 240 360

09/04 09/24 10/14

0

10

20

[cm]

Loop Current area

2011

80

120

160

200

[103km2

]

SSHbcb mode 1: 57%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

10−3 days

phase [degrees]

% variance in 10−3 day modes

 mode 1: 57 mode 2: 23 mode 3: 6 0 120 240 360

09/04 09/24 10/14

0

10

20

[cm]

Loop Current area

2011

80

120

160

200

[103km2

]

Figure 3.4-15. CEOFs determined from band-passed baroclinic sea-surface height referenced to the 

bottom, SSH_bcb, during the Icarus time period. Two frequency bands are shown, 20 to 

10 days, and 10 to 3 days. Conventions same as in Figure 3.4-12a.
164

10-day mode has a swath of elevated amplitude along the LC propagating anti-cyclonically. It 

has a slight minimum just downstream of the Mississippi Fan, and branches off to the east rather 

than accompany the LC southward.

CEOF Spatio-Temporal Summary

The strongest variability is in the 100- to 40-day band. The peak amplitudes coincide temporally 

with and persist for a cycle or two after eddy detachment and separation. Spatially these 100- to 

40-day modes are restricted to east of the Mississippi Fan, growing and propagating downstream 

along the eastern portion of the LC. There is excellent agreement between PIES-mapped and 

CCAR-SSH regarding the 10- to 40-day CEOF spatio-temporal structure. The CCAR-SSH 

amplitudes are slightly weaker and their wavelengths (and hence phase speeds) are slightly 

larger. 

Meanders between 40 and 20 days propagate along the full, encompassed length of the LC. 

Their temporal amplitudes peak at the time of eddy detachment and separation. Meanders with 

shorter periods than 20 days grow in amplitude during the one or two month interval preceeding 

eddy detachment. Judging from the difference in spatial amplitudes among the above cases, it is 

speculated that their ability to propagate along the full length of the LC may depend on the 

location of the LC. If the Loop Current is positioned to the east, flowing close to the Florida 

Shelf, then these short period (20 to 10, and 10 to 3 day) waves do not propagate southward 

along the eastern edge of the LC. But when the LC forms slightly farther to the west, the 20-10 

day meanders can follow its entire mean path. 

The highest frequency bands (20 to 10 day, and 10 to 3 day) CEOFs suggest several interesting 

scientific questions. Why don’t the high frequency meanders (< 20 days) propagate along the 

entire length of the LC? Do they slow down as they approach the northern tip of the LC? Do 

they undergo a non-linear eddy rectification process? Do the high frequency meanders feed the 

downstream growth of lower frequency meanders, which peak later during the eddy detachment 

and separation process? 

CEOF Phases – Meander Wavenumbers and Phase Speeds

Figure 3.4-16 and Table 3.4-2 show the wavenumber and phase speed estimates from the CEOF 

analysis. Wavenumber is determined by calculating the amplitude of the spatial phase gradient 

(δφ/δs, where φ is phase and s is distance). For each CEOF, the spatial phase gradient is 

calculated for regions where the corresponding spatial amplitude is greater than 0.5. Phase speed 

is determined by 2πω (δs/δφ) where ω is the central frequency of the band-passed frequency. 

The wavenumber-speed dispersion relationship for Loop Current meanders agrees particularly 

well at wavelengths longer than 300 km with that for Gulf Stream (GS) meanders in the region 

northeast of Cape Hatteras (Kontoyiannis and Watts 1994; Lee and Cornillon 1996). The shortperiod (10 to 3 day) LC meanders have somewhat longer wavelengths and higher phase speeds 

than their counterparts in the GS. In both regions, the dispersion relation resembles a parabolic 

shape, c = Ak2 – B, as is consistent with a simple 1 1⁄2 layer analytical thin-jet prediction by 

Cushman-Rosin et al. (1993). The constant B is similar for the LC and GS cases, governed 

mainly by the beta effect. The constant A for the LC appears to be somewhat larger than for the 

GS, and this would be consistent with the lower latitude and smaller cross-stream change in
0 0.01 0.02 0.03 0.04

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

phase speed [ms−1]

wavenumber [km−1]

 628 314 209 157 

Lee and Cornillon 1997

Kontoyiannis and Watts 1994

Altimeter

PIES

 165

 wavelength [km]

Figure 3.4-16. Wavenumber (km-1) versus phase speed (ms-1). Values are determined from the phase 

information in the CEOFS (Figures 3.4-12 through 3.4-15). Wavelengths are noted along 

the upper edge of the plot. PIES mapped SSH_bcb estimates (CCAR sea-surface 

height) shown by blue triangles (red plusses). Horizontal lines indicate standard deviation. Estimates from Lee and Cornillon (1996) and Kontoyiannis and Watts (1994) for the 

Gulf Stream (gray triangles) are also included. 
166

thermocline depth in the LC than in the GS. Altimeter estimates produce slightly longer 

wavelengths and correspondingly faster phase speeds than from the PIES maps.

Table 3.4-2. Average Propagation Speeds Determined from the CEOF Analysis

Period (days) Wavenumber

(rad km-1)

Wavelength

(km)

Phase Speed

(km day-1)

57.14 PIES 0.0121 518 9.1

0.0150 419 7.3

0.0136 463 8.1

57.14 CCAR-ALT 0.0115 544 9.5

0.0129 486 8.5

0.0109 576 10.1

26.67 0.0182 345 12.9

0.0151 417 15.6

0.0177 355 13.3

0.0202 311 11.7

13.33 0.0245 257 19.2

0.0249 252 18.9

0.0222 284 21.3

0.0207 304 22.8

4.62 0.0278 226 48.9

0.0271 232 50.2

0.0306 205 44.5

0.0247 255 55.2

3.4.4 Horizontal Variability in the Lower Layer

In contrast to the broad anticyclonic mean flow observed in the upper ocean, the mean deep 

circulation exhibits more structure (Figure 3.4-17). Along the western side of the array, an 

anticyclonic gyre with ~200 km lateral extent is centered near B1 (26.3°N, 87.3°W) with mean 

speeds near 6 cm s

-1

. To the east, a weaker cyclonic gyre, speeds near 3 cm s

-1

, is centered near 

C2 (26.2°N, 85.7°W). These gyres were discussed in Section 3.4.1 using means from the lowerlayer current meters. Along the southern boundary of the array, mean flow is to the northwest. 

Standard deviation ellipses are mainly isotropic with a tendency for more elongated ellipses 

along the West Florida Shelf (D2: 26.4°N, 87.9°W). 
24o

N

26o

N

28o

N

89o

W 87 oW 85 oW

10 cms−1

mean Loop Current

(a) near−bottom eddy kinetic energy [cm 2

 s−2]

0 40 80 120 160

100

200

300

[cm 2 s−2]

 (b) Near−bottom eddy kinetic energy

Ek nam narF klin aH d la

0

10

20

30

(c) Array−average SSH

[cm]

Jul2009 Jan2010 Jul2010 Jan2011 Jul2011

100

150

200 (d) Loop Current area

[103km2

]

 167

Figure 3.4-17. (a) Near-bottom mapped and directly-measured mean currents (thin and bold vectors, 

respectively). Standard-deviation ellipses superimposed on the time-mean near-bottom 

eddy kinetic energy (color-bar). Scale for vectors and elipses shown in lower left corner. 

Red line denotes the mean Loop Current position defined by the CCAR SSH 17-cm 

contour. Bathymetry plotted with gray contours every 500-m depth. Time mean is taken 

over the 30-month experiment duration from 3 May 2009 through 23 October 2011. (b) 

Time series of array-averaged near-bottom eddy kinetic energy. (c) Time series of 

array-average CCAR SSH. (d) Loop Current area. 
168

Elevated time-mean EKE is found beneath the mean position of the LC (Figure 3.4-17). This 

swath of high EKE can be traced from the Mississippi Fan, where it is offset slightly to the north 

of the mean LC position, across the array to the southeast where the EKE maxima lies slightly 

westward of the LC. Highest-mean EKE values occur in the central portion of the array (26.2°N, 

86.5°W) and the southeast corner (25.3°N, 86.0°W). Array-averaged EKE also shows the 

influence of the LC. Values are enhanced during LC-eddy-shedding events (Figure 3.4-17). 

During Ekman, Franklin, and Hadal peak EKE occurs at or near the first eddy detachment. An 

additional EKE peak occurs in June 2011 – during this time, the LC necks down but does not 

form a LC eddy.

In contrast to the upper ocean, there is proportionally more energy in the high-frequency bands 

(Figure 3.4-18): 72 % of the variance is in periods shorter than 100 days. Within the 100- to 3-

day mesoscale band, variance is distributed as follows: 57% within 100 to 40 day, 24% within 40 

to 25 day, 12% within 25 to 16 day and 7% within 16 to 3 day. By casting the upper and deep 

circulation in terms of sea surface height, one can compare the relative contributions of upper 

and deep variance to total sea surface height. Deep, SSH_ref, variance is only 2% of the upper 

SSH_bcb variance. This proportionality increases slightly to 10% for periods shorter than 100

days. However, the CEOF depth analysis of the velocities in Section 3.4.2 indicates that the 

lower water column below ~ 1000 m may have higher total depth-integrated EKE because of the 

greater thickness of the lower water column and the lack of depth variability of the currents.

Similar to the upper ocean, the spatial structure of the variance changes as a function of 

frequency band (Figure 3.4-18). Within the highest frequency band, 16 to 3 days, elevated 

values occur along the base of the Mississippi Fan in the northwest portion of the array. As 

frequency decreases, this ridge of high variance shifts to the southeast within the array. In the 

lowest frequency band, 100 to 40 days, the spatial pattern resembles the time-mean EKE (Figure 

3.4-17). 

Figure 3.4-19 shows the time series of SSH_ref variance as a function of frequency band. 

Similar to the array-average EKE shown in Figure 3.4-17, variance is also elevated during LC 

eddy events within each band. During each LC eddy event, peak variance tends to occur at 

successively later times as the frequency band increases. This contrasts the upper ocean where 

high-frequency variability preceded low-frequency variability. Because the juxtaposition of the 

LC, LC eddies, and the array, dictate the timing of observed elevated deep energy, a case-based 

CEOF analysis was performed. The focus of the CEOF analysis is on three time intervals that 

span the peaks in the four frequency bands that are designated, Ekman_deep, Franklin_deep and 

Hadal_deep to distinguish them from the time intervals used in the LC meander results. Loop 

current positions during these time intervals are shown in Figures 3.4-20, 3.4-21, and 3.4-22. 

Corresponding CEOF results are shown in Figures 3.4-23, 3.4-24 and 3.4-25, respectively. 

Ekman_deep and Franklin_deep CEOF case studies are remarkably similar in their spatial 

structure, phase speeds and propagation as well as timing relative to LC eddy detachments 

(Figures 3.4-23 and 3.4-24).
Total

25o

N

26o

N

27o

N

88o

W 86 oW 84 oW

 a

100 to 40 days

 b

40 to 25 days

 c

25 to 16 days

25o

N

26o

N

27o

N

88o

W 86 oW 84 oW

 d

16 to 3 days

 e

SSHref, barotropic, p3000/(ρ g), sea surface height standard deviation [cm]

0 0.4 0.8 1.5 4

Figure 3.4-18. Standard deviation of reference sea-surface height (SSH_ref) as a function of frequency band. SSH_ref is the 3000-dbar pressure 

converted to a height equivalent (pressure anomaly divided by gravity and density). Upper left (a): Total variance. Four right 

panels (b-e): Standard deviation in four frequency bands noted in the title of each panel. Bathymetry contoured in grey every 

500-m depth. Note that the color contour interval is not uniform.

169 
100

150

200

[103km2

]

 Loop Current area

 a

0

20

40

[cm]

 array−mean ssh

 bold−altimeter

 b

5

10

15

[cm2

]

 SSHref 100−40 day

 variance in frequency bands

Ekmandeep Franklindeep Hadaldeep

 c

2

4

6

[cm2

]

 SSHref 40−25 day

 d

2

4

6

[cm2

]

 SSHref 25−16 day

 e

2009 2010 2011 2012

2

4

6

8

10

[cm2

]

 SSHref 16−3 day

 f

 170

Figure 3.4-19. (a) Loop Current area. (b) Array-mean baroclinic sea-surface height referenced to the 

bottom, SSH_bcb (thin line) and CCAR sea-surface height (bold line). The mean of the 

baroclinic sea-surface height referenced to the bottom has been adjusted to match the 

CCAR sea-surface height. (c-f) Variance of array-averaged reference sea-surface height, 

SSH_ref, within frequency bands, as noted in the title of each panel. Grey-filled boxes 

correspond to the time period over which complex empirical orthogonal functions have 

been calculated.
 May.01 May.08 May.15 May.22 May.29

24oN

25o

N

26o

N

27o

N

28o

N

88o

W 86oW 84oW

 Jun.05 Jun.12 Jun.19 Jun.26 Jul.03

Ekmandeep 02−May−2009 to 30−Nov−2009

 Jul.10 Jul.17 Jul.24 Jul.31 Aug.07

 Aug.14 Aug.21 Aug.28 Sep.04 Sep.11

24oN

25o

N

26o

N

27o

N

28o

N

88o

W 86oW 84oW

 Sep.18 Sep.25 Oct.02 Oct.09 Oct.16 Oct.23 Oct.30 Nov.06 Nov.13 Nov.20

 171

Figure 3.4-20. CCAR SSH-determined Loop Current positions during Ekman_deep CEOF time period. 

For each panel, the position of the 17-cm contour is plotted every seven days and color 

coded by date, as noted at top of each panel. Location of the PIES represented by open 

blue circles. The mean Loop Current position is shown by the bold black line. Bathymetry 

contoured every 500-m depth.
 Jan.30 Feb.06 Feb.13 Feb.20 Feb.27

24oN

25o

N

26o

N

27o

N

28o

N

88o

W 86oW 84oW

 Mar.06 Mar.13 Mar.20 Mar.27 Apr.03

Franklindeep 31−Jan−2010 to 31−Oct−2010

 Apr.10 Apr.17 Apr.24 May.01 May.08

 May.15 May.22 May.29 Jun.05 Jun.12

24oN

25o

N

26o

N

27o

N

28o

N

88o

W 86oW 84oW

 Jun.19 Jun.26 Jul.03 Jul.10 Jul.17 Jul.24 Jul.31 Aug.07 Aug.14 Aug.21

 Aug.28 Sep.04 Sep.11 Sep.18 Sep.25

24oN

25o

N

26o

N

27o

N

28o

N

88o

W 86oW 84oW

 Oct.02 Oct.09 Oct.16 Oct.23 Oct.30

 172

Figure 3.4-21. CCAR SSH-determined Loop Current positions during Franklin_deep CEOF time period. 

For each panel, the position of the 17-cm contour is plotted every seven days and color 

coded by date, as noted at top of each panel. Location of the PIES represented by open 

blue circles. The mean Loop Current position is shown by the bold black line. Bathymetry contoured every 500-m depth.
 Feb.27 Mar.06 Mar.13 Mar.20 Mar.27

24oN

25o

N

26o

N

27o

N

28o

N

88o

W 86oW 84oW

 Apr.03 Apr.10 Apr.17 Apr.24 May.01

Hadaldeep 28−Feb−2011 to 31−Aug−2011

 May.08 May.15 May.22 May.29 Jun.05

 Jun.12 Jun.19 Jun.26 Jul.03 Jul.10

24oN

25o

N

26o

N

27o

N

28o

N

88o

W 86oW 84oW

 Jul.17 Jul.24 Jul.31 Aug.07 Aug.14

 173

Figure 3.4-22. CCAR SSH-determined Loop Current positions during Hadal_deep CEOF time period. 

For each panel, the position of the 17-cm contour is plotted every seven days and color 

coded by date, as noted at top of each panel. Location of the PIES represented by open 

blue circles. The mean Loop Current position is shown by the bold black line. Bathymetry contoured every 500-m depth.
 174

SSHref mode 1: 72%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

Ekmandeep

amplitude

0 0.4 0.8

100−40 days

phase [degrees]

% variance in 100−40 day modes

 mode 1: 72 mode 2: 20 mode 3: 7 0 120 240 360

05/07 08/15 11/23

0

5

10

[cm]

Loop Current area

2009

0

100

200

[103km2

]

SSHref mode 1: 83%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

40−25 days

phase [degrees]

% variance in 40−25 day modes

 mode 1: 83 mode 2: 14 mode 3: 2 0 120 240 360

05/07 08/15 11/23

0

5

10

[cm]

Loop Current area

2009

0

100

200

[103km2

]

SSHref mode 1: 69%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

25−16 days

phase [degrees]

% variance in 25−16 day modes

 mode 1: 69 mode 2: 19 mode 3: 7 0 120 240 360

05/07 08/15 11/23

0

1

2

3

4

[cm]

Loop Current area

2009

0

50

100

150

200

[103km2

]

SSHref mode 1: 65%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

16−3 days

phase [degrees]

% variance in 16−3 day modes

 mode 1: 65 mode 2: 12 mode 3: 7 0 120 240 360

05/07 08/15 11/23

0

5

[cm]

Loop Current area

2009

0

200

[103km2

]

Figure 3.4-23. CEOFs determined from band-passed deep reference sea-surface height, SSH_ref, 

during the Ekman_deep time period. Four frequency bands are shown. For each CEOF, 

left panel: normalized spatial amplitude, middle panel: phase in degrees, right panel: 

amplitude time series in cm. In the left panel, in addition to the mode amplitudes (blue), 

the mean position of the LC (17-cm contour) during the time interval of the CEOF is 

represented by the red line. In the middle panel, phase is plotted for regions where the 

spatial amplitude exceeds 0.5. Propagation is in the direction of increasing phase. 

Bathymetry is contoured every 1000-m depth. In the right panel, mode time series is 

blue; Loop Current area is red. 
 175

SSHref mode 1: 87%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

Franklindeep

amplitude

0 0.4 0.8

100−40 days

phase [degrees]

% variance in 100−40 day modes

 mode 1: 87 mode 2: 7 mode 3: 3 0 120 240 360

03/03 06/11 09/19

0

5

10

15

20

[cm]

Loop Current area

2010

0

50

100

150

200

[103km2

]

SSHref mode 1: 75%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

40−25 days

phase [degrees]

% variance in 40−25 day modes

 mode 1: 75 mode 2: 17 mode 3: 5 0 120 240 360

03/03 06/11 09/19

0

5

10

[cm]

Loop Current area

2010

0

100

200

[103km2

]

SSHref mode 1: 60%

25oN

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

25−16 days

phase [degrees]

% variance in 25−16 day modes

 mode 1: 60 mode 2: 22 mode 3: 9 0 120 240 360

03/03 06/11 09/19

0

1

2

3

4

[cm]

Loop Current area

2010

0

50

100

150

200

[103km2

]

SSHref mode 1: 55%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

16−3 days

phase [degrees]

% variance in 16−3 day modes

 mode 1: 55 mode 2: 15 mode 3: 10 0 120 240 360

03/03 06/11 09/19

0

1

2

3

4

[cm]

Loop Current area

2010

0

50

100

150

200

[103km2

]

Figure 3.4-24. CEOFs determined from band-passed deep reference sea-surface height, SSH_ref, 

during the Franklin_deep time period. Conventions are the same as in Figure 3.4-23.
 176

SSHref mode 1: 90%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

Hadaldeep

amplitude

0 0.4 0.8

100−40 days

phase [degrees]

% variance in 100−40 day modes

 mode 1: 90 mode 2: 6 mode 3: 3 0 120 240 360

04/07 05/27 07/16

0

5

10

15

20

[cm]

Loop Current area

2011

100

150

200

250

300

[103km2

]

SSHref mode 1: 84%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

40−25 days

phase [degrees]

% variance in 40−25 day modes

 mode 1: 84 mode 2: 12 mode 3: 4 0 120 240 360

04/07 05/27 07/16

0

2

4

[cm]

Loop Current area

2011

100

140

180

220

260

300

[103km2

]

SSHref mode 1: 81%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

25−16 days

phase [degrees]

% variance in 25−16 day modes

 mode 1: 81 mode 2: 10 mode 3: 7 0 120 240 360

04/07 05/27 07/16

0

5

10

[cm]

Loop Current area

2011

100

200

300

[103km2

]

SSHref mode 1: 81%

25o

N

26o

N

27o

N

88o

W 86oW 84oW

amplitude

0 0.4 0.8

16−3 days

phase [degrees]

% variance in 16−3 day modes

 mode 1: 81 mode 2: 9 mode 3: 3 0 120 240 360

04/07 05/27 07/16

0

5

10

15

20

[cm]

Loop Current area

2011

100

150

200

250

300

[103km2

]

Figure 3.4-25. CEOFs determined from band-passed deep reference sea-surface height, SSH_ref, 

during the Hadal_deep time period. Conventions are the same as in Figure 3.4-23.
177

Ekman_Deep and Franklin_Deep 100 to 40 Day Band

Ekman_deep and Franklin_deep CEOF-mode amplitudes grow to maxima during detachments. 

The spatial modes reveal a high amplitude ridge extending north-to-south along the eastern side 

of the array. These modes propagate anticyclonically with phase speeds near 7 km day-1

, and 

wave number near 0.015 km-1

. A noticeable phase speed increase is apparent in the southeast 

near where the LC necks down. 

Ekman_Deep and Franklin_Deep 40 to 25 Day Band

The 40- to 25-day CEOF mode also peaks during the LC eddy detachments, but at a slightly later 

time than the 100- to 40-day band. This mode propagates anticyclonically within the array. 

Phase speeds are near 10 km day-1

, and wave number near 0.02 km-1. The 100- to 40- and 40- to 

25-day band-passed SSH_ref data are separately mapped every seven days for the time intervals 

when these modes have high amplitudes within the Franklin_deep time interval (Figures 3.4-26 

and 3.4-27). These map sequences are next examined together with the CEOF analysis to 

elucidate the close relationship between the nearly depth-independent mode and the eddyformation process in the LC.

Prior to the first detachment, a deep anticyclone-cyclone pair propagates along the LC. As they 

move southward, both features intensify jointly with a growing upper meander crest and trough 

along the eastern edge of the LC. On 9 July 2010, the deep strong cyclone is positioned at the 

southernmost extent of the array, near 25.3°N, 86.0°W. While the ultimate fate of this feature is 

unknown, due to the array’s limited spatial extent, it is speculated that this deep cyclone 

facilitates Franklin’s first detachment and the trailing deep anticyclone aids the subsequent 

reattachment that occurs 1 August 2010. During this same Franklin_deep time interval, in the 

40- to 25-day band, several cyclones and anticyclones move successively along the LC from the 

northwest corner to the central portion of the array, and they continue on an anticyclonic path 

southwestward to cross the LC. The passage of the strong anticyclone-cyclone pair occurs 8 

August to 7 September 2010, just prior to and during the final separation of eddy Franklin. 

Ekman_Deep and Franklin_Deep 25 to 16 Day Band

These mode amplitudes peak after LC eddy separation. The spatial structure is slightly different 

between the Ekman_deep and Franklin_deep. The Ekman_deep pattern has two maxima, one 

along the Mississippi Fan propagating slightly down-slope and another along the southern 

portion of the array propagating northwestward. The Franklin_deep pattern also has two maxima, 

one along the Mississippi Fan and another extending from the southern portion with 

northwestward propagation. The Franklin_deep amplitude is slightly greater in the array interior 

compared to Ekman_deep, revealing connected propagation across the array. Phase speeds in 

this band are near 20 km day-1

, and wave number = 0.016 km-1.

Ekman_Deep and Franklin_Deep 16 to 3 Day Band

In this highest-frequency band, both Ekman_deep and Franklin_deep have their largest mode 

amplitudes along the Mississippi Fan with southwest along-slope propagation. Phase speeds are 

rapid, near 60 km day-1

, and wave numbers are between 0.016 and 0.020 km-1. As noted in 

Hogg (2000), while shorter-wavelength (<100 km) topographic Rossby waves would have a
15 JUN 2010

25°N

26°N

27°N

21 JUN 2010 27 JUN 2010 3 JUL 2010

9 JUL 2010

25°N

26°N

27°N

15 JUL 2010 21 JUL 2010 27 JUL 2010

2 AUG 2010

25°N

26°N

27°N

8 AUG 2010 14 AUG 2010 20 AUG 2010

26 AUG 2010

88°W 86°W 84°W

25°N

26°N

27°N

−24 −16 −8 0 8 16

SSHref [cm]

1 SEP 2010

88°W 86°W 84°W

7 SEP 2010

88°W 86°W 84°W

13 SEP 2010

frequency: 100−40

88°W 86°W 84°W

 178

Figure 3.4-26. Snapshots of 100 to 40 day band-passed deep reference sea-surface height (SSH_ref) 

for a portion of the Franklin_deep time interval. The date of each snapshot is given in 

each panel title. In each panel, the location of the CCAR SSH 17-cm contour is plotted 

with a bold black line. Color bar in the lower left corner notes the SSH_ref contour 

interval in cm. The 3000-m depth isobath is shown by the grey contour. 
15 JUN 2010

25°N

26°N

27°N

21 JUN 2010 27 JUN 2010 3 JUL 2010

9 JUL 2010

25°N

26°N

27°N

15 JUL 2010 21 JUL 2010 27 JUL 2010

2 AUG 2010

25°N

26°N

27°N

8 AUG 2010 14 AUG 2010 20 AUG 2010

26 AUG 2010

88°W 86°W 84°W

25°N

26°N

27°N

−24 −16 −8 0 8 16

SSHref [cm]

1 SEP 2010

88°W 86°W 84°W

7 SEP 2010

88°W 86°W 84°W

13 SEP 2010

frequency: 40−25

88°W 86°W 84°W

 179

Figure 3.4-27. Snapshots of 40 to 25 day band-passed deep reference sea-surface height (SSH_ref) for 

a portion of the Franklin_deep time interval. The date of each snapshot is given in each 

panel title. In each panel, the location of the CCAR SSH 17-cm contour is plotted with a 

bold black line. Color bar in the lower left corner notes the SSH_ref contour interval in 

cm. The 3000-m depth isobath is shown by the grey contour. 
180

high-frequency cutoff around a 30-day period in this region, these longer-wavelength features 

(~300 to 400 km) are only weakly bottom trapped and resemble barotropic-topographic Rossby 

waves, which can support much shorter period variability. 

It is worth noting that in both high-frequency bands, the upper-ocean (SSH_bcb) and nearly 

depth-independent mode (SSH_ref) signals are strongest along the northwest corner of the array, 

along the Mississippi Fan, yet the phase propagation is in the opposite sense: northeastward in 

the SSH_bcb fields; southwestward in the SSH_ref fields.

Hadal_Deep 100 to 40 Day Band 

Hadal_deep 100- to 40-day spatial mode shows anticyclonic propagation (Figure 3.4-25). Phase 

speeds and wavenumbers are similar to Ekman_deep and Franklin_deep. Also similar to 

Ekman_deep and Franklin_deep is the slight increase in phase speed where the LC necks down 

near 25.5°N, 87.0°W. The temporal amplitudes peak about a month prior to Hadal separation. 

The sequence of mapped SSH_ref for this frequency band (Figure 3.4-28) shows that as cyclones 

and anticyclones move off the Mississippi Fan, they further intensify. These long-period deep 

cyclones interact with and jointly intensify with an upper-layer trough in the LC. For example, 

the LC develops a steep trough as the cyclones move through the array during 15 to 22 May 

2011 and 10 to 24 July 2011, however, no LC eddy detachment occurs during these two LC 

neck-downs. 

Hadal_Deep 40 to 25 Day Band

The 40- to 25-day variability exhibits the signature of baroclinic instability, as exemplified by 

deep cyclones leading upper troughs on 1 to 15 May 2011 and 10 to 24 July 2011, and by a deep 

anticyclone leading an upper crest on 10 to 24 July 2011 (Figure 3.4-29). These features jointly 

intensify in the region just downstream of the Mississippi Fan. Nevertheless, the amount of 

steepening in these cases was not sufficient to close the LC neck and cause a LC eddy 

detachment. The mode amplitude peaks well in advance of Hadal detachments, propagation is

anticyclonic and mainly along or very close to the mean path of the LC during this time interval 

(Figure 3.4-25). 

Hadal_Deep 25 to 16 Day and 16 to 3 Day Band

In several respects, the 25- to 16-day and 16- to 3-day CEOFs for the Hadal_deep time interval 

closely resemble Ekman_deep and Franklin_deep: spatial amplitudes and phases indicate 

southwestward propagation along the base of the Mississippi Fan (Figure 3.4-25). In 

severalother respects, these frequency bands differ from Ekman_deep and Franklin_deep: the 

Hadal_deep amplitudes are larger (see also bottom two panels of Figure 3.4-19), and in the 25- to 

16-day band the CEOF maximum amplitude coincides in time and space with Hadal’s 

separation. This is clearly shown in Figure 3.4-30, for 26 June 2011 through 14 August 2011. 

Note that as the deep cyclones and anticyclones propagate along the Mississippi Fan, they 

intensify and after the passage of a strong cyclone on 7 August 2011, Hadal separates.
1 MAY 2011

25°N

26°N

27°N

8 MAY 2011 15 MAY 2011 22 MAY 2011

29 MAY 2011

25°N

26°N

27°N

5 JUN 2011 12 JUN 2011 19 JUN 2011

26 JUN 2011

25°N

26°N

27°N

3 JUL 2011 10 JUL 2011 17 JUL 2011

24 JUL 2011

88°W 86°W 84°W

25°N

26°N

27°N

−24 −16 −8 0 8 16

SSHref [cm]

31 JUL 2011

88°W 86°W 84°W

7 AUG 2011

88°W 86°W 84°W

14 AUG 2011

frequency: 100−40

88°W 86°W 84°W

 181

Figure 3.4-28. Snapshots of 100 to 40 day band-passed deep reference sea-surface height (SSH_ref) 

for a portion of the Hadal_deep time interval. The date of each snap-shot is given in 

each panel title. In each panel, the location of the CCAR SSH 17-cm contour is plotted 

with a bold black line. Color bar in the lower left corner notes the SSH_ref contour 

interval in cm. The 3000-m depth isobath is shown by the grey contour. 
1 MAY 2011

25°N

26°N

27°N

8 MAY 2011 15 MAY 2011 22 MAY 2011

29 MAY 2011

25°N

26°N

27°N

5 JUN 2011 12 JUN 2011 19 JUN 2011

26 JUN 2011

25°N

26°N

27°N

3 JUL 2011 10 JUL 2011 17 JUL 2011

24 JUL 2011

88°W 86°W 84°W

25°N

26°N

27°N

−24 −16 −8 0 8 16

SSHref [cm]

31 JUL 2011

88°W 86°W 84°W

7 AUG 2011

88°W 86°W 84°W

14 AUG 2011

frequency: 40−25

88°W 86°W 84°W

 182

Figure 3.4-29. Snapshots of 40 to 25 day band-passed deep reference sea-surface height (SSH_ref) for 

a portion of the Hadal_deep time interval. The date of each snap-shot is given in each 

panel title. In each panel, the location of the CCAR SSH 17-cm contour is plotted with a 

bold black line. Color bar in the lower left corner notes the SSH_ref contour interval in cm. 

The 3000-m depth isobath is shown by the grey contour. 
1 MAY 2011

25°N

26°N

27°N

8 MAY 2011 15 MAY 2011 22 MAY 2011

29 MAY 2011

25°N

26°N

27°N

5 JUN 2011 12 JUN 2011 19 JUN 2011

26 JUN 2011

25°N

26°N

27°N

3 JUL 2011 10 JUL 2011 17 JUL 2011

24 JUL 2011

88°W 86°W 84°W

25°N

26°N

27°N

−24 −16 −8 0 8 16

SSHref [cm]

31 JUL 2011

88°W 86°W 84°W

7 AUG 2011

88°W 86°W 84°W

14 AUG 2011

frequency: 25−16

88°W 86°W 84°W

 183

Figure 3.4-30. Snapshots of 25 to 16 day band-passed deep reference sea-surface height (SSH_ref) for 

a portion of the Hadal_deep time interval. The date of each snap-shot is given in each 

panel title. In each panel, the location of the CCAR SSH 17-cm contour is plotted with a 

bold black line. Color bar in the lower left corner notes the SSH_ref contour interval in 

cm. The 3000-m depth isobath is shown by the grey contour. 

185

CHAPTER 4: DYNAMICS 

4.1 INTRODUCTION

This chapter investigates LC physical processes, including frontal cyclones, the development of 

large-scale meanders, deep eddies and topographic Rossby waves (TRWs), and attempts to relate 

them generation mechanisms such as baroclinic instabilities. The role of topography is important 

both as a constraint on the flows, but also through topographic slopes, the generation of lowerlayer eddies and waves. The emphasis will be on meso-scale variability that is resolved by the 

arrays. Discussion of longer time scales than 1-2 years, and the role of external influences from 

the Caribbean and Atlantic is given in Chapter 5. As before, the interface between the upper and 

lower layers is taken to be the depth of the 6 °C isotherm (Bunge et al. 2002), and much of the 

analysis will make use of vertical relative vorticity (ζ) fields. The calculation of ζfrom plane fits 

to 40-HLP velocity components, at a given depth level, is given in Chapter 2, and the locations 

of the ζ-points were given earlier in Figure 2.9-2 where they are similar, and similarly numbered, 

to the equivalent PIES position. Because the CICESE N-transect plus A4, B3 and C1 tall 

moorings span the LC from the Campeche Bank almost to the west Florida escarpment, it allows 

simultaneous examination of processes on both the east and west sides of an extended LC. This 

section will be referred to as the N1-C1 transect.

4.2 RELATIVE VORTICITY, UPWELLING AND LC EDDY SEPARATIONS

The array area-averaged EKE, deviations of ζ from the mean at 200 m and 100 mab, and vertical 

velocity at 900 m, are given in Figure 4.2-1. The EKE time series are equivalent to the 

baroclinic and barotropic variability discussed in Chapter 3 and show marked increases in EKE 

for the lower layer during eddy detachments (as for Ekman and Franklin) or just prior to eddy 

detachments (as for Hadal). There are also increases in lower-layer ζ′ fluctuations for these 

events with periodicities ~40 to 60 days. Whereas the bottom EKE decreases rapidly to a low 

level after separation, the ζ′ fluctuations decay more slowly. In the upper layer, ζ′

 

is bi-modal, 

being negative (anticyclonic) during the later growth stages where the LC is over the array, with 

an abrupt shift to cyclonic when an eddy detaches. Again Hadal differs from the previous two 

eddies in that the large pulses of positive ζ′, and increases in lower-layer EKE occur before the 

separation and roughly correspond to episodes of large east-side meander activity discussed in 

the previous chapter. At 200 m, intervals of positive and negative ζ′ have similar magnitudes 

(~0.1f), indicating that when the LC or LC eddy is not present, cyclonic flows predominate, even 

though they have lower velocities and EKE than the LC. This implies that when the LC is 

absent, smaller scale (compared to the LC) cyclonic eddies predominate. It is noteworthy that 

for Franklin and Hadal, the first switch from negative to positive ζ′ at 200 m corresponds to a 

positive pulse of ζ′ in the lower layer and a large increase in lower-layer EKE and to some extent 

an increase in upper-layer EKE, indicating that stronger layer coupling occurs or is initiated at 

these times. Something similar happens for Ekman except that the positive ζ′ pulse and less 

abrupt increase in EKE in the lower layer precede the upper layer switch to positive ζ′.

Chang and Oey (2010b) derive a canonical eddy-separation scenario and its coupling with the 

deep flows by using the numerical model in a free running mode with no surface forcing and 

invariant boundary conditions. In this mode, the model sheds eddies at regular intervals of 8.1
LC Area & Area + Eddy

Ekman Franklin Hadal

200 m

200 m

900 m

100 mab

100 mab

cm2 s-2 cm2 s-2 m/day

Fractional

f

Fractional

f 103 km2

EKE

EKE

ζ

ζ

w

Figure 4.2-1. Array averaged relative vorticity anomaly (ζ′), eddy kinetic energy (EKE) at 200 m and 100 mab, with area averaged 7-DLP 

vertical velocities (w) at 900 m. LC area (green) and LC+Eddy area (blue) are given in the top panel to show LC growth and eddy 

deatchments.

186 
187

months and a total of 12 shedding events were combined for the analysis. Chang and Oey (2011) 

use a control volume approach with an interface between the upper and lower layers at 1000 m, 

and a division between the east and west basins of the Gulf at 90°W. Transports through these 

interfaces, including the upper and lower layers at the Yucatan Channel, were generated from the 

model outputs. The LC cycle was divided into three stages. Stage A is “Loop-reforming” with 

downward flux and deep divergence under the LC. Stage B is “incipient-shedding” with strong 

upward flux and deep convergence. Stage C is “eddy-migration” with waning upward flux and 

deep through flow from the western Gulf into the Yucatan Channel. Because of the strong deep 

coupling between the eastern and western Gulf, the LC expansion is poorly correlated with deep 

flows through the Yucatan Channel. This pattern of transports is sketched in Figure 4.2-2. The 

mean vertical flux due to the Loop Current Cycle is downward, so that since the net circulation 

around the abyssal basin is zero, the deep Gulf’s gyre must be cyclonic. Observations indicate 

that the deep circulation in the western Gulf is cyclonic (DeHaan and Sturges 2005; Hamilton 

2009). The gyre’s strength is strongest when the LC is reforming, and weakest after an eddy is 

shed. The numerical study suggests that the LC Cycle can force a surprisingly strong, low 

frequency (shedding periods) abyssal oscillation in the Gulf of Mexico.

Examination of the average vertical velocity for the array at 900 m gives some support to Chang 

and Oey’s (2011) results for stage B. Both Ekman and Hadal show intervals of upwelling when 

the eddy or the extended LC moves off to the west. For Ekman, August-September 2009 has 

sustained upward velocities that slightly precede the upper-layer ζ′ switching from negative to 

positive (marked by dashed event lines in Figure 4.2-1). Similarly for Hadal, the three large 

upwelling events, beginning in the middle of April 2011, also correspond to positive ζ′ pulses 

that in turn correspond to Hadal events that extend the LC to the northwest and away from the 

array, and thus towards or into the western Gulf. The third upwelling event in August 2011 

corresponds to the separation of Hadal. Because Franklin essentially faded away after 

separation, the Chang and Oey (2011) scenario does not apply and any upwelling flux would be 

weak and is not definitively observed in the vertical velocity (w) time series. The mean of w

over the 2.5 years is -0.52 ± 0.7 m d-1

, which corresponds to a net downwelling under the LC for 

the experimental period. Moreover, for the intervals during Franklin and Hadal where the area 

average relative vorticity is negative (Figure 4.2-1), the calculated average w’s are also negative 

(-0.5 ± 1.4 and -3.7 ± 2.0 m d-1, respectively), lending support to the idea that the extending LC 

generates a downward mass flux to the lower layer of the Gulf. 

4.3 LOOP CURRENT FRONTAL VARIABILITY

The east-west excursions of the front, as given by the 17-cm SSH contour, were found to differ 

in amplitude and characteristic wavelengths between the east and west side of an extended LC. 

The discussion in the previous chapter centered on detachments and separations of the three 

eddies. In general, when the LC is extended into the Gulf, the front along the Campeche Bank 

shows only small displacements until a separation event occurs, but the east side often develops 

large scale (~300 km wavelength), large amplitude meanders with periods of ~40 to 60 days that 

propagate south or southeastwards towards the Florida Straits. The consistency of the 

wavelength and periods of the east-side meanders for the three eddy shedding events do not have 

an explanation at this time, though vortex instabilities are a possible process. This section 

examines the variability along the extended LC front in more detail.
188

Figure 4.2-2. A schematic illustration of the three stages of the LC cycle. Lower box shows the mass 

balance in the deep control volume bounded by 90°W, the Yucatan Channel, and the 

depth of z = -1000 m. Arrows and symbol circles indicate the directions and 

(approximate) magnitudes of the transports. Yellow shading indicates a closed boundary. 

Projected upper layer shows the condition of the LC during stage (A) Loop reforming, (B) 

incipient eddy-shedding, and (C) westward eddy migration across 90°W (from Chang and 

Oey 2011). 
189

The depth of the 6 °C isotherm along the N1-C1 transect is given in Figure 4.3-1. The location

of fronts along the transect are overlaid and show a close correspondence with the 800-850 m 

isotherm depth contour. The isotherm depths are constructed from both the moorings and the 

PIES temperature profiles to increase the horizontal resolution, and because the PIES locations 

are not exactly on the transect, and differences in vertical resolution between mooring-based 

temperature sensors and acoustic travel-time-derived temperature profiles, there are some bulls 

eyes in the plot. However, the major features are well observed and include a clear northeast to 

southwest propagation of isotherm depth signal during the warm intervals when the LC is 

present. The periodicity of these fluctuations is about 40 days and the propagation time from C1 

to N4 is around one to two months. Water depth increases from C1 to N4 by about 250 m, and 

thus phase propagation along the depth gradient could suggest TRWs with group velocities 

towards the northwest. Hamilton (2009), using data from a long-term mooring (L7) deployed 

near A4, showed that the lower-layer fluctuations were compatible with TRWs with periods of 

40 to 70 days. However, the apparent southwestward propagation could also be a consequence 

of the southward propagation of east-side meander crests and troughs. Fluctuations of ~ 40-60 

days are also present during the cold intervals when the LC or LC eddy is not present in the 

transect. However, the propagation of the signal along the transect is not clear and where events 

seem to propagate (e.g., between Franklin and Hadal), they are much slower than when the eddy 

is present.

The velocity component normal to the N1-C1 transect, which is approximately parallel to the 

mean LC front on the western side, is shown in Figure 4.3-2. Magnitudes on the western side are 

a maximum near the front location and show rapid fluctuations that are associated with cyclonic 

LCFEs (note that the SSH contour does not resolve fluctuations with time scales < ~10 to 20 

days, and length scales < ~50 to 100 km). For the purposes of this analysis LCFEs are defined as 

having along-front length scales of 50-100 km and periodicities of < 20 days. These rapid 

fluctuations are also observed in the isotherm depths (Figure 4.3-1), and are most strongly 

present when the front is between N2 and N3 (e.g., June 2009 for Ekman, March through June 

2010 for Franklin, and February through May 2011 for Hadal). When the front moves closer and 

away from the Campeche bank, the intensity of the fluctuations decreases indicating that the 

relative location of the western front to the shelf break influences the development and 

propagation of the LCFEs. On the eastern side of the transect, the oppositely directed current 

fluctuations have smaller magnitudes, and generally occur inside the front location. The

fluctuations have longer periodicities and less amplitude than on the western side (Figure 4.3-2). 

The same high-frequency fluctuations, but with less magnitude, are observed at E2 and E3 on 

transect E when the front is in the vicinity of these stations (not shown).

The velocities at 120 m along the N1-C1, and E transects are interpolated to the front location 

and the coordinates rotated so that the v-component is directed along the front as defined by the 

17-cm SSH contour, where it crosses the transects. The resulting vectors are denoted as alongfront velocities, and approximately directed northwestward on the west and southeastward on the 

east side of the LC. They are given, along with the front displacements relative to E2, N2 and 

C1, in Figure 4.3-3. During the Franklin and Hadal intervals, the west-side front displacements 

relative to the 500 m (i.e., N2 and E2) isobaths are very similar. However, both the intensity of 

the fluctuations and the means are larger on the N1-C1 transect than the E transect. There is also
Depth (m) 

C1

B3

A4

N4

N3

Distance (km)

N3 to C1 Depth of 6°C Isotherm

66

67

64

65

Figure 4.3-1. Depth of the 6 °C isotherm along the N3-C1 transect. The locations of the SSH 17-cm contour on the transect are given by the 

thick lines for the east (green) and west (purple) sides, respectively.

190 
N1 to C1 120-m 40-hlp Velocity Component (310°T)

-150 -100-125 -75 -50 -25 0 25 50 75 100 125 150

cm/s

C1

B3

A4

N4

N3

N2

N1

Distance (km)

Figure 4.3-2. Velocity components, directed 310°T, at 120 m for moorings along the N1-C1 transect. The locations of the SSH 17-cm contour 

on the transect are given by the thick lines for the east (green) and west (purple) sides, respectively.

191 
Front Location

(km)

Front Location

(km)

C1

N2

cm/s

Along Front Velocities

East Side

West Side

120 m

103 km2

LC Area & Area + Eddy

Ekman Franklin Hadal

N2

C1

E2

E2

Figure 4.3-3. Along-front velocity vectors for the E and N1-C1 transects for the west (E2 and N2) and east (C1) sides, respectively. Lower panel 

gives the displacement relative to the 500-m isobath of the 17-cm SSH contour along the E (red) and N1-C1 (blue) transects where 

positive is towards the northeast. The top panel is the displacement of the front on the N1-C1 transect relative to C1 where 

positive is towards the southwest along the transect. 

192 
193

a reduction in mean flow on the east side of the N1-C1 transect compared with the west side, 

however, the fluctuations are larger and generally of longer periodicities. 

The variability of the fluctuation EKE is analyzed through spectra of the along-front velocities in 

the vicinity of E2, N2 and C1 for the Franklin and Hadal intervals, when the western fronts were 

close to the slope and LCFE activity is evident (Figure 4.3-4). The increase in EKE from the E 

to N1-C1 transects is clear in both eddy intervals (the spectra are variance preserving with equal 

areas under the curve representing equal variances), implying that small perturbations in the front 

north of the Yucatan, grow as the current flows north along the Campeche slope. The 

mechanism is most likely the mixed instability analyzed by Luther and Bane (1985) for the 

analogous Gulf Stream flowing along the slope of the South Atlantic Bight (SAB). The EKE 

energy for the frontal velocities near N2 has peaks at 5-7 days and ~10 days, most prominently 

for the Franklin interval. These periodicities are characteristic of propagating cyclonic frontal 

eddies, as is the characteristic “haystack” configuration of the stick vectors in Figure 4.3-3 (Lee 

and Atkinson 1983). Transects E and N1-C1 are too far apart to definitively track propagating 

signals (this may also be a consequence of displacements of the jet core when the mooring 

spacing is relatively coarse), and sequences of clear sky satellite SST images are rare, but 

previous work has established along-front length scales of ~100 km (Walker et al. 2009). For the 

northeast LC front, the along-front velocity EKE show little energy at periods shorter than 10 

days, and relatively more EKE variance at longer periods than near N2 (Figure 4.3-4). This 

implies either that short-period cyclonic frontal eddies decay after the main current leaves the 

slope, and/or there is non-linear transformation to longer-period fluctuations. The latter could be 

consistent with the observed merging of LCFEs in satellite imagery along the northern boundary 

of an extended LC (Walker et al. 2011). There is an analogy with the Gulf Stream leaving the 

slope and flowing into deep water at Cape Hatteras, which also occurs for the northward-flowing 

branch of the extended LC that leaves the slope at the northeast corner of the Campeche Bank. 

The Gulf Stream downstream of Cape Hatteras develops long-period meanders and the frontaleddy perturbations, prominent in the SAB, are not observed.

4.4 RELATIVE VORTICITY 

The Hadal interval (January to May 2011) mean upper-layer cross-sectional vorticity and 

velocity component, normal to the section, are given for the N1-C1 and E transects in Figure 4.4-

1. On the cyclonic side of the LC jet, ζ has a strong horizontal gradient and is fairly depth 

independent down to 500 to 900 m. The jet is centered around N3 and between E2 and E3, and 

is slightly wider on the northern section, which reflects the greater movement of the front 

because of LCFE activity. On the anticyclonic side of the front, i.e., within the LC, ζ is nearly 

constant horizontally but decreases in depth. This is consistent with solid body rotation with 

speeds that decrease with depth, and is, not surprisingly, similar to the solid body rotation found 

in detached eddies (Hamilton et al. 2003). For the N1-C1 transect, the center of the solid body 

rotation is between N4 and A4. Thus, the isolines of speed spread out with increasing depth on 

the anticyclonic side, but remain parallel, constrained by slope of the bottom on the cyclonic 

side.
 194

Figure 4.3-4. EKE Spectra of the along-front interpolated velocities on the N2-C1 and E transects. 

Western LC front spectra are red and yellow (N2-C1), and green and dark green (E) and 

the Eastern LC front spectra are blue and magenta, for the Franklin and Hadal intervals, 

respectively. The Hadal interval differs slightly between the E and N2-C1 transects. 
E1 E2 E3 E4 E5

0

25 75 50 100

0 0

25

50 75

-25

N1 N2 N3 N4 A4 B3 C1

-0.15

-0.20

-0.25

-0.10

-0.05

0

0.05

0.10

0.15

0.20

0.25

Relative Vorticity / f

 195

Figure 4.4-1. Mean along-front velocities (cm s-1) and relative vorticity (fraction of f) for the indicated 

interval and sections across the Campeche slope during the LC formation of Hadal. 
196

The variation of ζ through the water column is given in Figures 4.4-2 for ζ locations 78 and 82 

(derived from moorings N2 and N3, and E2, E3 and EN, respectively; see Figure 2.9-2). The 

vertical fluctuations are consistent with the means (Figure 4.4-1) in that cyclonic (positive) ζ

does not have much depth attenuation, and anticyclonic (negative) ζ events are attenuated with 

depth. At 78, for Ekman (June-July 2009) and Franklin (April-May 2010), the greater seaward 

slope with depth of the location of maximum velocity (e.g., Figure 4.4-1) creates intervals where 

the upper water column is anticyclonic, and the lower water column is cyclonic. Moving down 

stream from N2 into deeper water, the depth distribution of ζ is given for location 56 (derived 

from moorings A1, A2 and B1) in Figure 4.4-3. At 56, ζ is predominantly anticyclonic, being 

within the LC or a LC eddy most of the time. The mean location of the 17-cm contour is 20 km 

northwest of A1. The dominance of negative ζ extends to the lower layer where anticyclonic 

fluctuations are larger and longer lasting than cyclonic pulses. A mean anticyclonic ζ is 

consistent with the mean lower-layer anticyclone given by the mean velocities (see Section 3.4) 

for the west side of the LC, and attributed to weakly shoaling topography, and the tendency of 

LC/LC eddies to move westward under the influence of β that leads to compression of the lower 

water column. The lower-layer ζ is relatively depth independent with some anticyclonic events 

showing evidence of weak bottom trapping during intervals when the LC is advancing to the 

north.

There are visual indications in Figure 4.4-3 that the upper and lower layer have coherent events, 

and this is analyzed using frequency domain EOFs, where the ζs are depth-range weighted, and 

the frequency bands (100-40, 40-20, 20-10, and 10-3 days) are the same as used for quasibarotropic and baroclinic analysis using the PIES array in Section 3.4. The EOF modes for 

location 56 are given in Figure 4.4-4, where for 100-40 days there is a strong connection between 

lower-layer and upper-layer fluctuations with a 90° phase lead of bottom ζwith the upper layer. 

The lowest frequency band has a significant surface-intensified mode 2 with little expression in 

the lower layer that accounts for upper-layer fluctuations associated with the northwest part of 

the LC. With increasing frequency bands, the mode 1 fluctuations become more bottom trapped 

with much weaker connections to the surface layer, and are typical (high coherence and inphase) of TRWs. Highest bottom amplitudes occur for the 20-10 day period band, and the 

lowest for the 10-3 day band. The shortest period band has a significant second mode that is 

surface trapped, indicating that short-period motions of less than 20 days, associated with LCFEs 

propagating along the front, are not extending into the lower layer.

Further downstream at location 67, ζ (from velocities at B2, B3, C1 and C2) is given in Figure 

4.4-5. Lower-layer fluctuations have large amplitude, longer periods, and more dominant 

cyclonic pulses, when compared with 56 (Figure 4.4-3) on the northwest side of the LC. Similar 

characteristics are seen in the upper layer, except for some relatively weak higher-frequency 

fluctuations in the Franklin (January-April 2010) growth interval. The EOF modes for location 

67 (Figure 4.4-4) show that periods longer than 40 days have a strong connection between layers 

with only small (< 90°) phase leads of the lower over the upper, with the longer periods having 

larger amplitudes, which are about twice those of the equivalent modes at 56. Mode 1 for this 

lowest frequency band combines the near-surface intensification with the barotropic mode. 
-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Relative Vorticity at 82 Fractional f

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Relative Vorticity at 78 Fractional f

103 km2

LC Area & Area + Eddy

Ekman Franklin Hadal

 197

Figure 4.4-2. Time series of relative vorticity (normalized by f) for locations 78 (from N2 and N3 velocities), and 82 (from E2, E3 and EN velocities) as a function of depth.
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

900 m

1300 m

2000 m

Fractional f Relative Vorticity at 56

103 km2

LC Area & Area + Eddy

Ekman Franklin Hadal

Figure 4.4-3. Time series of relative vorticity (normalized by f) for location 56 (from A1, A2 and B1 velocities), as a function of depth.

198 
67

56

67 56

 199

Figure 4.4-4. Frequency domain EOFs of vertical profiles of relative vorticity (units f-1) at locations 56 

and 67. Frequency bands are 100-40 days (red: mode 1, orange: mode 2), 40-20 days 

(blue), 20-10 days (green: mode 1), and 10-3 days (purple: mode 1, cyan: mode 2).
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Fractional f Relative Vorticity at 67

900 m

2000 m

103 km2

LC Area & Area + Eddy

Ekman Franklin Hadal

Figure 4.4-5. Time series of relative vorticity (normalized by f) for location 67 (from C1, C2, B2 and B3 velocities), as a function of depth.

200 
201

Unlike at 56, a separate upper-layer mode is not present. The significant high-frequency mode 2, 

for the 10-3 day band, is again surface trapped with these fluctuations having smaller amplitudes 

than at 56. Thus, ζprofiles on the east side of the LC are more barotropic, energetic, and have 

longer periods than further upstream along the front. This is consistent with motions being 

dominated by large-scale meanders (i.e., ~ 300 km wavelength with periods of 40 to 60 days) 

that are strongly connected to the lower layer.

To further illustrate the along-front and eddy-event changes in ζ fluctuations from transect E 

through N around to the west Florida slope at C1, wavelet power and cross-power have been 

calculated for locations 82, 78, 56 and 67, respectively. Wavelet analysis for the two Campeche 

slope locations (Figure 4.4-6) at 82 on transect E, show that short-period fluctuations, < 8 days, 

are weak and do not rise above the 95% significance level, estimated as in Torrence and Compo 

(1998). Ten-to-twenty-day power is significant during the earlier growth stages of Franklin and 

Hadal, but signals longer than 30 days, particularly for Hadal, resulting from longer-scale 

variations of the LC front, tend to dominate. Further downstream, at section N, the shorter 

period LCFEs are prominent for Franklin; less so for Hadal. At longer periods, 16-32 days, there 

are events during the growth phase and first detachment of Franklin and in the early growth 

phase of Hadal. However, they are not coincident, even allowing for 1-2 weeks propagation lag 

times, with the events on transect E. This is consistent with the spectral analysis (Figure 4.3-4) 

and indicates that short-period LCFEs undergo growth between the Yucatan and the northern 

part of the Campeche slope. It has been speculated from numerical modeling studies that similar 

period wind forcing, acting through a coastal-trapped wave, could be the trigger for these short 

period instabilities on the LC front on the Campeche slope (Sheinbaum, personal 

communication).

Moving into deeper water, the connections between upper layer and lower layer are investigated 

using cross-wavelet power (Figure 4.4-7). At 56 there is little connection between layers at 

periods less than 10 days, and between 10 and 20 days the most significant connection occurs for 

Hadal just before the separation, where the phase angles indicate a 90° phase lag of upper against 

lower layer ζ (Grinsted et al. 2004). At periods longer than 30 days, where cross power is 

significant, the lower layer tends to lead by ~ 90°, which is consistent with baroclinic instability, 

except for detachment and separation intervals where the layers tend to be in phase or in antiphase. On the east side of the LC, at 67, all the significant cross power is at longer than 20 days. 

Phase leads of the lower layer are generally less than 90°, as was indicated by the EOFs in Figure 

4.4-5.

The main conclusions from this section on relative vorticity are that short-period, upper-layer 

frontal eddies grow along the Campeche slope north of the Yucatan. When they transition to 

deep water, growth stops and decreases in amplitude are seen from the northwest to the east side 

of the extended LC. In the northwest, periodicities tend to be shorter than in the northeast, 

consistent with evidence of baroclinic instabilities at periods longer than 20 days. Short period 

cyclones have little or no signal in the lower layer. In the northeast, periods longer than 30-40 

days dominate with larger amplitudes than in the northwest, with less evidence of baroclinic 

instability, but still strong connections at these longer periods between the layers. 
78 at 155 m Normalized 

Wavelet Power Relative 

Vorticity

82 at 160 m Normalized 

Wavelet Power Relative 

Vorticity

103 km2

LC Area & Area + Eddy

Ekman Franklin Hadal

 202

Figure 4.4-6. Normalized wavelet power for relative vorticity at 160 m at locations 82 (transect E), and 

78 (transect N) using the Morlet wavelet. The thick solid contours encloses regions of 

greater than 5% significance against a red-noise process. The lighter shades indicate the 

“cone of influence” where edge effects are important.
56 Wavelet X-power btwn 166 and 2000 m Relative Vorticity

56

67

67 Wavelet X-power btwn 166 and 2000 m Relative Vorticity

103 km2

LC Area & Area + Eddy

Ekman Franklin Hadal

 203

Figure 4.4-7. Cross-wavelet normalized power between 166 and 2000 m at locations 56 and 67. The 

5% significance level against red noise is shown as a thick contour. The relative phase 

relationship is shown as sticks emanating from the crosses (with in-phase pointing right, 

anti-phase pointing left, and lower leading upper by 90° pointing straight down).
204

4.5 BAROCLINIC INSTABILITY ANALYSIS

During LC eddy detachment and separation events, a marked increase in lower-layer eddy 

kinetic energy occurred coincident with the development of a large-scale meander along the 

northern and eastern parts of the LC (Figure 4.5-1). In this section, it is shown that these lowerlayer eddies gain their high-energy levels in a pattern consistent with developing baroclinic 

instability (Cushman-Roisin and Beckers 2011; McWilliams 2006). Coherence estimates and 

case studies reveal that the deep streamfunction perturbations lead corresponding perturbations 

in the upper streamfunction, as they jointly intensify. This baroclinic instability is intrinsically a 

whole-water-column process, and the interaction between the upper and lower water column is 

quantified by evaluating the mean-eddy potential-energy budget. Within that budget, as will be 

treated in this section, the baroclinic energy conversion term, represented by down-gradient eddy 

heat fluxes, is found to be largest along the eastern side of the LC. In those peak conversion 

regions there is a near balance between horizontal down-gradient eddy heat fluxes (baroclinic 

conversion rate) and vertical down-gradient eddy heat fluxes, indicating that eddies extract 

available potential energy from the mean baroclinic field and further convert that eddy potential 

energy to eddy kinetic energy.

A signature of growing baroclinic instability events is a vertical phase tilt; along the direction of 

propagation, deep leads upper. Consequently, at a fixed location, deep leads upper in time also. 

Here we illustrate that characteristic phase tilt, as was done in Donohue et al. (2006). More 

comprehensive discussions are presented in ocean-atmosphere texts such as Cushman-Roisin 

(1994) and Cushman-Roisin and Beckers (2011). The schematic in Figure 4.5-2 presents an 

eastward jet with a meander crest and trough in the pattern conducive to baroclinic instability. A 

deep anticyclone (high-pressure center) leads the anticyclonic crest in the upper jet; a deep 

cyclone (low-pressure center) leads the upper cyclonic trough. In this configuration the upper 

baroclinic jet can intensify the deep eddies as follows. As the upper crest intensifies and shifts 

its sloped thermocline structure northward, this squashes the lower water column, adding 

anticyclonic vorticity to the deep eddy. As the upper trough intensifies and shifts southward, the 

rising sloped thermocline stretches the lower water column, adding cyclonic vorticity to the deep 

eddy. Complementing this, the deep eddies can also intensify the upper meander under this 

illustrated phase shift. Consider a water parcel translating along the upper jet from crest to 

trough. The deep eddy contribution to this circulation draws the parcel across the baroclinic front 

deeper into the trough. This stretches the upper water column and adds cyclonic vorticity, 

tending to grow the trough. Cold advection due to cyclonic turning with height further intensifies 

the upper trough. Correspondingly, an upper-layer water parcel, passing from trough to crest, is 

drawn by the deep eddy to move higher into the crest; this squashes the upper column and adds 

anticyclonic vorticity, and the upper crest grows. Warm advection due to the anticyclonic turning 

with height intensifies the upper crest. The consequence of this vertical phase tilt is joint growth 

and development of upper meanders and deep eddies acting upon each other, where this 

configuration allows them to draw upon the mean potential energy in the sloped thermocline of 

the baroclinic jet.

To investigate vertical coupling, coherences and phases between upper and deep streamfunctions 

(SSH_bcb and SSH_ref, respectively) were estimated using the averaged periodogram method of 

Welch (1967) (256-day length segment with 50% overlap). Upper and deep streamfunctions are 

coherent over large portions of the array for frequencies between 1/64 d-1 and 1/32 d-1. Figure
24o

N

26o

N

28o

N

89o

W 87 oW 85 oW

10 cms−1

mean Loop Current

(a) near−bottom eddy kinetic energy [cm 2

 s−2]

0 40 80 120 160

100

200

300

[cm 2 s−2]

 (b) Near−bottom eddy kinetic energy

Ek nam narF klin aH d la

0

10

20

30

(c) Array−average SSH

[cm]

Jul2009 Jan2010 Jul2010 Jan2011 Jul2011

100

150

200 (d) Loop Current area

[103km2

]

 205

Figure 4.5-1. (a): Near-bottom mapped and directly measured mean currents (thin and bold vectors, 

respectively). Standard deviation ellipses superimposed on the time-mean near-bottom 

eddy kinetic energy (color-bar, cm2s-2). Scale for vectors and ellipses shown in lower left 

corner. Red line denotes the mean Loop Current position defined by the CCAR-SSH 

17-cm contour. Bathymetry plotted with gray contours every 500 m depth. Time mean is 

taken over the 30-month experiment duration from 3 May 2009 through 23 October 2011. 

(b): Time series of array-averaged near-bottom eddy kinetic energy (cm2s-2). (c): Time 

series of array-averaged CCAR-SSH. (d): Loop Current area in units of 103 km2.
UPPER

 JET

deep eddies

HIGH

LOW

Figure 4.5-2. Schematic representation of the characteristic phase offset between upper and lower-layer cyclonic or anticyclonic perturbations 

that favor baroclinic instability. A meander trough and crest propagate east along the upper eastward baroclinic jet (bold black 

contours). Leading the upper trough is a deep cyclone (thin dashed blue contours); leading the upper crest is a deep anticyclone 

(thin red contours). The phase offset (vertical tilt of the low-pressure centers and the high-pressure centers, respectively) would 

favor meander growth. Reproduced from Donohue et al. (2006). 

206 
207

4.5-3 shows the spatial pattern of coherence and phase for three frequencies within this band. A 

tongue of high coherence extends from the northeast trending south-southwest toward the central

portion of the array. Two additional peaks occur, one near the base of the Mississippi Fan and 

another in the southeastern corner. Where statistically coherent, the phase offset is such that the 

deep leads the upper. Phase estimates range between 60 and 150 degrees. Frequencies outside 

the band 1/64 d-1 and 1/32 d-1 do not show statistically significant coherence between upper and 

deep. This spectral approach characterizes the overall mean statistics, yet each LC eddy 

shedding event differs, e.g., location of final separation, number of brief detachments that 

precede the separation, location of the LC within the Gulf and within the array. In the remainder 

of the discussion, the focus is on each LC eddy shedding event separately, as case studies.

To illustrate the evolution of LC eddy-shedding events and the relationship between upper and 

deep, maps of upper and deep streamfunction were plotted with a five-day interval. In each plot, 

mapped baroclinic SSH referenced to the bottom (SSH_bcb, filled colored contours) is 

embedded within altimetric SSH that covers the broader region. The 17-cm contour denotes the 

location of the LC and LC-eddy fronts. The deep-pressure fields (deep ref streamfunction) are 

expressed in centimeters of water height as SSH_ref, so that relative strengths of the upper (bcb) 

and deep (ref) fields are evident. Mapped SSH_ref reveals the presence of deep cyclones (blue

contours) and deep anticyclones (red contours). Two sets are provided for each shedding event: 

full frequency (3-day low pass quasigeostrophic), and 100 to 40-day band pass fields (Figures 

4.5-4a-d for Ekman, 4.5-5a-d for Franklin and 4.5-6a-d for Hadal). The following discussion 

focuses upon the 100 to 40 day band where coherence between upper and deep was found to be 

high.

Eddy Ekman: 3 May to 31 August 2009 

A long-wavelength meander developed along the northern edge of the LC in early July (Figure 

4.5-4b). The 3 July map depicts two deep eddies labeled as cyclone A and anticyclone B. These 

two deep eddies are positioned on this date such that the deep anticyclone B leads an upper high 

and the deep cyclone A slightly leads an upper low. This classic pattern associated with 

baroclinic instability remains with varying vertical phase-tilt as the meander and deep eddies 

propagate together anticyclonically along the LC periphery from 3 July to 27 August. While the 

amplitude of deep cyclone A remains nearly constant during this interval, deep anticyclone B’s 

strength modulates. Anticyclone B intensifies from 8 to 18 July, remains constant in strength 

until 28 July, then weakens over the next 10 days. A slight re-amplification occurs 27 August. 

On 23 July (Figure 4.5-4d), another deep cyclone labeled C, located on the Mississippi Fan, 

begins to develop. It is positioned slightly downstream of a developing upper trough. This trough 

and deep cyclone C jointly intensify 23 July through 22 August. During this interval, the trough 

deepens to nearly pinch off the neck of the LC, and the vertical phase tilt gets smaller as deep 

cyclone C becomes nearly vertically aligned under the trough. By 27 August, the phasing of deep 

leading upper no longer exists, Eddy Ekman is nearly separated, and deep cyclone C has 

weakened and subsequently propagates southwestward out of the array.

Eddy Franklin: 15 February to 14 September 2010 

Similar to Eddy Ekman, during the formation of Eddy Franklin, the signature vertical phase tilts 

of baroclinic instability are present. This case study includes upper and deep events leading to an
central frequency 64.0 days

coherence

25°N

26°N

27°N

phase [degrees]

central frequency 51.2 days

25°N

26°N

27°N

central frequency 32.0 days

88°W 86°W 84°W

25°N

26°N

27°N

0 0.4 0.8

88°W 86°W 84°W

ref leads bcb bcb leads ref

−180 −60 60 180

 208

Figure 4.5-3. Coherence (left) and phase (right) between upper, SSH_bcb, and lower, SSH_ref, 

streamfunction for three frequency bands: top (1/64 d-1), middle (1/51.2 d-1), and bottom 

(1/32 d-1), estimated using the averaged periodogram method of Welch (1967) (256-day 

length segment with 50% overlap). Phase (in degrees) contoured where coherence 

exceeds 95% confidence limits denoted by the thick black contour in the coherence 

maps. Negative phase indicates that deep leads upper. PIES locations shown by black 

diamonds. Bathymetry (thin black line) contoured every 1000-m depth. 
4 MAY 2009

25°N

26°N

27°N

9 MAY 2009 14 MAY 2009 19 MAY 2009

24 MAY 2009

25°N

26°N

27°N

29 MAY 2009 3 JUN 2009 8 JUN 2009

13 JUN 2009

25°N

26°N

27°N

18 JUN 2009 23 JUN 2009 28 JUN 2009

3 JUL 2009

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−50−25 0 25 50

8 JUL 2009

88°W 86°W 84°W

13 JUL 2009

SSHref increment: 2 cm

88°W 86°W 84°W

18 JUL 2009

frequency: full

88°W 86°W 84°W

 209

Figure 4.5-4a. Loop Current eddy-shedding event Ekman, 4 May through 18 July 2009. Maps of 

baroclinic SSH referenced to the bottom (SSH_bcb) embedded within altimetric SSH 

(filled color contours; colorbar and contour interval on the bottom left). Maps shown 

sequentially left to right, top to bottom at 5-day intervals. The 17-cm contour (green, 

SSH_bcb within array, altimeteric SSH outside array) denotes the location of the Loop 

Current. Mapped reference level SSH (SSH_ref) reveals the presence of deep cyclones 

(blue contours) and deep anticyclones (red contours) contoured every 2 cm. Diamonds 

denote PIES sites. Grey lines denote the 3000-m depth contour. The frequency band of 

the SSH data is listed below the bottom right panel.
4 MAY 2009

25°N

26°N

27°N

9 MAY 2009 14 MAY 2009 19 MAY 2009

24 MAY 2009

25°N

26°N

27°N

29 MAY 2009 3 JUN 2009 8 JUN 2009

13 JUN 2009

25°N

26°N

27°N

18 JUN 2009 23 JUN 2009 28 JUN 2009

3 JUL 2009

B

88°W 86°W 84°W

25°N

26°N

27°N

A

SSHbcb [cm]

−30−15 0 15 30

8 JUL 2009

88°W 86°W 84°W

13 JUL 2009

SSHref increment: 2 cm

88°W 86°W 84°W

18 JUL 2009

frequency: 100−40

88°W 86°W 84°W

 210

Figure 4.5-4b. Loop Current eddy-shedding event Ekman, 4 May through 18 July 2009. Maps of 100-40 

day band-passed baroclinic SSH referenced to the bottom (SSH_bcb) embedded within 

altimetric SSH (filled color contours; colorbar and contour interval on bottom left). Maps 

shown sequentially left to right, top to bottom at 5-day intervals. The 17-cm contour 

(green, SSH_bcb within array, altimeteric SSH outside array) denotes the location of the 

Loop Current. Mapped 100-40 day band-passed reference level SSH (SSH_ref) reveals 

the presence of deep cyclones (blue contours) and deep anticyclones (red contours) 

contoured every 2 cm. Diamonds denote PIES sites. Grey lines denote the 3000-m 

depth contour. The frequency band of the SSH data is listed below the bottom right 

panel. The 3 July map indicates deep cyclone A and deep anticyclone B, discussed in the 

text. 
23 JUL 2009

25°N

26°N

27°N

28 JUL 2009 2 AUG 2009 7 AUG 2009

12 AUG 2009

25°N

26°N

27°N

17 AUG 2009 22 AUG 2009 27 AUG 2009

1 SEP 2009

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−50−25 0 25 50

6 SEP 2009

88°W 86°W 84°W

11 SEP 2009

SSHref increment: 2 cm

88°W 86°W 84°W

16 SEP 2009

frequency: full

88°W 86°W 84°W

 211

Figure 4.5-4c. Loop Current eddy-shedding event Ekman, 23 July through 16 September 2009. (full 

frequency as in Figure 4.5-4a). 
23 JUL 2009

25°N

26°N

27°N C

28 JUL 2009 2 AUG 2009 7 AUG 2009

12 AUG 2009

25°N

26°N

27°N

17 AUG 2009 22 AUG 2009 27 AUG 2009

1 SEP 2009

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−30−15 0 15 30

6 SEP 2009

88°W 86°W 84°W

11 SEP 2009

SSHref increment: 2 cm

88°W 86°W 84°W

16 SEP 2009

frequency: 100−40

88°W 86°W 84°W

 212

Figure 4.5-4d. Loop Current eddy-shedding event Ekman, 23 July through 16 September 2009 (100-40 

days frequency as in Figure 4.5-4b). 
11 APR 2010

25°N

26°N

27°N

16 APR 2010 21 APR 2010 26 APR 2010

1 MAY 2010

25°N

26°N

27°N

6 MAY 2010 11 MAY 2010 16 MAY 2010

21 MAY 2010

25°N

26°N

27°N

26 MAY 2010 31 MAY 2010 5 JUN 2010

10 JUN 2010

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−50−25 0 25 50

15 JUN 2010

88°W 86°W 84°W

20 JUN 2010

SSHref increment: 2 cm

88°W 86°W 84°W

25 JUN 2010

frequency: full

88°W 86°W 84°W

 213

Figure 4.5-5a. Loop Current eddy-shedding event Franklin, 11 April through 25 June 2010. Maps of 

baroclinic SSH referenced to the bottom (SSH_bcb) embedded within altimetric SSH 

(filled color contours; colorbar and contour interval on bottom left). Maps shown sequentially left to right, top to bottom at 5-day intervals. The 17-cm contour (green, SSH_bcb 

within array, altimeteric SSH outside array) denotes the location of the Loop Current. 

Mapped reference level SSH (SSH_ref) reveals the presence of deep cyclones (blue 

contours) and deep anticyclones (red contours) contoured every 2 cm. Diamonds 

denote PIES sites. Grey lines denote the 3000-m depth contour. The frequency band of 

the SSH data is listed below the bottom right panel.
11 APR 2010

25°N

26°N

27°N

16 APR 2010 21 APR 2010 26 APR 2010

1 MAY 2010

25°N

26°N

27°N

6 MAY 2010 11 MAY 2010

A

B

16 MAY 2010

21 MAY 2010

25°N

26°N

27°N

26 MAY 2010 31 MAY 2010 5 JUN 2010

A

B C

10 JUN 2010

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−30−15 0 15 30

15 JUN 2010

88°W 86°W 84°W

20 JUN 2010

SSHref increment: 2 cm

88°W 86°W 84°W

25 JUN 2010

frequency: 100−40

88°W 86°W 84°W

B

C

 214

Figure 4.5-5b. Loop Current eddy-shedding event Franklin, 11 April through 25 June 2010. Maps of 

100-40 day band-passed baroclinic SSH referenced to the bottom (SSH_bcb) embedded 

within altimetric SSH (filled color contours; colorbar and contour interval on bottom left). 

Maps shown sequentially left to right, top to bottom at 5-day intervals. The 17-cm contour 

(green, SSH_bcb within array, altimeteric SSH outside array) denotes the location of the 

Loop Current. Mapped 100-40 day band-passed reference level SSH (SSH_ref) reveals 

the presence of deep cyclones (blue contours) and deep anticyclones (red contours) 

contoured every 2 cm. Diamonds denote PIES sites. Grey lines denote the 3000-m 

depth contour. The frequency band of the SSH data is listed below the bottom right 

panel. The 11 May map indicates deep anticyclone A and deep cyclone B discussed in 

the text. The 5 June map indicates deep anticyclone C discussed in the text. 
30 JUN 2010

25°N

26°N

27°N

5 JUL 2010 10 JUL 2010 15 JUL 2010

20 JUL 2010

25°N

26°N

27°N

25 JUL 2010 30 JUL 2010 4 AUG 2010

9 AUG 2010

25°N

26°N

27°N

14 AUG 2010 19 AUG 2010 24 AUG 2010

29 AUG 2010

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−50−25 0 25 50

3 SEP 2010

88°W 86°W 84°W

8 SEP 2010

SSHref increment: 2 cm

88°W 86°W 84°W

13 SEP 2010

frequency: full

88°W 86°W 84°W

 215

Figure 4.5-5c. Loop Current eddy-shedding event Franklin, 30 June through 13 September 2010 (full 

frequency as in Figure 4.5-5a). 
30 JUN 2010

25°N

26°N

27°N

B

5 JUL 2010 10 JUL 2010 15 JUL 2010

20 JUL 2010

25°N

26°N

27°N

25 JUL 2010 30 JUL 2010 4 AUG 2010

C

D

9 AUG 2010

25°N

26°N

27°N

14 AUG 2010 19 AUG 2010 24 AUG 2010

29 AUG 2010

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−30−15 0 15 30

3 SEP 2010

88°W 86°W 84°W

8 SEP 2010

SSHref increment: 2 cm

88°W 86°W 84°W

13 SEP 2010

frequency: 100−40

88°W 86°W 84°W

 216

C

D

Figure 4.5-5d. Loop Current eddy-shedding event Franklin, 30 June through 13 September 2010. The 

30 June map indicates deep cyclones B, D and deep anticyclone C discussed in the text. 

The 4 August map also indicates deep cyclone D and deep anticyclone C (100-40 day 

frequency as in Figure 4.5-5b).
217

eddy detachment in early July 2010 and final separation in early August 2010. Consider the 

large-scale LC meander that is developing in early May 2010. The 11 May map (Figure 4.5-5b)

shows two deep eddies, anticyclone A and cyclone B. They are positioned such that the deep 

anticyclone resides downstream of and leads the upper crest. The deep cyclone B resides 

upstream of that upper crest, and in subsequent days (5 June to 25 June) cyclone B intensifies as 

it leads a developing upper trough within the array. Anticyclone C comes into view 5 June with 

an upper crest following close behind it. During June, the B and C deep eddies and their slightly 

trailing upper meander trough and crest propagate downstream around the Loop. The trough and 

deep eddy B jointly intensify, and by early July (Figure 4.5-5d) the LC neck pinches off into a 

short-lived detachment. The 30 June map shows three deep eddies; a deep cyclone, labeled D, 

appears near the Mississippi Fan. The northern limit of the array leaves the question open as to 

whether these deep eddies (A, B, C or D) initially propagate into the array from further north, or 

whether they originate upstream along the LC front. During July, deep eddies C and D and their 

slightly trailing upper meander crest and trough propagate downstream around the LC. For 

example, on 10 and 15 July 2010, the vertical phase tilt is evident, and the features jointly 

intensify. Eventually, the trough ‘necks down’ again, and eddy separation occurs in August. The 

recurrent structure observed in these map sequences is that as deep eddies propagate through the 

array they lead their upper counterpart. For example, from 5 June to 10 July (Figures 4.5-5b and 

4.5-5d), deep cyclone B leads an upper cyclone (trough); from 15 July to 4 August, deep 

anticyclone C leads an upper anticyclone. Finally, we note that during the Franklin event, the 

largest amplitude deep eddies occur during the early to mid-July detachment, prior to the final 

separation of a relatively small LC eddy in August.

Eddy Hadal: 1 March to 14 September 2011 

Upper-deep coupling with the vertical phase tilt of baroclinic instability also characterizes the 

Hadal shedding cycle. Figures 4.5-6b and 4.5-6d show that during Hadal, long-wavelength 

meanders develop along the eastern side of an extended LC. The eastern side of the LC runs 

through the middle of the array during much of this time, and the associated deep eddies are 

relatively well centered within the observational window. This case study will follow a sequence 

of four deep eddies, anticyclones A and C, and cyclones B and D. Their propagation starts 

southward and downstream along the LC, and as they intensify they turn southwestward across 

the neck of the LC. As seen in our Ekman and Franklin case studies, while these deep eddies 

translate along the LC, they lead their upper counterpart as they jointly develop and tend to 

constrict the neck. For example, on 13 April, deep anticyclone A sits just downstream of an 

upper crest (high SSH_bcb), and during the subsequent 15 days the upper and deep highs jointly 

intensify. Shortly after that, on 3 May deep cyclone B leads an upper trough (low SSH_bcb), and 

both intensify during the subsequent 20 days. Immediately following that, on 23 May, the deep 

anticyclone C leads an upper crest downstream, intensifying during the next 20-30 days to about 

22 June. Deep-cyclone D follows this train of upper-deep coupling interactions. From 22 June 

to 17 July 2011 deep-cyclone D leads and jointly develops with an upper low SSH_bcb and 

trough, constricting the LC neck greatly. Shortly afterward Hadal separates. Limits to the 

growth phase of the upper and deep perturbations appears to occur where the deep eddy 

trajectory turns to the southwest, not following the downstream path of the upper jet. 

Subsequently, their vertical phase tilt becomes non-conducive to baroclinic instability, and they 

jointly decay. Deep-cyclone B decays after 28 May together with its upper-strong low. 

Analogously deep-anticyclone C decays after 22 June together with its upper strong high. Similar
9 MAR 2011

25°N

26°N

27°N

14 MAR 2011 19 MAR 2011 24 MAR 2011

29 MAR 2011

25°N

26°N

27°N

3 APR 2011 8 APR 2011 13 APR 2011

18 APR 2011

25°N

26°N

27°N

23 APR 2011 28 APR 2011 3 MAY 2011

8 MAY 2011

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−50−25 0 25 50

13 MAY 2011

88°W 86°W 84°W

18 MAY 2011

SSHref increment: 2 cm

88°W 86°W 84°W

23 MAY 2011

frequency: full

88°W 86°W 84°W

 218

Figure 4.5-6a. Loop Current eddy-shedding event Hadal, 9 March through 23 May 2011. Maps of 

baroclinic SSH referenced to the bottom (SSH_bcb) embedded within altimetric SSH (filled 

color contours; colorbar and contour interval on bottom left). Maps shown sequentially left 

to right, top to bottom at 5-day intervals. The 17-cm contour (green, SSH_bcb within 

array, altimeteric SSH outside array) denotes the location of the Loop Current. Mapped 

reference level SSH (SSH_ref) reveals the presence of deep cyclones (blue contours) and 

deep anticyclones (red contours) contoured every 2 cm. Diamonds denote PIES sites. 

Grey lines denote the 3000-m depth contour. The frequency band of the SSH data is 

listed below the bottom right panel.
9 MAR 2011

25°N

26°N

27°N

14 MAR 2011 19 MAR 2011 24 MAR 2011

29 MAR 2011

25°N

26°N

27°N

3 APR 2011 8 APR 2011 13 APR 2011

A

B

18 APR 2011

25°N

26°N

27°N

23 APR 2011 28 APR 2011 3 MAY 2011

A

C

8 MAY 2011

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−30−15 0 15 30

13 MAY 2011

88°W 86°W 84°W

18 MAY 2011

SSHref increment: 2 cm

88°W 86°W 84°W

23 MAY 2011

frequency: 100−40

88°W 86°W 84°W

 219

B

B

C

Figure 4.5-6b. Loop Current eddy-shedding event Hadal, 9 March through 23 May 2011. Maps of 

100-40 day band-passed baroclinic SSH referenced to the bottom (SSH_bcb) embedded 

within altimetric SSH (filled color contours; colorbar and contour interval on bottom left). 

Maps shown sequentially left to right, top to bottom at 5-day intervals. The 17-cm contour 

(green, SSH_bcb within array, altimeteric SSH outside array) denotes the location of the 

Loop Current. Mapped 100-40 day band-passed reference level SSH (SSH_ref) reveals 

the presence of deep cyclones (blue contours) and deep anticyclones (red contours) 

contoured every 2 cm. Diamonds denote PIES sites. Grey lines denote the 3000-m 

depth contour. The frequency band of the SSH data is listed below the bottom right 

panel. The 13 April, 3 May and 23 May maps indicate deep anticyclone A, deep cyclone 

B, and deep anticyclone C, respectively. 
28 MAY 2011

25°N

26°N

27°N

2 JUN 2011 7 JUN 2011 12 JUN 2011

17 JUN 2011

25°N

26°N

27°N

22 JUN 2011 27 JUN 2011 2 JUL 2011

7 JUL 2011

25°N

26°N

27°N

12 JUL 2011 17 JUL 2011 22 JUL 2011

27 JUL 2011

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−50−25 0 25 50

1 AUG 2011

88°W 86°W 84°W

6 AUG 2011

SSHref increment: 2 cm

88°W 86°W 84°W

11 AUG 2011

frequency: full

88°W 86°W 84°W

 220

Figure 4.5-6c. Loop Current eddy-shedding event Hadal, 28 May through 11 August 2011 (full frequency 

as in Figure 4.5-6a). 
28 MAY 2011

25°N

26°N

27°N

B

2 JUN 2011 7 JUN 2011 12 JUN 2011

17 JUN 2011

25°N

26°N

27°N

22 JUN 2011

C

27 JUN 2011 2 JUL 2011

7 JUL 2011

25°N

26°N

27°N

12 JUL 2011 17 JUL 2011 22 JUL 2011

27 JUL 2011

88°W 86°W 84°W

25°N

26°N

27°N

SSHbcb [cm]

−30−15 0 15 30

1 AUG 2011

88°W 86°W 84°W

6 AUG 2011

SSHref increment: 2 cm

88°W 86°W 84°W

11 AUG 2011

frequency: 100−40

88°W 86°W 84°W

 221

C

D

Figure 4.5-6d. Loop Current eddy-shedding event Hadal, 28 May through 11 August 2011. The 28 May 

map indicates deep cyclone B and deep anticyclone C discussed in the text. The 22 June 

map indicates deep cyclone D discussed in the text (100-40 day frequency as in Figure 

4.5-6b).
222

to the Franklin event, large amplitude deep eddies and joint intensification (mid-April through

late June) occur prior to the final eddy separation (mid-August).

In summary, our case studies of upper and deep coupling reveal several interesting aspects of 

upper-deep coupling:

• Joint intensification is intermittent, lasting only tens of days while the vertical phase tilt is 

optimal for baroclinic growth.

• Due to the limited spatial domain of the array, we cannot unambiguously distinguish 

between locally generated deep eddies and external deep eddies that may enter and 

intensify when they encounter favorable phasing with the upper thermocline waters. 

• Strongest upper-deep interaction and the most energetic deep eddies can occur well in 

advance of the final eddy separation. A train of upper-deep eddy interactions precedes 

each eddy separation. 

4.5.1 Eddy Potential Energy 

The terms in the time-mean eddy potential-energy budget are evaluated so as to diagnose the role 

of eddies in the system. The goal is to show that eddies extract potential energy from the mean 

field (stored in the sloping isopycnals of the LC) and ultimately convert that energy to eddy 

kinetic energy.

Following Cronin and Watts (1996), a quasigeostrophic framework (small Rossby number) is 

assumed to be valid for our diagnostics. Temperature will be a proxy for density: ρ=ρo(1-αT), 

where α is an effective thermal expansion coefficient (10-4 oC-1). Potential energy budget terms 

are evaluated near 400 m depth. This avoids the near-surface depth of Subtropical Underwater 

where otherwise the role of salinity would have to be independently included when calculating 

density.

In a Boussinesq incompressible fluid, the temperature equation is:

 u!"T = #w!z # "!u$T$ , (4.5.1)

where u=(u,v) is geostrophic velocity, T is temperature, w is vertical velocity and θz is the 

regional background vertical temperature gradient. Overbars indicate a time mean and primes 

indicate deviation from the mean. In the following discussion, u′T′ is referred to as ‘eddy heat 

flux’ since eddy temperature flux multiplied by density and specific heat at constant pressure 

(ρoCp) is a heat flux. Equation 4.5.1 states that mean horizontal advection is balanced by mean 

vertical advection and the divergence of horizontal eddy heat flux. Note that the dynamically 

important part of the eddy heat flux term is the divergent component of eddy heat flux:

 u! "#T! = #"u!T! . (4.5.2) 
223

Eddy heat flux can be decomposed into rotational and divergent components by Helmholtz’ 

theorem. The rotational component merely recirculates heat whereas the divergent component 

provides the net lateral heat flux that transfers potential (baroclinic) energy into eddies. It is a 

challenge, numerically and observationally to isolate these divergent eddy heat fluxes from the 

total eddy heat flux (see Griesel et al. (2009) for a recent discussion). 

The approach will be to take advantage of the velocity vector decomposition, expressed as the 

baroclinic velocity relative to the bottom plus a bottom reference velocity, u = u_bcb + u_ref. 

Mean ψ_bcb streamlines are nearly parallel to mean temperature contours and therefore do not 

advect mean temperature. Figure 4.5-7 shows the linear relationship between mean ψ_bcb and 

mean T at 400 m within our array. The divergent component of the heat flux arises from the 

nearly depth-uniform reference current of which a component can cross the time-varying 

baroclinic LC front. The dynamically important heat flux is entirely contained in u'_refT'. 

Figure 4.5-8 shows the mean eddy heat fluxes for the three LC eddy-shedding events 

superimposed on temperature variance. Eddy heat flux is calculated three ways for this 

illustration, using the total eddy velocity (u'T'), baroclinic eddy velocity (u'_bcbT'), and 

reference eddy velocity (u'_refT'). For each eddy event, u'T' has the largest magnitudes. As 

expected u'_bcbT' circulates around temperature variance. u'_refT' shows downgradient heat 

fluxes in all events with strongest fluxes along the eastern side of the LC. 

The eddy potential energy budget in steady state is determined by multiplying the temperature 

equation by gαT′/θz,

 0 = !u"# g!

2"z

T$

2 ! #"u$

g!

2"z

T$

2 ! g!

"z

u$T$ "#T ! g!T$w$.

 (4.5.3)

where eddy potential energy is defined as

 EPE = g!

2"z

T!

2

. (4.5.4)

Dividing by αg/θz and rearranging yields, 

 u!" 1

2

T#

2

MAP

!#"#$

+ "!u#

1

2

T#

2

EAP

!#"#$

+!zT#w#

PKC

!"$ = $u#T# !"T

BC

!#"#$. (4.5.5)

Equation 4.5.5 states that the horizontal down-gradient eddy heat flux (BC) is balanced by the 

mean advection of eddy potential energy (MAP), eddy advection of eddy potential energy (EAP) 

and the vertical down-gradient heat flux (PKC). In baroclinic instability, the eddy conversion 

term (BC) of mean potential energy to eddy potential energy is balanced by the eddy conversion 

of eddy potential to eddy kinetic energy (PKC). 

If we decompose our velocity field as described above into the baroclinic-referenced-to-thebottom and reference components, we can rewrite the eddy energy budget: 
10 11 12 13 14 15

15.5

16

16.5

17

17.5

ψb c b[m2 s− 2]

T [ °C]

400 m depth

 224

Figure 4.5-7. A linear relationship (black line) exists between mean ψ_bcb and mean T at 400 m (grey 

dots). 
1000 [kW m−2]

ρoC p( u T , v T )

Ekman

total velocity

25°N

26°N

27°N 1000 [kW m−2]

ρoC p( u b c bT , v b c bT )

bcb only

1000 [kW m−2]

ρoC p( u r ef T , v r ef T )

ref only

1000 [kW m−2]

Franklin

total velocity

25°N

26°N

27°N 1000 [kW m−2]

bcb only

1000 [kW m−2]

ref only

1000 [kW m−2]

Hadal

total velocity

88°W 86°W 84°W

25°N

26°N

27°N

T variance [°C2 0 5 10 ]

1000 [kW m−2]

bcb only

88°W 86°W 84°W

1000 [kW m−2]

ref only

88°W 86°W 84°W

Figure 4.5-8. Eddy heat flux vectors at 400-m depth for the three LC eddy-shedding events superimposed on the 400-m depth temperature 

variance. Rows correspond to the LC eddy-shedding events: Ekman, 3 May through 31 August 2009 (top); Franklin, 15 February 

through 14 September 2010 (middle); Hadal, 1 March through 14 September 2011 (bottom). Columns correspond to the perturbation velocity used in the eddy heat flux calculation: total (left), baroclinic-referenced-to-the-bottom (center), reference (right). The 

bold black line denotes the mean position of the 17-cm altimeter-mapped SSH contour; grey contours indicate the 10, 17, 27, and 

37-cm contour. The 3000-m isobath contoured with thin black line. 

225 
226

ubcb !" 1

2

T#

2

MAPbcb

!#"#$

+ uref !" 1

2

T#

2

MAPref

!#"#$

+ "!u#

bcb

1

2

T#

2

EAPbcb

!#"#$

+ "!u#

ref

1

2

T#

2

EAPref

!#"#$

+!zT#w#

PKC

!"$ = $u#

bcbT# !"T

BCbcb

!#"#$ + $u#

refT# !"T

BCref

!#"#$.

(4.5.6)

Because the baroclinic-referenced-to-bottom velocities flow along mean temperature contours, 

there is a relationship between mean temperature and velocity:

fubcb = 2! k ! "T (4.5.7)

where γ is an empirical constant,

 ! = 1

2

d" bcb

dT .

 (4.5.8)

Equations 4.5.7 and 4.5.8 state that the baroclinic-referenced-to-the-bottom field is aligned 

vertically with the front (“equivalent barotropic”), which is a good approximation in our array 

(Figure 4.5-7). With this decomposition, the following relationships hold:

 

ubcb !" 1

2

T#

2

MAPbcb

!#"#$

= $u#

bcbT# !"T

BCbcb

!#"#$

and

"!u#

bcb

1

2

T#

2

EAPbcb

!#"#$

= 0,

 (4.5.9)

 (4.5.10)

Therefore, the mean eddy potential energy budget can be reduced to the following: 

 uref !" 1

2

T#

2

MAPref

!#"#$

+ "!u#

ref

1

2

T#

2

EAPref

!#"#$

+!zT#w#

PKC

!"$ = $u#

refT# !"T

BCref

!#"#$. (4.5.11)

Hereafter the subscript ref will be dropped from Equation 4.5.11.

To calculate these terms, one needs to determine vertical velocity w and mean θz. θz is 

determined by the mean stratification within the array and at 400 m depth has a value of 0.023 

°C.m-1. Following Lindstrom and Watts (1994) and Howden (2000), vertical velocity is 

estimated near the base of the thermocline from the depth of the 6° isotherm (Z6 )

 w = !Z6

!t

+ u !"Z6. (4.5.12)

Z6 is negative and becomes increasingly negative with depth. 
227

Figures in the following eddy-specific discussions show the results of calculating the terms in the 

mean eddy potential energy budget (Eqn. 4.5.11), and it is noted that the energetics for the three 

shedding events share the following characteristics:

• The magnitude of eddy advection of eddy potential energy, EAP, a triple-correlation term 

which has often been assumed small, must in fact be included in the budget, because it is 

of the same order as the baroclinic conversion (BC) and vertical down-gradient heat flux 

(PKC). The mean advection of eddy potential energy (MAP) by the ref field is small 

compared to the other four terms. The spatial pattern and magnitude of the combined 

PKC+EAP+MAP terms is very similar to the BC term. 

• At any particular location, the time series that contribute to the terms in the eddy energy 

budget are event-like in the LC, often with only a few events dominating the mean. The 

maps summarize the energy conversion rates over the time interval of each respective 

case study. They are not individually intended as statistical studies, but there is obviously 

a strong similarity amongst them. Conversion of eddy potential energy to eddy kinetic 

energy occurs primarily along the eastern edge of the LC.

Eddy Ekman 

The BC term nearly balances the sum of the PKC, EAP and MAP terms (Figure 4.5-9). The BC 

term is positive (indicating down-gradient fluxes) along the northwestern corner near the 

Mississippi Fan and along the eastern side of the LC. Overall, the pattern in the PKC term 

corresponds well to the BC term, although the maxima and minima are slightly displaced from 

one another. Time series of the BC′ and PKC′ terms in three regions where both terms are strong 

and positive are shown in Figure 4.5-10. Here BC′ is defined as !u"

refT" #$T and PKC′ is 

defined as!z

T!w!. Time series track each other well and are positively correlated with one 

another, with correlation coefficients (r) ranging from 0.51 to 0.74. The peaks in the time series 

can be traced back to dates when the deep eddies and upper SSHbcb 40-to-100 day band passed 

fields jointly intensify. For the three time series shown here, located at the correspondingly 

color-coded stars on the map at the top of the figure, the peaks are associated with times when 

deep cyclone A intensifies as it propagates along the LC periphery: near the Mississippi Fan 

(magenta star in Figure 4.5-10) in mid-July, at the northeast corner (blue star) in late July and in 

the southeast corner (cyan star) in early August. 

Eddy Franklin 

Similar to Ekman, during the Franklin event, the BC term nearly balances the sum of the PKC, 

EAP and MAP terms (Figure 4.5-11). The BC term is positive (indicating down-gradient fluxes) 

near the base of the Mississippi Fan, along the eastern side of the LC as well as in the central 

portion of the array. Overall, the pattern in the PKC term corresponds well to the BC term, 

although the maxima and minima are slightly displaced from one another. Additionally, the 

range of PKC values is larger than the BC range, particularly in the central array. Time series of 

the BC′ and PKC′ terms in three regions where both terms are strong and positive are shown in 

Figure 4.5-12. Note the vertical scale extends to higher rates than for the other two eddy 

separation case studies discussed here. Time series track each other well and are positively
Ekman: 3 May 2009 through 31 Aug. 2009 400-m depth

 88°W 86°W 84°W

 25°N

 26°N

 27°N

P K C + E A P + M A P

 88°W 86°W 84°W

 25°N

 26°N

 27°N

P K C w T Θz

 88°W 86°W 84°W

 25°N

 26°N

 27°N

10−3 cm2s−3

−3 −1 1 3

B C − u T T

Δ .

 88°W 86°W 84°W

 25°N

 26°N

 27°N

E A P 1

2 u T Δ 2 .

 88°W 86°W 84°W

 25°N

 26°N

 27°N

M A P u 1

2 T

Δ 2 .

 228

Figure 4.5-9. Four terms in the steady eddy potential-energy budget (Equation 4.5.5) determined for the 

Ekman event, 3 May through 31 August 2009 at 400-m depth (contour interval is 0.5×10-3

cm2s-3; colorbar indicates that blue hues are negative and orange hues are positive). The 

horizontal down-gradient eddy heat flux (BC) is balanced by the mean advection of eddy 

potential energy (MAP), eddy advection of eddy potential energy (EAP) and the vertical 

down-gradient heat flux (PKC). Top right panel shows the sum of the PKC, EAP and MAP 

terms. The red line denotes the mean position of the 17-centimeter-mapped SSH contour. 

Bathymetry (black lines) contoured every 1000-m depth. 
Ekman: 3 May 2009 through 31 Aug. 2009 400-m depth

 88°W 86°W 84°W

 25°N

 26°N

 27°N

P K C w T Θz

 88°W 86°W 84°W

 25°N

 26°N

 27°N

10−3 cm2s−3

−3 −1 1 3

Jun Jul Aug Sep

−20

0

20 B C P K C r = 0.51

10−3 cm2

s−3

Jun Jul Aug Sep

−20

0

20 r = 0.74

10−3 cm2

s−3

Jun Jul Aug Sep

−20

0

20 r = 0.62

10−3 cm2

s−3

B C − u T T

Δ .

 229

Figure 4.5-10. Top panels: BC (left) and PKC (right) at 400-m depth determined for the Ekman event 

(contour interval is 0.5×10-3 cm2s-3; colorbar indicates that blue hues are negative and 

orange hues are positive). The red line denotes the mean position of the 17-cm altimetermapped SSH contour. Bathymetry (black lines) contoured every 1000-m depth. Bottom 

three panels: time series of BC′ (red) and PKC′ (blue) at locations indicated by colored 

stars in the mapped energetic terms (top panels) and denoted on the top left corner of 

each time series plot. 
Franklin: 15 Feb. 2010 through 14 Sept. 2010 400-m depth

 88°W 86°W 84°W

 25°N

 26°N

 27°N

P K C + E A P + M A P

 88°W 86°W 84°W

 25°N

 26°N

 27°N

P K C w T Θz

 88°W 86°W 84°W

 25°N

 26°N

 27°N

 88°W 86°W 84°W

 25°N

 26°N

 27°N

 88°W 86°W 84°W

 25°N

 26°N

 27°N

10−3 cm2s−3

−3 −1 1 3

B C − u T T

Δ .

E A P 1

2 u T Δ 2 . M A P u 1

2 T

Δ 2 .

 230

Figure 4.5-11. Four terms in the steady eddy potential-energy budget (Equation 4.5.5) determined for 

the Franklin event, 15 February through 14 September 2010 at 400-m depth (contour 

interval is 0.5×10-3 cm2s-3; colorbar indicates that blue hues are negative and orange 

hues are positive). The horizontal down-gradient eddy heat flux (BC) is balanced by the 

mean advection of eddy potential energy (MAP), eddy advection of eddy potential energy 

(EAP) and the vertical down-gradient heat flux (PKC). Top right panel shows the sum of 

the PKC, EAP and MAP terms. The red line denotes the mean position of the 17-cm 

altimeter-mapped SSH contour. Bathymetry (black lines) contoured every 1000-m depth. 
Franklin: 15 Feb. 2010 through 14 Sept. 2010 400-m depth

 88°W 86°W 84°W

 25°N

 26°N

 27°N

P K C w T Θz

 88°W 86°W 84°W

 25°N

 26°N

 27°N

10−3 cm2s

−3

−3 −1 1 3

Mar Apr May Jun Jul Aug Sep

−20

0

20

40 B C P K C r = 0.49

10−3 cm2

s−3

Mar Apr May Jun Jul Aug Sep

−20

0

20

40 r = 0.67

10−3 cm2

s−3

Mar Apr May Jun Jul Aug Sep

−20

0

20

40 r = 0.49

10−3 cm2

s−3

B C − u T T

Δ .

 231

Figure 4.5-12. Top panels: BC (left) and PKC (right) at 400-m depth determined for the Franklin event 

(contour interval is 0.5×10-3 cm2s-3; colorbar indicates that blue hues are negative and 

orange hues are positive). The red line denotes the mean position of the 17-cm 

altimeter-mapped SSH contour. Bathymetry (black lines) contoured every 1000-m depth. 

Bottom three panels: time series of BC′ (red) and PKC′ (blue) at locations indicated by 

colored stars in the mapped energetic terms (top panels) and denoted on the top left 

corner of each time series plot.
232

correlated with one another, with correlation coefficients (r) ranging from 0.49 to 0.67. Positive 

BC and PKC peaks along the eastern side of the LC coincide with the propagation of several 

deep eddies. In the southeast (magenta star in Figure 4.5-12), peaks are due to the intensification 

of deep anticyclone A (Figure 4.5-5b) in early May. Along the northeast (blue star in Figure 4.5-

12) the peak is due to the intensification of deep cyclone B. In the central array (cyan star), the 

mid-June BC and PKC peaks occur when deep anticyclone C is intensified. 

Eddy Hadal 

Just as for the Ekman and Franklin case studies, the BC term nearly balances the sum of the 

PKC, EAP and MAP terms (Figure 4.5-13). The BC term has a maximum just downstream of the 

Mississippi Fan near 26.2°N, 86.2°W. The PKC term is also high here, indicating that eddies 

gain potential energy from the mean LC and convert that energy to eddy kinetic energy. An 

additional maximum occurs in the PKC field, near 26.2°N, 87.5°W, and here the balance is 

mainly between PKC and EAP. Figure 4.5-14 shows the time series of BC′ and PKC′ centered 

on a location where both terms sum to a strong positive peak. Again, the time series track each 

other well; the correlation coefficient is 0.86. The two large peaks in the time series, late April 

and mid-May, coincide with the intensification of deep cyclone B and deep anticyclone C, 

respectively (Figure 4.5-6b). 

4.6 TOPOGRAPHIC ROSSBY WAVES 

In a review of lower-layer current observations in the Gulf, Hamilton (2009) showed that 

bottom-trapped low frequency motions were consistent with TRWs in almost all deep water 

regions. He speculated that the LC could generate TRWs that would propagate towards the 

Sigsbee escarpment where high-speed near-bottom currents had been observed (Hamilton and 

Lugo-Fernandez 2001). Moreover, the variation of the frequency bands of the dominant EKE 

along the Sigsbee, from ~10 days in the east to ~60 days in the west, could be explained by the 

dispersion of TRWs of different periodicities having different paths to the slope. Using a highresolution numerical model, Oey (2008) proposed a mechanism where the growth of LCFEs 

along the western and northern parts of the LC front generated corresponding deep eddies that 

detached from the LC and translated to the west. The decay of these westward translating deep 

eddies generated the TRWs that radiated towards the northern slope. As discussed above, there 

is little evidence of a direct generation of deep eddies by LCFEs over this part of the LC front. A 

more direct generation mechanism that is consistent with the models of Malanotte-Rizzoli et al. 

(1987) is that as the LC advances to the northwest over shoaling topography, there is 

compression of the water column, which leads to the observed mean anticyclonic deep 

circulation, but would also radiate broad band TRWs. Because TRW motions have a highfrequency cut off proportional to the bottom slope, above which propagating waves are not 

supported (Rhines 1970), short-period waves would only be generated over the steeper 

topography of the Mississippi Fan, and the relatively gentle abyssal slopes under the LC would 

favor the longer periods of 40 to 60 days that are prominent in the velocity records. LaCasce 

(1998) discusses the stability of geostrophic vortices over a slope, and in many cases both an 

initially barotropic and a surface-intensified vortex will radiate TRWs and still maintain a stable 

upper-layer vortex. This seems possible for the barotropic modes under the LC, but would also 

be true for a separated westward-translating LC eddy (also pointed out by Oey and Lee (2002)). 

So it is unclear, from theoretical arguments, whether the barotropic modes of the LC or the
Hadal: 1 Mar. 2011 through 14 Sept. 2011 400-m depth

 88°W 86°W 84°W

 25°N

 26°N

 27°N

P K C + E A P + M A P

 88°W 86°W 84°W

 25°N

 26°N

 27°N

P K C w T Θz

 88°W 86°W 84°W

 25°N

 26°N

 27°N

 88°W 86°W 84°W

 25°N

 26°N

 27°N

 88°W 86°W 84°W

 25°N

 26°N

 27°N

10−3 cm2s−3

−3 −1 1 3

B C − u T T

Δ .

E A P 1

2 u T Δ 2 . M A P u 1

2 T

Δ 2 .

 233

Figure 4.5-13. Four terms in the steady eddy potential-energy budget (Equation 4.5.5) determined for 

the Hadal event, 1 March through 14 September 2011, at 400-m depth (contour interval is 

0.5×10-3 cm2s-3; colorbar indicates that blue hues are negative and orange hues are 

positive). The horizontal down-gradient eddy heat flux (BC) is balanced by the mean 

advection of eddy potential energy (MAP), eddy advection of eddy potential energy (EAP) 

and the vertical down-gradient heat flux (PKC). Top right panel shows the sum of the 

PKC, EAP and MAP terms. The red line denotes the mean position of the 17-cm 

altimeter-mapped SSH contour. Bathymetry (black lines) contoured every 1000-m depth. 
Hadal: 1 Mar. 2011 through 14 Sept. 2011 400-m depth

 88°W 86°W 84°W

 25°N

 26°N

 27°N

P K C w T Θz

 88°W 86°W 84°W

 25°N

 26°N

 27°N

10−3 cm2s

−3

−3 −1 1 3

Mar Apr May Jun Jul Aug Sep

−20

0

20 B C P K C r = 0.86

10−3 cm2

s−3

B C − u T T

Δ .

Figure 4.5-14. Top panels: BC (left) and PKC (right) at 400-m depth determined for the Hadal event 

(contour interval is 0.5×10-3 cm2s-3; colorbar indicates that blue hues are negative and 

orange hues are positive). The red line denotes the mean position of the 17-cm 

altimeter-mapped SSH contour. Bathymetry (black lines) contoured every 1000-m depth. 

Bottom panel: time series of BC′ (red) and PKC′ (blue) at location indicated by colored 

star in the mapped energetic terms (top panels) and denoted on the top left corner of the 

time series plot.

 234
235

surface-intensified large (relative to the Rossby deformation radius) LC eddies are more efficient 

at generating the TRWs that impinge on the lower-northern slope.

To investigate whether TRWs are supported by deep-current fluctuations under the LC, a 

wavenumber analysis was performed for the interval during the detachments of Franklin when 

deep EKE and relative vorticity fluctuations increase in magnitude (Figure 4.2-1). This interval 

was defined to be from 15 March to 15 October 2010. Using the velocity records at 100 mab in 

subsets of three or four locations surrounding a PIES location, frequency domain EOF modes 

were calculated for the 100 to 20-day band. This is consistent with the periodicities chosen for 

the PIES baroclinic instability analysis given in the previous section. The velocity stations used 

for each nominal PIES location are exactly the same as for the relative vorticity calculations (see 

Section 2.9). In most cases two EOF modes were significant, and using a least square fit to the 

phase angles, east and north wave numbers were estimated as in Hamilton (1990; 2009). The 

direction of the local isobaths at each PIES location was determined from a least square plane fit 

to the latest version (13) of the Smith and Sandwell (1997) global topography data base, where 

the one minute resolution topography was smoothed with a 25 km median filter. Where the 

wavenumber was directed into the second or third quadrant in the local isobath coordinate frame 

where the shallower water is to the left of the along-isobath coordinate, the mode was considered 

a candidate for being a TRW. Thus, the along-isobath wavenumber component (k) is negative in 

the isobaths coordinate frame, as is required by the theory (Rhines 1970). The cross-isobath 

wavenumber component (l) usually dominates and may be directed up or down slope. The group 

velocity is perpendicular to the phase velocity and also directed into the 2nd or 3rd quadrants, and 

for long-period waves, this is a small angle to the negative along-isobath direction. The results 

are given in Figure 4.6-1 where the size of the dot gives the variance of the mode divided by the 

number of velocity locations (three or four). Under the east side of the LC, amplitudes are small 

or non-existent (locations 71 and 76), with the largest amplitudes in a north-south band between 

86.5 and 87°W. Most of the wavenumbers are directed up slope, but are nearly parallel to the 

across-isobath axes. This indicates that the TRWs would propagate along the isobaths to the 

west. Wavenumber magnitudes indicate wavelengths ranging from ~50 to 200 km, which is 

typical of short wavelength TRWs in the Gulf (Hamilton 2009). Conclusions are that lowerlayer currents have some characteristics of TRWs under the LC, but only in the north and central 

part of the array. Amplitudes may be small (maximum of ~7 cm s

-1

), but would involve the 

whole of the ~3000-m water column as the mode is barotropic. The western side of the LC front, 

over deep water where measurements were not made (Figure 4.6-1), is also a candidate for a 

source region for TRWs.

4.7 NUMERICAL MODELING

Numerical modeling studies were largely devoted to understanding LC variability and its effects 

on the Gulf basin, particularly looking at the intra-annual variability and its relation to largescale wind systems including those over the Caribbean. In addition, research was made into 

more efficient assimilation schemes that produce more skillful forecasts and hindcasts. The 

latter has been published (Xu et al. 2013a) and shows that a local ensemble transform Kalman 

filter was better than optimal interpolation and persistence of AVISO SSHA in forecasting the 

location, size, and slow separation velocity of Franklin in 2010. This was particularly 

challenging because Franklin’s separation speed, caused by its small size and weak circulation 

after August 2010, was not determined by Rossby wave propagation, as is more usual. The 
1000 m

2000 m

2500 m

1000 m

3000 m

3500 m

200 m

200 m

Wave Number

1/100 km-1

Mode Variance/Station

25 cm2 s-2

Lower Layer EOF 100-20 day Wavenumber Analysis for Eddy Franklin 

15 March to 15 October 2010

 236

Figure 4.6-1. Wavenumbers from 100 to 20-day EOFs for the 100-mab currents for Franklin where the 

propagation is compatible with TRWs. The wavenumber and direction is given by the red 

lines, and the total variance (normalized by the number of stations (three or four) in the 

EOF mode) by the diameter of the blue dot. Isobath coordinate axes are given by the 

dashed lines where the arrowhead denotes the direction of the local isobaths, where the 

shallower water is to the left. The mean location of the 17-cm SSH cotour for the analysis period is given by the purple line.
237

reader is referred to the paper for details of the techniques and comparisons, which will not be 

repeated here.

In section 4.2, tentative observational support was given, in terms of array-averaged vertical 

velocity, for Chang and Oey’s (2011) modeling study of canonical LC growth and separation, 

driving large-scale upwelling and downwelling. The translation of a model LC eddy to the west 

drives deep exchanges between the western and eastern basins. The phasing of these transports

provides an explanation of why deep counter flows in the Yucatan Channel do not directly relate 

to LC growth and retreat. Chang and Oey (2011) give dynamical arguments that, because of 

essentially closed topographic contours in the lower layer, a cyclonic gyre must exist in the 

western Gulf as a compensation of the net downward flux imposed by the LC in the eastern 

basin. Observations support (DeHaan and Sturges 2005; Hamilton 2009), at least in the northern 

abyssal Gulf, a cyclonic deep gyre. They predict that the gyre strength is modulated by the LC 

cycle such that it is strongest when the LC is reforming, and weakest when an eddy separates and 

translates into the western basin. At present, there are not enough long-term observations to 

confirm this prediction.

Chang and Oey (2010a) discuss the effect of large-scale wind fields over the Gulf on the 

shedding of eddies. They postulate that LC eddy shedding is largely mediated by the PichevinNof mechanism, and thus does not involve the lower layer. An eddy separation occurs when the 

westward translation of the eddy, as a Rossby wave, exceeds the growth of the LC from upperlayer volume transport imbalances between the Yucatan Channel and the Florida Straits. Note 

that the Pichevin-Nof theory (Pichevin and Nof 1997) per-se does not predict that eddies will 

separate, but merely accounts for an extended LC to bend and stretch towards the west. The 

results from this program’s observations indicate that baroclinic instabilities involving the upper 

and lower layers act as the main agent for eddy detachments. Further discussion of these points 

is reserved for Chapter 7. However, it is noted that after an eddy has separated, it will translate 

westwards at Rossby wave speeds if the western basin upper layer is quiescent. Chang and Oey 

(2010a) apply a spatially uniform, constant, westward wind over the Gulf (i.e., excluding model 

regions external to the Gulf) that mimics the trades. They find, compared to the no wind case, 

that substantial westward transports are forced on the northern (Louisiana and Texas) and 

southern (Campeche Bank) shelf regions. The compensating eastward upper-layer transport 

occurs mainly in the center of the basin that opposes the westward translation of LC eddies, and 

therefore would impede an eddy attempting to detach from a fully extended LC. A recent study 

by Sturges and Bozec (2013), using historical databases of ship drift and surface-layer drifters 

from many decades of observations, show that there are substantial westward mean flows over 

the northern and southern shelves, but these westward drifts are not compensated by mid-basin 

eastward surface mean flows. Indeed, the mean flow in mid basin from their calculations is still 

westward. Sturges and Bozec (2013) compare their surface-transport results with a couple of 

numerical-model calculated means, and find that the model results approximately obey 

continuity with westward and eastward transports in balance. This model-data discrepancy has 

yet to be resolved, but has profound implications for mean circulations. If the surface transport 

is westward across the 91°W meridian, as indicated by Sturges and Bozec’s (2013) calculations, 

then the compensating return flow must occur at depth and involve downwelling in the western 

part of the Gulf. If the eastward return flow is at a shallow depth, then the Chang and Oey 

(2010a) mechanism for delaying LC eddy shedding may be valid. Observations are too sparse 
238

below the surface layer to resolve this dilemma. When more realistic but still idealized winds 

are used, as in Chang and Oey (2013a), the delaying effect of westward winds over the Gulf is 

less apparent. This is discussed in more detail in Chapter 5 where the historical record of eddy 

separations is subjected to a rigorous analysis, and suggests that westward winds over the Gulf 

do not play a significant role.

Chapter 5 discusses the historical record of LC eddy shedding, and establishes that there is an 

annual signal in average LC metrics, with maxima in the spring, minima in the fall and early 

winter. This leads to higher and lower probabilities for eddy shedding in these respective 

seasons. A number of reduced-gravity model experiments were performed to establish possible 

mechanisms behind these seasonal preferences. These experiments are reported in Chang and 

Oey (2013a). In a single-layer reduced gravity model, eddy separation is attributed to the 

Pichevin-Nof mechanism where the Rossby wave westward translation of the northern part of an 

extended LC exceeds the growth of the LC. Thus, this mechanism does not involve the lower 

layer, and Xu et al. (2013b) indicate that in their fully 3D model, wind effects and baroclinic 

instability modify the timing of separations, but the Pichevin-Nof mechanism is the fundamental 

process. This differs from the observational analysis of Section 4.5 where baroclinic instability 

has a much more prominent role.

Nevertheless, the numerical experiments established a relation with the biannual signal of the 

Caribbean trade winds, which have westward component maxima in June-July and December, 

with minima in April-May and September-October. The biannual wind cycle is not symmetric, 

but was approximated by a biannual sinusoidal modulation, which (in the model) drives a 

biannual northward transport anomaly in the Yucatan Channel. The flow patterns and biannual 

cycles of wind and Caribbean transports are shown in Figure 4.7-1 (taken from Chang and Oey 

(2013a); their Figures 7 and 9). The YC northward transport anomaly promotes LC growth 

when it is positive, and promotes a shedding event by the Pichevin-Nof mechanism when it is 

negative, if the LC is well extended. The SSHA monthly composite in the northwest Caribbean 

(from the model) is compared to the equivalent AVISO-derived signal in Figure 4.7-1f. If the 

model leads by one month, the correlation (R) is 0.66, with a 95% significance level of 0.52. 

The reanalysis of the historical SSH altimeter record is performed in Chapter 5, where the 

significance of the Caribbean anomalies is discussed, and an alternate mechanism involving 

coastal-trapped waves that perturb the LC within the Gulf, rather than winds in the northwest 

Caribbean, is proposed and analyzed. These somewhat contradictory investigations indicate that 

several processes that still need more study may be the causes of the complex variability of the 

LC.
(F)

 239

Figure 4.7-1. (a)-(d): Schematic illustrations of the dominant flow anomalies in the northwestern 

Caribbean Sea for the indicated months based on monthly composites derived from EOF 

analysis of model SSH; grey vector shows total (i.e., not anomaly) wind. (e) 12-year 

composite of monthly transport anomalies (Sv = 106 m3s-1) in the control volume shown 

in the rectangle in (a). The mean ± fluctuation (in Sv) for each term is shown. Grey curve 

is the specified zonal wind stress in m2s-2. (f) Monthly AVISO SSHA and scaled reduced 

gravity (RG) model SSH averaged over 17.5°-22.5°N; 87°-80°W in the northwestern 

Caribbean Sea with standard error bars. Plots are repeated for two years (from Chang 

and Oey 2013a). 

(a)

(f)

(e)

(b) (c) (d)

241

CHAPTER 5: LONG TERM AND SEASONAL VARIABILITY 

5.1 INTRODUCTION 

Continuous monitoring of the LC is required to accurately identify LC eddy separation events, 

since eddies frequently detach and re-attach before ultimately separating, and separation may 

occur at any time of the year. Multi-satellite altimetric mapping of the ocean mesoscale afforded 

by the ERS-1 and TOPEX/Poseidon missions, and later follow-on missions, provided the 

satellite sampling required to achieve this monitoring capability in the early 1990s. Continuous 

multi-satellite altimetric mapping has remained to the present day. 

Before the advent of satellite altimetry, a number of observational technologies were exploited 

for LC monitoring. Studies of LC intrusion and eddy separation in the 1970s relied on a variety 

of data sources, including in-situ and satellite data to identify separation events, and were subject 

to periods of poor sampling. The earliest studies were based on upper-ocean temperature sections 

along shipboard survey cruise transects (Leipper 1970; Maul 1977; Behringer et al. 1977). Most

of these observations were made during the spring, summer and fall. In those studies an annual 

cycle of LC intrusion was hypothesized based on earlier observations of an annual cycle in 

Yucatan Current inflow, with maximum currents in May and June and a minimum in October 

and November (Cochrane 1965). Leipper (1970) proposed an annual cycle of LC intrusion in the 

spring followed by either a deeply intruded LC in the fall or a separated eddy and retreated LC. 

That study was based on in-situ data collected primarily during 1965 and 1966. Maul (1977) 

found a similar cycle in 1972 and 1973, and was able to track the frontal position of the LC over 

14 months. Thus, by the mid-1970s the emerging consensus was that the LC exhibited a mean 

annual cycle, with significant deviations due to highly variable eddy-separation events. 

Separation periods had been observed to range from as short as eight months to as long as 17 

months (Behringer et al. 1977). During an average annual cycle, the LC intruded northward into 

the Gulf in the spring, followed by maximum intrusion with probable eddy separation during 

summer and fall, and retreat to the south during winter, since the few winter observations over 

this time period did not show a LC intrusion north of 26°N. 

In the mid-1970s, satellite radiometry imagery became available at sufficient resolution and 

precision to observe synoptic-scale and mesoscale fronts in the Gulf. Maul (1975) demonstrated 

that satellite imagery could be used to detect the western margin of the LC during winter. 

Legeckis (1976) reported the first wintertime deep intrusion and eddy separation determined 

from direct observations during the winter of 1974 and 1975. Later, Molinari et al. (1977) used 

both satellite and in-situ data to identify intrusions of the LC north of 26° N from 1974 through 

1977, and LC eddy separation events in both winter and spring. They concluded that, since the 

earlier observational dataset was limited during the wintertime, it was not clear whether winter 

intrusions occurred before the mid-1970s. Their work provided the first evidence, however, that 

eddy separation could occur in any season. 

By the late 1970s, “monthly” sea-surface temperature (SST) frontal analyses in the Gulf were 

being made from the very high-resolution radiometer (VHRR) instruments onboard polar 

orbiting NOAA satellites (Vukovich et al. 1979). These analyses were typically based only on a 

few clear-sky SST images and could not be made throughout the year. From June through 
242

October, the LC and LC eddy fronts could not be distinguished in the SST imagery when the 

warm seasonal surface mixed layer developed in the Gulf. In May, when the seasonal mixed 

layer was developing, intense image enhancement of some of the imagery was needed to identify 

the fronts. For this reason, there were times when the accuracy of some features in May frontal 

analyses were questioned and earlier analyses were used instead. In the time periods when LC 

and LC eddy SST thermal fronts were masked by the mixed layer, information on the LC and 

warm rings were also obtained from MMS, Navy, NSF, NOAA, and the various oil companies 

that sponsored ship surveys in the Gulf. That information was supplemented with available 

Coastal Zone Color Scanner (CZCS) data to estimate the LC and LC eddy positions, the position 

of the northern boundary of the LC, the diameter of the ring, etc. Though frontal analyses could 

not be created from those data, they were entered into an unpublished database maintained by 

Dr. Fred Vukovich (Vukovich 2012).

Infrared images from the Geostationary Operational Environmental Satellite (GOES) were also 

used for LC monitoring in the late 1970s. Imagery processed by the NOAA Miami Satellite Field 

Services Station was geo-registered using photographic techniques and animated in order to 

attempt to map daily locations of the LC front (Maul et al. 1978). The 24-hour coverage 

provided by GOES geostationary sampling reduced data outages associated with cloud cover, 

and oceanic fronts in the Gulf Stream system could be mapped about half of the days (Maul et al. 

1984).

Several significant technological advancements in satellite oceanography occurred in the 1970s 

that contributed to the development of operational satellite monitoring of the LC and LC eddies. 

These advancements included the first successful tests of satellite-tracked drifting buoys, satellite 

altimetry, and satellite ocean-color radiometry. Satellite-tracked drifting ocean buoys were 

developed using data collected by the NASA Nimbus-6 satellite, which carried a Tracking and 

Data Relay experiment that was used to determine drifting buoy positions using Doppler tracking 

(Kirwan et al. 1976). Nimbus-6 was launched on 12 June 1975 and operated until 29 March 

1983. This research mission led to the development of the Advanced Research Global 

Observation Satellite (ARGOS) system, which collects, processes, and disseminates data from 

fixed and mobile platforms using polar orbiting NOAA satellites to the present day. Kirwan et al. 

(1984) documented the first use of satellite-based tracking of drifting buoys within a LC eddy. 

Three satellite-tracked drifting buoys were air deployed in November 1980 by the NOAA Data 

Buoy Center into a fall-separated LC eddy and permitted satellite tracking of the LC eddy into 

the western Gulf, well into spring 1981. The drifters were undrogued, but had 200-m thermistor 

cables attached. It is noteworthy that this is the only mention of a LC eddy separation event in 

the fall of 1980 reported in the peer-reviewed literature. This event does not appear in published 

LC eddy separation event censuses (Vukovich 1988; Sturges 1994) or their re-publication 

(Sturges and Leben 2000; Leben 2005; Vukovich 2012). In the late 1970s, the first oceanaltimetry and ocean-color satellite missions were flown by NASA. Seasat, launched on 27 June 

1978, carried the first satellite altimeter capable of measuring ocean-surface topography with the 

accuracy required to resolve ocean-mesoscale signals (Cheney et al. 1983). The first instrument 

devoted to the measurement of ocean color, the CZCS, was launched aboard the Nimbus-7 

satellite on 24 October 1978. These were experimental missions and little of these data made it 

into the general user community for use in operational ocean monitoring or into the published 

LC eddy separation censuses. Later, Müller-Karger et al. (1991) demonstrated that the combined 
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use of CZCS ocean-color and Advanced Very High Resolution Radiometer (AVHRR) SST 

images permits year-round monitoring of LC intrusion and eddy separation. The LC eddy 

separation event in the fall of 1980, mentioned above, can be seen clearly in the August and 

September ocean-color images shown in Plate 1b of that paper.

In the early 1980s, the hypothesis that the LC sheds eddies in response to annual variations in the 

inflow through the Yucatan Channel was challenged by a study of LC intrusion and eddy 

shedding using a numerical ocean model (Hurlburt and Thompson 1980). They found that a 

modeled LC could penetrate into the Gulf, bend westward, and shed realistic LC eddies at a 

quasi-annual natural shedding frequency with steady inflow. The quasi-annual period was about 

290 days. This was the first numerical model of the Gulf that was integrated to statistical 

equilibrium and simulated the basic repetitive features of the LC eddy shedding (Hurlburt and 

Thomson 1982). They also found that realistic time varying upper-layer inflow could 

significantly influence the eddy separation. Nevertheless, the eddy shedding was dominated by 

the natural period, not the period of forcing in the model experiments. At about the same time, 

Sturges and Evans (1983) speculated that there were wind-forced annual variations in the northsouth position of the LC. They relied on hydrographic data to determine the northernmost 

position of the LC. Difficulties were noted in reconciling the in-situ estimates of the LC position 

with surface observations determined from satellite images, so only in-situ data were used in 

their analyses. Thus, the basic hypotheses determined from modeling and observational studies 

were at odds with each other, with the state-of-the-art modeling studies indicating a natural 

shedding period (a quasi-annual period of about 10 to 11 months) and some unidentified external 

forcing contributing to the limited observational evidence of a true annual cycle. Given that the 

annual signal amplitude in the northern LC boundary was only 1.7 degrees, it seemed reasonable 

that the annual signal detected in observations was just an artifact of under sampling and 

averaging over the observed highly variable LC eddy shedding cycles.

All subsequent analyses of the LC annual cycle and LC eddy separation periods published in the 

late 1980s and early 1990s relied heavily on monitoring of the LC using SST imagery (Vukovich 

1988; Maul and Vukovich 1993; Sturges 1992; 1993; 1994) and were affected by outages due to 

seasonal heating of the mixed layer and the lack of consistent sampling. There was also limited 

access to satellite altimetry, satellite ocean color, and industry monitoring. This led to 

inaccuracies in the published record and misrepresentation of the annual cycle in the prealtimetric record when SST imagery was relied on too heavily for LC monitoring, as will be 

shown in this chapter. Thus, the general consensus from the 1980s and through the 1990s was 

that the LC exhibited little or no annual cycle.

Late in the 1990s and into the new century, satellite altimetric and industry monitoring made 

tracking of the LC and its associated eddies fully operational. Nevertheless, the seasonality of 

LC eddy separation only became apparent over time as the length of the continuous record of 

altimetric monitoring of the LC and LC eddies increased enough to resolve the seasonal signal, 

independent of the earlier historical and published records. Industry concerns, about the joint 

probability of eddy-hurricane events in the Gulf (Cooper and Stear 2009) and the potential 

impact of LC seasonality on the joint probability, motivated a preliminary re-analysis of the prealtimetric and altimetric record of LC intrusion and eddy shedding. 
244

The following sections in this chapter describe the detailed observational analyses that were 

performed using the available historical and satellite records, and what has been learned about 

the dynamics contributing to LC seasonality and eddy separation. Section 5.2 describes the reanalysis of the pre-altimetric LC record; Section 5.3 provides comparisons of the re-analysis with 

previously published separation dates; Section 5.4 describes the 20-year-long altimetric LC 

record; and Section 5.5 presents a detailed statistical analysis of LC seasonality. Section 5.6 

presents the present study’s investigation of the dynamics contributing to LC seasonality and 

identifies the dominant signal contributing to the observed LC seasonality and annual cycle.

5.2 RE-ANALYSIS OF THE “PRE-ALTIMETRIC” LOOP CURRENT RECORD

Continuous multi-satellite altimetric sampling required for accurate mapping of the SSH 

associated with mesoscale circulation in the Gulf and monitoring of the LC and LC eddies did 

not exist prior to late 1992. NASA Seasat altimetry, NASA CZCS ocean color, AVHRR SST, 

and ESA ERS-1 satellite altimetry data were used to perform a re-analysis of the separation 

events during the “pre-altimetric” LC record before 1993. LC and LC eddy positions determined 

from Horizon Marine Inc. (HMI) EddyWatchTM reports and the Climatology and Simulation of 

Eddies/Eddy Joint Industry Project (CASE/EJIP) Gulf Eddy Model (GEM) analyses were used to 

supplement the satellite observations. Table 5.2-1 lists the dates of all 20 identified separation 

events in the record along with HMI industry names (if available), separation periods, and retreat 

latitudes. The separation period is the length of time between separation events. Retreat latitude 

is the maximum latitude of the LC immediately following separation of a LC eddy (Leben 2005). 

The mean separation period over this time period is 270.5 days and the mean retreat latitude is 

25.7°N.

Seasat along-track altimetry data are available from July through October 1978 from the NASA 

Ocean Altimeter Pathfinder program (Koblinsky et al. 1998). The data were processed as nonrepeat track data similar to the processing described for ERS-1 geodetic mission data in Leben et 

al. (2002). CZCS data are available from November 1978 into June 1986 from the NASA Ocean 

Color Webpage (CZCS 2008). Level-3 chlorophyll-a concentration 8-day composite images at 4-

km resolution were used in the re-analysis (downloaded 10 July 2008). AVHRR data, described 

in Casey et al. (2010), are available from the National Ocean Data Center (NODC) Pathfinder 

SST Program website (Casey et al. 2010 [Internet]). The September 1981 through January 1985 

Pathfinder SST data were first released on 13 April 2009 by NODC, which was the first time that

these data had been available in the nearly 20-year history of the AVHRR Pathfinder program. 

The weekly-averaged 4-km resolution SST product, Version 5.1, was used (downloaded in May 

and September of 2009 and February 2010). Example images of the LC from CZCS ocean-color 

and AVHRR SST images, in the time period before industry analyses from HMI became 

available in 1984, are shown in Figure 5.2-1. The CZCS ocean-color image shown is an 8-day 

composite from 13-20 August 1979. The AVHRR SST image is the weekly mean from 19-25 

February 1982. Along-track 35-day repeat ERS-1 altimeter data, from the multidisciplinary 

mission phase (14 April 1992 through 21 December 1993), were extracted from the Radar 

Altimeter Database System (RADS) and were processed as described in Leben et al. (2002) and 

Section 2.6.1 of this report.
245

Table 5.2-1. Eddy separation events with the corresponding retreat latitudes and 

separation periods from July 1978 through December 1992

No. YearLetterIndustry

Name

Separation

Date

Best Available 

Imagery/Chart

Retreat

Latitude (°N)

Separation

Period 

(days)

1 1978 - 15 Jul 1978 *†SSH 24.7§ -

2 1980a - 18 Feb 1980 *Chlorophyll-a 26.2 583

3 1980b - 16 May 1980 *Chlorophyll-a 26.4 88

4 1980c - 04 Aug 1980 *Chlorophyll-a 26.0 80

5 1981a - 04 Jul 1981 Chlorophyll-a 25.5 334

6 1981b - 24 Oct 1981 *Chlorophyll-a 26.4 112

7 1982 - 21 Aug 1982 *Chlorophyll-a 26.0 301

8 1983a - 08 Mar 1983 *SST 26.8 199

9 1983b - 23 Aug 1983 *†SST 26.0 168

10 1984a - 25 Jan 1984 *SST 25.8 155

11 1984b Arnold 28 Aug 1984 Chlorophyll-a 25.6 216

12 1985 Fast 18 Jul 1985 *†EddyWatchTM 25.6 324

13 1986a Hot Core 18 Jan 1986 SST 25.7 184

14 1986b Instant 12 Sep 1986 *†SST 25.7 237

15 1987 Kathleen 08 Nov 1987 SST 25.6 422

16 1988 Murphy 25 Apr 1988 *SST 24.5 169

17 1989 Nelson 01 Sep 1989 *†EddyWatchTM 25.3 494

18 1990 Quiet 14 Sep 1990 *†EddyWatchTM 25.0 378

19 1991 Triton 01 Nov 1991 *SST 26.4 413

20 1992 Unchained 10 Aug 1992 SSH 24.7§ 283

Mean 25.7 270.5

* GEM P&C analyses (Evans Hamilton 1992) were available to verify separation date estimate.

† GEM P&C analyses determined separation date estimate.

§ An offset of 0.36° must be added to SSH-derived retreat latitudes to make them consistent with values estimated from satellite 

SST and ocean-color frontal analyses. The offset was applied when calculating the mean.

The HMI EddyWatchTM reports, used in the re-analysis to help identify both LC eddy separation 

and LC retreat latitude, span the time period from 4 September 1984 through 31 December 1992. 

However, there were several time spans when the weekly reports were not published: 30 August 

1986 through 5 February 1987, 15 August 1987 through 30 March 1988, 12 November 1988 

through 16 February 1989, and 1 April 1992 through 3 September 1992. The available reports 

were digitized from hardcopies provided by CASE/EJIP for the development of a statistical LC 

hindcast model (Forristall et al. 2010). An EddyWatchTM report is shown in Figure 5.2-2 for LC 

eddy “Hot Core”, which separated from the LC on 18 January 1986. This is a representative 

example of the type of information provided in the EddyWatchTM reports used in the re-analysis 

to help identify both LC eddy separation and LC retreat latitude. Although the GEOSAT 

Geodetic and Exact Repeat Missions (ERM) spanned many of the time periods when 

EddyWatchTM reports were not published, GEOSAT altimeter data were not used in the reanalysis because of the frequent data outages in the eastern Gulf during this mission. These 
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<18

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(a)

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Figure 5.2-1. Examples of the “best” LC images from (a) CZCS ocean color and (b) AVHRR SST in the 

time period before EddyWatch analyses from Horizon Marine, Inc. became available in 

1984 (see Figure 5.2-2). The CZCS ocean-color image is an 8-day composite from 13-20 

August 1979. The AVHRR SST image is a weekly mean from 19-25 February 1982. 
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Figure 5.2-2. Sample HMI EddyWatch map from week of 10-17 January 1986 showing frontal analysis 

of “Fast Eddy”, “Hot Core Eddy”, and the Loop Current based on satellite-tracked drifters, 

SST, and a ship-of-opportunity transect.
248

outages occurred whenever the passive-gravity gradient stabilization system allowed the satellite 

to point too far off nadir, which caused the on-board tracker to fail to regain lock on the returned 

waveform over the ocean when coming off of land (Sandwell and McAdoo 1988). Continuous 

satellite altimetry from 35-day repeat sampling during the ERS-1 multidisciplinary phase, 

however, provided altimetric coverage during the time period in 1992 when EddyWatchTM

reports were not published. This was fortunate because no ocean-color data were available 

during the summer of 1992 for monitoring of the LC and LC eddy fronts.

GEM Path and Configuration (P&C) daily analyses (Evans Hamilton 1992) were also used in the 

re-analysis to help determine LC eddy separation dates. GEM is both a model and a database and 

is the standard industry tool for hindcasting LC and LC eddy currents. Gulf metocean 

engineering designs rely on hindcasts from the model to provide a database for the location of 

the LC and LC eddies and the associated currents (Forristall et al. 2010). GEM is based on the 

feature model developed by Glenn et al. (1990) to support exploratory deepwater-drilling 

operations off the U.S. east coast. The model fits an idealized isolated translating elliptic 

paraboloid with a swirl velocity to: surface fronts in satellite imagery, expendable 

bathythermograph survey data, and satellite-tracked drifting-buoy data associated with 

anticyclonic recirculation embedded within the intruding LC and LC eddies, both separating 

from and propagating away from the LC. GEM eddy tracks from 1966 to 1991, including the 

initial portion of the track that corresponds to LC eddies embedded in the intruding LC, are 

shown in Figure 3 of Kantha et al. (2005).

Animations of the combined time series of color maps, SST images, HMI EddyWatchTM charts, 

and GEM P&C analyses were used to identify LC eddy separation and LC retreat following 

separation, supplemented with satellite altimetry maps from Seasat and ERS-1. CZCS images 

and GEM analyses showed conclusively that there were no LC eddy separation events from 

November 1978 through 1979. The one separation event reported in the literature during this 

time period, in April 1979 (Vukovich 1988; Vukovich 2012), was identified in the reanalysis as 

an eddy detachment, not an eddy separation. The first LC eddy separation event was identified 

using GEM analyses and occurred in July 1978, after which a continuous record of separation 

events and LC retreats following separation could be derived using the satellite and industry data 

records. Remarkably, the short-lived NASA Seasat Mission sampled this initial LC eddy 

separation event with both the Seasat satellite altimeter and the Seasat Synthetic-Aperture Radar 

(SAR) (Fu and Holt 1982), confirming the industry observations of a separation event. Figure 

5.2-3 shows Gulf SSH calculated by adding Seasat SSH anomaly to the CUPOM model mean. 

The Seasat altimetric sampling allows an estimate of the LC retreat latitude, which was one of 

the most southern retreats observed in the historical record. Consistent with the far southern 

retreat of the LC after the first LC eddy separation, the second LC eddy separation event was 

detected in color images in February 1980, approximately 19 months later, which is the longest 

LC eddy separation period observed in the entire 35-year record from 1978 through 2012.

The retreat latitudes of the LC following LC eddy separation derived from SSH are not 

equivalent to retreat latitudes derived from SST or ocean-color fronts. In Forristall et al. (2010) 

the edge of the LC, as defined by the 17-cm SSH tracking contour used to track the LC in the 

CCAR Mesoscale SSH data products, was estimated to lie inside the surface thermal or oceancolor front by about 40 km. This offset is 0.36° along the northern edge of the LC front, which
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(a)

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Figure 5.2-3. LC eddy 1978 as observed by Seasat approximately two weeks after eddy separation. 

Shown (a) as color-mapped along-track data overlaid on a contour plot of the objectivelymapped SSH (contour increment = 5 cm), and (b) as a SSH color image with the 17-cm 

LC tracking contour overlaid. Along-track data are from 16 July through 9 August 1978. 

The analysis date of the mapped data is 28 July 1978.
250

must be added to each SSH-derived retreat latitude value to allow consistent analyses of the LC 

retreat latitudes when combining the altimetric estimates with non-altimetric estimates. The two 

retreat latitudes derived from altimetry during the pre-altimetry time period, shown in Table 5.2-

1, do not incorporate the offset, but the offset was applied before calculation of the mean.

Figures 5.2-4, 5.2-5 and 5.2-6 show imagery of all pre-altimetric eddies with exception of the 

two SSH-derived events shown in Figures 5.2-3 and 5.2-7, respectively, for the separation events 

detected using Seasat and ERS-1 altimetry. The black dashed lines show the derived LC retreat 

latitudes. Each eddy in Table 5.2-1 has been given a year or year-letter designation since 

multiple LC eddies were shed in some years. Note that the EddyWatchTM chart in Figure 5.2-6 

(q) shows a deeply retreated Loop Current, although the SST data for the respective date suggest 

that the LC maximum latitude was further north. Two eddy separation events, LC eddy 1984b 

(#11, 28 August 1984) and LC eddy 1986b (#14, 12 September 1986), do not fall within the date 

range of the corresponding image/chart. For those events, images have been provided where the 

LC and LC eddy can be most clearly seen, although the movie sequences of satellite imagery and 

GEM P&C analyses suggest that separation happened a week to a month before the images 

shown in Figure 5.2-5 (j) and Figure 5.2-6 (m). Table 5.2-2 gives the data type and date range 

for the data used to create each image in Figures 5.2-4, 5.2-5 and 5.2-6. For the most part, the 

dataset used to create each image was also used to determine the respective separation date. The 

exceptions used GEM P&C analyses to set the separation date and are marked by a “†” symbol 

in Table 5.2-2, These include two SST images, #9 and 14, and all three EddyWatchTM maps, #12, 

17, and 18. Otherwise, for the event dates derived from composite chlorophyll-a images, the first 

date of the corresponding image-date range was selected as the separation date. The date of the 

earliest image swath within the composite, providing evidence of LC eddy separation, was not 

identified, so the first date in the date range used to form the composite image was used for 

convenience. The separation dates derived from weekly SST images were set to mid-week.

The goal of the re-analysis was to derive a pre-altimetric LC record as consistent as possible with 

the LC eddy separation record derived from satellite altimetry, using the automated LC tracking 

procedure based on tracking the 17-cm LC contour in CCAR SSH maps (Leben 2005). Since 

altimetry well-resolves only the dominant Gulf mesoscale ocean circulation, small anticyclonic 

eddies generated near the periphery of the LC are typically not detected at the 17-cm level in the 

gridded CCAR SSH data products. SST imagery, however, may show warm surface features on 

the periphery of the LC that are not LC eddies per se because the subsurface waters below these 

features are not warm Caribbean water comprising the LC and LC eddies. These features are 

usually smaller in diameter and exhibit a weaker surface thermal expression than LC eddies. 

They may also be associated with cyclonic circulation that can be identified by the timeevolution of the SST pattern. Nevertheless, SST signatures of some of the smallest LC eddies in 

the 20-year altimetry record (i.e., Zapp, Walker, Brazos, etc.) were compared with the signatures 

of the pre-altimetry eddies to ensure that all eddies identified in the pre-altimetric record were 

large enough to be counted as LC eddies. Since all of the LC eddies in the altimetry record are 

“verified” – that is, all LC eddies appearing in the SST during the altimetry time period have 

been confirmed by the corresponding altimetry – eddies in the pre-altimetry record are 

considered LC eddies as long as their surface areas or surface thermal signatures are comparable 

or larger than the smallest LC eddies observed during the altimetry period. All the pre-altimetry 

LC eddies identified in the reanalysis meet this criterion. Neither was a minimum lifetime nor
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(a) (b)

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(e) (f)

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Figure 5.2-4. LC eddy separation events with LC retreat latitude following separation shown by dashed 

black lines. Date ranges for which the plots are valid are given in Table 5.2-2. LC eddy 

separation date: (a) 18 February 1980; (b) 16 May 1980; (c) 4 August 1980; (d) 4 July 

1981; (e) 24 October 1981; (f) 21 August 1982.
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(g)

(i)

(k)

(h)

(j)

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Figure 5.2-5. LC eddy separation events with LC retreat latitude following separation shown by dashed 

black lines. Date ranges for which the plots are valid are given in Table 5.2-2. LC eddy 

separation date: (g) 8 March 1983; (h) 23 August 1983; (i) 25 January 1984; (j) 28 August 

1984; (k) 18 July 1985; (l) 18 January 1986.
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(m) (n)

(o) (p)

(q) (r)

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Figure 5.2-6. LC eddy separation events with LC retreat latitude following separation shown by dashed 

black lines. Date ranges for which the plots are valid are given in Table 5.2-2. LC eddy 

separation date: (m) 12 September 1986; (n) 8 November 1987; (o) 25 April 1988; (p) 1 

September 1989; (q) 14 September 1990; (r) 1 November 1991.
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30°N

Sea Surface Height (cm)

−30 −20 −10 0 10 20 30

(a)

(b)

 254

Figure 5.2-7. LC eddy 1992 “Unchained” as observed by ERS-1 on the date of separation, 10 August 

1992. Shown (a) as color-mapped along-track data overlaid on a contour plot of the 

objectively-mapped SSH (contour increment = 5cm), and (b) as a SSH color image with 

the 17-cm LC tracking contour overlaid. Data are from 24 July through 27 August 1992. 
255

Table 5.2-2. Date ranges for LC eddy separation events shown in Figures 5.2-4, 

5.2-5 and 5.2-6

No. Fig. No. Separation Date Best Available 

Imagery/Chart

Date Range for

Data in the Image/Chart

2 5.2-4 (a) 18 Feb 1980 *Chlorophyll-a 18 Feb 1980 – 25 Feb 1980

3 5.2-4 (b) 16 May 1980 *Chlorophyll-a 16 May 1980 – 23 May 1980

4 5.2-4 (c) 04 Aug 1980 *Chlorophyll-a 04 Aug 1980 – 11 Aug 1980

5 5.2-4 (d) 04 Jul 1981 Chlorophyll-a 04 Jul 1981 – 11 Jul 1981

6 5.2-4 (e) 24 Oct 1981 *Chlorophyll-a 24 Oct 1981 – 31 Oct 1981

7 5.2-4 (f) 21 Aug 1982 *Chlorophyll-a 21 Aug 1982 – 28 Aug 1982

8 5.2-5 (g) 08 Mar 1983 *SST 05 Mar 1983 – 11 Mar 1983

9 5.2-5(h) 23 Aug 1983 *†SST 20 Aug 1983 – 26 Aug 1983

10 5.2-5 (i) 25 Jan 1984 *SST 22 Jan 1984 – 28 Jan 1984

11 5.2-5 (j) 28 Aug 1984 Chlorophyll-a 05 Sep 1984 – 12 Sep 1984§

12 5.2-5 (k) 18 Jul 1985 *†EddyWatchTM 12 Jul 1985 – 19 Jul 1985

13 5.2-5 (l) 18 Jan 1986 SST 15 Jan 1986 – 21 Jan 1986

14 5.2-6 (m) 12 Sep 1986 *†SST 01 Oct 1986 – 07 Oct 1986§

15 5.2-6 (n) 08 Nov 1987 SST 05 Nov 1987 – 11 Nov 1987

16 5.2-6 (o) 25 Apr 1988 *SST 22 Apr 1988 – 28 Apr 1988

17 5.2-6 (p) 01 Sep 1989 *†EddyWatchTM 26 Aug 1989 – 01 Sep 1989

18 5.2-6 (q) 14 Sep 1990 *†EddyWatchTM 07 Sep 1990 – 14 Sep 1990

19 5.2-6 (r) 01 Nov 1991 *SST 29 Oct 1991 – 04 Nov 1991

* GEM P&C analyses (Evans Hamilton 1992) were available to verify separation date estimate.

† GEM P&C analyses determined separation date estimate.

§ Images shown in Figure 5.2-5 (j) and Figure 5.2-6 (m) do not depict the official separation dates but do show the LC eddy more 

clearly separated than the corresponding images.

minimum separation interval required of the LC eddies counted in the re-analysis. Beyond these 

caveats, the guidelines used for counting events were necessarily subjective: cohesive masses of 

water separating from the LC and causing significant change in LC area were deemed to be LC 

eddies provided they did not reattach to the LC at a later date.

Each LC eddy in the altimetry record was assigned a discrete date marking the completion of the 

eddy-separation process, objectively derived using the continuous sampling afforded by the 

multi-satellite altimetry and the breaking of the LC-tracking contour. Yet, eddy separation is a 

slow, continuous process that happens over the entire depth of the LC water column and can take 

months to complete. The estimated uncertainty in objective altimetric estimates, when compared 

with coincident subjective estimates, is ±1 month (Leben 2005). SST and ocean-color sampling, 

however, are frequently interrupted by cloud-cover, often preventing clear views of ongoing 

separation processes. Therefore, LC and LC eddy signatures in SST and ocean-color imagery can 

be difficult to identify. Complex surface flows may obscure the northern boundary of the LC and 

the connectivity of the LC with a separating LC eddy. GEM analyses also may show large 

changes in LC eddy diameters and large variations in LC eddy positions. These uncertainties 

impact retreat latitude and separation-date estimates in the pre-altimetric record. As such, the 
256

separation dates derived in the reanalysis are probably accurate to only ±1.5 months, and the 

retreat latitudes to only ±0.25°, at best.

5.3 COMPARISONS OF PREVIOUSLY PUBLISHED SEPARATION DATES WITH THE

RE-ANALYSIS

Various versions of the LC eddy separation record over the pre-altimetry time period have been 

published and republished in the peer-reviewed literature (Vukovich 1988; Sturges 1993; Sturges 

1994; Sturges and Leben 2000; Leben 2005) with the most recent being Vukovich (2012). 

Present comparisons and discussion focus on Vukovich (2012), since that work replicates and 

extends the pre-1988 separation record published in Vukovich (1988) and provides more 

information on the sampling available during the pre-altimetry time period. The other studies 

cited above, and recent publications supported by this study program (Chang and Oey 2012; 

Chang and Oey 2013a; 2013b), relied on the record published in Vukovich (1988). Therefore, it 

is important to review these early records of LC eddy separation and compare them with the 

reanalysis included in this report.

Table 5.3-1 shows the LC eddy separation dates from the re-analysis (Table 5.2-1) and 

corresponding dates in Vukovich (2012). For the pre-altimetry time period (1978-1992), 

Vukovich (2012) employed NASA CZCS ocean-color (or chlorophyll-a) data from 1979 through 

1985, “ship-of-opportunity” data, and SST data to identify LC eddy separations. SST data came

primarily from NOAA AVHRR instruments, though SST data from NOAA VHRR, GOES, 

Seasat, and the Heat Capacity Mapping Mission (HCMM) were also used. Vukovich (2012) 

relied heavily on NOAA VHRR SST to derive dates from 1972 through 1978, but does not 

specify which SST data source was used to identify specific separation events. The last usable 

VHRR data were collected on 1 March 1979 (NOAA 5 satellite), before the second LC eddy 

separation event in early 1980 (Table 5.3-1). AVHRR coverage began with the launch of the first 

four-channel AVHRR instrument (TIROS-N satellite) on 13 October 1978. The AVHRR 

instrument was later enhanced to include five channels and was then put into operational use 

onboard NOAA 7 on 23 June 1981 (Casey et al. 2010; Kramer 2002; Schnapf 1981). AVHRR 

coverage lasted through the end of the pre-altimetry time period and beyond. VHRR LC 

monthly-frontal analyses, including copies of the original SST maps over the time period from 

1972 through 1977, are found in Vukovich et al. (1978) and Vukovich et al. (1979). Other 

AVHRR SST monthly-frontal analyses and imagery are found in Vukovich (1986), Vukovich 

and Maul (1985), Vukovich and Crissman (1986), Vukovich (1988), Vukovich (2007), and 

Vukovich (2012). GOES SST may have been used for any number of events, but were minimally 

used according to the description in Vukovich (2012). Seasat recorded both microwave and 

infrared SST, although these data were only available from July to October 1978, after the first 

and before the second Vukovich (2012) LC eddy separation found in Table 5.3-1. No separation 

events could have been directly observed with the Seasat data, given the identified separation 

dates. Additionally, Table 5 of Vukovich (2012) indicates that no usable data were available in 

the Gulf during the entire lifetime of Seasat. The HCMM satellite was launched in April 1978 

and was decommissioned in August 1980, so it could only have been used to help identify the 

first three of the Vukovich (2012) separation events listed in Table 5.3-1 (Kramer 2002). Table 4 

of Vukovich (2012) indicates which data type – ocean color, SST, or ship-of-opportunity – was 

used to derive each of the LC eddy separation dates.
257

Table 5.3-1. Comparison of re-analysis LC eddy separation dates with those 

from Vukovich (2012)

No. YearLetterIndustry 

Name

Re-analysis *Vukovich 

(2012)

†Difference 

(days)

1 1978 - 15 Jul 1978 Jun 1978 30

- - - - Apr 1979 -

2 1980a - 18 Feb 1980 Jan 1980 34

3 1980b - 16 May 1980 - -

4 1980c - 04 Aug 1980 - -

5 1981a - 04 Jul 1981 Mar 1981 111

6 1981b - 24 Oct 1981 - -

7 1982 - 21 Aug 1982 May 1982 98

8 1983a - 08 Mar 1983 Mar 1983 -7

9 1983b - 23 Aug 1983 - -

10 1984a - 25 Jan 1984 Feb 1984 -21

11 1984b Arnold 28 Aug 1984 - -

12 1985 Fast 18 Jul 1985 Jul 1985 3

13 1986a Hot Core 18 Jan 1986 Jan 1986 3

14 1986b Instant 12 Sep 1986 Oct 1986 -33

15 1987 Kathleen 08 Nov 1987 Nov 1987 -7

16 1988 Murphy 25 Apr 1988 May 1988 -20

17 1989 Nelson 01 Sep 1989 May 1989 109

18 1990 Quiet 14 Sep 1990 Sep 1990 -1

19 1991 Triton 01 Nov 1991 Sep 1991 47

20 1992 Unchained 10 Aug 1992 Jul 1992 26

Mean 24.8

RMS 52.1

Mean without #5, 7, and 17 4.5

RMS without #5, 7, and 17 24.1

* Dates for LC eddy separation events that occurred in the 1970s and after 1992 are listed in Vukovich (2012).

† Differences assumed that all Vukovich (2012) separation events occurred on the 15th of the given month.

All available information on ocean features was integrated into monthly frontal-analysis maps 

indicating the location of LC and LC eddy fronts (e.g., Vukovich (2012), Figure 1). As noted in 

the preceding discussion, satellite SST data played a major role in the development of these 

analyses. In the time periods 1972 through 1978, and 1986 through 1991, only satellite SST data 

were available to develop the frontal analyses. (Details in Vukovich (2012) describing events 

preceding 1978 are largely omitted from this chapter since online data archives do not exist for 

satellite data from that time period.) Information provided in Table 5 of Vukovich (2012) 

indicates that satellite data were insufficient to map LC and LC eddy fronts during June through 

October every year from 1978 through 1983 and for two to five months every summer and fall 

for the years 1984 through 1991. This is because the LC and LC eddy fronts could not be 

detected in SST imagery when the warm seasonal mixed layer masked the surface thermal 
258

signature of the fronts. According to Vukovich (1988), there were generally only five to nine 

clear-sky images during the months from November through May, and only occasionally were 

images in late October and early June usable. When SST frontal analyses were insufficient for 

LC tracking, Vukovich (2012) used ship-of-opportunity data. Specifically, ship-of-opportunity 

data were used to identify LC eddy separations #1, 12, 18, 19, and 20 in Table 5.3-1 (ship-ofopportunity data were used exclusively to derive #18, 19, and 20). According to Table 5 of 

Vukovich (2012), there were no data available during the time periods when LC eddy separation 

events #1, 12, 14, 18, and 19 occurred, and LC eddy #20 was ambiguously reported to have 

“missing” data. Five of these six LC eddy separation events were derived with ship-ofopportunity data. However, since there was either missing or no data at the actual times of 

separation for the five events, the ship-of-opportunity data may not have provided much useful 

information. Therefore, it is difficult to evaluate the efficacy of the LC or LC eddy monitoring 

during these time periods or to confirm the reported results.

The criteria met by each LC eddy separation listed in Vukovich (2012) are the following: only 

LC eddy separation events shedding eddies with a diameter of ~300 km or greater at the time of 

separation, that persisted for five months or more, and propagated into the western Gulf were 

counted. There are significant differences between the re-analysis dates and the Vukovich (2012) 

dates in Table 5.3-1. Vukovich (2012) identified one separation event in April 1979 that GEM 

analyses and CZCS imagery showed was an eddy detachment since the eddy later reattached to 

the LC. As a result, that event was ignored in the re-analysis. Five eddies detected in the reanalysis do not appear in Vukovich (2012) (#3, 4, 6, 9, and 11 in Table 5.3-1), four of which 

relied primarily on chlorophyll-a data. Three of the five eddies (#4, 6, and 9) separated in time 

periods when Vukovich (2012) reported no data were available. This includes the event that was 

identified using SST imagery (#9). The other two (#3 and 11) may have been undetected in the 

chlorophyll-a or failed to meet LC eddy diameter criteria. Diameter approximation using 

chlorophyll-a or SST imagery is a subjective process since cloud cover, meanders, surface-layer 

masking, and peripheral cyclones frequently conceal full-eddy areal coverage. Vukovich (2012) 

may have estimated that the diameters of these two LC eddies were less than 300 km. These 

eddies may also have been ignored because they could not be tracked for five months into the 

western Gulf. In the re-analysis, LC eddies were often impossible to track systematically beyond 

about three months after separation unless trajectory information from GEM P&C analyses were 

available. In SST and chlorophyll-a images, LC eddy surface signatures typically fade into the 

background less than five months after eddy separation. If the five-month eddy lifetime 

requirement had been strictly enforced in the re-analysis, many of the early LC eddy events 

including eddy #3 and #11 would have been eliminated.

Beyond differences in the number of LC eddy separations listed in Table 5.3-1, there are also 

some differences between the separation dates in the re-analysis and those in Vukovich (2012) 

for the events that were identified in both studies. Assuming that each date in Vukovich (2012) 

corresponds to the 15th day of the respective month, nine separation dates differ by one month or 

less (#1, 8, 10, 12, 13, 15, 16, 18, and 20) and three events (#2, 14, and 19) differ by between one 

and two months. These twelve events show good agreement (mean = 4.5 days, RMS = 24.1 

days), comparable to uncertainty estimates of LC eddy separation dates found between 

subjective tracking by an expert and automated-altimetric tracking in Leben (2005) (mean = 3 

days, RMS = 28 days). The three other events, however, differ by more than three months (#5, 7, 
259

and 17) and degrade uncertainty estimates substantially (mean = 24.8 days, RMS = 52.1 days). 

The re-analysis separation dates for these separation events fell in summer, when Vukovich 

(2012) reported that no satellite data were available.

Satellite data and industry analyses used in the re-analysis were significantly different than the 

data used in Vukovich (2012). Pathfinder AVHRR SST data (August 1981-1992) were employed 

extensively in the re-analysis. The Pathfinder SST program began in the early 1990s and is a 

NASA/NOAA/NODC joint effort to produce a long, accurate, and consistent AVHRR data 

record. Newly reprocessed SST data from 1985 through 2001 were released by NODC in April 

2003, and reprocessed SST data from 1981 through 1984 were released in April 2009 (Casey et 

al. 2010). AVHRR data prior to August 1981, VHRR, Seasat, HCMM, and GOES SST were not 

used at all in the re-analysis, though they were also minimally used by Vukovich (2012). CZCS 

ocean-color data were employed considerably more in the re-analysis. Table 4 in Vukovich 

(2012) shows that in no instance during the pre-altimetry time period was a separation event 

identified using exclusively ocean-color data, and there were only two instances (#7 and 12) for 

which ocean color was used. Conversely, the re-analysis used CZCS to derive seven event dates 

(#2, 3, 4, 5, 6, 7, and 11), two of them exclusively (#5 and 11). See Table 5.2-1. In the reanalysis, CZCS chlorophyll-a images were reliable from May through August and also at times 

during the months of February, March, April, September and October. Missing frontal analyses 

during the summer and fall of 1978 through 1985, listed in Table 5 of Vukovich (2012), indicate 

little or no reliance on CZCS ocean-color data for LC tracking. This may be an artifact of the 

CZCS data processing available at the time that the original published analyses in Vukovich 

(1988) were performed. The re-analysis reported here benefited greatly from the comprehensive 

reprocessing of the CZCS archive by NOAA and NASA (Gregg et al. 2002). Ship-of-opportunity 

data were not used in the re-analysis per se. However, 15 of the 20 pre-altimetry separation dates 

were covered by GEM analyses (see Table 5.2-1), which incorporate ship-survey data and offer 

additional kinematic information about LC eddy separation from satellite-tracked drifting-buoy 

trajectories. EddyWatchTM reports were also available, providing frontal analyses as well as ship 

surveys and satellite-tracked drifting-buoy tracks used by the offshore industry for operational 

monitoring of the LC. Seasat altimetry data were used to map SSH in the Gulf just after the 

separation of the first event counted in the re-analysis (LC eddy 1978). ERS-1 altimetry was used 

to derive event #20, LC eddy 1992 “Unchained”.

In summary, time periods were noted in both the re-analysis, and by Vukovich (2012) when 

satellite data quality was poor, with the eastern Gulf obscured by clouds or the LC masked by 

seasonal warming of the mixed layer. Subsequently, identification of LC and LC eddy fronts 

and LC eddy separation events during the summer and fall were difficult without ancillary 

information such as that provided from ship-board surveys and satellite-tracked drifting buoys. 

Nevertheless, in the re-analysis, more satellite coverage was found than was described in 

Vukovich (2012). Compared to the datasets used to estimate the separation dates in Vukovich 

(2012), the re-analysis included more satellite data during summer and late fall, and had access 

to supplementary information provided by the EddyWatchTM and GEM analyses. Thus, the 

separation dates in the re-analysis are likely more accurate and less affected by seasonal data 

outages than those reported in Vukovich (2012). Discussion of whether date discrepancies like 

those found in the data comparison shown in Table 5.3-1 prevented identification of a seasonal 

LC signal will be pursued in Section 5.5 of this report.
260

5.4 THE ALTIMETRIC LOOP CURRENT RECORD

The 20-year multi-satellite altimeter data record was used to investigate LC intrusion and LC 

eddy separation events over the time period from January 1993 through December 2012. 

Analyzed altimetry datasets included daily CCAR and AVISO SSH and a hybrid daily SSH 

based on AVISO SSHA added to the University of Colorado Princeton Ocean Model (CUPOM) 

mean (AVISO-CUPOM). The daily AVISO and AVISO-CUPOM datasets were created from 

the delayed-time weekly 1⁄4° AVISO SSH (absolute dynamic topography) dataset, linearly 

interpolated to daily maps. AVISO and AVISO-CUPOM datasets were both demeaned in the 

deepwater by subtracting the daily-averaged values of SSH in water deeper than 200 m in the 

Gulf to remove the steric signal associated with seasonal heating of the mixed layer. The steric 

signal appears approximately as an annual sine wave with 5.8 cm amplitude in AVISO SSH, 

with the peak near 15 September and the trough near 16 March. The demeaning procedure was 

not applied to the CCAR SSH because the along-track altimeter data are de-trended before 

gridding of the CCAR SSH fields, which effectively removes the steric signal. Satellite altimeter 

missions that provided the sampling used in the CCAR SSH product are shown in Figure 5.4-1. 

Coincident satellite coverage, from different satellites, was available during nearly the entire 

record, except for three months in early 1994 when ERS-1 was placed into a 3-day exact repeat 

orbit for ice sheet mapping and only TOPEX/Poseidon altimeter data were available. Additional 

information about the CCAR SSH product is provided in Chapter 2. Specifics of satellite 

coverage used in the AVISO (and AVISO-CUPOM) dataset are not documented, but are likely 

comparable to that used in the CCAR dataset.

LC eddy separation dates and LC metrics (Leben 2005) were derived using a MATLAB® 

toolbox developed during this research program at CCAR called the Loop Current Toolbox 

(LCT). The LCT automatically identifies and tracks the LC and LC eddies in gridded SSH 

datasets. LC and LC eddy boundaries are defined by the location and breaking of the 17-cm 

tracking contour. CCAR separation dates are given in Table 5.4-1 along with the corresponding 

retreat latitudes and separation periods. Retreat latitude is defined as the maximum latitude of the 

LC immediately following separation of a LC eddy (Leben 2005). In the LCT, the retreat latitude 

is equal to the minimum value of the maximum latitude of the LC tracking contour observed in 

SSH maps during the first five days after LC eddy separation. In the CCAR SSH dataset, the 

mean separation period is 243.3 days, and the mean retreat latitude is 26.2° (with offset; see 

Section 5).

Table 5.4-2 compares the CCAR LC eddy separation dates with the corresponding dates derived 

from the AVISO and AVISO-CUPOM SSH datasets. Also, Tables 5.4-1 and 5.4-2 contain two

anomalous events, LC eddies Zorro and Franklin, which were large anticyclonic eddies that 

formed after deep LC intrusions and yet exhibited little or no westward propagation away from 

the LC during their lifetimes. Zorro separated from the northwestern edge of the LC in June 2007 

and dissipated in 10 weeks without any significant westward propagation. Satellite-tracked 

drifting buoys deployed in Zorro at the time of separation showed that the entire recirculation of 

the separated anticyclonic eddy was entrained along the outer edge of the LC and advected out of 

the Gulf (Coholan et al. 2008). This was the first time that the rapid and total dissipation of a 

major anticyclonic eddy in the Gulf had been observed. Franklin was one of the LC eddies 

observed during the study program, and its formation and ultimate separation is described in 

detail in Section 3.2.2. Franklin was a relatively large eddy when it initially detached from the
261

Figure 5.4-1. Satellite usage in the CCAR gridded altimeter dataset during the time period from 1993 

through 2012.

LC in June 2010; however, the eddy became progressively smaller as repeated reattachment and 

detachment cycles reduced the size and intensity of the recirculation. The weakening of the eddy 

circulation resulted in little or no β-induced westward propagation, since the induced velocity is 

a function of eddy amplitude (Nof 1981). As a result, the eddy remained near the LC and 

continued to interact with the LC until early 2011.

Counting Zorro and Franklin, the number of LC eddy separation events identified in the CCAR, 

AVISO, and AVISO-CUPOM datasets over the 20-year satellite-altimeter record totaled 30, 28, 

and 30 events, respectively. The difference in the totals is because Quick and Zorro were not 

distinct events in the AVISO SSH record. According to the AVISO SSH maps, Pelagic and 

Quick were connected and appeared as one eddy at the 17-cm contour level when they separated 

from the LC and then later split into the two observed eddies. In the CCAR and AVISO-CUPOM 

SSH maps, Pelagic separates first from a deeply intruded LC followed quickly by the separation 

of Quick, hence the name. The difference in the order of eddy separation versus splitting in the 

two scenarios is a consequence of the means used to estimate the total SSH. As was discussed in 

Section 2.7.4, there are differences in both the amplitude and spatial structure of the CCAR and 

AVISO mean SSH maps in the eastern Gulf (Figure 2.7-11). When the two datasets have been 

referenced to the same level, the CCAR mean SSH, which depends on CUPOM for the 

unobserved stationary signal not observable by altimetry, is as much as 15 cm higher than the 

AVISO mean SSH in the central eastern Gulf where the LC tracking contour tends to break 

during LC eddy separation. Consequently, the CUPOM mean contributes SSH signal in the 

CCAR and AVISO-CUPOM SSH products that keeps Quick attached until after the separation 

of Pelagic, as was determined by Horizon Marine, Inc. (HMI) at the time these events occurred. 

This is not the case for the AVISO SSH that is based on the CNES/CLS 2009 Mean Dynamic 

Topography (Rio and Larnicol 2010). In the case of Zorro, AVISO SSH shows a reattachment 

of the eddy to the LC at the 17-cm contour level that is not detected in the CCAR or AVISOCUPOM datasets, which may also be attributed to the differences in the mean. In most cases, the 

separation dates of the CCAR and AVISO-CUPOM datasets are more similar, as is the case of 

Xtreme (two days apart) and Albert (1 day apart) – and both of them dissimilar to the 

corresponding AVISO product dates. For example, the separation dates of Xtreme and Albert are 

different by 20 and 18 days and 26 and 25 days, respectively, from the LC eddy separation dates 

determined from the CCAR and AVISO-CUPOM datasets.
262

Table 5.4-1. LC eddy separation event dates with the corresponding retreat 

latitudes and separation periods from January 1993 through 

December 2012, derived from CCAR SSH dataset

No. YearLetterIndustry

Name*

Separation

Date

Confirmation 

Dataset

Retreat 

Latitude (°)

Separation 

Period (days)

21 1993a Whopper 10 Jul 1993 SSH 27.1 334

22 1993b Xtra 11 Sep 1993 SSH 26.5 63

23 1994 Yucatan 26 Aug 1994 SSH 26.2 349

24 1995a Zapp 19 Apr 1995 SSH 26.8 236

25 1995b Aggie 07 Sep 1995 SSH 25.5 141

26 1996a Biloxi 15 Mar 1996 SSH 26.2 190

27 1996b Creole 25 Oct 1996 SSH 24.6 224

28 1997 El Dorado 30 Sep 1997 SSH 25.2 340

29 1998 Fourchon 22 Mar 1998 SSH 24.7 173

30 1999 Juggernaut 28 Sep 1999 SSH 25.2 555

31 2001 Millennium 10 Apr 2001 SSH 25.7 560

32 2002a Pelagic 28 Feb 2002 SSH 27.3 324

33 2002b Quick 13 Mar 2002 SSH 24.7 13

34 2003 Sargassum 05 Aug 2003 SSH 26.6 510

35 2004a Titanic 08 Feb 2004 SSH 25.8 187

36 2004b Ulysses 26 Aug 2004 SSH 25.0 200

37 2005 Vortex 13 Sep 2005 SSH 26.8 383

38 2006a Walker 08 Feb 2006 SSH 27.3 148

39 2006b Xtreme 04 Mar 2006 SSH 26.0 24

40 2006c Yankee 26 Sep 2006 SSH 25.8 206

41 2007a Zorro 07 Jun 2007 SSH 26.1 254

42 2007b Albert 16 Nov 2007 SSH 26.2 162

43 2008a Brazos 06 Mar 2008 SSH 26.3 111

44 2008b Cameron 01 Jul 2008 SSH 26.0 117

45 2009a Darwin 24 Feb 2009 SSH 25.4 238

46 2009b Ekman 29 Aug 2009 SSH 24.9 186

47 2010 Franklin 01 Oct 2010 SSH 25.0 398

48 2011 Hadal 14 Aug 2011 SSH 25.9 317

49 2012a Icarus 03 Feb 2012 SSH 25.9 173

50 2012b Jumbo 04 Aug 2012 SSH 24.3 183

Mean 26.2† 243.3

* Using an earlier version of the CCAR SSH dataset, Leben (2005) identified HMI eddy Odessa/Nansen as a minor eddy. In the 

current CCAR SSH dataset Odessa/Nansen was completely insignificant and was excluded from further analysis.

† An offset of 0.36° must be added to SSH-derived retreat latitudes to make them consistent with the pre-altimetry retreat latitude 

values in Section 5.2 estimated from satellite SST and ocean color frontal analyses. The offset was not added to the retreat latitudes 

listed in the table, but was applied when calculating the mean. The mean of the values listed in the table is 25.8°.
263

Table 5.4-2. Comparison of LC eddy separation event dates derived from CCAR, 

AVISO, and AVISO-CUPOM SSH datasets from January 1993 

through December 2012

No. Industry Name CCAR

Separation Date

AVISO

Separation Date

AVISO-CUPOM

Separation Date

21 Whopper 10 Jul 1993 08 Jul 1993 08 Jul 1993

22 Xtra 11 Sep 1993 04 Sep 1993 06 Sep 1993

23 Yucatan 26 Aug 1994 19 Aug 1994 24 Aug 1994

24 Zapp 19 Apr 1995 17 Apr 1995 15 Apr 1995

25 Aggie 07 Sep 1995 01 Sep 1995 08 Sep 1995

26 Biloxi 15 Mar 1996 08 Mar 1996 15 Mar 1996

27 Creole 25 Oct 1996 20 Jul 1996 17 Aug 1996

28 El Dorado 30 Sep 1997 25 Sep 1997 29 Sep 1997

29 Fourchon 22 Mar 1998 12 Feb 1998 20 Feb 1998

30 Juggernaut 28 Sep 1999 28 Sep 1999 05 Oct 1999

31 Millennium 10 Apr 2001 29 Mar 2001 07 Apr 2001

32 Pelagic 28 Feb 2002 24 Feb 2002 26 Feb 2002

33 Quick 13 Mar 2002 * 02 Mar 2002

34 Sargassum 05 Aug 2003 11 Aug 2003 11 Aug 2003

35 Titanic 08 Feb 2004 20 Dec 2003 24 Dec 2003

36 Ulysses 26 Aug 2004 19 Aug 2004 21 Aug 2004

37 Vortex 13 Sep 2005 11 Sep 2005 10 Sep 2005

38 Walker 08 Feb 2006 06 Feb 2006 03 Feb 2006

39 Xtreme 04 Mar 2006 12 Feb 2006 02 Mar 2006

40 Yankee 26 Sep 2006 15 Sep 2006 18 Sep 2006

41 Zorro 07 Jun 2007 † 09 Jun 2007

42 Albert 16 Nov 2007 21 Oct 2007 15 Nov 2007

43 Brazos 06 Mar 2008 02 Mar 2008 04 Mar 2008

44 Cameron 01 Jul 2008 27 Jun 2008 30 Jun 2008

45 Darwin 24 Feb 2009 14 Feb 2009 23 Feb 2009

46 Ekman 29 Aug 2009 22 Jun 2009 03 Jul 2009

47 Franklin 01 Oct 2010 27 Jun 2010 04 Jun 2010

48 Hadal 14 Aug 2011 22 Jul 2011 28 Jul 2011

49 Icarus 03 Feb 2012 05 Nov 2011 11 Nov 2011

50 Jumbo 04 Aug 2012 28 May 2012 16 Jun 2012

* In the AVISO product, Pelagic and Quick separate from the LC as one eddy, though they split from each other only days after

separation.

† Zorro appears as a detachment event in the AVISO product.
264

Direct comparison of the LC eddy separation dates derived from each of the datasets shows that 

separation occurs later in the CCAR SSH dataset than the other two datasets for the majority of 

the events, sometimes even months later. Of the 28 LC eddy separation events identified in all 

three datasets at the 17-cm level, a total of 24 separation dates were later in the CCAR dataset 

versus those derived from the datasets based on AVISO SSHA. Thus, the “delay” is likely 

caused by differences in smoothing applied during objective analysis of the CCAR and AVISO 

SSHA datasets rather than differences in mean SSH used to produce the synthetic SSH. Several 

specific examples implicating the smoothing are the CCAR separation dates for Titanic, 

Franklin, and Icarus, which are one month, three months, and two months later, respectively, 

than the corresponding AVISO and AVISO-CUPOM dates even though the CCAR and AVISOCUPOM datasets are both based on the CUPOM model mean.

In addition to LC eddy separation detection, the LCT uses the breaking of the 17-cm LC tracking 

contour for detachment detection and continuously tracks each detached LC eddy contour until 

reattachment to the LC. Dates of LC eddy detachment detected in the CCAR, AVISO, and 

AVISO-CUPOM datasets are listed in Table 5.4-3. Although separation events can be matched 

up relatively well between the three datasets, finding correspondence between detachment events 

is more difficult since the eddy typically remains detached from the LC for less than one month. 

The number of detachment events detected in the CCAR, AVISO, and AVISO-CUPOM datasets 

totaled 30, 27, and 13, respectively. The CCAR and AVISO datasets have approximately the 

same number of detachment events as separation events. The detachment event count for 

AVISO-CUPOM, however, is significantly less, indicating that when the smoother, higher 

amplitude AVISO SSHA is combined with the higher amplitude mean SSH field from CUPOM 

fewer detachments are detected.

Detachment events were matched up by assuming that LC eddy detachments detected in the 

datasets correspond to the same event when the dates differ by less than one month. The number 

of detachment events separated by less than one month occurred 12 times in the CCAR and

AVISO datasets, nine times in the CCAR and AVISO-CUPOM datasets, and 12 times in the 

AVISO and AVISO-CUPOM datasets. There were eight times that all three datasets showed 

detachment events separated by less than one month. AVISO and AVISO-CUPOM show the 

best agreement since all but one of the AVISO-CUPOM dates were within one month of an 

AVISO-derived date. Even so, AVISO-CUPOM did not match AVISO 15 times. Overall the 

results for LC eddy detachment events agree less than LC eddy separation events indicating that 

detachment is sensitive to both differences in the smoothing and differences in the mean between 

the three datasets.

Monthly histograms of LC eddy separation and detachment dates from Table 5.4-2 and 5.4-3 

respectively, are shown in Figure 5.4-2. The histograms from all three datasets show peaks in the 

February/March and August/September time periods. The CCAR dataset histogram peaks are the 

most sharply defined, while AVISO-CUPOM peaks are least distinct. Seasonality of LC eddy 

separation will be discussed in greater detail in Section 5.5. The seasonal distribution of 

detachment events is inconsistent among the datasets. CCAR detachments peak strongly in July 

– September. AVISO dates show two small peaks, one in January and one in May. The AVISOCUPOM annual monthly distribution is close to uniform, with a minor peak in July. Detachment 

events are complex processes that merit further exploration in the future. 
265

Table 5.4-3. Comparison of LC eddy detachment event dates derived from 

CCAR, AVISO, and AVISO-CUPOM SSH datasets from January 1993 

through December 2012. The HMI industry name of the LC eddy 

separation event following each date is also listed

No. Impending Event/

Industry Name

CCAR

Detachment Date

AVISO

Detachment Date

AVISO-CUPOM

Detachment Date

1 Whopper 28 May 1993 24 May 1993 27 May 1993

2 Xtra 15 Aug 1993 22 Aug 1993

3 Zapp 11 Mar 1995 06 Mar 1995 12 Mar 1995

4 Biloxi 25 Jan 1996 04 Feb 1996

5 Creole 20 Aug 1996

6 Creole 12 Sep 1996

7 Creole 14 Oct 1996

8 El Dorado 26 Jul 1997

9 Fourchon *30 Sep 1997

10 Fourchon 02 Mar 1998

11 Juggernaut 28 May 1999 20 Jun 1999 19 Jun 1999

12 Millennium 20 Jan 2000

13 Millennium 27 Oct 2000

14 Millennium 24 Jan 2001 27 Jan 2001

15 Pelagic 10 Sep 2001

16 Pelagic 26 Nov 2001 10 Dec 2001

17 Sargassum 26 May 2003

18 Sargassum 14 Jul 2003 08 Jul 2003 12 Jul 2003

19 Titanic 26 Sep 2003 19 Sep 2003 25 Sep 2003

20 Titanic 31 Dec 2003

21 Ulysses 24 May 2004

22 Vortex 25 Feb 2005 20 Feb 2005 28 Feb 2005

23 Vortex 22 Jun 2005 17 Jun 2005

24 Vortex 04 Aug 2005 23 Jul 2005

25 Walker 24 Sep 2005

26 Yankee *12 Feb 2006

27 Yankee 11 Jul 2006 08 Jul 2006 16 Jul 2006

28 Yankee 19 Aug 2006

29 Zorro 10 Apr 2007 02 Apr 2007 08 Apr 2007

30 Albert 06 Jun 2007

31 †Albert/Brazos 27 Sep 2007 *21 Oct 2007

32 Brazos 30 Jan 2008
266

Table 5.4-3 (Continued)

No. Impending Event/

Industry Name

CCAR

Detachment Date

AVISO

Detachment Date

AVISO-CUPOM

Detachment Date

33 Cameron 21 May 2008

34 Darwin 06 Nov 2008 29 Nov 2008

35 Ekman 05 Jul 2009

36 Ekman 10 Aug 2009

37 Franklin 07 Jun 2010 23 May 2010

38 Franklin 11 Jul 2010

39 Franklin 18 Aug 2010

40 Hadal 27 Jul 2011

41 Icarus 07 Nov 2011

42 Icarus 23 Nov 2011

43 Icarus 25 Dec 2011

44 Jumbo 20 Jun 2012

45 Jumbo 13 Jul 2012

* Detachment occurred on same date as a separation event. See Table 5.4-2. Detachment event was associated with the following 

separation event, not the separation event occurring on the same day.

† CCAR detachment date is associated with Albert. AVISO detachment date is associated with Brazos.

Figure 5.4-3 shows LC metrics computed from the CCAR dataset: area, volume, anticyclonic 

circulation, westernmost longitude, and northernmost latitude. The metrics are shown both as 

time series and as histogram distributions over the 20-year record. Red dashed lines on the time 

series plots identify separation events. Identical statistics were computed for AVISO and 

AVISO-CUPOM datasets. Figure 5.4-4 shows monthly composite annual cycles (CACs) 

calculated from all three datasets for each of the metrics given above. The CAC of LC area plus 

the area of detached LC eddies are also shown. The 95% confidence intervals show that monthly 

means in February are statistically different than means in either October or November or both 

for all three data types and all six metrics. The metrics from all three datasets largely follow the 

same trends: a maximum in February (there are a few exceptions) and a minimum in October or 

November. AVISO data show the lowest values per month for all metrics with the exception of 

latitude; latitude CACs are similar among all three datasets. Though the AVISO dataset mean is 

weaker than CUPOM overall, it is comparable to the CUPOM mean on the northern boundary of

the LC. CCAR data show the highest magnitudes for area, area including detachments, volume, 

and longitude metrics. AVISO-CUPOM has the highest in anticyclonic circulation, indicating 

that the AVISO SSHA objective analyses have higher geostrophic speeds parallel to the 17-cm 

contour when combined with the CUPOM model mean SSH.
(a)

(c)

(b)

 267

Figure 5.4-2. Monthly histograms of separation and detachment dates (Tables 5.4-2 and 5.4-3) determined from the (a) CCAR, (b) AVISO, and (c) AVISO-CUPOM SSH datasets by automated 

tracking of the 17-cm SSH contour.
0.9

1.5

2.1

3.5

6.5

0.8

1.6

2.4

86.8

90.4

94.0

1993 1996 1999 2002 2005 2008 2011

24.5

26.5

28.5

Year

0 900 1800

 Count

(a)

(b)

(c)

(d)

(e)

Figure 5.4-3. Daily LC (a) area (x105 km2), (b) volume (x104 km3), (c) anticyclonic circulation (x106 m2s-1), (d) westernmost longitude (°W), and 

(e) northernmost latitude (°N) time series and corresponding histograms, derived from CCAR SSH data.

268 
1.0

1.2

1.4

1.6

1.8

1.0

1.2

1.4

1.6

1.8

Jan Mar May Jul Sep Nov

25.0

25.5

26.0

26.5

27.0

3

4

5

6

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Jan Mar May Jul Sep Nov

86.5

87.0

87.5

88.0

88.5

89.0

89.5

CCAR

AVISO

AVISO−CUPOM

(a)

(b)

(c)

(d)

(e)

(f)

 269

Figure 5.4-4. Monthly mean plots of LC (a) area (x105 km2), (b) area including detachments (x105

km2), (c) northernmost latitude (°N), (d) volume (x104 km3), (e) anticyclonic circulation 

(x106 m2s-1), and (f) westernmost longitude (°W) statistics, derived from the CCAR, 

AVISO, and AVISO-CUPOM SSH datasets.
270

To highlight the effects of different tracking methods on derived separation dates, Table 5.4-4 

compares the AVISO re-analysis LC eddy separation dates given in Table 5.4-2 with LC Eddy 

separation dates published in Chang and Oey (2013b), Vukovich (2012), and Lindo-Atichati et 

al. (2013). All LC eddy separation dates listed in Table 5.4-4 were derived from altimetry data; 

however, only Vukovich (2012) used CCAR SSH. The AVISO dataset re-analysis dates were 

used in the Table 5.4-4 comparison instead of CCAR or AVISO-CUPOM re-analysis dates 

because two of the three publications compared, Chang and Oey (2013b) and Lindo-Atichati et 

al. (2013), used AVISO datasets to derive separation dates. As described previously in this 

report, the AVISO re-analysis used 1/4° daily AVISO SSH (interpolated from the weekly 

AVISO delayed-time product), which was demeaned in water deeper than 200 m to remove the 

steric signal (see Section 2.7.4). Tracking of separation events was performed using the LCT.

Analyses of LC eddy separation dates derived from AVISO SSH data were presented in both 

Chang and Oey (2012) and Chang and Oey (2013b). Chang and Oey (2012) derived a set of 

monthly LC eddy separation dates from 1993 through 2009, but did not publish the actual dates. 

Instead, the analyzed dates were presented in the form of a monthly histogram (Figure 1(a) in 

Chang and Oey (2012)), from which the actual year and month of each event cannot be 

determined. However, Chang and Oey (2013b) showed separation dates plotted as month versus 

year. LC eddy separation months were determined by manually tracking the 1.65 m SSH 

contour in an animation of AVISO SSH. The animation was based on the release of AVISO data 

just prior to that used in the preparation of this report. Comparison of the event dates from 1993 

through 2009 in Chang and Oey (2013b) with the annual monthly histogram in Chang and Oey 

(2012) shows that the Chang and Oey (2013b) dates have one more March separation event and 

one less June separation event. Since the two papers use different altimeter-derived separation 

dates, the two datasets will be treated independently throughout the statistical discussion of LC 

eddy separation presented in Section 5.5. In the remainder of this section, only the dates given 

graphically in Chang and Oey (2013b) will be used.

Vukovich (2012) used SST, ocean color, and in-situ data from various sources in addition to 

satellite altimetry to derive LC eddy separation events. Altimeter data from TOPEX/Poseidon, 

JASON, and ERS missions were mentioned specifically, and altimeter data from the CCAR 

website were cited in the acknowledgments. Lindo-Atichati et al. (2013) used a weekly 1/4° 

AVISO SSH dataset, which was based on the Rio and Hernandez (2004) mean dynamic 

topography.

For quantification of the differences in the derived LC eddy separation dates in Table 5.4-4, only 

month and year (without day-of-month, if given) were considered for each event. The numbered 

events that do not have dates from all four sources (event #22, 33, 39, 41, 43, 47, 48, 49, and 50) 

and all the unnumbered events (Odessa/Nansen, “unnamed1”, “unnamed2”, and “unnamed3”) 

are ignored because one or more of the date list sources would be otherwise unrepresented. This

leaves 21 “ubiquitous” LC eddies. Of those events, all dates agreed for two events (#25 and 34); 

there were no events where no dates agreed; the difference between the earliest and latest dates 

was one month for 15 events (#21, 23, 24, 26, 28, 29, 30, 31, 32, 35, 36, 37, 38, 42, and 45); and 

the difference was two months for four events (#27, 40, 44, and 46). Table 5.4-5 shows how 

many times each eddy separation analysis had the earliest or latest eddy separation date. For 

example, AVISO re-analysis dates (first row of table) were earlier than all respective dates from 
271

Table 5.4-4. Comparison of altimetry record LC eddy separation dates from 

AVISO re-analysis (from Table 5.4-2), Chang and Oey (2013b), 

Vukovich (2012), and Lindo-Atichati et al. (2013)

No. Industry Name AVISO 

Re-analysis

Chang and Oey 

(2013b)

Vukovich 

(2012)

Lindo-Atichati 

et al. (2013)

21 Whopper 08 Jul 1993 Jul 1993 Jun 1993 21 Jul 1993

22 Xtra 04 Sep 1993 * * 08 Sep 1993

23 Yucatan 19 Aug 1994 Aug 1994 Sep 1994 31 Aug 1994

24 Zapp 17 Apr 1995 Apr 1995 Mar 1995 26 Apr 1995

25 Aggie 01 Sep 1995 Sep 1995 Sep 1995 13 Sep 1995

26 Biloxi 08 Mar 1996 Mar 1996 Feb 1996 20 Mar 1996

27 Creole 20 Jul 1996 Oct 1996 Aug 1996 21 Aug 1996

28 El Dorado 25 Sep 1997 Sep 1997 Oct 1997 24 Sep 1997

29 Fourchon 12 Feb 1998 Mar 1998 Mar 1998 04 Mar 1998

30 Juggernaut 28 Sep 1999 Oct 1999 Oct 1999 29 Sep 1999

31 Millennium 29 Mar 2001 Apr 2001 Apr 2001 11 Apr 2001

Odessa/Nansen † Sep 2001 † 21 Sep 2001

32 Pelagic 24 Feb 2002 Feb 2002 Mar 2002 13 Mar 2002

33 Quick § § Mar 2002 17 Apr 2002

34 Sargassum 11 Aug 2003 Aug 2003 Aug 2003 20 Aug 2003

א (unnamed1) 24 Sep 2003

35 Titanic 20 Dec 2003 Jan 2004 Jan 2004 24 Dec 2003

36 Ulysses 19 Aug 2004 Sep 2004 Sep 2004 01 Sep 2004

37 Vortex 11 Sep 2005 Sep 2005 Sep 2005 03 Aug 2005

38 Walker 06 Feb 2006 Mar 2006 Feb 2006 08 Mar 2006

39 Xtreme 12 Feb 2006 ℘ ℘ 19 Apr 2006

א (unnamed2) Jun 2006

40 Yankee 15 Sep 2006 Aug 2006 Oct 2006 27 Sep 2006

41 Zorro ◊ May 2007 ◊ 11 Apr 2007

42 Albert 21 Oct 2007 Oct 2007 Nov 2007 14 Nov 2007

43 Brazos 02 Mar 2008 Mar 2008 Mar 2008 ∀

44 Cameron 27 Jun 2008 Jul 2008 Aug 2008 02 Jul 2008

א (unnamed3) 03 Dec 2008

45 Darwin 14 Feb 2009 Mar 2009 Mar 2009 04 Mar 2009

46 Ekman 22 Jun 2009 Jul 2009 Jul 2009 02 Sep 2009

47 Franklin 27 Jun 2010 Aug 2010

48 Hadal 22 Jul 2011

49 Icarus 05 Nov 2011

50 Jumbo 28 May 2012
272

* Chang and Oey (2012) considered Whopper and Xtra to be one event because they separated less than two months apart and 

reported the separation date of the first eddy only. Vukovich (2012) may have also identified Whopper and Xtra as one event.

† Odessa/Nansen dissipates in less than a month in the AVISO re-analysis with little westward propagation and is, therefore, not 

considered a separation event. Vukovich (2012) provides no specific information on the LC or LC eddies during this time period.

§ Pelagic and Quick appear as a single separation event in the AVISO re-analysis, but the eddy splits into two pieces less than a 

week after separation. Since the two eddies separate less than two months apart, Chang and Oey (2012) considered the two eddies 

to be one event and reported the date of the first eddy only.

א The eddy appears as a detachment event in the re-analysis AVISO dates, not a separation. Reasons for why the eddy is not a 

separation event in the other publications are unknown.

℘ Chang and Oey (2012) do not mention a short-period separation (less than two months) to have occurred in 2006. Due to how 

the SSH data were processed, Walker and Xtreme may have appeared as one eddy originally such that combining the two was not 

necessary. Similarly, Vukovich (2012) may have also identified Walker and Xtreme as one event.

◊ Zorro appears as a detachment event in the AVISO re-analysis. Vukovich (2012) provides no specific information on the LC or LC 

eddies during this time period.

∀ The objective tracking technique in Lindo-Atichati et al. (2013) missed this event.

the other three sources (e.g., event #27) for seven events. For another seven events, the AVISO 

re-analysis shared the earliest separation dates with one or two of the other sources, but at least 

one source had a later date (e.g., event #23). For four events, the AVISO re-analysis shared the 

latest separation dates with one or two of the other sources, but at least one source had an earlier 

date (e.g., event #21). The AVISO re-analysis dates were never later than all of the respective 

dates from the three other sources. The three other LC eddy separation date sources listed in the 

second, third, and fourth rows of Table 5.4-5 can be interpreted similarly. The two events where 

all dates agreed (#25 and 34) were excluded from the counts in the table. 

“Earliest” and “latest” sum columns are also given. The AVISO re-analysis provided the earliest 

separation date 14 times, far greater than the other three sources. Likewise, the AVISO reanalysis provided the latest separation date four times, far less than the others. Chang and Oey 

(2013b), Vukovich (2012), and Lindo-Atichati et al. (2013) all seem to be very comparable.

Table 5.4-5. LC eddy separation timing of the 19 events where each source – the 

AVISO re-analysis (from Table 5.4-2), Chang and Oey (2013b), 

Vukovich (2012), and Lindo-Atichati et al. (2013) – reported a 

separation event, excluding events #25 and 34

Analysis Earliest 

Alone

Earliest 

Shared

Sum of

Earliest

Latest 

Shared

Latest 

Alone

Sum of 

Latest

AVISO Re-analysis 7 7 14 4 0 4

Chang and Oey (2013a) 1 4 5 11 1 12

Vukovich (2012) 3 1 4 9 4 13

Lindo-Atichati et al. (2013) 1 4 5 10 1 11

Tracking procedures in all four sources were different. As discussed previously, for the AVISO 

re-analysis, the LC and LC eddies were defined by the 17-cm contour in deepwater-demeaned 

AVISO SSH fields to derive the dates. Breaking of the 17-cm contour objectively established 
273

each date. Chang and Oey (2012) also identified LC eddies by tracking on a fixed contour level 

in AVISO data. However, the steric signal was retained in the data, eddy-separation periods less 

than or equal to two months were ignored, and each separation date may have been somewhat 

determined based on expert opinion. Testing suggests that retention of the steric signal would 

have had the affect of advancing separation events in winter and spring and delaying separation 

events in summer and fall in comparison to the same event dates derived without the steric 

signal.

To perform the tests, separation dates were objectively derived using the AVISO re-analysis 

dataset with (steric) and without the steric signal (nosteric) at the 13-cm level for both. 

(Combining AVISO mean SSH with the steric signal caused several persistent LC and LC eddy 

tracking issues in winter and spring months at the 17-cm level that made a 17-cm level 

comparison invalid.) Table 5.4-6 contains reprinted AVISO re-analysis 17-cm nosteric 

separation dates with 13-cm nosteric dates and 13-cm steric dates for comparison. The 13-cm

nosteric dates were subtracted from the 13-cm steric dates to yield delay (last column in 

Table5.4-6). To interpret the delays, the events were separated into two groups, the group where 

events should be delayed and the group where events should be advanced. Based on the annual 

peak and trough of the steric signal (15 September and 16 March, respectively), steric signal 

sinusoidal inflection points were estimated to be 15 June and 15 December. Between 15 June 

and 15 December, separation events were expected to be delayed by the steric signal. Between 

15 December and 15 June, events were expected to be advanced. Expected-delayed events are 

highlighted in red in Table 5.4-6, while expected-advanced events are highlighted in blue. Events 

that behaved as expected are highlighted in green in the last column. (Event #26 was disregarded 

since no separation event occurred in the 13-cm steric AVISO data.) Only events #27, 49, and 50 

did not behave as expected. Events #49 and 50 were both near an inflection point. Steric heating 

in the Gulf has some inter-annual variation, and so the actual inflection points can fluctuate from 

year-to-year about the estimates. If the events whose nosteric separation dates occurred within 

plus or minus ten days (arbritrary) of the estimated inflection points are ignored (#35, 46, 49, and 

50), the RMS of the remaining date differences is 3.2 days. Delays are between zero and four 

days. Advances are between three and eight days. Notice that event #46, eliminated in the 

calculation, is an outlier (42 days), showing that delays (and maybe advances) caused by the 

steric signal can be upwards of a month. However, it seems more likely that the effect of the 

steric signal on events will usually be less than one week, though this result is dependent on 

tracking contour level. Thus, the effect of the steric signal could be to shift the separation month 

in Chang and Oey (2013b) by one month, depending on the day of the month the separation 

occurred. However the separation day-of-month is critical information in assessing the impact 

on individual events. Even so, for the 21 ubiquitous events mentioned previously, based on 

month only, re-analysis dates are just as early or earlier than the corresponding Chang and Oey 

(2013b) dates for all events but one (#40). This one event has a summer/fall date, thus, 

contradicting the expected trend. If one assumes that each Chang and Oey (2013b) date in Table 

5.4-4 corresponds to the fifteenth day of the given month, the mean delay of the 21 events 

between the Chang and Oey (2013b) dates and the re-analysis is 13 days. Using the ten-day 

window about the inflection points, events expected to be delayed have an average delay of 10.6 

days. Events expected to be advanced are actually also delayed on average by an even larger 

value, 13.8 days. These results are not consistent, and the source of the discrepancy is unknown.
274

Table 5.4-6. Comparison of LC eddy separation events

No. Industry 

Name

(1) AVISO

17-cm

No Steric

(2) AVISO

13-cm

No Steric

(3) AVISO

13-cm

Steric

(2) - (1)

Days

(3) - (2)

Days

21 Whopper 08 Jul 1993 11 Jul 1993 13 Jul 1993 3 2

22 Xtra 04 Sep 1993 05 Sep 1993 07 Sep 1993 1 2

23 Yucatan 19 Aug 1994 21 Aug 1994 22 Aug 1994 2 1

24 Zapp 17 Apr 1995 18 Apr 1995 15 Apr 1995 1 -3

25 Aggie 01 Sep 1995 03 Sep 1995 04 Sep 1995 2 1

26 Biloxi 08 Mar 1996 11 Mar 1996 * 3

27 Creole 20 Jul 1996 24 Jul 1996 24 Jul 1996 4 0

28 El Dorado 25 Sep 1997 27 Sep 1997 29 Sep 1997 2 2

29 Fourchon 12 Feb 1998 16 Feb 1998 12 Feb 1998 4 -4

30 Juggernaut 28 Sep 1999 30 Sep 1999 04 Oct 1999 2 4

31 Millennium 29 Mar 2001 31 Mar 2001 27 Mar 2001 2 -4

32 Pelagic 24 Feb 2002 25 Feb 2002 24 Feb 2002 1 -1

33 Quick † † †

34 Sargassum 11 Aug 2003 13 Aug 2003 16 Aug 2003 2 3

35 Titanic 20 Dec 2003 22 Dec 2003 21 Dec 2003 2 -1

36 Ulysses 19 Aug 2004 20 Aug 2004 22 Aug 2004 1 2

37 Vortex 11 Sep 2005 12 Sep 2005 14 Sep 2005 1 2

38 Walker 06 Feb 2006 09 Feb 2006 05 Feb 2006 3 -4

39 Xtreme 12 Feb 2006 15 Feb 2006 11 Feb 2006 3 -4

40 Yankee 15 Sep 2006 17 Sep 2006 19 Sep 2006 2 2

41 Zorro § § §

42 Albert 21 Oct 2007 09 Nov 2007 11 Nov 2007 19 2

43 Brazos 02 Mar 2008 09 Mar 2008 01 Mar 2008 7 -8

44 Cameron 27 Jun 2008 28 Jun 2008 30 Jun 2008 1 2

45 Darwin 14 Feb 2009 17 Feb 2009 14 Feb 2009 3 -3

46 Ekman 22 Jun 2009 25 Jun 2009 06 Aug 2009 3 42

47 Franklin 27 Jun 2010 09 Aug 2010 13 Aug 2010 43 4

48 Hadal 22 Jul 2011 23 Jul 2011 26 Jul 2011 1 3

49 Icarus 05 Nov 2011 17 Dec 2011 18 Dec 2011 42 1

50 Jumbo 28 May 2012 07 Jun 2012 13 Jun 2012 10 6

* A very small eddy separates from the LC for this event on 4 March 1996, too small to be considered a LC eddy.

† In all three versions of the AVISO data, Pelagic and Quick separate from the LC as one eddy, though they split from each other 

days after separation.

§ Zorro appears as a detachment event in all three versions of the AVISO data.
275

If the AVISO re-analysis had been performed on a lower-tracking contour than 17 cm 

throughout, it could have had the effect of delaying all separation event dates. The second to last 

column in Table 5.4-6 shows that tracking the LC at the 13-cm level in nosteric AVISO data 

delayed every separation event, compared to tracking at the 17-cm level. Delays ranged from one 

to 43 days. The mean delay is 6.1 days, and the median is two days. Four delays were greater 

than one week (#42, 47, 49 & 50). Two delays were greater than one month (#47 & 49). 

Unfortunately, effects of changing contour level are unpredictable and event-dependent. Even so, 

re-derived event dates from lower-contour tracking may be more consistent with Chang and Oey 

(2013b) dates.

Comparison of Loop Current eddy separation events derived from AVISO SSH without steric 

signal at the 17-cm level, without steric signal at the 13-cm level, and with steric signal at the 13-

cm level, from January 1993 through December 2012, is presented in Table 5.4-6. The last two 

columns show resulting event separation delay (in days) when changing the tracking contour 

from 17-cm to 13-cm and when changing from data without the steric signal to data with the 

steric signal. The 13-cm events that were expected to be delayed by the steric signal are 

highlighted in red, while events that were expected to be advanced are highlighted in blue. 

Events that behaved as expected for either case are highlighted in green in the last column.

Vukovich (2012) provided no explicit information as to how LC eddies were tracked, although 

specified lifetime and diameter criteria were mentioned, as discussed in Section 5.3. Given that 

GOES SST, SeaWiFS and MODIS ocean color, and CCAR altimetry were used in combination, 

event dates may have been derived entirely subjectively. Vukovich (2012) dates were later than 

re-analysis dates for 14 events and earlier for only three events. Lindo-Atichati et al. (2013) used 

maximum gradient in AVISO SSH fields to determine the boundaries of the LC and LC eddies. 

Removing the steric signal would have had no affect on separation dates since a constant offset 

applied to a SSH field would not affect the gradient calculation. Lindo-Atichati et al. (2013) 

dates were later than re-analysis dates for ten events and earlier for only one event. Combinations 

of the contour level and SSH gradient techniques described are likely to yield similar results. For 

instance, Dukhovskoy et al. (in preparation) tracked the LC and LC eddies in HYbrid Coordinate 

Ocean Model (HYCOM) data using a predictor-corrector method in which SSH contour level 

defined the first estimation of LC and LC eddy boundaries and SSH gradient improved the first 

estimation. Separation dates derived using the predictor-corrector routine were only slightly 

later than dates found using SSH contour level alone, as implemented in the LCT.

Tracking techniques applied in the LCT, in Chang and Oey (2012) and Lindo-Atichati et al. 

(2013) are Eulerian approaches to separation detection. The techniques use SSH or SSH gradient 

at specified grid points to track LC and LC eddy positions at every time-step following 

streamlines or the instantaneous velocity field. Because ocean flows are quasi-geostrophic, they 

evolve slowly enough that streamlines well-approximate path lines of the flow field, and since 

the flow is unsteady, path lines do cross streamlines, and the fluid contained within a closed 

streamline is not conserved. Nevertheless, tracking of a SSH contour or velocity fronts can 

identify separation dates relatively accurately. It could be argued that the Vukovich (2012) 

tracking technique, although subjective, is Lagrangian through the use of time-evolving SST and 

ocean-color patterns in satellite images as a Lagrangian tracer. However, neither SST nor 

chlorophyll concentrations are conserved quantities, so a subjective technique based on satellite 
276

imagery is, at best, a mixed Eulerian/Lagrangian approach that relies heavily on expert judgment. 

In contrast, explicit Lagrangian tracking focuses on specific fluid parcels moving with the flow 

rather than Eulerian flow-field variables specified at fixed points in space. For example, 

Andrade-Canto et al. (2013) presented a method for finding manifolds – Lagrangian coherent 

structures (LCSs) – in velocity fields using finite-time Lyapunov exponents. These LCSs are 

material boundaries that follow parcel path lines through a flow. In the case of the LC, LCSs can 

show whether the main circulation coming into the Gulf through the Yucatan Channel is flowing 

northward around a presently detached LC eddy or is cutting immediately east to exit through the 

Florida Straits. A northward flow typically means that the detached LC eddy will re-attach, but 

an eastward flow means that the LC eddy is separated. Euclidean methods often require more 

than a month of data beyond separation of a LC eddy to confirm that the LC eddy is truly 

separated and not just detached from the LC. The technique given in Andrade-Canto et al. (2013) 

confirms separation more promptly. Even so, separation dates derived using this Lagrangian 

technique, which is significantly more complicated to implement, are comparable to dates 

derived from Eulerian tracking techniques.

In conclusion, dates of LC eddy separation (and detachment) events are affected by two main 

factors: data processing and tracking technique. Original CCAR, AVISO, and AVISO-CUPOM 

datasets were all derived from similar along-track altimetric sampling (SSHA), were free of 

steric heating and cooling affects, and were used to identify LC eddy separation events by the 

breaking of the 17-cm contour. Yet, corresponding LC eddy separation dates derived from the 

three datasets (Table 5.4-2) were usually different, sometimes by more than a month. Date 

differences were as much caused by differences in SSHA smoothing as they were caused by 

differences in mean SSH. In-depth testing of the AVISO dataset showed that steric heating of the 

Gulf can have the effect of delaying separation of LC eddies in summer and fall seasons and 

advancing separation in winter and spring seasons, relative to the same events in nosteric data 

(RMS of 3.2 days). Aside from data processing, the tracking technique employed can also affect 

LC eddy separation event results in significant ways. Variations in the application of a specific 

tracking technique can impact all derived separation dates. For example, decreasing the 

tracking-contour level in nosteric AVISO data, from 17 cm to 13 cm, delayed the separation time 

for all events in the altimeter record by an average of 6.1 days (Table 5.4-6). Different Eulerian 

tracking techniques, whether objective (Lindo-Atichati et al. 2013), semi-objective (Chang and 

Oey 2012), or subjective (Vukovich 2012), all yield different results (Table 5.4-4). Just as in the 

pre-altimetry era, separation dates derived from altimetry data are very much analyst dependent,

in spite of the fact that most use similar altimetry products.

The pre-altimetry and altimetry time periods were compared to determine in which time period 

LC eddy separation dates were more consistent. Revisiting the Table 5.3-1 pre-altimetry dates, 

29% (six) of the 21 listed events (both numbered and unnumbered events) were only recognized 

by one date list, the re-analysis or Vukovich (2012), not both. Similarly, 30% (nine) of the 30 

listed altimetry events in Table 5.4-4 occurring from 1993 through 2009 (both numbered and 

unnumbered events) were unacknowledged by at least one of the date lists. This means that 

uniformity of LC eddy separation event identification has remained a problem regardless of Gulf 

data used. In the pre-altimetry time period, LC eddy counts were misrepresented due to poor data 

quality and seasonal satellite data outages. Now, with higher-quality altimetry data, LC eddy 

counts still differ among authors due to application of different eddy size, lifetime, and 
277

propagation criteria, allowance of short-period events, and ambiguity of separation status 

(detachment or separation). Of the 15 ubiquitous pre-altimetry events, re-analysis and Vukovich 

(2012) dates differed by a month or less for 73% (11) of the events (ignoring day-of-month, as in 

the present section). Slightly better, 81% (17) of the 21 ubiquitous altimetry events in Table 5.4-

4 differed by one month or less. Lastly, 20% (three) of the ubiquitous pre-altimetry dates and 0% 

of the ubiquitous altimetry dates differed by three months or greater. These results indicate that 

the altimetry dates have better agreement overall than the pre-altimetry dates, especially since a 

total of four altimetry date lists exhibited more consistency than only two pre-altimetry date lists. 

With full consideration of the various tracking techniques compared, the SSH contour-tracking 

technique used in the CCAR LCT to identify LC eddy separation events in this report is 

relatively simple to apply, although the 17-cm level would need to be decreased to make derived 

separation dates more comparable to dates derived by the other analyses. Changing the tracking 

contour level is a user-selectable option within the LCT to allow general use of the LCT on Gulf 

observational and modeling data. As the use of more accurate SSH data improves, in 

combination with objective tracking techniques, LC eddy separation dates will likely become 

more consistent in the future.

Although the LCT was used only by the remote sensing component of this study, the tool has 

been used in other studies. For example, the LCT was used extensively to test the sensitivity of 

LC eddy separation event dates to changes in Gulf satellite-altimetric sampling. SSHA fields 

from a Gulf 54-year high-resolution HYCOM run were sub-sampled along four different satellite 

(TOPEX/Poseidon, TOPEX/Poseidon interleaved, Geosat, and Envisat) ground tracks to 

generate simulated along-track data. The simulated along-track data were then smoothed and 

gridded using the CCAR altimetry-processing procedures described in Section 2.6 and combined 

with the HYCOM mean SSH to create seven different 54-year synthetic SSH time series. The 

objective 17-cm tracking employed in the LCT made counting of LC eddies fast and unbiased. 

The effects of the various satellite sampling were then compared systematically. This suite of 

sensitivity tests revealed relatively weak sensitivity of the probability distribution of the LC eddy 

shedding to uncertainties and biases related to the derivation of the SSH fields from altimetric 

sampling (Dukhovskoy et al., in preparation).

5.5 STATISTICAL ANALYSIS OF LOOP CURRENT SEASONALITY

Several recent studies have suggested that the LC may exhibit seasonality in the timing of LC 

eddy separation. Alvera-Azcárate et al. (2009) found 21 LC eddies in a survey of altimetry data 

from October 1992 into February 2006, 12 of which separated in the months of July, August, or 

September. Leben and Hall (2010) presented monthly-binned histograms of pre-altimetry and 

CCAR altimetry LC eddy separation dates as additional observational evidence that separation 

timing has a seasonal preference. Chang and Oey (2012) similarly suggested that pre-altimetry 

separation dates in past literature combined with altimetry dates derived from an AVISO product 

also support seasonality. More rigorously, Lindo-Atichati et al. (2013) calculated the mean 

annual cycle of the northern boundary of the LC with error bars, and concluded that northern 

penetration at some times of the year is statistically different than at other times. The 95% 

confidence intervals in Figure 5.4-4 of this report similarly support that there are two distinct LC 

seasons, one of maximums and one of minimums, though the extents of the two are not clearly 

defined. In the current study, a number of pre-altimetry, altimetry, and combined (both pre-
278

altimetry and altimetry) datasets were compared to assess seasonality and the statistical 

significance and boundaries of seasons where LC eddy separation is most likely. 

Statistical χ2 tests were performed on the re-analysis pre-altimetry dates (N=20) shown in Table 

5.3-1 to assess the null hypothesis that LC eddy separation dates come from a uniform 

distribution. Since expected bin counts using monthly binning would be too low to test for 

statistical significance, the data were binned quarterly (not shown) to increase expected counts in 

each three-month bin to five. Bins larger than three months (e.g., four months or six months) can 

begin to conceal seasonality and are, therefore, undesirable. Quarterly binning proceeded in three 

different ways: first with the bins Feb-Apr, May-Jul, Aug-Oct, and Nov-Jan (binning1), second 

with the bins Jan-Mar, Apr-Jun, Jul-Sep, and Oct-Dec (binning2), and third with the bins MarMay, Jun-Aug, Sep-Nov, and Dec-Feb (binning3). Results from the χ2 tests indicate that at the 

95% confidence level, the null hypothesis is rejected for binning1 and binning2 (Ott and 

Longnecker 2001), implying that separation timing is seasonal. The tests of binning3 did not 

yield statistical significance at the 95% confidence level. Statistical significance can be a 

function of bin boundaries and size; therefore, suppression of seasonality in at least one of the 

three-month binning schemes is expected. There are too few pre-altimetry dates from Vukovich 

(2012) in Table 5.3-1 (N=16) to statistically determine whether the separation dates are from a 

uniform distribution. The χ2 distribution is not well approximated whenever 20% or more of the 

bins have expected values less than five (Ott and Longnecker 2001). Vukovich (2012) LC eddy 

separation dates fail this requirement since all four bins have an expected value of four. 

However, Table 5.3-1 contains only a portion of the pre-altimetry dates given in Vukovich 

(2012) from 1978 through 1992. If all pre-altimetry separation dates from Vukovich (2012), 

from 1972 through 1992, are tested (N=23), the expected bin counts are sufficient, but none of 

the three sets of bins show statistical significance of seasonality.

Monthly-binned histograms of the pre-altimetry re-analysis dates and the pre-altimetry dates 

from Vukovich (2012) listed in Table 5.3-1 are shown in Figures 5.5-1a and 5.5-1b, respectively. 

The blue dashed line in each subplot represents the average number of LC eddies to separate per 

month, per year. Randomization tests were performed on both datasets to determine which peaks 

in the histograms, if any, were significant. Re-analysis LC eddy separation event testing 

proceeded as follows: The events were randomly reordered 100,000 times, forming 100,000 

separation date sequences. Each sequence used each original separation event exactly once 

(selection without replacement) so that every sequence had exactly 20 events, just as the original 

sequence, and the separation periods and duration of the record were preserved. The initial day 

of the year to start each sequence was also randomized. Then all 100,000 sequences were binned 

by month to produce a distribution of LC eddy separation counts for each month. Significance 

was determined from the random outcomes. For example, if there were no seasonal signal in the

original re-analysis LC eddy separation sequence, then each of the 12 monthly counts 

represented by bars in the original histogram (Figure 5.5-1a) would be frequently replicated 

among the 100,000 random sequences. However, Figure 5.5-1a shows that the count in August is 

significant. The value 1.7% above the bar means that of all 100,000 sequences, only 1.7%, or 

1,700, of the randomized sequences contained, in this case, five or more separation events in 

August. Any count with a value of 5% or less was considered significant at the 95% confidence 

level. The only significant month of separation in the re-analysis dates is August. Even so, one 

month is enough to indicate that there is some seasonal preference in the re-analysis pre-
Ave. No. Eddies per Year 

52.5% Jan

52.7% Feb47.4% Mar49.4% Apr47.6% May

16.8% Jun

23.3% Jul

1.7% Aug

22.0% Sep

47.6% Oct

50.6% Nov

0

15.7% Dec

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

1

2

3

4

5

6

7

Total Eddies 

Ave. No. Eddies per Year 

38.8% Jan

61.6% Feb

38.6% Mar

61.4% Apr

15.2% May

61.5% Jun

38.6% Jul

26.5% Aug

38.6% Sep

61.4% Oct61.6% Nov

0

26.6% Dec

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

1

2

3

4

5

6

7

Total Eddies 

(a)

(b)

 279

Figure 5.5-1. LC eddy separation dates (Table 5.3-1) binned monthly from (a) reanalysis and (b) 

Vukovich (2012) pre-altimetry (1978-1992). Blue dashed lines show the average number 

of LC eddies to separate per month, per year. The percent likelihood of observing an LC 

eddy count as extreme or more extreme by chance is displayed for each monthly bar. All 

bars at 5% or less are considered significant at the 95% confidence level and colored 

red.
280

altimetry dates. The same randomization testing was performed on the pre-altimetry Vukovich 

(2012) dates in Figure 5.5-1b and on the complete pre-altimetry record from 1972 through 1992 

in Vukovich (2012) (not plotted as histogram). There were no significant months found, 

indicating no seasonality in the Vukovich (2012) pre-altimetry dates. Traditional histograms of 

Figures 5.5-1a and 5.5-1b are shown in Figures 5.5-2a and 5.5-2b for comparison.

These two types of statistical tests, χ2 and randomization, complement each other. The χ2 test 

indicates whether a distribution of LC eddy separation dates exhibits statistically significant 

seasonality; if the dates are not from a uniform distribution, then the distribution exhibits 

seasonality. However, the χ2 test does not indicate in which month or season LC eddy separation 

is more likely or less likely to occur. Conversely, if the randomization test shows any months as 

being significant, the test not only indicates that the respective dates exhibit seasonality, but also 

provides information on the seasonal preference. If no months are significant, then the 

randomization test is a null result, and no information on seasonality is obtained. Table 5.5-1 

summarizes results of the χ2 and randomization tests on the pre-altimetry re-analysis and 

Vukovich (2012) datasets along with results of the same tests performed on additional datasets. 

Of all pre-altimetry datasets shown, the re-analysis LC eddy separation date list is the only one to 

show a statistically significant peak and is one of two lists to show significant χ2 test results. The 

other list with a significant χ2 test is given in Sturges (1994). Sturges (1993), Sturges (1994), 

and Vukovich (2012) dates were all based on dates in Vukovich (1988), which had too few 

events to make the χ2 test valid. Vukovich (2012) continued the list presented in Vukovich 

(1988) through the pre-altimetry time period. Note that the dates in Vukovich (2012) over the 

longer time period from 1972 though 1992 exhibited no statistically significant seasonality by 

either test. Because seasonality was not evident in Vukovich (1988), seasonality was 

indiscernible until the altimetry record became sufficiently long to overcome the lack of 

seasonality in these earlier published pre-altimetry LC eddy separation dates.

Figures 5.5-3a, 5.5-3b and 5.5-3c display, respectively, the CCAR (N=30), AVISO (N=28), and 

AVISO-CUPOM (N=30) altimetry separation dates from Table 5.4-2, binned monthly. (The 

same separation date lists are plotted as traditional histograms in Figures 5.5-2c, 5.5-2d, and 5.5-

2e, respectively.) All three histograms have bimodal distributions. The CCAR histogram is 

strongly bimodal, while the AVISO-CUPOM shows weak bimodality, with one peak in the late 

winter/early spring (February/March) and the other in late summer/early fall (August/ 

September). Henceforth, these peaks will be called the “spring” and “fall” seasons since they 

represent time periods of preferred LC eddy separation and reach maximums near the spring and 

fall equinoxes. Randomization tests performed on the three datasets show that August and 

September are significant months in the CCAR dataset, and August is significant in the AVISO 

dataset. None of the other months’ eddy counts in any of the three histograms are significantly

different from the mean. There are no significant months in the AVISO-CUPOM dataset. These 

results indicate that the spring peak is not significant; although, it may become significant with a 

longer satellite altimeter-derived time series based on more observations of separation events if 

the statistics remain stationary. The fall peak is likely significant; however, Figure 5.5-3c 

demonstrates that different versions of SSHA and mean SSH do affect the significance of the fall 

peak. Although CCAR and AVISO-CUPOM datasets both use the same mean SSH, the fall
0

2

4

6

0

2

4

6

0

2

4

6

8

10

12

Jan Apr Jul Oct

0

2

4

6

8

Jan Apr Jul Oct Jan Apr Jul Oct

Number of Loop Current Eddies

(a) (b)

(c) (d) (e)

(f ) (g) (h)

(i) (j) (k)

281

Figure 5.5-2. Monthly-binned histograms of pre-altimetry, altimetry, and combined LC eddy separation 

date datasets. First row: (a) reanalysis and (b) Vukovich (2012) pre-altimetry separation 

dates (1978-1992) from Table 5.3-1. Second row: (c) CCAR, (d) AVISO, and (e) AVISOCUPOM altimetry (1993-2012) from Table 5.4-2. Third row: reanalysis pre-altimetry 

(1978-1992) and (f) CCAR, (g) AVISO, and (h) AVISO-CUPOM altimetry (1993-2012) 

combined. Fourth row: Vukovich (2012) pre-altimetry (1978-1992) and (i) CCAR, (j) 

AVISO, and (k) AVISO- CUPOM altimetry (1993-2012) combined.
Ave. No. Eddies per Year 

8.3% Jan

8.6% Feb11.6% Mar

55.1% Apr

8.2% May

29.7% Jun

52.8% Jul

4.5% Aug3.9% Sep

52.8% Oct

29.7% Nov

0

8.2% Dec

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

1

2

3

4

5

6

7

8

9

10

Total Eddies 

Ave. No. Eddies per Year 

9.3% Jan

7.0% Feb

42.5% Mar

33.2% Apr31.2% May

40.6% Jun42.4% Jul

42.5% Aug

3.0% Sep

31.2% Oct33.1% Nov31.1% Dec

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

1

2

3

4

5

6

7

8

9

10

Total Eddies 

Ave. No. Eddies per Year 

7.1% Jan

20.1% Feb24.7% Mar

55.0% Apr

7.0% May

23.2% Jun

47.7% Jul

24.8% Aug

9.5% Sep

26.9% Oct

54.5% Nov

26.4% Dec

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

1

2

3

4

5

6

7

8

9

10

Total Eddies 

(a)

(b)

(c)

 282

Figure 5.5-3. LC eddy separation dates (Table 5.4-2) binned monthly from (a) CCAR, (b) AVISO, and 

(c) AVISO-CUPOM altimetry (1993-2012). Blue dashed lines show the average number 

of LC eddies to separate per month, per year. The percent likelihood of observing an LC 

eddy count as extreme or more extreme by chance is displayed for each monthly bar. All 

bars at 5% or less are considered significant at the 95% confidence level and colored red.
283

Table 5.5-1. Results of significance testing of various sources of LC eddy 

separation event dates

χ2 Test Randomization 

Test

Source bin1 bin2 bin3 Significant 

Months

PRE-ALTIMETRY

Re-analysis, 1978-1992 x x Aug(+)

Sturges (1993), 1965-1990 None

*Sturges (1994), 1973-1993 x x None

Vukovich (1988), 1973-1987 N/A None

Vukovich (2012), 1972-1992 None

Vukovich (2012), 1978-1992 N/A None

ALTIMETRY

CCAR, 1993-2012 x x Aug(+), Sep(+)

†AVISO, 1993-2012 x x Sep(+)

AVISO-CUPOM, 1993-2012 x x None

§Alvera-Azcarate et al. (2009), 1993-2006 x x Mar(+), Sep(+)

אChang and Oey (2012), 1993-2009 x x Sep(+)

Chang and Oey (2013b), 1993-2009 x x x Mar(+), Sep(+)

Leben (2005), 1993-2004 N/A Sep(+)

Lindo-Atichati et al. (2013), 1993-2009 x x x Sep(+)

Vukovich (2012), 1993-2010 x x Mar(+)

COMBINED

Re-analysis, 1978-1992+CCAR, 1993-2012 x x x Aug(+), Sep(+), 

Dec(-)

℘Re-analysis, 1978-1992+AVISO, 1993-2012 x x x Aug(+), Sep(+)

Re-analysis, 1978-1992+

AVISO-CUPOM, 1993-2012

x x x Aug(+), Sep(+)

Vukovich (2012), 1978-1992+CCAR, 1993-2012 x x Sep(+), Dec(-)

◊Vukovich (2012), 1978-1992+

AVISO, 1993-2012

x x Sep(+)

Vukovich (2012), 1978-1992+

AVISO-CUPOM, 1993-2012

x None

אChang and Oey (2012), 1974-2009 x x x Dec(-)

Chang and Oey (2013b), 1974-2009 x x x Mar(+), Dec(-)

Sturges and Leben (2000), 1973-1999 x x None

Vukovich (2012), 1972-2010 x x Mar(+), Dec(-)

For the χ2 tests, binning1 (bin1) used month groupings Feb-Apr, May-Jul, Aug-Oct, and Nov-Jan, binning2 (bin2) used Jan-Mar, AprJun, Jul-Sep, and Oct-Dec, and binning3 (bin3) used Mar-May, Jun-Aug, Sep-Nov, and Dec-Feb. “x” means the distribution was not 

uniform at the 95% confidence level. “N/A” means there are not enough separation events for the test to be valid. For the 

randomization tests, months with “+” signs are peaks, and months with “-“ signs are troughs.

Additional notes on next page.
284

* Sturges (1994) presented one separation event occurring in 1993, beyond the limits of the pre-altimetry “era” ending in 1992. 

Even so, most of the dates in Sturges (1994) are pre-altimetry dates, and so Sturges (1994) is placed in the pre-altimetry category. 

Sturges (1994) was submitted before the end of 1993. Thus, the study year 1993 was not completed.

† In the AVISO date list (Table 5.4-2), two LC eddies shed in February 2006. However, if those two events are combined into one, 

the results of the χ2 tests and randomization test remain the same.

§ Alvera-Azcarate et al. (2009) analyzed data ending in February 2006. Thus, the study year 2006 was not completed. AlveraAzcarate et al. (2009) noted two separation events to have occurred on the same day, 6 March 2002. If those two events are 

combined into one, the results of the χ2 tests remain the same, but the March peak is no longer significant.

א No dates were explicitly given in Chang and Oey (2012), but we know the dates are very similar to dates in Chang and Oey 

(2013b). All dates in Chang and Oey (2013b) were taken to be dates in Chang and Oey (2012) “as is”, with the exception of three: 

Chang and Oey (2013b) dates in March 1996, April 1995 and May 2007 were included in Chang and Oey (2012), after each being

shifted forward a month to ultimately match the altimetry histogram in Chang and Oey (2012). See further explanation in Section 

5.4. Since the estimated Chang and Oey (2012) dates can be binned monthly to match the histogram in Chang and Oey (2012), the

χ2 test results included herein are valid even if the exact estimated dates are wrong. However, the corresponding randomization

test will be impacted by incorrect dates.

℘ In the AVISO date list (Table 5.4-2), two LC eddies shed in February 2006. However, if those two events are combined into one, 

the results of the χ2 and randomization tests on the combined re-analysis/AVISO date set remain the same.

◊ In the AVISO date list (Table 5.4-2), two LC eddies shed in February 2006. However, if those two events are combined into one, 

the results of the χ2 and randomization tests on the combined Vukovich (2012)/AVISO date set remain the same.

season is significant in the CCAR seasonal distribution but not in the AVISO-CUPOM seasonal 

distribution. Differences in SSHA processing methods between CCAR and AVISO resulted in

smaller and larger spreads, respectively, of separation dates around the center of the fall season. 

In addition, AVISO dates were clustered closer to the fall center than the AVISO-CUPOM dates, 

indicating that both SSHA processing and mean SSH impact the overall spread of the 

distribution. If the AVISO-CUPOM dates were the only dates available for analysis, there would 

have been insufficient evidence to prove seasonality based on the randomization test. With the 

null hypothesis that the counts come from a uniform distribution, χ2 tests show that the null 

hypothesis can be rejected at the 95% confidence level for all three subplots with binning1 and 

binning2, indicating a seasonal preference. Thus, seasonality is also confirmed in the AVISOCUPOM dataset although the preferred seasons cannot be identified.

Results of the statistical tests performed on the CCAR, AVISO, and AVISO-CUPOM datasets 

are given in Table 5.5-1 along with results of testing on additional LC eddy separation dates 

derived from altimetry. September is a significant month in all data sets except for AVISOCUPOM, as mentioned before, and the Vukovich (2012) dates from 1993 through 2010. 

Vukovich (2012) was the only source in the Table 5.5-1 altimetry list to rely also on SST and 

ocean-color data besides altimetry to derive dates during the altimetry time period, which may 

have resulted in event dates different enough from other sources to suppress fall season 

significance. However, March was a significant month in the Vukovich (2012) altimetry dates. 

This month was also significant in Alvera-Azcarate et al. (2009) and Chang and Oey (2013b), 

but not Chang and Oey (2012). Lack of significance of the March peak in Chang and Oey (2012) 

illustrates the extreme sensitivity of significance testing to small changes in separation dates. 

(Please refer to Section 5.4 and Table 5.5-1 notes for details on the Chang and Oey (2012) dates.)

The pre-altimetry re-analysis date list is nearly consistent with the majority of the altimetry date 

lists because of its significant peak in August, close to the significant altimetry September peak. 

This rough agreement serves as additional evidence that the LC eddy separation dates 

determined by the re-analysis presented in this report are likely more accurate than the Vukovich 

(2012) dates.
285

Figure 5.5-4 displays the three altimetry date sets CCAR, AVISO, and AVISO-CUPOM paired 

with the pre-altimetry re-analysis dates. (Traditional histograms of the three combined lists are 

presented in Figures 5.5-2f, 5.5-2g, and 5.5-2h, respectively.) All three combined lists have 

significant peaks in August and September, including the combined list using the AVISOCUPOM dates shown in Figure 5.5-4c. December has become a significant trough in the prealtimetry/CCAR combined histogram (Figure 5.5-4a). Figure 5.5-5 displays the three altimeterderived LC eddy separation date sets paired with the Vukovich (2012) pre-altimetry dates from 

1978 through 1992. (Traditional histograms of the three combined lists are presented in Figures 

5.5-2i, 5-5-2j, and 5.5-2k, respectively.) The August peak that appeared in the CCAR altimetry 

dates alone (Figure 5.5-3a) is no longer significant in the combined date list in Figure 5.5-5a. 

However, December has become a significant trough. Other months besides March, August, 

September, and December may also become significant as more separation events occur and are 

added to the record. The September peaks in the CCAR and AVISO altimetry lists (Figures 5.5-

3aand 5.5-3b) are still significant in the combined lists (Figures 5.5-5a and 5.5-5b). No peaks are 

significant in the AVISO-CUPOM combined list (Figure 5.5-5c), which is not unexpected since 

neither the Vukovich (2012) pre-altimetry dates (Figure 5.5-1b) nor the AVISO-CUPOM 

altimetry dates (Figure 5.5-3c) had any significant peaks. The Vukovich (2012) pre-altimetry 

dates tend to suppress seasonal preference when combined with the altimeter record, whereas the 

pre-altimetry re-analysis dates tend to accentuate seasonality. Table 5.5-1 presents significance

testing results for all six combinations of LC eddy separation dates along with results from 

published dates by other studies.

Significance testing indicates that the annual cycle of LC eddy separation has a strong significant 

peak in September, with a less distinct peak suggested in March. Therefore, it is natural to divide 

the cycle into the two seasons previously introduced, the spring and the fall, respectively peaking 

near the spring (March) and fall (September) equinoxes. Though the peaks of the two seasons are 

evident, the centers and boundaries are not. The seasonal centers (means), which account for all 

events within the respective season, may not necessarily match the seasonal peaks determined by 

significance testing of the distribution. To precisely define the boundaries of the seasons, it is 

useful for separation events to be arranged in a “circular” sense. “Linear” annual histograms, 

such as in Figure 5.5-1 through Figure 5.5-5, show the existence of seasonality well, but poorly 

represent the cycle of the seasons from year to year. Some publications such as Chang and Oey 

(2012) concatenate two identical annual cycles to illustrate the flow of one year into the next. 

However, regardless of how the data are plotted, January and December observations are often 

kept separate for statistical analyses. Since it is possible that a separation season can begin at the 

end of one year and end at the beginning of the next, it is imperative that all events have

connectivity with each other mathematically so that seasonal boundaries can be objectively 

defined.

As an alternative to traditional “number-line” representations, separation event dates can be 

represented in a circular manner around the unit circle on a complex plane. First, the 

corresponding day-of-year (DOY) for each separation event date is converted to an angle with 

units of radians using: 

! = (5.5.1) 2"(DOY)

365
Ave. No. Eddies per Year 

18.6% Jan

34.5% Feb42.2% Mar

39.9% Apr

6.3% May

60.7% Jun

24.3% Jul

2.0% Aug

4.6% Sep

18.5% Oct

60.8% Nov

6.2% Dec

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

2

4

6

8

10

12

14

16

Total Eddies 

Ave. No. Eddies per Year 

21.3% Jan

16.4% Feb

61.3% Mar

23.5% Apr21.3% May

43.4% Jun

22.0% Jul

4.5% Aug

1.4% Sep

21.2% Oct

43.5% Nov

7.8% Dec

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

2

4

6

8

10

12

14

16

Total Eddies 

Ave. No. Eddies per Year 

19.1% Jan

18.6% Feb24.7% Mar

40.1% Apr

6.6% May7.4% Jun

42.1% Jul

0.2% Aug

1.8% Sep

37.6% Oct40.2% Nov

0

1.1% Dec

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

2

4

6

8

10

12

14

16

Total Eddies 

(a)

(b)

(c)

 286

Figure 5.5-4. LC eddy separation dates binned monthly from combined pre-altimetry reanalysis (1978-

1992) and (a) CCAR, (b) AVISO, and (c) AVISO-CUPOM altimetry (1993- 2012). Blue 

dashed lines show the average number of LC eddies to separate per month, per year. 

The percent likelihood of observing an LC eddy count as extreme or more extreme by 

chance is displayed for each monthly bar. All bars at 5% or less are considered significant 

at the 95% confidence level and colored red.
Ave. No. Eddies per Year 

24.4% Jan

33.4% Feb

17.6% Mar

45.5% Apr45.4% May

33.5% Jun33.4% Jul

54.7% Aug

8.0% Sep

24.4% Oct

45.5% Nov

8.8% Dec

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

2

4

6

8

10

12

14

16

Total Eddies 

Ave. No. Eddies per Year 

29.8% Jan

15.0% Feb

28.9% Mar

29.8% Apr

48.5% May48.2% Jun

29.0% Jul

51.7% Aug

2.7% Sep

30.0% Oct29.7% Nov

12.2% Dec

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

2

4

6

8

10

12

14

16

Total Eddies 

Ave. No. Eddies per Year 

25.7% Jan

18.4% Feb

8.8% Mar

46.0% Apr46.1% May

25.4% Jun

53.8% Jul

18.4% Aug

3.7% Sep

46.3% Oct

25.4% Nov

0

1.9% Dec

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

2

4

6

8

10

12

14

16

Total Eddies 

(a)

(b)

(c)

 287

Figure 5.5-5. LC eddy separation dates binned monthly (1978-2012) from combined Vukovich (2012) 

pre-altimetry (1978-1992) and (a) CCAR, (b) AVISO, and (c) AVISO-CUPOM altimetry 

(1993-2012). Blue dashed lines show average number of LC eddy separations per 

month, per year. The percent likelihood of observing an LC eddy count as extreme or 

more extreme by chance is displayed for each monthly bar. All bars at 5% or less are 

considered significant and colored red.
288

Since DOY can be at most equal to 365 days and at least one day, α is always greater than zero 

and less than or equal to 2π. (Note that for a separation date falling in a leap year, the leap day is 

ignored and the DOY is calculated as for a non-leap year. In the case that a separation occurs on 

the leap day, Feb. 29, the DOY for Feb. 28 is used to keep the separation event in the correct 

month.) Then each angle α is transformed into a complex number:

. (5.5.2)

Separation dates in the form of complex numbers can then be plotted around the unit circle.

Figure 5.5-6 displays the pre-altimetry re-analysis date list from Table 5.3-1 plotted around the 

unit circle. Similar plots for the CCAR, AVISO, and AVISO-CUPOM altimetry date lists in 

Table 5.4-2 are shown in Figure 5.5-7, and plots of the combined pre-altimetry and altimetry date 

lists are shown in Figure 5.5-8. A k-means clustering algorithm was applied to each date list 

(seven altogether) to divide the events in each list into two distinct groups per plot, the spring 

(red dots) and fall (blue dots) seasons. (The results of a k-means scheme are dependent on the 

initialization of the algorithm; different initializations can result in different clusterings and, thus, 

different standard deviations of the two clusters in this situation. The k-means algorithm was 

semi-randomly initialized many times to identify the two event groups yielding the minimumRMS of their standard deviations.) For each date list, the complex numbers corresponding to all 

dates in a season were averaged with Eq. (5.5.3) to find the geometric center or centroid of each 

season, 

, (5.5.3)

where the variable N represents the total number of events in the season. Then the mean angle 

was found as

, (5.5.4)

where .

(Equation 5.5.1 can be used to calculate the DOY corresponding to the center of the season.) The 

colored triangles in each subplot of Figures 5.5-6 through 5.5-8 represent the centers of the two

seasons. The spring and fall equinoxes occur after the respective centers of the separation 

seasons are reached during the year (moving counterclockwise around the circle). The dashed 

lines plotted between the seasonal means, each nearly pass through the origin of the 

corresponding unit circle, meaning that the centers of the two seasons are about six months apart 

in all seven date lists. (In fact, the dashed line in the pre-altimetry re-analysis figure, Figure 5.5-

6, crosses through the origin almost exactly.) Notice that the triangles do not lie on the unit 

circles as the dots do. The distance between each triangle and the unit circle is a measure of 

dispersion (standard deviation) in the dates in each season. The approximate circular analogue of 

the basic linear standard deviation is given by the following equation:

. (5.5.5)

z = cos(!) + isin(!)

z = 1

N

zj

j=1

N

!

! = arg(z )

0 <! " 2#

!std = 2(1" z )
Spring Equinox

 Summer Solstice

 Fall Equinox

Winter Solstice

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Spring

Season

Fall

Season

 289

Figure 5.5-6. Pre-altimetry reanalysis LC eddy separation dates from 1978-1992 (Table 5.3-1) plotted 

as days-of-year on the unit circle in the complex plane, divided into two seasons. Each 

dot represents a separation event. The triangles represent the means of the two seasons.
 Spring Equinox

 Summer Solstice

 Fall Equinox

 Winter Solstice

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Spring

Season

Fall

Season

 Spring Equinox

 Summer Solstice

 Fall Equinox

 Winter Solstice

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Spring

Season

Fall

Season

 Spring Equinox

 Summer Solstice

 Fall Equinox

 Winter Solstice

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Spring

Season

Fall

Season

(a)

(b)

(c)

 290

Figure 5.5-7. LC eddy separation dates (Table 5.4-2) from (a) CCAR, (b) AVISO, and (c) AVISOCUPOM altimetry (1993-2012) plotted as days-of-year on the unit circle in the complex 

plane, and divided into two seasons. Each dot represents a separation event. The 

triangles represent the means of the two seasons.
(a)

(b)

(c)

 Spring Equinox

 Summer Solstice

 Fall Equinox

 Winter Solstice

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Spring

Season

Fall

Season

 Spring Equinox

 Summer Solstice

 Fall Equinox

 Winter Solstice

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Spring

Season

Fall

Season

 Spring Equinox

 Summer Solstice

 Fall Equinox

 Winter Solstice

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Spring

Season

Fall

Season

 291

Figure 5.5-8. LC eddy separation dates (1978-2012) combining the reanalysis pre-altimetry with (a) 

CCAR, (b) AVISO, and (c) AVISO-CUPOM altimetry dates plotted as days-of- year on the 

unit circle in the complex plane, and divided into two seasons. Each dot represents a 

separation event. The triangles represent the means of the two seasons.
292

The angle αstd in Eq. 5.5.5 can be substituted into Eq. 5.5.1 to yield standard deviation in units of 

days (Berens 2009; Jammalamadaka and SenGupta 2001).

The centers and standard deviations obtained from circular statistical methods are given in Table 

5.5-2. Linear means and standard deviations calculated using DOYs instead of complex numbers 

are also presented in the table for comparison. Considering all seven date lists, circular results 

indicate that the spring mean lies within approximately a two-week period from Feb. 22 through 

7 March (~1 March); standard deviations are between 22 and 34 days. Linear results are much 

less reliable. They indicate that the spring mean lies within a period larger than a month, from 24 

February through 2 April; standard deviations are between 23 and 96 days. The fall mean, 

according to circular methods, lies within approximately a two-week period from 16 August 

through 1 September (~24 August); standard deviations are between 37 and 45 days. Linear 

methods also indicate the mean lies in a two-week window from 16 August through 31 August; 

standard deviations are between 39 and 49 days. Mean circular and linear method results for the 

fall season are comparable. However, circular methods have a clear advantage for estimating the 

spring mean. The reason for this is because the AVISO and AVISO-CUPOM altimetry spring 

seasons start in December according to the clusterings in Figures 5.5-7b and 5.5-7c. In Table 5.5-

2, the CCAR spring circular mean is very similar to its corresponding linear mean, but the 

AVISO and AVISO-CUPOM spring linear means are significantly different than their respective 

circular means. Also, in comparison to the CCAR spring linear standard deviation, the standard 

deviations of the other two date lists are very large. This discrepancy is caused by the DOY bias 

of Titanic, which separated in December in AVISO and AVISO-CUPOM but is part of the 

spring cluster. The Titanic DOY is high in the AVISO (354) and AVISO-CUPOM (358) date 

sets and low in the CCAR (39) dataset. Titanic not only has a noticeable impact on spring linear 

AVISO and AVISO-CUPOM altimetry statistics, but also the linear combined AVISO and 

AVISO-CUPOM statistics in Table 5.5-2 and Figures 5.5-8b and 5.5-8c.

Circular statistics account for relative positioning of the events better than standard linear 

(number-line) statistics, resulting in superior mean estimates. Note that each circular standard 

deviation in Table 5.5-2 is lower than the corresponding linear standard deviation, indicating that 

circular statistics have higher reliability. Linear statistics in Vukovich (2012) should be 

interpreted in light of the statistical discussion above. Instead of grouping separation events into 

two seasons, Table 2 of Vukovich (2012) reports that the average separation month of all events 

for three different year ranges is June, with a standard deviation of three months. The standard

deviation was likely calculated assuming a normal distribution. However, none of the histograms 

in Figure 5.5-2 appear normally distributed. The mean of a normal distribution is equal to the 

most likely value, which Vukovich (2012) indicates is June, but most of the histograms in Figure 

5.5-2 show that LC eddies are unlikely to separate in that month. Table 4 of Vukovich (2012) 

lists 48 LC eddy separation events from 1972 through 2010, only three (6%) of which were June 

events. Because the series of 12 calendar months repeats in a perpetual cycle, giving an 

“average” separation month on a number line, such as June, is meaningless and misleading since 

one might be led to believe that June events happen frequently. To the author’s credit, Vukovich 

(2012) also provides separation month mode, March, which has more statistical significance.
293

Table 5.5-2. Centers (means) and standard deviations (std.) of Table 5.2-1 and 

5.4-2 separation events analyzed separately and combined, 

separated into spring and fall seasons and presented circularly and 

linearly

Circular Linear

spring fall spring fall

PRE-ALTIMETRY

Re-analysis, 1978-1992

center (DOY) 53.2 (22 Feb) 236.0 (24 Aug) 54.8 (24 Feb) 235.5 (24 Aug)

std. (days) 33.6 42.5 38.9 47.3

ALTIMETRY

CCAR, 1993-2012

center (DOY) 65.6 (07 Mar) 243.8 (01 Sep) 65.8 (07 Mar) 242.9 (31 Aug)

std. (days) 22.0 37.4 23.3 40.6

AVISO, 1993-2012

center (DOY) 53.9 (23 Feb) 227.7 (16 Aug) 90.0 (31 Mar) 227.8 (16 Aug)

std. (days) 28.9 41.3 95.4 44.7

AVISO-CUPOM, 1993-2012

center (DOY) 59.8 (01 Mar) 228.9 (17 Aug) 92.3 (02 Apr) 229.7 (18 Aug)

std. (days) 27.4 44.6 90.4 48.7

COMBINED

Re-analysis, 1978-1992+CCAR, 1993-2012

center (DOY) 65.8 (07 Mar) 242.6 (31 Aug) 66.7 (08 Mar) 242.8 (31 Aug)

std. (days) 30.3 37.2 32.1 39.6

Re-analysis, 1978-1992+AVISO, 1993-2012

center (DOY) 53.7 (23 Feb) 231.5 (20 Aug) 78.3 (19 Mar) 231.3 (19 Aug)

std. (days) 30.6 42.0 81.1 45.3

Re-analysis, 1978-1992+AVISO-CUPOM, 1993-2012

center (DOY) 61.8 (03 Mar) 234.5 (23 Aug) 83.8 (25 Mar) 235.2 (23 Aug)

std. (days) 33.5 41.9 77.3 45.0

Re-analysis, 1978-1992+CCAR+AVISO+AVISO-CUPOM, 1993-2012

center (DOY) 61.0 (02 Mar) 235.3 (23 Aug) 79.9 (21 Mar) 235.2 (23 Aug)

std. (days) 29.5 40.9 70.2 43.5

Seasonal clusterings in the analysis of the pre-altimetry re-analysis and CCAR, AVISO, and 

AVISO-CUPOM altimetry LC eddy separation date sets separately are somewhat sensitive to 

changes in event dates. The addition of a single new event to a list can cause events to be reclustered into opposite seasons, shifting seasonal means by weeks. A larger number of events in 

each season must be observed before the seasons will “stabilize” and seasonal boundaries can be 

estimated. However, this number is not known a priori and depends on the stationarity of the 

process being observed. Even with the combined date sets, which include more separation 

events than do the pre-altimetry or altimetry date sets separately, the seasonal boundaries are not 
294

well isolated. In Figure 5.5-8a, one boundary is between mid-May and early June, and the other 

between mid-November and mid-January. In Figure 5.5-8b, the boundaries are sometime in early 

May and between mid-November and mid-December. In Figure 5.5-8c, the boundaries are 

sometime in late May, and between mid-November and mid-December. For the best possible 

estimate of seasonal boundaries, the pre-altimetry re-analysis dates and the CCAR, AVISO, and 

AVISO-CUPOM dates were all combined together into one date list and clustered as before (not 

shown). The results indicate that the boundary between spring and fall is between 16 May and 28 

May 28 (~22 May), and the boundary between fall and spring is between 16 November and 20 

December (~3 December). Center and standard deviation statistics for this combined date list are 

included in Table 5.5-2. The spring center is 2 March, and the fall center is 23 August.

General Conclusions

In contrast to the new pre-altimetry re-analysis dates derived for this report, previously published 

pre-altimetry LC eddy separation dates do not exhibit seasonality. The re-analysis date list is 

thought to be more accurate than older date lists because the re-analysis is based on a more 

complete observational record and a careful re-analysis of that record. In addition, re-analysis 

significance- testing results are relatively consistent with altimetry-based results – that is, both 

the re-analysis dates and the dates from most altimetry lists show a significant LC eddy 

separation peak in the late summer/early fall – and most altimetry date lists are consistent with 

each other. Nevertheless, identification of LC eddy separation events in the pre-altimetry datasets 

(SST, chlorophyll-a, EddyWatchTM) is necessarily subjective. Caution is advised when using 

these data in combination with the more objective and quantitative altimetric record to detect 

subtle changes in long-term climate trends or seasonality since changes found could be an 

artifact of the heterogeneous record.

Analyses shown indicate at the 95% confidence level that the LC follows a seasonal pattern 

throughout the year. Figure 5.4-4 shows with a variety of different LC metrics and three different 

datasets that LC characteristics are different at some times of the year than at others. Statistical 

tests, using χ2 on most date lists, indicate that there is seasonal preference to the timing of LC 

eddy separation since the distribution is not uniform. Randomization tests indicate that 

separations are most likely to occur in September and possibly March. Events are unlikely to 

happen in December. The annual cycle of LC eddy separation can be split into two seasons, the 

“spring” centered around 2 March and the “fall” centered around 23 August. The boundaries 

between these two seasons are approximately 22 May and 3 December.

5.6 INVESTIGATION OF DYNAMICS CONTRIBUTING TO LOOP CURRENT

SEASONALITY

Statistically significant seasonality has been identified in this analysis, not only in the annual 

cycle of LC metrics (Section 5.4), but also in the biannual distribution of LC eddy separation 

events (Section 5.5). The primary cause of this seasonality can now be explored in detail. 

As discussed in the introduction to this chapter, seasonality of LC eddy separation became more 

apparent over time as the length of the continuous record of altimetric monitoring of the LC and 

LC eddies increased. Industry concerns about the joint probability of eddy-hurricane events in 

the Gulf (Cooper and Stear 2009) and the potential impact of LC seasonality on the joint 
295

probability motivated a preliminary re-analysis of the pre-altimetric and altimetric record of LC 

intrusion and eddy shedding. This information was presented at the 2010 Ocean Sciences 

Meeting (Leben and Hall 2010), and at the 2011 Gulf of Mexico Information Transfer Meeting 

(Leben et al. 2012). This generated a number of modeling studies supported by the LC study 

program that were performed independently from the observational studies. In those studies 

Chang and Oey (2012) hypothesized that the “biannually” varying combination of Gulf and 

Caribbean winds affect Gulf and Caribbean transports, which cause more LC eddies to shed in 

summer and winter and fewer to shed in spring and fall, based on a series of process-oriented 

modeling experiments. Chang and Oey (2013a) further stated that the LC shows bimodal, 

asymmetric growth/wane captured by the first two empirical orthogonal function (EOF) modes 

of SSH in the eastern Gulf/northern Caribbean Sea, with the more dominant growth/wane from 

summer to fall and the less dominant from winter to spring. In the following section, EOF 

analyses will be used to re-visit the findings determined from the process modeling studies and 

preliminary altimetric data analysis performed by Chang and Oey (2013a).

Deepwater EOF Analysis

EOFs are a powerful tool for identifying the dominant variability in a dataset and are useful for 

exploring seasonal variations in the LC as well. The following analysis 1) uses EOFs to capture 

the dominant LC variability in the 20-year altimeter time series, 2) shows that the dominant LC 

variability also contains seasonal variability, 3) extracts the seasonal EOF modes containing the 

annual variability, and 4) evaluates proposed physical mechanisms causing the seasonal modes 

and the annual LC variability.

Monthly SSH fields from 1993 through 2012 were generated from delayed-time weekly 1⁄4° 

AVISO mapped SSH fields. A small amount of daily near-real-time data were included to 

complete the dataset through the end of the year 2012. The monthly data were demeaned in the 

deepwater by subtracting the averaged values of SSH from the monthly maps in Gulf waters 

deeper than 200 m to remove the steric signal associated with seasonal heating of the mixed 

layer. The steric signal is removed since it is an annual signal in the Gulf that would otherwise 

dominate the first mode of an EOF decomposition of SSH, but does not contribute to the 

dynamical variability of the LC. All data over the shelf were masked so that the EOF 

decomposition would reflect LC variability, which is predominately confined to the deep waters 

of the Gulf. This also prevents mode mixing (Kim and Wu 1999) of the deepwater and shelf 

variability in the EOF analyses. An EOF decomposition was calculated over the domain 98°W80°W, 18°N-31°N. This is different than the EOF domain used by Chang and Oey (2013a) for 

analysis of the AVISO data, which covered 92°W-80°W, 15°N-31°N and included the 

continental shelf. In all deepwater EOF analyses shown in this chapter, the spatial signal over 

the shelf was reconstructed for each spatial EOF loading vector. This was accomplished by 

regressing the corresponding principal component time series (PCTS) onto the original SSH time 

series, over the shelf, to map the shelf signal correlated with the deepwater SSH variability.

The first two EOF loading vectors are shown in Figure 5.6-1 and account for 24.6% and 16.6% 

of the deepwater SSH variance. Gray dashed lines plotted on the loading vectors define the data 

masking boundaries of the EOF decomposition. With the exception of the lines that transect the 

Yucatan Channel and Florida Strait, the lines follow the 200-m isobath. In comparison to the first
98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

Sea Surface Height (cm)

<−30

−20

−10

0

10

20

>30

(a)

(b)

 296

Figure 5.6-1. Deepwater (a) EOF mode 1 and (b) EOF mode 2 loading vectors, derived from monthly 

AVISO SSH with the steric signal removed. Mode 1 explains 24.6% of the variance, and 

mode 2 explains 16.6%. Black contours are at 5-cm intervals. Gray dashed lines signify 

the boundaries of the EOF decomposition. The lines follow the 200-m isobath everywhere 

except across the Yucatan Channel and Florida Strait.
297

two loading vectors, corresponding EOF modes shown in Figure 10 of Chang and Oey (2013a) 

accounted for 29.5% and 17.2% of the variance, slightly higher in both cases. This is due to 

differences in steric signal removal procedures, to differences in EOF decomposition domains, 

and likely to other differences in methods. The third and fourth EOF loading vectors are shown 

in Figure 5.6-2 and account for 11.1% and 6.6% of the deepwater variance. All together, the first 

four modes account for 58.9% of the variance in the monthly averaged data. EOF mode 1 leads 

EOF mode 2 by 55 days (EOFs derived from daily data were used to improve lag estimation 

only) based on a cross-correlation between PCTS 1 and 2. Further cross-correlation testing 

shows that mode 3 leads mode 4 by 65 days (see Figure 5.6-3).

When combined with the PCTS modes shown in Figure 5.6-3, the spatial patterns in Figures 5.6-

1 and 5.6-2 blend into a continuous three-event sequence: LC penetration, LC eddy separation, 

and westward LC eddy propagation. Table 5.4-2 shows that 28 LC eddies were detected in the 

20-year AVISO altimetry record. This averages out to about one LC eddy separation every 8.6 

months. An approximate count of local peaks is 27 in PCTS 1 (using monthly EOFs); 26 in 

PCTS 2; 25 in PCTS 3; 29 in PCTS 4. There are about as many peaks in the PCTS as there are 

separation events, meaning that, on average, the propagating LC eddy pattern in the first four 

EOF modes repeats about as frequently as LC eddies separate in the AVISO data, between eight 

and nine months. This is approximately commensurate with the periods associated with the two 

quadrature pairs formed by the first four EOF modes, which are 7 1/3 months (4 x 55 days) for 

modes 1 and 2, and 8 2/3 months (4 x 65 days) for modes 3 and 4. The four deepwater EOFs in 

Figures 5.6-1 and 5.6-2 represent most of the LC and LC eddy SSH variability in the eastern 

Gulf. 

These results are in contrast to the 3-month lagged correlation found between the first two EOF 

PCTS by Chang and Oey (2013a) in their EOF analysis of the monthly AVISO data. A 3-month 

lagged correlation corresponds to an annual period for the dominant quadrature pair. Why is 

there such a discrepancy, 7 1/3 months versus 12 months, between the periods of the dominant 

quadrature pairs from these two EOF analyses of AVISO monthly data? An attempt was made to

duplicate the EOF decomposition performed by Chang and Oey (2013a) to confirm the 3-month 

lag. The authors used monthly 1/3° AVISO mapped SSH fields from January 1993 through 

December 2010. The steric signal was removed by averaging over the Gulf and northwestern 

Caribbean Sea (98°W-80°W, 15°N-31°N). Then, EOFs were computed over the domain 92°W80°W, 15°N-31°N. Variance explained by the first EOF mode was 25.4%, and by the second 

EOF 15.9%, both still lower than the values quoted by Chang and Oey (2013a). Also, the lag 

computed between their first and second PCTS was two months, not three. Another EOF 

decomposition on the monthly AVISO dataset prepared for this report (not shown) was 

performed over the domain 92°W-80°W, 18°N-31°N, ignoring the western Gulf. Mode 1 led 

mode 2 by 54 days, and mode 3 led mode 4 by 65 days, comparable in both instances to the 

original lagged analysis results of 55 and 65 days, respectively. Including the western Gulf or 

northwestern Caribbean Sea, variability does not significantly affect the decomposition of the 

dominant LC variability modes.
98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

Sea Surface Height (cm)

<−30

−20

−10

0

10

20

>30

(a)

(b)

 298

Figure 5.6-2. Deepwater (a) EOF mode 3 and (b) EOF mode 4 loading vectors, derived from monthly 

AVISO SSH with the steric signal removed. Mode 3 explains 11.1% of the variance, and 

mode 4 explains 6.6%. Black contours are at 5-cm intervals. Gray dashed lines signify 

the boundaries of the EOF decomposition. The lines follow the 200-m isobath everywhere except across the Yucatan Channel and Florida Strait.
1993 1995 1997 1999 2001 2003 2005 2007 2009 2011

−2

−1

0

1

2

Mode 1

Mode 2

1993 1995 1997 1999 2001 2003 2005 2007 2009 2011

−3

−2

−1

0

1

2

3

Mode 3

Mode 4

(a)

(b)

Figure 5.6-3. Deepwater principal component time series: (a) PCTS 1 and PCTS 2 and (b) PCTS 3 and PCTS 4, derived from monthly AVISO 

SSH with the steric signal removed.

299 
300

Returning again to the original EOF decomposition, Figure 5.6-4 shows the composite annual 

cycle (CAC) of the PCTS computed by averaging all PCTS values shown in Figure 5.6-3 for 

each month, with 95% confidence intervals included. The CAC of PCTS 1 is dominantly annual, 

with the trough in October being statistically different than the months January through June. 

The CAC is weakly biannual with two small peaks in February and May, though this biannual 

signal is not significant. The CAC of PCTS 2 has no statistically significant monthly variance, 

but does exhibit some biannual variation with one peak in February and the other in July. 

February peaks in the CACs of both PCTS 1 and PCTS 2 are indicative of LC northward 

penetration and westward spreading. In contrast, the two-month delay between the May and July 

peaks of the first and second CACs, respectively, indicates LC northward penetration and LC 

eddy detachment or separation. The CAC of PCTS 3 is mainly annual with a significant trough 

in November, while the CAC of PCTS 4 is nondescript.

Figure 5.6-5a shows the sum of monthly variance of the AVISO data in the Gulf and 

northwestern Caribbean Sea, and Figure 5.6-5b provides the fraction of that variance contained 

within a monthly reconstruction of the first four deepwater EOF modes. The map shows that LC 

variance has been largely isolated and is upwards of 80% represented by the four modes. 

Notably, SSH variations along parts of the shelf are correlated with LC variations since the four 

EOF modes account for more than 30% of the variance in some areas of the Texas-Louisiana 

Shelf and more than 40% over some areas of the Campeche Bank. The map also shows that the 

variations in the western Gulf and northwestern Caribbean deep water are uncorrelated with the 

dominant LC variability.

The CACs of the LC metrics shown in Figure 5.4-4, derived from the complete 20-year AVISO 

monthly SSH dataset, capture the annual variability of the LC in the AVISO dataset very well. 

The CACs were computed by averaging all LC metric values for each month and each LC metric 

(area, area including detachments, volume, anticyclonic circulation, northernmost latitude, and 

westernmost longitude) to create a monthly mean time series for each metric. Using a different 

technique, CACs of the same LC metrics mentioned were computed from CAC SSH map sets 

derived from various monthly reconstructions using the first four deepwater EOF loading vectors 

shown in Figure 5.6-1 and Figure 5.6-2 to verify that the EOF modes contribute the majority of 

LC seasonal variability. Note that the LC metric CACs shown in Figure 5.4-4 were generated by 

averaging monthly LC metric values. The LC metric CACs shown here were created by 

generating an “average year” map set and then computing the corresponding LC metrics from 

that set. The first CAC SSH map set was calculated from the monthly-reconstructed deepwater 

EOF mode 1. SSH maps from each specific month were averaged to create a composite sequence 

of twelve maps, January through December, corresponding to the annual cycle, called CAC1. 

The second CAC SSH map set was calculated from the monthly reconstruction of modes 1 and 2 

together and is CAC12. Similarly, two more EOF CAC map sets were calculated called CAC123 

and CAC1234, and a final reference CAC map set was calculated from the original monthly 

AVISO SSH data called CAC_raw. The six listed LC metrics were calculated from each of the 

five CAC map sets. The names CAC_raw, CAC1, CAC12, CAC123, and CAC1234 will be used 

to refer to each respective twelve-month map sequence as well as individual LC metric CACs 

depending on the context. Since the LC metrics exhibit similar trends, only the maximum 

northern latitude and area are shown in Figures 5.6-6 and 5.6-7, respectively. Figures 5.6-6a and
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Mode 1

Mode 2

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Mode 3

Mode 4

 (a) 

 (b) 

 301

Figure 5.6-4. CACs generated from deepwater EOF mode (a) PCTS 1 and PCTS 2 and (b) PCTS 3 

and PCTS 4. Error bars are 95% confidence intervals.
98°W 95°W 92°W 89°W 86°W 83°W 80°W

18°N

21°N

24°N

27°N

30°N

Variance (cm

2

)

0

100

200

300

400

500

600

700

800

900

98°W 95°W 92°W 89°W 86°W 83°W 80°W

18°N

21°N

24°N

27°N

30°N

Fraction of Variance Explained

0

0.2

0.4

0.6

0.8

1

(a)

(b)

 302

Figure 5.6-5. (a) Sum variance of monthly AVISO maps. Contour increment 150 cm2. (b) Fraction of 

total variance captured by first four deepwater EOF modes including correlated signals at 

depths less than 200 m. Contour increment 0.1.
25

25.2

25.4

25.6

25.8

26

26.2

26.4

26.6

26.8

27

Northern Latitude (°N)

CAC raw

CAC1

CAC12

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

25

25.2

25.4

25.6

25.8

26

26.2

26.4

26.6

26.8

27

Northern Latitude (°N)

CAC raw

CAC123

CAC1234

(a)

(b)

 303

Figure 5.6-6. CAC of Loop Current northern boundary latitude. CAC_raw is plotted with: (a) CAC1 and 

CAC12; (b) CAC123 and CAC1234. 
0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Area (x10−5 km2

)

CAC raw

CAC1

CAC12

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Area (x10−5 km2

)

CAC raw

CAC123

CAC1234

(a)

(b)

 304

Figure 5.6-7. CAC of Loop Current area. CAC_raw is plotted with: (a) CAC1 and CAC12; (b) CAC123 

and CAC1234. 
305

5.6-7a show CAC_raw (metrics) compared to CAC1 and CAC12. Figures 5.6-6b and 5.6-7b 

show CAC_raw compared to CAC123 and CAC1234.

Figures 5.6-6 and 5.6-7 both show that CAC1 reproduces the dominant LC metric variability: 

relatively high values from January through June, low values during September and October, and 

then a rise to the end of the year. The next two EOF modes added in the CAC12 and in the 

CAC123 reconstructions additionally improve the metric approximation. Variance values are 

given in Table 5.6-1 for CACs and for the corresponding monthly-reconstructed time series for 

comparison. Area CAC variance explained reaches a maximum with only the first two modes. In 

contrast, monthly variance explained by the first two modes computed from the entire monthly 

time series is at a minimum for both northern latitude and area. The impact of the fourth EOF 

mode in CAC1234 is minimal. Minor improvements to the northern latitude approximation are 

found in April, May, and October of Figure 5.6-6b, and minor improvements to the area 

approximation are found in April and May of Figure 5.6-7b. The metric approximation will 

converge to the actual metric time series, CAC_raw, slowly as more EOF modes are added, 

though some EOF modes will “locally” make the approximation worse. Since approximation 

adjustments caused by the fourth EOF mode were so slight and since the fifth EOF mode (not 

shown) appeared to be more of a central/western Gulf mode than an eastern Gulf mode, it is 

likely that the dominant LC variability was captured by the first four EOF modes, so no further 

modes were added. In terms of fit, the LC northern latitude correlation between CAC_raw and 

CAC1234 is 0.9871 (variance 0.9744). The LC area correlation (R) is 0.9632 (R2 = 0.9277). 

Table 5.6-1. Proportion of LC northern latitude and area variance explained by 

first four deepwater EOF modes reconstructed as monthly time 

series and as CACs (CAC1, CAC12, CAC123, and CAC1234) with 

reference to complete monthly time series and CAC of original 

AVISO data (CAC_raw)

EOF LC Northern Latitude Variance LC Area Variance

Monthly CAC Monthly CAC

EOF 1 0.2643 0.7668 0.2263 0.9212

EOF 1,2 0.1374 0.9084 0.1457 0.9574

EOF 1,2,3 0.5921 0.9662 0.6099 0.9179

EOF 1,2,3,4 0.6149 0.9744 0.6367 0.9277

Between the 20-year complete AVISO dataset and the 20-year reconstruction of the first four 

EOF modes, the LC northern latitude correlation is 0.7842 (R2 = 0.6149), and the LC area 

correlation is 0.7980 (R2 = 0.6367).

EOF modes of monthly data, as in Figures 5.6-1 and 5.6-2, capture LC variability very well, but 

are not optimal for describing seasonal signals. For instance, the CAC of PCTS 2 in Figure 5.6-4 

indicates that the corresponding loading vector in Figure 5.6-1 has biannual power within a 

monthly context. However, the same biannual signal may not appear in an average year since the 

signal averages out. Additional EOF decompositions were performed on CAC_raw and 

CAC1234 for further insight into the LC variability. Figure 5.6-8 shows the deepwater mode 1 
98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

Sea Surface Height (cm)

<−15

−10

−5

0

5

10

>15

(a)

(b)

 306

Figure 5.6-8. CAC_raw deepwater (a) EOF mode 1 and (b) EOF mode 2. Mode 1 explains 43.0% of 

the variance. Black contours are at -5, -2, 0, 5, 10, and 15 cm. Mode 2 explains 30.2% of 

the variance. Black contours are at 3-cm intervals. Gray dashed lines signify the boundaries of the EOF decomposition. The lines follow the 200-m isobath everywhere except 

across the Yucatan Channel and Florida Strait.
307

and mode 2 loading vectors of the CAC_raw EOF decomposition. Mode 1 in Figure 5.6-8a 

accounts for 43.0% of the SSH variance within CAC_raw, and mode 2 in Figure 5.6-8b accounts 

for 30.2%. Most of this variance is in the eastern Gulf. CAC_raw mode 3 and mode 4 loading 

vectors in Figure 5.6-9 account for 10.7% (Figure 5.6-9a) and 8.6% (Figure 5.6-9b) of the 

variance, respectively. The eight remaining EOF modes account for 7.5% total. PCTS 

corresponding to the first four EOF modes are shown in Figure 5.6-10. The PCTS of mode 1 and 

mode 2 are both mainly annual signals. Mode 1 has one main trough in October, which is 

associated with the fundamental variation of the LC metric CACs shown in Figure 5.4-4. The 

dominant peak in mode 2 is in August. Mode 2 also exhibits some weakly biannual signal 

associated with a small peak in March. In comparison, the monthly deepwater EOF mode 2 

PCTS CAC in Figure 5.6-4 shows two noteworthy peaks in February and July (though the 

second one is larger), each occurring one month earlier than the respective peaks in March and 

August of the present CAC in Figure 5.6-10. The biannual variation mechanism present in the 

monthly AVISO data is mostly averaged away in CAC_raw with other inseparable variation 

mechanisms and noise. The CAC_raw EOF mode 2 loading vector in Figure 5.6-8b shares little 

in common with the monthly EOF mode 2 loading vector in Figure 5.6-1b except for a strong 

anticyclone at 88°W. Additionally, CAC_raw EOF mode 3 and mode 4 loading vectors in Figure 

5.6-9 look nothing like monthly EOF mode 3 and mode 4 loading vectors in Figure 5.6-2. 

Conversely, the CAC_raw EOF mode 1 loading vector in Figure 5.6-8a closely resembles the 

monthly EOF mode 1 loading vector in Figure 5.6-1a. Both the CAC PCTS in Figure 5.6-10a 

and the CAC of PCTS 1 in Figure 5.6-4a follow an annual cycle remaining relatively stable from 

January through June, dropping to a minimum in October, and increasing to the end of the year. 

Since the first EOF mode of the monthly AVISO data and of the CAC of the monthly data 

(CAC_raw) are very similar with strongly annual Loop Current growth and subsidence. This is a 

mainly annual – not biannual – process.

The LC metrics plotted in Figures 5.6-6b and 5.6-7b demonstrate that the CAC of the first four 

EOF modes (CAC1234) captures most of the annual LC variability. Loading vectors of an EOF 

decomposition of CAC1234 are shown in Figures 5.6-11 and 5.6-12. The CAC1234 EOF 

decomposition captures 100% of CAC1234 variability as expected in the first four modes: 

66.4%, 28.9%, 4.3%, and 0.4%, respectively. Note, however, that these modes do not capture 

100% of the variability in CAC_raw. Figures 5.6-13 and 5.6-14 show, respectively, LC northern 

latitude and area CAC metrics of different reconstructions of the first three EOF modes of 

CAC1234 in comparison to CAC_raw and CAC1234. For both northern latitude and area, 

CAC1234 is almost perfectly reproduced by the reconstruction of the first three modes only, 

which is not surprising since the fourth mode captures only 0.4% of the variance in CAC1234.

The contribution of mode 4 to the seasonal signal is insignificant. The corresponding loading 

vector in Figure 5.6-12b reflects minimal impact on the LC. Table 5.6-2 lists proportions of 

variances explained using different reconstructions of the first four EOFs of CAC1234 in 

comparison to CAC1234 and CAC_raw. The first three modes explain about 97% of the northern 

latitude and 93% of the area variance in the annual cycle of the original AVISO data 

(CAC_raw). Note that the EOF 1 loading vector in Figure 5.6-11a closely resembles the 

CAC_raw EOF 1 loading vector in Figure 5.6-8a. However EOF 2, 3, and 4 loading vectors in 

Figures 5.6-11b and 5.6-12 do not match their CAC_raw EOF 2, 3, and 4 counterparts in Figures 

5.6-8b and 5.6-9. The EOF loading vectors corresponding to CAC1234 have much less
98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

Sea Surface Height (cm)

<−15

−10

−5

0

5

10

>15

(a)

(b)

 308

Figure 5.6-9. CAC_raw deepwater (a) EOF mode 3 and (b) EOF mode 4. Mode 3 explains 10.7% of 

the variance, and mode 4 explains 8.6%. Black contours are at 2-cm intervals. Gray 

dashed lines signify the boundaries of the EOF decomposition. The lines follow the 

200-m isobath everywhere except across the Yucatan Channel and Florida Strait.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

−1.5

−1

−0.5

0

0.5

1

1.5

Mode 1

Mode 2

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

−1.5

−1

−0.5

0

0.5

1

1.5

Mode 3

Mode 4

(a)

(b)

 309

Figure 5.6-10. CAC_raw deepwater PCTS for (a) EOF mode 1 and EOF mode 2 and (b) EOF mode 3 

and EOF mode 4.
98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

Sea Surface Height (cm)

<−15

−10

−5

0

5

10

>15

(a)

(b)

 310

Figure 5.6-11. CAC1234 deepwater (a) EOF mode 1 and (b) EOF mode 2. Mode 1 explains 66.4% of 

the variance. Black contours are at -5, -0.9, 5, 10 and 15 cm. Mode 2 explains 28.9% of 

the variance. Black contours are at -6, -4, -2, -1, 2, 4 and 6 cm. Gray dashed lines signify 

the boundaries of the EOF decomposition. The lines follow the 200-m isobath everywhere except across the Yucatan Channel and Florida Strait.
98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

Sea Surface Height (cm)

<−15

−10

−5

0

5

10

>15

(a)

(b)

 311

Figure 5.6-12. CAC1234 deepwater (a) EOF mode 3 and (b) EOF mode 4. Mode 3 explains 4.3%, and 

mode 4 explains 0.4%. Black contours are at 2-cm intervals. Gray dashed lines signify 

the boundaries of the EOF decomposition. The lines follow the 200-m isobath everywhere except across the Yucatan Channel and Florida Strait.
25.4

25.6

25.8

26

26.2

26.4

26.6

26.8

27

Northern Latitude (°N)

CAC raw

CAC1234

EOF1 of CAC1234

EOF1,2 of CAC1234

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

25.4

25.6

25.8

26

26.2

26.4

26.6

26.8

27

Northern Latitude (°N)

CAC raw

CAC1234

EOF1,2,3 of CAC1234

(a)

(b)

 312

Figure 5.6-13. CAC of Loop Current northern boundary latitude. CAC_raw and CAC1234 are plotted 

with (a) CAC1234 EOF mode 1 and EOF modes 1 and 2 combined; (b) CAC1234 EOF 

modes 1, 2 and 3 combined and EOF modes 1, 2, 3 and 4 combined. 
0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Area (x10−5 km2

)

CAC raw

CAC1234

EOF1 of CAC1234

EOF1,2 of CAC1234

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Area (x10−5 km2

)

CAC raw

CAC1234

EOF1,2,3 of CAC1234

(a)

(b)

 313

Figure 5.6-14. CAC of Loop Current area. CAC_raw and CAC1234 are plotted with (a) CAC1234 EOF 

mode 1 and EOF modes 1 and 2 combined; (b) CAC1234 EOF modes 1, 2 and 3 combined and EOF modes 1, 2, 3 and 4 combined. 
314

extraneous variations and are, spatially, much less complex. The EOF processing and monthly 

averaging required to produce and decompose CAC1234 have reduced the degrees of freedom 

required to separate the dominant LC variability at seasonal time scales from the original 

monthly time series.

Table 5.6-2. Proportion of CAC_Raw and CAC1234 LC northern latitude and area 

variance explained by CACs of reconstructions of first four 

deepwater EOF modes of CAC1234

EOF LC Northern Latitude Variance LC Area Variance

CAC_raw CAC1234 CAC_raw CAC1234

EOF 1 0.8532 0.8801 0.8703 0.9265

EOF 1,2 0.9711 0.9952 0.9276 0.9915

EOF 1,2,3 0.9725 0.9994 0.9317 0.9984

EOF 1,2,3,4 0.9744 1.0000 0.9277 1.0000

The evidence presented so far of annual LC variability can be compared with the results 

published by Chang and Oey (2013a). Similar to Figure 5.6-4, Chang and Oey (2013a) also show 

CACs of EOF mode 1 and mode 2 PCTS (their Figure 10) derived from monthly AVISO data 

over the 18-year time period from 1993 through 2010, which are described as annual signals. In 

Figure 4 of Chang and Oey (2013a), the authors show the first two EOF modes of an ocean 

model, with the CACs of the PCTS showing clear biannual signals. Figure 8c of Chang and Oey 

(2013a) shows six CAC monthly LC fronts, indicating relatively steady LC shape from January 

to March, LC growth from March to July, LC wane from July to November, and LC growth 

again from November to January. All together, the fronts create an annual – not biannual – cycle 

with a maximum in July and minimum in November. Figure 8d is a Hovmöller CAC plot of SSH 

along the latitude 26.5°N (crossing the northern tip of the LC). Figure 8e shows a CAC of 

maximum SSH along 26.5°N, based on Figure 8d. Figure 8e is biannual and would be 

convincing if the results presented were achieved at a constant longitude. This would suggest 

that SSH and, thus, the LC varies biannually at a fixed point in space. However, the “maximum 

SSH” criterion enables capturing of the center of the January and June SSH peaks in Figure 8d, 

though they occur at different locations. The northern latitude of the LC and other metrics 

discussed in this chapter depend less on sensitive spatial amplitude variation and choice, and are 

therefore more likely indicators of LC variability. While it is true that most LC metrics in Figure 

5.4-4 exhibit some biannual signal with local troughs in March or April and in October or 

November, the error bars show that the troughs in March or April are not significant. Assuming 

stationarity, these spring troughs may become statistically significant with more observations, 

but will still amount to only a small portion of seasonal LC variability.

Chang and Oey (2013a) explain that their Gulf-Caribbean model incorporated idealized wind 

forcing. The modeled Caribbean wind is a biannual sinusoid, maximum westward in December 

and June and minimum westward in March and September. This disagrees with observational 

wind data in that Caribbean wind is biannual but asymmetric, maximum westward in January 

and July and minimum westward in May and September (see Chang and Oey 2013a; Figure 8a). 

The September minimums are consistent with observations. The idealized modeled Gulf winds 

were 180° out of phase with modeled Caribbean winds, with westward peaks in March and 
315

September and westward minimums in December and June. The modeled westward maximums 

are not a good match with observed Gulf wind peaks in either May or October. The modeled 

minimum in December matches the observed December/January minimum, but the modeled 

June minimum occurs earlier than the observed August minimum. Table 2 of Chang and Oey 

(2013a) indicates that the model run chosen for most of the analyses in the paper, “Exp.Carib” 

(or just “Carib”), showed most LC eddies separating in the months of June, December, and 

January, times when LC eddies are unlikely to separate in reality. Chang and Oey (2013a) 

attribute the discrepancy between the peak LC eddy separation months in the model and 

observations, to both the misalignment of the modeled wind peaks with the observed wind peaks 

and the symmetry of the modeled wind signal in comparison to the asymmetry of the observed 

wind data. In a separate comparison, the authors also attribute some of the discrepancy between 

modeled and observed north Caribbean CAC monthly maps (their Figure 9) to the idealized wind 

forcing in the model. Discrepancies between modeled results and observations need to be 

resolved by using more realistic annual wind forcing.

Chang and Oey (2013a) also note that two of the four model runs the authors performed, 

“Exp.Carib” and “Exp.GOMCarib,” show similar results. Peak eddy-shedding months are June, 

December, and January for both. Chang and Oey (2010a) argued that strong Gulf easterlies 

delay eddy separation, as discussed in Section 4.7. Both “Exp.Carib” and “Exp.GOMCarib” 

incorporate winds over the northwestern Caribbean Sea, but only “Exp.GOMCarib” incorporates 

winds over the Gulf also. If the same peak shedding times can be achieved with and without Gulf 

winds, the Gulf winds must not be causing any significant delay. The other two model runs the 

authors performed in Chang and Oey (2013a), “Steady22Sv,” with only far-field forcing, and 

“Exp.GOM,” incorporating Gulf winds as well, show no seasonal preference for eddy separation. 

“Steady22Sv” eddy separation periods are seven and eight months, while “Exp.GOM” separation 

periods are six, seven, and eight months. The authors state that though the Gulf winds in 

“Exp.GOM” do not cause seasonal preference, they still have the effect of delaying separation, 

even though their experiments seem to imply that Gulf winds decrease separation intervals.

Both Chang and Oey (2012) and Chang and Oey (2013a) use a Yucatan Channel transport CAC 

from Rousset and Beal (2010) to support their modeling result that the biannual LC eddy 

shedding is caused by biannual transport variations in the Yucatan Channel. However, Rousset 

and Beal (2010) do not claim any statistical significance for a biannual signal in their transport 

results. Figure 9e of Chang and Oey (2013a) presents a biannually varying CAC of SSHA 

within a specific domain capturing the Yucatan Channel and northern Caribbean Sea (17.5°N22.5°N, 87°W-80°W), which the authors use to imply that SSHA variations in the region force 

biannual Yucatan Channel variations. The SSHA CAC does look somewhat like the Yucatan 

transport CAC in Figure 4b of Rousset and Beal (2010). However, the SSH anomalies that 

appear in the northern Caribbean Sea do not seem to propagate through the Channel in the 

corresponding CAC map set in Figures 9b and 9d. Evidence of a connection between SSHA and 

transport requires more extensive transport studies and more rigorous analyses. There may be 

some biannual transport through the Yucatan Channel forcing the LC, but that variation must 

account for only a small fraction of LC variability. The only clear evidence of biannual power 

associated with the LC is in the seasonal timing of LC eddy separation events. 
316

In contrast to Chang and Oey’s (2013a) results, all of the EOF analyses presented in this section 

indicate that variations of the LC itself are dominantly annual. Further inspection of the first two 

EOF loading vectors shown in Figure 5.6-11 indicates that annual LC variability is linked to 

coastal anomalies. The EOF 1 loading vector shows a nearly continuous low SSH anomaly 

around the entire Gulf shelf. The EOF 2 loading vector also shows a strong anomaly on the 

Campeche Bank. In the following subsection, results are shown from a coastal EOF analysis. It 

independently verifies the result that the LC co-varies with shelf signals and identifies coastal 

forcing as a possible dynamical source of the dominant LC annual variability. 

Coastal EOF Analysis

Sea-level measurements from coastal tide gauges and satellite altimetry show that an inter-annual 

sea-level signal extends all around the Gulf (Li and Clarke 2005). This signal is both remotely 

and locally forced. Remotely forced inter-annual sea-level signals propagate along the U.S. 

Atlantic coast and into the Gulf as coastal-trapped waves (CTWs). Some of this coastal signal is 

forced by inter-annual Rossby waves that form in the Atlantic, propagate westward, cross the 

Gulf Stream, and impinge on the coast. Coastal Kelvin waves are generated as the Rossby waves 

reflect off of the southeast U. S. Atlantic coast. This mechanism is consistent with observations 

that show that the inter-annual sea-level signal on the coast is driven by wind-stress curl over the 

Atlantic, and oceanic Rossby wave propagation to the coast (Hong et al. 2000) and with the high 

correlation found between U.S. east coast annual mean sea level and sea level along the northern 

coast of the Gulf (Maul and Hanson 1991). Along the northern Gulf shelf, the remotely forced 

inter-annual coastal signal is amplified from Pensacola to the Louisiana-Texas shelf by interannual alongshore wind forcing (Li and Clarke 2005). 

Li and Clarke (2005) identified inter-annual CTWs in the first EOF mode of historical monthly 

tide-gauge data (1986-2002) collected at 12 locations along the U.S. coast from Wilmington, 

North Carolina to Port Isabel, Texas. The first EOF mode captured 70% of the variance in the 

tide-gauge measurements, indicating an in-phase (at monthly resolution) signal spanning nearly

4500 km along the coast. 

To ensure that the AVISO data in shallow waters are reliable in the Gulf, coastal EOF analyses 

were performed using monthly gridded 1⁄4° AVISO SSH from 1993 through 2012 and compared 

with the tide-gauge results shown by Li and Clarke (2005). Near-coast SSH measurements are 

often excluded from gridded altimeter data products since wet tropospheric, high-frequency 

oceanographic, tidal, and other corrections applied to the altimetric range measurement tend to 

cause errors in the SSH values within 25 to 50 km of the coast (Saraceno et al. 2008). Consistent 

with the Li and Clarke (2005) analysis, the CAC was removed from the AVISO time series, and 

the data were low-pass-filtered using the Lanczos filter described in Trenberth (1984) to retain 

only inter-annual frequencies. After de-trending the data, all data in waters deeper than 500 m 

were masked to isolate the sea-level variations on the shelf and continental slope, and an EOF 

decomposition was then performed over the domain 98°W-70°W, 18°N-35°N. The EOF bounds 

were sufficiently far north to include the zone where the CTWs originate along the U.S. east 

coast and sufficiently far south to allow detection of the waves along the Gulf and northwestern 

Caribbean Sea coasts. The resulting PCTS and the original SSH were used to project the signal 

into the deep water (using a linear regression onto the original SSH time series as described in 

the earlier subsection on Deepwater EOF Analysis), yielding the monthly “low-passed” coastal 
317

EOF mode 1 loading vector shown in Figure 5.6-15a. A second coastal EOF decomposition was 

performed on the monthly AVISO data without removing the CAC or low-pass filtering the data. 

This “raw” monthly coastal EOF mode 1 (CM1) loading vector is shown in Figure 5.6-15b for 

comparison. 

The low-passed EOF mode 1 explains 60.4% of the low-frequency coastal AVISO variance, 

whereas CM1 explains 70.6% of the unfiltered coastal AVISO variance. Gray dashed lines in the 

Figure 5.6-15 maps designate the 500 m isobath. Loading vector sea level at the 12 tide gauge 

coastal locations from Figure 3 of Li and Clarke (2005) are plotted with corresponding loading 

vector sea-surface heights in Figure 5.6-16a. The low-passed loading vector SSH (blue curve) 

closely approximates the tide gauge loading vector (black curve) from Wilmington, North 

Carolina to about Pensacola, Florida, 2550 km down the coast. Beyond that point, the two 

loading vectors differ. Figure 5.6-16b shows the PCTS of the first tide gauge and AVISO coastal 

EOF modes. Note that though Li and Clarke (2005) used tide gauge data from 1986 through 

2002, only tide gauge PCTS results from roughly June of 1993 into October 2001 were given. 

The correlation between the tide gauge PCTS and the low-passed AVISO PCTS is 0.5941, which 

is quite good considering the differences in the processing of the two datasets. There are several 

key differences: 1) EOF decompositions of the altimetry were not performed over the same time 

period as the tide gauge data since reliable gridded satellite altimetry products cannot be made 

prior to late 1992; 2) the AVISO analysis includes both shelf and slope variability; and 3) 

altimetry-derived values in the AVISO maps at the tide gauge locations are extrapolated from 

altimeter measurements further offshore. Given these processing differences and possible 

sources of error, the similarity of the two EOF analyses indicates that coastal AVISO data 

analyses are able to resolve most of the dominant signal observed by the coastal tide gauges.

Veracity of the near-coast AVISO data was also tested by analysis of the northward boundary 

current speeds using the CAC_raw SSH dataset. Note that CAC_raw was created from unmasked 

monthly AVISO data and possesses no intrinsic deepwater or coastal characteristics associated 

with the various EOF decompositions presented in this chapter of the report. Northward 

geostrophic speed anomalies were computed in the Gulf Western Boundary Current at 25.25°N 

between 97.5°W and 95.5°W using CAC_raw and were compared with Western Boundary 

Current ship-drift speed anomalies from Sturges (1993) in Figure 5.6-17a. Ship-drift speeds fall 

within the 95% confidence interval error bars for all months except February, April, and 

September, indicating that the near-shore geostrophic speeds derived from CAC_raw coastal 

SSH are reliable. Figure 5.6-17b plots the derived Gulf Western Boundary Current northward 

geostrophic speed anomaly CAC with CACs derived from Florida Current speed anomalies at 

27.0°N between 80°W and 79°W and from Yucatan Current speed anomalies at 21.75°N 

between 86.75°W and 84.75°W. The CACs are consistent among the three currents in both speed 

and annual variation. Note that there is very little biannual seasonal variability in any of the 

western boundary currents.

Since comparison of the AVISO SSH with independent datasets indicates that coastal AVISO 

SSH data are valid, CM1 shown in Figure 5.6-18b can be compared with the first deepwater EOF 

loading vector derived from CAC1234 in Figure 5.6-18a. The two loading vectors are very 
98°W 94°W 90°W 86°W 82°W 78°W 74°W 70°W

18°N

21°N

24°N

27°N

30°N

33°N

98°W 94°W 90°W 86°W 82°W 78°W 74°W 70°W

18°N

21°N

24°N

27°N

30°N

33°N

Sea Surface Height (cm)

<−15

−10

−5

0

5

10

>15

(a)

(b)

 318

Figure 5.6-15. Coastal EOF mode 1 loading vector derived with monthly AVISO data from 1993 through 

2012: (a) with CAC removed, low-pass-filtered using Lanczos filter design presented in 

Trenberth (1984), and detrended; (b) unfiltered (CM1). Black contours are at 5-cm 

intervals. Gray dashed lines follow the 500-m isobath and signify the boundaries of the 

EOF decomposition. 
0 500 1000 1500 2000 2500 3000 3500 4000 4500

0

2

4

6

8

10

12

Distance (km) Along the Coast from Wilmington, NC

Sea Level (cm)

1993 1995 1997 1999 2001 2003 2005 2007 2009 2011

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Amplitude (unitless)

Tide Gauges

AVISO Monthly

AVISO Monthly − Filtered

(b)

(a)

 319

Wilmington, NC Pensacola, FL

Figure 5.6-16. Interannual EOF mode 1 (black) from monthly tide gauge SSH data for June 1993 

through October 2001 (Li and Clarke 2005) compared to EOF mode 1 derived from 

coastal AVISO SSH data low-pass-filtered with CAC/linear trend removed (blue) and 

unfiltered (red): (a) shows loading vector sea levels at specific distances along the coast 

south of Wilmington, North Carolina; (b) shows corresponding PCTS. 
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

−20

−15

−10

−5

0

5

10

15

20

Northward Speed Anomaly (cm/sec)

Sturges (1993) Ship Drift Speed Anomaly

Gulf of Mexico Western Boundary Current

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

−20

−15

−10

−5

0

5

10

15

20

Northward Speed Anomaly (cm/sec)

Gulf of Mexico Western Boundary Current

Florida Current

Yucatan Current

(a)

(b)

 320

Figure 5.6-17. (a) Gulf Western Boundary Current ship drift speed anomaly CAC (Sturges 1993) as 

compared to the northward geostrophic speed anomaly derived from CAC_raw. (b) 

Northward geostrophic speed anomalies derived from CAC_raw within the Gulf Western 

Boundary Current, the Florida Current, and the Yucatan Current. Speed anomalies were 

computed in the Gulf Western Boundary Current at 25.25°N between 97.5°W and 95.5°W, 

in the Florida Current at 27°N between 80°W and 79°W, and in the Yucatan Current at 

21.75°N between 86.75°W and 84.75°W. Error bars are 95% confidence intervals.
98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

98°W 96°W 94°W 92°W 90°W 88°W 86°W 84°W 82°W 80°W

18°N

20°N

22°N

24°N

26°N

28°N

30°N

Sea Surface Height (cm)

−15

−10

−5

0

5

10

15

(a)

(b)

 321

Figure 5.6-18. (a) CAC1234 EOF mode 1 loading vector (same as in Figure 5.6-11a). (b) CM1 loading 

vector with 5.07-cm offset applied. Black contours are at -5, -0.9, and 2 cm and then 

upwards at an interval of 2 cm. Gray dashed lines follow the 500-m isobath and signify the 

boundaries of the EOF decomposition.
322

similar in that they both show large anticyclonic anomalies over the LC and noticeable shelf 

signals as well, though the coastal loading vector shows a stronger coastal signal, as would be

expected. The SSH correlation between the two loading vectors in the deepwater (deeper than 

200 m) is 0.93 and is 0.85 overall. Figure 5.6-19a shows the sum of monthly variance of the 

AVISO data, and figure 5.6-19b provides the fraction of that variance contained within a 

monthly reconstruction of CM1. Variance explained is greater than 10% on the coast all the way 

around the Gulf from the West Florida Shelf to the Campeche Bank and within the LC. Variance 

explained is greater than 50% in some areas of the northern shelf.

Figure 5.6-20a compares the LC northern latitude metric of CAC_raw, CAC1234, and the CAC 

of the monthly CM1 reconstruction, while Figure 5.6-20b shows a similar comparison with LC 

area. Though no LC variance was included in the coastal EOF decomposition, LC variance is 

correlated with the coastal signal in the deepwater, and accounts for a large portion of the 

variance in the complete AVISO CAC, CAC_raw. Table 5.6-3 shows the proportion of 

CAC_raw and CAC1234 variance explained by the CAC of the monthly CM1 reconstruction for 

both LC metrics. The proportions in the table indicate that the CAC of the monthly CM1 

reconstruction comes closer to approximating true LC area than LC intrusion/retreat 

characteristics. Minimum and maximum area values are approximately reproduced; only 

minimum northern latitudes are reproduced. In Figure 5.6-20a, the CAC of CM1 remains close 

in magnitude to CAC_raw from January through April. Then it drops below CAC_raw, 

providing a poor approximation to observed northern latitude from May through August. Then 

from September through December, it follows true northern latitude closely. For area in Figure 

5.6-20b, the CAC of CM1 shows a similar trend as described for northern latitude from January 

through August. Then the CAC of the monthly CM1 reconstruction closely resembles CAC1234 

for the rest of the year.

Table 5.6-3. Proportion of CAC_Raw and CAC1234 LC northern latitude and area 

variance explained by the monthly reconstruction of CM1

Variance CAC_raw CAC1234

LC Northern Latitude Variance 0.65 0.75

LC Area Variance 0.85 0.82

Clearly there is a close connection between CM1 and the dominant LC annual variability. The 

question then is why do the Kelvin waves have such a dramatic affect on the LC? At inter-annual 

time scales, flow on the shelf and at the shelf edge induces parallel flow in the adjacent 

deepwater as discussed by Li and Clarke (2005). Beyond the shelf break, the shelf wave SSH 

signal decays causing seaward changes in geostrophic velocities along the continental slope. 

These deepwater near-shelf flow velocities vary depending on the orientation of the shelf (Li and 

Clarke 2005), but western boundaries theoretically induce the highest current speeds. In the Gulf, 

the Campeche Bank acts as a western boundary for the LC, which rapidly dissipates Kelvin wave 

energy in the form of eastward-propagating Rossby waves. The resulting changes in SSH at the 

shelf break induce a high-velocity jet over the continental slope that can either accelerate or 

decelerate the LC flow depending on the sign of the waves. The dynamics involved are valid at 

both annual and inter-annual frequencies. This effect may not be directly resolvable by satellite 
98°W 95°W 92°W 89°W 86°W 83°W 80°W

18°N

21°N

24°N

27°N

30°N

0

100

200

300

400

500

600

700

800

900

98°W 95°W 92°W 89°W 86°W 83°W 80°W

18°N

21°N

24°N

27°N

30°N

Fraction of Variance Explained

0

0.2

0.4

0.6

0.8

1

(a)

(b)

 323

Figure 5.6-19. (a) Sum variance of monthly AVISO maps. Contour increment 150 cm2. (b) Fraction of 

total variance generated by monthly reconstruction of CM1. Contour increment 0.1. Variance (cm

2

)
25.4

25.6

25.8

26

26.2

26.4

26.6

26.8

27

Northern Latitude (°N)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Area (x10−5 km2

)

CAC raw

CAC1234

CAC of Monthly CM1 Reconstruction

(a)

(b)

 324

Figure 5.6-20. (a) CAC of Loop Current northern boundary latitude. (b) CAC of Loop Current area. Each 

of the two subplots shows CAC_raw, CAC1234 and CAC of monthly CM1 reconstruction.
325

altimetry since the shelf break SSH gradient is large over only a short distance; however, the net 

effect at seasonal, annual, and inter-annual time scales is apparent in the response of the LC in

deepwater at these timescales. Reid (1972) has explained this type of LC response using a simple 

vorticity model that predicts the LC northern penetration as a function of current speed at the 

northern Campeche Bank shelf break and the departure angle of the LC at the shelf break. 

Greater current speed results in greater LC penetration for a fixed departure angle. Thus, CTWs 

propagating along the Gulf coast can and do affect LC variability through the generation of 

along-slope currents. This is one possible forcing mechanism for the observed annual variability 

in the LC. It is also possible that some LC variability is forced by the interaction of the eastern 

side of the LC with the remote shelf and slope along the West and South Florida slope. Further 

study of the CTW-induced currents is in progress using the in-situ data collected during the study 

program and an analysis of along-track altimeter data as performed by Li and Clarke (2005).

Conclusions

The seasonal LC variability is mainly annual. Altimeter-derived LC northern-boundary latitude 

and area metrics are relatively high from January through about July and low in September and 

October. The first three deepwater EOF modes of CAC1234 capture about 97% and 93% of the 

annual variability of LC northern latitude and area, respectively. Biannual LC seasonal 

variability is insignificant. It appears that inter-annual and annual coastal-trapped waves, 

energized mostly by wind-stress curl in the Atlantic and alongshore wind in the Gulf, are 

responsible for a large portion of LC variability. The CAC of the monthly CM1 reconstruction 

explains 65% of the variance in LC northern boundary latitude and 85% of the variance in LC 

area. Discussion and analysis of coastal EOF modes beyond CM1 will be the focus of future 

work.

327

CHAPTER 6: INERTIAL OSCILLATIONS 

6.1 INTRODUCTION

Inertial oscillations are common in the Gulf of Mexico, and are the principal high-frequency 

motions observed in deep water. On the shallow continental shelves, diurnal and semi-diurnal 

tides become important, but in deep water, tidal fluctuations are generally very small. Windforced near-inertial internal waves are the major signal propagating down from the surface. 

During hurricanes, energetic inertial oscillations can penetrate to depths of 1000 m or more 

(Brooks 1983, Shay and Elsberry 1987, Shay et al. 1992). Hurricanes and tropical storms 

generate intense inertial-internal wave activity. In many cases, however, inertial oscillations may 

be generated by an abrupt shift in wind stress, and are observed throughout the year with less 

magnitude in summer, except for hurricanes, and larger magnitudes in winter as a response to 

cold fronts that are frequent in the northern and eastern parts of the Gulf. This chapter will be 

principally concerned with the observed and modeled response to Hurricane Ida, the only 

hurricane in the dataset. This will be discussed first, followed by a section on the variability of 

inertial motions through the 21⁄2 years of current measurements. 

The upper-ocean response to a moving hurricane has been studied extensively (e.g., Leipper 

1967, Price 1981, Greatbatch 1983, Brink 1989, Dickey et al. 1998). The major response is 

characterized by sea-surface cooling and inertial oscillations that are most energetic to the right 

of the hurricane track. The hurricane-induced inertial energy then propagates both horizontally 

and vertically (Gill 1984). It is well known that under the β-effect, the inertial oscillations can 

only propagate equatorward into regions of smaller f as a result of beta-dispersion (Anderson and 

Gill 1979, Garrett 2001). On the other hand, the interaction of the inertial oscillations with the 

background flow can also influence its propagation. First derived by Mooers (1975), Kunze 

(1985) showed that the presence of relative vorticity, ζ, can alter the propagation of near-inertial 

waves through a change in the effective Coriolis parameter, ƒeff , in the form of ƒeff = f + ζ/2. 

When the near-inertial wave approaches positive vorticity, the increase of ƒeff prohibits the 

further free propagation of near-inertial waves; while when it approaches negative vorticity, ƒeff

becomes lower than f, creating a free propagation. Thus, to some extent, the horizontally nonuniform relative vorticity has the similar effect as the β-effect on the propagation of near-inertial 

energy. Numerical simulation work (Zhai et al. 2005a, Zhai et al. 2007) also shows that the 

distribution of near-inertial energy is strongly influenced by the background mesoscale eddy 

field and that anticyclonic eddies are important in draining near-inertial energy from the surface 

to the deep ocean.

Other than the effect of wave processes on the redistribution of hurricane-induced near-inertial 

energy, geostrophic advection is also important in carrying energy away from the hurricane 

track. Zhai et al. (2004) showed that the Gulf Stream can advect hurricane-induced near-inertial 

energy away from its generation site based on numerical simulations. Through mooring 

observations, Park et al. (2010) showed that the strong advection of the Kuroshio Extension 

dominates the near-inertial wave dispersion process, blocking the equatorward propagation of 

near-inertial energy.
328

In this study, the inertial oscillations induced by Hurricane Ida in November 2009 in the Gulf of 

Mexico (GOM) have been analyzed using both mooring observations and numerical models. 

Hurricane Ida was a category 2 storm that originated in the southwestern Caribbean Sea on 4

November and struck the Nicaraguan coast within 24 hours. It entered the GOM on 8 November, 

weakened and became an extratropical cyclone in the northern GOM before landfall in Alabama 

at Mobile Bay. It only took two days for Ida to cross the GOM (Figure 6.1-1; red line). To 

investigate the hurricane-induced inertial oscillations and the underlying mechanisms on the 

distribution of near-inertial energy, both mooring observations in the LC area and numerical 

models were utilized.

6.2 DATA AND METHODS

The LC mapping-array moorings (A-B-C transects) and CICESE moorings (E-transect) in the 

GOM have been employed for this inertial-wake study (Figure 6.1-1). The analysis concentrates 

on the upward-looking ADCPs that were deployed at 450 m (SAIC) and 500 m (CICESE) as 

these resolve the velocity profiles below ~ 60 m. Hurricane Ida went through the CICESE 

mooring transect, while the mapping-array moorings were on the right-hand side of the track 

(Figure 6.1-1), and both provide observational evidence on hurricane-induced motions. 

For Hurricane Ida, the 3-HLP hourly velocity data from these moorings were extracted from 1 

November 2009 to the end of December 2009. The currents were then 45-hour high-pass (45-

HHP) filtered to extract the near-inertial components. The clockwise and anticlockwise rotary 

spectra were calculated from the U and V velocity components for a one-month period from 6 

November to 6 December 2009. The relative vorticity normalized by local ƒ (i.e., ζ /ƒ) were also 

calculated using either triangle or least-square interpolation for the mapping array moorings, and 

direct computation for the CICESE moorings, as described in Section 2.9.

For the numerical model simulation, a 4-year ocean circulation hindcast from 2007 through 2010 

was performed using the Regional Ocean Modeling System (ROMS) (Haidvogel et al. 2008; 

Shchepetkin and McWilliams 2005). ROMS is a free-surface, hydrostatic, primitive-equation 

model that employs split-explicit separation of fast-barotropic and slow-baroclinic modes and 

vertically-stretched terrain-following coordinates. 

The model domain covers the entire Intra America Sea (IAS) including the Caribbean Sea, the 

GOM and the South Atlantic Bight. The model has a horizontal resolution of ~6 km (Figure 6.2-

1). Vertically, there are 30 terrain-following levels in the water column with higher resolution 

near the surface and bottom to better resolve boundary-layer dynamics. The model is free 

running, forced by winds and atmospheric fluxes, with open boundary conditions given by data 

assimilated into the global Hybrid Coordinate Ocean Model (HYCOM data server [unknown 

date]) 

For the surface-wind forcing during Hurricane Ida, the 6-hourly, 6-km resolution Hurricane 

Research Division (HRD) wind, (Moon et al. 2008; Powell et al. 1998; HRD database) was 

blended with the National Center for Environmental Prediction (NCEP) reanalysis wind. Figure 

6.2-2 shows the comparison of wind vector between the merged wind and National Data Buoy 

Center (NDBC) buoy 42003, whose location is indicated in Figure 6.1-1. It shows that the
11/08:1800

11/09:0600

11/09:1800

SAIC Tall Moorings

CICESE Moorings

42003

NDBC Buoy

329

Figure 6.1-1. Locations for the mooring array in the Gulf of Mexico, the NDBC buoy and the track of 

Hurricane Ida.
Figure 6.2-1. Six-kilometer (6-km) Intra-Americas Sea (IAS) circulation model domain. Both model boundaries and bathymetry (in meters) are 

shown.

330 
Comparison of NCEP + Hurricane Center and NDBC Winds for 42003

North

East

m/s m/s

331

Figure 6.2-2. Time series comparison of east and north wind components between hourly 42003 buoy 

observations (black) and the merged 6-hourly product (red) used to drive the model in 

late 2009. 
332

merged wind product agrees well with buoy observations, with a strong wind shift in early 

November when Hurricane Ida passed through.

In addition to the atmospheric conditions, the general ocean circulation condition is also 

presented. Figure 6.2-3 presents the time evolution of the wind field and LC conditions during 

Hurricane Ida, in the eastern Gulf of Mexico. From altimetry maps of SSH, a few weeks before 

the passage of Hurricane Ida, the LC had shed anticyclonic eddy Ekman and had retreated 

southward with its northern front south of 25° N. A very similar LC condition is found in a 4-

year numerical simulation just before the passage of Hurricane Ida (Figure 6.2-4). Thus, because 

of similarity of the model-simulated LC and shed eddy at the beginning of November 2009 to 

observations, the model simulation for November 8, 2009 was taken as the initial conditions for 

the Hurricane Ida simulation. Over a 2-4 week period, the low-frequency flow evolves slowly 

and thus only small deviations in the background flow are expected. Together with the merged 

realistic wind field, the model was reinitialized and the circulation hindcast from 1 November to 

7 December 2009, encompassing the entire life span of Hurricane Ida and its primary ocean 

response. The model hindcast along with model diagnostics were both saved at hourly intervals 

to keep the high frequency signals. To compare with observations, the simulated velocities at 

mooring locations were extracted and the same 45-HHP filter was applied. The model’s 

diagnostics were also used in uncovering the possible mechanisms of hurricane induced inertialoscillation distributions.

6.3 DESCRIPTION OF INERTIAL RESPONSE TO HURRICANE IDA

The hurricane-induced inertial oscillations are found in most of the mapping array moorings in 

the upper water column. For example, Figure 6.3-1a shows the time-series plot of 45-HHP 

filtered horizontal velocity at mooring A4 at various depth levels. It can be seen that near-inertial 

oscillation signals are present after the passage of Hurricane Ida (4-10 November 2009), starting 

around 10 November and lasting for 9-10 days at 84 m. The wave packets gradually propagate 

downward. At around 412 m, the inertial-oscillation signals are in the second half of November. 

Throughout the upper 400 m where ADCP measurements are available, a clear downward 

propagation of the near-inertial oscillation signal is well captured. Similar results are found in 

model simulations (Figure 6.3-1b). Although the model has approximately two inertial-wave 

packets, it successfully captured the hurricane induced inertial-oscillation signal though the 

downward propagation is not as well defined as in the observations.

On the other hand, observations from the CICESE E-transect moorings, deployed on the 

Campeche bank, show little inertial energy, though they were near the track of Hurricane Ida. 

Figure 6.3-2 shows an example of time series of high-pass-filtered horizontal velocity at E5. 

Throughout the upper water column, no strong inertial oscillations are induced after the passage 

of Hurricane Ida in early November. 

Figure 6.3-3 shows a series of clockwise rotary spectra for the upper-water-column ADCP at 

nine selected moorings. In near-inertial waves, the velocity vector rotates clockwise with the 

wave period when viewed from above. It can be seen that for the A-B-C transects, the nearinertial power-spectral peaks are found and their near-inertial frequency is around f to ~1.07f, 

increasing with the increase in depth, which indicates the near-inertial waves have both local and 

far-field (north) origins. While further south, at the CICESE E-transect moorings, the inertial
11/ 8/2009:1200H 11/ 8/2009:1800H 11/ 9/2009:0000H

11/ 9/2009:0600H 11/ 9/2009:1200H 11/ 9/2009:1800H

15 m/s

Figure 6.2-3. Winds during the passage of Hurricane Ida over the eastern Gulf from merged Hurricane Center and NCEP 10-m data. Mooring 

locations are indicated with red squares. The track of the central low pressure of Ida is given by the orange line, and the location 

of the 17-cm LC and eddy Ekman SSH front contour from the altimetry maps is given by the purple line.

333 
334

Figure 6.2-4. Model simulated Sea-Surface Height (SSH) in early November 2009. Purple line is the 

17-cm SSH contour.
cm/s cm/s

(a)

(b) 

335

Figure 6.3-1. Time series of high-pass filtered horizontal velocity at various depths (a) from 450-m 

ADCP measurements at mooring A4 and (b) from model simulations at the same location. 

Blue line is the V-velocity (positive northward) and black line is U-velocity (positive 

eastward). Red arrow lines indicate the vertical packet propa-gation.
cm/s

75 m

155 m

235 m

315 m

395 m

475 m

 336

Figure 6.3-2. Time series of high-pass filtered horizontal velocity at various depths from 500-m ADCP 

measurements at mooring E5. Blue line is the V-velocity (positive north-ward) and black 

line is U-velocity (positive eastward).
Variance/cpd

A4 A3 A2

B1 B3 C1

E5 E4 E2

 337

Figure 6.3-3. Clockwise rotary power spectra for high-pass filtered horizontal velocity at moorings for 

the upper 500 m. Orange vertical line shows the local inertial frequency.
338

oscillations are weaker and the frequencies corresponding to the power-spectral peaks are near 

the frequency of local diurnal tides, with a range of ~1.13f to1.25f throughout the water column.

In addition, the diurnal tidal energy at the E-transect moorings is much smaller than the nearinertial energy at the A-B-C transects (note the scale difference). Thus, the reduced amplitude 

high-frequency signal at the Campeche bank slope is dominated mainly by the local internal 

diurnal tides. 

6.4 DISCUSSION

The different upper-ocean responses to the passage of Hurricane Ida in the two mooring groups 

in the vicinity of the hurricane track is an interesting phenomena and two possible factors in 

modulating the propagation of near-inertial waves are investigated here: relative vorticity and 

background advection. Because the LC had retreated, the trapping and deep penetration of nearinertial internal waves by anticyclonic eddies (Kunze, 1985) is not a factor for the mapping-array 

observations.

6.4.1 The Effect of Relative Vorticity on the Distribution of Inertial Oscillations

The presence of relative vorticity could alter the propagation of near-inertial waves through the 

effective Coriolis parameter ƒeff. The mean distribution of normalized relative vorticity ζ /ƒ at 

200 m, as an example for the mapping-array moorings from 6 November to 6 December 2009 

(Figure 6.4-1a), shows that the month-long mean relative vorticity is positive or cyclonic with a 

maximum of 0.11f near the center. According to Kunze (1985), the maximum ƒeff then will be 

1.05f, which is still in the near-inertial frequency band. In that sense, this small positive relative 

vorticity in the region of the mapping-array moorings would not inhibit the propagation of nearinertial waves. Similar conditions are found at other depths, not limited to 200 m. However, the 

same month-long mean relative vorticity from the E-transect (Figure 6.4-1b) shows that the 

maximum relative vorticity appears at station 3 (between the E5 and E4 moorings) in the upper 

200 m with a value of 0.4f. This positive vorticity would increase the ƒeff to 1.2f, which exceeds 

the near-inertial frequency band, thus leading to the suppression of the propagation of nearinertial waves at these stations. Therefore, the strong positive relative vorticity is shown to be an 

important factor at the E-transect in prohibiting the propagation of near-inertial wave signals.

6.4.2 The Effect of the Loop Current on the Distribution of Inertial Oscillations

In addition to the suppression of the wave propagation process, strong background geostrophic 

advection may also be an important factor. This advection is shown in the altimeter SSH maps 

(Figure 6.2-3), with the E-transect moorings located near the front of the LC during the passage 

of Hurricane Ida. Using the theoretical approach of Zhai et al (2005b), the ratio between the 

dispersion processes of near-inertial waves and background circulation advective processes near 

the LC area can be estimated for the meridional component as:

R1 = dispersive_ process

advective_ process = N2

l

m

2

(! !Vl)V (6.4.1)
Southwest Northeast

(a) (b)

Figure 6.4-1. (a) Mean normalized relative vorticity plot for 6 November to 6 December 2009 at 200 m for the Loop Current study moorings 

(A-B-C transects). (b) Vertical plot of mean normalized relative vorticity at CICESE E-transect moorings for the same period.

339 
340

and$for$the$zonal$component$as:

R2 = dispersive_ process

advective_ process = N2

k

m

2

(! !Vk)U (6.4.2)

where N is the buoyancy frequency near the thermocline, ω is wave frequency, l is the 

meridional wave number that is negative, k is zonal wave number, m is vertical wave number, V

is meridional background flow and U is the zonal background flow. Typical values for N = 0.01 

s

-1

, l = 2π / 50 km, k = 2π / 50 km, m = 2π / 200 m are used. At the E-transect, typically, ω = 7.3 

x 10-5 s

-1

, and for the true northward flow of the LC (V=1.5 m s-1, U=0), the estimated ratio from 

Equation 6.4.1 is -0.0325, and the negative sign shows the equatorward propagation; for true 

eastward flow of the LC (V=0, U=1.5 m s-1), the estimated ratio from Equation 6.4.2 is 0.1163. 

Therefore, in both extreme conditions (true northward and true eastward flow) near the LC area, 

the estimated ratios indicate that at the Campeche bank slope, strong advection from the 

background flow dominates over the wave-dispersion processes, which is sufficient to block or 

reflect the equatorward propagation of near-inertial energy. Conversely, at the A-B-C transects, 

ω = 6.4 x 10-5 s

-1

, and the monthly means are V=0.15 m s-1 and U=0.013 m s-1. The estimated 

ratios for meridional and zonal components are -1.0245 and 21.7 respectively, indicating that the 

wave dispersion process overwhelms background advection, favoring the free propagation of 

near-inertial waves.

The model diagnostic output also provides some confirmation of the above conclusions. Figure 

6.4-2 shows the time evolution of zonal-momentum budgets in November 2009 at moorings A4 

and E5. On the left-hand side of the momentum equation is acceleration, while horizontal 

advection, Coriolis, the pressure gradient term and vertical viscosity are all on the right-hand 

side. The same 45-HHP filter was applied to all of these momentum terms to extract the highfrequency signal. It can be seen that at A4, the main momentum balance in the high-frequency 

band is between acceleration and the Coriolis term, resulting in strong inertial oscillations as 

observed, and these two terms are much larger compared to the rest of the terms in the 

momentum budget. However, at E5, which is near the LC front, horizontal advection becomes a 

major contributor in the momentum budget. It is comparable to the acceleration and Coriolis 

terms, dampening the inertial-oscillation signals. 

Therefore, both ratio estimates from observations and model diagnostics confirm that on the 

Campeche bank slope, strong LC advection plays an important role in dampening the inertialoscillation signals and blocking propagation. Conversely, at the A-B-C transect, with the retreat 

of the LC, after shedding of an anticyclonic eddy, inertial oscillations dominate and near-inertial 

waves propagate freely.

6.5 LONG-TERM VARIABILITY OF INERTIAL OSCILLATIONS

The variability of inertial oscillations over the 21⁄2-year field program has been investigated using 

velocity observations in the eastern Gulf of Mexico. Complex demodulation (see Section 2.9) 

has been applied to the current velocity data to extract the amplitudes of fluctuations near the 

Coriolis frequency. Figure 6.5-1 shows time series of amplitude of velocity from complex 

demodulation at mooring locations A4, B2 and C1 as examples. For the observational interval, 

large amplitudes are generally found in winter, for instance from November 2009 to March 2010,
Coriolis

Acceleration

Horizontal Advection

Pressure Gradient

Vertical Viscosity

E5

A4

10-6 m s-2

84 m

132 m

172 m

252 m

332 m

412 m

75 m

155 m

235 m

395 m

Figure 6.4-2. Time series evolution of zonal momentum budget at moorings A4 and E5 during the Hurricane Ida period (November 2009), red 

line is the Coriolis term, black line is acceleration term, purple line is horizontal advection, cyan line is pressure gradient term, and 

brown line is the vertical viscosity.

341 
A4 100 m

A4 300 m

B2 100 m

B2 300 m

C1 100 m

C1 300 m

cm/s

Figure 6.5-1. Time series (2.5 years long - from May 2009 to November 2011) of inertial frequency velocity amplitudes from com-plex demodulation at moorings A4, B2 and C1 for depths of 100 and 300 m, respectively.

342 
cm/s

(a) (b)

Figure 6.5-2. Time series of high-pass filtered horizontal velocity components at various depths from the 450-m ADCP measurements at mooring A4 for two periods (a) November 2009 and (b) January 2011.

343 
344

and from November 2010 to March 2011. Although the specific peak amplitude time varies 

among mooring locations, they all peak in the winter season. 

A 45-HHP filtered time series at these mooring locations further indicates the presence of inertial 

oscillations during the winter months. Figure 6.5-2 shows time series of the filtered velocity at

various depths of mooring A4 for two winter periods. One is from November to the end of 

December 2009. In it, strong inertial-oscillation signals are present and inertial energy 

propagates downward. The other period is from January to the end of February 2011. In it, largeamplitude inertial oscillations are also present, but with less consistency with depth. This 

suggests the possibility that they are not of the same origin. Corresponding atmospheric 

conditions for these time periods (Figure 6.5-3) show that strong inertial oscillations occur when 

there is stronger wind, lower atmospheric temperature and lower atmospheric pressure.

Similar features are found at other mooring locations. At B2 (Figure 6.5-4), inertial oscillations 

are present throughout the upper 400 m in the second half of November 2009, as well as toward 

the end of December 2009 (Figure 6.5-4a). The inertial oscillations are also stronger at deeper 

depths from mid-January, 2011, while there is only a weak inertial-oscillation signal for the 

upper 200 m during this period (Figure 6.5-4b). The corresponding atmospheric conditions are 

shown in Figure 6.5-3.

At C1 (Figure 6.5-5), clear and strong inertial-oscillation signals are present in December 2010 

and January 2011 throughout the upper 400 m, and in late February 2011 for the upper 250 m. 

Corresponding atmospheric conditions (Figure 6.5-6) show that strong winds had a direction 

shift along with a decrease in atmospheric temperature when there were strong inertial 

oscillations, indicating that the passage of winter cold fronts can cause these ocean velocity 

signals. Similar strong inertial oscillations are found at most of the A-B-C mooring sites. It is 

important to note that the inertial amplitudes generated by these winter storms and cold front 

passages appear to be as energetic and long lasting as those generated by Hurricane Ida.

6.6 SUMMARY AND CONCLUSIONS

Through the analyses of both moored-current observations in the Loop Current area in the 

eastern GOM and numerical model simulations, inertial oscillations induced by the passage of 

Hurricane Ida have been investigated. Strong hurricane-induced inertial oscillations are found in 

most of the mapping array moorings at all upper-layer depths, with the energy being transmitted 

downward as near-inertial waves. Similar features are well captured in the model simulations. 

The observations from the Campeche bank slope moorings, however, show that inertial 

oscillations are only weakly present. Instead, here, high-frequency oscillations are mainly 

dominated by local internal diurnal tides. It is noted that these may be the only observations of 

an internal diurnal tide in the Gulf, and warrant further investigation in the future. 

This pattern of ocean response to the northward moving Hurricane Ida is found to be closely 

related to the background relative vorticity as well as background geostrophic advection. The 

slowly varying background relative vorticity changes the propagation of near-inertial waves 

through the change of the effective Coriolis parameter ƒeff. From the relative vorticity analyses 

for the time of the storm, the mapping array moorings are located in the small positive relative 

vorticity area with a maximum around 0.1f, resulting in a small change of ƒeff to 1.05f, which is 
m/s °C mbar-1000 m/s °C mbar-1000

 345

Figure 6.5-3. Time series of atmospheric pressure, atmospheric temperature, and wind vectors for two 

winter periods for NDBC buoy 42003.
cm/s

(a) (b)

Figure 6.5-4. Time series of high-pass filtered horizontal velocity components at various depths from the 450-m ADCP measurements at mooring B2 for two periods (a) November 2009 and (b) January 2011.

346 
cm/s

 347

Figure 6.5-5. Time series of high-pass filtered horizontal velocity components at various depths from 

the 450-m ADCP measurements at mooring B2 for the 2010-2011 winter.
m/s °C mbar-1000

 348

Figure 6.5-6. Time series of atmospheric pressure, atmospheric temperature, and wind vectors for the 

2010-2011 winter periods for NDBC buoy 42003.
349

still in the near-inertial frequency band. However, for the Campeche bank slope moorings, the 

maximum relative vorticity on the cyclonic side of the LC front could be as high as 0.4f, 

resulting in a big change of ƒeff to 1.2f, which exceeds the near-inertial frequency band, and 

suppresses the free propagation of near-inertial waves. Therefore, the presence of strong positive 

relative vorticity on the Campeche bank slope could be a contributor in suppressing the 

hurricane-induced inertial-oscillation signals. On the other hand, from the altimeter maps, when 

Hurricane Ida passed through the Gulf, the LC had shed an anticyclonic eddy and retreated 

southward, making its front close to the E-transect moorings on the Campeche bank slope. Thus, 

the background geostrophic flow near the E-transect moorings was just the strong LC, whose 

advection is non-negligible in modulating the propagation of near-inertial signals. From the ratio 

estimate of dispersive processes versus advective processes, using the method of Zhai et al. 

(2005b) in the Loop Current region, it is shown that over the Campeche bank slope, the Loop 

Current advection processes overwhelmed the wave dispersion processes, sufficiently blocking 

the inertial oscillation signals. Therefore, the strong background advection from the Loop 

Current serves as another factor in suppressing hurricane-induced inertial oscillations at the Etransect moorings. This evidence is also supported by the numerical model diagnostics.

Besides the inertial response to tropical storms and hurricanes, the observations show that nearinertial internal waves were present in the array most of the time with maximum amplitudes in 

the winter season. These winter events had magnitudes that were comparable to the response to 

Hurricane Ida. In the eastern Gulf, winter cold fronts generally move from west to east, but 

northward propagating fronts may also occur. The cause of these winter inertial events is most 

likely the passage of these cold fronts across the northern Gulf that produce abrupt shifts of 

strong winds that can initiate near-inertial waves that may be trapped and enhanced in 

anticyclonic flows such as the LC and LC eddies (Kunze 1985). 

351

CHAPTER 7: SUMMARY DISCUSSION AND 

RECOMMENDATIONS

7.1 INTRODUCTION

This study was a measurement-based program into the characteristics, variability and dynamics 

of the LC. It consisted of a mapping array of PIES, tall and short current meter moorings 

deployed in U.S. waters, and tall mooring transects across the eastern slope of the Campeche 

Bank deployed in Mexican waters by CICESE. The U.S. array was deployed for 2 1⁄2 years 

beginning in May 2009, and the CICESE array began in June 2009 and is still ongoing, though 

only two years of coincident observations are available. This report is not meant to supplant the 

future CICESE report on their observations, however, where appropriate, the two datasets have 

been combined to get a more complete description of LC processes. Because of the type of 

measurements and the lengths of the programs, the emphasis is on meso-scale variability. 

However, long-term interannual and intraannual variability has been addressed through a 

thorough analysis of the historical altimeter and SST records, and numerical modeling. Most of 

the numerical modeling performed under this program has been published (Chang and Oey 

2010a, 2010b, 2011, 2012, 2013a; Xu et al. 2013a, 2013b), and therefore, in this report, model 

results are simply summarized and only results that are directly related to the observations have 

been highlighted. Numerical modeling was also used to study the ocean’s inertial response to 

Hurricane Ida (Chapter 6). The reader will note some disagreements between the interpretations 

of published model results on some aspects of LC eddy-shedding processes as well as long-term 

variability, but this is the nature of scientific research, and will most likely be resolved in the 

future. Clearly, with such an extensive and comprehensive dataset, this report cannot hope to 

cover all aspects of complex phenomena associated with the LC, but it can be expected that these 

data will serve as a source for many future studies that will expand on the results presented here. 

These data are also an important resource for numerical modelers to evaluate the performance of 

their Gulf of Mexico models.

The LC is the most important circulation feature of the deep Gulf of Mexico because it is the 

feature with the highest energy. Remote effects, through the shedding of eddies, radiating TRWs, 

forcing mean flows, and influencing shelf flows, are felt throughout the Gulf. Until this study, 

there had been no comprehensive observational program for the LC, with most of the previous 

studies (summarized by Schmitz et al. (2005) and Vukovich (2007)) relying on remote sensing to 

investigate LC variability, which of course only describes the upper-layer patterns. Numerical 

models of the Gulf have also concentrated on upper-layer variability (see Oey et al. (2005) for a 

review), often seeking to reproduce eddy shedding. Model simulations have been used to 

speculate on LC processes controlling circulation (e.g., Oey (2008), Le Hénaff et al. (2012), and 

Morey and Dukhovskoy (2013)), but rarely have been directly compared with in-situ 

observations. 

Perhaps the most important findings of the study are a significant revision of the ideas of how an 

eddy detachment takes place. The role of LCFEs is deemphasized in favor of baroclinic 

instabilities extracting energy from the mean flow, and jointly amplifying both the large scale 

meanders of the LC front, and the barotropic deep eddies. It is a steepening meander trough, in 

combination with the southwestward propagation of deep eddies, guided by the topography of 
352

the southern part of the Mississippi Fan, that effects a detachment (see Section 7.4 for a more 

detailed discussion). Some of these mechanisms have been put forward in the literature, but 

have not been brought together in a proper sequence. For example, Schmitz (2005) discusses 

detachments by cyclones on the east and west side of the neck based on an analysis of SSH maps 

(the role of a large independent cyclone against the Campeche slope is not supported by this 

study’s observations), and Xu et al. (2013b) discuss the role of baroclinic instabilities in model 

simulations, where they consider it a secondary mechanism that accelerates a detachment that is 

primarily a result of the Pichevin-Nof momentum paradox. The strong coupling of the upper and 

lower layers through barotropic flows has been observed in other strong baroclinic jets (e.g., the 

Gulf Stream); however, it has not been observed until this study for the LC. Coupling of 

barotropic and baroclinic flows is also not observed in other parts of the deep Gulf where moored 

velocity observations have been made (Hamilton 2009).

The other important results of the study pertain to the variability of the LC. In particular, the 

multi-decadal mean seasonal growth and wane of the LC has a dominant annual structure, with 

the consequence that eddy separation events have higher probabilities around the fall equinox 

and lower probabilities in late fall/early winter. This mean annual signal is correlated with the 

mean annual sea level signal along the U.S. southeastern coast, with the connection made 

through southward propagating coastal-trapped waves. How the remote signal on the west 

Florida shelf and slope affects the LC is not resolved by this study, nor is the tendency of eddy 

separation events to occur around the spring equinox.

 

This chapter is organized by first summarizing the results on statistics and dynamics (Chapters 3 

and 4), followed by long-term and inertial variability (Chapters 5 and 6). These summaries are 

then followed with a discussion of processes that are not understood very well in the 

observational results, and some new study recommendations to fill the gaps.

7.2 LC EDDY SHEDDING EVENTS

The formation, detachment and separation of three major LC eddies were contained in the 

datasets. The three eddies were Ekman, Franklin and Hadal with first detachment dates of 6 July 

2009, 8 June 2010, and 15 August 2011, respectively. All three followed similar sequences and 

the common features include a northward growth to an extended LC where the west-side front is 

relatively stationary along the Campeche upper slope. This western front then develops smallscale (50-100 km, 7 to 10-day period) cyclonic perturbations that grow in amplitude northwards 

along the slope, but then decay or are non-linearly transformed to longer period fluctuations over 

deep water on the northern part of the LC front. The east-side front of an extended LC, which is 

over the deep water of the eastern basin and thus not affected by the west Florida slope, develops 

large amplitude, long wavelength (~300 km), 40 to 60-day period meanders that propagate 

southward towards the Florida Straits. There is a simultaneous increase in lower-layer EKE, and 

the development of barotropic eddies that are displaced from the surface-layer crests and troughs 

by approximately 1⁄4 wavelength (i.e., bottom-layer fluctuations lead the surface by ~90°), which 

is a characteristic of a baroclinic instability. The interactions between the deep eddies (which are 

blocked from following the surface-layer meanders by the topography of the southern part of the 

eastern basin) with the meanders, causes a steepening of a trough that extends across the LC to 

cause a detachment. 
353

According to theory, supported by numerical modeling (Chang and Oey, 2013a), if a detached 

eddy is large enough, and its center is far enough north so as not to be impeded by the Campeche 

Bank, it will move off to the west by β-advection, and a separation will be achieved. The 

Rossby wave westward velocity of -βR0

2

, where R0 is the eddy’s 1st baroclinic radius based on 

upper-layer depth, must exceed the LC growth for separation to occur, and LC growth depends 

on transport through the Yucatan Channel. Therefore, Yucatan transport is sometimes observed 

to decrease just before a detachment, which would facilitate a separation (Xu et al. 2013b). This 

reduction apparently occurred just prior to Franklin’s final separation, based on CICESE’s 

Yucatan transport calculations for 2010. However, the separated Franklin was small and weak 

and thus the westward β-advection did not apply.

The three individual eddies showed some differences in their behavior from this generalized 

pattern.

Ekman

The first detachment occurred in the south, along transect E, but the eddy remained in the 

southern part of the eastern basin and so was blocked from separating by the Campeche Bank. 

Final separation occurred when the LC and attached eddy extended to the west. After that time, 

meanders developed on the northern boundary and grew downstream until a separating trough, 

extending southwestward across the observational array, pinched off the LC neck. The final 

Ekman was smaller than for the first detachment. Ekman’s final detachment illustrates that 

steepening meander troughs can occur anywhere along the northern or eastern front as long as 

they are over deep water, and deep barotropic flows can develop. Detachments are not restricted 

to regions just north of the Florida Straits.

Franklin

Franklin initially developed very similarly to Ekman and the first detachment occurred along 

transect E in the south, producing a southern eddy, also blocked by the Campeche Bank. The 

eddy remained in this southern position where the LC rejoined it multiple times, and instead of 

contributing to its growth, it extracted mean flow KE from the eddy. During this period of 

multiple reattachments and detachments, the CICESE-calculated Yucatan transports showed an 

overall increase of ~10 Sv, and may have been a factor in draining energy from the eddy. 

Eventually Franklin faded away under this repeated assault by the LC, and only separated a 

trivial anticyclone into the western Gulf.

Hadal

The LC underwent three extensions or growth spurts to the northwest. After each growth phase, 

large meanders developed on the eastern front, but seemed to be suppressed when the next 

extension of the LC and attached eddy occurred. Just prior to the first detachment and final 

separation, the steepening meander trough advected cyclonic vorticity of the trough from the 

eastern side of the extended LC to the western side, where it appeared as a large cyclonic

displacement of the western front. Viewed as a frontal phenomena using SSH, it appeared that a 

large cyclone suddenly developed on the western boundary adjacent to the Campeche Bank. 

However, the transfer, primarily by advection with possible assistance by westward propagating 

deep cyclones, of relative vorticity from the eastern frontal boundary generated this apparent 
354

western frontal perturbation growth. This observation contradicts Schmitz (2005) where it is 

asserted that some separations are effected by the simultaneous occurrence of cyclones on the 

eastern and western sides of the LC. Such occurrences may be artifacts of the SSH mapping 

algorithms. However, the formation of the west-side cyclone did assist in moving the separated 

Hadal, which was a large LC anticyclone, to the west. Numerical simulation using a freerunning model over several months had some success in hindcasting Hadal’s separation (Xu et 

al. 2013b) where the validation was provided by AVISO SSH.

7.3 STATISTICS AND DYNAMICS

Means and variances of velocity profiles are accounted for by two modes: a surface intensified 

unidirectional flow at the tall mooring location that occupies the upper layer from the surface to 

~700 to 900 m, and a nearly depth-independent barotropic mode that is not always aligned with 

the surface-intensified baroclinic mode. These characteristics make the LC ideally suited to 

analysis by the PIES mapping array where geopotential height anomalies and bottom pressure 

accompany the bottom-referenced baroclinic mode, and its referencing barotropic velocity 

modes. The barotropic mode is not present along Campeche slope in water depths less than 1000 

m, where mean flows and the baroclinic-mode fluctuations have about equal KE. In deep water, 

the KE is dominated by the barotropic mode, followed by the baroclinic and mean flow. 

Baroclinic and mean KE become more important in the vicinity of the LC or LC eddy fronts. 

Mean flows are strongly sheared in the upper layer and essentially depth-independent in the 

lower layer. Upper-layer means correspond to the mean LC configuration, but the lower-layer 

mean flows consist of an anticyclone-cyclone pair under the LC with the anticyclone to the west. 

This is consistent with potential vorticity conservation with the lower layer being squeezed and 

stretched on the leading and trailing edges, respectively, of a LC extending to the northwest. The 

shoaling topography of the Mississippi Fan to the northwest tends to intensify the deep 

anticyclone.

An illustration of how the weakly depth-dependent barotropic mode observed in the LC becomes 

more strongly bottom-trapped further north and west, away from the direct influence of the LC, 

is given in Figure 7.3-1. Here, depth-range-weighted CEOFs are given for mooring A3 (repeated 

from Figure 3.4-3), and mooring L4 that was deployed in a similar depth, west of the Mississippi 

Fan and near the Sigsbee escarpment, during the Exploratory study (Donohue et al. 2006). The 

modes have similar shapes at both locations, but at L4 the quasi-barotropic mode is distinctly 

more bottom trapped, decaying in amplitude towards the surface. Conversely, under the LC, at 

A3, the mode is essentially depth-independent. Though the near-surface-intensified mode at L4 

has about half the amplitude of that at A3, the near-bottom amplitudes of the quasi-barotropic 

modes are quite similar. This suggests that barotropic signals originating in the LC propagate 

out to the west, becoming more bottom-trapped with the characteristics of TRWs, and thus 

become more disconnected from surface-layer eddies. TRW ray tracing in Hamilton (2009) [his 

Figure 15] shows possible connections of the L4 site with the LC for 60-day waves.

Neglecting the long periodicities associated with the LC eddy-shedding cycle, fluctuations in 

both layers are dominated by 100 to 20-day variability. Shorter period (< 20 days) fluctuations 

are important in the upper layer especially along the western front where it overlies the 

Campeche slope, and in the northwestern part of the array. These are characteristic of LCFEs 

propagating along the front. An analysis of ~10-day fluctuations along the Campeche slope 
L4 A3

355

Figure 7.3-1. Depth range weighted CEOF modes for LC mooring A3 and Exploratory mooring L4.
356

shows that these fluctuations grow in amplitude between transects E, near the Yucatan, and N, 

near the northeast corner of the Campeche Bank. Bursts of LCFEs occurred during the 

northward extension or growth stage of the LC for all three eddies. After LCFEs leave the slope, 

growth appears to be inhibited, and they either decay or are transformed into longer period 

frontal perturbations. On the northeast side of the array, ~10-day fluctuations are only weakly 

observed. Furthermore, northeastward of the Campeche bank, along the LC front, over deep 

water, vertical coherence is low with similar weak fluctuations in the lower layer. This implies 

that LCFEs do not play an important role in developing deep eddies. This result does not support 

Oey’s (2008) interpretation of model simulations where deep eddies were generated in this 

region from frontal eddies. The deep eddies in the model propagated off to the west and formed 

sources for TRWs radiating towards the Sigsbee escarpment.

The most energetic fluctuations are in the 100 to 20-day period band, and the large meander 

periods of 40 to 60 days tend to dominate. In the upper layer, 100 to 20-day fluctuations 

propagate clockwise around the LC with the highest amplitudes east of the Mississippi Fan. In 

the lower layer, amplitudes at these periodicities increase just prior to and during detachments, 

and are associated with baroclinic instabilities that feed the growth of both the eastern side 

meanders and lower-layer eddies. Lower-layer propagation is from the Mississippi Fan towards 

the southeast at periods > 40 days, but with more of a cross-LC direction towards the southwest 

in the higher 40 to 20-day band.

In the 20 to 10-day-period band, fluctuations tend to show an increase later in the detachment 

process, and are a relatively minor component of the total EKE. They are most prominent in the 

regions around the base of the Mississippi Fan, where stronger bottom slopes can support higherfrequency westward-propagating TRWs, and towards the southeast, where propagation is 

towards the northwest. The vertical modes of velocities and relative vorticity suggest that 

barotropic and bottom-trapped planetary wave motions, distinct from baroclinic instability, are 

possible and indeed likely. A wavenumber analysis indicates that the northwestern part of an 

extended LC has down or up-slope phase components that are consistent with longer-period (~ 

40 to 60 days) TRWs. It is not clear, from observations, how such waves may be generated by 

the advance of the LC and/or LC eddy over shoaling topography, and whether wave dispersion, 

which depends on bottom slope, can radiate lower-layer EKE to the west and northwest.

7.4 LC EDDY SEPARATION DYNAMICS

In this section an attempt is made to concisely summarize the dynamics associated with a LC 

eddy detachment, as derived from the new observations. There are some aspects, particularly 

those related to the initiation of upper-lower layer baroclinic instabilities that were not resolved 

by the array. However, the authors are aware that the present study’s results revise some of the 

earlier ideas on LC eddy separation, which were mainly derived from remote sensing (e.g., 

Schmitz (2005)) as a purely upper-layer phenomenon, or model studies.

The analysis does not support a paradigm where small LC meanders progressively grow 

downstream along their path, starting from small amplitudes near the Yucatan Channel and 

reaching large amplitudes along the eastern and southbound portion of the LC, where the 

resulting trough extends across the neck and pinches off an eddy. The reasons are: (1) Using the 

fine spatial and temporal resolution afforded by these new observations, meanders could be 
357

traced along entering segments or northern or southward segments of the LC path, but it was 

difficult to connect any cases that transited this full path. (2) Meander frequencies along the 

northward and southward flowing portions were factors of two to four apart. (3) The path 

around the LC could not remain connected while neighboring portions oscillated at different 

frequencies. (4) Upper-deep coupling occurred along the southward-flowing portion of the LC 

for periods between 40 and 100 days, whereas meanders with these periods could not be traced 

back to the Yucatan Channel. Altogether, the observational evidence collected during this 

experiment, based upon spatial and temporal resolution capable of resolving the short spatial and 

temporal scales of the meanders, strongly argues against the concept of a continuous frontalperturbation growth from the Yucatan around to the pinch-off near the Dry Tortugas. 

The following multi-part scenario is suggested. The location of the LC within the Gulf and its 

positioning relative to the Mississippi Fan play important roles in determining the stability of the 

LC. It is speculated that the timing of this is related to the annual cycle discussed in Chapter 5. 

When the LC has extended sufficiently far north, with the well-observed tendency to lean 

towards the northwest (explained by the Pichevin-Nof momentum paradox), the following 

processes develop, involving vertical coupling with deep eddies that appear to depend upon 

interactions with the bottom topography of the southern extent of the Mississippi Fan. 

A. Along the western edge of the LC, flowing northward from Yucatan Channel, smallamplitude meanders of 20 to 10-day period propagate northward. They became more energetic 

near the times that the three LC eddies detached and separated. However, in the case of 

Franklin, this variability notably preceded detachment and final separation, and in the case of 

Hadal the energy peaks followed the separation event. Furthermore, the deep eddies within the 

20 to 10-day period exhibited southward phase propagation in that region, and the downstreampropagating upper meanders and deep-eddy perturbations did not couple effectively to jointly 

develop. Hence, they did not exhibit baroclinic instability that would enable them to draw 

efficiently upon the potential energy of the LC. Instead, they decayed in amplitude as they 

approached the northern section of the LC. Their fate suggests that they may either radiate deep 

eddies and deep topographic-wave variability as they approach the northern section, or they may 

simply feed their relatively meager energy and momentum back into the upper-current mean 

potential and kinetic energy field.

B. Along the northeastern portion of the LC, as it turns southward, deep eddies approach this 

section of the LC’s path from the NNE. Deep eddies that may have originated externally 

encounter preexisting small-amplitude upper-jet meanders or they may have developed from 

baroclinic instability of the LC itself in this location. The combined upper and deep 

eddy/meander structures jointly intensify via baroclinic instability. These meanders are strongly 

energetic at 100 to 40-day periodicities, and they translate downstream (southward) and grow. 

This was a characteristic pattern in Ekman, Franklin, and Hadal, and the regional average EKE 

built to a peak in the 100 to 40-day band prior to eddy detachments and separation. The process 

involved a sequence of two or three deep eddies entering at the NNE side and the development 

of progressively steeper meanders. After this steepening – a sort of 1-2 or 1-2-3 punch sequence 

of anticyclones and cyclones – the meander trough amplified sufficiently to reach across the neck 

of the LC and pinch it off. The intensified deep eddies followed the topographic contours of the 

Mississippi Fan and propagated across the LC neck. Consequently, the location where this mode 
358

of pinch-off occurred, enabled a conjoined process involving the full water-column. Deep eddies 

jointly intensify with upper meanders with a phase offset that drew upon the enormous pool of 

available potential energy in the LC and bottom topography. Subsequently, the deep eddies 

propagated across the neck and radiated energy northwesterly into the Gulf.

The observations did not extend far enough north to identify the source of the deep eddies that 

initiated the large-scale meander growth on the east side of the LC. Possible sources are eddies 

to the northeast of the array. Le Hénaff et al. (2012) indicate, from model studies, that the flow 

of the LC itself over the Mississippi Fan could generate a deep cyclone on the downstream side 

by the stretching of the lower water column through potential vorticity conservation. Against 

this concept, it is noted that the northern LC front barely reached the Mississippi Fan for Ekman 

and Franklin, and yet the meanders still developed. Le Hénaff et al.’s (2012) model LC tends to 

extend further into the Gulf than is usually observed, so in that case the Mississippi Fan 

topography is more a factor. Interpretations of remotely sensed SSTs have mentioned the 

merging and stalling of LCFEs on the northern LC boundary, producing a large cyclone in the 

surface layer. An example is Walker et al.’s (2011) “super” cyclone on the northern boundary of 

Franklin. Given the arguments above, it is thought more likely that northern cyclone 

development is from the generation of a large meander trough by the baroclinic instability 

process.

7.5 LONG-TERM AND SEASONAL VARIABILITY

Gulf of Mexico datasets, over the time period from 1978 through 1992, were reviewed to derive 

pre-altimetry LC eddy separation dates. Datasets used included Seasat and ERS-1 altimetry, 

CZCS chlorophyll-a, AVHRR SST, HMI EddyWatchTM reports, and CASE/EJIP GEM analyses. 

The reanalysis identified 20 separation events. Separation dates were estimated to be accurate to 

approximately ± 1.5 months and sufficient to detect statistically significant LC eddy separation 

seasonality, which was not the case for previously published records because of misidentification 

of separation events and their timing.

The reanalysis indicated that previous reported LC eddy separation dates, determined for the 

time period before the advent of continuous altimetric monitoring in the early 1990s, are 

inaccurate because of extensive reliance on SST imagery from polar orbiting satellites. Satellite 

sensors and sampling used were insufficient to detect the thermal signal of the LC and LC eddies 

due to the warm seasonal mixed layer and extensive cloudiness during the months of June 

through October, a limitation that was recognized at that time. 

Automated LC tracking techniques were used to derive LC eddy separation dates in three 

different altimetry datasets over the time period from 1993 through 2012. Between 28 and 30 LC 

eddy separation events were identified. Differences in dataset means and in objective-analysis 

smoothing caused differences in corresponding separation events between the datasets. 

Significance tests on various altimetry and pre-altimetry/altimetry combined date lists show that 

LC eddy separation events are more likely in the months March, August, and September, and 

less likely in December. LC eddy separation event dates were objectively divided into spring 

and fall seasons using a k-means clustering algorithm. The estimated spring and fall centers are 2 

March and 23 August, respectively, with seasonal boundaries on 22 May and 3 December. LC 
359

growth and wane is dominantly an annual process. LC metrics such as area, northern latitude, 

etc. are relatively high from January through about July and low in September and October. 

The SSH dominant mode of a coastal EOF analysis of the Southeast U.S. and Gulf of Mexico 

continental shelves indicates that the dominant coastal signal co-varies with the LC, and accounts 

for 65% and 85% of the annual variance in LC northern latitude and LC area, respectively. There 

is a statistically significant annual cycle embedded within the highly variable cycle of LC 

intrusion, eddy separation, and retreat. This annual cycle is primarily driven by and dynamically 

linked to geostrophic currents, seaward of the shelf break, forced by coastal-trapped waves 

generated on the Southeast U.S. and Gulf of Mexico continental shelves.

7.6 RECOMMENDATIONS

Some fundamental questions on LC dynamics have been raised by the results of this study that 

will require some detailed model investigations in relation to the observations. One group of 

questions relates to the east-side meanders: Why when meanders form, do they have seemingly 

preferred wavelengths of ~ 300 km and periods of 40 to 60 days? What mechanisms trigger the 

baroclinic instabilities that promote meander growth? What is the fate of the westward 

propagating deep cyclones after a detachment is achieved? Another set of questions arises from 

remote forcing mechanisms for the LC: How does the mean annual signal in LC growth and 

wane arise? How does the baroclinic instability mechanism for LC eddy detachments fit in with 

the mean annual variability in eddy separations? Statistical connections have been made 

between the remote SSH signal on the west Florida shelf and slope with LC variability, but 

dynamical connections are largely speculative. On a more practical level, models need to show 

that meander formation and growth and the interaction of barotropic and baroclinic flows 

conform to these observational results. A comparative analysis of multiple model diagnostics of 

these processes would likely be illuminating. 

From the above discussion, some aspects of the LC circulation processes remain unclear, and 

could be tackled with a follow-on study. Principally, the mechanisms that trigger the baroclinic 

instability that grow the east-side meanders through coupling with the lower layer appear to be 

the primary agent for LC eddy detachment. The observations suggest that a possible triggering 

mechanism is the propagation of deep eddies from the northeast, a region with almost no 

previous in-situ measurements. If these eddies are pertinent, then a number of questions arise 

such as how are they formed, and how do they interact with the surface-layer circulation? The 

LC itself may be an agent through remote forcing in generating deep eddies in the northeast, 

perhaps using the combined topography along the Mississippi Fan and the west Florida 

escarpment as wave-guides for disturbances initiated further south. It is also noted that the 

southeastern part of the deep basin has had no significant long-term measurements, and would 

also be a candidate region for a comprehensive observational study.

The second set of major questions relate to how the LC radiates deep energy into the western and 

northwestern Gulf. The Mississippi Fan is the major abyssal topographic feature in the area and 

it may act as a wave-guide for TRWs and eddies, and also perhaps as a barrier for LC deep EKE 

reaching some parts of the northern slope. It is observed that velocity measurements along the 

base of the northern continental slope are very inhomogeneous in both frequency content and 

energy levels (Cox et al. 2010, Donohue et al. 2006, Hamilton 2009). An explanation is that the 
360

flows along the base of the slope are primarily due to the impingement of TRWs of differing 

frequencies and wavelengths that are radiated from the LC and separated LC eddies translating 

westward across the basin (Oey and Lee 2002). Rectification of such waves by shoaling 

topography (Mizuta and Hogg 2004) was invoked as the driving force for the strong mean 

westward flows observed along the Sigsbee escarpment (DeHaan and Sturges 2005), though 

Chang and Oey (2011) argue that a cyclonic deep gyre is also a response to the LC eddy 

shedding cycle. Chang and Oey’s (2011) model result of upwelling across the base of the upper 

layer (1000 m) in the eastern basin, after an eddy is shed, was partially supported by the 

calculation of area-averaged vertical velocities at 900 m from the moored velocity 

measurements. Thus, observations of the westward pathways of energetic flows emanating from 

the LC, along with the role of topography, would be an advance in the understanding of Gulf 

circulation processes.

The deployment of PIES/mooring arrays in various regions of the deep Gulf has proved to be a 

cost-effective means of observing the 3-D geostrophic currents, temperature and salinity, as well 

as SSH and bottom pressure on a daily basis over relatively large areas which also resolve 

important eddy scales. Mapping arrays that have been deployed in the eastern Gulf under 

BOEM/MMS funding are shown in Figure 7.6-1. It is clear that there is a large gap in deepwater coverage in the northeast (and also in the southeast). Though the LC and Exploratory 

arrays are adjacent, the deployments are not coincident in time, and that would be required for 

signals to be traced from the LC to the Sigsbee escarpment. To fulfill the objectives listed 

below, a minimal PIES/mooring mapping array is given in Figure 7.6-2 as a starting point for 

further LC related studies.

• Determine the pathways of deep energy generated under the Loop Current.

• Quantify the upper and deep-layer interaction along those pathways.

• Identify trigger mechanisms for Loop Current meanders that lead to Loop Current eddy 

separations.

• Provide benchmarks/metrics to validate processes simulated by general ocean circulation 

models.

The experimental design covers the northern part of the LC from the west Florida escarpment 

across the Mississippi Fan to the eastern part of the Sigsbee escarpment. Resolution is 40 to 50 

km, which is adequate for mapping lower-layer eddies and TRWs. The array could be 

supplemented to cover a greater area with additional PIES, CPIES, near-bottom moorings and 

full-depth moorings. The measurements can also be supplemented with simultaneous 

deployments of upper and lower-layer RAFOS and APEX floats. Simultaneous Lagrangian and 

Eulerian measurements in the context of a PIES/mooring mapping array would provide a more 

fine-grained perspective on wave and eddy propagation. Similarly, the deployment of APEX 

profiling floats within the array would map water properties and provide calibration data for the 

PIES. It is recommended that this type of array be deployed for a minimum of two to three years 

so as to catch two to three LC eddy separations. Being able to compare three eddy separations 

during the present LC study was important to the subsequent analysis and made the results much 

more robust.
PIES

Full-Depth Moorings

Near-Bottom Moorings

LC Study

4/09-11/11

Eastern Gulf 01/05-01/06

Deep DeSoto 04/99-09/01

Exploratory 03/03-04/04

LSU Moorings

100 m

100 m

500 m

500 m

1000 m

1500 m

2000 m

3000 m

3500 m

BOEM/MMS Funded Mooring and PIES Measurements in the Eastern Gulf

 361

Figure 7.6-1. PIES/mooring arrays deployed in the eastern Gulf for this and prior BOEM/MMS 

programs.
100 m

100 m

500 m

500 m

1000 m

1500 m

2000 m

3000 m

3500 m

LC Deep Radiation Minimal Array

PIES

Mooring

 362

Figure 7.6-2. A possible configuration of PIES and moorings for a LC radiation experiment. The mean 

location of the 17-cm SSH contour for the 2 1/2 year LC study period is shown by the 

purple line. Previous locations of PIES and moorings from Figure 7.6-1 are shown in 

faded colors.
363

7.7 DEEPWATER HORIZON OIL SPILL

The Deepwater Horizon disaster on 20 April 2010, and the subsequent discharge of large 

quantities of oil and gas into the northern Gulf of Mexico over the next three months (Liu et al. 

2011a) took place during the growth and first detachments of Franklin. Because the LC/Franklin 

had intruded north of 26°N, there was considerable concern at the time, that oil could be 

transported southwards to the Florida Keys and further east to Miami (Weisberg 2011), 

particularly as a large patch of surface oil accumulated in a northern meander trough or “super” 

cyclone in mid-May 2010 (Walker et al. 2011). However, hydrocarbon measurements made at 

PIES sites in July 2010 under the auspices of this program (Wade et al. 2011) showed no 

significant accumulation of oil within the LC. The implications of this finding were that any 

surface oil entrained into the LC was rapidly dispersed, or the Lagrangian flow fields within the 

meander trough and in the LC were distinct “manifolds” (Kuznetsov et al. 2002), and water 

parcels in the trough did not interact with those south of the LC boundary. Oil slicks were not 

observed south of the northern LC boundary, and surface drifters in the two regions did not 

intermingle and cross the LC front (Liu et al. 2011b). This may be explained by the relative 

isolation of LC and LC eddy water masses from external Gulf waters. In particular, as a further 

example of this isolation, it is noted that the sub-tropical underwater (SUW) salinity maximum 

(> 36.5 psu) at 100 to 200 m depth in LC eddies is still identifiable all the way to the western 

boundary of the basin (Brooks 1984; Donohue et al. 2008).

365

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385

APPENDIX: BAROTROPIC TIDES 

Tidal response analysis (Munk and Cartwright, 1966) determined the amplitude and phase for 

eight major tidal constituents (O1, K1, Q1, P1, M2, K2, N2, S2) from the twenty-five recovered 

bottom pressure records (PIES 51 through 75) within the array (Figures A-1 and A-2, and Tables 

A-1 and A-2). Estimated phase and amplitude vary smoothly across the array as expected. Tidal 

amplitudes are generally small. The largest tidal amplitudes are near 13 cm for O1 and K1, near 

5 cm for P1 and M2, and less than 5 cm for the remaining four constituents. Amplitudes have 

been converted to meters by dividing pressure by density times gravity, ρg = 1.02.
−200 −100 0 100

−150

−100

−50

0

50

100

O1 AMPLITUDE [cm] 

distance [km]

13.5

13

12.5

−200 −100 0 100

−150

−100

−50

0

50

100

O1 PHASE [deg]

13

12

11

10

9

−200 −100 0 100

−150

−100

−50

0

50

100

K1 AMPLITUDE [cm] 

distance [km]

13.5

13

12.5

−200 −100 0 100

−150

−100

−50

0

50

100

K1 PHASE [deg]

20

18

16

−200 −100 0 100

−150

−100

−50

0

50

100

Q1 AMPLITUDE [cm] 

distance [km]

2.9

2.8

2.7

−200 −100 0 100

−150

−100

−50

0

50

100

Q1 PHASE [deg]

5

4

3

2

−200 −100 0 100

−150

−100

−50

0

50

100

P1 AMPLITUDE [cm] 

distance [km]

distance [km]

4.2

4.4

4.6

−200 −100 0 100

−150

−100

−50

0

50

100

P1 PHASE [deg]

distance [km]

20

18

16

386

Figure A-1. Amplitude (left column) and phase (right column) of the O1, K1, Q1, and P1 constituents 

determined with the tidal response method (Munk and Cartwright, 1966) from the 25 

bottom pressure records. PIES locations denoted by open diamonds.
−200 −100 0 100

−150

−100

−50

0

50

100

M2 AMPLITUDE [cm] 

distance [km]

2

3

4

5

−200 −100 0 100

−150

−100

−50

0

50

100

M2 PHASE [deg]

97

92

87

82

−200 −100 0 100

−150

−100

−50

0

50

100

K2 AMPLITUDE [cm] 

distance [km]

0.6

0.7

.0 8

−200 −100 0 100

−150

−100

−50

0

50

100

K2 PHASE [deg] 105

100

95

−200 −100 0 100

−150

−100

−50

0

50

100

N2 AMPLITUDE [cm] 

distance [km]

0.4

0.6

0.8

1

−200 −100 0 100

−150

−100

−50

0

50

100

N2 PHASE [deg]

124

114

104

94

84

−200 −100 0 100

−150

−100

−50

0

50

100

S2 AMPLITUDE [cm] 

distance [km]

distance [km]

2

2.5

3

−200 −100 0 100

−150

−100

−50

0

50

100

100

95

387

Figure A-2. Amplitude (left column) and phase (right column) of the M2, K2, N2, and S2 constituents 

determined with the tidal response method (Munk and Cartwright, 1966) from the 25 

bottom pressure records. PIES locations denoted by open diamonds. 
388

Table A-1. Amplitude in CM and Phase in Degrees for Four Major Tidal 

Constituents (O1, K1, Q1, P1)

Determined with the Tidal Response Method of Munk and Cartwright (1966)

O1 K1 Q1 P1

Amplitude Phase Amplitude Phase Amplitude Phase Amplitude Phase

Site (cm) (degrees) (cm) (degrees) (cm) (degrees) (cm) (degrees)

P51 13.65 12.54 13.90 20.43 2.93 4.64 4.73 20.55

P52 13.69 13.27 13.87 21.20 2.94 5.28 4.72 21.32

P53 13.69 14.16 13.86 22.05 2.95 6.24 4.72 22.18

P54 13.59 11.59 13.84 19.32 2.93 3.65 4.71 19.48

P55 13.47 12.05 13.70 19.87 2.89 4.40 4.66 19.96

P56 13.42 12.83 13.64 20.59 2.89 5.25 4.64 20.69

P57 13.37 14.04 13.54 21.36 2.95 6.60 4.59 21.55

P58 13.43 11.04 13.67 18.49 2.91 3.37 4.65 18.66

P59 13.14 11.70 13.36 19.31 2.83 4.02 4.54 19.44

P60 13.19 12.24 13.40 19.88 2.84 4.78 4.56 19.98

P61 13.01 13.47 13.18 21.24 2.80 5.93 4.48 21.33

P62 13.27 9.88 13.48 17.12 2.87 2.42 4.58 17.28

P63 13.08 10.99 13.26 18.30 2.83 3.50 4.51 18.45

P64 12.88 11.50 13.04 19.01 2.78 4.24 4.43 19.11

P65 12.76 12.56 12.88 20.14 2.75 5.18 4.38 20.24

P66 13.09 9.56 13.22 16.32 2.84 2.16 4.50 16.54

P67 12.92 10.24 13.01 16.52 2.91 2.51 4.40 16.94

P68 12.61 10.58 12.69 17.96 2.72 3.10 4.32 18.10

P69 12.41 11.64 12.42 19.03 2.68 4.21 4.23 19.16

P70 12.98 8.92 12.92 14.69 2.93 1.47 4.37 15.13

P71 12.77 9.17 12.73 15.37 2.86 1.54 4.31 15.78

P72 12.41 9.34 12.36 16.59 2.68 1.81 4.21 16.76

P73 11.96 10.63 11.87 17.65 2.59 3.23 4.05 17.84

P74 12.58 7.48 12.47 14.10 2.83 359.56 4.23 14.51

P75 12.10 7.64 12.01 14.94 2.61 0.12 4.10 15.10
389

Table A-2. Amplitude in CM and Phase in Degrees for Four Major Tidal 

Constituents (M2, K2, N2, S2)

Determined with the Tidal Response Method of Munk and Cartwright (1966)

M2 K2 N2 S2

Amplitude Phase Amplitude Phase Amplitude Phase Amplitude Phase

Site (cm) (degrees) (cm) (degrees) (cm) (degrees) (cm) (degrees)

P51 2.10 99.88 0.57 105.20 0.41 122.09 1.99 103.83

P52 1.75 102.13 0.55 106.97 0.36 131.90 1.88 105.44

P53 1.37 106.66 0.52 108.59 0.31 146.62 1.77 106.94

P54 2.91 94.04 0.64 101.66 0.54 106.23 2.26 100.45

P55 2.66 93.71 0.62 102.34 0.49 108.00 2.18 101.01

P56 2.33 93.53 0.60 102.99 0.42 111.75 2.07 101.53

P57 1.97 93.52 0.57 104.42 0.34 118.45 1.97 102.79

P58 3.49 90.98 0.70 100.01 0.64 98.19 2.47 98.89

P59 3.23 89.13 0.67 99.76 0.58 97.83 2.36 98.47

P60 3.01 88.06 0.65 99.96 0.53 97.26 2.29 98.60

P61 2.66 86.44 0.62 100.56 0.44 97.26 2.17 99.05

P62 4.09 88.49 0.75 97.64 0.76 92.98 2.67 96.61

P63 3.86 87.25 0.72 98.05 0.70 91.53 2.57 96.91

P64 3.67 84.43 0.70 97.22 0.65 89.10 2.50 95.92

P65 3.41 82.33 0.68 96.96 0.59 86.71 2.41 95.58

P66 4.67 86.92 0.80 96.77 0.87 88.80 2.88 95.80

P67 4.55 85.20 0.78 96.82 0.85 86.39 2.80 95.75

P68 4.32 82.10 0.76 94.87 0.79 82.29 2.70 93.78

P69 4.15 79.86 0.73 94.30 0.74 79.29 2.62 93.11

P70 5.23 86.17 0.85 96.02 1.00 86.60 3.05 95.12

P71 5.16 83.15 0.84 94.62 0.97 81.83 3.01 93.71

P72 5.07 80.21 0.82 93.01 0.94 78.02 2.94 92.03

P73 4.88 77.68 0.79 91.95 0.90 73.78 2.84 90.96

P74 5.77 82.12 0.89 93.04 1.12 79.53 3.19 92.26

P75 5.76 78.03 0.88 90.65 1.09 74.19 3.16 89.78
The Department of the Interior Mission

As the Nation’s principal conservation agency, the Department of the Interior has 

responsibility for most of our nationally owned public lands and natural 

resources. This includes fostering the sound use of our land and water 

resources; protecting our fish, wildlife, and biological diversity; preserving the 

environmental and cultural values of our national parks and historical places; 

and providing for the enjoyment of life through outdoor recreation. The 

Department assesses our energy and mineral resources and works to ensure 

that their development is in the best interests of all our people by encouraging 

stewardship and citizen participation in their care. The Department also has a 

major responsibility for American Indian reservation communities and for people 

who live in island communities.

The Bureau of Ocean Energy Management Mission

The Bureau of Ocean Energy Management (BOEM) works to manage the 

exploration and development of the nation's offshore resources in a way that 

appropriately balances economic development, energy independence, and 

environmental protection through oil and gas leases, renewable energy 

development and environmental reviews and studies.