OCS Study

MMS 2010-015

Low-Frequency Variability of Currents

in the Deepwater Eastern Gulf of Mexico

U.S. Department of the Interior

Minerals Management Service

Gulf of Mexico OCS Region
U.S. Department of the Interior

Minerals Management Service

Gulf of Mexico OCS Region

OCS Study

MMS 2010-015

Low-Frequency Variability of Currents

in the Deepwater Eastern Gulf of Mexico

Authors

K.L. Cole

S.F. DiMarco

Prepared under MMS Contract

1435-01-04-CT-34239 (M04PC00008)

by

Texas A&M University

College Station, TX 77808

Published by

New Orleans

March 2010
iii

DISCLAIMER 

This report was prepared under contract between the Minerals Management Service (MMS) and 

Science Applications International Corporation. This report has been technically reviewed by the 

MMS, and it has been approved for publication. Approval does not signify that the contents 

necessarily reflect the views and policies of the MMS, nor does mention of trade names or 

commercial products constitute endorsement or recommendation for use. It is, however, exempt 

from review and compliance with the MMS editorial standards. 

REPORT AVAILABILITY 

This report is available only in compact disk format from the Minerals Management Service, 

Gulf of Mexico OCS Region, at a charge of $15.00, by referencing OCS Study MMS 2010-015. 

The report may be downloaded from the MMS website through the Environmental Studies 

Program Information System (ESPIS). You will also be able to obtain this report form the 

National Technical Information Service in the near future. You may also inspect copies at 

selected Federal Depository Libraries. 

Minerals Management Service U.S. Department of Commerce 

Gulf of Mexico OCS Region National Technical Information Service 

Public Information Office (MS 5034) 5285 Port Royal Road 

1201 Elmwood Park Blvd. Springfield, Virginia 22161 

New Orleans, LA 70123-2394 Phone: (703) 605-6040 

Telephone requests may be placed at Fax: (703) 605-6900 

(504) 736-2519, 1-800-200-GULF or 

Rush orders: 1-800-553-6847 

Fax: (504) 736-2620 

CITATION 

Cole, K.L. and S.F. DiMarco. 2010. Low-frequency variability of currents in the deepwater 

eastern Gulf of Mexico. U.S. Dept. of the Interior, Minerals Management Service, Gulf 

of Mexico OCS Region, New Orleans, LA. OCS Study MMS 2010-015. 136 pp. 

ABOUT THE COVER 

The cover shows contours of the frequency-averaged wavelet power in the inertial band (0.5 – 2 

day period) during the weeks after Hurricanes Katrina and Rita in the upper 500 m of the water 

column at moorings M1 (top), M2 (middle), and M3 (bottom). 
v

ACKNOWLEDGMENT 

We would like to thank the U.S. Department of the Interior, Mineral Management Service, 

whose funding for the Survey of Currents in the Eastern Gulf of Mexico Study under contract 

number 1435-01-04-CT-34239 made this research possible. We especially appreciate the support 

and guidance of Dr. Alexis Lugo-Fernández at MMS. Thanks also goes to Dr. Robert Leben, 

whose sea surface height product I’ve used extensively in this report, Mr. Jeff Cox, who was 

Program Manager of the project, Dr. Matt Howard, and Dr. Ann Jochens. Thanks to Phyllis 

Bonifazi of the Texas A&M Research Foundation for her awesome administrative support, and 

to Susan Martin for assistance with editing this report. 

Thanks also goes to John Klinck of ODU, who developed the dynamic mode subroutine, and to 

Christopher Torrence and Gilbert P. Compo, who developed the wavelet codes used in these 

analyses. Credit must also go to Paul Wessel and Walter H. F. Smith, the creators of the Generic 

Mapping Tools (GMT) software package, which was used to create some of the maps in this 

report. 

Kelly L. Cole 

Steven F. DiMarco 
vii

TABLE OF CONTENTS 

 Page

LIST OF FIGURES ....................................................................................................................... ix 

LIST OF TABLES ....................................................................................................................... xiii 

1 EXECUTIVE SUMMARY ................................................................................................... 1

2 INTRODUCTION ................................................................................................................. 3

 2.1 Overview of the Physical Oceanography of the Gulf of Mexico .................................. 3

 2.2 Surface Circulation of the Gulf of Mexico ................................................................... 4

 2.3 Loop Current Ring Shedding ........................................................................................ 6

 2.4 Loop Current Frontal Eddies ........................................................................................ 6

 2.5 Deep Flows in the Yucatan Channel ............................................................................. 7

 2.6 Effects of Topography on Gulf of Mexico Circulation ................................................ 7

 2.7 Partitioning of Kinetic Energy Amongst Dynamic Modes ........................................... 8

 2.8 Scientific Questions and Hypotheses ............................................................................ 9 

3 DATA AND METHODS .................................................................................................... 13

 3.1 EGOM Mooring Study and Hydrographic Cruises .................................................... 13

 3.2 Historical Hydrography, Wind and Sea-Surface Height ............................................. 16

 3.3 EGOM Data ................................................................................................................ 16

 3.4 Data Processing ........................................................................................................... 18

 3.5 EOF Analysis .............................................................................................................. 19

 3.6 Dynamic Mode Decomposition .................................................................................. 20

4 RESULTS ............................................................................................................................ 21

 4.1 Velocity Record Length Time-series .......................................................................... 21

 4.2 Basic Statistics ............................................................................................................ 22

 4.3 Velocity Spectra .......................................................................................................... 25

 4.3.1 Upper Ocean Spectra ...................................................................................... 26

 4.3.2 Deep Ocean Spectra ........................................................................................ 26

 4.4 Coherency Spectra ...................................................................................................... 28

 4.4.1 Current – Wind Coherence ............................................................................. 28

 4.4.2 Vertical Current – Current Coherence ............................................................ 28

 4.4.3 Horizontal Current – Current Coherence ........................................................ 32

 4.5 Vertical Structure of Low-frequency Variability ........................................................ 34

 4.5.1 Empirical Orthogonal Function Analysis ....................................................... 34

 4.5.2 Dynamical Mode Analysis .............................................................................. 38

 4.5.3 Model Utility Tests and Summary Statistics for the Dynamic Mode Fit ....... 43

 4.5.4 EOF and Dynamic Mode Comparison ............................................................ 44
viii

 4.5.5 Temporal Correlation of First Baroclinic Mode and Sea Surface 

Height Gradient ............................................................................................... 45

 4.5.6 Spectra and Temporal Scales of Modes .......................................................... 48

 4.5.7 Dynamic Mode Kinetic Energy and Modal Coupling .................................... 50

 4.5.8 Modal Decomposition of EGOM Data Versus Historical Data ...................... 52

 4.5.9 Dynamic Mode Analysis of Hydrographic Data and Vertical Profiles 

of Horizontal Velocity .................................................................................... 54

5 DISCUSSION AND CONCLUSIONS ............................................................................... 59

6 REFERENCES .................................................................................................................... 67 

APPENDIX A: Graphical Information ......................................................................................... 73 

APPENDIX B: Tabular Information .......................................................................................... 127 
ix

LIST OF FIGURES 

Page

Figure 1. Sea-surface height in the Gulf of Mexico on August 5, 2005 ............................. 4 

Figure 2. Schematic diagram of MMS Eastern Gulf of Mexico Circulation Study 

mooring M1 configuration during deployment 1 ................................................. 15 

Figure 3. MMS Eastern Gulf of Mexico Circulation Study site and MMS Deepwater 

Physical Oceanography Reanalysis and Synthesis of Historical Data stations 

in the eastern Gulf of Mexico .............................................................................. 17 

Figure 4. Temperature-salinity relations in the Eastern Gulf of Mexico ............................ 18 

Figure 5. Gap-filled, gridded current speed from five moored ADCP depths and 

moored current meters for deployments 1 and 2 at mooring M3 ........................ 22 

Figure 6. Vertical profiles of record-length mean, standard deviation, minimum, and 

maximum velocity components for mooring M3 ................................................ 23 

Figure 7. Sea-surface height in the Gulf of Mexico on September 15, 2005 ...................... 25 

Figure 8. Power spectra at mooring M3 .............................................................................. 27 

Figure 9. Coherence, admittance, power, and phase spectra between current and wind

v-velocity components at 100 m at mooring M1 during deployment 1 ............... 29

Figure 10. Detided, gap-filled, gridded u-velocity time-series at mooring M1 during 

deployment 1 at 100 m and 428 m ....................................................................... 30 

Figure 11. Coherence, admittance, power, and phase spectra of east-west (u) velocity 

components at 100 m and 428 m at mooring 1 during deployment 1 .................. 31 

Figure 12. Coherence, admittance, power, and phase spectra of north-south (v) velocity 

components at 70 m and 494 m at mooring M2 during deployment 2 ................ 32 

Figure 13. Coherence, admittance, power, and phase spectra between v-velocity 

components at 749 m at mooring M1 and mooring M2 during deployment 1 .... 33 

Figure 14. Detided, gap-filled, gridded east-west velocity time-series at mooring M2 

and mooring M3 during deployment 1 at 1,995 m and 2,699 m respectively. .... 34

Figure 15. Coherence, admittance, power, and phase spectra between u-velocity 

components at mooring M2 and mooring M3 during deployment 1 at 1,995 

m and 2,699 m respectively ................................................................................. 35 

Figure 16. Vertical EOFs of east-west and north-south current velocity at mooring M3 

during deployment 1 ............................................................................................ 37 

Figure 17. Vertical profiles of Brunt-Väisälä frequency at or nearest to each mooring 

site ........................................................................................................................ 40 

Figure 18. Normalized barotropic and first two baroclinic modes calculated with 

averaged casts at M3 from cruises in January and August 2005 ......................... 41 
x

Page

Figure 19. Modal fit to mooring M3 u-velocity data ............................................................ 42 

Figure 20. Modal fit to mooring M3 v-velocity data ............................................................. 43 

Figure 21. Comparison of EOF mode 1 and the temporal amplitudes of the first 

baroclinic mode for M1 v-velocity during deployment 2 .................................... 45 

Figure 22. Comparison of EOF mode 1 and the temporal amplitudes of the first 

baroclinic mode for M3 u-velocity during deployment 1 .................................... 45 

Figure 23. Temporal amplitudes of the first baroclinic mode for the east-west velocity 

component at mooring M3 during deployment 1 and the SSH gradient in the 

north-south direction ............................................................................................ 46 

Figure 24. Coherency and phase spectra of the temporal amplitudes of the first 

baroclinic mode for the east-west velocity component at mooring M3 

during deployment 1 and the SSH gradient in the north-south direction ............ 47 

Figure 25. Power spectra of the time-series of amplitudes of the first three theoretical 

modes at mooring M3 during deployment 1 ........................................................ 48 

Figure 26. Normalized autocovariance functions of mode amplitudes from the mode fit 

to east-west and north-south velocity component data at mooring M3 during 

deployment 1 ........................................................................................................ 49 

Figure 27. Kinetic energy percentages of the dynamic modes at each depth level in 

Table 4 ................................................................................................................. 51 

Figure 28. Temporal amplitudes of the first baroclinic mode and second baroclinic 

mode for M1 v-velocity during deployment 2 calculated using EGOM CTD 

cast data and historical CTD data analyzed in the MMS Deepwater Physical 

Oceanography Reanalysis and Synthesis of Historical Data project. .................. 53 

Figure 29. Temporal amplitudes of the first baroclinic mode and second baroclinic 

mode for M3 u-velocity during deployment 1 calculated using EGOM CTD 

cast data and historical CTD data analyzed in the MMS Deepwater Physical 

Oceanography Reanalysis and Synthesis of Historical Data project ................... 54 

Figure 30. Normalized barotropic and first two baroclinic modes calculated with 

averaged casts at M3 from cruises in January and August 2005. ........................ 55 

Figure 31. Spatial correlation between observed u velocity at mooring M3 from 

deployment 1 and the modeled u velocity from CTD cast data on the 

EGOM hydrographic cruises. .............................................................................. 56 

Figure 32. Percentage of variance of time series record by depth attributed to 

barotropic, first baroclinic, and second baroclinic dynamic modes. .................... 57 

Figure 33. Representative vertical profiles of north-south current velocity from M3 

mooring during deployment 2 with fit of barotropic and first baroclinic 

mode and the same current velocity profile with first three theoretical 

modes superimposed. ........................................................................................... 58 
xi

Page

Figure 34. (Left) Sea-surface height in the Gulf of Mexico on March 25, 2005. (Right) 

Sea-surface height in the EGOM study region. ................................................... 60 

Figure 35. (Left) Sea-surface height in the Gulf of Mexico on June 11, 2005. (Right) 

Sea-surface height in the EGOM study region. ................................................... 61 

Figure 36. (Left) Sea-surface height in the Gulf of Mexico on August 9, 2005. (Right) 

Sea-surface height in the EGOM study region. ................................................... 61 

Figure 37. Contours of the frequency-averaged wavelet power in the inertial band 

during the weeks after Hurricanes Katrina and Rita in the upper 500 m of 

the water column at moorings M1, M2, and M3 ................................................. 63 
xiii

LIST OF TABLES 

Page

Table 1. MMS Eastern Gulf of Mexico Circulation Study Mooring Instruments ............. 14 

Table 2. Percentage of Variance in EOF Modes 1, 2, and 3 for Moorings M1, M2, 

and M3 for Horizontal Velocity Components during Deployment 1 and 

Deployment 2 ....................................................................................................... 38 

Table 3. East-west and North-south Velocity First Baroclinic Mode Amplitude 

Correlations to the Orthogonal Sea-Surface Height Gradient at Moorings 

M1, M2, and M3 for Deployments 1 and 2 ......................................................... 47 

Table 4. Percentages of Kinetic Energy in the Barotropic, First Baroclinic, and 

Second Baroclinic Modes at Each Depth Level at Mooring M3 during 

Deployment 1 ....................................................................................................... 50 

Table 5. Summary of Dynamic Mode Decomposition Statistics for EGOM 

Deployment 2 ....................................................................................................... 57 
1

1 EXECUTIVE SUMMARY 

Vertical structure of the low frequency horizontal currents at the northern edge of the Loop 

Current during eddy shedding events is observed using concurrent hydrographic, moored, and 

satellite altimetry data from 2005. Dynamic modes are calculated at three deep (~3000 m), full 

water-column moorings in the eastern Gulf of Mexico. Time-series of the barotropic and first 

two baroclinic modes are found using a least squares minimization that fits theoretically derived 

modes to observed moored velocity data. 

Empirical orthogonal function (EOF) analyses show that the majority of observed variance is 

explained by a surface-trapped mode that is highly coherent with the temporal amplitudes of the 

first baroclinic mode, and a lower, but significant percentage of variance is captured in bottomintensified modes. Amplitudes of the second empirical mode indicate that currents are more 

coherent in the ocean interior approaching the Loop Current, as more variance is explained by 

this mode at the southernmost mooring near the Loop Current. 

A dynamic mode decomposition of the horizontal currents reveals that the barotropic and first 

baroclinic modes exhibit low frequency variability and eddy time scales of 10 – 40 days. Second 

baroclinic mode amplitudes show higher frequency variability and shorter time scales. A model 

utility test for the least squares fit of modeled to observed velocity shows that the second 

baroclinic mode is useful to the statistical model during 50 – 85 % of the mooring deployment, 

and is particularly necessary to the model when cyclonic features are present in the study area. 

The importance of the second baroclinic mode to the model increases significantly closer to the 

Loop Current. 

High-speed currents associated with the Loop Current and anticyclones stimulate a strong first 

baroclinic response, but the second baroclinic mode amplitudes are found to be similar in 

magnitude to the first baroclinic mode amplitudes at times. This happens episodically and could 

be an indication of higher order dynamics related to frontal eddies or Loop Current eddy 

shedding. 
3

2 INTRODUCTION 

This chapter discusses a brief introduction and background to the physical oceanography of the 

Gulf of Mexico. Surface circulation in the Gulf is summarized and Loop Current dynamics are 

discussed. The theories behind the physics of Loop Current ring shedding and Loop Current 

frontal eddies are introduced. Deep flows in the Yucatan Channel and the effects of topography 

on Gulf of Mexico circulation is discussed, and studies involving the partitioning of kinetic 

energy amongst dynamic modes are summarized as well. Scientific questions and hypotheses for 

this research are presented at the end of this section. 

2.1 Overview of the Physical Oceanography of the Gulf of Mexico 

The Gulf of Mexico is a subtropical, semi-enclosed basin rich with complex dynamics and 

diverse mesoscale circulation features in the near-surface and at depth. It is host to a unique, 

inspiring physical setting that is at the forefront of contemporary oceanographic research 

(Sturges et al. 2005). In the last fifty years, physical understanding of the currents in this region 

has progressed considerably. Gulf of Mexico circulation is clearly important on a global level 

because of its position in western boundary flow and transport. Studies on its shelves have a 

wide range of applications as well, as the basin is incident with the critical latitude, and the 

resonance effect of the inertial and diurnal wind and tidal forcings on currents is a phenomenon 

of present interest. 

The Loop Current, the portion of the Gulf Stream system that connects the Yucatan and Florida 

Currents, drives the deepwater circulation throughout the Gulf, and therefore has been the focus 

of many studies in the region (Sturges and Leben 2000). Recently, an effort has been made to 

examine the circulation in the Gulf with a series of projects funded by the U.S. Department of 

the Interior Minerals Management Service (MMS). In 2003, instruments to measure physical 

parameters were deployed in the deepwater region of the north central Gulf as part of the 

Exploratory Study of Deepwater Currents in the Gulf of Mexico (Donohue et al. 2006). In 2004, 

deep currents in the northwest Gulf were observed in the Survey of Deepwater Currents in the 

Western Gulf of Mexico Study, and in 2005, the deep northeast Gulf was investigated in the 

Survey of Deepwater Currents in the Eastern Gulf of Mexico Study (EGOM). This research is 

focused on the dynamics of the eastern Gulf, and thus all analyses in this report use the EGOM 

dataset. 

The primary forcing in the Gulf of Mexico is the Loop Current, which is a portion of the Atlantic 

western boundary current that flows northward through the Yucatan Channel and makes a sharp 

90 clockwise turn at approximately 26N to exit the Gulf at the Florida Straits (Leben 2005). 

Altimeter derived sea surface height anomaly on August 5, 2005 is presented in Figure 1. The 

Loop Current is observed as the red region in the southeast Gulf extending northwest from Cuba 

with sea surface height anomaly above 30 cm (can range up to 80 cm). The Loop Current 

position in the eastern Gulf varies with periods on the order of months between a port-to-port 

regime, i.e., where the current follows almost a direct path between the Yucatan Channel and the 

Straits of Florida, and an extended position into the northern Gulf (Chérubin et al. 2005; Coats 

1992; Nowlin and McLellan 1967; Cochrane 1972; Hofmann and Worley 1986). Loop Current 

eddies (the circular feature with high sea surface height in the north central Gulf in Figure 1), 
4

which are large-scale anticyclones up to 400 km in diameter, separate from the Loop Current at 

an average frequency of 11 months and travel westward in the Gulf due to the topographic and 

planetary beta effects (Sturges and Leben 2000). These warm core rings have strong current 

velocities (core speeds up to 2.5 m/s) in the surface layer (depths > 800 m) and demonstrate 

average translation speeds of 3 - 6 km/day (Elliot 1982; Hamilton and Lee 2005). Typically, a 

Loop Current eddy will remain distinguishable for approximately a year, and a large portion of 

that time is spent decaying near the shelf break in the western Gulf. Some eddies have been 

observed to interact with the continental slope and move northward impacting circulation on the 

Texas-Louisiana Shelf, while some eddies lose their energy and dissipate before they reach the 

western Gulf (Walker 2005; Lewis and Kirwan 1985; Vidal et al. 1992). 

Figure 1. Sea-surface height in the Gulf of Mexico on August 5, 

2005. Contours are 5 cm apart. (image from R. Leben) 

2.2 Surface Circulation of the Gulf of Mexico 

The general surface circulation of the Gulf of Mexico was identified from dynamic height fields 

by Dietrich (1937), in which the Loop Current and the ubiquitous anticyclonic circulation in the 
5

western-central Gulf was inferred from very few hydrographic stations (DiMarco et al. 2005). 

Ichiye (1962) first proposed the detachment and westward translation of anticyclonic rings from 

the Loop Current in the Gulf of Mexico (Elliott 1982). Since this conjecture was presented, 

observational studies of the circulation in the eastern Gulf of Mexico, focused on the Loop 

Current and its associated eddies have been prevalent. 

While comparing circulation patterns between summers of 1966 and 1967, Nowlin and Hubertz 

(1972) gave the first account of an anticyclonic ring separated from the Loop Current in the 

eastern Gulf. They found that the current regimes were distinctly different between the summers 

of two consecutive years; one summer presented a Loop Current extended far into the 

northeastern Gulf and the next summer revealed a large detached anticyclone and a Loop Current 

positioned in the southern portion of the basin. Cochrane (1972) reported on the eddy 

detachment recorded in the same 1967 dataset and determined that cold ridges develop from 

cyclonic meanders off of the northern Campeche and West Florida Shelves and promote eddy 

detachment. 

Several studies in the Gulf have aimed to quantify the periodicity of the Loop Current’s northern 

penetration and eddy separation. Maul (1977) evaluated ocean color sensing satellite data to 

determine if there was an annual cycle to the currents in the eastern Gulf related to the growth 

and decay of the Loop Current. He was able to correlate an in-phase relationship between the 

annual cycle of the extension of the Loop Current into the eastern Gulf and the annual cycle of 

current speeds and transports of the Gulf Stream, which is in-phase with the annual cycle of trade 

wind stress (Fuglister 1951). He also noted that eddy shedding is a vital part of this cycle. 

Sturges (1994), Vukovich (1995), and Sturges and Leben (2000) have since investigated time 

scales of separation events based on satellite infrared data and altimetry since 1972, and have 

found that the shedding cycle is not annual. Leben (2005) has given the most complete analysis 

of the range of shedding periods and has showed it to be from a few weeks up to 18 months 

using additional satellite data. 

Lugo-Fernández (2007) applied a dynamical systems approach to determine if the Loop Current 

is a chaotic oscillator that demonstrates aperiodic behavior related to transport and vorticity input 

at the Yucatan channel. He hypothesized that because of its irregular shedding behavior, the 

Loop Current can be compared to a non-linear, driven, dampened oscillator with an amplitudedependent period. His study determined that the Loop Current is not a chaotic oscillator, and that 

the short memory of the current limits forecasting to one cycle in the future, as shedding events 

are found to be independent of each other. 

DiMarco et al. (2005) reports the latest, comprehensive description of the upper ocean 

circulation from direct velocity estimates in the Gulf of Mexico using 1397 drifters drogued at 50 

m between 1989 and 1999. The inflow and outflow of the Loop Current was witnessed in 

averaged data from all seasons, but only data from winter months revealed a continuous Loop 

Current. This was attributed to the frequent eddy detachment during other seasons. The spring 

and fall months presented a central Gulf with significantly variable currents, attributed to the 

presence of complex eddy systems, and the summer months revealed an energetic Loop Current 

extended further north than in winter. Furthermore, during the spring and winter, circulation in 

the eastern and western Gulf is decoupled, i.e., there is not much interaction between the two 
6

zones, and during the summer and fall, when eddy shedding is at a maximum, the zones are 

coupled. 

2.3 Loop Current Ring Shedding 

Chérubin et al. (2005) summarized three mechanisms for Loop Current eddy shedding, and 

hypothesized that a combination of all three mechanisms are involved in the shedding process. 

First, the ballooning mechanism responsible for the growth of the Loop Current and its 

northward migration, first described by Pichevin and Nof (1997) and Nof and Pichevin (2001), 

states that to conserve momentum, the current balloons northward near its source and forms an 

anticyclonic bulge followed by the shedding of an a warm core eddy. Second, cyclonic and 

anticyclonic circulations beneath the eddy form from the motion of the anticyclone in the upper 

layer. These deep currents are presented by Sturges et al. (1993), Welsh and Inoue (2000), and 

Cushman-Rosin et al. (1990). Third, baroclinic instability takes place to form a deep modon 

(Hurlburt and Thompson, 1980). This instability manifests as a deepening and spinning of the 

base of the Loop Current. The instability-generated cyclone contributes to the separation of the 

ring but the beta and/or topographic effects remain the control mechanism of the separation 

(Chérubin et al., 2005). The dynamical signature of the instability can extend 2000 m, leading to 

barotropic motion, which has also been observed by Hamilton (1990), as well as N. Walker 

(personal comm.). 

Chérubin et al. (2006) used a numerical simulation to study the quasigeostrophic linear and nonlinear instability of the Loop Current by modeling a shielded ring, as a vortex with an 

anticyclonic core, surrounded by a band of cyclonic circulation in the surface layers. A shielded 

ring is a simple, but reasonable modeling tool for this region, evidenced by Candela et al. (2002), 

who observed a strong potential vorticity anomaly on the western side of Yucatan Current that 

creates an outer sheared belt around the Loop Current (Chérubin et al. 2005). Higher, unstable 

azimuthal modes of the vortex were excited as the width of the cyclonic potential vorticity belt 

decreased, which increased the horizontal shear. The fourth azimuthal mode of the vortex 

appeared to be most unstable. 

Lewis and Kirwan (1987) studied the evolution of a Loop Current ring using drifters drogued at 

100 – 200 m in the Gulf. They hypothesized an alternative means of ring development and 

separation to the instability theory proposed by Hurlburt and Thompson (1980) based on lateral 

shearing stress the Loop Current encounters off the northwest coast of Cuba. The interaction of 

the Loop Current with the West Florida Shelf creates negative vorticity in this region because of 

the direction of the flow in and out of the Gulf. They found an anticyclonic rotational feature, 

called the Cuban eddy, can form in this region before the previous Loop Current ring is detached, 

indicating shorter time scales for ring shedding in the Gulf. 

2.4 Loop Current Frontal Eddies 

As ring separation has been associated with the steepening of potential vorticity gradients in the 

eastern Gulf, the importance of cyclonic circulation to the eddy shedding cycle has been 

evaluated through observations and numerical studies. Cold features observed on the northern 

edge of the Loop Current travel southward around the west Florida shelf and form cold tongues 

or ridges off Dry Tortugas that constrict the northern portion of the Loop, prompting eddy 
7

detachment (Vukovich 1986). Cyclones of 80 – 120 m diameter can form on the eastern side of 

the Loop and move into the southern Florida Straits, but observations show that they are not 

advected into the Atlantic (Vukovich and Maul 1985). Fratantoni et al. (1998) hypothesized that 

these large quasi-stationary cyclonic eddies in the southern Florida Straits, called Tortugas 

eddies, could be the downstream expression of Loop Current frontal eddies. They used three 

years of advanced very high-resolution radiometer measurements to show the relationship 

between the generation of Loop Current rings and the development of Tortugas eddies. Cyclonic 

frontal eddies on the outer edge of the Loop Current were observed by Walker et al. (2003) using 

GOES-8 high temporal resolution sea surface temperature measurements. They observed four 

fast-moving frontal eddies travel around the periphery of the Loop Current in May of 1999, 

which were detected as warm wavelike perturbations. The frontal eddies advect warm water 

around their centers of circulation but have cold centers below the surface and are usually seen 

east of the Campeche Bank and grow in diameter as they move clockwise around the Loop 

Current (Zavala-Hidalgo et al. 2003; Walker et al. 2003). 

2.5 Deep Flows in the Yucatan Channel 

The flow structure and transport of the Yucatan Channel and its influence on the circulation in 

the Gulf of Mexico has been investigated by Sheinbaum et al. (2002). They found a net transport 

of ~23 Sv into the Gulf from observations of the channel between September 1999 and June 

2000. A somewhat surprising result because it is smaller than the transport out of the Gulf in the 

Florida current (~30 Sv), and smaller than the transport necessary to close the mass budget of the 

Caribbean Sea. The reason for this anomaly could be due to transport through smaller passages 

that were not well monitored and remain less understood, or it could be that summer months 

were not included in the record. However, it is clear from their study that the dynamics of the 

circulation in the upper layer of the Gulf is controlled by the deep flow of the channel. 

Coherency between deep currents in the channel and the rate of change of the surface area of the 

Loop Current was shown by Bunge et al. (2002) based on the same observations. 

Using numerical simulations. Chérubin et al. (2005) linked the deep transport of the Yucatan 

Channel to Loop Current ring separation. They found that the outflow into the Caribbean through 

the channel is in phase with the shift of the Loop Current maximum velocity position and is 

reflected in transport variations through the channel. Chérubin et al. (2005) also affirmed from 

spectral analysis of Yucatan Channel transport that a dominant period of transport change and 

the lateral shifting of the Loop Current correspond to the presence of Caribbean eddies in the 

Yucatan Current. 

2.6 Effects of Topography on Gulf of Mexico Circulation 

The steep topography of the West Florida Shelf/Slope contributes to the dynamics of the eastern 

Gulf of Mexico by affecting the oceanic pressure fields along the shelf break. Hetland et al. 

(2001) employed a series of numerical experiments to investigate the presence of a northward 

flowing jet just seaward of the West Florida Shelf induced by forcing from the deep ocean (i.e., 

the Loop Current) and frictional processes on the shelf. They found that the structure and decay 

of the high-pressure tongue along the shelf break was dependent on the modeling of the West 

Florida Slope as a wall or a slope, and that this slight difference resulted in a change of the nature 

of eddy shedding in the Gulf of Mexico. Essentially, when the slope was modeled as a wall, a jet 
8

formed and transported mass from the Loop Current, effectively halting eddy shedding, but when 

the slope was modeled realistically, the jet formed such that mass was leaked onto the shelf to 

join a southward flow in response to the jet, and possibly return to the Loop Current. 

Observations of high-speed deep currents in the northern Gulf of Mexico by Hamilton (1990), 

Hamilton and Lugo-Fernández (2001), and Hamilton (2007) indicate the presence of lowfrequency topographic Rossby waves. At the base of the Sigsbee Escarpment and in the western 

Gulf, large amplitude wave trains of varying periods (~10 – 25 days) appear and decay over a 

period of 2 – 3 months. Ray tracing shows the source to be on the western side of an extended 

Loop Current, and could be caused by the interaction of Loop Current rings with shoaling 

topography or the ring shedding process itself, as two of the three wave trains observed at the 

escarpment were concurrent with the shedding and westward passage of anticyclones. Hamilton 

(2007) observed coherent currents at the escarpment, decaying away from the bottom, up to 300 

m from the surface in a 2000 m water column; evidence that topographic waves can be nearly 

full depth. In support of the idea the deep disturbances are linked to the upper layer dynamics 

associated with the Loop Current, Hamilton and Lugo-Fernández (2001) related observed deep 

currents to the coupling of the upper and lower layers of the water column during the passage of 

two cyclonic frontal eddies near the mooring site in the central Gulf. 

The underlying conclusion of all previous studies in the eastern Gulf is that mesoscale circulation 

in this region varies rapidly and seemingly aperiodically. The ubiquitous Loop Current, Loop 

Current eddies, Loop Current frontal eddies, and other cold and warm core eddies reshape the 

currents on the order of days. This study examines the role of these energetic and highly time 

fluctuating features on the horizontal current velocity field. 

2.7 Partitioning of Kinetic Energy Amongst Dynamic Modes 

Eddy motion is generated in regions with strong mean shear flow, which makes the eastern Gulf 

of Mexico a prime area to study eddy energy (Wyrtki et al. 1976). The research presented here is 

designed to investigate the roles of the Loop Current, Loop Current eddies, Loop Current frontal 

eddies, and anticyclonic and cyclonic eddies derived therefrom, on the upper and lower layer 

circulation. These energetic features will be investigated based on an EOF and dynamic normal 

mode decomposition of the horizontal current velocity time-series. Decomposition into 

theoretical modes allows the separation of low frequency currents into barotropic and baroclinic 

components, which represent net transport and current shear respectively (Inoue 1985). Eddy 

motion in the eastern Gulf is important to the energy transfer processes related to circulation, and 

the partition of horizontal velocity components into vertical modes is an effective way to study 

the vertical partition of kinetic energy (Wyrtki et al. 1976). This research expands the work of 

Wunsch (1997) in the vertical partitioning of oceanic horizontal kinetic energy to three full water 

column moorings in the eastern Gulf of Mexico. 

Dominant vertical EOF modes can often be represented as a superposition of the first few 

theoretical dynamic modes, and thus it is reasonable to assume that the vertical structure of 

horizontal quasigeostrophic velocity can be well represented by a linear combination of 

theoretical modes. McWilliams and Shen (1980) have affirmed that mid-ocean mesoscale 

currents can be represented by a few vertical empirical modes and these modes are similar to 

theoretical modes for linear quasigeostrophic waves. 
9

EOF analyses on widespread historic current data collected in the Gulf indicate that most current 

variance is explained by a surface-trapped mode that decays with depth, and higher modes 

explain a smaller fraction of variance relative to this mode (Nowlin et al. 2001). This surfaceintensified mode appears to be an arrangement of the barotropic and first baroclinic modes. The 

east Gulf has been hypothesized as a potential source region for topographic Rossby waves (Oey 

and Lee 2002; Hamilton 1990), whose presence would give rise to a bottom-trapped mode 

explaining a good portion of current variance as well, particularly in areas with sloping 

bathymetry. 

McWilliams and Flierl (1975) hypothesized that the barotropic and first baroclinic components 

are often correlated rather than independent, as evidenced by the linear relationship of the 

leading theoretical modes for a flat bottom ocean representative of the first EOF modes. 

McWilliams and Shen (1980) found that the barotropic and first baroclinic modes covary with 

greatest spatial correlation at lags of approximately an eddy radius. One motivation for this 

research is to investigate whether this coupling phenomenon is present in the eastern Gulf of 

Mexico as well. 

Wunsch (1997) performed a similar deep ocean investigation in which he partitioned the oceanic 

kinetic energy into barotropic and baroclinic components using vertically well-resolved current 

meter moorings and altimeter data. Both the partition of kinetic energy throughout the water 

column and in the surface layer amongst the buoyancy modes was considered. He showed that in 

the Gulf Stream region, the barotropic motions are amplified, but the first baroclinic mode is 

maximum over the mid-Atlantic Ridge. The modal decomposition of the surface kinetic energy, 

which reflects the motion of the thermocline layer, revealed that globally, the barotropic mode 

was significantly reduced relative to the first baroclinic mode, with the exception of the Gulf 

Stream region, where the energy was found to be 40% barotropic. Although Wunsch did not use 

the same method of mode amplitude computation used here (he used a priori assumptions about 

the fraction of energy amongst the modes instead of a least-squares sense), and fit 5 modes to 

data in most cases, it is expected that the eastern Gulf of Mexico will yield similar results. 

2.8 Scientific Questions and Hypotheses 

The following questions and hypotheses will be assessed in this study: 

1. What is the vertical structure and temporal variability of the most energetic dynamic modes? 

What is the horizontal spatial variability of dynamic modes in the northeast Gulf of Mexico? 

Hypothesis 1: Lower order modes exhibit predominantly low frequency temporal variability and 

higher order modes exhibit higher frequency variability. Time scales of the dynamic modes 

increase southward towards mooring M3. 

Most of the current energy in the EGOM study region can be explained in two modes or less, 

especially given the surface intensified flow that dominates the region, which is strongest at the 

mooring closest to the Loop Current. Time scales of the modes are hypothesized to increase 

southward towards mooring M3, as the currents there are exposed to more variability at 

mesoscale (dimensions on the order of the Rossby radius – around 100 km and time scales of a 
10

few months to a year) and longer periods. It is probable that the lower order theoretical modes 

(barotropic and first baroclinic) will possess low frequency variability on mesoscale eddy and 

secular (low- frequency mesoscale variability termed by Schmitz (1978)) time scales, while 

higher order modes will exhibit higher frequency variability of an episodic nature. Lower order 

modes will likely be prevalent throughout the deployment, with the first baroclinic mode 

amplified when the Loop Current is in the study area. Atmospheric tropical storms might also 

excite higher order modes in the water column. 

2. How do anticyclones and cyclones on the periphery of the Loop Current and the Loop Current 

itself affect the barotropic and baroclinic mode amplitudes? 

Hypothesis 2: The first baroclinic mode amplitudes will be affected by the surface 

intensification of the eddy field. The barotropic mode becomes significant in the vicinity of deep 

eddies. Higher order modes become significant during eddy shedding.

The first baroclinic mode will be strongest at the region of largest sea surface height gradient, 

i.e., near the edge of the Loop Current, anticyclones, and cyclones, and not directly in these 

features. Chérubin et al. (2005) noted that Loop Current instabilities that lead to ring detachment 

could reach 2000 m, leading to barotropic velocities, which might cause considerable variability 

in the barotropic mode. Also, eddies are surface intensified, but can affect the abyssal circulation 

as well. Thermal signatures of some rings are seen as deep as 1000 m (Kuznetsov et al. 2002). 

Eddies that affect the circulation this deep would alter the barotropic mode amplitude by 

accelerating mean flow over the water column. Higher order baroclinic modes (modes 2 and up) 

will most likely become significant during eddy shedding (with a lag since the study region is 

north of the separation region), as vertical shear plays an important role in the separation 

instability process. 

3. Are temporal amplitudes of lower order modes correlated? 

Hypothesis 3: Barotropic and first baroclinic modes are coupled, while higher order baroclinic 

modes are not correlated to other modes.

The barotropic and first baroclinic modes will be coherent at low frequencies during mesoscale 

processes and obtain the largest correlation at lag distances of approximately an eddy radius, 

consistent with previous studies by McWilliams and Shen (1980). 

At present, the ultimate goal of all deep Gulf of Mexico physical research is to make progress in 

understanding three phenomena: 1) quantifying processes responsible for Loop Current eddy 

detachment, 2) generation, propagation, and dissipation of topographic Rossby waves, and 3) 

quantifying the variability of the transport in and out of the Gulf through the Yucatan Channel 

and Florida Straits. This effort is focused on better understanding the current regime in the 

eastern Gulf of Mexico, as all of these can be better explained by further study of this region. 

While all of these phenomena are not directly addressed in this report, the results of the research 

herein will help explain the importance of eastern Gulf circulation to these processes. 
11

In this study, an investigation of the dynamics of the eastern Gulf of Mexico is employed by 

means of an empirical orthogonal function (EOF) and dynamic mode decomposition of 

horizontal currents measured from three full water column instrumented mooring arrays. All data 

used in this analysis, data processing methods, statistics for EOF analysis, and the dynamic mode 

calculation are explained in the data and methods section (Section 3). Results of the analysis are 

presented in the results section (Section 4) and their implications for our understanding of the 

circulation in the eastern Gulf of Mexico and goals for future research in this region are 

addressed in the discussion and conclusions section (Section 5). 
13

3 DATA AND METHODS 

This section summarizes the EGOM mooring and hydrographic studies. Historical hydrographic 

data, altimetry derived sea surface height, and the gridded wind product used in the analyses in 

this report are presented. EGOM data return and data processing methods for this study are 

discussed. The theory of empirical orthogonal function (EOF) analysis and dynamic mode 

decomposition of current velocity is briefly summarized as well as the calculations involved in 

these methods. 

3.1 EGOM Mooring Study and Hydrographic Cruises 

In January of 2005, three tall moorings, henceforth referred to as M1, M2, and M3 in this text, 

and one short mooring, M4, were deployed in the eastern Gulf of Mexico by Evans Hamilton 

Inc. (EHI), an oceanographic services company, aboard the R/V Pelican. A summary of moored 

instruments, parameters measured, sample intervals, and start and stop times, separated by 

mooring is given in Table 1. A schematic of the mooring M1 instrument array during 

deployment 1 is presented in Figure 2. The other two tall moorings were configured similarly. 

M1, M2, and M3 were equipped with one Rowe-Deines Instruments (RDI) Broadband 75 kHz 

Long-Ranger Acoustic Doppler Current Profiler (ADCP) with 8 meter bin spacing to measure 

current velocity components in the upper 500 meters of the water column. A string of six S4 and 

Aanderaa RCM current meters spaced ~ 250 meters apart were used to measure horizontal 

current velocity of the lower water column, as well as pressure, temperature, and conductivity 

when available. Moored current meter and ADCP data were recorded hourly. Tall moorings were 

also outfitted with three Sea-Bird MicroCAT 37SM conductivity-temperature-depth (CTD) 

sensors at ~75 m, ~150 m, and ~225 m to measure pressure, temperature, and conductivity in the 

thermocline layer, and four Hugrun temperature sensors positioned ~100 m apart in the upper 

500 m of the water column. These instruments collected data every 30 minutes, but will not be 

used in the analyses presented in this report. 

The short mooring, M4, was instrumented with Aanderaa RCM8 and RCM8s current meters at 

approximately 2530 m (200 m from the bottom) and 2630 m (100 m from the bottom) depth. 

These instruments collected hourly velocity data as well. 

The instruments were deployed for one year with a servicing and maintenance recovery after 

seven months. The servicing therefore divides the total deployment into two shorter 

deployments: D1 and D2. The first deployment, D1, was from January 21, 2005 to August 20, 

2005, and the second deployment, D2, was from August 22, 2005 to January 24, 2006. Three 

hydrographic cruises for this project took place in the study area, during which numerous SeaBird SBE 9 CTD and XBT casts took place. CTD casts were averaged into half-meter bins 

during post-collection processing. Vertical profiles of temperature from the XBT casts were 

spaced approximately 0.6 meters apart. The first cruise, HC1, occurred January 19–23, 2005, 

during the mooring deployment, the second cruise, HC2, occurred August 19–25, 2005, during 

the servicing and maintenance of the moorings, and the last cruise, HC3, occurred January 21–

28, 2006, during the mooring recovery. Detailed analysis of CTD data is used in this report as the 

basis for the modal analysis described in section 2.6. 
14

Table 1 

MMS Eastern Gulf of Mexico Circulation Study Mooring Instruments 
15

Figure 2. Schematic diagram of MMS Eastern Gulf of 

Mexico Circulation Study mooring M1 

configuration during deployment 1. 
16

3.2 Historical Hydrography, Wind and Sea-Surface Height 

This research is based on ADCP and current meter velocity data from M1, M2, and M3 from 

both deployments and CTD cast data from HC1, HC2, and HC3 at each of the mooring sites, as 

well as CTD, XBT, and Nansen and Niskin bottle data analyzed in the MMS Deepwater Physical 

Oceanography Reanalysis and Synthesis of Historical Data (DW) Report (Nowlin et al. 2001). 

These historic data include all good quality hydrographic data collected in the Gulf of Mexico 

since the early 1900s. Approximately 280 historic datasets from the eastern Gulf of Mexico (east 

of 89W) are included in the analyses in this report. 

Sea surface height (SSH) anomaly is obtained from Jason, TOPEX/Poseidon (T/P), Geosat 

Follow-On (GFO), ERS-2 and Envisat altimeter data processed by the Colorado Center for 

Astrodynamics Research (data courtesy of R. Leben). SSH data ranging from January 1, 2005 to 

January 31, 2006 were interpolated to a Gulf-wide grid of quarter-degree resolution and averaged 

to daily values. Wind velocity data for the full years of 2005 and 2006 is provided by the 

National Centers for Environmental Prediction (NCEP) at the nearest Eta grid point to each 

mooring at 3-hour intervals. 

3.3 EGOM Data 

The moorings of the EGOM study are depicted in Figure 3 by pink triangles; blue dots indicate 

stations in the eastern Gulf (east of 89W) where CTD, XBT, and bottle data were collected on 

various cruises between 1915 and 2000, and evaluated in the DW Report (Nowlin et al. 2001). A 

typical position of the Loop Current (estimated from sea surface height fields from the Gulf of 

Mexico in January 2005) is delineated by the orange line. The inertial period in this region is 

close to one day: 0.9496 cpd at mooring M1, 0.9389 cpd at mooring M2, and 0.9268 cpd at 

mooring M3. Also note that the eastern Gulf is bordered by two broad, shallow shelves, with 

steep escarpments: the West Florida Shelf and the Campeche Shelf, north of the Yucatan 

Peninsula (Maul 1977). The EGOM moorings were deployed in approximately 2700 m of water, 

in a flat-bottomed region, with M3 nearest to the Loop Current, and M1 closest to the steep 

Florida Slope. 

EHI was responsible for initial data quality control and processing. Generally, current velocity 

data for the mooring study was good. Suspect and bad data were flagged and excluded from 

further analysis. During the first deployment, the ADCP on M2 suffered interference from the 

mooring cable after the surface flotation was lost. This resulted in some low, atypical velocity 

measurements and these data were excluded from the analysis. The Aanderaa RCM7 and 

Aanderaa RCM8 current meter rotors stall at 1.1 cm/s, and the Aanderaa RCM8s stalls at 1.5 

cm/s, thus below these thresholds, velocity is recorded as zero. There were three cases of current 

meter rotors being lost, but direction was unaffected. 

Figure 4 shows the temperature-salinity (T-S) relationship of the hydrographic data collected 

from years 1915 – 2000 analyzed in the DW report and CTD data from all three EGOM cruises 

at each of the tall mooring sites. The temperature-salinity relations characteristic of Caribbean 

near surface water (Subtropical Underwater, or SUW, characterized by salinity > 36.5 at ~22.5 

C) and Gulf Common Water (salinity of ~36.4 at 22 – 23.3 C) at 0–250 m depth are clearly 

identified (Morrison and Nowlin 1982; Morrison et al. 1983). Typically, the T-S relationship in 
17

the upper ocean (at densities above sigma-theta of ~27) is scattered, while in the deep ocean 

there is very little variance in the T-S relationship. At depth there is a discrepancy between the 

EGOMcast data and the DW data, as the deep salinity and temperature data for the different 

projects are not incident with each other. This is likely a calibration problem, and will have very 

little affect the analyses herein. 

Figure 3. MMS Eastern Gulf of Mexico Circulation Study site and MMS Deepwater 

Physical Oceanography Reanalysis and Synthesis of Historical Data stations 

in the eastern Gulf of Mexico (east of 89°W). Triangles represent the EGOM 

mooring locations, blue dots indicate the Deepwater Reanalysis (DW) sites. 

The orange line signifies the nominal position of the Loop Current. 
18

Figure 4. Temperature-salinity relations in the Eastern Gulf of Mexico. 

Temperature versus salinity from MMS Eastern Gulf of Mexico 

Circulation Study CTD casts (red, pink, and green dots) and MMS 

Deepwater Physical Oceanography Reanalysis and Synthesis of 

Historical Data casts (blue dots) in the eastern Gulf of Mexico (east of 

89°W). Contours are of density (sigma-theta). 

3.4 Data Processing 

During the spring and summer of 2005, there were at least three separation and three 

reattachment events of the northern lobe of the Loop Current, which culminated in the permanent 

detachment of Eddy Vortex in September 2005. The passage of the northern extension of the 

Loop Current and the nascent anticyclone over the study area caused the portion of the mooring 

above 500 m to become drawn down in the water column; a result of the convergence of water in 

these features. Mooring draw down caused the instruments on the upper portion of the mooring 

to record at varying depths. Depth displacements of the instruments ranged up to 50 m at times, 

especially during spring, when the Loop Current was at its maximum penetration into the 

northeast Gulf. 
19

Prior to analysis of the ADCP current data, mooring draw down was corrected for by fitting eastwest and north-south component time series to a regular grid such that data recorded in an 8 m 

depth range were assimilated into a single time series. Because the ADCP was originally set to 8 

m bins, this method assures there is only one measurement for any sample time. A consequence 

of this method is gaps in the surface velocity data when the mooring was drawn down, as the 

uppermost instruments and bins were pushed downward at this time. Gaps over a period of less 

than 2 weeks and more than 1 day were filled using the spectral Method of Maximum 

Likelihood, a method which utilizes data before and after the gap to predict values in the gap 

(Press et al. 1986; DiMarco et al. 1997). All remaining gaps less than one day were linearly 

interpolated. The same gap filling procedure was performed on the single point current meter 

data. Most analyses outlined here require regularly spaced, gapless time series, and due to the 

gaps caused by the gridding procedure, time series above ~ 60 m were eliminated from further 

analysis. This also eliminates the portion of the water column that is contaminated by direct 

Ekman pumping (upper 50 m). For the study of low frequency circulation, all time series were 

filtered using a 96+1+96 point 40-hour low pass Lanczos-Cosine kernel (Emery and Thompson 

2001), which eliminates tidal and inertial signals form the data (DiMarco et al. 1997). For 

correlation between sea surface height (SSH) anomaly and current, and wind and current, current 

data was 40-hour low pass filtered and resampled at 24-hour intervals and 3-hour intervals 

respectively. 

3.5 EOF Analysis 

Empirical orthogonal function (EOF) analysis, is useful in the interpretation of oceanographic 

time series because it condenses the variability in a collection of datasets into a countable set of 

orthogonal modes (Emery and Thompson 2001; Preisendorfer 1988; Kundu et al. 1975). A linear 

combination of these modes multiplied by their spatial amplitudes should restore the total 

variance of a time-series, reconstituting the original data. Stationary patterns in the temporal or 

spatial domains can be identified as well as propagating features. The objective of EOF analysis, 

as described by Emery and Thompson (2001), is to write a single time series  m (t), t 1,2,...,N, 

of a collection of M time series (1 m  M ) from different locations in the form: 

 m (t)  aimi(t)

i1

M

 , 

where aim is the amplitude of the i

th mode at the mth location and  i

(t) is the i

th principal 

component (PC) time-series, or mode. Modes are found by casting the data series as a matrix, D, 

and solving the eigensystem: 

C   , 

where C (N 1)

-1 DDT

 is the covariance matrix of the data series,  is the matrix of 

eigenvectors, which are the spatial modes, and  are the eigenvalues, which are equal to the 

variance of each mode (Emery and Thompson 2001). 

(1) 

(2) 
20

3.6 Dynamic Mode Decomposition 

A complete set of linear vertical structure dynamic normal modes, Fn , for n 1,2,3,..., for a flatbottomed, resting ocean can be evaluated using the Taylor-Goldstein equation: 

1

N2

(z)

d2Fn

dz2   n

2

Fn (z)  0 , 

where N(z) is the Brunt-Väisälä frequency and  n is related to the phase speed of the growing 

waves of normal modes (Wunsch 1997). Boundary conditions require Fn (z)  0 for z  0,H

(surface and bottom). Fn is related to horizontal velocity structure modes, n , for n 1,2,3,..., 

by: 

n (z)  Fn

z



1

 n

2 , 

where  is the mean water column density; taken to be ~ 1028 kg/m3

 in this analysis. 

The second derivative in Equation 3 is cast as a matrix and solved numerically for the 

eigenvalues and eigenvectors,  n

2

 and Fn , respectively. 

Horizontal velocity modes can be fit to the moored current data using a least squares multiple 

regression described by Inoue (1982). The following residual is minimized: 

  [v(zm,t)  Dn (t)n (zm )]2

n 0

N

 m1

M

 , 

where v(zm,t) is the observed velocity at depth m and time t , Dn (t) (unknown) is the amplitude 

of mode n at time t , and n (zm ) is the n

th mode value at depth m. We minimize the error to 

find the temporal amplitudes of the k th mode by taking the partial derivative with respect to Dk

and setting it equal to zero as such: 



Dk

 2 k (zm )[v(zm,t)  Dn (t)n (zm )]  0

n 0

N

 m1

M

 , 

The set of these equations for all modes included in the least squares fit form a square matrix 

system and D0 , D1, D2 , ... can be solved for at every sample time t using simple inverse 

methods. 

(3) 

(4) 

(5) 

(6) 
21

4 RESULTS 

This section begins by obtaining an initial impression of the physical processes recorded in the 

data through examination of the time-series, basic statistics, and spectra of velocity components 

at various depths in the water column from the EGOM array. Current-wind coherence and 

current-current coherence is investigated for each velocity component. The vertical structure of 

low frequency variability is examined through EOF analysis and by a dynamic mode 

decomposition of the EGOM moored current velocity data, then these two methods are 

compared. The first baroclinic mode is assessed and related to the sea surface height gradient and 

spectra and time scales of the first three theoretical modes are evaluated. Next, the kinetic energy 

in the first three theoretical modes by depth and temporal modal correlation is calculated. Lastly, 

the results from EGOM data are compared to results from historical data. 

4.1 Velocity Record Length Time-series 

An initial impression of the physical processes under examination can be acquired by a simple 

visual assessment of the moored time-series data plotted in composite form at several depths that 

span the entire water column. Gridded, interpolated current velocity at five ADCP depths and all 

single point current meters for each mooring deployment at M3 are illustrated in Figure 5 

(Figures A-1 and A-2 in Appendix A give velocity time-series at M1 and M2). Tick marks along 

the y-axis are spaced at 70 cm/s intervals; tick labels indicate record depth. Clearly, currents 

during both deployments in this region show a high degree of coherency at water depths above 

500 m. High-speed current events (near surface speeds exceeding 100 cm/s) are more frequent as 

observations approach the Loop Current from mooring M1 to M3. 

Occasionally, the observations indicate a strong barotropic component to the flow structure. For 

example, in mid-August 2005, at mooring M3, there is a barotropic event associated with the 

detachment and reattachment of a eddy Vortex. The feature is coherent throughout the water 

column, and peaks in the upper ocean with only gradual diminishment with depth. In midDecember 2005, there is a second barotropic current event that is seen in the velocity data 

collected at M2 and M3. During this second event, the increase in current speed is associated 

with a Loop Current meander into the study area. 

Large-amplitude inertial oscillations excited immediately after the passages of Hurricanes 

Katrina, in late August 2005, and Rita, late September 2005, are easily identified in the timeseries. The current oscillations persist for at least two weeks after the passage of the storms. 

Inertial motions are strongest at M3 and penetrate down to at least 500 m. Inertial oscillations 

after the storms are present in the deep ocean as well, but these motions are present throughout 

deployment and might not be caused by the storms; the phase of these motions would have to be 

examined to attribute them to the hurricanes. Hurricane Dennis, which entered the Gulf on July 

9th, and later passed very close to the study area, is evidenced in the less intense inertial 

oscillations at M1 around this time. Note also in Figure 5, the periods of uncharacteristically 

linear data collected at mooring M3 during deployment 2 by the current meter at 997 m, which 

indicates a malfunction with this instrument. 
22

Figure 5. Gap-filled, gridded current speed from five moored ADCP depths and moored current 

meters for deployments 1 and 2 at mooring M3. Time periods when tropical storms 

traversed the Gulf are indicated by vertical dotted lines. 

4.2 Basic Statistics 

Figure 6 shows vertical profiles of summary statistics of record-length mean, mean plus and 

minus one standard deviation, minimum, and maximum values for u (east-west) and v (northsouth) velocity components for all instruments and ADCP depth bins on mooring M3 (Figures 

A-3 and A-4 in Appendix A give basic statistics for instruments on M1 and M2). The basic 

pattern revealed in this series of figures is that current velocity is generally greatest near-surface 

and decreases with depth. The statistics below depths of 1000 m are typically constant to the 

bottom. Some of the profiles show that for the uppermost surface velocity bins the record-length 

mean, standard deviation, and minimum/maximum envelopes tend to have a slightly different 

character with smaller or slightly shifted statistics compared to measurements at deeper bins, i.e., 

around 100 m. This may be due to fewer observations associated with surface bins due to 

instrument drawdown and the effects of gridding the data to non-overlapping depth bins. This 

effect is particularly relevant since most data dropout at these levels occurs during strong storms 

or eddy events. 
23

Figure 6. Vertical profiles of record-length mean, standard deviation, minimum, 

and maximum velocity components for mooring M3 (left: east-west 

component; right: north-south component). Top row: Deployment 1. 

Bottom row: Deployment 2. 
24

Current velocity at mooring M3 (Figure 6) is predominantly to the southeast during deployment 

1 and eastward during deployment 2. This is attributed to the relative location of the mooring to 

the northern limb of the Loop Current and the developing anticyclonic eddy during the early 

months of 2005. The southern limb of a cyclonic eddy passed over this region during a large 

period of deployment 2 producing mostly eastward-directed currents. Sea surface height in the 

Gulf is given in Figure 7, and the cyclone is clearly seen in the study region. The southward 

velocity at M3 is attributed to the position of the Loop Current relative to the mooring in early 

April 2005. In May, the northeastern limb of the Loop Current moves into the study area, 

producing large southward current velocities. During the second deployment, the mean northsouth velocity component at M3 is close to zero. 

Indications of energetic current events near the ocean surface are present at moorings M1 (Figure 

A-3) and M2 (Figure A-4) as well. During deployment 1, current velocity is primarily 

southeastward at mooring M2, and to the east at mooring M1. However, during the second 

deployment, currents are dominated by various cold core eddies moving in and out of the study 

area and the result is relatively small mean current velocities. 

At mid-water depths, i.e., around 750 m, the magnitude of the minimum and maximum currents 

for deployment 2 at mooring M1 is a maximum. An examination of the time series show that the 

large currents associated with this peak occurred in early September 2005 as a long period 

oscillation with inertial motions superimposed. Comparison with records above and below show 

little phase-locked or lagged correlation to any one particular event. The timing of these inertial 

oscillations at this depth are consistent with the interpretation that they were initiated at the 

surface by Hurricane Katrina on August 26 and propagated downward in the water column. 

However, the forcing of the longer period oscillation is not certain. Inertial band energy is seen at 

these depths at Moorings M2 and M3, however, there are no low-frequency motions and 

therefore no mid-water peak in basic statistics. 

Near-bottom (~2500 m) statistics from deployment 2 at mooring M1 show slightly larger 

extreme values than values 500 m above bottom. This is the only deployment showing evidence 

of bottom intensification. We note that at M1 there is no indication of low-frequency oscillations 

that extend throughout the water column and that bottom motions are not coherent with surface 

motions. Basic statistics for M4 are not plotted, however, record-length mean and standard 

deviation at M4 are near zero for both deployments and are consistent with values at similar 

depths at other moorings. 

Sea surface height is used in some of the analyses within this document, and therefore it is 

necessary to report basic statistics on those data as well. Mean standard deviation, maximum, 

and minimum of altimeter derived sea surface height anomaly are presented in Figure A-5 in 

Appendix A. The mean profile of the Gulf shows a Loop Current extended into the north central 

Gulf, which can be attributed to the Loop Currents extended position during most of the spring 

and summer; a time of heavy eddy formation and shedding activity. Most importantly, observe 

that eddy separation introduces the highest sea surface height variance south of the study area, 

and therefore the currents at mooring M3 are more affected by Loop Current variability than the 

currents at the other moorings. 
25

Figure 7. Sea-surface height in the Gulf of Mexico on September 15, 2005. (Left) Sea-surface 

height over the entire Gulf from several satellites. (Right) Sea-surface height in the 

EGOM study region. Arrows represent velocity at 50 m and 250 m depth at M1, M2, 

and M3. Contours are 5 cm apart. (images from R. Leben) 

4.3 Velocity Spectra 

Power spectral density profiles for velocity components at all depth levels, for both mooring 

deployments, were generated using Fast Fourier Transform (FFT) methods. Following Welch’s 

Method, the velocity time series were subsampled into overlapping segments of 512 points. 

Segments were preconditioned using a 512-point Kaiser-Bessel window; segments overlapped 

by 50%. The periodogram for each segment was computed using the FFT and then all 

periodograms for a given record were averaged to produce the spectra shown in this section. A 

convenient property of the Kaiser-Bessel window is that it allows each 512-segment to be treated 

as statistically independent. This technique significantly increases the degrees of freedom and, 

therefore, the statistical confidence of each spectra estimate. If the size of the longest, gapless 

segment of the time series was less than 512 points, which was the case for some records at the 

surface, the data were sub-sampled, and a Kaiser-Bessel window the size of the sub-sample was 

used for preconditioning. As previously stated, records were corrected for mooring draw down, 

interpolated, and eight tidal constituents were removed using the method of cyclic descent before 

analysis. Tidal amplitudes were small (~1 cm/s) during this study; common for this region. 

Spectra (non-variance preserving) estimates for mooring M3 east-west and north-south velocity 

components are presented at selected depths throughout the water column in loglog form for 

each deployment in Figure 8 (Figures A-6 and A-7 in Appendix A illustrate velocity spectra 

from M1 and M2). The purpose of these figures is to investigate how the spectral character of 

current velocity at each mooring location changes with depth. A typical velocity spectrum 
26

derived from a time series from the Gulf of Mexico displays a red energy distribution (weighted 

to low frequencies), with a distinct peak centered near the inertial frequency (i.e., close to 1 cpd). 

There is an energy minimum commonly seen in the 3-5 cpd range as well. Near-surface motions 

having periods ranging from 2-15 days are usually attributable to atmospheric weather 

conditions. Velocity spectra from the EGOM project support this energy partition. 

4.3.1 Upper Ocean Spectra 

In general, spectral energy throughout the frequency domain shown in Figure 8 is greatest in the 

shallow ocean (< 300 m depth). As expected, surface records (~ 50 m) contain larger weatherband variance than deeper records since the influence of winds on currents generally diminishes 

with depth. This is especially true at moorings M2 and M3, where the variance steadily increases 

between 0.9 cpd and 0.1 cpd. Inertial band energy is present throughout the water column, 

however, the amplitude of the inertial peak tends to narrow and decrease with depth. During the 

first deployment, the moorings each had similar inertial energy amplitudes. Spectral estimates 

based on data from the second deployment show moorings M2 and M3 had significantly more 

energy in the inertial band than mooring M1, owing to the closer proximity of this mooring to the 

centers of Hurricanes Katrina and Rita. 

Near-surface spectral variance associated with periods of ~20 days are typically associated with 

mesoscale processes such as the Loop Current and it’s eddies. Low-frequency spectral estimates 

in the upper ocean at moorings M1, M2, and M3 are roughly equal. There is slightly more subinertial energy present during deployment 1, especially at the 10 – 20 day period. As this is in the 

range of an eddy time scale, it is consistent with increased eddy presence observed in other 

analyses. 

The super-inertial domain, i.e., frequencies greater than 1 cpd, generally decreases with 

increasing frequencies. There is some evidence of semi-diurnal variance, likely associated with 

residual semi-diurnal tides. However, the variance associated with the semi-diurnal tides rarely 

rises above background levels. 

4.3.2 Deep Ocean Spectra 

Relative to the surface, spectral estimates found in deeper records of the eastern Gulf of Mexico 

are less energetic. However, the overall shapes of the trends of the spectral estimates of the 

deeper records closely resemble those estimated from records of the upper ocean. Generally, 

estimates at super-inertial frequencies tend to decrease faster with increasing frequency in the 

deeper records. Sub-inertial variability, particularly in the lowest bands shown, decreases from 

south to north, i.e., from mooring M3 to M1, This may be attributed to the motions associated 

with the Loop Current and eddy events at each mooring. There are some cases where low 

frequency variance (10 - 20 day period band) in the deepest record (usually 2500 m) is greater 

than the energy in the record at ~1000 m, which could be evidence of topographic Rossby waves. 

This is consistent with findings from the DW report, in which it was concluded that there is an 

energy minimum at ~700 - 1000 m in the Gulf of Mexico due to the sill depth of the Florida 

Straits. 
27

Figure 8. Power spectra at mooring M3. Panels A and B give power spectral 

density of detided, gap-filled u and v-velocity respectively at 6 

depths at mooring M3 from deployment 1. Panels C and D give 

power spectral density of u and v-velocity respectively at 6 depths 

at mooring M3 from deployment 2. 
28

4.4 Coherency Spectra 

4.4.1 Current – Wind Coherence 

Coherency, coherence of spectral estimates of independent records, was estimated for all 

combinations of u and v wind velocity and u and v current velocity at all ADCP depths with 

gapless time-series. In general, no statistical coherency of currents with wind was observed, 

except for incidental coherency near the inertial frequency. The coherency at this frequency is 

associated with random phase and are not seen deeper than the shallowest two or three velocity 

time-series for each mooring. The coherency near the inertial frequency was present at all 

moorings from data collected during deployment 2. This is likely related to the occurrences of 

Hurricanes Katrina and Rita, which caused high amplitude inertial currents in the study region 

for weeks after their passage through the Gulf. 

At mooring M1, during deployment 1, there is a weak low frequency correlation between current 

and wind. The coherency between north-south current velocity and north-south wind velocity 

shows a significant peak at ~ 20 - 50 day period. The coherency penetrates downward into the 

water column to 300 m with constant phase. Coherency, phase, admittance, and power spectra 

for the wind and M1 current north-south velocity records at 100 m during deployment 1 are 

given in Figure 9. Note that there is no diurnal peak in the wind data. 

4.4.2 Vertical Current – Current Coherence 

The coherency spectrum was estimated for current velocity components at different depths, i.e., 

vertically relative to the uppermost time-series at each mooring and horizontally between 

velocity components at similar depths at different moorings. To increase statistical reliability, the 

coherency spectra were smoothed in the frequency domain over 9 points. Summary plots of 

significant vertical coherency and horizontal coherency are given in Figures A-8 – A-19 and 

Figures A-20 – A-25 respectively in Appendix A. Phase information is not included in these 

plots for figure clarity purposes, but is briefly addressed in the following text. Super-inertial 

coherencies are mostly noisy signals, evidenced by their random phase. Significant coherent 

current patterns are demonstrated by solid vertical columns of dots penetrating deep into the 

water column at near and sub-inertial frequencies. These coherent structures are for the most part 

phase locked (sub-inertial motions) or exhibit propagating phase (near-inertial motions) with 

depth. It is also interesting to observe the shifting of inertial motions to neighboring frequencies 

throughout the water column. 

The vertical coherence at low frequencies (< 0.5 cpd) between velocity time-series at ~100 m 

and records to depths of ~500 m were mostly significant for every mooring deployment. 

Coherency was also observed at near-inertial frequencies. Coherency in the inertial band 

between near-surface velocity and records between 100 – 200 m diminished owing to the 

location of the pycnocline at these depths. Below this depth, inertial motions may be attributable 

to other forcing processes such as eddy features. Inertial oscillations at the surface and at depth 

therefore would not be expected to be coincident or phase locked. The exception to this is when a 

powerful hurricane is able to affect layers below the pycnocline. 
29

Figure 9. (Clockwise from top left) Coherence, admittance, power, and 

phase spectra between current and wind v-velocity components 

at 100 m at mooring M1 during deployment 1. Magenta 

asterisks in the phase spectrum indicate significant coherency 

at the corresponding frequency. 

At mooring M1, deployment 1, there is significant low frequency coherency between current 

velocity at 100 and 428 m depth at periods above five to six days as evidenced by a comparison 

of the individual time series (Figure 10). The coherency spectrum (Figure 11, upper left) further 

indicates significant coherency at the low frequencies (<0.2 cpd). The coherency phase spectrum 

(Figure 11, lower left) shows the phase between the low frequency components being close to 

zero indicating in-phase oscillations. The admittance spectrum (Figure 11, upper right) shows the 

gain between the spectral components of the two series and indicates that the variance in the 428 

m record is about 10% of that of the record at 100 m. The admittance at super-inertial 

frequencies is close to one, indicating nearly equal variances. 

At mooring M2, deployment 1, significant coherency is distributed similar to that seen at 

mooring M1. In the upper layer, low frequency coherency is seen at periods longer than about 

eight days and at near inertial peaks. However, this coherency extends deeper than at mooring 

M1. For example, north-south velocity is coherent with the surface at depths reaching 1244 m 

and east-west velocity is coherent with surface east-west velocity down to 750 m. For the second 

deployment, north-south velocity at mooring M2 is coherent throughout the upper water column 

(to about 500 m depth) at low frequencies with zero phase lag, as seen in Figure 12. This is not 

the case for the east-west velocity component, as it is only correlated at the lowest frequency 
30

estimate (~40 day period). The near-inertial correlation in both velocity components between the 

surface and at depth diminished around 120 m at mooring M2 during deployment 2. 

Vertical coherency at mooring M3 during deployment 1 presents a similar picture to moorings 

M1 and M2, with significant zero lag low frequency correlation throughout the upper water 

column (to ~500 m) for east-west velocity component, but only to 350 m for the north-south 

velocity component. Data at mooring M3 from deployment 2 are only significantly correlated to 

300 m for the east-west velocity component and 100 m for the north-south velocity component. 

Figure 10. Detided, gap-filled, gridded u-velocity time-series at mooring 

M1 during deployment 1 at 100 m and 428 m. Strong low 

frequency in phase coherency indicates significant 

correlations between currents at these two depths. 
31

Figure 11. (Clockwise from top left) Coherence, admittance, power, and 

phase spectra of east-west (u) velocity components at 100 m 

and 428 m at mooring 1 during deployment 1. Magenta 

asterisks in the phase spectrum indicate significant coherency 

and phase at the corresponding frequency. 
32

Figure 12. (Clockwise from top left) Coherence, admittance, power, and 

phase spectra of north-south (v) velocity components at 70 m 

and 494 m at mooring M2 during deployment 2. Magenta 

asterisks in the phase spectrum indicate significant coherency 

and phase at the corresponding frequency. 

4.4.3 Horizontal Current – Current Coherence 

Estimates of the coherency spectra for horizontal separations were calculated between moorings 

for all velocity component combinations at the same depth. East-west velocity at moorings M1 

and M2 were coherent at the lowest frequency band (~50 day period) and with zero phase lag. 

Near the inertial frequency in the upper water column, coherency was found at 750 m, 1244 m, 

and 1492 m. The phase of the correlation at the near inertial peak is variable with depth. The 

east-west velocity component at mooring M1 and north-south velocity component at mooring 

M2 are also coherent at low frequencies, but with phase difference of about 1 radian (~90°) at the 

lowest frequency, which indicates that M1 velocity leads M2 velocity. Coherency between M1 vvelocity and M2 u-velocity, as well as coherency between v-velocity at both moorings indicate 

coherency at low frequency with phase of ~ -1.0 radian, which means that M2 leads M1. Deeper 

current meter records, except for the records at 1995 m, are only significantly correlated between 

north-south velocity components at both moorings in the inertial band and at low frequencies (> 

10 day period), as seen in Figure 13. This may be an indication of topographic steering along the 

bathymetry. 
33

Figure 13. (Clockwise from top left) Coherence, admittance, power, 

and phase spectra between v-velocity components at 749 m 

at mooring M1 and mooring M2 during deployment 1. 

Magenta asterisks in the phase spectrum indicate significant 

coherency at the corresponding frequency. 

Mooring M1 and mooring M3 east-west velocities are coherent at near-inertial frequencies at 

every depth in the upper layers. M1 u-velocity and M3 v-velocity are correlated at the 

fundamental frequency at a phase of ~2 radians (180°) throughout the water column and near 

inertial peaks were present down to 998 m. North-south velocity at M1 and M3 were correlated 

at low frequencies down to 998 m with zero phase difference. Only near-inertial correlation was 

present between M1 v-velocity and M3 u-velocity. 

East-west velocity at moorings M2 and M3 illustrate very little significant coherency beyond 

some intermittent near-inertial correlations in the upper water column. However, the east-west 

velocity was coherent between moorings M2 and M3 in all current meter records in the deep 

ocean at periods of about 20 days (Figures 14 and 15). 
34

4.5 Vertical Structure of Low-frequency Variability 

4.5.1 Empirical Orthogonal Function (EOF) Analysis 

Empirical orthogonal function (EOF) analysis, also known as principal component analysis is an 

accepted tool to quantify patterns of variability in large sets of time-series data that are of 

sufficient spatial distribution (Emery and Thomson 2001; Preisendorfer 1988). We employed an 

EOF analysis to the EGOM current meter data in a manner consistent with previous studies in 

the Gulf of Mexico (Nowlin et al. 2001). In those previous studies, mooring locations that had at 

least 5 depth levels distributed in a manner consistent with previous studies in the Gulf of 

Mexico (Nowlin et al. 2001). In those previous studies, mooring locations that had at least 5 

depth levels distributed throughout the water column were chosen for analysis. At the time, only 

one mooring contained high vertical resolution from moored current profilers that were publicly 

available. EOF analysis was also performed on current output from a three-dimensional general 

circulation model of the full Gulf of Mexico basin (Kantha et al. 2005). The general conclusion 

of the previous studies showed consistent vertical modal structure at several locations across the 

northern slopes of the Gulf of Mexico. The structure was consistent for course and fine vertically 

resolved current observations. 

Figure 14. Detided, gap-filled, gridded east-west velocity time-series 

at mooring M2 and mooring M3 during deployment 1 at 

1,995 m and 2,699 m respectively. 
35

Figure 15. (Clockwise from top left) Coherence, admittance, power, and 

phase spectra between u-velocity components at mooring M2 

and mooring M3 during deployment 1 at 1,995 m and 2,699 m 

respectively. Magenta asterisks in the phase spectrum indicate 

significant coherency at the corresponding frequency. 

Nowlin et al. (2001) found that the first mode, Mode 1, defined as the mode with the greatest 

percentage of variance, has a surface maximum that decreased exponentially with depth. Mode 2, 

containing the second largest percentage of variance, is bottom intensified with a zero-crossing 

or minimum in the upper 500 meters and barotropic (nearly constant) at depth. The interpretation 

of these previous results concluded that the dynamics of the low-frequency variability of the Gulf 

of Mexico can be interpreted as a two-layer system; the dynamics of the upper layer associated 

with the exponentially decaying with depth motions of the Loop Current and Loop Current 

eddies, and the depth defining the transition to the lower layer being coincident with the sill 

depth of the Florida Straits. The bottom intensification for this analysis was attributed to the 

influence of the sloping topography on available normal dynamic modes estimated from stability 

theory (Charney and Flierl 1981). 

It is important to recall, however, that EOF modes are purely statistical constructs and in 

themselves do not represent physical processes. Therefore, the decomposition of statistically 

derived EOF modes are typically regressed onto dynamic modes to refine their interpretation and 

provide physical basis. 
36

The vertical EOF decomposition of east-west and north-south velocity component data was 

performed at each mooring, for each deployment, using data at approximately 12 depth levels 

that were distributed though out the water column. Due to computational considerations of 

computer memory and computing time, data from each gap-filled single point current meter and 

five depth levels of the ADCP data were used in the calculation. All current data were 40-hr lowpassed filtered to remove tidal, inertial, and other high frequency motions. 

Figure 16 (EOF of M3 u and v-velocity during deployment 1) and the sequence of plots shown in 

Figures A-26 – A-30 in Appendix A shows the results of the EOF analyses. These plots affirm 

that the horizontal current structure in this region of the Gulf resembles a 2-layer system. The 

eddy field causes intensification of the surface currents, which exponentially decay in magnitude 

with depth to ~ 800 m. This structure is observed in the Mode 1 amplitudes, which contain the 

largest percentage of variance (~ 80 - 95 %). This mode shows maximum amplitudes at the 

surface that decrease with depth to nearly zero below 1000 m. The dynamic effect of eddies are 

rarely seen below 800 m; the sill depth of the Florida Straits. 

The second mode, Mode 2, explains the second largest percentage of variance. In general, the 

amplitude crosses zero near 200 meters depth and is nearly constant or gradually increasing with 

increasing depth. During deployment 1, the amplitudes of Mode 2 at mooring M1 shows a midwater maximum at 300 m and barotropic amplitudes below1000 m. The structure of this mode, 

however, is more similar to the vertical structure found in Mode 3 at moorings M2 and M3. 

Furthermore, the percentage of variance in the second and third modes increases from M1 to M3, 

indicating more variance in the higher order modes closer to the Loop Current. During the 

second deployment, Mode 2 at mooring M1 again resembles higher order modes at M2 and M3. 

The vertical structure of Mode 3 is more complex with two zero crossings typically in the upper 

1000 m and relatively constant in water depths below 1000. The amount of variance contained in 

this mode is a small fraction of the current variance (< 4 %). A summary table of the percentage 

of variance explained by the first three modes for u and v-velocity EOFs at each mooring is 

presented in Table 2. 
37

Figure 16. Vertical EOFs of east-west and north-south current velocity at 

mooring M3 during deployment 1. Top three panels: Principal 

component (PC) time-series of first three empirical modes. Bottom 

panel: Amplitudes of empirical modes corresponding to PC timeseries. 
38

Table 2 

Percentage of Variance in EOF Modes 1, 2, and 3 for Moorings M1, M2, and M3 for Horizontal 

Velocity Components during Deployment 1 and Deployment 2 

(Deployment 2 is shown in parentheses) 

Component Mode 1 Mode 2 Mode 3 

 

M1 

u-component 96.51 (88.12) 2.33 (6.38) 0.47 (2.62) 

v-component 95.43 (88.37) 2.80 (6.44) 0.72 (2.21) 

 

M2 

u-component 93.53 (79.48) 3.24 (12.77) 1.81 (5.82) 

v-component 95.58 (96.06) 2.52 (1.98) 0.86 (1.24) 

 

M3 

u-component 84.67 (88.47) 10.36 (6.83) 3.23 (3.18) 

v-component 87.66 (85.96) 8.09 (11.49) 2.85 (1.43) 

 

4.5.2 Dynamical Mode Analysis 

The estimation of dynamic modes is motivated by the desire to identify horizontally propagating 

wave solutions under the Boussinesq approximation for a rotating fluid (LeBlond and Mysak 

1978). The method solves an eigenvalue equation for a prescribed stability profile, N(z). The 

resulting vertical eigenfunctions are the allowable structures for that stability. “The 

eigenfunctions are real, orthogonal with real eigenvalues. The gravest mode is identified as the 

barotropic mode, and the modes n=1, 2, 3, ... are the sequence of baroclinic modes (LeBlond and 

Mysak 1978)”. The calculations that follow presume a flat ocean bottom. A sloping bottom 

yields a bottom trapped gravest (barotropic) mode 

Stability profiles were derived from temperature and salinity (CTD) data from hydrographic data 

collected during the EGOM study. CTD data at mooring locations on HC1, HC2, and HC3 were 

used to calculate vertical buoyancy modes that represent the mean horizontal current structure at 

the three mooring locations. Note that the modes were calculated using a discretized version of 

the Taylor-Goldstein equation for a linear, flat-bottomed ocean (Klinck et al. 2004). Temporal 

and spatial means were not removed from the CTD data prior to mode calculation. Although the 

theoretical modes are based on a resting ocean, neutral modes of an ocean with a surfaceintensified mean flow are important for studies of baroclinic instability. The results should vary 

significantly when mean flow is included in the model, as the modes in this case become 

dependent on lateral scales of motion (Gill et al. 1974, Wunsch 1997). The density field in the 

upper 500 m is vital to the determination of mode structure (Wunsch 1997). Because 

hydrographic data was only available from three EGOM cruises at two different times of year in 
39

a region where the Loop Current is constantly altering the density field, hydrographic cruise data 

evaluated in the DW Study (Nowlin et al. 2001) were also analyzed for comparison, and yielded 

similar results. 

Vertical profiles of Brunt-Väisälä frequency (N2

), shown in Figure 17, were found to be 

maximum between 100 - 200 m during the winter and near surface (< 20 m depth) during the 

summer. Dynamic modes calculated from CTD casts at (or closest to) the mooring sites during 

deployment, maintenance, and recovery cruises were used to create an average set of modes to fit 

to the velocity data collected during mooring deployment. Some features of the N2

 profile might 

be smeared out because of averaging dynamic modes. 

Figure 18 in this section (normalized dynamic modes at M3 from profiles in January 2005 and 

August 2005) and Figures A-31 – A-35 in Appendix A give the first three normalized dynamic 

modes constructed from the averaged casts at each mooring. The barotropic mode is simply 

equal to one throughout the water column. First and second baroclinic modes have similar shapes 

at each mooring. The first mode crosses zero around 600 m; the second mode crosses zero twice, 

around 200 and 900 m. Below 1200 m all modes are barotropic, i.e., nearly constant with 

increasing depth. As can be seen, the general shape of these modes is the same for each mooring 

deployment. The relative amplitudes are nearly identical; the principal difference between casts 

is the depth of zero-crossing of the modes. Please note that the normalized modes in these figures 

are not the dynamic modes fit to the observed velocity. The baroclinic modes have much smaller 

magnitude than the barotropic mode, and normalization was performed to put the barotropic and 

baroclinic components on the same scale, while still maintaining the character of the curves. 

The temporal variation of the barotropic and first two baroclinic modes were estimated using a 

least squares minimization that fits the calculated set of vertical modes to synoptic vertical 

profiles of the moored ADCP and single-point current meter data. Three modes were used in the 

least squares fit. The modes were not normalized prior to fit. Figures 19 and 20 show a threepanel representation of the results of the least squares fit of the first three dynamic modes to the 

current profiles at M3. The sequence of Figures A-36 – A-45 in Appendix A show the results of 

the least squares fit of the dynamic modes to velocity components at the other moorings. Each 

tri-plot corresponds to a single deployment, mooring, and velocity component. The top panel 

represents the spatial (vertical) correlation of the fit with the observed profile. Correlation of one 

indicates a perfect fit with no residual error, less than one indicates higher order (n > 2) modal 

variability. The bottom panel shows the time-series of the first three dynamic mode amplitudes 

resulting from the fitting procedure. The right panel shows the time correlation between the 

observed and modeled time series at a particular depth. This is an indication of the vertical 

structure of the goodness of fit. Generally, the barotropic time-series amplitudes are significantly 

smaller than the baroclinic amplitudes at all moorings, both deployments, and both velocity 

components. As found previously in the EOF analysis, most of the variance in the observed 

velocity data can be explained by a surface trapped mode that decays exponentially with depth. 

Therefore, it is expected that the temporal amplitudes of the first baroclinic mode be large, 

indicating the presence of surface trapped, i.e., eddy related, motions. 

The amplitudes of the second baroclinic mode are more variable, i.e., possess higher frequency 

motions than the first baroclinic mode. During the first deployment, the east-west velocity mode 
40

amplitudes are mostly positive, i.e., eastward, because of the location of the mooring relative to 

the northeastern edge of the Loop Current. The high correlation between mode 1 amplitudes and 

CTD pressure records, which fluctuate due to mooring draw down, are also validation of the first 

baroclinic mode amplitudes as indicators of eddy activity in the eastern Gulf. 

Figure 17. Vertical profiles of Brunt-Väisälä frequency at or 

nearest to each mooring site. Casts from three EGOM 

hydrographic cruises in January 2005, August 2005, 

and January 2006. 
41

Figure 18. Normalized barotropic and first two baroclinic modes 

calculated with averaged casts at M3 from cruises in January 

and August 2005. 

Spatial correlation at every sample time between observed and modeled velocity from the least 

squares fit of dynamic modes shows that when the first baroclinic mode amplitudes are close to 

zero, the correlation is poor. The low correlation could possibly indicate during times of relative 

quiescence in the wake of eddies, that higher-order modes characterize the vertical structure. 

Correlations in the time domain were determined between record length velocity data and 

modeled velocity at every current meter depth and five ADCP layer depths. The model fits well 

above 500 m, and below 500 m, the correlation decreases. In some cases, e.g., the fit to velocity 

components collected during the second deployment, the correlation is minimum between 800 – 

1000 m, and may be associated with the kinetic energy minimum at this level in the Gulf. 
42

Figure 19. Modal fit to mooring M3 u-velocity data. (Top) Spatial correlation between 

observed u-velocity at mooring M3 from deployment 1 and the modeled u-velocity 

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of 

the first three theoretical modes based on the least squares regression. (Right) 

Temporal correlation between the modeled and observed velocity. 
43

Figure 20. Modal fit to mooring M3 v-velocity data. (Top) Spatial correlation between 

observed v-velocity at mooring M3 from deployment 1 and the modeled v-velocity 

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of 

the first three theoretical modes based on the least squares regression. (Right) 

Temporal correlation between the modeled and observed velocity. 

4.5.3 Model Utility Tests and Summary Statistics for the Dynamic Mode Fit 

Two types of model utility tests were performed on the modal fit to the observed currents in the 

space domain. The first test utilizes the F statistic to assess whether a useful relationship between 

the observed data and any of the modal predictors exists. The null hypothesis, that the 

coefficients of all modes included in the model equal zero, is rejected if the test statistic is greater 

than or equal to the F critical value found in an F distribution table. The test statistic is a function 

of degrees of freedom, the number of modes included in the fit, and spatial correlation, and the F 

critical value is determined by the degrees of freedom, the number of modes included in the fit, 

and the significance level, . For these data, the significance level of  = 0.05 was chosen. 
44

The second statistical test is an inference for a single mode coefficient, which determines if a 

certain mode needs to be included in the fit. This test is a two-tailed test using the t -statistic to 

reject or accept the null hypothesis that the targeted mode coefficient is equal to zero, i.e., it is 

not necessary in the multiple regression. The null hypothesis is rejected if the test statistic, 

calculated from the amplitude of the mode, the error sum of squares, and the error degrees of 

freedom, falls outside of the rejection region determined by the critical values, which are given 

in a t table and determined by the degrees of freedom and the significance level . This test 

indicates that the first baroclinic mode is necessary to explain the current structure during most 

of the deployment and surprisingly, the second baroclinic mode is useful to the model for a 

significant portion of the deployment. 

These calculations were performed at each time step during both deployments, providing a timeseries of test statistics. Figures A-46 – A-48 in Appendix A give time series of the model utility 

test statistics. The top panel gives the F-test statistic to evaluate the necessity of all of the modes 

included in the model. At each time step, when the F test statistic (blue line) is greater than the 

critical value (red line), at least one of the first two baroclinic modes are helpful to the fit of the 

statistical model to the data. The percentage of time these higher modes are useful to the model 

during the two deployments are summarized in Tables B-1 and B-2 in Appendix B (the fourth 

column labeled F-test). The bottom two panels illustrate t-test statistics to specifically test the 

necessity of the first baroclinic mode (middle panel) a second baroclinic mode (bottom panel) to 

the model. When the test statistic (blue line) is between the critical values (red lines), the mode is 

not useful to the model. 

The goodness of fit test confirms that the barotropic and at least one of the baroclinic modes are 

necessary to the regression approximately 80 - 100 % of the time. Although the second 

baroclinic mode is not necessary to the model as frequently as the first baroclinic mode, it is a 

useful predictor of the observed currents for a large portion of the record (columns 5 and 6 

labeled t-test in Tables B-1 and B-2 in Appendix B). 

Tables B-1 and B-2 in Appendix B summarize the least squares regression of the dynamic modes 

onto the moored velocity data. Notice that the mode amplitude means and standard deviations 

are much larger for the baroclinic modes over the barotropic mode, given their relative 

amplitudes. When the normalized modes are fit to the data instead of the raw modes calculated 

via the discretized Taylor-Goldstein equation (Klink et al. 2004), the mode amplitudes change in 

time such that the barotropic mode exhibits higher amplitudes on the same order as the first 

baroclinic mode. Also note that in general, the standard deviation of mode amplitudes calculated 

at mooring M3 are larger, likely due to the higher variance in the eddy field near this mooring. 

4.5.4 EOF and Dynamic Mode Comparison 

To verify the physical meaning of the surface-trapped first empirical mode, EOF mode 1 was 

compared to the temporal amplitudes of the first baroclinic mode. This comparison for velocity 

data at moorings M1 and M3 is shown in Figures 21 and 22 respectively. Clearly, the modes are 

coherent, especially at low frequencies. EOF modes are centered around zero because temporal 

means were removed prior to the calculation. This procedure was not followed for the dynamic 

mode calculation, hence the time series is shifted in the positive direction. 
45

Figure 21. Comparison of EOF mode 1 and the temporal amplitudes of the first baroclinic 

mode for M1 v-velocity during deployment 2. 

Figure 22. Comparison of EOF mode 1 and the temporal amplitudes of the first baroclinic 

mode for M3 u-velocity during deployment 1. 

4.5.5 Temporal Correlation of First Baroclinic Mode and Sea Surface Height Gradient 

This section investigates potential causes of the observed current structure. Since geostrophic 

current velocity should be perpendicular to the sea surface height gradient we expect a 

relationship between sea surface height gradient and the first baroclinic mode. We calculated 

time series of sea surface height gradient in the north-south and east-west directions in the 

vicinity of each mooring (sea surface height difference between points 30 km north and south or 

east and west of the moorings) and correlated that with time series of the first baroclinic mode 

for the perpendicularly oriented velocity component. In general, significantly large correlation 

was found between the orthogonal SSH gradient and the first baroclinic mode amplitudes, i.e., 
46

east-west velocity mode 1 amplitudes are compared to sea surface height gradient in the northsouth direction, and north-south velocity mode 1 amplitudes are compared to sea surface height 

gradient in the east-west direction (Figure 23 in this section for mode fit to M3 u-velocity during 

deployment 1 and odd numbered Figures A-49 – A-69 in Appendix A). 

Table 3 summarizes the zero lag correlations between the first baroclinic mode and the sea 

surface height gradient. Significant correlations, based on the effective degrees of freedom 

between the two time-series, are bolded, and are not as common as expected. However, the 

coherency between the two variables indicate in phase coherence at low frequencies despite the 

insignificant correlation. The coherency spectra show that the coherency is significant only at 

low frequencies, thus reinforcing that mode 1 amplitudes are related to the pressure gradient, 

indicating geostrophic currents (Figure 24 in this section for mode fit to M3 u-velocity during 

deployment 1 and even numbered Figures A-50 – A-70 in Appendix A). 

Figure 23. Temporal amplitudes of the first baroclinic mode for the east-west 

velocity component at mooring M3 during deployment 1 (blue) and 

the SSH gradient in the north-south direction (green). 
47

Table 3 

East-west and North-south Velocity First Baroclinic Mode Amplitude Correlations to the 

Orthogonal Sea Surface Height Gradient at Moorings M1, M2, and M3 for Deployments 1 and 2

(Bold values indicate significant zero lag correlation at the 90% confidence level) 

Mooring Deployment 1 Deployment 2 

 East-West Velocity North-South Velocity East-West Velocity North-South Velocity 

 

M1 0.56 0.28 0.33 0.43 

M2 0.55 0.63 0.66 0.58 

M3 0.76 0.59 0.80 0.70 

 

Figure 24. Coherency (top) and phase (bottom) spectra of the temporal amplitudes 

of the first baroclinic mode for the east-west velocity component at 

mooring M3 during deployment 1 and the SSH gradient in the northsouth direction. 
48

4.5.6 Spectra and Temporal Scales of Modes 

Power spectra and autocorrelation functions are generated for the dynamic mode time-series 

using FFT methods (as discussed previously). The results from these analyses are consistent 

between data from each mooring deployment. Spectra of modal amplitudes for the mode fit to 

mooring M3 velocity data during deployment 1 are presented in Figure 25. Spectra for mode fits 

to u and v-velocity exemplify a typical energy and enstrophy-conserving velocity spectrum, with 

an energy cascade in the red direction, i.e., from high to low frequencies. The barotropic 

amplitudes exhibit less energy than the first baroclinic modes at low frequencies. Also recall that 

variance at frequencies greater than 1 cpd is small because 40-hour low-passed filtered versions 

of the data were used in these calculations. The second baroclinic mode spectra are nearly white 

(constant) at frequencies less than 1 cpd. 

Figure 25. Power spectra of the time-series of amplitudes of the first three theoretical 

modes at mooring M3 during deployment 1 (top: barotropic mode; middle: 

first baroclinic mode; bottom: second baroclinic mode). Spectra for fits to 

the u-component and v-component are shown in the left and right columns 

respectively. 
49

A scales analysis is performed by estimating the first zero-crossing of the normalized 

autocovariance function (NACF) derived for each modal time-series. This calculation quantifies 

the temporal lag in which the data becomes decorrelated from previous observations. Results 

showing the NACF for the fit to the velocity data from mooring M3 during deployment 1 are 

given in Figure 26. The first baroclinic mode amplitudes have the longest time scales (13-39 

days), and the second baroclinic mode amplitudes have the shortest time scales (6-7 days). For 

most of the moored data, the barotropic and first baroclinic mode time series display eddy time 

scales (~ 25 days), which is expected because of the active eddy regime in the eastern Gulf. Time 

scales for the three dynamic modes by velocity component, mooring, and deployment are given 

in Tables B-3 and B-4 in Appendix B. 

Figure 26. Normalized autocovariance functions of mode amplitudes from the mode fit to 

east-west and north-south velocity component data at mooring M3 during 

deployment 1. 
50

4.5.7 Dynamic Mode Kinetic Energy and Modal Coupling 

Record length mean kinetic energy, T(zm ), at a fixed level zm was calculated at each current 

meter and ADCP bin depth used in the dynamic mode analysis by: 

T(zm )  1

2L { (Dun

n 0

N

 t1

L

 (t)n (zm ))2  (Dvn (t)n (zm ))2

n 0

N

 } , 

where L is the length of the time series of mode amplitudes, N is the number of modes used in 

the calculation (in this experiment N  2), Dun (t) is the amplitude at time t of the nth mode fit 

to u-velocity data and Dvn (t) is the amplitude at time t of the nth mode fit to v-velocity data. 

n (zm ) is the n

th mode value at depth zm (Wunsch 1997). Similarly, the kinetic energy in mode 

k at a fixed depth level zm , Tk (zm ), is given by: 

Tk (zm )  1

2L {

t1

L

 (Duk (t)k (zm ))2  (Dvk (t)k (zm ))2

} , 

The ratio Tk (zm )

T(zm )

 is presented as percentages of kinetic energy in the barotropic, first 

baroclinic, and second baroclinic modes (record length means) at M3 during deployment 1 at 

every depth level in Table 4 (Figure 27) in this section, and for the other mooring deployment in 

Tables B-5 – B-9 with summary figures in Appendix B. 

Table 4 

Percentages of Kinetic Energy in the Barotropic (BT), First Baroclinic (1BC), and Second 

Baroclinic (2BC) Modes at Each Depth Level at Mooring M3 during Deployment 1 

Depth %TBT (zm) %T1BC (zm) %T2BC (zm)

 

90 m 5.82 93.70 0.49 

170 m 13.72 84.38 1.90 

258 m 24.75 68.03 7.22 

346 m 34.81 53.83 11.36 

458 m 51.58 34.06 14.37 

750 m 93.37 1.51 5.12 

998 m 70.07 29.86 0.07 

1245 m 56.69 42.03 1.28 

1492 m 53.33 44.86 1.80 

1996 m 52.17 45.82 2.01 

2499 m 52.07 45.90 2.03 

2699 m 52.07 45.90 2.03 

 

(7) 

(8) 
51

Figure 27. Kinetic energy percentages of the dynamic modes at each 

depth level in Table 4. 

The energy distribution is similar for all of the mooring deployments. From these tables and 

figures it is clear that the second baroclinic mode makes a small contribution to the water column 

kinetic energy, except for at the base of the upper layer around 500 m. For deployment 2 data, 

the second baroclinic mode exhibits more kinetic energy closer to the Loop Current from 

mooring M1, to mooring M3, but for deployment 1 data, the distribution of kinetic energy in the 

second baroclinic mode is about the same at each mooring. 

The other interesting pattern to observe is the energy exchange between the barotropic mode and 

the first baroclinic mode above 1500 m. Near the surface, most of the kinetic energy is in the first 

baroclinic mode, and there is only slightly more energy in the barotropic mode than the second 

baroclinic mode. The kinetic energy in the first baroclinic mode decreases as the energy in the 
52

barotropic mode and second baroclinic mode increases. The second baroclinic mode reaches 

maximum kinetic energy at ~500 m and then decreases to near zero around 1000 m. The 

barotropic mode continues to grow and the first baroclinic mode continues to wane to ~750 m 

were they reach their respective maximum and minimum. The barotropic and first baroclinic 

mode contribute approximately the same amount of kinetic energy below 1500 m. This energy 

division is a reflection of the importance of the first baroclinic mode in the upper water column 

and the increasing importance of the barotropic mode with depth. 

Mode correlations were investigated using a simple coefficient of determination and a 

significance test based on the statistical t-distribution. Correlations between mode amplitudes 

from the mode fit to data from the same mooring deployment for the same velocity component 

are presented in Tables B-10 – B-15 in Appendix B. Significant correlations are bolded. 

Correlations between mode amplitudes of different velocity components yielded no significant 

correlation, and therefore are not included in the tables. 

The significant correlation between the barotropic and first baroclinic mode is nearly always 

present for all mooring deployments, especially for the u-velocity component. Interestingly, all 

modes are correlated for mooring M2 v-velocity during deployment 2, which is unusual since no 

modes are correlated for the u-velocity component at M2 or the v-velocity components at 

moorings M1 and M3 from the same deployment. This might be an effect of the relative position 

of mooring M2 to the frontal cyclone during deployment 2. Mooring M2 was usually in the 

center of the frontal cyclone, as opposed to the position of the other moorings predominantly on 

the edge of the cyclone.

4.5.8 Modal Decomposition of EGOM Data Versus Historical Data 

The dynamic modes used in the previous analyses were calculated from Brunt-Väisälä frequency 

profiles at or closest to the mooring measured before and after each deployment. The use of an 

average of two profiles to construct dynamic modes to fit the velocity data collected throughout 

deployment is somewhat unrealistic, given that in the eastern Gulf of Mexico the density 

(temperature and salinity), and hence the dynamic modes, change shape rapidly in the eddy field 

(this usually affects the zero crossings of the prevalent modes). To assure the results previously 

discussed are sound, the same analyses were carried out using historical CTD data. In the DW 

Report, historical data collected since the early 1900s were reanalyzed. All good quality 

historical data in the eastern Gulf (east of 89W) was used to create an average Brunt-Väisälä 

frequency profile for the eastern Gulf of Mexico. Dynamic modes calculated from this profile 

were fitted to EGOM velocity data using the methods previously discussed and yielded mode 

amplitudes comparable to those found from the fit of modes assembled from the sparse EGOM 

CTD data. Some examples from moorings M1 and M3 are illustrated in Figures 28 and 29. 

The amplitudes are coherent, probably because the fluctuation in mode shape due to the density 

field happen on smaller scales than the vertical spacing of data used in the mode calculation or 

possibly shallower than the shallowest moored time series. However, it is necessary to space the 

data like this because, statistically, to use all of the ADCP data would weight the abundant (~50) 

measurements in the surface ocean too much over the fewer (~7) current meter records in the 

deep ocean, thereby skewing the EOF and dynamic modes amplitudes. 
53

Figure 28. Temporal amplitudes of the first baroclinic mode (top) and second 

baroclinic mode (bottom) for M1 v-velocity during deployment 2 

calculated using EGOM CTD cast data (red) and historical CTD data 

analyzed in the MMS Deepwater Physical Oceanography Reanalysis and 

Synthesis of Historical Data project (blue). 
54

Figure 29. Temporal amplitudes of the first baroclinic mode (top) and second 

baroclinic mode (bottom) for M3 u-velocity during deployment 1 

calculated using EGOM CTD cast data (red) and historical CTD data 

analyzed in the MMS Deepwater Physical Oceanography Reanalysis and 

Synthesis of Historical Data project (blue). 

4.5.9 Dynamic Mode Analysis of Hydrographic Data and Vertical Profiles of Horizontal 

Velocity 

Stability profiles were derived from temperature and salinity (CTD) profiles from hydrographic 

data collected during the EGOM study (K. Cole, M.S. thesis, TAMU). Figure 30 gives the first 

three normalized dynamic modes constructed from the averaged casts at mooring M3 from 

profiles in January and August 2005. Note: the modes are most variable in the upper 1000 m, and 

are mostly constant with depth below 1000 m. 

The temporal variation of the barotropic and first two baroclinic modes were estimated using a 

least squares minimization that fits the calculated set of vertical modes to synoptic vertical 

profiles of the moored ADCP and single-point current meter data. The results of this 

computation for mooring M3 (deployment 2) are shown in Figure 31. The 2nd baroclinic mode 

(light blue) is seen to have large amplitude, i.e., comparable in magnitude to the first mode 

(green), at several times through out the record (bottom left panel). 
55

Figure 30. Normalized barotropic (BT) and first two 

baroclinic (BC) modes calculated with averaged 

casts at M3 from cruises in January and August 

2005. 

The top panel in Figure 31 shows the r-squared of the spatial correlation of the first three 

dynamical modes fit with the u component of current velocity. The estimates of spatial 

correlation show that the r-squared is largest, i.e., closest to 1, when the first baroclinic mode 

amplitude is large. However, there are often times when the r-squared is low, at times falling less 

than 0.1. These low values typically occur when the first baroclinic amplitude is close to zero. 

The poor correlation indicates that higher order modes (mode number greater than 2) are 

necessary to account for the observed vertical current structure. The right panel of Figure 31 

shows the record-length temporal correlation between the observed current and the fitted current 

at the specified depth. Note the correlation is poorest at 750 m. 

The amount of current velocity variance accounted in each mode in each depth layer is shown in 

Figure 32. The variances are based on record length variances. During this deployment, it is clear 

that up to almost 30% of the record can be attributed to second baroclinic mode (BC2). Other 

analysis shows that based on the EGOM Study results, the amount of variance in higher order 

modes increases with proximity to the LC. 

The statistical relevance of the modes is indicated in Table 5. Here, a summary of the dynamic 

mode decomposition of the EGOM data for east-west and north south velocity components 

during deployment 2 is given (see, e.g., Figure 33). In the table, F-test (t-test) refers to the 

fraction of time when F > 95 % confidence level (t  95 % confidence level). Correlation (C) and 

percent root mean squared error (% ERROR) of the mode fit to the data are depth-averaged 
56

values. The results of the F test indicate the percentage of time that the barotropic mode is 

necessary for the modal fit. The t-test results for BC1 and BC2 indicate the percentage of time 

that those modes are necessary for the fit. Note that the percentage increases from M1 to M3. 

This indicates that second order motions are increasingly relevant as observations move closer to 

the Loop Current. 

For this reason, the second order baroclinic mode is necessary to describe the vertical structure of 

horizontal currents in the Gulf of Mexico and that this mode and likely higher modes are 

increasing important with proximity to the Loop Current. The second baroclinic mode is 

necessary up to 80% of the time and can explain up to 30% of the current variability between 

250 and 750 m. 

Figure 31. (Top) Spatial correlation between observed u velocity at mooring M3 from 

deployment 1 and the modeled u velocity from CTD cast data on the EGOM 

hydrographic cruises. (Bottom) Amplitudes of the first three theoretical modes 

based on the least squares regression. (Right) Temporal correlation between the 

modeled and observed velocity. 
57

Figure 32. Percentage of variance of time series record by depth attributed to 

barotropic (BT), first baroclinic (1BC), and second baroclinic (2BC) 

dynamic modes. Note: up to 30% of variability between 100-500 m depth 

can be attributed to BC2. Percentages based on second deployment of M3 

(closet to LC) during the East GOM Study (Source: K. Cole, TAMU). 

Table 5 

Summary of Dynamic Mode Decomposition Statistics for EGOM Deployment 2 

Velocity 

Component 

by Mooring 

D0

mean (std) 

D1

mean (std) 

D2

mean (std) F-test t-test BC1 

t-test 

BC2 C % ERROR 

 

M1 

u -5.70 (3.27) -59.64 (40.49) 17.34 (25.96) 94.45% 93.70% 57.92% 0.92 19.54% 

v 3.03 (3.07) 26.04 (37.09) -4.35 (22.64) 83.70% 82.85% 39.64% 0.92 19.74% 

M2 

u -1.53 (4.05) -18.38 (58.65) 35.47 (39.15) 94.90% 90.92% 67.97% 0.96 11.70% 

v 1.09 (7.47) 15.62 (74.46) 0.33 (47.85) 96.58% 96.06% 63.48% 0.97 8.76% 

M3 

u 4.83 (7.10) 87.50 (80.15) -38.68 (75.52) 98.94% 97.46% 78.92% 0.97 8.41% 

v 0.74 (7.05) 8.35 (72.60) -21.37 (85.14) 91.18% 83.82% 81.22% 0.98 4.72% 

 
58

Figure 33. Representative vertical profiles of north-south current velocity (blue) from M3 

mooring during deployment 2 with (top) fit of barotropic and first baroclinic 

mode (red) and (bottom) the same current velocity profile with first three 

theoretical modes (barotropic plus first and second baroclinic mode) 

superimposed. 
59

5 DISCUSSION AND CONCLUSIONS 

The importance of low-frequency motion to the circulation in the eastern Gulf of Mexico was 

addressed in this report. Low frequency currents observed by the EGOM array were decomposed 

into empirical and theoretical modes to observe the effects of the eddy field on horizontal current 

velocity. There was a strong similarity between dynamical and empirical modes. The high 

contribution of the first baroclinic mode relative to the other dynamic modes was observed and 

assessed. 

The passage of the northern lobe of the Loop Current and the developing anticyclone over the 

study area cause intensified surface velocities which amplify the first baroclinic mode, also 

called the eddy or surface-trapped mode. The barotropic and first baroclinic mode amplitudes 

exhibit low frequency variability, substantiating the first hypothesis stated in the introduction. 

First baroclinic mode amplitudes are coherent with moored CTD pressure and a scales analysis 

of the temporal amplitudes of the first baroclinic mode indicate eddy time scales of 10 – 40 days. 

Clearly, the first baroclinic mode amplitudes are influenced by the Loop Current and eddy field. 

For example, during deployment 1, the amplitudes of the u-velocity first baroclinic mode are 

mostly positive at mooring M3, indicating eastward flow. This is caused by the moorings 

position at the northern edge of the loop current and the growing eddy. 

The second baroclinic mode contributes a relatively large amount of vertical shear and promotes 

mixing in the upper ocean. For a given level of wave energy, if the modal distribution of energy 

is weighted towards the second baroclinic mode, low Richardson numbers and high shear 

variance occur, which in turn increases the probability of shear instabilities (MacKinnon and 

Gregg 2003). In this study, energy was found to be concentrated in lower modes, and the second 

baroclinic mode amplitudes showed higher frequency variability and were not significant to the 

regression model as often as the first baroclinic mode. However, the regression analysis shows 

second baroclinic mode amplitudes comparable to first baroclinic mode amplitudes at times, 

especially at mooring M3, indicating higher order dynamics that could be related to eddy 

shedding or frontal eddies present in the study region. 

Inoue (1985) found that some mooring locations in Drake Passage showed a higher contribution 

of the higher baroclinic modes (he hypothesized this was due to topographic effects in the 

southern part of the passage), but in the EGOM region, higher modes are not favored at any 

mooring site. Time scales of the modes in the EGOM study area do not monotonically increase 

or decease towards the loop current as hypothesized. For north-south velocity barotropic and first 

baroclinic modes, the time scales are fairly consistent between moorings (most within 10 days of 

each other). 

There is higher spatial correlation between modeled and observed horizontal velocity when mode 

one amplitudes are large. There also seems to be poor correlation between modeled and observed 

velocity in the time domain at 500 – 1000 m, where an energy minimum is present in the Gulf. 

The first baroclinic mode amplitudes and SSH gradient are coherent at low frequencies, but the 

correlation is not always significant at zero lag. 
60

In agreement with the second hypothesis, the first baroclinic mode amplitudes were affected by 

the surface intensification of the eddy field. Figure 34 shows sea surface height on March 25, 

2005 in the EGOM study region and in the entire Gulf. The arrows in the figure on the right 

represent velocity at 50 m (black arrows) and 250 m (pink arrows) depth at moorings M1, M2, 

and M3. The moorings appear to be in a cyclonic eddy in an area of weak vertical shear, which is 

reflected in the small first and second baroclinic mode amplitudes (Figures 19, 20, A-36, A-37, 

A-40, and A-41). Similarly, Figure 35 shows the sea surface height on June 11, 2005 in the Gulf 

of Mexico. The amplitudes of the u-velocity first baroclinic mode are large at this time at all of 

the moorings, especially at mooring M1, as it is positioned at the greatest gradient of sea surface 

height (Figures 19, A-36, and A-40). It is clear from these images that the position of the Loop 

Current and it’s eddies relative to the moorings is manifested in the temporal evolution of the 

first baroclinic mode. 

Changes in vorticity with depth are characterized by vertical shear and are vital to eddy 

shedding, but the EGOM study site is too far north of the Loop Current eddy shedding region 

and there are too few separation events in this dataset to adequately evaluate the impact of eddy 

shedding on the second baroclinic mode amplitudes. There is one interesting event that should be 

noted. Figure 36 shows sea surface height on August 9, 2005 in the Gulf of Mexico. The eddy in 

this figure in the north central Gulf reattaches to the Loop Current at the end of August just 

before separating a final time in September and traveling west. The second baroclinic mode at 

mooring M3 on this date is highly amplified (Figure 19), which could be a result of the shear 

related to instabilities tied to eddy separation. 

Figure 34. (Left) Sea-surface height (from R. Leben) in the Gulf of Mexico on March 25, 2005. 

(Right) Sea-surface height in the EGOM study region. Arrows represent velocity at 

50 m and 250 m depth at M1, M2, and M3. Contours are 5 cm apart. 
61

Figure 35. (Left) Sea-surface height (from R. Leben) in the Gulf of Mexico on June 11, 2005. 

(Right) Sea-surface height in the EGOM study region. Arrows represent velocity at 

50 m and 250 m depth at M1, M2, and M3. Contours are 5 cm apart. 

Figure 36. (Left) Sea-surface height (from R. Leben) in the Gulf of Mexico on August 9, 2005. 

(Right) Sea-surface height in the EGOM study region. Arrows represent velocity at 

50 m and 250 m depth at M1, M2, and M3. Contours are 5 cm apart. 
62

Contrary to the second hypothesis, the barotropic mode amplitudes were found to be small 

throughout deployment at all of the moorings. This is a surprising result, as previous studies have 

found the barotropic mode amplitudes along with the first baroclinic mode amplitudes to 

dominate in most deepwater regions. Wunsch (1997) concluded that most areas are dominated by 

a barotropic and first baroclinic component to flow, from a modal analysis of data from the north 

Atlantic, a latitude band in the north Pacific, and a few stations in the south Atlantic. This is 

likely simply a difference in the method of the applied statistics in the analysis. In this study, the 

temporal mean was not removed from the time-series data for fear of altering the barotropic 

mode amplitudes, and the dynamic modes were not normalized before they were fit to the 

moored velocity data through a multiple regression. Thus, the baroclinic modes were quite small 

relative to the barotropic mode, which was taken to be one throughout the water column (the 

barotropic mode can be thought of as the y-intercept in traditional regression analysis). This is 

not the same procedure followed by others, for which the barotropic mode was found to attain 

amplitudes almost as large as the first baroclinic mode’s. To compare these results to others, it 

must be understood that the mode amplitudes simply give half of the information, and only by 

multiplying the amplitudes by the mode values can useful quantities be obtained (as seen in 

section 3.5.7 with the kinetic energy calculation). 

This is not to say that trends cannot be analyzed by looking at the dynamic mode amplitudes. 

Corroborating the third hypothesis, the barotropic mode amplitudes and first baroclinic mode 

amplitudes were found to be correlated in almost every case, which suggests that the barotropic 

and first baroclinic modes follow the same driving mechanisms and ultimately net transport and 

current shear are coupled. The strong vertical shear in the mean currents could lead to baroclinic 

instability and eddy shedding. This is in agreement with the findings of McWilliams and Shen 

(1980), who determined that there were significant barotropic and first baroclinic modal 

covariances between both streamfunction and velocity fields. Furthermore, it is the combination 

of the first baroclinic and barotropic modes that gives the vertical structure for the first empirical 

mode (Inoue, 1985). Higher order modes were correlated in some cases in this analysis, but it 

was more variable than the barotropic – first baroclinic coupling. The results of the partition of 

kinetic energy amongst the dynamic modes presented in section 3.5.7 indicate that the barotropic 

mode contains more than (or approximately the same) amount of kinetic energy as the first 

baroclinic mode below ~ 500 m. 

During the EGOM Study mooring deployment, five hurricanes and one tropical storm traversed 

the Gulf; the most severe being Hurricanes Katrina and Rita, which caused devastating loss of 

life and property damage to the Gulf coast. Hurricane Katrina entered the Gulf of Mexico on 

August 26, 2005 and was nearest the study area on August 28, 2005; Hurricane Rita entered the 

Gulf of Mexico on September 20, 2005 and was nearest the study region on September 22, 2005. 

The signature of these storms is not evidenced in the dynamic mode amplitudes, as they were 

created from low-pass filtered data. 

A direct response of the ocean to this atmospheric forcing is a wake of near-inertial oscillations, 

characterized by the downward propagation of energy and upward propagation of leading phase. 

Near-inertial motions are an essential and ubiquitous element of ocean circulation, evidenced by 

the high degree of coherency in the near inertial band discussed in sections 4.4.2 and 4.4.3. Xing 
63

and Davies (2005) found that inertial-internal waves propagate at near-inertial frequencies 

modified by the nonlinear effects associated with vorticity in the eddy. 

Figure 37 gives contours of the frequency-averaged wavelet power in the inertial band (0.5 – 2 

day period) during the weeks after Hurricanes Katrina and Rita in the upper 500 m of the water 

column at moorings M1, M2, and M3. The wavelet method estimates the temporal variability of 

energy in specified frequency bands. Wavelet power spectra were generated for all detided, gapfilled, gridded ADCP and current meter records using a Morlet basis function. The method 

described in Torrence and Compo (1998) was used to transform observed time-series into 

Fourier space. 

Figure 37. Contours of the frequency-averaged wavelet power in the inertial band (0.5 – 

2 day period) during the weeks after Hurricanes Katrina and Rita in the upper 

500 m of the water column at moorings M1 (top), M2 (middle), and M3 

(bottom). 
64

The downward propagation of inertial energy after Katrina and Rita to at least 500 m is indicated 

in this figure. The strongest response to the storms is seen at moorings M2 and M3, as the storm 

track was just southwest of the moorings. Note that there are generally two subsurface maxima 

of energy present after the storms and two paths for inertial energy are revealed. There is a direct 

influence on the entire water column that occurs during or immediately after the storm due to the 

storm’s intensity, evidenced by the nearly vertical column of high inertial energy around 

September 1, 2005. There is also the downward propagation of inertial energy, evidenced by the 

diagonal streak of high energy following the storm. It seems that the initial response to the 

storms is strongest at M3, while the propagation response is strongest at M2. Inertial waves after 

Katrina are present more than 2 weeks after the storm and penetrate quickly to the base of the 

upper layer. It is interesting to note the energy minimum between 200 and 300 m at mooring M3, 

which may represent the effect of the pycnocline on the downward energy propagation. Inertial 

oscillations are usually confined to the upper 100 m of the ocean and decay rapidly below the 

mixed layer (Pollard, 1970). The amplitudes of inertial oscillations after Hurricane Rita are not 

as large as the motions excited by Hurricane Katrina and don’t penetrate as deep, but appear to 

persist at the surface longer. The presence of a cold core eddy in the study region during the 

passage of these storms has likely affected the inertial motions. The rate of downward inertial 

energy propagation is roughly 30 m/day. Brooks (1983) estimated the vertical energy transport 

velocity of the wake of inertial oscillations in the western Gulf after Hurricane Allen in 1980 to 

be ~ 60 m/day. Pollard (1970) established that variance in the wind field on the order of an 

inertial period or shorter can initiate and destroy inertial motions, which could be the cause of the 

fingering of inertial energy down into the water column. 

The EOF analysis in this report does not suggest the propagation of topographic Rossby waves 

through this region. The deep ocean spectra presented in section 3.3.2 show some indication of 

bottom intensification, i.e. elevated energy at sub-inertial frequencies, but there are no dominant 

spectral peaks that distinguish topographic Rossby waves (18 – 37 day period) in the Gulf 

(Hamilton, 1990). Horizontal coherency of deep ocean time-series between the moorings 

indicate minimal coherency. The weak coherence between moorings M2 and M3 u-velocity in 

the deep records during deployment one (Figures 14 and 15) is the best indication of topographic 

effects. The conjecture that this could be a generation region for topographic Rossby waves was 

not tested in this analysis, but since the EGOM study area is flat bottomed and a great distance 

form the Loop Current eddy shedding region, topographic Rossby wave generation is not likely 

to be observed in these data. 

Future research objectives in the Gulf of Mexico should include studies focused on the stochastic 

formation and separation of rings from the Loop Current, as they are an important part of the 

heat and salt budgets of the Gulf. Studies directed at understanding the exact mechanism of 

generation of topographic Rossby waves, which could be related to eddy shedding, ring-ring 

interaction, or ring-topography interaction (Oey and Lee, 2002), should be conducted as well. 

From the EGOM data, it is clear that a study of the Loop Current, further south of the EGOM 

region, would be helpful to our understanding of these phenomena. 

The Eastern Gulf of Mexico Circulation Study provides a complete, good quality, year-long data 

set that encapsulates the current regime of this region. Furthermore, signatures of atmospheric 

and oceanic events of great magnitude are evident in these data, such as the passages of 
65

Hurricanes Katrina and Rita through the Gulf and the separation of Eddy Vortex from the Loop 

Current. The analyses presented in this report were somewhat limited by the depth and duration 

of the measurements. Longer time-series from moored instruments would be useful to investigate 

the inter-annual variability of currents, and data closer to the surface would provide a means of 

studying the current-wind relationship in the eastern Gulf. Diurnal variability of currents related 

to sea breeze and the tropical storm induced affects on currents in the surface ocean of the 

eastern Gulf could be better evaluated with data in the upper 40 m of the water column. Wavelet 

coherency between wind and current velocity would be interesting to calculate as well. 

Low-frequency waves have a different modal energy distribution than high-frequency waves 

(MacKinnon and Gregg, 2003). Sub-inertial variability was explored in this report, but inertial 

band and super-inertial variability in the EGOM dataset should be considered as well. An in 

depth analysis of the cold core eddy in the study region during the second deployment and its 

affect on the inertial-internal wave propagation after the hurricanes would be helpful in 

understanding the Doppler shift of the inertial frequency due to the vorticity of the Loop Current 

and the eddy field. EGOM observations could be paired with modeling and theory to evaluate if 

the presence of the cold core eddy in the study site damps the wake of internal waves caused by 

the storm or possibly advects them away. It is unlikely that packets of inertial oscillations at 

great depths are generated by a single atmospheric event at the surface (Pollard, 1970); they 

could be the result of an eddy. 

The conclusion of this study is that the low-frequency currents in the eastern Gulf of Mexico can 

be accurately depicted by a linear combination of the first three theoretical dynamic modes. The 

barotropic and first baroclinic modes alone represent the horizontal current structure ~ 20 - 40% 

the time, but there are significant excursions from this regime that correspond to higher order 

structure as well as deviations from geostrophy, and it is plausible that they are linked to 

complex Loop Current dynamics. The vertical structure of low-frequency horizontal currents in 

the eastern Gulf of Mexico is driven by the northward extent of the Loop Current and the 

temporally and spatially varying eddy field. Frontal eddies play an important role in the 

mesoscale circulation; perhaps more so than Loop Current anticyclones, but it is an amalgam of 

these dynamic features that comprise the currents. 
67

6 REFERENCES 

Brooks, D.A. 1983. The wake of Hurricane Allen in the western Gulf of Mexico. J. Phys. 

Oceanogr. 13(1):117-129. 

Bunge, L., J. Ochoa, A. Badan, J. Candela, and J. Sheinbaum. 2002. Deep flows in the Yucatan 

Channel and their relation to changes in the Loop Current extension. J. Geophys. Res. 

107(C12):3233 doi:10.1029/2001JC001256. 

Candela, J., J. Sheinbaum, J.L. Ochoa, A. Badan, and R. Leben. 2002. The potential vorticity 

flux through the Yucatan Current and the Loop Current in the Gulf of Mexico. Geophys. Res. 

Lett. 29(22):2059 doi:10.1029/2002GL015587. 

Charney, J.G. and G.R. Flierl. 1981. Oceanic analogues of large-scale atmospheric motions. In: 

Warren, B.A. and C. Wunsch, eds. Evolution of Physical Oceanography. MIT Press, 

Cambridge, MA. Pp. 504-548. 

Chérubin, L.M., W. Sturges and E.P. Chassignet. 2005. Deep flow variability in the vicinity of 

the Yucatan Straits from a high-resolution numerical simulation. J. Geophys. Res. 110(C4): 

C04009 doi:10.1029/2004JC002280. 

Chérubin, L. M., Y. Morel and E. P. Chassignet. 2006, Loop Current ring shedding: the 

formation of cyclones and the effect of topography, J. Phys. Oceanogr., 36(4), 569 – 591. 

Coats, D.A. 1992. The Loop Current. In: Millman, J.D. and E. Imamura. The Physical 

Oceanography of the U.S. Atlantic and Eastern Gulf of Mexico, U.S. Dept. of the Interior, 

Minerals Management Service, Atlantic OCS Region, Herndon, VA. 

Cochrane, J.D. 1972. Separation of an anticyclone and subsequent developments in the Loop 

Current. In: Capurro, L.R.A. and J.L. Reid. Contributions on the Physical Oceanography of 

the Gulf of Mexico, Texas A&M Oceanographic Studies, Vol. 2. Gulf Press, Houston, TX. 

Pp. 91-106. 

Cushman-Roisin, B.E., E.P. Chassignet, and B. Tang. 1990. Westward motion of mesoscale 

eddies. J. Phys. Oceanogr. 20(5):758-768. 

Dietrich, G. 1937. Die Lage Meeresoberfläche im Druckfeld Ozean und Atmosphäre mit 

besonderer Berücksichtigund des westlichen Nordatlantischen Ozeans und des Golfs von 

Mexiko. Veröffentlichungen des Institut für Meereskunde an der Universität Berlin, Heft 

33:5-52. 

DiMarco, S.F., A.E., Jochens, and M.K. Howard. 1997. LATEX Shelf data report: current meter 

moorings, April 1992 through December 1994. Technical Report No. 97-01-T. Texas A&M 

University, Oceanography, College Station, TX. 61 pp. 

DiMarco, S.F., W.D. Nowlin, Jr., and R.O. Reid. 2005. A statistical description of the velocity 

fields from upper ocean drifters in the Gulf of Mexico. In: Sturges, W. and A. LugoFernandez. Circulation in the Gulf of Mexico: Observations and Models. American 

Geophysical Union, Washington, DC. Pp. 101-110. 

Donohue, K., P. Hamilton, K. Leaman, R. Leben, M. Prater, E. Waddell, and R. Watts. 2006. 

Exploratory study of deepwater currents in the Gulf of Mexico. U.S. Dept. of the Interior, 
68

Minerals Management Service, Gulf of Mexico OCS Region, New Orleans, LA. OCS Study 

MMS 2006-073. 76 pp. 

Elliott, B.A. 1982. Anticyclonic rings in the Gulf of Mexico. J. Phys. Oceanogr. 12(11):1292-

1309. 

Emery, W.J. and R.E. Thompson. 2001. Data Analysis Methods in Physical Oceanography. 

Amsterdam: Elsevier. 

Fratantoni, P.S., T.N. Lee, G.P. Podesta, and F. Muller-Karger. 1998. The influence of Loop 

Current perturbations on the formation and evolution of Tortugas eddies in the southern 

Straits of Florida. J. Geophys. Res. 103(C11):24759-24779. 

Fuglister, F.C. 1951. Annual variations in current speeds in the Gulf Stream. J. Mar. Res. 

10(1):119-127. 

Gill, A.E., J.S.A. Green, and A.J. Simmons. 1974. Energy partition in the large-scale ocean 

circulation and the production of mid-ocean eddies. Deep-Sea Res. 21(7):499-528. 

Hamilton, P. 1990. Deep currents in the Gulf of Mexico. J. Phys. Oceanogr. 20(7):1087-1104. 

Hamilton, P. 2007. Deep-current variability near the Sigsbee Escarpment in the Gulf of Mexico. 

J. Phys. Oceanogr. 37(3):708-726 doi:10.1175/JPO2998.1. 

Hamilton, P. and T.N. Lee. 2005. Eddies and jets over the slope of the Northeast Gulf of Mexico. 

In: Sturges, W. and A. Lugo-Fernandez. Circulation in the Gulf of Mexico: Observations and 

Models. American Geophysical Union, Washington, DC. Pp. 123-142. 

Hamilton, P. and A. Lugo-Fernández. 2001. Observations of high speed deep currents in the 

northern Gulf of Mexico. Geophys. Res. Lett. 28(14):2867-2870. 

Hetland, R., Y. Hsueh, and D. Yuan. 2001. On the decay of a baroclinic jet flowing along a 

continental slope. J. Geophys. Res. 106(C9):19797-19807. 

Hofmann, E.E. and S.J. Worley. 1986. An investigation of the circulation of the Gulf of Mexico. 

J. Geophys. Res. 91(C12):14221-14236. 

Hurlburt, H.E. and J.D. Thompson. 1980. A numerical study of Loop Current intrusion and eddy 

shedding. J. Phys. Oceanogr. 10(10):1611-1651. 

Ichiye, T. 1962. Circulation and water mass distribution in the Gulf of Mexico. Geofis. Int. 2:47-

76. 

Inoue, M. 1982. Vertical structure of the low-frequency currents at Drake Passage. Ph.D. 

dissertation, Texas A&M University, College Station, TX. 

Inoue, M. 1985. Modal decomposition of the low-frequency currents and baroclinic instability at 

Drake Passage. J. Phys. Oceanogr. 15(9):1157-1181. 

Kantha, L., J. Choi, K.J. Schaudt, and C.K. Cooper. 2005. A regional data-assimilative model for 

operational use in the Gulf of Mexico. In: Sturges, W. and A. Lugo-Fernandez. Circulation in 

the Gulf of Mexico: Observations and Models. American Geophysical Union, Washington, 

DC. Pp. 165-180. 
69

Klinck, J.M., E.E. Hofmann, R.C. Beardsley, B. Salihoglu, and S. Howard. 2004. Water-mass 

properties and circulation on the west Antarctic Peninsula Continental Shelf in austral fall 

and winter 2001. Deep-Sea Res. II 51(17-19):1925-1946 doi:10.1016/j.dsr2.2004.08.001. 

Kundu, P.K., J.S. Allen, and R.L. Smith. 1975. Modal decomposition of the velocity field near 

the Oregon coast. J. Phys. Oceanogr. 5(4):683-704. 

Kuznetsov, L., M. Toner, A.D. Kirwan Jr., C.K.R.T. Jones, L.H. Kantha, and J.Choi. 2002. The 

Loop Current and adjacent rings delineated by Lagrangian analysis of the near-surface flow. 

J. Marine. Res. 60(3):405-429. 

LeBlond, P.H. and L.A. Mysak. 1978. Waves in the Ocean. New York: Elsevier. 

Leben, R.R. 2005. Altimeter-derived Loop Current metrics. In: Sturges, W. and A. LugoFernandez. Circulation in the Gulf of Mexico: Observations and Models. American 

Geophysical Union, Washington, DC. Pp. 181-201. 

Lewis, J.K. and A.D. Kirwan, Jr. 1985. Some observation of ring topography and ring-ring 

interactions in the Gulf of Mexico. J. Geophys. Res. 90:9017-9028. 

Lewis, J.K. and A.D. Kirwan, Jr. 1987. Genesis of a Gulf of Mexico ring as determined from 

kinematic analyses. J. Geophys. Res. 92(C11):11727-11740. 

Lugo-Fernández, A. 2007. Is the Loop Current a chaotic oscillator. J. Phys. Oceanogr. 

37(6):1455-1469 doi:10.1175/JPO3066.1. 

MacKinnon, J.A. and M.C. Gregg 2003. Shear and baroclinic energy flux on the summer New 

England Shelf. J. Phys. Oceanogr. 33(7):1462-1475. 

Maul, G.A. 1977. The annual cycle of the Gulf Loop Current part I: Observations during a oneyear time series. J. Marine. Res. 35(1):29-47. 

McWilliams, J.C. and G.R. Flierl. 1975. Quasi-geostrophic wave analyses: Dynamics and the 

analysis of MODE-1. Report of the MODE-1 dynamics group. Dept. of Meteorology, MIT. 

250 pp. 

McWilliams, J.C. and C.Y. Shen. 1980. Mesoscale modal coupling. J. Phys. Oceanogr. 

10(5):741-752. 

Morrison, J.M. and W.D. Nowlin, Jr. 1982. General distribution of water masses within the 

eastern Caribbean Sea during the winter of 1972 and fall of 1973. J. Geophys. Res. 

87(C6):4207-4229. 

Morrison, J.M., W.J. Merrell, Jr., R.M. Key, and T.C. Key. 1983. Property distributions and deep 

chemical measurements within the western Gulf of Mexico. J. Geophys. Res. 88(C4):2601-

2608. 

Nof, D. and T. Pichevin. 2001. The ballooning of outflows. J. Phys. Oceanogr. 31(10):3045-

3058. 

Nowlin, W.D., Jr. and J.M. Hubertz. 1972. Contrasting summer circulation patterns for the 

Eastern Gulf. In: Capurro, L.R.A. and J.L. Reid, eds. Contributions on the Physical 

Oceanography of the Gulf of Mexico, Texas A&M Oceanographic Studies, Vol. 2. Gulf 

Press, Houston, TX. Pp. 119-137. 
70

Nowlin, W.D., Jr. and H.J. McLellan. 1967. A characterization of the Gulf of Mexico waters in 

winter. J. Mar. Res. 25(1):29-59. 

Nowlin, W.D., Jr., A.E. Jochens, S.F. DiMarco, R.O. Reid, and M.K. Howard. 2001. Deepwater 

physical oceanography reanalysis and synthesis of historical data: Synthesis Report. U.S. 

Dept. of the Interior, Minerals Management Service, Gulf of Mexico OCS Region, New 

Orleans, LA. OCS Study MMS 2001-064. 528 pp. 

Oey, L.Y. and H.C. Lee. 2002. Deep eddy energy and topographic Rossby waves in the Gulf of 

Mexico. J. Phys. Oceanogr. 32(12):3499-3527. 

Pichevin, T. and D. Nof. 1997. The momentum imbalance paradox. Tellus, Ser A., 49(2):298-

319. 

Pollard, R.T. 1970. On the generation by winds of inertial waves in the ocean. Deep-Sea Res., 

17(4):795-812. 

Preisendorfer, R.W. 1988. Principal Component Analysis in Meteorology and Oceanography. 

Amsterdam: Elsevier. 

Press, W.H., B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling. 1986. Numerical Recipes: The 

Art of Scientific Computing. New York: Cambridge University Press. 

Sheinbaum, J., J. Candela, A. Badan, and J. Ochoa. 2002. Flow structure and transport in the 

Yucatan Channel. Geophys. Res. Lett. 29(3):1040 doi:10.1029/2001GL013990. 

Schmitz, W.J. 1978. Observations of the vertical distribution of low-frequency kinetic energy in 

the western North Atlantic. J. Mar. Res. 36(2):295-310. 

Sturges, W. 1994. The frequency of ring separations from the Loop Current. J. Phys. Oceanogr. 

24(7):1647-1651. 

Sturges, W., and R. R. Leben. 2000. Frequency of ring separations from the Loop Current in the 

Gulf of Mexico: A revised estimate. J. Phys. Oceanogr. 30(7):1814-1818. 

Sturges W., J.C. Evans, S. Welsh, and W. Holland. 1993. Separation of warm core rings in the 

Gulf of Mexico. J. Phys. Oceanogr. 23(2):250-286. 

Sturges, W., A. Lugo-Fernández, and M.D. Shargel. 2005. Introduction to circulation in the Gulf 

of Mexico. In: Sturges, W. and A. Lugo-Fernandez. Circulation in the Gulf of Mexico: 

Observations and Models. American Geophysical Union, Washington, DC. Pp. 1-10. 

Torrence, C. and G.P. Compo. 1998. A practical guide to wavelet analysis. Bull. Amer. Meteor. 

Soc. 79(1):61-78. 

Vidal, V.M.V., F.V. Vidal, and J.M. Pérez-Molero. 1992. Collision of a Loop Current 

anticyclonic ring against the continental shelf slope of the western Gulf of Mexico. J. 

Geophys. Res. 97(C2):2155-2172. 

Vukovich, F.M. 1986. Aspects of the behavior of cold perturbations in the Eastern Gulf of 

Mexico: A case study. J. Phys. Oceanogr. 16(1):175-188. 

Vukovich, F.M. 1995. An updated evaluation of the Loop Current’s eddy-shedding frequency. J. 

Geophys. Res. 100(C5):8655-8659. 
71

Vukovich, F.M. and G.A. Maul. 1985. Cyclonic eddies in the Eastern Gulf of Mexico. J. Phys. 

Oceanogr. 15(1):105-117. 

Walker, N.D. 2005. Wind and eddy-related shelf/slope circulation processes and coastal 

upwelling in the northwestern Gulf of Mexico. In: Sturges, W. and A. Lugo-Fernandez. 

Circulation in the Gulf of Mexico: Observations and Models. American Geophysical Union, 

Washington, DC. Pp. 295-313. 

Walker, N., S. Myint, A. Babin, and A. Haag. 2003. Advances in satellite radiometry for the 

surveillance of surface temperatures, ocean eddies and upwelling processes in the Gulf of 

Mexico using GOES-8 measurements during summer. Geophys. Res. Lett. 30(16):1854 

doi:10.1029/2003GL017555. 

Welsh, S.E. and M. Inoue. 2000. Loop Current rings and the deep circulation in the Gulf of 

Mexico. J. Geophys. Res. 105(C7):16951-16959. 

Wunsch, C. 1997. The vertical partition of oceanic horizontal kinetic energy. J. Phys. Oceanogr. 

27(8):1770-1794. 

Wyrtki, K., L. Magaard, and J. Hager. 1976. Eddy energy in the oceans. J. Geophys. Res. 

81(15):2641-2646. 

Xing, J.X. and A.M. Davies. 2005. Nonlinear interaction between wind-forced currents and nearinertial oscillations and internal waves in the nearshore frontal regions. J. Geophys. Res. 

110(C5):C05003 doi:10.1029/2004JC002579. 

Zavala-Hidalgo, J., S.L. Morey, and J.J. O’Brien. 2003. Cyclonic eddies northeast of the 

Campeche Bank from altimetry data. J. Phys. Oceanogr. 33(3):623-629. 
73

APPENDIX A: GRAPHICAL INFORMATION 
75

Figure A-1. Gap-filled, gridded current speed from five moored ADCP depths and moored 

current meters for deployments 1 and 2 at mooring M1. Time periods when 

tropical storms traversed the Gulf are indicated by vertical dotted lines. 
76

Figure A-2. Gap-filled, gridded current speed from five moored ADCP depths and moored 

current meters for deployments 1 and 2 at mooring M2. Time periods when 

tropical storms traversed the Gulf are indicated by vertical dotted lines. 
77

Figure A-3. Vertical profiles of record-length mean, standard deviation, minimum, and 

maximum velocity components for mooring M1 (left: east-west component; right: 

north-south component). Top row: Deployment 1. Bottom row: Deployment 2. 
78

Figure A-4. Vertical profiles of record-length mean, standard deviation, minimum, and 

maximum velocity components for mooring M2 (left: east-west component; right: 

north-south component). Top row: Deployment 1. Bottom row: Deployment 2. 
79

Figure A-5. (Clockwise from top left) mean, standard deviation, maximum, and minimum of 

altimeter derived sea surface height anomaly in centimeters (from Leben) in the 

Gulf of Mexico between January 1, 2005 and January 31, 2006. 
80

Figure A-6. Panels A and B give power spectral density of detided, gap-filled u and v-velocity 

respectively at 6 depths at mooring 1 from deployment 1. Panels C and D give 

power spectral density of u and v-velocity respectively at 6 depths at mooring 1 

from deployment 2. 

A 

B 

C 

D 
81

Figure A-7. Panels A and B give power spectral density of detided, gap-filled u and v-velocity 

respectively at 6 depths at mooring 2 from deployment 1. Panels C and D give 

power spectral density of u and v-velocity respectively at 6 depths at mooring 2 

from deployment 2. 

A 

B 

C 

D 
82

Figure A-8. Significant coherence (at 5% level) between mooring M1 deployment 1 current uvelocity component by depth relative to the upper-most time-series. 

Figure A-9. Significant coherence (at 5% level) between mooring M1 deployment 1 current vvelocity component by depth relative to the upper-most time-series. 
83

Figure A-10. Significant coherence (at 5% level) between mooring M2 deployment 1 current uvelocity component by depth relative to the upper-most time-series. 

Figure A-11. Significant coherence (at 5% level) between mooring M2 deployment 1 current vvelocity component by depth relative to the upper-most time-series. 
84

Figure A-12. Significant coherence (at 5% level) between mooring M3 deployment 1 current uvelocity component by depth relative to the upper-most time-series. 

Figure A-13. Significant coherence (at 5% level) between mooring M3 deployment 1 current vvelocity component by depth relative to the upper-most time-series. 
85

Figure A-14. Significant coherence (at 5% level) between mooring M1 deployment 2 current uvelocity component by depth relative to the upper-most time-series. 

Figure A-15. Significant coherence (at 5% level) between mooring M1 deployment 2 current vvelocity component by depth relative to the upper-most time-series. 
86

Figure A-16. Significant coherence (at 5% level) between mooring M2 deployment 2 current uvelocity component by depth relative to the upper-most time-series. 

Figure A-17. Significant coherence (at 5% level) between mooring M2 deployment 2 current vvelocity component by depth relative to the upper-most time-series. 
87

Figure A-18. Significant coherence (at 5% level) between mooring M3 deployment 2 current uvelocity component by depth relative to the upper-most time-series. 

Figure A-19. Significant coherence (at 5% level) between mooring M3 deployment 2 current vvelocity component by depth relative to the upper-most time-series. 
88

Figure A-20. (Clockwise from top left) Significant coherence (at 5% level) between D1M1 u-velocity and D1

u-velocity and D1M2 v-velocity, D1M1 v-velocity and D1M2 u-velocity, and D1M1 v-velocity 

by depth. 
89

Figure A-21. (Clockwise from top left) Significant coherence (at 5% level) between D1M1 u-velocity and D1M

velocity and D1M3 v-velocity, D1M1 v-velocity and D1M3 u-velocity, and D1M1 v-velocity and depth. 
90

Figure A-22. (Clockwise from top left) Significant coherence (at 5% level) between D1M2 u-velocity and D1

u-velocity and D1M3 v-velocity, D1M2 v-velocity and D1M3 u-velocity, and D1M2 v-velocity 

by depth. 
91

Figure A-23. (Clockwise from top left) Significant coherence (at 5% level) between D2M1 u-velocity and D2

u-velocity and D2M2 v-velocity, D2M1 v-velocity and D2M2 u-velocity, and D2M1 v-velocity 

by depth. 
92

Figure A-24. (Clockwise from top left) Significant coherence (at 5% level) between D2M1 u-velocity and D2

u-velocity and D2M3 v-velocity, D2M1 v-velocity and D2M3 u-velocity, and D2M1 v-velocity 

by depth. 
93

Figure A-25. (Clockwise from top left) Significant coherence (at 5% level) between D2M2 u-velocity and D2

u-velocity and D2M3 v-velocity, D2M2 v-velocity and D2M3 u-velocity, and D2M2 v-velocity 

by depth. 
94

Figure A-26. Vertical EOFs of east-west and north-south current velocity at mooring M1 

during deployment 1. Top three panels: Principal component (PC) time-series of 

first three empirical modes. Bottom panel: Amplitudes of empirical modes 

corresponding to PC time-series. 
95

Figure A-27. Vertical EOFs of east-west and north-south current velocity at mooring M1 

during deployment 2. Top three panels: Principal component (PC) time-series of 

first three empirical modes. Bottom panel: Amplitudes of empirical modes 

corresponding to PC time-series. 
96

Figure A-28. Vertical EOFs of east-west and north-south current velocity at mooring M2 

during deployment 1. Top three panels: Principal component (PC) time-series of 

first three empirical modes. Bottom panel: Amplitudes of empirical modes 

corresponding to PC time-series. 
97

Figure A-29. Vertical EOFs of east-west and north-south current velocity at mooring M2 

during deployment 2. Top three panels: Principal component (PC) time-series of 

first three empirical modes. Bottom panel: Amplitudes of empirical modes 

corresponding to PC time-series. 
98

Figure A-30. Vertical EOFs of east-west and north-south current velocity at mooring M3 

during deployment 2. Top three panels: Principal component (PC) time-series of 

first three empirical modes. Bottom panel: Amplitudes of empirical modes 

corresponding to PC time-series. 
99

Figure A-31. Normalized barotropic and first two baroclinic modes calculated with averaged 

casts at mooring M1 from cruises in January and August 2005. 

Figure A-32. Normalized barotropic and first two baroclinic modes calculated with averaged 

casts at mooring M1 from cruises in August 2005 and January 2006. 

0 

2 

1 

0 

1 

2 
100

Figure A-33. Normalized barotropic and first two baroclinic modes calculated with averaged 

casts at mooring M2 from cruises in January and August 2005. 

Figure A-34. Normalized barotropic and first two baroclinic modes calculated with averaged 

casts at mooring M2 from cruises in August 2005 and January 2006. 

1 

0 

2 

1 

0 

2 
101

Figure A-35. Normalized barotropic and first two baroclinic modes calculated with averaged 

casts at M3 from cruises in August 2005 and January 2006. 

1 

2 

0 
102

Figure A-36. (Top) Spatial correlation between observed u-velocity at mooring M1 from deployment 1 and th

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of the first three th

on the least squares regression. (Right) Temporal correlation between modeled and observed veloc
103

Figure A-37. (Top) Spatial correlation between observed v-velocity at mooring M1 from deployment 1 and th

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of the first three th

on the least squares regression. (Right) Temporal correlation between the modeled and observed ve
104

Figure A-38. (Top) Spatial correlation between observed u-velocity at mooring M1 from deployment 2 and th

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of the first three th

on the least squares regression. (Right) Temporal correlation between the modeled and observed ve
105

Figure A-39. (Top) Spatial correlation between observed v-velocity at mooring M1 from deployment 2 and th

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of the first three th

on the least squares regression. (Right) Temporal correlation between the modeled and observed ve
106

Figure A-40. (Top) Spatial correlation between observed u-velocity at mooring M2 from deployment 1 and th

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of the first three th

on the least squares regression. (Right) Temporal correlation between the modeled and observed ve
107

Figure A-41. (Top) Spatial correlation between observed v-velocity at mooring M2 from deployment 1 and th

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of the first three th

on the least squares regression. (Right) Temporal correlation between the modeled and observed ve
108

Figure A-42. (Top) Spatial correlation between observed u-velocity at mooring M2 from deployment 2 and th

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of the first three th

on the least squares regression. (Right) Temporal correlation between the modeled and observed ve
109

Figure A-43. (Top) Spatial correlation between observed v-velocity at mooring M2 from deployment 2 and th

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of the first three th

on the least squares regression. (Right) Temporal correlation between the modeled and observed ve
110

Figure A-44. (Top) Spatial correlation between observed u-velocity at mooring M3 from deployment 2 and th

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of the first three th

on the least squares regression. (Right) Temporal correlation between the modeled and observed ve
111

Figure A-45. (Top) Spatial correlation between observed v-velocity at mooring M3 from deployment 2 and th

from CTD cast data on the EGOM hydrographic cruises. (Bottom) Amplitudes of the first three th

on the least squares regression. (Right) Temporal correlation between the modeled and observed ve
112

Figure A-46. Goodness of fit tests for A. M1 u-velocity during deployment 1, B. M1 v-velocity during dep

velocity during deployment 2, and D. M1 v-velocity during deployment 2. Panels labeled with 1 

of the necessity of the first three modes in the model. Panels labeled 2 and 3 are tests for the baroclinic and second baroclinic modes respectively to the model. 

A.1 B.1 A.2 B.2 

C.1 D.1 C.2 C.3 

D.2 

D.3 

A.3 B.3 
113

Figure A-47. Goodness of fit tests for A. M2 u-velocity during deployment 1, B. M2 v-velocity during dep

velocity during deployment 2, and D. M2 v-velocity during deployment 2. Panels labeled with 1 

of the necessity of the first three modes in the model. Panels labeled 2 and 3 are tests for the baroclinic and second baroclinic modes respectively to the model. 

A.1 A.2 A.3 C.1 C.2 C.3 

B.1 B.2 B.3 D.1 D.2 D.3 
114

Figure A-48. Goodness of fit tests for A. M3 u-velocity during deployment 1, B. M3 v-velocity during dep

velocity during deployment 2, and D. M3 v-velocity during deployment 2. Panels labeled with 1 

of the necessity of the first three modes in the model. Panels labeled 2 and 3 are tests for the baroclinic and second baroclinic modes respectively to the model. 

A.1 A.2 A.3 

C.1 C.2 C.3 

B.1 

B.2 B.3 D.1 D.2 D.3 
115

Figure A-49. Temporal amplitudes of the first baroclinic mode for the east-west velocity 

component at mooring M1 during deployment 1 (blue) and the SSH gradient in the 

north-south direction (green). 

Figure A-50. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the east-west velocity component at mooring M1 during 

deployment 1 and the SSH gradient in the north-south direction. 
116

Figure A-51. Temporal amplitudes of the first baroclinic mode for the north-south velocity 

component at mooring M1 during deployment 1 (blue) and the SSH gradient in the 

east-west direction (green). 

Figure A-52. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the north-south velocity component at mooring M1 during 

deployment 1 and the SSH gradient in the east-west direction. 
117

Figure A-53. Temporal amplitudes of the first baroclinic mode for the east-west velocity 

component at mooring M1 during deployment 2 (blue) and the SSH gradient in the 

north-south direction (green). 

Figure A-54. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the east-west velocity component at mooring M1 during 

deployment 2 and the SSH gradient in the north-south direction. 
118

Figure A-55. Temporal amplitudes of the first baroclinic mode for the north-south velocity 

component at mooring M1 during deployment 2 (blue) and the SSH gradient in the 

east-west direction (green). 

Figure A-56. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the north-south velocity component at mooring M1 during 

deployment 2 and the SSH gradient in the east-west direction. 
119

Figure A-57. Temporal amplitudes of the first baroclinic mode for the east-west velocity 

component at mooring M2 during deployment 1 (blue) and the SSH gradient in the 

north-south direction (green). 

Figure A-58. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the east-west velocity component at mooring M2 during 

deployment 1 and the SSH gradient in the north-south direction. 
120

Figure A-59. Temporal amplitudes of the first baroclinic mode for the north-south velocity 

component at mooring M2 during deployment 1 (blue) and the SSH gradient in the 

east-west direction (green). 

Figure A-60. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the north-south velocity component at mooring M2 during 

deployment 1 and the SSH gradient in the east-west direction. 
121

Figure A-61. Temporal amplitudes of the first baroclinic mode for the east-west velocity 

component at mooring M2 during deployment 2 (blue) and the SSH gradient in the 

north-south direction (green). 

Figure A-62. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the east-west velocity component at mooring M2 during 

deployment 2 and the SSH gradient in the north-south direction. 
122

Figure A-63. Temporal amplitudes of the first baroclinic mode for the north-south velocity 

component at mooring M2 during deployment 2 (blue) and the SSH gradient in the 

east-west direction (green). 

Figure A-64. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the north-south velocity component at mooring M2 during 

deployment 2 and the SSH gradient in the east-west direction. 
123

Figure A-65. Temporal amplitudes of the first baroclinic mode for the north-south velocity 

component at mooring M3 during deployment 1 (blue) and the SSH gradient in the 

east-west direction (green). 

Figure A-66. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the north-south velocity component at mooring M3 during 

deployment 1 and the SSH gradient in the east-west direction. 
124

Figure A-67. Temporal amplitudes of the first baroclinic mode for the east-west velocity 

component at mooring M3 during deployment 2 (blue) and the SSH gradient in the 

north-south direction (green). 

Figure A-68. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the east-west velocity component at mooring M3 during 

deployment 2 and the SSH gradient in the north-south direction. 
125

Figure A-69. Temporal amplitudes of the first baroclinic mode for the north-south velocity 

component at mooring M3 during deployment 2 (blue) and the SSH gradient in the 

east-west direction (green). 

Figure A-70. Coherency (top) and phase (bottom) spectra of the temporal amplitudes of the first 

baroclinic mode for the north-south velocity component at mooring M3 during 

deployment 2 and the SSH gradient in the east-west direction. 
127

APPENDIX B: TABULAR INFORMATION 
129

Table B-1. 

Summary of the Dynamic normal mode decomposition of the EGOM data for east-west and north-south velocity co

deployment 1. F-test (t-test) refers to the fraction of time when F > 95 % confidence level (t  95 % confiden

Correlation (C) and percent root mean squared error (% ERROR) of the mode fit to the data are depth-averag

D 0 D1 D2 t-test t-test 

 mean (std) mean (std) mean (std) F-test BC1 BC2 C 

M1 u-component 1.43 (6.27) 30.17 (83.16) 27.25 (46.73) 93.83 % 93.99 % 59.60 % 0.96 v-component 1.07 (4.81) 6.26 (61.40) -4.55 (36.06) 95.41 % 93.51 % 54.58 % 0.96 M2 u-component 5.04 (7.41) 89.59 (91.50) 29.80 (47.97) 91.48 % 92.02 % 63.41 % 0.95 v-component -1.08 (8.13) -14.94 (96.07) -18.87 (46.03) 91.15 % 89.62 % 58.98 % 0.94 M3 u-component 6.67 (7.00) 107.96 (92.61) 20.02 (60.32) 95.10 % 92.19 % 70.49 % 0.97 v-component -1.86 (8.14) -47.17 (91.65) -29.81 (58.62) 94.09 % 92.62 % 68.16 % 0.98 
130

Table B-2. 

Summary of the Dynamic normal mode decomposition of the EGOM data for east-west and north-south velocity co

deployment 2. F-test (t-test) refers to the fraction of time when F > 95 % confidence level (t  95 % confiden

Correlation (C) and percent root mean squared error (% ERROR) of the mode fit to the data are depth-averag

D 0 D1 D2 t-test t-test 

 mean (std) mean (std) mean (std) F-test BC1 BC2 C 

M1 u-component -5.70 (3.27) -59.64 (40.49) 17.34 (25.96) 94.45 % 93.70 % 57.92 % 0.92 v-component 3.03 (3.07) 26.04 (37.09) -4.35 (22.64) 83.70 % 82.85 % 39.64 % 0.92 M2 u-component -1.53 (4.05) -18.38 (58.65) 35.47 (39.15) 94.90 % 90.92 % 67.97 % 0.96 v-component 1.09 (7.47) 15.62(74.46) 0.33 (47.85) 96.58 % 96.06 % 63.48 % 0.97 M3 u-component 4.83 (7.10) 87.50 (80.15) -38.68 (75.52) 98.94 % 97.46 % 78.92 % 0.97 v-component 0.74 (7.05) 8.35 (72.60) -21.37 (85.14) 91.18 % 83.82 % 81.22 % 0.98 
131

Table B-3. 

Time scales of the barotropic and first two baroclinic modes for east-west and north-south velocity 

components for EGOM data during deployment 1 based on the first zero crossing of the autocovariance 

function.

 Time Scale (days) 

 BT BC 1 BC 2 

 

M1 

u-component 21 22 29 

v-component 23 23 24 

 

M2 

u-component 34 33 5 

v-component 23 23 9 

 

M3 

u-component 13 13 6 

v-component 25 39 7 

 

Table B-4. 

Time scales of the barotropic and first two baroclinic modes for east-west and north-south velocity 

components for EGOM data during deployment 2 based on the first zero crossing of the autocovariance 

function.

 Time Scale (days) 

 BT BC 1 BC 2 

 

M1 

u-component 10 11 12 

v-component 40 37 10 

 

M2 

u-component 7 21 12 

v-component 38 36 12 

 

M3 

u-component 19 17 11 

v-component 34 31 33 

 
132

Table B-5. 

Percentages of kinetic energy in the barotropic (BT), first baroclinic (1BC), and second baroclinic (2BC) 

modes at each depth level at mooring M1 during deployment 1. The figure on the right is a summary plot 

of the Kinetic energy percentages in the table. 

Depth %TBT (zm ) %T1BC (zm ) %T2BC (zm )

 

100 m 6.53 % 91.40 % 2.07 % 

172 m 12.46 % 86.39 % 1.15 % 

252 m 18.73 % 74.54 % 6.73 % 

332 m 26.05 % 60.84 % 13.11 % 

428 m 36.56 % 44.43 % 9.01 % 

749 m 88.84 % 0.81 % 10.36 % 

1244 m 50.80 % 47.30 % 1.91 % 

1492 m 47.02 % 50.20 % 2.78 % 

2499 m 45.82 % 51.09 % 3.09 % 

 

Table B-6. 

Percentages of kinetic energy in the barotropic (BT), first baroclinic (1BC), and second baroclinic (2BC) 

modes at each depth level at mooring M2 during deployment 1. The figure on the right is a summary plot 

of the Kinetic energy percentages in the table. 

Depth %TBT (zm ) %T1BC (zm ) %T2BC (zm )

 

90 m 6.05 % 92.94 % 1.02 % 

154 m 13.73 % 85.16 % 1.11 % 

226 m 21.39 % 73.71 % 4.90 % 

322 m 32.94 % 57.56 % 9.50 % 

418 m 46.16 % 41.28 % 12.57 % 

749 m 92.47 % 4.15 % 3.38 % 

997 m 65.99 % 33.87 % 0.14 % 

1244 m 52.55 % 46.03 % 1.42 % 

1492 m 49.45 % 48.65 % 1.89 % 

1995 m 48.67 % 49.30 % 2.03 %

 
133

Table B-7. 

Percentages of kinetic energy in the barotropic (BT), first baroclinic (1BC), and second baroclinic (2BC) 

modes at each depth level at mooring M1 during deployment 2. The figure on the right is a summary plot 

of the Kinetic energy percentages in the table. 

Depth %TBT (zm ) %T1BC (zm ) %T2BC (zm )

 

65 m 8.03 % 88.71 % 3.26 % 

161 m 17.21 % 82.48 % 0.32 % 

265 m 28.20 % 67.65 % 4.15 % 

369 m 40.80 % 51.08 % 8.11 % 

489 m 58.35 % 30.92 % 10.73 % 

749 m 95.02 % 0.70 % 4.28 % 

997 m 74.57 % 25.42 % 0.00 % 

1492 m 57.05 % 41.68 % 1.28 % 

1995 m 56.01 % 42.57 % 1.42 % 

2499 m 55.98 % 42.59 % 1.42 %

 

Table B-8. 

Percentages of kinetic energy in the barotropic (BT), first baroclinic (1BC), and second baroclinic (2BC) 

modes at each depth level at mooring M2 during deployment 2. The figure on the right is a summary plot 

of the Kinetic energy percentages in the table. 

Depth %TBT (zm ) %T1BC (zm ) %T2BC (zm )

 

70 m 6.92 % 88.77 % 4.31 % 

166 m 18.51 % 79.30 % 2.18 % 

270 m 30.03 % 57.21 % 12.75 % 

374 m 42.41 % 36.08 % 21.51 % 

494 m 60.13 % 15.57 % 24.29 % 

749 m 88.03 % 6.85 % 5.12 % 

997 m 64.08 % 35.15 % 0.77 % 

1244 m 53.47 % 43.23 % 3.30 % 

1492 m 51.05 % 44.86 % 4.10 % 

1995 m 50.56 % 45.18 % 4.26 % 

 
134

Table B-9. 

Percentages of kinetic energy in the barotropic (BT), first baroclinic (1BC), and second baroclinic (2BC) 

modes at each depth level at mooring M3 during deployment 2. The figure on the right is a summary plot 

of the Kinetic energy percentages in the table. 

Depth %TBT (zm ) %T1BC (zm ) %T2BC (zm )

 

82 m 6.10 % 93.00 % 0.89 % 

170 m 18.29 % 73.87 % 7.84 % 

266 m 33.26 % 44.43 % 22.31 % 

362 m 45.49 % 26.08 % 28.43 % 

466 m 61.49 % 10.72 % 27.79 % 

750 m 88.56 % 7.11 % 4.33 % 

997 m 67.46 % 31.13 % 1.41 % 

1245 m 58.56 % 37.30 % 4.14 % 

1492 m 56.30 % 38.68 % 5.02 % 

1996 m 55.45 % 39.19 % 5.37 % 

2499 m 55.44 % 39.19 % 5.37 % 

2699 m 55.44 % 39.19 % 5.37 % 

 

Table B-10. 

East-west and north-south velocity mode amplitude correlations at mooring M1 for deployment 1. 

Bold values indicate significant zero lag correlation at the 90% confidence level.

 East-west velocity North-south velocity 

 BT BC 1 BC 2 BT BC 1 BC 2 

 

BT 1.00 0.91 0.31 1.00 0.86 0.22

BC1 0.91 1.00 0.48 0.86 1.00 0.42 

BC2 0.31 0.48 1.00 0.22 0.42 1.00 

 
135

Table B-11. 

East-west and north-south velocity mode amplitude correlations at mooring M2 for deployment 1. 

Bold values indicate significant zero lag correlation at the 90% confidence level.

 East-west velocity North-south velocity 

 BT BC 1 BC 2 BT BC 1 BC 2 

 

BT 1.00 0.52 0.07 1.00 0.87 0.01

BC1 0.52 1.00 0.03 0.87 1.00 0.01

BC2 0.07 0.03 1.00 0.01 0.01 1.00 

 

Table B-12. 

East-west and north-south velocity mode amplitude correlations at mooring M3 for deployment 1. 

Bold values indicate significant zero lag correlation at the 90% confidence level.

 East-west velocity North-south velocity 

 BT BC 1 BC 2 BT BC 1 BC 2 

 

BT 1.00 0.35 0.00 1.00 0.52 0.01

BC1 0.35 1.00 0.00 0.52 1.00 0.01 

BC2 0.00 0.00 1.00 0.01 0.01 1.00

 

Table B-13. 

East-west and north-south velocity mode amplitude correlations at mooring M1 for deployment 2. 

Bold values indicate significant zero lag correlation at the 90% confidence level.

 East-west velocity North-south velocity 

 BT BC 1 BC 2 BT BC 1 BC 2 

 

BT 1.00 0.65 0.04 1.00 0.67 0.02

BC1 0.65 1.00 0.00 0.67 1.00 0.01

BC2 0.04 0.00 1.00 0.02 0.01 1.00 

 
136

Table B-14. 

East-west and north-south velocity mode amplitude correlations at mooring M2 for deployment 2. 

Bold values indicate significant zero lag correlation at the 90% confidence level.

 East-west velocity North-south velocity 

 BT BC 1 BC 2 BT BC 1 BC 2 

 

BT 1.00 0.10 0.02 1.00 0.85 0.61 

BC1 0.10 1.00 0.01 0.85 1.00 0.60 

BC2 0.02 0.01 1.00 0.61 0.60 1.00 

 

Table B-15. 

East-west and north-south velocity mode amplitude correlations at mooring M3 for deployment 2. 

Bold values indicate significant zero lag correlation at the 90% confidence level.

 East-west velocity North-south velocity 

 BT BC 1 BC 2 BT BC 1 BC 2 

 

BT 1.00 0.60 0.20 1.00 0.34 0.57

BC1 0.60 1.00 0.29 0.34 1.00 0.60

BC2 0.20 0.29 1.00 0.57 0.60 1.00 

 
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

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;

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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

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Moreover, in working to meet its responsibilities, the Offshore Minerals Management Program

administers the OCS competitive leasing program and oversees the safe and environmentally

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efficient, timely and accurate collection and disbursement of revenue from mineral leasing and

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The MMS strives to fulfill its responsibilities through the general guiding principles of: (1) being

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development and environmental protection.