OCS Study

MMS 2003-049 

 

Deepwater Observations in the 

Northern Gulf of Mexico from 

In-Situ Current Meters and PIES 

Volume II: Technical Report

I1

I2

I3

500 m

1000 m

2000 m

2500 m

1500 m

Sigsbee Escarpment

Sigsbee Escarpment

Green Knoll

U.S. Department of the Interior

Minerals Management Service 

Gulf of Mexico OCS Region 
OCS Study

MMS 2003-049 

Deepwater Observations in the 

Northern Gulf of Mexico from 

In-Situ Current Meters and PIES 

Volume II: Technical Report 

Authors 

Peter Hamilton 

James J. Singer 

Evans Waddell 

Science Applications International Corporation 

Kathleen Donohue 

University of Rhode Island 

Prepared under MMS Contracts 

1435-01-00-CT-31132 

and 

1435-01-96-CT-30825 

by 

Science Applications International Corporation 

615 Oberlin Rd., Suite 100 

Raleigh, North Carolina 27605 

Published by 

U.S. Department of the Interior

Minerals Management Service 

Gulf of Mexico OCS Region 

New Orleans

August 2003 
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 

Extra copies of the report may be obtained from the Public Information Office (Mail Stop 5034) 

at the following address: 

 U.S. Department of the Interior 

 Minerals Management Service 

 Gulf of Mexico OCS Region 

 Public Information Office (MS 5034) 

 1201 Elmwood Park Boulevard 

 New Orleans, Louisiana 70123-2394 

 Telephone Number: 1-800-200-GULF or 

 504-736-2519 

CITATION 

Suggested citation: 

Hamilton, P., J.J. Singer, E. Waddell, and K. Donohue. 2003. Deepwater Observations in the 

Northern Gulf of Mexico from In-Situ Current Meters and PIES. Final Report. Volume

II: Technical Report. U.S. Dept. of the Interior, Minerals Management Service, Gulf of 

Mexico OCS Region, New Orleans, LA. OCS Study MMS 2003-049. 95 pp. 

ABOUT THE COVER 

The map shows the Sigsbee Escarpment south of New Orleans that was the primary focus of 

measurements from instruments on the indicated moorings. Moorings I1-4 and J1 were normal 

tautline moorings. Moorings K1-K3 were Inverted Echo Sounders with Pressure (PIES). The 

picture is of a PIES on the back deck of the mooring deployment vessel. The “orb” contains all 

the instrumentation associated with operations and recovery of the instrument. The stand is used 

in regions where strong bottom currents are expected, such as the present study area. 

iii 
ACKNOWLEDGMENT 

The insight of Dr. Willis Pequegnat was verified with this project. One of the authors 

remembers well listening to Willis many years ago describe how his biological sampling gear

lowered near the present study area could not reach the bottom due to very strong bottom 

currents. 

Both the MMS and BP provided support to this measurement program. This cooperative funding 

was essential to acquisition of the resulting horizontal and vertical coverage as well as the 

measurement duration. Dr. Alexis Lugo-Fernandez, the MMS COTR, and Mr. David Driver, the 

BP representative, worked cooperatively to define a program that accomplished both industry

and government objectives. 

v 
TABLE OF CONTENTS 

 Page

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

LIST OF TABLES.........................................................................................................................xv 

1.0 INTRODUCTION .................................................................................................................1 

 1.1 Background..................................................................................................................1 

 1.2 Organization of the Report...........................................................................................5 

2.0 CURRENT MEASUREMENTS ...........................................................................................7 

 2.1 Data ..............................................................................................................................7 

 2.2 Methods........................................................................................................................7 

 2.3 Upper-Layer Event Description.................................................................................10 

 2.4 Deep Currents ............................................................................................................18 

3.0 ANALYSIS OF CURRENTS..............................................................................................29 

 3.1 Basic Statistics...........................................................................................................29 

 3.2 Topography Rossby Waves.......................................................................................32 

 3.3 Spectra........................................................................................................................33 

 3.4 Vertical EOF Analysis at I1.......................................................................................36 

 3.5 Horizontal EOF Analysis...........................................................................................41 

 3.6 TRW Ray Tracing......................................................................................................45 

 3.7 Upper Layer Circulations...........................................................................................52 

 3.8 Inertial Currents.........................................................................................................58 

4.0 ECHO SOUNDERS WITH PRESSURE (PIES) ................................................................73 

 4.1 Introduction................................................................................................................73 

 4.2 Methodology..............................................................................................................73 

 4.2.1 Instrumentation .............................................................................................73 

 4.2.2 Initial Data Conditioning ..............................................................................76 

 4.2.3 Data Processing and Reduction - Gravest Empirical Mode..........................77 

 4.3 PIES in the Gulf of Mexico .......................................................................................84 

 4.4 Conclusion .................................................................................................................84 

5.0 SUMMARY.........................................................................................................................91 

6.0 REFERENCES ....................................................................................................................93 

vii 
LIST OF FIGURES 

Figure Page

1-1. Map of the deployment region in the northern Gulf of Mexico................................2 

1-2. Detailed bathymetric map of the Sigsbee Escarpment in the region 

south of the Mississippi delta. ...................................................................................3 

2-1. Time lines of data return for the current meter moorings. ........................................8 

2-2a. The first year of 40-HLP velocity, temperature and salinity data from 

the upper-layer records at mooring I1 for the indicated depths. .............................11 

2-2b. The second year of 40-HLP velocity, temperature and salinity data 

from the upper-layer records at mooring I1 for the indicated depths......................12 

2-3 (a-d). Sea surface height anomaly maps from TOPEX/ERS-2 altimetric 

data (courtesy of R. Leben, CCAR). September 12, 1999 (a), 

December 12, 1999 (b), March 5, 2000 (c), and July 2, 2000 (d)...........................13 

2-3 (e-h). Sea surface height anomaly maps from TOPEX/ERS-2 altimetric 

data (courtesy of R. Leben, CCAR). September 24, 2000 (e), 

November 27, 2000 (f), January 31, 2001 (g), and April 30, 2001 (h). ..................15 

2-3 (i-k). Sea surface height anomaly maps from TOPEX/ERS-2 altimetric 

data (courtesy of R. Leben, CCAR). May 21, 2001 (i), July 23, 2001 

(j), and August 22, 2001 (k). ...................................................................................16 

2-4a. The first year of upper layer isotherm depths as a function of time........................17 

2-4b. The second year of upper layer isotherm depths as a function of time. ..................19 

2-5a. The first year of 40-HLP velocity vectors from below 1000 m at I1......................20 

2-5b. The second year of 40-HLP velocity vectors from below 1000 m at I1. ................22 

2-6a. The first year of 40-HLP velocity vectors from below 1000 m at I1, I2, 

I3 and J1. .................................................................................................................24 

2-6b. The second year of 40-HLP velocity vectors from below 1000 m 

at I1, I2, I3 and I4....................................................................................................25 

2-7a. The first year of 3-HLP speed records from 200 m above the bottom 

at I1, I2, I3 and J1....................................................................................................26 

ix 
LIST OF FIGURES (continued) 

Figure Page

2-7b. The second year of 3-HLP speed records from 200 m above the 

bottom at I1, I2, I3 and I4........................................................................................27 

3-1. Standard deviation ellipses and mean velocity vectors from 40-HLP 

current data for 200 m and 1000 m above the bottom.............................................31 

3-2. Kinetic energy spectra in variance preserving form, for 40-HLP 

velocities from instruments 200-m above the bottom, for moorings 

I1, I2, I3, J1 and I4. .................................................................................................35 

3-3. Kinetic energy spectra in variance preserving form, for 40-HLP 

velocities from instruments 1000-m, 1400-m, 1800-m and 1979-m 

(Period 5 only) depths, for mooring I1....................................................................37 

3-4. Mode 1, represented as hodographs, resulting from EOF analyses of 

current records at I1 below 1000 m for the indicated periods 

(see Table 3-2) and frequency bands.......................................................................38 

3-5. Mode 1, represented as hodographs, resulting from EOF analyses of 

current records at I1 for the complete water column...............................................40 

3-6a. Mode 1, represented as hodographs, resulting from EOF analyses of 

current records 200-m from the bottom for analysis periods 1 

(14-7 days) and 2 (17-8 days)..................................................................................42 

3-6b. Mode 1, represented as hodographs, resulting from EOF analyses of 

current records 200-m from the bottom for analysis periods 3 

(25-8 days) and 4 (25-7 days)..................................................................................43 

3-6c. Mode 1, represented as hodographs, resulting from EOF 

analyses of current records 200-m from the bottom for analysis 

period 5 using frequency bands 30-11 days and 11-5 days.....................................44 

3-7. Mode 1, represented as hodographs, resulting from EOF analyses 

of current records 200-m from the bottom for the two-year period 

using frequency bands 30-15 days and 15-7 days...................................................46 

3-8. Bathymetry after applying a 50 km median filter and smoothing 

splines to GOTOPO 30 gridded data.......................................................................47 

x 
LIST OF FIGURES (continued) 

Figure Page

3-9. Backward and forward ray traces from the center of the I mooring 

triangle for waves of 8-day period and 76-km initial wavelength 

and 20 day period and 87 km wavelength...............................................................49 

3-10. Backward and forward ray traces from the center of the I mooring 

triangle for waves with indicated periods................................................................50 

3-11. Paths of the center of Eddy Millenium derived from a kinematic 

model analysis of smoothed drifter tracks...............................................................54 

3-12. Elliptical orbit from model kinematic equations.....................................................55 

3-13. Time series from translating ellipse model and observations at I1. ........................56 

3-14. Composite AVHRR Images for March 23 and April 5, 2001 

(Courtesy John Hopkins University Applied Physics Laboratory ..........................59 

3-15. Radial (Ur) and azimuthal (Vm) components of daily averaged velocity 

profiles, at I1, for Eddy M on the given Julian days, 2001. ....................................61 

3-16. Daily averaged temperature and azimuthal (Vm) velocity component 

profiles, at I1, for Eddy M on the given Julian days, 2001. ....................................62 

3-17. Azimuthal velocities (adjusted for effects of eddy translation) as a 

function of distance from the center of the eddy for the period 

March 13 to June 5 (excluding May 19 -21). .........................................................64 

3-18. 3-HLP velocity components from selected depths of mooring I1 for 

the indicated period. ................................................................................................66 

3-19. Amplitudes of inertial (26 hour) current oscillations at the 

indicated depths of mooring I1................................................................................68 

3-20. Rotary spectra for the indicated upper layer current records for three 

59-day periods. ........................................................................................................69 

3-21. Amplitudes (cm/s) and phases from EOF analyses of inertial period 

motions for periods 1 and 2.....................................................................................70 

3-22. Amplitudes (cm/s) and phases from an EOF analysis of inertial period 

motions for period 3. ...............................................................................................71 

xi 
LIST OF FIGURES (continued) 

Figure Page

4-1. PIES on the back deck of the deployment vessel in a cradle used in 

regions of expected strong bottom currents. ...........................................................74 

4-2. Schamatic drawing of the major components of the PIES instrument....................75 

4-3. Spatial and temporal distribution of historical hydrocasts used to 

construct of the Gravest Empirical Mode................................................................78 

4-4. Scatter plots of temperature versus tau 100-1000 for five representative 

 pressure levels. ........................................................................................................79 

4-5. Scatter plots of salinity versus tau 100-1000 for five representative 

pressure levels. ........................................................................................................80 

4-6. Scatter plots of specific volume anomaly versus tau 100-1000 for five 

representative pressure levels..................................................................................81 

4-7. Contour plot of the cubic smoothing spline fits for the temperature 

GEM field................................................................................................................82 

4-8. Contour plot of the cubic smoothing spline fits for the salinity 

GEM field................................................................................................................83 

4-9. Three PIES (Inverted Echo Sounders with pressure) 

arranged in a triangle around the I1 mooring for approximately 

6 months, February through August 2001...............................................................85 

4-10. Comparison of temperature time series measured by the I1 mooring 

and temperatures estimated at the same set of depths by the 3 

nearby PIES using the GEM interpretation of the tau (τ) measurements................86 

4-11. Comparison of salinity time series measured by the I1 mooring 

and salinity estimated at 450 dbar by the 3 nearby PIES 

using the GEM interpretation of the tau (t) measurements....................................87 

4-12. Comparison of velocity measured by the I1 mooring and velocity 

estimated at the same set of depths by the 3 nearby PIES using the 

GEM interpretation of the tau (τ) measurements and referencing 

geostrophic shears to deep geostrophic velocity determined from 

the bottom pressure measurements..........................................................................88 

xii 
LIST OF FIGURES (continued) 

Figure Page

4-13. Comparison of velocity measured by the I1 mooring and 

velocity estimated at the same set of depths by the 3 nearby PIES 

using the GEM interpretation of the tau (τ) measurements 

and referencing geostrophic shears to the deep current meter on the 

I1 mooring. ..............................................................................................................89 

xiii 
LIST OF TABLES

Table Page

2-1. Moored instrument and PIES measurement levels for the 

Desoto Canyon Extension Program.........................................................................9 

3-1. Statistics of currents measured during this project. ...............................................30 

3-2. Spectra and TRW Analysis Periods.......................................................................34 

3-3. TRW Wave Parameters..........................................................................................39 

3-4. TRW initial conditions with Start and End Wavelengths......................................48 

xv 
1.0 INTRODUCTION 

As an extension of the MMS-Funded DeSoto Canyon Eddy Intrusion Study (Hamilton et al.,

2000) additional current/temperature measurements were made at the base of a Sigsbee 

Escarpment in water depths of approximately 2000 m. Deepwater and near-current

measurements in this specific area, supported by BP, indicated the occurrence of periodic higher 

speed events that could be of considerable importance to expected oil/gas exploration and 

development in this deepwater area. In order to have available representative and pertinent 

knowledge of conditions in these development areas, the MMS funded a series of fairly sitespecific, deepwater current measurements. In conjunction with MMS support, BP provided 

support to expand the depth and areal coverage of these measurements in what was a

cooperatively government-industry measurement program. 

The specifics of the various components of measurement program and a characterization 

interpretation of many of the key attributes of the observations are presented in this report. 

1.1 Background 

In August 1999, the Minerals Management Service (MMS) funded the deployment of an array of 

three moorings, clustered near the 2000 m isobath at the base of the continental slope, south of

the Mississippi delta (Figure 1-1). This array was designed to study energetic deep currents that 

had been previously observed by a mooring deployed for BP Exploration Inc. in Block 618 of 

the Atwater Valley lease area (Hamilton, 1998). Both the previous BP mooring and the MMS 

array were situated south of a relatively steep slope known as the Sigsbee Escarpment which is 

an extensive approximately east-west geological feature across the deep northern slope between 

the Mississippi delta and east Texas. The MMS array consisted of one, extensively 

instrumented, full depth mooring (I1) and two short bottom moorings (I2 and I3). In order to 

discover how far up the slope high speed deep currents might extend from the Atwater site, BP 

funded another short bottom mooring on a block (Green Canyon 782) north of the escarpment 

(Figure 1-2). This mooring, denoted J1, was deployed in conjunction with the three MMS 

moorings. This four mooring array was deployed in August 1999. Mooring J1 was retrieved in 

August 2000 after one rotation in January 2000. Moorings I1, I2, and I3 were redeployed and 

after a further rotation in February 2001, finally retrieved in September 2001. During the final 

six months, BP and MMS jointly funded the near bottom moorings at I1, I2, I3 measurements 

and another deep mooring, named I4, on the middle part of the escarpment, just west of I2. The 

MMS also supported extending Mooring I1 from a near bottom to a full depth mooring. During 

these final six months, the MMS further supported deploying three Inverted Echo Sounders, 

equipped with precision bottom pressure sensors (known as PIES), positions approximately 

equidistant from the full depth mooring, I1. These positions are denoted K1, K2 and K3. These 

latter were deployed to use PIES to estimate measurements of temperature and salinity depth 

profiles, and through the geostrophic equations combined with bottom currents on absolute 

velocity profiles. The gravest empirical mode (GEM) method is used to convert travel time

between the bottom mounted PIES and the surface, and back, to salinity, temperature and density

profiles (Watts et al., 2001). Pairs of density profiles can then be used to compute geostrophic 

velocity profiles (He et al., 1998). 

1
200-m

1000-m

2000-m

3000-m

J1

K1

K3

I3

I4 I1

K2

I2

Figure 1-1.Map of the deployment region in the northern Gulf of Mexico. Solid dots and 

squares are the positions of current meter moorings and bottom-mounted PIES, 

respectively. The C-MAN meteorological station at Southwest Pass, LA is 

indicated by the solid diamond.

BURL1

Louisiana

2
I1

I2

I3

500 m

1000 m

2000 m

2500 m

1500 m

K1

K2 K3

Figure 1-2. Detailed bathymetric map of the Sigsbee escarpment in the region south of the 

Mississippi delta. The positions of the MMS moorings (I1, I2 and I3, black circles) 

and PIES (K1, K2 and K3, red squares), and the BP moorings (J1 and I4, green 

circles) are shown. 

J1 I4

Sigsbee Escarpment

Sigsbee Escarpment

Green Knoll

3
Such derived profiles can be compared to the time series measured at I1. Successful use of PIES 

would allow economical mapping of low-frequency current, salinity and temperature profiles 

over larger regions of the deep Gulf of Mexico than might be possible using conventional current

meter moorings. PIES have been used successfully, for this purpose, in many regions of the 

world’s oceans (e.g., Sun and Watts, 2001; Howden et al., 1994; Kelly and Watts, 1994). This 

report discusses the measurements made at all moorings and PIES over the two-year period. A 

discussion of the first six months of current measurements is given in Hamilton and LugoFernandez (2001). Aspects of the first year of bottom currents at I1, I2, I3 and J1 were also 

analyzed in a report to BP by Hamilton et al. (2000). 

Observations of the water column over the deeper portions in the Gulf of Mexico basin indicate 

that there is a basic two-layer structure. Above ~800 to 1200 m depth, the circulation is 

dominated by the Loop Current (LC) in the east, anticyclonic rings shed from the Loop Current 

in the central and western basin, and smaller-scale cyclones and anticyclones that are probably

generated by the LC rings. This upper layer has vigorous flows that result from eddies, and 

interactions between eddies. These flows often have strong vertical shears (Kirwan et al., 1984; 

Elliott, 1982; Hamilton, 1992). 

Below ~1000 m, eastern Gulf measurements have shown that currents are nearly depthindependent with a tendency for bottom intensification. These lower-layer flows do not appear 

to have a strong relationship to simultaneous current fluctuations in the upper layer. Hamilton 

(1990) suggested that these deep motions may result from topographic Rossby waves (TRW)

propagating westward across the continental slope and rise of the basin. Similar kinds of deep 

motions have been extensively studied in the Mid-Atlantic Bight where there is evidence that 

they are generated by meanders of the Gulf Stream (Hogg, 1981; Pickart, 1995). In the Gulf, it 

seems plausible that deep TRW's are generated by Loop Current fluctuations, Loop Current eddy 

(LCE) shedding events, and the propagation of LCE's across the Gulf. The latter could include 

the interaction of LCE's with topography and other eddies in the basin. However, the generation 

mechanisms of TRW's are not presently well understood. 

Previous analyses of deep current data, from the BP Atwater 618 block (Hamilton, 1998) and the 

MMS moorings (Hamilton et al., 2000; Hamilton and Lugo-Fernandez, 2001) were also 

interpreted in terms of TRW's. However, these current magnitudes were exceptional (~ 50 cm/s) 

and the periods were short (~ 10 days) compared to other regions of the central and western Gulf. 

A source for such short period TRWs was not obvious. Current measurements made on a single 

mooring under the LC showed almost no energy at periods shorter than about 15 days (Hamilton, 

1990). It was speculated that LC/LCE frontal eddies had space and time scales that matched the 

observed high-frequency TRW's and therefore could be a source (see Pickart, 1995). In a recent 

paper, Hogg (2000) has also observed energetic, short period TRW's on the western flanks of the

Grand Banks in the North Atlantic. He attributed these TRW's to transient behavior of the Gulf 

Stream as it passes over the tail of the Grand Banks, though direct evidence of this mechanism 

was lacking. The analogy with the LC extending over the Mississippi fan is striking, and thus, 

similar phenomena may be responsible for both the Gulf and North Atlantic TRW motions. 

4
1.2 Organization of the Report 

Chapter 2 discusses the database of measurements used in this report. It includes a basic 

description of the characteristics of the observed current, temperature and salinity fields.

Analysis and statistics of the observations are given in Chapter 3. The results from the PIES and 

the comparison to the moored data at I1 are discussed in Chapter 4, and the study is summarized 

in Chapter 5.

5
2.0 CURRENT MEASUREMENTS 

2.1 Data 

Instrumentation on each of the moorings is shown in Table 2-1 with locations shown in Figure 1-

2. Each instrument has an ID of the form DSC-xx-#, where xx is the mooring ID (e.g. I1) and # 

is the number of the instrument from the top of the mooring. Because of the number of 

instruments on I1, where # > 9, letters of the alphabet are used (e.g. A through O). Because the 

instrumentation changed slightly between deployments, the additional or replacement of 

instruments on I1 have instrument numbers or letters that are out of sequence. Time lines of the

data return for all instruments are given in Figure 2-1. Note that six of the instruments are 

ADCP's that measure velocity profiles at intervals of either 4 or 8 m. These instruments were

directed to measure profiles up or down from their positions on mooring I1 (see Table 2-1.). All

instruments in the lower layer (depths > 800 m) were conventional current meters. 

All data records underwent basic quality assurance during which suspect data values were 

flagged. Current records were corrected for magnetic variation. Short gaps of a few hours

caused by flagged data or the rotation of the moorings were subsequently filled by linear 

interpolation. Long gaps of up to 2 days were filled with a proven procedure that preserves the 

spectral content and has similar energy levels to the rest of the records. In the mooring rotation

gaps (mainly for I1), care was taken that the vertical coherence between levels were similar to 

other portions of the mooring's records. This is particularly important for the closely spaced 

depth levels generated by the ADCP's. The records at each depth level were merged into 

continuous time series where possible. The original data was recorded at 30 or 60-minute 

intervals and show varying degrees of noise in the records. To minimize this, all records were

filtered with a three-hour low-pass (3-HLP) Lazcos kernel and decimated to 1-hour intervals.

The axes of the current velocity records were rotated so that the V-component was directed along

the general trend of the isobaths. A rotated record has the notation Rθ after the ID, where θ is 

the clockwise rotation angle of the V- or along isobath component from true north. The U- or

cross-isobath component is then directed at angle θ+90°. To analyze efficiently the current

motions with periods greater than one day that dominate deepwater flows, the 3-HLP records 

were further filtered with a 40-HLP kernel and resampled at 6-hour intervals. The processing 

and calibration of the PIES is given in Chapter 4. 

2.2 Methods 

Methods for analyzing time series generally follow established techniques such as those used by 

Hamilton (1990) to characterize TRW motions in the deep Gulf. These include spectra, 

coherence and phase calculations, and EOF or principal component analysis (PCA). Spectra are 

used to determine the periods (frequency bands) of the energetic motions. Coherence squared 

and phase differences show the relationships between pairs of spectra. EOFs provide 

information on the coherent spatial structures associated with a frequency band using multiple

records. Spectra are calculated by standard FFT methods that allow record lengths that are not a 

power of 2. The time series are demeaned and a 10% cosine taper applied before the FFT. The

7
ADCP

ADCP

ADCP

ADCP

ADCP

ADCP

Figure 2-1. Time lines of data return for the current meter moorings. Solid and dashed lines 

represent velocity and scaler (e.g. Temperature and Salinity), respectively. On 

Mooring I1, a 150 kHz, up-directed ADCP failed near the end of the first six months 

and was replaced by various in-situ current meters for the remainder of the mooring 

deployments.

C/T/P

C/T/P

C/T

T

T

T

T

T

S4

C/T

GO/MKII

T

S4

S4

RCM

RCM

RCM

RCM

RCM

GO/MKII

GO/MKII

RCM

RCM

GO/MKII

RCM

RCM

GO/MKII

RCM

RCM

GO/MKII

RCM

RCM

Instr. Failure - Not Deployed

Not Deployed

Not Deployed

Not Deployed

Not Deployed

Not Deployed

72m

90m

95m

100m

150m

175m

200m

240m

250m

300m

400m

410m

450m

452m

525m

600m

602m

650m

225m

800m

1000m

1200m

1400m

1600m

1800m

1989m

1979m

1600m

1800m

1989m

1775m

1975m

2164m

972m

1172m

1361m

1557m

1757m

8
Table 2-1. Moored instrument and PIES measurement levels for the 

DeSoto Canyon Extension Program. 

Mooring 

Water 

Depth 

(M) 

Instrument 

Depth 

(M) 

Instrument 

Type 

I1 2000 72

90 

95 

100 

150 

175 

200 

225 

240 

250 

300 

400 

410 

450 

452 

525 

600 

602 

650 

800 

1000

1200

1400

1600

1800

1979

1989

C/T/D 

ADCP (300 kHz) - up

C/T/D 

ADCP (300 kHz) - down

C/T 

TEMP (Mini) 

TEMP (Mini) 

TEMP (Mini) 

ADCP (300 kHz) - up

ADCP (300 kHz) - down

TEMP (Mini) 

TEMP (Mini) 

S4 (Deployments 3 and 4 only)

C/T 

MK2 (Deployment 2 only)

TEMP (Mini) 

ADCP (150 kHz) (Deployment 1 only) - up

S4 (Deployments 3 and 4 only)

ADCP (75 kHz) - down 

S4 (+ 75 kHz ADCP Overlap)

RCM-7 (+ 75 kHz ADCP Overlap) 

RCM-7 

RCM-7 

RCM-7 

RCM-8 

MK2 (Deployments 3 and 4 only)

MK2 

I2 2000 1600

1800

1989

RCM-7/MK2 

RCM-7 

MK2 

I3 2175 1775

1975

2164

RCM-7 

RCM-7/MK2 

MK2 

I4 1950 1550

1750

1939

RCM-7 

RCM-7 

MK2 

J1 1372 972

1172

1361

RCM-7

RCM-7/MK2

MK2

K1 (1NE) 1771 1770 PIES 

K2 (1W) 2060 2059 PIES 

K3 (1SE) 2108 2107 PIES 

9
raw spectral estimates are smoothed using a rectangular Daniel window (Koopmans, 1974). 

EOF in the frequency domain uses spectra from multiple time series to separate the spatial and 

frequency content in terms of orthogonal modes. Preisendorfer (1988) has given a 

comprehensive treatise on EOFs. 

2.3 Upper-Layer Event Description

The I1 mooring site was strongly impacted by major Loop Current anticyclones and sometimes

the LC itself. Peripheral eddies that translate along the fronts of these major features also 

frequently affect the study location. To place the measurements in context, a brief description is 

given of the major features found in the upper-layer records that can be related to circulation 

events observed by remote sensing. Figure 2-2 shows selected 40-HLP velocity records in the 

upper 800 m of the water column. Included in Figure 2–2 are the salinity and temperature 40-

HLP records from the main thermocline at 150-m depth. At the beginning of September 1999, 

the LC was well extended to the northwest with the main front just east of the site (Figure 2-3a).

A regular sequence of warm and cold events accompanied by rotating current vectors occurred. 

The cold and warm events were accompanied by generally westward and northward flows, 

respectively. This is consistent with a sequence of frontal eddies with warm crests and cold

troughs propagating northwards along the LC front. Figure 2-3a suggests the existence of these 

cold (negative SSH anomalies) features even though they are poorly resolved by the altimetric 

maps. The warm and cold events had large and small vertical shears, respectively. The more 

depth-independent velocities in the cold events were consistent with circulation in cold eddies 

(Berger et al. 1996; Hamilton et al. 2002). The extended LC shed a large anticyclone (named “

Juggernaut”) which moved slowly westward between October 1999 and February 2000. Eddy J 

was highly elliptical in shape and as it moved westward the major axis rotated clockwise. The 

consequence of this is that I1 was sometimes just outside the front and sometimes just inside 

with the eddy center about 100 to 150 km south of the mooring. The general rotation of the 

current vectors from northwards to eastward between October 1999 and February 2000 and the 

relatively high temperatures and salinities are consistent with this scenario (Figure 2-2a). 

A particularly interesting event occurred around December 24, 1999. The current vectors rotated

clockwise from east to south, and there was a strong cooling at depth that is shown in the 

isotherm contours (Figure 2-4). Figure 2-3b gives the SSH map for December 12, 1999. It 

shows a cold eddy, centered north of the site, on the northern side of Eddy J. This eddy 

subsequently moved rapidly to the southeast, in the direction of Eddy J's swirl currents, as Eddy 

J translated further to the west. The rapid rotation of the upper-layer current vectors is consistent 

with the southeastward translation of a cold eddy through the I1 mooring site. 

During February 2000, Eddy J only peripherally affected the near-surface currents at the site and 

by the beginning of March it was centered about 26°N, 92°W (Figure 2-3c). Some large 

temperature fluctuations occurred in the surface layer at this time (Figures 2-2b and 2-4), but 

they only penetrated to about 400 m (Figure 2-4) and were accompanied by weak currents 

(Figure 2-2b). There is little sign of any peripheral eddy activity in Figure 2-3c, therefore it 

appears the upper 200 m was influenced by an anticyclone that was too small to be resolved by 

the altimetry. 

10
Eddy J

Figure 2-2a. The first year of 40-HLP velocity, temperature and salinity data from the upper-layer 

records at mooring I1 for the indicated depths.

N

Velocity (cm/s)

Temperature (°C)

Velocity (cm/s)

11

Salinity (psu)
Eddy M

Figure 2-2b. The second year of 40-HLP velocity, temperature and salinity data from the upperlayer records at mooring I1 for the indicated depths.

N

Velocity (cm/s)

Temperature (°C) Salinity (psu)

Velocity (cm/s)

12
TOPEX/ERS-2 Analysis Sep 12 1999

96W

96W

93W

93W

90W

90W

87W

87W

84W

84W

81W

81W

18N 18N

21N 21N

24N 24N

27N 27N

30N 30N

1 m/s

Sea surface height (cm)

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

TOPEX/ERS-2 Analysis Dec 12 1999

96W

96W

93W

93W

90W

90W

87W

87W

84W

84W

81W

81W

18N

21N

24N

27N

30N

1 m/s

TOPEX/ERS-2 Analysis Jul 2 2000

96W

96W

93W

93W

90W

90W

87W

87W

84W

84W

81W

81W

18N

21N

24N

27N

30N

1 m/s

TOPEX/ERS-2 Analysis Mar 5 2000

96W

96W

93W

93W

90W

90W

87W

87W

84W

84W

81W

81W

18N 18N

21N 21N

24N 24N

27N 27N

30N 30N

1 m/s

Figure 2-3a-d. Sea surface height anomaly maps from TOPEX/ERS-2 altimetric data (courtesy 

of R. Leben, CCAR). Geostrophic surface velocities are overlaid. The data is 

composited from about 7-days of satellite passes centered on the given date: 

September 12, 1999 (a), December 12, 1999 (b), March 5, 2000 (c), and July 2, 

2000 (d).

13

(a) (b)

(c) (d)
Eddy J subsequently interacted and was partially absorbed by an old major anticyclone in the 

western Gulf (April and May, 2000). The LC did not retreat very far to the south when Eddy J

was shed. It remained extended to the north for most of the first six months of the study (e.g. 

Figure 2-3b), and was probably still interacting with Eddy J up to the middle of December. 

During the middle of May 2000, a small LC eddy, that was highly elongated in the east-west 

direction, partially detached from the LC. This eddy was reabsorbed into the LC by the end of 

the month. However, as part of this process, a weak anticyclonic circulation was shed from the 

west-side of the LC. This anticyclone was named Eddy “Kinetic” (K) by the oil industry even 

though it did not qualify as a major LC eddy. By July, this weak anticyclone (Eddy K) had 

moved north and was centered over the mooring site (Figure 2-3d). Upper layer currents 

remained weak throughout this March through August, 2000 interval. When Eddy K began to 

affect the site in June 2000, the highest currents were observed in the upper 100 m along with a 

general warming of the water column (Figures 2-2b and 2-4). As Eddy K moved further over the 

site, the near-surface currents decreased and the deeper levels increased and then decreased as

the center approached. Current magnitudes were generally less than 20 cm/s. This behavior is 

characteristic of a bowl shaped depression of the isotherms and associated geostrophic current 

field slowly moving across the study area. The maximum depth of the isotherms occurred at the 

beginning of July 2000 and it is noteworthy this was similar to the observed maximum depths 

that occurred during Eddy J. However, the center of Eddy J did not pass over the site and the 

depth of the 10°C isotherm would be expected to be 600 to 650 m in the center of such a 

vigorous eddy. It is also noteworthy that the salinity in the center of the weak eddy during July 

and August, 2000 only increased to ~36.4 psu. This implies that water from the core of the LC 

(salinities > 36.6 psu) was not incorporated into this anticyclone. 

The marked contrast of the vigor of the current and temperature fluctuations between the first 

and second six months is clearly shown in Figures 2-2a and 2-4a. In the first interval, the upperlayer currents at the site were dominated by the peripheries of the LC and Eddy J. In the second 

half, Eddy J had moved away from the study area and the upper-layer flows were relatively 

quiescent. This distinction in the nature of the flows was not reflected in the deep current fields

that are discussed in the next section. 

The weak, warm Eddy K remained over the site until November 2000. It interacted with the LC 

and a large cyclone to the northwest of an extended LC. These interactions appear to have

strengthened this eddy and the temperatures and salinities increased indicating that LC derived 

water had been entrained in this circulation. An example of these interactions is given in Figure 

2-3e for September 24, 2000. In November 2000, Eddy K began to move westward and the 

cooling and weak southward flows indicate that the site was being influenced by the western side 

of a cold cyclone situated north of the LC (Figure 2-3f). At the beginning of January 2001, the 

LC front moved over the study site with northeastward currents, and high salinities and 

temperatures. This was followed by a peripheral cyclone (Figure 2-3g) that moved through the 

site towards the northwest. The current vectors (Figure 2-2b) rotated anticlockwise and the 

temperatures were relatively cool. 

The high eastward and northeastward currents associated with a detaching LC eddy (known as

“Millenium”), arrived over Mooring I1 in March 2001 and dominated the records for the next 

three months. After being shed, Eddy M was a moderate size, relatively circular LC anticyclone 

14
TOPEX/ERS-2 Analysis Sep 24 2000

96°W

96°W

93°W

93°W

90°W

90°W

87°W

87°W

84°W

84°W

81°W

81°W

18°N 18°N

21°N 21°N

24°N 24°N

27°N 27°N

30°N 30°N

1 m/s

TOPEX/ERS-2 Analysis Nov 27 2000

96 ̊W

96 ̊W

93 ̊W

93 ̊W

90 ̊W

90 ̊W

87 ̊W

87 ̊W

84 ̊W

84 ̊W

81 ̊W

81 ̊W

18 ̊N

21 ̊N

24 ̊N

27 ̊N

30 ̊N

1 m/s

TOPEX/ERS-2 Analysis Jan 31 2001

96 ̊W

96 ̊W

93 ̊W

93 ̊W

90 ̊W

90 ̊W

87 ̊W

87 ̊W

84 ̊W

84 ̊W

81 ̊W

81 ̊W

18 ̊N 18 ̊N

21 ̊N 21 ̊N

24 ̊N 24 ̊N

27 ̊N 27 ̊N

30 ̊N 30 ̊N

1 m/s

TOPEX/ERS-2 Analysis Apr 30 2001

96 ̊W

96 ̊W

93 ̊W

93 ̊W

90 ̊W

90 ̊W

87 ̊W

87 ̊W

84 ̊W

84 ̊W

81 ̊W

81 ̊W

18 ̊N

21 ̊N

24 ̊N

27 ̊N

30 ̊N

1 m/s

Sea surface height (cm)

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

15

(f)

(g) (h)

(e)

Figure 2-3e-h. Sea surface height anomaly maps from TOPEX/ERS-2 altimetric data (courtesy 

of R. Leben, CCAR). Geostrophic surface velocities are overlaid. The data is 

composited from about 7-days of satellite passes centered on the given date: 

September 24, 2000 (e), November 27, 2000 (f), January 31, 2001 (g), and April 

30, 2001 (h).
TOPEX/ERS-2 Analysis May 21 2001

96 ̊W

96 ̊W

93 ̊W

93 ̊W

90 ̊W

90 ̊W

87 ̊W

87 ̊W

84 ̊W

84 ̊W

81 ̊W

81 ̊W

18 ̊N 18 ̊N

21 ̊N 21 ̊N

24 ̊N 24 ̊N

27 ̊N 27 ̊N

30 ̊N 30 ̊N

1 m/s

TOPEX/ERS-2 Analysis Jul 23 2001

96 ̊W

96 ̊W

93 ̊W

93 ̊W

90 ̊W

90 ̊W

87 ̊W

87 ̊W

84 ̊W

84 ̊W

81 ̊W

81 ̊W

18 ̊N

21 ̊N

24 ̊N

27 ̊N

30 ̊N

1 m/s

TOPEX/ERS-2 Analysis Aug 22 2001

96 ̊W

96 ̊W

93 ̊W

93 ̊W

90 ̊W

90 ̊W

87 ̊W

87 ̊W

84 ̊W

84 ̊W

81 ̊W

81 ̊W

18 ̊N 18 ̊N

21 ̊N 21 ̊N

24 ̊N 24 ̊N

27 ̊N 27 ̊N

30 ̊N 30 ̊N

1 m/s

Sea surface height (cm)

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

Figure 2-3i-k. Sea surface height anomaly maps from TOPEX/ERS-2 altimetric data (courtesy 

of R. Leben, CCAR). Geostrophic surface velocities are overlaid. The data is 

composited from about 7-days of satellite passes centered on the given date: 

May 21, 2001 (i), July 23, 2001 (j), and August 22, 2001 (k).

16

(i) (j)

(k)
Figure 2-4a. The first year of upper layer isotherm depths as a function of time. Temperatures 

are in degrees Celcius. The depths of the 40-HLP temperature measurements used 

are indicated on the right side of the figure..

17

8°

10°

12°

14°

16°

18°

20°

Eddy J 25°
(Figure 2-3h). As with the passage of Eddy J, the upper layer temperature fluctuations (Figure 2-

4b) were considerably more energetic than the previous 9 months (March 2000 to January 2001) 

when no major LC eddies were affecting the site. Similar to Eddy J, the center of Eddy K was 

south of the site and the displacements and the clockwise axis rotations of the eddy as it 

translated westward caused large changes in temperatures. However, the site was generally

closer to the center of Eddy M than it was for Eddy J as can be seen by the greater depths (~ 600 

m) of the 10°C isotherm in the former compared to the latter (~ 450 m). This is also shown by 

the generally higher salinities at 150 m during March through May, 2001 than in the earlier 

September 1999 through January 2000, interval. Eddy M moved away to the west-southwest and 

when the front was over the site there was a cold event through the upper water column around 

May 16, 2001 (Figure 2-4b). The current vectors rotated anticlockwise (Figure 2-2b) and the 

temperature and velocity signals were similar to the cold event in December 1999 when Eddy J 

was moving away from the site. The major axis of both eddies at the time of these events were

directed northwest to southeast (Figures 2-3b and 2-3i). The implication is that this position and

orientation of a major LC eddy was favorable for the rapid translation of frontal cyclones. 

By early June 2001, Eddy M was no longer directly influencing the site. A cyclonic eddy on the 

northwest side of the LC caused the weak westward and southwestward flows in June and July 

2001. These strengthened as this cyclone apparently interacted with a slope anticyclone (Figure 

2-3j). In August and September, the vectors rotated anticlockwise and there were two cold 

events in the temperature records which may be interpreted as the cyclone moving off to the

northeast, around the LC front, accompanied by an intrusion of the southern side of the slope 

anticyclone over the site (Figure 2-3k). 

2.4 Deep Currents

The 40-HLP currents from the lower 1000 m of the water column at I1 are given in Figure 2-5. 

Currents and temperatures at 100 m below the water surface are also shown so that the lower 

layer currents can be compared to the presence or absence of major eddies. The lower layer 

currents were characterized by energetic fluctuations with periods of 10 to 20 days that persisted 

for several months. At I1, the amplitude of the fluctuations increased suddenly and then decayed 

slowly over several months. This can be considered to be characteristic of trains of wave-like 

energy propagating through the site. Motions were coherent through the lower 1000 m of the

water column and there is evidence of larger magnitude currents closer to the bottom than at 

1000 to 1200 m depth. This is known as bottom intensification and is characteristic of planetary 

motions known as topographic Rossby waves (Rhines, 1970). At least three of these energetic 

wave events can be identified in the two years of the records. The first event was already in

progress when the moorings were deployed in September 1999. This generated some of the 

highest bottom speeds observed in the two-year study. A second possible event began in 

December 1999, coincident with the cold cyclone passage discussed above, but it is not clear if it 

can be considered as distinct from the earlier wave train. After a period of quiescence in 

February and March 2000, another energetic wave train appearred and the fluctuations persisted 

until at least the beginning of August 2000 (Figure 2-5a). Bottom current fluctuations were 

small from August through November. In December 2000, bottom speeds increased to about 20 

cm/s and the fluctuations could be considered to be a weak wave train. However, in February 

2001, a major event occurred, just prior to the arrival of Eddy M, which persisted through June 

18
Eddy M

8°

10°

12°

14°

16°

18°

20° 25°

Figure 2-4b. The second year of upper layer isotherm depths as a function of time. Temperatures 

are in degrees Celcius. The depths of the 40-HLP temperature measurements used are 

indicated on the right side of the figure..

19
N

Figure 2-5a. The first year of 40-HLP velocity vectors from below 1000 m at I1. The top two 

panels show the velocities and temperature at 100 m depth.

Velocity (cm/s)

Velocity (cm/s)

Temperature (°C)

20
(Figure 2-5b). Finally, at the end of the measurement period, in August 2001, the initial part of 

another energetic wave train was observed, again coincident with the passage of a cold cyclone.

Thus, the lower layer currents at I1 were dominated by energetic events that persisted over 

several months separated by intervals of low amplitude fluctuations. 

An important question is whether the waves in the lower-layer had have any relation to upperlayer flows. The September 1999 and February 2001 wave trains occurred when the upperlayers were dominated by Eddies J and M, respectively. The wave train occurred in April 2000

when there was no major eddy activity in the central Gulf (Figure 2-5). For most of the records 

the 1800 m and 100 m currents appear to have had little or no relationship. However, some of 

the major current fluctuations that occurred in September 1999, December 1999, February 2001 

and August 2001, had a similar character to those of the surface-layer that were associated with 

cyclones moving through the site. In particular, the westward event around September 8, 1999 

was similar at all depths at I1 (see also Figures 2-2a and 2-5a). Similar events were observed at 

all the bottom records at this time though there were some phase differences. There were also 

similar current fluctuations at all depths of I1 for the event around December 24, 1999. In this 

case the flows were eastward at all depths and were attributed to a cold cyclone interacting with 

Eddy J. In early February 2001, the initial, smaller amplitude fluctuations had some similarity 

with the anticlockwise rotating current vectors in the upper layer associated with a propagating 

peripheral cyclone (Figures 2-2b and 2-5b). However, the large eastward fluctuation around 

August 10, 2001 was in the opposite direction to the upper-layer currents at this time, even 

though they were again associated with a cyclone. These events suggest that occasionally there 

may have been connections between rapidly varying upper-layer flows and wave-like events in 

the lower-layer. However, these apparent relations could be just circumstantial with the 

observed waves propagating into to the region from distant sources. It is also difficult to test 

statistically the significance of such brief events where the currents appear to have had some

coherence through the water column when in general the upper and lower level flows had very 

different characteristics. 

The April 2000 wave train also showed some relation with the upper-layer currents (Figure 2-

5a). However, the fluctuations at the 100 m level were smaller than at 1800 m on I1. This may

be an indication of the lower-layer TRW activity penetrating up into the upper-layer when the 

latter is quiescent. There was no obvious large change in the configuration of the LC in this

March-April period that could be considered as a possible distant source of such energetic

waves. 

Comparison of the lower-layer currents across the arrays (I1, I2, I3 and J1 in the first year, and 

I1, I2, I3 and I4 in the second year) shows how the wave energy changed with position and water 

depth. The 40-HLP lower-layer velocity vectors from the four moorings in each year are given

in Figure 2-6. It is immediately apparent that the fluctuations on each mooring were highly

coherent and thus the lower part of the water column moved like a slab. Mooring I2 had the 

highest amplitude currents, with I1 and I3 being a little less energetic and J1 and I4 considerably

less energetic. The fluctuations at the deepest mooring, I3, were also a little more rotary than the 

strongly rectilinear fluctuations at the other moorings. The pattern of the fluctuations through 

time is also quite similar at all the moorings. The records begin in September 1999 with a burst 

of very strong currents. These events produced the highest speeds observed at I2 (Figure 2-7), 

21
N

Figure 2-5b. The second year of 40-HLP velocity vectors from below 1000 m at I1. The top two 

panels show the velocities and temperature at 100 m depth.

Velocity (cm/s)

Velocity (cm/s)

Temperature (°C)

22
and clearly the effect of the event was felt at J1 where the highest speeds of that one-year record

was also observed. From these initial events, the energy slowly decayed through March 2000. 

The decay rates were not uniform across the array. The fluctuations persisted more strongly at I2 

than at I3 and I1, and the decay at J1 occurred over a much shorter period. By the middle of 

October 1999, the maximum speeds at J1 were below 20 cm/s (Figure 2-7a). 

In April 2000, the burst of energetic activity also had uneven distributions of magnitude and the 

change of activity with time also differ from the September 1999 waves. The April 2000 set of 

waves was again observed at all three I moorings though the maximum speeds were less than for 

the September 1999 events (Figure 2-6a). Again, I2 had the highest speeds and the high speeds 

persisted longer than at the other moorings. Some of the speed pulses were also observed at J1, 

but again their amplitudes were considerably diminished (Figure 2-7a). 

In contrast, the February 2001 bottom currents at I1 had the highest speeds with more persistant 

high speeds at I3 than occurred in the previous wave trains. Again, the energetic fluctuations

continued at I2 much longer than at the other two moorings and seem to merge with the August 

2001 event (Figures 2-6b and 2-7b). Current amplitudes at I4 were considerably reduced over 

those at I2 during the last six months of the records. I2 and I4 were separated by a distance of 

only 6 km, with I4 having been slightly higher (50 m) up the escarpment slope (Figure 1-2). It is 

clear that the higher speed events at I4 (> 25 cm/s) occurred only for eastward flows at both I2 

and I4. The speeds at I2 were approximately double those at I4. This very large change in short 

distance implies very strong horizontal shears and strong influence by the local topography of the 

escarpment slope. It is possible that I4 was situated in a flow separation zone, however, flow 

directions at both I2 and I4 oscillated both eastwards and westwards, and because the change in

magnitude was also observed at the upper current meters, which are 400 m above the bed, makes

this unlikely (Figure 2-6b). 

Interpretation of these bottom layer records in terms of TRWs is given in Chapter 3. This will 

include diagnosis of characteristic periods and how bottom-trapped the motions were. It can be 

seen that the amplitude of the record at 200 and 400 m from the bottom were often similar 

(Figure 2-6) implying a depth-independent flow. However, the dense instrumentation of I1 

shows that the records at 800 and 1000-m from the bottom have weaker fluctuations than the 

deeper records. It is clear, however, that the major events of the first six-months are more 

barotropic than the fluctuations that began in April 2000 and February 2001 (Figure 2-5). 

23
I3

I1

I2

J1

N

N

N

N

Figure 2-6a. The first year of 40-HLP velocity vectors from below 1000 m at I1, I2, I3 and J1. 

The direction of the y (V-component) axis with respect to North for each mooring 

is indicated.

Velocity (cm/s)

Velocity (cm/s)

Velocity (cm/s)

Velocity (cm/s)

24
I2 N

N I4

Figure 2-6b. The second year of 40-HLP velocity vectors from below 1000 m at I1, I2, I3 and I4. 

The direction of the y (V-component) axis with respect to North for each mooring is 

indicated.

Velocity (cm/s)

Velocity (cm/s)

Velocity (cm/s)

Velocity (cm/s)

N I3

N I1

25
Figure 2-7a. The first year of 3-HLP speed records from 200 m above the bottom at I1, I2, I3 and 

J1. Note the change of velocity scale for J1.

Speed (cm/s) Speed (cm/s) Speed (cm/s) Speed (cm/s)

3-HLP Speeds

26
Figure 2-7b. The second year of 3-HLP speed records from 200 m above the bottom at I1, I2, I3 

and I4. Note the change of velocity scale for I4.

Speed (cm/s) Speed (cm/s) Speed (cm/s) Speed (cm/s)

3-HLP Speeds

27
3.0 ANALYSIS OF CURRENTS 

3.1 Basic Statistics 

The basic statistics for all current records below 1000 m, and selected records from the upperlayer at I1, are given in Table 3-1. The means, standard deviations and extremes are given for 

the 3-HLP east and north components and speeds. The standard deviations are also given for the 

40-HLP velocities along with the ratio between the 40 and 3-HLP kinetic energy, and principal 

axis directions. The latter are calculated with the 40-HLP data and the ratio shows how the 

degree the low frequency motions dominate the variances of each record. In the lower layer 

(normally below 1000 m water depth), the maximum standard deviations and speeds are found at 

the I2 mooring followed by I3, I1, J1 and I4 in decreasing order. However, I4 and J1 are very 

similar and the higher speeds observed at J1 were caused by the initial September event when

maximum speeds at J1 were comparable to I1 (~ 50 cm/s). This first strong event in the record 

also produced the 95 cm/s maximum speed at I2. If you exclude the first two weeks of the 

record at J1, then the maximum speed observed at 1361 m was 29.2 cm/s which is smaller than 

the maximum speeds measured at I4. It is noted that all the near-bottom instruments, which were

in the frictional boundary layer, show a 10° anticlockwise rotation of the principal axis compared 

to the instrument 200 m from the bottom. This is consistent with Ekman turning in the bottom 

boundary layer. 

A summary of the low-frequency variance of the deep current data is given in Figure 3-1 in the 

form of standard deviation ellipses. The amplification of the KE from I1 to I2 on the same

isobath, separated by only 23 km is clearly evident. The variance at I3 is similar to I1, but is less

polarized with the major axis being at an angle to the isobaths. Motions at J1, above the 

escarpment and 30 km from I2, and I4, only 6 km west of I2, however, had small variances 

compared to the I1, I2, and I3 moorings. Therefore, the steep slope of the escarpment appears to

have insulated the region to the west and north from the energetic deep water motions. The 

ellipses at 200 m and 1000 m from the bottom are shown for I1, and clearly demonstrate the 

bottom trapped nature of the current fluctuations. Mean currents are also given in Figure 3-1 for 

the two-year 40-HLP records. There was a small mean southwestward current at I3, but at the 

base of the escarpment (I1 and I2) the means were of order 5 cm/s at 200-m from the bottom.

Smaller mean flows were observed at I4 and J1 for shorter averaging periods. Again, it is 

unknown if the escarpment slope had a role in generating a moderate westward near-bottom

mean current that again had considerable variation over the short distances between I3 and J1. 

In the upper layer at I1, means, maxima and standard deviations decreased with depth. This is 

mainly the influence of the two major LC eddies that were over the measurement site for 

approximately 9 months out of the 24 months. The minimum in the statistics of the whole water

column at I1 occurred at 1000 m and illustrates the two-layer nature of the deep Gulf. Energy in 

the currents increased both above and below this level with the maxima occurring near the water 

column boundaries (i.e. surface and bottom). 

29
Table 3-1. Statistics of currents measured during this project. The first column shows the mooring ID and th

surface of the measured current time series. Positive U is east; positive V is north. All velocities acm/s. 

Mean 

(3-HLP) 

Standard Deviation 

(3-HLP) 

Maximum (3-HLP) Minimum (3-HLP) Standard De

(40-HLP

Depth 

(m) U V Speed U V Speed U V Speed U V 

% of Time

with

Records 

U V 

I1 Time Period: 8/29/1999 – 9/06/2001 Coordinate Rotation 0° Water Depth: 2000 m

32 12.00 7.02 44.04 37.03 29.84 29.14 139.6 154.8 154.8 -113.0 -112.0 83 36.40 28.79 

106 15.63 0.47 35.95 30.72 28.33 26.24 118.1 98.5 123.7 -72.6 -106.6 100 30.36 27.57 198 7.54 0.76 22.04 20.34 18.31 17.72 76.3 71.0 83.7 -55.7 -68.1 100 20.06 17.66 300 5.35 0.32 18.02 16.11 15.08 13.66 69.1 53.6 74.3 -49.5 -55.7 100 15.77 14.50 410 4.72 -0.45 15.33 16.10 11.31 13.08 59.9 49.6 60.0 -46.5 -41.1 46 15.53 10.74 

588/602 4.04 1.56 12.08 10.75 9.34 8.32 45.8 34.5 47.3 -36.7 -26.1 51 10.24 8.49 

802 0.48 -0.21 7.40 7.28 5.33 5.11 30.7 20.1 47.6 -45.0 -25.3 100 6.50 4.32 

1000 -0.80 0.03 6.01 6.46 4.15 4.76 27.5 20.0 40.3 -38.8 -19.1 100 6.01 3.77 1200 -1.12 0.20 7.31 8.59 5.33 6.96 34.6 31.8 49.7 -49.3 -30.9 81 8.19 4.96 1400 -1.49 0.15 8.87 9.66 6.48 7.58 42.2 32.6 53.4 -52.9 -37.0 94 9.46 6.27 

30 1600 -2.74 0.96 9.01 10.16 6.11 8.22 42.8 30.8 52.3 -52.1 -43.6 72 9.92 5.87 

1800 -2.76 1.31 10.30 11.07 7.05 8.64 54.9 38.3 66.3 -53.9 -44.1 100 10.85 6.82 1979 -1.43 0.78 10.64 11.27 8.88 9.72 50.2 49.5 67.5 -36.7 -47.3 50 11.08 8.60 

I2 Time Period: 8/29/1999 - 9/06/2001 Coordinate Rotation 0° Water Depth 1998 m

1600 -4.73 0.37 16.97 19.54 6.08 12.13 47.7 23.5 95.0 -95.0 -29.0 73 19.15 5.76 1800 -4.53 0.39 17.15 20.27 6.60 13.31 49.9 30.2 85.6 -72.5 -49.6 100 19.91 6.21 1989 -4.09 -0.91 16.75 16.88 8.05 9.15 40.9 21.5 90.1 -76.9 -58.6 100 16.46 7.49 

I3 Time Period: 8/29/1999 – 9/06/2001 Coordinate Rotation 0° Water Depth 1158 m

1775 -0.97 -0.44 13.09 14.42 9.04 10.46 50.2 43.3 73.7 -72.5 -41.9 68 14.07 8.80 1975 -1.00 -0.94 13.33 13.64 8.58 9.00 47.2 39.5 66.1 -65.0 -40.1 100 13.31 8.34 2164 -1.28 -1.45 12.79 13.69 7.75 9.22 48.6 22.5 68.1 -59.1 -46.0 100 13.37 7.58 

 J1 Time Period: 8/28/1999 - 8/28/2000 Coordinate Rotation 0° Water Depth 1373 m

972 -1.20 -0.53 5.07 5.38 3.45 4.07 21.6 10.8 36.6 -36.5 -24.7 100 4.60 2.33 

1172 -2.00 -0.56 4.88 5.90 3.13 4.99 15.1 16.4 48.8 -48.7 -27.1 100 5.27 2.04 1361 -4.34 0.00 6.54 6.84 4.38 6.43 12.2 22.7 49.5 -47.1 -24.4 88 5.87 3.20 

I4 Time Period: 2/13/2001 - 9/06/2001 Coordinate Rotation 0° Water Depth 1957 m

1557 -0.90 0.71 7.43 7.74 3.75 4.32 22.6 19.2 30.2 -29.3 -12.3 28 7.23 2.89 1757 -1.86 0.74 6.44 7.63 3.49 5.68 15.0 15.5 42.5 -41.7 -11.6 28 6.87 2.69 
1999/9/2 to 2001/9/3

Figure 3-1. Standard deviation ellipses and mean velocity vectors from 40-HLP current data for 

200 m and 1000 m (green and dashed) above the bottom. Two-year long records 

used except for J1 (12 months - magenta) and I4 (6 months - red). Only I1 provided 

measurements 1000 m above the bottom.

31

I1 I2

I3

I4

J1
3.2 Topographic Rossby Waves 

The basic description of the lower-layer currents in Chapter 2 emphasized the wave-like nature 

of the nearly barotropic fluctuations in the lower 1000 m of the water column. Rhines (1970) 

first gave the theory of topographic Rossby waves. Important features of TRW theory are: 

1. The wave motion is bottom intensified; thus current amplitudes increase in magnitude

towards the bottom.

2. There is no phase difference between currents at different depths; therefore at any 

particular wave frequency, the motion is columnar. 

3. The maximum frequency or cutoff frequency for TRW's is Nα where α is the bottom 

slope, defined as normal to the general trend of the isobaths, and N is the Brunt-Vaisala 

frequency of the lower water column. Bottom slopes are defined over scales similar to 

the wavelengths of TRW's (~ 50 to 100 km). The effect of small or large perturbations of 

the bottom slope on TRW propagation is not covered by present linear theories. The 

wave frequency, ω, is proportional to the bottom slope and the cosine of the angle that

the wavevector makes with the isobaths. At the highest allowed frequency, the phase 

velocity is parallel to the isobaths such that shallow water is on the right of the direction 

of wave propagation. 

4. At the highest allowed frequency, wave motions are rectilinear and perpendicular to the

phase vector and isobaths. At lower frequencies the wave motions become more parallel 

to the isobaths. Longer wave-length motions are also less bottom trapped than high 

frequency waves. 

5. TRW's are dispersive and it can be shown that if the phase vector is directed into deeper 

water, then the energy flux has component towards the shallower water (Thompson, 

1977). TRW's are refracted by changing topography. These ray-paths can be calculated 

by WKB theory which assumes that the environment (e.g. bottom slopes) change 

"slowly" compared to the wavelength of the motions. This is rarely strictly true in

practice. 

TRW ray paths in this study were calculated using the full dispersion relation. The basis of the 

method is given in Meinen et al. (1993b) and used by Pickart (1995) to calculate TRW ray paths 

generated by the deep Gulf Stream in the Middle Atlantic Bight. The dispersion relation for 

TRW’s is given by the coupled equations (Pickart, 1995): 

λ2 = ( k

2

 + l2 + βk/ω ) ( N/f )2 (1)

λ tanh( λh ) = N2/(ωf ) ( khy – lhx ) (2)

where h is the water depth, 

N is the constant Brunt-Väisälä frequency, 

f is the Coriolis parameter using the β-plane assumption, 

 k = (k, l) is the wavenumber vector in east and north (x, y) coordinates, 

ω is the wave frequency, and 

 1/λ is the vertical trapping scale of the wave. 

32 
Under the WKB approximation, where changes in wave amplitude and phase caused by the 

environment are assumed to vary on scales larger than the local wavelength, the equations 

governing the path of a wave and its wavenumber are (LeBlond and Mysak, 1978): 

Dt x = ∂ω / ∂k = cg (3) 

Dt k = ∑ - ∂ω / ∂γi ∇γi (4)

where Dt = ∂ / ∂t + cg • ∇

is the derivative following the wavegroup, x is the path of the ray, and cg is the group velocity. 

The γI are the environmental parameters that cause refraction of the wave. There are three such

parameters for TRWs: h (water depth), ∇h (bottom slope), and N (Brunt-Väisälä frequency). N 

is assumed constant for these calculations. The WKB assumption is marginal though it is often 

used under conditions that have sharp changes in the environmental parameters. Therefore, the 

topography must be smoothed over at least the wavelength scale for the method to apply. This is 

discussed in Section 3.6. The ray tracing equations, (3) and (4), are solved using 4th order 

Runge-Kutta methods to determine ray paths, and the change in the wavenumbers along the rays. 

Essentially the same method was used by Oey and Lee (2002) for an investigation of TRWs

generated by a numerical circulation model of the Gulf of Mexico basin. 

3.3 Spectra 

The kinetic energy (KE) spectra, in variance preserving form, i.e. equal areas under the curve 

represent equal contributions to the variances, were calculated for lower-layer instruments. 

Because there were differences between the various wave trains observed in the lower layer 

records, KE spectra were calculated for five periods of 100 to 120 days that included the events 

discussed in the previous section. Table 3-2 summarizes these periods and includes the complete

two-year period that is used for analysis of longer period motions. 

The KE spectra for the currents, 200 m from the bottom are given in Figure 3-2. The two-year 

spectra show the dominance of the motions at I2 over the frequency band 0.02 to 0.09 cpd (50 to 

11 day periods). At periods shorter than 8 days, the spectra at the three I instruments are similar.

Between 8 and 11 days, I1 had about half the KE of I2 and I3. The maximum energy difference 

between I2 and its neighbors occurred at periods of about 16 to 20 days. The spectral peak at 16 

to 20 days and the lack of energy at periods longer than about 30 to 40 days are similar to spectra

of deep currents in the western and central Gulf (Hamilton, 1990). In the eastern Gulf, under the

LC, spectra did show high energy at 20 to 25 days, but also at longer periods (Hamilton and 

Lugo-Fernandez, 2001). The difference between the spectra for this site (Figure 3-2) and other 

regions of the Gulf is the high-energy peak at 8 to 11 day periods. The lack of energy at periods 

shorter than about 5 to 7 days corresponds to the cut-off frequency for TRWs that depends on 

bottom slope and lower-layer stratification. 

33 
Table 3-2. Spectra and TRW Analysis Periods 

Period Start Date 

(yyyy-mm-dd) 

Length 

(days) 

Upper-Layer Circulations 

1 1999-09-03 100 Eddy J

2 1999-12-01 100 Cyclones on J 

3 2000-04-01 120 Eddy K (weak anticyclone) 

4 2000-09-02 120 Cyclones

5 2001-02-19 120 Eddy M

Two-Year 1999-09-03 730 Complete Observation Period 

The spectra, for the September to December, 1999 interval (Period 1, Figure 3-2), show that the 

dominant response at I1 and I2 was at about the 8 – 9 day period. Both I1 and I2 were amplified 

over the broadband red spectra at I3. The energy at J1, which was above the escarpment, was 

negligible compared to the I moorings, as it is for all the periods where comparisons can be made 

(Figure 3-2). The second period has about a 10-day overlap with period 1, but even so the 

spectral peaks show a shift to a lower frequencies, with periods of 11 to 12 days. Energy levels 

were much lower because this period includes February and March 2000, which was relatively 

quiescent. However, I1 and I2 were still elevated above I3. In the April to August period (3), 

the spectral peak shifted to 12- to 15-day periods with relatively little energy at periods shorter 

than 10 days. The amplification of I2 over I1 and I3, which had similar energy levels, was larger 

than in the earlier periods. In period 4, another interval of relatively low energy, the 

characteristic peak remained at about 14 days, but I3 had similar variances to period 3 and both 

I1 and I2 diminished considerably. I2, however, still had the largest variances. For the last wave 

train that begins in February 2001 (period 5), there was a distinct change in characteristics. 

Unlike all the previous periods, I2 did not have the highest energy levels over most of the 

energetic frequencies. I3 dominated and there were two spectral peaks, at about 8 days, and 17 

to 20 days, respectively. The energy levels at I4 were much smaller than at the other three

moorings, with most of its energy at shorter periods than 10 days. 

These results imply that the wave trains, which can be identified in Figures 2-5 and 2-6, had 

distinctly different characteristics with different dominant periods and horizontal distributions of 

KE. These differences between wave trains suggest that they may have had different origins. 

KE spectra calculated for the BP mooring, which was within a few kilometers of I1, showed that 

fluctuations at 7- to 10-day periods dominated the September 1997 to April 1998 measurement 

period (Hamilton, 1998). 16-day motions were present at a spectral peak, but with lesser

amplitudes. The two-year KE spectra in Figure 3-2 are an indication of “average” conditions and

indicate there were two dominant periods, around 8 to 12 days and 16 to 20 days. The shorter 

periods dominated at I3, which had similar energy levels to I2, and the longer periods at I2 and 

I1. I2 had two to three times the variance of I1 and I3 at this longer period. The records at J1 

and I4 show that this high energy only intermittently penetrated west and upslope of I2. This 

34 
Two-Year Period 1 Period 2

Period 3 Period 4 Period 5

Figure 3-2. Kinetic energy spectra in variance preserving form, for 40-HLP velocities from instruments 200-m ab

moorings I1, I2, I3, J1 and I4 (see color code). The analysis periods are given in Table 3-2. Degrees 

18 for the two-year and period calculations, respectively.

35

1 cycle/10 days
spatial inhomogeneity implies, perhaps, that topography was strongly influencing the TRW wave

trains through focusing and reflection of energy; there was non-linear transfer of energy between

frequency bands; and/or that this could have been a genesis region. 

It is useful to examine how the motions at 200 m from the bottom decay with increasing distance

above the seabed. Figure 3-3 shows the KE spectra at the 1000, 1400 and 1800-m levels of I1 

for the intervals defined in Table 3-2. The two-year spectra are split, approximately equally,

between the 7 to 12 day and 12 to 30 day period bands. Both bands show decay with height with 

the shorter periods showing less penetration to the 1000-m level than the longer periods. This is 

in agreement with TRW theory as shorter period, and therefore, shorter wavelength TRW's are

more strongly bottom trapped. However, spectra during period 1, 2 and 4 show that motions 

were nearly depth-independent when the 1400 and 1800-m levels are compared. Spectra for

periods 3 and 5, on the other hand, show strong decay with height above the bottom for periods 

longer than 7-days. This, again, implies that the wave trains had different characteristics at 

different periods and thus, could have been generated by very different processes. Hogg (2000) 

also found strongly bottom intensified and nearly barotropic motions in the same region of the

tail of the Grand Banks. 

3.4 Vertical EOF Analysis at I1 

The spectra for I1 (Figure 3-3) were used for frequency domain EOF analyses of the depth 

dependence of the energetic currents. The resulting structures of the coherent motions in the

lower water column are given in Figure 3-4 where the frequency bands are centered on the 

spectral peak of each of the analysis periods. Only one frequency band was used for each 

interval except period 5 where the high and low frequency peaks were about equal. The first 

mode, in all cases, accounted for a very high percentage (85 to 95%) of the total variance of both 

the U and V-components at the available instrumented levels below 1000 m. The exception is

the quiescent period 4 where the relatively weak fluctuations accounted for 72% of the total 

variance of the 6 depths used for this analysis. This is consistent with the fluctuations being

dominated by highly coherent TRWs. The fluctuations were also in-phase through the water 

column and all the modes show a decrease in amplitude with height above the bottom. Themajor 

axes of the fluctuations were aligned approximately with the general trend of the isobaths. In 

period 5, the longer period motions were rotated anticlockwise from the shorter period 

fluctuations, and thus the former had a larger cross-isobath component. This is a departure from 

linear TRW theory in that it is expected that the major axes of shorter period motions should be 

more perpendicular to the isobaths than the longer period motions. This inconsistency will be 

discussed further when the horizontal structure of the waves is presented. Otherwise the longer

period band showed less decay with height than the shorter which implies a smaller trapping

depth with higher frequency. This is the behavior expected from the theory. 

The periods (1, 3 and 5) with major events had similar energy levels but different degrees of 

bottom intensification. Periods 1 and 2 had almost uniform motion at the bottom three levels 

(1400, 1600 and 1800 m) with decrease in amplitudes only observed at the two levels above 

these. The short period motions in periods 3 and 5 had a marked decay with height above the 

bottom. Period 3 peak frequency was lower than period 1, which should favor more barotropic 

fluctuations rather than the opposite. This further confirms that the different wave trains had 

36 
Two-Year Period 1 Period 2

Period 3 Period 4 Period 5

Figure 3-3. Kinetic energy spectra in variance preserving form, for 40-HLP velocities from instruments 1000-m, 

1979-m (Period 5 only) depths, for mooring I1 (see color code). The analysis periods are given in Ta

freedom are 30 and 18 for the two-year and period calculations, respectively.

1 cycle/10 days

37
-8 -6 -4 -2 2 4 6 8

1

14 - 7 days

2

17 - 8 days

3

25 - 8 days

4

25 - 7 days

5

30 - 11 days

5

11 - 5 days

Period

93.1% 95.4% 96.1% 72.2% 93.5% 85.2%

Percentage of Total Variance

1000 m

1200 m

1400 m

1600 m

1800 m

1989 m 1979 m 1979 m

Figure 3-4. Mode 1, represented as hodographs, resulting from EOF analyses of current records 

at I1 below 1000 m for the indicated periods (see Table 3-2) and frequency bands.

38
different characteristics, and thus, may not have been generated by exactly the same processes. 

During period 3, the wave train occurred when the surface layer currents were small and is of

interest to determine how far into the surface layer, bottom trapped TRWs can be traced. The 

other events occurred when energetic LC eddies were present and any TRW signal above 800 to 

1000 m would be overwhelmed by the eddy currents. Figure 3-5 shows the hodographs for 

period 3, using records fairly equally spaced with depth through the water column. The signal 

was significantly coherent with the mode at all levels below 300 m. The upper 3 levels can 

probably be regarded as being primarily noise. The second mode (not shown) accounted for 

15% of the total variance and was surface intensified with only the top 4 levels being significant. 

Therefore, in this period, when the surface circulation was dominated by a weak anticyclone 

(Eddy K), strong TRW motions accounted for the majority (73%) of the energy in the 2000-m

water column at I1. This is interesting because TRW theory (Rhines, 1970) indicates that such

wave motions involve the whole water column, but this has not been previously observed to the

author’s knowledge, except during a similar quiescent period at the BP Atwater mooring 

(Hamilton, 1998). 

The trapping depths can be found by least-square fitting of the major axis amplitudes to the 

function A0 cosh (λz) where the depth z is measured upwards from the ocean surface (depth

below the sea surface is negative) and (1/λ) is the trapping depth. The wavelength of the TRW's

is then related to λ by equation (1) with β = 0, i.e. 

 λ = NK/f 

where K = (k2 + l2)1/2 is the wavenumber magnitude and f, the Coriolis parameter (= 6.67 10-5

s-1). The resulting trapping depths and wavelengths (= 2π/K) for the six profiles, shown in 

Figure 3-4, are given in Table 3-3. 

Table 3-3. TRW Wave Parameters

Analysis 

Period 

Frequency 

Band (days) 

Trapping 

Depth (m) 

Wavelength

(km) 

Wavelength and 

Direction from 

Horizontal EOFs 

1 14-7 1588 151 76 180°T

2 17-8 893 85 50 189°T

3 25-8 896 85 62 188°T

4 25-7 793 75 70 198°T

5 30-11 1237 118 87 191°T 

5 11-5 683 65 73 191°T 

Two-year 30-15 - - 68 187°T 

Two-year 15-7 - - 68 194°T 

39 
-6 -4 -2 2 4 6 1800 m

1600 m

1400 m

1200 m

1000 m

800 m 48 m

106 m

198 m

300 m

452 m

658 m

Period 3

Frequency Band: 30 - 8 days

Percentage of Total Variance: 73.4%

Figure 3-5. Mode 1, represented as hodographs, resulting from EOF analyses of current records 

at I1 for the complete water column. Analysis period 3 (April - August, 2000) when 

surface layer currents are weak.

40
Table 3-3 shows that trapping depth decreased with shorter periods for the period 5 EOF

analysis, and the period 1 was less bottom trapped than the later periods. The inferred 

wavelengths are short and range from 60 to 150 km.

3.5 Horizontal EOF Analysis 

The investigation of how the TRW motions varied in space used the records measured 200 m

from the bottom at all of the moorings. The same frequency bands and periods were used as for 

the vertical analysis at I1. The results from the EOF analyses are given in Figure 3-6. The first 

modes dominate for all periods and exceed 76% of the total variances of the velocity records 

used. In the first year, the coherent responses at J1 were very small (amplitude ~ 1 cm/s) for all 

three wave trains. In the last six months, the coherent response at I4 (Figure 3-6c) was also small

compared with the moorings to the east. The distribution of amplitudes across the main array 

(I1, I2 and I3) also varied with measurement period. Thus, maximum amplitudes were observed 

at I2 for periods 1, 3 and 4. I1 dominated for period 2, and I3 for period 5. Generally, I1 had 

less variance than I3, except for period 1. The phase relationships between the moorings were 

similar for all periods with I3 lagging I2 and I1, and I1 usually having a small lead over I2. The

directions of the principal axes were consistent with this for the most part. Phase propagation 

was perpendicular to the principal axes such that the wavevector was directed into the 3rd or 4th

quadrant in a isobath coordinate system with y normal to the trend of the isbaths and directed 

into shallow water. Usually the offshore propagation of phase (i.e. the wavevector directed into 

the 4th quadrant) is consistent with onshore propagation of wave energy from presumed

deepwater generation regions. This was the case always for I3 and the principal axes of I2 were

always nearly parallel to the escarpment. However, in period 2 (Figure 3-6a) and for the lower 

frequency waves in period 5, the wave vector at I1 (Figure 3-6c), the principal axis was rotated

anticlockwise from the isobaths, implying onshore phase propagation. This may be an indication 

that the escarpment was reflecting some of the wave trains. 

The differences between the directions of the major axes between frequency bands and between 

I3 and the records at the base of the escarpment are quite interesting. The major axis of I3 was at 

a distinct angle to the isobath and this angle usually increased, in a clockwise direction, as the 

period becomes shorter. Compare period 1 (Figure 3-6a) with period 3 (Figure 3-6b) and the low 

frequency variance ellipse for period 5 (Figure 3-6c). This is exactly how rectilinear fluctuations

resulting from TRW's behave with increasing frequency. Therefore, it appears that the steep 

slope of the escarpment changes the direction of the water particle displacements causing the

fluctuations to be along the slope and perhaps amplifying the signal as it propagated to the west. 

If the steep slope is considered to be a wall so that the cross-slope velocities are zero, then the 

TRW velocities are forced to be a long-slope, as observed. This would also imply that TRW 

energy would be reflected back into deep-water. 

As a summary of average TRW characteristics, the two-year spectra were used to calculate the

characteristic motions at 200 m from the bottom for I1, I2 and I3. The EOF analysis was divided 

into two frequency bands corresponding to the major peaks in the spectra (Figure 3-4). The

energy at the 20- and 11-day periods was approximately the same and in both frequency bands, 

I1 and I2 had the maximum and minimum amplitudes, respectively. The phase relations were as 

41 
Period 1

Period 2

Figure 3-6a. Mode 1, represented as hodographs, resulting from EOF analyses of current records 

200-m from the bottom for analysis periods 1 (14-7 days) and 2 (17-8 days). 

J1

I1

I3 I2

J1

I1

I3

I2

42
Period 3

Period 4

Figure 3-6b. Mode 1, represented as hodographs, resulting from EOF analyses of current records 

200-m from the bottom for analysis periods 3 (25-8 days) and 4 (25-7 days). 

I1

I3

I2

I1

I3

I2

43
Period 5

Period 5

Figure 3-6c. Mode 1, represented as hodographs, resulting from EOF analyses of current records 

200 m from the bottom for analysis period 5 using frequency bands 30-11 days 

(upper panel), and 11-5 days (lower panel). 

I4

I1

I3

I2

I4 I1

I3

I2

44
given above and the principal axes of I1 and I3 rotated clockwise with increasing frequency 

(Figure 3-7). 

The horizontal wavenumbers and their directions can be directly estimated by least squares fit

from the phase differences between the moorings. These calculations were done without J1and 

I4 because of their low amplitudes compared to the other records. The results are given in the 

last column of Table 3-3 and are reasonably consistent with the wavelengths estimated from the 

trapping depths using the lower layer I1 records. Wavelengths of all cases were estimated to be 

between 50 and 90 km and the direction of phase propagation was south or slightly west of

south. The two-year analysis suggests that 70 km is a reasonable value for the wavelength for 

both 20- and 11-day TRWs. This suggests similar source regions for the waves even though 

different period motions dominate at different times and their genesis may not be the same. The

direction of phase propagation, calculated from the horizontal EOFs, was approximately 

perpendicular to mean direction of the major axes of the mooring data. This is an indication that 

estimating wave propagation direction from a single mooring may be misleading close to large

topographic features. 

3.6 TRW Ray Tracing 

The WKB approximation assumes that the depth, h, and the bottom slope, ∇h, vary smoothly 

over length scales similar to the wavelength of the TRWs. For this study, the GTOPO 30 world 

ocean bathymetry data set was used as a starting point. Nominal resolutions are 2’ of latitude 

and longitude. The northern slope region of the Gulf of Mexico has extremely rough 

bathymetry, so the challenge was to smooth the topography while keeping major features, such 

as the escarpment, but not introducing spurious features with surface fitting spline routines (e.g. 

oscillations where slopes have sharp changes). This was accomplished, after much 

experimentation, by first using a 50-km square median filter on the Gulf of Mexico subset of the 

bathymetry, and then fitting bivariate cubic smoothing splines to h and ∇h (Dierckx, 1982). The 

smoothing spline compromises between closeness-of-fit and smoothing by varying the number 

of knots over the grid. The resulting smoothed bathymetry is given in Figure 3-8. 

The ray tracing equations (1-4) require initial conditions for the period and wavelength of the 

wave. Equations (3) and (4) were integrated forwards or backwards in time from the initial

conditions to give an estimate of where the TRW has come from, and where it could propagate 

to, given the parameters at the measurement site. The integrations were terminated if the water 

becomes too shallow (i.e. no longer on the slope) or the group speed, cg, becomes < 0.1 cm/s. 

For a given wavelength and period, the dispersion relation, (1) and (2), can be solved for the 

wavenumber components (k,l). If the bottom slope is aligned with l, then k is always negative, 

and there is a choice of sign for the upslope component of the wavenumber. For l directed up 

and down slope, the energy propagation has a component in the opposite direction and 

determines whether the wave propagates into deeper or shallower water, respectively. Thus, four

ray paths can be traced from the starting point for a given period and initial wavelength. For

each of the analysis periods, the TRW wave period was taken from the spectral peaks and the 

initial wavelengths from the results of the horizontal EOF analysis given in Table 3-3. These are 

given in Table 3-4, and the paths for the 20- and 8-day waves observed in period 5 are shown in 

45 
Figure 3-7. Mode 1, represented as hodographs, resulting from EOF analyses of current records 

200 m from the bottom for the two-year period using frequency bands 30-15 days 

(upper panel), and 15-7 days (lower panel). 

I1

I3

I2

I1

I3

I2

46
Figure 3-8. Bathymetry after applying a 50 km median filter and smoothing splines to GOTOPO 30 gridded data

meters.

47
Figure 3-9. The 8-day wave in period 5 had the same wavelength as period 1. The starting point 

was the center of the triangle formed by the positions of I1, I2 and I3. 

The backward ray traces, with negative initial upslope wavenumber components, begin east and 

south of the site as might be expected if the LC is involved with their generation. If a positive 

upslope wavenumber component is used for the backward trace then the ray paths are in shallow 

slope water to the north and east (Figure 3-9). Very limited evidence from moorings indicate 

that bottom energy is low in these regions. In particular, the DeSoto Canyon Eddy Intrusion 

Study (Hamilton et al. 2000) had moorings on the 1200 m isobath near the path of the 20-day

wave. Energy at the near-bottom current meters was small with rms amplitudes < 3 cm/s though

20-day periods were present in the spectra. Therefore, it seems unlikely that large amplitude 

fluctuations observed at the site originate from these regions. Similarly, forward ray traces with 

negative upslope wavenumber, that continue the paths which originated in the south and east, 

continue into shallower water. Again, the evidence from the J1 and I4 moorings, as well as 

deepwater moorings, in water depths less than 2000 m, on 92°W (Hamilton, 1990), indicate that 

high energy at the site was not propagating directly west along the escarpment or above the 

escarpment. Therefore, an explanation of the decrease in energy across the escarpment is that 

the upslope propagating TRW’s are reflected in the region of the site. The ambiguous directions, 

Table 3-4. TRW Initial Conditions with Start and End Wavelengths.

Backward Forward 

Analysis 

Period 

Initial 

Wave 

Period 

(days) 

Initial 

Wavelength

(km) 

Initial 

Group 

Speed cg 

(cm/s) 

Start 

Time 

(days) 

Wavelength 

(km) 

End 

Time 

(days) 

Wavelength 

(km) 

1 & 5 8 76 9.4 -11.5 56 +12 86 

2 12.5 50 8.4 -41 64 +34 56 

3 13 62 10.4 -32 100 +29 69 

4 14 70 12.0 -31 160 +27 75 

5 20 87 15.9 -12 300 +37 225 

relative to the bathymetry, of the principal axes of I1 and I2 have been discussed previously. If

reflection occurs, and the upslope wavenumber component changes sign, the forward ray traces

show paths to the south and west. The 8-day wave does not penetrate far, but the 20-day wave

reaches the center of the basin in about 35 days. The lower-layer current observations made at 

92°W, 25.7°N (Mooring GG in; Hamilton, 1990) showed prominent oscillations, with maximum 

amplitudes < 20 cm/s, with periods of 20 – 25 days. The 20-day forward ray path passes within 

about 50 km of this position. 

Based on the analysis of periods and initial wavelengths, the rays were traced backwards and 

forwards from the site position with the assumption that reflection occurred. The results are

shown in Figure 3-10 for all the analysis periods (see Table 3-4). The elapsed times to the start 

and ends of the rays, where the site position is t=0, are given in Table 3-4, along with the average 

wavelength found for the last two days of each forward and backward integration. For wave 

48 
20 day

20 day

20 day

8 day

8 day

3000 m

2000 m

1000 m

200 m

Figure 3-9. Backward and forward ray traces from the center of the I mooring triangle for waves 

of 8-day period and 76 km initial wavelength (blue and red), and 20-day period and 

87 km wavelength (tan and green). Arrow heads are at 5-day intervals. Ray paths 

to the SE and NW (NE and SW) have down (up) slope directed initial phase vectors.

49
20 day

20 day 8 day

3000 m

2000 m

1000 m

200 m

Figure 3-10. Backward and forward ray traces from the center of the I mooring triangle for 

waves with indicated periods. Initial wavelengths are given in Table 3-4. Arrow 

heads are at 5-day intervals. Ray paths to the SE (SW) have down (up) slope 

directed initial phase vectors.

12.5 day

13 day

14 day

50
periods less than 14 days, the generation zone appears to be on the west side of the LC and the 

shorter the period the more likely the generation takes place close to the site. This was noted for 

the fluctuations associated with peripheral cyclones that had some degree of coherence through 

the water column at I1 at the beginnings of periods 1, 2 and 5. Thus, this is consistent with 

Pickart’s resonance theory of TRW generation in that rapidly northwards moving cyclones on 

the west side of the LC would have the right length and time scales to couple with lower layer 

TRWs. This is a region of explosive growth of peripheral frontal eddies as the LC flows

northwards past the Campeche Bank. The ray tracing also indicates that this short period energy

is confined to a region between 88.5° and 91.5°W, north of about 3000 m water depth and south 

of the escarpment. This agrees with the observations that energetic propagating signals with 

periods less than about 16 days were not observed in the deep water on the east side of the LC 

and west of 92°W (Hamilton, 1990). This may explain why the energy of the lower-layer 

currents at the site was so exceptionally large, if the TRW’s are partially trapped in its vicinity. 

A longer wavelength 20-day TRW is able to penetrate into the central basin as indicated by the 

observations. The origin of these waves is more over the Mississippi Fan and may be associated 

with an eddy shedding event because the wavelengths in this region are quite large (Table 3-4). 

However, the travel time to the site is about the same as the 8-day TRWs and this may explain 

why both period TRW’s appearred at about the same time in period 5, as Eddy M was in the

process of being shed. 

In the theory of TRW motions, waves do not propagate at frequencies above Nα, where α is the

bottom slope perpendicular to the isobaths. Therefore, short period waves propagating into 

regions of decreasing bottom slope will eventually become evanescent. This is indicated in the 

ray tracing when the group-velocity becomes very small and the calculation is terminated. To 

the author’s knowledge, the behavior of TRW motions where the bottom slope decreases has not 

been investigated either analytically or numerically. Since linear TRW’s can only propagate 

with shallow water on the right of the direction of propagation, reflection appears to be unlikely.

Therefore, it is speculated that in this situation, wave motions must dissipate or be transformed 

into different types of planetary waves, perhaps changing frequencies and wavelengths by nonlinear processes. Evidence from observations (Hamilton, 1990) and models (Oey and Lee, 2002) 

indicate that longer period (> 20 days) TRW’s can reach the western Gulf, however, the paths of 

such waves seem to be complex with possible contributing sources from the LC and westward

propagating LCE’s. 

The features of the TRW wave parameters and the distribution of energy by measurement 

interval across the site moorings suggest that TRW genesis is at multiple sites along the LC front 

and these change with time as the LC extends and sheds major anticyclones. Reflection of

TRWs by the escarpment appears to be consistent with the observations, however, the dynamics

of this process and the effects of trapping energy in a small part of the lower Gulf slope have not 

yet been studied either theoretically or with numerical simulations. This seems quite different 

from the Mid-Atlantic Bight where Gulf Stream generated 40-day period TRWs propagate large

distances over the slope region (Pickart, 1995). The similarity of these observations to Hogg’s 

(2000) measurements over the slope of the Grand Banks has been noted. 

51 
3.7 Upper Layer Circulations 

The upper layer currents at I1 have been described in Section 2.3. Energetic events were 

dominated by Eddies J and M. Eddy J’s path was further to the south than the later eddy, and 

mooring I1 was primarily affected by events on the periphery of its main circulation. 

Documentation of these events in the upper 100 m was hampered by the failure of the ADCP at 

90 m after the middle of October 1999. Eddy M, on the other hand, affected the mooring 

between March and May 2001, during which time the mooring was measuring currents within 

the core of the eddy. Previous surveys of LC eddy currents have been ship-based (Cooper et al. 

1990). The high-resolution temperature and current measurements on mooring I1 allow another 

view of the vertical and horizontal structures of part of a major LC eddy. To analyze the radial 

and azimuthal velocity components of Eddy M, it is necessary to identify its center path, as it 

moved past the mooring. The location of an eddy center is often difficult using remote sensing 

data. However, satellite-tracked (ARGOS) drifters were deployed in Eddy M by Horizon Marine 

as part of the industry program “Eddy Watch”. The “Far Horizon Drifters” used in that program

have a parachute-like drogue at a nominal depth of 50 m. The original data is proprietary to 

Horizon Marine. Use of the drifter tracks for Eddy M was purchased by the present study and 

two of these paths have been analyzed to provide the estimates of the locations of the center as it 

evolved between 89° and 91.5°W. The method uses the Glenn et al. (1990) translating ellipse 

kinematic model as adapted by Hamilton et al. (1999). The drifter tracks were initially smoothed 

and resampled at 6-hour intervals as discussed in Hamilton et al. (1999). The model uses a leastsquare fit of a diverging, translating ellipse to smoothed drifter paths. The equations fit to a 

drifter orbit are: 

x(t) = x0 + ut + (1 + Dt)[acosθ cos(-ωt + φ) - bsinθ sin(-ωt + φ) ] (5)

y(t) = y0 + vt + (1 + Dt)[asinθ cos(-ωt + φ) + bcosθ sin(-ωt + φ) ] (6) 

where 

x, y are the coordinates of the modeled drifter track; 

x0, y0 is the t = 0 center position of the ellipse; 

u, v are the x and y components of the center translation velocity; 

a, b are the major and minor axes of the ellipse; 

θ is the inclination of the major axis to east; 

ω is the orbital frequency; 

φ is the t = 0 phase of the orbit; 

D is the divergence. 

The orbits are fit for t ε [-T/2,T/2], where T = 2π/ω is the orbital period. Latitudes and 

longitudes are transformed to (x, y) coordinates using standard f – plane projections. The results 

of the model fits are shown in Figure 3-11 where the center paths and major and minor axes are 

shown for two drifters (00815 and 00850) orbiting in Eddy M. The orbital periods during this 

time were fairly constant at about 8 to 10 days. Some of the early orbits of 00815 were large and 

had longer periods, indicating that the drifter was probably outside the eddy’s core. After the 

parameters were estimated, the distance from the center, on a given day, to the mooring position 

was easily calculated (Figure 3-12). The position of the major axis allows the mooring to be

52 
placed in a quadrant of the eddy. The angle, A, is defined as α - θ, where tan-1α = (ym - y0)/(xm – 

x0), and (xm, ym) is the position of the mooring (Figure 3-12). Therefore, if A is ~ 0 or ±180°, 

then the mooring is closest to the location of the major axis, and if A is ~ ±90°, then the mooring 

is closest to the position of the minor axis. The orbit solutions (5) and (6) can be used to 

estimate the velocity at the mooring caused by the eddy, if solid body rotation holds from the 

center to the mooring location. The position, B, of the drifter when it crosses the line between

the mooring and the center is given by t = tB, which is the solution to 

(ym – y0)(x(t) – x0) = (y(t) – y0)(xm – x0) (7) 

Using (5) and (6), the orbit is redefined to go through (xm, ym) for new values of a and b, subject 

to the constraint a′/b′ = a/b (Figure 3-12). The eddy velocity, Vm, at the mooring is then given by 

(dx/dt, dy/dt) for t = tB and (a, b) = (a′, b′). The direction of Vm can then be used to define the 

azimuthal velocity direction at the mooring for a given day. A comparison of the time series of 

Vm, and one-day averaged currents at 50 m from I1, is given in Figure 3-13. While the eddy was 

influencing the mooring, the observed velocities at I1 and modeled drifter-based currents have 

very similar characteristics. 

The path of Eddy M’s center (Figure 3-11) shows some interesting deviations from a more usual 

track to the southwest (Hamilton et al. 1999). During the later half of March, the eddy made a 

rapid movement towards, and then away from the slope so that the path of the center forms a 

loop with the eddy translating eastwards for a few days after March 28. This was the closest 

approach (~ 50 km) of the eddy to I1. SST imagery shows that Eddy M was attached to the 

Loop Current through March and early April (Figure 3-14). The March 23 image shows a 

roughly circular eddy (see also the similar major and minor axis lengths in Figure 3-11). Soon 

after this, the eddy developed a large westward extrusion over the northern slope, apparently 

formed by a large cyclone that developed and propagated northwestward along the west side of

the LC and Eddy M. The large cyclone is seen in the April 5 image (Figure 3-14), and it is likely 

that the interaction between the anticyclonic Eddy M and the cyclone caused the northward loop 

of the eddy center in late March. The warm westward extension, or large filament, eventually 

detached from M, in late April, as the cyclone continued to move up onto the slope. No drifters 

were entrained in this filament, indicating that it may not have been an active circulation feature 

(i.e. a separate anticyclone). 

In April, the Eddy M translated due westward towards the slope, presumably because of the 

influence of the cyclone to its west. At the beginning of May, as the center approached the 2000 

m isobath, the eddy stalled and then moved rapidly southward, away from the slope. It also 

became more elliptical with the major axis directed northwest to southeast. This apparent 

"bounce off the slope" could be a result of the shoaling depths of the slope. (In our experience, 

eddy centers never cross the 2000 m isobath on the eastern and central Gulf slope – see Hamilton

et al. 1999; 2002). However, the path of the eddy center was similar, but more extreme, to that 

of Eddy Y, in November 1994, caused by interaction with a lower slope cyclone on its

northwestern side (Hamilton et al. 1999; 2002). The cyclone in Figure 3-14 apparently moved

onto the slope in late April and early May, and may have caused the interaction that moved Eddy 

M away from the slope. Available evidence (Hamilton 1992; Hamilton et al. 2002), indicates

that once a large cyclone has moved onto the lower slope, it usually becomes fairly stationary

53 
2000 m

200 m

I1

Figure 3-11. Paths of the center of Eddy Millenium derived from a kinematic model analysis of 

smoothed drifter tracks (heavy lines). Solid squares mark the start of each path. 

The major and minor (dashed) axes from the model are shown every 5 days. Dates 

(month/day) are given every 10 days. 

54
I1

O

A

V

m

2000 m

200 m

Figure 3-12. Elliptical orbit from model kinematic equations (heavy solid line). Case shown 

with no translation or divergence. Distance to the eddy center = I1-O; angle 

between I1-O and major axis = A. Fitted ellipse expanded to go through the site 

shown as thin line, which also defines the eddy velocity, Vm, assuming solid body 

rotation within the trajectory. 

Definitions of Distance to Center and Eddy Velocity

for Mooring Position

B Ur

55
Temperature

Observed

Eddy

Speed

Distance to

Center

Figure 3-13. Time series from translating ellipse model and observations at I1. From top to 

bottom, the panels are: Angle of line to center with respect to major axis, distance 

from I1 to the center, current speed from one-day averaged observations at 50 m 

(black) and eddy model (red), eddy model current vectors at I1 (red), observed 

current vectors at I1, and temperature at 200 m at I1.

Temperature (°C)

Velocity (cm/s)

Velocity (cm/s)

Velocity (cm/s) Distance (km)

2001

Eddy Millennium Parameters at I1

Angle (°)

Angle w/ respect 

to major Axis

56
and would block further westward movement of a LC anticyclone to its east. Unfortunately, SST 

imagery was obscured by extensive cloud cover at this time, so it has not been possible to 

confirm directly the existence of a large lower slope cyclone around 92° to 93°W. Between May 

15 and 25, the observed velocities and temperatures at I1 decrease, and the mooring was not 

under the direct influence of the eddy (Figures 3-12 and 3-13). Eddy M currents returned for a 

short period after May 25, even though the eddy was further away. The elliptical shape of the 

eddy and the rotation of the major axis from northwest to northeast, after the southward 

displacement, was the cause of this. In June, Eddy M again became more circular and had a 

southwestward path, approximately parallel to, and ~100 km south of, the 2000 m isobath. This

is a fairly typical path for central Gulf LC eddies (see path of Eddy Y in Hamilton et al. 1999). 

The azimuthal and radial velocity profiles were calculated using daily averaged 40-HLP records 

where the azimuthal direction is defined by the kinematic model fits to the smoothed buoy tracks 

as discussed above. The radial direction is defined as orthogonal to Vm (Figure 3-12) and has the 

opposite sign to conventional definitions of radial velocities for circular eddies (e.g. Kunze 

1986). The results are given at seven-day intervals for the period March 13 (Julian Day 72) to 

June 5 (day 156), 2001, in Figure 3-15. The directions (relative to North), of the azimuthal 

components, are given by the arrows, and the distance of the mooring, from the estimated eddy 

center position, is given by the color scale. The velocities include the translation of the eddy. In 

general, the closer to the center, the more uniform with depth are the azimuthal profiles, but there

are differences in profiles that fall into the same "distance from the center bins". For example, 

compare the azimuthal profiles for days 93, 100 and 121 (April 3, 10, and May 1). The first two 

dates are when the eddy was still attached to the LC, and the eddy center was looping to the 

north (Figure 3-11), and the latter was after the eddy had detached and was approaching the 

slope. Prior to detachment, two of the azimuthal profiles had maximum currents at 100 to 150 m 

below the surface (days 79 and 86; March 20 and 27). This is associated with a reversal of the

radial velocities (most clearly seen for day 86), from divergent near the surface to convergent, in

the region of the maximum, and divergent below. After day 107 (April 17), when the mooring 

was in the trailing quadrants of the eddy, these features in the profiles were not present. It is not 

known whether the increased structure in the velocity profiles in the first part of the record, 

compared to the later, is because the mooring was in the leading part of the eddy, or because the 

eddy was still attached to the LC. 

The azimuthal vertical shears are expected to be related closely to the eddy temperature field 

through the cyclogeostrophic momentum balance (Kunze 1986). Figure 3-16 shows the vertical 

temperature profiles and their corresponding azimuthal velocity profiles. Thus, the warmest 

water at I1, on day 107 (April 17), when the 12°C isotherm reached its deepest depth, 

corresponds to relatively depth independent currents. The sequence of plots for days 107 to 135, 

show increasing shears and shoaling isotherms as would be expected for a station moving from 

close to the center to edges of the eddy. On day 135 (May 15), the observed 50-m current was 

less than the solid-body rotation current, which indicates that the mooring was in the outer 

cyclonic shear zone of the eddy’s circulation (Figure 3-13). Of this sequence of 5 profiles, the 

one occurring on day 128 (May 8) is more characteristic of a position closer to the center than

the profiles on either side. The isotherms, however, had only slightly deepened from day 121. 

May 8 was during the interval when the eddy moved rapidly to the southeast and elongated.

Therefore, the interaction with the slope cyclone appears to have increased the radius of the

57 
region of solid body rotation and the mooring appears to have been relatively nearer the center. 

Some of the velocity in the upper 600 m for this profile was caused by the southeastward 

translation as can be seen by the positive radial component in Figure 3-15. This analysis 

indicates that the motion of the eddy and its interactions with surrounding circulation features 

could change swirl and radial velocity fields from that expected by a fixed –size translating 

elliptical bowl shaped circulations. The last part of the eddy velocity record at I1 can be used to 

estimate the width of the cyclonic shear zone. On May 25 (day 145), eddy and observed speeds 

were similar (Figure 3-13). By June 5, the observed speeds had dropped to zero as the eddy 

moved away from the site at a fairly constant speed. During this interval, the orientations of the 

ellipse major axis were fairly constant and directed towards I1. This indicates that the length of 

the semi-major axis or the distance from the center to the maximum surface velocity was ~ 150 

km. Using the drifter calculated a/b for May 25, results in the estimate for the semi-minor axis

of ~ 100 km. The width of the cyclonic shear zone, where the swirl velocities decrease from a 

maximum to zero, is about 50 km. Thus, a rough estimate of the cylonic shear zone width was 

~1/3 the eddy radius to the maximum swirl velocity. This would indicate that the positive 

vorticity anomaly associated with the outer edges of the eddy is about three times the negative 

vorticity anomaly associated with the eddy core. Using a rotation period of 9 days, the relative 

vorticity of the eddy is ~ -0.13f. Therefore, the high positive vorticity anomaly associated with 

the cyclonic shear zone implies instabilities and non-linear dynamics. 

The profiles can also be used to estimate the changes in horizontal velocity shear within the eddy 

with depth. The azimuthal velocities were corrected for the translation of the eddy by 

subtracting the center velocity vector for each day. These swirl velocities were then plotted as a

function of distance from the eddy center for five selected depths from the daily profiles for the

March 13 to June 5, period. The May 19 to 21 period, when the edge of the eddy briefly moved 

away from the mooring (Figure 3-13), was excluded. The results are given in Figure 3-17. 

There is scatter because of the evolving velocity fields and the elliptical shape, which results in

higher velocities closer to the center when the minor axis is directed towards I1 and vice-versa.

The lines on the plots are subjective attempts to define the anticyclonic and cyclonic shear zones, 

interior and exterior to the velocity maximum at each depth, respectively. Both the cyclonic and 

anticyclonic shears decrease with depth with the former showing the larger relative decrease. 

This is because the interior of the eddy is closer to solid body rotation, particularly in the upper 

100 m. Since the maximum velocity occurs closer to the center with increasing depth, and the 

eddy velocities fall to zero at about the same distance (~ 200 km) from the center, the cyclonic 

shears become weaker with depth. Thus, the positive relative vorticity region has strong depth 

gradients, where as the eddy interior has a more uniform negative vorticities. The radial fields of 

swirl velocities suggested by Figure 3-17 are more complex than used by most eddy models that 

assume depth independence and/or isolation from surrounding waters. 

3.8 Inertial Currents 

High frequency currents in deep-water regions of the northern Gulf are dominated by inertial 

oscillations. These are clockwise rotating currents (viewed from above) with periods near but

58 
50 cm/s 50 cm/s

Figure 3-14. Composite AVHRR Images for March 23 (left panel) and April 5 (right panel), 2001 (Courtesy John 

Applied Physics Laboratory). One day mean 40-HLP velocities from I1, centered on these times, ar250 m depth (black and purple arrows, respectively). 

59
shorter than 2π/fe, where fe, the effective Coriolis parameter given by (Mooers, 1975), is defined 

as: 

fe

2

 = f ( f + ζ ) 

where ζ is the relative vorticity of the background current field. At mooring I1, the inertial 

period, 2π/f, is 26.2 hours (frequency 0.92 cpd). At periods longer than 2π/fe, inertial waves

cannot propagate. The background vorticity field of an anticyclone is negative in the center 

surrounded by a positive annulus where the anticyclone is not in solid body rotation. Inertial 

energy can be trapped in the center of the eddy by this type of vorticity field and this leads to 

enhanced inertial velocities (Kunze, 1985; 1986). Inertial-internal waves propagate horizontally 

and vertically though vertical group velocities are small (Lighthill, 1978). Thus, at positions

below the surface, inertial wave packets can exhibit slightly different frequencies and 

propagation characteristics, since they may have propagated from different source regions. 

The sources of inertial oscillations are generally rapid changes in atmospheric forcing. Thus, 

hurricanes over deep water usually generate strong inertial wakes. Examples in the Gulf of

Mexico include Hurricanes Allen (Brooks, 1983), Frederic (Shay and Elsberry, 1987), Georges 

and Earl (Hamilton et al. 2000). Surface inertial current magnitudes of ~ 100 cm/s are not

uncommon during the passage of major hurricanes and the oscillations can persist several days or

even weeks after the hurricane has left the area. Other sources of inertial currents are winter 

storms. Over the DeSoto Canyon slope region to the east of the delta, Hamilton et al. (2000) 

found persistent inertial oscillations in the upper water column throughout the year. The 

ubiquitous nature of these upper-layer inertial currents, particularly in summer, was partly 

ascribed to trapping by the vorticity of the lower slope eddies and the eastward flowing slope jet.

This was in contrast to the Louisiana-Texas shelf-break region to the west of the delta where 

Chen et al. (1996) found that near inertial energy could be related to storms and decayed rapidly

seaward of the shelf-break. 

The records at I1 contain events for two winters and two LC eddies. No major hurricanes or

tropical storms passed near the site during the two-year deployment period. A short section of 

the 3-HLP current records from I1 are shown in Figure 3-18. The nearly daily period 

fluctuations were present at all depths above about 800 m. Amplitudes varied with time and

different depth levels varied in intensity. Around the depth of the main thermocline, at 250 m, 

the fluctuations were relatively more energetic and sustained in time, suggesting that trapping 

may have been occurring. Generally, however, amplitudes decayed with depth as would be

expected for surface forced oscillations. The v-components lead the u-components by about 90° 

which indicates clockwise rotation of the current vectors. At this site inertial current oscillations

did not penetrate deeper than about 1200 m.

To determine how inertial current magnitudes vary over the two-year duration of the mooring 

deployments, complex demodulation (Priestley, 1981) was performed for all current records in 

the upper layer using a period of 26 hours. A running 52-hour mean was subtracted from the 

records and the results filtered with a 4-Day Low Pass Lanzcos kernel. The amplitudes at

selected depths are given in Figure 3-19 where the speeds of the 40-HLP winds from the C-MAN 

meteorological station (see Figure 1-1) at the southwestern tip of the Mississippi delta (BURL1)

60 
-50 0 50 150

-50 0 50 150

60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

Distance (km) of I1 from Eddy Center

cm/s

cm/s

Julian Days 2001

Figure 3-15. Radial (Ur -upper panel) and azimuthal (Vm-lower panel) components of daily 

averaged velocity profiles, at I1, for eddy M on the given Julian days, 2001. The 

profiles are color coded according to distance from the eddy center. The vectors, 

above the plots, show the direction of the azimuthal component as defined in Figure 

3-12.

Depth (m) Depth (m)

Azimuthal Radial

61
0 20 40

°C

Julian Days 2001

Depth (m)

20°C

-50 0 50 150

60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

Distance (km) of I1 from Eddy Center

cm/s

Depth (m)

Azimuthal

Temperature

Figure 3-16. Daily averaged temperature (upper panel) and azimuthal (Vm-lower panel) velocity 

component profiles, at I1, for eddy M on the given Julian days, 2001. The profiles 

are color coded according to distance from the eddy center. The vectors, above the 

plots, show the direction of the azimuthal component as defined in Figure 3-12.

12°C

62
are also displayed. Intervals with high currents caused by Eddies J and M and their associated

cyclones (see Figure 2-2) are also indicated. During the passage of Eddy J, the 90-m level 

ADCP did not produce any data after October 1999, so it is unclear whether the upper layer had 

enhanced inertial activity. However, at 126 m depth during December and January, energy 

levels were elevated. At this time, the 126 m level was above the main thermocline (Figure 2-4) 

and therefore, this may be an indication of trapping within the ring. Below the thermocline, 

amplitudes (< 5 cm/s) were quite small except for occasional bursts (e.g. at 428 m at the end of

September and the beginning of November). Between March and October 2000, when surfacelayer eddy currents were weak, and wind speeds relatively low, inertial amplitudes were also 

small at all depths. In October, November and December 2001, when eddy currents were still 

weak, inertial amplitudes increased in the upper 100 m of the water column, somewhat 

corresponding to the increased in storm activity in the fall and early winter. In January and

February 2001, inertial amplitudes increase dramatically in the near surface, even though wind 

events were no stronger than in the fall and a little less frequent. This interval was characterized 

by vigorous currents associated with cyclones that preceded Eddy M, suggesting that eddy-eddy 

interactions may have been generating these inertial currents. As Eddy M moved over the site, 

inertial amplitudes decreased in the near surface but increased at deeper levels corresponding to

the increasing depth of the thermocline (see the 16°C isotherm in Figure 2-4b). This again 

suggests that the inertial energy generated in January and February propagated downward into 

the approaching warm eddy and appears to have been trapped in the negative vorticity region 

above the thermocline. In July and August 2001, after Eddy M had moved into the western Gulf, 

there was again strong currents caused by cyclones associated with the LC (Figure 2-3j and k), 

and again there was an increase in inertial amplitudes in the near surface, even though winds

were weak, as is typical of the summer period. 

Based on the above discussion, more detailed analysis of inertial motions was carried out for 

three two-month interals corresponding to parts of the records with large amplitude oscillations 

in the surface layer. These are 1) October 27 to December 25, 2000, when low-frequency

currents were quiescent; 2) January 1 to March 1, 2001, when cyclones were present; and 3) 

March 1 to April 29, 2001, when Eddy M was over the site (Figure 3-19). These periods had 

good depth coverage from 20 m to 1000 m, except for a gap between 410 and 600 m. Spectra 

from four representative depths in the upper 400 m, for the three intervals, are given in Figure 3-

20. The spectra are for velocities that have been decomposed into anticlockwise (+) and 

clockwise (-) rotating components (Gonella, 1971). Only the frequency band around the inertial 

period, f = 0.917 cpd, is shown and for all the spectra the clockwise rotating component

dominated over the anticlockwise, which is characteristic of inertial currents in the upper layers 

of the ocean. In the first interval, the peaks of the spectra are at frequencies that are 5 to 10% 

greater than f. Amplitudes decreased with depth and the energy was spread over a broad range 

of frequencies that is a consequence of spectral analysis of highly intermittent signals. In the

second interval, clockwise amplitudes increased at the deeper levels and the spectral peaks were

more centered about f. The near surface level (20 m) had a peak at a frequency at about 5% less

than f. This could indicate that this signal was not propagating (i.e., evanescent), or was being 

generated in a region that had negative (anticyclonic) relative vorticity, and was therefore, 

probably trapped in the surface layer. In Eddy M, the relative vorticity of the core was negative

and fe decreased. Thus, in interval three, the spectral peaks, except at 20 m, were at frequencies

that are more than 10% less than f, and the energy levels at the three deeper depths had increased 

63 
0 50 100 150 200 250

0

25

50

75

100

125

150

Distance from Center

(km)

Azimuthal Speed (cm/s)

Eddy Millennium

48 m

106 m

206 m

310 m

410 m

658 m

Figure 3-17. Azimuthal velocities (adjusted for effects of eddy translation) as a function of 

distance from the center of the eddy for the period March 13 to June 5 (excluding 

May 19 -21). Depths are indicated by the color code, and estimated mean shears 

on the cyclonic and anticyclonic sides of the maximum swirl velocity are given 

by the straight lines.

64
over interval two. The deepest level (410 m) has the highest energy levels, indicating that 

trapping may have been occurring at the base of the upper layer that had the anticyclonic rotation 

of the eddy (Kunze, 1986). 

Further investigation of the depth distribution of energy in the inertial band was carried out for 

the three intervals by using frequency domain EOF analysis. The frequency bands were centered 

about the dominant spectral peaks for each interval and in all cases at least two modes were 

significant. Analyses were done for all depths above 1000 m and it was found that below about 

400 m, amplitudes were small. Therefore, the analysis was repeated for all records above 400 m

and the mode amplitudes and phases for the U and V-components are given in Figures 3-21 and 

3-22. In all cases where the mode amplitudes were significant, the V-component leads the Ucomponent by approximately 90°, and component amplitudes had similar magnitudes. This is 

characteristic of all clockwise (anticyclonic) rotary motions. Phases also generally increased 

with depth so that deeper fluctuations led those at higher levels. Upward phase propagation for 

internal waves indicates that energy propagation (vertical group velocity) is downwards, 

suggesting surface forcing. The slope of the phase lines is an indication of the vertical 

wavelength of the coherent motions represented by the modes (i.e. the phase changes by 360° 

over a vertical wavelength). 

In interval one, when eddy activity was weak, mode 1 was surface intensified above 100 m with 

almost constant phase (Figure 3-21). This indicates slab-like motions in the upper 100 m, with 

no downwards flux of energy, and suggests that a well-mixed surface layer extended down to 

about 80 m, with these fluctuations being directly forced by local winter storms. Below the 

surface layer, both modes 1 and 2 had subsurface maxima at about 200 m depth. Because modes

were not correlated, this suggests that the inertial waves represented by these modes had 

different origins, with mode 1 energy being propagated down from the local surface layer, and

mode 2 perhaps from more remote regions. The depth of the 15°C isotherm (see Figure 2-4b), 

which is characteristic of the main thermocline, was at about 200 m at this time. Both modes had 

similar characteristic wavelengths of 400 to 500 m, below the surface layer. 

In the next interval (Figure 3-21), the upper layers were dominated by cyclones prior to the

arrival of Eddy M. Despite this positive vorticity, the spectral peaks shifted to lower frequencies

when compared with the previous interval (Figure 3-20). This suggests that the inertial waves 

were being trapped in the outer parts of the cyclones where there was an annulus of negative 

vorticity surrounding the positive cores. Mode 1 was again surface intensified but the 

fluctuations were no longer slab-like. Depth of penetration was shallower at about 50 to 60 m, 

which is consistent with the uplift of the isotherms by the cyclones (Figure 2-4b). Mode 2 had a 

subsurface maximum at about 150 m, with implied vertical wavelengths of about 400 m. When 

Eddy M arrived, interval 3 amplitudes and phases (Figure 3-22) changed in character. Mode 1 

was no longer surface intensified, rather showed almost constant amplitudes below 100 m and 

above 450 m. The vertical wavelengths were again large (~ 500 m) and coupled with the shift of 

the spectral peaks to frequencies less than f (Figure 3-20). This suggests trapping above the 

thermocline in the core of the eddy. In this interval, three modes were significant. However, 

modes 2 and 3 had relatively constant amplitudes in the upper 400 m and the main difference

between them was vertical wavelengths of about 200 and 400 m, respectively. The significance 

of these latter modes is not clear, and they may just represent background inertial energy 

65 
cm/s cm/s

December

2000

January 

2001

East Component - Dashed/Shaded

North Component - Solid Black

Inertial Currents at I1 (2000 m)

Figure 3-18. 3-HLP velocity components (east - dashed and shaded, north - solid) from selected 

depths of mooring I1 for the indicated period.

66
resulting from events earlier in this ring’s history. The mode 1 results are consistent with 

Kunze’s (1986) analysis of the trapping of inertial oscillations in a Gulf Stream warm-core ring. 

They also suggest that instability processes on the edge of a large anticyclone (i.e. the presence 

of peripheral cyclones), may have been a source of inertial energy. The high surface energies of 

interval 2, exceeded, for several events, the supposed wind forced response of interval 1 (Figure

3-19). The temperature profiles in the upper ocean were similar for both intervals and the winds 

were generally weaker in interval 2 than earlier. The strong surface-layer fluctuations then 

propagate horizontally and vertically into the approaching anticyclone, which showed decreasing 

inertial amplitudes in the surface layer and accumulation of energy at depths above the 

mainthermocline. This speculation cannot be proved because information on the horizontal

propagation of inertial packets is lacking. 

The trapping of inertial oscillations at the base of the thermocline, in rings, has been observed in

the Mid-Atlantic (Kunze, 1986), and is suggested by these measurements in Eddy M. 

Concentration of inertial energy at depth could result in subsurface inertial jets that could be a

hazard to oil industry operations. However, this type of phenomena seems most likely to occur 

within LCE’s, and therefore the background low-frequency surface currents are likely to be 

energetic. This is somewhat different than reported occurrences of subsurface jet-like currents 

when surface currents are quiescent (DiMarco, personal communication) and LCE’s were not 

present. 

67 
40-HLP

Wind Speed at

BURL1

C Eddy J C Eddy M Cyclone(s)

Figure 3-19. Amplitudes of inertial (26 hour) current oscillations at the indicated depths of 

mooring I1. Top panel shows the 40-HLP wind speed at the BURL1 C-MAN 

Station. Vertical lines show intervals when LC eddies and their peripheral 

cyclones (C) dominate the upper layer at the site.

Quiescent

cm/s m/s

68

Amplitudes of 26-hour current oscillations
f f f

October 27 - December 25, 2000 January 1 - March 1 2001 March 1 - Apri

Figure 3-20. Rotary spectra (clockwise - dashed, anticlockwise - solid) for the indicated upper layer current reco

periods. The inertial frequency, f, at I1 is indicated on the plots.

Variance/CPD

Rotary Spectra

69

1 cycle/day
Figure 3-21. Amplitudes (cm/s) and phases from EOF analyses of inertial period motions for 

periods 1 (top) and 2 (bottom).

Depth (m) Depth (m)

70
Figure 3-22. Amplitudes (cm/s) and phases from an EOF analysis of inertial period motions for 

period 3.

71
4.0 ECHO SOUNDERS WITH PRESSURE (PIES) 

4.1 Introduction 

For the final six months (nominally February through August 2001) of this extended set of 

DeSoto Canyon measurements, the MMS supplemented support from BP to extend the mooring 

at I1 to the full water column depth and to support placement of three PIES in a triangle around 

this full-depth mooring. The support to extend Mooring I1 to full depth was to help provide 

information that may provide additional insight about linkage of upper and lower layer current 

patterns. The PIES were used to provide an independent estimate of the vertical profiles of 

temperature salinity and hence density and geostrophic velocities. Placement of three PIES

around the instrumented mooring provides a basis for comparing velocity and temperatures as 

estimated by the PIES and GEM methodology with nearby actual Eulerian current/temperature

measurements made at various depths below the sea surface.

4.2 Methodology 

4.2.1 Instrumentation 

The Model 6.1 Inverted Echo Sounders (IES) deployed in the Gulf of Mexico is a bottommounted instrument that measures the vertical acoustic travel time (VATT) round-trip from the

sea floor to the sea surface and back. The Model 6.1E used in this study (Figure 4-1) is a 

combined IES, data-logger and acoustic release, with bottom pressure and temperature

measurements. From its position on the seafloor, the upward directed transducer at the top of the

instrument (Figure 4-2), transmits a burst of four 10kHz acoustic pulses every 10 minutes. The 

time (τ or tau) required for the round trip from the instrument, to the water surface and back to 

the instrument is recorded internally. Pressure and temperature are also measured and recorded

at 10-minute intervals (six/hour). 

Features of the PIES: (See Figure 4-2) 

• Entirely self-contained in a single, non-eroding, glass sphere: acoustic & timed 

release, flotation buoyancy and optional recovery aids (radio beacon, xenon flasher 

and flag) 

• 32-bit microcontroller combines high-performance data manipulation with low-power 

operation modes. 

• Data stored on removable (type ATA compact flash) memory cards (16-512Mbyte 

capacity) 

• Data stored as engineering units n MS-DOS file formats 

• Many self-test features 

• “Through-the-glass” communications - high speed data download without opening 

the instrument housing 

• Acoustic command subsystem, including data telemetry option 

73 
Figure 4-1. PIES on the back deck of the deployment vessel in a cradle used in regions of 

expected strong bottom currents. Prior to deployment, the ropes to the weights 

(chain links) were removed, as were the rubber "stoppers" around the equatorial rib. 

This configuration orients vertically on a sloping bottom since the weights tend to 

orient the instrument toward the vertical. The transducer is at the top of the sphere 

in this picture, and the release, radio and light are at the bottom. When the acoustic 

release is activated, the unit seperates from the chain links and the rises to the 

surface with the transducer pointing downward. This causes the light and radio to 

be at the water surface.

Transducer

Assembly

74
Figure 4-2. Schematic drawing of the major components of the PIES instrument.

75
• Acoustic command and data logging circuitry and batteries are independent 

• 17-inch (43 cm) diameter glass-sphere instrument housing provides buoyancy for 120 

or 180 Amp-Hr Lithium battery. Typical deployment durations of 2-5 years, 

depending on measurement schedule, water depth (output power) and battery 

capacity. 

• Pressure/temperature sensors 

• Long-term stability and barotropic pressure resolution better than 10μPa - 0.1 mbar

(equivalent to 0.001 m water) 

The IES processes 24 individual echo measurements to produce a single travel time. In a typical 

deep-sea experiment, the ocean acoustic travel time sensitivity to changes in actual water surface

height is about +1.3 milliseconds/meter (ms/m) with thermocline depth variations changing the 

travel time by approximately 0.05 ms/m. 

To eliminate early echoes from reverberation and false targets, the IES echo detector is disabled 

immediately after the acoustic transmission for a period of time called the lockout time. The 

detector is enabled again just before the anticipated surface echo. To minimize false echoes from 

fish and other weak targets, the IES acoustic output power level is adjusted for depth under 

firmware control so that the sea surface is the most viable target. The optimal lockout time and 

output power level are suggested by the IES firmware after the user estimates the deployment

depth. This setting can be overridden/set manually by the user. 

An IES equipped for pressure measurements (PIES) uses a quartz sensor made by Paroscientific, 

Inc. for high accuracy and resolution. Paroscientific's stated accuracy of 0.01% for this line of 

sensor is well established. Typical resolution of Paros sensors is better than 1 part per million,

and under stabilized conditions, resolution can approach 1 part per billion. In the typical PIES

application, where the temperature and pressure are changing slowly and are relatively stable, the

estimated sensor resolution is one part in 10 million. In the PIES, the pressure channel 

electronics measure with a resolution of about 1:64,000,000; that's about 0.00016 lbs/inch2

 (psi) 

or about 0.16 mm H2O for a 10,000 psi sensor. This ensures that the PIES pressure measurement 

resolution is limited by the capabilities of the sensor and not by the PIES electronic circuits. 

4.2.2 Initial Data Conditioning 

The IES internally processed 24 individual echo measurements to produce a single travel time 

(one averaged travel time per hour, i.e. four echos per 10-minute interval averaged over six 10-

minute intervals). In a typical deep-sea experiment, the ocean acoustic travel time sensitivity to

changes in actual water surface height is about +1.3 milliseconds/meter (ms/m) with thermocline 

depth variations changing the travel time by approximately 0.05 ms/m. Any obvious spikes in 

the hourly records were replaced with interpolated values during subsequent data quality control. 

Processing of the pressure measurements included removing spikes, long-term drifts and the 

tides. Tidal response analysis (Munk and Cartwright, 1965) was used to determine the tidal 

constituents for each record. Long-term drifts were identified by fitting exponential-linear

curves in a least-squares sense to the detided pressure records. The travel time, pressure and 

temperature records were low-pass filtered using a second-order Butterworth filter with a cutoff 

period of 40 hours. The filter was passed forward and backward in time to avoid introducing

76 
phase shifts. Twenty hours of data at each end of the filtered series were discarded to avoid 

startup transients. After filtering all time series were subsampled at 12-hour intervals.

4.2.3 Data Processing and Reduction – Gravest Empirical Mode 

In the present experiment, an empirical relationship has been established between τ100-1000, round 

trip travel time between 100 and 1000 dbar surfaces, and vertical profiles of temperature, 

salinity, and specific volume anomaly using historical hydrography, the so-called Gravest

Empirical Mode (GEM) representation (e.g., Meinen and Watts, 2000 and Watts et al., 2001) 

For the GEM construction in the present study, we utilized 446 hydrographic stations from the

Gulf of Mexico HYDRO Database compiled by TAMU as part of MMS-funded Deepwater 

Reanalysis as well as additional stations provided by SAIC. Due to the integral nature of τ and 

the fact that this study represents an initial attempt to establish a GEM field for the Gulf of 

Mexico, only high vertical resolution CTD hydrocasts were retained in the analysis. The spatial 

and temporal distribution of these hydrocasts are shown in Figure 4-3. The northwestern Gulf of 

Mexico is well sampled; hydrocasts represent about 20 years of sampling; hydrocasts sample 

most the annual cycle, except December; the bulk of casts extend between 1000 to 2000 dbar 

with relatively few cast below 2000 dbar. 

The upper limit of the τ (tau) integration was chosen as 100 dbar in an effort to avoid the 

influence of the seasonal cycle; the bulk of the 'contamination' of τ from seasonal variability

should be above the mixed layer. In the future, further refinement to the GEM field will include 

a seasonal correction (e.g., Watts et al., 2001). The lower limit of the τ integration was chosen as 

1000 dbar in an effort to balance two needs: extend the integration below the thermocline and 

retain as many of the acquired historical hydrocasts as possible. 

The GEM field was determined as follows. First, the historical hydrocasts were linearly 

interpolated to a uniform 25 dbar grid. Second, for every 25 dbar, a cubic smoothing spline was 

fitted to the temperature measurements as a function of τ100-1000. The same procedure was 

applied to salinity and specific volume anomaly. Figures 4-4, 4-5, and 4-6 illustrate this fit for 

several pressure surfaces. Root-mean-square residual, rms, for each curve provides an indication 

of the departure any individual profile might have from the GEM curve. The rms values for 

temperature, salinity, and specific volume anomaly are small and decrease with increasing

pressure (depth). The curves show that a functional relationship exists between the integrated

variable τ100-1000 and vertical profiles of temperature, salinity, and specific volume anomaly. 

Figures 4-7 and 4-8 show contours of the temperature and salinity fits for all pressure surfaces as 

a function of τ100-1000, the two-dimensional ``GEM fields.'' Note the lack of deep casts (> 2000 

dbar) for τ100-1000 less than about 1.188 s. There is little structure in the temperature and salinity 

GEM fields below about 1000 dbars and this reflects the uniform deep water properties observed 

on the Gulf of Mexico. The GEM field provides a look-up table; given a τ100-1000 value, profiles 

of temperature, salinity, and specific volume anomaly can be determined. 

77 
446 casts with depth > 1000 dbar

 98oW 94oW 90oW 86oW 

 18oN 

 20oN 

 22oN 

 24oN 

 26oN 

 28oN 

 30oN 

0 2000 4000

0

50

100

150

200

max pressure [dbar]

number of casts

1980 1990 2000

0

20

40

60

80

100

120

year

1 2 3 4 5 6 7 8 9101112

0

20

40

60

80

month

 18oN 

 20oN 

 22oN 

 24oN 

 26oN 

 28oN 

 30oN 

Figure 4-3. Spatial and temporal distribution of historical hydrocasts used to construct of the 

Gravest Empirical Mode. Data provided by the Gulf of Mexico HYDRO Database 

compiled by TAMU as part of the MMS-funded Deepwater Reanalysis and 

additional stations provided by SAIC. Top panel. Spatial distribution of the 

hydrocasts with bathymetry contoured every 1000 m. Histograms of the maximum 

hydrocast pressure (bottom left), year of hydrocast (middle), and month of hydrocast 

(right).

78
10

15

20

25

30

Temperature rms = 0.72 °C 150 dbar

temperature [°C]

5

10

15

20

25

rms = 0.36 °C 300 dbar

temperature [°C]

5

10

15

rms = 0.23 °C 500 dbar

temperature [°C]

4

6

8

10

rms = 0.16 °C 800 dbar

temperature [°C]

1.182 1.184 1.186 1.188 1.19 1.192 1.194 1.196 1.198

4

4.2

4.4

tau100-

1000 [s]

rms = 0.03 °C 1500 dbar

temperature [°C]

Figure 4-4. Scatter plots of temperature versus tau100-1000 for five representative pressure 

levels. At each pressure, the temperature versus tau100-1000 data are fitted by a 

cubic smoothing spline (solid curve).

79
35.5

36

36.5

37

Salinity rms = 0.11 150 dbar

34

35

36

37

rms = 0.06 300 dbar

34.5

35

35.5

36

rms = 0.03 500 dbar

34.8

35

rms = 0.01 800 dbar

1.182 1.184 1.186 1.188 1.19 1.192 1.194 1.196 1.198

34.92

34.94

34.96

34.98

35

tau 100-1000 [s]

rms = 0.01 1500 dbar

salinity (psu) salinity (psu) salinity (psu) salinity (psu) salinity (psu)

80

Figure 4-5. Scatter plots of salinity versus tau100-1000 for five representative pressure levels. At 

each pressure, the salinity versus tau100-1000 data are fitted by a cubic smoothing 

spline (solid curve).
10

20

30

40

50

Specific Volume Anomaly rms = 1.57 107 m3 kg-1

 150 dbar

δ [107 m3kg-1] 5

10

15

20

25

rms = 0.34 107 m3kg-1

 300 dbar

δ [107 m3kg-1] 5

10

15

rms = 0.21 107 m3kg-1

 500 dbar

δ [107 m3kg-1] 4

6

8

10

rms = 0.23 107 m3kg-1

 800 dbar

δ [107 m3kg-1]

1.182 1.184 1.186 1.188 1.19 1.192 1.194 1.196 1.198

4.5

5

5.5

tau100-1000 [s]

rms = 0.09 107 m3kg-1

 1500 dbar

δ [107 m3kg-1]

81

Figure 4-6. Scatter plots of specific volume anomaly versus tau100-1000 for five representative 

pressure levels. At each pressure, the specific volume anomaly versus tau100-1000

data are fitted by a cubic smoothing spline (solid curve).
tau100—1000

pressure [dbar]

Temperature [°C]

 6

 6

 6

 8

 8

 8

12

12

12

16

16

16

20

20

20

24

24

24

1.182 1.184 1.186 1.188 1.19 1.192 1.194 1.196 1.198

0

500

1000

1500

2000

2500

(s)

Figure 4-7. Contour plot of the cubic smoothing spline fits for the temperature GEM field. 

Grey dots indicate positions of CTD data.

82
tau100 1000 [s]

pressure [dbar]

Salinity (psu)

35.2

35.2

35.2

35.6

35.6

35.6

35.6 36

 36

 36

 36

36.4

36.4 36.4

1.182 1.184 1.186 1.188 1.19 1.192 1.194 1.196 1.198

0

500

1000

1500

2000

2500

Figure 4-8. Contour plot of the cubic smoothing spline fits for the salinity GEM field. Grey dots 

indicate the positions of CTD data.

83
4.3 PIES in the Gulf of Mexico 

The tau (τ) time series measured by the three Gulf of Mexico PIES were calibrated to τ100-1000 as 

described by Meinen and Watts (1998). For each τ100-1000 the GEM parameterizations provide 

look-up tables for temperature, salinity, and specific volume anomaly for any pressure; the 

calibrated τ times series from the 3 PIES combined with the GEM parameterization yields

estimates of vertical profiles of temperature, salinity, and specific volume anomaly. These 

estimates compared well to the independent measurements from the nearby I1 mooring (Figure 

4-9). RMS temperature differences range from 1.3°C at 150 dbar to 0.5°C at 650 dbar (Figure 4-

10); RMS salinity differences are near 0.08 psu at 450 dbar (Figure 4-11). The time series have 

been weekly averaged to eliminate small-scale features. These differences derive not only from 

instrument and parameterization errors but also reflect horizontal density gradients as the 

instruments are not co-located. The largest differences between the PIES temperature records

occur in the early part of the record (February through June) as the Loop Current extends 

northward to 27°N and the Eddy Millennium forms and detaches from the Loop Current. At that 

time upper-ocean velocities were strong (>50 cm/s, upper right panel of Figure 4-12); 

corresponding horizontal temperature gradients were necessarily large (geostrophy).

Geostrophic velocity shears were estimated from horizontal density gradients. Again, density at

any pressure can be determined via the GEM parameterization. These shears were referenced 

with either deep geostrophic velocity calculated from the near-bottom pressure gauges (Figure 4-

12) or with the deepest current meter record from the I1 mooring (Figure 4-13) Note equipment

failures of the pressure sensors for a portion of the deployment have reduced the time series to 

span late April through mid July. The triangular configuration of the PIES (a 2-D array) permits 

the estimate of the velocity vector (i.e., zonal and meridional velocity components). Comparison 

between the PIES estimated velocities referenced with the deep geostrophic velocities to the 

directly-measured velocity records reveals RMS velocity differences near 7 cm/s at 120 dbar and 

5 cm/s at 1980 dbar (Figure 4-12). Note that the bottom left panel in Figure 4-12 shows the

geostrophic velocity determined solely from deep pressure gauge while the bottom panels in 

Figure 4-13 is the deepest current meter record from the I1 mooring. Although the weekly 

averaging of the time series greatly reduces the amplitude of small-scale features, part of the 

discrepancy may be attributed to the fact that the mooring velocities are point measurements and 

the PIES velocities are geostrophic, and hence, represent the average velocity between the PIES. 

The comparison is encouraging in several aspects: the upper-ocean velocity vectors illustrate the 

strong currents associated with the Loop Current and Loop Current Eddy detachment and the 

deep velocity vectors show the strong current pulses as topographic Rossby waves pass through 

the mooring. 

4.4 Conclusion 

Although refinements may be made to the Gulf of Mexico GEM parameterization with future 

availability of additional appropriate hydrographic profiles, the present analysis illustrates that a 

robust empirical relationship exists between τ (tau) and vertical profiles of salinity, temperature

and density. A two-dimensional array of PIES will provide the basis for estimating a time series

of vertical profiles of the geostrophic velocity vector that can be referenced by measured deep 

velocities. The comparison of PIES-based velocity estimates and measured velocities was good. 

84 
500

1000

1500

2000

2500

I1 Mooring

PIES

 91oW 30’ 90oW 30’ 89oW 30’ 88oW 

 30’

 27oN 

 30’

 28oN 

 30’

Placement of PIES Relative to Mooring I1

Figure 4-9. Three PIES (red triangles) (Inverted Echo Sounders with pressure) arranged in a 

triangle around the I1 mooring (circle) for approximately 6 months, February 

through August 2001. Bathymetry is contoured every 500 m.

85
15

20

25

I1 MOORING PIES

150 m ; rms = 0.62,1.28,0.68 °C

temperature [°C]

5

10

15

20

300 m ; rms = 0.59,1.11,0.75 °C

temperature [°C]

5

10

15

20

400 m ; rms = 0.59,0.93,0.59 °C

temperature [°C]

6

8

10

12

14

525 m ; rms = 0.52,0.48,0.42 °C

temperature [°C]

4

6

8

10

Feb Mar Apr May Jun Jul Aug

2001

650 m ; rms = 0.52,0.23,0.41 °C

temperature [°C]

 Figure 4-10. Comparison of temperature time series measured by the I1 mooring (red) and 

temperatures estimated at the same set of depths by the 3 nearby PIES (blue) using 

the GEM interpretation of the tau (τ) measurements.

86
34.5

35

35.5

36

Feb Mar Apr May Jun Jul Aug

2001

I1 MOORING PIES

450 m ; rms = 0.08,0.06,0.08 

salinity (psu)

Figure 4-11. Comparison of salinity time series measured by the I1 mooring (red) and salinity 

estimated at 450 dbar by the 3 nearby PIES (blue) using the GEM interpretation of 

the tau (τ) measurements.

87
-50

0

50

PIES I1 Mooring Depth = 122 m

RMS = 6.7, 6.7 cm s-1

-20

0

20

40

300 m

RMS = 6.2, 7.3 cm s-1

-20

0

20

410 m

RMS = 7.1, 7.1 cm s-1

-10

0

10

20

1400 m

RMS = 5.9, 6.0 cm s-1

0

10

1800 m

RMS = 4.8, 4.4 cm s-1

-20

-10

0

10

May Jun Jul

2001

1979 m

RMS = 4.5, 4.4 cm s-1

May Jun Jul

2001

velocity (cm s-1) velocity (cm s-1) velocity (cm s-1) velocity (cm s-1) velocity (cm s-1) velocity (cm s-1)

Figure 4-12. Comparison of velocity measured by the I1 mooring (right) and velocity estimated 

at the same set of depths by the 3 nearby PIES (left) using the GEM interpretation 

of the tau (τ) measurements and referencing geostrophic shears to deep 

geostrophic velocity determined from the bottom pressure measurements.

88

-20

-10
-50

0

50

PIES I1 Mooring Depth=122 m

RMS = 11.9,11.2 cm s-1

-20

0

20

40

300 m

RMS = 10.3,11.0 cm s-1

-20

0

20

40

410 m

RMS = 12.2,10.0 cm s-1

-20

0

20

1400 m

RMS = 8.7, 6.5 cm s-1

-20

0

20

1800 m

RMS = 3.3, 2.6 cm s-1

-20

0

20

Feb Mar Apr May Jun

2001

1979 m

Feb Mar Apr May Jun Jul

2001

velocity (cm s-1) velocity (cm s-1) velocity (cm s-1) velocity (cm s-1) velocity (cm s-1) velocity (cm s-1)

Figure 4-13. Comparison of velocity measured by the I1 mooring (right) and velocity estimated 

at the same set of depths by the 3 nearby PIES (left) using the GEM interpretation 

of the tau (τ) measurements and referencing geostrophic shears to the deep current 

meter on the I1 mooring.

89
5.0 SUMMARY 

The two-years of data, from the three main moorings in the region of the Sigsbee Escarpment on 

the lower slope south of the Mississippi Delta, have shown unusual deep current flows. The

bottom intensified, nearly depth-independent motions are typical of topgraphic Rossby waves 

observed in this and other regions of the deep Gulf. However, energy levels are exceptional and 

the dominant periods of the motions are about 10 to 14 days and short compared to other regions 

of the eastern and western Gulf (Hamilton, 1990). Maximum currents at the I2 mooring were of

order 85 to 95 cm/s for an event early in the record. This energy seems to spill over the 

escarpment to the BP J1 site at the top of the Escarpment on some occasions when very-high

energy events occurred at I2. Otherwise, the velocities at J1 were much less energetic than at the

moorings south of the Escarpment. Similarly, bottom velocities at another site (I4), just west of 

I2, on the Escarpment, were also much weaker than measured at the base of the escarpment, and 

in deeper water depths. 

The records show a number of distinct wave trains passing through the site. The first, between 

September 1999 and January 2000, showed the highest current speeds and at the beginning of the 

record there were indications that upper-layer disturbances, caused by cyclonic frontal eddies on 

the LC front, were coherent with the lower layer flows. In this first period, upper-layer currents 

were vigorous due to the presence of the LC and later, the recently shed eddy J. The second 

period began in April 2000 and lasted to the end of the record in August 2000. These TRW’s

were also energetic though with slightly longer characteristic periods, stronger bottom trapping, 

and larger westward amplification between I1 and I2, than observed in the first period. The 

upper layer currents were quiescent during this second period as Eddy J had moved off into the 

western Gulf. Thus, there was no evident connection with the initiation of the April TRW’s with 

simultaneous fluctuations of the upper-layer currents. A third interval of energetic TRW’s, 

beginning in February 2001, was associated with the shedding of Eddy M and associated 

cyclonic circulations. In all, five wave trains, with differing periods and wavelengths were 

identified in the bottom records. Ray-tracing suggests that the west side of the LC is the most 

likely source region for these waves and that it is difficult for such short period waves to 

penetrate into the western Gulf basin. This is an accord with earlier measurements (Hamilton 

1990) that showed 20 to 30 day TRW’s dominating in the central and western Gulf. If the 

mechanism for coupling of surface propagating eddies or meanders with deep TRW motions that 

has been put forward for TRW generation by the Gulf Stream in the North Atlantic (Pickart, 

1995) applies here, then small cyclonic frontal eddies on the LC and LCE fronts could be 

candidates for generating deep, short-period TRW’s in the eastern Gulf. 

It is apparent from these measurements and the previous one-year of current data obtained by BP

at a site close to I1 (Hamilton, 1998), that TRW activity is fairly continuous at the base of the

escarpment in this region. The distribution of energy across the array was quite inhomogeneous, 

and varied with the different observed wave trains. The rotation of the principal axes of the 

motions from partly across-isobath at I3 to along-isobath at I1 and I2 suggests that the steep 

escarpment may be influencing the propagation of the TRW’s, possibly by reflecting the energy

back into deep water. The weak currents at J1 and I4 suggest that it is an effective barrier to 

TRW motions propagating into shallower water. 

91 
Upper layer currents were dominated by the passage of the two major LC anticyclones. The 

periphery of these eddies seem to have produced the most energetic temperature and velocity 

fluctuations that were often associated with rapidly translating cold cyclones. The passage of 

Eddy M into the western Gulf, between February and June 2001, allowed partial analysis of 

radial and azimuthal flows from mooring I1. This eddy moved further north than the previous 

Eddy J, and the center of the eddy passed within 60 km of the mooring, so that a substantial 

portion of the eddy interior was measured. The path and characteristics of the eddy were 

analyzed using drifters deployed by Horizon Marine. Eddy M was probably forced northwards 

and towards the slope by a large cyclone on its western side that formed while the eddy was still 

attached to the LC. This cyclone eventually moved up onto the slope and blocked further 

westward passage of Eddy M, which moved rapidly southwards during May 2001, and then 

resumed a more usual southwestward path into the western deep Gulf. The azimuthal velocity 

and temperature profiles behaved roughly as expected for an elliptical eddy in solid body rotation 

with a period of 8 to 10 days. However, there were significant anomalies that were associated 

with either attachment to the Loop Current or interactions with the cyclone and slope. The

passage of the eddy allowed estimation of the distances from the center to the maximum 

velocity, along the semi-major axis, and the width of the cyclonic shear zone outside the 

maximum velocity position. These were 150 and 50 km, respectively. The narrow cyclonic 

shear zone implies a large positive vorticity anomaly and thus a generation region for non-linear 

instabilities.

Upper layer inertial currents were also analyzed. In the January – February, 2001 period, before 

the arrival of Eddy M, when the upper layer velocities were dominated by vigorous interacting 

cyclones, strong inertial currents were generated in the surface layer. These were more vigorous 

than in the fall and winter of 2000, when background currents were small and wind forcing was 

stronger. It was speculated that the interacting eddies were partially responsible for the increased 

amplitudes of the inertial oscillations. The January – February inertial waves did not propagate

to deeper depths until Eddy M arrived. In Eddy M, the region just above the main thermocline 

had greater inertial energy than the surface indicating the propagating inertial internal waves

were being trapped by the negative vorticity anomaly in the center of the eddy. Below 800 to 

1000 m, inertial oscillations had negligible amplitudes. 

This study deployed, around I1, three bottom-mounted PIES to test the viability of using the 

gravest empirical mode (GEM) method to generate low-frequency temperature, salinity and

geostrophic velocity depth profiles. Deployment of an array of PIES and bottom current meter 

moorings is much more cost effective for large-scale measurement programs in deep water, than 

deploying arrays of full-depth moorings like I1. A preliminary GEM was constructed from 

historical CTD data for the Gulf and applied to the bottom pressure and travel time records from 

the three PIES deployed in the last 6-months of the study. The resulting derived profiles of 

temperature, salinity and geostrophic currents were compared with appropriate direct 

measurements of these quantities from mooring I1. The time series comparisons were good for 

all depths with high statistical significance and confidence. The last six months of the

deployment included part of the passage of Eddy M. This work will allow the confident use of 

PIES in future deep Gulf physical oceanographic measurement programs. 

92 
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95 
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