OCS Report 

MMS 2005-049 

A Circulation Model of the Gulf of Mexico and the Caribbean Sea: 

Development of the Princeton Regional Ocean Forecast (& Hindcast) 

System – PROFS, and Hindcast Experiment for 1992-1999 

LCE

Loop

Caribbean Current

Current

Florida Current

ACE

Cyclone

LCE Atlantic Ocean

Eddy Field

Shelf Current

Shelf

Current

Yucatan

Current

Gulf of 

Mexico

Caribbean Sea

CARE

Cyclonic

Gyre

Cyclonic

Gyre

CARE

YC: Yucatan Current CARE: Caribbean Eddy

LC: Loop Current ACE: (Smaller) Anticyclone

LCE: Loop Current Eddy

Cyclone

ACE

Cyclone

Greater Antilles

Venezuela

Lesser Antilles

Windward

Passage

Mona Passage

Columbian 

Basin

Cayman 

Basin

Anegada Passage

Nicaragua 

Rise

U.S.A

Mexico Jamaica

Netherlands

Antilles

0.0 0.2 0.4 0.6 0.8 1.0 (m/s)

Hispaniola
 Page 

 

II

OCS Study 

MMS 2005-049 

A Circulation Model of the Gulf of Mexico and the Caribbean Sea: 

Development of the Princeton Regional Ocean Forecast (& Hindcast) 

System – PROFS, and Hindcast Experiment for 1992-1999 

Final Report 

Author 

Lie-Yauw Oey 

Princeton University 

Prepared under MMS Contract 

1435-01-00-CT-31076 

by 

Princeton University 

Program in Atmospheric and Oceanic Sciences 

Sayre Hall 

Princeton, NJ 08544 

Published by 

U.S. Department of the Interior 

Minerals Management Service 

Herndon, Virginia 

October 2005 
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III

DISCLAIMER 

This report was prepared under contract between the Minerals Management Servie 

(MMS) and Princeton University. This report has been technically reviewed by the 

MMS and approved for publication. Approval does not signify that the contents 

necessarily reflect the views and policies of the Service, nor does mention of the trade 

names or commercial products constitute endorsement of 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 at the 

following address: 

U.S. Department of the Interior 

Minerals Management Service 

Headquarters (HDQRS)

Information Center, MS 4063 

Information Technology Division 

Minerals Management Service 

381 Elden Street 

Herndon, VA 20170-4817 

(703) 787-1080 

FAX (703) 787-1050 

tech.pubs @mms.gov

CITATION 

Suggested Citation: 

Oey, L.-Y., 2003: A Circulation Model of the Gulf of Mexico and the Caribbean Sea: 

Development of the Princeton Regional Ocean Forecast (& Hindcast) System - 

PROFS, and Hindcast Experiment for 1992-1999. Final Report, OCS Study 

MMS 2005-049, U.S. DOI Minerals Management Service, Herndon, Virginia. 

174 pp. 

ABOUT THE COVER

An example of model output over the Gulf of Mexico and Caribbean Sea: near-surface 

current and eddy fields obtained from a combination of satellite data and model. Shown 

are ten-day trajectories from Jul/19 through Jul/28, 1997. Colors indicate speeds such 

that greenish blue is ≈ 0.5 m/s and red is ≥ 1 m/s. From Oey, Lee and Schmitz (2003a). 
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IV

ACKNOWLEDGEMENTS 

Sponsor Acknowledgments: The development and application of the Princeton 

Regional Ocean Forecast (& Hindcast) System to the Gulf of Mexico and northwest 

Atlantic Ocean was sponsored by the Minerals Management Service/DOI, under 

Contract#1435-01-00-CT-31076. The Contract Officer was Dr. Walter Johnson and 

period of study was from Oct/2000 through Sep/2003. The author is also grateful to the 

Office of Naval Research/DOD for additional supports, and to the Geophysical Fluid 

Dynamics Laboratory/NOAA, Princeton University for the permission to use their 

supercomputing facilities. 

Other Acknowledgments: This work is an accumulated work of several staff members 

of AOS: S.J. Fan, H.-C. Lee, T. Ezer, H.-C. Zhang and M.-Z. Wei, to all of whom I am 

much indebted. I am also grateful to our departmental manager, Ms. L. Rossi for her 

gracious handling of complex contractual matters. I benefited from discussions with 

outside colleagues: Peter Hamilton, Walter Johnson, Bill Schmitz, Tony Sturges and D.-

P. Wang. Peter provided much of the observational data used for model validation, and 

Walter provided the ECMWF wind data. Finally, I thank my family for their supports, 

and for putting up with many missed weekends and occasions during the course of this 

study. 
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V

TABLE OF CONTENTS 

 Page 

 

COVER PAGE I 

TITLE PAGE II 

DISCLAIMER & OTHER REPORT INFORMATION III 

ACKNOWLEDGEMENTS IV 

TABEL OF CONTENT V 

EXECUTIVE SUMMARY 1 

1. INTRODUCTION 4 

 

2. PROFS – MODEL EQUATIONS, INPUTS & FORCING 8 

3. DATA ASSIMILATION SCHEMES 21 

4. GRID NESTING 27 

5. EXPLORATORY MODEL EXPERIMENTS 30 

6. MODEL EXPERIMENTS WITH ASSIMILATION 42 

7. CONCLUSIONS 53 

8. FUTURE DEVELOPMENTS & IMPROVEMENTS 55 

9. REFERENCES 56 

APPENDIX: ABSTRACTS OF PUBLICATIONS 61 

Table 1 69 

Table 2 70 

FIGURES 71 
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1

EXECUTIVE SUMMARY

The objective is to provide the Minerals Management Service (MMS) with multi-years of 

hindcast currents obtained from a numerical ocean circulation model for the Gulf of 

Mexico and the adjacent U.S. southeastern shelf and slope regions. These currents are to 

be used in MMS’ OSRA computer program to derive statistics regarding impacts of 

offshore spills. To achieve the objective, a comprehensive circulation model for the 

region has been developed based on the Princeton Ocean Model. This report describes 

the extensive development, testing and evaluation of the model that have been carried 

out. The hindcast period was 1993-1999. The model, all inputs and outputs (including 

all 60-day ‘restart’ files and standard plots) were delivered to MMS in July 2003. A 

Users’ Guide for the model was delivered to MMS in September 2003. Dr. Oey went to 

MMS’ Herndon (VA) offices in October/2003 to give a ‘training session’ on how to use 

the model. The model was demonstrated to run correctly on MMS’ workstations. 

The model hindcast attempts to portray as best as we can the ocean circulation state in the 

Gulf for the period 1992-1999, given the data available to us and the time constrains 

imposed by the contract performance period of 3 years. The data included (but were not 

restricted to) six-hourly wind field obtained from a combination of NDBC buoy data and 

the ECMWF analysis, daily river discharges from 34 U.S. rivers in the Gulf of Mexico, 

and satellite sea-surface height (SSH) anomaly and sea-surface temperature (SST). The 

satellite data were used in an assimilation scheme based on optimum interpolation. 

These data are deemed the most basic for a successful hindcast estimation of the 

circulation in the Gulf and adjacent seas. Other data, such as drifters, hydrographic 

measurements, and current meters were also utilized for testing and evaluation purposes. 

It is shown that the hindcast has yielded mean circulation and variances that are 

consistent with observations. In the Gulf of Mexico, the model gives generally anticyclonic circulation near the surface and a cyclonic circulation in the deep layers, though 

with considerable spatial variability. Variance ellipses show current intensities that are in 

general agreement with historical data, both near the surface and in deep layers. The 

model also gives consistent results when evaluated in details against observations at two 

locations in the Gulf: DeSoto Canyon and Yucatan Channel. The model gives Loop 

Current and eddy-shedding variability, circulation structures and transport variability that 

generally agree with those observed. Data assimilation enables correct placements of the 
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locations of the Loop Current and Loop Current eddies. It is shown for example that the 

correct placement of the Loop Current in the Florida Straits southwest of Florida is 

crucial in remotely driving currents over the west Florida shelf. 

The model was also tested to simulate drifters’ trajectories, and a drifter-assimilating 

scheme was developed and tested. Drifter-assimilation provides important supplemental 

information (in addition to satellite data) to the model in that smaller-scale eddy 

structures generally not resolved by satellite can now also be included. It is shown that a 

combination of both satellite data and drifter assimilations yields the least RMS errors in 

drifter positions. The two assimilations are complementary: satellite gives Gulf-wide 

coverage of large-scale Loop Current and Loop Current Eddies, while drifters enable 

more realistic simulations of localized (small-scale) eddy field. Simulating drifters are 

challenging however; their movements are sensitive to wind, waves and associated 

turbulence mixing that the model parameterizes. 

An important part of the model development and improvement process is the publications 

of results in peer-reviewed journals. Constructive critiques of model results and findings 

by anonymous peers are often useful in improving the model and our understanding of 

the flow physics. As of this writing, findings from this and another MMS’ Deep-Water 

supports have been reported in a number of publications: Oey and Lee (2002; JPO) on 

topographic Rossby waves; Oey et al. (2003a; JGR) on Loop Current variability and eddy 

shedding; Ezer et al. (2003; JGR) and Oey et al. (2004; JGR) on current variability in the 

Yucatan Channel; Wang et al. (2003; JPO) on model evaluations in DeSoto Canyon; Fan 

et al. (2004; CSR) on drifters assimilation and comparison; Oey and Zhang (2004; CSR) 

on subsurface jets and cyclones; Oey (2004b, JGR) on vorticity fluxes and Loop Current 

eddy-shedding, Oey et al. (2005a) on test-forecasting Loop Current and eddies, and Oey 

et al. (2005b; AGU Monograph) on review of models and physical processes. There are 

also three MMS reports (Oey et al. 2003b; Oey, 2003; and this one, Oey, 2004a; plus 

numerous bi-monthly and quarterly reports), as well as various reports in Proceedings

and Invited Talks (2001 and 2004 European Geophysical Union; and 2002 Japan 

Oceanographic Society Symposium). 

Though we have provided the MMS with hindcast currents that account for realistic wind 

forcing, river discharges and correct placements of Loop Current and Loop Current 
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3

eddies, there is plenty of room for further improvements. First, more validations may be 

carried out, either with newer data or with focus on different dynamics and processes; for 

examples, subsurface processes in DeSoto Canyon; different modes of Loop Current and 

shedding variability; topographic Rossby waves over the upper slope (≈ 2000 m isobath) 

and new MMS/SAIC exploratory study of deep currents in the central Gulf, and 

northwestern and western Gulf study. Secondly, the potential usefulness of drifterassimilation, as well as assimilation with SOFAR and new MMS/SAIC data sets should 

be further explored; so is the development of more sophisticated assimilation schemes: 

Kalman filtering and 3D-Var, for examples. Thirdly, the model’s surface physics can be 

further improved to include effects of wind waves. This improvement should prove 

particularly relevant to MMS’ objectives of obtaining more accurate statistics for oil spill 

trajectory studies. Finally, some fundamental questions should be explored. These 

include (i) small-scale eddies and strong jets (birth, development, interaction and decays), 

and the closely related (we suspect) topic of ring/topography interaction; (ii) Loop 

Current variability and eddy-shedding; (iii) transport variability through Yucatan Channel 

and Florida Straits (especially in view of the recent Canek data); (iv) deep currents; and 

(v) Caribbean Sea and Gulf of Mexico connection (both large-scale and smaller-scale 

effects such as eddy-squeezing through the channel). 
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4

1. INTRODUCTION 

The Loop Current (LC) is the dominant feature of the circulation in the eastern Gulf of 

Mexico and the formation region of the Florida Current-Gulf Stream system. Intense 

speeds occur in the Loop, up to 1.7 m s-1 (Forristal et al., 1992). This and the broad 

ranges of spatial and temporal scales of variability that exist in the Loop pose an 

enormous challenge in our attempt to describe, understand and predict its behaviors. 

Compounded to the difficulty is the well-known fact that the Loop Current can become 

unstable and episodically sheds warm-core eddies or rings (e.g. Cochrane, 1972; 

Vukovich, 1995). These rings have diameters ≈ 300 km, vertical extent ≈ 1000 m, swirl 

speeds ≈ 1.8~2 m s-1, and they generally translate westward at 2~5 km day-1 (Elliott, 

1982; Cooper et al. 1990; Forristal et al., 1992). The Gulf has a relatively small central 

deep basin (depth ≈ 3500 m) surrounded by continental rise, slope and shelves. The 

Loop Current and rings readily interact with topography. The interaction strongly affects 

how energy of the currents is distributed in the water column, and how the energy 

propagates along and across isobaths (Oey and Lee, 2002). Ancillary smaller cyclones 

and anti-cyclones, many of them subsurface, can develop around rings’ and Loop 

Current’s edges. These smaller-scale features develop through flow instability, eddysplitting and/or interaction of the strong current with topography (Brooks and Legeckis, 

1982; Vukovich and Maul, 1985; Cooper et al. 1990; Vidal et al. 1992; Biggs et al. 1996; 

Hamilton et al., 2002; Oey and Zhang, 2004). The resulting redistributions of intense 

energy to deep layers, and to locations that can be quite remote from rings and the Loop 

make it difficult to predict the occurrences of these small-scale phenomena. 

This report is concerned with modeling currents in the Gulf of Mexico. A subordinate 

interest is the related circulation dynamics of the Caribbean Sea. It will be seen that a 

significant portion of the Loop Current and Loop Current Eddy (LCE) dynamics depends 

on current variability in the Caribbean Sea. The complexity of currents in the combined 

system can perhaps be appreciated by even a simple map such as that in the Title Page 

Illustration (TPI). Here, a ‘snapshot’ of near-surface current and eddy fields in the Gulf 
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5

of Mexico and the Caribbean Sea is obtained by combining altimetry sea-surface height 

(SSH) anomaly (from satellite) with the result of a general circulation model (GCM), and 

plotted as ten-day trajectories from Jul/19 through Jul/28, 1997. Colors indicate speeds 

such that greenish blue is ≈ 0.5 m/s and red is ≥ 1 m/s. (How we construct a circulation 

map like this will be detailed later in the report.) In addition to the more conspicuous 

high-speed (≈1 m/s), jet-like features, which show up in red in the map: the Caribbean 

Current (CC) along the southern portion of the Caribbean Sea, the Yucatan Current (YC) 

and Loop Current (LC) at the Yucatan Channel and in the eastern Gulf of Mexico, and 

the Florida Current in the Florida Straits and along the slope of the South Atlantic Bight, 

the figure also shows eddies and meanders at smaller scales: Loop Current Eddies 

(LCE’s), Caribbean Eddies (CARE’s), and smaller cyclones. These currents and eddies 

constitute an important component of the subtropical gyre circulation of the North 

Atlantic Ocean, and play an important role in the regional as well as basin-scale 

transports of heat, salt and other tracers. 

 On a more practical level, in regions where there exist earnest oil and gas 

explorations, in the Gulf of Mexico, in particular, one is also interested in the fate and 

trajectories of possible contaminant spills, for which knowledge of currents is required. 

Indeed, a main objective of the present study is to provide the Minerals Management 

Service (MMS), our sponsor, with hindcast of currents in the Gulf of Mexico. It is 

necessary that the hindcast currents are produced using as realistic forcing and input as 

possible, and are for a sufficiently long period (multi-years) that meaningful statistics of 

the modeled trajectories may be obtained using the MMS’ Oil Spill Risk Analysis 

(OSRA; Smith et al. 1982) computer program. The development of such a hindcast 

system and its application to the Gulf of Mexico for the period 1993-1999 are detailed in 

this report. It is also necessary to skill-assess the model in general, and the hindcast in 

particular. I will therefore also compare the hindcast results with observations, and will 

summarize general assessments of the model dynamics. For some results, I have liberally 

taken materials from recent work by my colleagues and myself, and this report will then 

serve as a (hopefully) succinct summary. 
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6

 The outline of the report is as follows. Section 2 describes the model: the 

Princeton Regional Ocean Forecast (and Hindcast) System - PROFS, as it is applied to 

the Gulf of Mexico, Caribbean Sea and the U.S. east coast. The governing equations, 

boundary conditions, and modeling strategy are described. I also discuss inputs and 

forcing in the model. Inputs include shelf as well as deep-ocean bathymetry, three-hourly 

wind, monthly climatological (potential) temperature (T) and salinity (S), daily river 

discharges, ten-daily altimetry SSH anomaly, weekly Multi-Channel Sea Surface 

Temperature (MCSST) data, and drifter data. Section 3 describes the PROFS’ dataassimilation scheme using SSH anomaly, MCSST and drifter data. Grid-nesting (for 

doubled resolution calculation in the Gulf of Mexico) is used in some experiments, and 

the technique is described in section 4. Section 5 summarizes the various exploratory 

experiments that have been conducted, from simple no-wind cases to fully assimilated 

cases. Section 6 describes in more details model experiments with data assimilation, 

inter-experiment comparison, comparison with observations, and model predictability. I 

will discuss model results in terms of characteristics that have become quite standard in 

the modeling literature of the Gulf: Loop Current, Loop Current Eddy shedding, and 

Loop Current eddies. There are by far the most energetic and ubiquitous circulation 

features of the Gulf, as well as being the ‘best known’ observation-wise (though by no 

means we understand them well!). I will detail one example to assess the model’s ability 

to simulate a Loop Current Eddy’s evolution. I will also discuss model results in terms of 

quantities which are less-often discussed in the literature: transports through various 

straits and channels, the Caribbean Current, mean and variance field maps in the deep as 

well as near the surface. Comparisons with observations will be made. I will also 

describe our experience with assimilating drifters and show how in some cases they can 

improve the model hindcast. Recently MMS (and others) are interested in subsurface and 

deep currents, and these will be discussed in terms of topographic Rossby waves 

generated by Loop Current and eddies, and also in terms of subsurface cyclones and jets 

when Loop Current or Loop Current eddy smashes onto the continental slope. The report 
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7

ends with a concluding summary in section 7, and section 8 contains some thoughts on 

future directions. 
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8

2. PROFS 

 At the core of PROFS is POM, the Princeton Ocean Model (Mellor, 2002). The 

following description begins with a general presentation of the governing equations, then 

POM’s numerical scheme and specializations to the Gulf of Mexico region. The reader 

is referred to Mellor (2002) and Oey (2003) for details on numerics. 

2.1 Governing Equations 

 PROFS uses the time-dependent three-dimensional, incompressible Navier-Stokes 

equations on a rotating plane (earth) assuming hydrostaticity and Bousinesq 

approximation, and appropriately Reynolds-averaged (Hinze, 1975; Gill, 1982): 

 + + = 0 u v w

xyz

∂∂∂

∂∂ ∂ (2.1) 

2 1 + + + - + ' + + a

o

o

M x o z

u u uv uw u g p fv g dz K F t x y z x x xz z ρ∂∂ ∂ ∂ ∂ ∂ ∂η ∂ρ ∂

∂ ∂ ∂ ∂ ∂ρ ∂ ∂ ∂ ∂

⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

′ + = ∫ (2.2) 

 

2 1 + + + + + '+ + a

o

o

M y o z

v uv v vw v g p fu g dz K F t x y z y y yz z ρ∂∂ ∂ ∂ ∂ ∂ ∂η ∂ρ ∂

∂ ∂ ∂ ∂ ∂ρ ∂ ∂ ∂ ∂

⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

′ + = ∫

 (2.3) 

 - p g

z

∂

ρ ∂ = (2.4) 

Here, (u, v, w) are three components of velocities in west-east (x; positive eastward), 

south-north (y; positive northward) and upward (z; z = 0 at the mean sea-surface), t is 

time, f is the Coriolis parameter, in general a function of latitude, g is acceleration due to 

gravity, η(x,y,t) is the free surface measured from z = 0, ρ is density of sea-water (ρo is 

some reference density, a constant ≈ 1025 kg m-3; recall Bousinesq approximation), 

pa(x,y,t) is the atmospheric pressure, assumed known, KM is the sum of (kinematic) 

molecular and parameterized eddy viscosities in the z-direction, and similarly Fx and Fy

represent the horizontal viscosity terms in the x and y directions, respectively. They are 

given by: 
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9

 

Fx = + ( ) xx xy ( ) x y

∂ ∂ τ τ ∂ ∂ (2.5a) 

 

 

Fy = + ( ) xy yy ( ) x y

∂ ∂ τ τ ∂ ∂ 

(2.5b) 

where 

 = 2 , = = + , = 2 xx xy yx yy MM M

u uv v AA A

x yx y

∂ ∂∂ ∂

τ ττ τ ∂ ∂∂ ∂

⎛ ⎞ ⎜ ⎟

⎝ ⎠

 

(2.6a,b,c) 

AM is the sum of (kinematic) molecular and parameterized eddy viscosities in the x and y

directions, assumed equal. 

 Equation (2.1) is the continuity equation for an incompressible fluid, and 

equations (2.2) and (2.3) are the x and y momentum equations, respectively. The zmomentum equation (2.4) expresses the hydrostatic condition, which upon integration in 

z gives: 

 + ' ' o

a o z

p p g dz = + gρ η ρ ∫ (2.7) 

Taking the horizontal gradients of (2.7) then yields the three terms in (2.2) (or (2.3)) that 

involve the x (y) gradients of η, ρ and pa. 

 The density ρ is a function of the potential temperature T, salinity S, and pressure 

p: 

 ρ = ρ(S, T, p) (2.8) 

where T and S are governed by the following heat and salt conservation equations: 

 

 

+ + + = + H T

T Tu Tv Tw T K F

tx y zz z

∂∂ ∂ ∂ ∂ ∂

∂∂ ∂ ∂∂ ∂

⎡ ⎤

⎢ ⎥ ⎣ ⎦ (2.9) 
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10

 

+ + + = + H S

S Su Sv Sw S K F

tx y zz z

∂∂ ∂ ∂ ∂ ∂

∂∂ ∂ ∂∂ ∂

⎡ ⎤

⎢ ⎥ ⎣ ⎦ (2.10) 

Here, similar to the momentum equations, KH is the sum of (kinematic) molecular and 

parameterized eddy diffusivities in the z-direction, and FT and FS represent the horizontal 

diffusive terms for heat and salt, respectively. They are modeled by: 

 + qx qy F

x y φ

∂ ∂

∂ ∂ ≡ (2.11) 

where 

 , x y H H qA qA

x y

∂φ ∂φ

∂ ∂ ≡ ≡ , (2.12a,b) 

φ represents T or S, and AH is the sum of (kinematic) molecular and parameterized eddy 

diffusivities in heat and salt, assumed equal. 

 Except for the eddy viscosity and diffusivity terms, the seven equations (2.1) 

through (2.3), and (2.7) through (2.10), together with some appropriate initial and 

boundary conditions (to be detailed below), form a closed system for the seven unknowns 

(the so called prognostic variables): u, v, w, T, S, ρ and p (or equivalently, η). 

 Reynolds averaging leads to turbulent stress terms which we have parameterized 

above using eddy viscosities, KM and AM, and eddy diffusivities, KH and AH, and relating 

the stresses to gradients of the mean fields, equations (2.6) and (2.12). 

The Vertical Eddy Viscosity & Diffusivity: 

 We model the vertical eddy viscosity and diffusivity, KM and KH, using Mellor 

and Yamada’s (1982) level 2.5 turbulence closure scheme. The reader is referred to that 

paper for a detailed derivation. In summary, a pair of advective-diffusive equations with 

turbulence sources and sinks is solved, one for q

2

 (twice the turbulence kinetic energy) 

and another one for q

2 A ( A = turbulence length scale). The KM and KH are then related to 
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11

q and A through Richardson number-dependent stability functions SM and SH according 

to: 

 = K qS M M A (2.13a) 

 = K qS H H A (2.13b) 

 

where SM and SH are given by 

22 12 2 1 1 [1 (3 + 18 ) ] = [1 6 / ] H H S AB AA G A A B − − (2.14a) 

 

12 1 12 1 1 1 1 [1 9 ] [(18 2 + 9 ) ] = [1 3 6 / ] M HH H S AAG S A AA G A C A B − − −− , (2.14b) 

and where 

⎥

⎦

⎤ ⎢

⎣

⎡ − z

p

z c

g

q

G

o s

H ∂

∂

∂

∂ρ

ρ 2 2

2 1 = 

A (2.15c) 

 

is a Richardson number. The quantity cs

2 is the speed of sound squared. The five 

constants in (2.14a,b) are evaluated from neutral homogeneous and near surface 

turbulence data (law-of-the-wall region) and are found (Mellor and Yamada, 1982) to be 

(A1, B1, A1, B2, C1 ) = (0.92, 16.6, 0.74, 10.1, 0.08). The stability functions limit to 

infinity as GH approaches the value = 0.0288. 

The Horizontal Eddy Viscosity & Diffusivity: 

 In the Navier-Stokes framework, the horizontal eddy viscosity and diffusivity are 

also micro-scale (O(cm) and less) turbulence quantities. In practice, however, numerical 

models typically use grid sizes so large (10’s and 100’s of km) that the AM and AH must 

be parameterized using the properties of the mean field. The AM and AH (or more exactly 

the F’s on the right-hand-side of equations (2.2), (2.3), (2.9) and (2.10)) then 

parameterize mixing by small-scale (100’s m to km’s) ocean eddies. Smagorinsky 

(1963), for example, proposes the following formula, 

 

 ( ) 1

 = + 

2

T

A Cxy M ∆∆ ∇ ∇ V V (2.16) 
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12

where 

( ) 2 2 2 1/2 + 2 [( / ) ( / / ) / 2 ( / ) ] T ∇ ∇ V V = × ∂ ∂ + ∂ ∂ +∂ ∂ + ∂ ∂ ux vx uy vy (2.17) 

and ∆x and ∆y are grid sizes. The Smagorinsky constant C ≈ 0.05 ~ 0.20. An advantage 

of the Smagorinsky relation is that C is non-dimensional. Also, note that AM decreases 

as resolution improves and that AM is small if velocity gradients are small. 

 

2.2 The Numerical Scheme 

 Given an ocean domain, POM solves the above governing equations and 

associated boundary conditions (to be presented later1) on a discrete set of orthogonal 

curvilinear grid in the horizontal, and terrain-following sigma (σ) coordinate in the 

vertical (Phillips, 1957): 

 - = 

+

z

H

η σ

η (2.18) 

where H (x, y ) is the bottom topography. Thus σ ranges from σ = 0 at z = η to σ = −1 

at z = −H. Figure 2-1a shows the σ-coordinate system and Figure 2-1b the horizontal 

curvilinear grid that covers the domain of interest in this study: the northwest Atlantic 

Ocean west of 55o

W (to 98oW) and 6oN-50oN. A staggered Arakawa C-grid is used, as 

shown in Figure 2-1c. 

 A leap-frog time-stepping and center-space differencing scheme is used in POM 

which formally renders the model second-order accurate in time and space for a uniform 

grid (Richtmyer and Morton, 1957). To take advantage of the different time scales that 

exist between the external (barotropic; ~ L/Ce) and internal (baroclinic; ~ L/Ci) gravity 

wave modes, L/Ce << L/Ci, and also the different spatial scales between the vertical (H) 

and horizontal (L) directions, H << L, where Ce and Ci are typical phase speeds of 

barotropic and baroclinic waves respectively, a split time-stepping (called mode splitting, 

Simons, 1974; Madala and Piacsek, 1977) is used and time-integration in the vertical is 

implicit. The external mode equations are obtained by integrating the governing 

 

1 Boundary and initial conditions are of course an integral part of the total solution. They depend on a particular model’s 

domain and will be discussed later focusing on the Gulf of Mexico and Caribbean Sea region. 
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13

equations (2.1), (2.2) and (2.3) and applying the boundary conditions that fluid parcel 

must remain at the material surfaces at z = η and z = −H. This leads to an equation for η: 

 + + = 0 UD VD

tx y

∂η ∂ ∂

∂∂ ∂ (2.19) 

where (U , V) is depth-averaged velocity and D = H + η, and two other equations for (U ,

V) . These (two-dimensional) external-mode equations can be solved rapidly at small 

time step ∆te (limited by the Courant-Friedrichs-Lewy’s (1928) or CFL condition) and 

supply the surface elevation η and transport (i.e. (U , V) ) information to the full threedimensional (internal-mode) equations (2.1-2.3). The internal-mode equations in turn 

supply the external-mode equations with near-bottom velocity (for bottom drag), vertical 

integrals of pressure (density) gradients, and the so called dispersion terms in terms of 

integrals of velocity differences arising from advections (and Smagorinsky diffusion) of 

momentum. The upshot is that the internal-mode equations can be solved at ∆ti >> ∆te, 

thus making the scheme efficient. These and other details of the numerical scheme can 

be found in Mellor (2002). In PROFS, we use ∆ti = 675 seconds and ∆te = 15 seconds. 

2.3 Inputs, Forcing and Boundary and Initial Conditions 

Topography

 Figure 2-2 shows the model topography. The set we use is GTOPO30, a satellitederived topography dataset (using the global digital elevation model) with a horizontal 

spacing of 30 arc seconds (approximately 1 km; http://edcwww.cr.usgs.gov/landdaac/ 

gtopo30/gtopo30.html). We further supplemented the data with direct National Ocean 

Survey topography charts especially over the shelves, and checked carefully for 

inconsistencies and errors. Unlike some commonly used topography (e.g. DBDB5) the 

present topography is valid for both the near-coast as well as open-ocean regions. 

Lateral Open Boundary at 55o

W & Closed Boundaries

 At the model’s only open boundary at 55o

W, time-independent total transports are 

specified according to Schmitz (1996). Except for experiments in which we assimilate 
 Page 

 

14

sea-surface height anomaly from the satellite, the steady transports effectively filter out 

propagating signals from the region east of 55o

W. These transports determine the twodimensional depth-integrated velocities at the open boundary and are meant to account 

for the large-scale transports (windcurl + thermohaline) through 55o

W.

2 The openboundary conditions are then a combination of these transport specifications along with 

radiation and advection as detailed in Oey and Chen (1992a). Monthly T and S are 

interpolated to the model grid from the Generalized Digital Environmental Model 

(GDEM) climatology (Teague et al. 1990), and one-sided differencing is used for T and 

S, such that GDEM values are used when the local flow is westward (i.e. into the 

modeled domain), and the T and S are advected out when flow is eastward. Orlanski 

(1970) radiation condition is used for the baroclinic, depth-dependent velocities. These 

open-boundary specifications also set the baroclinic structure, which is largely 

geostrophic through the thermal-wind balance. All normal fluxes are zero across closed 

boundaries. Because of the C-grid, it is not necessary to specify the tangential 

component of the velocity at lateral coastal boundaries. However, POM masks out all 

land points, and a no-slip condition is implicitly imposed by the use of a non-zero lateral 

viscosity AM (equation 6; Oey, 1996c). Near the ocean floor, a quadratic drag 

formulation is used to model the bottom stress: 

( ) , , 1/2 2 2 , = u v u v d C

z

v

z

u

MK ⎥

⎦

⎤ ⎢

⎣

⎡ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ + ∂

∂

∂

∂ z Æ − (H+η) (2.20) 

where the bottom drag coefficient, Cd, is given by: 

 

{ }

2

2 = , 0.0025

ln /

d

b o

C MAX

z z

κ

⎡ ⎤

⎢ ⎥

⎡ ⎤ ⎣ ⎦ ⎣ ⎦

 (2.21) 

and where κ = 0.4 is the von Karman constant, zo = 0.01 m is the roughness parameter, 

and zb is the z-value of the grid cell closest to the bottom. The above formulation is 

equivalent to matching the near-bottom velocity to a logarithmic profile (i.e. law of the 

wall). 

 

2 We will for convenience refer to experiments that specify only these transports as “no-wind experiments,” though in fact the 

55o

W transports already include in part a windcurl-driven portion from east of 55oW. 
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15

Generalized Digital Environmental Model (GDEM) Climatology 

 The GDEM climatology is an important input to the hindcast. Figure 2-3 shows 

two examples of T-contours at selected depths for (a) January and (b) July, and figure 2-4 

shows the corresponding S-contours. The figures show the prominence of the warm and 

saline Gulf Stream water and cooler and fresher water to the north. However, the 

descriptions here will focus on the Caribbean and the Gulf. In winter (January), there is a 

strong contrast in (potential) temperature between the Caribbean and the Gulf, by as 

much as 5 o

C near the surface. In summer, the near-surface temperature contrast is 

obliterated in the Gulf because of strong warming, but the Caribbean becomes only 

slightly warmer, 1~2 o

C. The subsurface (z≈−200 m and below) temperatures remain 

essentially unchanged with season. The temperature remains at 3~5 o

C in the deeper 

portion of the water column both for winter and summer. The salinity displays less 

seasonal variation. 

Sea-Surface Boundary Conditions

The Wind: 

 At the sea-surface, six-hourly ECMWF (European Center for Medium-range 

Weather Forecast) wind stress (τ

ox, τoy) /ρo is specified: 

x y , = ( , )/ u v o o KM z z o

∂ ∂ τ τ ρ ∂ ∂

⎛ ⎞ ⎜ ⎟ ⎝ ⎠ z Æ η (2.22) 

We compare the ECMWF wind for the hindcast period 1993 through 1999 with all 

available National Data Buoy Center (NDBC) buoy and CMAN stations in the Gulf of 

Mexico (Figure 2-5). Figure 2-6 gives examples (for 1997 at four stations) of comparison 

between NDBC (green) and ECMWF (red) time series. In each panel along the bottom 

in the figure, we show also the mean/variance values (for both ECMWF and NDBC), the 

skill ‘Sk’ defined by 

Sk = {1 - [<(um-uo)•(um-uo)>]/[<um•um>.<uo•uo>]} × 100%, (2.23) 
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16

where u is the wind vector, subscripts ‘m’ and ‘o’ denote model (i.e. ECMWF) and 

observation (i.e. NDBC) respectively and <.> denotes time averaging (one year), and also 

CO = the correlation coefficient between ECMWF and NDBC. (The ‘sig’ is the 95% 

significance level). Thus perfect agreement gives Skill = 100%. It is visually clear from 

figure 2-6 that ECMWF winds are in general less energetic: peaks in NDBC time-series 

are often missing from ECMWF. However, the phase agreement is excellent, and the 

ECMWF time-series follow remarkably well the lows and highs of NDBC time-series, 

both for high and low-frequency fluctuations. Figure 2-7 summarizes this correspondence 

with plots of the correlation coefficients (upper two panels) and skills Sk (lower two 

panels) for all 33 stations (indicated along the x-axis). The correlations are all significant 

at the 95% significance level (sg < 0.1 for all stations) and values at all but four stations 

are 0.8 and higher. The four stations that have lower values (~0.5), namely SAUF1, 

41008, 41009 and 41010, are outside the Gulf off east Florida and in the South Altantic 

Bight. The skills are also similarly high, Sk~80% and higher, for all but the four stations 

where Sk drops to about 60%. Figure 2-8 summarizes the comparison of mean and 

standard deviation between ECMWF and NDBC. Points that lie on the 45o

 line would 

indicate perfect agreements. It is seen that there is a fairly good agreement of the mean 

west-to-east U (top left panel) component, in that both ECMWF and NDBC show 

westward-blowing winds with most points lying near the 45o

 line indicating 

approximately equal intensities. On the other hand, the south-to-north V (bottom left 

panel) component for ECMWF is more positive (i.e. blowing more northward) than 

observed. Also, as mentioned above for the time-series plots, figure 2-6, the standard 

deviations for ECMWF are weaker than NDBC (there are more points above the 45o

 line 

on the right panels of figure 2-8), by as much as 40% at some stations. 

Thus while the ECMWF time-series show good matching of the lows and highs 

of the NDBC time-series, resulting in high correlations (>0.8) and skills (>80%) for 

stations inside the Gulf, both the variance and meridional wind component need to be 

improved. We found that we were able to match the variance quite well by simply 

increasing the magnitude of ECMWF fluctuations by 7%, while keeping its means 

unchanged. To derive an improved wind data to be used as forcing into the model, we 

therefore take this 7% increased variance in ECMWF and use it together with NDBC 

data as input to optimally interpolate (Bretherton et al. 1976) onto the model grid points. 
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17

Near the NDBC locations, the optimally-interpolated wind coincides with the NDBC 

time series, while at points away from NDBC stations, the wind merges with ECMWF. 

 The wind is generally from the east (i.e. trade wind), strongest in the Caribbean 

Sea where the mean wind stress curl is also strongest (Figure 2-9). In the Gulf of 

Mexico, the mean wind stress is weaker and the corresponding curl is generally 

anticyclonic (and weak) over most of the Gulf, except over the southwestern Gulf where 

the curl is cyclonic. 

Surface Heat and Salt Fluxes: 

 We specify surface fluxes of heat and salt so that they are consistent with 

climatological values of surface T and S (Oey and Chen, 1992a). To illustrate, consider 

the following one-dimensional (in z) example for T: 

 

= ⎥

⎦

⎤ ⎢

⎣

⎡

z

T K

t z

T

H ∂

∂

∂

∂

∂

∂ (2.24) 

Integrate (2.24) over a near-surface layer z = −ho to z = η: 

 

o @ z @ z -h

0

= = =

−

⎥

⎦

⎤ ⎢

⎣

⎡ − ⎥

⎦

⎤ ⎢

⎣

⎡

∫ z

T K

z

T Tdz t K H H

ho

∂

∂

∂

∂ ∂ ∂ η (2.25) 

The first term on the right hand side of (2.25) is heat flux through the sea surface, while 

the second term is heat flux through the bottom of the layer. For illustrative purpose (and 

without loss of generality), set the latter to zero and write the first as: 

 

C ( ) H @ z 1 T Tsurf z

T K = − − ⎥

⎦

⎤ ⎢

⎣

⎡ =η ∂

∂ , (2.26) 

where Tsurf is the sea-surface temperature (to be specified from observation) and 

 dT

dQ C

C p /( ) o

1

ρ = ≥ 0. (2.27) 
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18

Here, Q is surface heat flux in J/(m2.s), ρo density of water (≈ 103 kg.m-3), and Cp the 

specific heat of water (≈ 4×103

 J/(kg.oK)) (Oey, 1986). Over the Atlantic, climatological 

atlases give dQ/dT ≈ 50 J/(m2

.s oK), hence C1 ≈ 1.25×10-5 m s

-1 ≈ 1 m day-1 = the value 

used in the program (c.f. Gill, 1982). In the model, the GDEM climatological surface 

temperature is used for Tsurf. As a limiting example, assume that in the surface layer the 

water is well-mixed, and T ≈ constant through the layer. Equation (2.25) with second 

term on the right = 0 and first term replaced by (2.26) then gives: 

 ( / ) 1 ( (0) ) ho C t

surf surf T T T T e − = + − (2.28) 

where T(0) is T at time t=0. Thus the e-folding time scale for the modeled temperature to 

adjust to Tsurf is ho/C1, ≈ 10 days if ho is taken as ≈ 10 m. The same surface relaxation 

formulation, with the same value of C1, is assumed for salinity. 

Rivers: 

 Time series of (daily) discharges at thirty-four rivers in the northern Gulf are 

shown in Figure 2-10 and their locations on the model grid are given in Figure 2-11. The 

Mississippi and Atchafalaya rivers have the largest discharges, about 2×104

 m

3

s

-1 and 

7×103

 m

3

s

-1 respectively. These and most other rivers show clear seasonal variation in 

their discharge. Some smaller ones do not however (e.g. Rio Grande Basin), and depend 

more on local conditions (episodic storms etc). It is also clear that the raw data contain 

some anomalously large peaks (Guadalupu river for example), which we could remove 

prior to their usage in the model. However, their occurrence is rare and tests indicate that 

the model remain stable even when they are included. 

 Following Oey (1996a), rivers are specified by downward velocity at the river 

mouth. This is equivalent to including a source term in the continuity equation (2.19). 

Recall that equation (2.19) is obtained by a vertical integration of equation (2.1), which 

gives two terms involving the vertical velocities at surface and bottom. These vertical 

velocities are such that the bottom and sea-surface are material surfaces, which results in 

a vertical velocity in the transformed σ-coordinate that is zero at the bottom, but at the 

surface it is equated to discharge per unit area at the river’s mouth. Equation (2.19) is 

modified to: 
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19

 + + = R

UD VD W

tx y

∂η ∂ ∂

∂∂ ∂ (2.29) 

where WR(x,y) is the river discharge per unit area specified at the (x,y) location of each of 

the 34 rivers shown in Figures 2-10 and 2-11. This change does not affect the ∂(Sw)/∂z

term in (2.10) because S = 0 where WR ≠ 0. But the governing equation for T, equation 

(2.9), is changed. We use the climatological temperature for the surface temperature at 

the river points. In theory, the change also affects momentum equations. But the effect 

is small and we set the downward momentum = 0 (Oey, 1996a). 

Robust Diagnostic Calculation

 To prevent drift in multi-year integration, a weak relaxation is incorporated in the 

equations for φ (= T or S) such that at levels deeper than about 500 m T and S are relaxed 

to their respective climatological values (Oey and Chen, 1992a), with a time scale λ

-1 ≈

200 days. Thus, 

 + ) ( ) = ( ) ( Adv Dif c t

∂φ φ φ λ φ φ ∂ − − (2.30a) 

 R z z

d s d G G G e

/ λ = + ( − ) (2.30b) 

where φc is monthly climatology, λ is inverse relaxation time scale which is a function of 

z, Adv(φ) and Dif(φ) represent the advection and horizontal diffusion terms, respectively, 

Gs (=0) and Gd (= 5.787×10-8

 s

-1, i.e. = 1/200 day-1) are the reciprocals of the relaxation 

time sales at the surface and at deep levels respectively, and zR (= −500 m) is the 

relaxation depth scale. Thus no relaxation is used for T (and S) at levels shallower than 

about 500 m (λ ≈ 1/300 day-1 at z = 500 m), and model dynamics (and data assimilation; 

see later) dictate the simulated physical process. At deeper levels, equation (2.30) 

prevents long-term drift of the simulated mass field. 

 

Initial Conditions

 The hindcast period is 1992 through 1999. January values of GDEM T and S are 

used as initial conditions. To obtain a corresponding geostrophically-balanced velocity 
 Page 

 

20

field and allow a smooth transition to assimilated simulation that begins on Oct/20/1992 

(when the first satellite data becomes available, see later), we let λ be a function of time 

for the first nine months of 1992, such that Gs = Gd = 1 day-1 at t = 0 and they 

exponentially approach Gs =0 and Gd = 1/200 day-1 at t = 270 days. Thus the calculation 

is essentially diagnostic for the first half of 1992. Such a mixed ‘prognostic-diagnostic’ 

spin-up provides an initial field for satellite data assimilation that is closer to smooth 

climatology than that derived from a wholly prognostic spin-up. The latter generates 

eddies and Loop Current with mass fields which do not necessarily correspond to those 

from data assimilation and the resulting mismatch may take some time (months) to 

recover. 

 Figure 2-12 shows the results of two months of calculation in the above robust 

diagnostic mode in terms of sea-surface height, speeds, temperatures and surface salinity. 

They represent typical early stages (initial conditions) of the model hindcast. The 

Caribbean Current, Loop Current, Florida Current and Gulf Stream are clearly seen in 

these plots. Speeds in these major currents exceed 1 m s-1 and there exist strong contrast 

in surface elevation as well as temperature (at depths) across the currents. The elevation 

difference across the Loop Current and Gulf Stream is ≈ 1 to 1.5 m, while that across the 

Caribbean Current is ≈ 0.5 m. Temperature differences are ≈ 10 o

C. In the salinity plot 

(Figure 2-12b), effect of rivers along the northern Gulf coast is seen as a band of low 

salinity on the shelf. 

2.4 Sigma-Level Pressure-Gradient Error 

We check that the sigma-level pressure gradient error (Haney, 1991) in the model 

is not large when compared with the physically meaningful modeled currents. The error 

is reduced by removing the basin-averaged density distribution (in z-only) from the timedependent density field before evaluating the pressure gradient terms (Mellor et al., 

1998). A one-year test calculation using an initially level density field with perturbations 

(see Mellor et al. 1998) and zero forcing was conducted. Figure 2-13 shows that the 

maximum error asymptotes to ≈ 0.15 cm/s, which is relatively small in comparison to, 

say, the Loop Current speeds ≈ 1 m/s. The maximum occurs off Cape Haterass under the 

Gulf Stream where the slope is steep and density contrast is strong. 
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21

3. DATA ASSIMILATION 

 I begin with a brief introduction of the various assimilation schemes that have 

been used in PROFS. Specialization to the present hindcast using satellite SSH and SST 

are then discussed. I conclude the chapter with a brief description of the satellite SSH 

data used. 

3.1 Data Assimilation in PROFS 

 PROFS has a number of options for different data assimilations. The various 

forms are all based on standard optimal interpolation (or Multivariate OI or MVOI; e.g. 

Daley, 1991). They differ only in the details in which the various data are utilized and 

how the error covariance matrix is defined. The data (at present) consist of satellite seasurface height anomaly (SSH), sea-surface temperature (SST), moored temperatures and 

currents, hydrography, and drifters. One can in principle also incorporate other data (e.g. 

CODAR, SOFAR etc). Given the observed (anomaly) vector o wβ , the model ‘forecasts’ 

(or first-guess) f wi at N grid points, ‘i’, that is corrected to obtain an analyzed vector 

a wi according to: 

∑ ∑ = =

= + −

M N

i

f

i i

o

i

f

i

a wi w K w H w

1 1

[ ( )]

β

β β β . (3.1) 

Greek subscripts denote the M observational locations, Kiβ is the Gain matrix (or 

weights), and Hβ interpolates modeled values onto the observational point. Kiβ is 

obtained by minimizing the square of the analysis error =< − >2 ( )i

a

i

a Ei w w , where 

wi is the ‘truth’ and the angle brackets denote (time or ensemble) averaging. Thus, 

 α

β

β βα i

f

M

f T o Ki (HP H P ) (P H)

1

∑ + = =

, (3.2a) 

where 

Pαβ =< (wα − wα )(wβ − wβ ) > f f f (3.2b) 
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22

Pαβ =< (wα − wα)(wβ − wβ ) > o o o (3.2c) 

are the space-time correlations of the ‘forecast’ error and observational error, 

respectively. Since wα is usually not known, various levels of approximation must be 

made for f Pαβ and o Pαβ , hence Kiβ . 

Level 1: 

Here the Kiβ is analytically specified (and in general not “optimum”), and 

 Kiβ = ΓijΛjβ and i j ij Λ H = I β β , (3.3a) 

where 

 ∑=

− − ∆ Γ =

M

ij i

d

i

a

ij M

t

t t

t

t

1

0 exp( ) ( )/ 2

β

δ λ β , (3.3b) 

 

∑=

Λ = M

i

i

i

β 1

β

β

β

λ

λ (3.3c) 

 exp( ) 2

2

2

2

2

2

z

i

y

i

x

i

i

R

z

R

y

R

x β β β λ β = − − − , (3.3d) 

Iij is the unit matrix, δ ij is the Kronecker delta function, ∆t is the assimilation time step, 

at is the assimilation time scale (shorter for stronger assimilation), i t0 is the most recent 

time when observation is available at point ‘i,’ td is the time influence of the observational 

data, (x,y,z)iβ is the distance between the model and observational grid points, and Rx,y,z

are (x, y, z) scales, respectively, that measure the radius of influence of observation. 

Typically (ta, td) ≈ hours to days, and (Rx, Ry, Rz) ≈ (10’s km, 10’s km, 10’s m), taken to be 

independent of grid point ‘i.’. To put in more ‘physical flavor,’ it can be shown that if 

∆t = model time step (using a ‘leap-frog’ scheme), (3.1) and (3.3) lead to: 
 Page 

 

23

∑=

= + Γ − ∂

∂ N

j

f

j

o

ij j

f

i physics w w

t

w

1

) ~ ( ) ( (3.4a) 

 ∑ ∑ = =

=

M M

i

o

i

o wi w

1 1

( )/( ) ~

β β

λ β β λ β , (3.4b) 

which is the nudging method. Fan et al. (2003) used this scheme to assimilate observed 

drifters (see Chapter 5). 

Level 2 (“Standard OI”): 

Here, o Pαβ is diagonal and f Pαβ is Gaussian: 

 Pαβ

o = σ2

δαβ (3.5a)

exp( ) 2

2

2

2

2

2

2

2

2

x y z t

f

R

t

R

z

R

y

R

x

P w αβ αβ αβ αβ

αβ =< δ α > − − − − , (3.5b) 

where σ is the standard deviation of observational error (assumed constant), < >2 δwα is 

the (model) variance, and as before xαβ = xα − xβ etc., and Rx etc. are scales. This 

(equations 3.5, 3.2 and 3.1) is the scheme used in POM for assimilating the satellite SSH 

and SST (Mellor and Ezer, 1991; Wang et al. 2003; Oey et al. 2003a,b; Oey et al. 2004a). 

Level 3a: 

Here, o Pαβ is given by (3.5a) but f Pαβ is computed from (3.2b) by assuming the model and 

observed climatologies are the same and ‘truths.’ Then f Pαβ is just the model covariance. 

Level 3b: 

Here, the observed are assumed to be ‘truths.’ Thus = 0 o Pαβ and f Pαβ is computed from 

(3.2b) with o wα = wα . 
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24

Level 3c: 

Here, a complete hindcast is first made with the Level-1 scheme. This is then used in 

Level-3b to pre-compute f Pαβ . This hindcast is then repeated but at each time step, the 

pre-computed f Pαβ , hence Kiβ from (3.2), are used to correct the first-guess f wi . Dong 

and Oey (2003; unpublished work) found this scheme to give good ‘prediction’ at points 

where no data were assimilated. 

3.2 Specialization Using Satellite Data 

 Mellor and Ezer (1991) describe a clever way that specializes the Level-2 (i.e. 

standard OI) assimilation scheme above. The model is first integrated without 

assimilation, from 1992-1999, forced by 6-hourly ECMWF winds and surface heat and 

salt fluxes as described in chapter 2. This experiment produces its own ‘eddy’ field, from 

which the correlations between SSH anomaly δη and subsurface temperature and salinity 

(T/S), and also between SST and subsurface T/S are calculated. Figure 3-1 shows 

contours of the correlation coefficient for SSH and sub-surface temperature (SBT) in the 

Gulf of Mexico. A similar plot for sea-surface temperature (SST) and SBT is given in 

Figure 3-2. The SSH-SBT remains relatively high (>0.6) over a substantial portion of the 

Gulf down to a sub-surface depth of 500m. There is, therefore, a strong eddy influence 

over deeper (>500m) waters, so that geopotential fluctuations are good indicators of subsurface ‘bowling’ and ‘doming’ of isopycnals. On the other hand, the SST-SBT 

correlation is high (≈1) near the surface over (nearly) the entire Gulf – the shelf in 

particular, and becomes small (<0.4) at depths. This can be expected as SST fluctuations 

are primarily caused by mixed-layer dynamics 

Given the satellite SSH anomaly, δηsa, the model subsurface temperature anomaly 

δT is calculated as: 

δT(x,y,z ,t) = FT(x,y,z) δηsa(x,y,t) (3.6) 

where the correlation factor is 
 Page 

 

25

FT = <δT δη>/<δη2>, (3.7a) 

and the corresponding correlation coefficient is 

CT = <δT δη>/[<δT2

><δη2>]1/2. (3.7b) 

Mellor and Ezer (1991) then show that the standard OI is reduced to the following 

scheme. After each assimilation time step ∆tA (= 1 day), the model temperature T is 

replaced by the assimilated temperature TA: 

 TA = T + [2 RACT

2

/(1 + 2 RACT

2 − CT2

)] (TO − T) (3.8) 

where RA is the ratio of ∆tA to the de-correlation time scale ∆tE of the model eddy field (≈

30 days), and TO is the ‘observed’ temperature inferred from satellite SSH anomaly, 

which from (3.6) is: 

 TO = <T> + FT δηsa. (3.9) 

In (3.9) <T> = TC, the climatological mean temperature. The assimilation effect is such 

that TA ≈ TO in regions where the correlation is high, but TA ≈ T, where the correlation is 

small. Also, to minimize potential satellite errors near the coast, the assimilation is 

restricted to regions where water depths are > 500 m, thus excluding the shelves. A 

similar assimilation of SST is also carried out after (3.8), with the same ∆tA but with CT

and FT replaced by the corresponding functions that use δ(SST) in place of δη in (3.7). 

Weekly Multi-Channel satellite SST maps, obtained from the Jet Propulsion Laboratory 

(JPL), are used for this purpose. The SST-assimilation is applied to the entire region, 

over the shelves as well as deep waters. Sensitivity experiments indicate that the SSH and 

SST assimilations complement each other – the former is effective over the deep portions 

of the Gulf while the latter is most effective over the shelves. We comment however that 

since satellite does not resolve well the smaller-scale peripheral eddies (diameters ≈ 150 

km and less), the assimilation is biased towards larger, usually, anticyclones. We are 

therefore more reliant on the model’s intrinsic dynamics for small-scale physics. 

3.3 Satellite Data 
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26

Satellite altimeter data, AVISO (Archiving, Validation, and Interpretation of 

Satellites Oceanographic), are obtained from the French Space Agency. The data product 

was created by merging TOPEX/Poseidon (T/P) and ERS-1 & -2 altimeter measurements 

(Ducet et al., 2000). The combined, inter-calibrated altimeter data are interpolated in time 

and space using a global objective analysis. The length scale of the interpolation varies 

with latitudes, and is about 200 km at mid-latitudes. The e-folding time scale is set at 10 

days in the tropics and 15 days elsewhere. The resulting satellite product has a spatial 

resolution of 0.25o

 x 0.25o and is provided at 10-day intervals. The merged T/P + ERS1&2 SSH anomaly maps provide reduced and more homogeneous mapping errors than 

either individual data set, and thus, more realistic statistics. Fratantoni (2001) compared 

AVISO- and drifter-derived kinetic energy and found reasonable agreements. Wang et 

al. (2003) checked the AVISO data against two-year direct current measurements in the 

DeSoto Canyon, and found that their first two SVD (Singular Value Decomposition; 

Bretherton et al. 1992) modes agreed. We have checked that in the Gulf the AVISO data 

agreed well with those obtained from the Colorado Center for Astrodynamics Research 

(Leben et al. 2002). We use the AVISO data from 1992/October through 1999. Figure 

3-3 shows an example of the satellite SSH anomaly added to the model mean SSH on 

Dec/25/1999. In the Gulf, the figure shows a fully-developed Loop Current, and also a 

Loop Current eddy that has just been shed. The Gulf Stream shows a number of 

meanders. In the Caribbean, there exists a warm eddy just southwest of Hispaniola (Oey 

et al. 2003a), and also in the Cayman Sea just south of Cuba. 
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4. GRID NESTING 

 To achieve high resolution in the Gulf of Mexico, we embed (or nest) a doubledresolution grid within the large-domain model of Figure 2-2. In some calculations, this 

doubled-resolution grid is used. This chapter describes the embedding technique. 

A smaller-domain model that encompasses only the Gulf of Mexico (and a 

portion of the Caribbean Sea; such as that given in Oey, 1996a) is driven by inflow 

transports from the Cayman Sea, and outflow through the Florida Straits. The smaller 

domain allows rapid model execution and the model resolution can be improved without 

unduly sacrificing efficiency. However, since the (time-dependent) inflow structures and 

magnitudes are generally poorly known, inconsistent specifications can generate false 

vorticity (potential vorticity) along open boundaries which, due to their proximity to the 

Gulf, may produce false information that can alter the interior Gulf solution. Moreover, 

there is new evidence that remote forcing from the Atlantic affects Loop Current eddy 

shedding (Oey et al. 2003a), so there is incentive to incorporate remote effects into the 

open-boundary formulation of the smaller high-resolution model. A nested-grid 

formulation in which the Gulf domain is embedded within a larger parent grid (the outer 

model) ensures that, at least in the larger scale resolvable by the parent grid, the structure 

and intensity of transport along the nest’s open boundaries are dynamically consistent 

with a Caribbean circulation deduced from an outer model. To ensure dynamical 

consistency, the outer solution comes from a model, rather than directly from 

observations. However, the latter can be injected into the outer model through boundary 

conditions of the outer model, and also by means of data-assimilation. In this way, 

observations are melded into the model dynamics before being used as boundary forcing 

in the nested Gulf model. The requirement of outer- and inner-solution compatibility can 

be dealt with using a two-way nested-grid approach (Oey and Chen, 1992b; Oey, 1996b). 

However, two-way nesting requires the execution of two models in tandem. We have 

therefore developed a variant of a more efficient one-way nesting technique (based on 

Oey and Chen, 1992b), or ‘embedding,’ in which both the outer and inner grids share an 

overlapped (inner) region where the two grids are the same except that the inner grid has 

twice the number of grid lines. Once the general circulation features (transport 

distribution in particular) have been computed from the outer model, the inner model 

utilizes the outer information and is run independently. The method resolves the 
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28

uncertainty in open-boundary treatments of the smaller-domain model, and allows 

efficient and rapid parametric sensitivity studies. 

For the present application, the nested domain is as shown in Figure 2-2. The 

vertical sigma levels of both the parent and nested grids are the same. In the horizontal, 

at every other grid, the nested grid lines coincide exactly with the parent grid lines. The 

nested grid lines that do not coincide with the parent grid lines exactly halve the latter, 

thus doubling the resolution within the nested domain (Figure 4-1). The parent grid is 

then run for the entire hindcast period, and all prognostic variables are saved along the 

open boundaries of the nest, say every one day. Unlike two-way nesting, in which 

prognostic variables actively interact between the two grids, we find that in the present 

one-way nesting case the most important variables that need to be transferred from the 

outer grid are transports. We impose these transports by using Flather’s (1976) radiation 

condition (Oey and Chen, 1992a). For example, across the eastern parent-nest boundary, 

( ) n p np

g U U H =+ − η η (4.1a) 

where subscripts n and p denote the nested and parent variables, respectively, and 

capitalized U (or V) denotes depth-averaged x (y) component velocity. Similarly, across 

the southern parent-nest boundary: 

( ) n p np

g V V H = − − η η . (4.1b) 

The (U, V) are specified at the locations indicated by the diamond symbols in figure 4-1. 

To preserve volume conservation, the topography at the parent-nest boundary must be the 

same for both the nested and parent grids. While within the nest we use higher-resolution 

topography, this is made to smoothly merge with the parent-grid topography for points 

near the parent-nest boundary. A tanh profile is used for this purpose, over 12 nested 

grid points. Also, the parent-grid variables in equation (4.1) (and also below) are actually 

values defined at the fine-grid points. For (Up, Vp) we simply use the nearest parent-grid 

values (i.e. two nested Up or Vp are equal, and equal to their nearest parent-grid U or V). 

For ηp (and other variables below), linear interpolation is used, and values nearest the 

parent-nest boundary in the nested side are used. 
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29

 For the tangential depth-averaged velocity, a simple one-sided advection scheme 

is used. For the three-dimensional baroclinic velocities, Orlanski (1976) radiation 

condition, together with a Kurihara and Bender’s (1980) relaxation scheme, is used. For 

T and S, a flow relaxation scheme is used (Martinsen Engedahl, 1987): 

Tn = α Tp + (1−α) Tn (4-2) 

and similarly for S. Here, α varies over 12 nested grid points from zero inside the nest to 

one at the parent-nest boundary. According to Martinsen and Engedahl, we use quadratic 

variation for α for inflow, and tanh variation for outflow (see also Oey and Chen, 1992b). 

 Oey and Lee (2002) used the above nested-grid technique to verify a doubledresolution experiment involving bottom-trapped topographic Rossby waves inside the 

Gulf of Mexico. Wang et al. (2003) used the method wherein the nest and parent grid 

had actually the same grid sizes. The method was then used to incorporate remote 

forcing into their regional model of the Gulf. We will later present more detailed results 

of the nested-grid calculations. 
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5. EXPLORATORY MODEL EXPERIMENTS 

 We have conducted a multitude of experiments to check the code as well as to 

explore the model physics. I will report some of the more significant and interesting 

ones, and these are listed in Table 1. Of these, I consider the first five experiments to be 

fundamental as they explore the effects of various forcing on the model solution. I will 

first report on these five experiments, and draw conclusions on the model transports 

through various straits and channels in the Gulf of Mexico and Caribbean Sea, on Loop 

Current and Loop Current eddy shedding variability, and also on current and eddy 

variability in the Caribbean Sea. 

5.1 Fundamental Experiments 1 Through 5 

 The simplest of these (apart from even simpler barotropic or reduced-gravity 

experiments) is Expt.1 in which the model is forced only with steady transport and 

annual-mean T and S climatology specified at 55o

W, and all other forcing such as wind, 

surface fluxes and river are zero. Experiment 2 is the same as Expt.1 except that monthly 

T and S are specified at 55o

W. Experiment 3 adds six-hourly ECMWF wind to Expt.2. 

Experiment 4 adds both the wind and surface-flux relaxation of heat and salt to Expt.2. 

Finally, experiment 5 includes also satellite data assimilation. 

 Figure 5-1 shows 80-month (May/93-Dec/99) averaged stream function for these 

experiments, plotted for model sub-region that includes the Gulf of Mexico and the 

Caribbean Sea. A comparison between expt.1 and expt.2 (figure 5-1a,b) shows that they 

are very similar. Oey et al. (2003a) also found that these two experiments yield almost 

identical Loop Current eddy shedding characteristics. Thus the time-dependent nature of 

the T and S (i.e. monthly in expt.2 versus time-independent annual-mean in expt.1) at 

55o

W does not have a significant effect on currents in the Gulf of Mexico and in the 

Caribbean Sea. The stream function contours in Figure 5-1a,b show some interesting 

features that indicate the dominance of transports through the model’s open boundary at 

55o

W. It is seen that major circulation features, the Caribbean Current, Loop Current, 

Florida Current remain despite the simplicity of the forcing. One also sees a number of 

smaller gyres or eddies, whose existence therefore does not depend in a crucial way to 
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wind stress curl or surface forcing, since these are nil in expt.1 or expt.2.3 The most 

interesting of these gyres are (1) the cyclonic gyre just south of the Caribbean Current in 

the Columbian Basin (73o

W-78oW and 11oN-13oN), and (2) cyclonic cells north and west 

of the Loop Current in the Gulf of Mexico. The former may be forced by the Caribbean 

Current, while the latter indicate cyclonic flow in the deep basin of the Gulf of Mexico. 

We will further discuss these features in Part 2. 

 Important changes to the circulation occur with the addition of surface forcing: 

wind in expt.3, and wind and surface heat and salt fluxes in expt.4. Transports through 

various straits and channels are now altered, as I show more clearly in Figure 5-2 with 

transport vectors at selected sections. The Yucatan transport is now increased from 22.5 

Sv for expt.2 (or expt.1, same below) to 26.5~26.7 Sv for expts.3 and 4. As noted also in 

Oey et al. (2003a), the increase is due to an additional wind-curl driven Svedrup transport 

of about 4 Sv from the Atlantic into the Caribbean Sea through the channels of the 

Greater Antilles.4 In expt.2, a significant (about 4 Sv) portion of the transport through the 

Lesser Antilles channels in the eastern Caribbean Sea exits into the Atlantic through the 

Windward and Mona Passages. With wind, this exit transport is reversed (reduced in 

expt.3 at the Windward Passage). In addition to these large-scale changes in the 

transports, there are also important differences in smaller gyre circulations. The abovementioned cyclonic gyre in the southern Columbian Basin spreads more southward, 

though its intensity is reduced. The wider spread is wind-related, and is most likely 

forced by the predominantly positive wind stress curl that occurs in this region (Figure 2-

9). The cyclonic cells in the Gulf of Mexico still exist, though they become less intense 

(than in expt.1 or 2). This weakening is again wind-induced, probably directly by a 

generally negative curl that exists over the Gulf, albeit weak (figure 2-9). On the other 

hand, it may also be indirectly wind-induced. The wind produces larger Yucatan 

transport, in the mean as well as variance, and the Loop Current intrudes farther north 

and west into the Gulf, as shown in figure 5-3. The figure superimposes the zero-stream 

function contour of expt.3 (taken from figure 5-1c) onto the stream function contours of 

expt.1 (i.e. figure 5-1a) in the Gulf of Mexico. The zero-stream function is taken as a 

 

3 The gyres and eddies might implicitly be a function of surface forcing however through the model’s use of the GDEM 

climatology as initial and boundary conditions. A separate set of experiments in which an area-averaged GDEM climatology 

is used is now being conducted to check if this implicit dependency is important. 

4 Oey et al.’s (2003) average is for a much longer spin-up period of 16~32 years, which results in slightly different transport 

values. However, the conclusions are the same. 
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proxy for the mean outer-edge position of the Loop Current. The westward and 

northward extension of the Loop Current in expt.3 is clearly seen. As a result of forcing 

by the fluctuating wind, the model Loop Current in expt.3 tends to shed eddies at a higher 

rate, hence more eddies in a given time period (Oey et al. 2003a). Both the production of 

more eddies and also the more extensive westward and northward intrusion of energetic 

Loop Current are consistent with the weakening of the cyclonic stream-function cells in 

the Gulf in expt.3. 

 The addition of surface heat and salt fluxes (expt.4) has relatively minor effects 

on the overall circulation and Yucatan transport (c.f. expt.3). However, detailed 

transports through the Greater and Lesser Antilles straits differ. We have not analyzed 

their causes. 

 With data assimilation, the Yucatan transport is further increased to 28.8 Sv. The 

cyclonic cells in the Gulf further weaken, and the Caribbean and the Atlantic become 

more populated with eddies. Assimilation adds sinks and sources to the governing 

equations. Thus apart from some general statements about the transports and distribution 

of eddies, it is difficult to interpret this experiment except in specific situations when the 

results are compared with moored data, which I will defer till later. 

5.2 Loop Current Variability: The Caribbean Connection 

 One important conclusion of the present hindcast study is that the Caribbean Sea 

and Gulf of Mexico are dynamically connected. We first raised this issue in Oey (1996a) 

but only until Oey et al. (2003a) did we realize the importance of the connection. I 

summarize here the essence of our findings. The most significant of these is that the 

Loop Current variability and Loop Current eddy separation (or shedding) strongly depend 

on conditions in the Caribbean Sea. The disparate periods of eddy separation, which are 

known to range from 3 to 17 months, can be explained in terms of two forcing: transport 

and vorticity fluctuations caused by remote (Atlantic) wind and Caribbean eddies. 

Figure 5-4 gives histograms of Loop Current eddy shedding periods for four experiments. 

The first two are basically expt.2 and expt.3 extended for 16 and 32 years, respectively. 

They are renamed here as experiments B and C respectively following Oey et al. (2003a). 

The third experiment, CS, also for 16 years, is one in which only the steady part of 
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ECMWF is used, taken as the mean over eight years 1992-1999. The fourth experiment, 

D, again for 16 years, is one in which eddies are injected into the model in the eastern 

Caribbean Sea by assimilating satellite SSH anomaly (see Chapter 3). This experiment 

will test effects on Loop Current variability of eddies originating in the Caribbean Sea. 

 In expt.B, the Caribbean Sea circulation is in general ‘quiet’ void of energetic 

large-scale eddies, transport in the Caribbean Current is fairly steady, and the Loop 

Current sheds at periods of around 9~10 months. Figure 5-5 gives an example with two 

shedding events separated by about 9 months. Circulation in the Caribbean Sea is 

dominated by the Caribbean Current. There are meanders but they are of small scales 

and amplitudes. Figure 5-6 gives an example from expt.C. This shows large-scale (≈

300 km in diameter) eddies that originate just southwest of Hispaniola (referred to as the 

Hispaniola eddies by Oey et al. 2003a) and propagate into the Yucatan Channel. The 

first panel shows a snapshot 50 days after a Loop Current eddy separates, and another 

eddy separates approximately 100 days later (5~10 days after panel 4). The Caribbean 

Current also displays large-amplitude meanders. In comparison to figure 5-5 of expt.B, it 

is clear that expt.C gives more energetic circulation in the Caribbean Sea. Oey et al. 

(2003a) showed that Yucatan transport variability in expt.C is caused by high-frequency 

wind-induced transports through the Greater Antilles passages, with periods ~ 3-6 

months, and also by Hispaniola eddies that squeeze through the channel. They also 

showed that Hispaniola eddies are spun up by the steady portion of the wind stress (curl) 

southwest of Hispaniola (figure 2-9). The third panel of figure 5-4 shows that when the 

model is forced by this steady wind, eddy-shedding shifts to longer periods, which 

suggests that forcing by eddies alone (i.e. without fluctuating transport caused by wind) 

tend to give longer shedding periods. This interesting result is confirmed by expt.D (last 

panel in figure 5-4) in which eddies are injected (and allowed to propagate westward into 

the Yucatan Channel) in the eastern Caribbean Sea. This experiment too shows the 

tendency for eddies to shed at longer periods. We conclude then that the short-period 

sheddings in expt.3 are caused by wind, while long-period sheddings are due to 

Caribbean eddies. Oey et al. (2003a) explain these results by invoking the conservation 

potential vorticity for flow with velocity and vorticity specified at the Yucatan Channel. 

They showed that Caribbean eddies with anticyclonic vorticity tend to short-circuit the 

Loop Current thus preventing it from intruding far north into the Gulf. The consequence 

is a Loop Current that on average stays close to the channel and the Florida Straits, and 
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34

hence has a less tendency to shed eddies, thus prolonging shedding periods. On the other 

hand, transport fluctuations by wind produce velocity fluctuations which tend to produce 

episodic northward intrusions of the Loop Current, hence a more likelihood to shed 

eddies. 

5.3 The Caribbean Current: Mean and Variability 

 Currents through the Caribbean Sea, the Gulf of Mexico and the Florida Straits 

constitute an important component of the subtropical gyre circulation of the North 

Atlantic Ocean. The Caribbean Sea serves as a heat reservoir and the Caribbean Current 

a ‘conveyor’ by which heat is transported into the Florida Current and the Gulf Stream 

system. Fratantoni’s (2001) drifter analysis shows that surface velocities in the 

Caribbean Sea are highest (0.7 m s-1) in the Caribbean Current near the southern 

boundary along the coast of Venezuela and the Netherlands Antilles (Title Page 

Illustration; also figures 5-7 and 5-8). The Caribbean Current departs from the 

continental slope and into the open Columbian Basin around 72o

W, where it appears to 

behave like a ‘free jet.’ After crossing the Columbian Basin, the Caribbean Current 

flows along to the southern and western slopes of the Cayman Basin, and continues into 

the Yucatan Channel, where the current is more commonly referred to as the Yucatan 

Current. These inferences are consistent with comparatively early descriptions of the 

circulation in the Caribbean Sea by Parr (1937), Wust (1963, 1964), and Gordon (1967). 

 Despite its importance, relatively little attention (especially in comparison to the 

Loop Current and the Gulf of Mexico) has been devoted to a study of the Caribbean Sea 

in general, and the Caribbean Current in particular. Hurlburt (1986) studies the 

instability of the Current in its formation region in the eastern Caribbean Sea, and 

suggests that the current may be baroclinically unstable. Murphy et al. (1999) focus on 

the westward propagation of large-scale eddies in the Caribbean Sea. Oey et al. (2003a) 

connect transport and vorticity (eddy) variability originating in the Caribbean Current and 

Yucatan Current to the Loop Current, but the focus is primarily on Loop Current eddy 

shedding. This was discussed above in section 5.2. Although a model with wind and 

assimilation appears to have captured some of the observed characteristics of the 

Caribbean Current (e.g. figure 5-8), a more complete study still requires more extensive 

observations. At present, a model with simpler forcing, such as expt.1, can be useful for 
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studying some basic questions regarding the natural variability of the Caribbean Current. 

Since surface forcing is zero, and since transport and T/S specified at the eastern 

boundary at 55o

W are time-independent, expt.1 excludes variability caused by the wind 

and Rossby waves that originate from east of 55o

W. Under these relatively simple 

settings, we pose three questions. Firstly, what is the resultant mean transport, and is it 

consistent with available observations? Secondly, is the Caribbean Current inherently 

unstable, and what are its spatial and temporal variability? Also, does this variability 

contribute also to the variability of the Yucatan Current? Finally, we know that the 

variability does not cause the Loop Current to shed eddies; models with a fixed inflow at 

Yucatan are known to produce eddy shedding at reasonable periods (albeit nearly 

constant) of about 9~10 months (Hurlburt and Thompson, 1980). The question is: can 

disturbances by Loop Current shedding significantly affect the Caribbean Current? The 

analysis below is taken from Lee and Oey (2003; manuscript under preparation). 

 Figure 5-9 shows the mean transport in terms of stream function contours (upper 

panel) and vectors at selected sections in the Caribbean Sea. These show approximately 

27 Sv into the eastern Caribbean Sea through the passages of the Lesser Antilles. A 

major portion of this transport, about 21 Sv, flows through the southern two passages, the 

Grenada and St. Vincent, and continues westward to feed the Caribbean Current. At the 

Bertha Ridge (≈ 64o

W), approximately 5 Sv branches northward along the ridge. The 

main branch with 15 Sv continues westward as the Caribbean Current. These two 

branches rejoin at approximately 72o

W where the Caribbean Current departs from the 

continental slope of Venezuela. The flow continues westward across the Columbian 

Basin, and along the southern and western continental slopes of the Cayman Basin into 

the Yucatan Channel. Thus, of the 27 Sv that flows through the Lesser Antilles passages, 

only about 22 Sv flows into the Yucatan Channel, while approximately 5 Sv leaks out of 

the Caribbean and into the Atlantic through the Windward Passage of the Greater 

Antilles. The 22 Sv through Yucatan Channel is probably an underestimate. Oey et al. 

(2003a) shows that wind-curl driven transport from the subtropical gyre inhibits or 

diminishes the leak through the Windward Passage, and the Yucatan Channel transport 

becomes more realistic ≈ 27 Sv. 

 To study variability, we examine flow variables at sections placed across the 

Caribbean Current. Nine such sections are shown in figure 5-10, labeled from ‘1’ at the 
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36

eastern Caribbean Sea to ‘9’ at Yucatan Channel. Figure 5-11 shows section-time 

contours of surface velocity normal to seven of the nine sections. These plots show 

widths of westward or northward velocity cores to be about 100~150 km. Maximum 

speeds are about 0.3~0.4 m s-1 in the eastern and central Caribbean Sea (‘1’ through ‘7’) 

but greater than 1 m s-1 over the Yucatan slope (‘8’) and in the Yucatan Channel (‘9’; i.e. 

a western boundary current is formed off Yucatan). At ‘1,’ ‘8’ and ‘9’ (also at ‘2’, not 

shown) the flow is constrained by sloping topography and shows little meanders. At 

about 72o

W, the Caribbean Current separates from the Venezuela coast. At sections ‘3’ 

through ‘7’ the flow is less constrained by topography and shows cross-stream meanders 

with amplitudes 50~150 km’s. A more detailed analysis indicates that westward 

propagation speeds of these meanders to be about 9 km day-1. Figure 5-12 shows the 

standard deviation of sea-surface height. This is highest in the Loop Current and 

southwestward across the Gulf of Mexico along where modeled Loop Current eddies 

propagate (Oey and Lee, 2002). For this idealized experiment 1 with only steady forcing 

at 55o

W, values in the Caribbean Sea are less but larger values are found west of 72oW

where the Caribbean Current separates from the Venezuela coast, and also along the 

southern and western slopes of the Cayman Sea. Results of flow instability in a channel 

may be used to indicate if instability can cause the variability seen in the Caribbean 

Current. Figure 5-13 shows cross-sectional contours of velocity normal to the section 

(solid) and isopycnals (dash), and the sign of sectional potential vorticity, gradient 

∂Πo/∂s, where s is the across-section coordinate, is also indicated (shaded is where 

∂Πo/∂s < 0; Pedlosky, 1979), at sections ‘3’ and ‘9.’ Here, 

2

2

1

= o un n u

s s z B z

ρ

ρ

∂ β ∂

⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

∂ ∂ ∂

∂ ∂ ∂

Π − −

 (5-1) 

where un is velocity normal to the section and B is the Burger number (= baroclinic 

Rossby radius divided by horizontal length scale; here B is taken as 1). At ‘3’ the current 

is over deep water away from sloping topography. That ∂Πo/∂s is positive in some subregion of the corss-sectional plane and negative in others (figure 5-13, top panel) 

indicates that the flow may be unstable with respect to small-amplitude perturbations. At 

Yucatan Channel (section ‘9’), ∂Πo/∂s also changes sign. However, the slope of 

isopycnals near the bottom is less than topographic slope, which would tend to stabilize 
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the flow. These inferences are consistent with the higher-amplitude cross-current 

meanders found at ‘4’ than ‘9’ (figure 5-10). 

 Current spectra (not shown here) show significant energies at short periods 

30~100 days, and also at longer periods, 180 days and 256~300 days. The shorter 

periods correspond to cross-current meanders. For baroclinic instability waves, lowerlayer fluctuations lead upper layer. An example is shown in figure 5-14, which plots 

cross-coherence spectra between transports above and below 800 m at section ‘3.’ It can 

be seen that at the significant coherences at 34, 64 and 91 days, lower layer leads (i.e. 

positive phase differences) upper layer. We also conduct cross-spectra coherency 

analyses of cross-current displacements between different sections to examine how shortperiod meanders relate to one another. Figure 5-15 shows such an analysis for ‘2-3’, ‘3-

4’, ‘4-7’ and ‘8-9.’ For ‘2-3’ significant coherences occur at 38, 46, 53, and 70~100 

days. (Other peaks, for example, at short periods < 30 days and also at 213 days have 

little energies). Here ‘2’ leads ‘3’ by 13 days (at 38 days) to 25 days (at 70~100 days), 

which give propagation speed C2-3 ≈ 9~15 km day-1. For ‘3-4’ significant coherences 

occur at 36, 49, 58~91 days, and ‘3’ leads ‘4’ by 16 days (at 36 and 91 days) and 22~25 

days (at 58 and 49 days). The propagation speed C3-4 ≈ 8~13 km day-1. For ‘4-7’ 

significant coherences occur at 32 and 64~71 days, and ‘4’ leads ‘7’ by 44 days (at 32 

days) and 74 days (at 64~71 days).5 The propagation speed C4-7 ≈ 9~16 km day-1. Along 

the Yucatan slope, for ‘8-9’, significant coherences occur at 36, 64, and 128~213 days. 

Section ‘8’ leads ‘9’ by 17 days (at 36 days) and 20 days (at 64 days). The propagation 

speed C8-9 ≈ 8~10 km day-1. Ezer et al. (2003) analyzed velocity profile at Yucatan 

Channel, and showed that the first EOF mode corresponds to cross-channel meander of 

the Yucatan Current. They found energy peaks from 34 to 93 days as well as longerperiods at 171 days and 256 days. That shorter-period fluctuations are ‘meander modes’ 

are consistent with the present findings, and we would suggest that these fluctuations are 

meanders that propagate downstream into the Yucatan Channel from the Caribbean 

Current. Figure 5-15d also shows that at 128~213 days, ‘9’ slightly leads ‘8.’ This 

indicates the influence of upstream propagation at longer periods over the Yucatan slope 

(see below). 

 

 5 Note that ‘4’ and ‘7’ are separated by a large distance ≈ 700 km, and a full period is added to the phase 

difference. 
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At longer periods (> 100 days), Oey (1996a) also noted a period of around 180 

days in the fluctuations of the upper-layer (above 750 m) transport in the Yucatan, similar 

to the 171 days period found by Ezer et al (2003) and the 180 days we have found here. 

As in Oey (1996a) and Ezer et al. (2003), these 171~180 days fluctuations are caused by 

north-south vacillations of the Loop Current as well as (occasional short-period) eddy 

sheddings. Therefore, these longer periods and the 256~300 days (dominant) shedding 

period, are caused by Loop Current and Loop Current shedding variability. We now 

check for upstream propagation (from the Gulf of Mexico to the Caribbean Sea) at these 

long periods and also at shorter periods. Oey’s (1996a) and Ezer et al.’s (2003) studies 

indicate that lower-layer transport (below 800 m) serves as a good proxy of Loop Current 

vacillations and eddy-shedding at the long periods. It is also clear from the surface 

meander analysis presented above (figure 5-15) that upstream propagation at short 

periods (< 100 days) can only occur in the lower layer. Figure 5-16 shows the crossspectral coherency analysis for (a) sections ‘9-6’ and (b) ‘9-4.’ Good correlations are 

found for ‘9-6’ at the long periods 125~300 days, and also at short periods 36~50 days. 

The phases are negative, meaning that ‘9’ leads ‘6’ consistent with propagation from the 

Yucatan Channel into the Caribbean Sea. At the longer periods 125~300 days, the 

propagation speeds are about 3~6 km day-1. At the shorter periods 36~50 days, 

propagation speeds are more ambiguous owing to the large distance from ‘9’ to ‘6’ (≈

1000 km). For section pair ‘9-4’ (figure 5-16b), the correlations are not as high, though 

still significant, at periods 280, 100, and around 30 days. Negative phases again indicate 

that ‘9’ leads ‘4.’ For the longer periods, the phase relation may be further analyzed by 

low-passing the time-series. Figure 5-17 shows time lag-correlation plots for ‘9-8’ and 

‘8-7’ both for the upper and lower layer transports. The time-series has been low-passed 

to remove periods shorter than 100 days. In the upper layer, both pairs ‘9-8’ and ‘8-7’ 

are nearly in phase or even show negative lags meaning that the first time-series lags the 

second. In other words, the upper-layer transports are such that there is apparently a very 

fast propagating signal from the Cayman Sea to the Yucatan Channel: 7Æ 8 Æ 9. Since 

the source for these long-period fluctuations is at the Yucatan Channel (Loop Current 

vacillations and shedding), the paradox can be explained that upstream propagating 

signal from the Yucatan is swept downstream by the strong Caribbean Current in the 

upper layer (i.e. Doppler effect). In the lower layer (figure 5-17c,d), the correlations are 

lower.6 Lags are clearly positive meaning that signal propagates from the Yucatan to 

 

6 The correlations are increased by band-passing the time-series to focus only in the 170~300 days period. These details are 
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Caribbean: 9 Æ 8 Æ 7. The 28 and 10 days lags from ‘9’ to ‘8’ then ‘8’ to ‘7’ suggest a 

propagation speed of about 10~14 km day-1. 

In summary, we have discussed above the mean circulation of the Caribbean Sea 

and its current variability using a model with simple forcing. The mean transport is about 

27 Sv through the passages of the Lesser Antilles in the eastern Caribbean Sea. The 

major portion of this transport, about 21 Sv, flows through the southern two passages, the 

Grenada and St. Vincent, and continues westward to feed the Caribbean Current 

concentrated along the southern portion of the Caribbean Sea. In the absence of wind, 

about 5 Sv (of the total 27 Sv) leaks out through the Greater Antilles passages into the 

Atlantic Ocean, and the remaining 22 Sv flows through the Yucatan Channel. The 

Caribbean Current is unstable after separating from the Venezuela slope/coast at about 

72o

W. Meanders develop near the surface and propagate downstream into the Cayman 

Sea and the Yucatan Channel. It is unlikely however that individual meanders can be 

identified (or even survive) over such vast distances. Spectral and cross-spectral analyses 

indicate that periods of these meanders are 30~90 days, and their propagation speeds are 

10~15 km day-1. Contours of cross-current gradients of potential vorticity show that 

these change sign in the cross-current section, which suggest that the current is 

dynamically unstable. The meanders are largest (amplitudes up to 150 km) in the 

Columbian Basin where topographic constraints are least, and smallest off the Yucatan 

Slope and in the Yucatan Channel. Lower-layer current fluctuations lead upper layer, 

which suggests instability of the baroclinic type. At longer periods, > 100 days, the 

source of fluctuations is at the Yucatan Channel, caused by Loop Current vacillations and 

eddy-shedding. In the upper layer, these fluctuations cannot propagate upstream into the 

Caribbean because of the swift speeds of the Caribbean Current. The fluctuations 

therefore appear to be stationary. In the lower layer, our analysis indicates upstream 

propagation at speeds of 10~14 km day-1, probably by topographic Rossby waves (Oey 

and Lee, 2002). 

5.4 A Summary of Other Experiments and Physical Insights Derived From Them 

 not shown here. 
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40

An important part of our model development and improvement process is the 

publications of results in peer-reviewed journals. Constructive critiques of model results 

and findings by anonymous peers (who at times can be quite ‘harsh’) are often useful in 

improving the model and our understanding of the flow physics. Here I will highlight the 

findings from these publications, and show also other results. 

Oey and Lee (2002) verify the existence of topographic Rossby waves (TRW’s) in 

PROFS’ deep currents in the Gulf of Mexico (Figure 5-18). They show that TRW’s are 

triggered by frontal meanders around the Loop Current and rings, and demonstrate that 

the simulated TRW properties agree with those observed (Hamilton, 1990). The TRW 

ray paths have also been shown to agree well with those deduced from observations 

(Oey, Hamilton and Lee, 2003b). Oey and Lee (2002) further infer (and demonstrate in 

the model) that the deep circulation in the Gulf is cyclonic – a large-scale feature that has 

recently been confirmed in observations (DeHaan and Sturges, 2004). 

Oey, Lee and Schmitz (2003a) examine eddy-shedding characteristics of PROFS. They 

show that shedding irregularity strongly depends on fluctuating transport and vorticity at 

Yucatan Channel. Through extensive experiments, they were able to isolate the different 

forcing that cause shedding irregularity (Figure 5-4). They show that with realistic wind 

and eddy forcing, the model was able to produce shedding periods from 3~16 months

consistent with those observed (Sturges and Leben, 2000). The transport and its 

fluctuations at Yucatan Channel are also quite realistic: mean ≈ 23-27 Sv, and range ≈

15~35 Sv. 

Ezer, Oey, Lee and Sturges (2003) analyze PROFS results at Yucatan Channel. They 

show velocity profiles and current fluctuations that agree well with Maul (1977), Maul et 

al. (1985), Ochoa et al. (2001), Sheinbaum et al. (2002) and Bunge et al. (2002). Figure 

5-19 compares the observed and modeled mean velocity profiles in Yucatan Channel. 

Good agreements may be seen. There is a strong western boundary current near the 

surface and a weaker return flow on the eastern side of the channel. Deep flow shows 

northward current in the center, flanked by returned currents on both sides of the channel. 

Ezer et al. also computed EOF’s of currents in the channel, and identify the different 

modes as being caused by different physical processes: meander of the core current is 

contained in mode 1, upper-layer transport in mode 2 and deep sill current in mode 3 etc. 
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41

Figure 5-20 summarizes these findings. Candela et al. (2003) recently note the difference 

between Ezer et al.’s EOF’s and those computed from observations. Oey et al. (2004b) 

show that the discrepancy can be explained by the existence of an additional upper-slope 

and shelf meander mode that is probably missing from the observations (and inadequately 

represented by z-level models). 

Oey and Zhang (2004) study the generation of small-scale sub-surface cyclones and jets 

as a warm-core ring ‘smashes’ upon a continental slope. Idealized (periodic channel) and 

Gulf (PROFS) bathymetries were used. Slope-trapped cyclones are formed to the left 

(looking on-slope) of the ring. The resulting jet propagates away from the ring and 

upward into the water column in a series of dynamical events involving bottom boundary 

layer (BBL) mixing, hydraulic front, and upward-propagating super-inertial disturbance 

that is trapped at about 250 m below the surface as the front spreads. Figure 5-21 shows 

a schematic of the pertinent processes. A model without BBL does not produce hydraulic 

front and upward-propagating super-inertial disturbances. The authors demonstrate the 

process over west Florida slope in a nested-grid, high-resolution PROFS simulation. 

The above summarizes PROFS applications without the use of real-time data other than 

the wind forcing. They are non-trivial exercises however. For example, we know that 

the remarkable layer model HYCOM does not produce cyclonic deep circulation in the 

Gulf (Sturges, pers. comm.). We also know of at least 2 apparently good basin models 

(with comparable resolution) that fail to shed eddies after some years of integration 

(Smith et al. 1999, who used POP; Candela et al. 2003, who used Océan Parallélisé 

(OPA) z-level primitive equation model). In our view, eddy sheddings and, to a lesser 

extent the deep cyclonic circulation, are robust observable features that should be 

simulated by a model; i.e. they should be part of the intrinsic characteristic of a model. 

Figures 5-22 and 5-23 show two other examples of more detailed intrinsic characteristics 

that PROFS simulates. I now summarize experiments when satellite and/or drifter 

assimilations are turned on in PROFS. 
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6. MODEL EXPERIMENTS WITH DATA ASSIMILATION, INTEREXPERIMENT COMPARISONS, COMPARISONS WITH OBSERVATIONS & 

MODEL PREDICTABILITY 

 We have conducted a multitude of experiments to check the code as well as to 

explore the model’s sensitivity to different assimilations. I will report some of the more 

significant and interesting findings. 

Some Example Model Results and Comparison with Satellite-Derived Data

Figure 6-1a compares the modeled and satellite-derived SSH and SST on Dec/26/1997. 

This winter-time date is chosen as an illustration of effects of not only the SSH 

assimilation over the deep Gulf region, but also the SST assimilation over the shallow 

shelves where cooler water temperatures prevail. While correct eddy features are 

simulated, the modeled fields appear smoother than those observed. In the case of SST, 

satellite data contain ‘holes’ due to cloud covers, so that the model provides a useful 

dynamical interpolator (as opposed to optimum-interpolation one may use to fill in the 

‘holes’). This is illustrated in the case of Figure 6-1a by the warm LCE over the central 

Gulf, seen in both the modeled and satellite-derived SSH fields, for which the model 

shows distinct feature in its SST field, while the feature is barely discernible in the 

corresponding satellite-derived SST. Over the shelves, the model (on this date) shows 

almost zero SSH variability, while altimetry SSH indicates small but non-zero anomaly. 

The modeled SST shows cool waters over the shelves, though the coldest (SST < 10 o

C) 

near-coast regions are not simulated. 

Figure 6-1b gives another example that ensures that the assimilation indeed reproduces 

main eddies in the Gulf. Here, rather than comparing our result with the satellite SSH 

anomaly added to our own model mean, which would yield very similar features as those 

shown in the assimilated result shown in the upper panel of Figure 6-1b, we have chosen 

to compare with the SSH map from the Colorado Center for Astrodynamics Research, 

which uses a different model mean). 

Figure 6-2 compares the modeled and satellite-derived SSH-anomaly rms (or standard 

deviation STD), √<(δηM)

2

> (left panel) and √<(δηO)

2

> (right panel), respectively, where 
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43

<.> denotes time-averaging over three years from 1997 through 1999. As should be 

expected from this model experiment with data-assimilation, both the shape and intensity 

of the SSH STD agree well with those derived from satellite. The maximum STD is 

somewhat larger: 37 cm compared to 33 cm derived from satellite. It is of interest to 

compare similar maps for an otherwise identical experiment, but without data 

assimilation. This comparison in Figure 6-3 shows a maximum STD over the LC larger 

than that derived from satellite, and suggests that the larger modeled STD of Figure 6-2 is 

due to the natural variability of the model and perhaps also the excitation of this natural 

mode to forcing by the SSH assimilation. Also evident in Figure 6-3 are the model’s bias 

for a predominantly southwestward LCE propagation and lower variability over shelves 

(surprisingly) and in the Cayman (Caribbean) Sea. That the shelf variability is still lower 

than that indicated by the altimetry data (assumed believable over shelves) in a model that 

includes ECMWF winds (Figure 6-3) suggests shelf motions which are not purely winddriven, local or remote. Other possible forcing agents include current fluctuations by 

river-borne buoyancy, and perhaps also spillage of energy from energetic LC and LCEs. 

Since rivers are not explicitly specified in our experiments, their effects are indirectly 

reflected by the SST fluctuations on the shelves, which are assimilated in Figure 6-2. To 

also eliminate these, we conducted another experiment without SST assimilation, but 

retaining the SSH assimilation (for region of Gulf deeper than 500m as before). Figures 

6-4 and 6-5 compare, respectively, the SSH and velocity STD’s derived from satellite 

(panel D) with the corresponding contours for the three experiments: (A) with both SSH 

and SST assimilations, (B) with SSH assimilation only and (C) without any assimilation, 

in the northern Gulf and shelf region. The satellite velocity STD was calculated from 

SSH by assuming geostrophy. On each STD map, the three-year mean velocity vectors 

are also superimposed. Note that the ‘satellite mean’ is actually the model climatology 

computed from the ten-year model run for the large domain of Figure 2-1b. Of 

significance is that for ‘C,’ little variability exists over the slope and rise (≈200m to 

2000m), with STD values half of those found for ‘A’, ‘B’ and ‘D’. The latter three maps 

also show higher SSH STD over the shelf7. The mean vectors with assimilation (A or B) 

show weaker shelfbreak currents, which as we will see shortly are more realistic when 

compared with the moored observations. We conclude therefore that without 

assimilation, little ‘eddy’ activities exist over the slope/rise (≈ 200m to 2000m) portion of 

 

7 Note that the localized high variability seen in the data (panel D of Figure 11) near the Louisiana-Texas shelf corner at 

94o

W, and also at the Florida ‘Big-Bend’ at 83.5oW maybe artifacts of the satellite data. 
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44

the northern Gulf, and that these activities account for energy leakage onto the shelf. The 

reasons maybe that without assimilation, the model LCE’s tend to take a more 

southwestward path, and also that smaller-scale eddies (diameters ≈ 200km and smaller, 

which are observed over the slope/rise, Hamilton, 1992; Hamilton et al. 2002) are not 

simulated. The actual physical mechanisms remain to be resolved in future work 

Assimilations with Drifters and Satellite Data

Fan, Oey and Hamilton (2004) conduct a detailed drifter comparison study that examines 

the possibility of assimilating observed drifters into the model. The 1998 NEGOM 

drifters (Figure 6-6) were used to test the scheme. Drifter data were collected by the U.S. 

Minerals Management Service (MMS) program: “Collection of Environmental Data for 

Oil Spill Risk Analysis Model Verification (CEDOMV)”, which was part of the MMS 

Northeastern Gulf of Mexico Shelf Physical Oceanography Program (NEGOM, 

DiMarco, et al., 2001). A total of 30 drifters, designed to drift at the surface within the 

upper 1 m and tracked by the ARGOS satellite system, were deployed from November 

1997 to December 1999. For the present study, eight of the nine drifters deployed from 

11-May-1998 to 10-July-1998 are used (negom20011 to negom20019). Negom20015 

went ashore and is excluded from our analysis. Different experiments were conducted so 

that the sensitivity of the model to various assimilation schemes using satellite SSH, SST, 

and/or surface drifters can be tested (Table 2). A simple nudging scheme is used to 

assimilate drifters, as follows. 

Positions of the drifters were smoothed using a Gaussian-filter scale of 24 hours to 

eliminate tidal and inertial currents, and were sub-sampled at 3-h intervals. The method 

is given in Hamilton et al. (1999). Velocity vn

o

(m) is then computed from drifter 

positions rn

o

(m), n = 1, 2, ...N = number of drifters, at time t = m∆t, m = 1, 2 ... M, 

where ∆t is the time step, as: 

 vn

o

(m) = (rn

o

(m) − rn

o

(m−1))/∆t (6.1) 

 

The vn

o

 is then used as a nudging term in the momentum equation: 
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45

 ( )

1

( )

N o n n

n

physics N

t

λ

=

∂ = −− ∂ ∑ u

u v (6.2a) 

 λn = (1/ta) exp(- r2

n/R2nudge)exp(- (t - ton)/td) exp(z/zd), (6.2b) 

where rn is the distance between the model grid point and the nth drifter’s position and (t - 

t

o

n) is the difference between the model time and the last time when the nth drifter is 

observed. The assimilation timescale, ta, determines the strength of the nudging factor, 

and the damping timescale, td, and lengthscale, Rnudge, are parameters of the nudging 

term. The exp(z/zd) term, where zd = 10 m, is used to restrict the effect of the 

assimilation to approximately the near-surface. The td should correspond approximately 

to Lagrangian correlation time scale. Fan et al. (2004) used td = 1 day, ta ≈ ∆t, and Rnudge

= 0.4o

. Equation (6.2) shows that, through the space and time-dependent nudging 

parameter λn, model’s velocity u at a grid cell is mainly influenced by the most recent 

nearby drifters. 

Through extensive experiments, Fan et al. (2004) show that a combination of both 

satellite data and drifter assimilations (Experiment E of Table 2) yields the least RMS 

errors in drifter positions (Figure 6-7). Satellite data and drifter assimilations are 

complementary: satellite gives Gulf-wide coverage of large-scale LC and LCE’s, while 

drifters enable more realistic simulations of localized (small-scale) eddy field. Figure 6-8 

illustrates this finding. Here, modeled circulation fields for experiments A (without any 

assimilation), B (with satellite SSH and SST assimilations), and E (with satellite and 

drifter assimilations) are shown. The geostrophic velocity field computed from satellite 

is also shown. We see that with drifter assimilation, experiment E, a small anticyclonic 

eddy located approximately at (87o

W, 28oN) (this is the “Lone Drifter” shown in Figure 

6-6) is simulated, while experiment B with satellite data assimilation alone does not show 

such a feature. A small anticyclone is also seen in the geostrophic velocity field, but the 

eddy is displaced to the southeast and is oriented northwest to southeast rather than west 

to east. In this case, the RMS error of drifter positions using the geostrophic field is 

actually largest (c.f. Figure 6-7), even larger than that for Experiment A which shows 

weak currents near (87o

W, 28oN). In other words, drifter positions are very sensitive to 

the detailed velocity fields used to track them, and fields with misaligned and/or 

misplaced eddies may not be more superior than a field with weak currents and no 

eddies. 
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On a larger scale, Figure 6-8 shows that with data assimilation (both experiments B 

and/or E) the position of the Loop Current in its retracted southern position is correctly 

modeled. In the Florida Straits the Current’s northern edge brushes near the southwest 

Florida continental shelfbreak. The Loop Current in experiment A (without 

assimilation), on the other hand, extends into the Gulf, and the Current is away from the 

southwest Florida shelfbreak. The consequence to currents over the west Florida shelf is 

significant. We note from Figure 6-8 that shelf currents are southeastward and quite 

strong in experiments B and E, but weak in experiment A and misaligned in the 

geostrophic field. It turns out that winds during the period mid-May through mid-August 

1998 were very weak (shown in top panel of Figure 6-9), so that the weak shelf currents 

in experiment A are expected. On the other hand, since satellite data is not assimilated 

over the shelf, the strong southwestward currents seen in experiment B must be remotely 

forced. This is indeed the case as proposed by Weisberg and He (2003), who inferred 

that the forcing was due to the Loop Current brushing near the southwest Florida 

shelfbreak. Figure 6-9 shows a more detailed comparison that illustrates the 

phenomenon. At the beginning of the year (1998), winds were strong and modeled 

(without and with assimilations, experiments A and B) currents show fluctuations similar 

to those seen in the observation. From March and later, winds weakened and currents in 

experiment A began to show fluctuations quite unrelated to those observed. Experiment 

B, on the other hand, began to show strong southeastward flow after March, as were also 

observed. Experiment E with drifter assimilation also shows similar southeastward shelf 

currents (Figures 6-8 and 6-9). On the other hand, currents derived from the geostrophic 

field derived from satellite SSH data (not shown) gives very poor comparison. 

Model-Data Comparison in DeSoto Canyon

Wang, Oey, Ezer and Hamilton (2003) evaluated PROFS against 2 years (1997-1999) of 

current-meter observations in DeSoto canyon over the northeastern Gulf slope and shelfedge. The moorings were on the 100 m ~ 1500 m isobaths, and the regional circulation is 

‘tricky’ to simulate with satellite data-assimilation because (i) satellite data is of more 

questionable quality in the (small-scale) canyon, at the shelfbreak, and near the coast, and 

(ii) the surface-subsurface correlations used in the assimilation scheme weaken across the 

slope. The authors show that PROFS performs reasonably well in terms of means and 
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variances (Figure 6-10). We previously showed (Figure 5-22) the first two SVD modes. 

Figures 6-11 compares observed and modeled details in DeSoto Canyon. The 

development of the second mode is particular interesting. Earlier PROFS simulations 

(presented in Wang et al. 2003) only showed a weak second-mode signal in the model. 

Later simulations (with improved boundary conditions and bathymetry) appear to capture 

this mode quite well, as shown on the right panels of Figure 5-22. Figure 6-12 shows the 

development of the second mode in the model, and compare it with that seen from 

satellite SST frontal analysis (P. Fratantoni et al. 1998). The mode appears as a Loop 

Current eddy is shed and the Loop itself extends far northward along the west Florida 

slope. In the eight-year simulation (1992-1999), this feature occurs 12% of the time. 

Combined Hydrographic and Satellite Data Assimilations

A different kind of data assimilation study using nested PROFS was reported in chapter 4 

of Oey, Hamilton and Lee (2003b). This slope-eddy study focuses on the following 

scientific problem. Given an observed slope eddy field (spatial scales ≈ 50~150 km) over 

the north-central Gulf, can a model generate its temporal and spatial evolution, hence we 

may deduce its properties (e.g. eddy energy, stability etc), and check the ‘prediction’ 

against observations? Two surveys are taken from LATEX-C and Gulfcet-I 

measurements (Hamilton, Berger and Johnson, 2002) for the observed eddy fields: (A) 

Dec/03-14/1993 and (B) Dec/16-23/1993. Data from Period-A is used to initialize the 

model, while that from Period-B is used to check model’s prediction. To initialize the 

model, the larger-scale circulations of LC and LCE’s are generated by assimilating 

satellite altimeter and SST data using an optimal interpolation scheme over the whole 

model domain. The observed temperature and salinity measurements from Period-A are 

‘injected’ by nudging them into the heat/salt equations. The model ‘predicts’ growth of 

the eddy energy of this initial field. The growth agrees with the observed increase of the 

kinetic energy of the geostrophic flow from Period-A to Period-B. Stability analysis 

indicates that the growth is caused by mixed barotropic and baroclinic instabilities. The 

success of this use of hydrographic surveys in a model assimilation scheme is a first step 

along the path that will allow the incorporation of in-situ, ocean observing systems into 

real-time model predictions. 
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Comparison with Historical Data and Sensitivity to Different Data Assimilation 

Parameters and Grid Resolution

Variance Ellipses: 

We can check energies of the modeled currents by comparing variance ellipses with those 

computed from historical data set from moored current meters in the Gulf. The dataset 

we have is from SAIC. Data descriptions are available in SAIC reports as well as papers 

published by Peter Hamilton (e.g. Hamilton, 1990). Figure 6-13 compares the observed 

and modeled variance ellipses. The model in this case has satellite data assimilations, 

and the variances were computed based on results from 1993-1999. Surface data are for 

moorings where z > −200 m, and subsurface z < −200 m. Modeled currents were 

interpolated to the observed levels. If there is more than one current meter for either the 

surface or subsurface group, then one with the longest time series is used. Except for the 

two moorings off southwest Florida slope where the model produces larger variances, 

modeled surface variances compare well with those observed. The data assimilation 

therefore seems to have produced the correct level of energy near the surface. The reason 

for the overestimation of energy off southwest Florida slope is not known, though we 

found that elevated energy also exists for the simulation without assimilation (not 

shown). 

Mean Currents: 

We find that the modeled mean circulation in the Gulf is robust irrespective of the forcing 

details and grid resolution: generally anticyclonic near the surface and cyclonic near the 

bottom. Figure 6-14 shows 1993-1999 mean current vectors near the surface and bottom 

for the case with ECMWF wind forcing (left), with ECMWF and doubled resolution 

(middle), and without wind (right). The near-surface anticyclonic circulation was also 

previously noted in Figure 6-5, and it is more intense for the coarse-grid than for the finegrid particularly along the northern slope. As for the case with data assimilation (Figure 

6-5), the abundance of more energetic smaller-scale eddies over the northern Gulf in the 

doubled-resolution run appears to drain the energy of the mean current, hence weakens it. 

Deep Mean Currents: 
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49

That deep currents are generally westward over the northern half of the Gulf was 

proposed by Oey and Lee (2002). Westward currents are needed to ‘channel’ 

propagating TRW rays so they are consistent with distribution of deep energy computed 

from their model. The authors’ Figure B.1 shows deep cyclonic circulation patterns 

similar to those seen in Figure 6-14. A recent, careful analysis of observations confirms 

that the deep flow is cyclonic (DeHaan and Sturges, 2004). Figure 6-15 compares timeaveraged zonal currents at a meridional section at 90o

W for four different experiments: 

(a) with wind forcing, (b) with wind and data assimilation, with wind and doubled 

resolution, (c) one with the Smagorinsky’s constant = 0.1, and (d) the other one = 0.05. 

Deep (z < -500 m say) cyclonic circulation is seen in the original-resolution case with 

wind (i.e. “a”) as distinct slope-bound currents on both sides. With assimilation, 

westward current over the northern slope (right side) remains, but eastward current over 

the southern slope becomes much narrower. Westward current over the northern slope 

also exists for the doubled-resolution experiments, but eastward current on the south side 

moves off the slope, and is only seen for z > −1200 m over the upper slope, and below z 

≈ −2500 m. These differences are caused by small-scale eddy field that exists in both the 

assimilation case and also in the doubled-resolution cases. 

Comparisons between Fine and Coarse Grids, with and without Data Assimilation: 

Figure 6-16 compares spectra of currents at about 100 m below the surface north of 26o

N

for three experiments: CGE (Coarse, i.e. original grid), FGE (Fine grid or doubledresolution grid), and CGE with satellite SSH assimilation. We see that that eddy energy 

is lower for the original-grid experiment without data assimilation. In that experiment, 

Loop Current eddies propagate predominantly to the southwest and there is little eddy 

activity over the northern slope. In the FGE, Loop Current eddies tend to take a more 

direct westward path and there are also more smaller-scale eddies. Curiously enough, the 

reason for this is because the FGE’s Loop Current eddies tend to be weaker than the 

CGE’s. The stronger CGE eddies produce stronger southward drift due to beta 

dispersion. We do not know why FGE eddies are weaker, but the reason may be because 

there is a greater transfer of energy to smaller scales. With data assimilation, the CGE’s 

eddy paths are ‘corrected’ and its spectrum becomes more similar to the FGE. 
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That fine-grid and data-assimilated simulations give similar levels of eddy energy may be 

useful in practice. Given limited satellite coverage to resolve eddy scales smaller than 

about 200 km, and in the present case a model resolution 2~8 times more refined than 

satellite’s even when compared with the “original model resolution” case, data 

assimilation on the doubled-resolution grid may not yield more information than that on 

the original-resolution grid. 

Effects of Different Assimilations and Comparisons with Observations:

Data assimilations introduce sources and sinks into the model’s thermodynamics, which 

over time can erode the density structures. We have checked the modeled temperatures 

at different locations in the Gulf and give some examples here. Figure 6-17 compares 3-

year time series of model temperature at (25.9N, 93.6W) for different experiments with 

observation. With no assimilation, the modeled temperature follows the climatological 

variation. The temperature variation for the SSH assimilation experiment at times 

displays irregularities, but otherwise follows the observed quite well. The best match 

between model and observation is for the case with both SSH and SST assimilations. 

The effects of assimilation on the vertical structure of the temperature is summarized in 

Figure 6-18 in terms of Gulf area-averaged temperature profiles and their respective 

standard deviations for experiments with and without assimilations. Most of the change 

is in the upper 300 m near the surface. Note that the temperature as well as its 

fluctuations are larger for the case with both SSH and SST assimilations. In terms of 

velocity fluctuations, it is of interest to know how deep the assimilated eddy energy 

penetrates into the water column. Figure 6-19 shows such a plot in terms of Gulf-wide 

area-averaged kinetic energy of the mean current (MKE) and also the eddy kinetic energy 

(EKE). The energy penetrates deep into the water column. It is interesting that increases 

in energies are least at the main thermocline (z ≈ −300 m to −500 m), and that there is an 

increase in EKE near the bottom. Our interpretation here is that as the upper layer is 

perturbed by eddies that are assimilated, stretching and compression generate responses 

in the lower layer in the form of bottom-intensified TRW’s (c.f. Oey and Lee, 2002). 

Another interesting feature is that SST assimilation tends to damp the response. Thus 

SST serves to dampen ‘noises’ (or unrealistic fluctuations; c.f. 6-17) associated with SSH 

assimilation. 
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51

We next compare modeled temperature profiles with in situ data. Figures 6-20 is for a 

slope location and Figure 6-21 for a shelf location. The first profile was taken at the 

northern edge of a ring. In comparison to the June climatology, the observed profile 

shows generally warmer water down to 800 m, by as much as 4 o

C at z ≈ −170 m. Data 

assimilations also show generally warmer waters, though not as much as observed. For 

the shelf station, assimilation produces much improved vertical stratification (Figure 6-

21). This is note-worthy as SSH assimilation was not applied over the shelf and for the 

result shown in Figure 6-21, the model had no rivers. This result suggests that over the 

shelf, surface heating alone is responsible for the bulk of top to bottom temperature 

difference in summer. Observation shows interesting temperature inversion very near the 

surface. This is likely due to the less-saline water near the surface from river discharge 

(Oey, 1995). 

Over the shelf, river-borne buoyancy plays an important role especially very near the 

surface (Oey, 1995) and the model and model results we provided MMS do include 

rivers. Figure 6-22 shows snapshots of surface salinity contours on the LATEX shelf 

from winter (February) through late summer (August). These show structures consistent 

with those explained in details by Oey (1995; see also references quoted therein). In 

winter, down-shelf (i.e. westward) wind tends to confine less-saline waters near the coast 

as near-shore jet develops. In spring/summer, weak up-shelf winds and large discharges 

produce off-shelf spreading of less-saline waters, and give rise to meandering of the 

salinity front. In late summer/fall, less-saline waters are ‘stacked up’ against the 

Louisiana coast. 

Finally, we now illustrate the effect of passage of Hurricane Georges on the near-surface 

current and thermal structures. Figure 6-23 shows Georges’ path and satellite SST (upper 

panel) and modeled (assimilated) SSH and surface currents. Note the cooling of waters 

under the path and the SSH low. Cyclonic circulation is produced at the wake as the 

Loop Current is depressed to the south near the Yucatan Channel and Florida Straits. 

Figure 6-24 shows that one day after the hurricane passage, satellite SST indicates rapid 

warming behind the wake, while the cyclone persists. Associated with the SSH low and 

cyclone is upwelled cool water that extends deep to z ≈ −50 m. 
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Sensitivity to Assimilation Parameters and Model Predictability

While the problem of model predictability is not of direct interest to MMS, it is fitting in 

a data assimilation study to assess the model intrinsic dynamics in response to 

initialization from satellite observations. In other words, given an initial analysis field 

that is a combination of satellite observation and first-guess hindcast field, we will assess 

how far into the future the model predicts before its solution becomes totally devoid of 

reality. (Note that for drifters’ paths, we know from the previous subsection that the 

answer is only about 10 days). 

Figure 6-25 shows modeled calculations in which the model was not assimilated, was 

assimilated every one day, and also was assimilated every five days. These are compared 

with satellite-derived geostrophic currents. The 1-day assimilated eddy tracks the 

satellite-derived geostrophic eddy well. The 5-day case retains the eddy position quite 

well but the intensity deteriorates with time. The no-assimilation case begins to depart 

from both satellite and 1-day assimilated case in about 1 month. Figure 6-26 summarizes 

various characteristics of the eddy being tracked in Figure 6-25. These (and other 

diagnostics) plots show that time scale for model predictability (i.e. model without 

assimilation) is about 30 days. Beyond this time the model without assimilation (blue) 

departs significantly in terms of the eddy path and intensity (as measured by the SSH at 

eddy center) from the assimilated case (green). The 5-day assimilated case (brownish red) 

retains the path but its intensity degrades after about 30 days. Assimilating SST only 

(black) produces results which are essentially not different from the no-assimilation case, 

while assimilating SSH only (orange) produces results similar to the full assimilated case 

(green). 
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7. CONCLUSIONS 

The model hindcast described in this report attempts to portray as best as we can the 

ocean circulation state in the Gulf for the period 1992-1999, using available data. The 

data included six-hourly wind field obtained from a combination of NDBC buoy data and 

the ECMWF analysis, daily river discharges from 34 U.S. rivers in the Gulf of Mexico, 

and satellite sea-surface height (SSH) anomaly and sea-surface temperature (SST). The 

satellite data were used in an assimilation scheme based on optimum interpolation. In 

addition, monthly climatological T/S data and surface fluxes were also used for boundary 

specifications. These data are deemed the most basic for a successful hindcast estimation 

of the circulation in the Gulf and adjacent seas. Other data, such as drifters, 

hydrographic measurements, and current meters were also utilized for testing and 

evaluation purposes. 

It is shown that the hindcast has yielded mean circulation and variances that are 

consistent with observations. In the Gulf of Mexico, the model gives generally anticyclonic circulation near the surface and a cyclonic circulation in the deep layers, though 

with considerable spatial variability. Variance ellipses show current intensities that are in 

general agreement with historical data, both near the surface and in deep layers. The 

model also gives consistent results when evaluated in details against observations at two 

locations in the Gulf: DeSoto Canyon and Yucatan Channel. The model gives Loop 

Current and eddy-shedding variability, circulation structures and transport variability that 

generally agree with those observed. Data assimilation enables correct placements of the 

locations of the Loop Current and Loop Current eddies. It is shown that the correct 

placement of the Loop Current in the Florida Straits southwest of Florida is crucial in 

remotely driving currents over the west Florida shelf. 

The model was also tested to simulate drifters’ trajectories, and a drifter-assimilating 

scheme was developed and tested. Drifter-assimilation provides important supplemental 

information (in addition to satellite data) to the model in that smaller-scale eddy 

structures generally not resolved by satellite can now also be included. It is shown that a 

combination of both satellite data and drifter assimilations yields the least RMS errors in 

drifter positions. The two assimilations are complementary: satellite gives Gulf-wide 

coverage of large-scale Loop Current and Loop Current Eddies, while drifters enable 
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more realistic simulations of localized (small-scale) eddy field. Simulating drifters are 

challenging however; their movements are sensitive to wind, waves and associated 

turbulence mixing that the model parameterizes. 
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8. FUTURE DEVELOPMENTS & IMPROVEMENTS 

First, more validations may be carried out, either with newer data or with focus on 

different dynamics and processes; for examples, subsurface processes in DeSoto Canyon; 

different modes of Loop Current and shedding variability; topographic Rossby waves 

over the upper slope (≈ 2000 m isobath) and new MMS/SAIC exploratory study of deep 

currents in the central Gulf, and northwestern and western Gulf study. Secondly, the 

potential usefulness of drifter-assimilation, as well as assimilation with SOFAR and new 

MMS/SAIC data sets should be further explored; so is the development of more 

sophisticated assimilation schemes: Kalman filtering and 3D-Var, for examples. Thirdly, 

the model’s surface physics can be further improved to include effects of wind waves 

(Craig and Banner, 1994; Mellor, 2004). This improvement should prove particularly 

relevant to MMS’ objectives of obtaining more accurate statistics for oil spill trajectory 

studies. Finally, some fundamental questions should be explored. These include (i) 

small-scale eddies and strong jets (birth, development, interaction and decays), and the 

closely related (we think) topic of ring/topography interaction; (ii) Loop Current 

variability and eddy-shedding; (iii) transport variability through Yucatan Channel and 

Florida Straits (especially in view of the recent Canek data); (iv) deep currents; and (v) 

Caribbean Sea and Gulf of Mexico connection (both large-scale and smaller-scale effects 

such as eddy-squeezing through the channel). 
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9. REFERENCES 

Bunge, L., J. Ochoa, A. Badan, J. Candela and J. Sheinbaum, 2002: Deep flows in the 

Yucatan Channel and their relation to changes in the Loop Current extension, J. 

Geophys. Res, 107(C12), 3233, doi:10.1029/2001JC001256, 2002.

Biggs, D.C., G.S. Fargion, P. Hamilton, and R.R. Leben, 1996. Cleavage of a Gulf of 

Mexico Loop Current Eddy by a deep water cyclone, J. Geophys. Res., 101: 

20629-20642. 

Bretherton, F.P., R.E. Davis, and C.B. Fandry, 1976: A technique for objective analysis 

and design of oceanographic experiments applied to MODE-73. Deep Sea Res., 

23, 559-582. 

Bretherton, C.S., C. Smith, and J.M. Wallace, 1992: An intercomparison of methods for 

finding coupled patterns in climate data. J. Climate, 5, 541-560. 

Brooks, D.A. and R.V. Legeckis, 1982: A ship and satellite view of hydrographic 

features in the Gulf of Mexico. J. Geophys. Res., 87, 4195-4206. 

Candela, J., S. Tanahara, M. Crepon, B. Barnier and J. Sheinbaum, 2003: Yucatan 

Channel flow: observations versus CLIPPER ATL6 and MERCATOR PAM 

models. J. Geophys. Res., 108 (C12), 3385, doi:10.1029/2003JC001961, 2003. 

Cochrane, J.D., 1972: Separation of an anticyclone and subsequent developments in the 

Loop Current (1969). Texas A & M Univ. Ocean Studies. Eds: L.R.A. Capurro 

and J.L. Reid, Gulf Publishing Co., Houston, 2, 91-106. 

Cooper, C., G.Z. Forristall and T.M. Joyce, 1990: Velocity and hydrographic structure of 

two Gulf of Mexico warm-core rings. J. Geophys. Res., 95, 1663-1679. 

Courant, R., K.O. Friedrichs, and H. Lewy, 1928: Uber die partiellen 

differenzengleichurgen der mathematischen physik. Mathematische Annalen, 100, 

32-74. 

Craig, P. D. and M. L. Banner, 1994: Modeling wave-enhanced turbulence in the ocean 

surface layer. J. Phys. Oceanogr., 24, 2546-2559. 

Daley, R., 1991: “Atmospheric Data Analysis,” Cambridge University Press, 455 pp., 

NY. 

DeHaan, C.J. and W. Sturges, 2004: Deep cyclonic circulation in the Gulf of Mexico. J. 

Phys. Oceangr. In press. 

DiMarco, S.F., Howard, M.K., Jochens, A.E., 2001. Deepwater Gulf of Mexico historical 

Physical Oceanography and data inventory. Department of Oceanography, Texas 

A&M University, Technical Report 01-01-D. 196pp. 

Ducet, N., P.Y. Le Tron, and G. Reverdin, 2000: Global high-resolution mapping of 

ocean circulation from TOPEX/Poseidon and ERS-1&2. J. Geophys. Res., 105,

19,477-19,498. 

Elliott, B.A., 1982: Anti-cyclonic rings in the Gulf of Mexico. J. Phys. Oceanogr., 12, 

1292-1309. 

Ezer, T., L.-Y. Oey, W. Sturges and H.-C. Lee, 2003: The variability of currents in the 

Yucatan Channel: analysis of results from a numerical ocean model, J. Geophys. 

Res. 10.1029/2002JC001509. 

Fan, S.J., L.-Y. Oey, and P. Hamilton, 2004. Assimilation of drifters and satellite data in 

a circulation model of the northeastern Gulf of Mexico. Cont. Shelf Res., 24(9): 
 Page 

 

57

1001-1013. 

Forristal, G.Z., K.J. Schaudt, and C.K. Cooper, 1992: Evolution and kinematics of a 

Loop Current eddy in the Gulf of Mexico during 1985. J. Geophys. Res., 97: 

2173-2184. 

Flather, R., 1976: A tidal model of the northwest European continental shelf, Mem. Soc. 

R. Sci. Liege Coll. 8, 6(10), 141-164. 

Fratantoni, D.M., 2001: North Atlantic surface circulation during the 1990’s observed 

with satellite-tracked drifters. J. Geophys. Res., 106, 22,067-22,093. 

Fratantoni, P.S., T.N. Lee, G.P. Podesta, and F. Muller-Karger, 1998: The influence of 

Loop Current perturbations on the formation and evolution of Tortugas eddies in 

the southern Strait of Florida. J. Geophys. Res., 103, 24,759-24,799. 

Gill, A.E., 1982: “Atmosphere-Ocean Dynamics.” Academic Press, New York, 662pp. 

Gordon, A.L., 1967: Circulation of the Caribbean Sea. J. Geophys. Res., 72, 6207-6223. 

Hamilton, P. 1990. Deep currents in the Gulf of Mexico. J. Phys. Oceanogr., 20: 1087-

1104. 

Hamilton, P., 1992: Lower Continental Slope Cyclonic Eddies in the Central Gulf of 

Mexico. J. Geophys. Res., 97: 2185-2200. 

Hamilton, P., Fargion, G. S., and Biggs, D. C., 1999. Loop Current eddy paths in the 

western Gulf of Mexico. J.Phys. Oceanogr., 29, 1180-1207. 

Hamilton, P., T.J. Berger, and W. Johnson, 2002: On the structure and motions of 

cyclones in the northern Gulf of Mexico. J. Geophys. Res., 107,3208 doi:10.1029, 

1-18. 

Haney, R.L., 1991: On the pressure gradient force over steep topography in sigma 

coordinate ocean models. J. Phys. Oceanogr., 21, 610-619. 

Hinze, 1975: “Turbulence.” McGraw-Hill Book Co., 2nd edition. New York, 790pp. 

Hurlburt, H.E., 1986: Dynamic transfer of simulated altimeter data into subsurface 

information by a numerical ocean model. J. Geophys. Res., 91, 2372-2400. 

Hurlburt, H.E., and J.D. Thompson, 1980: A numerical study of Loop Current intrusions 

and eddy shedding. J. Phys. Oceanogr., 10, 1611-1651. 

Kurihara, Y. and M.A. Bender, 1980: Use of a movable nested-mesh model for tracking a 

small vortex. Mon. Wea. Rev., 108: 1792-1809. 

Leben, R.R., G.H. Born and B.R. Engebreth, 2002: Operational altimeter data processing 

for mesoscale monitoring. Marine Geodesy., 25, 3-18. 

Madala, R. V., and S. A. Piacsek, 1977: A semi-implicit numerical model for baroclinic 

oceans, J. Comput. Phys., 23, 167-178. 

Martinsen and Engedahl, 1987: 

Maul, G. A, 1977: The annual cycle of the Gulf Loop Current. Part I: Observations 

during a one-year time series, J. Mar. Res., 35, 29-47. 

Maul, G. A., D. A. Mayer and S. R. Baig, Comparisons between a continuous 3-year 

current-meter observation at the sill of the Yucatan Strait, satellite measurements 

of Gulf Loop Current area, and regional sea level, J. Geophys. Res.,90, 9089-

9096. 

Mellor, G.L., 2002: User guide for a three-dimensional, primitive equation, numerical 
 Page 

 

58

ocean model (Jul/2002 version), 42pp., Prog. In Atmos. And Oceanic Sci., 

Princeton University, 2002. [See 

http://www.aos.princeton.edu/WWWPUBLIC/htdocs.pom/ PubOnLine 

/POL.html]. 

Mellor, G. L. 2004: Wave breaking and ocean surface layer thermal response. J. Phys. 

Oceanogr. In Press.

Mellor, G.L. and T. Ezer, 1991: A Gulf Stream model and an altimetry assimilation 

scheme. J. Geophys. Res. 96, 8779-8795. 

Mellor, G.L., L.-Y. Oey, and T. Ezer, 1998. Sigma coordinate pressure gradient errors 

and the seamount problem. J. Atmos. Oceanic Tec., 15: 1122-1131. 

Mellor, G.L., and T. Yamada, 1982: Development of a turbulence closure model for 

geophysical fluid problems, Rev. Geophys. Space Phys., 20, 851-875. 

Murphy, S. J., H. E. Hurlburt and J. J. O’Brien, 1999: The connectivity of eddy 

variability in the Caribbean Sea, the Gulf of Mexico, and the Atlantic Ocean. J. 

Geophy. Res., 104, 1431-1453. 

Ochoa, J., J. Sheinbaum, A. Baden, J. Candela and D. Wilson, 2001: Geostrophy via 

Potential vorticity inversion in the Yucatan Channel, J. Mar. Res., 59, 725-747. 

Oey, L-Y., 1986: The formation and maintenance of density fronts on the U.S. 

southeastern continental shelf during winter. J. Phys. Oceanogr., 16, 1121-1135. 

Oey, L.-Y., 1995: Eddy- and wind-forced shelf circulation, JGR, 100: 8621-8637. 

Oey, L-Y., 1996a: Simulation of mesoscale variability in the Gulf of Mexico, J. Phys. 

Oceanogr., 26, 145-175. 

Oey, L.-Y., 1996b: The accuracy of a nested-grid ocean model. Princeton University 

Atmospheric & Oceanic Sci. Report#1996-03, pp.28, 25 figures. 

Oey, L.-Y. 1996c: Flow around a coastal bend: a model of the Santa Barbara Channel 

eddy. JGR-Oceans, 101, 16,667-16,682. 

Oey, L.-Y., 2003: USERS GUIDE for The Princeton Regional Ocean Forecast (& 

Hindcast) System - PROFS: for the Gulf of Mexico & Northwest Atlantic Ocean, 

Including the Gulf Stream & the Caribbean Sea. Report submitted to U.S. DOI 

Minerals Management Service, Herndon, Virginia, Contract# 1435-01-00-CT31076, by Princeton University, AOS Program, Sayre Hall, Princeton, NJ 08544, 

Oct/2003, 22 pp., 3 illustrations. 

Oey, L.-Y., 2004. Vorticity Flux in the Yucatan Channel and Loop Current Eddy 

shedding in the Gulf of Mexico. J. Geophys. Res. 109, C10004, 

doi:10.1029/2004JC002400. 

Oey, L.-Y. & P. Chen, 1992a: Simulation of circulation in NE-Atlantic shelves & seas, J. 

Geophys. Res, 97: 20,087-20,115. 

Oey, L.-Y. & P. Chen, 1992b: A nested-grid simulation of the Norwegian coastal current, 

J. Geophys. Res., 97: 20,063-20,086. 

Oey, L.-Y. and H.-C. Lee, 2002: Deep eddy energy and topographic Rossby waves in the 

Gulf of Mexico, J. Phys. Oceanogr., 32: 3499-3527. 

Oey, L.-Y., H.-C. Lee and W. J. Schmitz Jr., 2003a: Effects of Winds and Caribbean 

Eddies on the Frequency of Loop Current Eddy Shedding: A Numerical Model 

Study, J. Geophys. Res., 108 (C10), 3324, doi:10.1029/2002JC001698, 2003. 

Oey, L.-Y., P. Hamilton, and H.-C. Lee, 2003b: “Modeling and Data-Analyses of 
 Page 

 

59

Circulation Processes in the Gulf of Mexico.” Final Report to the Minerals 

Management Service, Contract#1435-01-99-CT-31028; 116 pp, 56 figures. 

Available from Science Applications International Corporation, 615 Oberlin Rd., 

Suite 100, Raleigh, NC 27605. 

Oey, L.-Y. and H.-C. Zhang, 2004. A mechanism for the generation of subsurface 

cyclones and jets. Cont. Shelf Res., 24, 2109-2131. 

Oey, L.-Y., C. Winnant, E. Dever, W. Johnson and D.-P. Wang, 2004a: A model of the 

near-surface circulation of the Santa Barbara Channel: comparison with 

observations and dynamical interpretations. J. Phys. Oceangr., 34, 23-43. 

Oey, L.-Y., T. Ezer & T. Sturges, 2004b. Modeled and Observed Empirical Orthogonal 

Functions of Currents in the Yucatan Channel. J. Geophys. Res., 109, C08011, 

10.1029/2004JC002345. 

Oey L.-Y., T. Ezer, G. Forristall, C. Cooper, S. DiMarco, S. Fan, 2005a: An exercise in 

forecasting loop current and eddy frontal positions in the Gulf of Mexico, 

Geophys. Res. Lett., 32, L12611, doi:10.1029/2005GL023253. 

Oey L.-Y., T. Ezer & H.J. Lee, 2005b: Loop Current, Rings and Related Circulation in 

the Gulf of Mexico: A Review of Numerical Models and Future Challenges. 

AGU Monograph. In press. 

Orlanski, I., 1976: A simple boundary condition for unbounded hyperbolic flows. J. 

Comp. Phys. 21, 251-269. 

Parr, A.E., 1937: A contribution to the hydrography of the Caribbean and Cayman Seas, 

based on the observations made by the research ship “Atlantis” 1933-34. Bull. 

Bingham Ocean. Coll., 5, 110 pp. 

Pedlosky, J., 1977: On the radiation of meso-scale energy in the mid-ocean. Deep Sea 

Res., 24, 591-600. 

Phillips, N. A., 1957: A coordinate system having some special advantages for numerical 

forecasting, J. Meteorol., 14, 184-185. 

Richtmyer, R.D. and K.W. Morton, 1957: “Difference Methods for Initial-Value 

Problems,” Interscience Publishers, John Wiley & Sons, New York, 405 pp. 

Schmitz, W.J., Jr., 1996: On the World Ocean Circulation: Volume I – Some Global 

Features/North Atlantic Circulation. WHOI Technical Report WHOI-96-03, 141 

pp. 

Sheinbaum, J., J. Candela, A. Badan and J. Ochoa, 2002: Flow structure and transports in 

the Yucatan Channel, Geophys. Res. Let., 29(3), 10.1029/2001GL0139990. 

Simons, T. J., 1974: Verification of numerical models of Lake Ontario. Part I, circulation 

in spring and early summer, J. Phys. Oceanogr., 4, 507-523. 

Smagorinsky, J., 1963: General circulation experiments with the primitive equations. Part 

I: the basic experiment. Mon. Wea. Rev., 91, 99-164. 

Smith, R.A., J.R. Slack, T. Wyant, and K.J. Lanfear, 1982: The oil spill risk analysis 

model of the U.S. Geological Survey. Geological Survey Professional Paper 

1227. USGS, Reston, VA, USA. 

Smith, R.D., M.E. Maltrud, F.O. Bryan and M.W. Hecht, 1999: Numerical simulation of 

the North Atlantic Ocean at 1/10 deg. J. Phys. Oceanogr., 30, 1532-1561. 

Sturges, W. and R. Leben, 2000: Frequency of ring separations from the Loop Current In 

the Gulf of Mexico: A revised estimate, J. Phys. Oceanogr., 30, 1814-1818. 
 Page 

 

60

Teague, W. J., M. J. Carron and P. J. Hogan, 1990: A comparison between the 

Generalized Digital Environmental Model and Levitus climatologies, J. Geophy. 

Res. 95, 7167-7183, 1990. 

Vidal, V.M.V., F.V. Vidal and J.M. Perez-Molero, 1992. Collision of a Loop Current 

anticyclonic ring against the continental slope of the western Gulf of Mexico. J. 

Geophys. Res. 97, 2155-2172. 

Vukovich, F.M., 1995: An updated evaluation of the Loop Currents eddy-shedding 

frequency. J. Geophys. Res. 100, 8655-8659. 

Vukovich, F.M. and G.A. Maul, 1985: Cyclonic eddies in the eastern Gulf of Mexico. J. 

Phys. Oceanogr. 15, 105-117. 

Wang, D.-P., L.-Y. Oey, T. Ezer and P. Hamilton, 2003: Nearsurface currents in DeSoto 

Canyon. J. Phys. Oceanogr., 33: 313-326. 

Weisberg, R.H., He, R., 2003. Local and deep-ocean forcing contributions to anomalous 

water properties on the West Florida Shelf. J. Geophys. Res. in press. 

Wust, G., 1963. On the stratification and circulation in the cold-water sphere of the 

Antillean-Caribbean basins. Deep-Sea Res. I, 10, 165 – 187. 

Wust, G., 1964. Stratification and circulation in the Antillean-Caribbean basins. Part 1, 

spreading and mixing of the water types with an Oceanographic Atlas. Columbia 

Univ. Press. New York. 
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APPENDIX: ABSTRACTS OF PUBLICATIONS 

Paper#1: Oey, L.-Y. and H.-C. Lee, 2002: Deep eddy energy and topographic Rossby 

waves in the Gulf of Mexico, J. Phys. Oceanogr., 32: 3499-3527. 

Observations (Hamilton, 1990) suggest the hypothesis that deep eddy kinetic energy 

(EKE) in the Gulf of Mexico (GOM) can be accounted for by topographic Rossby waves 

(TRWs). Presumably, the TRWs are forced by Loop Current (LC) pulsation, Loop 

Current eddy (LCE) shedding, and perhaps also by LCE itself. While the hypothesis is 

supported by model results such as those presented in Oey (1996), the existence of TRWs 

in the model, and how they can be forced by larger-scale LC and LCEs with longerperiod vacillations have not been clarified. In this paper, results from a ten-year 

simulation of LC and LCEs, with double the resolution of that used by Oey, are analyzed 

to isolate the TRWs. It is shown that along an east-to-west band across the Gulf, 

approximately over the 3000m isobath, significant EKE that accounts for over half of the 

total spectrum is contained in the 20 to 100 day periods. Bottom energy intensification 

exists in this east-west band with vertical decay scales ~ 600 to 300m decreasing 

westward. The decrease agrees with TRW solution. The band is also located within the 

region where TRWs can be supported by the topographic slope and stratification used in 

the model, and where wavenumber and frequency estimates are consistent with the TRW 

dispersion relation. The analysis indicates significant correlation between pairs of 

east/west stations, over distances of approximately 400km. Contours of lag-times suggest 

offshore (i.e. down-slope) phase propagation, and thus the east-west band indicates 

nearly parabathic and up-slope energy propagation. Ray-tracing utilizing the TRW 

dispersion relation and with and without (for periods>43 days) ambient deep currents 

shows that TRW energy paths coincide with the above east-west high-energy band. It 

also explains that the band is a result of TRW refraction by an escarpment (with 

increased topographic gradient) across the central Gulf north of the 3000m isobath, and 

also by deep current and its cyclonic shear, and that ray convergence results in localized 

EKE maxima near 91o

W and 94o~95oW. Escarpment and cyclonic current shear also 

shorten TRW wavelengths. Westward deep currents increase TRW group speeds, by 

about 2-3 km/day according to the model, and this and ray-confinement by current shear 

may impose sufficient constraints to aid in inferring deep flows. Model results and ray 

paths suggest that the deep EKE east of about the 91o

W originates from under the LC, 

while further west the EKE also originates from southwestward propagating LCEs. 
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Finally, the near-bottom current fluctuations at these source regions derive their energy 

from short-period (<100 days) and short-wavelength (<200km) near-surface fluctuations 

that propagate around the LC during its northward extrusion phase, and also around 

LCEs as they migrate southwestward in the model. 

Paper#2: Ezer, T., L.-Y. Oey, W. Sturges and H.-C. Lee, 2003: The variability of 

currents in the Yucatan Channel: analysis of results from a numerical ocean model, J. 

Geophys. Res. 10.1029/2002JC001509. 

The flow through the Yucatan Channel and into the Gulf of Mexico is a major 

component of the Gulf Stream and the subtropical gyre circulation. Surprisingly, 

however, little is known about the forcing and physical parameters that affect the current 

structures in the Channel. This paper attempts to improve our understanding of the flow 

through the Channel with a detailed analysis of the currents obtained from a primitiveequation model that includes the Gulf and the entire Caribbean Sea and forced by 6-

hourly wind from ECMWF. The analysis includes two parts: Firstly, the overall statistics 

of the model results, including the Loop Current (LC) variability, the frequency of LC 

eddy-shedding, and the means and standard deviations (SD) of transports and currents, 

are compared with observations. Secondly, an Empirical Orthogonal Function (EOF) 

analysis attempts to identify the forcing and physical parameters responsible for the 

dominant modal fluctuations in the Channel. 

The model LC sheds seven eddies in four years at irregular time intervals (6.6, 7.1, 5.3, 

11.9, 4.2, 10.9 months). The model’s upper (thickness ~800m) inflow into the Gulf of 

Mexico occupies two-thirds of the Channel on the western side, with a near-surface 

maximum (4-year) mean of around 1.5 m s-1 and SD ≈ 0.4 m s-1. Three (return) outflow 

regions are identified, one in the upper layer (thickness ~ 600m) on the eastern third of 

the Channel, with mean near the surface of about 0.2 m s-1 and SD ≈ 0.14 m s-1, and two 

deep outflow cores, along the western and eastern slopes of the Channel, with (Mean, 

SD) ≈ (0.17,0.05) and (0.09,0.07) m s-1, respectively. The total modeled Channel 

transport varies from 16 to 34 Sv (1 Sverdrup = 106

 m3 s-1) with a mean around 25 Sv. 

The above velocity and transport values agree quite well with observations by Maul et al. 

(1985), Ochoa et al. (2001), and Sheinbaum et al. (2002). The deep return transport 
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below 800 m was found to correlate with changes in the Loop Current extension area, in 

agreement with the observational analysis by Bunge et al. (2001). 

The EOF mode#1 of the along-channel currents contains 50% of the total energy. It is 

surface-trapped, is 180o

 out of phase across the channel, and correlates well (correlation 

coefficient γ ≈ 0.8) with the cross-channel vacillations of the LC frontal position. The 

EOF mode#2 contains 18% of the energy, and its structure mimics that of the mean flow: 

dominated by two vertically more coherent regions that are 180o

 out of phase across the 

Channel. The mode is dominated by two periods, approximately 11 months and 2 months 

respectively, and correlates (γ ≈ 0.7) with the upper-channel inflow transport. The third 

and fourth modes, together, account for 18% of the total energy. Their combined timeseries correlates (γ ≈ 0.66) with the deep current over the sill, and is dominated by 

fluctuations with a period ≈ 205 days coincident with the dominant low-frequency 

fluctuations inherent in Maul et al.’s (1985) sill measurement. It is concluded that the 

dominant mode of flow fluctuations in the Yucatan Channel is caused by LC crossfrontal movements not directly related to LC eddy-sheddings, while higher modes 

correspond to transport fluctuations that affect eddy-sheddings, and to a bottom-trapped 

current fluctuations, the cause of which has yet to be fully uncovered. 

Paper#3: Fan, S.J., L.-Y. Oey, and P. Hamilton, 2004. Assimilation of drifters and 

satellite data in a circulation model of the northeastern Gulf of Mexico. Cont. Shelf Res., 

24(9): 1001-1013. 

Drifter and satellite data are assimilated into a circulation model that hindcasts nearsurface currents in the Northeastern Gulf of Mexico. Experiments without assimilation, 

and using assimilation of drifter, satellite sea-surface height (SSH) and sea-surface 

temperature (SST) data, in various combinations, were conducted. Currents derived from 

these experiments were used to compute drifter trajectories that were compared against 

observations. Surface geostropic current fields, calculated from satellite SSH, were also 

used to generate drifter paths. Assimilation that used a combination of drifter and 

satellite data reproduced the drifter trajectories with position errors ≈ 30 to 80 km over a 

10-day period. Comparisons of the modeled currents with moored observations on the 

West Florida Shelf show improvement when data assimilation is used, because of better 

simulation of deepwater processes (primarily the Loop Current). 
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Paper#4: Wang, D.-P., L.-Y. Oey, T. Ezer and P. Hamilton, 2003: Nearsurface currents 

in DeSoto Canyon. J. Phys. Oceanogr., 33: 313-326. 

This study evaluates a data-assimilated model simulation of nearsurface circulation in 

DeSoto Canyon (DSC), Gulf of Mexico, with emphasis on analyzing moored currentmeter observations and comparing them with satellite data and model results. The study 

period is for two years from April 1997 to April 1999. The model results are from a highresolution Gulf of Mexico model forced by analyzed wind and surface heat flux. Two 

types of data are used to deduce nearsurface circulation: moored current meters at 

thirteen locations in the DSC, and satellite sea level anomaly. The moored currents are 

mapped through multivariate objective analysis to produce surface currents and surface 

geopotentials, against which satellite and model derived sea surface heights and 

geostrophic currents are compared. Coupled patterns between the observations, model 

results, and satellite data, are obtained using the Singular Value Decomposition (SVD) 

analysis. There are two dominant modes: a ‘single-eddy’ mode where currents are 

concentrated at the foot of the canyon and an ‘eddy-pair’ mode where one eddy is at the 

foot of the canyon and the other, a counter-rotating eddy, is over the head of canyon. 

Mode-1 appears to be associated with the mesoscale eddy travelling around the Loop 

Current crest and trough, and mode-2 is associated with the intrusion of Loop Current 

crest and trough over the West Florida shelf. The observed and model currents are in 

good agreements about the means and variances. The model currents also appear to be 

well constrained by the steep topography. However, the model velocity field contains 

only the first mode. The satellite-derived velocity field, on the other hand, contains both 

the first and second modes; though, the satellite field does not adequately resolve the 

velocity structures over the slope. 

Paper#5: Oey, L.-Y., H.-C. Lee and W. J. Schmitz Jr., 2003: Effects of Winds and 

Caribbean Eddies on the Frequency of Loop Current Eddy Shedding: A Numerical 

Model Study, J. Geophys. Res., 108 (C10), 3324, doi:10.1029/2002JC001698, 2003. 

The Loop Current (LC) is known to shed eddies at irregular intervals from 3~17 months. 

The causes of this irregularity have not, however, been adequately identified previously. 

We examine effects of various types of external forcing on shedding with a model of the 

western North Atlantic Ocean (96o

W-55oW, 6oN-50oN). We force the model with steady 
 Page 

 

65

transport at 55oW, with winds, and include eddies in the Caribbean Sea. We examine 

their separate effects. With steady transport only, the model sheds rings at a dominant 

period of 9~10 months. Wind-induced transport fluctuations through the Greater Antilles 

passages cause shedding at shorter intervals (≈ 3~7 months). Caribbean eddies 

(anticyclones) cause shedding at longer periods (≈ 14~16 months). Potential vorticity 

conservation indicates that Caribbean eddies tend to deter northward extension of the LC 

into the Gulf, which can lead to longer periods between eddy shedding. Fluctuating 

inflow at the Yucatan Channel that is associated with winds and/or Caribbean eddies can 

cause a LC eddy to temporarily (~ 1 month) detach from, and then reattach back to the 

LC, a phenomenon often observed. Model results also suggest that southwest of 

Hispaniola warm eddies are spun up by the local wind stress curl. This type of eddy drifts 

southwestward, then westward after merging with the Caribbean Current, and then 

northward as it progresses towards the Yucatan Channel; these eddies significantly affect 

the shedding behavior of warm-core rings. The time scale for spin-up and drift from 

Hispaniola is about 100 days. Satellite data indicate the existence of these eddies in the 

real ocean. 

Paper#6: Oey, L.-Y. and H.-C. Zhang, 2004. A mechanism for the generation of 

subsurface cyclones and jets. Cont. Shelf Res., 24, 2109-2131. 

A mechanism for the generation of subsurface cyclones and jets when a warm ring 

smashes onto a continental slope and shelf is proposed based on the results of a primitiveequation three-dimensional numerical model. The warm ring initially ‘sits’ over a slope 

with an adjoining shelf in a periodic channel, and its subsequent evolution is examined. 

The ‘inviscid’ response is cyclonic ‘peeling-off’ of the on-slope portion of the warm ring. 

The cyclone propagates away (to the left looking on-slope) from the warm ring, and is 

bottom-intensified as well as slope-trapped (cross-slope scale ≈ Rossby radius). The 

near-surface flow ‘leaks’ further onto the shelf while subsurface currents are blocked by 

the slope. The ‘viscous’ response consists of the formation of a bottom boundary layer 

(BBL) with a temporally and spatially dependent displacement thickness. The BBL 

‘lifts’ the strong along-slope (leftward) current or jet (> 0.5 m s-1) away from the bottom. 

The jet, coupled with weak stratification within the BBL and convergence due to 

downwelling across the slope, becomes supercritical. Super-inertial disturbance in the 

form of a hydraulic jump or front, with strong upwelling and downwelling cell, and the 
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66

jet, propagate along the slope as well as off-slope and upward into the water column. 

The upward propagation is halted at z ≈ ztrap when mixing smoothes out the ‘jump’ to an 

along-slope scale λtrap that allows the ambient jet to bend the propagation path horizontal. 

At this ‘matured’ stage, ztrap ≈ −250 m, λtrap ≈ 50 km, and the jet’s cross-slope and 

vertical scales are ≈ 30 km and 50 m respectively. An example that illustrates the process 

under a more realistic setting in the Gulf of Mexico when the Loop Current impinges 

upon the west Florida slope is given. The phenomenon may be relevant to recent oil 

industry’s measurements in the Gulf, which at times indicate jets at z ≈ −150 m through 

−400 m over the slope. 

Paper#7: Oey, L.-Y., 2004. Vorticity Flux in the Yucatan Channel and Loop Current 

Eddy shedding in the Gulf of Mexico. J. Geophys. Res. 109, C10004. 

Recent observations (the CANEK Program; Candela et al., 2002) suggest that potential 

vorticity (PV) flux anomaly (VFA) at Yucatan Channel may serve as a useful indicator of 

Loop Current variability, including Loop Current extension, retraction and eddy 

shedding. Intuitively, anticyclonic VFA extends the Loop Current into the Gulf of 

Mexico and cyclonic VFA causes retraction or even shedding. However, this intuition is 

inconsistent with PV-conservation. The problem is reexamined here by careful analyses 

of the relation between VFA and Loop Current variability using (i) the results of a 15-

year numerical simulation of shedding specified with simple forcing, and (ii) CANEK 

and satellite observations. Both model and observations indicate that Loop Current eddy 

shedding or retraction tends to occur shortly (1~2 months) after the influx of VFA at 

Yucatan has turned anticyclonic, and that these events are sometimes preceded by a more 

prolonged period of influx of cyclonic VFA. These findings suggest that, contrary to 

intuition, influx of cyclonic VFA tends to extend the Loop Current into the Gulf, thus 

making the Current more susceptible to retract or shed an eddy, and influx of anticyclonic 

VFA may then ‘trigger’ retraction or eddy shedding. However, the Loop Current’s 

behaviors are much more complex than can be prescribed by these simple rules. A much 

longer observational dataset, coupled with more refined model experiments and 

sophisticated analyses, is required to further quantify the phenomenon. 
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67

Paper#8: Oey, L.-Y., T. Ezer & T. Sturges, 2004b. Modeled and Observed Empirical 

Orthogonal Functions of Currents in the Yucatan Channel. J. Geophys. Res., 109, 

C08011, 10.1029/2004JC002345. 

Candela et al. (2003) have reported Empirical Orthogonal Function (EOF) analyses based 

on 23-month current-meter and Acoustic Doppler Current Profiler measurements in the 

Yucatan Channel. Those authors noted the difference between EOF’s obtained from 

observations and their z-level models and EOF’s calculated by Ezer et al. (2003) from the 

results of a terrain-following model. Here a new analysis is reported that explains this 

difference, and that also suggests the importance of shelf-edge meander mode of the core 

Loop Current in the channel. We show that the terrain-following model gives EOF’s 

with characteristics similar to those observed when the upper slope and shelf in the 

western portion of the model channel are omitted. Modes 1 and 2 have tripole and dipole 

structures respectively with energies = (35%, 26%) of total energy, and correlate with 

‘slow’ vacillation of the core-current for periods > 50 days. Exclusion of upper-slope 

and shelf topography eliminates a short-period and energetic component inherent in Ezer 

et al.’s original mode-1 EOF. This mode correlates with frontal meanders of the core 

current over the shelf edge in the western portion of the channel. The short-period mode 

may be missing or underestimated in observational and z-level models’ analyses, since 

there were only a few moorings over the upper slope and shelf, and z-level models have 

step-like topography with generally lower resolution in shallower seas. 

Paper#9: Oey L.-Y., T. Ezer, G. Forristall, C. Cooper, S. DiMarco, S. Fan, 2005a: An 

exercise in forecasting loop current and eddy frontal positions in the Gulf of Mexico, 

Geophys. Res. Lett., 32, L12611, doi:10.1029/2005GL023253. 

As part of a model-evaluation exercise to forecast Loop Current and Loop Current eddy 

frontal positions in the Gulf of Mexico, the Princeton Regional Ocean Forecast System 

(PROFS) is tested to forecast 14 4-week periods 8/25/99-9/20/00, during which a 

powerful eddy, Eddy Juggernaut (Eddy-J) separated from the Loop Current and 

propagated southwestward. To initialize each forecast, PROFS assimilates satellite sea 

surface height (SSH) anomaly and temperature (SST) by projecting them into subsurface 

density using a surface/subsurface correlation that is a function of the satellite SSH 

anomaly. The closest distances of the forecast fronts from seven fixed stations in the 
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68

northern Gulf over a 4-week forecast horizon are then compared against frontal 

observations derived primarily from drifters. Model forecasts beat persistence and the 

major source of error is found to be due to the initial hindcast fields. 

Paper#10: Oey L.-Y., T. Ezer & H.J. Lee, 2005b: Loop Current, Rings and Related 

Circulation in the Gulf of Mexico: A Review of Numerical Models and Future 

Challenges. AGU Monograph. In press. 

Progress in numerical models of the Loop Current, rings, and related circulation during 

the past three decades is critically reviewed with emphasis on physical phenomena and 

processes. 
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69

Table 1. Model Experiments. All experiments have steady transport specified at 55o

W, taken from 

Schmitz (1996) and shown in figure 2-1b. The “−” means that the particular forcing is not imposed, i.e. 

is zero. 

--------------------------------------------------------------------------------------------------------------------------- 

 Forcing Boundary Wind Surf. Satellite 

Expt. T/S @ 55o

W Relax. Assimilation 

--------------------------------------------------------------------------------------------------------------------------- 

1 Steady+

 − − − 

2 Monthly# − − −

3 Monthly ECMWF − −

4 Monthly ECMWF Yes −

5 Monthly ECMWF Yes SSH Anomaly

 

--------------------------------------------------------------------------------------------------------------------------- 

+ Annual climatology 

# Monthly climatology
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70

Table 2. Fan, Oey and Hamilton’s (2004) model experiments designed to test the sensitivity of PROFS 

to various data assimilation schemes using satellite and/or surface drifters. 

Experiment # SSH and SST Drifter 

 Assimilation Assimilation 

A N=No N 

B Y=Yes N 

C Y Y (Local) 

D N Y (Local) 

E Y Y (Weighted) 

F N Y (Weighted) 
 Page 71

z = 0

σ = 0

σ = −1

z = −H(x,y)

η

Figure 2-1a. The sigma coordinate system. 
 Page 72

Figure 2-1b. PROFS’ orthogonal curvilinear grid over the northwest Atlantic Ocean 

and the nested, doubled-resolution Gulf of Mexico region. The “parent” grid lines are 

shown at every seventh grid point, and the approximate distribution of doubledresolution grid sizes in the nested Gulf is indicated. There are 25 sigma levels in the 

vertical, with vertical grid sizes less than 5m near the surface over the deepest region of 

the Gulf (~3500m). Time-independent inflow and outflow transport profile, as a 

function of latitude (y), is specified across the 55o

W as shown. See text for details. 
 Page 73

Ui,j,k Ui+1,j,k

Vi,j,k

Vi,j+1,k

ηi,j

Ti,j,k

x Plan View

y

Ui,j,k Ui+1,j,k

Vi,j,k+1

Wi,j,k

Si,j,k

Ti,j,k

x Elevation View

σ

Qi,j,k

Qi,j,k+1

σk

σk+1

Figure 2-1c. The Arakawa C-Grid in POM shown with the positions of variables: u, v, 

w, T, S, η and q (or q

2

). Not shown are density ρ and pressure p points, which coincide 

with the T and S points, and also turbulence variables q

2 A , KM and KH, which coincide 

with the q point. Note that the variables u, v, w and q are capitalized in the figure and 

that σk > σk+1. 
 Page 74

Figure 2-2. PROFS domain and bottom topography of the northwest Atlantic Ocean including the 

Gulf of Mexico and the Caribbean Sea. Time-independent inflow and outflow that account for the 

large-scale transports (Svedrup + thermohaline) are specified across the open boundary at 55o

W as a 

function of latitude. Isobaths are in meters. 
 Page 75

Figure 2-3a. GDEM climatology: potential temperature (o

C) in January at z = −10 m, 

−200 m, −1000 m and −2000 m. 
 Page 76

Figure 2-3b. GDEM climatology: potential temperature (o

C) in July at z = −10 m, 

−200 m, −1000 m and −2000 m. 
 Page 77

Figure 2-4a. GDEM climatology: salinity (psu) in January at z = −10 m, −200 m, 

−1000 m and −2000 m. 
 Page 78

Figure 2-4b. GDEM climatology: salinity (psu) in July at z = −10 m, −200 m, −1000 m 

and −2000 m. 
 Page 79

 

Figure 2-5. NDBC and C-MAN wind stations used for checking and correcting the ECMWF winds. 

See text for details. 
 Page 80

Figure 2-6a. Comparison of filled NDBC time-series of wind in m/s at buoy 42020 and 

42035 in the western Gulf with ECMWF time-series for the year 1997. The U (V) is 

west/east (south/north) component and numbers along the bottom of each panel are 

discussed in text.
 Page 81

Figure 2-6b. Comparison of filled NDBC time-series of wind in m/s at buoy 42054 and 

CMAN station BURL1 in the east/central Gulf with ECMWF time-series for the year 1997. 

The U (V) is west/east (south/north) component and numbers along the bottom of each 

panel are discussed in text.
 Page 82

Figure 2-7. The correlation coefficients between NDBC and ECMWF time-series (upper 2 panels) and 

skills (defined in text; lower 2 panels), computed for the period 1993 through 1999 at all 33 NDBC buoy 

and CMAN stations (the x-axis) in the Gulf of Mexico (see fig.2 or 3 for station locations). The U is 

west-to-east wind component and V south-to-north component.
 Page 83

Figure 2-8. Comparison of the mean (left panels) and standard deviation (right panels), in 

units of m/s, between the NDBC (observed) and ECMWF (model) time-series for the 

period 1993 through 1999 at all 33 NDBC buoy and CMAN stations in the Gulf of Mexico 

(see figs.2 or 3 for station locations). Upper row shows the west-to-east U-wind 

component and lower row the south-to-north V component. 
 Page 84

Figure 2-9. Upper panel: 1992-1999 mean ECMWF wind stress vectors (m2/s2; 

plotted every 10 grid points); lower panel: the corresponding mean wind stress curl 

(contour interval = 10-10 m/s2

, negative contours are dashed). 
 Page 85

Figure 2-10. Daily river discharges from 34 locations in the northern Gulf of Mexico 

for 1992 through 1999. See Figure 2-10 for locations of the rivers. The names of some 

locations are repeated as the rivers are very close to each other. 
 Page 86

Figure 2-10. Continued. 
 Page 87

Figure 2-10. Continued. 
 Page 88

Figure 2-10. Concluded. 
 Page 89

Figure 2-11. Locations of 34 rivers in the northern Gulf of Mexico used in PROFS 

hindcast for 1992 through 1999. Contours show isobaths in meters. 
 Page 90

Figure 2-12a. Contours of (a) upper-left: surface elevation, (b) upper-right: satellitederived SSH (purposely left blank, i.e. no data on this date), (c) lower-left: surface 

speed and (d) lower-right: speed at z = −500 m, two months after PROFS’ robust 

diagnostic calculation using GDEM climatology, Mar/01/1992. See text for details. 
 Page 91

Figure 2-12b. Contours of (a) upper-left: surface temperature, (b) upper-right: 

temperature at z = −100 m, (c) lower-left: temperature at z = −500 m, and (d) lowerright: surface salinity, two months after PROFS’ robust diagnostic calculation using 

GDEM climatology, Mar/01/1992. See text for details. 
 Page 92

Figure 2-13. The maximum speed that results from a one-year test calculation using initially 

level density field with perturbation: ρ(z) = ρr + ρ’, where ρr = area-averaged and annual-mean 

climatological density, and ρ’ = −0.1 kg/m3 × exp(z/1000m) and zero forcing (see Mellor, Oey 

& Ezer 1998). For this perturbation, the maximum speed asymptotes to 1.45×10-3 m/s in about 

60 days. Only the first 60 days is shown in the plot. The error is approximately proportional to 

the amplitude of perturbation.
 Page 93

Figure 3-1. Contours (CI=0.2) of correlation coefficients between SSH and 

subsurface temperature fluctuations at z=0, −50, −100 and –500m, calculated 

from the results of a ten-year model integration forced by the ECMWF wind and 

monthly climatological T/S in the large-model domain of Figure 4. The portion 

in the Gulf of Mexico only is shown. Regions with values greater than 0.6 are 

stippled, and those with values greater than 0.8 is dark-shaded.
 Page 94

Figure 3-2. Contours (CI=0.2) of correlation coefficients between SST and 

subsurface temperature fluctuations at z=−10, −20, −50 and –100m, calculated 

from the results of a ten-year model integration forced by the ECMWF wind and 

monthly climatological T/S in the large-model domain of Figure 4. The portion 

in the Gulf of Mexico only is shown. Regions with values greater than 0.6 are 

stippled, and those with values greater than 0.8 is dark-shaded.
 Page 95

Figure 3-3a. The sea-surface height (SSH) over the entire model domain 

including the western Atlantic, Gulf of Mexico and Caribbean Sea, derived 

from combining a ten-year model mean SSH (shown in figure 3-3b) and 

satellite SSH anomaly, for Dec/25/99. Contour interval = 10cm. Note high 

SSH’s in red and yellow that signify the anticyclonic eddies in the 

Caribbean Sea, the LC and LCE in the Gulf of Mexico, and meanders along 

the Gulf Stream front. Cyclonic eddies and shelf/slope waters are generally 

of low SSH’s (i.e. cooler), in blue and purple. 
 Page 96

Figure 3-3a. The 10-year mean modeled sea-surface height (SSH) for the 

western Atlantic, Caribbean Sea and Gulf of Mexico. The contour interval 

is 10cm. 
 Page 97

u

v

η

T

v

u

T

η

Figure 4-1. A schematic sketch of a doubled-resolution grid nested or embedded 

within a parent grid (thick lines). Large dots denote locations of the η, T, S, w and 

turbulence variables (see figure 2-1c) in the parent grid, and small dots are the 

corresponding locations in the nested grid. The u and v points are also shown. 

Diamonds denote the u or v points at the parent-nest boundary where transports from 

the parent grid are imposed onto the nested grid through a radiation condition. The 

parent-grid variables are used in a flow-relaxation scheme within approximately 12

nested grid points next to the parent-nest boundary. See text for details. 
 Page 98

Figure 5-1a,b. Eighty month averaged stream function for Expt.1 (upper panel) and 

Expt.2 (lower panel). Note that negative contours indicate generally anticyclonic 

circulation, and positive contours cyclonic circulation. 
 Page 99

Figure 5-1c,d. Eighty month averaged stream function for Expt.3 (upper panel) and 

Expt.4 (lower panel). Note that negative contours indicate generally anticyclonic 

circulation, and positive contours cyclonic circulation. 
 Page 100

Figure 5-1e. Eighty month averaged stream function for Expt.5. Note that negative 

contours indicate generally anticyclonic circulation, and positive contours cyclonic 

circulation.
 Page 101

Figure 5-2. Eighty month averaged inflow and outflow transports (Sv) in the Gulf 

of Mexico and the Caribbean Sea for simulations with steady transport across 55o

W 

(expt.2; upper-left panel), with six-hourly ECMWF wind added (expt.3; upper 

right), with ECMWF wind and monthly surface heat and salt fluxes (expt.4; lower 

left), and with ECMWF wind, surface fluxes and satellite data-assimilation (expt.5; 

lower right). See text for details. 
 Page 102

Expt.3

Expt.1

Figure 5-3. Eighty month averaged stream function for Expt.1 (dark contours; from 

figure 5-1a), enlarged in the Gulf of Mexico. The zero contour indicates the 

(averaged) position of the Loop Current for this experiment. The red thick contour 

line indicates the corresponding zero contour from expt.3 (sketched from figure 5-1c). 

This shows that the Loop Current in expt.3 intrudes farther north and west into the 

Gulf. 
 Page 103

Figure 5-4. Histograms of Loop Current eddy shedding periods for experiment B: without 

the ECMWF wind; experiment C: with the ECMWF wind; experiment CS: in which only 

the mean ECMWF wind is specified; and experiment D: in which eddies over the eastern 

Caribbean Sea are “injected” into the model by assimilation of satellite SSH anomaly. 

The abscissa is time interval in months between shedding and the ordinate is the number 

of shed eddies. The result for expt.C (second panel) is from a 32-year time series, while 

others are from 16-year time series. From Oey et al. (2003).
 Page 104

Figure 5-5. Experiment B: examples of Eulerian trajectories launched for 10 days centered around the indicated 

date in each panel, and at every 8th grid point at the first sigma level (i.e. surface), superimposed on color image of 

surface elevation (red for values ≥ 0.4 m, blue < -0.6 m). Colors on trajectories indicate speeds such that [light-blue, 

blue, purple, black] = [<0.25, 0.25-0.5, 0.5-0.75, >0.75] m s-1. Light contours are the 200m and 2000m isobaths. In 

terms of day#, let to=94/10/17 (first panel) when an LCE has just shed, then subsequent panels are to+100d: when the 

LCE has reached the western Gulf and is merging with an older eddy, to+230d: when the merged eddy stalls in the 

southwestern Gulf and the LC expands northward, to+250d: when a small cyclone off the southwestern slope of 

Florida appears and the LC is on the verge of shedding, to+270d: when the cyclone appears to cleave the LC and an 

eddy is shed, and to+290d: when the shed eddy moves west. Note also in all panels the Caribbean Current – a narrow 

blue-purple belt along the southern basin.
 Page 105

Figure 5-6. Experiment C: examples of Eulerian trajectories launched for 10 days centered around the indicated 

date in each panel, and at every 8th grid point at the first sigma level (i.e. surface), superimposed on color image of 

surface elevation (red for values ≥ 0.4 m, blue < -0.6 m). Colors on trajectories indicate speeds such that [light-blue, 

blue, purple, black] = [<0.25, 0.25-0.5, 0.5-0.75, >0.75] m s-1. Light contours are the 200m and 2000m isobaths. In 

terms of day#, let to=96/11/26 (first panel) when an eddy begins to form southwest of Hispaniola, then subsequent 

panels are to+30d: when the eddy has intensified; to+60d: when the eddy drifts to south of Jamaica; to+90d: when the 

eddy merges with the Caribbean Current and intensifies as it crosses over the Nicaragua Rise, and a new Hispaniola 

eddy begins to form; to+120d: when the eddy moves westward and the new eddy intensifies; and to+150d: when the 

eddy begins to enter the Yucatan Channel, and the new eddy drifts to south of Jamaica. These snapshots also 

illustrate the Loop Current and shedding behaviors as discussed in the text. 
 Page 106

Figure 5-7. Decadal-mean surface velocity field in the North Atlantic Ocean, based on 

quasi-Eulerian averaging of drifter trajectories in 1o

 square boxes. Blue vectors indicate 

speeds > 30 cm s-1, light-blue vectors 15 cm s-1 < speeds ≤ 30 cm s-1. Adapted from D. 

Fratantoni (2001). 
 Page 107

LCE

Loop

Caribbean Current

Current

Florida Current

ACE

Cyclone

LCE Atlantic Ocean

Eddy Field

Shelf Current

Shelf

Current

Yucatan

Current

Gulf of 

Mexico

Caribbean Sea

CARE

Cyclonic

Gyre

Cyclonic

Gyre

CARE

YC: Yucatan Current CARE: Caribbean Eddy

LC: Loop Current ACE: (Smaller) Anticyclone

LCE: Loop Current Eddy

Cyclone

ACE

Cyclone

Greater Antilles

Venezuela

Lesser Antilles

Windward Passage

Mona Passage

Columbian 

Basin

Cayman 

Basin

Anegada Passage

Nicaragua 

Rise

U.S.A

Mexico Jamaica

Netherlands

Antilles

Figure 5-8. An example model output over the Gulf of Mexico and Caribbean Sea: nearsurface current and eddy fields obtained from a combination of satellite data and model. 

Plotted are ten-day Eulerian trajectories x = xo + ∫ u dt, where x and u are position and 

velocity vectors respectively, and the integration is over ten days. The trajectories are 

launched from Jul/19 through Jul/28, 1997, and from every 8th grid point at the first sigma 

level (i.e. surface). Colors indicate speeds such that greenish blue is ≈ 0.5 m/s and red is ≥ 1 

m/s. The lower inset shows the near-surface zonal velocity profile along 66o

W in the eastern 

Caribbean (dotted in upper panel) as observed using drifters (Fratantoni, 2001), and ADCP at 

20m (Hernández-Guerra and Joyce, 2000), taken from Fratantoni (2001), and we superimpose 

on it the modeled near-surface velocity profiles: 10-day average centered around Jul/23/1997 

(dashed) and 1993-1999 mean (dash-dot).
 Page 108

Figure 5-9. The mean transport in terms of stream function contours (upper panel) and 

vectors at selected sections in the Caribbean Sea (lower panel). Experiment 1. 
 Page 109

LCE

Loop

Caribbean Current

Current

Florida Current

ACE

Cyclone

LCE Atlantic Ocean

Eddy Field

Shelf Current

Shelf

Current

Yucatan

Current

Gulf of 

Mexico

Caribbean Sea

CARE

Cyclonic

Gyre

Cyclonic

Gyre

CARE

YC: Yucatan Current CARE: Caribbean Eddy

LC: Loop Current ACE: (Smaller) Anticyclone

LCE: Loop Current Eddy

Cyclone

ACE

Cyclone

Greater Antilles

Venezuela

Lesser Antilles

Windward

Passage

Mona Passage

Columbian 

Basin

Cayman 

Basin

Anegada 

Passage

Nicaragua 

Rise

U.S.A

Mexico

Jamaica

Netherlands

Antilles

4 3 1

5

7

9

8 2

6

Figure 5-10. As in title-page figure with locations of sections 1 through 9 shown. 

These sections are where flow variability across the Caribbean Current are examined. 
 Page 110

Time

Cross-Channel

1

3

4

5

7

8

9

Section

Figure 5-11. Section-time contours of surface velocity normal to seven of the nine 

sections shown in figure 5-10. Experiment 1. 
 Page 111

Figure 5-12. Standard deviation of sea-surface height for Experiment 1. 
 Page 112

Figure 5-13. Cross-sectional contours of velocity normal to the section (solid) and 

isopycnals (dash), and the sign of sectional potential vorticity, gradient ∂Πo/∂s, where s 

is the across-section coordinate, is also indicated (shaded is where ∂Πo/∂s < 0; 

Pedlosky, 1979), at sections ‘3’ (upper panel) and ‘9’ (lower panel). Experiment 1. 
 Page 113

Section 3

Figure 5-14. Cross-coherence spectra between transports above and below 800 m at 

section ‘3.’ Experiment 1. 
 Page 114

Sections 7 & 4

Sections 7 & 4

Sections 4 & 3

Sections 4 & 3

Sections 9 & 8

Sections 9 & 8

Sections 3 & 2

Sections 3 & 2

Figure 5-15. Cross-spectra coherency analyses of cross-current displacements between 

the different indicated sections. Experiment 1. 
 Page 115

(a) Sections 9 & 6 (b) Sections 9 & 4

Figure 5-16. Lower-layer cross-spectral coherency analysis for (a) sections ‘9-6’ and 

(b) ‘9-4.’ Experiment 1. 
 Page 116

(a) Sections 9 & 8 

Upper

(b) Sections 8 & 7 

Upper

(c) Sections 9 & 8 

Lower

(d) Sections 8 & 7 

Lower

Figure 5-17. Cross-spectra coherency analyses of cross-current displacements (i.e. 

meanders) between the different sections for the upper and lower layers as indicated in 

each panel. Experiment 1. 
 Page 117

Figure 5-18. Top panel: wave rays (in blue; lighter blue for wavelength < 30km) traced 

using the TRW dispersion relation indicating deep energy paths in the Gulf that 

originate under the Loop Current and Loop Current Eddies. The outer rims of LC and 

LCEs are indicated in red by the 10-year assemblage of the ζ/f=−0.2 contours at 

z=−50m obtained from PROFS-IAS. The green arrows indicate wavenumber vectors, 

plotted every 10 days along the path, with lengths equal to wavelengths (the 100km 

scale is shown below the panel). Bottom panel: the 20-100day modeled deep energy. 

Superimposed is a comparison of rays from the top panel (thin solid) with those derived 

by including effects of deep mean flow (thick green curves). From Oey & Lee, 2002. 
 Page 118

Observation: 97/01 Model (Exp.C): 93-99

Observed & Modeled V’s: Comparison in Yucatan Channel

1.3 m/s

1.4 m/s

From Sheinbaum et al. 2002, GRL

Figure 5-19. The observed and modeled mean velocity profiles in Yucatan Channel. 
 Page 119

1993 1993.5 1994 1994.5 1995 1995.5 1996 1996.5 1997 85.2

85.3

85.4

85.5

85.6

85.7

85.8

85.9

86

 Inflow Position and EOF−Mode 1

Year

Lon (W)

CORR=0.83

1993 1993.5 1994 1994.5 1995 1995.5 1996 1996.5 1997 28

30

32

34

36

38

40

Inflow Transport and EOF−Mode 2 (filtered)

CORR=0.7

Year

Sv

E

E

E

E E

E

E

1993 1993.5 1994 1994.5 1995 1995.5 1996 1996.5 1997 −10

−5

0

5

10

15

20

25

 Sill Velocity and EOF−Mode 3 & 4 (filtered)

CORR=0.66

Year

cm/s

Inflow Position w/Mode 1 (γ = 0.83) Inflow Transport w/Mode 2 (γ = 0.7)

Sill Currents w/Modes 3&4 (γ = 0.66)

Mode 1

(50%)

Mode 2

(18%)

Mode 3

(11%)

Mode 4

(7%)

10−3 10−2 10−1 0

0.2

0.4

0.6

0.8

1

1.2

(a) Observed

Freq. (cycle/day)

(cm/s)**2

205

114

37

32 18

Spectra of Observed Sill Currents

205 days

10−3 10−2 10−1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

 EOF Mode 3 and Mode 4

Freq. (cycle/day)

(cm/s)**2

205

45

29

Spectra of Modes 3 & 4

205 days

EOFs at Yucatan

 

Figure 5-20. A summary of EOF analysis in Yucatan Channel. The first four modes 

are shown and their connections to physical quantities indicated. The observations over 

the sill are from Maul et al. (1985). For details please see Ezer, Oey, Lee and Sturges 

(2003). 
 Page 120

Surface Flow of 

a Warm Eddy

Subsurface Flow 

of a Warm Eddy

Secondary 

Surface Flow

The Coast The Shelf

~ 1000 m

The Slope

x

z

y

The Slope

Main 

Surface 

Anticyclone

Deep 

Anticyclone

Subsurface 

Anticyclone

Deep Cyclone

Weaker 

Subsurface 

Cyclone

Weak 

Surface 

‘Cyclone’

Trapping 

Height

Mixing Front

Jet’s Path

BBL

The Slope

Figure 5-21. A schematic sketch of deep cyclone-anticyclone pair that results when a warm 

eddy (thick red line) impinges upon a continental slope and shelf. The subsurface portion of the 

warm eddy ‘feels’ the slope while the surface flow intrudes further onshore and ‘spills’ over the 

shelf (thin red line). Thus cyclone-anticyclone pair is formed in the deep (thick blue and brown 

dashed lines). Nearer the surface, the cyclone weakens (green dashed and thin red lines) as the 

flow follows the main anticyclonic path of the warm eddy (thick red line). In the presence of a 

bottom boundary layer (BBL), a mixing front is formed and the bottom-intensified current or jet 

is lifted up. The front-jet system propagates along-slope, off-slope, and also upward as a superinertial disturbance, until it is trapped as indicated here (dotted dark line). From Oey and 

Zhang, 2004.
 Page 121

−89 −88 −87 −86

26

26.5

27

27.5

28

28.5

29

29.5

30

30.5

−0.05

0

0

0

0.05

0.05

−89 −88 −87 −86

26

26.5

27

27.5

28

28.5

29

29.5

30

30.5

−0.1

−0.05

−0.05 0

0

0.05

0.05

0.05

0.1

Figure 5-22. Regression coefficients of satellite sea level anomaly with first (upper left; 87%) 

and second (upper right; 10%) observed modes of currents in DeSoto Canyon, from Wang et al. 

(2003), and the corresponding near-surface modeled currents (lower panels) obtained by the 

nested PROFS.
 Page 122

Figure 5-23. On February 9, 2002, altimeter-derived SSH shows a rather unusual elongated 

extension of the Loop Current into the western Gulf of Mexico (left panel, from Colorado Center 

for Astrodynamic Research). The right panel shows a PROFS-IAS counterpart. Plotted are 10-

day Eulerian trajectories launched every 14 grid points (scale=1m/s per 200km) at 150m below 

the surface, colored with the local value of relative vorticity/f: dark-blue is cyclonic (≥+0.3) and 

red is anticyclonic (≤ -0.3). Model horizontal resolution ranges from ~5km in the southern Gulf 

to ~1km in the north and there are 25 vertical sigma levels. The (nested) model is forced by 

transports through its southern and eastern boundaries supplied by PROFS-IAS, and six-hourly 

ECMWF wind at the surface, with date as indicated in the panel's title. This experiment has no 

data assimilation so that its date has little meaning, and the elongated Loop Current is a 

characteristic of the model's intrinsic dynamics. The feature is rare however, occurring only one 

time during the 1992-1999 simulation period.
 Page 123

Figure 6-1a. An example of the model results: comparisons of the modeled and 

satellite-derived SSH (panels A & B; CI=10 cm) and SST (panels C & D; CI=1 

o

C) on Dec/26/1997. 
 Page 124

Figure 6-1b. Data-assimilated surface trajectory colored with local values of relative 

vorticity/f (blue=cyclone and red=anticyclone; upper panel), averaged from Apr/06 through 

Apr/15/1998, and the satellite SSH on Apr/15/1998 (lower panel) from an independent 

source: the Colorado Center for Astrodynamics Research. The latter uses a different model 

mean than that used in our calculation.
 Page 125

Figure 6-2. A comparison of the modeled and satellite-derived SSH-anomaly rms, 

√<(δηM)

2

> (left panel) and √<(δηO)

2

> (right panel), respectively, where <.> denotes timeaveraging over three years from 1997 through 1999, for the experiment with assimilation. 

The contour interval CI=5 cm. 
 Page 126

Figure 6-3. A comparison of the modeled and satellite-derived SSH-anomaly rms, 

√<(δηM)

2

> (left panel) and √<(δηO)

2

> (right panel), respectively, where <.> denotes timeaveraging over three years from 1997 through 1999, for the experiment without

assimilation. The contour interval CI=5 cm. 
 Page 127

Figure 6-4. The SSH-anomaly rms (CI=2 and 1 cm) for model experiments 

(A) with both SSH and SST assimilations, (B) with SSH assimilation only 

and (C) without any assimilation, in the northern Gulf and shelf region. The 

corresponding contours derived from satellite are shown in bottom panel (D). 

White contours show the 200m and 2000m isobaths. 
 Page 128

Figure 6-5. The three-year (1997-1999) mean velocity vectors near the surface 

superimposed on the velocity rms (CI=10 cm/s) for model experiments (A) with both 

SSH and SST assimilations, (B) with SSH assimilation only and (C) without any 

assimilation, in the northern Gulf and shelf region. The corresponding vectors and 

contours derived from satellite assuming geostrophy are shown in bottom panel (D). 

Note that the ‘satellite’ mean velocities are equivalent to those from the ten-year model 

climatology of the model run over the entire domain shown in Figure 4, hence their 

similarity with panel (C). 
 Page 129

Figure 6-6. Drifter trajectories in the northeastern Gulf of Mexico from 11-May-1998 to 

10-July-1998. Initial drifter deployment locations are marked (*). We groups these 

trajectories into three groups: Shelf Group (thin solid curves), Canyon Group (mediumsolid curves), and Lone Drifter (thick solid curve). The NOAA buoy 42036 and the 

ADCP site at the 50 m (AS1/CM2) isobath from the University of South Florida are also 

shown. The two dotted curves are 200m and 2000 m isobaths. From Fan, Oey & 

Hamilton (2004).
 Page 130

Figure 6-7. The prediction errors for ten-day re-sampled drifters for all experiments. 

From Fan, Oey & Hamilton (2004). 
 Page 131

 

Figure 6-8. Five-day averaged surface velocity (z=−27 m; plotted as Eulerian 

trajectories) from July-6-1998 to July-10-1998 for experiments A, B, satellite 

geostrophic velocity and experiment F. The asterisk denotes ADCP site AS1/CM2. The 

two solid line are 200 m and 2000 m isobaths. Dark (blue) curves (trajectories) 

emphasize west Florida shelf currents and lone-drifter eddy (exp.E or F) as discussed in 

text. From Fan, Oey & Hamilton (2004). 
 Page 132

 

Figure 6-9. Time series of winds, AS1/CM2 (on west Florida shelf, see figures 6-6 for 

locations) mid-depth currents for experiment A, B, and E, and observation (bottom 

panel; Weisberg and He, 2003). The shaded area for experiment E is the time period 

with drifter assimilation. The year is 1998. From Fan, Oey & Hamilton (2004). 
 Page 133

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

30 cm/s

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

30 cm/s

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

x3

10 cm/s

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

x3

10 cm/s

Figure 6-10. Mean surface currents (left) and variances (right) at mooring locations 

from observations (upper) and model (lower). Note that the velocity scale for means is 3 

times larger. Dotted are isobaths: 2000, 1000, 200 and 100m. From Wang, Oey, Ezer 

and Hamilton, 2003. 
 Page 134

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

Observed: 97/99 Æ

Modeled: 97/99 Æ

1st SVD Mode

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

−89 −88 −87 −86

28

28.5

29

29.5

30

30.5

Observed: 97/99 Æ

Satellite: 97/99 Æ

2nd SVD Mode

Figure 6-11. First and second SVD modes of observed and modeled currents in DeSoto 

Canyon. From Wang, Oey, Ezer and Hamilton (2003). 
 Page 135

The Development of the 2nd Mode

Satellite (from P. 

Fratantoni et al, 1998)

Modeled Currents 

No Assimilation

Figure 6-12. The development of the second SVD mode in the model (right panels) 

and comparison with that observed from satellite SST frontal analysis (left panels; from 

P. Fratantoni et al. 1998). 
 Page 136

Surface 97/99 DeSoto 

Canyon Study

Model Observation

Subsurface

Figure 6-13. Observed and modeled variance ellipses. The model in this case has 

satellite data assimilations, and the variances were computed based on simulation from 

1993-1999. Surface data are for moorings where z > −200 m, and subsurface z < −200 

m. Modeled currents were interpolated to the observed levels. If there is more than one 

current meter for either the surface or subsurface group, then one with the longest time 

series is used. 
 Page 137

Near-Surface Currents

ECMWF ECMWF; Doubled-Resolution Run No Wind

1 m/s

0.3 m/s

1 m/s

ECMWF ECMWF; Doubled-Resolution Run No Wind

Near-Bottom Currents

Figure 6-14. Modeled mean currents near the surface (upper panels; sigma (σ) level 1, or about 0.2 m 

to 2.5 m below the surface depending on the local water depth) and near the bottom (lower panels; σlevel 19, or about 0.5 m to 120 m above the bottom) for the case with ECMWF wind forcing (left), 

ECMWF wind forcing and doubled resolution (middle) and no wind forcing (right). The averaging is 

taken over 8 years from 1993 through 1999. 
 Page 138

Wind Wind & Assimilation

Doubled-Resolution Run 

with Wind; Smag.C=0.1

Doubled-Resolution Run 

with Wind; Smag.C=0.05

(d) (c)

(a) (b)

Figure 6-15. Time-mean (1993-1999) zonal currents at a meridional section at 90o

W in the 

Gulf of Mexico. The view is westward so that Yucatan Peninsula, Mexico is on the left and 

Louisiana, USA is on the right. Positive (yellow/red/brown) current is directed out-of page 

(i.e. eastward) and negative (green/blue/violet) is into page (i.e. westward). 
 Page 139

Figure 6-16. Time-mean (1993-1999) velocity spectra expressed in m/s at sigma-level 6 

(≈100m below the surface) as a function of the spatial scale for model region north of 26o

N 

but deeper than the 500m isobath. Here CGE means “Coarse-Grid or the original-grid 

Experiment” and FGE means “Fine-Grid or the doubled-resolution-grid Experiment.” 
 Page 140

Figure 6-17. A comparison with NDBC near-surface temperature of 3-year time series of 

model temperature at (25.9N, 93.6W) for different experiments. 
 Page 141

Figure 6-18. Gulf-wide area-averaged temperature profiles and their respective standard 

deviations for experiments with and without assimilations. 
 Page 142

 

Figure 6-19. Gulf-wide area-averaged kinetic energy of the mean current (MKE) and eddy 

kinetic energy (EKE) for experiments with and without assimilations. 
 Page 143

Figure 6-20. Comparison of in situ (solid curve) with climatological and modeled 

temperature profiles at the indicated date and location over the northern Gulf slope. Panel A 

shows the location on the modeled SSH map. 
 Page 144

Figure 6-21. Comparison of in situ with climatological and modeled temperature profiles at 

the indicated date and location over the LATEX shelf. The assimilation in this case includes 

SST assimilation. 
 Page 145

Figure 6-22. Ten-day averaged surface salinity contours over the LATEX shelf for the 

indicated period from late winter (February) through late summer (August). 
 Page 146

Figure 6-23. Satellite-derived SST and path of hurricane Georges (upper panel). The lower 

panel shows the corresponding modeled (with assimilation) SSH and surface currents. 
 Page 147

Figure 6-24. (A) Satellite-derived SST and path of hurricane Georges; (B) modeled SSH 

(assimilated); (C) model 25 m temperature and (D) model 50 m temperature. 
 Page 148

Satellite Assimilation 

Every 1 day

Assimilation 

Every 5 days

No 

Assimilation

Figure 6-25. A comparison of the satellite-derived surface currents in the vicinity of a newly-shed Loop 

Current Eddy (left column) with model assimilated every 1-day (2nd column) and 5-day (3rd column), and 

no assimilation (right-most column). All cases are initialized with fields on Oct/2nd/1997 (i.e. 10 days prior 

to the first-row panels shown here), the date when the eddy is shed. Shown are Eulerian trajectories 

launched for 5 days centered around the indicated date in each panel, and from every 10th grid point at the 

first sigma level (i.e. surface). Colors indicate speeds such that greenish blue is ≈ 0.5 m/s and red is ≥ 1 

m/s. Black contours are the 200m and 2000m isobaths. Day-interval going down the column is 30 days. 
 Page 149

Position of Eddy Center

SSH at Eddy Center

Departure of Eddy 

Center from Initial 

(Fixed) Position

Position of Eddy Center

SSH at Eddy Center

Departure of Eddy 

Center from Initial 

(Fixed) Position

SSH+SST 1_day Assim

SSH+SST 5_day Assim

No Assimilation SST_Only 1_day Assim

SSH_Only 1_day Assim

Figure 6-26. Inter-comparison of various eddy characteristics amongst different model runs with and 

without assimilation, and with various assimilations. 
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lands, and distribute those revenues. 

Moreover, in working to meet its responsibilities, the Offshore Minerals Management Program 

administers the OCS competitive leasing program and oversees the safe and environmentally 

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The MMS strives to fulfill its responsibilities through the general guiding principles of: (1) being 

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development and environmental protection.