Eddy Energy and Shelf Interactions
in the Gulf of Mexico
J. Carter Ohlmann and P. Peter Niiler
Scripps Institution of Oceanography,
University of California, San Diego
Chad A. Fox and Robert R. Leben
Colorado Center for Astrodynamics Research,
University of Colorado, Boulder
Submitted to: JGR Oceans
Revision #1
July 5, 2000
Abstract
Sea-surface height anomaly data from satellite are continuously available for the
entire Gulf of Mexico. Surface current velocities derived from these remotely sensed
data are compared with surface velocities from drifting buoys. The comparison shows
that satellite altimetry does an excellent job resolving Gulf eddies over the shelf-rise
(depths between ~200 and 2000 m) if the proper length scale is used. Correlations
between altimeter and drifter derived velocities are statistically significant (r > 0.5) when
the surface slope is computed over 125 km, indicating that remotely sensed sea-surface
height anomaly data can be used to aid the understanding of circulation over the shelfrise. Velocity variance over the shelf-rise from the altimetry data shows regions of
pronounced eddy energy south of the Mississippi outflow, south of the Texas-Louisiana
shelf, and in the northwest and northeast corners of the Gulf. These are the same
locations where surface drifters are most likely to cross the shelf-rise, suggesting Gulf
eddies promote cross-shore flows. This is clearly exemplified with both warm and cold
eddies. Finally, the contribution of Gulf eddies and wind stress to changes in the mean
circulation are compared. Results indicate that the eddy generated vorticity flux to the
mean flow is greater than the contribution from the surface wind stress curl, especially in
the region of the Loop current and along the shelf-rise base in the western Gulf. Future
modeling efforts must not neglect the role of eddies in driving Gulf circulation over the
shelf-rise.
1. Introduction
A predictive understanding of ocean circulation in the Gulf of Mexico (Gulf) is
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necessary to track and manage the Gulf’s rich supply of physical and biological
resources. For instance, Gulf ocean circulation models are required to forecast the
movement of harmful algal blooms and to assess potential environmental impacts of
future oil and gas drilling efforts. Existing ocean models for the Gulf show considerable
skill in determining surface currents on the continental shelf (Oey 1995, Herring et al.
1997). However, model skill is poor in the region of the continental shelf-rise (Herring et
al. 1997). Model inaccuracies are largely due to the limited understanding of how Gulf
eddies interact with the shelf-rise and their role in shelf-water exchange (Sturges 1993,
Oey 1995, Cho et al. 1998).
Ocean circulation in the Gulf is dominated by the Loop current. This current is a
portion of the Atlantic’s western boundary current that enters the Gulf through the
Yucatan Channel, extends mostly northward, and exits through the Florida Straits (e.g.
Vukovich et al. 1979). Large anticyclonic eddies separate from the Loop current and
travel westward across the basin. These warm rings have a significant influence on
currents, heat, and salt in the entire Gulf, and have thus been the focus of numerous
studies. Historical data suggests the time between eddy separations varies from 3 to 17
months (Elliott 1982, Maul and Vukovich 1993). The exact mechanism for eddy
formation and detachment has yet to be identified (e.g. Hurlburt and Thompson 1980,
Vukovich and Crissman 1986, Maul and Vukovich 1993). At the time of separation the
anticyclonic eddies have diameters mostly between 200 and 400 km (Vukovich et al.
1979, Elliot 1982, Lewis et al. 1989) and current speeds near 50 to 75 cm s-1 (Kirwan et
al. 1984). The eddies decay with an e-folding time of ~1 year while migrating westward
at ~2 to 5 km day-1 (Elliot 1982, Vukovich and Crissman 1986, Oey 1996).
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Comparatively, little is known about the fate of Loop current eddies and their
influence on continental shelf and shelf-rise flows once they reach the western boundary.
The modeling study by Smith (1986) suggests that the western boundary imposes an
asymmetry in the flow that results in northward movement of anticyclonic rings. Both
northward and temporary eastward movement of Loop current eddies in the western Gulf
have been observed (Kirwan et al. 1984, Lewis et al. 1989). Upon colliding with the
shelf-break, anticyclonic eddies can shed a significant portion of their volume and
angular momentum to the south setting up adjacent cyclonic rings (Vidal et al, 1992).
Advection of shelf water offshore on the north side of a warm ring can also produce an
adjacent cyclonic eddy as relative vorticity increases with flow into deeper water (Smith
1986). The existence of both warm and cold eddies in the shelf-rise region certainly
influences the local flow field and provides an efficient mechanism for shelf-water
exchange.
This study uses current data from drifting buoys and satellite altimetry to investigate
eddy driven circulation over the continental shelf-rise. Drifting buoys provide an
efficient and accurate way of capturing synoptic scale circulation patterns through their
spatial and temporal resolution. Satellite altimetry can potentially provide continuous
real-time shelf-rise flow data. Surface velocity data from drifters and altimetry are
compared to determine how well altimetry resolves the actual circulation patterns in the
Gulf. This is particularly important near continental margins where high frequency
variations in the flow field are easily aliased, and ageostrophic velocities can be large.
We show that surface velocities from satellite altimetry and drifters are well correlated
offshore of the shelf-break (200 m). Altimetry data is then used to identify regions of
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large eddy energy and significant cross shelf-rise flows. Finally, the role of eddies in
Gulf circulation is discussed. Eddies play a large role in the Gulf’s shelf-rise flow field
by promoting shelf water exchange and contributing energy to the mean circulation.
Satellite altimetry can provide continuous circulation information useful for monitoring
shelf-rise eddies, for further understanding shelf-rise currents, for model validation, and
for data assimilation.
2. Data and Methods
2.1. Drifter data
The Surface Current and Lagrangian-drift Program (SCULP) was developed to
improve the understanding of ocean circulation over continental margins in the northern
Gulf of Mexico. Drifters deployed during SCULP are similar in design to those used
during the U.S. Coastal Dynamics Experiment (Davis 1985). The drifters are composed
of four rectangular vanes (50 cm wide, 90 cm tall) extending radially from a thin,
vertically oriented, tube held in place at 0.5 m depth by four small surface floats. The
drifters are initially packaged in soluble cardboard boxes with attached parachutes and
dropped from aircraft. Continuous position transmissions are through service ARGOS
for a period of 90 days. Drifter slip has previously been observed to be less than 3 cm/s
(Davis 1985).
The SCULP field program consists of 3 distinct segments identified here as SCULP-I,
-II, and -III. SCULP-I drifter deployments occurred primarily at 15 stations (distributed
as a 3 by 5 grid) within a 125 km square on the Louisiana-Texas shelf. The abundance of
oil and gas activity and the presence of current meter moorings in this region make it a
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prime location for a drifter study. SCULP-I drifter deployments occurred from October,
1993, through July, 1994. The grid was reinitialized weekly for the first three months,
then biweekly for three months, and finally monthly, giving roughly one year of data.
The SCULP-II drifters were deployed within a ~400 by 150 km rectangle on the
northwest Florida shelf to investigate cross-shore flows. The initial SCULP-II
deployment occurred in February, 1996, and consisted of 15 units. The grid was
reinitialized every two weeks for roughly a year. The SCULP-III study was specifically
concerned with eddies on the shelf-rise of the Louisiana and North Florida coasts. Four
deployments of 20 drifters seeded the edge of warm eddies identified with remotely
sensed sea-surface temperature (AVHRR) and SSH (TOPEX/Poseidon) data.
Deployments occurred during April, 1998, on the Louisiana shelf, and during July, 1998,
on the continental margin south of the Florida-Louisiana border.
Drifter positions, recorded at various times throughout each day, were organized
temporally and de-spiked by eliminating displacements requiring velocities greater than
250 cm sec-1. Data points recorded within 15 minutes were averaged together to
eliminate erroneous displacements associated with observations by multiple satellites.
The data were then interpolated onto a uniform time grid and daily averaged values
computed. This was done by fitting a three-parameter analytic correlation function for
each day to the Fourier transform of spectral estimates obtained from ten days of
unequally sampled observations centered on the day of interest. The three fit parameters
represent a low-frequency amplitude, a tidal amplitude, and a width for the tidal peak.
Each correlation function was then used to produce an interpolated time-series that
accounts for tidal and inertial signals that may have been aliased in the original unequally
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sampled data. Interpolated values were sub-sampled every three hours and daily
averaged velocities calculated. Tidal and inertial signals are effectively removed in daily
averaged velocities for the Gulf region. A thorough description of the data processing
scheme is given by Van Meurs (1995).
The regions of drifter deployment and the spatial density of daily averaged velocity
values are shown in Figure 1. The number of observations in ¼ by ¼ bins is largest off
the Texas-Louisiana and northwest Florida coasts (the areas of deployment). Counts
generally decrease with distance from these regions. There are a significantly greater
number of drifter observations along the Texas shelf than along the Louisiana shelf
suggesting a predominantly westward flow from the Texas-Louisiana deployment region.
However, the number of drifter observations along the Louisiana coast is sufficiently
large that observational biases due to flow direction should to be small (e.g. Davis 1991).
Mean westward velocities along the Louisiana shelf further suggest the absence of large
sampling biases in this region. Drifter counts in the northeast Gulf are distributed much
more uniformly around the deployment region. Drifters move mainly southward, both
offshore of the Panhandle and along the Florida shelf. Practically the entire Gulf (give
exception to the southernmost region off the Yucatan coast) is eventually sampled
(Figure 2). Statistics are computed on data in ¼ by ¼ bins that are located over the
continental shelf-rise (200-2000 m) and contain more than 10 daily average velocity
observations. The 10-value threshold was arbitrarily selected so that statistics are
determined for the majority of the shelf-rise region north of 24.
2.2. Altimeter data
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Altimeter data used in this study are the near real-time and archival data streams
available from the TOPEX/Poseidon (T/P; Fu et al. 1994) and ERS-1 and -2 satellites.
Processing of the SSH data is based on a near real-time mesoscale analysis technique
designed to exploit the tandem altimetric sampling by these satellites (Lillibridge et al.
1997). This method has been used to operationally monitor the Gulf of Mexico since
November, 1995.
Space/time sampling provided by the 10-day repeat orbit of the T/P satellite (selected
to map topography associated with large-scale variations in ocean circulation) is not ideal
for monitoring mesoscale oceanic variability due to the large distance (~300 km) between
satellite ground tracks. Altimetric sampling with the ERS satellite offers better
mesoscale sampling characteristics due to the improved spatial resolution afforded by a
35-day repeat period. The longer ERS repeat orbit is still sufficient for resolving the 30day decorrelation scale typical of mid-latitude eddy variability (Stammer 1997).
Intuitively, the combination of data from multiple altimeters should improve mesoscale
sampling. However, the fields produced from combined SSH data sets may not be
significantly better than those constructed from T/P data alone if uniform errors and
wavelength/frequency resolution satisfying the Nyquist criteria are required of the
space/time gridded product estimated from the along-track sampling (Greenslade et al.
1997). While these metrics may be reasonable for theoretical sampling studies or mission
design, the constraints are too limiting at mesoscale wavelengths for the design of an
operational space/time objective smoother for interpolating T/P and ERS data.
Operational tandem or multiple satellite objective mapping of the mesoscale circulation
must therefore rely on sub-optimal smoothing to resolve eddy scale wavelengths (albeit
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with the commensurate errors caused by sampling limitations and aliasing). The efficacy
of the final product can, however, be compared with coincident data for quantitative
evaluation of the processing and gridding strategies.
2.2.1. Mesoscale analysis
The processing of the T/P and ERS-2 data over the Gulf is designed to retain
mesoscale signals while removing the substantial orbit error (~50 cm) that may be
present in the fast-delivery products. The procedure blends data from the two satellites,
treating both data sets in a consistent fashion. All along-track T/P and ERS-2 data are
referenced directly to the Ohio State University Mean Sea Surface (Yi 1995). This saves
a significant amount of computational effort during near real-time processing and allows
referencing of the non-repeat track ERS-1 data from the geodetic mission phase. A data
archive is created from collinear exact repeat mission data based on final versions of the
geophysical data records (GDRs) by interpolation to reference ground-tracks. By
referencing all altimeter data to an independent mean sea surface, the climatology based
on the blended T/P and ERS-1 data can be extended to include past, present and future
altimeter mission data referenced in the same manner, such as have been produced from
the historical GEOSAT data (Berger et al. 1996a,b). Along-track loess filtering is used to
remove residual orbit and environmental correction errors. The loess filter removes a
running least squares fit of a tilt and bias from the along track data within a sliding
window. The window width is approximately 15 degrees of latitude (200 seconds alongtrack). This high pass filter retains the short wavelength mesoscale signals while
removing the longer wavelength orbit and environmental correction errors. A fast
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multigrid preconditioned Cressman analysis (Hendricks et al. 1996) with spatial/temporal
weighting is used to interpolate the along-track data to quarter-degree daily analysis
fields over the Gulf of Mexico.
2.2.2. Along-track data
Along-track T/P data are from the reprocessed T/P GDRs provided by the NASA
Physical Oceanography Distributed Active Archive Center at the Jet Propulsion
Laboratory (JPL/PO.DAAC). ERS-1 and -2 data are based on the ERS Altimeter Ocean
Products (ALTOPR) CD-ROMs obtained from the Centre ERS d'Archivage et de
Traitement (CERSAT), the French processing and archiving facility for these satellite
data. Daily maps have been produced from the corrected and loess filtered along-track
altimeter data for the time period spanned by SCULP.
The T/P data were corrected using standard corrections supplied on the
JPL/PO.DAAC reprocessed T/P GDRs and based on the JGM-3 orbits (Marshall et al.
1995). Inverter barometer, electromagnetic bias, ionosphere and wet/dry troposphere
corrections, were applied as recommended in the GDR handbook (Callahan 1993).
Ocean tides were removed using the tide solution derived from the Colorado Center for
Astrodynamics Research (CCAR) barotropic tide model (version 1.0) assimilating T/P
data (Tierney 1998). The ERS data were corrected similarly using standard corrections
supplied on the ALTOPRs, including inverter barometer, electromagnetic bias,
ionosphere, and wet/dry troposphere. Orbit, and tide corrections were also applied to the
ERS data.
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Each cycle of corrected 10-day repeat T/P and 35-day repeat ERS data was linearly
interpolated to reference ground tracks based on computed ephemeredes for the satellites.
The T/P reference track is based on a ground track computed for cycle 18. This ground
track has a fixed spacing of the sub-satellite reference points at one second along-track,
corresponding to ~7-km. The ERS 35-day reference ground track is based on one-second
along-track points computed for cycle 6 of the ERS-1 Multidisciplinary 1 mission. No
along-track gridding of the non-repeat ERS-1 geodetic mission was performed.
Coverage available from T/P and ERS-1 and -2 varied throughout the SCULP
sampling period. During SCULP-I, tandem coverage by T/P and ERS-1 was only
available before December 20, 1993, and after April 10, 1994, because of the intervening
ERS-1 Ice-2 mission phase. Data collected after April 10, 1994 was from the ERS-1
Geodetic-1 mission phase. Tandem coverage was available from T/P and ERS-2
throughout SCULP-II and -III.
2.2.3. Gridded data (space/time interpolation)
Daily analysis maps of height anomaly relative to the mean sea surface were
estimated using an objective analysis procedure (Cressman 1959) to interpolate the
along-track data to a ¼ grid over the entire Gulf. The method uses an iterative
difference-correction scheme to update an initial guess field and converge to a final
gridded map. A multi-grid procedure (Hendricks et al. 1996) provides the initial guess.
Five iterations with 200, 175, 150, 125 and 100 km radii of influences were used while
employing a 100-km spatial decorrelation length scale in the isotropic Cressman
weighting function. Data were also weighted in time using a 12-day decorrelation time-
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scale relative to the analysis date, with +-10-day and +-17 day windows applied to the
T/P and ERS data, respectively. The resultant sea-surface height anomaly data are
subsequently referred to as the “CCAR gridded altimetry data”, or “gridded data”. If an
estimate of the total dynamic height is desired, a model or climatological mean seasurface height can be added to the anomaly field.
3. Comparison of Velocities from Altimetry and Drifting Buoys
Current velocities derived from altimetry and drifting buoy data are compared to
determine the accuracy of altimeter-derived velocities over the continental shelf-rise in
the Gulf of Mexico. First, cross-track velocities computed along T/P ground tracks are
compared at locations where drifters are coincident in time and space with altimeter overflights. This most basic comparison isolates discrepancies in the directly determined
velocity estimates. Next, comparisons are performed with the CCAR gridded altimetry
data. The gridded data provides circulation information for the entire Gulf basin.
Comparisons are performed over four arbitrarily chosen depth regions (continental shelf,
0 – 200 m; inshore portion of the shelf-rise, 200 – 1000 m; offshore portion of the shelfrise, 1000 – 2000 m; offshore of the shelf-rise base, > 2000 m) to examine how well the
gridded altimetry data resolve flow variations near the coast.
3.1. Local cross-track velocity comparison
Local cross-track velocity comparisons are made using daily averaged drifter
velocities that fall within ¼ by ¼ bins over which the altimeter crosses and within 24
hours of a crossing. The mean cross-track velocity values for each bin computed from
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all drifters meeting these criteria are compared with T/P cross-track velocities determined
from the sea-surface height slope computed over a given length of the altimeter track
(“window width”). This is done separately for ascending and descending altimeter tracks
to avoid biases in regions where the cross-track velocity component is small. Although
the drifters measure total velocity and T/P gives only variations from the mean,
correlations should be meaningful outside the Loop current where mean velocities are
small relative to variations.
Correlations between local cross altimeter track velocities from SSH anomaly and
drifter data for various window widths and depth ranges are illustrated in Figure 3. The
curves show that velocity relationships are a strong function of window width and that
correlations generally increase with distance offshore. The correlations between drifter
and altimeter derived cross-track velocities for the descending track and depths greater
than 2000 meters ranges from 0.40, using a ~20 km window width, to 0.75, using a ~105
km window width. Correlations for the descending track over the shelf-rise range from
0.20 (window width ~10 km) to 0.52 (window width ~125 km). Correlations between
cross-track velocities for ascending tracks show similar ranges (Figure 3b).
The window width for which the cross-track velocities are most strongly correlated
depends on the depth range, and is fairly consistent between the ascending and
descending tracks. Over the continental shelf and the inshore region of the shelf-rise
correlations are strongest near a window width of 200 km. In comparison, correlations
are strongest using a ~125 km window width for the offshore region of the self-rise and
beyond the shelf-rise base. This 125 km length is roughly half the diameter of eddies
observed near the base of the shelf-rise with SCULP drifters, and previously found in the
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western Gulf (e.g. Hamilton et al. 1999), suggesting that sea-surface height anomaly data
is capturing Gulf eddies beyond the shelf-break. The widow width corresponding to
maximum correlation is much larger than the length scales of the dominant circulation
patterns on the shelf, and over the inshore edge of the shelf-rise.
The maximum correlation over the continental shelf is only ~0.30 for both the
ascending and descending tracks. The Correlation increases to ~0.53 over the shelf-rise,
and further increases to 0.62/0.75 for the ascending/descending tracks beyond the shelfrise base. Overlapping error bars suggest little statistical difference in correlations for the
inshore and offshore regions of the shelf-rise (Figure 3a,b; red and black curves). The
dependence of velocity correlation on depth is illustrated spatially in Figure 4.
Correlations between cross-track altimeter and drifter derived velocities are generally
greater offshore of the shelf-break than over the shelf. Reduced correlations across
descending tracks over the shelf-rise in the eastern and western Gulf are due largely to
the alignment of these tracks with bathymetry and small cross-shore (and thus crosstrack) velocity components.
This analysis indicates T/P sea-surface height data can be used for a statistically
significant representation of cross-track currents offshore of the shelf-break. However,
the degree to which currents can be accurately determined from T/P depends strongly on
the window width used to determine the sea-surface height slope along the altimeter
track. A window with of near 125 km is appropriate for resolving Gulf eddies over the
shelf-rise and just offshore of the shelf-rise base.
3.2. Comparison using gridded sea-surface height values
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The comparative analysis for the cross-altimeter-track velocity component discussed
above illustrates that currents over the shelf-rise can be determined locally with remotely
sensed T/P SSH data. A gridded SSH field is necessary to obtain a complete picture of
Gulf circulation from altimetry. Fifteen-day drifter velocity averages centered on the 8th
and 23rd days of each month (on a ¼ by ¼ grid) are compared with velocities from the
gridded sea-surface height anomaly data for these days. To account for the fact that
neither drifter nor altimeter derived velocities are completely independent, and sampling
errors are inherent in both data sets, comparisons are performed using a scheme that
bridges the gap between linear correlation and least-squares regression analysis (Emery
and Thomson 1998). Initially correlation coefficients are calculated to determine how
well the velocities co-vary in space and time. Next, linear regressions are performed
using a “geometric mean functional regression” whereby each variable is regressed on the
other and a mean slope is computed. This gives the best regression line estimate, a useful
result for assessing energy differences between the two flow fields.
Initial comparisons reveal a poor correlation between drifter and altimeter derived
velocities in the southern Gulf (south of ~24). The low correlation values are due
primarily to the mean Loop current flow that is not resolved by sea-surface height
anomalies alone, and to a lesser extent, sparse drifter coverage. To eliminate such biases,
velocity comparisons are performed only with data collected north of 24. Results are
essentially the same when only data north of 25 is considered. Velocity comparisons are
performed separately for the eastern and western portions of the basin. The regional
comparisons serve to isolate Loop current eddies that exist the primarily in the west.
Scatter-plots of drifter and altimeter derived surface velocities over various depth
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ranges in the northwestern and northeastern Gulf are illustrated in Figures 5 and 6,
respectively. In the northwestern region, drifter and altimeter derived velocities are
poorly correlated over the continental shelf (r=0.17; Figure 5a). The gridded altimetry
product is not expected to resolve the small-scale, high frequency features found in shelf
waters. Beyond the shelf-break, drifter and altimeter derived velocities demonstrate
statistically significant correlations (at the 95% confidence level). Correlations are 0.62
and 0.64 over the inshore and offshore regions of the shelf-rise, respectively (Figures
5b,c). The correlation increases to 0.70 for the region beyond the shelf-rise base (Figure
5d). Regression lines for the regions beyond the shelf-break have slopes that increase
with depth from ~0.65 to near 0.70. This indicates that altimeter data captures between
~65 and 70% of the energy in drifter velocities beyond the shelf-break. Both
ageostrophic flows and small-scale motions are unresolved in altimeter derived
velocities.
In the northeastern region of the Gulf, drifter and altimeter derived velocities also
show statistically significant correlation (at the 95% confidence level) only offshore of
the shelf-break. However, correlation coefficients are ~15% less, on average, than for the
northwestern Gulf. Correlations between gridded velocities from drifters and altimetry
are 0.51 and 0.55 over the inshore and offshore regions of the shelf-rise, respectively.
Beyond the shelf-rise break the correlation increases to 0.56. The reduced correlations in
the northeast are due to dynamic height features off the Florida coast that are not tracked
by drifters, and effects of the Loop current that are not captured in sea-surface height
anomalies. Regression lines for the depth regions beyond the shelf-break in the
northeastern Gulf have slopes mostly near 0.55, also slightly less than in the northwestern
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region. This is likely due to Loop current energy, present in the drifter data, that is absent
in the surface height anomaly data.
The comparative analysis presented here indicates geostrophic currents determined
from the CCAR gridded altimetry product for the Gulf’s shelf-rise region north of ~24
are well correlated with surface flows obtained from drifting buoys. Large semipermanent and synoptic scale eddies evident in drifter data in the northwestern Gulf are
resolved by the CCAR gridded altimetry product. Small eddies appearing in the dynamic
height field in the northeastern region are not always sampled by drifters. Neither are
topographic eddies within the Loop current region seen in drifter data. The altimetry
derived flow field captures much variability, especially in the northwest region, and can
provide a continuous description of flows associated with large eddies over the shelf-rise.
4. Shelf-Rise Velocity Variance from Altimeter Data
Variance ellipses computed with over 2000 daily velocity averages from the CCAR
gridded SSH anomaly data show the distribution of eddy energy over the Gulf’s shelf-rise
region (Figure 7). Velocity variance is greatest near the Yucatan channel and Florida
Straits due to perturbations in the strong (often greater than 100 cm s-1) Loop current.
Beyond the Gulf’s inflow and outflow regions, variance is greatest south of the
Mississippi outflow, south of the Texas-Louisiana border, and near the shelf-rise base in
the northwest (26.5, 265) and northeast (28, 273) corners of the Gulf. Root mean
square velocity perturbations reach nearly 20 cm s-1 in all four of the high variance zones.
These data clearly show that eddy energy is not isotropic over the shelf-rise; rather,
isolated areas of large eddy energy exist.
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Variance ellipses computed from altimeter data near the shelf-rise base in the
northwestern Gulf are oriented mainly along bathymetry (northeast-southwest direction)
with an exception at 25.5, 264.5 (Figure 7). Ellipses for this region are oriented roughly
in the direction of the mean flow. In contrast, ellipses along the shelf-rise base south of
the Texas-Louisiana border are oriented mainly across bathymetry, ~45 out of phase
with mean velocities. This indicates that eddies influence cross-shelf transport both by
introducing cross-shelf variations in mean long-shore flows and by altering magnitudes
of mean cross-shelf flows.
Variance ellipses in the northeastern Gulf further support the previous finding and
point to the existence of a specific eddy flow. Altimeter derived variance ellipses inshore
of the shelf-rise base in the northeastern Gulf are largely aligned along isobaths, in phase
with the southeastward mean flow. The large variance ellipses along the shelf-rise base
are oriented partly cross-shore, and more than 45 out of phase with the mean flow.
Orientation of the largest variance ellipses (located on either side of DeSoto canyon) are
such that they could arise from flows associated with an eddy in DeSoto canyon that
impinges against the shelf-rise. Drifter data often indicates the existence of a warm core
ring in the DeSoto canyon area. It is likely that the regions of pronounced eddy energy
correspond to regions where cross shelf-rise flows are most significant. This idea is
explored below.
5. Cross Shelf-Rise Drifter Movement
Variance ellipses computed from the entire SCULP drifter data set are illustrated
in Figure 8. Although much noisier than the variance ellipse field computed from SSH
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anomaly data, the drifter derived variance ellipses suggest similar findings. The region of
largest variance exists near the Florida Straits and is associated with variations in the
Loop current outflow. Regions of large eddy energy also exist south of the Mississippi
outflow, south of the Texas-Louisiana border, and in the northwest and northeast corners
of the Gulf. These are exactly the regions of large variance found in the altimetry data,
with exception of the Yucatan Straits that was not sampled during SCULP. The variance
computed from drifter data is roughly 40% larger (on average) than that from sea-surface
height data. High frequency energy is aliased in the CCAR altimetry data. Variance
ellipses determined from drifter and altimetry data over the shelf-rise display similar
orientations in the northeastern and northwestern gulf. Ellipses from altimeter data are
near 45 out of phase with ellipses from drifter data in the regions south of the
Mississippi outflow and south of the Texas-Louisiana border. Variance ellipses for both
the drifter and altimetry data are mainly oriented across bathymetry in these regions
despite the phase difference.
Cross-isobath flow can be simply and accurately assessed with a statistical analysis of
Lagrangian drifter tracks. Table 1 indicates the number of drifters that cross the shelfbreak (200 m isobath) and the shelf-rise base (2000 m isobath) in both the offshore and
onshore directions. Crossings are counted in three different ways. First, all drifters
crossing a given isobath in a given direction are counted. Second, only those drifters that
do not re-cross the isobath for at least 14 days are counted. Third, only those drifters that
never re-cross the isobath are counted. Drifters that repeatedly cross the shelf-break or
shelf-rise base on daily time-scales and drifters that move offshore and onshore following
synoptic scale features are isolated in this scheme.
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Of the 719 drifters deployed on the continental shelf, roughly half move into waters
deeper than 200 m (Table 1a). Of those drifters that move off the shelf, ~70% don’t recross the shelf-break for at least 14 days, and nearly 60% stay offshore. Statistics for the
2000 m isobath crossings are similar. Just under half of the drifters that move off the
continental shelf cross the shelf-rise and reach waters deeper than 2000 m. Almost 70%
of the drifters that move offshore of the shelf-rise base (2000 m) don’t re-cross the 2000
m isobath for at least 14 days, and ~50% never re-cross. These statistics indicate a
moderate propensity for cross-shore flows. Water parcels that move offshore generally
remain there. However, re-crossings after 14 days suggest that currents can remove
drifters from the shelf and subsequently replace them. Finite drifter lives impose a lower
limit on the number of re-crossings after 14 days, as drifters can “die” while en route
back across an isobath.
Counts of onshore drifter crossings computed in the same fashion are given in Table
1b. Roughly 60% (76%) of the drifters offshore of the shelf-break (shelf-rise base) move
onshore into shelf (shelf-rise) waters. Of the drifters that cross the 200 m isobath in the
onshore direction ~72% stay in shelf waters for at least 14 days and ~60% remain in shelf
waters indefinitely. Statistics for onshore drifter movement across the 2000 m isobath are
similar. Roughly 76% of the drifters that move onshore of the shelf-rise base stay
onshore for at least 14 days and ~64% stay indefinitely. The large fraction of drifters that
move onshore is further indicative of strong cross shelf-rise flows in the northern Gulf.
The fraction of drifters that move onshore and then return offshore after 14 days is
remarkably similar to the offshore-then-onshore case, lending support to the existence of
eddy flows that can move water across bathymetry in both directions.
20
Drifters that cross the shelf-rise base in the offshore direction do so mainly in the
northwest corner of the Gulf, and in a region just south of the Florida Panhandle (Figure
9). Offshore crossings for the 1000, 500, and 200 m isobaths show a slight increase in
the fraction of drifter crossings south of the Panhandle, and along the west Texas shelf,
with decreased depth (figures not shown). In contrast, shelf-break crossings in the
onshore direction occur primarily in the northeast Gulf. The fraction of onshore shelfbreak crossings is also significant south of the Louisiana peninsula (~15%) and in the
northwest Gulf (8%). The region of pronounced onshore crossings in the northeast Gulf
displays a westward migration to the DeSoto canyon area, and a decrease, as deeper
isobath crossings (500, 1000, and 2000 m) are considered (figures not shown). The
distribution of cross-isobath drifter movement clearly illustrates that drifters do not just
percolate across the shelf-rise, but rather are advected cross-shore in preferential regions.
Regions characterized by a large number of drifters moving across isobaths could
easily be biased by the spatial distribution of drifters. For example, if cross-shore flow
were completely homogeneous in space and time, cross isobath drifter counts would
depend on the number of drifters locally available. Such a bias exists, but is not
significant here. Drifter densities are similar over the shelf-rise in the northwest and
northeast Gulf, with ¼ bins containing ~25 drifter-days of data (Figure 1). Quarterdegree bins on the shelf-rise between deployment regions contain closer to 15 drifterdays of data (Figure 1). Thus, the fraction of shelf-rise crossings occurring in this area is
likely underestimated. A hypothetical doubling of drifter density in the under-sampled
areas suggests only one noteworthy change in the spatial analysis of cross shelf-rise
drifter movement. That is, significant cross shelf-rise flow may occur in a region south
21
of the Louisiana Peninsula.
Direct evidence from Lagrangian surface drifters indicates that cross shelf-rise
flows are a significant component of ocean circulation in the Gulf. The locations of
largest variance correspond with regions where a significant fraction of cross-shore
drifter activity occurs. This spatial agreement points to variations about the mean flow in
promoting cross shelf-rise flows. The cross-isobath transport is due largely to Gulf
eddies that are observed to be semi-permanent or act on synoptic time-scales.
6. Discussion
6.1 Comparison for flows associated with two particular eddies
The CCAR gridded sea-surface height anomaly data does not alone provide a
complete picture of ocean circulation in the Gulf, and is not expected to do so. However,
the altimetry data is useful for identifying synoptic scale eddies that often exist near the
continental shelf-rise and contribute to the overall circulation in the Gulf.
“Instantaneous” images of remotely sensed SSH anomaly data and velocity vectors
from drifter data directly illustrate the kind of eddy driven flows that exist on the shelfrise (Figure 10). A large eddy was present in the Desoto Canyon area of the northeastern
Gulf during most of the SCULP period, although its size and exact location varied
synoptically (Figure 10a). The correlation between velocities from the altimetry and
drifter data in the region of the large eddy is 0.70. The slope of the mean regression line
is also ~0.70. Although the CCAR gridded SSH anomaly data does not provide an exact
quantification of currents, it is clearly useful in identifying the general flow pattern
associated with the Desoto Canyon eddy that extends from the deep Gulf onto the shelf-
22
rise.
Lack of agreement between altimeter and drifter derived velocities on the continental
shelf is illustrated with the Gulf eddy located just west of Tampa Bay (Figure 10a).
Although strong southward currents along the inshore edge of the eddy appear well
correlated (r=0.74), this is just by chance. Drifters continue southward in a coastal jet
and do not follow dynamic height contours around the warm ring evident in the altimetry
data. We have previously pointed out the poor overall correlation between velocities
from drifter and SSH data on the continental shelf. This analysis directly illustrates that
eddies appearing in remotely sensed dynamic height imagery over the continental shelf
are not necessarily part of the actual flow field.
A cold eddy over the shelf-rise in the northwestern Gulf and an adjacent warm feature
are illustrated with coincident drifter derived velocity observations in Figure 10b. Cold
eddies exist in the northwestern Gulf during each of the SCULP deployment periods.
The correlation between velocities from altimetry and drifters is 0.79 and the slope of the
mean regression line is 0.86. Velocity vectors determined from drifters follow dynamic
height contours nicely, further illustrating the utility of CCAR gridded sea-surface height
data in providing a real time description of eddy driven flows over the shelf-rise.
6.2. Eddy forced circulation in the Gulf
Time dependent motions in the ocean can rectify the transfer of momentum and
vorticity to the mean flow. This transfer is expressed in the Reynolds’ averaged
momentum equations
1
1

(ξ  f ) kˆ  u  kˆ  (ξ u )  - ( g   u   u   u   u ) 
2
2
z
23
(1)
where u is velocity expressed as a mean (overbar) and fluctuating (prime) component, 
is vorticity (also expressed with a mean and fluctuating components), f is the Coriolis
parameter,  is sea-surface height, g is gravitational acceleration,  is the wind stress, z is
depth, and k̂ is the unit vector in the vertical. The mean vorticity equation can be
obtained by taking the curl of Equation 1, which eliminates the Bernoulli function and
gives

kˆ  (  (  f ) kˆ  u)  kˆ   - kˆ   u)
z
(2)
Equation 1 indicates that the transfer of momentum to the mean flow by eddies exists
both through a Bernoulli function (term proportional to u’u’) as well as through
covariations in  and u (term proportional to ’u’). In our view, Equation 1 is an
expression for sea level given both the mean and time dependent velocities. Equation 2
illustrates how eddies transfer vorticity to the mean flow.
Traditionally, the vertical convergence of wind stress curl is believed to be the
primary driver of the mean circulation in the Gulf beyond the region of the Loop current
(e.g. Blaha and Sturges 1981, Sturges 1993). To better understand the role of eddies in
Gulf circulation we examine the fluctuating terms in Equation 1 to determine how eddies
influence the sea-level setup. The influence of Gulf eddies on the mean vorticity is then
compared with that of the vertical wind stress curl convergence (terms on the right hand
side of Equation 2).
Mean values of eddy momentum convergence over the shelf-rise computed from six
years of sea-surface height anomaly data are shown in Figure 11. Regions characterized
by large values of eddy momentum convergence correspond with regions of large
24
velocity variance and significant cross-shore drifter movement (Figures 7-9). Eddy
momentum convergence values are greatest near the Yucatan and Florida Straits where
strong flows in and out of the Gulf exist. Values are also large south of the Mississippi
outflow, south of the Texas-Louisiana border and in the Gulf’s northwest corner. In
general, eddy momentum is being put into the Gulf and onto the Gulf’s northern shelf.
The absolute value of sea-level gradient generated by eddy momentum transfer
(Equation 1) is illustrated for the entire Gulf in Figure 12. The maximum value of this
gradient is ~5*10-8, or ~0.5 cm per 100 km, and exists in the region of the Loop current.
Such a gradient could influence the mean sea level by ~3 cm across the entire Loop
current. A 3 cm change corresponds to near 4% of the mean sea-surface height for the
Loop current. Beyond the Loop current region, the maximum absolute value of the eddy
induced sea level gradient is ~2*10-8. This gradient suggests a sea level influence of only
~1.5 cm across the entire western Gulf. Our calculations indicate that Gulf eddies do set
up sea level gradients, but that these gradients are small. Eddy momentum is more likely
to directly influence the mean flow. This direct eddy forcing will now be quantified.
The eddy vorticity flux to the mean (Figure 13) shows the strongest fluxes to be
associated with the Loop current. Near the edge of the Loop current eddies act to reduce
positive vorticity. Near the center of the Loop current positive vorticity is being gained.
Another noticeable feature in Figure 13 is the band of vorticity gain that follows the
shelf-rise base (2000 m contour) in the western Gulf. The mean vorticity flux computed
over the western Gulf region (22 - 26; 262 - 270) where depths are between 1900 and
2300 m is -6.3*10-14 sec-2. The true magnitude of this estimate may be near 50% greater
as surface velocities from remotely sensed altimeter data capture only ~67% of the drifter
25
energy in the northwestern Gulf (Figure 5). The standard error associated with the mean
is 2.2*10-14 sec-2, an upper bound computed with the assumption that only 4 Gulf eddies
exist within the region of interest giving only 4 independent observations. Additional
error may exist due to poor altimeter coverage in the region. By comparison, the mean
eddy vorticity flux and associated standard error computed for the western Gulf (22 26; 262 - 270) where depths are greater than 2500 m are an order of magnitude smaller
(and of opposite sign). The large negative vorticity flux along the shelf-rise base
suggests that Gulf eddies enhance positive vorticity over the shelf-rise in the western
Gulf. Positive vorticity is also being added to the shelf-rise in isolated regions south of
the Texas-Louisiana border and in the DeSoto Canyon area. Negative vorticity is being
added to the shelf-rise primarily in the northeastern Gulf. In summary, altimetry data
suggests pronounced regions of eddy vorticity flux exist along the edge of the Loop
current and over the shelf-rise base in the western Gulf. It remains to compare the role of
eddies with the wind stress curl in forcing Gulf flows.
Wind stress forcing is estimated from the Comprehensive Ocean-Atmosphere
Data Set (COADS) climatological mean surface winds (Woodruff et al. 1987). The
COADS winds employed here are based on observations from 1950 through 1993,
primarily by ships of opportunity. Mean COADS winds on a 2 by 2 grid are used to
compute wind stress following the standard bulk formula with a wind speed dependent
drag coefficient (Large and Pond 1981). The wind induced vorticity flux is then
calculated as   ( z) where a 50 m surface mixed layer is assumed. This surface
stress induced vorticity flux is illustrated in Figure 14. Values are in agreement with the
mean wind stress curl for the period 1990 to 1993 given by Gutierrez de Velasco and
26
Winant (1996). The wind stress curl contributes to anticyclonic vorticity over most of the
Gulf. Wind induced positive vorticity exists only in the southwest and in a small region
in the extreme northeast. Absolute values of the wind forced vorticity flux are mostly
near 4*10-14 sec-2, and reach 8*10-14 sec-2. Wind forced vorticity fluxes are roughly 75%
less in magnitude than eddy driven vorticity fluxes in the Loop current region and along
the shelf-rise base in the western Gulf. Wind and eddy induced vorticity fluxes are much
closer in magnitude (within ~10%) over the remainder of the Gulf.
The above comparison indicates that eddies are at least equally important as surface
stresses in driving Gulf circulation on long timescales. Gulf eddies may play a
significantly larger role than wind stress in forcing circulation over the shelf-rise in the
western Gulf. Thus, Gulf eddy influences must not be neglected in further attempts to
understand and forecast ocean circulation over the shelf-rise in the Gulf of Mexico.
7. Conclusions
Surface velocity statistics computed from drifting buoys provide a comprehensive
view of circulation in the northern Gulf of Mexico. Roughly 775 surface drifters
deployed on the shelf and shelf-rise in the northern Gulf eventually sampled almost the
entire basin. Comparisons between surface velocities determined from satellite altimetry
and drifting buoys indicate that flows offshore of the shelf-break (~200 m) can be
resolved with remotely sensed sea-surface height anomaly data. Comparisons of crossaltimeter track velocity components made locally indicate that correlations generally
increase with distance offshore and are a strong function of the spatial scale over which
sea-surface slope is calculated. Local cross-altimeter track velocities from SSH and
27
drifter data are poorly correlated on the continental shelf where high frequency and small
spatial scale motions not well resolved with altimetry are significant. Over the shelf-rise,
and beyond the base of the shelf-rise break, correlations are statistically significant (at the
95% confidence level) with coefficients near 0.5 and 0.7, respectively. Correlations can
be much worse if the length scale over which sea-surface slope is calculated is not
properly selected.
Sea-surface height anomaly maps for the entire Gulf are computed daily using an
objective analysis procedure. Comparisons between surface velocities from gridded data
give results similar to those for the local cross-track component analysis. Velocities
display statistically significant correlations only offshore of the shelf-break. Correlation
coefficients increase from ~0.56 for the 200 to 1000 m depth range to ~0.63 for depths >
2000 m. Altimeter derived velocities contain near 65% of the energy found in drifter
derived velocities. The comparative analysis indicates that the gridded SSH anomaly
data captures much of the variance in surface currents over the Gulf’s northern shelf-rise
region. The altimeter data can be used to accurately monitor Gulf eddies offshore of the
shelf-break and to provide further information about Gulf circulation.
Velocity variance over the shelf–rise computed from six years of daily gridded SSH
anomaly data shows regions of enhanced eddy energy south of the Mississippi outflow,
south of the Texas-Louisiana border, and in the northwestern and northeastern corners of
the Gulf. These areas characterized by large velocity variance correspond to regions
where drifters are most likely to move across bathymetry. More than half of the drifters
that cross the shelf-rise base do so in the four regions indicated above. Our data suggests
that shelf-rise eddies and cross shelf-rise flows are significant aspects of Gulf circulation.
28
Flows associated with individual eddies can be adequately resolved with remotely sensed
sea-surface height anomaly data. Comparisons between surface velocities from altimetry
and drifter data for two specific eddies located over the shelf-rise give correlation
coefficients ranging from 0.70 to 0.80.
Gulf eddies influence circulation by directly forcing motion, and by setting up sealevel gradients. Calculation of mean eddy momentum convergence from the remotely
sensed SSH anomaly data indicates eddies set up sea-level gradients that reach 0.5 cm per
100 km in the Loop current region, and 0.2 cm per 100 km in the western Gulf. These
sea-level gradients correspond to height influences of ~3 and 1.5 cm across the Loop
current and western Gulf regions, respectively, and near 10% of mean surface heights for
the regions. Calculation of the mean direct eddy vorticity flux to the mean flow indicates
eddies significantly reduce positive vorticity near the edge of the Loop current, and
increase positive vorticity along the shelf rise-base in the western Gulf. The mean
vorticity flux along the shelf-rise in the western gulf due to eddies is 6.3*10-14 sec-2. For
comparison, the mean vorticity flux due to the wind stress curl in the region is 4.0*10-14
sec-2. This comparison suggests eddy vorticity fluxes are greater than wind forced
vorticity fluxes over the shelf-rise base in the western Gulf. Wind and eddy induced
vorticity fluxes are closer in magnitude over the shelf-rise in the northern Gulf. We
conclude that Gulf eddies play a significant role in driving Gulf circulation over the shelfrise and must be considered along with wind forcing. The improved understanding of
ocean circulation obtained through this study will ultimately enhance modeling and
monitoring efforts in the Gulf of Mexico.
29
Acknowledgements. Sharon Lukas and Judy Gaukel provided assistance with data
processing. Discussions with Norman Barth and Sean Kennan were always helpful.
Presentations and conversation at the 31st International Liege Colloquium on Ocean
Hydrodynamics provided information and motivation for completion of this work.
Support has been provided by the Minerals Management Service under grant 136870029.
30
Figure List
Figure 1 - The number of daily averaged surface current observations from Lagrangian
drifters in 0.25 x 0.25 bins. Observations are for the period October, 1993, through
September, 1998. Drifter deployment locations are indicated by squares, diamonds and
stars for SCULP-I, -II, and –III, respectively. Bathymetric contours are shown at 200 and
2000 m.
Figure 2 - Tracks for each of the drifters (~775) deployed during the SCULP field
program. Tracks are from daily averaged values of position. The red, green, and blue
tracks are for drifters deployed during SCULP-I, -II, and –III, respectively.
Figure 3 - Correlation between cross-altimeter track velocities determined from T/P and
SCULP data as a function of window width and ocean depth for the descending (3a) and
ascending (3b) altimeter tracks. Window width is the length of the altimeter track over
which sea-surface height slope is determined. Correlations are computed with data on the
continental shelf (0-200 m), the inshore portion of the shelf-rise (200-1000 m), the
offshore portion of the shelf-rise (1000-2000 m), and beyond the self-rise base (> 2000
m). Drifter velocities are from buoys that lie within ¼ of an altimeter track and within 1
day of a pass.
Figure 4 - Correlation between cross-altimeter track velocities determined from T/P and
SCULP data as a function of space. T/P velocities are calculated from a sea-surface
height slope over ~125 km. Drifter velocities are from buoys that lie within ¼ of an
31
altimeter track and within 1 day of a pass.
Figure 5 - Comparison of current velocities determined from gridded drifter and SSH
anomaly data for the depth ranges (a) 0 – 200 m, (b) 200 – 1000 m, (c) 1000 – 2000 m,
and (d) 2000 – 5000 m. Both the u (eastward) and v (northward) velocity components
are shown for latitudes > 24 and longitudes <= 270. Drifter derived velocities are 15day averages centered on the 8th and 23rd days of each month. Altimeter derived
velocities are from the CCAR gridded data for the 8th and 23rd of each month. Dashed
lines show linear regressions of drifter velocities on altimeter velocities, and visa-versa,
fit in a least-squares sense. The solid line shows the average of the two dashed regression
lines. Correlation coefficients are 0.17, 0.62, 0.64, and 0.70 for (a) through (d),
respectively.
Figure 6 - Same as Figure 5 for latitudes > 24 and longitudes > 270. Correlation
coefficients are 0.24, 0.51, 0.55, and 0.56 for (a) through (d), respectively.
Figure 7 - Velocity variance ellipses computed from altimeter derived velocities.
Variance is computed from daily values (1992 through 1998) in ¼ by ¼ bins located on
the shelf-rise. Bathymetric contours are shown at 200 and 2000 m.
Figure 8 - Velocity variance ellipses computed from drifter velocities. Variance is
computed from daily averaged values in ¼ by ¼ bins located on the shelf-rise. Variance
ellipses are shown only for those bins with more than 10 drifter-days of data.
32
Bathymetric contours are shown at 200 and 2000 m.
Figure 9 - The percentage of the total number of drifters that cross the 2000 m (200 m)
isobath in the offshore (onshore) direction and do not re-cross in the opposite direction
for at least 14 days. Offshore and onshore crossings are shown along the 2000 and 200 m
isobaths, respectively. Roughly 40% of the offshore crossings occur between ~265 and
268, and ~40% of the onshore crossings occur between 272.5 and 275.5. The display
of whole fractions for bins with values > 1% prevents summing to 100.
Figure 10a - Sea-surface height anomaly contours from the CCAR gridded altimetry data
(for 22 August 1998) and velocity vectors from drifters showing the representation of
surface currents near two eddies in the northeastern Gulf. Vectors are 15-day averages
centered on 22 August 1998. The 200 and 2000 m isobaths are shown. The coefficient
of variation (r2) between velocities from drifter and altimeter data is 0.49 in the region of
the large eddy where agreement is evident.
Figure 10b - Same as Figure 10a for a cold eddy and adjacent warm feature in the
northwestern Gulf. Sea-surface height anomaly data is for 15 December 1993. Vectors
are 29-day averages centered on 15 December. The time averaging period was selected
to show vectors around the entire cold ring. The coefficient of variation (r2) between
velocities from drifter and altimeter data is 0.63.
Figure 11 - Mean eddy momentum convergence (u  u) computed from 6 years of
33
sea-surface height anomaly data (1/93 – 12/98).
Figure 12 - The absolute contribution of eddy momentum convergence to the sea-surface
height gradient. Values are calculated as | (u  u) | /g. The eddy momentum
convergence used in the calculation is illustrated in Figure 11.
Figure 13 - The mean flux of eddy generated vorticity into the mean circulation. Values
are computed from six years of remotely sensed sea-surface height anomaly data on a ¼
by ¼ grid.
Figure 14 - The mean flux of wind stress curl generated vorticity into the mean
circulation. Values are computed from COADS climatological winds on a 2 x 2 grid.
An upper ocean mixed layer depth of 50 m is assumed.
34
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38
Table 1. Cross-shelf drifter counts in the offshore and onshore directions.
200 m
2000 m
total crossings
382
171
14-day crossings
273
113
no-return crossings
224
86
Number of drifting buoys that cross the 200 and 2000 m isobaths in the offshore
direction. Total possible crossings are 778 and 719 drifters for the 200 and 2000 m
isobaths, respectively.
200 m
2000 m
total crossings
267
133
14-day crossings
194
101
no-return crossings
158
85
Number of drifting buoys that cross the 200 and 2000 m isobaths in the onshore direction.
Total possible crossings are 441 and 175 drifters for the 200 and 2000 m isobaths,
respectively.
39
------------------------- THIS IS STUFF THAT WAS CHANGED ----------------------
We will now make a direct comparison of the terms on the RHS of expression 2. The
data necessary to accurately determine the contribution of Gulf eddies to the mean flow,
is only recently available. Here we use the complete CCAR altimetry data set to quantify
the mean eddy momentum convergence over the shelf-rise, to identify that portion of the
eddy vorticity that contributes to direct forcing of the mean flow, and to compare it with
the contribution of the wind stress curl. The analysis is performed using a scheme that
requires only knowledge of the fluctuating velocity components.
The shallow water momentum equations with wind forcing provide the starting point.
Written in vector form after Reynolds averaging, they are
du
 u   u  u   u   f  ( u  u ) = - g  
dt
(1)
where u is velocity expressed as a mean and fluctuating component, f is the Coriolis
parameter,  is sea-surface height,  is the wind stress, t is time, and bold symbols
represent vectors. Expressing the fluctuating advective component of velocity in terms of
vorticity and a potential using the familiar vector identity
1
u  u =   u   ( u 2 )
2
(2)
with  defined as the vorticity vector, and retaining only vorticity components in the
vertical (k direction) gives an equation where the rotational and irrotational terms
involving perturbation velocities are isolated
du
1
 - u   u - f  u - k  (  u) - (g  u 2 )  
dt
2
40
(3)
Finally, taking the curl of Equation 3 eliminates potential terms leaving an equation for
the contribution of eddies to the circulation, or
d
 -   ( u   u ) -   ( f  u ) - k    k  (   u )    
dt
(4)
The left-hand side of Equation 2 gives the total eddy momentum convergence when
computed with velocity values from remotely sensed sea-surface height anomaly data.
The two terms on the right-hand side of Equation 2 represent the direct contribution
of eddies to circulation and the contribution to a potential, or Bernoulli function,
respectively. Mean values of each of these terms computed from six years of sea-surface
height anomaly data are shown in Figures 11b and c. Gulf eddies act to move the mean
circulation onto the shelf-rise in the region north of ~25. Off the Yucatan shelf, gulf
eddies are acting to combine the mean flow over the shelf-rise with the branch of the
Loop current extending into the Gulf (Figure 11b). The dynamic and potential terms in
Equation 2 are of the same order and act in mostly opposite directions. Figure 11c shows
(again) the enhanced regions of eddy energy that exists on the shelf-rise south of the
Mississippi outflow, south of the Texas-Louisiana border, and in the northwestern region.
Eddy energy is also large near the Yucatan and Florida Straits where the Loop current
enters and exits the Gulf, respectively. Eddy energy is generally greater over the shelfrise than offshore of the shelf-rise base, and eddies likely cause a meandering mean flow
over the northern shelf-rise.
Dividing the potential term in Equation 2 by gravitational acceleration enables the
potential contribution to be expressed in terms of sea-surface height. Figure 12 shows
that Gulf eddies themselves are responsible for generating sea-surface height
41
perturbations that are ~10% of typical surface height anomalies. The greatest
contribution to sea-surface height (up to ~1 cm) is in the region of the Loop current. The
regions over the shelf-rise in the northern Gulf where eddies contribute the most to seasurface height changes are the same as those where eddy momentum convergence is
greatest (south of Mississippi outflow, south of Texas-Louisiana border, northwest
corner).
The mean eddy contribution to Gulf circulation is illustrated in Figure 13. Although a
noisy field, discernable patterns do exist. The largest contribution of eddies to the change
in mean circulation is along the edge of the Loop current where eddies act to reduce
positive vorticity. Near the center of the Loop current positive vorticity is being gained.
Perhaps the most noticeable feature in Figure 13 is the band of vorticity gain that follows
the shelf-rise base in the western Gulf. This suggests that Gulf eddies are enhancing
positive vorticity on the shelf-rise in this regions. Positive vorticity is also being added to
the shelf-rise in the regions south of the Texas-Louisiana border and in the DeSoto
Canyon area. Negative vorticity is being added to the shelf-rise region primarily in two
small regions in the northeastern Gulf. In general, Gulf eddies are acting to increase
vorticity on the shelf-rise.
The relative influence of eddies and wind-stress curl on Gulf circulation are
determined by scaling arguments on their respective terms. The influence of eddies is
given in Equation 4 as
k    k  (   u)
(5)
42
Typical values of vorticity and velocity perturbations in the Gulf’s shelf-rise region are
10-7 sec-1 and 10 cm sec-1, respectively. Plugging these values into Equation 5 and
assuming a length scale of 100 km gives values of order 10-13 sec-2 (Figure 13).
The wind-stress curl influence (also given in Equation 4) is simply    . Typical
wind-stress values for the Gulf are near 0.5 cm2 sec-2. Assuming horizontal and vertical
length scales of 300 km and 15 m, respectively, also gives values of order 10-13 sec-2 as
estimates for changes in circulation due to the wind-stress curl. This indicates that Gulf
eddies are equally important in driving circulation over the shelf-rise as the wind-stress
curl. If waters over the shelf-rise are assumed barotropic, thus suggesting that eddy
energy extends to roughly 1000 m, then the role of eddies on circulation could be much
larger than wind-stress curl influences which act only in the upper layer. Thus Gulf
eddies play a significant role in driving circulation over the shelf-rise and must not be
neglected in further attempts to understand and forecast ocean circulation in the Gulf of
Mexico.
The contributions of the mean eddy momentum convergence (Figure 11a) directly
into circulation and into a potential are shown in Figures 11b and c, respectively. Gulf
eddies act to move the mean circulation onto the shelf-rise in the region north of ~25.
Off the Yucatan shelf, gulf eddies are acting to combine the mean flow over the shelf-rise
with the branch of the Loop current extending into the Gulf (Figure 11b). The dynamic
and potential contributions are of the same order and act in mostly opposite directions.
Figure 11c shows (again) the enhanced regions of eddy energy that exists on the shelfrise south of the Mississippi outflow, south of the Texas-Louisiana border, and in the
northwestern region. Eddy energy is generally greater over the shelf-rise than offshore of
43
the shelf-rise base, and eddies likely contribute to a meandering mean flow over the
northern shelf-rise.
Figure 11 - Mean eddy momentum convergence computed from 6 years of sea-surface
height anomaly data (1/93 – 12/98). Figure 11a shows the total convergence (u  u) ,
11b shows the component that goes directly into circulation (  u ) , and 11c shows the
1
potential component ( u   u ).
2
44