A Two-Dimensional Response to a Tropical Storm
on the Gulf of Mexico Shelf
J. Carter Ohlmann and P. Peter Niiler
Scripps Institution of Oceanography,
University of California, San Diego
Submitted to: Journal of Marine Systems; Proceedings of the 31st International
Colloquium on Ocean Hydrodynamics Special Issue
Revision #1: May 6, 2000
Abstract
Surface current data from drifting buoys and remotely sensed wind data recorded over
the continental shelf in the northeastern Gulf of Mexico during the passage of tropical
storm Josephine in October, 1996, are examined. Drifter data show the existence of a
strong surface jet (velocities reaching 1 m s-1) that moves up the west Florida shelf and
westward along the Louisiana-Texas shelf, and lasts for near one week. The coastal jet
occurs during an intense synoptic scale wind event where wind speeds reach 15 m s-1. A
simple force balance and statistical analysis are performed to assess the role of strong
wind forcing. The primary balance shows an Ekman-type current. The role of local
acceleration is greatest when winds are directed along bathymetry. A simple twodimensional strongly forced shelf response model developed from the linear steady-state
momentum equations also indicates larger along-shore currents due to both Ekman-type
forcing by cross-shore winds and a cross-shore pressure gradient arising from
conservation of mass. Model parameters fit empirically are within 15% of theoretical
values. The simple model explains 30 and 46% of the variance in the observed alongshore and cross-shore surface currents, respectively.
1. Introduction
The Gulf of Mexico (Gulf) is rich with mineral resources, such as oil and natural gas.
Gulf circulation models are used to manage these resources by forecasting their
movement in the case of a spill or leak. Observational studies are necessary to improve
the understanding of ocean circulation in the Gulf and for validation and constant
refinement of Gulf circulation models. The documentation of circulation during extreme
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forcing conditions is of particular interest as data during these times is, by definition,
limited.
Wind stress plays a primary role in forcing ocean circulation over continental shelves.
Observational studies by Marmorino (1982) and Cragg et al. (1983) show coherence
among atmospheric pressure, wind stress, and sea-level over the west Florida continental
shelf on synoptic scales. Mitchum and Sturges (1982) indicate that currents and sea-level
are coherent with along-shore, but not cross-shore, wind stress. These and other
observational studies of the Gulf’s response to wind forcing over the continental shelf
include data collected during periods of strong synoptic wind events. However, no recent
studies focusing specifically on intense wind forcing over the Gulf’s continental shelf are
known to exist. Tropical storm winds may provide a mechanism for circulating water
great distances in short periods of time. Knowledge of the response to intense wind
forcing is an important component of understanding and forecasting Gulf circulation as
an average of 5 tropical storms pass through the basin each year.
In this paper, in-situ drifter data and remotely-sensed wind data recorded over the
continental shelf in the northeast Gulf during the passage of tropical storm Josephine in
October, 1996 are presented and analyzed to investigate relationships between intense
wind stress forcing and surface currents. Results show the strongest surface currents are
oriented along bathymetry, with cross isobath surface flows also occurring. This suggests
that both geostrophic and Ekman components are important. Empirical coefficients for a
simple two-dimensional shelf response model are within 15% of theoretical values. The
model explains a significant portion of variance in the surface currents for the continental
shelf region.
3
2. Data and Methods
2.1 Drifter data
Observations of near-surface currents were made with drifting buoys in the northern
Gulf of Mexico as part of the Surface Current and Lagrangian-drift Program (SCULP).
The drifters used in SCULP 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 small surface floats. The SCULP drifters are similar in design to those used during
the U.S. Coastal Dynamics Experiment (CODE), shown to exhibit slip less than 3 cm s-1
in west coast upwelling wind conditions (Davis 1985). Drifters for the second portion of
SCULP (hereafter referred to as SCULP-II) were initially deployed at 26 stations within a
400 by 150 km rectangle on the northwest Florida shelf in February 1996. The 26-station
grid was reinitialized every two weeks for nearly a year.
Drifter positions were recorded at various times throughout each day, for roughly 90
days from the time of deployment, by service ARGOS. Position data 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 calculating an analytic correlation function for each day
from the Fourier transform of a model spectrum obtained from ten days of unequally
spaced observations centered on the day of interest (Van Meurs, 1995). Each correlation
function was then used to produce an interpolated location time-series. Interpolated
values were sub-sampled every three hours and daily averaged velocities calculated.
4
Tidal and inertial signals are effectively removed in daily averages. More detailed
descriptions of SCULP and the SCULP-II data are given by Ohlmann et al. (in review).
Drifter tracks over the Gulf’s continental shelf during the period September 29 to
October 14, 1996 are illustrated in Figure 1. Drifters generally move counterclockwise
along the Florida shelf following bathymetry during the first four-days of the period
(Sept. 29 through Oct. 2). Most drifters move less than 80 km during the four-day period,
corresponding to average surface velocities less than 23 cm s-1. Drifters show westward
movement over the shelf, mostly along bathymetry, during the second four-day interval.
However, drifters on the Gulf’s northern shelf travel up to 250 km in four days, requiring
average velocities near 70 cm s-1. This suggests a threefold increase in average surface
velocity, presumably due to winds associated with the passage of tropical storm
Josephine. Large westward drift along bathymetry continues for drifters on the Florida
panhandle, Texas, and Louisiana shelves during the third four-day period. Northward
moving drifters on the west Florida shelf show velocity increases and a reversal in
direction, becoming southward. During the final four-day period (October 11 - 14),
drifters on the northern shelf resume typical velocities near 15 cm s-1, continuing their
counterclockwise path along bathymetry. Drifters on the west Florida shelf reverse
direction and move southward along bathymetry at near the same speed. In summary, the
effect of Josephine is to move drifters from as far as the eastern edge of the Florida
Panhandle shelf and to deposit them on the Louisiana-Texas shelf over the course of a
week.
Surface current vectors derived from the SCULP-II drifter data are shown with wind
vectors in Figure 2. On October 5, 1996, surface currents in the northeastern Gulf are
5
moving mostly westward. This results in cross-shore currents over the west Florida shelf
and along-shore currents on the northern shelf. Cross-shore velocities are only a few cm
s-1, whereas along-shore velocities reach nearly 1 m s-1 west of the Mississippi outflow.
On October 6, surface currents over the west Florida shelf increase (to near 10 cm s-1)
and become northward, aligned with bathymetry. Currents over the Gulf’s northern shelf
remain westward along bathymetry and show a slight velocity increase. Current speeds
begin to decrease on October 8 following the passage of Josephine. Finally, currents in
the northeastern Gulf become southeastward along bathymetry at typical speeds of a few
cm s-1 on October 10 (not shown).
2.2 Wind data
Wind data used in this study are from the NASA Scatterometer (NSCAT), a Ku band
radar that measures sea-surface roughness used to estimate wind speed and direction.
NSCAT was launched on the Japanese Advanced Earth Observing System (ADEOS)
satellite and recorded data globally (under most all weather conditions) from September
1996 through June 1997. Measurements of backscattered energy and the determination
of wind velocity and stress vectors every 12 hours on a 0.5 by 0.5 grid are described by
Naderi et al. (1991) and Liu et al. (1998). Daily wind stress values collocated with
surface current data are determined by linear interpolation in space, and time averaging.
The presence of NSCAT offers a unique space-time resolution of this tropical storm not
given by standard operational surface sensors.
Wind vectors for the Gulf during the passage of tropical storm Josephine are
illustrated in Figure 2. The cyclonic wind pattern associated with Josephine (centered
6
near 94 W, 24 N) first becomes clearly evident on October 5. Winds in the northern
and eastern portions of the Gulf are mostly westward with velocities near 10 m s-1 at this
time. The cyclone moves slightly to the east-northeast on October 6. Winds in the
northeastern Gulf remain westward with velocities mostly near 10 m s-1. Winds over the
southwest Florida shelf become more northward and winds in the northeast corner of the
Gulf become more southward. On October 7, the center of tropical storm Josephine
moves into the northeastern Gulf. Winds on the northern shelf become more southward
and winds on much of the west Florida shelf become northwestward. Velocities remain
between 10 and 15 m s-1 over most of the northern Gulf. Finally, on October 8, the center
of Josephine is no longer evident in the Gulf. Winds over most of the basin are now
southward except in the southeast Gulf where winds turn and become directed toward the
northeast. Decreased velocities are now evident in the western Gulf as Josephine’s
influence leaves the region.
3. Discussion
3.1 Dynamic balance
The surface circulation momentum balance over the continental shelf can be
described accurately with
du
  x
 fv  - g

dt
x  z
,
(1a)
dv
  y
,
 fu  - g

dt
y  z
(1b)
where u and v are velocity components in the x and y directions, respectively, t is time, f
is the Coriolis parameter, g is gravitational acceleration,  is sea-surface height, x and y
7
are the x and y turbulent stress components, respectively, at the sea-surface,  is density,
and (d/dt) is the rate of change following drifter motion. Here, daily average surface
current and wind stress components collocated in space and time are used with linear
regression analysis to investigate the dynamic balance given above. The assumption is

that (  z ) is proportional to the surface stress 0. Local downwind acceleration terms
in Equation 1 are computed as a first difference. Sea-level gradient terms are, for the
moment, assumed negligible. Strong correlations between the sum of terms on the lefthand-side of Equation 1 and wind stress terms support this assumption as long as the sealevel itself is not a strong function of local winds. As we show later, this is not the case.
An initial investigation into the dynamic balance for the northeast Gulf during
tropical storm Josephine shows a strong spatial dependence in relationships between the
wind stress and local acceleration terms, and the wind stress and Coriolis terms. The
spatial dependency is presumably due to the curved coastline in the northeast Gulf. The
along-shore and cross-shore wind components for a large-scale spatially uniform wind
field change dramatically from the west Florida shelf (oriented north-south) to Florida
panhandle shelf (oriented east-west). The analysis is thus performed for two distinct
regions, that to the west of 87W where bathymetry is oriented mainly east-west, and that
to the east of 87W where bathymetry is oriented mainly north-south. Winds are
primarily alongshore to the west of 87W (on the northern shelf) and cross-shore to the
east of 87W (on the west Florida shelf). We discuss the forcing and response in an
along-shore - cross-shore coordinate system, with the positive along-shore component in
the direction where shallow water is to the left, and the positive cross-shore component in
the onshore direction.
8
As a first step in this analysis the magnitude of the terms on the left-hand-side of
Equation 1 are compared to identify how wind stress forcing during the passage of
tropical storm Josephine is rectified in ocean circulation (Figure 3). This comparison also
gives information about how the orientation of the wind, relative to bathymetry,
influences the ocean’s response to its forcing. The first result is that Coriolis terms are an
order of magnitude larger than the local acceleration terms, regardless of how the
coordinate system is oriented. This suggests that the wind forcing associated with
Josephine gives rise primarily to equilibriated flows.
Having established the relative roles of the downwind and Coriolis acceleration terms
in Equation 1, statistical relationships with the wind-stress terms are determined. Linear
regressions between the wind stress, and acceleration terms are illustrated in Figures 4
and 5 for the west Florida and northern Gulf shelves, respectively. Strong correlations (r2
= 0.96) exist between the cross-shore component of wind stress and both the local
acceleration and Coriolis terms for the west Florida shelf region (Figures 4b,d).
However, the slope for the cross-shore wind stress vs. local acceleration regression is –
0.02 cm2 kg-1, whereas the slope for the cross-shore wind stress vs. Coriolis term
regression is 0.72 cm2 kg-1. A strong correlation (r2=0.90) also exists between the alongshore wind stress and the downwind acceleration (Figure 4c). There is no relationship
(r2=0.00) between along-shore wind stress and the cross-shore Coriolis term (Figure 4a).
This analysis indicates that strong winds in the eastern Gulf associated with Josephine
primarily drive along-shore currents, regardless of the wind direction. The primary
balance demonstrates an Ekman-type current for cross-shore winds. Along-shore winds
9
set up along-shore acceleration, although this response is much weaker than that for
cross-shore wind forcing.
Linear regressions for wind stress forcing and the ocean’s dynamic response over the
Gulf’s northern shelf are illustrated in Figure 5. During tropical storm Josephine the
ocean responds primarily to along-shore wind stress forcing in this region. The strongest
correlation (r2=0.82) is between along-shore wind stress and the Coriolis term (Figure
5a). A strong correlation (r2=0.71) also exists between the along-shore wind stress and
along-shore acceleration terms (Figure 5c). The slope of the former correlation (0.55 cm2
kg-1) is nearly an order of magnitude larger than the latter (0.07 cm2 kg-1). Statistical
relationships with cross-shore wind stress terms are not statistically significant (Figures
4b,d). The primary balance on the Gulf’s northern shelf during Josephine thus appears to
contain elements of an Ekman-like response forced by along-shore winds. The alongshore winds also force along-shore acceleration. Cross-shore winds have comparatively
little influence on shelf currents in this region. The fact that shelf width decreases along
the transition from the west Florida shelf the Northern shelf may partially explain the
reduced correlations over the northern shelf; this due to the role of continuity of mass.
An analysis requiring consideration of the sea-level gradient terms reveals a more
complete picture.
3.2 Two-dimensional shelf response
Consider the linear, steady-state momentum equations with constant vertical
diffusivity to provide the starting point for developing a simple model of strongly forced
shelf response. Because the data show the net accelerations to be smaller than the
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Coriolis force on daily time scales, continental shelf waves do not play an important role
on such scales. We will be modeling the simplest form of an “arrested wave”. The
equations are defined here for the along-shore – cross-shore coordinate system used in
the above analysis (x and y are the along- and cross-shore directions, respectively, x is
positive with shallow water to the left, and y is positive in the onshore direction). The
water depth, h, increases with distance offshore (decreasing y). Density is homogenous.
The existence of a coastal boundary allows for the set-up of horizontal pressure gradients
in the cross-shore direction due to the conservation of mass. Along-shore pressure
gradients are not allowed to occur. The approximate resultant horizontal equations of
motion are then
 fv  
 2u
z 2
(2a)
fu  - g

2v
  2
y
z
(2b)
where  is a viscosity coefficient. Boundary conditions are

u
 x ,
z
at z  0 ;
(3a)

v
 y ,
z
at z  0 ;
(3b)
;
(3c)
uv0
,
at - h(y)
0
 v dz  0
;
(3d)
-h
or, via Equation 2a, the surface stress in the along-shore direction is equal to the bottom
stress in the along-shore direction. A similar linear shelf model is presented and solved
by Csanady (1982). The solution to Equations 2a and 2b, subject to conditions stated in
11
3, can found directly or by decomposing velocity into Ekman and geostrophic responses.
For the case where 2 f << h, or the Ekman layer depth is much shallower than total
water depth, the surface currents (uz=0, vz=0) are:
u z 0 
v z 0 
1
 2f
1
 2f
[3 x   y ]
(4a)
[ y   x ]
(4b)
This simple Ekman-like model shows that uz=0 ~ 3x + y, and vz=0 ~ y - x. Theory
supports the dynamic balance analysis performed above. The larger along-shore current
is due to the role of both the cross- and along-shore wind stress in forcing along-shore
motion in the Ekman sense and the addition of the cross-shore pressure gradient that
results from conservation of mass. In contrast, cross-shore currents are driven almost
solely by Ekman dynamics and are thus expected to be smaller.
The current and wind stress data collected over the Gulf’s northeast continental shelf
near the time of tropical storm Josephine are used to check the theoretical solution given
above. Eight days (October 3 – 10) of data recorded in water depths between 50 and 200
m and multiple regression analysis are used to solve the linear system of equations
u z 0  A x  B y
(5a)
v z 0  C x  D y
(5b)
The regression solution yields coefficients A=1.90, B=0.67, C=-0.63, and D=0.57 m2 s
kg-1. These coefficients are such that A = 2.84B, C = -0.94B, and D = 0.85B.
Empirical values are remarkably close in sign and amplitude to those predicted by theory
(A = 3B, -C = D = B). The model explains 30 and 46% of the variance in the uz=0 and
12
vz=0 velocity components, respectively. The 95% confidence intervals for coefficients
extend ~15% in either direction.
An Ekman depth can be computed for each empirical regression coefficient by
combining Equations 4 and 5 and substituting the Ekman depth equation ( D E  2 f ).
Values of Ekman depth range from 20 m (for coefficient B; 0.67 m2 s kg-1) to 23 m (for
coefficient D; 0.57 m2 s kg-1), suggesting bottom stress is not a first order term in this
analysis. Model coefficients determined with data recorded in water depths between 20
and 200 m (A=3.65*B, C=-1.27*B, and D=1.46*B) are much further from theoretical
values, and the empirical model explains less of the variance in both surface velocity
components, compared with the 50 to 200 m case. This is presumably due to the
increased importance of bottom stress that accompanies the shallower depths considered.
Model coefficients determined with data recorded in water depths between 100 and 200
m are similar to those for the 50 to 200 m case; the explained variance is slightly greater
(31% for uz=0; 50% for vz=0). This analysis shows the simple model holds for the Gulf’s
northeast shelf region during one particularly large wind event. Additional surface
current and wind data over the continental shelf during periods of intense wind forcing
are necessary for further validation
4. Summary
Surface current data were collected from drifting buoys over the Gulf’s eastern and
northern shelves during Fall, 1996, as part of SCULP. The drifter data show a strong
coastal jet that follows bathymetry up the west Florida shelf and westward along the
Gulf’s northern shelf. The jet begins to develop on October 4, and last for near a week.
13
Peak surface velocities reach 1 m s-1 over the Gulf’s northern shelf and 50 cm s-1 over the
west Florida shelf. The observed coastal jet occurs in conjunction with an intense
synoptic scale wind event. The jet transports water from as far as the eastern edge of the
Gulf’s northern shelf to the Louisiana-Texas shelf over the course of a week. Wind
velocity and stress data obtained remotely from NSCAT show the development of
cyclonic flow associated with the evolution of tropical storm Josephine on October 4.
The cyclone is first evident in the western Gulf and moves to the east. Josephine’s winds
reach 15 m s-1. The strongest winds are first directed westward in the north and eastern
Gulf, then become southwestward, and finally southward as Josephine moves across the
basin. The near five days of intense wind forcing from Josephine sets up the strong
coastal jet.
A simple force balance is performed whereby terms in the depth integrated linear
momentum equations are compared for a first-order description of the coastal jet. The
balance is carried out with linear regression analysis in an along-shore – cross-shore
coordinate system. Results differ dramatically between the region east of ~87W, where
the coastline is oriented north-south, and west of ~87W, where the coastline is oriented
east-west, and the region. Results for the west Florida shelf (< 87W) show a strong
relationship (in a statistical sense; r2 > 0.96) between cross-shore wind stress and the
Coriolis term. Results for the Gulf’s northern shelf (>= 87W) show strong relationships
between along-shore wind stress and the Coriolis term, and along-shore wind stress and
local downwind acceleration. The observed coastal jet is forced primarily by offshore
winds over the west Florida shelf and along-shore winds over the Gulf’s northern shelf.
A simple theoretical model for the coastal jet is obtained through a solution to the
14
equilibrated momentum equations in homogenous water with constant diffusion
coefficients. Empirical fits give model parameters that are within 15% of the theoretical
values and explain nearly half of the variance in surface currents. Synoptic scale wind
events such as Josephine provide a specific mechanism for moving water great distances
along the coast, rapidly.
Acknowledgements. Sean Kennan was always willing to listen and provide comments.
Sharon Lukas assisted with data processing. Three anonymous reviewers provided
thoughtful criticism and ideas. Support for this work, and attendance at the 31st
International Liege Colloquium on Ocean Hydrodynamics, was provided by the Minerals
Management Service under grant 136870029.
15
Figure List
Figure 1. Surface drifter tracks for 4-day periods from: a) 29 September through 2
October, b) 3-6 October, c) 7-10 October, and d) 11-14 October 1996. Only drifter tracks
in waters between 20 and 200 meters deep are shown. The set of drifters shown changes
from figure to figure as drifters were continually added and continually “die”. The 200 m
isobath is plotted.
Figure 2. Wind (gray) and surface current (black) velocity vectors during the passage of
tropical storm Josephine. Daily averaged values are shown for: a) 5 October, b) 6
October, c) 7 October, and d) 8 October 1996. Current vectors are derived from the
drifter tracks shown in Figure 1. The 200 m isobath is illustrated.
Figure 3. Local acceleration verses the Coriolis term (Eq. 1) for the along-shore and
cross-shore components. Daily average values for the 8-day period from 3 through 10
October 1996 are illustrated. Shown are: a) along-shore acceleration vs. Coriolis, and b)
cross-shore acceleration vs. Coriolis for the Texas-Louisiana continental shelf region
(longitudes >= 87W). Similar plots for the west Florida shelf region (longitudes <
87W) are shown in c and d.
Figure 4. Linear regressions between wind stress components and Coriolis terms for the
west Florida shelf (longitude < 87W). Shown are: a) along-shore wind stress versus
Coriolis (r2=0.00; slope=0.00 cm2 kg-1), b) cross-shore wind stress and the Coriolis term
(r2=0.96; slope=0.72 cm2 kg-1), c) along-shore wind stress and along-shore acceleration
16
(r2=0.90; slope=0.07 cm2 kg-1), and d) cross-shore wind stress and cross-shore
acceleration (r2=0.96; slope=-0.02 cm2 kg-1). Regressions are determined by binning
daily average values of accelerations for the 8-day period from 3 through 10 October
1996 by corresponding wind-stress values. Wind stress bins are 0.07 N m-2 wide and
begin at –0.4 N m-2. Mean values for each bin are plotted and used for the regressions.
Error bars show the standard deviation associated with the mean acceleration for each
bin. Only data recorded in water depths between 20 and 200 m are included.
Figure 5. Linear regressions between wind stress components and Coriolis terms for the
Gulf’s northern shelf region (longitude >= 87W). Shown are: a) along-shore wind stress
versus Coriolis (r2=0.82; slope=0.55 cm2 kg-1), b) cross-shore wind stress and the Coriolis
term (r2=0.00; slope=0.01 cm2 kg-1), c) along-shore wind stress and along-shore
acceleration (r2=0.71; slope=0.07 cm2 kg-1), and d) cross-shore wind stress and crossshore acceleration (r2=0.13; slope=-0.02 cm2 kg-1). Regressions are determined in the
manner described for Figure 4.
Figure 6. Linear regressions between the along-shore wind stress and the cross-shore
sea-surface height gradient for a) the west Florida shelf region (longitude < 87W;
r2=0.97, slope=0.74*10-5 m2 N-1) and b) the northern shelf region (longitude >= 87W;
slope=0.13*10-5 m2 N-1). Sea-surface height gradients are computed with daily average
values of velocity and wind stress data for the period from 3 through 10 October 1996
using Equation 1b. Regressions are determined in the manner described in Figure 4.
17
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18