OCS Study 

MMS 2005-039 

 

Coastal Marine Institute 

Aspects of the Louisiana Coastal Current 

Cooperative Agreement

Coastal Marine Institute 

Louisiana State University 

U.S. Department of the Interior

Minerals Management Service 

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

Minerals Management Service Coastal Marine Institute 

Gulf of Mexico OCS Region Louisiana State University 

OCS Study 

 MMS 2005-039 

 

Coastal Marine Institute 

Aspects of the Louisiana Coastal Current 

Authors 

Larry J. Rouse, Jr. 

William J. Wiseman, Jr. 

Masamichi Inoue 

June 2005 

Prepared under MMS Contract 

14-35-0001-30660-19936 

by 

Coastal Marine Institute 

Louisiana State University 

Baton Rouge, Louisiana 70803 

Published by 
iii

DISCLAIMER 

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

Louisiana State University. This report has been technically reviewed by the MMS and approved 

for publication. Approval does not signify that the contents necessarily reflect the view and 

policies of the Service nor does mention of trade names or commercial products constitute 

endorsement or recommendation for use. It is, however, exempt from review and compliance 

with MMS editorial standards. 

REPORT AVAILABILITY 

Extra copies of the report may be obtained from the Public Information Office (MS 5034) at the 

following address: 

U.S. Department of the Interior 

Minerals Management Service 

Public Information Office (MS 5034) 

Gulf of Mexico OCS Region 

1201 Elmwood Park Boulevard 

New Orleans, Louisiana 70123-2394 

Telephone Number: (504) 736-2519 

 1-800-200-GULF 

CITATION 

Suggested Citation: 

Rouse, L. J., Jr, W. J. Wiseman, Jr., and M. Inoue. 2005. Aspects of the Louisiana Coastal 

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

Region, New Orleans, LA. OCS Study MMS 2005-039. 50 pp. 

ABOUT THE COVER 

The cover art shows a schematic diagram of the westward (downcoast) flowing Louisiana 

Coastal Current (LCC). The sea surface tilts up towards the coast. The low salinity waters of the 

LCC are separated from the higher salinity mid-shelf waters by a strong bottom-to-surface 

frontal boundary. The westward current is indicated by the circle with a dot inside (an 

arrowhead coming out of the page). 
v

TABLE OF CONTENTS 

LIST OF FIGURES ...................................................................................................................... vii 

LIST OF TABLES......................................................................................................................... ix 

I. INTRODUCTION........................................................................................................................1 

 1.1 Morphology of the Northwestern Gulf of Mexico Shelf ..............................................1 

 1.2 River Discharge ............................................................................................................1 

 1.3 Winds ............................................................................................................................2 

 1.4 Louisiana Coastal Current.............................................................................................2 

 1.5 Historical Investigations ...............................................................................................7

 1.6 Summary.......................................................................................................................8 

II. OVERVIEW OF EXISTING MODELS..................................................................................11 

 2.1 Introduction.................................................................................................................11 

 2.2 One-dimensional Models............................................................................................11 

 2.3 Two-dimensional Models ...........................................................................................13 

 2.4 Fully Three-dimensional Model .................................................................................14 

 2.5 Conclusions.................................................................................................................15 

III. VERTICALLY-INTEGRATED, WIND-DRIVEN MODEL OF VERY 

 LOW-FREQUENCY FLOW .................................................................................................17 

 3.1 Introduction.................................................................................................................17 

 3.2 Model ..........................................................................................................................17 

 3.3 Comparison to Observations and Discussion .............................................................19 

IV. APPLICATION OF THE YANKOVSKY AND CHAPMAN (1997) MODEL ...................27 

 4.1 Introduction.................................................................................................................27 

 4.2 Comparison to LATEX-B Data ..................................................................................27 

 4.3 Critique .......................................................................................................................28 

V. POSSIBLE IMPORTANCE OF PRESSURE GRADIENTS..................................................33 

 5.1 Introduction.................................................................................................................33 

 5.2 Results from Recent Field Studies..............................................................................33 

 5.3 Discussion...................................................................................................................39 

VI. SUMMARY............................................................................................................................43 

VII. REFERENCES.......................................................................................................................45 
vii

LIST OF FIGURES

1. Northwestern Gulf of Mexico shoreline and bathymetry interpolated to 0.1 degree from 

 DBDB5 data...............................................................................................................................3 

2. Annual discharge of the Mississippi River as measured at Tarbert Landing. ...........................4 

3. Long-term daily mean Mississippi River discharge at Tarbert Landing with maximum 

 and minimum observed discharge .............................................................................................5 

4. A ten-year record of the major and minor axes of the wind-stress variance ellipse from a 

station along the Texas coast. ....................................................................................................6 

5. Model output at the end of March 1993...................................................................................20 

6. Model output at the end of June 1992......................................................................................21

7. Comparison of the model output eastward velocity and monthly mean data plotted 

 at 15-day intervals for LATEX-A station 2 (27.284o

 N, 96.980o W). .....................................22 

8. Comparison of the model output northward velocity and monthly mean data plotted 

 at 15-day intervals for LATEX-A station 2 (27.284o

 N, 96.980o W). .....................................23 

9. Comparison of the observed depth where the coastal front intersects the bottom with 

that predicted by the theory of Yankovsky and Chapman (1997) for 25 sections collected 

during LATEX-B (Murray, 1997). ..........................................................................................29 

10. Plot comparing the ratio of water depth at the toe of the salinity front versus the 

 cross-frontal salinity difference for 29 sections west of the Atchafalaya River 

 mouth collected during LATEX-B cruises. .............................................................................30 

11. Example of a salinity section across a well-defined coastal front ...........................................32 

12. Location map indicating the ADCP and pressure gauge locations..........................................35 

13. Discharge of the Mississippi River during 2002 and vertical difference between 

 7 and 20 m depth at the ADCP mooring..................................................................................36 

14. Mean alongshore and cross shore flows during the ADCP deployment. ................................37 

15. First and second empirical orthogonal functions from the ADCP data...................................38 

16. Estimates of coherence squared between alongshore current and alongshore 

 pseudostress. ...........................................................................................................................40 
viii

17. Estimates of coherence squared between alongshore current and alongshore bottom 

pressure gradient during deployment 1 and alongshore current and alongshore 

bottom pressure gradient during deployment 2. ......................................................................41 
ix

LIST OF TABLES 

1. Complex correlation coefficients between model output and observations. ............................24 
I. INTRODUCTION 

1.1 Morphology of the Northwestern Gulf of Mexico Shelf 

In the following, we will define the northwestern Gulf of Mexico shelf as originating at the 

birdfoot or Belize delta of the Mississippi River and extending westward to the Mexican border 

(Figure 1). The shelf is extremely narrow near the birdfoot delta and broadens dramatically to 

the west. Immediately west of the delta, the shelf is cut by the Mississippi Canyon. There are 

indications in some data sets that the presence of this canyon influences the local circulation and 

allows cross shelf transport of waters with deepwater characteristics (A. E. Jochens, personal 

communication). Offshore of the Texas-Louisiana border the shelf attains its maximum width of 

approximately 191 km. Further west, it narrows considerably. At approximately 96o

 W, the 

shelf begins to turn to a north-south orientation as it continues to narrow. The shelf width at the 

Texas-Mexican border is only 76 km. 

Assuming the shelf break lies at approximately 100 m, the mean cross shelf slope varies from 

0.008 near the Mississippi delta to .0005 offshore of the Texas-Louisiana border to 0.001 near 

the Mexican border. The slope, though is not uniform. Nearshore, the bottom topography is 

concave upwards. Despite the relatively smooth character of the shelf, there are a number of 

shoals over the inner shelf such as Ship Shoals near 91o

 W, Trinity Shoal near 92.25o W, and the 

Sabine Bank near the Texas-Louisiana border. There is a break in bottom slope at mid-shelf 

over the broadest regions of the shelf. The offshore slope is steeper than that over the inner 

portions of the shelf. This feature is important for the formation of dense water over the midshelf during some winters (Nowlin and Parker, 1974), but is of little importance to the dynamics 

of the inner shelf and the Louisiana Coastal Current. 

1.2 River Discharge 

The Mississippi River discharge to the northwestern Gulf of Mexico shelf is the dominant source 

of fresh water to the region (Cochrane and Kelly, 1986; Dinnel and Wiseman, 1986). The 

Mississippi River system drains 41% of the contiguous United States and parts of two Canadian 

provinces. It discharges 94% of the fresh water emptied onto the northwestern Gulf of Mexico 

shelf (Cochrane and Kelly, 1986). Natural processes cause the river to change the location of its 

major delta lobe approximately every 1000 years. The birdfoot delta has been dominant since 

European settlement, but the river is seeking a more efficient route to the sea through the 

Atchafalaya delta, which enters into Atchafalaya Bay. The US Corps of Engineers has been 

tasked with maintaining 70% of the river system's flow through the birdfoot delta. 

The annual (1979-2002) discharge of the system is 692 km3

 (Figure 2). This discharge has a 

strong seasonal signal (Figure 3). Maximum discharge is associated with snowmelt in the upper 

portions of the drainage basin. Interannual variability is strong. Due to the integrating effect of 

the large drainage basin, the ratio of maximum to minimum discharge during a year is 

significantly less than observed in smaller systems. Long-term discharge data from Tarbert 

Landing just north of Baton Rouge, but below the Old River control structure, were obtained. A 
2

seasonal Kendall-tau test for trends (Hirsch et al., 1982) indicated that discharge has increased 

significantly (α=0.05) over the length of the record (1930-2002) in the later months of the year. 

When the record is shortened to include the period since 1979, when the ratio of Mississippi 

River to Atchafalaya River discharge was stabilized at its mandated ratio, only the month of 

September indicated a significant trend in discharge and this trend is negative! 

1.3 Winds 

Winds in the region are significantly influenced by the Bermuda high pressure system. When the 

system is strong and in a southwesterly location, typical of summer conditions, the northwestern 

Gulf of Mexico shelves are subject to breezes from the south and southeast. The only persistent 

strong winds are associated with the occasional tropical storm or hurricane. When the high 

pressure system retreats to the northeast during winter, the dominant synoptic weather pattern is 

the cold air outbreak (DiMego et al., 1976). These recur with time scales of 3 to 10 days. 

Preceding the frontal passage, strong winds blow from the south. Following the front, intense 

winds blow cold, dry air off the continent. During frontal passage, wind stress changes direction 

by 180 degrees (Dinnel, 1988), wind-driven currents may intensify and change direction (Crout 

et al., 1984; Wiseman and Kelly, 1994), and latent air-sea heat flux increases significantly 

(Nowlin and Parker, 1974; Huh et al., 1984). 

Because of subtle changes in the coastal orientation, subtle changes in wind stress direction may 

have significant effects on currents as the winds change from downwelling to upwelling 

favorable (Cochrane and Kelly, 1986; Howard, 1996). Gutierrez de Velasco and Winant (1996) 

describe the larger, low-passed wind patterns for the entire Gulf of Mexico for the three-year 

period 1991-1993 with a focus on the seasonal and annual means. Howard (1996) discusses the 

monthly mean stress distribution for the LATEX period (1992-1994) with emphasis on the 

spring transition from downwelling favorable to upwelling favorable conditions. Wiseman et al. 

(1998) stress the importance of seasonal and interannual variability in the wind stress distribution 

over the region. An example of this variability is presented in the plots of wind pseudo-stress 

variance ellipse characteristics presented in Figure 4. 

1.4 Louisiana Coastal Current 

In response to the massive freshwater discharge of the Mississippi River system and the 

predominantly downwelling favorable winds of the northwestern Gulf of Mexico shelf, a 

strongly stratified coastal current, known as the Louisiana Coastal Current (Wiseman and Kelly, 

1994), flows westward along the Louisiana inner shelf. During much of the year, this flow 

extends into Texas waters and even onto the Mexican shelf (Cochrane and Kelly, 1986). 

Seasonal cycles of both the stratification (Wiseman et al., 1997) and currents (Nowlin et al., 

1998) are observed to occur in response to similar cycles in the river discharge and winds. 

The seasonal cycle of stratification within the Louisiana Coastal Current between the Mississippi 

and Atchafalaya River deltas was described from eight years of occasional CTD casts at a site in 

20 m of water by Wiseman et al. (1997). Although the buoyancy flux associated with fresh 
3

Figure 1. Northwestern Gulf of Mexico shoreline and bathymetry interpolated to 0.1 degree from DBD
4

Figure 2. Annual discharge of the Mississippi River as measured at Tarbert Landing. 
5

Figure 3. Long-term daily mean Mississippi River discharge (solid) at Tarbert Landing with 

 maximum and minimum observed discharge (dotted). 
6

Figure 4. A 10-year record of the major (top) and minor (middle) axes of the wind-stress 

 variance ellipse from a station along the Texas coast. Parameters are computed over a 

 60-day window. The orientation of the ellipse is also shown (bottom). (Wiseman et 

 al., 1998) 

water from the river system represents the dominant control on stratification, vernal and summer 

solar heating are not without influence. On a classical temperature and salinity diagram, the path 

of surface water mass characteristics for surface and bottom waters rotate in contrasting 

directions. The surface waters are cold and saline at the onset of the year. In response to the 

spring flood and increasing length of day, the waters heat and freshen through the spring months. 

After the spring flood ends, salinity drops gradually, but the waters continue to increase in 

temperature. By late summer/early fall, they begin to cool dramatically, while continuing to 

increase slowly in salinity. The bottom waters increase in salinity throughout the spring and 

summer months as the halocline precludes freshening through mixing with the overlying waters 

and weak vertical entrainment of lower layer waters into the upper layers results in a 

hypothesized weak replacement flow from offshore. Throughout the fall and early winter, the 

bottom waters cool dramatically and freshen as the halocline begins to weaken. This counterrotation of water mass characteristics on the T-S diagram reflects increasing density stratification 
7

throughout the first half of the year and decreasing stratification in the latter part of the year. 

Data at 7 and 20 m depth from a recent mooring at the same location as this station data confirm 

this picture of a seasonal pattern of stratification, but also indicate the importance of highfrequency perturbation of the stratification by wind-driven mixing (Wiseman et al., 2004). 

Current understanding of the dynamics of this region remains less than satisfactory. Winter flow 

regimes are highly frictional. The dominant time scales of the sub-tidal currents are associated 

with the synoptic weather band (3 - 10 days). Currents are highly coherent with wind stress 

(Crout et al., 1984) and the currents are coherent both vertically and horizontally (F. J. Kelly, 

personal communication). As stratification increases, coherence of near-bottom currents with 

the local winds may decrease, e.g. Chuang and Wiseman (1983). Recent observations confirm 

these results. During summer, near-bottom flows may oppose the near-surface flows or stagnate 

(Crout, 1983). It is not yet clear whether results observed west of the Atchafalaya Delta, where 

the Louisiana Coastal Current flows over somewhat shallower water, are directly comparable to 

flows between the Mississippi and Atchafalaya Deltas, since the initial discharge plume of the 

latter rapidly detaches from the bottom while that of the former is bottom attached. Seasonal 

changes in very low-frequency flow in direct response to changes in the local wind have been 

noted for many years (Cochrane and Kelly, 1986). Cho et al. (1998) confirm these results, but 

stress the interannual variability of flows. A recent eight-month record from an ADCP in 20 

meters of water at 91.25o

 W suggests a mean circulation consistent with downwelling flow. 

Variability about this pattern, though, is significant. The dominant EOF, accounting for 82% of 

the sub-inertial flow variance, is barotropic and moderately sheared. The second EOF mode, 

which is consistent with a two-layered system, accounts for only 13% of the variance. Flows 

consistent with upwelling and downwelling are frequent in the subinertial cross shelf current 

structure. 

The frequency band over which wind forcing is important overlaps that where quasi-geostrophic 

dynamics may be expected to contribute significantly to the transport. It is unclear, with existing 

data sets, how one might determine the importance of geostrophic dynamics in this region. As a 

first attempt to accomplish this, ten-day low-pass filtered current shear data in 10 m of water 

were compared with local thermal wind shear. The results exhibited an approximately one-toone linear fit of one data set to the other, suggesting a nearly geostrophically balanced shear in 

these shallow, but highly stratified, waters. 

1.5 Historical Investigations 

Some of the earliest concerted efforts devoted to understanding the circulation and stratification 

of the Texas-Louisiana shelf were Lagrangian (Kimsey and Temple, 1963, 1964; Hill et al., 

1975; Schideler, 1979). These, though, were rapidly followed by a series of Eulerian studies that 

were reported in the gray literature (Oetking et al., 1973; Armstrong, 1976; Gosselink et al., 

1976; Angelovic, 1977; Gunn, 1978; Frey, 1981; Hann and Randall, 1981; Nowlin et al., 1998). 

The data collected during these studies often was reanalyzed for publication in the refereed 

literature and was supplemented by other small-scale efforts. These efforts focussed on two 

aspects of the Louisiana Coastal Current: stratification and velocity structure. 
8

The seminal work by Cochrane and Kelly (1986) synthesized existing knowledge of the 

Louisiana-Texas shelf. This effort was based largely on observed temperature and salinity 

characteristics of the water, but also included the isolated observations of flow and existing 

climatologies of coastal wind fields. They defined a seasonal cycle of near-surface circulation 

that remains essentially unchanged today. The shelf circulation was seen to be dominated by a 

cyclonic circulation cell, driven by Mississippi and Atchafalaya River discharge and 

downwelling favorable winds, during most of the year. A nearshore reversal of flow, in response 

to upwelling favorable winds along the Mexican and south Texas shelves occurred from late 

spring to summer and extended into Louisiana waters during mid-summer. Recent observations 

confirm this pattern, although they stress the interannual variability associated with it (Nowlin et 

al., 1998). Dinnel and Wiseman (1986) elaborated on the distribution of Mississippi River water 

over the shelf and its seasonal and interannual variability. The question of the cross shelf 

dispersion of this water, though, remained open. Wiseman et al. (1982) described the seasonal 

and spatial distribution of water properties within the plume of the Mississippi River delta, while 

Wiseman et al. (1975) focussed attention on the fine-structure in the water column in the same 

region. 

Working alone, Ned Smith produced some of the first publications describing the nearshore 

flows along the Texas inner shelf (Smith, 1975, 1978). These strongly influenced Cochrane and 

Kelly as they developed their synthesis of the shelf circulation. Later, much of the historical 

data, originally confined to the gray literature, was reanalyzed and published in the open 

literature. Crout et al. (1984) described the relationship of inner shelf currents, during the 

energetic winter season, to the local winds and found strong evidence that a simple local linear 

model would describe much of the observed variability. Wiseman and Kelly (1994) described 

the changes in flow structure across the inner shelf and the response of the flow field to the 

spring flood of the Mississippi River system. Daddio et al. (1978) were the first to focus 

attention on the strong inertial oscillations over the inner shelf in response to cold air outbreaks 

in the presence of strong stratification. 

More recent studies have used extensive data sets collected with modern instrumentation to 

describe the flow and stratification variability near the Mississippi River delta (Hitchcock et al., 

1997; Wiseman et al., 1997; Wiseman et al., 2004). Downcoast of the Atchafalaya River delta, 

data from the LATEX program (Nowlin et al., 1998) have been analyzed and reported on 

extensively, e.g. Cho et al. (1998); DiMarco and Reid (1998); Li et al. (1997). Finally, Dinnel et 

al. (1997) performed a seasonal analysis of the low-order seasonal statistics of available upper 

layer current observations from the inner shelf from south Texas to the Florida panhandle, 

documenting the spatial variability of these characteristics. 

1.6 Summary 

From the abbreviated preceding paragraphs, it should be clear that much information and 

extensive data sets are available from the Louisiana-Texas inner shelf region. These data, while 

incomplete and occasionally misleading, provide a vast source of information for model 

development, model forcing, and model verification. In the next chapter, we briefly review the 

level of success achieved by existing models of the region. It will become clear that existing 
9

models of the region have had some limited success in hindcasting observations, but that issues 

remain with all of these. In light of this, it may be of interest to investigate how successful 

simple local models are in hindcasting observations. Thus, we follow the review of existing 

models with application of simple concepts to the Louisiana Coastal Current. In Chapter III, we 

investigate the ability of a vertically-integrated model forced by low-frequency winds to explain 

the observed current fields at frequencies below the weather band. Yankovsky and Chapman's 

model of a coastal current controlled by bottom boundary layer processes is compared to 

observations in Chapter IV. We discuss the potential role of pressure gradients in Chapter V. 

Finally, we summarize and critique these results, in Chapter VI, and offer suggestions for fruitful 

areas of future progress. 
11

II. OVERVIEW OF EXISTING MODELS 

2.1 Introduction 

The noted statistician George P. E. Box once stated “All models are wrong-but some models are 

useful”. It would be easy to ignore, refute, or criticize historical modeling efforts over the 

LATEX inner shelf. A more useful approach might be to consider the assumptions and goals of 

the models, to determine their success at achieving their stated goals, and to assess the degree to 

which their lack of success is attributable to their assumptions. It is only recently that long 

simultaneous records from multiple sites have become available for comparison to model output. 

Necessarily, therefore, early models focused on short time scales, usually subinertial, and 

specific sites and seasons when stratification clearly was either a dominant or second-order 

concern. Approaches to modeling have generally involved a numerical solution to equations that 

often were of reduced dimensionality. 

2.2 One-dimensional Models 

While the focus of this chapter is on subinertial motions, it should be mentioned that the strong 

stratification and the impulsive wind forcing found over the Louisiana-Texas shelf result in the 

generation and persistence of energetic inertial oscillations. These were first noted and modeled 

by Daddio et al. (1978), following the approach of Pollard and Millard (1970), and later by Chen 

et al. (1996). A full understanding of the dynamics of these currents across the breadth of the 

shelf remains an open topic of investigation. 

Much of the one-dimensional modeling of the currents on the Louisiana-Texas shelf is based on 

the early observations of strong coherence between local wind and currents, e.g. Crout et al. 

(1984). These observations suggested that a local linear balance between wind stress and bottom 

stress could explain the measured flows within the weather band. Following Scott and Csanady 

(1976), Crout (1983) attempted to estimate the intensity of an alongshore pressure gradient term 

in an expanded model that included wind stress, bottom stress, and alongshore pressure 

gradients. (This will be discussed further in Chapter V.) Murray (1998) and Walker et al. (2001) 

were moderately successful in describing observed currents, for brief periods of time, with a 

similar model that supplemented the wind stress/bottom stress balance with a local acceleration 

term. 

Chuang and Wiseman (1983) considered the linearized, vertically-integrated equations of motion 

and continuity. They assumed alongshore homogeneity and forcing by an oscillatory wind 

stress. Bottom topography was allowed to vary in the cross-shore direction. Thus, the equations 

to be solved were 

∂U/∂t - fV = -gh∂ζ/∂x + τx -rU/h (1) 

∂V/∂t + fU = τy -rV/h (2) 
12

∂U/∂x = -∂ζ/∂t (3) 

with boundary conditions 

 U = 0 at x = 0 (the coast) (4) 

 

ζ = 0 as x → ∞ (5) 

where U and V are the transports in the alongshore (x) and cross-shore (y) directions, f is the 

Coriolis parameter, h is the water depth, τx and τy are the wind stress components in the x and y 

directions, respectively, r is a linear drag coefficient, ζ is the sea level elevation and t is time. 

Assuming a wind stress that varies as eiσt

, taking the Fourier transform of the governing 

equations, and eliminating U and V, one obtains a second order differential equation for ζ, which 

can be solved numerically. The solution, assuming a realistic cross-shore bottom profile, 

indicated insensitivity to the frequency of cross-shore wind forcing, but a sensitive dependence 

upon the water depth at the coast; sea level set-up being higher for shallower nearshore waters. 

These results compared well with observations from five-month records during the winter of 

1962-1963 at Galveston, TX and Eugene Island, LA. Similarly, the strong, frequency-dependent 

response of sea level to an oscillatory alongshore wind stress at Galveston suggested a drag 

coefficient equal to 0.01 cm/s. The relative insensitivity of the sea level response to forcing 

frequency at Eugene Island indicated a much larger drag coefficient, near 0.1 cm/s, at this site. 

Chuang and Wiseman argue that the increased drag coefficient appropriate to the solution at 

Eugene Island may be due to wave-current interactions during intense cold air outbreaks. 

Nevertheless, they suggest that this explanation is not sufficient to account for the abnormally 

large coefficient required to fit the model solution to observations. An alternative explanation is 

that some other important process is missing from the model formulation. It has been suggested 

that alongshore pressure gradients of small spatial scale may be the source of the mismatch. 

Another possibility is the absence of an appropriate lateral mixing scheme in the model. Finally, 

the assumption of alongshore homogeneity was made for mathematical convenience rather than 

being justified from physical arguments. 

The models of Chuang and Wiseman (1983), Murray (1998) and Walker et al. (2001), as well as 

the statistical analyses of Crout et al. (1984), discussed thus far have assumed non-stratified flow 

and focused on vertically-integrated transport rather than on the sheared flow expected in a real 

system. This assumption was common both for mathematical convenience and because there 

were few data sets available for model verification that resolved the vertical structure of the flow 

field. Nevertheless, the importance of stratification was clearly recognized (see Chapter I). As 

more and better data sets became available, including more than a single current meter in the 

vertical, the possibility of verifying models that included vertical structure became a reality. The 

first such model for this region was that of Lewis and Reid (1985). They solved the normal 

mode equations (Veronis and Stommel, 1956) for a linearized, two-layered system given 

oscillatory wind stress forcing and assuming alongshore homogeneity. They were quite 

successful in hindcasting the autumn and winter energy levels in both the surface and lower 

layers, but underpredict the energies across the weather band during the summer months. They 

note that their normal mode approach implies that their baroclinic friction represents energy loss 
13

from both layers as a function of vertical shear rather than energy transfer between layers – a 

more typical interpretation. The underprediction of summer energy levels is attributed to shelf 

wave phenomena. Evidence of propagating shelf waves over the Texas-Louisiana shelf is 

sparse. The model by Current (1996), to be discussed below, is based on the assumed existence 

of such waves. Unpublished data sets (E. Jarosz, personal communication; J. She, personal 

communication) suggest the existence of such waves, but the results are only marginally 

significant in a statistical sense. Again, the reduced dimensionality of the model and missing 

physics may be the culprit, as was suggested for the Chuang and Wiseman model. Alongshore 

pressure gradients are still missing from the model, lateral mixing processes are absent, and 

vertical mixing and dissipation is highly idealized. 

2.3 Two-dimensional Models 

Building on the success of the previous modeling efforts and the assumption that shelf wave 

motion may account for a portion of the mismatch between observations and model hindcasts, 

Current (1996) developed a spectral shelf wave model of the Texas-Louisiana shelf that could be 

verified using the extensive data sets from LATEX-A (Nowlin et al., 1998). Current assumes a 

quasi-linear, viscous conservation of horizontal momentum, locally hydrostatic pressure, and 

three-dimensional non-divergence of the velocity field. A bottom slip condition and a rigid lid 

are imposed. The upstream boundary condition is data driven, while a radiation boundary 

condition is imposed at the downstream boundary. The effects of the seasonally-varying density 

structure are imposed and the derived equations ultimately are solved for the volume transport on 

a boundary fitted coordinate system. The dissipative terms in the equations depend upon a 

careful evaluation of the bottom stress. A non-linear formulation of this term was carefully 

derived to yield results that were significantly improved over those obtained with a linear bottom 

friction coefficient. 

The model was verified by comparing 40-hr low-passed current and water level observations 

from the shelf with the subinertial response of the tuned model. The average r-squared value 

between the hindcast and observed currents over the inner shelf (depths less than 50 m) was 0.46, 

but at individual meters the model explained nearly two-thirds of the variance observed. The 

comparisons were generally best at the inshore meters. When the comparisons are made on a 

monthly basis, it is interesting to note that the comparison was worst during the months of July 

and August, similar to the results of Lewis and Reid (1985), when the dynamics of the inner 

shelf are different from those prevalent during non-summer months. Alternatively, the 

explanation could lie in a degraded forcing field as many of the LATEX meteorological sensors 

were removed during the hurricane season for protection (S. A. Hsu, personal communication). 

Comparisons of simulated and observed water levels proved even superior to the current 

comparisons. Mean r-squared values were 0.55. 

Chen et al. (1997) used a two-dimensional version of the Princeton Ocean Model (Blumberg and 

Mellor, 1987), overlain with a simple NPZ model of the biological dynamics, to study the 

physical-biological coupling offshore of the Atchafalaya River delta. The model was structured 

as a vertical slice across the shelf with longshore homogeneous conditions. The onshore 

boundary conditions allowed for a specified mass flux per unit longshore distance from the river. 
14

The offshore boundary condition was a radiation condition applied at the edge of a sponge layer. 

A free surface was specified to allow for tidal forcing from the open basin. A Mellor-Yamada 

level 2.5 turbulence closure scheme was used. When run with river flow parameters 

characteristic of spring 1993 and no wind forcing, the model was able to reproduce the observed 

nutrient and phytoplankton distributions inshore of the haline front that separates the low salinity 

inshore waters from saltier midshelf waters. This suggests that the dominant physics affecting 

the biology were adequately reproduced by the model, including the cross-shelf circulation and 

stratification. The alongshore flow after 30 days of model run was significantly higher than 

observed in the region studied (Nowlin et al., 1998; Dinnel et al., 1997). The reasons for the 

accelerated current are unclear. Longshore pressure gradients are absent from the model. Their 

influence cannot be estimated. The bottom topography used in the model is deeper than the 

observed bathymetry, thus frictional dissipation of the highly stratified flows may be too weak. 

Finally, the Mellor-Yamada turbulence closure scheme may be inappropriate for such highly 

stratified situations (Garvine, 2001). 

2.4 Fully Three-dimensional Model 

A fully three-dimensional version of the Princeton Ocean Model (Blumberg and Mellor, 1987) 

was implemented on a curvilinear grid covering the entire Gulf of Mexico, the northern 

Caribbean Sea, and parts of the Atlantic Ocean (Herring et al., 1999). The grid had maximum 

resolution over the northwestern shelf of the Gulf of Mexico. The model assumed a fixed 

horizontal eddy viscosity for most of the domain, but used a Smagorinsky (1963) closure scheme 

over the shelf. River inflow from 34 rivers was specified using real data. Evaporation was 

assumed to balance precipitation and surface heat flux was imposed from climatology. The 

model output was compared with current meter and water level data, as well as salinity data 

(Wiseman et al., 2000). This latter data was believed to represent an integrated response to the 

time-varying flows over the shelf. The mean flows for the 33-month data set available compared 

well. Flow means were of essentially the same magnitude and the same direction in all but a few 

sites. The r-squared values of the comparison between complex observed and hindcast current 

vectors generally ranged from 0.36 to 0.5. When only the alongshore components were 

considered, the r-squared values increased to values approaching those obtained by Current 

(1996). (It should be remembered that Current's analysis imposed an upstream boundary 

condition derived from current observations, while the present model used only wind stress and 

river flow as input. When the shelf wave model domain was extended to the Mississippi Delta 

and forced by wind only, the r-squared values dropped slightly at the upstream moorings, 

reducing the overall r-squared values slightly as well - C. Current, personal communication.) 

The phase of the complex correlation coefficient between observations and hindcast currents was 

near zero. Coherence-squared between the observed and hindcast currents of Herring et al. 

(1999) was only significant at the very lowest frequencies resolved. Visual comparison of the 

records suggest that the two signals exhibit periods of excellent correlation interspersed with 

periods of much poorer correlation. This may be due to the quality of the wind stress field used 

to force the model (Wiseman et al., 2000). Furthermore, there were indications in the data that 

momentum did not mix downward sufficiently rapidly in the model, suggesting issues with the 

turbulence closure scheme that needed further work. Comparisons did not improve when the 

grid size was halved. Thus, grid resolution does not appear to be the dominant cause of the 
15

model-data discrepancies of the Herring et al. (1999) three-dimensional modeling study. 

Comparison with the water levels was better than for the currents, as is to be expected. The 

salinity fields hindcast by the model did not differ significantly from the observations at the 95% 

level. Nevertheless, there were consistent patterns in the error signal that should be remedied. 

The surface salinities were, on average, saltier than the observations and the deeper modeled 

salinities were fresher than observations. Furthermore, the low-salinity surface waters west of 

the Atchafalaya Bay were confined closer to the shore in the model results than in the 

observations. It has been suggested (Wiseman et al., 2000) that the turbulence closure schemes 

used in the model were a primary source of this discrepancy. 

Recent improvements have been made to the model under funding from the National Ocean 

Partnership Program (R. Patchen, personal communication), but output from these model runs 

were not available for comparison with observations. 

2.5 Conclusions 

While it is esoterically pleasing to be able to model the shelf circulation and water properties 

using fully three-dimensional, time-dependent models, it is intriguing that the improvements in 

hindcast skill associated with today's models over lower dimensional models do not appear to be 

extreme. The cause of this is unclear, but may be related to the extremely frictional behavior of 

the water column at weather-band frequencies in this shallow environment, particularly during 

winter periods. While awaiting the next generation of three-dimensional models, it might be 

useful to try to understand some of the aspects of the shelf dynamics that can be readily 

understood using simple models. We have already mentioned the appeal and success of linear, 

one-dimensional balances between wind stress and bottom friction, e.g. Murray (1998), Walker 

et al. (2001). In the remainder of this report, we consider three such simple models. The first is 

a steady-state linear model forced by monthly mean winds. This is meant to approximate the 

Arrested Topographic Wave approach of Csanady (1978). The second is based on the model of 

Yankovsky and Chapman (1997), who propose that, in the absence of wind forcing, the structure 

and offshore extent of a buoyancy-driven coastal current will be controlled by bottom boundary 

layer processes. The final simple approach to be considered is to explore improvements to the 

understanding of the nearshore current dynamics by including alongshore pressure gradients. 
17

III. VERTICALLY-INTEGRATED, WIND-DRIVEN MODEL 

OF VERY LOW-FREQUENCY FLOW 

3.1 Introduction 

Initially, we had intended to try to compare predictions from the arrested topographic wave 

model of Csanady (1978) to the observed low frequency current fields. A simpler approach, 

though, was to compare these current observations to predictions from a vertically-integrated, 

homogeneous, wind-forced model. There is some rational justification, other than ease of 

application, for this. Csanady’s elegant solution of the steady problem resulted from ignoring the 

linearized friction associated with cross-shore flow. He made the assumption that this term 

would always be small and was able to derive a consistent solution to the resulting equations. 

We treat a slowly varying problem, not a steady one. Observationally, we recognize that, at least 

for brief periods of a few days duration, cross-shelf flows may be significant and contribute to 

important bottom friction. How this affects the force balance of the slowly-varying flow field is 

not immediately evident. By using the full equations, though, we can assess the importance of 

the various terms in the equations of motion, a posteriori. 

3.2 Model 

The model we used was one developed earlier for estuarine studies (Inoue and Wiseman, 2000; 

Park, 1998). The model equations are those for conservation of mass and momentum. They are 

written in Cartesian coordinates in terms of the depth-integrated transport (Leendertse, 1967) as: 

 ( ) ( ) A U

H

V

H

U

H

U

C

g

x

fV gH

y

UV H

x

U H

t

U x 2

2 2

2

2

 + + ∇ 

 



  +  



 



 









 



 − ∂

∂

+ = − ∂

∂

+

∂

∂

+

∂

∂

ρ

ς τ (6) 

 ( ) ( ) A V

H

V

H

U

H

V

C

g

y

fU gH

y

V H

x

UV H

t

V y 2

2 2

2

2

 + + ∇ 

 



  +  



 



 









 



 − ∂

∂ − = − ∂

∂

+

∂

∂

+

∂

∂

ρ

ς τ

 (7) 

= 0

∂

∂

+

∂

∂

+

∂

∂

y

V

x

U

t

ς (8) 

∫− = ς

h

U udz (9)

∫− = ς

h

V vdz (10) 

 H = h + ς (11) 
18

Where t represents time, x, y, and z are the coordinates of an orthogonal, right-handed Cartesian 

system, u and v are the horizontal velocity components in the x and y directions, respectively, ζ 

is the elevation of the free surface above mean sea level, h is the depth of the water when at rest, 

f is the Coriolis parameter, which is assumed to be constant, g is the acceleration due to gravity, 

τx and τy are the x and y components of the wind stress, respectively, ρ is the density of water, 

assumed to be constant, A is the horizontal eddy viscosity, assumed to be constant, and C is the 

depth dependent Chezy coefficient. The Chezy coefficient is represented using Manning’s 

coefficient, n, such that 

 n

H C

1 6

= . (12) 

Manning’s n was set to a constant value of 0.025. 

No normal flow and no-slip boundary conditions are used along the land boundaries. Along the 

southern and eastern open boundaries, radiation boundary conditions (Camerlengo and O’Brien, 

1980) are imposed. These boundaries are along the 26 degree parallel of latitude and the 88 

degree meridian of longitude. 

The model equations are discretized in a finite-difference formulation on the staggered mesh C 

grid of Arakawa (Mesinger and Arakawa, 1976). The Grammeltvedt C scheme (Grammeltvedt, 

1969), which conserves mass and total energy, is employed. For time integration, the leapfrog 

scheme is used with an Euler step inserted at regular time intervals to eliminate the 

computational mode due to the central time differencing. For numerical stability, the frictional 

terms are lagged in time. 

The model bathymetry was based on the ETOP05 data set and interpolated onto a grid size of 2.5 

minutes in both the latitudinal and longitudinal directions. The minimal depth was set to 5 m and 

the maximum depth was set to 500 m in order to satisfy the CFL criterion with a reasonable time 

step. 

Monthly wind speed components for the LATEX experimental period were made available by 

Texas A&M University (courtesy of Matt Howard). These were interpolated onto the model grid 

and monthly mean wind stress components were estimated using the formula of Thompson, et al. 

(1983), 

 ( ) 0 ρ aCd a aV0 τ = (13) 

 2 2

0

2

a = V + 4σ (14) 

where τ0 is the magnitude of the monthly mean wind stress, V0 is the magnitude of the monthly 

mean wind speed, and σ is an estimate of the monthly root mean squared wind speed. In this 

study, we have assumed that σ is approximately 5 m/s. Cd is estimated from the WAMDI (1988) 

third generation wave model formulation as 
19

 ( ) 1.2875 10 ,if 7.5m/s 10

3 = × < − Cd a a (15) 

 () ( ) 0.8 0.065 10 ,if 7.5m/s 10

3 = + 10 × ≥ − Cd a a a (16) 

where a10 is the wind speed at 10 m height. The monthly mean wind stress, estimated in this 

manner, was assigned to the last day of the month and linear interpolation between these values 

was used to assign a wind stress at any particular time step. 

The model was spun up from rest. The horizontal viscosity was set to a constant value of 100 

m2

/s everywhere except at those grid points where the water depth was 500 m. At these points, 

which were closest to the open boundaries, the viscosity was set to a value of 1000 m2/s in order 

to damp out small-scale noise generated near the open boundaries. 

3.3 Comparison to Observations and Discussion 

The output of such a simple model is qualitatively consistent with expectation. Transport 

velocities are only high over the inner shelf. They are generally downcoast (in the sense of 

Kelvin wave phase propagation) (Figure 5). This is the direction that would be expected from an 

examination of the monthly mean wind vectors (Cochrane and Kelly, 1986). Along the Texas 

coastline, the flow reverses during late spring/early summer in response to the strongly upwelling 

favorable winds along the south Texas coast at that time of year (Figure 6). 

Two-week mean currents from the upper current meters at each mooring were smoothed with a 

two-point box-car filter to produce thirty-day means. These were compared with the model 

output. Since the moorings did not lie over model grid-points and some smoothing was applied 

to the ETOP05 bathymetry, the data was compared with model output at the closest point that 

exhibited a similar depth to that at the mooring. (This is a technique that produced acceptable 

results when used to evaluate the Princeton-Dynalysis model in Herring et al., 1999). The 

magnitude and phase of the complex correlation coefficients are presented in Table 1. Assuming 

a thirty-day decorrelation time scale, Tchebycheff significance levels were estimated for the 

correlation coefficients. When the correlation coefficients are significant at or above the 80% 

level, this is indicated in the table. It is interesting to note that this model, forced solely by lowfrequency winds, compares most favorably with observations at the same stations where the 

models of Current (1996) and Herring et al. (1999) compared well. These latter models were 

forced, though, by high-frequency winds that included the energetic weather band and, in the 

case of the Herring et al. model, buoyancy flux. 

While the correlations, i.e. the comparisons of the shape of the fluctuating component, were 

often acceptable, the point by point comparisons were not, e.g. Figures 7 and 8. The observed 

velocities exhibited much higher peak-to-peak variations that did the model output. 

Furthermore, the model output was often significantly biased with respect to the observations. 

One might suggest that the observations represent the surface Ekman layer flow and would be 

expected to be more energetic than the vertically-averaged flow. Yet, the current meters were 

frequently about 10 m below the sea surface. Also, for the inshore stations considered and 
20

Figure 5. Model output at the end of March 1993. Every fourth velocity vector is printed. The 

 maximum velocity vector shown represents a speed of 14.4 cm/s. The ordinate and 

 abscissa are grid points. Grid point spacing is 2.5 minutes. The origin of the grid 

 points is located at 26o

 N, 98o W.
21

Figure 6. Model output at the end of June 1992. Every fourth velocity vector is printed. The 

 maximum velocity vector shown represents a speed of 9.5 cm/s. The ordinate and 

 abscissa are grid points. Grid point spacing is 2.5 minutes. The origin of the grid 

 points is located at 26o

 N, 98o W.
22

Figure 7. Comparison of the model output eastward velocity (solid line) and monthly mean data 

 (asterisks) plotted at 15-day intervals for LATEX-A station 2 (27.284o

 N, 96.980o W).
23

Figure 8. Comparison of the model output northward velocity (solid line) and monthly mean 

data (asterisks) plotted at 15-day intervals for LATEX-A station 2 (27.284o

 N, 96.980o W). 
24

Table 1 

Complex Correlation Coefficients between Model Output and Observations 

LATEX-A 

Station 

Number

North 

Latitude

West 

Longitude

Mooring 

Depth 

(m)

Complex 

Correlation 

Coefficient 

Magnitude

Complex 

Correlation 

Coefficient 

Angle (o

)

1 27.256 97.246 20 0.60* 1

2 27.284 96.980 37 0.60* -18

3 27.290 96.736 65 0.38** 6

14 28.395 90.493 47 0.46** -6

15 28.6608 90.492 27 0.59* -8

16 28.867 90.491 18 0.19 -5

17 29.196 91.965 8 0.17 -18

18 28.963 91.983 22 0.34 4

19 28.465 92.035 53 0.30 -13

20 29.261 94.064 14 0.15 -17

21 28.837 94.080 24 0.35** -2

22 28.356 93.956 55 0.30 12

23 28.713 95.536 15 0.65* -18

24 28.474 95.437 28 0.40** -11

25 28.162 95.426 37 0.67* 0 

 * Significant at the 95% level; ** Significant at the 80% level. (Tchebycheff confidence 

intervals were used. A 30-day decorrelation scale was assumed.)

for those within the 30 m isobath, one would expect the surface and bottom Ekman layers to 

overlap, at least in a homogeneous fluid. Thus, one is lead to believe that, at least a portion of 

the discrepancy can be attributed to stratification that was present at the measurement site. The 

bias between the two signals might also be attributable to a geostrophic flow driven by the 

slowly-varying ambient stratification. 

A comparison of the terms in the model output is revealing. The local accelerations are 

negligible, as was to be expected from simple scaling arguments, since the time-scale of the 

forcing is significantly longer than a pendulum day. The lateral dissipation terms are small in 

comparison to the Coriolis terms. The bottom friction terms, though, are also small. The friction 

formulation used is, based on prior experience, appropriate for tidal flows and flows in the 

weather band within the shallow estuaries and nearshore environments of the northwestern Gulf 

of Mexico. In the model formulation, we accounted for the absence of high frequency 

components of the wind spectrum in the forcing by enhancing the drag coefficient. Similar 

arguments have been used to suggest that the bottom drag coefficient should be enhanced in such 

low frequency models (Current, 1996; discussion in Chuang and Wiseman, 1983). An enhanced 

bottom drag coefficient, though, would result in a further reduction in the amplitude of the winddriven flows. We have already noted above that the modeled currents were smaller in amplitude 

than the observed ones. 
25

The dominant terms in the momentum balance in the model, as presently formulated, are the 

Coriolis term, the pressure gradient term, and the wind stress term. (In the cross-shore direction, 

the non-linear term is, on occasion, important, but never makes an order one contribution to the 

momentum balance.) Although probably unproductive, at this time, it would be intriguing to 

speculate on the similarities of the balance of forces in this model and those of the steady, central 

ocean wind-driven flow (Sverdrup, 1947). 

Consequently, one is lead to conclude that a simple wind-driven model of the low frequency 

flows is inadequate. It may capture the qualitative structure and variability of the flows, if the 

bottom drag coefficient is appropriately tuned. It is unclear whether such tuning merely would 

be correctly representing bottom frictional processes or would be parameterizing additional 

processes that are not included in the model formulation, such as baroclinic processes (Chapter 

IV, this report; Wiseman et al. 1997). 
27

IV. APPLICATION OF THE YANKOVSKY AND CHAPMAN (1997) MODEL 

4.1 Introduction 

It has been noted above and elsewhere, e.g. Crout et al. (1984), Current (1996), that flows in the 

wind-driven band are highly coherent with the alongshore wind stress over the Louisiana/Texas 

inner shelf. At longer periods, there are also indications that wind forcing is a significant 

contributor to the observed flow variability (Cochrane and Kelly, 1986; Walker et al., 2001; 

Chapters III and V, this report). At these same longer time scales, baroclinicity has also been 

implicated as significant to the observed dynamics. Wiseman et al. (1997) have noted that lowpassed current shear over the inner shelf near the Texas-Louisiana border is correlated with 

geostrophic shear. Garvine (2004) has noted similar behavior off the New Jersey coast. It is, 

thus, reasonable to ask whether the data sets collected during the LATEX-B surveys (Murray, 

1998) might contain additional evidence supporting or belying the importance of geostrophy in 

the dynamics of the Louisiana/Texas inner shelf. 

Yankovsky and Chapman (1997) have developed a theory that predicts important length scales 

associated with a buoyant coastal discharge. They note that, for a bottom-advected discharge, 

such as is expected to occur offshore and downstream of the Atchafalaya River mouth, the 

transport eventually would be expected to be confined to the width of the offshore density front, 

W. If this front is trapped at an equilibrium depth, hb, then the transport, Tb, is approximately 0.5 

uz hb

2

 W, where uz is the vertical shear of the horizontal flow. (It is assumed that u is zero at the 

bottom.) The shear, uz, is given by the thermal wind equations as g ρy/ρ f, where g is the 

acceleration due to gravity, ρ is water density, and f is the Coriolis parameter. Substituting for 

the current shear in the equation defining the transport, one finds hb = √(2 Tb W ρ f/ g ρy) ≈ √(2 

Tb ρ0 f/ g ∆ρ), where ρ0 is a characteristic density and ∆ρ is the density difference across the 

coastal front. 

4.2 Comparison to LATEX-B data 

The LATEX-B program (Murray, 1998) monitored numerous intensely-sampled CTD sections 

across the Louisiana Coastal Current perpendicular to the isobaths. These were snap-shots of the 

hydrographic structure of the current and included effects due to storms and tides. Thus, it may 

not be expected that the theory developed by Yankovsky and Chapman would be very successful 

in reproducing observations. The sections did not always sample the offshore edge of the frontal 

boundary separating the low salinity coastal waters from those of the middle shelf. Nevertheless, 

they always allowed estimation of the depth at which the coastal front intersected the bottom, hb. 

Since the full width of the current was not sampled, the transport within the frontal region could 

not be unequivocally estimated from the field data. To obtain an estimate of this quantity, we 

noted the measured discharge of the Atchafalaya River at Simmsport, LA and adjusted this 

figure upwards to account for offshore waters that had been entrained into the flow to produce 

the salinity observed inside the front. Finally, we estimated reduced gravity, g ∆ρ/ρ0, assuming a 

linear equation of state based solely upon the salinity of the waters. Both these estimates 

depended upon knowledge of the cross-frontal salinity difference, which was estimated 
28

subjectively from plots of the salinity distribution along the section in question. We estimated 

hb, from the observed salinity distributions. We depended heavily upon the salinity distributions 

because these provided the clearest identification of the frontal structure and its intersection with 

the bottom. We then compared the observed depth at which the front intersected the bottom with 

that predicted by the theory of Yankovsky and Chapman (1997). Figure 9 indicates the results of 

this comparison. 

4.3 Critique 

In the interests of full disclosure, a few points should be noted. Generally, only data from the 

first few sections observed downstream of the Atchafalaya River outlet were used in this 

comparison. The discharge of the Atchafalaya is not steady, while the theory is a steady state 

theory. It became progressively more difficult to estimate the river discharge appropriate to a 

given section, and consequently the transport through the section, as the sections were displaced 

from the mouth of the river. Furthermore, dispersion processes not included in the theory were 

more likely to have affected the structure of the coastal current the farther downcoast a section 

was sampled. Finally, it was quickly noted that the comparison broke down, if data from further 

down the Texas coast were included in the comparison. In some cases, even in the sections 

retained, a well-defined frontal boundary between the inner shelf, low-salinity waters and the 

higher salinity, mid-shelf waters was not apparent. In these cases, data from the given section 

was not utilized in the analyses. 

Despite the restricted size of the data set included in this analysis, the theory appears to represent 

an upper bound on the observed depth of the toe of the front. The clear linear relationship 

between the predicted and observed parameters when a strong front is present (cross-frontal 

salinity differences of 7 or higher) is impressive, particularly when one considers the differences 

between the characteristics under which the observations were collected and those assumed by 

the theory. The ratio of estimated to observed water depth at the toe of the front is plotted 

against the cross-frontal salinity difference in Figure 10. It is obvious that the analysis does not 

produce acceptable estimates of the depth at which the front intersects the bottom when the 

estimated cross-frontal salinity difference is small. It is unclear, though, whether this results 

from inabilities of the theory to handle such situations or from difficulties in estimating the 

inputs to the theory in such weakly stratified situations. 

Although the Atchafalaya River discharge is large, its variability is small compared to rivers with 

a more restricted catchment basin, such as the Eel River 

(http://ca.water.usgs.gov/archive/waterdata/96/11477000.html). Thus, estimates of the discharge 

of the Atchafalaya River should be relatively well defined and characteristic of waters that have 

been recently debouched, since the time scales of discharge variability are long. These estimates 

should contribute little to the relative error in the estimates of hb. Estimates of the cross-frontal 

salinity difference, though, are far less concise and contribute much more to the relative error in 

hb. An example of a section exhibiting a very clearly defined salinity front is presented in Figure 

11. It should be obvious that, even in such cases of a well-defined front, a certain level of 

subjectivity and error is incurred in estimation of the various parameters needed to enter into the 

comparison of observations with theory. In this situation, for example, we have estimated the toe 
29

Figure 9. Comparison of the observed depth where the coastal front intersects the bottom with 

 that predicted by the theory of Yankovsky and Chapman (1997) for 25 sections 

 collected during LATEX-B (Murray, 1998). A line with unit slope is overlain on the 

 data. Data points indicated by a square surrounding an asterisk are from sections where 

 the cross-frontal salinity difference is estimated to be at least 7. 
30

Figure 10. Plot comparing the ratio of water depth at the toe of the salinity front versus the 

 cross-frontal salinity difference for 29 sections west of the Atchafalaya River mouth 

 collected during LATEX-B cruises. 
31

of the front to intersect the bottom at a depth of 12 m, although one could argue coherently for 

any value between 10 and 14 m. Similarly, we have estimated the cross-frontal salinity 

difference to be 6 (33 – 27), but slightly different values could also be justified. In situations 

where the front is less well defined, these estimates become even more imprecise.

While the errors, mentioned above, in estimating input parameters for the comparison are 

important, they are not the sole cause of discrepancies between the observations and the theory. 

Dynamical processes occurring at short time scales not accounted for by the theory, particularly 

wind forcing and non-Fickian dispersion processes, must influence the structure of the front. 

Perhaps more important is the fact that the theory describes a situation where the system is 

approaching steady-state. In fact, the model calculations shown in Yankovsky and Chapman 

(1997) are for a structure that has developed over a 90 day period since river flow was initiated. 

The sections observed during LATEX-B were probably sampling waters within 10 days of 

discharge. If the flow structure had not achieved a near steady situation, one might assume that 

the transport was not fully confined to the frontal region and that transport within the bottom 

boundary layer was still advecting the observed toe of the front offshore. Indeed, ADCP sections 

taken during LATEX-B often indicate significant transport inshore of the toe of the front. Such a 

situation may explain why the theory seems to overestimate the observed depth of intersection 

between the front and the bottom. 

The theory of Yankovsky and Chapman (1997) is based on a simple geostrophic balance in the 

interior of the flow, which is coupled to a bottom boundary layer. While clearly ignoring many 

dynamical processes known to be important in the vicinity of the Louisiana Coastal Current, it is 

intriguing that the theory does as well as it does in predicting the depth at which the coastal 

salinity front intersects the bottom. This appears to be a clear indication of the dynamical 

importance of the baroclinic pressure gradients associated with the buoyant discharge from the 

Mississippi-Atchafalaya system. The data used in this comparison were all collected downcoast 

of the Atchafalaya River mouth. It remains to be determined how well a similar comparison may 

describe the coastal current upcoast of the Atchafalaya River mouth, which is associated with the 

bottom-separated plumes discharged from the Mississippi Delta. The apparent success of the 

theory at describing structures associated with Atchafalaya River discharge suggest that further 

development of a robust, time-dependent theory would be beneficial. 
32

Figure 11. Example of a salinity section across a well-defined coastal front. (The depth scale is 
33

V. POSSIBLE IMPORTANCE OF PRESSURE GRADIENTS 

5.1 Introduction 

As mentioned earlier, longshore pressure gradients have been proposed as a possible mechanism 

to explain the disparity between the predictions of a local balance between wind stress and 

bottom (and/or internal) stress and observations. The first person to suggest and estimate the 

importance of these pressure gradients appears to have been Crout (1983), who followed the 

formalism of Scott and Csanady (1976). He estimated monthly mean longshore pressure 

gradient values that were positive in January and March and negative in February and April. He 

argued that the local frictional balance was more complete in January and March, producing 

meaningful estimates of the longshore pressure gradients. 

Wiseman et al. (1992) analyzed a single month of data and found that only 20% of the pressure 

gradient variance could be explained by a model including bottom stress, wind stress, and time 

rate of change of bottom currents in 20 m of water. However, the pressure was strongly coherent 

with the longshore currents, suggesting cross-shore pressure gradient and longshore currents 

were coherent. They noted, though, the short duration of the record and its anomalous 

characteristics when compared to data from other years. 

More recently, She (personal communication), has examined a series of long-term, near-surface 

current records from the east Texas inner shelf and concluded that seasonal geopotential 

gradients associated with changes in the large scale wind field are important in controlling the 

regional flow patterns. 

5.2 Results from Recent Field Studies 

Walker et al. (2001) have analyzed a series of pressure, water level, and current meter records 

from the LATEX inner shelf region for the period 1994-1998. They suggest that the character of 

sub-surface pressure changed depending upon the seasonal characteristics of the regional wind 

field. During the autumn-winter-spring period, when winds were generally downwelling 

favorable and strong, the pressure signal was coherent with both the longshore and cross-shore 

winds within the weather band. In contrast, during the summer, when the winds were upwelling 

favorable along the Texas and west Louisiana coasts, the pressure signal was coherent, at the low 

end of the weather band, with the longshore winds, but generally incoherent with the cross-shore 

winds. 

They estimate the longshore pressure distribution, but do not mention the reference level used. 

We assume that the reference is either the record mean at each station, which is then removed, or 

the mean over a shorter period of time appropriate to concurrent data at all stations. Both 

methods have potential associated problems. The means derived from the entire data set are not 

of equal length, i.e. the data sets are gappy. Thus, the means that are removed from the data 

would be biased. If the means from concurrent data records are used, the means would be 

computed from very short data sets. (These same problems plague our own data to be described 
34

later in this chapter.) In either case, only the strongest variations would be significant. 

Fortunately such large gradients do appear in the data. Over periods of a few days, pressure 

gradients of 30 mb are seen to develop between Padre Island Coast Guard Station and Freeport, 

Texas. As a cautionary note, though, it should be mentioned that some tide gauges used were 

situated within passes and bays where local set-up and set-down could affect the data. 

A statistical comparison of pressure gradients between Padre Island, Texas and Sabine Pass, 

Texas and current measurements over the inner shelf offshore of Cameron, Louisiana, though, 

suggested significant coherence at periods between 5 and 10 days during the summer upwellingfavorable regime and no strongly significant coherence during the downwelling-favorable 

regime. 

From 14 March through 12 November 2002, under another project (Rabalais et al. 2002a), an 

acoustic Doppler current profiler (ADCP) was deployed twice at a station in 20 meters of water 

midway between the Mississippi River birdfoot delta and the Atchafalaya River delta (29.5o

 N 

91.25o

 W) (Figure 12). Ancillary data included bottom mounted pressure cells, roughly at the 

same isobath, east and west of the mooring and temperature-salinity recorders at the site of the 

ADCP mooring. Weather data were obtained from a station at Grand Isle (29.27o

 N 89.96o W). 

All data were similarly processed. The semi-diurnal and diurnal tides, as well as the strong 

inertial oscillations present near 30o

 N, were eliminated by applying a 101-point, zero-phase 

filter approximating a flat response out to 40 hours and a linear decay to 27 hour periods 

(Ormsby, 1961). The resultant low-passed currents and pseudostress were rotated 12o

counterclockwise into an alongshore/cross-shore coordinate system. 

The expected strong dominance of the alongshore currents was clear in the data. More surprising 

was the highly variable structure of the flow. Periods of strong vertical shear were interspersed 

with long periods of very weakly sheared flow. Long periods of flow contrary to the expected 

westward flow regime were also observed. The vertical density difference between sensors at 

approximately 7 and 20 m depth showed reduced density difference associated with strong upper 

layer flow and, consequently, strong shear, even when the river was in flood and the downcoast 

flow was responsible for a strong lateral buoyancy flux (Figure 13). A significant importance for 

shear-induced mixing is suggested by these results. 

The mean flow is consistent with expectations. The flow is strongly sheared in the alongshore 

direction. The lower layer flow is weak (Figure 14). The cross shore flow is consistent with a 

wind-driven downwelling regime as would be expected under the predominantly southeasterly 

winds affecting the region and a weak indication of reversal is present near bottom. 

Both theory and prior isolated observations, led us to anticipate two-layered flows or flow 

confined to the upper layer, particularly during the highly stratified summer season. Yet, a 

complex EOF analysis (Kundu and Allen, 1976) indicates that 82% of the variance in the lowpassed currents is accounted for by the first mode, which describes nearly unidirectional, 

vertically-sheared flow (Figure 15). The second EOF mode accounts for only 13% of the 

variance and describes a two-layered flow field. However, the vertical sigma-t gradient during 
35

Figure 12. Location map indicating the ADCP and pressure gauge locations. All were deployed 

 at approximately 20 m water depth. (Redrawn from Wiseman et al., 2004.) 
36

Figure 13. Discharge of the Mississippi River during 2002 (top) and vertical difference 

between 7 and 20 m depth at the ADCP mooring (bottom). (Redrawn from 

Wiseman et al., 2004.) 
37

Figure 14. Mean alongshore and cross shore flows during the ADCP deployment (Wiseman et 

 al., 2004). 
38

Figure 15. First (left) and second (right) empirical orthogonal functions from the ADCP data. 

 Values associated with every second ADCP bin are plotted (Wiseman et al., 2004). 
39

the analysis period was strong, generally greater than .075 m-1 and often 2 or 3 times this (Figure 

13). 

Such a strong stratification would be expected to isolate the lower layer from direct local wind 

forcing. 

Depth-frequency spectra (not shown) of the alongshore flow indicate significant energy in the 

diurnal and semi-diurnal tidal-inertial band currents. At the lowest frequencies, intense flows 

penetrate to the bottom, particularly the alongshore component of flow, while the higher 

frequency signals suggest surface trapping of the energy. A similar structure is evident in the 

depth-frequency spectra of the cross shore flows. 

The alongshore wind pseudostress is generally coherent with the alongshore currents, at the 95% 

significance level, below 0.025 cph, except in a narrow band around 0.015 cph (Figure 16). This 

coherence is slightly stronger at depth than in the upper layers, but it is significant throughout the 

entire water column. During the first of the two deployments, the upper layer alongshore 

currents were coherent with the alongshore pressure gradient in bands near 0.01 and 0.02 cph 

(Figure 17). Similar coherence was observed during the second deployment, but with a more 

barotropic response, and in a third band of significant coherence near 0.005 cph (Figure 17). It is 

important to note, though, that two hurricanes passed through the region, approximately a week 

apart, during the second deployment. The associated signals were very strong in all records and 

may dominate the cross-spectrum analyses. 

5.3 Discussion 

These observations raise a number of questions concerning the dynamics of the local flow. What 

momentum source forces the lower layer flow? Our normal concepts of highly stratified coastal 

flow as two-layered would preclude local wind forcing of the lower layer. Csanady (1981) 

suggests that, if the lower layer moves cross-shore as a column in response to the downwelling 

winds, then Coriolis force acting on this motion will cause an alongshore motion in the correct 

direction to match observations. This conceptual model, though, assumes two-dimensional and 

frictionless flow. These assumptions are inconsistent with the real environment. Is lateral 

advection of alongshore, wind-driven waters associated with the downwelling system 

sufficiently intense to account for the lower layer observations or are they associated with 

alongshore pressure gradients? Allen et al. (1995) and Allen and Newberger (1996) have 

described the flows arising within a two-dimensional model of upwelling and downwelling 

dynamics and the multiple circulation cells that may result, even without the addition of a coastal 

buoyancy source. The existing data does not contain the spatial complexity of these models, but 

the observed cross-shore flows are often multi-layered. Another possibility is that the wind field, 

interacting with the strong stratification and the crenulated shoreline, produces spatially and 

temporally varying alongshore pressure gradients that drive the flow in the lower layer. Some 

evidence for this may be seen in the coherence analyses discussed above, but, without 

simultaneous cross-shore ADCP records, answers remain largely conjectural. If the lateral flows 

are important mechanisms for the advection of momentum, how does this affect the oxygen 
40

Figure 16. Estimates of coherence squared between alongshore current and alongshore 

 pseudostress. The solid contour is the 95% significance level (0.28), the dashed 

 contour is 0.5, and the dotted contour is 0.75. (Redrawn from Wiseman et al., 2004) 
41

Figure 17. Estimates of coherence squared between alongshore current and alongshore bottom 

 pressure gradient during deployment 1 (top) and alongshore current and alongshore 

 bottom pressure gradient during deployment 2 (bottom). The solid contour is the 

 95% significance level (0.28), the dashed contour is 0.5, and the dotted contour is 

 0.75. (Redrawn from Wiseman et al., 2004.) 
42

dynamics? Our near-bottom oxygen records corresponding to the current measurements 

presented above are still being processed, but historical records (Rabalais et al., 2002b) suggest 

that near-bottom dissolved oxygen concentrations are modulated at a variety of advective scales, 

including those associated with upwelling/downwelling cycles. 
43

VI. SUMMARY 

We have briefly reviewed the status of existing, reduced dimensionality models of the dynamics 

of the Louisiana Coastal Current. Many of these are successful at reproducing the qualitative 

features of the circulation at specific time scales and periods of the year. Local, wind-driven 

models reproduce credibly the flow variability over the shallow regions of the west 

Louisiana/east Texas inner shelf, particularly during the winter season, at sub-tidal frequencies 

within the weather band (Crout et al, 1984; Lewis and Reid, 1985; Walker et al., 2001). Results 

are noticeably improved when care is taken to accurately account for variability of the bottom 

dissipation and far-field forcing (Current, 1996). The earlier models were unable to account for 

alongshore pressure gradients, while that of Current (1996) did. We were, thus, encouraged to 

assess the importance of such pressure gradients from observations. 

The success of such wind-driven models is surprising, since they ignore the riverine buoyancy 

flux and consequent strong stratification that is characteristic of this region of the Gulf of 

Mexico. A fully three-dimensional, time-dependent model of the region (Herring et al., 1999) 

did not perform significantly better at reproducing observations, although it did a good job of 

capturing the long term mean flows and very low frequency variability. It was also able to 

reproduce observed stratification moderately well (Wiseman et al., 2000). 

In an attempt to discern the plausibility of treating the Louisiana Coastal Current as an arrested 

topographic wave (Csanady, 1978), we applied an existing vertically-integrated, non-linear 

numerical model forced by monthly mean wind fields. The results were intriguing but 

inconclusive. While the momentum balance generally appeared to be in quasi-steady state, i.e. 

the local accelerations were negligible compared to other forces, the advective accelerations in 

the model were, at specific sites, non-negligible. More interesting was the fact that the 

dominant balance of forces in the model was between the Coriolis forces, the surface wind 

stress, and the pressure gradients. This may have resulted from not appropriately increasing 

the bottom drag coefficient to account for motions at frequencies higher than the forcing 

frequency. Typically, the choice of a constant bottom friction coefficient for subtidal flow 

modeling is justified by arguing that deterministic tidal currents are much stronger that the 

subtidal flows being modeled and, thus, dominate the dissipation processes. We selected a 

friction coefficient that has been used successfully to model tidal flows in the shallow waters of 

the northwestern Gulf of Mexico. We did not modify the formulation to account for the 

unresolved tidal flows or the significantly more energetic unresolved weather-band flows. Such 

modifictions were beyond the scope of this effort, although similar adjustments were made to the 

wind stress based on the literature. It was also interesting to note that the observations that 

compared least closely with the model results tended to be the same sites where comparison with 

prior model results forced by higher frequency winds (Current, 1996; Wiseman et al., 2000) was 

poor, possibly for many of the same reasons suggested in these references. 

Observations of the water depth at which the salinity front, defining the offshore edge of the 

Louisiana Coastal Current, intersected the bottom were compared with the predictions of a 

steady-state theory for bottom-trapped, buoyant, coastal discharges (Yankovsky and Chapman, 

1997). The comparison was qualitatively successful for the available data. The model appears 

to predict an upper bound for the intersection depth and the comparison is best when the front is 
44

most clearly developed. The good comparison of the Yankovsky and Chapman model with 

observations suggests that further development of a robust, time-dependent theory would 

be beneficial.

Recent results by Walker et al. (2001) suggest that inner shelf currents over the west Louisiana 

shelf are significantly coherent with longshore pressure gradients, during the summer period of 

upcoast mean flow, at periods between 4 and 10 days. They also suggest weak, but statistically 

significant, coherence during the downcoast flow regime at periods longer than 10 days. Our 

comparisons of full water column velocity measurements from a bottom-mounted ADCP and 

alongshore bottom pressure gradients at a site further east are far less satisfying. The bottom 

layer alongshore currents are significantly coherent with the observed alongshore pressure 

gradients in bands between 25 to 33 hours and near 50 and 100 hours. The source of the 

pressure gradient is unclear. We assume that it is dominated by the sea surface slope, but 

available data is insufficient to rule out a significant contribution from the baroclinic component. 

The weaker coherence between the upper layer alongshore currents and the alongshore bottom 

pressure gradient, as well as the weak coherence between the same currents and the alongshore 

wind stress is disconcerting. This may be due to instabilities in the flow field, which are 

observed in numerical models (L. Oey, personal communication) and satellite images, but 

observations are not available with which to verify this conjecture. 

There appear to exist situations in time and space along the Louisiana-Texas inner shelf where 

the bathymetry is sufficiently simple and a single forcing function sufficiently strong that a 

simplified balance of forces realistically describes the first order dynamics of the coastal current. 

Such conclusions, though, cannot be generalized to the entire coast or to all time periods. The 

Lousiana Coastal Current is a fully three-dimensional, time-dependent system. True 

understanding of the system will only result from field, theoretical, and numerical 

simulation studies that account for all four dimensions. 
45

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