Introduction to Circulation in the Gulf of Mexico

W. Sturges

Florida State University, Tallahassee, Florida

A. Lugo-Fernandez

US. Minerals Management Service, New Orleans, Louisiana

M. D. Shargel

Florida State University, Tallahassee, Florida

The Gulf of Mexico is a jewel among the natural resources of the western hemisphere. Its wetlands are the source of an important seafood and shellfish industry. Offshore waters support rich commercial and sport fisheries. Its oil and gas resources are prime incentives for commercial development. Its glistening coastal beaches provide recreation to millions and are the economic backbone of numerous coastal com­munities. If we are to understand how to use and manage such resources, it is crucial that we understand the waters that flow in and through the Gulf.

In recent years our understanding of the physical ocean­ography of the Gulf of Mexico, the patterns of circulation in its waters, has grown considerably. Beyond describing the current state of the science for physical oceanogra-phers, the authors in this book believe it is important—per­haps vitally important—to approach the broader group of people concerned with the Gulf to whom this new body of information will be useful. So it is also to those readers whose professional lives are intimately connected with the Gulf—and who, though scientifically literate, are unfamiliar with the jargon of physical oceanography—that this book is directed.

Thus, this brief introduction is directed to the scientifi­cally literate general reader and focuses on the questions that physical oceanographers are asking and some of the answers they have found during the past several years.

Circulation in the Gulf of Mexico: Observations and Models Geophysical Monograph Series 161 Copyright 2005 by the American Geophysical Union. 10.1029/161GM02

For the reader who wants a more detailed overview of the content in this volume and of the preceding research in which it is grounded, we provide a synopsis by Schmitz et al. Readers who are familiar with particular topics in our understanding of the Gulf of Mexico can go directly to the papers here, many of which contain introductory material and authoritative reviews.

The majority of papers present state of the art research results in specific areas. But we intend the results, which we believe will serve as the basis for solving a host of practical problems, to be accessible to readers in fields related, con­tiguous, or parallel to physical oceanography. For example, designers and operators of offshore oil and gas facilities need to know how strong and persistent currents are; the Loop Current and its rings can shut down deepwater drill­ing rigs for weeks (at a cost of nearly half a million dollars per day). Fisheries management often requires detailed knowledge of regional circulation. Biologists and fisheries scientists concerned with wetlands and marshes will find the chapter on sea level rise essential. Knowledge of ocean circulation has proven indispensable to sedimentologists and marine geologists who seek to understand the heterogeneous distribution of sediment on the ocean floor. In addition, currents are a key factor in understanding many environ­mental and biological issues involving hypoxia (such as the "dead zone" near the Mississippi River outflow), harmful algal blooms, oil spill impacts, produced water, and so on. Developing mitigation and management strategies for these issues demands an accurate and thorough knowledge of circulation in the Gulf.

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2 INTRODUCTION TO CIRCULATION IN THE GULF OF MEXICO

Many of the new results are comprehensive time series that lend themselves better to video presentations (we call them "movies" or "animations") than to standard print format. In response, we have included a CD with a variety of materials that can be viewed both as basic research tools and as introductory views of what Gulf circulation "really looks like." Many of us who have studied Gulf circulation for decades have been surprised and delighted by insights emerging from animations of daily or weekly images of data sets concerned with sea surface temperature, the shape of the sea surface from satellite altimetry, ocean color, and so on. This is true not only of data collected in the real world, but also of the valuable sets of "simulated data" produced by numerical models; movies of their output are included here as well.

Numerical models have become a valuable research tool, unquestionably essential as an aid to the analysis of direct observations. Both are valid tools of exploration and of analysis (as is theory). Speaking recently at a conference on the "World Ocean Circulation Experiment," C. Wunsch, a leading physical oceanographer at MIT, commented that in the early days of numerical modeling it was sometimes suggested that models would make the need for direct obser­vations much less important; actually the opposite is true. Models are now so detailed and complex that it takes many more real-world observations to identify where a model has correctly or incorrectly configured any number of phenom­ena. Consequently we have rejected the difference between numerical and observational studies as a useful organizing principle in this book (and Introduction) and, though admit­tedly arbitrarily, simply divided papers into two groups: papers that concentrate on issues in deep water and papers that concentrate on issues in coastal water areas.

CIRCULATION IN DEEP WATER

Overview

Just as the currents on the U.S. east coast are dominated by the Gulf Stream, the currents in the Gulf of Mexico are dominated by the Loop Current. The Loop Current forms as the pre-Gulf Stream waters flow from the Caribbean Sea, through the Gulf of Mexico, and on into the Atlantic. The Loop Current is as strong as the Gulf Stream, but since the Gulf is only about one-fifth the width of the Atlantic, the Loop Current is relatively more dominant. Large fragments of the Loop Current form "rings," sometimes called eddies, which shed almost randomly and drift to the west, driving the deep circulation just about everywhere in the Gulf.

Because it is so common for almost everything in nature to operate on an annual cycle, ring shedding was first assumed

to have an annual cycle, too. A discernable cycle exists but with no annual clock. We are still asking why. The paper by Leben (this volume) describes and explores this shedding in detail. He has provided a movie of satellite data (found on the CD) showing the motion of the Loop Current and its rings since 1993. If you wish to obtain a decent understanding of the behavior of the Loop Current, you may want to watch this movie many times.

Loop Current Rings are big, -300 km in diameter, and they rotate in the anticyclonic direction (clockwise, in this hemisphere). Smaller rings that spin the other way tend to collect around the edge of the Loop Current. The chapter by Schmitz on cyclonic rings is a thorough study of how smaller rings affect the shedding of larger warm-core rings.

The image of sea-surface height (SSH) in Plate 1 was chosen for its clear image of the large ring that is gradually becoming detached from the Loop Current. The flow around the high (red) is clockwise; the cyclonic (counter-clockwise, cold-core) features are ubiquitous. One danger with our ideas of the Loop Current and ring shedding is the ease with which we can assume a firm picture of what is "typical;" which usually translates to "the best I have ever seen" or, more often, "it agrees with my previous biases." We look, sometimes with dismay, at Leben's movie in the CD and find that our "typical" view is not always present.

Plate 2, by contrast, shows the fantastic level of detail available in the high-resolution imagery of sea-surface tem­perature (SST). This view is at a different time from the pre­vious image; tendrils of warm water can be seen everywhere. Cold water coming from inshore is evident. (The color scale was lost in cropping the figure but can be seen on plate 3.)

The SeaWiFS movie by Hu andMueller-Karger uses com­pletely different satellite data and on a different time scale. But the same large-scale features of irregular ring detach­ment come through clearly. The additional information, such as chlorophyll concentrations, found in the "color" images is what makes these pictures of such great biological interest.

Having more than one source of similar and complemen­tary data immediately raises the question of whether both show what we can call "the same thing." As a practical mat­ter, the answer is yes. The SST data can be obtained over a time of roughly one hour, although several days of data are usually combined to produce images in which clouds have been filtered out. The SSH data from several satellites are combined and then averaged using filters that extend nearly two weeks both before and after the "day of the image." So, though it is impossible to expect exact agreement between a temperature image averaged over a short interval and a SSH image averaged over +/- 12 days, the height contours agree quite well with what we think we are seeing in temperature, as Plate 3 will illustrate.

STURGES ET AL.

Real-Time Mesoscale Altimetry - Aug 3, 2005

30 N

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-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 Plate 1. Sea surface height (from Leben) centered on August 3, 2005, using data from several satellites; arrows indicate surface currents; red is high, blue is low, about a local mean value. The color scale at bottom is in cm; height contours are 5 cm apart. Note the speed scale at lower right.

4 INTRODUCTION TO CIRCULATION IN THE GULF OF MEXICO

Plate 2. Sea Surface temperature, April 13,2003. The Mississippi delta is at the top, Cuba at the bottom right, the Yucatan Peninsula at the bottom left. A few clouds are evident. Red is warm, blue is cold; image provided by N. Walker, LSU.

STURGES ET AL. 5

The large warm-core rings that separate from the Loop Current carry a huge volume of water, roughly 300 km across and 800 - 1000 m deep, across the Gulf. The swirl speeds can be as great as 3-4 knots, but the rate at which the ring as a whole moves to the west is about 5 cm/s (~1/10 of a knot). Because the high-speed currents in a ring are a serious threat to drilling rigs, our ability to predict ring shedding and motion has been of great concern to the oil industry. Despite our best efforts, however, we have yet to build numerical models with the capacity to predict with good reliability when a warm-core ring will separate from the Loop Current. The reader interested primarily in numerical modeling may wish to refer to Oey, Ezer, and Lee's paper, which presents a comprehensive survey of recent progress in numerical modeling in the Gulf.

Specific Features of Deep- Water Flow

The flow from the Caribbean Sea between Mexico and Cuba is the "input" to the Loop current. The paper by Badan et ah describes the results of a major current-meter mooring program in the Yucatan Straits. Longstanding political prob­lems between the U.S. and Cuba have kept oceanographers from the U.S. from working in the Yucatan Channel, lying between Cuba and Mexico. But research resulting from an arrangement with Mexican oceanographers at Ensenada has produced an excellent new set of data. The flow pat­tern found in the upper layers (above 800 m) is essentially in keeping with traditional ideas. But as less flow is found in Yucatan than in the Straits of Florida, some additional flow (~5 Sv) from east of Cuba is a required. Therefore we have been intrigued by the deep flow, which does not look at all like what most of us had anticipated. The deep flow (below ~ 1000 m) goes in and out like a plunger on each cycle of Loop Current intrusion, agreeing with ideas put forward by G. Maul decades ago. Surprisingly, as the Loop Current intrudes to the north, deep Gulf water flows back to the south, carrying a transport roughly one-fifth that of the upper flow that becomes the Florida Current.

Chassignet et ah describe the overall flow in the Gulf. Using surface color data from the SeaWiFS satellite, they compare five different numerical models, seeking to answer how well each performs and what features of biological interest seem to be clearly connected to circulation patterns. As can be seen on many of the color images, chlorophyll (and other water-borne particles) is taken from the shelf and transported in convoluted paths as a result of the strongly time-dependent placement of eddies found offshore. Simple ideas of how such transport might have taken place are clearly inadequate without a knowledge of how the material is extracted from the shelf region and how it is moved around by and within the eddy field.

Kantha et ah describe their work with a full-Gulf numerical model that has been in operational use for some years. They perform a hind-cast of the ability of their model to describe the large-scale circulation of the Gulf since 1993, asking: Is it good enough for use by the oil industry? Their model, like the others, is primarily wind-forced; they show that it requires the inclusion (or assimilation) of satellite altimeter data to improve the model sufficiently for it to reach a level of usefulness that will benefit the oil industry.

The large-scale flow of the Gulf has been explored with near-surface drifters for many years. DiMarco et ah have studied nearly 1400 drifter tracks. They ask whether, despite great variability, they can deduce reliable patterns of mean flow from these ~10 years of data. And they find that they can. (Movies of surface drifters on the CD are described later.)

Weatherly et ah have studied a set of data from drifters at a depth of 900 m. As expected, they find an enormous vari­ability in the flow as rings pass by. Nonetheless, by using several years of data, they successfully squeeze the statistics with the intention of finding features of mean flow where such results are statistically reliable. Although such mean flows are small, the variability is large. In a separate study using deep floats in the Pacific and Indian Oceans, Davis [2005] has shown that the mean values will be uncertain to roughly ~1 cm/sec even after a full year of data. Many years of data are required before a reliable mean emerges.

The Bay of Campeche is a region in the southwestern Gulf whose circulation is somewhat shielded from Loop Current rings. The paper by Vazquez et ah examines a variety of historical data, asking whether or not the mean flow there can persist in defiance of the rings' influence. The authors are able to affirm that the flow is consistent with what is expected from wind forcing.

The Inner Edge of the Deep Water and the Outer Edge of the Coastal Circulation

The flow near the outer edges of the continental shelf cre­ates an area where nutrients (or pollution) from continental sources enter, or as we more formally say, "exchange with" deep waters. Some studies of coastal flow examine this phenomenon. The paper by Hamilton and Lee is an excellent example of a planned experiment at the edge of the conti­nental shelf. Their paper as well as their movies and data in the CD show how eddies can intrude onto the edge of the shelf and dominate the circulation in that area. We usually expect eddies to "drift along " but Hamilton and Lee show that sometimes they are trapped by the topography and sit there for a month or more.

Slightly farther west, the study by Biggs et ah describes the area just offshore of the Mississippi River. In an exemplary

INTRODUCTION TO CIRCULATION IN THE GULF OF MEXICO

Plate 3. Drifter tracks showing motion of a surface drifter influenced by two large warm-core (anticyclonic-ACl, etc.) rings. Near the top of the figure, both the blue and the black tracks begin in shallow water and move around in counter­clockwise patterns. The SSH contours, from Leben, have been added to the SST image. Note that although they are centered on the same day, the two images contain data taken over different time intervals. The color scale for SST is shown; SSH contours are spaced every 5 cm. From Walker (this volume).

STURGES ET AL. 7

multipurpose study involving both currents and whales, they show an interesting series of eddy patterns at the edge of the shelf; they use satellite data, currents measured from their ship's Doppler acoustic profiler, and traditional hydro casts. The flow around and between these eddies can bring fluid off the shelf to exchange with deeper waters.

The transfer of particles (or of anything) between the shelf and deep water is an important and difficult topic, as it involves turbulent exchange. Many practical issues arise. How long do particles (larvae, pollutants, sediment) stay on the shelf before they get into deep water? Will particles in river runoff settle out on the shelf before getting into deep water? Can we predict in advance and under what conditions this material will linger on the shelf, or will it be whisked quickly offshore? Conversely, how do fish larvae get from deep offshore spawning regions into the shallow grass beds? Following the track of a surface drifter can give insight into how particles move. In Walker's discussion of flow on the shelf off Louisiana and Texas, she shows a surface drifter that not only leaves the shelf to be carried around a large anticyclone, but which also is brought back to the shelf again by another anticyclone, as shown in Plate 3.

The chapter by Morey et al, though primarily a study of the coastal flow in the western Gulf, also explores the cross-shelf transport of coastal waters. The authors emphasize the cross-shelf export of shelf and river water by wind- and buoy­ancy-driven coastal circulations as well as by the mesoscale eddy field (as seen in Plate 3, for example). Loop Current rings propagate to the west, reaching the coast of Mexico and Texas in a few months. Some of the large-scale flow in the western half of the Gulf is driven by these decaying Loop Current Rings while some is driven by wind. Oceanogra-phers have yet to determine which force is dominant here despite considerable speculation over three decades. The new orbit recently given to the TOPEX/Poseidon satellite in 2003 should shed light on the issue. The shift of 1.42 degrees of longitude, which interleaves the TOPEX/Poseidon and Jason ground tracks, will provide greatly enhanced cover­age of the far western Gulf. It will improve our ability to deal with many practical issues of ocean transport as varied as oil spills (remember Ixtoc?), young turtles leaving their hatching grounds, search and rescue, or effects on shrimp fisheries.

Deep and Near-Bottom Flow

The majority of papers presented here are concerned with the circulation in the upper layers of the Gulf. The paper by Sturges examines the waters that originate in the Atlantic, flow through the Caribbean, and ultimately refresh the deeps of the Gulf. Sturges questions not only inflow of waters, but

also return flow: what goes out? A remarkable three-layer overturning pattern is found that can be traced in the deep water from the Atlantic to the Gulf and back.

Tides

Kantha has contributed a brief summary paper on tides in the Gulf. His title includes the term "barotropic," which derives from fluid mechanics and refers to that part of the flow that is uniform from top to bottom. In addition to his main paper, he has provided a brief movie of the daily aver­age tidal flow over a 24-hour period. We can ask where the tidal inflow is and where the tides are primarily diurnal and semi-diurnal and actually see the answers.

COASTAL CIRCULATION

At the risk of belaboring the obvious, the shallowest water is found at the coast. B. Douglas, a leader in the study of sea level rise, explores the issue. He compares the Gulf and Atlantic coasts, pointing out exceptions to the general rule that they are quite similar. Despite wide variability, the trend in the Gulf is unmistakable; a rise o f -20 cm in 75 years is almost a foot per century. (A plot of data from San Francisco or New York would look similar, the differences being in the details.) Who can argue with the kind of data that Douglas presents? Note, however, his use of the term "relative" when related to sea level rise. A single tide gauge does not tell whether the water is coming up, the land is going down, or some mix of both. The rate here, however, is close to the world average at mid latitudes.

Johnson's paper gives us a description of movies (found on the CD) of satellite-tracked drifters in the waters of the Gulf coast between Florida and Texas. These drifters show

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1920 1940 1960 1980 2000 Figure 1. Annual means of Relative Sea Level (RSL), dots, at Pensacola, FL. Note the large low frequency fluctuations around the upward trend. Taken from the chapter by B. Douglas.

8 INTRODUCTION TO CIRCULATION IN THE GULF OF MEXICO

how the near-surface currents on the shelf consist largely of back-and-forth motions. Monthly means as well as movies of daily motions show how irregular the motions can be. The mean flow, averaged over many weeks, is remarkably small when compared with the transient or daily currents, which respond mostly to local winds. (There are notable exceptions to this general rule; coastal trapped waves propagate for long distances. See for example reviews by Brink [1991], Davis and Bogden [1989] or Huyer et al. [2002]). The question is often asked, What is the mean flow just offshore (of point X)? The questioner may have seen occasional strong flow, and is surprised to hear, "Well, the average over which week? The mean flow this week is to the north; last week it was to the south, and the long-term average may not be reliably different from zero."

Using current-meter moorings and a numerical model, Weisberg et al. explore the flow on the very wide west Florida shelf. Although the simplest wind-forced models can explain a major fraction of the wind-forced currents fairly well, they ignore vertical motions. However, as the authors show here, a full 3-D model can depict where upwelling and downwelling regions become important.

On the north coast of the Gulf, the general area to the west of the Mississippi River is commonly called the LATEX (Louisiana-Texas) region (to be distinguished from a major experiment referred to by the same acronym). The year-long mooring array discussed by Jarosz and Murray measured the currents close inshore at the eastern end of this region, west of the outflow from the Mississippi River, from the coast out to a depth of ~ 20 m. They found the reversal of the coastal current in the summer, as expected; while the mean speeds were ~ 6 cm/sec or less, they found persistent peak speeds well over a knot.

Farther to the west, Nowlin et al. discuss the flow on the northern Gulf coast, using the nearly three-year-long data set from the LATEX experiment. The shelf off Texas is wide, and a persistent gyre-like pattern develops there. Currents over the inner shelf flow eastward, toward the Mississippi River in summer and reverse during the rest of the year. The flow pattern appears to be driven mainly by the annual cycle of winds. Because the fresh river outflow usually tends to be toward the west, the reversing flow pattern off Texas leads to an annual signal in salinity as well as in the currents.

WHAT IS IN THE CD?

The CD on the inside back cover of this book allows us to incorporate a range of extra material of interest, including appendices to some of the articles and a large number of color figures. But above all, it lets us include the animations, our "movies " from which we have learned so much. Leben's

movie alone, showing sea surface height since 1993, presents over a decade of continuous data.

An "ocean color" movie by Muller-Karger and Hu, using images from the SeaWiFS satellite sensor, records ocean radia­tion in the visible and near infrared wavelengths. This allows us to detect patterns of chlorophyll (or color interpreted as such) and to spot the occurrence of phytoplankton blooms and trace their motion. Though daily coverage of the entire Gulf is available, weekly and bi-weekly versions are used for these movies in an attempt to suppress cloud cover, a standard averaging technique used with sea surface temperature as well. For comparison, Leben has contributed a brief movie of chlo­rophyll at the sea surface, computed with a slightly different algorithm, superimposed on his contours of SSH.

Anderson and Walker have made a movie that combines data from many surface drifters collected with SST maps over the whole Gulf. The drifter motions are plotted so that the colors of the track show the speeds. What is particularly interesting is the extent to which the drifters follow (or do not!) the patterns of SST.

The ocean data from the DeSoto Canyon experiment (from the paper by Hamilton and Lee) are combined into a movie show­ing velocity and temperature data at several depths. Johnson's movies show results of two separate year-long surface drifter experiments, and Kantha's animation shows deep-water tides. A movie produced from Oey andEzer's numerical model shows a time series of velocity, top to bottom, on a N-S section at 90° W; it is remarkable to see how the pattern changes so thoroughly as Loop-Current rings pass through the section.

Hamilton compiled views of the deep mean flow as measured by long-term moorings and has contributed an extremely valuable set of figures. His diagrams show the mean flow as well as the variability at several levels for all available moorings longer than 6 months and deeper than 800 m. These direct measurements of the variability are at least as valuable as the means, as the operative question in deep water usually is "At what level of confidence can the computed mean values be reliably distinguished from zero?"

CONCLUDING THOUGHTS

This is being written in the summer of Hurricane Katrina, another terrifying reminder of the fragility of the Gulf and all other coasts. How will the witch's brew of polluted water affect the sea life along the coast as it drains from New Orleans?

An important and relevant question is whether the pres­ence of a large intrusion of the Loop Current affected the increase in Katrina's strength from a Category 1 to a 4 or 5. We thank N. Walker and R. Leben, who prepared Plate 4, which superimposes the storm track, the sea surface temper­ature, and the position of the Loop Current. A large eddy-like

STURGES ET AL.

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LSU ESL GOES-12 SST Composite Color UC CCAR Sea Surface Height (cm) 08/27 Weekly Composite 08/23-08/30. Max winds in miles/hr

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Plate 4. The track of Hurricane Katrina: dates show position of the center; black numbers show maximum wind speed (mph). Contours of SSH show the position of the Loop Current and a large not-yet-detached ring. Color scale shows SST in °F.

10 INTRODUCTION TO CIRCULATION IN THE GULF OF MEXICO

feature extends to the west but has not yet separated from the main current.

A hurricane draws energy from warm surface water. See for example the recent study of Hurricane Ivan [Walker and Leben, 2005] and the more general study by Price et al. [1994]. The warm upper layer in the Gulf in late sum­mer may be only 25-30 m thick. Within the Loop Current, however, the warm upper layer is quite deep and thus has the potential for providing a great deal more stored heat energy. The availability of a large quantity of stored heat from the Loop Current and its eddies is clear and unambiguous. Yet because the Loop Current does not have a significant annual cycle, its position in the summer is nearly random; at the onset of a major storm, the Loop Current may extend only a small distance into the Gulf or have a major intrusion as shown here. The questions involving these interactions are complex: there is vertical mixing as well as a feedback cycle; the cyclonic (counterclockwise) surface winds drive upwell-ing beneath the hurricane, so stronger hurricanes will drive stronger upwelling. The stored heat in the deep upper layer clearly influences hurricanes, but whether the effect is large or small is an open question. Hurricane prediction models "know about" sea-surface temperature, but because the models do not yet couple the atmosphere and the ocean, the depth of the warm layer is not part of the calculation (T. N. Krishnamurti,pers. comm.).

In looking over the papers in this book and the materi­als on the CD, we are struck by two things. The first is the enormous progress in physical oceanography in general,

and that of the Gulf of Mexico in particular, since the major summary by Capurro and Reid in 1972. Technology has advanced much more than we could possibly have anticipated three decades ago. The second is the increasing realization of how much we have not yet learned. Most of us were drawn to oceanography because it seemed exciting and fun. It still is.

REFERENCES

Brink, K. H., Coastal-Trapped Waves And Wind-Driven Currents Over The Continental Shelf. Ann. Rev. Fluid Mech., 23: 389-412. (doi:10.1146/ annurev.fl.23.010191.002133), 1991.

Capurro, L. R. A., and J. L. Reid, Jr., eds, Contributions on the Physical Oceanography of the Gulf of Mexico. Gulf Publishing, Houston, TX, 288 pp, 1972.

Davis, R. E. and P. S. Bogden, Variability on the California shelf forced by local and remote winds during the Coastal Ocean Dynamics Experiment. /. Geophys. Res., 94, C4, p. 4763-4783, 1989.

Davis, R. E., Intermediate-depth circulation of the Indian and South Pacific Oceans measured by autonomous floats. / . Phys. Ocean., 34, 683-707, 2005.

Huyer, A., R. L. Smith, and J. Fleischbein, The coastal ocean off Oregon and northern California during the 1997-8 El Nino. Progr. Ocean., 54, 311-341,2002.

Price, J. E , Sanford, T. B. and Forristall, G. Z., Forced stage response to a moving hurricane, / . Phys. Oceanogr. 24, 233-260, 1994.

Walker, Nan D., Robert R. Leben and Shreekanth Balasubramanian, Hurri­cane-forced Upwelling and Chlorophyll a Enhancement within Cold-core Cyclones in the Gulf of Mexico. Geophys. Res. Lett., 2005.

W. Sturges, Florida State University, Tallahassee, FL 32303-4320 A. Lugo-Fernandez, U.S. Minerals Management Service, New Orleans,

Louisiana 70123-2394 M. D. Shargel, Florida State University, Tallahassee, FL 32303-4320