1. Introduction
The currents in the Gulf of Mexico are dominated by the Loop Current, by the rings that detach from it, and by the myriad other eddies that occur. Although our focus in this paper will be the mean flow, both horizontal and vertical, the eddy motions are dominant and are important to the consideration of how all the pieces fit together. Figure 1 shows a presumably typical pattern of sea surface height: an anticyclonic ring has recently separated from the Loop Current and is drifting to the west. In this instantaneous view, rings and eddies dominate the circulation though in most means, whether from numerical models or from hydrographic data, we see a “mean Loop Current” in the east and a persistent anticyclone in the western gulf.
The winds over the gulf have a clear annual cycle; the near-shore currents along the western and northern shelf regions have vigorous annual cycles as well. The Loop Current has a great deal of variability: yet for reasons that are not understood it does not have any significant energy at 12.0 months. These flow patterns have recently been discussed by many authors (see, e.g., Ohlmann and Niiler 2005; Leben 2005; Schmitz et al. 2005; DiMarco et al. 2005) and by others on the basis of model results (e.g., Oey et al. 2005; Chassignet et al. 2005; in addition, W. Schmitz has developed a Web page devoted to a summary of our knowledge of the Gulf of Mexico, http://www.serf.tamus.edu/gomcirculation/).
The availability of essentially continuous data from satellites, both for temperature and for sea surface height, has given us a new understanding of events at the sea surface. Leben’s (2005) animation of sea surface height is particularly helpful in our attempts to understand the behavior of rings and the interaction between eddies. In contrast to the older view that a single anticyclonic ring existed almost in isolation, it is clear that several eddies of both signs are present at any given time. After looking at many figures, such as Fig. 1, one realizes that the western gulf is so dominated by eddy motions that forming a reliable mean is a difficult task.
This paper deals with several long-term datasets of winds and currents. (There is a major concern in all areas of science about climate change.) Many papers show datasets beginning in the 1800s (e.g., Mann and Emanuel 2006), but the only such long-term dataset on surface currents in the ocean is that from the well-known archives of ship drift. One of our original motivations in this work was not only to understand the implications of the ship-drift data in the gulf but also to better understand the errors in that data. We soon realized, however, that we were finding an unexpected signal that was much larger than any possible errors in the data; therefore, we were obliged to try to understand the observations. Thus, the primary purpose of this paper is to explain the implications of the unexpected finding of a net mean upper-layer flow to the west in the central gulf.
Further, as we began to appreciate how the different datasets all fit together, it became apparent that a mean vertical flow must be an essential component of the circulation. This result should not be surprising, as the curl of the wind stress over the gulf is remarkably similar to the curl over the central North Atlantic; on most maps of wind curl, the near-maximum contours that pass near Bermuda continue into the Gulf of Mexico. The analogous vertical component of flow that feeds the thermocline in the midlatitude anticyclones of the ocean is well known (e.g., McDowell et al. 1982; Luyten et al. 1983; and many others), even though it is not a component of circulation in the gulf that is often discussed. The primary mean circulation in the upper Gulf of Mexico is anticyclonic; we should not be surprised that the flow is remarkably analogous to the flow in the central North Atlantic.
Our paper is arranged as follows: we first briefly describe the surface wind field; next, from different sets of data, we describe the observed near-surface flow. Putting these together leads to the typical internal Sverdup flow regime and the associated downwelling beneath a convergent wind system. To track the deep water paths, we then study the distribution of salinity and potential temperature in the deep water. We then examine the density distribution in detail to estimate the mean north–south dynamic height difference in the central gulf. Finally, we estimate the deep mean flow from calculation of potential vorticity (PV).
2. Surface winds
Many analyses of surface winds are available, and useful plots can be found in many forms. The dataset from the National Centers for Environmental Protection, usually referred to as “NCEP reanalysis winds,” is widely available. Useful insights can be drawn from the set of monthly mean maps prepared by Rhodes et al. (1989), who compared the computed geostrophic winds with observations at a central gulf buoy to find the necessary correction factors. The “FSU Winds” (Shriver and O’Brien 1995) are widely used; the results of Isemer and Hasse (1985) are widely respected as well. Boning et al. (1991) computed the Sverdrup transport in the North Atlantic using the wind stress values of both the Hellerman–Rosenstein and the Isemer–Hasse climatologies. They found substantially increased transports when using the Isemer–Hasse values.
In the present application (to the Gulf of Mexico), we take the point of view that the surface velocity observations are the basic results to be understood. Both the wind stress and surface velocities have errors that are difficult to quantify, so we assume that it is important primarily to ask whether the long-term mean downward pumping is reasonably consistent with the enigmatic mean surface flow into a closed western gulf.
The basic features of the wind field are 1) the prevailing flow is from east to west and 2) the speeds decrease from south to north. The curl of the wind stress is typically negative except in the southwestern corner of the gulf (Vazquez et al. 2005). The curl has a substantial annual cycle with a maximum in the summer (e.g., Sturges 1993). The monthly mean maps of Hastenrath and Lamb (1977) show that the winds tend to be from the northeast from November through January, while from the east or the southeast during the rest of the year; the mean speeds are typically ∼4 m s−1 in the south and ∼2 m s−1 in the north. To focus on the issue of most importance here, the wind signal can be represented adequately by the simplified view in Fig. 2, which shows the north–south distribution of annual-mean westward wind speeds in the central gulf from Isemer and Hasse (1985). This result is consistent with the other long-term atlas compilations, but the speeds are weaker, by almost a factor of 2, than the observations at the NOAA/NDBC buoy 42001 in the central gulf. There are various ways to try to explain this discrepancy, but that is not the focus of the work here. Note that Fig. 2 shows the essentially linear distribution of mean wind speed, not stress.
The Ekman transport is clearly to the north everywhere, so the flow in the upper layers is convergent across the full north–south extent of the basin. As in the North Atlantic south of Bermuda, the Ekman flow is to the north but the Sverdrup interior flow is to the south (see, e.g., Mayer and Weisberg 1993). The near-surface flow will be at an angle to the right of due west. Price et al. (1987) found that the daily averaged flow at ∼5 m would be roughly 60° to the right; McWilliams and Huckle (2006), however, show that the angle between the surface current and wind increases with increasing wind variability. In the North Atlantic, the northward transport in the Ekman layer flow south of Bermuda vanishes where the wind stress changes sign. In the gulf, by contrast, the mean wind stress does not reach zero, so the northward Ekman transport runs into the coastal boundary flow along the southern United States. The effect is the same: the convergent flow must be pumped down.
This flow regime is analogous in part to the well-known Sverdrup flow as exemplified by Fig. 8-4 of Cushman-Roisin’s (1994) text. It is important to remember, however, that the wind pattern over the gulf is similar to only the southern third of the wind pattern over the typical open ocean gyre. Because the curl of the wind stress never goes to zero (in theoretical models at least), the flow to the north along the western boundary does not easily leave the coast but extends to the northern boundary, looping back around into the interior. Because the wind stress has such a large annual cycle and the large Loop Current rings are so often present, realizations of the ideal solution will only be seen rarely. The interior flow field is also rather like that shown by Warren (1982) in his modeled Indian Ocean. In the middle section of his Fig. 18, the source on the eastern boundary can be compared with the (wind driven) flow in the 20°–23° band here.
3. Surface currents
Recent observations of surface currents have been made with remotely tracked drifters. Nowlin et al. (2005) give a full description of the currents on the wide Texas shelf; Ohlmann and Niiler (2005) confirmed that the mean flow along the northern coast of the gulf south of Texas is to the west and has an annual cycle. DiMarco et al. (2005), in a study that is particularly important to our work here, analyzed a long-term comprehensive set of near-surface drifter data. They show seasonal means as well as an annual mean over the entire gulf. Weatherly et al. (2005) examined a set of drifter data different from that of DiMarco, with values both at the surface and at ∼900 m.
a. Ship drift data
The largest available dataset, and the one that has by far the longest records, is based on ship drift; the data are available as a CD set from the National Oceanographic Data Center. Figure 3 shows annual-mean surface currents based on the most recent compilation of which we are aware—an analysis carried out at the Naval Oceanographic Office, Stennis, Mississippi; copies were distributed widely (D. Thompson 1989, personal communication). Note that the similar Fig. 1 shown in Sturges (1993) is not the annual mean, but is for the month of July.
A more detailed view of this dataset is in the published atlas of the Naval Oceanographic Office (1981). Each data point is from a track of either 12 or 24 h. It is common practice for U.S. ships to use 12 h, but many foreign vessels use 24 h. It is unlikely, therefore, that a ship’s result can place a data point in two (or even three) adjacent 1° boxes.
Thus, for example, the boxes between 23° and 24°N, 90° and 93°W, which are not along major shipping lanes, have sparse data, a combined total of ∼400 independent observations. A ship’s drift velocity is commonly reported to 0.1 kt (5 cm s−1); if we suspect that the error in a single data point is perhaps 4 times that, the standard error of the mean of 400 observations is reduced to ∼ 20 cm s−1/20, or ∼1 cm s−1, if we assume that the errors are random. This seems a reasonable assumption, as the currents and winds on any given day are likely much larger than the mean. Most of the individual 1° boxes have substantially more observations than a few hundred. We therefore suspect that the random errors in the mean values of reported ship drift are a much smaller source of concern than the fraction of the ship’s drift induced by windage on the ship, from Stokes drift, or perhaps by the action of reflected waves.
Several features in Fig. 3 can be found in all of these current observations. The Loop Current in the eastern gulf is obvious but not very well resolved. Ship-drift data are Lagrangian results based on a ship’s track over 12 or 24 h, so structure at scales of the width of the Loop Current will be smoothed or lost. There is a concentrated flow to the west along the northern coast of Mexico; this flow is consistent with the interior Sverdrup flow to the south. Along the western boundary of the gulf there is flow to the north. Most noticeable is the main point addressed here: If all the flow in the central Gulf is to the west, where is the return flow? This last, puzzling feature is present in almost all months of all such analyses in the Gulf of Mexico.
Ship-drift data contain a large store of potentially valuable observations of near-surface flow. These data extend throughout many years and are reasonably well distributed across the seasons. Where the signal is strong, Richardson and Walsh (1986) were able to use the ship-drift data very well (see also Arnault 1987). A nice example of analysis comparing ship drifts, Ekman-layer velocities, and the geostrophic component is given in Richardson et al. (1992). In a particularly noteworthy paper, Richardson (1997) studied the effects of winds from different directions blowing directly on the ship. He was able to deduce a correction term that can be applied to reduce that specific error in the data. Richardson found that, in the cases he studied, the error in leeway was 0.6% of the wind speed for vessels steaming normal to the wind and half that for random orientations. We assume that his result (at similar latitudes) is appropriate to our data here.
Figure 4a shows the mean north–south distribution of westward surface speeds in the central gulf from ship-drift data. It is straightforward to apply Richardson’s correction term; it is immediately clear, however, that the mean flow to the west is hardly affected at all by this correction (∼0.6–1.2 cm s−1), so it has not been applied in this figure. The primary flow to the west in the current along the north coast of Mexico has speeds O(20 cm s−1); a correction term on the order of 1 cm s−1 is lost in the noise. Because the sign of the wind correction is unambiguous, however, in general it should be retained.
b. Surface drifter data
Figure 4b shows a similar plot of westward surface velocity using the data of the 10-yr study from drifters drogued at 50 m, from the work of DiMarco et al. (2005). It is important to realize that this dataset is independent of the ship-drift data, both in method and in time. While in principle the drifters also provide Lagrangian data, their analysis method uses a smoothed velocity estimate computed from adjacent 6-h positions that fall into a box 1½° on a side. Thus, these values have a finer spatial resolution than do the ship-drift data based on 12- or 24-h fixes.
Figure 4c shows the number of observations in both datasets. DiMarco et al. (2005) chose to report the degrees of freedom of data in the individual bins. Because the decorrelation time scale of the data is ∼8 days, the degrees of freedom are determined as the total number of 6-hourly observations divided by 32, the number of observations in an 8-day time window.
c. Comparison of datasets
Figure 5 is a primary result: it compares the two measures of near-surface velocity by the two methods. The two data sources agree remarkably well in the strong flow to the west along the coast of Mexico. Within that region of strong current the two values, when integrated across the flow, are essentially identical. The two means are noticeably in disagreement, however, at 25.5° and 26.5°N. Because large rings that separate from the Loop Current drift through these latitudes, it is reasonable to expect that the resolutions of the two datasets would show a different result. The difference in the mean flow between the two datasets in Fig. 5 in this region is so great, however, that the difference appears to be real. The north–south mean for the ship drift is 12 cm s−1 and for the drifters, 7 cm s−1. The drogues at 50 m are not in the surface mixed layer in the summer, so the two methods are measuring different quantities, but this is true in the south as well. The two datasets are from vastly different times, and this difference may be important.
In the band of strong flow in the region 22°–24°N along the Mexican coast, the ships are preferentially traveling with the wind and current, so the effects of wind and waves will be smallest there. It is possible that the reflection of waves from the ships’ hulls could make a significant difference in the central region, where the ships are traveling at a greater angle to the wind and waves. This topic will be addressed in a separate paper. The net difference in the north–south mean near-surface flow between the two datasets is thus ∼4–5 cm s−1. This, in fact, could be an indication of the errors as well as a problem with the signal-to-noise ratio. Whereas that difference is troublesome and as yet unexplained, it is not central to the main point of our work, so will not be pursued further here.
In the northern gulf (Fig. 5) the speeds from ship drift are greater than those from the 50-m drifters. The tracks of ships in this region are primarily along shipping lanes from the Yucatan Channel to the Texas coast; thus, because they have come preferentially from the region of the Loop Current, we can speculate that this difference is symptomatic of a bias arising from the remnants of strong Loop Current speeds in a portion of the Lagrangian tracks. Further, because the ship-drift data in the central latitudes could also contain remnants of Loop Current velocities, it is possible that the differences there are evidence of this bias. The flow to the west along the northern boundary of the gulf could arise from coastal currents that are driven by the prevailing alongshore winds reenforced by the inflowing Ekman surface drift.
Several aspects of the ship-drift data, however, give us confidence that the data have genuine value. First, in the central gulf at 25°–26°N, where the large Loop Current rings drift across to the west, the ship-drift data show an essentially bimodal flow: roughly half the values are to the east and roughly half are to the west. There is a small mean value, to within error bars, that is appropriate for the drift of rings.
Second, the strong flow to the west along the northern Mexican coast not only agrees with the drifters but is consistent with classical ideas of Ekman pumping and interior Sverdrup flow. Third, the velocity values in the strong flow to the west are much larger than the suspected errors in the data or the correction terms suggested by Richardson (1997). Fourth, the concentrated flow along the western boundary is to the north while the winds are out of the east, so it is highly unlikely that errors from wind or wave effects could lead to erroneous results of that kind. Moreover, the surface Ekman flow is too small to account for the observed ship drift.
4. Wave effects
Richardson’s (1997) work appears to be the best study to date of the errors in ship drift. Yet one issue remains. His analysis, and its clever execution in the North Atlantic shipping lanes, is based on the assumption that the errors in ship drift are caused almost exclusively by the effects of winds blowing on the exposed area of the ship. It is possible, however, that two effects of waves should be explicitly considered: 1) the well-known Stokes drift and 2) the effect of waves being reflected from the ship hulls. These effects are included in Richardson’s results but are implicitly attributed to wind forces. We therefore merely mention here brief comments about these two issues as they may affect the results of ship-drift data.
a. Stokes drift
Our attitude toward the effects of Stokes drift in the present case is a bit ambiguous. In most oceanographic settings, we think of the large-scale, near-surface flow as extending much deeper than a few meters, whereas the Stokes drift is limited to the upper layer in which wave orbital velocities are prevalent. In regions of weak currents, however, the Stokes drift can be as large as the reported ship-drift speeds, so inclusion of the Stokes drift component can be important in understanding the motion of the ship through the water. Because this effect is usually small and is well described in the literature, we merely give here the results of our calculations (see, e.g., Kenyon 1969). McWilliams and Restrepo (1999) have accorded the Stokes drift a new level of importance by incorporating it into numerical wind-driven circulation models applied over whole ocean basins. Our conclusion, however, is that under the mean wind conditions of the Gulf of Mexico, the effect of Stokes drift on a typical ship here is O(4 cm s−1).
b. Wave reflection
While Stokes drift is often discussed, a potentially larger effect arises from the reflection of waves from a ship’s hull. We point this out explicitly because the major influence from Stokes drift in the Gulf of Mexico is largely the result of the longer waves. By contrast, the waves that will be reflected from a hull will be those that have lengths on the same order as depth of the hull (see, e.g., Kenyon 2004; Kenyon and Sheres 2006). Thus, the momentum imparted by reflected waves will largely be from shorter waves. The long waves and swell will not be reflected, of course, as the ship merely rides over them. Because the shorter waves are in equilibrium with local wind, while the longer waves tend to be preferentially from swell, it may be possible to distinguish between the two effects. This issue is not central to the main point of this paper, so will be reported separately.
5. How can there be a net flow into a closed basin?
The principal result thus far is the finding that 1) there is an observed mean surface flow to the west and 2) the curl of the wind stress is negative over the central gulf. In an attempt to explain the curious observation of a mean surface flow into a closed basin, DeHaan (1998) made a series of geostrophic calculations that use the ship-drift values (corrected by Richardson’s method) as a surface boundary condition. He found that the mean net flow to the west has an annual mean of ∼3 Sv. This mass transport of 3 Sv may all be contained in the boundary current along the northern Mexican coast. If the surface flow to the west in the latitude band 21°–24°N decreases from 20 cm s−1 linearly to zero at 300 m, the resulting mass transport is precisely that amount. If the net transport is all contained in the flow along the southern boundary, there need be no transport north of there—a point to which we return in section 10.
6. Ekman convergence and the Sverdrup interior
The gulf-specific wind values of Rhodes et al. (1989) allowed Sturges (1993) to determine the curl of the wind stress in the central basin along 24°N. There is a seasonal variation of (−5 to −18) × 10−9 dyn cm−3 with a mean of ∼−10. A large annual cycle is typical of these latitudes. Using the traditional linear Sverdrup relation and β = 2 × 10−13 s−1 cm−1, these values lead to transports (to the south) of −2.5 to −7.5 Sv with a mean of ∼5 Sv.
The Sverdrup transport is the portion of the interior flow that must be returned to the western boundary. It is the horizontal part of the flow. It agrees, within reasonable error estimates, to the flow to the west along the coast of Mexico as discussed above. In the main anticyclonic gyres of all oceans this feature has been well understood for a long time. We emphasize it here only because we are not aware of a discussion of it previously as it relates to the Gulf of Mexico. The three separate parts of the flow field described here are summarized in Table 1. They are computed independently; although they are subject to discouragingly large uncertainties, we assume that these values are correct to somewhat better than an order of magnitude. The magnitudes of the annual cycles are of course subject to larger uncertainties.
7. But where does the water go?
The final issue to deal with is the question of how there can be a net downward pumping out of the bottom of the Ekman layer over essentially the whole (closed) western half of the basin. That is, even if there is a mean Sverdup flow, where does it eventually go? In a discussion of this general topic for circulation in the open ocean, the issue would usually be ignored; the water somehow simply “goes away.” Here, however, because the basin is closed to the west, one is curious about the manner of outflow.
The most straightforward answer is that water is pumped down below the westward-flowing near-surface flow so that it can return at depth and leave the gulf via either the Straits of Florida or the Yucatan Channel. For the near-surface waters to reach sufficient depth to leave below the upper-layer flow, there are many potentially operative mechanisms: winter surface cooling, flow along steeply sloping isopycnals, the pumping of the Loop Current intrusion cycle, and the downward pumping of the convergent Ekman layer, where momentum and energy are supplied by wind stress.
The idea of a vertical flow, pumped down out of the upper surface layer, is well known in the major ocean basins, although to our knowledge it has not been discussed in the Gulf of Mexico. The speed of these vertical flows is difficult to grasp intuitively; because it is only on the order of ∼100 m yr−1, it is clearly buried in the much larger signals of internal and inertial wave motions and horizontal flows. The downward path occurs partly as a tiny addition to horizontal flow and is carried in eddies of both signs. The descent of surface water along sloping isopycnals has been studied for decades (e.g., McDowell et al. 1982; Luyten et al. 1983).
Keffer (1985) shows maps of density surfaces in the open Atlantic and discusses the presumably similar downward Ekman pumping in the North Atlantic that takes place south of the zero wind stress curl line.
a. Surface cooling
Although the Gulf of Mexico is not usually thought of as a source of deep-water formation, the cold fronts that sweep off the continent often bring below-freezing (air) temperatures. Temperatures as low as ∼12°–13°C are often found on SST maps after a cold front sweeps across the western gulf. The sea surface is usually obscured by clouds during frontal passages, however, and the coldest water sinks rapidly. When examining records of surface water temperature at the buoys offshore of the west Texas coast (e.g., National Data Buoy Center buoy 42035, 22 n mi from Galveston) it is not difficult to find temperatures of ∼10°C in randomly selected February data; surface temperatures can occasionally reach 8°C. Nowlin and Parker (1974) reported a band of water approximately 10°–14°C along the coast immediately after the passage of a cold front, consistent with the cold bands seen in the SST images.
It is worth remembering that surface cooling is not totally restricted to winter months; Loop Current rings carry to the west a large volume of water whose dominant surface signature is its warm core, which erodes in all seasons. Furthermore, other mechanisms (discussed next) could initiate a deepening process, with the actual cooling taking place several months later. Niiler and Stevenson (1982) suggest that much of the heat loss from these upper-layer warm waters is by turbulent diffusion that mixes the heat downward. Dewar et al. (2006) have suggested a new mechanism of vertical mixing induced by biological migrations; this mechanism has very broad implications here and elsewhere.
b. Steeply sloping isopycnal surfaces
In the open Atlantic, winter cooling in the far north brings many deep isotherms to the surface; this is the mechanism by which the thermocline is ventilated. An analogous mechanism in the Gulf of Mexico is provided by the steeply sloping isotherms that are found in rings and “ring pairs.” In an XBT section across a cyclonic–anticyclonic ring pair, the 14°C isotherm rises above 200 m and reaches down below 400 m. In strong eddy flows or in the Loop Current, isopycnals slope downward another ∼200 m. The 10°C isotherm in the northwestern gulf in winter is found as shallow as 200 m and at much shallower depths along the left-hand side of the Loop Current or Florida Current. Along the right-hand side of these flows, however, the 10°C isotherm reaches well below 600 m. Thus, it is plausible that the upper waters forced down by Ekman pumping can be carried along isopycnals to depths perhaps greater than ∼600 m.
c. Pumping action of the Loop Current intrusion cycle
The final mechanism for removing this extra mass flux from the western gulf is the pumping action of the Loop Current as it goes through a ring-shedding cycle. Bunge et al. (2002) and Sheinbaum et al. (2002) found surprisingly strong deep exchanges between the gulf and the Caribbean Sea. They found that, when the Loop Current is advancing to the north, a compensating deep flow to the south is observed in the Yucatan Channel well below the depth of the Straits of Florida. During a Loop Current shedding cycle, the southward deep flow had transports greater than ∼5 Sv for periods longer than a month. They found a deep mean flow to the south on the Mexican as well as the Cuban side. It is crucial to recall that this “pumping action” of the Loop Current intrusion is a one-way process. After the Loop Current has intruded to the north, a ring separates (roughly once a year) so that most of the mass that has intruded remains in the gulf. The essential idea here is that mass is added in the upper layers but is removed from the deeper layers, which is an answer to the issue to be resolved. (The mean addition of warm water in the surface and loss of cold deep water also has to be considered in heat-budget scenarios.) There may also be a deep flow to the east along the southern boundary of the basin as part of a mean deep cyclonic flow (see, e.g., DeHaan and Sturges 2005).
d. Comparison with Loop Current rings
The previous sections have been an attempt to deal with getting rid of the extra mass flux to the west and, to a lesser extent, the heat flux. It is most instructive, therefore, to compare these with the mass and heat fluxes contained in the approximately annual shedding of a Loop Current ring. Using typical values (∼300 km diameter, ∼1000 m depth) one finds that the mass flux associated with a single ring is ∼3 Sv.
It seems appropriate also to mention the work of Hoffmann and Worley (1986), who used an inverse solution to find an estimate of the mean flow in the gulf. They chose a three-layer scheme in which they assumed no net flow in each layer; their uppermost layer reached down to ∼600 m, thereby ruling out by assumption the mean flow from the ship-drift and drifter data that form the basis of our work here.
e. Evidence from water property distributions
One traditional method of searching for weak flows is to examine water properties on density surfaces. It is well known that the Loop Current brings the high salinity “Tropical Water” into the gulf in the near-surface layers. When rings detach and drift to the west, they carry this high salinity layer into the western gulf. If this high salinity water is pumped or mixed downward and then carried back to the east by the flow postulated here, the requisite higher salinity might show up on maps of deeper density surfaces. Figure 6a shows the depth, and Fig. 6b the salinity, on the 27.4 sigma-theta potential density surface derived from a carefully constructed long-term mean density dataset. At these depths the Loop Current water has the low salinity signature of Antarctic Intermediate Water (AAIW). In the western gulf, however, the salinity is higher than the incoming AAIW. This higher salinity can result from both vertical mixing and downward pumping of higher salinity water that is above this density surface. While this result is based on a collection of averaged data, a similar result showing higher salinity in the western gulf at these depths was found by Nowlin (1972) based on nearly synoptic data from a single cruise. This evidence is completely consistent with the idea of downward pumping.
As far as we can tell, the existing database of typical tracers (oxygen, nitrogen, or isotopes) in the gulf is not yet adequate to allow their use in a long-term-averaged sense.
8. Inferences from potential vorticity
Examining the potential vorticity between two density surfaces allows us to determine whether a deep mean flow as proposed here is dynamically possible. Figure 7 shows potential vorticity between the 26.8 and 27.65 sigma-theta surfaces at depths of ∼250 to 1000 m; the exact choice of these two surfaces does not significantly affect this result. The contours (6.3–7.3) × 10 −13 cm−1 s−1 found in the western gulf can also be found in the Caribbean Sea near and south of the Yucatan Channel with some eddy noise in between. Thus, because geostrophic flow takes place along PV contours, it is likely that deep water from the western gulf does, indeed, flow to the Yucatan Channel and back into the Caribbean. The direction of the flow, of course, is not implied on such maps, but from the basic ideas here it surely must be from west to east.
9. Can we find these results in dynamic height?
Most oceanographers familiar with the Gulf of Mexico will know that the mean surface flow to the west as described here is not a feature that is “known” from conventional maps of dynamic height. The reason, of course, is that maps of dynamic height typically assume that a reference surface (such as 1000 db) is level or, equivalently, that the flow at those depths is vanishingly small. There is a plausible alternative assumption.
If we assume that the surface flow suggested by the data here is correct, it is straightforward to compute the vertical geostrophic shear, use the surface velocity to set the unknown constant of integration, and examine the resulting flow profile.
To compute the dynamic height is straightforward: below 300 m the signal is weak. Table 2 shows the values of density at the north and south edges of the basin in the center of the gulf, interpolated at longitudes ∼90°–93°W, at a series of depths as determined from maps similar to Fig. 6a, except plotted at high resolution and with finescale contours.
There is a small mean difference of ∼10 m across the gulf on these surfaces, with the deeper value at the southern edge of the basin. Thus, density surfaces slope upward from south to north. The net dynamic height difference across the basin between 300 and 1000 db is ∼10 cm. (The uncertainty is ∼3 cm.) While the deeper data are “noisy,” the persistent difference shown in Table 2 is unmistakable. The conclusion here, therefore, is that, if the mean surface flow is to the west, so as to satisfy continuity, the velocity must reverse at depths of approximately 300 m, and the 1000-db pressure surface slopes down from south to north. The slope of these pressure surfaces is small but appears to be well above the noise, which means that the deep flow is eastward, providing the return flow necessary to balance the westward near-surface flow. A deep mean velocity O(1 cm s−1) and a net transport of ∼3 Sv is a straightforward result. Because the frequent passage of rings provides much larger velocities, such a result will emerge only in a long-term mean.
The alternative is to assume that the deep surfaces are level. This assumption gives ∼3 Sv of deep flow to the west below 300 m, thus doubling the mass transport problem, which is an untenable result.
10. Discussion
The primary result of this work is that there is a net surface flow into the western gulf of Mexico that is pumped downward, out of the surface layers, and leaves the gulf via a deep flow in the Yucatan Channel and perhaps partly through the Straits of Florida. Given the various bits of evidence, we are now in a position to (try to) understand how the flow patterns fit together, using the values from Table 1. The net mass flux in the flow to the west along the southern boundary of the gulf is estimated to be ∼3 Sv, which is the same as the annual mean westward flow estimated from ship drift (plus hydrographic data). Independent data from surface drifters confirms the net westward flow. We would, of course, expect to find a balancing flow back to the east in the northern gulf, but it is not found in the observations. We conclude, therefore, that the mass carried to the west by Loop Current rings, also ∼3 Sv, must balance the expected mass flux coming out of the western boundary flow, although in a most complex way. As these two flows converge, the combined flow is pumped down by the various mechanisms discussed earlier. The winds have a clear annual cycle, but the shedding of Loop Current rings does not, so the details of the phases of these different parts of the flow are completely obscure.
Because it is so hard to see how these different pieces fit together, it may be helpful to emphasize the lack of any simple, direct connection between the downward Ekman pumping and the Sverdrup interior flow. The surface Ekman layer is directly driven by the local wind stress; the Sverdrup transport by contrast represents (in part) the mean accumulated effects of convergent Ekman pumping and has no direct forcing terms in its calculation. Using typical values here, the maximum mean wind stress of ∼1 dyn cm−2 at 25°N, over the width of the gulf west of 88°W, yields only ∼1.3 Sv of Ekman surface transport. Clearly several years of such input must accumulate to develop an interior Sverdrup flow of ∼5 Sv shown in Table 1.
It is important to be aware of the very small values of velocity that are able to support a mass flux out of the western gulf. The vertical shear in the western gulf below ∼300 m is quite weak, and the observed deep flow to the south in the Yucatan Channel penetrates very deep. If we assume that a deep, broad flow leaves the western gulf over the full north–south extent of the gulf with a vertical extent of ∼1000 m, as discussed in the previous section, the associated average velocity required to provide 3 Sv is only ∼0.5 cm s−1. The early work of Fofonoff (1954) suggests that, while strong flows to the west are allowable, strong flows to the east would be unstable. Thus, we suspect that a deep flow to carry the transport of ∼3 Sv back to the east should be distributed across a wide area in the southern part of the basin; if it were concentrated along the boundary, it would be easier to observe.
Sturges (2005) deduced a deep mean southerly outflow from the gulf back into the Caribbean Sea at depths below ∼1100 m. Mooring results in the Yucatan Channel show a deep outflow along the western wall (on the Mexican side) below ∼500 m that is completely consistent with these results. J. Sheinbaum (2007, personal communication) has found that the salinities observed in the Yucatan flow show lower salinities in the region of AAIW in the inflowing waters and higher salinities in the similar T, S properties in the outflowing waters. This increase in salinity from inflow to outflow properties is consistent with the mixing and downward motions suggested here.
One other mechanism should perhaps be mentioned, if only for completeness: the loss of surface waters by evaporation. The magnitudes of evaporation minus precipitation over the gulf are orders of magnitude smaller than the ∼3 Sv values described here (e.g., Schmitt 1998): The inflow from rivers tends to offset this loss.
The observations of Sheinbaum et al. (2002) from deep moorings showed southward-directed mean flow on the Mexican side in the Yucatan Channel at depths of ∼600 m and deeper. The standard deviation is large, however, and flow to the south occurs often at shallower depths. Thus, it is abundantly clear that the water pumped down out of the Ekman layer can leave the gulf through the Yucatan Channel and flow back to the Caribbean. The possibility that some of the water pumped down leaves the gulf with the flow through the Straits of Florida is also equally plausible but is not pursued here; the dataset used in the construction of Fig. 7 is not sufficiently resolved in the region of the outflow.
While almost all numerical models show strong flow to the west in the southern part of the basin, none that we have examined shows a net upper-layer flow to the west; all show the balancing surface flow coming from the western boundary. Whether this disagreement with the observations is from imperfect physics and forcing, inadequate resolution, or some other cause, we cannot say. Perhaps model runs that use our full knowledge of the Loop Current ring shedding after 1993, such as given by Leben (2005), could clarify these issues. The downward pumping of surface waters requires mixing and water mass transformations, which are difficult modeling issues.
One other result emerges from this work. The results here are based heavily on ship-drift data. Most of our early understanding of ocean surface currents came from these observations. To our knowledge, ship-drift data are no longer being collected. Ship-drift data are rarely used in modern studies, in large measure because of concern for their accuracy. The results here suggest that ship-drift data have an accuracy approaching that of modern drifters. Considering the remarkable accuracy available with modern navigation techniques, ship-drift data could provide a continuing major source of surface current data, which, while relatively cheap, would nicely complement the data taken from modern methods.
Acknowledgments
We are grateful to many colleagues for discussions of this topic: in particular, D. Nof, L. Oey, W. Schmitz, M. Stern, and B. Warren have been most helpful; the work of C. DeHaan was essential. Steve DiMarco was generous in sharing the drifter data, and Mia Shargel provided admirable editorial help. We are happy to acknowledge the helpful comments from Phil Richardson over many years; Robert O. Reid and Julio Sheinbaum made thoughtful and helpful comments on the original manuscript that improved it considerably. During this work W.S. had support from NSF Grant 0326233 and the Minerals Management Service, Cooperative Agreement 1435-1-04-CA32645.
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Transport estimates of the three flow components.
Depths of potential density surfaces at the northern and southern limits of the central Gulf of Mexico interpolated at longitudes ∼90°–93°W.