• Bunge, L., J. Ochoa, A. Badan, J. Candela, and J. Sheinbaum, 2002: Deep flows in the Yucatan Channel and their relation to changes in the Loop Current extension. J. Geophys. Res., 107, 3233, https://doi.org/10.1029/2001JC001256.

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  • DeHaan, C. J., and W. Sturges, 2005: Deep cyclonic circulation in the Gulf of Mexico. J. Phys. Oceanogr., 35, 18011812, https://doi.org/10.1175/JPO2790.1.

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  • DiMarco, S. F., W. D. Nowlin Jr., and R. O. Reid, 2005: A statistical description of the velocity fields from upper ocean drifters in the Gulf of Mexico. Circulation in the Gulf of Mexico: Observations and Models, Geophys. Monogr., Vol. 161, Amer. Geophys. Union, 101–110.

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  • Enkoji, R., 2010: Current - Direction and other data from multiple ships from world-wide distribution from 18940101 to 19931231 (NODC Accession 9400068), version 1.1. National Oceanographic Data Center, accessed 15 December 2016, https://catalog.data.gov/dataset/current-direction-and-other-data-from-multiple-ships-from-world-wide-distribution-from-1894010.

  • Fuglister, F. G., 1951: Annual variations in current speeds in the Gulf Stream system. J. Mar. Res., 10, 119127.

  • Hamilton, P., 2009: Topographic Rossby waves in the Gulf of Mexico. Prog. Oceanogr., 82, 131, https://doi.org/10.1016/j.pocean.2009.04.019.

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  • Leben, R. R., 2005: Altimeter-derived Loop Current metrics. Circulation in the Gulf of Mexico: Observations and Models, Geophys. Monogr., Vol. 161, Amer. Geophys. Union, 181–201.

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  • Maximenko, N., P. Niiler, L. Centurioni, M. Rio, O. Melnichenko, D. Chambers, V. Zlotnicki, and B. Galperin, 2009: Mean dynamic topography of the ocean derived from satellite and drifting buoy data using three different techniques. J. Atmos. Oceanic Technol., 26, 19101919, https://doi.org/10.1175/2009JTECHO672.1.

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  • Pérez-Brunius, P., H. Furey, A. Bower, P. Hamilton, J. Candela, P. Garcia-Carrillo, and R. Leben, 2018: Dominant circulation patterns of the deep Gulf of Mexico. J. Phys. Oceanogr., 48, 511529, https://doi.org/10.1175/JPO-D-17-0140.1.

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  • Ralph, E. A., and P. P. Niiler, 1999: Wind-driven currents in the tropical Pacific. J. Phys. Oceanogr., 29, 21212129, https://doi.org/10.1175/1520-0485(1999)029<2121:wdcitt>2.0.co;2.

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  • Richardson, P. L., 1997: Drifting in the wind: Leeway error in ship-drift data. Deep-Sea Res. I, 44, 18771903, https://doi.org/10.1016/S0967-0637(97)00059-9.

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  • View in gallery

    Mean speeds in the western Gulf of Mexico from ship drift, drifters, and from SSH in mean dynamic topography.

  • View in gallery

    Mean absolute dynamic sea surface topography, from the work of Maximenko et al. (2009). Such maps can be created easily from their web page (see text).

  • View in gallery

    All ship drift tracks in the western Gulf in September. The box shows the region of focus in this study.

  • View in gallery

    Histogram of the E–W speed component of all ship-drift observations in September, with those in the north shown in gray. The y axis is number of observations. The speed is in cm s−1. A Gaussian curve is superposed, with the mean shifted to lie at −12 cm s−1, the mean of the observations.

  • View in gallery

    Histogram of the number of data points in each year for ship-drift data in the Gulf of Mexico.

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    Annual cycle of pseudo stress from E–W wind components within 22.5°–29°N, 90°–95°W. The dashed line shows the N–S mean annual cycle.

  • View in gallery

    Ship drift speeds in the northern section, plotted as a function of wind pseudo stress along 25.5°N. Components are to the west; vertical bars show an estimated two standard deviation error on speeds. The linear least squares fit is merely an aid to the eye and is not statistically significant. Data are monthly means from the northern half of the boxed area in Fig. 3, as in Table 1.

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On the Mean Flow in the Western Gulf of Mexico and a Reappraisal of Errors in Ship-Drift Data

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  • 1 Earth, Ocean and Atmospheric Sciences, Florida State University, Tallahassee, Florida
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Abstract

Ship-drift data in the Gulf of Mexico have led to a perplexing result, that the near-surface flow in the west has a north–south mean, of the east–west flow, ~5–10 cm s−1 into a closed basin. Ship-drift data have been used in the past hundred years under the assumption that they are reasonably accurate; the present study examines that assumption carefully, finding that the standard deviation of individual observations is typically ~20 cm s−1. In a monthly mean composed of order 400 observations or more, as examined here, the standard error of the mean will be reduced accordingly. In the southern part of the western Gulf of Mexico, the observed upper-layer flow is clearly to the west and is consistent with our expectations. In the northern part, however, the apparent flow as reported by ship drift in deep water is not significantly different from zero. Thus, the puzzling result remains: three different datasets in the southern half of the basin clearly show flow to the west, with speeds of 10 cm s−1 or more, yet there is no clear evidence of a near-surface return flow back to the east. The convergent wind stress forces downwelling of the upper layer; its return flow could be at some intermediate depth. The transport to the west from Loop Current rings is possibly returned in a deep boundary flow driven by the rectification of deep topographic Rossby waves.

Corresponding author: Wilton Sturges, wsturges@fsu.edu

Abstract

Ship-drift data in the Gulf of Mexico have led to a perplexing result, that the near-surface flow in the west has a north–south mean, of the east–west flow, ~5–10 cm s−1 into a closed basin. Ship-drift data have been used in the past hundred years under the assumption that they are reasonably accurate; the present study examines that assumption carefully, finding that the standard deviation of individual observations is typically ~20 cm s−1. In a monthly mean composed of order 400 observations or more, as examined here, the standard error of the mean will be reduced accordingly. In the southern part of the western Gulf of Mexico, the observed upper-layer flow is clearly to the west and is consistent with our expectations. In the northern part, however, the apparent flow as reported by ship drift in deep water is not significantly different from zero. Thus, the puzzling result remains: three different datasets in the southern half of the basin clearly show flow to the west, with speeds of 10 cm s−1 or more, yet there is no clear evidence of a near-surface return flow back to the east. The convergent wind stress forces downwelling of the upper layer; its return flow could be at some intermediate depth. The transport to the west from Loop Current rings is possibly returned in a deep boundary flow driven by the rectification of deep topographic Rossby waves.

Corresponding author: Wilton Sturges, wsturges@fsu.edu

1. Introduction

Two separate mechanisms force the circulation in the western Gulf of Mexico. The curl of the wind stress leads to an anticyclonic gyre which includes a western boundary current. This flow has an annual cycle (Sturges 1993). In addition, the irregular parade of Loop Current rings propagating into the western Gulf forces a nearly chaotic pattern of eddies of both signs which transport fluid to the west. The Loop Current ring separation spectrum has maxima at periods of order 6–11 months, but no clear annual cycle (see, e.g., Schmitz 2005; Leben 2005; Sturges and Leben 2000).

There are two basic ideas about mean flow in the western Gulf of Mexico that have been unresolved for decades. One idea is based on observations of surface currents from ship drift; these show a mean flow, integrated north–south (N–S), of order 5–10 cm s−1 into the western Gulf, which is a closed basin. The other idea, based on the anticyclone, requires flow to the west in the southern half of the basin and compensating flow back to the east in the north.

Figure 1 shows a comparison of velocity distributions based on these observations. The curve from ship drift is patterned after the work of Sturges and Kenyon (2008), who used data from 91° to 93°W. The results in the present work are based on data from a slightly expanded area, as shown by the box in Fig. 3. The curve (Fig. 1) marked “from SSH” shows the geostrophic speeds computed from the map of sea surface slope along 92°W in Fig. 2. The curve marked “drifters” is from DiMarco et al. (2005); the variance ellipses for the region we examine have values of ~7 (cm s−1)2. It may be important to realize that the drifters were nearly all launched into Loop Current rings, so that dataset may be biased toward the circulation associated with rings. The present work does not include data north of 28°, as being on the continental shelf, nor south of 22°, as not being part of the anticyclonic gyre. The realization that these mean values, computed over spans of decades, show differences greater than 10 cm s−1 emphasizes that each method has errors that may not be well understood. We cannot be certain that data from different times of observations are observing the same phenomena, although we usually assume that averages over decades are adequate.

Fig. 1.
Fig. 1.

Mean speeds in the western Gulf of Mexico from ship drift, drifters, and from SSH in mean dynamic topography.

Citation: Journal of Physical Oceanography 50, 7; 10.1175/JPO-D-19-0260.1

Fig. 2.
Fig. 2.

Mean absolute dynamic sea surface topography, from the work of Maximenko et al. (2009). Such maps can be created easily from their web page (see text).

Citation: Journal of Physical Oceanography 50, 7; 10.1175/JPO-D-19-0260.1

Figure 2 shows a calculation of mean absolute sea surface topography, SSH (Maximenko et al. 2009). That topography leads us to expect a geostrophic flow as required by the anticyclone. In the southern half of the basin the ship drift and drifter results agree with such flow, at least in sign, but the ship drift has the sign opposite to that required by the mean dynamic heights north of ~25°N. Results similar to Fig. 2 can also be downloaded directly from the AVISO web pages.1

One obvious issue is that a mean flow of order 5–10 cm s−1 across the full basin, as indicated by the ship-drift results, requires a mean rise of sea level from south to north of order half a meter, assuming geostrophic balance. Figure 2 suggests that there is essentially no mean N–S slope across the basin. Furthermore, modern high-resolution numerical models do not show the mean flow found by ship drift. Sturges and Bozec (2013) examined the mean flow of three well-regarded numerical models and found no obvious net mean near-surface flow to the west, but with upper-layer flow more in agreement with that suggested by Fig. 2. The upper-layer net flow could be returned at some intermediate depth.

Since the early 1900s, mariners have assumed that the ship-drift results are fairly reliable, and for that reason those data have been considered meaningful in many previous studies. For example, Fuglister (1951) studied flow in the Gulf Stream, and Richardson and Walsh (1986) and Richardson et al. (1992) studied equatorial currents. The U.S. Naval Oceanographic Office (1981) has published many atlases of surface currents based on this dataset, and at this writing some prominent web pages (e.g., Mariano2) use ship drift as a basic data source. I have not seen careful studies of the resulting accuracy, however. One purpose of this paper, therefore, is to estimate the errors in the mean flow in the western Gulf. The importance of this result is that a substantial mean flow into the closed basin requires a return flow.

2. Data

Ship drift data have been collected since the late 1800s and are available at NOAA web pages3 and can be purchased on a set of CDs (Enkoji 2010). The method for determining currents is straightforward: the ship’s navigator plots positions as determined by available methods (historically by star sights) to compare with the intended positions from dead reckoning. The difference vector is assumed to be the effect of surface currents, called ship drift. For accurate results, the navigator must include windage and the Ekman flow as well. The calculation of ship drift (SD) in the u, east–west (E–W) direction is

SD(u)=Ut+w+Ek+errors,
Ut=TMGDRwEk+errors,

where TMG is ship’s speed determined from the “track made good,” presumably over 12 or 24 h, Ut is the resulting true speed of the near-surface flow; DR is the dead reckoning done by the ship’s navigator to estimate the speed the ship was expected to make, w is the windage term, and Ek is the Ekman flow. If pre–World War II (WWII) merchant vessels make ~8 kt (1 kt ≈ 0.51 m s−1), over the course of 24 h they travel on the order of 200 n mi (1 n mi = 1.852 km). If the navigation error at each end is order of 0.2 mi, the expected uncertainty in speed is ~0.35 kt, or 18 cm s−1, for a single observation.

Richardson (1997) found that the effect of winds blowing against the hull could cause an error of ~0.6% of wind speed in the worst case of winds normal to the ship’s track and ~0.3% of wind speed for random directions. In the northern Gulf of Mexico, this effect (based on mean winds) is small, as described below. One reason the ship-drift data are thought to be reliable is that ships are underway, so the effect of direct wind action in the results is greatly reduced in comparison with a drifting object.

Figure 3 shows a map of all ship tracks in the Gulf from the September ship-drift data, in which the number of data points (~1600) is unusually large; the box shows the region used for data in this work. Results in other months differ only in detail. The ship tracks can be seen to go to ports on the coast of Texas and Mexico, but the central region is poorly sampled. The study area was extended to 94°W to include a larger dataset than in previous work. Because the cyclonic gyre and the effects of Loop Current eddies are deep-water phenomena, the data selected extend to only 28°N, the approximate edge of the continental shelf.

Fig. 3.
Fig. 3.

All ship drift tracks in the western Gulf in September. The box shows the region of focus in this study.

Citation: Journal of Physical Oceanography 50, 7; 10.1175/JPO-D-19-0260.1

Figure 4 shows a histogram of the E–W speeds from all the September data points inside the box of Fig. 3, with the data north of 25°N emphasized. The scale on the x axis extends to over 250 cm s−1 in the easterly direction and 160 cm s−1 toward the west to include all the data. Normally we would remove or prefilter such data. I had originally planned to clip all such data points at 50 cm s−1; however, the purpose here is to search for sources of error, so these points were retained. A Gaussian curve is superposed to address the issue of whether the values are normally distributed. The Gaussian has the standard deviation of the data and is shifted so that its peak lies at the mean value of the data, −12 cm s−1, to retain the focus on the observed values. I have ignored the large number of values near zero; it is difficult to distinguish a reported value of zero from a simple missing value. The data points fall along the Gaussian curve well, except for the few that are possible outliers from errors.

Fig. 4.
Fig. 4.

Histogram of the E–W speed component of all ship-drift observations in September, with those in the north shown in gray. The y axis is number of observations. The speed is in cm s−1. A Gaussian curve is superposed, with the mean shifted to lie at −12 cm s−1, the mean of the observations.

Citation: Journal of Physical Oceanography 50, 7; 10.1175/JPO-D-19-0260.1

A possibly surprising result is in Fig. 5, showing the years of the observations; most of the observations are concentrated in two decades prior to WWII. One’s reaction is to suspect that this region of the Gulf of Mexico is not sampled so well as the rest of the ocean. So I examined the results of a similar swath across the Atlantic, from 30° to 70°W and the same latitude band as in Fig. 3, making plots similar to those of Figs. 35 here. The results are remarkably similar, although they differ in detail.

Fig. 5.
Fig. 5.

Histogram of the number of data points in each year for ship-drift data in the Gulf of Mexico.

Citation: Journal of Physical Oceanography 50, 7; 10.1175/JPO-D-19-0260.1

It is instructive to examine details of the three sets of results in Fig. 1. Each of the three represents an attempt to determine a mean value over a span of at least a decade, yet they differ by ~10 cm s−1 or more in the means. The differences vary, depending on latitude, as to which one is nearer or farther from the other. The ship drift data are mainly from 1920 to 1940, the drifters are from 1989 to 1999, and the SSH (or mean dynamic topography) begin in 1993; they are mainly based on the satellite SSH but also include the drifter data as well as being based on a numerical model and knowledge of the geoid.

3. Results

We could adjust these data for the windage corrections found by Richardson (1997). Figure 6 shows the annual cycle of wind pseudo stress. The ship tracks are almost never normal to the winds, so these effects are small, but not negligible in comparison with the uncertainties of the data (as seen below), particularly in the north, where our concern is the greatest: 0.3% of 3 m s−1 would produce an error (or bias) of order ~1 cm s−1, and to the west. In our earlier studies, we assumed that an error of this order could be neglected in a result of order 10 cm s−1 N–S.

Fig. 6.
Fig. 6.

Annual cycle of pseudo stress from E–W wind components within 22.5°–29°N, 90°–95°W. The dashed line shows the N–S mean annual cycle.

Citation: Journal of Physical Oceanography 50, 7; 10.1175/JPO-D-19-0260.1

Ekman flow will be across the geostrophic contours, as deduced from Fig. 2, but may be less important. The winds are predominantly from east to west. Even though the full Ekman-layer transport is to the north, for shallower draft pre-WWII vessels the near-surface flow will be closer to 50° from the wind. This concern is addressed in the discussion around Fig. 7. Moreover, the speeds in the upper part of the Ekman layer are small relative to those we see in Fig. 4 (e.g., Price et al. 1987; Ralph and Niiler 1999). This point is further developed below, in the discussion of the values in Table 1.

Fig. 7.
Fig. 7.

Ship drift speeds in the northern section, plotted as a function of wind pseudo stress along 25.5°N. Components are to the west; vertical bars show an estimated two standard deviation error on speeds. The linear least squares fit is merely an aid to the eye and is not statistically significant. Data are monthly means from the northern half of the boxed area in Fig. 3, as in Table 1.

Citation: Journal of Physical Oceanography 50, 7; 10.1175/JPO-D-19-0260.1

Table 1.

Summary of ship-drift results in the western Gulf of Mexico. E–W and N–S speeds are for the full box. Values for the northern half are shown as uNorth. Speeds are in cm s−1. The region, as in Fig. 3, is 22°–28°N, 90.5°–94.5°W.

Table 1.

The archived ship-drift data were sorted by months; Table 1 shows the monthly mean values. The final columns show results for the region north of 25°N, where the primary concern is that the sign of the ship-drift values is in the direction opposite to that of the geostrophic flow.

4. Discussion

The values in the “std dev” columns of Table 1 are consistent with the earlier estimate of ~20 cm s−1. Of greater interest is the uncertainty of the monthly mean values. The standard error of the mean is the standard deviation of the individual values divided by the square root of the number of observations. There are ~400 values or more in each month, so the standard error of the mean is of order 1.4 cm s−1.

The idea that a surface current greater than 1 kt has repeatedly been reported, however, makes one suspect that some navigation fixes are less accurate than intended for this purpose, or are errors in reporting. It does not seem possible to determine the source of these large values using the archived data.

All the data in Fig. 1 show a flow to the west, south of ~24°N. A major concern, therefore, is with flow in the north of the basin. Given the obvious westward flow in the south, it would be physically reasonable to expect a return flow to the east in the north. Figure 7 shows the data in the northern half from Table 1. The standard deviation of the mean in each month is ~1.4 cm s−1. Using this value, and two standard deviations about the means, Fig. 7 shows that for most of the year, and in the mean, the speeds in the north are not significantly different from zero. The windage error could add ~1 cm s−1 back to the east. In addition to the direct effect of winds blowing against the ship’s hulls, there is also the effect of waves. It is reasonable to assume, however, that these effects are included in Richardson’s result. A plot similar to Fig. 7 (not shown) for the full dataset in Table 1 shows that there is no significant correlation between the monthly mean observed speeds and the wind stress.

The main conclusion, therefore, is that flows of the order of ~10 cm s−1, as found in the southern part of the basin, are not observed in the northern part. So the dilemma remains: the flow to the west in the southern half of the basin is well above the noise level, yet there is no direct evidence for significant flow back to the east. Because these are all surface observations, computing their associated transports merely adds uncertainty. There are two reasonable assumptions about the return flow. Because the wind stress over the basin is convergent over all seasons, the flow into the closed western basin associated with the wind-driven gyre is pumped downward into the main thermocline and returns at some intermediate depth. It is therefore not observed in surface observations. The HYCOM and ECCO2 models show, at 92°W, such return flow, although the depth extents differ (see Sturges and Bozec 2013, their Fig. 8).

The other transport to the west is by Loop Current rings, which separate from the flow in the east at irregular intervals of ~6–11 months. The fluid in rings extends down to 1000–1500 m. The steep isotherms in the rings allow fluid to be pumped downward even farther by vertical motion and by mixing.

The existence of a cyclonic deep flow, driven by the rectification of topographic Rossby waves, is well known. DeHaan and Sturges (2005) found clear evidence of such boundary layer flow at depths below ~1000 m. Hamilton (2009) showed results of deep flow to the south along the western boundary in several moorings. Weatherly et al. (2005) found, surprisingly, that the boundary flow at 900 m in the west extended 200–300 km out into the interior. Pérez-Brunius et al. (2018), with floats as deep as 1500 m and more, show a flow to the east along the northern coast of Mexico. Some of the floats continue along the boundary, and because of the rich eddy field, some are pulled away. And finally, in a mooring section across the Yucatan Channel, Bunge et al. (2002) found flow to the south, contained within oscillating flow, along the western side at depths from ~1000 m to the bottom. It is important to realize that these transports have mean speeds of order a few centimeters per second, buried within a stronger time-dependent flow. At such speeds, moving fluid over a distance of a few thousand kilometers is a very long time-scale process, so mixing, both vertical and lateral, must be important. For a mean deep flow of order 2 cm s−1, one circuit around the Gulf would take on the order of 10 years. The HYCOM and ECCO2 models (Sturges and Bozec 2013, their Fig. 8) both show a region of flow back to the east along the steep Mexican boundary from above 1000 m down to the bottom.

One comment is relevant here on the more general issue of the validity of ship-drift data in other regions. Where the flow tends to be in one direction, as in the Gulf Stream (Fuglister’s studies) or in the shipping lanes, it is likely that the standard deviations will be smaller and the means may therefore be more reliable than in the Gulf of Mexico, where the Loop Current rings cause large shifts in speed and direction.

Acknowledgments

The wind data used here are made conveniently available by NOAA at their web page https://www.esrl.noaa.gov/psd/data/reanalysis/reanalysis.shtml. I am grateful to Profs. Steve DiMarco, Kern E. Kenyon, and Carl Wunsch, who have consistently provided helpful ideas and data. Two anonymous reviewers provided very useful comments on mistakes in an earlier draft.

REFERENCES

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    • Crossref
    • Export Citation
  • Enkoji, R., 2010: Current - Direction and other data from multiple ships from world-wide distribution from 18940101 to 19931231 (NODC Accession 9400068), version 1.1. National Oceanographic Data Center, accessed 15 December 2016, https://catalog.data.gov/dataset/current-direction-and-other-data-from-multiple-ships-from-world-wide-distribution-from-1894010.

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    • Crossref
    • Export Citation
  • Maximenko, N., P. Niiler, L. Centurioni, M. Rio, O. Melnichenko, D. Chambers, V. Zlotnicki, and B. Galperin, 2009: Mean dynamic topography of the ocean derived from satellite and drifting buoy data using three different techniques. J. Atmos. Oceanic Technol., 26, 19101919, https://doi.org/10.1175/2009JTECHO672.1.

    • Crossref
    • Search Google Scholar
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