Abstract

In recent years the acoustic Doppler current profiler (ADCP) has found increasing use on commercial vessels to measure currents and their variability along selected routes in the ocean. One such dataset, in operation since late 1992, is the ADCP record from the Container Motor Vessel (CMV) Oleander, which operates between New Jersey and Bermuda. Because the Oleander ADCP system measures upper-ocean currents of O(10−2) m s−1 accuracy every 2.5 km, it provides excellent coverage of the mesoscale and submesoscale velocity field, and also of transport. The question addressed here is how well do estimates of fluxes between the continental shelf break and Bermuda compare with corresponding geostrophic estimates derived from satellite altimeter measurements of sea level extracted from weekly mapped fields along the same route. The Oleander route spans three distinct deep-sea regions: the Slope Sea, the Gulf Stream, and the Sargasso Sea. Agreement in sea surface height variability depends principally upon the length of the section being compared, and not upon eddy kinetic energy levels. Thus, yearly averages for short subsections such as across the quiet Slope Sea and energetic Gulf Stream both have correlation coefficients in excess of 0.9, whereas across the longer Sargasso Sea the correlation coefficient drops to 0.64 and to 0.58 for the 950-km-long Slope–Bermuda section. The principal cause of decrease in correlation with increasing distance appears to be due to ageostrophic flow, principally the Ekman layer and inertial motion, measured by the ADCP but not represented in the altimeter-derived geostrophic fluxes.

1. Introduction

Accurate measurements of ocean currents over a wide range of space and time scales serve a broad array of observational needs. Knowledge of transports and their temporal variability, parameterization of submesoscale processes, and the role of bottom topography in shaping fluid pathways in the ocean are required for accurate representation of ocean circulation in numerical studies. A very powerful tool for probing the spatial structure of currents is the remote sensing acoustic Doppler current profiler (ADCP). Prior to the advent of the global positioning system (GPS), ADCPs were most effective on moorings to resolve the vertical structure of currents as a function of time. In these applications the movement of the instrument was minor, and its orientation could be determined with a magnetic compass. With the advent of GPS and especially the GPS compass, a major advance in measuring ocean currents took place. With continuous accurate knowledge of vessel speed and heading, it became possible to measure currents at high horizontal resolution from ships even when ship speeds exceed 20 kt (1 kt = 0.51 m s−1; Flagg et al. 1998). The Oleander Project has been maintaining a vessel-mounted ADCP since the fall of 1992 on the Container Motor Vessel (CMV) Oleander, which operates on a weekly schedule between Port Elizabeth, New Jersey, and Bermuda (Rossby and Gottlieb 1998). Three other vessels operating in the North Atlantic are similarly equipped: the recently restarted ADCP program on the Motonave (M/N) Nuka Arctica, in service between Greenland and Denmark (Knutsen et al. 2005); the Motor Ship (M/S) Explorer of the Seas, which cruises in the Sargasso Sea and Caribbean (Beal et al. 2008); and the M/S Norröna, which sails out of the Faroe Islands to Denmark and Iceland (Rossby and Flagg 2012).

The Oleander Project was initiated to study long-term variability on interannual and decadal time scales across the Gulf Steam and surrounding waters in the northwest Atlantic (Rossby et al. 2005, 2010). The ADCP measures velocity over a wide range of scales: 16-m vertical resolution and 2.5-km horizontal resolution (5-min averages at 16–17 kt vessel speeds) over the 1000-km span of the CMV Oleander’s transit between the mid-Atlantic shelf break and Bermuda (Fig. 1). The fundamental strength of the ADCP is its ability to accurately profile currents with high horizontal resolution with respect to the mesoscale eddy field. The question addressed here is the effectiveness of the ADCP at determining transports as the length of the section, the range of integration, increases. The ADCP measurements have inherent uncertainties at the O(0.01) m s−1 accuracy level that will accrue as the integration length increases. And the ocean itself possesses variability that adds noise to the integration process. To assess these uncertainties we use satellite altimetry, which via geostrophy gives us accurate information on the variability of surface currents, especially on scales greater than O(50) km. Stammer and Theiss (2004) found fair agreement between sea surface height (SSH)-estimated velocities during the Jason–Ocean Topography Experiment (TOPEX) tandem mission coincident in time and space with Oleander velocities. Notably, Oleander velocity variance was greater than altimeter-derived velocity variance by about 25%. Stammer and Theiss (2004) were unable to determine the relative contributions of different spatial and temporally sampling of the two measurement systems and the influence of ageostrophic signals. For an excellent overview of the early development and applications of satellite altimetry, the reader is referred to Fu and Cazenave (2000).

Fig. 1.

Sea surface height (color shades) and velocity vectors measured by the ADCP at 52-m depth during a mid-September Oleander crossing. The large vector magnitudes between 38° and 39°N indicate the Gulf Stream, while the vectors in opposite directions between 36° and 37°N indicate a cyclonic cold-core ring. Land is shaded white. Depth contours every 1000 m from 1000- to 4000-m depth are gray.

Fig. 1.

Sea surface height (color shades) and velocity vectors measured by the ADCP at 52-m depth during a mid-September Oleander crossing. The large vector magnitudes between 38° and 39°N indicate the Gulf Stream, while the vectors in opposite directions between 36° and 37°N indicate a cyclonic cold-core ring. Land is shaded white. Depth contours every 1000 m from 1000- to 4000-m depth are gray.

On large scales, altimetric estimates of transport depend primarily upon knowledge of the reference geoid, the accuracy of which continues to improve. This is evident in the increasingly accurate representation of the mean sea level ands mean dynamic topography (MDT). The most recent estimate, MDT Centre National d’Études Spatiales (CNES)–Collecte Localisation Satellites (CLS09) [produced by CLS’s Space Oceanography Division and distributed by Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO), with support from CNES], reproduces a number of frontal features, such as the Gulf Stream and North Atlantic Current with remarkable spatial detail (Rio et al. 2011). Yet uncertainties remain in contemporary MDT products. For example, Griesel et al. (2012) show that a suite of MDT products, including the CNES-CLS09, overestimates the strength of the Antarctic Circumpolar Current. Validation requires independent observations and that is a challenge because the products utilize a diverse dataset—e.g., in situ surface drifter and hydrographic measurements and satellite altimeter and gravity measurements. The Oleander dataset provides an independent dataset to evaluate MDT products, especially in regions of strong frontal features.

In summary, ADCP and altimetric measurements of ocean currents complement each other. The ADCP resolves the mesoscale and submesoscale velocity field quite accurately, whereas SSH works best at the mesoscale and larger scales, with a small-scale cutoff at about 50 km. Here, altimetry is used to assess the effectiveness of the ADCP in estimating transports over larger scales. The paper has three main sections. Section 2 summarizes the datasets and methods applied in the analysis. Section 3 compares transport estimates from the ADCP with altimeter-derived estimates, and section 4 discusses in errors in both datasets and their contribution to the transport uncertainties. A brief summary in section 5 ends the paper.

2. Data and methods

a. The ADCP operation

The ADCP measures currents by transmitting coded signals in four narrow oblique beams and determining the Doppler shift of the return signals. Range gating these return signals produces velocity estimates as a function of distance from the transducer. The Doppler shift itself is an accurate measure of the velocity component along the axis of each beam; these can then be remapped into their horizontal and vertical components relative to the instrument. In September 1992, an RD Instruments 150 kHz narrowband ADCP was installed in the hull of the CMV Oleander. The unit could profile currents to as deep as about 250-m depth in the Sargasso Sea. The high-operating frequency (150 kHz) and especially the low density of backscattering material (mostly zooplankton) in the 18°C water precluded profiling to greater depths. In 2004, the ADCP was replaced with a RD Instruments 75-kHz Ocean Surveyor ADCP, which can profile to about 600-m depth; it is still in operation. The earlier 150 kHz (later 75 kHz) provides 8-m (16 m) vertically binned velocity data collected weekly along the Oleander line with gaps due to maintenance of the vessel and ADCP downtime. Five-minute averages yield velocity estimates with about 2.5-km horizontal resolution based on an average ship speed of 16–17 kt. The calibration of ADCP speed and heading is done in the bottom-track mode; the ADCP measures the ship’s speed over the bottom. Integrating this gives instrument translation, which is then compared with GPS-estimated translation. Any difference is used to correct speed calibration and instrument heading. This calibration check, done for every transect, ensures that the 5-min ensemble profiles are accurate to about ±0.01 m s−1. Prior to the summer of 1995, the gyrocompass provided heading but because the Oleander steams on a constant heading for most of the transit, the Schuler oscillations are kept to a minimum. From mid-1995 an Ashtech GPS receiver (3DF or ADU5) has resolved the ship’s heading independent of the gyrocompass. The Oleander makes the New Jersey–Bermuda trip every Friday to Sunday and the return trip Tuesday to Thursday. A typical southbound transit from the shelf break to Bermuda at 137° heading takes about 36 h to complete.

The data return is not uniform due to vessel-loading conditions, storms, and problems with the instrumentation. Bubbles drawn under the ship are by far the most common cause for data loss, since bubbles will attenuate and scatter the transmitted signal from the ADCP (Flagg et al. 1998). Bubble drawdown occurs more readily when the CMV Oleander is lightly loaded and draws less on return trips from Bermuda to New Jersey or when heading into the seas, which is more likely on northbound transits. Not every Oleander transect contains data along the full length of the transit, so a quality-control process is required to select acceptable data. Naturally, this algorithm depends upon how the data will be used. Here we require velocity to be available along the full 1000-km section between the shelf break and Bermuda. The distribution of transects that meet our criteria are shown in Fig. 2 as a function of time. The dataset consists of 542 velocity transects measured at 52-m depth between 1993 and 2004 (150-kHz ADCP) and 55 m from 2005 through 2009 (75-kHz ADCP). These depths were chosen to be close to the surface yet below the wind-driven Ekman layer. We return to the implication of this choice, in particular, whether the 55-m velocities are purely geostrophic in our discussion. The velocities are recorded every 5 min, corresponding to 2.5-km resolution.

Fig. 2.

Number of usable transects each year after applying the selection criteria. The total transects for each year are in blue. The usable transects are then presented by each of the four season. The numbers in parentheses indicate which months are included in a particular season with January being 1 and December 12.

Fig. 2.

Number of usable transects each year after applying the selection criteria. The total transects for each year are in blue. The usable transects are then presented by each of the four season. The numbers in parentheses indicate which months are included in a particular season with January being 1 and December 12.

b. Satellite altimetry

AVISO provides a gridded ⅓° mapped altimeter-derived SSH product every 7 days from 1992 to the present. The altimeter products were produced by Segment Sol multimissions d’ALTimétrie, d’Orbitographie et de localisation precise/Data Unification and Altimeter Combination System (SSALTO/DUACS) and distributed by AVISO with support from CNES (http://www.aviso.oceanobs.com/duacs). The gridded data provide SSH anomalies relative to a 7-yr mean, 1993–99. The SSH fields have a characteristic accuracy of about 0.02 m that varies with distance (in both space and time) to the nearest along-track measurement. The mapped SSH anomaly fields used in this analysis are the “reference” (Ref) products, which use only two “standard satellites” on the same two paths over the entire sampling period. The first satellite path has a 10-day repeat, with ground-track spacing at the equator of 315 km. This path was originally flown by TOPEX/Poseidon, which was replaced by Jason-1 in 2002. In 2009, Jason-2 replaced Jason-1. The second satellite path has a 35-day repeat and ground-track spacing is 80 km at the equator. This path was originally flown by European Remote Sensing Satellite-1 (ERS-1) and was replaced by ERS-2 in 1996, which was then replaced by the Environmental Satellite (Envisat) in 2002. Their paths are shown in Fig. 3. For completeness, we note that AVISO also produces an “updated” (Upd) mapped SSH anomaly product that uses all available altimeter data, for example, Geosat Follow-On (GFO) and/or TOPEX/Poseidon in a tandem mission. However, its quality is not homogeneous in time because the data density varies as individual satellite missions are added or removed, and therefore it is not used in this study.

Fig. 3.

Satellite ground tracks across the northwest Atlantic in the vicinity of Oleander’s route (red) between New Jersey (top left) and Bermuda (bottom right). Two satellite ground tracks are shown: green represents Envisat (from 2002 to present), ERS-2 (from 1996 to 2002), and ERS-1 (from 1991 to 1996); blue represents Jason-2 (from 2009 to present), Jason-1 (from 2002 to 2009), and TOPEX/Poseidon (from 1992 to 2002). The thin offshore line delineates the 200-m isobath.

Fig. 3.

Satellite ground tracks across the northwest Atlantic in the vicinity of Oleander’s route (red) between New Jersey (top left) and Bermuda (bottom right). Two satellite ground tracks are shown: green represents Envisat (from 2002 to present), ERS-2 (from 1996 to 2002), and ERS-1 (from 1991 to 1996); blue represents Jason-2 (from 2009 to present), Jason-1 (from 2002 to 2009), and TOPEX/Poseidon (from 1992 to 2002). The thin offshore line delineates the 200-m isobath.

An MDT product—MDT CNES-CLS09—is also available through AVISO, which provides absolute SSH when added to the anomaly (http://www.aviso.oceanobs.com). It represents the mean sea surface height above geoid for the 7-yr period 1993–99. This mean field uses 4.5 yr of Gravity Recovery and Climate Experiment (GRACE) data, 15 yr of altimetry, and in situ data including hydrographic data and drifters (http://www.aviso.oceanobs.com/en/data/products/auxiliary-products/mdt). MDT is mapped on a ⅓° grid.

3. Results

a. Mean SSH from AVISO and the ADCP

The CNES-CLS09 MDT interpolated to 20 km spacing along the Oleander line is shown in Fig. 4. The sea level jump across the Gulf Stream is about 1.3 m with reverse slopes elsewhere reflecting westward flows in the Slope and Sargasso Seas, such that the total difference between the shelf break and Bermuda is 0.80 m.

Fig. 4.

The heavy (dashed) black line is the estimated SSH calculated by integrating the average velocity normal to the Oleander track 1993–99 (1993–2009), plotted with 20-km resolution. The thin gray line is the CLS09 mean product distributed by AVISO interpolated to an average Oleander line using the same 20-km spacing along the track line. The northernmost SSH value has been subtracted from the CLS09 mean SSH to set the initial value to zero for comparison with the Oleander-derived mean SSH.

Fig. 4.

The heavy (dashed) black line is the estimated SSH calculated by integrating the average velocity normal to the Oleander track 1993–99 (1993–2009), plotted with 20-km resolution. The thin gray line is the CLS09 mean product distributed by AVISO interpolated to an average Oleander line using the same 20-km spacing along the track line. The northernmost SSH value has been subtracted from the CLS09 mean SSH to set the initial value to zero for comparison with the Oleander-derived mean SSH.

Next we use the Oleander data during 1993–99 set to construct a corresponding geostrophic sea level difference for comparison with CNES-CLS09. The velocity component normal to the ship’s track is integrated using the linear geostrophic momentum equation:

 
formula

where x is the distance from the shelf break toward Bermuda, υ(x) is the normal velocity component, f(x) is the local Coriolis parameter (varies as a function of latitude along the transect), g is gravity, and h(x) is the estimated surface elevation. In the construction of mean h(x), it is assumed that ageostrophic velocities average out. The ADCP estimate of sea level difference across the Gulf Stream of 1.1 m is less than that of AVISO by 0.3 m, but the two estimates of sea level difference across the entire distance of the Oleander line are comparable. Figure 4 also includes the ADCP-estimated mean sea level for the time period (1993–2009). The total sea level difference, shelf break to Bermuda as well as across the Gulf Stream, remains the same. There is a slight northward shift, about 15 km, in the Gulf Stream core position. Since the MDT is a construct using many diverse datasets, we cannot determine the reasons why the CNES-CLS09 Gulf Stream is so much larger. The maximum sea level difference is best examined in a Gulf Stream coordinate system. This has been estimated in several studies. Using the Oleander ADCP dataset, the long-term average equals 1.19 m (Rossby et al. 2010); this is still significantly less than the CNES-CLS09 estimate. The mean Gulf Stream curvature is quite small here and slightly anticyclonic. The geostrophic estimates would be less than the gradient wind estimates, in the opposite direction to the discrepancy found here. The contribution of the density gradient above 52 m is too small to account for these differences. Sato and Rossby (1995) report a 0.25-m dynamic height difference across the Gulf Stream at 300-m depth. A linear downscaling provides an estimate for the additional dynamic height difference above 50 of 0.04 m [0.25(50/300)]. This downscaling is an overestimate because it includes the shoaling main thermocline, which levels out below 50 m on the Slope Sea side of the Gulf Stream. It seems likely that much of the difference is due to MDT uncertainties, which may be larger here due to the meandering of the energetic and narrow Gulf Stream.

b. SSH variability from AVISO and the ADCP

To estimate SSH variability, we use the same procedure except in this analysis the AVISO SSH anomaly is an altimeter-only measurement. Chelton et al. (2011) suggest that eddies with a Gaussian e-folding scale of 40 km at 30° latitude and 30 km at 50° latitude have been filtered out of the AVISO reference product. To avoid the influence of small horizontal-scale variability, ADCP velocities are smoothed with a 50-km spatial filter; therefore, we do not include the northernmost and southernmost 25-km-long segments in the following comparison.

Agreement between ADCP and altimeter flux estimates will be quantified by the degree of correlation between the two. Altimeter flux Falt, between two locations, x1 and x2, along the Oleander line is defined by

 
formula

where h′(x, t) is altimeter SSH anomaly. The Oleander flux is defined by

 
formula

where υ(x, t) is the Oleander-measured velocity component normal to the ship’s track. To examine fluxes in the Slope Sea, the Gulf Stream, and Sargasso Sea, we define four points along the shelf break to Bermuda section: the shelf break, the northern bound or the limit of the Gulf Stream, its southern bound, and a point just north of Bermuda. The points bracketing the Gulf Stream were chosen to be close to the Gulf Stream, but also in areas where SSH variability shows a local minimum, Fig. 5. We further subdivide the Sargasso Sea into the northern and southern halves.

Fig. 5.

Color contours indicate the standard deviation (cm) of the SSH anomalies field for the period 1992–2009. Land is outlined in black, and the thin line delineates the 200-m isobath. The five dots from north to south represent the fixed index points used to delineate the three major subregions: Slope Sea, Gulf Stream, and Sargasso Sea. The fourth southward dot divides the Sargasso Sea into a northern and southern part.

Fig. 5.

Color contours indicate the standard deviation (cm) of the SSH anomalies field for the period 1992–2009. Land is outlined in black, and the thin line delineates the 200-m isobath. The five dots from north to south represent the fixed index points used to delineate the three major subregions: Slope Sea, Gulf Stream, and Sargasso Sea. The fourth southward dot divides the Sargasso Sea into a northern and southern part.

Absolute fluxes and their variability in these domains have been discussed by Rossby et al. (2010). Here the focus is on how well the ADCP and AVISO estimates agree. We consider each of the subsections first and the entire section last. All comparisons are annual averages stepped every 6 months to provide partial overlap and better continuity.

The AVISO and ADCP estimates of flux variability in the Slope Sea (Fig. 6, top curve) are almost identical over this short region. The length of this section is 75 km (225–300 km from New Jersey). Minor changes in flux anomalies are captured by both methods, indicating excellent agreement of the two methods. The RMS flux difference between the two curves is 1.9 × 103 m2 s−1, which per unit length is 0.025 m s−1.

Fig. 6.

Fluxes for five subregions—Slope Sea, Gulf Stream, and Sargasso Sea and its north and south sections—as well as for the total for all the subregions (bottom curve) from the shelf break to Bermuda. ADCP fluxes are shown in red and those calculated from AVISO are shown in blue. Data points are annual averages stepped every 6 months. Please note that there is a 5 × 104 m2 s−1 offset between successive segments starting with the total section. The r value to the right of each curve indicates the corresponding correlation coefficient. Standard error bars are determined using an integral time scale of 10 days based upon Gulf Stream analysis of Johns et al. (1995).

Fig. 6.

Fluxes for five subregions—Slope Sea, Gulf Stream, and Sargasso Sea and its north and south sections—as well as for the total for all the subregions (bottom curve) from the shelf break to Bermuda. ADCP fluxes are shown in red and those calculated from AVISO are shown in blue. Data points are annual averages stepped every 6 months. Please note that there is a 5 × 104 m2 s−1 offset between successive segments starting with the total section. The r value to the right of each curve indicates the corresponding correlation coefficient. Standard error bars are determined using an integral time scale of 10 days based upon Gulf Stream analysis of Johns et al. (1995).

Unlike the smoothly varying Slope Sea, the 300-km-long Gulf Stream section exhibits significant interannual flux variability (Fig. 6, second curve from the top) that is captured quite well by both methods and reflected in the high correlation coefficient, 0.88. This includes the striking decrease at the end of the record (the fluxes have since then recovered). Despite considerable effort we have not been able to identify the cause of the disagreements in 1999–2000 and 2005. The RMS flux difference between the two curves is 4.4 × 103 m2 s−1, which per unit length is 0.015 m s−1.

The Sargasso Sea is the longest of the three subsections (570 km). The flux variations are nearly as large as in the Gulf Stream (Fig. 6, third curve from the top). Whereas the Gulf Stream shows a large drop at the end of the record, the Sargasso Sea record is recovering from a large drop in flux at the start of the record, both of which are captured by both methods. While the two estimates of flux show similar patterns, at 0.64 the correlation coefficient is significantly lower than for the Gulf Stream and Slope Sea. The RMS flux difference between the two curves is 5.9 × 103 m2 s−1, which per unit length is 0.01 m s−1. Despite the significant drop in the correlation coefficient compared to the Gulf Stream, the standard error bars still overlap with the other variable. We also note that the disagreements occur at other times than for the Gulf Stream section.

The Sargasso Sea subsection includes the energetic cold-core ring region south of the Gulf Stream. To examine whether these could be a cause of the lower correlation, we divide the section into a northern part (250 km) and a southern part (320 km) at 850 km from New Jersey, approximately where eddy kinetic energy (EKE) shows a decrease in amplitude (Rossby et al. 2010). This division does two things: first, it creates shorter distances over which the ADCP fluxes are integrated, and second, it puts the high-variability region in part due to the passage of cold-core rings into its own subregion. The result is striking, as shown in Fig. 6. Both subregions show much higher correlations, at 0.93 and 0.94, respectively, indicating that the higher eddy activity in the northern subregion was not responsible for the low Sargasso Sea correlation coefficient. The RMS flux differences for the northern and southern regions are 3.8 × 103 and 3.0 × 103 m2 s−1, or 0.015 and 0.009 m s−1 per unit length, respectively.

The above-mentioned results indicate excellent agreement when integrating fluxes over a few hundred kilometers, but not as the length of the section increases. This does not come as a surprise, since the ADCP flux is an integral of velocity components from a wide range of space and time scales. The longest integral we can construct is the 950-km section from the shelf break to Bermuda. In this case the correlation between AVISO and ADCP drops to 0.58 (Fig. 6, bottom curve). Visual inspection reveals conspicuous short-term reversals and offsets, but the longer time scales, such as the rise over the first 10 yr and the decrease thereafter, are captured by both methods, suggesting that agreement will depend upon the number of degrees of freedom available in the comparison. Stated differently, in order to resolve the short-term variability of longer sections, more transects will be needed to compensate for accumulating errors in the integration process. But it is also interesting to note that the RMS flux difference between the two curves is 6.8 × 103 m2 s−1, which per unit length is 0.007 m s−1.

The above-mentioned flux comparisons are summarized in three panels in Fig. 7. The top panel shows the correlation coefficient between the two estimates of flux, the middle panel shows the equivalent velocity error per unit length, and the bottom panel shows the error variance for the six cases, all plotted as a function of section length. Results from flux comparisons along 15 subsections of the 570-km Sargasso section are also included in Fig. 7 (time series are not shown). The Sargasso section is split into eight segments (72-km length) and four segments (144-km length). In addition, we include a 286-km-length segment centered within the section and two overlapping 429-km-length segments, one at each end. The panels give complementary perspectives on the ADCP–AVISO SSH intercomparison. The correlation tells us that as distance increases and more degrees of freedom of measurement uncertainty are added to the integration, the agreement will decrease for the same ensemble size. The middle panel indicates that the uncertainty contributing to the integration uncertainty is largely independent, or possibly decreasing slowly with increasing distance. The high values near 75 km (which come from the quiet Slope Sea and the short Sargasso subsets) are likely influenced by altimeter uncertainties when differenced over such a short distance as well as the sensitivity to the high velocity variance in the northern Sargasso Sea and Gulf Stream. Within the cluster of values near 75 km, the lowest uncertainty occurs for segments located within the quiet southern Sargasso Sea. The lower limit of uncertainty for the quiet southern Sargasso Sea and the entire section lies just under 0.01 m s−1. The bottom panel indicates that the flux error variance increases linearly with the length of integration. This would be consistent with the assumption that velocity measurement uncertainties are additive along a section. It does not tell us from where they come.

Fig. 7.

The (top) correlation coefficient between ADCP and SSH estimates of flux variability, (middle) equivalent velocity uncertainty, and (bottom) flux error variance (the square of the RMS values for each case), all plotted as a function of section length. The gray line in (bottom) is a linear least squares fit with 0 and 1000-km intercepts at 0.03 and 5.519 × 107 (m2 s−1)2, respectively.

Fig. 7.

The (top) correlation coefficient between ADCP and SSH estimates of flux variability, (middle) equivalent velocity uncertainty, and (bottom) flux error variance (the square of the RMS values for each case), all plotted as a function of section length. The gray line in (bottom) is a linear least squares fit with 0 and 1000-km intercepts at 0.03 and 5.519 × 107 (m2 s−1)2, respectively.

To give the measurement uncertainty context, it can be expressed as a fraction of the average flux for the entire section. Figure 8 shows the 16-yr ensemble integral of flux across the Oleander line between the shelf break and Bermuda. The solid curve indicates a mean integral at 50-m depth starting at the shelf break, while the gray curve indicates the corresponding single transit uncertainty of the flux. The peak at about 500 km reflects the lateral meandering of the Gulf Stream. Measurement error modeled as the square root of the distance (dotted line) may represent the underlying uncertainty to which a dynamic variability is added (e.g., the Gulf Stream region).

Fig. 8.

Mean (black) and standard deviation (gray) of 542 sections between shelf break and Bermuda. The black mark near the top at 1200 km indicates a standard error of the 1000-km integral (=2% of the mean). The dotted line is proportional to the square root of the distance.

Fig. 8.

Mean (black) and standard deviation (gray) of 542 sections between shelf break and Bermuda. The black mark near the top at 1200 km indicates a standard error of the 1000-km integral (=2% of the mean). The dotted line is proportional to the square root of the distance.

Assuming each transect flux estimate to be independent, it is clear that an annual average with typically 20–25 sections for the full 1000-km section will have a standard error on the order of one-fifth the single transect uncertainty, or about 10% of the total. The overall uncertainty from all sections is 2% (thick bar located at 1200-km distance in Fig. 8).

4. Discussion

The question we address here concerns the source of the integration errors. In the following subsections we discuss possible instrument error, persistent (or biased) heading error, and wind-driven ageostrophic velocity components at the surface that should not be included in a comparison with AVISO SSH.

a. Instrument error

While we do not expect random errors to contribute to the integration error, it is worth reporting the velocity-measurement uncertainty. According to the manufacturer (http://www.rdinstruments.com/surveyor.aspx), the ADCP has an inherent single-ping measurement uncertainty of 0.30 m s−1. This reduces to about 0.025 m s−1 uncertainty in the 5-min (N > 100) ensemble profile estimates. These uncertainties are further averaged during the 1000-km (about 400 profiles 2.5 km apart) integration from the shelf break to Bermuda, such that the root-mean-square uncertainty due to instrument noise drops by a factor of (400)1/2 to <0.002 m s−1—a very small number.

b. Heading error

The GPS compass plays a central role in the accuracy of the ADCP data, since it is thanks to GPS that we can georeference the velocity data obtained from a fast-moving vessel. Further, the compass, an ADU5, is checked and calibrated for every transit by operating the ADCP in the bottom-track mode (while traversing the continental shelf), whereby the instrument determines its own displacement by integrating the measured speed and heading of the bottom relative to the ship. This integration determines two parameters, namely, the speed calibration of the ADCP and the instrument orientation in the hull (the GPS has been independently calibrated and referenced to the vessel). From an ensemble of 45 such calibrations over the course of 15 months, we know that heading error has a standard deviation of about 0.07°. This uncertainty decreases by a factor 4–5 when averaged over the roughly 20–25 transits used in the 1-yr ADCP–AVISO intercomparisons. An average heading error of, say, 0.015°, would lead to a constant track–track velocity error of 16 kt (vessel speed) × sin(0.015) = 0.0022 m s−1. For comparison, the middle panel of Fig. 7 shows that the ADCP–SSH misfit could be accounted for in terms of an error velocity at the 0.01 m s−1 level. Since this is greater by a factor 4 than the above-mentioned estimate of potential heading errors, it suggests that GPS error is not a source of integration errors.

An intermittent heading error could lead to a bias. One possible situation is a small but time-independent heading error combined with an unequal distribution of southbound and northbound transects. In the mean, total section fluxes estimated from southbound sections are only slightly higher than northbound sections at both 150 and 75 kHz. In terms of an error velocity, they are 0.0017 and 0.0044 m s−1 at 150 and 75 kHz, respectively. These estimates are consistent with our previous estimate of the heading error. In each year, roughly twice as many southbound sections compared to northbound sections contribute to the estimate. Nevertheless, these errors are quite small and do not account for the ADCP–AVISO SSH flux discrepancies. Another possible explanation could be weather-dependent errors. Heavy winds will cause rolling motion to the ship, such that the beams do not have the same vertical angle. We have assumed that this is a second-order effect, which will be further reduced in the ensemble averaging. Finally, the gyrocompass provides heading information when the GPS data are not available. We do not find larger errors in the pre-GPS years compared to years when the GPS was consistently available.

c. Ageostrophic components

The two obvious ageostrophic candidates are both wind driven: the Ekman layer and inertial motion. The Ekman layer is directly wind driven and is limited to the surface with velocities typically at a few centimeters per second with a yearly average flow almost straight south in the Oleander area (McGrath et al. 2010). Its vertical extent is essentially governed by the mixed layer depth and can be estimated using the Price and Sundermeyer (1999) stratified Ekman layer model. In summertime when the mixed layer may only be 10–20 m deep, the shallowest ADCP measurement (26 m) is already below most of the Ekman layer. In winter the mixed layer can be 50 m in the Slope Sea and Gulf Stream and 100–200 m deep in the Sargasso Sea such that the Ekman currents can be observed, even from fast-moving vessels (Stoermer 2002). Interestingly, while winds are stronger in winter, the depth of the mixed layer is such that the Ekman layer velocities are actually somewhat less (McGrath et al. 2010).

In a further effort to identify ageostrophic velocity components in the ADCP data, we take a closer look at the surface–near-surface ADCP data. Inertial oscillations appear in all Eulerian current meter records. They are excited by transient winds; however, their RMS amplitude decreases across the seasonal pycnocline from O(0.1) at the surface to O(0.05) m s−1 at 50 m, and O(0.03) m s−1 at 150-m depth (Pollard 1980; Briscoe and Weller 1984). The latter study, the Long-Term Upper Ocean Study (LOTUS) at 34°N, 70°W, was located about 250 km southwest of the Oleander line in the Sargasso Sea.

An attempt to relate ADCP data with the LOTUS results is presented in Fig. 9. The top panel shows RMS velocity at five levels across the Sargasso Sea, starting just south of the Gulf Stream. The energetic range between 600 and 850 km spans the corridor of westward drifting cold-core rings. While the overall velocities are obviously greater toward the north, they also show a consistent decrease with increasing depth. In an effort to isolate the wind-driven Ekman and inertial motions better, the bottom panel shows the same velocity statistics after subtracting the velocity field at 155 m from each and every section. The removal of this mesoscale eddy field reveals a residual velocity significantly richer in small-scale variability at the surface than the full velocity field, as can be seen from their transverse covariance functions in Fig. 10 (in both cases the ensemble mean velocity field was removed from each section before analysis). Estimated from 306 complete transects across the Sargasso Sea, the variance of the residual velocity field at 55-m depth equals 0.011 m2 s−2, with a half-power point about 15 km away, much less than the 35 km for the full field. Thus, the residual field has a much shorter correlation scale, that is, a whiter wavenumber spectrum than the full field. However, even with this drastic step, the RMS velocities in the quiet Sargasso Sea are still greater by a factor 2 than the O(0.05) m s−1 average at 50-m depth reported by Briscoe and Weller (1984). Most likely this is due to additional geostrophic shear present in the top 150 m, as is evident in the upper panel of Fig. 9 (particularly in the cold-core ring corridor).

Fig. 9.

RMS velocity (m s−1) in five layers from 55- to 155-m depth. (top) Observed velocity and (bottom) RMS velocity difference relative to the 155-m depth.

Fig. 9.

RMS velocity (m s−1) in five layers from 55- to 155-m depth. (top) Observed velocity and (bottom) RMS velocity difference relative to the 155-m depth.

Fig. 10.

Correlation function of the transverse (or cross track) velocity field between 700 and 1180 km. Variances and RMS velocities of the full (black) and surface residual (gray) velocity fields are 0.063 and 0.01 m2 s−2, and 0.25 and 0.1 m s−1, respectively.

Fig. 10.

Correlation function of the transverse (or cross track) velocity field between 700 and 1180 km. Variances and RMS velocities of the full (black) and surface residual (gray) velocity fields are 0.063 and 0.01 m2 s−2, and 0.25 and 0.1 m s−1, respectively.

d. Modeling the impact of the Ekman and inertial motion

We now model how these velocity fields might impact the velocity integration, beginning with the inertial motions. The approach is straightforward: we construct a random normal velocity field (1000 km long with 2.5-km spacing to simulate the full Oleander section) and low-pass filter it with a low-order Butterworth filter, such that it has a horizontal correlation scale and variance suggested by Fig. 10. The velocity field is then integrated to obtain a flux. This process is repeated many times to create an ensemble of flux estimates. The standard deviation of these is about 1.6 × 104 m2 s−1 compared to the standard deviation in flux error variance in Fig. 7: (4.8 × 107)1/2 = 6.9 × 103 m2 s−1. However, the latter estimate is based on annual averages that comprise about 25 sections per year. Thus, the single section error would be roughly a factor of 5 larger or roughly twice as large as the model estimate. While not grossly different we conclude from this that the small-scale velocity field at the surface cannot alone be responsible for the observed flux variance. We now consider the Ekman layer.

While it is true that the Ekman velocities are small, they are driven by large-scale wind systems and thus may have a weak undetected large-scale signature. We also note from the middle panel in Fig. 7 that the annual average flux errors could be accounted for in terms of an equivalent cross-track velocity error of O(0.01), or O(0.05) m s−1 for a single transect (at about 25 transects per year). This suggests that a large-scale correlated residual velocity field of this order might be able to account for the flux discrepancies. Very crudely this is saying that large wind systems introduce a coherent Ekman flow of this magnitude all along or at least along a significant fraction of the section.

Further evidence that the Ekman layer is a significant contributor to integration error can be seen in Fig. 11, which shows the error between the ADCP integrals and SSH for the 970-km section. One sees a striking decrease in error scatter during the summer months. This agrees with the fact that the mixed layer is quite shallow during the summer months everywhere. On the other hand, there are conspicuous outliers throughout the year. We do not know their cause, but storms can occur at any time. These can excite inertial oscillations that can ring for days. Some combination of Ekman velocity and inertial contribution seems to be the main source of error to the flux integration.

Fig. 11.

Difference between ADCP and AVISO SSH flux estimates for the 970-km transect. The 12 vertical bars indicate monthly standard deviations. The summer months (May–October) have twice as many sections as the winter months (November–April).

Fig. 11.

Difference between ADCP and AVISO SSH flux estimates for the 970-km transect. The 12 vertical bars indicate monthly standard deviations. The summer months (May–October) have twice as many sections as the winter months (November–April).

It is beyond the scope of this study to examine whether discrepancies between AVISO and ADCP fluxes can be attributed to or correlated with specific wind events, but this should be possible to do, and is worth further study. Interestingly, should further study prove wind-driven events to be the main cause of the ADCP–AVISO differences, it would suggest that vertically integrated flux measurements—for example, with the 75-kHz ADCP to 600 m or the 38-kHz ADCP to 1200 m—may be more accurate than is generally recognized, since the Ekman layer contribution will be comparatively minor. Moreover, since Ekman fluxes can be estimated directly from knowledge of the winds, it should be possible to determine the geostrophic component of flux provided the ADCP captures the full Ekman layer, that is, profiles from the surface down. This is possible with a high-frequency ADCP that resolves the surface waters. One could then partition the wind-driven flux from the total to obtain the net geostrophic flux, which should be in better agreement with AVISO. But there is another factor that should be addressed, namely, the effect of vessel roll to flux measurement, particularly if the roll is biased due to persistent winds (this should be less of an issue with large deep-draft shipping vessels).

5. Summary

Using the Oleander ADCP velocities, a mean SSH field is constructed for comparison with the recent CNES-CLS09 mean dynamic topography. The two estimates of sea level difference of 0.8 m across the entire distance of the Oleander line (shelf break to Bermuda) are comparable. But the ADCP estimate of sea level difference across the Gulf Stream of 1.1 m is 80% less than the CNES-CLS09 estimate.

The ADCP complements altimetry well in that it provides detail about the velocity field at scales as small as a few kilometers, and can measure currents and fluxes accurately over distances of a few 100 km. ADCP and AVISO SSH fluxes compare well when they are determined over small regions: the Slope Sea, the north Sargasso Sea, and the south Sargasso Sea regions all have correlation coefficients of 0.93 or above. Despite the excellent correlations of the smaller regions, the total flux across the entire Oleander transect shows a much smaller correlation coefficient of 0.58. Over longer distance scales, measurement (velocity and navigation) errors accrue, leading to increasingly large flux uncertainties even though in terms of an equivalent velocity these errors are small, near the 0.01 m s−1 level. The challenge ahead is to understand where these come from so they can be further reduced.

The comparison requires careful consideration of the end points for the flux estimates. Best agreement occurs in regions of low variance away from the influence of the Gulf Stream or the energetic cold-core ring region south of the Gulf Stream. This is likely due to the presence of small horizontal-scale features as well as high-frequency variability that are not adequately sampled by the satellite altimetry.

The decrease in error during the summer months points to two error sources: excitation of transient nongeostrophic motion at and near the surface and possible changes in the behavior of the ship. Teasing out these two contributions needs further study. Looking to the future, a better understanding of what contributes to the small residual biases in a shipboard ADCP system, whether it is a better understanding the integrated ADCP and navigation systems or deeper-reaching ADCPs, has enormous payoff. The U.S. merchant marine with its fleet of ships operating along regular routes offers the opportunity to estimate upper-ocean transport with ADCPs over a wide range of scales, from the submesoscale to distances exceeding 1000 km.

Acknowledgments

A graduate fellowship from the U.S. Coast Guard to the first author and NSF Grant OCE 0825845 supported this study. We are indebted to the Bermuda Container Line for their continued support of the ADCP operation on board the Oleander. We particularly thank our Oleander collaborator Dr. Charles Flagg for his continuing professional advice and Ms. Sandy Fontana for her careful attention to all aspects of the data acquisition system and data processing. Mr. George Schwartze has been a central figure in maintaining the continual operation of the equipment on board the Oleander. For the first 5 yr, the Oleander program was funded by NOAA; since then the activity has been supported by grants from the NSF. ONR has also provided very helpful assistance.

REFERENCES

REFERENCES
Beal
,
L. M.
,
J. M.
Hummon
,
E.
Williams
,
O. B.
Brown
,
W.
Baringer
, and
E. J.
Kearns
,
2008
: Five years of Florida Current structure and transport from the Royal Caribbean Cruise Ship Explorer of the Seas. J. Geophys. Res.,
113
,
C06001
, doi:.
Briscoe
,
M. G.
, and
R. A.
Weller
,
1984
:
Preliminary results from the Long-Term Upper-Ocean Study (LOTUS)
.
Dyn. Atmos. Oceans
,
8
,
243
265
, doi:.
Chelton
,
D. B.
,
M. G.
Schlax
, and
R. M.
Samelson
,
2011
:
Global observations of nonlinear mesoscale eddies
.
Prog. Oceanogr.
,
91
,
167
216
, doi:.
Flagg
,
C. N.
,
G.
Schwartze
,
E.
Gottlieb
, and
T.
Rossby
,
1998
:
Operating an acoustic Doppler current profiler aboard a container vessel
.
J. Atmos. Oceanic Technol.
,
15
,
257
271
, doi:.
Fu
,
L.-L.
, and
A.
Cazenave
,
2000
: Satellite Altimetry and Earth Sciences: A Handbook of Techniques and Applications. International Geophysics Series, Vol. 69, Academic Press, 463 pp.
Griesel
,
A.
,
M.
Mazloff
, and
S.
Gille
,
2012
:
Mean dynamic topography in the Southern Ocean: Evaluating Antarctic Circumpolar Current transport
.
J. Geophys. Res.
,
117
,
C01020
, doi:.
Johns
,
W.
,
T.
Shay
,
J.
Bane
, and
D.
Watts
,
1995
:
Gulf Stream structure, transport, and recirculation near 68°W
.
J. Geophys. Res.
,
100
,
817
838
, doi:.
Knutsen
,
Ø.
,
H.
Svendsen
,
S.
Østerhus
,
T.
Rossby
, and
B.
Hansen
,
2005
: Direct measurements of the mean flow and eddy kinetic energy structure of the upper ocean circulation in the NE Atlantic. Geophys. Res. Lett.,
32
, L14604, doi:.
McGrath
,
G.
,
T.
Rossby
, and
J.
Merrill
,
2010
:
Drifters in the Gulf Stream
.
J. Mar. Res.
,
68
,
699
721
, doi:.
Pollard
,
R.
,
1980
:
Properties of near-surface inertial oscillations
.
J. Phys. Oceanogr.
,
10
,
385
398
, doi:.
Price
,
J. F.
, and
M. A.
Sundermeyer
,
1999
: Stratified Ekman layers. J. Geophys. Res.,104, 20 467–20 494, doi:.
Rio
,
M.
,
S.
Guinehut
, and
G.
Larnicol
,
2011
:
New CNES-CLS09 global mean dynamic topography computed from the combination of GRACE data, altimetry, and in situ measurements
.
J. Geophys. Res.
,
116
,
C07018
, doi:.
Rossby
,
T.
, and
E.
Gottlieb
,
1998
:
The Oleander Project: Monitoring the variability of the Gulf Stream and adjacent waters between New Jersey and Bermuda
.
Bull. Amer. Meteor. Soc.
,
79
,
5
18
, doi:.
Rossby
,
T.
, and
C. N.
Flagg
,
2012
:
Direct measurement of volume flux in the Faroe-Shetland Channel and over the Iceland-Faroe Ridge
.
Geophys. Res. Lett.
,
39
,
L07602
, doi:.
Rossby
,
T.
,
C.
Flagg
, and
K.
Donohue
,
2005
:
Interannual variations in upper-ocean transport by the Gulf Stream and adjacent waters between New Jersey and Bermuda
.
J. Mar. Res.
,
63
,
203
226
, doi:.
Rossby
,
T.
,
C.
Flagg
, and
K.
Donohue
,
2010
:
On the variability of Gulf Stream transport from seasonal to decadal timescales
.
J. Mar. Res.
,
68
,
503
522
, doi:.
Sato
,
O. T.
, and
T.
Rossby
,
1995
:
Seasonal and low frequency variations in dynamic height anomaly and transport of the Gulf Stream
.
Deep-Sea Res. I
,
42
,
149
164
, doi:.
Stammer
,
D.
, and
J.
Theiss
,
2004
:
Velocity statistics inferred from the TOPEX/Poseidon-Jason-1 tandem mission data
.
Mar. Geod.
,
27
,
551
575
, doi:.
Stoermer
,
S. A.
,
2002
: Ekman flow and transports in the northwest Atlantic from acoustic Doppler current profiler data. M.S. thesis, Graduate School of Oceanography, University of Rhode Island, 93 pp.

Footnotes

*

Current affiliation: USCGC SEQUOIA (WLB 215), U.S. Coast Guard, Santa Rita, Guam.