Methodology

In designing the Line W array to monitor the Deep Western Boundary Current, the line was chosen to coincide with track 126 of the TOPEX/Poseidon altimeter (Pena-Molino and Joyce, 2008). Between January 2002 and December 2008, 249 passes of Line W were made by successor mission JASON, yielding an estimate of sea surface height anomaly every 10 days. These altimeter data were accessed using the Radar Altimeter Database System (http://rads.tudelft.nl/rads/index.shtml), which provides access to a harmonised, validated and cross-calibrated version of the data set (Naeije et al., 2000). Unfortunately, these data only provide sea surface height anomalies from a temporal mean and not the absolute SSH referenced to the geoid. Rio and Henrandez (2004) have recently constructed a global mean dynamic topography from a combination of altimetry, in situ measurements and a geoid model on a 1^◦ × 0.5^◦ grid; however this product lacks the spatial resolution along the Line W section to provide an accurate mean background field. In situ cruise data from Line W is thus used to estimate the absolute SSH differences, as outlined below.

Line W Cruise Sections

Nine CTD/LADCP sections taken as part of the Line W programme were used to estimate surface velocities and full-depth Gulf Stream transport. Details of these cruises are given in Table 3.7. A tenth section, occupied during April 2007, only occupied the slope waters inshore of the Stream and consequently was not used. Prior to estimating the Gulf Stream transport, the data were processed as follows:

1. The nine CTD sections were downloaded in the WOCE .ctd format from the Line W world wide web pages (http://www.whoi.edu/science/PO/linew/data/index.htm).

These CTD data were interpolated onto 2 dbar pressure surfaces and have an attached quality control flag, with one file per station. Temperature is reported correct to 0.001^◦C and salinity to 0.02 after laboratory calibration. All data flagged as good (quality flag 2) were used.

2. The lowered ADCP files for each station were downloaded from the same location as .dat files. These data had previously been detided using the Oregon State University Ocean Model (Egbert et al., 1994). In order to check the consistency of the data, the final processed u and v velocities in the bottom bin were compared with the bottom velocities derived using the bottom tracking only. Visual examination revealed strong agreement in the velocities near the bottom (an example is given in Figure 3.40) and the velocity values at the deepest common level between each set of stations were thus used to reference the geostrophic shear.

3. Geostrophic shear between each station was calculated from the CTD data and refer-enced using the deepest common level velocity of the LADCP between each station.

In a handful of cases where LADCP data were missing at a particular station (e.g. at

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V velocity (m/s)

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may20089017

Final velocity Bottom Velocity

Figure 3.40: Comparison of bottom v velocities derived from bottom tracking (in red) and the final choice of LADCP velocity (in blue) for Station 17 of the May 2008 section.

Station 9 in April 2006), deepest common level velocities were linearly interpolated from the nearest stations. The nine alongstream velocity sections are shown in Figure 3.41.

4. Bottom triangle transports were calculated by reproducing the deepest common level velocity throughout the bottom triangle and multiplying it by the triangle’s area. For the 10 sections used, the total bottom triangle transports of the section sum to between +0.04 Sv and −0.49 Sv.

5. The Gulf Stream transport was calculated by cumulating the cross-stream transport in the top 1000 dbar west to east across the Line W line and defining the inshore edge as the position of minimum cumulated northward transport and the outer edge as the location of maximum cumulated northward transport. This leads to different integra-tion limits between the secintegra-tions as the Gulf Stream meanders substantially between the individual sections. Whilst it is apparent from Figure 3.41 and from previous studies (e.g. Johns et al. (1995)) that northward Gulf Stream velocities extend to the bottom, the 1000 dbar level was used as the default bottom boundary in our study to make the results more easily comparable with the upper ocean interior transports of the mid-ocean section. The analysis was also repeated for the top 2000 dbar and for the full-depth.

It is apparent from Figure 3.41 that there is substantial interannual variability in the posi-tion, structure and peak velocity of the Gulf Stream. In April 2006, for instance, the Gulf Stream extends only to around 2000 dbar and is displaced inshore compared to most other years. In contrast, the April 2005 section has a strong Gulf Stream with peak velocities

00 0

Figure 3.41: Alongstream absolute geostrophic velocity (positive polewards and negative equatorwards) in cm/s for nine Line W cruises. The thick contour is at 0 cm/s. The vertical dashed line shows the position of 36^◦N.

Cruise dates Research Vessel Measurements taken

November 2003 R/V Knorr Shipboard measurements

May 2004 R/V Oceanus Full moored array deployed, shipboard measurments September 2004 R/V Cape Hatteras Shipboard measurements

April 2005 R/V Oceanus MMP turnaround, shipboard measurements

October 2005 R/V Oceanus Shipboard measurements

April 2006 R/V Oceanus MMP/VACM turnaround, shipboard measurements

October 2006 R/V Oceanus Shipboard measurements

October 2007 R/V Endeavor Shipboard measurements

May 2008 R/V Oceanus Mooring turnaround, shipboard measurements Table 3.7: Cruises conducted as part of the Line W programme with results included in our regression analysis. A further cruise conducted in April 2007 aboard R/V Oceanus. MMP stands for McLane Moored Profiler.

exceeding 2 ms⁻¹ and the core of the current is located further offshore; indeed some of the current is actually located south of 36^◦N. Moreover, the Stream is commonly separated into more than one velocity core (e.g. in May 2004 and April 2006). Integrating the transport from west to east above 1000 dbar yields transports of between 43 and 98 Sv, with the smallest transport in April 2006 and the largest in May 2004 (Figure 3.42). Some sections extend into the recirculation region to the east of the Gulf Stream (e.g. September 2004 and October 2007), whilst in other sections it is not clear that the Gulf Stream has been completely crossed (e.g. October 2005).

In order to quantify the relationship between the Gulf Stream transport and the sea surface height difference across the current, a correlation analysis was undertaken. The horizontal profile of sea surface height for each section was obtained using the absolute geostrophic velocity at the sea surface between the inner and outer edges of the Gulf Stream. This was obtained from the following equation:

η2− η₁ = vs×f

g × (x₂− x₁) (3.1)

where η₂and η₁are the sea surface heights at either end of the Gulf Stream, x₂−x₁represents the horizontal distance and v_s is the mean velocity at the surface between x₁ and x₂. A value of f at 38^◦N is used. The scatter plot of SSH difference against the total transport in the top 1000 dbar is shown in Figure 3.43, with the correlation and regression statistics presented in Table 3.8. A very high correlation coefficient (0.96) is observed, demonstrating that SSH changes are a reliable indicator of Gulf Stream transport variability. This result is even stronger than the 0.90 correlation observed by Imawaki et al. (2001) in the Kuroshio, and suggests that transport changes in the top 1000 dbar of the Gulf Stream are primarily driven by equivalent barotropic transport variability (i.e. an increase in total northward transport results from increased northward velocities in all layers down to 1000 dbar) . This is confirmed by Figure 3.44, which displays the mean transport per unit depth between the inner and outer edges of the Gulf Stream normalised by the mean surface velocity. The fact

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Figure 3.42: Total cumulated west to east transport (in the upper 1000 dbar) for the nine CTD sections reference to the deepest common level of the LADCP. Most sections show a southward transport close to the western boundary associated with the upper parts of the DWBC and then strong northward transport associated with the Gulf Stream further offshore. The dashed line indicates the position of the 36^◦N section.

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Sea surface height difference (m)

Gulf Stream transport (Sv)

Figure 3.43: Scatter plot of the Gulf Stream transport above 1000 dbar (in Sv) and the sea surface height difference across the current. The solid line shows the linear regression line.

For each cruise the inner and outer edges of the Stream are defined by the minimum and maximum cumulated transport (Figure 3.42).

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Normalised transport

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Figure 3.44: Mean transport per unit depth in the upper 1000 dbar between the inner and outer edges of the Gulf Stream normalised by the transport per unit depth at the sea surface for the nine sections. The profile to the left of the others below 500 dbar is the April 2006 section where the Gulf Stream is displaced onshore and largely confined to the upper 1000 dbar (Figure 3.41f).

that most curves overlie one another suggests that transport changes occur simultaneously across all layers, meaning the sea surface height is a reliable expression of the total transport change.

It is acknowledged here that the cruise-derived SSH differences only reflect the geostrophic changes and do not take into account the difference caused by the Ekman transport across the section. Nevertheless, the excellent agreement between SSH difference from the CTD and total Gulf Stream transport implies that the Ekman transport error is likely to be small.

Furthermore, the barotropic tide is largely removed from the data by the ADCP processing.

This correlation exercise was repeated for Gulf Stream transport in the upper 2000 dbar and for the full depth transport including the bottom triangles. As the depth range of the integration increases, the overall transport of the Gulf Stream increases but the size of the correlation coefficient decreases (Table 3.8). Although the regression relationship remains statistically significant at the 5% level even when the full depth transport is used, the first linear regression coefficient between SSH difference and transport is not significant for the 1000 to 2000 dbar depth range, with a strong anticorrelation for the region between 2000 dbar and the bottom. These results indicate that whilst the relationship can be used to infer transport changes down to 2000 dbar, the results are less certain than for the 0 to 1000 dbar depth range as baroclinic effects become important. The SSH is clearly not a suitable indicator of full-depth changes.

Depth range Correlation Regression R² F p value of transport coefficient coefficients value statistic

integration (a and b)

0 − 1000 dbar 0.9605 77.05/13.87 0.9221 83.4053 < 1 × 10⁻⁵ 0 − 2000 dbar 0.8843 47.76/45.07 0.7820 25.1106 0.0015

0− bottom 0.6892 64.18/41.86 0.4751 6.3347 0.0400

1000 − 2000 dbar 0.4175 4.38/16.44 0.1743 1.4775 0.2636 2000 dbar− bottom −0.6828 −28.26/51.40 0.4717 5.3565 0.0599 Table 3.8: Linear regression statistics for the regression of sea surface height difference de-termined from absolute surface velocity on Gulf Stream transport in different depth ranges.

The relationship expressed by the regression coefficients is GS transport (in Sv) = a× SSH difference (in m) +b.