1. Introduction

Observational studies targeting large-scale circulation changes have relied on “endpoint” measurement techniques to provide estimates of the net transport across vertical sections (e.g., Whitworth 1983; McPhaden and Zhang 2002; Johns et al. 2005; Kanzow et al. 2006). The large-scale flow in the ocean interior is in geostrophic balance to first order (away from the surface and bottom Ekman layers), and endpoint vertical density profiles can be used to compute the net geostrophic flow (relative to a level of reference) between them. The absolute geostrophic horizontal velocity U = (u, υ) can be deduced from the horizontal gradient in pressure P in the ocean, according to

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with Ω and ρ denoting the earth’s angular velocity and reference ocean density, respectively. On a zonal section, the Coriolis parameter f is constant and the horizontal pressure difference between the eastern and western endpoints (P_E, P_W) is proportional to the zonally integrated northward geostrophic volume transport per unit depth, T:

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with z and t denoting depth and time, respectively.

The pressure at z = −h can be written as the displacement of sea level from its time mean η and the density of the water column,

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where g is the earth’s gravitational acceleration. It is assumed that an inverted barometer correction has been applied to η, at a rate of ΔP_A(t) = gρ₀Δη(t) (e.g., Fu and Pihos 1994), so dynamically inactive changes (Δη) due to deviations in atmospheric pressure from the long-term mean (ΔP_A) are removed. The geostrophic balance is a valid approximation even in the strongest (fastest) ocean current systems, such as the Antarctic Circumpolar Current (ACC; Whitworth 1983), the Gulf Stream (Sato and Rossby 1995), the Kuroshio (Johns et al. 2001), the Agulhas Current (Beal and Bryden 1999), or the Atlantic deep western boundary current (DWBC; Johns et al. 2005).

Recently, the endpoint measurement technique has been used to infer meridional transport variations across a 6000-km transatlantic section between the Bahamas and the Moroccan coast at 26.5°N in the Atlantic (Fig. 1; Cunningham et al. 2007; Kanzow et al. 2007), hereafter referred to as midocean transport. Cunningham et al. (2007) show that the daily upper midocean transport shallower than approximately 1000 m displays fluctuations of 3.1 Sv (1 Sv ≡ 10⁶ m³ s⁻¹) RMS for the period between April 2004 and April 2005. As a consequence of the westward energy transfer effected by Rossby waves and eddies and of instabilities in the boundary current systems, significantly elevated levels of surface eddy kinetic energy are commonly found near the western boundaries of the ocean (see Fig. 9b in Wunsch and Stammer 1998). Using mooring-based observations of upper-ocean transports across 26.5°N, we investigate how eddy variability¹ within 500 km of the western boundary affects basinwide integrated transports. This question is important for the interpretation of the variability of both the Atlantic Meridional Overturning Circulation (AMOC) and the subtropical gyre at this latitude. Important currents in the western boundary region here include the southward-flowing DWBC below 1000 m and the northward-flowing Antilles Current in the upper 1000 m (Lee et al. 1990, 1996; Bryden et al. 2005; Johns et al. 2008).

Transient eddy variability is sometimes important for the horizontal redistribution of heat, salt, and momentum but may be a source of noise in experiments aimed at characterizing the temporal evolution of the large-scale ocean circulation using endpoint methods (e.g., Kanzow et al. 2008a). An eddy’s rotation-related maximum pressure anomaly is located at its center so that the rotational transport is largest when integrating over its radius. Integrating over the eddy’s diameter, the rotational transport cancels. Thus, if the eddy’s horizontal extent is fully contained within the section when passing across it, only the across-section eddy translation but not its rotational flow has an impact on net across-section transports. Conversely, eddies passing over one endpoint contribute to fluctuations in the net zonal pressure gradient, causing noise that has the potential to mask the temporal evolution of the pressure gradients associated with the large-scale flow field.

Altimetry might represent an efficient tool to estimate the time-variable strength of upper-ocean velocities. Transient features of geostrophic surface flow are proportional to the sea surface slope η and have been monitored by satellite altimetry. Numerous applications have been presented for the study of wind-driven gyres, mesoscale flows, and strong ocean currents (e.g., Stammer 1997; Chelton et al. 2007; Cunningham and Pavic 2007). The time-variable geostrophic transport T_η over the depth range [−h, 0] can be estimated by associating the geostrophic surface flow with one dominant vertical mode of horizontal velocity F(z) according to

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Away from the boundaries, the upper-ocean geostrophic flow on time scales longer than a few weeks exhibits a surface-intensified first mode baroclinic structure (Wunsch 1997), whose velocity zero crossing is typically found around 1500 m. Such motions mainly reflect westward-propagating baroclinic eddies and Rossby waves, as satellite observations reveal (Chelton et al. 2007). However, approximating the vertical structure of geostrophic flow by linear baroclinic modes can fail near the sea surface. A sign of failure is that there is no sea surface temperature signal to the linear mode. Observations from the Mid-Ocean Dynamics Experiment (MODE Group 1978) showed that temperature-inferred vertical displacements do not necessarily decrease toward the sea surface (Richman et al. 1977), with the near-surface departure from linear mode theory possibly being due to shear modes (Beckmann 1988).

Barotropic motions gain in importance in the less stratified deep ocean (Wunsch 1997; Johns et al. 2005; Kanzow et al. 2008a), and from a comparison of in situ observations and altimetry in the tropical North Atlantic, Kanzow et al. (2008a) concluded that variations of η are not representative of transport changes below 1000 m.

Near boundaries, a separation of the barotropic and baroclinic modes is ambiguous because an across-boundary integral of barotropic along-boundary velocities over sloping bathymetry inevitably results in a baroclinic transport profile. Topographically trapped waves may also become important (e.g., Johns and Watts 1986) such that the relationship between η and upper-ocean transports may vary across the boundary. In addition, competing dynamics and their manifestations as vertical modes mean that a stable relationship between η and upper-ocean transports might not exist.

Using density and current meter data from the Rapid Climate Change–Meridional Overturning Circulation and Heatflux Array (RAPID–MOCHA) moorings within 500 km of the western boundary at 26.5°N, we will investigate the relationship between transports and η. In particular, we test whether a robust relationship between η at the western boundary (or the boundary-to-boundary difference in η) and the upper midocean transport across 26.5°N can be established according to (4). If successful, this would enable us to estimate the strength of the AMOC at 26.5°N continuously since the launch of the Ocean Topography Experiment (TOPEX)/Poseidon altimeter in 1992 [combined with continuous estimates of the Gulf Stream and Ekman transports over this period from the Florida Current telephone cable measurements (Baringer and Larsen 2001) and wind field reanalysis products [such as those from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis]. A stable relationship between the differences in η within a few hundred kilometers from the western boundary and η at the eastern boundary may provide a proxy for the strength of the wind-driven subtropical gyre at this latitude.

The paper is structured as follows. In section 2 we present the underlying data and methods. Section 3 describes the midocean zonally integrated transports between Morocco and four locations up to 500 km east of the Bahamas; in addition, these transports are compared with the variability in altimetric observations. In section 4 we analyze the effects of eddies impinging on the western boundary on basinwide integrated flows by means of numerical model experiments. A theoretical explanation for the model results is presented in section 5. The effects of eddies close to and at the western boundary on endpoint measurements and the implications for measuring and interpreting basinwide integrated volume transports such as the AMOC are discussed in section 6, followed by a brief summary (section 7).

2. Data and methods

b. Methods

Meridional transports across 26.5°N zonally averaged between Florida and Africa and vertically averaged over the top 1000 m are a reliable measure of the strength of the Atlantic Meridional Overturning Circulation (Cunningham et al. 2007) because the middepth level of no motion exhibits fluctuations in vertical displacement of only 90 m RMS around its time mean of 1041 m for daily transport values. The basinwide integrated northward transport T_BASIN across 26.5°N is computed as the sum of (i) the zonally averaged Ekman transport T_EK, (ii) Gulf Stream transport integrated across the Straits of Florida (between Florida and the Bahamas) T_GS, and (iii) the midocean transport (the northward geostrophic transport integrated between the Bahamas and the African coast) T_MO:

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The notation T_GS(z, t), T_EK(z, t), T_MO(z, t), etc., indicates transports per unit depth z, while T_GS(t), T_EK(t), T_MO(t), etc., indicate vertically integrated transports. As each variable is a function of time t, the explicit mentioning of the time dependence will be dropped hereafter. Transport fluctuations are anomalies about the time mean, unless otherwise noted.

For the computation of T_EK, we used daily wind stress data from the Quick Scatterometer (QuikSCAT) mission (Kanzow et al. 2007) while daily estimates of T_GS are available from the telephone cable–based Florida Current monitoring system (Baringer and Larsen 2001). The midocean transport T_MO(z, t) can be divided into two components: (i) the transport in the 16-km-wide “western boundary wedge” between the Abaco shelf (AS) and site WB2 T_AS-WB2(z), derived from direct current meter measurements on moorings WBA, WB0, WB1, and WB2 (Fig. 2; for details see Johns et al. 2008; Kanzow et al. 2008b) and (ii) the surface to 4740 m geostrophic transport between WB2 and the eastern boundary. The geostrophic transport relative to the reference level z_REF = −4740 m between WB2 and the eastern boundary, referred to as internal transport T_INT, is computed from continuous observations of density profiles at the section endpoints (ρ_WB2 and ρ_EAST) according to

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To compute the absolute geostrophic transports, for each 12-hourly profile of T_INT(z), a reference transport T_C must be derived.

From the first year of the RAPID measurements, Kanzow et al. (2007) show that there is a strong negative correlation between T_MO and the sum of T_GS and T_EK at periods in excess of 10 days, such that the residual (zonally and vertically integrated) transport across 26.5°N displays much smaller fluctuations than either component. Kanzow et al. (2007) argue that the variability of the residual transport is mostly due to measurement uncertainties rather than real fluctuations that could have been caused by changes in the strength of the Arctic throughflow. Here, we assume that there is precise compensation among the different flow components, in the sense that the sea surface to seafloor (z = −h_BOT) integral yields zero residual mass transport across 26.5°N (Kanzow et al. 2007; Cunningham et al. 2007) according to

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The net upper midocean transport U_MO is defined as the midocean transport T_MO(z) integrated over the upper 1000 m, according to

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Formally, there is a small southward mass transport across 26.5°N associated with the sum of Bering Straits flow from the Pacific into the Arctic Ocean and of the net precipitation between the Bering Straits and 26.5°N. Because each of these components is less than 1 Sv and there is little information on how they vary in time (Woodgate and Aagaard 2005; Wijffels 2001), we assume zero residual mass transport at each moment of time and the referencing of T_INT(z) is carried out by computing a compensating transport profile T_C at each time step as follows:

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For the computation of the corresponding compensation transport profile T_C(z), we assume that the underlying compensating meridional velocity field V_C is spatially uniform (vertically and zonally) such that

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with X_E and X_W denoting the eastern and western boundaries, respectively, and L denoting the effective width of the ocean, which decreases with depth.

Throughout this study we apply a 10-day low-pass filter to U_MO (and to all other transport time series) as transport changes at periods shorter than 10 days may not be representative of AMOC fluctuations (Kanzow et al. 2007). As defined in (10) T_C(z) is nearly depth independent shallower than 3500 m, whereas below that the reduction in the effective zonal ocean width (below the crest of the Mid-Atlantic Ridge; see Fig. 1) makes the amplitude of T_C(z) decrease with depth. Overall, only about 25% of T_C(z) occurs at depths shallower than 1000 m.

To compute the upper-ocean transport east of WB2 U_WB2-EAST, we subtract from U_MO the transport west of WB2 in the upper 1000 m (U_AS-WB2):

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Similarly, to obtain the upper midocean transport east of WB3 (U_WB3-EAST), we subtract from U_MO the transport west of WB3 (U_AS-WB3) integrated over the top 1000 m:

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Here, U_AS-WB3 is computed from the direct current meter measurements on WBA, WB1, WB2, and WB3 (Fig. 3; Johns et al. 2008). Finally, to obtain the upper midocean transport east of WB5 (U_WB5-EAST), we subtract from U_MO the sum of U_AS-WB3 and the transport between WB3 and WB5 above 1000 m (U_WB3-WB5):

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Here, U_WB3-WB5 is computed in three steps. First, we compute the internal geostrophic transport relative to 4740 m between WB3 and WB5 from the density profiles at both sites (ρ_WB3 and ρ_WB5) as in (6). Second, both mooring sites comprise bottom pressure sensors, from which the near-bottom northward external transport (per unit depth) T_EXT(z) integrated between WB3 and WB5 can be computed (e.g., Kanzow et al. 2008b) according to

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Finally, adding internal and external transports gives geostrophic transport fluctuations between WB3 and WB5 T_WB3-WB5(z).

We will compare the dynamic sea surface heights at the mooring locations and the midocean transport anomalies to satellite-derived sea surface heights and their zonal differences. We use the “updated” delayed-time maps of sea level anomalies (DT-MSLA “Upd”) gridded multisatellite merged altimeter dataset described by Dibarboure et al. (2008) and provided by Aviso (information online at http://www.aviso.oceanobs.com). The altimetry dataset spans the period between October 1992 and January 2008 and has a nominal resolution of ⅓° in space and 7 days in time. The underlying satellite missions include TOPEX/Poseidon, Jason-1, European Remote Sensing Satellite-2 (ERS-2), and Envisat. We extract the sea surface height η along 26.5°N and at each time step we subtract the zonal mean η (Bahamas to Morocco) from each grid point. This suppresses the dynamically inactive portion of the seasonal variations of η that is mainly associated with seasonal near–sea surface thermal expansion.

The Jason-1 ground track closest to the Abaco shelf approaches to within about 4 km of WB2, crossing 26.5°N east of WB2. It is an ascending track that enters deep waters from the Nassau shelf about 200 km southwest of WB2 (Fig. 1b). The correlation between η at the point closest to WB2 from the Jason-1 along-track dataset and η at WB2 extracted from the gridded dataset (with the latter being subject to spatial and temporal averaging) is R = 0.79. A descending Jason-1 track approaches WB3 to within 15 km (minimum distance), crossing 26.5°N to the east of WB3 (Fig. 1b).

Throughout the paper anomalies of transport and sea surface height will be discussed such that T and η represent fluctuations with the time mean removed.

3. Upper-ocean transport and sea surface height

In the following, we test the extent to which altimetric observations of η can be used to gain information on the spatiotemporal characteristics of zonally integrated upper-ocean transport. Figure 5 shows η for the period between October 1992 and January 2008 within 700 km of the western boundary along 26.5°N. It reveals coherent westward propagation of η anomalies at roughly 6 cm s⁻¹, with periods between 2 and 6 months. However, some of the propagating anomalies entering the domain at 70°W disintegrate before they reach 76°W. For example, positive and negative anomalies appear at 70°W in June 1996 and July 2003 vanishing before crossing 74°W.

Superimposed on the propagation pattern are numerous isolated stationary anomalies that sometimes appear as dipolar structures. Three such events can be seen between 76° and 73°W during the period from October 2002 through July 2003. Interannual variations are also apparent, both propagating and stationary. The strongest interannual changes are centered around 75.8°W (Fig. 5b), where η displays anomalously negative values from February 2001 through June 2002 and from April 2006 through July 2007, and positive values from October 2002 through January 2004. Both stationary and propagating anomalies have in common that their RMS amplitudes and RMS variabilities appear to diminish west of 76°W.

In the western boundary region at 26.5°N, there is a gradual westward increase in the RMS fluctuations of η from 6.5 cm RMS at 65°W to its maximum 11.2 cm RMS at 75.8°W for the period of altimetric observations between October 1992 and January 2008 (solid line in Fig. 6). West of 75.8°W, there is a rapid decrease in the variability of η from 11.2 to 5.3 cm RMS at 76.75°W. Estimates of the RMS amplitude of η west of 76.75°W (WB2) are possibly unreliable due to a lack of altimetric observations. Similar reductions in RMS variability are confirmed for the shorter RAPID measurement period between April 2004 and October 2006 (red dashed line) and the Atlantic Climate Change Program (ACCP-3) measurement period (Johns et al. 2005) between October 1995 and June1997 (blue dashed line).

The rapid decrease of eddy energy toward the boundary may be due to the abrupt, clifflike topography of the Bahamian escarpment that deepens from 500- to 5000-m depth over 25 km. We show, however, that a decrease in eddy energy close to the western boundary is a general expectation from theory. This decrease in eddy energy within a few tens of kilometers of the western boundary differs from the general tendency for eddy energy to decrease away from energetic western boundary regions toward the ocean interior on scales of several hundred kilometers [as seen, e.g., in MODE-1 experiment a few degrees farther north (MODE-1 Atlas Group 1977)].

Also shown in Fig. 6 are RMS fluctuations of dynamic height at 200 m relative to the seafloor from the RAPID mooring measurements (red crosses) and from mooring C of the ACCP-3 experiment (Johns et al. 2005). Using a dynamic height at 200 m rather than at sea level suppresses the seasonal cycle of the near-surface thermal expansion. Dynamic heights at WB5, C, WB3, and WB2 vary by 9.1, 11.0, 5.9, and 3.9 dynamic cm RMS, respectively, and are in agreement with the altimetric observations (Fig. 6). In particular, the sharp decrease to the west of site C is reproduced. If RMS fluctuations of dynamic height from mooring C are representative of those during the RAPID measurement period, the implied decrease in dynamic height variations (or η) is 7.1 cm, declining from 11 cm at 76.1°W to 3.9 cm RMS at 76.75°W (i.e., over 65 km). This may be a steeper gradient than the gridded altimeter dataset can resolve with its resolution of about 33 km.

If η or the dynamic height near the sea surface can be used as a proxy for upper-ocean transport, then, according to (4), the meridional transport variations integrated between WB5 and the eastern boundary should be significantly larger than between WB2 and the eastern boundary. Note in passing that at the eastern boundary the RMS fluctuations of η amount to only 2.2 cm RMS at EBH4 (Fig. 2).

The 10-day low-pass-filtered basinwide integrated upper midocean transport U_MO exhibits fluctuations of 3.0 Sv RMS over the 30 months of observations (Fig. 7; Table 2). It shows pronounced seasonal variations that suggest a reduced southward flow in autumn and enhanced southward flow in spring. The standard error of U_MO (based on the degrees of freedom in Table 2) is 0.6 Sv for the 30-month-long time series and 0.9 Sv for a 12-month segment.

The upper-ocean transport between WB2 and the eastern boundary (U_WB2-EAST) displays a variability of 3.6 Sv RMS and a correlation of 0.81 with U_MO, which is significant at 5% error probability (Table 2; Fig. 8). Transports between WB3 and the eastern boundary (U_WB3-EAST) and between WB5 and the eastern boundary (U_WB5-EAST) exhibit variations of 6.0 and 10.8 Sv RMS, respectively (Table 2; Fig. 8). The correlations of U_WB3-EAST and U_WB5-EAST with U_MO are 0.45 and 0.10, respectively, with the first value being barely significant and the second not exceeding the 5% error probability threshold of 0.42 (Table 2). The differences U_WB2-EAST − U_MO and U_WB3-EAST − U_MO are 2.1 and 5.3 Sv RMS, respectively.

The following picture emerges within roughly 100 km of the western boundary of the Atlantic at 26.5°N. The farther away from the Abaco shelf the western endpoint of the section is moved to the east, the larger the variations of the zonally integrated transports become. We see that U_WB2-EAST, U_WB3-EAST, and U_WB5-EAST exceed U_MO by factors of 1.2, 2, and 3.6, respectively, in terms of RMS fluctuations. The increase in transport variations is in qualitative agreement with the offshore increase in the RMS amplitude of η in the vicinity of the western boundary. This holds both for intraseasonal and interannual fluctuations (Fig. 6). The correlation analysis suggests that U_WB2-EAST is moderately representative of U_MO with an RMS uncertainty of 2.1 Sv (which is not small compared to the 3.0 Sv RMS fluctuations of U_MO). The 2.1 Sv RMS is, according to (8), the RMS variability that the upper-ocean transports west of WB2 (U_AS-WB2) contributes. A negative correlation of −0.55 between U_WB2-EAST and U_AS-WB2 is observed—possibly resulting from Antilles Current meanders and eddies passing over WB2—and explains why U_WB2-EAST displays a larger transport fluctuations than does U_MO.

The transport components farther offshore (i.e., U_WB3-EAST, U_WB5-EAST) cannot serve as a reliable measure of U_MO. Thus, to estimate variations in U_MO reliably (as part of the AMOC at 26.5°N), density measurements have to be obtained as close to the boundary as possible (and not several tens of kilometers away from it).

We now test whether zonal differences in η provide a straightforward way of estimating zonally integrated upper-ocean transports across 26.5°N. The correlations of the differences in η between the eastern boundary and WB5, WB3, WB2, and WB1 (η_EAST − η_WBX, with X = 5, 3, 2, and 1 denoting the different WB mooring sites) with the corresponding transports U_WB5-EAST, U_WB3-EAST, U_WB2-EAST, and U_MO are 0.85, 0.71, 0.44, and 0.12, respectively (Fig. 9). The difference η_EAST − η_WB1 was used to compare to U_MO rather than η at the Abaco shelf break, because (i) variations of U_WB1-EAST (i.e., upper-ocean transport east of WB1) are representative of U_MO with their correlation being 0.95 and (ii) sea surface variations from the gridded altimetry dataset to the west of WB2 are unreliable due to a lack of measurements (section 2). A linear regression of the form U_WBX-EAST = s_WBX(η_EAST − η_WBX) gives s_WBX = 0.91, 0.68, and 0.32 Sv cm⁻¹ for U_WB5-EAST, U_WB3-EAST, and U_WB2-EAST, respectively. Subtracting the fit from the respective upper-ocean transports yields transport residuals U_WBX-EAST − s_WBX(η_EAST − η_WBX) of 5.7, 4.2, and 3.2 Sv RMS for X = 5, 3, and 2.

The linear fit using η_EAST − η_WBX explains 72%, 51%, and 19% of the variances of U_WB5-EAST, U_WB3-EAST, and U_WB2-EAST, respectively. Although the transport variance explained by η_EAST − η_WBX is largest at WB5, the absolute residual between the linear fit and the corresponding transport is largest, too. Both the relative prediction skill and the absolute error decrease toward the boundary. At WB2, the error of the transport prediction (3.2 Sv RMS) has roughly the same amplitude as U_MO. This means that reliable estimates of U_MO cannot be obtained by combining a current meter–based boundary current array (measuring the transports between the shelf and, say, WB2) with altimetric observations of η_EAST − η_WB2.

The fact that η_EAST − η_WB1 has no skill in determining U_MO could partly be related to the fact that the Jason-1 altimeter (or TOPEX/Poseidon) takes no measurements between Abaco and WB2. However, since there is a Jason-1 ground track 4 km east of WB2, we consider the relatively low level of the variance of U_WB2-EAST explained by η_EAST − η_WB2 to be a robust result.

It is interesting to note that it is particularly the low-frequency transport variability of periods in excess of 2 months that is gradually suppressed, as the western endpoint of the section is moved closer to the western boundary. The reduction in RMS transport variability is a factor of 4 comparing 2-month low-pass-filtered time series of U_WB5-EAST and U_MO from 10.2 to 2.5 Sv RMS (Table 2). For 2-month high-pass-filtered data, there is only a reduction by a factor of 2 between U_WB5-EAST and U_MO from 3.0 to 1.7 Sv RMS (Table 2). This will become relevant in section 6.

To investigate why the correlation between U_WB2-EAST. and η_EAST − η_WB2 is lower than the correlation between U_WB5-EAST and η_EAST − η_WB5, an EOF mode analysis is carried out. The first three leading EOF modes for U_MO(z), U_WB2-EAST(z), U_WB3-EAST(z), and U_WB5-EAST(z) [which are the transport per unit depth profiles in the upper 1000 m corresponding to the net upper-ocean transports defined in (8) and (11)–(13)] are displayed in Figs. 10a–d. The variances explained by the first modes are 69%, 76%, 83%, and 92%, respectively, while those of the second modes amount to 22%, 18%, 17%, and 7%.

For all four transport cases the first modes (blue lines in Figs. 10a–d) do not exhibit a zero crossing between the sea surface and 1000 m. Therefore, the transport at the sea surface associated with the first mode is of the same sign as the upper-ocean transport explained by the first mode (i.e., the vertical integral of that mode over the top 1000 m). All of the second modes (red lines in Figs. 10a–d) display a zero crossing shallower than 250 m. As a result, transports associated with the second modes at the sea surface have opposite signs to the vertically integrated transports. The first modes of U_WB5-EAST(z), U_WB3-EAST(z), U_WB2-EAST(z), and U_MO(z) explain 10.8, 5.9, 3.5, and 2.8 Sv RMS above 1000 m, respectively, according to , while the second modes account for 0.8, 0.9, 1.0, and 1.2 Sv RMS, respectively. Here, Mⁱ denotes the ith EOF mode and Aⁱ the corresponding principal component, and the angle brackets represent variance operators.

The gradient in the sea surface height is regarded as a measure of the surface geostrophic flow. For the former to be also a good indicator of depth-integrated upper-ocean transport requires surface and upper-ocean transport to fluctuate in phase. It is not surprising that η_EAST − η_WB5 is a good proxy of U_WB5-EAST (Fig. 9) given that the first EOF mode explains 92% of the variance (Fig. 10d). Flow reversals in the upper 1000 m—as represented by the second EOF modes—gradually gain in importance as the western endpoint of the transport integration is moved westward. As has been shown above, all of the second modes imply an out-of-phase relationship between the surface and the depth-integrated upper-ocean transport. In the particular case of the Bahamaian western boundary, this has to do with the superposition of the upper-ocean Antilles Current on the DWBC below, which have been shown to vary largely independently from one another (Lee et al. 1990, 1996). Further, the core of the Antilles Current, which is found near 400 m in the mean, is not strongly coupled to variations in the surface currents just above it (Lee et al. 1990, 1996).

The change of the modal structure over the continental slope implies that the clear relationship between the surface and the upper-ocean transport found offshore is gradually lost. As a consequence, variations in η_EAST − η_WB2 do not provide a reliable estimate of the temporal evolution of U_WB2-EAST (Fig. 9). In the case of U_MO, the second mode has an even higher relative importance than the first one, when compared to U_WB2-EAST (Figs. 10a and 10b). The fact that altimetric measurements effectively do not exist west of WB2 represents an additional practical problem when trying to infer the temporal evolution of U_MO (as part the AMOC) from the basinwide gradient of the sea surface height.

4. The signatures of eddies in basinwide integrated transports: A model simulation

Why are upper-ocean transport variations integrated between the western and eastern boundaries so much smaller than WB5-to-eastern boundary transports? And what is the dynamical reason for the sharp decline in RMS variations of the sea surface height anomalies within 100 km of the western boundary? Analysis of the altimeter data suggests that westward-propagating eddies are a major source of variability near the western boundary (Fig. 5). In this section we present numerical results from a nonlinear reduced-gravity model. We want to elucidate the fate of Rossby waves and eddies as they approach the western boundary and to investigate how they affect the sea surface height near and on the boundary. This allows us to put the observations into a dynamical context.

The model is similar to that described in Johnson and Marshall (2002) but is eddy permitting with a lateral resolution of 14 km. The domain extends 4500 km in the meridional direction (with the southern boundary at the equator) and 2800 km in the zonal direction. A beta-plane approximation is made, with f₀ = 0.65 × 10⁻⁴ s⁻¹ equal to the Coriolis parameter at 26.5°N. The background model layer thickness is 750 m, and the reduced gravity is 0.015 m s⁻² (broadly consistent with the North Atlantic density distribution). Dissipation is achieved through lateral friction, with a coefficient of 30 m² s⁻¹, and no-slip and no-normal flow boundary conditions are applied. A sponge region ramps up over the southernmost 1000 km of the domain, in which layer thickness is relaxed to the background value at a maximum rate of ⅙ h⁻¹; this efficiently damps any fast boundary waves as they approach the equator, preventing them from propagating right around the basin and contaminating the results.

The first integration (Fig. 11) is initialized with a single, anticyclonic eddy, located roughly in the center of the domain at y = 0 (equivalent to 26.5°N). The eddy has an approximate diameter of 500 km, and a layer thickness anomaly of 130 m, equivalent to a sea surface height anomaly, η′ = (g′/g)h′, of roughly 20 cm, as plotted in Fig. 11a. The eddy propagates westward at a speed of about 5 cm s⁻¹ (Fig. 11b) although it is somewhat dispersive. On reaching the western boundary, a fast Kelvin wave is generated, which propagates rapidly southward; subsequently, the eddy itself propagates northward along the boundary due to the nonlinear image effect (Minato 1982) and the rocket effect (Nof 1988), and short Rossby waves are also generated. The maximum amplitude of the free-surface height disturbance η on the boundary is roughly a factor of 4 smaller than that in the basin interior.

Figures 11c and 11d show integrated meridional transports within the moving layer of the reduced gravity model, as a function of latitude and time. In Fig. 11c, the transport is integrated from 56 km off the western boundary to the eastern boundary (U_56KM-EAST); Fig. 11d shows the meridional transport integrated from coast to coast, from the western to the eastern boundaries (U_WEST-EAST). These two transport values differ widely in terms of both their structures and their amplitudes. While U_56KM-EAST is dominated by the signature of the northward-moving eddy close to the western boundary, U_WEST-EAST is dominated instead by the much smaller-amplitude, southward-propagating boundary wave signals on the western boundary itself. It is clear from Figs. 11c and 11d that the net northward transport anomaly associated with an individual eddy is very different when the western endpoint of the section lies a short distance off the boundary compared with on the boundary. This is a direct consequence of the reduction in amplitude of variations in η at the boundary.

Figure 12 shows the same diagnostics for a calculation in which the model is initialized with a field of cyclonic and anticyclonic eddies (Fig. 12a). The Hovmöller plot shows the westward propagation of the eddies along y = 0 and subsequent propagation along the western boundary (Fig. 12b); again, the maximum amplitude of η on the boundary is smaller than that in the basin interior. This is consistent with the observed reduction in the amplitude of the dynamic height variability between site C and WB2 (Fig. 6). As with the single eddy, U_56KM-EAST exhibits large-amplitude variability (Fig. 12c), most of which disappears in U_WEST-EAST (Fig. 12d), and the remaining transport anomaly being associated with boundary waves generated when each eddy reaches the western boundary. Figure 13a shows variations of η along 26.5°N within 500 km from the western boundary (blow-up of image detail in Fig. 12b). As in the observation (Fig. 5), the simulated η anomalies display maximum amplitudes away from the western boundary. The RMS variability of η peaks at 100 km offshore (Fig. 13b) and there is then a decay of roughly a factor of 5 toward the western boundary. Both the scale over which the decay takes place and the degree of the decay are in good agreement with the observations (Fig. 6).

Note that the 1.5-layer reduced-gravity model used here includes no representation of topographic effects or boundary complexity, and as such does not accurately reproduce the details of the boundary propagation, which in more complex models involves a combination of Kelvin, mixed Kelvin–Rossby, and topographic Rossby wave dynamics (Huthnance 1978; Clarke and Shi 1991; Hallberg and Rhines 1996). However, we believe that the fact that the model exhibits a similar decay in the amplitude of variability as that observed, and over a similar distance from the boundary, suggests that these details are not necessary to explain the observed behavior. O’Rourke (2009) finds that the presence of topography in fact increases the speed of coastally trapped waves, provided that there are boundary waves with a group speed significantly faster than the interior Rossby wave speed, then a reduction in the amplitude of variability close to the boundary will occur.

The “eddy-filled ocean” experiment in Fig. 12 also highlights a potential attribution problem. The fast equatorward communication of transport anomalies may make it very difficult to distinguish between local and remotely forced fluctuations of U_MO (or the AMOC) because—at any given latitude—in addition to local anomalies U_MO also contains transport contributions resulting from eddies impinging on the western boundary poleward of the latitude of interest.

5. A theory for the reduction of SSH fluctuations close to the western boundary

The observations are in good qualitative agreement with the reduced-gravity model. In addition the model has highlighted boundary waves as a potential mechanism for reducing variability in η at the boundary. On the basis of linear dynamics, we now derive a relationship between the amplitude of η (or layer thickness anomaly) on the western boundary and the amplitude offshore.

First, consider an analytical model of linear Rossby waves in a β-plane basin. In the limit ω ≪ βL_d, the reduced-gravity equations admit long and short Rossby wave solutions,² satisfying the dispersion relations ω/k_l = −βL_d² (for long waves) and ωk_s = −β (for short waves), where ω is the angular frequency, k_l and k_s are the long and short wavenumbers, L_d is the deformation radius, and β is the meridional gradient of f.

Now suppose that incoming long Rossby waves are balanced by short Rossby waves generated at a meridional western boundary (x = 0). The total layer thickness anomaly is thus

View Expanded

The wave amplitudes, A_l(y) and A_s(y), may be complex and include phase information.

The zonal component of velocity is zero at the western boundary. Thus, the linear meridional momentum equation [e.g., see Cushman-Roisin 1994, Eqs. (12)–(35), for the nonlinear case] takes the following form on the boundary:

View Expanded

Here, g′ is the reduced gravity, we assume that the meridional velocity is geostrophic to leading order, and we neglect any frictional dissipation. Substituting for h′, and noting k_s ≫ k_l, we find

View Expanded

This, in turn, may be rewritten as

View Expanded

Finally, assuming that the total wave amplitude, A_s + A_l, vanishes to the north of the incoming long waves, and integrating the above expression, we obtain

View Expanded

Thus, the total wave amplitude on the boundary, A_s + A_l, is reduced relative to the interior by a factor βΔy/f, equal to the fractional change in the Coriolis parameter across the band of incoming long waves. The amplitude reduction is thus greater the smaller the meridional scale of the incoming wave (or eddy). If the incoming waves are confined to a small latitude band, then the wave amplitude, and hence the variability in sea surface height, are greatly reduced on the boundary. For Δy = 500 km, the reduction will be by a factor of f/(βΔy) = 6 (using f_26.5°N = 6.4 × 10⁻⁵ s⁻¹ and β = 2.1 × 10⁻¹¹ s⁻¹ m⁻¹).

Physically, this amplitude reduction occurs because an along-boundary pressure gradient is unable to be maintained, since the Coriolis force to balance it would require a flow into the boundary. Instead a fluid acceleration is generated, which rapidly propagates any pressure anomalies along the boundary. This is precisely the same mechanism that gives rise to coastal Kelvin waves, although the character of the wave motion is different in this Rossby wave limit (Clarke and Shi 1991). The result that the pressure anomaly is reduced on the boundary holds across a wide range of physical parameters, although precise details depend on frictional dissipation, boundary conditions, and wave frequency (D. P. Marshall and H. L. Johnson 2009, unpublished manuscript).

6. Discussion

7. Summary

The main results of this study can be summarized as follows. The meridional upper midocean transport U_MO integrated between Morocco and the Bahamas varies by 3.0 Sv RMS between April 2004 and October 2006. Zonally integrated upper-ocean transports between Morocco and stations 16, 40, and 500 km off the shelf of the Bahamas show fluctuations of 3.6, 6.0, and 10.8 Sv RMS, respectively, and thus exceed those of U_MO. In agreement with that, both the mooring and altimetric measurements of sea surface height variability show a threefold decline within roughly 100 km of (and toward) the shelf of the Bahamas. The findings imply that in order to capture the variability of U_MO (and the AMOC) reliable in situ density measurements need to be taken right at the ocean boundaries.

There is a gradual decrease in the correlation between upper-ocean transport (integrated between the eastern boundary and different sites within 500 km of the western boundary) and the difference in η between the corresponding section endpoints, as the western endpoint moves westward. The correlation coefficient drops from 0.85, for a station located 500 km offshore, to a statistically insignificant value of only 0.12 for the basinwide integration. We consider the gradual decrease in correlation, as the western section endpoint is moved westward, to be mainly a consequence of changes in the vertical structure of the integrated flow, because of flow reversals in the upper 1000 m becoming increasingly important over the continental slope compared to offshore conditions. The results imply that the basinwide difference of η does not provide reliable estimates of the temporal evolution of U_MO.

The nonlinear reduced-gravity model used to study eddy–boundary interaction is able to reproduce both the observed decline in the amplitude of η within 100 km from the western boundary and the corresponding reduction in the integrated transport fluctuations. It shows that eddies impinging on the western boundary kick off fast boundary waves that propagate equatorward and account for the observed decline.

An analytical linear model based on a simple budget of incoming long and reflected short Rossby waves at the western boundary provides a scaling for the reduction of thermocline thickness (or η) on the western boundary compared to offshore conditions according to f/(βΔy). At 26.5°N and for a meridional scale, Δy = 500 km of the incoming wave yields a decrease by a factor of 6.

Physically, this amplitude reduction occurs because an along-boundary pressure gradient cannot be maintained by a Coriolis force (since there cannot be flow into the boundary). Instead a fluid acceleration is generated, which rapidly propagates any pressure anomalies along the boundary.

Overall, our results suggest that the local eddy field does not have the potential to dominate AMOC variability at 26.5°N on interannual to decadal time scales. If a monitoring system based on boundary-to-boundary density gradient observations can be maintained in the ocean continuously over climate relevant time scales, it will document the temporal evolution of the strength of the AMOC, whether it be random fluctuations, regular oscillations, or a long-term trend.