It is quite widely accepted that the along-shelf pressure gradient (ASPG) contributes in driving shelf currents in the Middle Atlantic Bight (MAB) off the northeastern U.S. coast; its origin, however, remains a subject for debate. Based on analyses of 16 yr (1993–2008) of satellite, tide gauge, river, and wind data and numerical experiments, the authors suggest that river and Coastal Labrador Sea Water (CLSW) transport contribute to a positive mean ASPG (tilt up northward) in the ratio of approximately 1:7 (i.e., CLSW dominates), whereas wind and the Gulf Stream tend to produce a negative mean ASPG in the ratio of approximately 1:6.
Data also indicate seasonal and interannual variations of ASPG that correlate with the Gulf Stream’s shift and eddy kinetic energy north of the Gulf Stream (N-EKE) due to warm-core rings. A southward shift in the Gulf Stream produces a sea level drop north of Cape Hatteras, which is most rapid in winter. The N-EKE peaks in late spring to early summer and is larger in some years than others. A process model is used to show that ring propagation along the MAB slope and ring impingement upon the shelf break north of Cape Hatteras generate along-isobath density gradients and cross-shelfbreak transports that produce sea level change on the shelf; the dominant ageostrophic term in the depth-integrated vorticity balance is the joint effect of baroclinicity and relief (JEBAR) term. In particular, the shelf’s sea surface slopes down to the north when rings approach Cape Hatteras.
The Middle Atlantic Bight (MAB) is the continental shelf region off the northeastern coast of the United States stretching between Nantucket Shoals to the northeast and Cape Hatteras to the south (Beardsley and Boicourt 1981). The MAB is a dynamically complex region where cooler and fresher shelf water is separated from warmer and saltier slope water by a shelfbreak front (Csanady and Hamilton 1988). Understanding water properties and currents in MAB is of interest for navigation, fisheries, and coastal ecosystems.
The MAB circulation has been extensively studied through observations and modeling (Csanady 1976; Beardsley and Boicourt 1981; Chapman 1986; Csanady and Hamilton 1988; Linder and Gawarkiewicz 1998; Flagg et al. 2006; Lentz 2008a). Depth-averaged mean currents are predominantly along isobath directed equatorward, with speeds of 0.03–0.1 m s−1 that increase with distance offshore (Lentz 2008a, 2010). Currents are westward on the New England shelf, southwestward in the middle of MAB, and veer offshore just north of Cape Hatteras.
An important driving force for currents in the MAB is the along-shelf pressure gradient (ASPG) (Beardsley and Boicourt 1981). Stommel and Leetmaa (1972) concluded that an ASPG on the order of 10−7 is required to drive the southwestward flow. Csanady (1976) argued also that an ASPG must exist to account for the observed circulation in the MAB. Lentz (2008a) extended Csanady’s model, analyzed observations, and showed quite convincingly that the southwestward along-shelf current is consistent with an along-shelf sea surface slope; he estimated an ASPG value of approximately 3.7 × 10−8. Lentz (2008a) discussed the possibility of other types of forcing, but the hypothesis that ASPG exists seems reasonable.
Lentz (2008a) showed that ASPG is mainly due to the sea surface slope. The Gulf Stream (GS) and Slope Sea gyre (Csanady and Hamilton 1988) may drive an ASPG at the shelf break, but the penetration of the pressure field onto the shelf is limited (Wang 1982; Csanady and Shaw 1983; Chapman 1986). What drives the ASPG?
Observations also show seasonal variations in the depth-averaged along-shelf currents that are different in different subregions of the MAB (Lentz 2008b). Over the southern flank of Georges Bank, the along-shelf flow is maximum southwestward in September (Butman and Beardsley 1987; Brink et al. 2003; Flagg and Dunn 2003; Shearman and Lentz 2003). Farther west and south in the MAB, the seasonal variation is less clear (Mayer et al. 1979; Beardsley et al. 1985; Aikman et al. 1988). Along the Oleander line, Flagg et al. (2006) observed a shelfbreak jet (offshore of 100-m isobath) that was stronger southwestward in fall and winter and weaker in spring and summer. ADCP measurements at station 5 of the Coastal Ocean Bio-optical Buoy (COBY) transect (37.833°N, 75.029°W) show maximum southwestward currents in spring and weak currents in summer and fall (F-.H. Xu et al. 2011, unpublished manuscript). From analyses of 27 long-term measurements, many of which were taken in the New England shelf, Lentz (2008b) found that the alongshore currents have amplitudes of a few centimeters per second. The residual alongshore flow after the removal of the wind-driven component is maximum southwestward in spring onshore of the 60-m isobath. He suggested that the seasonality of the along-shelf currents is primarily driven by the cross-shelf density gradient induced by freshwater discharge. Does ASPG also have seasonal and interannual variations, and, if it does, how are they produced?
In this study, we carry out a set of model experiments and analyze them in conjunction with satellite, tide gauge, rivers, and wind data. We attempt to provide answers to the origin of ASPG: its mean as well as seasonal and interannual variability. Although the focus is on the shelf, it seems reasonable (from the literature) that the ASPG can be due to a larger-scale process (or processes) that requires careful considerations of forcing outside the MAB. We will examine mean, seasonal, and interannual variability and attempt to relate them to driving mechanisms: wind stress curl, Gulf Stream’s latitudinal shifts, rings, Coastal Labrador Seawater (CLSW; Csanady and Hamilton 1988) transport, and river discharge.
Sea level data for 16 yr (1993–2008; same for other data below; Fig. 1) off the eastern coast of the United States are obtained from the University of Hawaii Sea Level Center (UHSLC; http://ilikai.soest.hawaii.edu/uhslc/datai.html). The data have been corrected for atmospheric pressure and are then monthly running averaged for analyses.
Gridded sea surface heights (SSHs) and corresponding geostrophic velocities are from Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO; http://www.aviso.oceanobs.com/duacs/). This dataset has a temporal resolution of 7 days and a spatial resolution of ⅓° × ⅓° (Le Traon et al. 1998).
The cross-calibrated, multiplatform (CCMP) ocean surface wind data are used to force the numerical ocean model (below). This is a 6-hourly gridded (¼° × ¼°) product that combines the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) with satellite surface winds from SeaWinds on the Quick Scatterometer (QuikSCAT), SeaWinds on Advanced Earth Observation Satellite-II (ADEOS-II), Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E), Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), and Special Sensor Microwave Imager (SSM/I), as well as wind from ships and buoys.
Daily river data at 25 northeastern U.S. stations were downloaded from the U.S. Geological Survey (USGS; http://waterdata.usgs.gov/nwis). Missing data longer than 1 week were filled by regression using nearby stations, whereas shorter gaps were filled by linear interpolations.
The M2 tidal data are from Oregon State University’s (OSU) global assimilation model (http://www.coas.oregonstate.edu/research/po/research/tide/index.html) on a ¼° × ¼° grid. The data are not directly used for analysis; rather they are used to drive the numerical model at its open boundary (see below).
3. The numerical model
The terrain-following (i.e., sigma) coordinate and time-dependent numerical model for this study is based on the Princeton Ocean Model (Mellor 2002). Mellor and Yamada’s (1982) turbulence closure scheme modified by Craig and Banner (1994) to affect wave-enhanced turbulence near the surface is used (Mellor and Blumberg 2004). A fourth-order scheme is used to evaluate the pressure-gradient terms (Berntsen and Oey 2010) and, in combination with high resolution and subtraction of the area-mean density profile, guarantees small pressure-gradient errors of O(mm s−1) (cf. Oey et al. 2003). Smagorinsky’s (1963) shear and grid-dependent horizontal viscosity is used with a coefficient of 0.1, and the corresponding diffusivity is set 5 times smaller (cf. Mellor et al. 1994). The northwestern Atlantic Ocean model (NWAOM; Oey et al. 2003) uses an orthogonal curvilinear grid to cover the region 6°–50°N, 98°–55°W (Fig. 2). In the present study in which forcing and sensitivity are to be explored, such a regional model is efficient so that multiple long-term experiments can be conducted. Moreover, the NWAOM is used to test the sensitivity of the modeled dynamics in MAB to the CLSW transport, which is specified as a boundary inflow (see below). The drawback is that except for model’s variability due to the (global) CCMP wind forcing, larger, basin, or even global-scale variability are excluded. The assumption is that these variabilities are of secondary importance in the MAB circulation processes.
The NWAOM uses 25 vertical sigma levels and horizontal grid sizes Δ ≈ 8–12 km. The World Ocean Atlas data (“climatology”) from the National Oceanographic Data Center (NODC; http://www.nodc.noaa.gov/OC5/WOA05/pr_woa05.html) is used for the initial condition as well as the boundary condition along the eastern open boundary at 55°W. Across 55°W, a steady transport combined with radiation using also the geostrophically balanced surface elevation (Oey and Chen 1992a) specifies the Gulf Stream exiting near the Grand Banks south of Newfoundland, with a magnitude of 93 Sv (1 Sv ≡ 106 m3 s−1), following W. J. Schmitz (2002, personal communication; see also Schmitz 1996; Hendry 1982; Hogg 1992; Hogg and Johns 1995). This is balanced by transports specified as broad return flows south (the “Worthington gyre”; Worthington 1976) and north (the “north recirculation gyre”; Hogg et al. 1986) of the jet. The CLSW inflow is then specified (and changed in experiments below) as the northern portion of this north recirculation gyre with a jet shape, identified by Csanady and Hamilton (1988, their Fig. 20b) as the “offshoot of the Labrador Current” that “turns the other way and intrudes into the Slope Sea.” The CLSW also contains freshwater transport (FWT), which is estimated as , where the y integral is from offshore where the water depth H = 1000 m to the coast, the z integral is from the bottom to the surface, and SRef = 35 psu is the maximum salinity at the offshore and bottom location in the cross section. We then obtain an FWT ≈ 0.16 Sv per 1 Sv of CLSW volume transport. In addition to these steady transports, a combination of flow-relaxation, radiation, and advection schemes (Oey and Chen 1992a,b) are used to also specify monthly climatological (potential) temperature T and salinity S and OSU M2 tide at 55°W. Sea surface fluxes are specified as detailed below. To prevent temperature and salinity drift in deep layers in long-term integration, T and S for z < −1000 m are restored to annual-mean climatological values with a time scale of 600 days; this weak restoring does not impede short-period mesoscale variability. The NWAOM has been used for research primarily in the Gulf of Mexico, where we have also extensively compared the results against observations both in the surface and subsurface (Oey and Lee 2002; Ezer et al. 2003; Wang et al. 2003; Fan et al. 2004; Oey et al. 2005a,b, 2006, 2007; Lin et al. 2007; Yin and Oey 2007; Oey 2008; Wang and Oey 2008; Mellor et al. 2008; Oey et al. 2009; Chang and Oey 2010a,b).
The NWAOM is first run for 15 yr, forced by monthly climatological National Centers for Environmental Prediction (NCEP) surface fluxes. This 15-yr run establishes a statistically equilibrium ocean field, as verified by examining the domain-averaged kinetic energy and eddy potential energy time series (not shown). This run is then continued by applying the CCMP 6-hourly winds from 1 January 1993 through 2008. Surface heat and evaporative fluxes are relaxed to monthly climatological values with a time scale of 100 days.
To calculate wind stresses, we use a bulk formula with a high wind speed limited drag coefficient that fits data for low to moderate winds (Large and Pond 1981) and data for high wind speeds (Powell et al. 2003),
where |ua| is the wind speed.1 According to this formula, Cd is constant at low winds; linearly increases for moderate winds; reaches a broad maximum for hurricane-force winds, |ua| ≈ 30–50 m s−1; and then decreases slightly for extreme winds. It is necessary to use a Cd formula that accounts for high winds because, within the NWAOM domain, the study period (1993–2008) includes a few hurricanes. Donelan et al. (2004) suggest that the Cd leveling at high wind may be caused by flow separation from steep waves. Moon et al. (2004) found that Cd decreases for younger waves that predominate in hurricane-forced wave fields. Bye and Jenkins (2006) attribute the broad Cd maximum to the effect of spray, which flattens the sea surface by transferring energy to longer wavelengths.
Daily discharges from 25 major sources in the MAB (and also from 33 sources in the Gulf of Mexico) are specified. These are specified as point sources at the “heads” of major bays or rivers using the method described in Oey (1996). Although broad bathymetric outlines and dimensions of bays and rivers are included (Fig. 2), detailed estuarine circulation within them is not of interest for the purpose of this work. Their function is to allow a gradual transition of brackish waters onto the shelves. In other words, instead of inputting fresh river waters directly at the coast, they are allowed to mix (by tides and winds) with saline seawater within the bays or rivers before flowing out onto the continental shelves.
The northeastern corner of NWAOM domain is where the CLSW transport flows west-southwestward. We find that, for this model, a CLSW transport of 1.5 Sv is the minimum inflow that forces the model Gulf Stream to separate at Cape Hatteras (cf. Mellor and Ezer 1991). The (mean) Gulf Stream tends to separate too far to the north for a CLSW inflow below this minimum. It is convenient to nondimensionalize the CLSW by this “critical” transport of 1.5 Sv, which we will refer to as “1UA” or UA = UAcritical = 1. A CLSW transport of 4.5 Sv (i.e., 3UA, or UA = 3) is used, and this value will be adjusted in various experiments. The 3UA value may be compared with Csanady and Hamilton’s (1988) estimate of approximately 4 Sv for the CLSW transport.
The data-assimilated experiment (Ex.DA; Table 1) consists of all the forcing and specifications described above; additionally, the AVISO SSH anomaly data are assimilated into the model. The Gulf Stream and eddies are assimilated in deep-ocean regions only (water depth H > 1000 m) using Mellor and Ezer’s (1991) scheme, which is simple and yields fairly accurate upper-layer structures (z = 0 to approximately −800 m) of mesoscale currents and eddies (Oey et al. 2005b; Lin et al. 2007; Yin and Oey 2007). No assimilation is done in deep layers for z <≈ −800 m and over the slope and shelves where topography is shallower than 1000 m. The Ex.DA simulation may therefore be viewed as a shelf model with shelfbreak “open-boundary conditions” calculated through data assimilation to account for the effects of the deep sea: the Gulf Stream, rings, and the Slope Sea gyre. On the shelves where ASPG is calculated, the simulated fields satisfy the model’s conservation equations.
Figures 2 and 3a show the 16-yr (1993–2008) mean SSH from the Ex.DA simulation. A cyclonic gyre is seen in the Gulf of Maine (e.g., Pettigrew et al. 2005). The cyclonic flow branches eastward and south-southwestward off of Cape Cod. The eastward branch flows anticyclonically over Georges Bank and then merges with the weaker south-southwestward branch over the shelf off Cape Cod. Figure 3a thus shows two local high pressure cells on the New England shelf: one over the Georges Bank and a weaker one directly south of Cape Cod. It is clear that south of Cape Cod is where the sea level begins to slope down westward and southwestward along the entire length of the MAB shelf to Cape Hatteras. The SSH contours tend to be across shelf for water depths shallower than about 100 m, and over the shelf break and slope they are more closely aligned along isobaths.
Figure 3b plots the mean SSH along the 50-m isobath. Sea surface generally slopes down from north (x = 730 km) to south (x = 0). The linear fits yield slopes ranging from ASPG ≈ 5.4 × 10−8 (dashed line) between Chesapeake Bay (CHS) and Cape Cod (CC) in approximate agreement with Lentz’s (2008a) estimate of 3.7 × 10−8 based on long-term observations, to a larger ASPG ≈ 8.4 × 10−8 (solid line) over a shorter distance between Delaware (DEL) and eastern Long Island (ELS). The larger value is caused by local rivers, especially by the Long Island Sound plume (note the slight dip in sea level from ELS to Cape Cod in Fig. 3b), and is in closer agreement with Scott and Csanady’s (1976) estimate ≈ 1.44 × 10−7 off (the southern coast of) Long Island. There are also significant seasonal and interannual fluctuations of ASPG. Figure 3c shows a clear seasonal signal of maximum (positive) ASPG in winter and minimum ASPG in summer; the exceptions are 1993 and 1998. The range is approximately from 10−7, generally in winter, to −10−7, generally in summer. Note that steric effect alone cannot account for these fluctuations, because its contribution to ASPG is negative, largest in winter (about −3 × 10−8). The amplitudes of these seasonal fluctuations also vary at interannual time scales: larger in some years (1994–95 and 2003–07) and smaller in others (1997–99).
a. Tide gauge data
Accurate sea level measurement is difficult (Sturges 1977), so we focus on sea level variation only (seasonal and interannual) and calculate the EOF of the 16-yr data at the 12 tide gauge stations in MAB shown in Fig. 1 (excluding Bermuda and Wilmington, North Carolina). Only overlapping data are used, which (unfortunately) excludes the last three years (2006–08). Mode 1 explains 67% of the total variance (Fig. 4a); mode 2 (10%) is weak. The amplitude of sea level fluctuation is ≈0.08 m in the south near Duck Pier through Atlantic City and decreases to about 0.02 m in the north near Halifax. The corresponding principal component (PC1; Fig. 4b) is generally negative and minimum in summer through fall and positive and maximum in winter (December–February); the range is approximately −1 to +2. Because the sign of the eigenvector is negative (Fig. 4a), sea level then slopes up poleward in winter and slopes down in summer to fall, relative to an undetermined mean tilt. This result agrees with the modeled seasonal fluctuations shown in Fig. 3c. The linear regression of EOF mode 1 (Fig. 4a) yields a sea level slope of +4.8 × 10−8 from Halifax to Duck Pier (Fig. 4c). This gives an ASPG range of approximately −5 × 10−8, which generally occurs in summer, to 10−7, which generally occurs in winter (from Fig. 4b). If Lentz’s (2008a) estimate of a positive mean ASPG ≈ 3.7 × 10−8 is used, we then have estimates of the absolute sea level tilt of approximately 1.4 × 10−7 sloping up poleward in winter and −1.3 × 10−8 sloping down in summer. This range is smaller than but is consistent with the model-predicted range of approximately ±10−7 mentioned previously. The tide gauge mode-1 time series also shows interannual variations (Fig. 4b). The amplitudes are generally larger in 1994–95 and 2001–04 and smaller in 1997–2000 and 2004–05. These seasonal and interannual ASPG variations from tide gauge approximately agree with those modeled. The correlation coefficient for monthly tide gauge PC1 (Fig. 4b) and model ASPG fluctuations (Fig. 3c) (with the annual cycle removed) is about 0.45, above the 95% significance level of 0.20.
b. Depth-averaged along-shelf currents
The mean along-shelf current varies with location (Fig. 5a). Over the southern flank of Georges Bank and the Nantucket Shoals, the mean along-shelf currents are westward (speeds ≈ 0.03 m s−1). Between the Hudson Shelf Valley and Long Island, the current is weak (speeds ≈ 0.01 m s−1). South-southwest of the Hudson Shelf Valley, the along-shelf mean currents strengthen (speeds > 0.02 m s−1). Just north of Cape Hatteras, the mean flow turns eastward. Variances are larger than the means in most locations, except over the southern flank of Georges Bank and the Nantucket Shoals. From the Nantucket Shoals toward Cape Hatteras, these spatial variations in the magnitude and direction of mean flow are generally consistent with observations (Fig. 1 of Lentz 2008a).
Time series of 3-month-mean depth-averaged along-shelf current averaged along the 50-m isobath is shown in Fig. 5c (the cross-shelf currents are very weak and are not shown). The along-shelf current fluctuates from about −0.06 m s−1 in winter–spring to about 0.01 m s−1 in summer–fall. The along-shelf mean value is −0.025 m s−1, which is approximately 2 times weaker than Lentz’s value. The discrepancy is due to the spatial averaging (i.e., along 50-m isobath) and perhaps also the model’s resolution (Δx ≈ Δy ≈ 10 km). The zero-lag correlation between the along-shelf current and ASPG (plotted in Fig. 5b) is −0.69, above the 95% significance level of 0.31.
It is of interest to check that the above mean values for the model ASPG and along-shelf current are self-consistent. The ASPG is one of the driving force for the mean equatorward along-shelf current (Lentz 2008a). The steady, linearized, and depth-averaged along-shelf (x, positive poleward) momentum equation is
where η is surface elevation; H is water depth, and τbx and τox are the x-component kinematic bottom and wind stresses, respectively. For τox ≈ 1.4 × 10−5 m2 s−2 in MAB, Lentz (2008a) shows that the RHS of (1) is negative (ASPG overcomes wind stress; both are positive). Using the above value for the model mean ASPG (=5.4 × 10−8) between Chesapeake Bay and Cape Cod and parameterizing τbx as ru where from the model r ≈ 5 × 10−4 m s−1 is the linear bottom friction coefficient, then u is also negative (i.e., equatorward), ≈−0.026 m s−1, in agreement with the above model estimate based on Fig. 5c.
5. What drives the ASPG?
We consider the following mechanisms:
latitudinal shifts of the Gulf Stream;
wind stress and wind stress curl;
southwestward-propagating warm-core rings;
CLSW transport; and
We first examine the process (or processes) responsible for the mean ASPG; this is then followed by an examination of the cause (or causes) for the seasonal and interannual variability of ASPG.
a. Mean ASPG
To identify the importance of various mechanisms, we conduct free-running experiments without data assimilation (Table 1)2 and systematically alter the forcing. The Gulf Stream is included in all but the last experiment in Table 1. Although in Ex.DA we do not assimilate over slope and shelves where topography is shallower than 1000 m, it is inappropriate to use the data-assimilated solution to infer dynamics that involves wind, Labrador Sea transport, and Gulf Stream and its eddies, all of which should interact freely with the shelf response that gives rise to ASPG. The free-running experiments include a simulation forced by the same forcing as Ex.DA (except with no data assimilation; Ex.RivLab3Wind); a simulation forced by wind (Ex.Wind); a simulation forced by river and 3UA CLSW transport (Ex.RivLab3); a simulation forced by 1.5UA CLSW transport (Ex.Lab1.5); a simulation forced by river and 1UA CLSW transport (Ex.RivLab1); and a simulation forced by 1UA CLSW transport (Ex.Lab1). Finally, a simulation forced by river only (Ex.Riv; in particular, without the Gulf Stream) is also included. For each experiment, we compute the mean ASPG (Fig. 6) as the slope of the linear best fit of the corresponding mean SSH along the 50-m isobath between DEL and ELS (as in Fig. 3b, solid line).
The combined influence of CLSW transport, rivers, wind and the Gulf Stream on ASPG is summarized by the following expression:3
where terms on the RHS represent the ASPG contributions from various processes: RIV = 2 is the contribution from rivers (=0 for no rivers); UAcritical = 1 is the nondimensionalized critical CLSW transport (described previously); Hυ is the Heaviside (step) function Hυ(n) = 1 for n ≥ 0 [Hυ(n) = 0 otherwise]; WIND = 1 is the wind contribution (=0 for no wind); and GS = 6 is the contribution from the Gulf Stream (=0 for no Gulf Stream). Equation (2) says that rivers cause the sea level to slope up poleward, whereas the Gulf Stream and the mean westerly wind have the opposite effect. The contributions to ASPG from the separate terms in Eq. (2) are now explained using Table 1. The wind effect is deduced from Ex.RivLab3 and Ex.RivLab3Wind, giving ASPGwind = −10−8. The Gulf Stream’s influence is then obtained from Ex.Wind, and has a much larger effect on the poleward setdown of sea level, ~6 times larger than the wind, ASPGGS = −6 × 10−8. The river influence is from the simplest experiment Ex.Riv of an initially resting ocean forced by rivers. The corresponding sea level increases poleward, with ASPGriv = 2.1 × 10−8. The effect of river is also checked by comparing Ex.Lab1 with ASPG ≈ 2.3 × 10−8 and Ex.RivLab1 with ASPG ≈ 4.3 × 10−8, giving a difference of ≈2 × 10−8, which agrees well with the ASPG from Ex.Riv. Finally, the contribution of CLSW is obtained from Ex.Lab1.5 and Ex.Lab1, as well as from Ex.RivLab1, Ex.RivLab3, and Ex.RivLab3Wind, taking into account also the effects of rivers, wind, and the Gulf Stream derived above. The upshot is a CLSW contribution given by the second term on the RHS of (2). The contribution is idealized by a step function, so that, for UA < UAcrit and GS ≠ 0, it is assumed that the Gulf Stream dominates. It is interesting that, from Ex.Lab1, the critical CLSW transport of 1.5 Sv (i.e., UA = 1) gives an ASPG (=2.3 × 10−8) that is nearly equal to the ASPG contribution from rivers (=2.1 × 10−8). We also note that the CLSW transport is dynamically linked to the Gulf Stream in forcing the Slope Sea circulation (Csanady and Hamilton 1988). This can be seen by expressing the second term on the RHS of (2) as (7 × UA − 4.7 + GS) × H(UA − UAcritical), so that the “pure” CLSW contribution is actually (7 × UA − 4.7).
In summary, Gulf Stream and wind tend to produce a sea level setdown poleward over the MAB shelf. The Gulf Stream influence is particularly strong, and its seasonal and interannual variations are discussed below. Because the observed mean ASPG is positive (sea level tilts up poleward), only river and CLSW transport can contribute to this mean.
It is interesting to compare Ex.RivLab3Wind, for which APSG = 1.7 × 10−7, with its assimilated counterpart Ex.DA, which reduces APSG (=8.4 × 10−8) to a value closer to that observed (see section 4). Without assimilation, the CLSW transport of 3 × 1.5 Sv (i.e., UA = 3) is too strong and the corresponding Gulf Stream tends to separate south of Cape Hatteras (not shown). The reason is because the model’s Gulf Stream is too weak and produces too few warm-core rings when compared with the assimilated experiment. Stronger Gulf Stream and warm rings both contribute to negative ASPG (see below).
b. Seasonal and interannual variability of ASPG
We now examine the seasonal and interannual variations of ASPG (Figs. 3c, 4b) to the aforementioned five mechanisms. Note that the mechanisms are not necessarily independent of each other. In the following, interannual variability is defined by fluctuations of one-year running-averaged time series. Seasonal variations are then defined as the deviations of 3-month running-averaged time series from the interannual fluctuations. The time series are plotted in Fig. 7. Here, the ASPG (Fig. 3c) and CLSW are from Ex.DA, whereas the other time series are from observations. The CLSW is calculated off the southern coast of Nova Scotia (near 60°W; see Fig. 2) from the coast to the 1000-m isobath. The CLSW is therefore purely driven by unsteady forcing confined entirely within the model domain (west of 55°W); it does not reflect any outflow variation from the Labrador Sea transport, which is kept fixed at the northeastern corner of the model domain (~50°N, 55°W). Because assimilation is nil for the shelf region where the water depth is shallower than 1000 m, the ASPG and CLSW reflect dynamical responses to deep-sea observed forcing.
The Gulf Stream shifts northward in summer–fall and southward in winter–spring, and the path also fluctuates at interannual time scales (Lee and Cornillon 1995). Currents over the MAB shelf break and slope appear to respond to these shifts (e.g., Bane et al. 1988; Dong and Kelly 2003). The EOF analysis of surface velocity and SST anomalies in the Slope Sea by Peña-Molino and Joyce (2008) also shows that that Gulf Stream’s path shifts (GSS) can influence the generally southwestward-flowing slope currents both on seasonal and interannual time scales. In the northern MAB, the slope currents appear to strengthen southwestward when the Gulf Stream shifts southward in winter–spring but are weak or even reversed in summer–fall, when the Gulf Stream shifts northward (Dong and Kelly 2003; Peña-Molino and Joyce 2008). Bane et al. (1988) observed currents on the southern MAB slope off Delaware that appear to have the opposite response: stronger southwestward when the Gulf Stream shifts northward and vice versa.
Figure 7b shows that, at seasonal time scales, the zonally averaged GSS (relative to the 16-yr, 1993–2008, mean Gulf Stream’s position) is southward in winter–spring and northward in summer–fall, with values of ±0.4° latitude (Fig. 7b). The maximum lagged correlation between the (seasonal) ASPG (Fig. 7a) and GSS is R ≈ 0.74, with a 4-month lag (ASPG lags GSS; Table 2). Figure 7b shows that the Gulf Stream retreats southward from fall when the current is at its most northward position to spring when it is most southward. The ASPG therefore generally peaks during the time of the most rapid retreat: that is, in winter. This is explained as follows: The Gulf Stream’s southward retreat produces a sea level (hGS) drop north of Cape Hatteras ∂hGS/∂t < 0, which is therefore most rapid in winter (i.e., ∂hGS/∂t is large and negative). In the southern portion of the MAB (off Chesapeake Bay), this strong ∂hGS/∂t (<0) is accompanied by a correspondingly strong off-shelfbreak flow related to the joint effect of baroclinicity and relief (JEBAR) term in the integrated vorticity balance [see Eq. (3) below; figure not shown]. By continuity, this wintertime strong outflux is accompanied by an increased, equatorward along-shelf flow so that the corresponding current (ushelf < 0) is also strong in winter and is (approximately) balanced by the ASPG according to rushelf ≈ −gH∂hshelf/∂x. That ushelf is generally strongest (equatorward) in winter is seen in Fig. 5c. Therefore, ∂hshelf/∂x > 0 and is a maximum in winter. In other words, the maximum of ASPG occurs when hGS is falling most rapidly, with both occurring in winter, and both lag the maximum Gulf Stream’s most northward shift in fall. At the interannual time scales, GSS and ASPG are not significantly correlated.
d. Wind stress curl
The 16-yr 3-monthly-mean wind stress curl is calculated over the northwest Atlantic westward from 60°W to the 200-m isobath and from 35° to 42°N. The wind stress curl shows a significant seasonal cycle; it is positive in winter and weak and (in some years) negative in summer (Fig. 7c). Its correlation with ASPG is low and not significant. On the other hand, wind stress curl is negatively correlated with both GSS (R ≈ −0.65 at zero lag: i.e., the Gulf Stream shifts south in winter) and CLSW (R ≈ −0.81; CLSW lags wind stress curl by 1 month and strengthens southwestward as wind stress curl increases). Interestingly, CLSW is positively correlated with GSS (R ≈ 0.77) and lags it by 1 month.4 The CLSW then appears not to influence the Gulf Stream at the seasonal time scale. The most likely explanation is that the wind is locked to the Gulf Stream, especially in winter (Chelton et al. 2004). The CLSW is driven by the wind stress curl (Csanady and Hamilton 1988) and lags it and therefore GSS as well by 1 month.
e. Warm-core rings (N-EKE)
Large northward meanders of the Gulf Stream regularly break off as warm-core rings. These rings propagate southwestward in the slope water between the continental shelf break and the Gulf Stream until they are either absorbed by another meander or are forced to coalesce with the Gulf Stream off Cape Hatteras. Approximately 10 rings per year either form in or propagate into the region west of 60°W (Glenn et al. 1990). The average lifetime is 120–130 days, and the average propagation speed is approximately 6 km day−1 with a range of 2–10 km day−1 (Brown et al. 1986; Auer 1987; Cornillon et al. 1989; Glenn et al. 1990).
Effects of warm-core rings are estimated by calculating the eddy kinetic energy (EKE) density north of the Gulf Stream’s monthly-mean path from AVISO geostrophic current (N-EKE). The EKE density is defined as monthly EKE averaged over the area with SSH anomaly (SSHA) > 0 normally associated with warm eddies. Region north of the Gulf Stream is chosen to focus on warm-core rings only, because these are ones that give rise to ASPG fluctuations (see below). The use of the monthly path (instead of a 16-yr mean) eliminates fluctuations associated with shifts in the Gulf Stream’s axis. The presence of warm-core rings was also checked by visually inspecting the satellite data. Time series of N-EKE show larger values from spring through early summer than in fall and winter (Figs. 8a,b).5 The ASPG and N-EKE are significantly correlated (R = −0.57), with ASPG lagging N-EKE by approximately 3 months (Table 2). Thus, ASPG reaches a minimum in summer–fall after the N-EKE peaks in spring–summer (Figs. 7a,d). Physically, ring production peaks in spring–summer. These rings propagate southwestward. At speeds of approximately 6 km day−1, they arrive over the slope north of Cape Hatteras in approximately 3 months. The speed agrees with those of observed warm-core rings, typically 5.6–6.8 km day−1 (Glenn et al. 1990). We show below that the arrival of a ring produces high SSH over the shelf north of Cape Hatteras, and the high SSH in turn induces a negative ASPG anomaly.
The N-EKE also correlates with GSS (R = −0.41) with GSS leading N-EKE by about one month (Table 2). Table 2 also shows that the N-EKE/GSS correlation and lag are consistent with how each of N-EKE and GSS separately relates to ASPG. The influence of the Gulf Stream path on ASPG is therefore partly because of warm-core rings. Finally, the N-EKE lags wind stress curl by one month with R = 0.53.
At interannual time scales, N-EKE is positively correlated with ASPG (R = 0.4; zero lag). The sign is opposite from the corresponding correlation at the seasonal time scales (R = −0.57). The reason is because, at the seasonal period, the N-EKE has a clear spring–summer peak described above and, as we shall show below, the APSG then becomes negative because of arrivals of rings near Cape Hatteras. At long (interannual) time scales, N-EKE reflects mostly the contribution from eddies that are farther east and north, away from Cape Hatteras, near their generation locations as well as when they are propagating. These eddies tend to produce a shelf’s sea surface that slopes down toward Cape Hatteras (i.e., ASPG > 0).
At the interannual time scales, Table 2 shows also a small but significant correlation between N-EKE and wind stress curl (R = −0.3). This result is related to the North Atlantic Oscillation (NAO). We find that (cf. Dong and Kelly 2003) during a positive (negative) NAO, the wind pattern shifts north (south), producing a more negative (positive) wind stress curl (from 35° to 42°N). The wind stress curl (Fig. 7c) and NAO index (not shown) are significantly correlated at −0.4. Our result then agrees with Chaudhuri et al. (2009), who show that periods of increased number of warm-core rings (assuming that rings give rise to N-EKE) coincide with positive phases (PP) of NAO and vice versa.
f. How do warm-core rings produce fluctuations in ASPG?
To examine this mechanism, an idealized experiment of a shelf’s sea level and current responses to arrivals of warm-core rings along the MAB shelf break and slope was conducted. The simulation has the same domain and topography as the NWAOM, but all lateral boundaries are closed. The ocean is initially at rest with a density profile that varies in the vertical only, given by the basin average of the annual-mean climatology. Three warm-core rings each with radius = 100 km were “injected” every 360 days over the open ocean in the northeastern region of the model domain near (40°N, 62.5°W). The 360-day period mimics in a crude way the seasonal fluctuation of EKE (Fig. 8c). The simulation was run for 8 yr. The eddy-injection method follows Shaw (1994), wherein an isolated warm pool is gradually ramped up over a period of 10 days, during which time the model’s velocity field is allowed to geostrophically adjust. To conserve heat, the same heat is removed by also specifying a uniform upward surface heat flux (i.e., cooling) over the model domain. Because the area of this is much larger than the eddy size, the results are virtually unchanged with or without the surface cooling. Sensitivity experiments with a different number of eddies and rate of injection give similar results and are not shown. The relatively small number of eddies (compared to observation) allow effects of individual eddies on the shelf’s currents and sea level to be more clearly identified in the simulation. Because the idealized model does not include a Gulf Stream, all modeled rings survive (throughout their migrations) and eventually reach Cape Hatteras.
Figure 9a shows the 8-yr mean SSH. Large and positive SSH from northeast to southwest over the Slope Sea indicates the path of the southwestward propagation of warm-core rings. Maximum SSH is seen near the continental shelf break north of Cape Hatters, where warm-core rings tend to be trapped. The mean SSH slopes down northward from Cape Hatteras and off Chesapeake Bay to eastern Long Island (Fig. 9b). The SSH slope is steep for the first 200 km along shelf north of Cape Hatteras because of the large influence of rings there; the slope then is gentler from the shelf between Delaware Bay and Long Island, where linear regression gives ASPG ≈ −1.3 × 10−8 (Fig. 9b). This may be compared with the ASPGGS = −6 × 10−8 estimated from Eq. (2) for the Gulf Stream (plus eddies). We conclude that warm rings can contribute to as much as 20% of the total ASPG induced by the Gulf Stream.
Temporal variations of ASPG due to warm rings are also significant (Fig. 9c). The ASPG varies depending on the position of rings relative to the MAB shelf. We illustrate this with two examples: one during the negative phase (NP) of ASPG at day 1200 (Fig. 9c) and the other one when ASPG is positive at day 1610. As we now explain, the process in both cases involves convergences and divergences of shelf waters as the ring comes close to the shelf break. The negative phase at day 1200 occurs when the ring’s influence reaches far southwestward to the shelf break off Chesapeake Bay; the ring center is nearer Cape Hatteras, south of 38°N (Figs. 10a,b). Onshore convergence occurs south and west of the ring, producing a locally high SSH that extends onshore of the 50-m isobath off Chesapeake Bay to Delaware Bay (Fig. 10b). Offshore divergence occurs north of the ring, producing a locally low SSH that extends from offshore New Jersey northward to the mouth of Long Island Sound. Note that, although the main high-speed core of the ring is relatively small (<100-km radius), the ring’s interaction with the sloping topography produces an along-shelf response that covers almost the entire MAB from Chesapeake Bay to Long Island. Such an extensive along-shelf response (when an eddy interacts with continental shelf break) has been noted in previous studies (e.g., Oey and Zhang 2004). Figures 10c,d show the example of a positive phase of ASPG at day 1610, when the ring’s (a different one than at day 1200) influence is more confined to the middle portion of the MAB between Delaware and New Jersey; the ring center is north of 38°N, farther away from Cape Hatteras. Onshore convergence now produces high SSHs onshore of the 50-m isobath off New Jersey and New York, whereas the southern portion of the MAB remains relatively quiet, SSH ≈ 0. The SSH increases poleward along the shelf, and the ASPG is positive (Fig. 9c at day 1610). As the ring continues south-southwestward toward Cape Hatteras, the cycle repeats (Figs. 10a,b) and ASPG turns negative (beginning at day 1860 in Fig. 9c).
To examine how effects of warm-core rings penetrate onto the shelf, we analyze each term of the depth-averaged vorticity equation derived from the curl of the depth-averaged momentum equations (Oey et al. 2010, and references therein),
where ζ is the curl of the depth-averaged velocity U; H is local water depth; k is the z-unit vector; , b = gρ/ρ0; τ0 and τb are the surface (wind) and bottom stress vectors, respectively; and A lumps both horizontal advection and diffusion vectors. The second term on the LHS of Eq. (3) (denoted as CPVF) represents the horizontal advection of the geostrophic potential vorticity f/H. The first term on the RHS is the JEBAR term, which is nil if isopycnals are parallel to isobaths.
For slowly evolving flows, ∂ζ/∂t in Eq. (3) is small compared to the cross-isobath flux term CPVF, which is then determined by the ageostrophic terms on the RHS and indicates onshore flux if positive and offshore if negative. Our goal is to determine which (if any) of these ageostrophic terms dominate and why and how ASPG is then accordingly changed. A succinct way is to compute the weighted composites of each of the terms in Eq. (3) according to positive and negative phases of ASPG anomaly (i.e., Fig. 9c),
where the subscript n denotes time, υ is each term of Eq. (3), w is ASPG anomaly (serving as weights), and S+ means summing over the positive phase of ASPG anomaly. A similar formula is used for ASPG− using S−. Equation (4) gives a better composite than straight averaging because it reduces the influences of values of υn near small wn with potentially large uncertainty (Chang and Oey 2011).
Figure 11 plots the dominant terms CPVF and JEBAR together with the corresponding composites of SSH and surface velocity; note that the anomalies are plotted and −JEBAR is plotted so that its cancellation with CPVF may be seen. Other vorticity-balance terms in Eq. (3) are not shown; in general, they are one order of magnitude smaller than either CPVF or JEBAR. It is clear that negative ASPG− (Fig. 11, right, for which Figs. 10a,b at day 1200 are members of the composite) is induced by rings that are near Cape Hatteras; the SSH then shows an anticyclonic (warm) anomaly centered at approximately (37°N, 74°W) off Chesapeake Bay flanked by cyclonic (cold) anomalies to the north (off New Jersey) and south (off Cape Hatteras) (Fig. 11b). It is readily shown that χ is higher in a warm anomaly so that, south of the anticyclone, ∇χ points north/northeastward and JEBAR = k · [∇(χ) × ∇(H−1)] ≈ CPVF > 0 (i.e., onshore flux), whereas, north of the anticyclone, ∇χ points west/southwestward and JEBAR ≈ CPVF < 0 (i.e., offshore flux).6 The resulting shelfward convergence and divergence tend to produce a northward sea level setdown. A reversed situation applies for positive ASPG+ (Fig. 11, left, for which Figs. 10c,d at day 1610 are members of the composite). The resulting depth-averaged velocity across the 200-m isobath has a typical magnitude of ≈0.01 m s−1, which is sufficient to produce the necessary convergence/divergence over the outer shelf to induce the ASPG anomalies. We conclude that, for rings brushing against the outer MAB continental shelf and slope, the along-isobath density gradients result in JEBAR that becomes the dominant ageostrophic term accounting for the cross-isobath fluxes.
Because the idealized experiments exclusively isolate forcing by warm-core rings, the above clearly demonstrates that long-period variations of ASPG can be due to the shelf response to propagating warm-core rings. The amplitudes of variations of O(10−8) (Fig. 9c) are comparable to the observed variability (Fig. 4). In the model, the forcing is annual so that the resulting ASPG has a seasonal signal (Fig. 9c). Figure 9c shows that, in general, the ASPG reaches a minimum some 120–180 days after each eddy injection (days 0, 360, 720, etc.). Because the model eddies propagate at 6–8 km day−1, the time lag of 120–180 days coincides well with the time taken for eddies to traverse a distance of 1000–1200 km from their injection location (40°N, 62.5°W) to Cape Hatteras. This result agrees well with the conclusion reached previously on the correlation between N-EKE and ASPG (Figs. 7, 8; also Table 2). Figure 9c also shows interannual variations as eddies merge and dissipate (not shown) at different times in the region north of Cape Hatteras. The precise temporal phasing giving rise to these interannual fluctuations is not of interest because of the idealized nature of the model. However, our results do indicate the potential importance of Gulf Stream warm-core rings in contributing to the seasonal and interannual variations of ASPG.
g. CLSW transport
The mean CLSW transport is southwestward, about −4.3 Sv, and its standard deviation is about 1.8 Sv (Fig. 7e). The transport is strong in spring and is much weaker in fall. The one-year running average shows interannual variability (Fig. 7e). For example, from 1993 to 1996, the transport was weaker, whereas, from 1996 to 1997, the transport became stronger. This variation is consistent with Labrador Sea transport variability reported by Dong and Kelly (2003, their Fig. 4a). From Table 2, the transport correlates well with wind stress curl (R = −0.81) and suggests that the variations in CLSW transport are mainly forced by the wind (cf. Csanady and Hamilton 1988). Temperature and salinity anomalies over the MAB shelf (and slope) correlate well with the CLSW transport: colder and fresher shelf waters correspond to stronger southwestward transport (not shown). The correlations in both the seasonal and interannual time scales between CLSW transport and ASPG are low (Table 2) so that CLSW transport does not directly influence the seasonal and interannual variations in ASPG.
h. Freshwater discharge
The 3-monthly average of total river input has a clear seasonality and reaches its maximum in spring because of snow melting and precipitation (Fig. 7f). The correlation between river discharge and the ASPG is insignificant at the 95% significance level: (correlation, significance) = (0.36, 0.36) (though it is above the 90% significant level = 0.3), indicating insignificant influences of rivers on the seasonal and interannual variability of ASPG compared to those due to the N-EKE and GS path variations.
In this work, the question of what physical mechanisms contribute to the mean, seasonal, and interannual variability of the along-shelf pressure gradient (ASPG) in the MAB is addressed by analyzing observational data and results of numerical experiments both realistic (including data assimilations) and idealized. The realistic experiment simulates the circulation in the northwest Atlantic Ocean (including the Gulf Stream and the MAB) from October 1992 to December 2008. Realistic atmospheric forcing, freshwater discharge, and tidal forcing are included. Our results show that the model ASPG agrees with that deduced in other studies (Stommel and Leetmaa 1972; Scott and Csanady 1976; Lentz 2008a), and its variation is consistent with that deduced from tide gauge data. The mean ASPG is positive, about 5–8 × 10−8, but it also has seasonal and interannual variations of ±10−7.
We show that the observed, mean positive ASPG is caused by freshwater discharge and CLSW transport. The mean westerly wind produces a negative ASPG, though its effect is weak. The Gulf Stream produces a large sea surface setdown to the north, ASPG < 0, but the Gulf Stream in this case separates from the coast too far north from Cape Hatteras and clearly cannot by itself drive the observed positive ASPG. The CLSW and Gulf Stream are therefore closely tied, because a critical value of the former [=−1.5 Sv (flowing southwestward) in our model] is necessary to maintain the separation near Cape Hatteras and also to give a positive ASPG.
The seasonal and interannual variations in ASPG are produced by latitudinal shifts in the Gulf Stream, as well as by Gulf Stream’s warm-core rings that propagate southwestward in the Slope Sea and interact with the MAB shelf break. The Gulf Stream’s southward retreat produces a sea level drop north of Cape Hatteras (ASPG > 0). The effects of rings on ASPG are demonstrated with an idealized experiment that isolates eddy processes. We show that shelf convergences and divergences are forced by rings that interact with the shelf break. Though the penetration of the ring’s sea level signal across the shelf break is limited (because of the insulating effect of the slope; e.g., Wang 1982; Csanady and Shaw 1983; Chapman 1986), it is nevertheless sufficient to produce O(1–4 × 10−8) fluctuations that are consistent with the observed fluctuations from the tide gauge. Vorticity analysis shows that the JEBAR term, caused by along-isobath density gradients by virtue of rings brushing against the MAB continental slope, is the dominant ageostrophic term accounting for the cross-isobath fluxes. We show that the production of warm-core rings peaks in spring–summer. Rings propagate southwestward and produce a northward setdown of the shelf’s sea level (ASPG < 0) approximately 3 months later when the rings arrive over the slope north of Cape Hatteras. At interannual time scales, the response is opposite: the ASPG is positive in years of increased N-EKE. The reason is that, at long time scales, the net effect of eddies that spread throughout the entire northern portion of the Gulf Stream is to produce a sea surface sloping downward toward Cape Hatteras.
A number of outstanding issues remain. Although the mean ASPG as one of the important drivers of shelf’s currents is established, its seasonal and interannual effects are not (e.g., Lentz 2008b). The present work suggests that the effects should be most apparent on shelves near Cape Hatteras, and this can be examined from observations and modeling. Our focus in the present work is on ASPG, and the connections between the Gulf Stream, eddies, CLSW, and wind stress (curl), especially at the interannual time scales, have only been briefly discussed. These should be pursued in a future work perhaps in conjunction also with a basin-scale model.
We thank the two reviewers and editor Dr. Barth for their helpful comments that improve the MS. This research is supported by the Minerals Management Service Contract M09PS20004. Dr. Jose Blanco processed the river and tidal data. Computations were done at NOAA/GFDL, Princeton.
A more complicated function may give a better fit, but this is not attempted. The goal here is to summarize in a succinct way the response due to each of the different forcings.
Statistically, CLSW leads GS by about 11 months, which seems to agree with Rossby and Benway (2000) that strong CLSW can cause a southward shift of the Gulf Stream one year later. However, this would be a false interpretation because Rossby and Benway were looking at interannual rather than seasonal time scales.
The result is unchanged if N-EKE includes all points north of the Gulf Stream, except that the peak in Fig. 8b is less prominent and the various correlations (below) degrade slightly. Also, if warm and cold rings as well as Gulf Stream meanders are included, then the largest EKE is in summer (Zhai et al. 2008).
Another way is to write the vorticity equation using Salmon’s (1992) two-layer planetary geostrophic equations (see appendix in Oey et al. 2010), which yield the following for the CPVF ≈ JEBAR balance: , where g′ = reduced gravity and h1 = upper-layer depth. The vector ∇χ may be identified with , which points from cold to warmer anomalies.