The origin of along-shelf pressure gradient in the Middle Atlantic Bight

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The origin of along-shelf pressure gradient in the Middle Atlantic Bight
F.-H. Xu and L.-Y. Oey
Princeton University

July 09, 2010


Long-term mean and depth-averaged currents on the Middle Atlantic Bight (MAB) shelf are mainly alongshelf and southwestward. The circulation has a seasonal and inter-annual variability, such that currents are southwestward from late winter through spring, and are weaker or even reversed in summer and fall. Momentum balance considerations suggest that forcing for these seasonal fluctuations of shelf currents is the along-shelf pressure gradient (ASPG) whose origin, however, remains a subject for debate. The large-scale wind pattern over the North Atlantic, Gulf Stream path shift, the activity of Gulf Stream warm-core rings, Labrador Sea transport, and river discharge may all contribute to the ASPG. Sixteen years (1993-2008) of satellite data from AVISO, data-assimilated model reanalysis, and tide-gauge sea level data are analyzed. It is shown that the mean ASPG is primarily produced by the total river discharge along the east coast of North America and the Labrador Sea transport. The southwestward propagation and impingement of warm-core rings upon the shelf break north of the Gulf Stream near Cape Hatteras contribute to the seasonal and inter-annual variations in ASPG. Warm-core rings change the ASPG by forcing cross-shelfbreak transports that modify the sea surface height over the outer shelf. A process model shows that warm-core rings produce a sea surface sloping down to the north when they are near Cape Hatteras. It is shown that the large-scale wind pattern cannot directly affect the ASPG. However, north of the Gulf Stream, there exist seasonal and inter-annual variations of eddy kinetic energy which affect the ASPG, and which may be forced by the wind .

  1. Introduction

The Middle Atlantic Bight (MAB) off the east coast of the United States is the continental shelf region that extends from Nantucket Shoals in the north to Cape Hatteras in the south. The MAB is a dynamically complex region where cooler and fresher shelf water is separated from warmer and saltier slope water by a shelf break front. Understanding the water properties and currents in MAB are important for navigation, fisheries, and coastal ecosystem.

The MAB circulation has been investigated through observational and modeling studies over several decades (e.g. Beardsley and Boicourt 1981; Chapman et al. 1986; Linder and Gawarkievicz 1998; Flagg et al. 2006; Lentz 2008a). Depth-averaged mean currents are mainly along-isobath and were observed to be 0.03-0.1 m s-1 (Lentz 2008a). The mean currents are westward on the New England shelf, and southwestward in the middle of MAB. South of the Chesapeake Bay, mean currents veer offshore. The along-shelf mean currents also increase with distance offshore (Beardsley et al. 1976; Lentz 2010).

The primary driving force for the depth-averaged mean currents in the MAB is along-shelf pressure gradient (ASPG) (Beardsley and Boicourt 1981). Stommel and Leetmaa (1972) modeled the steady-state wintertime circulation. They proposed that an ASPG of order of 10-7 is required to drive the southwestward flow. Csanady (1976) argued that the cross-shelf density gradients may be prescribed and concluded also that an ASPG must exist to account for the observed circulation within 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 of about 3.710-8. Lentz (2008a) discussed the possibility of other types of forcing, but the hypothesis that ASPG exists seems reasonable.

What drives the ASPG? Lentz (2008a) showed that along-shelf density gradients are negligible, so that ASPG is mainly due to sea surface slope. The Gulf Stream 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 unclear (Wang 1982; Chapman et al. 1986). We will further investigate the contribution of large-scale forcing to the ASPG.

Observations also show seasonal variations in the depth-averaged along-shelf currents which are different in different sub-regions 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). Further west and south in the MAB, a well-defined seasonal along-shelf flow in mid and outer shelves was not, however, observed in several previous studies (Mayer et al. 1979; Beardsley et al. 1985; Aikman et al. 1988). Along Oleander line, Flagg et al. (2006) observed a shelfbreak jet (offshore of 100m-isobath) which was stronger southwestward in fall and winter and weaker in spring and summer. Currents measured by ADCP at the location of station 5 on the Coastal Ocean Bio-optical Buoy (COBY) transect (75.029W, 37.833N) show maximum southwestward in spring and weak in summer and fall. From analyses of 27 long-term current records, many of which were in the New England Shelf, Lentz (2008b) found that the alongshore currents have amplitudes of a few cm s-1,with maximum southwestward in spring onshore of the 60m isobath for the residual alongshore flow after the wind-driven component is removed. He suggested that the seasonality of along shelf currents is primarily driven by the cross-shelf density gradient induced by freshwater discharge. The role of ASPG in the seasonality of along-shelf currents remains unclear. Does ASPG have seasonal and inter-annual variations, and if it does, how are they forced?

In this study, we carry out a set of model experiments and analyze them in conjunction with observations. We attempt to provide (some) answers to the origin of ASPG: its mean as well as seasonal and inter-annual variability. Although the focus is on the shelf, the above descriptions suggest that ASPG can be due to larger-scale process(es) that requires careful considerations of forcing outside the MAB. We will examine mean, seasonal, and inter-annual variability. We examine the driving mechanisms, including the wind stress curl over the North Atlantic, Gulf Stream latitude shift, Gulf Stream warm-core rings, Labrador Sea transport, and river discharge.

The paper is organized as follows: Section 2 presents a description of the observation datasets used in the study. Section 3 describes the numerical experiments. In section 4, we analyze the mean, seasonal, and inter-annual variations in the along-shelf flow and ASPG in the MAB. The influence of wind, river, Gulf Stream, warm-core rings and Labrador Sea transport are discussed in section 5. The paper concludes in section 6.

  1. Data

Sixteen years (1993-2008) of quality-controlled sea level data are obtained from the University of Hawaii Sea Level Center (UHSLC, off the east coast of the United States. Data at 12 stations (excluding Bermuda and Wilmington NC, Figure 1) are monthly running-averaged and analyzed to study seasonal and inter-annual variations in sea surface slope.

The gridded sea surface heights (SSH) and the corresponding geostrophic velocities for the period 1993 to 2008 are from AVISO ( This dataset has a temporal resolution of 7 days and spatial resolution of . A detail description of the dataset is in Le Traon et al. (1998).

The Cross-Calibrated, Multi-Platform (CCMP) ocean surface wind velocity data is used to force the numerical ocean model (below). This is an ERA-40 Re-analysis, 6-hourly gridded () product that incorporates satellite surface winds from Seawinds on QuikSCAT, Seawinds on ADEOS-II, AMSR-E, TRMM TMI and SSM/I, and ships and buoys measurements..

  1. 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, 2004). Two nested domains are used. The 1/4o × 1/4o and 55 z-level SODA global analysis product [Carton and Giese, 2008] is used to specify temperature, salinity and transports along the open boundary at 55W of a northwestern Atlantic Ocean model (98W-55W and 6N-50N; hereinafter referred to as NWAOM; fig.1). The eastward Gulf Stream transport is approximately 100 Sv, while an inflow transport of 4.5 Sv is specified along the northeastern slope of the model domain (this will be denoted as the “Labrador Sea transport”). The NWAOM has 25 vertical sigma levels and horizontal grid sizes   10~15 km in MAOR. Except for SODA inputs and other changes described below, the NWAOM is the same as that used previously [e.g. Oey et al. 2005; Lin et al. 2006; Yin and Oey, 2007]. A doubled-resolution (  5~7 km, same 25 sigma levels) MAOR grid domain is then nested within the NWAOM domain. The nesting procedure follows Oey and Zhang [2004].

Our interest is on the shelf and shelf-edge transports (across the 200 m isobath). Therefore, the Gulf Stream and eddies are assimilated in deep ocean regions only (water depth H > 1000 m) using satellite sea-surface height anomaly data from AVISO ( We use the Princeton Regional Ocean Forecast System (PROFS; to hindcast the ocean state. The model integration and analysis are for 19931999. PROFS has been extensively tested against observations and also used for process studies in the Gulf of Mexico [Oey et al. 2005a and b, where a list of recent publications is given]. The Mellor and Ezer’s [1991; see also Ezer and Mellor, 1994] scheme is used to assimilate the AVISO data. In this scheme, the SSH anomaly is projected into the subsurface density field using correlation functions pre-computed from the model’s eddy statistics derived from a non-assimilated 15-year model run. The method is simple, yet it yields fairly accurate upper-layer structures (z = 0 to approximately 800 m) of mesoscale currents and eddies [Oey et al. 2005a; Lin et al. 2006; Yin and Oey, 2007]. No assimilation is done in deep layers for z < 800 m and as mentioned above in regions where the topography is shallower than 1000 m. In these regions, the simulated currents rely entirely on the model’s dynamics.

The Mellor and Yamada’s (1982) turbulence closure scheme modified by Craig and Banner (1994) to effect wave-enhanced turbulence near the surface is used. To account for mixing in stable stratification (e.g., internal waves; MacKinnon and Gregg, 2003), Mellor’s (2001) modification of a Ridchardson-number-dependent dissipation is introduced. A fourth-order scheme is used to evaluate the pressure-gradient terms [Berntsen and Oey, 2009] and, in combination with high resolution and subtraction of the mean -profile, guarantees small truncation errors of O(mm/s) [c.f. Oey et al. 2003].

Initial and Boundary Conditions, and Forcing:

The NWAOM is first run for 15 years, forced by monthly climatological NCEP surface fluxes. The World Ocean Atlas data (“Levitus” data) from NODC [] was used for initial condition as well as boundary condition along the eastern open boundary at 55oW. The transport across 55oW is also specified [Oey et al. 2003]. This 15-year 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 NCEP six-hourly reanalysis winds from Jan/01/1992 through 1999, during which the SODA inputs are also used along 55oW. Surface heat and evaporative fluxes are relaxed to monthly climatological values with a time scale of 100 days. A combination of flow-relaxation and radiation conditions described in Oey and Chen [1992a,b] are used to specify the SODA variables and the M2-tidal forcing from Oregon State University [;]. The nested NWAOM field is then used to initialize the finest MAOR nested grid, in which similar open-boundary conditions are also applied.

To calculate wind stresses, we use a bulk formula with a high wind-speed limited drag coefficient that curve-fits data for low-to-moderate winds (Large and Pond, 1981) and data for high wind speeds (Powell et al. 2003):

Cd 103 = 1.2, |ua|  11 m s-1;

= 0.49 + 0.065 |ua|, 11 < |ua|  19 m s-1;

= 1.364 + 0.0234 |ua|  0.00023158 |ua| 2, 19 < |ua|  100 m s-1


where |ua| is the wind speed.1 According to this formula, Cd is constant at low winds, is linearly increasing 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 since the study period (1993-1999) 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.

  1. Results

Model Sea Surface Height over the MAB shelf

Figure 2a shows the 16-year (1993-2008) mean SSH from the NWAOM simulation. A cyclonic gyre is seen in the Gulf of Maine. The cyclonic flow branches eastward and south-southwestward off 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 2a shows three local high pressure cells in this vicinity, one over the Georges Bank, one south of the Bank over the 1000 m isobath, 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 are across-shelf for water depths shallower than about 100 m, and over the shelf break and slope they are aligned along the isobaths.

Figure 2b plots SSH along the 50 m isobath. This confirms the generally downward sea-level tilt from the northern station off Cape Cod (x = 730 km) to the southern station off Cape Hatteras (x = 0); the corresponding ASPG  3~5×10-8 which is in excellent agreement with Lentz’s (2008a) estimate of 3.7×10-8 based on long-term observations. The ASPG is larger  8.4×10-8 between the east end of Long Island (ELS) and Delaware (DEL), where a linear sea-level slope is seen. This stronger ASPG seems to be consistent with Scott and Csanady’s (1976) estimate  1.44×10-7 off Long Island based on a 25-day time series in September 1975. There are, however, strong seasonal and inter-annual fluctuations (Fig.2c). The standard deviation is 8.6×10-8 and maximum and minimum peaks are 2×10-7, larger in some years (2003~2007) and smaller in others (1997~1999). There is a clear seasonal pattern of maximum (positive) ASPG in winter and minimum in summer; the exceptions are 1993, 1997 and 1998.

Sea-Level Fluctuations from Tide Gauge

To corroborate the above model results, we use an independent dataset from coastal tide gauges to estimate the ASPG. Accurate sea-level measurement is unreliable (Sturges, 1982), so sea-level variation is analyzed by calculating the EOF of the 16-year data at the tide gauge stations shown in Fig.1 (excluding Bermuda and Wilmington NC). Only overlapping data are used, which excludes the last three years (2006-2008).Mode 1 explains 67% of the total variance (Fig.3a). The amplitude of sea-level fluctuation is nearly constant  0.08 m from Duck Pier to Atlantic City, and then gradually decreases to about 0.02 m at Halifax. The corresponding principal component (PC1; Fig.3b) is generally positive and maximum in winter (Dec~Feb) and negative and minimum in summer through fall; the range is approximately 1 to +2. Since the sign of the eigenvector is negative (Fig.3a), sea level in winter (summer~fall) therefore increases (decreases) northward consistent with the modeled seasonal fluctuations shown in Figure 2. The linear regression of EOF mode 1 (Fig. 3a) yields a sea-level slope of +4.810-8 from Halifax to Duck Pier (Fig. 3c), giving a range of approximately 510-8 to 10-7. This is smaller than but consistent with the model-predicted range of 210-7 shown in Fig.2c. There are also inter-annual variations (Figure 3b), most notably in 1993~1996 when the PC1 was mostly positive, meaning that sea-level tends to slope more steeply northward, and in 1996~1999 when the reverse occurred.

Depth-Averaged Along-Shelf Currents

The mean along-shelf current varies with location (Figure 4a). 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 Hudson Shelf Valley and Long Island, the current is weak (speeds < 0.005 m s-1). South-southwest of Hudson Shelf Valley, the along-shelf mean currents strengthen (speeds > 0.01 m s-1). Just north of Cape Hatteras, the mean flow turns eastward. This spatial variation in the mean flow is generally consistent with observations (Lentz, 2008).

Time series of 3-month-mean depth-averaged along-shelf current averaged along the 50 m isobath is shown in Figure 4c (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 0.04 m s-1 in summer-fall. The along-shelf mean value is 0.015 m s-1 which is approximately 2-3 times weaker than Lentz’s value. The discrepancy is due to the spatial averaging (i.e. along 50 m isobath) and may also be due to model’s resolution (x  y  10 km). The along-shelf currents are correlated with the ASPG (Figure 4b). The lag correlation is maximum at zero lag, about -0.69, above the 95% significance level = 0.31.

The ASPG is one of the primary driving force for the mean equatorward along-shelf current (Lentz, 2008a). This can be deduced from the steady depth-averaged along-shelf (x, positive poleward) momentum equation which upon neglecting the nonlinear advective terms gives:

bx = oxgH/x, (1)

where  is surface elevation, H is water depth, bx and ox are the x-component bottom and wind stresses respectively. For the mean wind stress in MAB, Lentz (2008) shows that the RHS of (1) is negative (ASPG overcomes wind stress, both are positive), so that if bx is parameterized as ru where from the model r3×10-4 m s-1 is the linear bottom friction coefficient, then u is also negative (i.e. equatorward).

5. What drives the ASPG?

There exist various mechanisms that can cause the sea surface to vary along shelf in the MAB, including the sea-level gradient produced by the Gulf Stream and variations due to the latitudinal shifts of the Stream, wind stress and wind stress curl over the North Atlantic, southwestward propagating Rossby waves and Gulf Stream warm-core rings, Labrador Sea transport, and river discharge. The NWAOM simulation described in section 4 shows a clear mean ASPG sloping downward to the south. The value (= 8.4×10-8) is consistent with the ASPG estimated from observations by Lentz (2008a). In the followings, we first identify the dominant mechanism(s) responsible for the mean ASPG, we then examine the cause(s) for the seasonal and inter-annual variability of ASPG

Mean ASPG:

To understand the mechanism(s) responsible for the mean ASPG, we conducted the following three experiments: a simulation forced by river only (Ex.Riv); a simulation that includes both river and Labrador Sea transport (Ex.RivLab); and a simulation forced by wind only (Ex.Wind). No assimilations are used in any of these experiments. For Ex.Riv, the mean SSH increases to the north (Figure 5b), but the mean ASPG is only about 2.1×10-8, smaller than the ASPG from the standard run (Figure 5a). In Ex.RivLab, a Labrador Sea transport = 1.5 Sv (or 1/3 of the transport specified for the standard NWAOM run, Fig.2) at the northeastern boundary of the model domain is added to Ex.Riv. The mean ASPG is = 4.3×10-8. For the Ex.RivLab, the ASPG increment = 2.2×10-8 when the Labrador Sea transport of 1.5 Sv is added to Ex.Riv is consistent with the ASPG = 8.4×10-8 for the NWAOM experiment with the full transport of 4.5 Sv. On the other hand, the Ex.Wind produces a negative mean ASPG, -7.2×10-8 (Figure 5d). These results clearly indicate that the mean ASPG is caused by the combined forcing of river discharge and Labrador Sea transport.

Seasonal & inter-annual variability of ASPG:

Having now determined that river and Labrador Sea transport are the main forcing that give rise to the mean or steady portion of the ASPG, we now proceed to examine what drive its seasonal and inter-annual variations. The literature has largely ignored that the ASPG may be time-dependent, yet the NWAOM analysis shown in Fig.2 clearly shows that the seasonal and inter-annual variability are not insignificant. The contributions of aforementioned five mechanisms to ASPG variations are now examined. The mechanisms are not entirely independent however, and these will also be discussed.

Gulf Stream path shifts

The Gulf Stream’s path shifts northward in summer~fall, and southward in winter~spring, and the path also fluctuates at inter-annual 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 Molino and Joyce (2008) also shows that the Gulf Stream’s path-shifts can influence the generally southwestward-flowing slope currents both on seasonal and inter-annual time scales. Off the northern shelf break of 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; 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. Our concern here is on how the Gulf Stream’s path can affect ASPG. Shifts in the Gulf Stream can contribute to sea-level sloping up or down north of Cape Hatteras. Direct effects across the MAB shelf break further north are unlikely (Wang, 1982; Chapman et al. 1986). The 3-month running average, and zonally averaged Gulf Stream position anomalies (relative to the 16 year mean position, 1993-2008) from AVISO satellite SSH shows that the Gulf Stream shifts southward in winter-spring, and northward in summer-fall by about 0.60 latitude (Figure 6b). The maximum lagged correlation between the ASPG (Figure 6a) and the Gulf Stream path is about 0.74 with 4-month lag (Table 1). The Gulf Stream’s southward retreat from Fall to spring produces a sea-level drop north of Cape Hatteras and a maximum ASPG in winter~spring; i.e. the strong along-shelf divergence due to the maximum rate of fall of sea-level north of Cape Hatteras results in maximum ASPG in winter~spring.2 However, the one-year running averaged GS’s path and ASPG are not significantly correlated, so that at inter-annual time scales, the GS’s path does not appear to directly affect the ASPG. There are indirect effects of the Gulf Stream, however, due to warm-core rings, to be discussed later.

Large-scale wind stress curls

The 16-year 3-monthly mean wind stress curl is estimated over the Northwest Atlantic from 60W westward to the 200m isobath and from 35N to 42N. As expected, the wind stress curl shows a significant seasonal cycle; it is positive in winter and weak and negative in summer (Fig. 6c). Its correlation with ASPG is low and not significant, however. Thus the large-scale wind pattern does not directly influence the ASPG. On the other hand, as will be further discussed later, the wind stress curl is significantly correlated with the GS path and eddy kinetic energy (EKE) north of the Gulf Stream mean path with lags of a few months (Table 1). The wind stress curl also correlates well with the upstream transport. Thus strong wind stress curl in winter forces a strong southwestward transport.

Warm-core rings

Effects of warm-core rings are estimated by calculating the EKE north of the 16-year Gulf Stream mean path from AVISO geostrophic current anomaly (hereafter, N-EKE). The seasonal evolution of EKE is averaged over the region from 75W to 55W and from the north of the Gulf Stream mean path to 42.5N (Figure 7a). The N-EKE is large in late spring and late summer but weaker in fall and winter (Figures 7b, c). The reason for choosing the region north of the Gulf Stream is to focus on warm-core rings only, as these will most likely give rise to the ASPG fluctuations (see below). However, Zhai et al. (2008) computed the Gulf Stream EKE from satellite data but did not differentiate between the northern and southern regions. They found largest EKE in summer. The maximum correlation for 3-month running average of ASPG and N-EKE after the removal of one-year average values is about -0.48 with 3-month lag (Figure 6, Table 1). This implies that the southwestward propagation of warm-core rings with speed about 2-10 km d-1 can induce ASPG decrease after 3 months. Also, the correlation for one-year low pass filtered N-EKE and ASPG is also significant  0.40, suggesting that warm-core rings can influence ASPG at inter-annual time scales.

An Idealized Model of MAB Shelf Response to Warm-Core Rings

To examine how warm-core rings can generate ASPG in MAB, an idealized experiment of shelf sea-level and current responses to impingements of westward-propagating warm-core rings was conducted. The simulation has the same domain and realistic 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. Warm-core rings with radius = 125 km were “injected” every 360 days over the open ocean in the northeastern region of the model domain near (62.5oW, 40oN). The simulation was run for 6 years. 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 specifying upward surface heat flux (i.e. cooling) over 2/3 of the model domain south of 34oN. Since the area of this latter domain is much larger than the eddy size, the results are virtually unchanged with or without the surface cooling. We experimented with different number of eddies and rates of injection, but the results are similar and the conclusions are the same. In the followings, analyses from the experiment with 3 warm rings injected every 360 days are presented. Previous studies (e.g. Wei et al. 2008) have shown that on average 4~5 long-lived warm rings per year are formed.

Figure 8a shows the 6-year mean sea surface height (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. A mean ASPG = 1.5×10-8 sloping down northward from Delaware to Eastern Long Island is estimated using linear regression (Figure 8b). Temporal variations of ASPG are shown in Figure 8c. The red lines indicate times when new warm-core rings are injected.

The ASPG varies temporally depending on the position of the warm-core ring relative to the MAB shelf. The variations are illustrated using two examples, one during the positive phase of ASPG at day 1200 (Fig.8c), and the other one when ASPG is negative 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 positive phase at day 1200 occurs when a ring has propagated far southwestward to the shelf break off Chesapeake Bay (Figs.9a,b). Onshore convergence occurs south and west of the ring, producing a local high SSH that extends onshore of the 50m-isobath off Chesapeake Bay. Offshore divergence occurs north of the ring, producing a local low SSH that extends northward to the mouth of Long Island Sound. Note that while the main high-speed core of the ring is relatively small (100 km radius), the ring’s interaction with the sloping topography produces along-shelf response that covers almost the entire MAB from Chesapeake to Long Island. Such extensive along-shelf response (when an eddy interacts with continental shelf break) has been noted in previous studies (e.g. Oey and Zhang, 2004; Wei and Wang, 2008). Figures 9c,d show the example of a negative phase of ASPG at day 1610 when the ring is positioned off the middle portion of the MAB. Onshore convergence now produces high SSH’s onshore of the 50m-isobath off New Jersey and New York, while the southern portion of the MAB remains relatively quiet, SSH  0. The SSH increases poleward along the shelf, and the ASPG is positive (Fig.8c at day 1610).

We have checked that the temporal variation of ASPG shown in Fig.8c is due to the shelf response to propagating warm-core rings, illustrated above. This is the advantage of an idealized experiment that exclusively isolates forcing by the warm-core rings. In as far as the strengths of the modeled rings are realistic (with speeds ~ 1 m s-1), variations in the surface slope induced by the warm-core rings, in the order of 10-8, are also comparable with the observed variability (e.g. Fig.3). Figure 8c also shows seasonal and inter-annual variations. While these temporal scales are in part artificial depending on the frequency of eddy-injection in the numerical experiments, they do indicate the potential importance of Gulf Stream warm-cores rings in contributing to the seasonal and inter-annual variations in the MAB shelf and slope currents.

The variation in Gulf Stream path also correlates with N-EKE with about one-month lead from Table 1. The influence of the Gulf Stream path on the ASPG may therefore be partially induced through the activity of warm-core rings. This is corroborated by the time lags of Gulf Stream path variation and N-EKE with ASPG (Table 1). The time lag arises mainly from the time taken warm-core rings to propagate southwestward over the Slope Sea.

Labrador Sea transport

The Labrador Sea transport (Fig.6e) is calculated off the southern coast of Nova Scotia up to the 1000 m isobaths. The mean value is southwestward, about -4.3 Sv and its standard deviation is about 1.8 Sv. The transport is strong in spring, and is much weaker in fall. The one-year running average shows inter-annual variability (Fig.6e). From 1993 to 1996, the transport was weaker, while from 1996 to 1997, the transport became stronger. This variation is consistent with Labrador Sea transport variability reported by Dong and Kelly (2003; see their Fig.4a). From Table 1, the transport correlates well with wind stress curl (R=-0.81), and suggests that the variations in Labrador Sea transport are mainly forced by the large-scale wind. Temperature and salinity anomalies over the MAB shelf (and slope) also correlate well with the Labrador Sea transport (not shown). Colder and fresher shelf waters correspond to stronger southwestward transport. However, the correlations in both the seasonal and inter-annual time scales between transport and ASPG are low, indicating that the change in Labrador Sea transport cannot directly influence the seasonal and inter-annual variations in ASPG.

Freshwater discharge

Freshwater discharge from 17 rivers along the east coast from Cape Hatteras to the St. Lawrence River system was used in NWAOM. The 3-monthly average of total river input has a clear seasonality, and is maximum in spring due to snow melting and precipitation (Fig. 6f). From table 1, the correlation between river discharge and the ASPG is low  0.19, though it is above the 95% significant level (= 0.13), indicating weak influences of rivers on the seasonal and inter-annual variability of ASPG compared to those due to the N-EKE and GS path variations.

  1. Summary

In this work, the question of what physical mechanisms contribute to the mean, seasonal and inter-annual 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, process models. 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 is consistent with that deduced in other studies (Stommel and Leetmaa, 1972; Scotts and Csanady, 1976; Lentz 2008a), and its variation is consistent with that deduced from tide-gauge data. The mean ASPG is positive, about 3~5×10-8, but it also has strong seasonal and inter-annual variations of 5×10-8.

We show that freshwater discharge and Labrador Sea transport both contribute to the mean ASPG. On the other hand, the seasonal and inter-annual variations in ASPG are mainly produced by Gulf Stream’s warm-core rings that propagate southwestward in the Slope Sea, and that interact with the MAB shelf break. The effects of rings on ASPG were demonstrated with an idealized experiment that isolates the 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 signal across the shelf break is limited (e.g. Wang, 1982; Chapman et al. 1986), it is sufficient to produce O(1~4×10-8) fluctuations that are consistent with the observed fluctuations from tide-gauge. The influence of large-scale wind pattern on ASPG is also examined. Though the wind cannot directly affect ASPG, it is the major mechanism accounting for the GS path variations (Dong and Kelly, 2003), as well as the seasonality of EKE (Zhai et al. 2008).

1 This same formula was used in Oey et al. (2006), but the coefficient for |ua| 2 was erroneously rounded off to 0.0002.

2 GS/t  Hushelf/x. Also rushelf = gshelf/x. So if GS ~ cosine, then ushelf ~ sine, and ASPG (=gshelf/x) is also sine. When GS/t < 0, ushelf/x >0; i.e. ushelf near CH is more negative than currents further north, so that gshelf/x>0. In other words, the maximum of ASPG occurs when GS is falling most rapidly, both occurring in winter.

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