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

*Corresponding Author: fxu@princeton.edu

August 13, 2010


6000 words.


Abstract

It has been known for some time that the along-shelf pressure gradient (ASPG) is an important forcing that drives the time-mean, equatorward depth-averaged currents on the Middle Atlantic Bight (MAB) shelves off the U.S. northeastern coast. The origin of ASPG and its seasonal and inter-annual variations remain to be explained, however. Possible (though not necessarily independent) contributors to ASPG are: wind and wind stress curl, Gulf Stream’s path shift, warm-core rings, Labrador Sea transport, and river discharge. In this work, sixteen years (1993-2008) of satellite data, data-assimilated model reanalysis, and tide-gauge sea level data are analyzed. It is shown that the mean ASPG is produced by rivers discharging along the east coast of North America and by the Labrador Sea transport. The seasonal and inter-annual variations in ASPG are caused by southwestward propagation of warm-core rings along the MAB slope, and also by impingement of these rings upon the shelf break north of the Gulf Stream near Cape Hatteras. 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. On the other hand, north of the Gulf Stream, there exist seasonal and inter-annual variations of eddy kinetic energy which affect the ASPG, and which may be in part forced by the wind.



  1. Introduction

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 shelf break front (e.g. Flagg et al. 2006). Understanding the water properties and currents in MAB is important for navigation, fisheries, and coastal ecosystems.

The MAB circulation has been investigated through observational and modeling studies over several decades (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 directed equatorward, with speeds of 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, the currents veer offshore. The mean along-shelf currents also increase with distance offshore (Beardsley et al. 1976; Lentz 2010).

An important driving force for the depth-averaged mean currents in the MAB is the along-shelf pressure gradient (ASPG) (Beardsley and Boicourt 1981). Stommel and Leetmaa (1972) modeled the steady-state wintertime circulation, and concluded that an ASPG of order of 10-7 is required to drive the southwestward flow. Csanady (1976) argued that the cross-shelf density gradients are important 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 the 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). This work will further investigate the large-scale contributions to 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, the seasonal variation is less clear in previous observations (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 measurements, many of which were taken in the New England Shelf, Lentz (2008b) found that the alongshore currents have amplitudes of a few cm s-1. The residual alongshore flow after the wind-driven component is removed is maximum southwestward in spring onshore of the 60m isobath. He suggested that the seasonality of the along shelf currents is primarily driven by the cross-shelf density gradient induced by freshwater discharge. The role of ASPG in the seasonality of the along-shelf currents is unclear. Does ASPG have seasonal and inter-annual 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 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, 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 model and 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 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). 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 (http://www.aviso.oceanobs.com/duacs/). 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, as well as ships and buoys measurements.

  1. The Numerical Model and the Experiment with Data Assimilation

The terrain-following (i.e. sigma) coordinate and time-dependent numerical model for this study is based on the Princeton Ocean Model (Mellor, 2002). 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 (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 mean -profile, guarantees small pressure-gradient errors of O(mm/s) (c.f. Oey et al. 2003). The Smagorinsky’s (1963) shear and grid-dependent horizontal viscosity is used with coefficient = 0.1, and the corresponding diffusivity is set 5 times smaller (c.f. Mellor et al., 1994). The northwestern Atlantic Ocean model (NWAOM) uses an orthogonal curvilinear grid to cover the region 98W-55W and 6N-50N (fig.2). The model has 25 vertical sigma levels and horizontal grid sizes   8~12 km in the MAB and the Slope Sea. The World Ocean Atlas data (“Climatological” data) from NODC (http://www.nodc.noaa.gov/OC5/WOA05/ pr_woa05.html) was used for initial condition as well as boundary condition along the eastern open boundary at 55oW. Across 55W, a steady transport combined with radiation using also the geostrophically-balanced surface elevation g (Oey and Chen, 1992a) specifies the Gulf Stream exiting near the Grand Banks south of Newfoundland with a magnitude of 93 Sv following Schmitz (personal correspondence, 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 vertical structures of the currents (i.e. after a depth-averaged value is removed) are specified using radiation conditions. The velocity component tangential to the boundary, as well as turbulence kinetic energy and length scale, are specified using one-sided advection scheme at outflow grids and are set zero at inflow. The (potential) temperature (T) and salinity (S) are similarly advected during outflow, but are specified using climatological values at inflow grids. Radiation is used for the surface elevation , but since POM uses a staggered C-grid, and because transports are specified, the boundary  plays only a minor role and a zero-gradient condition on it works well also. Sea surface fluxes are specified as detailed below. To prevent temperature and salinity drift in deep layers in long-term integration, the T and S for z < 1000 m are (weakly) restored to annual-mean climatological values with a time scale of 600 days; this does not impede short-period mesoscale variability. More details are in Oey et al. (2003). 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, 2008, 2009; Lin et al. 2007; Yin and Oey, 2007; Oey, 2008; Wang and Oey, 2008; Mellor et al. 2008).

For the present application to the MAB, the NWAOM is first run for 15 years, forced by monthly climatological NCEP surface fluxes. 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 the CCMP3 six-hourly winds from Jan/01/1993 through 2008. 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 at the open boundary at 55oW the WOA T/S, the steady transport and the M2-tide interpolated from the Oregon State University’s tidal data [http://www.oce.orst.edu/research/po /research/tide/index.html].

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

(2)

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.



Daily discharges from 17 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 is not of interest for the purpose of this work. Their function is to provide for a more 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 with saline sea water within the bays or rivers before flowing out onto the continental shelves.

The northeastern corner of NWAOM domain is where the Labrador Sea slope transport flows west-southwestward. An inflow transport of 4.5 Sv is specified along the northeastern slope of the model domain, and this value will be adjusted (below) in sensitivity tests. For simplicity, we defined 1 UA = 1.5 Sv (UA: depth-averaged U velocity of Labrador Sea transport), and so 4.5 Sv = 3 UA.

Various experiments are carried out as discussed separately below (Table 1). Here we describe the standard experiment (Ex.DA) which consists of all the forcing and specifications described above. Additionally, satellite SSH anomaly data from AVISO (www.aviso.oceanobs.com) is also assimilated into the model. The purpose of this data-assimilative (DA) analysis is to provide a realistic open-ocean state – the Gulf Stream, rings and the Slope Sea gyre – to which the shelf then can respond. The Gulf Stream and eddies are assimilated in deep ocean regions only (water depth H > 1000 m) using the Mellor and Ezer’s [1991; see also Ezer and Mellor, 1994] scheme. 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.


  1. Results

Model Sea Surface Height over the MAB shelf

Figure 2 and Figure 3a shows the 16-year (1993-2008) mean SSH from the Ex.DA simulation. A cyclonic gyre is seen in the Gulf of Maine (Pettigrew et al., 2005). 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 3a shows two local high pressure cells on the 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 aligned along the isobaths.

Figure 3b 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 linear fits yield slopes ranging from ASPG  5.4×10-8 between Chesapeake Bay to Cape Cod in excellent agreement with Lentz’s (2008a) bight-wide estimate of 3.7×10-8 based on long-term observations, to the larger ASPG  8.4×10-8 between Delaware (DEL) and the east end of Long Island (ELS). The latter larger value is caused by local river effects especially to less saline waters from the Long Island Sound (note the slight dip in sea level from ELS to Cape Cod in fig.3b), and is in better agreement with Scott and Csanady’s (1976) estimate  1.44×10-7 off (the southern coast of) Long Island based on a 25-day time series in September 1975. There are also significant seasonal and inter-annual fluctuations (Fig.3c). There is a clear seasonal signal of maximum (positive) ASPG in winter and minimum in summer; the exceptions are 1993 and 1998. The range is 2×10-7 with model sea-level sloping poleward, generally in winter, and 10-7 sloping equatorward, generally in summer. The amplitudes of these seasonal fluctuations also vary at inter-annual time scales, they are larger in some years (1994~1995 and 2003~2007) and smaller in others (1997~1999).
Sea-Level Fluctuations from Tide Gauge

To check the seasonal and inter-annual variations in ASPG, we estimate it using coastal tide gauges. Accurate sea-level measurement is difficult (Sturges, 1982), so we focus on sea-level variation only, and analyze it 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.4a). 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 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.4a), sea level in winter (summer~fall) therefore increases (decreases) northward, relative to an undetermined mean tilt. This result is consistent with the modeled seasonal fluctuations shown in Figure 3c. The linear regression of EOF mode 1 (Fig. 4a) yields a sea-level slope of +4.810-8 from Halifax to Duck Pier (Fig. 4c). This gives an ASPG range of approximately 510-8 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 up equatorward in summer. This range is smaller than but is consistent with the model-predicted range mentioned previously. The tide-gauge mode-1 time series also shows inter-annual variations (Figure 4b). The amplitudes are generally larger in 1994~1995 and 2001~2004, and smaller in 1997~2000 and 2004~2005. The correlation coefficient for monthly PC1 (Fig. 4b) and ASPG fluctuations (Fig. 3c) is about 0.45, above the 95% significant level 0.20. However, the correlation of two-year average of PC1 and ASPG is not significant.



Depth-Averaged Along-Shelf Currents

The mean along-shelf current varies with location (Figure 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 Figure 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 may also be due to model’s resolution (x  y  10 km). The along-shelf currents are correlated with the ASPG which is plotted in Figure 5b. The zero-lag correlation coefficient is = -0.69, above the 95% significance level = 0.31.

It is of interest to check that the above mean values for the model ASPG and alongshelf current are self-consistent. The ASPG is one of the 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 kinematic bottom and wind stresses respectively. For the mean wind stress values of ox1.4×10-5 m2 s-2) in MAB, Lentz (2008) shows that the RHS of (1) is negative (ASPG overcomes wind stress, both are positive). Using the above value for the model mean ASPG, and parameterizing bx as ru where from Lentz (2008) r2.5×10-4 m s-1 is the linear bottom friction coefficient, then u is also negative (i.e. equatorward)  0.024 m s-1 in agreement with the above model estimate based on fig.5c.


5. What drives the ASPG?

We consider the following mechanisms that can cause the sea surface to vary along shelf in the MAB:

a. latitudinal shifts of the Gulf Stream;

b. wind stress and wind stress curl over the North Atlantic;

c. southwestward propagating warm-core rings;

d. Labrador Sea transport, and

e. river discharge.

The standard Ex.DA simulation described in section 4 shows a mean ASPG sloping downward from Cape Cod towards Cape Hatteras. In this section, we will conduct additional experiments to identify the mechanism(s) that drive ASPG. For each experiment, we compute (i) the mean ASPG as the slope of the linear best-fit of the corresponding mean SSH along the 50 m isobath between Delaware and the eastern end of Long Island (as in fig.3b, solid line), and (ii) the corresponding time-series (as in fig.3c). We first examine process(es) responsible for the mean ASPG, and then 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 seven sensitivity experiments: a simulation forced by the same forcing as Ex. DA except no data assimilation (Ex. RivLab3Wind); a simulation forced by both river and 3UA Labrador Sea transport (Ex. RivLab3); a simulation forced by 1.5UA Labrador Sea transport only (Ex.Lab1.5); a simulation that includes both river and 1UA Labrador Sea transport (Ex.RivLab1); a simulation forced by 1UA Labrador Sea transport only (Ex.Lab1); a simulation forced by wind only (ExWind); and a simulation forced by river only (Ex.Riv). The detail differences of the experiments are listed in Table 1.

For Ex.Riv, the mean SSH increases to the north (Fig. 6h), but the mean ASPG is only about 2.1×10-8, smaller than the ASPG from the standard run (Figure 6a). For Ex.Lab1, the ASPG is about 2.3×10-8 (Fig. 6f) and for Ex.RivLab1 the mean ASPG is = 4.3×10-8 (Figure 6e). Noticeably, the corresponding mean ASPG increment is = 2.0×10-8 when river is added to Ex.Lab1. The result is consistent with ASPG in Ex.Riv, and the contribution of river to the mean ASPG setup (2.0×10-8) is clear.

To explore the influence of Labrador Sea transport, the mean ASPG at different transport for Ex.RivLab3 (Fig. 6c), Ex.Lab1.5 (Fig. 6d), and Ex.Lab1 (Fig. 6f) are compared. The ASPG increases by about 8×10-8 when the Labrador Sea transport increases 1 UA. Then ASPG ×108 = -6 + 8UA is obtained.

Without river and Labrador Sea transport, the mean ASPG becomes negative. This is true with or without wind. For example, for the Ex.Wind simulation, the mean ASPG = 7.2×10-8 (Fig. 6g). This negative ASPG is mainly induced by the Gulf Stream. Also, in the experiments Ex.RivLab3Wind (Fig. 6b) and Ex.RivLab3 (Fig. 6c), the ASPGs are close, 17×10-8 and 18×10-8, respectively. This means that though the wind is not important for the mean ASPG, the Gulf Stream contributes to the negative setup of ASPG, about -7.2×10-8. This is consistent with estimates of ASPG ×108 = -6 + 8UA = 2 - 8+ 8UA, where ‘2’ is contributed by river and ‘-8’ may be induced by Gulf Stream. We conclude that the mean ASPG is caused by the combined forcing of river discharge, Labrador Sea transport, and Gulf Stream.
Seasonal & inter-annual variability of ASPG:

Having now determined that river and Labrador Sea transport contribute to the mean or steady portion of the ASPG, we now proceed to examine what drive its seasonal and inter-annual variations. The Ex.DA simulation shown in Fig.3 shows that seasonal and inter-annual variability exist. 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.

In the followings, inter-annual 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 inter-annual fluctuations.
Gulf Stream path shifts

The Gulf Stream 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. We examine how the Gulf Stream’s path can affect ASPG. Shifts in the Gulf Stream can contribute to sea-level change on shelf region immediately north of Cape Hatteras. At the seasonal time scales, the 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 0.40 latitude (Figure 7b). The maximum lagged correlation between the (seasonal) ASPG (Figure 7a) and the Gulf Stream path is about 0.74 with 4-month lag (ASPG lags Gulf Stream, Table 2). The correlation and lag are explained as follows. 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 generally peaks during the time of the most rapid retreat, i.e. in winter. Physically, the Gulf Stream’s southward retreat produces a sea-level GSdrop north of Cape Hatteras GS/t < 0 which is therefore most rapid in winter (i.e. GS/t is large and negative). From continuity, GS/t  Hushelf/x, where H = water depth and ushelf is the along-shelf velocity, positive poleward. In winter, the along-shelf flow is therefore maximally divergent (ushelf/x > 0 and large), and the southward along-shelf current strengthens towards Cape Hatteras, north of which on the shelf ushelf is therefore large and negative. Now, at seasonal and longer time scales, rushelf  gshelf/x, so that gshelf/x > 0 and is a maximum in winter. In other words, the maximum of ASPG occurs when GS is falling most rapidly, both occurring in winter, and both lag the maximum Gulf Stream’s northward shift in fall.

At the inter-annual time scales, fig.7a,b show that the Gulf Stream’s path and ASPG are not significantly correlated. 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. The wind stress curl shows a significant seasonal cycle; it is positive in winter and weak and negative in summer (Fig. 7c). 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 with lags of a few months (Table 2). Furthermore, the wind stress curl also correlates well with the Labrador Sea transport, i.e. strong wind stress curl in winter forces a strong southwestward transport (table 1 and Fig.7c,e).


Warm-core rings

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 60oW (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 EKE north of the Gulf Stream’s 16-year mean seasonal path from AVISO geostrophic current anomaly (hereafter, N-EKE). Between Gulf Stream north wall and the shelf break, the ratio of EKE and TKE (total kinetic energy) in the region offshore of 1000m isobaths clearly shows the southwestward propagating EKE (Fig. 8a). The EKE is calculated as 0.5(u’2+v’2), and TKE = 0.5(u2+v2). And the u=+u’ and v=+v’. The bracket indicates the long-term mean of the geostrophic velocity. South of the GS, the relative high EKE/TKE is due to the small values of and . From figure 8a, the N-EKE is relatively large in spring and summer and becomes weaker in fall and winter. To better illustrate this seasonal variation in N-EKE, the N-EKE is averaged over the region from 75W to 55W and from north of the Gulf Stream seasonal path to 42.5N (rectangular box in Fig. 8a). 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). It is necessary to use the seasonal path (instead of annual) so that N-EKE will not then include the high kinetic energy associated with the main Stream as it shifts with season. The N-EKE is large from spring through early summer but weaker in fall and winter (Figures 8b, c). Zhai et al. (2008) also 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 between the seasonal ASPG and N-EKE is -0.48 with ASPG lagging N-EKE by approximately 3 months (Table 2); i.e. ASPG reaches a minimum in summer~fall after the N-EKE peaks in spring~summer (Fig.7a,d). Physically, the production of warm-core rings 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 is consistent with the propagation speed of observed warm core rings, 5.6 km day-1 to 6.8 km day-1 (Glenn et al., 1990). We next show 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. It appears that the same mechanism can also explain the significant correlation ( 0.4) between N-EKE and ASPG at the inter-annual time scales (Table 2).

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 2).



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’s sea-level and current response to the 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. Warm-core rings with radius = 100 km were “injected” every 360 days over the open ocean in the northeastern region of the model domain near (62.5oW, 40oN). The 360-day period mimics in a crude way the seasonal fluctuation of EKE (Fig.8c). 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 do not affect the conclusions. In the followings, analyses from the experiment with 3 warm rings injected every 360 days are presented. This small number of eddies is intentionally chosen so that effects of individual eddies on the shelf can be clearly identified in the simulation. Since the idealized model does not include a Gulf Stream, all modeled rings survive and eventually reach Cape Hatteras.

Figure 9a 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. The mean SSH slopes down northward from Cape Hatteras and Chesapeake to Eastern Long Island. The SSH-slope is steep for the first 200 km alongshelf north of Cape Hatteras because of the large influence of rings there; the slope then equilibrates to a linear drop from the shelf between Chesapeake and Delaware, where linear regression gives ASPG  1.3×10-8 (Figure 9b).

Temporal variations of ASPG are shown in Figure 9c. The ASPG varies depending on the position of the warm-core ring relative to the MAB shelf. We illustrate this with two examples, one during the negative phase 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 a ring has propagated far southwestward to the shelf break off Chesapeake Bay (Figs.10a,b). Onshore convergence occurs south and west of the ring, producing a locally high SSH that extends onshore of the 50m-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 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 et al., 2008). Figures 10c,d show the example of a positive phase of ASPG at day 1610 when the ring is positioned off the middle portion of the MAB between Delaware and New Jersey. 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.9c at day 1610). As the ring continues south-southwestward towards Cape Hatteras, the cycle repeats (Fig.10a, b) and ASPG turns negative (beginning at day 1860 in fig.9c).

Since the idealized experiments exclusively isolate forcing by the 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 (when “N-EKE” is a maximum). Since the model eddies propagate at 6~8 km day-1, the time lag of 120~180 days coincide well with the time taken for eddies to traverse a distance of 1000~1200 km from their injection location (62.5oW, 40oN) 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 inter-annual 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 inter-annual fluctuations is not of interest due to 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 inter-annual variations of ASPG, hence also in the MAB shelf and slope currents.
Labrador Sea transport

The Labrador Sea transport (Fig.7e) 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.7e). 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 does not 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. 7f). 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. 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 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 nevertheless 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).



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


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