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

September 08, 2010


7915 words.


Abstract

It has been known for some time that the along-shelf pressure gradient (ASPG) contributes to driving 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 contributors to ASPG are: wind and wind stress curl, Gulf Stream’s path, warm-core rings, Coastal Labrador Sea Water (CLSW) 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 forced by river discharge and the CLSW transport. On the other hand, 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. It is shown that rings change the ASPG by forcing cross-shelfbreak transports that modify the sea surface height over the outer shelf, and by producing a sea surface sloping down to the north when they are near Cape Hatteras. It is also shown that the large-scale wind 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 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 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 (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; he estimated an ASPG value of approximately 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 limited (Wang 1982; Csanady and Shaw, 1983; Chapman 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 (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 100m-isobath) which 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 (75.029W, 37.833N) show maximum southwestward currents in spring, and weak currents in summer and fall (Xu et al., manuscript in preparation). 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 cm s-1. The residual alongshore flow after the removal of wind-driven component 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. Does ASPG also 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 satellite and tide-gauge 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, it seems reasonable (from the literature) to suggest that the 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’s latitudinal shifts, warm-core rings, Coastal Labrador Sea Water (CLSW; Csanady and Hamilton, 1988) 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 CLSW 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) level 3 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; Oey et al. 2003) uses an orthogonal curvilinear grid to cover the region 98W-55W and 6N-50N (Fig.2). In a process study in which forcing and sensitivity are to be explored, such a regional model offers some advantages compared to, e.g. a basin-scale North Atlantic model. The improved efficiency allows multiple long-term experiments to be conducted at a reasonably high resolution. Moreover, the NWAOM is used here 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 larger, basin or even global-scale variability are excluded. The assumption is then that these variability are of secondary importance in the interpretations of the MAB circulation processes.

The NWAOM 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 CLSW inflow is then specified (and adjusted; see below) as the northern portion of this “North Recirculation gyre.” The CLSW is identified here as being the same as Csanady and Hamilton’s (1988; their Fig.20b) “offshoot of the Labrador Current” that “turns the other way and intrudes into the Slope Sea.” Much of this west/southwestward transport turns eastward to join the Gulf Stream, however, near 60oW. In addition to these steady transports, a combination of flow-relaxation and radiation conditions (Oey and Chen, 1992a,b) are used to also specify the WOA T/S and the M2-tide interpolated from the Oregon State University’s tidal data [http://www.oce.orst.edu/research/po/research/tide/index.html] at the open boundary at 55oW. Thus 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; 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).

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 CCMP 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.

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, 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 since within the NWAOM domain, because 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 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 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 sea water 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 = 1.5 Sv is the minimum inflow that can give a “reasonable-looking,” time-mean separation and path of the Gulf Stream near Cape Hatteras (Mellor and Ezer, 1991; Ezer and Mellor, 1994a). The (mean) Gulf Stream tends to separate from the coast too far to the north for a CLSW inflow below this minimum. It is convenient to non-dimensionalize various values of the CLSW transport discussed below by this “critical” transport of 1.5 Sv, which we will refer to as “1UA” or UA=1. In the “standard experiment” (below), a CLSW transport of 4.5 Sv (i.e. 3UA or UA=3) is used, and this value will be adjusted (below) in sensitivity tests. The 3UA value may be compared with Csanady and Hamilton’s (1988) estimate of approximately 4 Sv for the CLSW transport.

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, 1994b] 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. 2007; 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 show the 16-year (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 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 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 the mean 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 (dashed line) between Chesapeake Bay (CHS) to Cape Cod (CC) in agreement with Lentz’s (2008a) estimate of 3.7×10-8 based on long-term observations, to the larger ASPG  8.4×10-8 (solid line) over a shorter distance between Delaware (DEL) and the east end of Long Island (ELS). The latter larger value is caused by local river effects 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 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 of ASPG. Figure 3c shows a clear seasonal signal of maximum (positive) ASPG in winter and minimum in summer; the exceptions are 1993 and 1998. The range is approximately from 10-7 with model sea-level sloping poleward, generally in winter, to 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

We check the seasonal and inter-annual variations in ASPG using coastal tide gauges. Accurate sea-level measurement is difficult (Sturges, 1977), 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 agrees 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 of approximately 10-7, 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 tide-gauge PC1 (Fig. 4b) and model ASPG fluctuations (Fig. 3c) is about 0.45, above the 95% significant level 0.20. However, the correlation of two-year running-averaged 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 (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, and parameterizing bx as ru where from the model r5×10-4 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 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. CLSW 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 (DEL) and the eastern end of Long Island (ELS; as in fig.3b, solid line) in Fig. 6, 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 numerous sensitivity experiments, seven of which (in addition to Ex.DA) are summarized in Table 1.2 Gulf Stream is included in all but the last experiment in Table 1, either through data-assimilation (Ex.DA), or through model dynamics. The 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.

The combined influence of CLSW transport, rivers, wind and the Gulf Stream on ASPG is summarized by the following expression:3

ASPG×108 = RIV + (7×UA+1.3)×Hv(UAUAcritical)  WIND  GS (2)

where RIV = 2 is the (constant) contribution from rivers (=0 for no rivers); UAcritical = 1 is the non-dimensionalized critical CLSW transport (described previously) that prevents the Gulf Stream from separating at a location too far north past Cape Hatteras; “Hv” is the Heaviside (step) function Hv(n) = 1 for n  0, = 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). Also, as mentioned previously, the symbol UA = 1 for 1UA, UA = 1.5 for 1.5UA etc. The contribution to ASPG from the CLSW transport is idealized by a step function for UA > UAcrit. Equation (2) says that rivers cause the sea-level to slope up poleward, while the Gulf Stream as well as the mean westerly wind have the opposite effect and cause the sea-level to decrease poleward. The contributions to ASPG from the separate terms in equation (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 note that it has a much larger effect on the poleward set-down 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  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). 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 set-down poleward over the MAB shelf. The Gulf Stream influence is particularly strong, and its seasonal and inter-annual variations are discussed below. Since the observed mean ASPG is positive (sea-level tilts up poleward), only river and CLSW transport can contribute to this mean. This result is consistent with the idea that pressure field is trapped on the shelf (Wang, 1982; Csanady and Shaw, 1983; Chapman 1986). Moreover, since the CLSW-contribution has a large factor “7” in “(7×UA4.7)”, it is relatively ineffective (compared to rivers) in producing the mean ASPG (compare Ex.Riv and Ex.Lab1 in Table 1). This is because a large portion of the CLSW transport is over the slope, while only the shelf portion is effective in producing the along-shelf pressure field (Wang, 1982).

Before concluding this subsection, we should comment on Ex.DA and its corresponding experiment without data assimilation, Ex.RivLab3Wind. It is clear that with UA =3, the APSG is unreasonably high. More detailed analyses on Ex.RivLab3Wind (also Ex.RivLab3) confirm that the CLSW transport is too strong, so that the corresponding Gulf Stream tends to separate south of Cape Hatteras. Assimilating satellite data (Ex.DA) corrects this and brings the ASPG to a more reasonable value (Fig.3). This and other detailed comparisons of various experiments with observations will be reported separately (Xu, Wang and Oey, 2010; manuscript in preparation).
Seasonal & inter-annual variability of ASPG:

Having now determined that river and CLSW 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 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 necessarily independent of each other however.

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. These time series are plotted in Figure 7a.
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 Peña-Molino and Joyce (2008) also shows that 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; 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. We will now show that shifts in the Gulf Stream can contribute to sea-level change on the shelf region immediately north of Cape Hatteras, and this change in turn affects ASPG. At seasonal time scales, the zonally averaged Gulf Stream’s position anomalies (relative to the 16 year mean position, 1993-2008) from AVISO SSH shows that the Gulf Stream shifts southward in winter-spring, and northward in summer-fall by about 0.40 latitude (Fig. 7b). The maximum lagged correlation between the (seasonal) ASPG (Fig. 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. Immediately north of Cape Hatteras, on the shelf, the 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, figure 7a and 7b 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 (in some years) 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 below, the wind stress curl is significantly correlated with the GS path and eddy kinetic energy (EKE) north of the Gulf Stream (Table 2). The wind stress curl also correlates well with the CLSW transport, i.e. strong wind stress curl in winter forces a strong southwestward transport (table 2 and Fig.7c,e), in general agreements with Csanady and Hamilton’s (1988) analytical model.


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).

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. We estimate EKE from 16-year AVISO geostrophic currents. The seasonal EKE in the middle Atlantic Ocean also shows maximum in summer (Fig. 8a), consistent with results from Zhai et al. (2008).

Effects of warm-core rings are estimated by calculating the EKE north of the Gulf Stream’s 16-year monthly seasonal mean path from AVISO geostrophic current anomaly (hereafter, N-EKE). Between the seasonal Gulf Stream north wall (black line in Fig. 8a) and the shelf break, the N-EKE offshore of 1000m isobaths clearly shows seasonal variability (Fig. 8a). The N-EKE is larger in spring and summer and becomes weaker in fall and winter. To further illustrate this seasonal variation in N-EKE, the N-EKE is averaged over the region from 75W to 55W (rectangular box in Fig. 8a) and from north of the Gulf Stream monthly path to 42.5N. The reason for choosing the region north of the Gulf Stream is to focus on warm-core rings only, as these are ones that give rise to ASPG fluctuations (see below). It is necessary to use the monthly path (instead of a 16-year mean) so that N-EKE will not then include the high kinetic energy associated with the main Gulf Stream as it shifts with season. The N-EKE is large from spring through early summer but weaker in fall and winter (Fig. 8b, 8c). The maximum correlation between the seasonal ASPG and N-EKE is -0.48 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 (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. (WHY???? N-EKE & ASPG (last row in table 2) is positive???)

The correlation in the inter-annual time scale between N-EKE and ASPG is relatively high, 0.40 (Table 2, the 95% significant level is 0.17). This correlation implies that more warm rings correspond to the larger ASPG. Note that the correlation is positive, opposite to the seasonal correlation between N-EKE and ASPG (-0.48). The reason for the inconsistency is because that 1-year average of N-EKE has removed the seasonal variability and represents only the annual generations of warm rings. Most of the warm rings are initially generated in the relative northeast locations, propagating southwestward, and then approaching the MAB shelf. When the warm rings are in the north of the 38N, they can contribute to the positive ASPG, discussed in the next section. So more warm rings are generated, larger ASPG is found.

The seasonal variation in Gulf Stream path also correlates with N-EKE with N-EKE leading by about one month (Table 2). The influence of the Gulf Stream path on the ASPG is therefore partly because of warm-core rings. This is corroborated by the time lags of Gulf Stream path variation and N-EKE with ASPG (Table 2).


How Do Warm-Core Rings Produce Fluctuations in ASPG?

To examine this mechanism, an idealized experiment of shelf’s sea-level and current responses 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 8 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 also specifying a uniform upward surface heat flux (i.e. cooling) over the model domain. Since the area of this is much larger than the eddy size, the results are virtually unchanged with or without the surface cooling. Three warm rings are injected every 360 days. Sensitivity experiments with different number of eddies and rates of injection, give similar results, and are not shown. The relatively small number of eddies allow effects of individual eddies on shelf’s currents and sea-level to be more clearly identified in the simulation. Since 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 7-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 off Chesapeake Bay to eastern Long Island (Fig. 9b). 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 is gentler from the shelf between Chesapeake and Delaware bays, where linear regression gives ASPG  1.3×10-8 (Fig. 9b). This may be compared with the ASPGGS = 6×10-8 estimated from equation (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 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 (Figs.10a,b). The ring center locates south of the 38N. 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 Bay 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’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 locates north of 38N. 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 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 (day 0, 360, 720 etc). 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.
CLSW transport

The CLSW transport is fixed at the northeastern corner of the model domain (~55oW, 50oN). However, because of other unsteady forcing (e.g. wind and Gulf Stream), the shelf and slope current that is the southwestward extension of the CLSW inflow is time-dependent (Fig.7e). For convenience we refer to this also as the CLSW transport; it is calculated off the southern coast of Nova Scotia (near 62oW; see fig.2) from coast to the 1000 m isobath. By this definition, the variation of CLSW is purely driven by unsteady forcing confined entirely within the NWAOM domain (west of 55oW); it does not reflect any outflow variation from the Labrador Sea. 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 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 (c.f. Csanady and Hamilton, 1988). Temperature and salinity anomalies over the MAB shelf (and slope) also correlate well with the CLSW transport (not shown). Colder and fresher shelf waters correspond to stronger southwestward transport.

There is also a strong correlation between the CLSW transport and Gulf Stream’s path-shifts. Stronger southwestward transport generally coincides with southward shift of the Gulf Stream.

The correlations in both the seasonal and inter-annual time scales between CLSW transport and ASPG are low (Table 2), so that CLSW 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 reaches its maximum in spring due to snow melting and precipitation (Fig. 7f). From table 2, 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.





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