T jpo, 2011, in press he origin of along-shelf pressure gradient in the Middle Atlantic Bight

The NWAOM uses 25 vertical sigma levels and horizontal grid sizes   8~12 km. The World Ocean Atlas data (“climatology”) from NODC (http://www.nodc.noaa.gov/OC5/WOA05/pr_woa05.html) is used for initial condition as well as boundary condition along the eastern open boundary at 55^oW. Across 55W, a steady transport combined with radiation using also the geostrophically-balanced surface elevation (Oey and Chen, 1992a) specifies the Gulf Stream exiting near the Grand Banks south of Newfoundland, with a magnitude of 93 Sv 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 changed in experiments below) as the northern portion of this “North Recirculation gyre” with a jet shape, identified by Csanady and Hamilton (1988; their Fig.20b) as the “offshoot of the Labrador Current” that “turns the other way and intrudes into the Slope Sea”. The CLSW also contains freshwater transport (FWT) which is estimated as FWT = u[1-S/S_Ref] dzdy, where the y-integral is from offshore where the water depth H = 1000 m to coast and the z-integral is from bottom to surface, and S_Ref = 35 psu is the maximum salinity at the offshore and bottom location in the cross-section. We then obtain an FWT  0.16 Sv per 1 Sv of CLSW volume transport. In addition to these steady transports, a combination of flow-relaxation, radiation and advection schemes (Oey and Chen, 1992a,b) are used to also specify monthly climatological (potential) temperature (T) and salinity (S) and OSU M₂ tide at 55^oW. 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 restored to annual-mean climatological values with a time scale of 600 days; this weak restoring does not impede short-period mesoscale variability. The NWAOM has been used for research primarily in the Gulf of Mexico where we have also extensively compared the results against observations both in the surface and subsurface (Oey and Lee, 2002; Ezer et al. 2003; Wang et al. 2003; Fan et al. 2004; Oey et al. 2005a,b, 2006, 2007; Lin et al. 2007; Yin and Oey, 2007; Oey, 2008; Wang and Oey, 2008; Mellor et al. 2008; Oey et al. 2009; Chang and Oey, 2010a,b).

The NWAOM is first run for 15 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):

C_d 10³ = 1.2, |u_a|  11 m s^-1;

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

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

where |u_a| is the wind speed.¹ According to this formula, C_d is constant at low winds, linearly increases for moderate winds, reaches a broad maximum for hurricane-force winds, |u_a|  30~50 m s^-1, and then decreases slightly for extreme winds. It is necessary to use a C_d formula that accounts for high winds since within the NWAOM domain, the study period (1993-2008) includes a few hurricanes. Donelan et al. (2004) suggest that the C_d-leveling at high wind may be caused by flow separation from steep waves. Moon et al. (2004) found that C_d decreases for younger waves that predominate in hurricane-forced wave fields. Bye and Jenkins (2006) attribute the broad C_d-maximum to the effect of spray, which flattens the sea surface by transferring energy to longer wavelengths.

Daily discharges from 25 major sources in the MAB (and also from 33 sources in the Gulf of Mexico) are specified. These are specified as point sources at the “heads” of major bays or rivers using the method described in Oey (1996). Although broad bathymetric outlines and dimensions of bays and rivers are included (Fig.2), detailed estuarine circulation within them is not of interest for the purpose of this work. Their function is to allow a gradual transition of brackish waters onto the shelves. In other words, instead of inputting fresh river waters directly at the coast, they are allowed to mix (by tides and winds) with saline 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 forces the model Gulf Stream to separate at Cape Hatteras (Mellor and Ezer, 1991; Ezer and Mellor, 1994a). The (mean) Gulf Stream tends to separate too far to the north for a CLSW inflow below this minimum. It is convenient to non-dimensionalize the CLSW by this “critical” transport of 1.5 Sv, which we will refer to as “1UA” or UA=UA_critical=1. A CLSW transport of 4.5 Sv (i.e. 3UA or UA=3) is used, and this value will be adjusted in various experiments. The 3UA value may be compared with Csanady and Hamilton’s (1988) estimate of approximately 4 Sv for the CLSW transport.

The data-assimilated experiment (Ex.DA; Table 1) consists of all the forcing and specifications described above; additionally, the AVISO SSH anomaly data is assimilated into the model. 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 which is simple and 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 over the slope and shelves where topography is shallower than 1000 m. The Ex.DA simulation may therefore be viewed as a shelf model with shelfbreak “open-boundary conditions” calculated through data assimilation to account for the effects of the deep sea: the Gulf Stream, rings and the Slope Sea gyre. On the shelves where ASPG is calculated, the simulated fields satisfy model’s conservation equations.

2. 
   Results
   

Figure 3b plots the mean SSH along the 50 m isobath. Sea surface generally slopes down from north (x = 730 km) to south (x = 0). The linear fits yield slopes ranging from ASPG  5.4×10^-8 (dashed line) between Chesapeake Bay (CHS) and Cape Cod (CC) in agreement with Lentz’s (2008a) estimate of 3.7×10^-8 based on long-term observations, to a larger ASPG  8.4×10^-8 (solid line) over a shorter distance between Delaware (DEL) and the eastern Long Island (ELS). The larger value is caused by local rivers especially by the Long Island Sound plume (note the slight dip in sea level from ELS to Cape Cod in Fig.3b), and is in better agreement with Scott and Csanady’s (1976) estimate  1.44×10^-7 off (the southern coast of) Long Island. There are also significant seasonal and 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, generally in winter, to 10^-7, generally in summer. Note that steric effect alone cannot account for these fluctuations, since its contribution to ASPG is negative, largest in winter (about -3.e-8). The amplitudes of these seasonal fluctuations also vary at inter-annual time scales: larger in some years (1994~1995 and 2003~2007) and smaller in others (1997~1999).

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 50m isobath) and perhaps also model’s resolution (xy10km). The zero-lag correlation between the along-shelf current and ASPG (plotted in Fig.5b) is = -0.69, above the 95% significance level of 0.31.

It is of interest to check that the above mean values for the model ASPG and alongshelf current are self-consistent. The ASPG is one of the driving force for the mean equatorward along-shelf current (Lentz, 2008a). The steady, linearized and depth-averaged along-shelf (x, positive poleward) momentum equation is:

_bx = ^ox  gH /x, (1)

where  is surface elevation, H is water depth, _bx and ^ox are the x-component kinematic bottom and wind stresses respectively. For ^ox  1.4×10^-5 m² s^-2 in MAB, Lentz (2008a) shows that the RHS of (1) is negative (ASPG overcomes wind stress, both are positive). Using the above value for the model mean ASPG, and parameterizing _bx as ru where from the model r  5×10^-4 m s^-1 is the linear bottom friction coefficient, then u is also negative (i.e. equatorward)  0.026 m s^-1 in agreement with the above model estimate based on Fig.5c.

2. 
   What drives the ASPG?
   

a. latitudinal shifts of the Gulf Stream;

b. wind stress and wind stress curl;

c. southwestward propagating warm-core rings;

d. CLSW transport, and

e. river discharge.

We first examine process(es) responsible for the mean ASPG; this is then followed by an examination of the cause(s) for the seasonal and inter-annual variability of ASPG.
Mean ASPG:

To identify the importance of various mechanisms, we conduct free-running experiments without data-assimilation (Table 1)², and systematically alter the forcing. Gulf Stream is included in all but the last experiment in Table 1. Although in Ex.DA we do not assimilate over slope and shelves where topography is shallower than 1000 m, it is inappropriate to use the data-assimilated solution to infer dynamics that involves wind, Labrador Sea transport and Gulf Stream and its eddies, all of which should interact freely with the shelf response that gives rise to ASPG. The free-running experiments include: a simulation forced by the same forcing as Ex. DA (except with no data assimilation; Ex. RivLab3Wind); a simulation forced by wind (Ex.Wind); a simulation forced by river and 3UA CLSW transport (Ex. RivLab3); a simulation forced by 1.5UA CLSW transport (Ex.Lab1.5); a simulation forced by river and 1UA CLSW transport (Ex.RivLab1); and a simulation forced by 1UA CLSW transport (Ex.Lab1). Finally, a simulation forced by river only (Ex.Riv; in particular, without the Gulf Stream), is also included. For each experiment, we compute the mean ASPG (Fig.6) as the slope of the linear best-fit of the corresponding mean SSH along the 50 m isobath between Delaware (DEL) and eastern Long Island (ELS; as in Fig.3b, solid line).

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

ASPG×10⁸ = RIV + (7×UA+1.3)×H_v(UAUA_critical)  WIND  GS (2)

where terms on the RHS represent the ASPG-contributions from various processes: RIV=2 is the contribution from rivers (=0 for no rivers); UA_critical=1 is the non-dimensionalized critical CLSW transport (described previously); “H_v” is the Heaviside (step) function H_v(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). 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. 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 ASPG_wind = 10^-8. The Gulf Stream’s influence is then obtained from Ex.Wind, and has a much larger effect on the poleward set-down of sea-level: ~6 times larger than the wind, ASPG_GS = 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 ASPG_riv = 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). The contribution is idealized by a step function, so that for UAcrit and GS0, it is assumed that the Gulf Stream dominates. It is interesting that, from Ex.Lab1, the critical CLSW transport of 1.5 Sv (i.e. UA =1) gives an ASPG (=2.3×10^-8) that is nearly equal to the ASPG-contribution from rivers (=2.1×10^-8). We also note that the CLSW transport is dynamically linked to the Gulf Stream in forcing the Slope Sea circulation (Csanady and Hamilton, 1988). This can be seen by expressing the second term on the RHS of (2) as (7×UA4.7+GS)×H(UAUA_critical), 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.

It is interesting to compare Ex.RivLab3Wind, for which APSG=1.7×10^-7, with its assimilated counterpart Ex.DA which reduces APSG (=8.4×10^-8) to a value closer to that observed (see section 4). Without assimilation, the CLSW transport of 3×1.5Sv (i.e. UA=3) is too strong, and the corresponding Gulf Stream tends to separate south of Cape Hatteras (not shown). The reason is because the model’s Gulf Stream is too weak and produces too few warm-core rings when compared with the assimilated experiment. Stronger Gulf Stream and warm rings both contribute to negative ASPG (see below).
Seasonal & inter-annual variability of ASPG:

We now examine the seasonal and inter-annual variations of ASPG (Fig.3c & Fig.4b) to aforementioned five mechanisms. Note that the mechanisms are not necessarily independent of each other. 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. The time series are plotted in Figure 7. Here, the ASPG (fig.3c) and CLSW are from Ex.DA, while the other time series are from observations. The CLSW is calculated off the southern coast of Nova Scotia (near 60^oW; see fig.2) from coast to the 1000 m isobath. The CLSW is therefore purely driven by unsteady forcing confined entirely within the model domain (west of 55^oW); it does not reflect any outflow variation from the Labrador Sea transport, which is kept fixed at the northeastern corner of the model domain (~55^oW, 50^oN). Since assimilation is nil for shelf region shallower than 1000m, the ASPG and CLSW reflect dynamical responses to deep-sea, observed forcing.

The Gulf Stream shifts northward in summer~fall, and southward in winter~spring, and the path also fluctuates at 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. In the northern MAB, the slope currents appear to strengthen southwestward when the Gulf Stream shifts southward in winter~spring, but are weak or even reversed in summer~fall when the Gulf Stream shifts northward (Dong and Kelly, 2003; Peña-Molino and Joyce, 2008). Bane et al. (1988) observed currents on the southern MAB slope off Delaware that appear to have the opposite response: stronger southwestward when the Gulf Stream shifts northward, and vice versa.

Figure 7b shows that, at seasonal time scales, the zonally averaged GSS (relative to the 16-year, 1993-2008, mean Gulf Stream’s position) is southward in winter-spring, and northward in summer-fall, with values of 0.4⁰ latitude (Fig. 7b). The maximum lagged correlation between the (seasonal) ASPG (Fig. 7a) and GSS is R  0.74 with a 4-month lag (ASPG lags GSS, Table 2). Figure 7b shows that the Gulf Stream retreats southward from fall when the current is at its most northward position to spring when it is most southward. The ASPG therefore generally peaks during the time of the most rapid retreat, 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). In the southern portion of the MAB (off Chesapeake Bay), this strong _GS/t (<0) is accompanied by a correspondingly strong off-shelfbreak flow related to the JEBAR term in the integrated vorticity balance (see equation 3 below; figure not shown). By continuity, this winter-time strong outflux is accompanied by an increased, equatorward along-shelf flow, so that the corresponding current (u_shelf < 0) is also strong in winter, and is (approximately) balanced by the ASPG according to ru_shelf  gH_shelf/x. That u_shelf is generally strongest (equatorward) is seen in Fig.5c. Therefore, _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-most shift in fall.

At the inter-annual time scales, GSS and ASPG are not significantly correlated.

The 16-year 3-monthly mean wind stress curl is calculated over the Northwest Atlantic westward from 60^oW 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. On the other hand, wind stress curl is negatively correlated with both GSS (R0.65 at zero-lag, i.e. Gulf Stream shifts south in winter) and CLSW (R0.81, CLSW lags wind stress curl by 1 month, and strengthens southwestward as wind stress curl increases). Interestingly, CLSW is positively correlated with GSS (R0.77) and lags it by 1 month.⁴ The CLSW then appears not to influence the Gulf Stream at the seasonal time scale. The most likely explanation is that the wind is locked to the Gulf Stream especially in winter (Chelton et al. 2004; Minobe et al. 2008). The CLSW is driven by the wind stress curl (Csanady and Hamilton, 1988) and lags it and therefore also GSS by 1 month.

Large northward meanders of the Gulf Stream regularly break off as warm core rings. These rings propagate southwestward in the slope water between the continental shelf break and the Gulf Stream until they are either absorbed by another meander or are forced to coalesce with the Gulf Stream off Cape Hatteras. Approximately 10 rings per year either form in or propagate into the region west of 60^oW (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 density north of the Gulf Stream’s monthly mean path from AVISO geostrophic current (hereafter, N-EKE). The EKE density is defined as monthly-averaged EKE divided by the number of points with SSH anomaly (SSHA) >0 normally associated with warm eddies. Region north of the Gulf Stream is chosen in order to focus on warm-core rings only, as these are ones that give rise to ASPG fluctuations (see below). The use of the monthly path (instead of a 16-year mean) eliminates fluctuations associated with shifts in the Gulf Stream’s axis. The presence of warm-core rings was also checked by visually inspecting the satellite data. Time-series of N-EKE shows larger values from spring through early summer than in fall and winter (Fig. 8a,b).⁵ The ASPG and N-EKE are significantly correlated (R=-0.57) with ASPG lagging N-EKE by approximately 3 months (Table 2). Thus ASPG reaches a minimum in summer~fall after the N-EKE peaks in spring~summer (Fig.7a,d). Physically, ring-production peaks in spring~summer. These rings propagate southwestward. At speeds of approximately 6 km day^-1 they arrive over the slope north of Cape Hatteras in approximately 3 months. The speed agrees with those of observed warm core rings, typically 5.6 km day^-1 to 6.8 km day^-1 (Glenn et al., 1990). We show below that the arrival of a ring produces high SSH over the shelf north of Cape Hatteras, and the high SSH in turn induces a negative ASPG anomaly.

The N-EKE also correlates with GSS (R=-0.41) with GSS leading N-EKE by about one month (Table 2). Table 2 also shows that the N-EKE/GSS correlation and lag are consistent with how each of N-EKE and GSS separately relates to ASPG. The influence of the Gulf Stream path on ASPG is therefore partly because of warm-core rings. Finally, the N-EKE lags wind stress curl by one month with R=0.53.

At inter-annual time scales, N-EKE is positively correlated with ASPG (R=0.4, zero lag). The sign is opposite from the corresponding correlation at the seasonal time scales (R=-0.57). The reason is because at the seasonal period, the N-EKE has a clear spring ~ summer peak described above and, as we shall see below, the APSG then becomes negative because of arrivals of rings near Cape Hatteras. At long (inter-annual) time scales, N-EKE reflects mostly the contribution from eddies that are further east and north, away from Cape Hatteras, near their generation locations as well as when they are propagating. These eddies tend to produce a shelf’s sea-surface that slopes down towards Cape Hatteras (i.e. ASPG>0).

At the inter-annual time scales, Table 2 shows also a small but significant correlation between N-EKE and wind stress curl (R=-0.3). This result is related to NAO (North Atlantic Oscillation). We find that (c.f. Dong and Kelly, 2003) during a positive (negative) NAO, the wind pattern shifts north (south), producing a more negative (positive) wind stress curl (from 35N to 42N). The wind stress curl (Fig. 7c) and NAO index (not shown) is significantly correlated at -0.4. Our result then agrees with Chaudhuri et al. (2009), who show that periods of increased number of warm-core rings (assuming that rings give rise to N-EKE) coincide with positive phases of NAO, and vice versa.

To examine this mechanism, an idealized experiment of shelf’s sea-level and current responses to arrivals of warm-core rings along the MAB shelf break and slope was conducted. The simulation has the same domain and topography as the NWAOM, but all lateral boundaries are closed. The ocean is initially at rest with a density profile that varies in the vertical only, given by the basin-average of the annual-mean climatology. 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 (62.5^oW, 40^oN). 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 rate of injection, give similar results, and are not shown. The relatively small number of eddies (compared to observation) allow effects of individual eddies on 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 8-year mean SSH. Large and positive SSH from northeast to southwest over the Slope Sea indicates the path of the southwestward propagation of warm-core rings. Maximum SSH is seen near the continental shelf break north of Cape Hatters, where warm-core rings tend to be trapped. The mean SSH slopes down northward from Cape Hatteras and off Chesapeake Bay to eastern Long Island (Fig. 9b). The SSH-slope is steep for the first 200 km alongshelf north of Cape Hatteras because of the large influence of rings there; the slope then is gentler from the shelf between Delaware bay and Long Island, where linear regression gives ASPG  1.3×10^-8 (Fig. 9b). This may be compared with the ASPG_GS = 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; the ring center is nearer Cape Hatteras, south of 38N (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 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 is north of 38N, farther away from Cape Hatteras. 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).

To examine how effects of warm-core rings penetrate onto the shelf, we analyze each term of the depth-averaged vorticity equation derived from the curl of the depth-averaged momentum equations [Oey et al. 2010 and references therein]:

ζ/t+(HU)•(f/H)=k.[(χ)×(1/H)]+×[(τ⁰-τ_b)/H]-×(A/H) (3)

whereζis the curl of the depth-averaged velocity U, H is local water depth, k is the z-unit vector, χ= ∫⁰_-Hzbdz, b=gρ/ρ₀, τ⁰ and τ_b are the surface (wind) and bottom stress vectors, respectively, and A lumps both horizontal advection and diffusion vectors. The second term on the LHS of Equation 3 (hereafter CPVF) represents the horizontal advection of the geostrophic potential vorticity f/H. The first term on the RHS is the JEBAR term, which is nil if isopycnals are parallel to isobaths.

For slowly-evolving flows, the ζ/t in (3) is small compared to the cross-isobath flux term CPVF which is then determined by the ageostrophic terms on the RHS, and indicates onshore flux if positive and offshore if negative. Our goal is to determine which (if any) of these ageostrophic terms dominate and why, and how ASPG is then accordingly changed. A succinct way is to compute the weighted composites of each of the terms in (3) according to positive and negative phases of ASPG-anomaly (i.e. fig.9c):

ASPG⁺(v) = ⁺(v_nw_n)/⁺w_n, (4)

where the subscript “n” denotes time, v is each term of (3), w is ASPG-anomaly (serving as ‘weights’), and ⁺ means summing over the positive phase of ASPG-anomaly. A similar formula is used for ASPG^- using ^-. Formula (4) gives a better composite than straight averaging since it reduces the influences of values of “v_n” near small “w_n” with potentially large uncertainty [Chang and Oey, 2011: the Philippines-Taiwan Oscillation, submitted manuscript].

Figure 11 plots the dominant terms CPVF and JEBAR together with the corresponding composites of SSH and surface velocity; note that the anomalies are plotted and –JEBAR is plotted so that its cancellation with CPVF may be seen. Other vorticity-balance terms in equation (3) are not shown; in general, they are one order of magnitude smaller compared to either CPVF or JEBAR. It is clear that negative ASPG^- (fig.11 right; for which fig.10a,b at day1200 is a member of the composite) is induced by rings that are near Cape Hatteras; the SSH then shows an anticyclonic (warm) anomaly centered at approximately (74^oW,37^oN) off Chesapeake Bay flanked by cyclonic (cold) anomalies to the north (off New Jersey) and south (off Cape Hatteras) (fig.11b). It is readily shown that χ is higher in a warm anomaly so that, south of the anticyclone, χ points north/northeastward and JEBAR= k.[(χ)×(H^-1)] CPVF>0 (i.e. onshore flux), while north of the anticyclone, χ points west/southwestward and JEBARCPVF<0 (i.e. offshore flux).⁶ The resulting shelfward convergence and divergence tend to produce a northward sea-level set-down. A reversed situation applies for positive ASPG⁺ (fig.11 left; for which fig.10c,d at day1610 is a member of the composite). The resulting depth-averaged velocity across the 200m-isobath has a typical magnitude of  0.01 m s^-1, which is sufficient to produce the necessary convergence/divergence over the outer shelf to induce the ASPG anomalies. We conclude that for rings brushing against the outer MAB continental shelf and slope, the along-isobath density gradients result in JEBAR that becomes the dominant ageostrophic term accounting for the cross-isobath fluxes.

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 (62.5^oW, 40^oN) 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.

The mean CLSW transport 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) correlate well with the CLSW transport: colder and fresher shelf waters correspond to stronger southwestward transport (not shown).

The correlations in both the seasonal and 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

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). The correlation between river discharge and the ASPG is insignificant at the 95% significance level: (correlation, significance) = (0.36, 0.36) (though it is above the 90% significant level = 0.3), indicating insignificant influences of rivers on the seasonal and inter-annual variability of ASPG compared to those due to the N-EKE and GS path variations.

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