## 1. Introduction

In the Middle Atlantic Bight (MAB), a persistent shelfbreak front near the 200-m isobath (Fig. 1) separates cooler, fresher continental shelf waters from the warmer, saltier waters of the slope sea (e.g., Wright and Parker 1976; Houghton et al. 1988; Linder and Gawarkiewicz 1998), which lies between the continental shelf and the Gulf Stream (Csanady and Hamilton 1988). The shelfbreak front supports a surface-intensified equatorward jet along the shelf break (Fratantoni et al. 2001), and secondary circulation at the front leads to upwelling and increased primary production (Marra et al. 1990), which ultimately support active commercial fisheries (Orphanides and Magnusson 2007).

Despite numerous observational, numerical, and theoretical studies over the past few decades, the inherent small-scale, short-period variability in the vicinity of the MAB shelf break has made a complete understanding of the region elusive. Quantification of the scales of variability in the region is a critical step so that observational campaigns can be designed to resolve the important features and processes. Gawarkiewicz et al. (2004) and Lee and Brink (2010) used SeaSoar observations within the MAB shelfbreak front and over the southern flank of Georges Bank, respectively, to show that the *e*-folding scales for spatial correlations of temperature and salinity are *O*(10 km) in both the alongshelf and cross-shelf directions, while the *e*-folding scales for temporal correlations are *O*(1 day); Gawarkiewicz et al. (2004) also found a shelfbreak frontal meander wavelength of 40 km. Chen and He (2010) found similar spatial decorrelation scales in a numerical hindcast model. Using sea surface temperature (SST) and ocean color observations obtained from satellite imagery with 1.25-km resolution, He et al. (2010) found alongshelf *e*-folding scales of 40–45 km and cross-shelf *e*-folding scales of 19–25 km over the shelfbreak region between Cape Cod and the Del-Mar-Va Peninsula. While these previous studies have focused on the MAB shelf break, horizontal variability farther offshore in the slope sea has not been analyzed before.

Here we use finescale observations (with horizontal resolution of a few kilometers or better) collected by autonomous underwater gliders (Rudnick et al. 2004) to examine horizontal spatial scales near the MAB shelf break and over the continental rise. Our results for the shelf break confirm prior results from other observing platforms, while our results for the slope sea are new. Section 2 presents the glider observations over the MAB shelf break and continental rise; section 3 presents a structure function analysis of the horizontal variability; and section 4 summarizes the results and implications.

## 2. Finescale glider observations

Two Spray gliders (Sherman et al. 2001) collected observations over the MAB shelf break and continental rise (Fig. 1). In March–April 2006, a glider completed one alongshelf transect in the slope sea east of Georges Bank and a second alongshelf transect near the Great South Channel (Fig. 1, dark blue dots); the eastern transect was always at least 50 km offshore of the shelf break while the western transect was 12–45 km from the 200-m isobath. Between these two transects, the glider passed around a large Gulf Stream warm core ring (Fig. 1, light blue dots) that is discussed by Cenedese et al. (2012, manuscript submitted to *J. Phys. Oceanogr.*). During July–October 2007, a second glider completed a series of 16 cross-shelf transects between about 39.0° and 40.2°N over the shelf break and continental rise south of Cape Cod, Massachusetts (Fig. 1, red dots). The eastern and western alongshelf transects were occupied over 8 and 11 days, respectively; cross-shelf transects were completed in an average of 6.6 days. The survey region in 2007 roughly corresponds to the extended domain of the upcoming Ocean Observatories Initiative (OOI) Pioneer Array (Fig. 1, dashed orange box).

The gliders profiled from the surface to 500–1000 m in deep water or to within a few meters of the bottom over the shelf. Horizontal resolution between profiles varied with the depth of the profiles (e.g., Fig. 2c); profiles to 1000 m were separated by about 6 km, profiles to 500 m by about 3 km, and shallow profiles over the continental shelf by less than 1 km. Profiles of conservative temperature (Θ, essentially equal to potential temperature; Intergovernmental Oceanographic Commission 2010), absolute salinity (*S _{A}*), and potential density were obtained by applying standard algorithms (Intergovernmental Oceanographic Commission 2010) to measurements from the pumped CTD system on the gliders. Profiles were binned to a common vertical coordinate with 10-m resolution and subsequently interpolated to isopycnal levels. The gliders measured vertically averaged horizontal ocean velocity, and cross-track geostrophic currents referenced to these vertically averaged currents were estimated as in Todd et al. (2011) using a 30-km Gaussian scale.

Observations from the two alongshelf transects in 2006 and the longest cross-shelf transect in 2007 are shown in Fig. 2. The two alongshelf transects offshore of the shelf break (Figs. 2a,b,d,e,g,h,j,k) show a weakly stratified layer of cool, fresh continental shelf water roughly 50 m thick overlying a warmer, saltier layer of slope water down to about 200 m, typical of early spring structure in the slope sea (cf. Zhang et al. 2011, their Fig. 3). A cross-shelf transect between 39° and 41°N in late October 2007 (Figs. 2c,f,i,l) shows the transition from cool, fresh waters on the shoreward side of the shelfbreak front to warmer, saltier waters in the slope sea. The cross-shelf transect clearly shows the westward-flowing shelfbreak jet with speeds as large as 0.55 m s^{−1} and an entrained filament of saltier slope water just north of 40°N. Along-isopycnal salinity (i.e., spice) on surfaces deeper than the 27.0 kg m^{−3} isopycnal has little horizontal variability indicating little water mass variability below the depth of the shelf break. Above the 27.0 kg m^{−3} isopycnal, a large cross-shelf spice gradient indicates the partially density-compensated transition from shelf to slope waters across the shelfbreak front.

The mean cross-shelf structure during July–October 2007 (Fig. 3) smooths over transect-to-transect variability to show typical features of the shelfbreak front and slope sea in summer. To construct the mean, we simply average the observations into latitude bins since the isobaths are oriented primarily east–west in the area surveyed in 2007 (Fig. 1); we use 5-km bins over the continental shelf and 20-km bins over the continental rise since the horizontal spacing between profiles is smaller over the shelf. To calculate mean zonal geostrophic velocity, we first project observations from each transect onto a meridional line through the observations, then calculate zonal geostrophic velocity referenced to vertically averaged zonal velocity for each transect by objective mapping (Todd et al. 2011), and finally average the transects in latitude bins.

In the summer 2007 mean, the shelfbreak front is most evident in salinity (Fig. 3b) since warming of surface waters throughout the region in summer obscures the thermal signature of the front (Linder and Gawarkiewicz 1998; Zhang et al. 2011). A layer of cooler water over the shelf, referred to as the “cold pool” (Ketchum and Corwin 1964; Beardsley and Flagg 1976), extends beyond the shelf break at depths of 50–100 m. Along isopycnal surfaces (Fig. 3c), the southward transition from cooler, fresher shelf waters to warmer, saltier slope waters is the dominant signal above 27.0 kg m^{−3}; below 27.0 kg m^{−3}, a single water mass with high salinity, the upper slope pycnostad (Wright and Parker 1976; Csanady and Hamilton 1988), is found. Mean zonal velocities (Fig. 3d) capture the offshore edge of the westward-flowing shelfbreak jet, a weak eastward flow just offshore of the shelf break, and a deep westward flow adjacent to the slope that may be the upper portion of the deep western boundary current (see Toole et al. 2011).

While the mean cross-shelf structure highlights the water mass contrast across the shelfbreak front, investigation of temperature–salinity diagrams (Fig. 4) reveals extensive cross-frontal exchange shallower than about 27.0 kg m^{−3}. Over the continental shelf (water depths less than 150 m; Fig. 4b, black points) during summer–fall 2007, observations are clustered along the low-salinity and low-temperature edges of the deployment-wide Θ-*S _{A}* distribution (Figs. 4b,c, gray points) that are indicative of shelf water. Over the continental rise (water depths greater than 2000 m; Fig. 4c, black points), observations are clustered along the warm, salty edges of the deployment-wide Θ–

*S*distribution that are characteristic of slope waters. However, we also find many observations of warm, salty slope water over the continental shelf and cool, fresh shelf water over the continental rise (Figs. 4b,c) suggesting interleaving of shelf and slope water masses from opposite sides of the shelfbreak front. Observations from the two alongshelf transects during spring 2006 (Fig. 4a) show along-isopycnal variability above 27.0 kg m

_{A}^{−3}within 50 km of the shelf break (gray points), but not further offshore (black points); interleaving of shelf and slope waters is constrained to within

*O*(50 km) of the shelf break.

## 3. Horizontal spatial scales

*e*-folding scales and dominant wavelengths for a given variable, but the calculation of autocorrelations strongly depends upon both the mean and variance, which themselves depend on spatial and temporal scales larger than those resolved by our observations. To work around this limitation, we instead consider the structure function,

*S*(

_{q}*r*), of a variable

*q*(

*x*) (Kolmogorov 1941; Davis et al. 2008), which is defined asthe mean square difference between observations separated by a distance

*r*, where 〈·〉

_{x}denotes averaging over all

*x*and, implicitly, time. The structure function does not have an explicit dependence on either the mean or variance of the variable

*q*(

*x*). The structure function is related to the autocorrelation

*C*(

_{q}*r*) bywhere 〈

*q*′

^{2}〉 is the variance of

*q*(

*x*). Thus, the structure function is an unscaled version of the autocorrelation with its asymptotic behavior reversed. The structure function starts at zero and approaches twice the variance at large separations, whereas the autocorrelation starts at unity and approaches zero at large separations; local minima in the structure function occur at the same separation as local maxima in the autocorrelation and vice versa. We consider structure functions of Θ and

*S*on depth surfaces and

_{A}*S*along isopycnals (i.e., spice).

_{A}*r*aswhere Δ

**q**is the

*N*-element column vector of differences between pairs of observations with separations between

*δ*= 10 km being the width of the separation bins used to calculate

*S*(

_{q}*r*). The weight matrix

*k*th diagonal element given by

*x*is the distance from the midpoint of the

_{k}*k*th pair of observations to the next nearest midpoint of a similarly separated pair of observations. Structure functions are only calculated for separation bins having at least three pairs of observations contributing to the bin average (

*N*≥ 3).

We calculate cross-shelf structure functions from the cross-shelf transects in summer–fall 2007 and alongshelf structure functions from the two alongshelf transects in March–April 2006. Since the structure function was originally conceived to analyze homogeneous turbulence (Kolmogorov 1941), we must remove trends from the observations before calculating the structure functions. For the cross-shelf structure functions, we subtract the cross-shelf mean over July–October 2007 (Fig. 3); for the alongshelf structure functions, we simply remove a linear trend from each transect. Cross-shelf structure functions are calculated for the entire latitudinal range (39.0°–40.2°N) and for subranges near the shelf break (39.5°–40.2°N) and in the slope sea (39.0°–39.5°N). Structure functions are averaged across depth ranges (0–50 or 100–200 m) or over densities between 25.0 and 27.0 kg m^{−3} (roughly corresponding to the upper 200 m, Figs. 2d–f); cross-shelf structure functions are additionally averaged across the 16 transects.

Suitable error estimation techniques for structure functions currently do not exist (Nichols-Pagel et al. 2008), but we conservatively estimate the number of degrees of freedom in our structure function estimates for a particular transect as the length of the transect divided by the spatial scale. We assume that individual cross-shelf transects are sufficiently separated in time and space to be considered independent, so we sum the number of degrees of freedom across transects to estimate the number of degrees of freedom for our cross-shelf structure functions. Cross-shelf structure functions have in excess of 20 degrees of freedom at all resolved separations and 150 or more degrees of freedom at the smallest separations; our cross-shelf structure functions are statistically reliable. Since they result from single transects, our alongshelf structure functions have fewer degrees of freedom. At the shortest separations, alongshelf structure functions have at least 10 degrees of freedom for all variables; at longer scales, the number of degrees of freedom for alongshelf structure functions is *O*(1) for all variables. Alongshelf structure functions are likely to be statistically reliable at short separations, but they must be interpreted with caution at longer separations. At longer separations, the finite horizontal speed of the glider (about 0.25 m s^{−1}) causes projection of temporal variability onto horizontal structure that further complicates the interpretation of horizontal variability (Rudnick and Cole 2011).

The magnitudes of structure functions calculated for different areas, depths, or density ranges are directly related to the relative amounts of variability in the respective locations. Mean square differences of Θ and *S _{A}* at a given separation are always larger in the upper 50 m (black lines in Figs. 5a–d) than at 100–200 m (gray lines in Figs. 5a–d). In most cases, mean square differences are also somewhat larger near the shelf break (triangles in Fig. 5) than over the entire cross-shelf range (circles) or in the slope sea alone (squares). Thus, the greatest variability in temperature and salinity is found in the uppermost water column in the immediate vicinity of the shelf break.

Structure functions of temperature and salinity along depth surfaces (Figs. 5a–d) show a transition to longer scales from the shelf break to the slope sea. To quantify horizontal scales, we perform a least squares fit of an exponential function to the structure functions; the exponential provides a better fit than a Gaussian. Table 1 gives the exponential (*e*-folding) scales for structure functions averaged over the upper 50 m of the water column; alongshelf structure functions are only fit for separations *r* less than 100 km to capture the initial behavior of the structure function and use the portion of the structure function with the greatest statistical reliability. Cross-shelf exponential scales near the shelf break are 12–13 km and alongshelf scales just offshore of the shelf break are 8–10 km; these scales compare favorably with the *O*(10 km) *e*-folding scales found using SeaSoar observations over the shelf break (Gawarkiewicz et al. 2004; Lee and Brink 2010) and are slightly smaller than the 20-km cross-shelf scale that He et al. (2010) found for SST in an *O*(100 km) wide band along the MAB shelf break. Cross-shelf structure functions calculated using the entire latitudinal range of observations from 2007 have *e*-folding scales roughly twice as long as in the shelfbreak region. With the exception of the cross-shelf scale for temperature, *e*-folding scales in the slope sea are larger still at approximately 30 km.

Exponential (*e*-folding) scales for least squares fits of an exponential function to selected structure functions shown in Fig. 5. Shelfbreak and slope sea subregions for cross-shelf scales are as defined in the text.

Alongshelf structure functions of temperature and salinity along depth surfaces (Figs. 5b,d) exhibit periodicity that is not apparent in the cross-shelf structure functions. For the western transect near the shelf break (triangles), the structure functions appear to have a wavelength of 40–50 km; this agrees well with the 40-km wavelength of a westward-propagating shelfbreak frontal meander reported by Gawarkiewicz et al. (2004) and with the alongshelf decorrelation scales of SST and sea surface color (He et al. 2010). Finding a 40–50-km wavelength at the location of this transect, which is tens of kilometers offshore of the mean axis of the shelfbreak jet (see Zhang et al. 2011, their Fig. 3), suggests that shelfbreak frontal meanders influence temperature and salinity structure well out into the slope sea. For the alongshelf structure functions of Θ and *S _{A}* from the eastern transect in the slope sea, we find an apparent periodicity with wavelength between 175 and 250 km that would again indicate an increase in dominant spatial scales away from the shelf break, but this result may be affected by the low statistical reliability of the structure functions at longer scales.

Structure functions of along-isopycnal salinity (i.e., spice; Figs. 5e,f) reveal further differences between variability near the shelf break and within the slope sea. Cross-shelf structure functions of spice averaged between 25.0 and 27.0 kg m^{−3} (Fig. 5e) closely resemble the structure functions of salinity on depth surfaces averaged over the upper 50 m (Fig. 5c, black); the slight reduction in magnitude of the along-isopycnal structure functions is to be expected since they are effectively averaged over the upper 200 m of the water column where waters with densities between 25.0 and 27.0 kg m^{−3} are found (Figs. 2 and 3). Since most of the cross-shelf horizontal variability in salinity is accounted for by along-isopycnal variability (i.e., spice variability), it follows that interleaving of shelf and slope water masses is the main source of cross-shelf variability; given the cross-shelf changes in water mass characteristics evident in individual transects (e.g., Fig. 2i) and the mean (Fig. 3c), it is reasonable to expect cross-shelf variability to be dominated by water mass changes. The structure function of along-isopycnal salinity from the western alongshelf transect near the shelf break (Fig. 5f, triangles) shows some similarities with the structure function calculated from observations on depth surfaces shallower than 50 m from the same transect (Fig. 5d, black triangles); the magnitudes of the structure functions are similar at separations less than 50 km, and both structure functions reach maxima around 20 km and have local minima near 35, 105, and 135 km. In contrast, the structure function of along-isopycnal salinity from the eastern transect that was farther from the shelf break shows virtually no variability along isopycnals at any alongshelf separation up to 300 km (Fig. 5f, squares). Near the shelf break, water mass variability due to meandering of the shelfbreak front and cross-frontal exchange contributes at least a portion of the alongshelf horizontal variability. Farther from the shelf break in the slope sea, alongshelf variability results from the projection of vertical movement of isopycnal surfaces onto the horizontal with little to no along-isopycnal variability.

Two pieces of evidence suggest that these results were not significantly impacted by projection of temporal variability onto spatial variability because of the relatively slow speed of the gliders (Rudnick and Cole 2011). First, the small *e*-folding scales found near the shelf break agree with prior results from more synoptic observations (Gawarkiewicz et al. 2004; Lee and Brink 2010; He et al. 2010). Second, structure functions of along-isopycnal salinity are nearly identical to those of salinity along depth surfaces at the smallest resolved scales, which would not occur if the slow speed of the gliders had resulted in substantial projection of temporal variability onto spatial structure (see Rudnick and Cole 2011).

## 4. Conclusions

Glider observations with fine horizontal resolution capture the along- and cross-shelf scales of variability in the Middle Atlantic Bight shelf break and slope sea regions. Horizontal spatial scales offshore of the MAB shelf break have not been examined previously. A structure function analysis shows that, in general, spatial scales increase offshore of the shelf break. Exponential scales for temperature and salinity are 8–13 km near the shelf break, where the shelfbreak front contributes significant variability, and increase to about 30 km over the continental rise. Just offshore of the shelf break, alongshelf structure functions exhibit periodic variability with a wavelength of 40–50 km, close to the alongshelf wavelength of shelfbreak frontal meanders (Gawarkiewicz et al. 2004). Farther out in the slope sea, our results suggest a dominant wavelength of 175–250 km, though the available observations barely resolve these scales. Comparison of structure functions calculated from observations at fixed depths to along-isopycnal structure functions shows that cross-shelf variability and alongshelf variability near the shelf break result primarily from interleaving of shelf and slope water masses from opposite sides of the shelfbreak front; farther offshore, alongshelf variability results from heaving of isopycnals. Future observational and numerical studies of the MAB shelf break and slope sea (e.g., the forthcoming OOI Pioneer Array) must resolve the small horizontal spatial scales that characterize variability in this ecologically and economically important region.

## Acknowledgments

We thank Ken Brink for helpful comments on the manuscript. Glider observations in March–April 2006 were supported by the National Science Foundation through Grant OCE-0220769. Glider observations in July–October 2007 were supported by a grant from Raytheon. RET was supported by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Cooperative Institute for the North Atlantic Region. GGG was supported by the National Science Foundation under Grant OCE-1129125.

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