• Austin, J. A., and S. J. Lentz, 1999: The relationship between synoptic weather systems and meteorological forcing on the North Carolina inner shelf. J. Geophys. Res.,104, 18 159–18 185.

  • Beardsley, R. C., J. Candela, R. Limeburner, W. R. Geyer, S. J. Lentz, B. M. Castro, D. Cacchione, and N. Carniero, 1995: The M2 tide on the Amazon Shelf. J. Geophys. Res.,100, 2283–2319.

  • Boicourt, W. C., 1981: Circulation in the Chesapeake Bay entrance:Estuary-shelf interactions. Proc. Chesapeake Bay Plume Study, NASA Conf. Publication 2188, 61–78. [Available from NASA, Scientific and Technical Information Branch, Washington, DC 20546.].

  • Butman, C. A., 1994: CoOP coastal ocean processes. Sea. Technol.,35, 44–49.

  • Chao, S. Y., 1990: Tidal modulation of estuarine plumes. J. Phys. Oceanogr.,20, 1115–1123.

  • Chapman, R. D., L. K. Shay, H. C. Graber, J. B. Edson, A. Karachintsev, C. L. Trump, and D. B. Ross, 1997: On the accuracy of HF radar surface current measurements: Intercomparisons with ship-based sensors. J. Geophys. Res.,102, 18737–18748.

  • Clarke, A. J., 1991: The dynamics of barotropic tides over the continental shelf and slope. Tidal Hydrodynamics, B. Parker, Ed., John Wiley and Sons, 79–108.

  • Cook, T. M., and L. K. Shay, 1998: Tidal variability observed with high frequency radar. Preprints, Second Conf. on Coastal Atmospheric and Oceanic Prediction and Processes, Phoenix, AZ, Amer. Meteor. Soc., 287–292.

  • Daifuku, P. R., and R. C. Beardsley, 1983: The K1 tide on the continental shelf from Nova Scotia to Cape Hatteras. J. Phys. Oceanogr.,13, 3–17.

  • Foreman, M. G. G., 1977: Manual for tidal currents analysis and prediction. Pacific Marine Science Report 78-6, Institute of Ocean Sciences, 57 pp. [Available from Institute of Ocean Sciences, P.O. Box 6000, Sidney, BC V8L 4B2, Canada.].

  • Garvine, R. W., 1987: Estuary plumes and fronts in shelf waters: A layer model. J. Phys. Oceanogr.,17, 1877–1896.

  • Godin, G., 1972: The Analysis of Tides. Liverpool University Press, 264 pp.

  • Goodrich, D. M., W. C. Boicourt, P. Hamilton, and D. W. Prichard, 1987: Wind-induced destratification in Cheasapeake Bay. J. Phys. Oceanogr.,17, 2232–2240.

  • Graber, H. C., B. K. Haus, R. D. Chapman, and L. K. Shay, 1997: HF radar comparisons with moored estimates of current speed and direction: Expected differences and implications. J. Geophys. Res.,102, 18 749–18 766.

  • Griffin, D. A., and K. R. Thompson, 1996: The adjoint method of data assimilation used operationally for shelf circulation. J. Geophys. Res.,101, 3457–3478.

  • Harrison, W., M. L. Brehmer, and R. B. Stone, 1964: Nearshore tidal and nontidal currents, Virginia Beach, Virginia. U.S. Army Corps of Engineers, Tech. Rep. No. 5, U.S. Army Coastal Engineering Research Center, Washington, DC, 20 pp. [Available from U.S. Army Coastal Engineering Research Center, 5201 Little Falls Road, Washington, DC 20016.].

  • Haus, B. K., H. C. Graber, L. K. Shay, S. Nikolic, and J. Martinez, 1998: Ocean surface current observations with HF Doppler radar during the Cope-1 experiment. RSMAS Tech. Report 95-010, University of Miami. Miami, FL, 104 pp.

  • Imasato, N., 1983: What is a tide-induced residual eddy? J. Phys. Oceanogr.,13, 1307–1317.

  • Kundu, P. K., 1976: Ekman veering observed near the ocean bottom. J. Phys. Oceanogr.,6, 238–242.

  • Lentz, S. J., M. Carr, and T. H. C. Herbers, 2001: Barotropic tides on the North Carolina Shelf. J. Phys. Oceanogr., in press.

  • Marks, F. D., L. K. Shay, and PDT-5, 1998: Landfalling tropical cyclones: Forecast problems and associated research opportunities. Bull Amer. Meteor. Soc.,79, 305–323.

  • Marmorino, G., L. K. Shay, B. K. Haus, R. A. Handler, H. C. Graber, and M. P. Horne, 1999: An EOF analysis of HF Doppler radar current measurements of the Chesapeake Bay outflow. Contin. Shelf Res.,19, 271–288.

  • Miller, J. L., Z. Hallock, L. K. Shay, and J. Zaitzeff, 1998: Tidal and subtidal surface salinity advection in a coastal plume: Estimates from remotely sensed fields. Eos, Trans. Amer. Geophys. Union,79, 168.

  • Mooers, C. N. K., 1973: A technique for the cross-spectrum analysis of complex valued time series with emphasis on properties of polarized components and rotational invariants. Deep-Sea Res.,20, 1129–1141.

  • Munchow, A., and R. W. Garvine, 1993: Dynamical properties of a buoyancy-driven coastal current. J. Geophys. Res.,98, 20 063–20 077.

  • ——, A. K. Masse, and R. W. Garvine, 1992: Astronomical and nonlinear tidal currents in a coupled estuary shelf system. Contin. Shelf. Res.,12, 471–487.

  • Officer, C. B., 1976: Physical Oceanography of Estuaries and Associated Coastal Waters. Wiley and Sons, 465 pp.

  • Otnes, R. K., and L. Enochson, 1978: Applied Time Series Analysis. Vol. 1. Basic Techniques. Wiley and Sons., 449 pp.

  • Pietrafesa, L. J., J. O. Blanton, J. D. Wang, V. Kourafalou, T. N. Lee, and K. A. Bush, 1985: The tidal regime in the South Atlantic Bight. Oceanography of the Southeastern U.S. Continental Shelf, L. P. Atkinson, D. W. Menzel, and K. A. Bush, Eds., Amer. Geophys. Union, 63–76.

  • Prandle, D., 1982: The vertical structure of tidal currents. Geophys. Astrophys. Fluid Dyn.,22, 29–49.

  • Redfield, A. C., 1958: The influence of the continental shelf on the tides of the Atlantic Coast of the United States. J. Mar. Res.,17, 432–448.

  • Rennie, S. E., J. L. Largier, and S. J. Lentz, 1999: Observations of a pulsed buoyancy current downstream of Chesapeake Bay. J. Geophys. Res.,104, 18 227–18 240.

  • Rosenfeld, L. K., and R. C. Beardsley, 1987: Barotropic semidiurnal tidal currents off Northern California during the Coastal Ocean Dynamics Experiment (CODE). J. Geophys. Res.,92, 1721–1732.

  • Shay, L. K., H. C. Graber, D. B. Ross, and R. D. Chapman, 1995: Mesoscale ocean surface current structure detected by HF radar. J. Atmos. Oceanic Technol.,12, 881–900.

  • ——, T. N. Lee, E. J. Williams, H. C. Graber, and C. G. H. Rooth, 1998a: Effects of low frequency current variability on near-inertial submesoscale vortices. J. Geophys. Res.,103, 18 691–18 714.

  • ——, S. J. Lentz, H. C. Graber, and B. K. Haus, 1998b: Current structure variations detected by HF radar and vector measuring current meters. J. Atmos. Oceanic Technol.,15, 237–256.

  • Simpson, J. H., and J. R. Hunter, 1974: Fronts in the Irish Sea. Nature,250, 404–406.

  • Teague, C. C., J. F. Vesecky, P. E. Hansen, N. G. Schwepf, J. M. Daidu, R. G. Orstott, K. Fisher, and D. M. Fernandez, 1997: Initital observations of ocean current and current shears, wind direction using multifrequency HF radar. Proc. Int. Geoscience and Remote Sensing Symp., Vol. 4, Singapore, IEEE, 1808–1810.

  • Weller, R. A., and J. F. Price, 1988: Langmuir circulation within the oceanic mixed layer. Deep-Sea Res.,35, 711–747.

  • Wheless, G. H., and A. Valle-Levinson, 1996: A modeling study of tidally driven estuarine exchange through a narrow inlet on a sloping shelf. J. Geophys. Res.,101, 25 675–25 687.

  • Zimmerman, J. T. F., 1978: Topographic generation of residual circulation by oscillatory (tidal) currents. Geophys. Fluid Dyn.,11, 35–47.

  • View in gallery

    Experimental HF radar domain (dots) of Naval Research Laboratory (NRL) Chesapeake Bay Outfall Plume Experiment during Sep and Oct 1996. The NRL acoustic Doppler current profiler (ADCP) moorings, NOAA National Ocean Survey sea-level station along the Chesapeake Bay Tunnel Bridge (CBTB), and NOAA Coastal Marine Automated Network (NOAA–CMAN) Chesapeake Bay Lighthouse Tower (CHLV2) station are given relative to the HF radar domain. Master and Slave sites were located at Fort Story U.S. Army Base in Virginia Beach, Virginia, and the U.S. Naval Fleet Training Center Atlantic at Dam Neck, Virginia.

  • View in gallery

    Surface current maps from COPE-1 experiment at 1200 UTC: (a) YD 258 (14 Sep), (b) YD 264 (20 Sep), (c) YD 271 (27 Sep), (d) YD 272 (28 Sep), (e) YD 277 (3 Oct), and (f) YD 280 (6 Oct) in 1996. Note that the color bar represents the velocity scale for each panel.

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    Vector plots of rotated current profiles (340°T) observed at ADCP mooring A for the smoothed and subsampled currents every hour at selected depths.

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    Low-pass filtered (a) wind vector (m s−1) and (b) atmospheric pressure (mb) from the NOAA-CMAN Chesapeake Bay Lighthouse Tower during the COPE-1 deployment. The wind is rotated into an oceanographic context and relative to the orientation of the coastline (340°T).

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    Observed time series at mooring A from YD 261 (17 Sep) to YD 271 (27 Sep) 1996 during COPE-1 for the surface (solid) and 1.5 m (dotted) (a) along-shelf component (cm s−1), (b) cross-shelf component (cm s−1), (c) vertical current shear (×10−1 s−1) over a 1.5-m layer relative to the cross-shelf coordinate (70°T) and (d) one-half daily-averaged (36 points) magnitudes of the complex correlation coefficients (⩽1) and complex phase angles (°) listed above each bar.

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    Regression analyses of surface (ordinate) and subsurface (abscissa) currents (left panels) and histograms for the current differences (uou1.5, υoυ1.5) (right panels) at ADCP moorings A (upper panels: a, b) and A′ (lower panels: c, d) at 1.5 m (cm s−1) for cross-shelf (a, c) and along-shelf (b, d) components, respectively. Regression curves (solid) represent the best fit to the data with the biases and slopes given on the graphs. The histograms include differences of less than ±80 cm−1, and the 95% confidence limits are depicted by arrows. Note that υ and u represent along-shelf and cross-shelf components, respectively.

  • View in gallery

    Time series of (a) observed sea level heights, (b) reconstructed tidal heights based on the harmonic analysis of (a), and (c) the residual sea level heights (a − b) during the COPE-1 experiment from 15 Sep (YD 259) to 8 Oct (YD 282) 1996. The data were acquired at the NOAA NOS Chesapeake Bay Tunnel Bridge station.

  • View in gallery

    Comparison of the surface (solid) and depth-averaged (dashed) tidal current (upper panel) and contoured baroclinic tidal currents (lower panel) for (a) cross-shelf component and (b) along-shelf component (cm s−1) from ADCP A′ deployed in the COPE-1 experiment from YD 261 to YD 271 in 1996. The contour interval is 4 cm s−1 for the velocity profiles from 1.5 to 14.5 m subsampled at a 20-min sample interval.

  • View in gallery

    Tidal ellipses of the (a) K1, (b) O1, (c) M2, and (d) S2 constituents superposed on the magnitude of the tidal current amplitude (color) from the COPE-1 experimental data over the radar domain based on 19 days of continuous data.

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    Explained variance of the summation of the four tidal constituents depicted in Fig. 9 for the (a) cross-shelf and (b) along-shelf surface currents.

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    Surface M2 tidal currents from the COPE-1 experiment on YD 280 (5 Oct 96) at (a) 0000 UTC, (b) 0200 UTC, (c) 0420 UTC, (d) 0620 UTC, (e) 0820 UTC, and (f) 1040 UTC. The color bar depicts the magnitude of the tidal current.

  • View in gallery

    Magnitudes of the complex correlation coefficients (color) and phases (contoured) based upon 23 days of measurements in COPE-1 relative to cell 125 (dark triangle) in the strong tidal regime for (a) observed surface currents and (b) M2 tidal currents. The appropriate color bar is below each panel.

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    Normalized M2 tidal vorticity by the local Coriolis frequency at the same times in Fig. 11.

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    Mixing parameter S induced by the M2 tidal currents over the cycle in Fig. 12. Lower values of S imply less dissipation of the kinetic energy of the tidal currents near the mouth of the Chesapeake Bay.

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    Simulated ampltitudes and tidal ellipses from the adjoint model encompassing a large fraction of the HF radar grid.

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    Spatial differences between the simulated and observed M2 surface tidal currents for (a) cross-shelf and (b) along-shelf amplitudes, and (c) cross-shelf and (d) along-shelf phases. Amplitudes were contoured at 2 cm s−1 intervals and phases at 10° intervals. Spatial smoothing was done in the northeast corner of the domain where the surface current measurement was not as reliable.

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    Comparisons between observed (o) and modeled (m) surface current for the M2 constituent for (a) cross-shelf ampltitude and (b) phase, (c) along-shelf amplitude and (d) phase, (e) semi-major axis, and (f) orientation relative to 0°N. A total of 85 cells were used in the comparison to the simulated fields.

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The Strength of the M2 Tide at the Chesapeake Bay Mouth

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  • 1 Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida
  • | 2 Naval Research Laboratory, Division of Physical Oceanography, Stennis Science Center, Mississippi
  • | 3 Applied Marine Physics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida
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Abstract

As part of the Naval Research Laboratory and Office of Naval Research sponsored Physics of Coastal Remote Sensing Research Program, an experiment was conducted in September–October 1996 off Virginia Beach. Ocean surface currents were measured using the high-frequency (25.4 MHz) mode of the Ocean Surface Current Radar at 20-min intervals at a horizontal resolution of 1 km over an approximate 30 km × 44 km domain. Comparisons to subsurface current measurements at 1–2 m beneath the surface from two broadband acoustic Doppler current profilers (ADCP) revealed good agreement to the surface currents. Regression analyses indicated biases of 4 and −3 cm s−1 for cross-shelf and along-shelf currents, respectively, where slopes were O(1) with correlation coefficients of 0.8.

Nine months of sea level heights from the NOAA National Ocean Survey Chesapeake Bay Bridge Tunnel tidal station revealed an energetic M2 tidal component having an amplitude of 37.5 cm and a phase of 357°. The S2 tidal constituent had an amplitude of 7 cm and a phase of 49°. By contrast, the diurnal band (K1, O1) tidal constituents were considerably weaker with amplitudes of 1–5 cm. From 19 days of HF-derived surface currents, the M2 and S2 tidal current amplitudes had a maximum of about 50 and 8 cm s−1 at the Chesapeake Bay mouth, respectively. Explained variances associated with these four tidal current constituents were a maximum of 60% at the mouth and decreased southward. Analyses at the ADCP moorings indicated that the semidiurnal tidal currents were predominantly barotropic with cross-shelf and along-shelf currents of 18 and 10 cm s−1. Energetic semidiurnal tidal currents were highly correlated over the HF-radar domain, and the phase angles indicated a consistent anticyclonic veering of the M2 tidal current with along-shelf distance from the mouth. Normalized tidal current vorticities by the local Coriolis parameter (f), which represent a proxy for the Rossby number, were ±0.25f near the mouth and ±0.05f in the southern part of the domain for the M2 constituent. Simulations from a linear, barotropic model were highly correlated with observed M2 tidal currents at 85 points within the HF-radar domain, consistent with the premise of weakly nonlinear flows.

Corresponding author address: Dr. Lynn K. Shay, Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, 4600 Rickenbacker Causeway, Miami, FL 33149-1098.

Email: nick@erg.rsmas.miami.edu

Abstract

As part of the Naval Research Laboratory and Office of Naval Research sponsored Physics of Coastal Remote Sensing Research Program, an experiment was conducted in September–October 1996 off Virginia Beach. Ocean surface currents were measured using the high-frequency (25.4 MHz) mode of the Ocean Surface Current Radar at 20-min intervals at a horizontal resolution of 1 km over an approximate 30 km × 44 km domain. Comparisons to subsurface current measurements at 1–2 m beneath the surface from two broadband acoustic Doppler current profilers (ADCP) revealed good agreement to the surface currents. Regression analyses indicated biases of 4 and −3 cm s−1 for cross-shelf and along-shelf currents, respectively, where slopes were O(1) with correlation coefficients of 0.8.

Nine months of sea level heights from the NOAA National Ocean Survey Chesapeake Bay Bridge Tunnel tidal station revealed an energetic M2 tidal component having an amplitude of 37.5 cm and a phase of 357°. The S2 tidal constituent had an amplitude of 7 cm and a phase of 49°. By contrast, the diurnal band (K1, O1) tidal constituents were considerably weaker with amplitudes of 1–5 cm. From 19 days of HF-derived surface currents, the M2 and S2 tidal current amplitudes had a maximum of about 50 and 8 cm s−1 at the Chesapeake Bay mouth, respectively. Explained variances associated with these four tidal current constituents were a maximum of 60% at the mouth and decreased southward. Analyses at the ADCP moorings indicated that the semidiurnal tidal currents were predominantly barotropic with cross-shelf and along-shelf currents of 18 and 10 cm s−1. Energetic semidiurnal tidal currents were highly correlated over the HF-radar domain, and the phase angles indicated a consistent anticyclonic veering of the M2 tidal current with along-shelf distance from the mouth. Normalized tidal current vorticities by the local Coriolis parameter (f), which represent a proxy for the Rossby number, were ±0.25f near the mouth and ±0.05f in the southern part of the domain for the M2 constituent. Simulations from a linear, barotropic model were highly correlated with observed M2 tidal currents at 85 points within the HF-radar domain, consistent with the premise of weakly nonlinear flows.

Corresponding author address: Dr. Lynn K. Shay, Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, 4600 Rickenbacker Causeway, Miami, FL 33149-1098.

Email: nick@erg.rsmas.miami.edu

1. Introduction

The Chesapeake Bay system is surrounded by tributaries along both the eastern and western shores of Virginia that contribute to a freshwater influx into this broad and complex estuary (Officer 1976). In this regime, terrestial–atmospheric–estuarine interactions have a pronounced impact on the coastal oceanic circulation by modulating buoyancy fluxes within Chesapeake Bay (CB). The largest amount of freshwater influx occurs during the spring due to increased precipitation by winter storms over the Middle Atlantic Bight (MAB). In the spring transition period, restratification generally occurs within the estuary due to this higher freshwater volume entering CB from its tributaries. By contrast, autumn months usually have a lower freshwater influx because of prevailing drier atmospheric conditions. However, the region is susceptible to landfalling tropical cyclones and the ensuing severe weather with increased precipitation and flooding (Marks et al. 1998). This effect leads to a significant contrast in buoyant outflows between the shelf and estuarine water that may persist for long-time periods following storm passage. While CB is a partially mixed estuary, wind-induced mixing events during the autumn months tend to destratify the upper part of the water column inside CB (Goodrich et al. 1987). Thus, atmospheric forcing conditions not only play an important role in the salt balance in this estuarine system but modulate the freshwater flux that freshens the adjacent continental shelf water along the MAB.

The fresher CB water is ejected as a thin lens (≈5 m) with salinity concentrations of 22–28 parts per thousand (ppt) into the adjacent coastal waters between Cape Henry and Cape Charles where water depths range from 10 to 20 m. This freshwater plume turns anticyclonically under the influence of planetary vorticity and is trapped against the coast (Boicourt 1981). This trapping scale has a width proportional to the internal Rossby Radius of deformation (λ = gd/f, where g′ represents the density difference between the fresher plume layer and the coastal water mass). Based upon recent in situ measurements, Marmorino et al. (1999) found values of about 5 to 6 km for the baroclinic deformation radius (note g′ ≈ 0.057 m s−2). This buoyant plume spreads laterally in the far-field and impacts on the inner-shelf circulation as far south as Duck, North Carolina (Rennie et al. 1999).

The extent of the anticyclonic turning of the plume is controlled by the geomorphology of the region (i.e., the width of the mouth) and the deformation radius associated with the plume structure (Garvine 1987). The Kelvin number, defined as the ratio of the mouth width to the deformation radius, is O(1), whereas in other bays and estuaries such as Delaware Bay, the Kelvin number may be less than 0.5. In Delaware Bay, Munchow and Garvine (1993) found strongly nonlinear flows using arguments based on the relative vorticity normalized by the local Coriolis parameter (f). In simulations from the Princeton Ocean Model, Wheless and Valle-Levinson (1996) found two counter-rotating vortices where the Kelvin number was <0.5. The implication here is that perhaps vorticity effects may not be as important in the response to the seasonal buoyancy forcing in smaller estuaries such as Delaware Bay compared to the larger CB regime.

Wheless and Valle-Levinson (1996) also found that a combination of the semidiurnal tides and a buoyant outflow caused stronger flows. This result suggests that the strength of tidal currents, and more importantly surface tidal currents, affect the radial spreading of buoyant plumes exiting the mouths of bays. Redfield (1958) examined tidal currents along the continental shelf and slope along the eastern seaboard of the United States based upon volumetric transport calculations. Pietrafesa et al. (1985) found reasonable agreement with Redfield’s semidiurnal tidal current estimates of 5–10 cm s−1 from measurements along the South Atlantic Bight due to tidal resonance (Clarke 1991). However, recent measurements between Cape Hatteras to CB have indicated more energetic semidiurnal tidal currents than those determined from Redfield’s analysis (Shay et al. 1995; Cook and Shay 1998; Lentz et al. 2000). Moreover, analytical tidal models require simplifying assumptions concerning along-shelf tidal current variability and bottom terrain. In cases with uniform bottom slopes and weak along-shelf variability, observed and modeled results in the cross-shelf direction have been in agreement as in Duck (Lentz et al.). In the Coastal Ocean Dynamics Experiment (CODE), Rosenfeld and Beardsley (1987) observed that coherence scales of the barotropic tides may be much less than the scales >100 km commonly assumed for deep ocean tides. That is, barotropic motion scales of 25 km were found to be more appropriate for the along-shelf variability. Thus, a key science issue is whether surface tidal current signals on the shelf can be ascribed to linear, barotropic dynamics over simple shelf topography.

Marmorino et al. (1999) examined surface current signatures acquired from an Office of Naval Research (ONR) sponsored Ocean Surface Current Radar (OSCR) deployment during the Naval Research Laboratory (NRL) Chesapeake Bay Outfall Plume Experiment (COPE-1) in September–October 1996. Analyses of surface current measurements indicated that 76% of the surface current variability could be ascribed to the first three EOF modes. While the buoyant outflow occurred within the 48-h low-pass filtered (i.e., low-frequency) current variability, the first and second modes were related to wind and tidal forcing (M2), respectively. Of particular relevance here was the behavior of the third mode that not only indicated large-scale horizontal shears and curvature in the offshore edge of the buoyant plume but also the spring–neap cycle when a transient (in time) and stationary (in space) vortex was located between Cape Henry and Rudee Inlet (Harrison et al. 1964). During this period, an atmospheric front propagated through the domain that further complicated the surface circulation. The relevant issue is the horizontal structure of the tidal flow with respect to the bottom terrain that impacts buoyant outflows in the plume turning regime (hereafter referred to as PTR) located just south of the CB mouth.

From September to October 1996, the HF-radar system provided continuous surface current measurements during COPE-1 (Haus et al. 1998). Since OSCR illuminated a large domain and measured the spatial evolution of the surface current patterns, tidal currents and low-frequency flows associated with the buoyant plume were well resolved. Embedded within the core of the OSCR domain were a pair of high-resolution, broadband acoustic Doppler current profilers (ADCP) deployed by NRL to examine the current structure. This study examines the strength of the spatially varying tidal currents based on these measurements and determines the relative importance of linear processes by including comparisons to barotropic model simulations (Hallock et al. 2000, manuscript submitted to J. Geophys. Res.) based on data assimilation using the adjoint technique (Griffin and Thompson 1996).

To achieve this goal, the experimental design is discussed in section 2, and the observations and data quality are described in section 3. Sea level observations and the surface and subsurface currents are analyzed for the dominant tidal content with an emphasis on the M2 and K1 constituents in section 4. The horizontal structure of the tidal current constituents, and in particular the M2 tidal current, its vorticity, and frontal location is determined in section 5. This section also includes comparisons to simulations from a linear, barotropic model followed by a summary of results and concluding remarks in section 6.

2. Experimental design

a. HF-radar observations

The HF-mode (25.4 MHz) of the OSCR system was deployed from 13 September to 6 October 1996 to include an intensive observation period of the NRL/ONR-sponsored COPE-1 experiment (Haus et al. 1998). As shown in Fig. 1, the “Master” site was located at Fort Story, a U.S. Army Military Reservation (36°55′N, 75°59.5′W), whereas the “Slave” site was deployed approximately 20 km south at the U.S. Navy Fleet Combat Training Center Atlantic (36°45.6′N, 75°57′W). Sixteen element receive arrays were oriented at 200°T and 120°T at the Master and Slave sites, respectively. These phased array orientations provided optimal coverage of the experimental domain with respect to the NRL Physics of Coastal Remote Sensing (CoRS) program objectives. Communications were facilitated by UHF between the two sites for real-time surface current mapping at 20-min sample intervals at 700 cells spaced 1 km apart.

Geometrically, HF radar coverage is constrained by the physical orientation and placement of the phased arrays. The angle (Δ) between two radial beams must fall between 30° ⩽ Δ ⩽ 150° for reliable vector current measurements (Graber et al. 1997), and the maximum effective range of the HF mode of OSCR is limited to 44 km. The beam intersection angle restriction can be relaxed to include cells with smaller intersection angles, however, the vector currents are not reliable under these circumstances. For example, intersection angles were inadequate to resolve the vector currents for seven cells in the northeast and southeast corners of the domain. Thus, affixing physical processes based upon these cells is avoided here.

The resulting dataset is 22.78 days in length starting at 2000 UTC 13 September [yearday (YD) 257] and extending to 1240 UTC 6 October (yearday 280) 1996. Of these time steps, 170 (∼11%) were linearly interpolated. The largest data gap occurred on YD 260–261 when 90 samples were missing due to a faulty generator at the Master site. In the following analyses, only data starting after this interpolation period (∼19 days) will be used to avoid any temporal aliasing of the M2 tidal current. These surface current data were subsequently smoothed with a three-point Hanning window (Otnes and Enochson 1978).

b. Current profiles

As part of the NRL CoRS research initiative, two upward-looking, broadband ADCP were deployed at moorings A (36°52.1′N, 75°47.2′W) and A′ (36°51.9′N, 75°47′W) in the central region of the OSCR domain in 17–18 m depth (see Fig. 1). The three-dimensional velocity vectors were acquired at 1-min intervals (60 pings per minute) with 1-m vertical bin widths starting at 13.6 and 14.5 m (approximately 3 m above the bottom) for moorings A and A′, respectively. In the subsequent analysis, the uppermost bins were not used since the measurements were noisy due to their proximity to the sea surface; the first usable bins were located at 1.5 to 1.6 m beneath the surface at A and A′, respectively. Previous studies have demonstrated that mooring and ship-based ADCP records have been effective in relating surface to subsurface flow structure (Chapman et al. 1997; Shay at al. 1998a). The approach here isolates the vertical structure of tidal currents at the moorings and relates them to the HF-radar-derived surface current measurements.

3. Observations

a. Chronology of surface currents

During the experimental period, episodic buoyant jet intrusions, wind-driven flows, tidal currents, and submesoscale vortices1 were evident in the surface current observations. As shown in Fig. 2a, a strong southward-flowing jet of about 80 cm s−1 occurred on 14 September (YD 258) as fresher, buoyant water was ejected and subsequently turned anticyclonically, presumably under the influence of the earth’s planetary vorticity. Using salinity measurements from aircraft, Miller et al. (1998) found inshore salinities of 25 ppt compared to 31 ppt over the shelf, implying a large surface-layer salinity gradient between the estuarine and shelf water. Their measurements indicated a series of cusps and troughs, suggestive of a wavelike feature with an along-shelf wavelength of 10–20 km. Similarly, on 20 September (YD 264), another episode of this buoyant outflow occurred with velocities of about 60 cm s−1 (Fig. 2b). This outflow was more diffuse as it widened downstream with salinities ranging from 10 to 15 ppt at the mouth and about 25 ppt over the shelf. A flooding tide into the bay was evident on 27 September (YD 271: Fig. 2c). At the mouth of the bay, currents exceeded 70 cm s−1, and one day later on 28 September (YD 272) a vortex appeared between the CB mouth and Rudee Inlet (Fig. 2d). The horizontal scale of this vortex was 10–12 km (∼2λ) during its apparent 6-h lifetime. This pattern may have been due to nonlinear effects resulting either from the interaction between wind-driven flow and spring tide (Marmorino et al. 1999) or by tidal modulation of the buoyant plume (Chao 1990). During the ebb cycle on 3 October (YD 277), tidally dominated flows indicated a pronounced current boundary extending south of the mouth to about 20 km offshore (Fig. 2e). The magnitude of the maximum velocity core was about 75 cm s−1 at the mouth, decreasing to 55 cm s−1 offshore. A nearly uniform flow pattern was observed on 6 October (YD 280), where the largest velocities occurred in the PTR (Fig. 2f). Thus, several events occurred in the surface circulation during the period of deployment that seem to be significantly influenced by tidal processes.

b. Velocity profiles

To facilitate direct comparisons between the high-resolution ADCP (subsurface currents) and OSCR (surface current) data, 1-min mooring data were smoothed using a running five-point Hanning window and subsampled at 20-min intervals (Otnes and Enochson 1978). Surface and subsurface data were combined to form profiler time series to assess data quality over a 10-d period from both ADCP moorings A and A′. The observed variations in the vertical structure of the horizontal currents at the ADCP mooring are shown in Fig. 3. Currents exceeded ±50 cm s−1 in the upper part of the water column. While there were periods of vertical coherence in the currents, the currents also indicated veering with depth, leading to periods of strong vertical current shear. For example, the predominant southward current decreased from 50 cm s−1 to about 20 cm s−1 at depth on YD 268. Presumably, a large fraction of this decrease is due to the frictional bottom boundary layer (Prandle 1982). Semidiurnal tidal currents with amplitudes of about 15 cm s−1 were also evident in the time series from YD 262 to 266. This profiler series is used below to determine the consistency of the surface current data, and quantify the barotropic and residual (observed less barotropic) tidal currents.

c. Surface winds

Winds and pressures observed at the Chesapeake Bay Light Tower, a Coastal Marine Automated Network Station (36.9°N, 75.7°W), revealed strong winds and the passage of low pressure systems over synoptic timescales of 3–7 days (Fig. 4). Austin and Lentz (1999) found similar timescales in observations acquired during Duck94. Surface winds ranged from 5 to 10 m s−1 during periods of high atmospheric pressure. By contrast, the passage of low pressure systems caused winds to increase beyond 20 m s−1. One particular event occurred on YD 273, when surface winds rotated abruptly from a northward to a southward direction over less than an inertial period (∼20 h in this region). The corresponding wind change was about 30 m s−1. As suggested by Marmorino et al. (1999), this strong atmospheric event excited an upper-ocean response, and coincided with the appearence of the transient submesoscale vortex during spring tide between the CB mouth and Rudee Inlet (Fig. 2d).

d. Time series comparisons

Based upon previous studies, reasonably good agreement between subsurface and surface current data has been found at depths ranging from 10 to 20 m beneath the surface. Given an observed current range of over 1 m s−1, Shay et al. (1998b) reported 7 cm s−1 rms difference between the surface and subsurface currents acquired at 4 m beneath the surface from vector measuring current meters deployed as part of the NSF-sponsored CoOP program in Duck, North Carolina (Butman 1994). The quality of the observed HF-radar-derived surface currents from COPE-1 will be assessed here by comparing these data to subsurface measurements at the ADCP moorings.

Rotated surface and subsurface current components (u positive toward 70°T defined as cross-shelf; υ positive toward 340°T defined as along-shelf) indicated consistent agreement with velocity records at 1.5 m beneath the surface at mooring A (Fig. 5). As anticipated, current records were dominated by semidiurnal tidal oscillations. Surface along-shelf currents ranged ±50 cm s−1 with a predominant southward flow during the first eight days of the experimental period followed by an oscillatory flow superposed on a northward drift current (Fig. 5a). The surface cross-shelf currents ranged ±25 cm s−1 and the subsurface currents followed the surface flows, but with generally weaker magnitudes. However, intermittent periods occurred when cross-shelf subsurface currents were larger than the surface currents by 5–10 cm s−1 (Fig. 5b). While the current magnitudes differed, the temporal phase differences were negligible between the two measurements over the 1.5-m vertical separation. Apart from the large difference on YD 265 that also appear in the ADCP records from 1.5 to 3.5 m, bulk current shears O(10−2 s−1) were aligned in the cross-shelf direction and were consistent with those found in High Resolution Remote Sensing (HIRES) and Duck94 experiments (Shay et al. 1995, 1998b) (Fig. 5c).

Statistical measures of the relationship between the surface (uo, υo) and subsurface (u1.5, υ1.5) current vectors are the complex correlation coefficient given by
i1520-0485-31-2-427-e1
and the phase angle
i1520-0485-31-2-427-e2
where 〈 · · · 〉 represents a half-daily average based upon 36 points (Kundu 1976). Geometrically, this phase angle represents the average cyclonic angle of the subsurface current vector with respect to the surface current vector. Magnitudes of the complex correlation coefficients exceeded 0.8 except for half-day period 7 due to weaker surface cross-shelf currents of 10 cm s−1 compared to subsurface currents of 25–30 cm s−1. The corresponding phase angles were also the largest at this point with an estimated value of 65°. Over the remainder of the time series, the phases ranged between −7° and 20° with similar results found at the A′ mooring (not shown).

e. Regression analyses

Subsurface (1.5 m) current components were regressed against the surface current components at both A and A′ moorings (Fig. 6). Based on a least squares fit, biases at mooring A were 3.7 and −2.7 cm s−1 with slopes of 1.03 and 1.16 for the cross- and along-shelf components, respectively. Histograms for the current differences revealed a variability envelope of ±20 cm s−1 at mooring A. Similar biases of 4.5 and −3.1 cm s−1 were found at mooring A′ for the cross-shelf and along-shelf currents, respectively. Regression curve slopes were less than those derived at the A mooring due to large scatter in the data (Figs. 6c,d). These results suggest that subsurface along-shelf currents exceeded the surface currents as reflected in the histograms of current differences where the data followed a theoretical Gaussian distribution. Notice that approximately 95% of the differences were within ±1.96 s, where s is the standard deviation. Over 50% of the current differences were within ±12 to 16 cm s−1 with the peak skewed toward positive values for cross-shelf currents and negative values for the along-shelf currents. Rms differences were 6–7 cm s−1 at the ADCP mooring locations, consistent with previous findings. That is, rms differences were similar between adjacent bins from 1.5 to 3.5 at both ADCP A and A′, particularly on YD 265 and 271 owing to both geophysical variability and inherent measurement error. These comparisons followed observed data trends and were also similar to results from HIRES (Shay et al. 1995; Chapman et al. 1997), Duck94 (Shay et al. 1998b), and Ocean Pollution Research Center (Shay et al. 1998a) experiments.

4. Tidal analysis

Local sea level variations observed at the NOAA National Ocean Survey Station (NOS) along the CB Tunnel Bridge (see Fig. 1) were used to determine the dominant tidal constituents from a nine-month record in 1996 encompassing the COPE-1 experiment. These results guide the harmonic analysis of the surface and subsurface current records in resolving the predominant tidal constituents in the diurnal and semidiurnal tidal bands.

a. Tidal heights

To resolve the dominant tidal constituents (Foreman 1977), observed sea level data from the NOS Station (ηo) are fitted to a series of sinusoidal waves from the expression:
i1520-0485-31-2-427-e3
where η is the time-average sea level height, m is the number of analyzed frequencies, ωn is the nth tidal constituent frequency, An is the corresponding tidal amplitude, ϕn represents its phase, and t is time. Harmonic analysis of this series (starting in January 1996 through September 1996) revealed that the dominant tidal contribution was associated with the semidurnal (M2) tidal constituent where the amplitude was 37.5 cm and the phase was 357° (Table 1). The next largest amplitude was 8.4 cm for the N2 constituent where the phase was 328°. The S2 constituent was nearly as energetic with an amplitude of 7 cm with a phase of 49°. Thus, a large fraction of the variability occurred within the semidiurnal tidal band for periods from 12 to 12.658 h. The predominant diurnal constituents (K1, O1) were resolved with amplitudes of 5.1 and 4.6 cm and phases of 188 and 187°, respectively. These tidal amplitudes were also consistent with those previously found at the CB mouth by Boicourt (1981). The remaining constituents were less energetic (1–5 cm), including the fortnight (Mf) tidal constituent.

Hourly sea level variations observed during the COPE-1 experiment are shown in Fig. 7a. Based upon tidal constituents in Table 1, reconstructed tidal height time series ranged between ±40 cm (Fig. 7b) except during spring tide when the lunar and solar semidiurnal tides interacted over 14-day timescale. The resultant tidal range increased to about ±50 cm s−1 between YD 270 and 274 (Fig. 7b). Residual sea-level variations (ηr), defined as the difference between the observed (ηo) sea level and the reconstructed tidal height (ηp) time series, indicated high-frequency oscillations superposed on lower-frequency variations in the sea level heights (Fig. 7c). Higher-frequency oscillations of 5–10 cm also tended to be more energetic during the first part of the time series (YD 262–268), than during the latter part of the time series. The lower-frequency signals in sea level were more energetic and reached 35–40 cm on YD 261 and 278. These large sea level changes were correlated to atmospheric frontal passage as suggested by the wind and pressure time series in Fig. 4. For example, on YD 261 and 278, sea level pressures changed by about 12–15 mb. In addition, winds increased significantly by about 20 m s−1 prior to these large changes of 20–30 cm on YD 261 and 278. Thus, its likely that the atmospheric frontal passage modulated the sea level heights during these periods.

The explained variance of the observed sea level variations (ηo) by the m tidal constituents (Σmp=1ηp) was determined from the expression
i1520-0485-31-2-427-e4
where k is the number of data points (6552) and m represents the number of tidal constituents (9) as per Table 1. The predicted tidal time series explained 74% of the observed variance in the sea level records. Equation (4) is also used below to estimate explained variance by the along-shelf (υ) and cross-shelf (u) tidal current components.

b. Tidal currents

Tidal current analyses were performed by replacing the sea level heights with the cross-shelf (u) and the along-shelf (υ) currents in (3) and restricting the analyses to the semidiurnal (M2) and diurnal (K1) tidal current constituents (Foreman 1977). It is convenient to represent orthogonal tidal current velocities u and υ as a complex rotating vector W = u + iυ. Following Mooers (1973), this vector is decomposed into two counterrotating complex vectors:
WW+entWent
where W+ is a cyclonic-rotating vector and W is an anticyclonic-rotating vector, and over a tidal cycle ent and ent describe two circles. The resultant W is an ellipse described by the following quantities: semi-major (M) and semi-minor (N) axes, ellipse orientations (θ), and phases (ϕ). These parameters, determined for each component at each grid point, are used to describe tidal motions in the domain.

c. Vertical structure

A summary of the ellipse characteristics for the M2 tidal constituent at the mooring A site is given in Table 2. Major axes for the M2 constituent were similar throughout the water column. The surface tidal current value was 17.2 cm s−1 compared to 14.3 and 16.4 cm s−1 at 1.5 and 2.5 m, respectively. The ellipses were oriented in the cross-shelf direction. Net differences were 1–3 cm s−1 between surface and subsurface major axes. In previous experiments, similar differences have been found in current amplitudes, which are within the resolving capability of the instruments (Shay et al. 1998b). Notice that the standard errors of 1–2 cm s−1, estimated from an approach by Beardsley et al. (1995) and Lentz et al. were well below signal levels. In addition, minor axes were about 25%–30% of the major-axis length, which suggested rectilinear motions, but with more uncertainty compared to the major axes. Both phase and orientation angles for the M2 tidal current were nearly uniform throughout the water column, consistent with barotropic M2 tidal flow.

For the K1 constituent (not shown), major axes were about 10 cm s−1 less than the M2 constituent. In addition, there was about a 2–3 cm s−1 difference in the surface major and minor axes compared to subsurface values at 1.5–2.5 m beneath the surface. Phase differences in the vertical were more erratic because of lower amplitudes (and major and minor axis values). Thus, the weaker K1 tidal currents may have been more influenced by frictional boundary layers (Prandle 1982).

For these two constituents, explained variances of the current structure based on (4) at mooring A (Table 3) increased from 18% at the surface to as large as 55% for the along-shelf tidal current at 13.5 m. Similarly, cross-shelf tidal currents explained as much as 43% of the variance at 5.5 m. In the near-bottom layers, explained variances in both tidal current components converged to values from 30% to 55%. A significant fraction of the observed current variability was due to the M2 tidal constituent.

d. Barotropic currents

Profiles of the tidal current time series, formed from the M2 and K1 constituents, were vertically integrated between 1.5 and 13.5 m (Fig. 8) and compared to the surface tidal current time series. For both along-shelf and cross-shelf current components, the depth-averaged and surface tidal currents were highly correlated. The along-shelf component (Fig. 8a) indicated a diurnal inequality when the combination of the diurnal and semidiurnal tidal currents was slightly larger in amplitude than those with just a semidiurnal current constituent. Similarly, cross-shelf tidal currents, which range ±18 cm s−1, exhibited a similar trend (Fig. 8b). Removal of the depth-averaged current from the tidal current profile series formed a tidal current residual series that revealed signals with a semidiurnal period. While a fraction of this variability may be ascribed to possible baroclinic effects due to a buoyant plume structure (Chao 1980), bottom frictional influences on the tidal current profile may have also contributed to residual effects (Prandle 1982). This effect is consistent with the decreased amplitude of the major axes oriented in the cross-shelf direction and eccentricity of the near-bottom tidal ellipses (Table 2).

5. Horizontal tidal structure

a. Current ellipses

The duration of the continuous HF-radar measurements of ≈19 days (17 September–6 October) was sufficient to determine semidiurnal (M2, S2) and diurnal (K1, O1) tidal constituents (Godin 1972). For this time series, diurnal and semidiurnal tidal ellipses indicated finescale variability over kilometer scales as suggested by previous studies. Major axes of the K1 tidal ellipses indicated along-shelf propagation with larger amplitudes (∼7 cm s−1) found 1 to 2λ from the coast (Fig. 9a). In the center of the domain, and close to the ADCP moorings, ellipses tended to be more circular with amplitudes of about 6 cm s−1. This tidal current amplitude was consistent with results reported by Daifuku and Beardsley (1983). By contrast, the O1 tidal constituent ellipses (Fig. 9b) were more erratic due to lower current amplitudes compared to those found for the K1 constituents. However, the O1 flow was more rectilinear and oriented in the cross-shelf direction in contrast to the K1 constituent.

Velocity amplitudes of the M2 semidiurnal constituent were more energetic with amplitudes exceeding 50 cm s−1 at the CB mouth (Fig. 9c). Ellipses were oriented in the cross-shelf direction toward the CB mouth, where inner-shelf ellipses were rectilinear rather than rotary. The M2 horizontal structure and its gradient south of CB in the PTR revealed submesoscale variability within 2λ of the coast. In the center of the domain near the ADCP moorings, these amplitudes were 15–18 cm s−1 as suggested by the vertical structure analysis (Table 2). The S2 tidal constituent amplitudes were less energetic ranging from 2 to 10 cm s−1 (Fig. 9d). These ellipses were oriented in the cross-shelf direction, and were more rotary close to the coast. Notice that the S2 constituents were more energetic than either of the diurnal constituents. For both of these semidiurnal constituents, horizontal structure analyses revealed strong tidal current variability well above Redfield’s (1958) results due in part to the geomorphology of the CB mouth. Additionally, horizontal changes coincided with the cross-shelf variability in the topographical gradient, indicative of barotropic tidal flows as noted in the vertical structure measurements. That is, tidal currents in the midshelf region were distributed over greater depths (20 m) compared to those over the inner-shelf where depths were 10 m.

Explained variances by these tidal constituents indicated spatial structure over the domain (Fig. 10). For cross-shelf tidal currents, the maximum explained variance of about 60% was located in the strong M2 tidal current region near the mouth. The explained variance decreased southward with values of 25%–30% in the PTR. Near the ADCP moorings, tidal currents accounted for 22% of the observed variability. This differs by a few percent from the results listed in Table 3 due to the inclusion of the additional tidal constituents in the horizontal analysis. Along-shelf tidal current variance was less with a maximum of only 15%–20% in the north-central region of the domain (Fig. 10b). At the ADCP moorings, explained variances were about 18%. In both directions, estimates of explained variance were dominated by the M2 tidal constituent. Lower values of explained variances by the tides in the along-shelf direction also suggested the importance of the buoyant flows over the inner-shelf (Rennie et al. 1999), and wind-driven currents over the domain (Marmorino et al. 1999).

b. M2 tidal currents

As shown in Fig. 11, a cycle of M2 tidal currents indicated significant differences between ebb and flood near the CB mouth. Currents during ebb (Figs. 11a,b) ranged from 30 to 40 cm s−1 close to the mouth of the bay. Notice the strong tidal current frontal boundary that developed in the PTR within 2λ from the coast. Over the next 2 h, maximum ebb flow occurred when tidal currents approached 50 cm s−1. At this stage, the current boundary encompassed about 30% of the radar domain. During the transitional period from ebb to flood, a southward current of about 10 cm s−1 remained in the PTR whereas over the remainder of the domain tidal currents were weaker. During flood, the tidal currents increased in the PTR to about 40 cm s−1 two hours later (Fig. 11d), and subsequently to about 50 cm s−1 (Fig. 11e). As during the ebb cyle, a strong boundary developed that encompassed about 30% of the domain. During the transitional phase, tidal currents of 10 cm s−1 were located within 2λ from the coast in the PTR (Fig. 11f). Notice that the transitional tidal currents exhibited curvature in the flow with significant horizontal gradients as suggested by EOF analyses (Marmorino et al. 1999).

The M2 current strength was not only above that predicted by Redfield (1958) but the structure revealed submesoscale variability that scaled well with the deformations radius λ, particularly in the PTR. Given the M2 current strength and its horizontal structural variations, fresher-water pulses emanating from CB (Miller et al. 1998) during the ebb cycle of the M2 tide may have induced additional curvature in the observed surface flow. Based upon model simulations, Wheless and Valle-Levinson (1996) found radial spreading of the buoyant outflow during this phase of the semidiurnal tide cycle.

c. Correlation scales of the M2 tidal current

Using (1) and (2), the magnitude of the horizontal complex correlation coefficients and phases relative to the current time series at cell 125 are shown in Fig. 12. As noted above, this phase angle represents the average cyclonic angle of the surface current vector with respect to the vector at cell 125. From the observed surface current records (Fig. 12a), high correlation coefficients (>0.75) were located in the northern and central portion of the domain. Here, current vectors were in-phase, whereas closer to the coast (∼2λ) these coefficients decreased to 0.6 or less, particularly in the PTR. In addition, correlation coefficients steadily decreased to 0.4 or less over the inner to mid shelf with nearly equal phases. Given the location of these lower correlation indices, the buoyant outflow plume and weaker outershelf currents degraded the spatial coherence of the observed flows. However, this coastally trapped buoyant outflow from the CB has been traced farther south along the MAB by Rennie et al. (1999), suggestive of large coherence scales over the inner shelf.

By contrast, the M2 tidal currents were spatially correlated because of larger wavelengths of the tidal waves propagating through the domain (Fig. 12b). However the coherence scale of these motions may not necessarily be O(>100 km), rather the coherent scale may be O(25 km) (Rosenfeld and Beardsley 1987). Further, the pattern of high correlations (>0.95) extended from the strong tidal current regime southward over the mid to inner shelf. The magnitude of the correlation coefficients decreased to 0.92 in the PTR as suggested by the correlations of the observed surface current time series. Complex spatial phases decreased to −40°, which indicated an anticyclonic veering of the tidal current vector by about −1° km−1. Perhaps this phase separation may have been a manifestation of the depth changes sensed by barotropic currents. These coefficients and phases were also estimated for diurnal (K1, O1) and semidiurnal (S2) constituents (not shown). For example, correlation coefficients for the S2 constituent tidal currents indicated similar results with a slightly higher phase change of almost −2° km−1. The diurnal tidal current phase variations were even more rapid with values of up to 5° km−1. However, amplitudes of the diurnal constituents were considerably less energetic than those associated with the M2 constituent (see Figs. 9a,b), implying erratic phases in these weaker current regimes. Thus, the M2 tidal constituent and to a lesser extent the S2 constituent dominated the coastal tidal currents as found in the CoOP experiment in Duck (Lentz et al. 2001).

d. M2 tidal vorticity

To examine the current gradients in Fig. 11, the relative vorticity is estimated from the expression;
i1520-0485-31-2-427-e6
where the alongshelf (υ) and cross-shelf (u) velocity components are the M2 tidal currents. The vorticities were normalized by the local Coriolis parameter f (0.87 × 10−5 s−1) to place the gradients into geophysical context as shown in Fig. 13.

During ebb (Fig. 13a), the maximum vorticities were about −0.25f and indicative of a strong anticyclonically rotating regime within the PTR. South of this strong vorticity regime was a region of weak cyclonic vorticity of approximately 0.05f. The contributions from both terms in (6) were nearly equal where the along-shelf variations in the cross-shelf tidal currents were slightly larger near the mouth and the PTR. Two hours later, anticyclonic vorticity affected the inner shelf with a relative maximum located ∼2λ from the coast. During the ebb-to-flood transition (Fig. 13c), residual vorticities of 0.05f were observed near the north-central part of the domain. As flood tide began (Fig. 13d), the relative vorticity changed sign in the PTR (0.25f) and the southern inner shelf (−0.05f). This tidal current vorticity maximum was located about 2λ from the coast (Fig. 13e). About two hours later, the transition back to ebb began as manifested by weaker vorticies over the domain.

This general pattern in normalized vorticities resembled a comma-cloud formation often associated with leading edges of atmospheric storms and fronts, but on a significantly smaller scale. During ebb tide, the vorticity regime changed from a cyclonically to anticyclonically rotating regime. Given the oscillatory nature of tidal currents, these patterns did not significantly change except that the gradients in the normalized vorticity alternated between ±0.25f in the PTR and ±0.05f south of the PTR. Still these large excursions in the M2 tidal vorticity gradients impacted inner to mid shelf dynamics during periods of strong wind forcing and presumably in the formation of the vortexlike feature (Harrison et al. 1964; Marmorino et al. 1999). Since the normalized vorticities can be thought of as a proxy for Rossby number (Munchow and Garvine 1993), the M2 tidal flow may be characterized as weakly nonlinear.

Given only one realization of the vortex, it remains unclear whether this feature occurs regularly or is the juxtaposition of a spring tide and a wind event. Zimmerman (1978) has shown that oscillating tidal current flows over irregular bottom terrain causes a net transfer of energy to the mean field via nonlinear advection in the vorticity balance. In his theory, the mean current increases as the intrinsic length scale of the bottom terrain approaches the tidal current excursions. Here, bottom terrain varies over scales less than 1 km whereas the tidal current excursions over a tidal cycle averages 3–5 km near the CB mouth. Clearly, longer time series such as those acquired during the recent COPE-3 experiment will provide additional insight into this vortex and its forcing mechanism (Imasoto 1983), which is beyond the scope of this manuscript.

Munchow et al. (1992) noted that strong tidal currents propagating over the shelf impact on the stratification and density fields due to increases in turbulence. Simpson and Hunter (1974) suggested that the occurrence of tidal mixing fronts can be predicted by
i1520-0485-31-2-427-e7
where u is the cross-shelf tidal current for the M2 constituent. The rate of kinetic energy dissipation is proportional to u3h−1 = 10S. As shown in Fig. 14, the tidal mixing parameter associated with the M2 tidal current varied from 2.2 at the CB mouth to as large as 4.2 in the southeast region of the surface current domain. Lower levels of S found near the mouth were indicative of less dissipation of M2 tidal current energy. By contrast, where the M2 tidal currents were weaker the corresponding values of this parameter were larger as more tidal energy is presumably dissipated. Notice the gradients in S also become more diffuse south and east of CB. Based on tidal current amplitudes and vorticity fields, S ≈ 3 depicted the transition between the highly energetic M2 tidal current regime near the CB mouth and the region where higher dissipation rates of tidal energy occurred. Munchow et al. (1992) found values of 2.6–4.6 for the range of the tidal mixing fronts with 3.4 selected as the location of the boundary between the Delaware Bay water and ambient shelf water. Based upon these results, the scales of variability for amplitudes, vorticities, and boundary locations were fairly consistent, yet less than anticipated for long, barotropic tidal waves propagating over the shelf. These scales were more on the order of 25 km as suggested by Rosenfeld and Beardsley (1987) during CODE. Thus, barotropic motions on the shelf may have shorter correlation scales than in the deep ocean.

e. Comparison to linear model simulations

Given these results, an important question that has emerged is whether the observed surface tidal current could be explained by linear, barotropic processes. To investigate this question, Hallock et al. assimilated several different sets of observations into a linear model using the adjoint technique of Griffin and Thompson (1996). The governing equations for this linear barotropic model with bottom friction are described by
i1520-0485-31-2-427-e8
where bottom frictional stress, τb, is related to a constant k(u, υ), surface elevation is given by η in a domain with finescale bottom topography h(x, y) augmented with ETOPO-5 data, and g is the acceleration of gravity. However, wind stress is not of primary concern in the present context and is excluded from the model.

Simulations presented here were from adjoint model experiments where all of the available data were used in the assimilation process. As noted in Hallock et al., even in that experiment, the correlation indices were ∼0.93. In terms of HF-radar-derived measurements, a small subset of data was used in the central part of the domain in the assimilation where the mean square error was 0.15. Further details can be found in Hallock et al. and Griffin and Thompson (1996).

As shown in Fig. 15, the simulated M2 tidal currents were a maximum of 65 cm s−1 in the CB mouth. The model simulations extended farther north and west of the surface current domain. That is, the maximum observed M2 tidal current amplitudes were 50 cm s−1 just south and east of the mouth as shown in Fig. 9c. However, in the observed surface current domain, similar amplitudes and tidal current gradient boundaries were evident in the simulated current. Ellipses of the simulated tidal currents were more rectilinear and were aligned in a north-northwest orientation compared to a predominant northwest orientation in the actual observations. Since the eccentricity of the ellipses was less than observed at the mouth, one possibility is that the observed tidal currents may have been affected by baroclinic effects or topographic variations. Given that the Rossby numbers were about 0.25 in this region (as deduced from the vorticity arguments), weak nonlinear interactions may have played a role in the dynamics (Wheless and Valle-Levinson 1996). Farther offshore, the simulated M2 tidal current ellipses were weaker, which is also consistent with the observed ellipses. It is useful to compare fields from the observed M2 tidal currents with those simulated by the model of Hallock et al. given the consistency in the model results.

Simulated cross-shelf and along-shelf amplitudes and phases for M2 tidal currents were subtracted from those observed as shown in Fig. 16. The amplitudes differed by a maximum of 12 and 8 cm s−1 in the region of highest tidal current signals of 45 to 50 cm s−1 in the energetic PTR. These larger differences along the PTR and inner shelf were located about 2 to 3λ from the coast, which lends support to the modulation of the tidal currents by buoyant jet excursions from the CB (Rennie et al. 1999). Notice that the net amplitude differences away from the inner shelf and PTR were 2–4 cm s−1, and the southeast part of the domain indicated good agreement between simulated and observed tidal currents. Similar results were also found using simple analytical treatments such as Clarke (1991) assuming negligible along-shelf variability. Phase differences tended to be in the 10°–20° range (Figs. 16c,d). The cross-shelf phases suggested two regions of large differences that correlated well with the normalized vorticities (see Fig. 13). By contrast, along-shelf phase differences were more uniform. Thus, away from the inner-shelf (∼2λ), linear barotropic dynamics dominated the M2 tidal current signals.

For 85 points over the HF-radar domain, detailed comparisons between the tidal current amplitudes and phases, semimajor axes and orientations revealed more insights into the tidal current physics (Fig. 17). The maximum observed tidal current amplitude in the cross-shelf direction was about 45 cm s−1 compared to the simulated value of 40 cm s−1. The phases of this flow component suggested about a 15°−20° bias. Along-shelf variability also suggested a direct relationship between the observed and simulated values of 20 cm s−1. Beyond this threshold current, more energy was found in the simulated tidal current. While in each of these first three cases a direct relationship was found between observed and simulated results, along-shelf phases indicated more disagreement (Fig. 17d). The observed phase ranged between 180° and 260°, whereas the corresponding range for the simulated values was 200° to 240°. The major axes were correlated as suggested by the scatter along the line observed Mo = Mm. This was not a surprising result given the strength of the M2 tidal currents over the domain. Generally, ellipse orientations indicated a difference of −20° due to an offset prescribed in the model based on the directional difference between the surface and depth-averaged M2 tidal current. That is, the simulated tidal current signals indicated more of an along-shelf orientation compared to observed tidal current ellipses.

6. Summary and concluding remarks

Observations acquired during the Cheasapeake Bay Outfall Plume experiment revealed complex circulation patterns influenced by the tides, winds, and intermittent freshwater intrusions associated with the coastally trapped buoyant jet (Haus et al. 1998; Marmorino et al. 1999). As in previous experiments, HF-radar-derived surface currents were well resolved over kilometer scales in the domain beginning at the CB mouth and extending southward approximately 30 km. The freshening of the continental shelf water was greater during this experiment due to the frequency of landfalling tropical cyclones (i.e., Fran, Bertha) and their associated precipitation patterns over the MAB (Miller et al. 1998). Notwithstanding, these surface currents when combined with ship-, aircraft-, and mooring-based measurements in support of CoRS provided data to improve our understanding of the complex coastal processes.

Comparisons of surface currents to subsurface current measurements at 1–2 m beneath the surface from two broadband ADCP agreed well over 10-day concurrent records. Maximum surface and subsurface currents ranged between ±75 cm s−1. Regression analysis showed good agreement between the current measurements, with small biases and slopes approaching unity. Generally, magnitudes of the correlation coefficients exceeded 0.8 with small phases, except on two occasions when vertical current shears were a maximum O(10−1 s−1). The results agreed with those found previously in the HIRES, Duck94, and OPRC experiments. Large vertical current shears were associated with processes other than tides such as surface wave-induced velocities (Graber et al. 1997), near-inertial motions (Shay et al. 1998a), and Langmuir cells (Weller and Price 1988). With the advent of multifrequency radar systems (Teague et al. 1997), detailed surface and subsurface measurements must be acquired with sufficient temporal sampling to characterize the spectrum of flow regimes that contribute to near-surface current shears and subsurface structure. This area of inquiry is required to improve our understanding of radar-derived signals and their relationship to near-surface vertical current shears.

The theme of this study was to determine the mesoscale variability in the tidal currents that contributed to the complex coastal circulation as measured by sea level stations, HF radars, and ADCPs. Tidal signals were dominated by the M2 and to a lesser extent the S2 tidal constituents. From the HF-derived surface current records, the M2 and S2 tidal current amplitudes had a maximum of about 50 and 8 cm s−1, respectively, at the CB mouth, where the phases were 30° and 0°. These tidal current estimates were larger than Redfield’s (1958) estimates of 5–10 cm s−1, based upon volumetric arguments at the shelf break, due to the shallower depths and the geomorphology of the CB mouth.

Explained variances associated with these four tidal current constituents were a maximum of 60% at the mouth and decreased southward. Energetic semidiurnal tidal currents were highly correlated over the HF-radar domain, and phases indicated an anticyclonic veering of the M2 tidal current with along-shelf distance from the mouth at a rate of approximately −1° km−1. Tidal current vorticities associated with the M2 constituent were ±0.25f (where f is the local Coriolis parameter) and about ±0.05f south of the plume turning region. Submesoscale spatial scales of these tidal vorticity pools were O(10 km), except near the mouth where the relevant cross-shelf scales were larger. It is clear from the analysis that the stationary submesoscale vortex formed between the CB mouth and Rudee Inlet warrants further attention as it may be a combination of both tidal and wind-forcing effects interacting with the buoyant outflow (Marmorino et al. 1999).

Analyses at the ADCP moorings indicated that the semidiurnal tidal currents were predominantly barotropic with cross-shelf and along-shelf current amplitudes of 18 and 10 cm s−1, respectively. Residual tidal currents were associated more with frictional effects (Prandle 1982) rather than internal tides due to the large distance to the shelf-break region from the CB. Given the modeling results of Hallock et al., data assimilation techniques of Griffin and Thompson (1996) hold promise in isolating coastal ocean physics. Even with a Rossby number of 0.25 as suggested by normalized vorticity arguments (Munchow and Garvine 1993), model simulations to within 2λ from the coast were governed to a large extent by linear, barotropic processes. Clearly, the M2 tidal currents play a pronounced role on coastal circulation patterns and modulate the buoyant outflow (Chao 1990). Exploiting linear physics in a weakly nonlinear regime is quite important, as it provides a framework for more complete numerical treatments that include baroclinic and wind-driven effects (Wheless and Valle-Levinson 1996). Gridded surface current observations are well suited for the evaluation of analytical and numerical results.

Since the buoyant outflow from the CB was well above the normal levels in September to October 1996 because of landfalling hurricanes Bertha and Fran (Marks et al. 1998), inner-shelf differences between modeled and observed currents reflected this variability in excess rainfall and the lower salinity water (Miller et al. 1998). In this context, terrestial–estuarine–atmospheric interactions were important to the adjacent shelf circulation. Along-shelf variability was sensitive to the coastal boundary conditions (sea level) as well as changes in the bottom topography particularly around the CB mouth used in the model. Thus, future experiments need to consider additional arrays of instruments (bottom-mounted pressure sensors, temperature, and salinity moorings) as well as meteorological moorings capable of withstanding harsh environmental conditions all embedded within an OSCR domain as in Duck94 (Butman 1994).

There is a wealth of information present in the COPE-1 and the recently acquired COPE-3 datasets, particularly episodic buoyant jet intrusions, the wind-driven response to frontal passages, and the strong tidal current interactions with these flows and the bottom. By combining subsurface data from the COPE datasets including mooring-, ship-, and aircraft-based data with these surface current observations, important fundamental questions regarding physical processes over the inner to mid shelf may now be addressed within a dynamical framework (Boicourt 1981; Garvine 1987; Munchow and Garvine 1993). By resolving the tidal current variability, further analysis of the wind- and buoyancy-driven circulations will provide a more complete picture of physical processes over the inner to mid shelf regime. These types of data and the ensuing analyses are central to improving conceptual and numerical models of complex coastal ocean circulation and their interactions with the atmosphere, which is relevant for a spectrum of societal needs.

Acknowledgments

Data were acquired as part of ONR Remote Sensing Program under Grants N00014-96-1-1065 and N00014-99-1-0057 by the RSMAS OSCR group. LKS and TMC further acknowledge funding support from the ONR Remote Sensing under Grant N00014-96-1-1011 and N00014-98-1-0818. Z. Hallock was funded by NRL Program Element 61153N-31 in the acquisition of the ADCP data. George Marmorino kindly provided insightful comments on earlier versions of the manuscript. Terry Faber and Mike Robozo participated in the field experiment. The authors also gratefully acknowledge the personnel at the Fort Story U.S. Army Base and the U.S. Navy Fleet Combat Training Center for the logistics and real estate required to sustain HF radar operations. Steve Lentz (WHOI) provided the error analysis code. The anonymous reviewers provided insightful comments that improved the quality of the manuscript.

REFERENCES

  • Austin, J. A., and S. J. Lentz, 1999: The relationship between synoptic weather systems and meteorological forcing on the North Carolina inner shelf. J. Geophys. Res.,104, 18 159–18 185.

  • Beardsley, R. C., J. Candela, R. Limeburner, W. R. Geyer, S. J. Lentz, B. M. Castro, D. Cacchione, and N. Carniero, 1995: The M2 tide on the Amazon Shelf. J. Geophys. Res.,100, 2283–2319.

  • Boicourt, W. C., 1981: Circulation in the Chesapeake Bay entrance:Estuary-shelf interactions. Proc. Chesapeake Bay Plume Study, NASA Conf. Publication 2188, 61–78. [Available from NASA, Scientific and Technical Information Branch, Washington, DC 20546.].

  • Butman, C. A., 1994: CoOP coastal ocean processes. Sea. Technol.,35, 44–49.

  • Chao, S. Y., 1990: Tidal modulation of estuarine plumes. J. Phys. Oceanogr.,20, 1115–1123.

  • Chapman, R. D., L. K. Shay, H. C. Graber, J. B. Edson, A. Karachintsev, C. L. Trump, and D. B. Ross, 1997: On the accuracy of HF radar surface current measurements: Intercomparisons with ship-based sensors. J. Geophys. Res.,102, 18737–18748.

  • Clarke, A. J., 1991: The dynamics of barotropic tides over the continental shelf and slope. Tidal Hydrodynamics, B. Parker, Ed., John Wiley and Sons, 79–108.

  • Cook, T. M., and L. K. Shay, 1998: Tidal variability observed with high frequency radar. Preprints, Second Conf. on Coastal Atmospheric and Oceanic Prediction and Processes, Phoenix, AZ, Amer. Meteor. Soc., 287–292.

  • Daifuku, P. R., and R. C. Beardsley, 1983: The K1 tide on the continental shelf from Nova Scotia to Cape Hatteras. J. Phys. Oceanogr.,13, 3–17.

  • Foreman, M. G. G., 1977: Manual for tidal currents analysis and prediction. Pacific Marine Science Report 78-6, Institute of Ocean Sciences, 57 pp. [Available from Institute of Ocean Sciences, P.O. Box 6000, Sidney, BC V8L 4B2, Canada.].

  • Garvine, R. W., 1987: Estuary plumes and fronts in shelf waters: A layer model. J. Phys. Oceanogr.,17, 1877–1896.

  • Godin, G., 1972: The Analysis of Tides. Liverpool University Press, 264 pp.

  • Goodrich, D. M., W. C. Boicourt, P. Hamilton, and D. W. Prichard, 1987: Wind-induced destratification in Cheasapeake Bay. J. Phys. Oceanogr.,17, 2232–2240.

  • Graber, H. C., B. K. Haus, R. D. Chapman, and L. K. Shay, 1997: HF radar comparisons with moored estimates of current speed and direction: Expected differences and implications. J. Geophys. Res.,102, 18 749–18 766.

  • Griffin, D. A., and K. R. Thompson, 1996: The adjoint method of data assimilation used operationally for shelf circulation. J. Geophys. Res.,101, 3457–3478.

  • Harrison, W., M. L. Brehmer, and R. B. Stone, 1964: Nearshore tidal and nontidal currents, Virginia Beach, Virginia. U.S. Army Corps of Engineers, Tech. Rep. No. 5, U.S. Army Coastal Engineering Research Center, Washington, DC, 20 pp. [Available from U.S. Army Coastal Engineering Research Center, 5201 Little Falls Road, Washington, DC 20016.].

  • Haus, B. K., H. C. Graber, L. K. Shay, S. Nikolic, and J. Martinez, 1998: Ocean surface current observations with HF Doppler radar during the Cope-1 experiment. RSMAS Tech. Report 95-010, University of Miami. Miami, FL, 104 pp.

  • Imasato, N., 1983: What is a tide-induced residual eddy? J. Phys. Oceanogr.,13, 1307–1317.

  • Kundu, P. K., 1976: Ekman veering observed near the ocean bottom. J. Phys. Oceanogr.,6, 238–242.

  • Lentz, S. J., M. Carr, and T. H. C. Herbers, 2001: Barotropic tides on the North Carolina Shelf. J. Phys. Oceanogr., in press.

  • Marks, F. D., L. K. Shay, and PDT-5, 1998: Landfalling tropical cyclones: Forecast problems and associated research opportunities. Bull Amer. Meteor. Soc.,79, 305–323.

  • Marmorino, G., L. K. Shay, B. K. Haus, R. A. Handler, H. C. Graber, and M. P. Horne, 1999: An EOF analysis of HF Doppler radar current measurements of the Chesapeake Bay outflow. Contin. Shelf Res.,19, 271–288.

  • Miller, J. L., Z. Hallock, L. K. Shay, and J. Zaitzeff, 1998: Tidal and subtidal surface salinity advection in a coastal plume: Estimates from remotely sensed fields. Eos, Trans. Amer. Geophys. Union,79, 168.

  • Mooers, C. N. K., 1973: A technique for the cross-spectrum analysis of complex valued time series with emphasis on properties of polarized components and rotational invariants. Deep-Sea Res.,20, 1129–1141.

  • Munchow, A., and R. W. Garvine, 1993: Dynamical properties of a buoyancy-driven coastal current. J. Geophys. Res.,98, 20 063–20 077.

  • ——, A. K. Masse, and R. W. Garvine, 1992: Astronomical and nonlinear tidal currents in a coupled estuary shelf system. Contin. Shelf. Res.,12, 471–487.

  • Officer, C. B., 1976: Physical Oceanography of Estuaries and Associated Coastal Waters. Wiley and Sons, 465 pp.

  • Otnes, R. K., and L. Enochson, 1978: Applied Time Series Analysis. Vol. 1. Basic Techniques. Wiley and Sons., 449 pp.

  • Pietrafesa, L. J., J. O. Blanton, J. D. Wang, V. Kourafalou, T. N. Lee, and K. A. Bush, 1985: The tidal regime in the South Atlantic Bight. Oceanography of the Southeastern U.S. Continental Shelf, L. P. Atkinson, D. W. Menzel, and K. A. Bush, Eds., Amer. Geophys. Union, 63–76.

  • Prandle, D., 1982: The vertical structure of tidal currents. Geophys. Astrophys. Fluid Dyn.,22, 29–49.

  • Redfield, A. C., 1958: The influence of the continental shelf on the tides of the Atlantic Coast of the United States. J. Mar. Res.,17, 432–448.

  • Rennie, S. E., J. L. Largier, and S. J. Lentz, 1999: Observations of a pulsed buoyancy current downstream of Chesapeake Bay. J. Geophys. Res.,104, 18 227–18 240.

  • Rosenfeld, L. K., and R. C. Beardsley, 1987: Barotropic semidiurnal tidal currents off Northern California during the Coastal Ocean Dynamics Experiment (CODE). J. Geophys. Res.,92, 1721–1732.

  • Shay, L. K., H. C. Graber, D. B. Ross, and R. D. Chapman, 1995: Mesoscale ocean surface current structure detected by HF radar. J. Atmos. Oceanic Technol.,12, 881–900.

  • ——, T. N. Lee, E. J. Williams, H. C. Graber, and C. G. H. Rooth, 1998a: Effects of low frequency current variability on near-inertial submesoscale vortices. J. Geophys. Res.,103, 18 691–18 714.

  • ——, S. J. Lentz, H. C. Graber, and B. K. Haus, 1998b: Current structure variations detected by HF radar and vector measuring current meters. J. Atmos. Oceanic Technol.,15, 237–256.

  • Simpson, J. H., and J. R. Hunter, 1974: Fronts in the Irish Sea. Nature,250, 404–406.

  • Teague, C. C., J. F. Vesecky, P. E. Hansen, N. G. Schwepf, J. M. Daidu, R. G. Orstott, K. Fisher, and D. M. Fernandez, 1997: Initital observations of ocean current and current shears, wind direction using multifrequency HF radar. Proc. Int. Geoscience and Remote Sensing Symp., Vol. 4, Singapore, IEEE, 1808–1810.

  • Weller, R. A., and J. F. Price, 1988: Langmuir circulation within the oceanic mixed layer. Deep-Sea Res.,35, 711–747.

  • Wheless, G. H., and A. Valle-Levinson, 1996: A modeling study of tidally driven estuarine exchange through a narrow inlet on a sloping shelf. J. Geophys. Res.,101, 25 675–25 687.

  • Zimmerman, J. T. F., 1978: Topographic generation of residual circulation by oscillatory (tidal) currents. Geophys. Fluid Dyn.,11, 35–47.

Fig. 1.
Fig. 1.

Experimental HF radar domain (dots) of Naval Research Laboratory (NRL) Chesapeake Bay Outfall Plume Experiment during Sep and Oct 1996. The NRL acoustic Doppler current profiler (ADCP) moorings, NOAA National Ocean Survey sea-level station along the Chesapeake Bay Tunnel Bridge (CBTB), and NOAA Coastal Marine Automated Network (NOAA–CMAN) Chesapeake Bay Lighthouse Tower (CHLV2) station are given relative to the HF radar domain. Master and Slave sites were located at Fort Story U.S. Army Base in Virginia Beach, Virginia, and the U.S. Naval Fleet Training Center Atlantic at Dam Neck, Virginia.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

 Fig. 2.
Fig. 2.

Surface current maps from COPE-1 experiment at 1200 UTC: (a) YD 258 (14 Sep), (b) YD 264 (20 Sep), (c) YD 271 (27 Sep), (d) YD 272 (28 Sep), (e) YD 277 (3 Oct), and (f) YD 280 (6 Oct) in 1996. Note that the color bar represents the velocity scale for each panel.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 3.
Fig. 3.

Vector plots of rotated current profiles (340°T) observed at ADCP mooring A for the smoothed and subsampled currents every hour at selected depths.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 4.
Fig. 4.

Low-pass filtered (a) wind vector (m s−1) and (b) atmospheric pressure (mb) from the NOAA-CMAN Chesapeake Bay Lighthouse Tower during the COPE-1 deployment. The wind is rotated into an oceanographic context and relative to the orientation of the coastline (340°T).

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 5.
Fig. 5.

Observed time series at mooring A from YD 261 (17 Sep) to YD 271 (27 Sep) 1996 during COPE-1 for the surface (solid) and 1.5 m (dotted) (a) along-shelf component (cm s−1), (b) cross-shelf component (cm s−1), (c) vertical current shear (×10−1 s−1) over a 1.5-m layer relative to the cross-shelf coordinate (70°T) and (d) one-half daily-averaged (36 points) magnitudes of the complex correlation coefficients (⩽1) and complex phase angles (°) listed above each bar.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 6.
Fig. 6.

Regression analyses of surface (ordinate) and subsurface (abscissa) currents (left panels) and histograms for the current differences (uou1.5, υoυ1.5) (right panels) at ADCP moorings A (upper panels: a, b) and A′ (lower panels: c, d) at 1.5 m (cm s−1) for cross-shelf (a, c) and along-shelf (b, d) components, respectively. Regression curves (solid) represent the best fit to the data with the biases and slopes given on the graphs. The histograms include differences of less than ±80 cm−1, and the 95% confidence limits are depicted by arrows. Note that υ and u represent along-shelf and cross-shelf components, respectively.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 7.
Fig. 7.

Time series of (a) observed sea level heights, (b) reconstructed tidal heights based on the harmonic analysis of (a), and (c) the residual sea level heights (a − b) during the COPE-1 experiment from 15 Sep (YD 259) to 8 Oct (YD 282) 1996. The data were acquired at the NOAA NOS Chesapeake Bay Tunnel Bridge station.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 8.
Fig. 8.

Comparison of the surface (solid) and depth-averaged (dashed) tidal current (upper panel) and contoured baroclinic tidal currents (lower panel) for (a) cross-shelf component and (b) along-shelf component (cm s−1) from ADCP A′ deployed in the COPE-1 experiment from YD 261 to YD 271 in 1996. The contour interval is 4 cm s−1 for the velocity profiles from 1.5 to 14.5 m subsampled at a 20-min sample interval.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 9.
Fig. 9.

Tidal ellipses of the (a) K1, (b) O1, (c) M2, and (d) S2 constituents superposed on the magnitude of the tidal current amplitude (color) from the COPE-1 experimental data over the radar domain based on 19 days of continuous data.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 10.
Fig. 10.

Explained variance of the summation of the four tidal constituents depicted in Fig. 9 for the (a) cross-shelf and (b) along-shelf surface currents.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 11.
Fig. 11.

Surface M2 tidal currents from the COPE-1 experiment on YD 280 (5 Oct 96) at (a) 0000 UTC, (b) 0200 UTC, (c) 0420 UTC, (d) 0620 UTC, (e) 0820 UTC, and (f) 1040 UTC. The color bar depicts the magnitude of the tidal current.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

 Fig. 12.
Fig. 12.

Magnitudes of the complex correlation coefficients (color) and phases (contoured) based upon 23 days of measurements in COPE-1 relative to cell 125 (dark triangle) in the strong tidal regime for (a) observed surface currents and (b) M2 tidal currents. The appropriate color bar is below each panel.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 13.
Fig. 13.

Normalized M2 tidal vorticity by the local Coriolis frequency at the same times in Fig. 11.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 14.
Fig. 14.

Mixing parameter S induced by the M2 tidal currents over the cycle in Fig. 12. Lower values of S imply less dissipation of the kinetic energy of the tidal currents near the mouth of the Chesapeake Bay.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 15.
Fig. 15.

Simulated ampltitudes and tidal ellipses from the adjoint model encompassing a large fraction of the HF radar grid.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 16.
Fig. 16.

Spatial differences between the simulated and observed M2 surface tidal currents for (a) cross-shelf and (b) along-shelf amplitudes, and (c) cross-shelf and (d) along-shelf phases. Amplitudes were contoured at 2 cm s−1 intervals and phases at 10° intervals. Spatial smoothing was done in the northeast corner of the domain where the surface current measurement was not as reliable.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Fig. 17.
Fig. 17.

Comparisons between observed (o) and modeled (m) surface current for the M2 constituent for (a) cross-shelf ampltitude and (b) phase, (c) along-shelf amplitude and (d) phase, (e) semi-major axis, and (f) orientation relative to 0°N. A total of 85 cells were used in the comparison to the simulated fields.

Citation: Journal of Physical Oceanography 31, 2; 10.1175/1520-0485(2001)031<0427:TSOTMT>2.0.CO;2

Table 1.

Tidal height amplitudes (η) and relative phases (ϕ) of nine constituents from the analyzed hourly sea level variations at a NOAA National Ocean Survey Station from nine months of measurements. The amplitudes (ηg) and phases (ϕg) are relative to Greenwich.

Table 1.
Table 2.

Summary of semimajor and semiminor axes (cm s−1), orientation, and phase angles (deg) at the ADCP mooring for M2 tidal constituent. Analyses include OSCR surface currents (z = 0) and the ADCP subsurface currents measurements (z > 1.5 m) during COPE-1 experiment. The approach is based on Foreman (1977), and the uncertainty in the least squares technique is given for each estimate following Beardsley et al. (1995) and Lentz et al. The phase is relative to zero phase at Greenwich.

Table 2.
Table 3.

Observed (σ2O) and percent of explained variance by a combination of the K1 and M2 tidal constituents are given for the 10-d time series at ADCP mooring A. The time series starts at 2200 UTC 17 Sep 1996 during the COPE-1 experiment.

Table 3.

1

Here the term submesoscale vortex refers to an isolated feature having similar scales to the deformation radius (λ ≈ 6 km).

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