surface m2 tidal currents along the north carolina shelf observed

Surface M2 tidal currents along the North Carolina shelf observed

with a high-frequency radar

Thomas M. Cook and Lynn K. ShayDivision of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science,University of Miami, Miami, Florida, USA

Received 24 January 2002; revised 19 July 2002; accepted 3 September 2002; published 21 December 2002.

[1] Surface tidal circulation over the continental shelf of Duck, North Carolina, wasexplored using surface current observations measured by a high-frequency (HF) radar.The Ocean Surface Current Radar (OSCR) was deployed at the U.S. Army Corps ofEngineers (USACE) Field Research Facility (FRF) in Duck, North Carolina, during 1–30October 1994 and measured surface current at 20-min intervals at 700 cells with a 1.2-kmresolution in a 25 � 44 km domain. Harmonic analysis of the surface current indicatesfine-scale (O(1 km)) variability in tidal amplitudes and phases within the study domain.The M2 tidal current amplitudes ranged from 2 to 10 cm s�1, with phases rangingfrom 100� to 120�, which compared well to previous results. Strong tidal currentamplitudes and fine-scale variability occurred near bathymetric features. Decreasing M2

surface tidal current amplitudes in the far field (�40 km) of the radar domain areconsistent with decreasing spectral quality of the HF radar returns. A 1-D barotropic tidalmodel is utilized to examine the physics of the M2 tidal currents over the shelf. ObservedM2 tidal currents compare well with those predicted by the model over the inner shelfto the midshelf. However, differences between the observed and the barotropic tidalcurrents of 5–8 cm s�1 are related to the decrease in spectral quality of the HF radar datain the far field. INDEX TERMS: 4219 Oceanography: General: Continental shelf processes; 4560

Oceanography: Physical: Surface waves and tides (1255); 4594 Oceanography: Physical: Instruments and

techniques; KEYWORDS: HF radar, surface currents, tidal currents, tidal models, USA, North Carolina, Duck

Citation: Cook, T. M., and L. K. Shay, Surface M2 tidal currents along the North Carolina shelf observed with a high-frequency radar,

J. Geophys. Res., 107(C12), 3222, doi:10.1029/2002JC001320, 2002.

1. Introduction

[2] Given the close proximity of the major populationcenters of the world to the ocean, it is not surprising thatthe coastal ocean circulation is regarded as sociallyrelevant. Motivating factors for this increased interest incoastal ocean research include the observation and pre-diction of its physical response to ordinary (i.e., tides) andextreme (i.e., hurricanes) events. While more attention isplaced on the latter due to its critical nature [Marks et al.,1998], important information about a region’s circulationcan be learned through detailed tidal investigations, par-ticularly with the use of Doppler radar technology [Pran-dle, 1987]. Accordingly, the surface tidal current responseover a broad continental shelf is the primary focus of thiseffort.[3] Since tidal currents represent an important contribu-

tion to the background flows over the continental shelf, theiraccurate determination and subsequent prediction are cen-tral to coastal circulation research. Over the past decade,surface current observations, as measured by University ofMiami’s high-frequency (HF) radar, the Ocean Surface

Current Radar (OSCR), have been acquired in severalvenues, including the North Carolina shelf during October1994 [Shay et al., 1998]. These data serve as the foundationof the present study as high-frequency (HF) radar representsan important observational tool capable of providing surfacecurrent measurements with a high spatial and temporalresolution, providing spatial context for mooring, ship,drifter, and autonomous underwater vehicle-based coastaloceanographic experimentation [Shay et al., 1995; Chap-man et al., 1997].[4] In a comprehensive study of the tides along the North

Carolina shelf, Lentz et al. [2001] found that the M2 semi-diurnal tidal constituent dominates both the sea level ele-vation and current tidal signals. Their moored observationscompared well to predictions from a one-dimensional bar-otropic tidal model [Clarke, 1991], which was used todescribe the cross-shelf tidal current structure. While theagreement between observed and predicted tidal currentswas high, the study was limited to five current metermoorings along a transect perpendicular to the shore. Giventhe variable bottom topography of the region, it is likely thatthese point measurements are not fully representative of thebroader region’s tidal circulation.[5] The motivation of the present work is the observa-

tion of fine-scale (O(1 km)) surface tidal current variations

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. C12, 3222, doi:10.1029/2002JC001320, 2002

Copyright 2002 by the American Geophysical Union.0148-0227/02/2002JC001320$09.00

15 - 1

with HF radar. Observations are compared with predictionsfrom a barotropic tidal model, given previous success incomparing surface tidal currents with simulations from alinear barotropic model in the Chesapeake Bay Mouthregion (100 km north of the study area) [Shay et al.,2001]. In this paper, surface current observations aredescribed in section 2, while the tidal current analysisfrom these observations are discussed in section 3, fol-lowed by an explanation of the one-dimensional barotropicmodel and a comparison between predicted and observedsurface tidal currents in section 4. Concluding remarks aregiven in section 5 including a summary and discussion ofthe results.

2. Experimental Setting

[6] Observations that will be used to address the objec-tives were acquired during October 1994 near the coast ofDuck, North Carolina, located along the southern MiddleAtlantic Bight (MAB) on the North Carolina shelf [Haus etal., 1995]. As shown in Figure 1, this region is unique as itlies between two distinct sources of forcing, the ChesapeakeBay (buoyancy forcing) to the north and the Gulf Stream(large-scale ocean current) to the south. The shelf off Duck,North Carolina, is relatively broad (80 km) and shallow,where depths typically range between 20 to 40 m depth,encompassing a complicated pattern of offshore sandbarsand canyons. The coast is oriented NW (340�T), and allcurrent velocity components are rotated (�20�) into a cross-and along-shelf coordinate system.[7] During October of 1994, a multiinstitutional near-

shore experiment, DUCK94, was conducted at the U.S.Army Corps of Engineers (USACE) Field ResearchFacility (FRF) and supported by the USACE, the Officeof Naval Research, the Naval Research Laboratory andthe United States Geological Survey. This experimentincluded surface current data acquired by an HF radarfrom 1 to 30 October 1994. The radar was deployedalong two ocean-front sites at FRF (master site) and inCorolla, North Carolina (slave) (Figure 1). The systemoperated at 25.4 MHz, mapping surface currents every 20min over a 25 km � 44 km domain, at 700 grid pointsspaced at 1.2 km, except in the far field where gridspacing was 2 km.

2.1. High-Frequency (HF) Radar

[8] Coastal HF radar represents an important observa-tional tool that provides surface current measurements witha high spatial and temporal resolution, and continues togain importance in coastal oceanographic experiments,addressing the need to resolve fine-scale coastal circulationprocesses [Brink et al., 1992]. The OSCR phased-arraysystem transmits at 25.4 MHz in HF mode and 49.9 inVHF mode and uses beam-forming and range-gating tech-niques to measure surface current at distinct, user-definedcells [Marex Technology Ltd., 1992]. The technique formeasuring surface currents from HF radar returns aredetailed in several studies, most notably Stewart and Joy[1974].[9] A single radar unit only measures the current along a

radial from the transmitter site, hence determination ofvector currents requires the use of two sequentially operat-

ing radars (Master and Slave) separated by several kilo-meters. OSCR observes the surface current (�30–50 cm)over a given sampling area (1200 km2 in HF mode, 70 km2

in VHF mode) at 700 locations with a given horizontalresolution (1.2 km in HF mode, 250 m in VHF mode). Theresultant surface current observations have compared wellto observations from independent, ‘‘proven’’ current meas-uring techniques such as the Vector Measuring CurrentMeter (VMCM) and the Acoustic Doppler Current Profiler(ADCP) with RMS differences of about 7 cm s�1 over arange of current of 100 cm s�1 [Chapman et al., 1997; Shayet al., 1998].

2.2. HF Radar Data Return and Quality

[10] The OSCR-derived surface currents during theDUCK94 experiment were characterized by a strong(95%) data return averaged over the OSCR domain, withfew temporal gaps, as only 69 of a possible 2073 sampleswere not acquired during a 29 day time series [Haus et al.,1995; Shay et al., 1998]. The OSCR system classifies thequality of the radial currents based on the strength of theBragg peaks relative to the noise level of the receivedbackscatter. Quality numbers range from 0 to 9, with a highquality number assigned to an observation where the Braggpeaks are strong and well resolved (narrow), such that theradial current is determined with a high degree of accuracy[Marex Technology Ltd., 1992]. The combined spectralquality numbers from the master and slave sites (Figure 2)illustrate that the overall spectral quality is reasonable forthe DUCK94 deployment, and is highest in the central partof the domain from nearshore to about 25 km offshore, and

Figure 1. High-resolution bathymetry from side-scanningsonar [Lentz et al., 2001] contoured at 5 m intervals alongthe North Carolina shelf. The experimental setup near Duck,NC during the DUCK94 and CoOP experiments is shown,including OSCR cells (dots), CoOP moorings (squares), andbottom pressure gauges (triangles). The inset shows theMiddle Atlantic Bight and the location of Duck, NC.

15 - 2 COOK AND SHAY: SURFACE M2 TIDAL CURRENTS

then begins to decrease toward the outer periphery of thedomain. The decreasing spectral quality in the far field isdue to the attenuation of the radio waves with distance,which is greatest during periods of storm-induced surfacewaves [Haus et al., 1995].[11] Forming reliable vector current fields from radial

measurements strongly depends on the intersection angle(y) between the radials emanating from the master and slavestations (Figure 3a). Optimal intersection angles (given by30� � y � 150�) encompassed nearly the entire domainexcept for the grid points closest to the shore, whereintersection angles exceeded the 150� limit. The GeometricDilution Of Precision (GDOP) also allows an examinationof the spatial dependence of the observed current differ-ences based on these geometrical constraints as describedby Chapman et al. [1997]. Using the radar’s mean lookdirection (a), and the half-angle (f) between intersecting

beams, expressions for the error in the along-shelf (v) andcross-shelf (u) current components are

sv ¼ 2sin2 að Þsin2 fð Þ þ cos2 að Þcos2 fð Þ

sin2 2fð Þ

� �12

s; ð1Þ

and

su ¼ 2cos2 að Þsin2 fð Þ þ sin2 að Þcos2 fð Þ

sin2 2fð Þ

� �12

s; ð2Þ

where s represent RMS current differences. The GDOPvalue is thus defined as the ratios of sv

s and sus for the along-

shelf and cross-shelf currents, respectively [Chapman et al.,1997]. Over most of the domain, GDOP values for u and vrange from 0.75 to 2 (Figures 3b–3c). However, close toshore where intersection angles increase, the GDOPincreases quickly to maximum of �4 in the u componentand �6 in the v component. Thus, these cells close to shore(�24 of 700) are excluded from all further analyses andcomparisons in this study.[12] Despite these physical constraints, the OSCR system

accurately measured high resolution surface currents duringvarious oceanographic conditions (Table 1). Shay et al.[1998] provides a detailed comparison of the surface cur-rents with the VMCMs at the 20- and 25-m moorings duringthe DUCK94 experiment. Over their entire shared recordlength, the 4 m VMCM at the 25-m mooring and the OSCRhad a complex correlation coefficient of 0.93 amplitude and7� phase, and an RMS difference in the cross- and along-shelf direction of 7.2, and 7.1 cm s�1, respectively. Dailyaveraged complex correlation coefficients exceeded 0.8during the experiment, indicative of a high quality data set.

3. Tidal Analysis

[13] The technique of harmonic analysis will be used toisolate the tidal variability in the data, where the observedvalues are least squaress fit to a harmonic representation ofthe tide. As horizontal velocity is a vector quantity, its scalarcomponents (u, v) are analyzed separately from the expres-sions,

u tð Þ ¼ u0 þXRn¼1

un cos wnt � bnð Þ þ ur tð Þ; ð3Þ

Figure 2. Spectral quality of OSCR data during theDUCK94 experiment based on strength of Bragg peaks inDoppler spectra.

Figure 3. a) Intersection angle of master and slave radials at each OSCR cell, and GDOP for b) v and c)u current components.

COOK AND SHAY: SURFACE M2 TIDAL CURRENTS 15 - 3

and,

v tð Þ ¼ v0 þXRn¼1

vn cos wnt � cnð Þ þ vr tð Þ: ð4Þ

where u and v are the observed component velocities, u0 andv0 are the mean component velocities, un and vn and bn andcn represent the amplitude and phase lag (i.e., harmonicconstants) for each of the n tidal constituent frequencies (wn)[Godin, 1972]. Here, R represents the number of resolvabletidal components, which depends on sampling interval andduration of the observed time series (Rayleigh criterion),and ur and vr represents the residual signals from physicalcontributions other than the tidal forcing. To interpret andvisualize results, the tidal current data are transformed intotidal ellipse parameters; semimajor axis (Ma), semiminoraxis (ma), orientation (q), and phase (f).[14] Foreman’s [1981] tidal analysis software, based on

Godin [1972], will be used in this study. In addition tosolving the harmonic constants in (3) and (4), this packagecalculates nodal corrections, which represent slow changesin amplitude and phase of major tidal constituents due inpart to interference from close, unresolvable constituents.The package computes the phase lag relative to the moon’stransit over Greenwich, England. This reduces the phase toa common zone, thus facilitating comparison of tidalanalysis of records without a common starting time. Finally,uncertainties (95% confidence limits) in the amplitude andphase for each constituent are estimated following theapproach of Lentz et al. [2001].[15] A record length of �29 days is sufficient to resolve

the most energetic tidal constituents, and is the traditionalminimum length for a short time series. This study isconfined to the M2 tidal constituent (12.42 hr period),typically the dominant tidal constituent, hence resolutionis not issue here. However, uncertainties may also exist inthe tidal analysis of current observations due to the lowersignal-to-noise ratio as compared to relatively smooth sealevel fluctuations. Contribution from wind and wave com-ponents may also complicate the surface current results[Prandle, 1997].

3.1. Tidal Variability at Duck, North Carolina

[16] Examination of the M2 cotidal chart for the MAB[Moody et al., 1984] indicates that the M2 tide is nearlyconstant in amplitude (45–50 cm) and phase along the shelfand occurs simultaneously along the MAB shelf break

about 12 h after the moon’s transit at Greenwich, England.The study region’s tides are dominated by the M2 tidalconstituent whose coastal sea level elevation amplituderanges between 46 and 48 cm over the 44 km study domain[Lentz et al., 2001]. The M2 constituent is responsible for70–80% of the observed sea level elevation variance [Cook,2000]. Variance explained by the cross- (u) and along-shelf(v) components of the M2 surface tidal currents is shown inFigure 4. Notice that a fair percentage (15–25%) of thealong- and cross-shelf current variance is explained by tidalcurrents in the outer domain (depths > 20 m), whereas lessvariance (5–10%) is explained closer to shore wherecurrents approach zero toward the coast.[17] Overall, the M2 surface tidal ellipses rotate clockwise

(not shown) and the additional parameters (Figure 5a) arespatially coherent, but exhibit fine-scale variability. An

Table 1. Chronology of Observed Surface Flow Features From

HF Radar During the Duck94 Experiment in October 1994 From

Shay et al. [1998]

Event Type

Start Date End Date

Day Time Day Time

1 Frontal Passage 1 1800 4 00002 Coastal Intensification 4 0100 6 23003 Low Winds and Tidal Forcing 7 0000 12 07004 Coastal Intensification 12 0800 14 12005 Nor’easter 14 1300 18 10006 Low Winds and Tidal Forcing 18 2200 26 18007 Frontal Passage 26 1900 29 02008 Low Winds and Tidal Forcing 29 0300 30 1200

Figure 4. Variance explained by the a) cross- and b)along-shelf surface M2 tidal surface currents.


example of this variability is seen in the M2 surface tidalellipse orientation, where ellipses are oriented in a cross-shelf direction offshore. These ellipses become morealigned in the along-shelf direction near the coast. Thisresult is expected as cross-shelf flow is restricted near thecoast and noted in other studies of the region [Lentz et al.,2001]. Fine-scale spatial variability of the M2 tidal current

amplitude is evident in the central and far-field areas of thedomain, especially in the vicinity of the 25 m isobath(Figure 6). It is likely that the local bathymetry affects theM2 tidal current amplitude here, as the bathymetry ischaracterized by a complex pattern of ridge-swale features.Generally, the M2 tidal current amplitude increases awayfrom the coast, but toward the far field begins to decrease,

Figure 5. Surface M2 tidal ellipses from tidal analysis of a 29-day series of HF radar derived surfacecurrent, a) Tidal amplitude (semimajor axis) is shown in color, and ellipses are plotted at selected cells, b)phase contoured at 5� intervals.


likely due to lower data quality indices that decrease in thefar field of the HF radar domain as suggested by Figure 2.[18] While the decrease of spectral quality limits a quan-

titative description of the relation between the M2 tidalcurrent amplitude and the bathymetry in the far field, theoccurrence of fine-scale variability near bathymetric fea-tures is evident. For example, in the far field of the northernpart of the domain, an isolated area of M2 tidal currentamplitude of 9 cm s�1 occurs near a relatively shallowsandbar (depth �25 m) surrounded by deeper water (depth�30 m). This also is evident in the north-central area of thedomain, where the M2 tidal current amplitude reaches amaximum (10 cm s�1), along a shallow sandbar (depth �20m) surrounded by deeper water (depth �27 m).[19] Another area of fine-scale spatial variability of M2

tidal current amplitude exists near the coast in the proximityof the slave site, where tidal current amplitude is 3 to 4 cms�1 greater than surrounding areas and the orientation of thetidal ellipses are perpendicular to the coast and to thesurrounding tidal ellipses. Although this area is consistentwith the strong currents found in the nearshore regionassociated with the along-shelf propagation of the Chesa-peake Bay freshwater plume, which occasionally extends 10km offshore [Rennie et al., 1999], it also borders on an areawhere the HF radar vector currents tend to be less reliabledue to intersection angles greater than 150� (Figure 3a).Furthermore, inspection of the M2 tidal current amplitudeuncertainty (Figure 7) reveals that this area contains thelargest uncertainty (>1.2 cm s�1) over the entire regime.Due to these factors, the fine-scale variability present in thisarea will be ignored.

[20] The phase of the surfaceM2 tidal currents (Figure 5b)varies only slightly throughout the domain, increasing from100� in the south to 120� in the north. Throughout the centralpart of the experimental domain, the phase is nearly constant,

Figure 6. Surface M2 tidal ellipse amplitude (color contours as in Figure 5a) superposed on localbathymetry (black contours).

Figure 7. Uncertainty of surfaceM2 tidal ellipse amplitudefrom tidal analysis of a 29-day series of OSCR derivedsurface current.


decreasing by 5 to 10� toward the outer edge of the domain.The variance of the observed surface phase slightly larger, butconsistent with the data presented by Lentz et al. [2001]. Thetidal currents over the study area lag the M2 sea level heightby roughly 60 to 80� [Cook, 2000]. Additionally, an area ofextremeM2 tidal current phase change exists in the nearshorearea described above, but this is likely an artifact of the largeM2 tidal amplitude uncertainty in this region (Figure 7).[21] The M2 ellipse parameters of the surface current

measurements corresponding to the 20- and 25-m moorings[Lentz et al., 2001] indicate good agreement to the near-surface (4 m) ellipses (Table 2). At both sites, surface andnear-surface tidal ellipses are oriented in the same direction,but the surface tidal ellipse has a greater phase. That is,subsurface tidal currents lead those at the surface. The phaselead of the near-bottom currents is predicted by analyticalsolutions for tidal current profiles [Prandle, 1982; Kundu,1976], which also indicate that maximum tidal currentamplitudes occur at middepth. Here, the M2 tidal currentshave maximum amplitude at middepth (13 to 18 m) at the25-m mooring, and near surface (4 m) at the other moorings[Cook, 2000]. Generally, the ellipses are more rotary in thesurface layer, but become more rectilinear with depth,suggestive of bottom friction influence. The results fromthe moorings suggest that the M2 current response isprimarily barotropic, consistent with results from previousstudies [Shay et al., 1998; Lentz et al., 2001]. This findingwill be explored in the next section within the context of alinear, barotropic tidal model.

4. Barotropic Tidal Model

[22] Tides over the continental shelf are independent ofdirect astronomical forcing as they represent a cooscillationof the open ocean tide, which is forced by the tidal potential[Mofjeld, 1976]. This allows one to treat shelf tides as afreely propagating wave from the open ocean at frequenciescorresponding to the frequencies of astronomical forcing.To understand the dynamics associated with the tidal currentobservations, the one-dimensional barotropic model ofBattisti and Clarke [1982] and Clarke [1991] is used todetermine the barotropic response to the tidal forcing on theNorth Carolina shelf.[23] Battisti and Clarke [1982], and subsequently Clarke

[1991] develop and evaluate an analytical one-dimensionalbarotropic model based on the Laplace Tidal Equations that

include along-shelf gradients of sea level height, Coriolisforce and linear friction. If one assumes the continental shelfis considered ‘‘smooth’’, such that the along-shelf (@/@y)variation in topography is assumed to be smaller than thecross-shelf (@/@x) variations (i.e., @h/@y @h/@x), solu-tions are given by,

iwh ¼ Qh iwþ r

h

� �hx

h ixþ Qhð Þx f hy; ð5Þ

u ¼ �Q hx iwþ r=hð Þ þ f hyh i

; ð6Þ

v ¼ Q f hx � hy iwþ r

h

� �h i; ð7Þ

Q ¼ g= iwþ r=hð Þ2þf 2h i

: ð8Þ

where h is sea level displacement, u and v are the cross- andalong-shelf velocity, respectively, f is the Coriolis para-meter, g is acceleration due to gravity, w is the frequency forthe M2 tidal constituent, and h is variable water depth. Thelinear friction coefficient, r, depends on the drag coefficientCD and the RMS velocity juj such that,

r xð Þ ¼ CD uj j: ð9Þ

Based on current meter records, Lentz et al. [1999]estimated r = 5 � 10�4 m s�1 from the depth-averagedmomentum balances from this region, and produced bottomstress estimates in agreement with observations.[24] The along-shelf wave number is defined, l = hy/lh,

which is independent of x [Clarke and Battisti, 1981], and isa complex parameter defining the along-shelf scale of thetidal forcing that can be approximated from availablecoastal observations. While the horizontal wavelength ofthe open ocean barotropic M2 tide is O(2000 km), itscoherent scale on the shelf has been found to be signifi-cantly decreased [Rosenfeld, 1987]. Thus, choosing anappropriate along-shelf scale is crucial in accurately pre-dicting the M2 tidal current on the shelf. Given that thecoastal tide can be represented by the form hc( y) = AeiG,where A( y) is the amplitude and G( y) is the phase of the

Table 2. Results of the Tidal Analysis for the Near-Surface

VMCMs at the 20- and 25-m Mooring for Selected Tidal

Constituents

Near-Surface Current Meters and Nearest OSCR Cell at theVMCM Moorings

Depth, m Ma, cm s�1 mI, cm s�1 q, � f, �

20-m VMCM Mooring—29-day Series M2OSCR 3.4 ± 1.0 �1.9 ± 0.8 126.6 ± 23.5 277.8 ± 25.44.0 4.9 ± 0.9 �1.3 ± 0.7 125.5 ± 9.1 292.2 ± 11.16.0 4.6 ± 0.8 �1.0 ± 0.6 124.7 ± 8.3 297.0 ± 10.5

25-m VMCM Mooring—29-day Series M2OSCR 7.1 ± 0.6 �2.9 ± 0.8 143.2 ± 7.5 282.5 ± 6.74.0 6.0 ± 0.6 �2.3 ± 0.6 136.4 ± 7.0 289.9 ± 6.86.0 5.8 ± 0.5 �2.2 ± 0.5 141.9 ± 6.3 290.1 ± 5.7

Figure 8. Map of DUCK94 HF radar domain with OSCRcells (dots), cross-shelf transects where currents from thebarotropic, 1-D model are computed (grey lines), andbottom pressure gauges (triangles).


tidal constituent along the coast, Clarke and Battisti [1981]estimate l as,

l ¼ Gy � iAy=A: ð10Þ

This parameter is often estimated from coastal tidal or sealevel stations, however few stations exist in the study area.Lentz et al. [2001] notes that the coastal tidal station nearthe Chesapeake Bay is further complicated due in part tononlinearities within 1–2 deformation radii of the Bay. Inthis study, l is estimated from (10) using amplitude andphases from the along-shelf array of bottom pressure gauges(J0–J4) (Figures 8 and 9) as in the work of Lentz et al.[2001]. Equation (5) can be solved numerically given l = hy/ih and the boundary conditions of a known tidal sea levelamplitude (hc = known), prescribing no flow through thecoast (u = 0 at x = 0). Cross-shelf, sea level estimates canthen be substituted into (6) and (7) to solve for the cross-shelf tidal current structure.[25] The predicted tidal currents, particularly the along-

shelf current, are sensitive to the values of r and l [Churchet al., 1985; Cook, 2000]. Generally, increasing rdecreases the along-shelf current amplitude and phase[Cook, 2000]. The value of r (5 � 10�4m s�1) used here

reasonably estimated the bottom stress at the 20-m moor-ing location [Lentz et al., 1999]. Along-shelf amplitudeand phase is also highly sensitive to the choice of along-shelf wave number (l). As lr increases, predicted amplitudeand phase decreases, and as li increases, predicted ampli-tude increases while predicted phase decreases [Cook,

Figure 9. Bottom pressure time series at along shelf pressure array for sensors a) J0, b) J1, c) J2, d) J3,from Lentz et al. [2001].

Figure 10. M2 tidal constants for the along-shelf pressurearray from Lentz et al. [2001], where a) M2 tidal amplitudevariations with latitude, and b) M2 tidal phase variationswith latitude. The along-shelf wave number estimated fromthis data and equation (10) is 5.2 � 10�7–1.0495 � 10�6i.


2000]. Since l was determined using high-quality pressuredata collected during the same period of current measure-ments used in this study, it is assumed that its value isaccurate.

4.1. Comparison With Surface Tidal Ellipses

[26] The one-dimensional model is applied along thirtycross-shelf transects spaced 1.2 km encompassing the HF

radar domain and nearshore pressure gauge [Alessi et al.,1996] coverage (Figure 10). Transects are taken along linesof constant latitude (i.e., f = constant) to correspond with HFradar grid cells, and are not necessarily perpendicular to thecoastline. However, these transects are perpendicular to theorientation of the shelf break and 100 m isobath. High-resolution bathymetry from side-scanning sonar is used forthe model depth measurement (h). Coastal sea level ampli-

Figure 11. Surface M2 tidal ellipses predicted from 1-D barotropic tidal model along 30 transectsspaced 1.2 km within the OSCR domain, where a) tidal amplitude (semimajor axis) is shown in color,and ellipses are plotted at selected cells, and b) phase contoured at 5� intervals.


tudes (h0) and along-shelf wave number (l) were thendetermined using a linear interpolation of the along-shelftransect of pressure gauges analyzed by Lentz et al. [2001](Figure 8).[27] The predicted barotropic M2 tidal current ellipses are

shown in Figure 11. Generally, predicted M2 semimajoraxis (Figure 11a) increases seaward to a maximum near 15cm s�1 on the outer edge of the OSCR domain. In the near-field, the M2 tidal current amplitudes increase in a linearmanner, however toward the central and far field the fine-scale variability of the M2 tidal amplitude increases. Overthe entire domain, modeled M2 tidal current ellipses areoriented in the shore parallel direction. This contrasts theobserved M2 tidal current ellipses which have a shoreperpendicular orientation in deeper water, and turn shoreparallel toward the coast. Predicted phase (Figure 11b) isgenerally constant across the shelf, but decreases towardthe coast due in part to bottom friction influence in shallowdepths.[28] A large fraction of the differences between observed

and predicted amplitudes (Figure 12) are generally smalland within the measurement accuracy of radar-derived sur-face currents (2 to 4 cm s�1). However, in the far field of theexperimental domain, observed amplitudes tend to be muchweaker than predicted tidal amplitudes (4 to 8 cm s�1). It islikely that the lower spectral quality data in this area, mayexplain some of these differences. In fact, the correlationcoefficient between the spectral quality and amplitudedifference is 0.83, suggestive of a strong relationshipbetween these quantities.[29] Generally, there is agreement between the harmonic

constants of the observed surface and predicted barotropictidal currents (Figure 13). For both the cross- and along-shelfcomponents (Figures 13a–13c), predicted barotropic tidalamplitudes exceed those at the surface. Slopes of the linear

regression of the predicted and observed amplitudes are 0.97and 1.67 for u and v, respectively. The extent to which thepredicted along-shelf component tidal amplitudes exceedthe surface is also evident in Figure 11a, which shows thatthe predicted ellipses are oriented more shore-parallel thanthose derived from the radar data. There is little agreementbetween the observed and predicted cross-shelf componentphase (Figure 13b), as the predicted cross-shelf phase varieslittle from 90�. The predicted along-shelf phase varies moreover the domain than the cross-shelf phase, and a fairagreement to the observed along-shelf phase (Figure 13d)is evident given the 0.71 value for the linear regressionslope. The slope of the regression line of the predictedsemimajor axis on the observed semimajor axis is 1.4,whereas the slope of the regression of the predicted versusobserved orientation is 0.72, as noted above.[30] Additionally, the model overestimates the depth-

averaged tidal current amplitude at each of the moorings(Figure 14). It is possible that the value of the bottomfriction coefficient, r, may be responsible for the discrep-

Figure 12. Difference in M2 tidal ellipse amplitude (cms�1) between observed (Figure 5a) and predicted (Figure10a) currents.

Figure 13. Comparison of observedM2 tidal parameters tothose predicted from the linear, barotropic model, a) cross-shelf tidal current amplitude, b) cross-shelf tidal currentphase, c) along-shelf tidal current amplitude, d) along-shelftidal current phase, e) major axis, f) ellipse orientation. Thelinear regression line is shown in black, and the slope (m)and bias (b) is included for each regression.


ancy. However, sensitivity studies show that a rather largechange in r is required to more accurately represent thecross-shelf currents [Cook, 2000]. The values of r needed to‘‘tune’’ the model to accurately predict the depth-averagedM2 tidal currents at the mooring locations is unrealistic, andan order of magnitude greater than the value currently used(5 � 10�4 m s�1).

5. Discussion and Conclusions

[31] The investigation of the M2 surface tidal circulationalong the North Carolina shelf has provided new insights onthe fine-scale current variability which occurs over a broadcontinental shelf. The tidal forcing on the shelf is due to thecooscillation of the open ocean tide, and explains up to 90%of the observed coastal sea level and 20 to 40% of thehorizontal current along the North Carolina shelf [Cook,2000].[32] The region’s dominant tidal constituent is the M2

semidiurnal constituent, which accounts for sea level dis-placements of 46 to 49 cm at the coast, and had amaximum current amplitude of 10 cm s�1 at the surfacenear an offshore sandbar. Spatially, the M2 tidal currentellipses were coherent over the HF radar domain, except inan area in the northern nearshore region, where tidalamplitudes were intensified by 2 to 4 cm s�1 and tidalphase varied 40 to 50� over a 5 km scale. While thisnearshore area is consistent with the depiction of Ches-apeake Bay buoyant outflow water on this shelf as shownby Rennie et al. [1999], the HF radar configuration for thisdeployment does not allow rigorous analysis over thenearshore region.[33] A 1-D barotropic tidal model [Clarke, 1991] is

employed to delineate the dynamics of the M2 tidal currentsacross the shelf. Overall, a large fraction of the surface M2

tidal current variability can be explained by linear baro-tropic dynamics. Generally, the spatial variability of thepredicted M2 tidal currents is similar to that the surface,however predicted amplitudes are greater than observed in amajority of the study domain. Around 70% of the differ-ences between the observed surface M2 tidal current ampli-tudes and predicted barotropic tidal current amplitudes are±2 cm s�1, which is within the measurement resolution ofthe OSCR system. The remainder of the differences arelocated in the far field of the HF radar domain, wherespectral data quality is decreased compared to those shore-ward areas.

[34] While a majority of these differences can beexplained by phenomena affecting the observation techni-que, it is not to say that a dynamical explanation, namely thestructure of the barotropic tidal depth profile, does not exist.First, the 1-D barotropic model assumes that the along-shelfvariations in bathymetry are small compared to those in thecross-shelf direction. This assumption may not be suitablefor this location as the shelf width doubles over a relativelyshort distance. Lentz et al. [2001] investigate the effects of awidening shelf on the along-shelf pressure gradient using aflat-bottom two-dimensional model, which produces M2

tidal current amplitudes closer to those observed at themoorings than the 1-D model with realistic topographydoes.[35] Finally, M2 tidal currents are observed to vary with

the bottom topography. In-depths deeper than 20 m, tidalcurrent variations somewhat follow topographic variations,as maximum observed currents occurred near offshoresandbars. With an extended deployment of HF radar (>3months), it is likely that the movement of these offshoresandbars could be observed. Prandle [1997] refers to thisas the ‘‘Grand Challenge’’ of HF radar studies. That is,sediment transport monitoring represents an excitingpotential application of HF radar, especially given thecost and increasing frequency of beach renourishmentprojects.[36] This study has shown the effectiveness of HF radar

for measuring well-resolved tidal currents on the continentalshelf. The observed M2 tidal currents may be less reliablealong the outer periphery of the experimental domain due toattenuation of the transmitted HF signal, as shown in thedifferences between observed and predicted tidal currents.However, these differences may be manifestations of thevariation of the tidal current profile in the differing dynam-ical regimes that exist on the North Carolina shelf [Lentz etal., 1999]. While most of the tidal variability on this shelfcan be explained using a 1-D tidal model, further under-standing of the relationship between surface and subsurfacetidal currents needs to be developed to fully utilize HF radarmeasurements in differing dynamical regimes. Combinedwith longer-term deployments and high quality subsurfacemeasurements, fine-scale, 3-dimensional tidal response willbe observed at a resolution which, at this point, has onlybeen approximated using numerical models. HF radar datahas been effectively assimilated into coastal numericalmodels [Shay et al., 2001], providing further insight intothe complications of coastal dynamics.

[37] Acknowledgments. The authors gratefully acknowledge fundingsupport by the Office of Naval Research Coastal Dynamics (321 CD)contract N00014-94-1-1016, Remote Sensing Program (321 RS) contractN00014-96-1-1101, and Numerical Modeling (322 OM) contract N00014-98-1-0818 in supporting the HF radar measurements. The National ScienceFoundation supported the Coastal Ocean Processes (CoOP) measurementprogram through OCE-92-21615 which provided the VMCM and pressuredata. The authors are indebted to numerous discussions with Steve Lentz,who provided the VMCM data, code for the 1-D barotropic model andcomments on the drafts of this manuscript. Additionally, Jacobus van deKreeke, Thomas Lee and Kevin Leaman provided comments instrumentalin the development of this manuscript. The staff of the United States ArmyCorps of Engineers at the Duck Field Research Facility shared resources inplanning and executing the experiment. Bill Birkemeier, Gene Bichner, andBill Grog provided real estate required for the OSCR trailer and thelogistical support that were needed for successful operations. Art Lefflersurveyed the master site and Kent Hathaway assisted with the electrical

Figure 14. Cross-shelf variation of M2 tidal amplitudeprofiles, with tidal amplitude from the VMCM (dot), thedepth-averaged tidal amplitude (black line), and thepredicted barotropic value (dashed line).


connections. Brian Haus, Chris Boyce, Nick Peters, Mike Rebozo, JorgeMartinez and Louis Chemi were involved in the experiment.

ReferencesAlessi, C. A., S. J. Lentz, and J. Austin, Coastal ocean processes innershelf study: Coastal and moored physical oceanographic measurements,Woods Hole Oceanogr. Inst. Rep. 96-06, 154 pp., Woods Hole, Mass.,1996.

Battisti, D. S., and A. J. Clarke, A simple method for estimating barotropictidal currents on continental margins with specific application to the M2

tide off the Atlantic and Pacific Coasts of the United States, J. Phys.Oceanogr., 12, 8–16, 1982.

Brink, K. H., et al., Coastal ocean processes: A science prospectus, WoodsHole Oceanogr. Inst. Tech. Rep. WHOI-92-18, 103 pp., Woods Hole,Mass., 1992.

Chapman, R. D., L. K. Shay, H. C. Graber, J. Edson, A. Karachintsev,C. Trump, and D. B. Ross, On the accuracy of HF radar surface currentmeasurements: Intercomparison with ship-based sensors, J. Geophys.Res., 102, 18,737–18,748, 1997.

Church, J. A., J. C. Andrews, and F. M. Boland, Tidal currents in the centralGreat Barrier Reef, Cont. Shelf Res., 4, 515–531, 1985.

Clarke, A. J., The dynamics of barotropic tides over the continental shelfand slope (review), in Tidal Hydrodynamics, edited by B. B. Parker, pp.79–108, John Wiley, New York, 1991.

Clarke, A. J., and D. S. Battisti, The effect of continental shelves on tides,Deep Sea Res., 28, 665–682, 1981.

Cook, T. M., Surface tidal current variability on the North Carolina shelfobserved with high frequency radar, M.S. thesis, 97 pp., Univ. of Miami,Miami, Fla., 2000.

Foreman, M. G., Manual for tidal heights analysis and prediction, Tech.Rep. Pac. Mar. Sci. 77-10, 97 pp., Inst. of Ocean Sci.,Victoria, B. C.,1981.

Godin, G., The Analysis of Tides, 264 pp., Univ. of Toronto Press, Toronto,Ont., 1972.

Haus, B. K., H. C. Graber, L. K. Shay, and J. Martinez, Ocean surfaceobservations with HF Doppler Radar during the DUCK94 Experiment,RSMAS Tech. Rep. 95-010, 104 pp., Rosenstiel Sch. of Mar. and Atmos.Sci., Univ. of Miami, Miami, Fla., 1995.

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

Lentz, S. J., R. T. Guza, S. Elgar, F. Feddersen, and T. H. C. Herbers,Momentum balances on the North Carolina inner shelf, J. Geophys.Res., 104, 18,205–18,226, 1999.

Lentz, S. J., M. Carr, and T. H. C. Herbers, Barotropic tides on the NorthCarolina Shelf, J. Phys. Oceanogr., 31, 1843–1859, 2001.

Marex Technology Ltd., OSCR User Manual, vol. 1, 124 pp., Cowes, U. K.,1992.

Marks, F. D., L. K. Shay, and PDT-5, Landfalling tropical cyclones: Fore-cast problems and associated research opportunities, Bull. Am. Meteorol.Soc., 79, 305–323, 1998.

Mofjeld, H. O., Tidal currents, in Marine Sediment Transport and Environ-mental Management, edited by D. J. Stanley and D. J. P. Swift, pp. 53–64, John Wiley, New York, 1976.

Moody, J. A., et al., Atlas of tidal elevation and current observations on theNortheast American Continental Shelf and Slope, U.S. Geol. Surv. Bull.1611, 122 pp., U.S. Govt. Print. Off., Washington, D. C., 1984.

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

Prandle, D., The fine-structure of nearshore tidal and residual circulationsrevealed by H.F. radar surface current measurements, J. Phys. Oceanogr.,17, 231–246, 1987.

Prandle, D., Tidal and wind-driven currents from OSCR, Oceanography,10, 57–59, 1997.

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

Rosenfeld, L. K., Tidal band current variability over the northern Californiacontinental shelf, Ph.D. thesis, Woods Hole Oceanogr. Inst. Rep. WHOI-87-11, 237 pp., Woods Hole, Mass., 1987.

Shay, K. L., H. C. Graber, D. B. Ross, and R. D. Chapman, Mesoscalesurface current structure detected by HF radar, J. Atmos. Oceanic Tech-nol., 12, 881–900, 1995.

Shay, L. K., S. J. Lentz, H. C. Graber, and B. K. Haus, Current structurevariations detected by high frequency radar and vector measuring currentmeters, J. Atmos. Oceanic Technol., 15, 237–256, 1998.

Shay, L. K., T. M. Cook, Z. Hallock, B. K. Haus, H. C. Graber, andJ. Martinez, Strength of M2 tide at the Chesapeake Bay, J. Phys. Ocea-nogr., 31, 427–449, 2001.

Stewart, R. H., and J. W. Joy, HF radar measurement of surface current,Deep Sea Res., 21, 1039–1049, 1974.

��T. M. Cook and L. K. Shay, Division of Meteorology and Physical

Oceanography, Rosenstiel School of Marine and Atmospheric Science,University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149,USA. ([email protected])


surface m2 tidal currents along the north carolina shelf observed

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