Observed tidal currents outside Block Island Sound: Offshore decay and effects of estuarine outflow

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2003jc001804, 2004 Observed tidal currents outside Block Island Sound: Offshore decay and effects of estuarine outflow Daniel L. Codiga and Laura V. Rear 1 Department of Marine Sciences, University of Connecticut, Groton, Connecticut, USA Received 31 January 2003; revised 15 November 2003; accepted 10 December 2003; published 5 June [1] An array of moored profiling current meters on the inner continental shelf m deep is used to investigate tidal currents outside the Block Island Sound and Long Island Sound estuarine system. The M 2 constituent dominates due to near-resonant semi-diurnal estuarine response. Vertical-mean M 2 currents rotate clockwise in time in ellipses elongated toward the estuary mouth with little sensitivity to complex local bathymetry; semi-major axes decay sharply offshore (55 to 20 cm/s over 10 km) in agreement with the nearly inverse-square radius dependence of a kinematic theory. Estimated tidal volume exchange out of Block Island Sound to the south is m 3 /s. Observed vertical structure of M 2 ellipses in the deepest m (amplitude decay, ellipse flattening, major axis turning clockwise, phase advance) is generally captured well by optimally fit frictional solutions despite the fact that they omit bathymetry and include stratification only indirectly through its influence on eddy viscosity. In the upper water column, vertical structure varies seasonally: Mid-depth ellipses enlarge in spring; near-surface ellipses are larger (smaller) than optimal-fit solutions in fall/winter (spring). Observed seasonal-average estuarine outflow includes surface-intensified Coriolisdeflected mean flow that strengthens and spreads farther offshore in spring. Richardson numbers based on moored hydrographic profiler records suggest spring stratification suppresses deep eddy viscosities, which in frictional solutions can explain mid-depth ellipse enlargement. An inviscid theory for mean-flow modifications due to ambient vorticity of estuarine outflow currents is shown to be the most plausible explanation for observed seasonal changes in near-surface tidal ellipses. INDEX TERMS: 4560 Oceanography: Physical: Surface waves and tides (1255); 4219 Oceanography: General: Continental shelf processes; 4235 Oceanography: General: Estuarine processes; 4508 Oceanography: Physical: Coriolis effects; KEYWORDS: tidal current, stratification, estuarine outflow Citation: Codiga, D. L., and L. V. Rear (2004), Observed tidal currents outside Block Island Sound: Offshore decay and effects of estuarine outflow, J. Geophys. Res., 109,, doi: /2003jc Introduction [2] This study addresses two processes by which inner shelf tidal motions can be modified in the presence of a nearby estuary. The first is amplification due to nearresonant tidal response within the estuary. The second is modification of tidal ellipses due to estuarine outflow and the associated changes to stratification and the frictional regime. Though they are largely independent from each other, the two processes are addressed together here, as needed for full description of horizontal and vertical structure of tidal currents. The importance of understanding mechanisms governing spatial structure of tidal currents near the mouth of an estuary includes the typically strong influence they have on mixing and dispersion that regulates 1 Now at Center for Operational Oceanographic Products and Services, NOAA/NOS, Silver Spring, Maryland, USA. Copyright 2004 by the American Geophysical Union /04/2003JC exchange with adjacent shelf waters thus impacting the ecological health of the estuary. [3] We analyze observations from the inner continental shelf outside the Long Island Sound (LIS) and Block Island Sound (BIS) estuarine systems (Figure 1a). In contrast to areas within LIS, where numerical models have been applied [e.g., Kenefik, 1985; Signell et al., 1998], tides on the adjacent inner shelf have received little attention. Observations of currents and hydrography were collected using an array of moored profiling instruments deployed as part of a multi-institution study (Front-Resolving Observation Network with Telemetry) funded through the National Ocean Partnership Program initiative for ocean observatories. The array design (Figure 1b) [see also Codiga and Houk, 2002] was motivated in part by the use of networked acoustic modems to relay its data to shore in real time [Codiga et al., 2004] for use in data-assimilative numerical modeling (C. E. Edwards et al., Combining ADCP records with a GCM using a linear depth-averaged inverse model: The effect of low-frequency motions on fronts near Block Island Sound, submitted to Journal of Geophysical Research, 2004). Ship- 1of19

2 Figure 1. Deployment locations. (a) Regional view. Contours indicate the 50-, 100-, and 150-m isobaths. (b) Boxed region from Figure 1a. Squares mark ADCP sites. Central array consists of 10 km 10 km five-point cross with North, West, Central, East, and South sites. Circles mark moored CTD profiler sites. Three deployment locations, referred to in the text as far-field sites, are labeled FA01-LI (Long Island), SP02-DP (Deep), and SP02-BI (Block Island). Diamond: origin for offshore decay calculation (section 4). based surveys [Kirincich, 2003] give a view of larger-scale hydrographic fields. HF radar provides good spatial resolution of both tidal flow and a seasonal jet [Ullman and Codiga, 2004] in surface currents. [4] The present focus is horizontal and vertical structure of observed tidal currents. Harmonic analysis demonstrates strong dominance by the principal lunar semi-diurnal M 2 constituent. Important seasonal changes to M 2 current ellipses are identified based on deployments that span the fall, winter, and spring seasons. They are investigated in the context of observed seasonal variations in mean currents and stratification associated with estuarine outflow. We do not examine characteristics of constituents other than M 2, owing to their much smaller amplitudes; also, we limit our focus to harmonic fits using records typically at least 2 months long, and do not address changes in tidal currents on timescales shorter than seasonal (spring-neap, weatherband, etc.). [5] Theory for tidal currents on broad continental shelves with coastal walls is advanced [e.g., Clarke, 1991], but of limited applicability near an estuary mouth. While tidal currents within estuaries can assume complicated patterns [e.g., Carbajal, 2000] due to combined standing and propagating responses as modified by coastal boundaries, we intend to address the region offshore from such influences. Tidal currents outside estuaries are commonly amplified due to near-resonant response of the estuary. Examples include Delaware Bay [Munchow et al., 1992] and Chesapeake Bay [Valle-Levinson et al., 1998]. A kinematic theory for estuaryshelf interaction regions [Whitney, 2003] indicates nearly inverse-square radius offshore decay of currents. We answer the question of how well the theory applies outside Block Island Sound. [6] Frictional theoretical solutions for vertical profiles of tidal ellipses are well developed (Soulsby [1990] gives a review). In general these solutions incorporate neither stratification (except indirectly as a changed eddy viscosity profile [e.g., Maas and van Haren, 1987; Visser et al., 1994]) nor non-uniform bathymetry, both of which are commonly important in coastal areas including the present study site. How important is complex bathymetry and stratification to the deep boundary layer? We perform optimal fits to measured profiles using existing frictional models to help address this issue. [7] Observed tidal currents are shown to exhibit distinct seasonal changes, notably a mid-depth increase in ellipse size during the spring. Is this tied to the estuarine outflow, and if so, by what mechanism? We present observed seasonal changes in the three-dimensional structure of estuarine outflow. We demonstrate a straightforward frictional mechanism for larger mid-depth springtime tidal ellipses: reduced nearbottom eddy viscosity, as suggested by increased deep springtime Richardson numbers we observe. [8] Near the surface, observed vertical structure of tidal ellipses appears inconsistent with frictional effects. This motivates an inviscid theory for modifications to tidal current ellipses due to mean currents. The theory shares with previous wave-mean flow modification literature [e.g., Mooers, 1975; Lighthill, 1978; Kunze, 1985; Codiga, 1997] the importance of ambient vorticity and an effective Coriolis parameter. We conclude that mean flow is the most plausible agent responsible for observed near-surface ellipse structure. [9] Section 2 describes the measurements. Vertical-mean currents quantify the tidal/non-tidal energy partition (section 3) and address offshore decay (section 4). Observed vertical structure is then (section 5) compared to frictional models. Section 6 presents seasonal changes in estuarine outflow, stratification, and Richardson number. A frictional mechanism for enlarged spring mid-depth ellipses (section 7) follows. Section 8 introduces and interprets mean-flow modification theory. Section 9 is a summary. 2. Measurements and Methods 2.1. Currents [10] Seventeen records from upward-looking bottommounted ADCPs are used. Thirteen are from a sequence of fall 2001, winter 2002, and spring 2002 deployments at sites designated North, West, Central, East, and South, which constitute a central array in the form of a five-point cross spanning water depths between about 15 and 55 m (Figure 1, Table 1). Instruments deployed at the South site in winter 2of19

3 Table 1. ADCP Record Information a Name Start, yy/mm/dd End, yy/mm/dd Duration, Days Lon, deg W Lat, deg N H, m z min,m z max, m Bin Size, m SP01 01/03/12 01/05/ FA01-LI 01/09/04 01/11/ FA01-W 01/09/04 01/12/ FA01-S 01/10/02 01/12/ FA01-N 01/10/02 02/01/ FA01-E 01/10/02 01/12/ FA01-C 01/10/03 02/01/ WI02-N 02/01/14 02/03/ WI02-E 02/01/14 02/03/ WI02-W 02/01/17 02/03/ WI02-C 02/01/22 02/03/ SP02-N 02/03/21 02/06/ SP02-C 02/03/21 02/06/ SP02-W 02/03/21 02/06/ SP02-S 02/03/21 02/06/ SP02-DP 02/03/21 02/06/ SP02-BI 02/04/19 02/06/ a Name includes season, year, and suffix corresponding to sites in the central array of Figure 1. Water depth is denoted H; center depths of the shallowest and deepest vertical bins are denoted z min and z max. Ensemble time is 20 min for all records; time between consecutive ensembles is 20 min for all records except 80 min for WI02-C. FA01-W, FA01-N, WI02-W, SP02-N, and SP02-W are from 600 khz units; all others are from 300 khz units. (The record denoted SP01 here is SP01-Cm of Codiga and Houk [2002]) and at the East site in spring 2002 showed evidence of trawling impacts on recovery; their records were of insufficient duration for inclusion in this analysis. Three records are from the following sites outside the central array, referred to as far-field (Figure 1a): south of Long Island, 20 km to the west and south of the central array, during Fall 2001; southeast of Block Island, 20 km to the east and north of the central array, during spring 2002; and the deepest site, 20 km offshore southward of the central array, during spring One record is from near the South site in the central array, during spring 2001, and is included because a moored CTD profiler (section 2.2) measured time series hydrographic profiles concurrently at that location. [11] All records are from 300-kHz or 600-kHz RDI Workhorse ADCPs with ensemble interval 20 min, bin sizes 0.5 or 1 m, and deployment duration between 45 and 117 days (Table 1). Data from the deepest bin, and from bins greater than 94% of the water depth from the seafloor, are considered contaminated and omitted. Standard error due to instrument uncertainty does not exceed 2 cm/s. Further information on deployments and data reduction is given by Codiga and Houk [2002]. [12] The analysis is carried out in terms of positive east and north velocity components (u, v) because the complex bathymetry (Figure 1) offers little justification for a coordinate rotation with respect to along- and across-isobath directions. Tidal currents for multiple frequency constituents are computed from raw velocities using the least squares harmonic method of Godin [1972] as implemented by Pawlowicz et al. [2002]. [13] Tidal current ellipses for the M 2 frequency are presented in terms of four parameters: the semi-major axis length or maximum current velocity (L maj, a positive quantity), the semi-minor axis length (L min, can be positive or negative; for positive/negative values the tip of the velocity vector traces the tidal ellipse in a counterclockwise/clockwise direction during one full tidal period T = 2p/w, where w is the radian frequency), the orientation angle (Q) or counterclockwise angle from east of the northward semi-major axis, and the Greenwich phase lag (F) where F/w is the time at which the current is directed along the northward semi-major axis. Appendix A provides the notational conventions and underlying equations with which these quantities are calculated, and shows them graphically (see Figure A1 in Appendix A). Error estimates are 95% confidence intervals [Pawlowicz et al., 2002] from a bootstrapping technique Hydrography From Moored CTD Profilers [14] Hydrographic profiles from two moored CTD profiler deployments, referred to as spring and fall, are used. The locations are within 1 km of each other, near (spring) or at (fall) the South site of the central array, in 47 m (55 m) water depth. The spring record spans 21 days in May 2001, while the fall record spans 24 days in October Sampling repeats each 2 hours and consists of an up-cast and a down-cast 10 min later. Values from individual casts, measured nominally each several centimeters in the vertical, are sorted such that density anomaly increases monotonically downward, and are used to calculate buoyancy frequency squared N 2, which is subsequently averaged in 1-m vertical bins and then across all casts (minimum 250) throughout the duration of the deployment. Each moored CTD profiler was deployed colocated with an ADCP (SP01 and FA01-S, Table 1), and the Richardson number calculation Ri = N 2 /S 2 (section 6) uses shears S 2 = (du/dz) 2 + (dv/dz) 2 based on currents averaged across the subset of the velocity record during the CTD profiler deployment period, because instrument noise limits usefulness of shears based on currents from individual ensembles. Profilers are buoyancy-driven Ocean Sensors Model APV500s, modified with oversized pistons and custom roller brackets and deployed on taut-wire moorings with subsurface flotation. 3. Energy Partition [15] This section presents the partition of kinetic energy variance among tidal and non-tidal components, and the partition of the tidal component among individual constituents. Vertical-mean currents, the average across all 3of19

4 Figure 2. Energy partition based on vertical-mean currents. Area of top-row pie chart indicates total, summed tidal and non-tidal, kinetic energy variance, with the largest pie representing 365 cm 4 /s 4 ; the tidal (non-tidal) portion is shown black (white). Histogram bars indicate percent kinetic energy E n in each of the five most energetic constituents. ADCP vertical bins, are used; differences of energy partition calculations using currents from individual depth bins (not shown) from vertical-mean results presented here are minor. [16] A kinetic energy variance percentage is used to assess the relative contribution of the tidal component to the total flow. This quantity, V E ¼ s2 KE fit s 2 KE dat 100; compares the kinetic energy variance s 2 KE, where KE = (u 2 + v 2 )/2 is the kinetic energy per unit mass, of the superposed multiple-constituent harmonics (subscript fit ) to that of the total measured flow (subscript dat, raw velocities). Relative energy in individual tidal constituents is gauged using the percentage E n ¼ P N i¼1 KE n KE i 100; where n is an index of the N tidal constituents included in the harmonic fit. The five most energetic constituents (O 1, K 1, N 2, M 2, and S 2, determined based on fits using 69 astronomical and shallow-water tidal constituents) are included because, while inclusion of fewer than five constituents reduces V E appreciably in some cases, results are very insensitive to inclusion of more than five constituents [Rear, 2002]. [17] The total kinetic energy variance varies with water depth and site location, and varies weakly with season (Figure 2, top row, pie charts). The general pattern in the total (summed tidal and non-tidal) kinetic energy variance (size of pie charts, top row) is a decrease from the shallow side of the central array to the deep side by roughly an order of magnitude. Total variances at the far-field sites are weaker than most sites in the central array. The percent of the total variance accounted for by the tidal component, V E, ranges from 47 to 95%. At shallower inshore sites, V E is higher than at deeper sites, and at the far-field sites, V E is only 25 35%. These energy distributions are due to the near-resonance of the LIS/BIS system to semidiurnal forcing [e.g., Kenefick, 1985; Signell et al., 1998] which causes strongly amplified tidal currents to dominate the total kinetic energy near the mouth of BIS relative to the far-field sites. Similar patterns occur outside the mouths of other estuaries [e.g., Munchow et al., 1992; Valle-Levinson et al., 1998]. [18] The M 2 constituent dominates at all sites (Figure 2, histograms) with percent energy (E n ) of 85 90%. The other four constituents, with N 2 the next most important, account for less than 10% each of the summed tidal kinetic energies. Higher N 2 than S 2 energy is similar to behavior seen in the lower Chesapeake Bay, and causes primary and secondary consecutive spring-neap cycles [Valle-Levinson et al., 1998]. At far-field sites, M 2 is less dominant and the relative contributions of O 1 and K 1 increase. This is consistent with selective resonance of the LIS/BIS system, for which the natural period better matches semidiurnal than diurnal constituents. 4. Horizontal Structure of Tidal Currents [19] The remainder of the study focuses on the M 2 constituent, given its dominance. This section continues analysis of vertical-mean currents, presenting the measured horizontal pattern of current ellipses, comparing the offshore decay to a kinematic theory, and estimating tidal volume transport between Montauk Point and Block Island Measured Current Ellipses [20] At sites in the central array, vertical-mean M 2 currents are generally at least as strong as record-mean flows, and decrease substantially in the offshore direction (Figure 3, top). Ellipse semi-major axes fall from 55 cm/s to 20 cm/s over the 10-km onshore-offshore span of the array, corresponding to nominal tidal advection lengths 2L maj /w of 7.8 km and 2.8 km, respectively. Currents rotate clockwise in time, and phases vary only weakly across the central array. Ellipses are oriented similarly at all sites in the array, elongated in the direction toward the mouth of BIS. Major axes are aligned either across or along local isobaths, indicating that the complex bathymetry plays a relatively minor role in determining ellipse orientation. Major axes are nearly perpendicular to a line spanning the mouth of BIS between Montauk Point and Block Island, consistent with a flow pattern set primarily by the kinematic constraint of largevolume tidal exchange between estuarine and coastal waters. [21] Characteristics of ellipses at the far-field sites differ from those in the central array (Figure 3, bottom). Amplitudes are substantially weaker. Off Block Island, the major axis points to the east of the island, though slightly westward relative to those in the central array, and there is a slight phase advance relative to flow in the central array. At the deeper offshore site, the ellipse is more nearly circular. To the south of Long Island, the ellipse is aligned closely with isobaths and roughly perpendicular to ellipses in the central array; in contrast to the other locations in this study, a theory for tidal 4of19

5 the presence of the estuary. With the neglect of surface height changes (as justified with scaling by Whitney [2003]), volume continuity in the radial coordinate system requires that e be independent of radius. Consequently, the estuary-enhanced component at any radius r is related to that at a reference radius r o as u e =u e (r o ) [(r o h (ro ))/(r h)(r)]. The expression u t ðþ¼ r ðu t ðr o Þ u a Þf½r o ðh c þ ð2a=pþr o ÞŠ= ½rh ð c þ ð2a=pþrþšgþu a ð1þ Figure 3. (top) Vertical-mean M 2 tidal ellipses for the central array, fall 2001 deployment. Ellipse size accurately represents distance by which a water parcel would move if subjected to M 2 tidal advection only. Isobaths are in 10-m intervals. (bottom) The three far-field sites (see Figure 1a), at the same scale. Currents amplify strongly with proximity to the estuary entrance, and elongated ellipses are oriented toward the estuary mouth with little sensitivity to the local bathymetry. currents on continental shelves has been shown [Battisti and Clarke, 1982] to account reasonably well for ellipses along a cross-shelf transect near this site Comparison to Kinematic Theory for Offshore Decay [22] We now compare the observations with a kinematic theory [Whitney, 2003] for offshore decay of tidal current amplitudes outside the mouth of an estuary. The theory addresses the region outside an estuary mouth of width b, and is strictly applicable only at radii greater than b/2. The coastline is straight, and the seafloor is a plane inclined at slope a having depth h c at the coast and deepening with distance perpendicular to the coast. Using a radial coordinate system with origin at the middle of the estuary mouth, the depth h(r, q) =h c + a(r cos q) is such that along each offshore semicircle the arc-averaged depth as a function of radius is h =h c +(2a/p)r. The total tidal current amplitude u t is treated as the sum of two components: an ambient current u a taken to be constant across the shelf and set by tidal flow on the outer shelf beyond the influence of the estuary, and an estuary-enhanced current u e associated with gives the theoretical offshore decay of the total tidal current amplitude. The dependence is nearly inverse-square radius, physically interpretable as inverse-radius decay due to the deepening water in addition to inverse-radius decay due to radial spreading. [23] Theoretical u t (r) for a field site follow from equation (1) with estimates of coastal depth h c, topographic slope a, ambient current u a, and total tidal current amplitude u t (r o ) at known radius r o. Outside Block Island Sound, using an origin midway between Montauk Point and Block Island (Figure 1b), arc-averaged depths increase roughly linearly with radius (Figure 4, top) with h c = 25 m and a = 0.6 m/km. On the basis of the semi-major axis of a measured M 2 tidal current ellipse on the outer shelf about 80 km offshore [Brown, 1984], a representative value for the ambient current is u a = 6 cm/s. [24] Two theoretical offshore decay curves, using above values with measured u t = 55 cm/s at the North site (r o = 6 km) in one case and u t = 20 cm/s at the South site (r = 15 m) in the second, are compared with the offshore decay of the semimajor axes from all experiment sites (Figure 4, bottom). Considering the limited confidence in estimated parameters h c, a, and u a, the agreement is adequate to confirm applicability of the theory. As the estuary mouth width b is 20 km, radii of shallow observation sites are smaller than b/2, yet disagreement from the theoretical curves remains minor Tidal Volume Transport Between Montauk Point and Block Island [25] Using the theory to estimate the average tidal volume transport between Montauk Point and Block Island Sound seems justified, given its ability to successfully account for offshore decay. Theoretical tidal volume transport is independent of radius and oscillates in time with peak amplitude V = pr h(r) u t (r), the instantaneous transport through a semicircular arc at radius r at peak flood or ebb current. Using u t (r) from observed M 2 semi-major axes and h(r) based on the topography (Figure 4), estimates of V are 2.9 ± m 3 /s. Given the underlying assumptions, and the fact that the total tidal volume transport includes constituents other than M 2, ±25% seems a reasonable limit to the precision of this estimate. Previous estimates of peak instantaneous tidal volume transport between the western side of Block Island Sound and Long Island Sound include m 3 /s using a tidal prism approach with measured tidal heights [Koppelman et al., 1976] and m 3 /s based on numerical modeling [Kenefik, 1985]. Taken together with the present result, they suggest that more than half the tidal transport entering Block Island Sound eastward from Long Island Sound exits to the south between 5of19

6 Figure 4. Comparison between observed and theoretical offshore decay of tidal current amplitudes. (top) Topographic depth (dots) averaged along constant-radius arcs, relative to origin shown as diamond in Figure 1 (bottom), with visually fit line from which h c and a characterizing a planar slope are determined. (bottom) Observations (dots) with confidence intervals, and theoretical offshore decay curves chosen to pass through the farthest inshore observation (dashed line) and that at radius 15 km (dotted line). The nearly inverse-square radius dependence of the theoretical curves agrees well with the observations. Montauk Point and Block Island instead of to the north of Block Island to the east. 5. Vertical Structure of Tidal Currents [26] This section describes measured tidal current ellipses as a function of depth and discusses which aspects are and are not captured well by one-dimensional frictional solutions. Observed seasonal changes in ellipses are then presented Measured Ellipse Parameter Profiles [27] Vertical structure of tidal current ellipses in the central array during the three main deployment seasons (fall 2001, winter 2002, and spring 2002) and from the far-field sites are presented (Figures 5, 6, 7, and 8, respectively) both as ellipses and as vertical profiles of the four current ellipse parameters (semi-major axis L maj, semi-minor axis L min, orientation angle Q, and Greenwich phase lag F). The ellipses are a physically intuitive graphical representation, while profiles of individual parameters provide full vertical resolution and show confidence intervals. [28] Many observed ellipse characteristics are common to all or most of the sites in the central array (Figures 5, 6, 7): [29] 1. Within the deepest m, as the bottom is approached from shallower depths: (1) Ellipse size decreases by cm/s, preferentially in the minor axis with narrowing of ellipse shape. In some records (FA01-E, FA01-S), rectilinear motion and counterclockwise rotation of the velocity vector in time are seen very close to the bottom. (2) Ellipse orientation angle decreases by 20 50, corresponding to a clockwise turning of the ellipse major axis. At some sites, orientation angle appears to increase with depth slightly in a thin bottom layer (e.g., FA01-E) or shows more complex vertical structure (e.g., FA01-S). (3) The Greenwich phase lag decreases (equivalently, there is a phase advance) by ; the time of maximum current occurs about min earlier. [30] 2. For all records other than at the North site, the maximum ellipse size is reached at depth below the surface. This is most clear in the spring records and least prominent at the South and East sites in fall and winter. [31] 3. In the upper water column, the orientation angle and Greenwich phase lag both increase, roughly linearly, toward the surface. In some records (e.g., SP02-S), more complex structure is seen in the orientation angle. [32] At the far-field sites (Figure 8), most features are qualitatively similar to those listed above. In contrast, they show more complex profiles in the upper water column, but their near-bottom changes are as described (see item 1 above) Optimally Fit Frictional Models for Vertical Structure [33] One-dimensional frictional models for vertical structure have been shown to account reasonably well for observed tidal current ellipse characteristics in previous studies [e.g., Thorade, 1928; Kundu et al., 1981; Prandle, 1982a, 1982b; Maas and van Haren, 1987; Soulsby, 1990]. The models are for a flat-bottom, rotating, homogenousdensity ocean without lateral boundaries and forced by a vertically and horizontally uniform rotating horizontal pressure gradient (Soulsby [1990] gives a review; equations are provided in Appendix B). Models have included effects of stratification indirectly through vertical profiles of eddy viscosity with reduced values [e.g., Maas and van Haren, 1987] with some success. Complex topography and seasonally varying estuarine outflow are known to be important at our experimental site yet are not included explicitly in the frictional model. We will show that the model nonetheless captures the observed ellipse characteristics near the bottom (section 5.1, item 1) quite well. [34] Optimal fits of five configurations of the frictional model (Table 2) were made to the measured ellipse profiles from each individual record. Using the notation of Appendix A, the cost function is the depth-averaged, time-averaged, summed squared magnitudes of the difference between data and model velocity vectors, CF ¼ 1 M ¼ 1 M X M i¼1 X M i¼1 Z 1 T T 0 h jr d ðz i Þ R m ðz i Þj 2 dt Ud þ ðz i Þ Um þ z i ð Þ 2 þ Ud ðz i Þ Um ð z i iþ 2 ; where subscript d (m) indicates observed data (model solution), and i is the index of the M depth bins of the 6of19

7 Figure 5. Vertical structure of M 2 tidal ellipse parameters at the North, Central, West, South, and East sites during fall 2001 deployment. A subset of plan view current ellipses, one nominally each 8 m for clarity, is shown at left. Horizontal lines indicate water depth. Dashed lines are optimally fit model solution. ADCP measurement. Disagreement between measured and modeled values of any of the four current ellipse parameters contributes to the cost function. The cost function weights all depth bins equally. The optimization is carried out using the downhill simplex method of Nelder and Mead [1965] as implemented in Matlab function fminsearch and variants. As discussed by Rear [2002] the optimally fit values of eddy viscosity ( m 2 /s) and linear bed stress coefficient ( m/s) lie in a similar range to previous estimates from model-data comparisons at other sites [e.g., Prandle, 1982a; Maas and van Haren, 1987; Soulsby, 1990; Souza and Simpson, 1996], as well as from microstructure measurements [Levine et al., 2002] and numerical modeling [Edwards et al., 2004] specific to the present site. Optimally fit eddy viscosity values do not exhibit a seasonal pattern with reduced values in spring (as would be expected based on the descriptions in section 6 below) because the cost function weighs equally heavily all depths and seasonal changes occur in near-surface profiles (discussed below) unrelated to the deep frictional layer. [35] A primary result of the optimal fits (Case 1, dashed lines, Figures 5 8) is that in the deepest m the 7of19

8 Figure 6. As in Figure 5, but for winter 2002 deployment (instrument at South site did not return adequate useful data). agreement between the frictional model and all observed characteristics (item 1, section 5.1) is very good. We conclude that at these depths the influences of bathymetric changes and of stratification, other than in its indirect effect on the eddy viscosity, are secondary to the physics. These results are robust to different choices of bottom boundary condition and eddy viscosity profile; none of the five cases (Table 2) showed substantially better ability to capture the observed characteristics listed in section 5.1. Differences among the five cases are minor and consist mainly of degraded fit to records from the North site, and improved fit to deep portions of FA01-E and FA01-S profiles, for Cases 3 and 4. Hence results of Cases 2 5 are not shown. [36] The optimal fits agree most poorly with records from the North site, where the model profiles differ qualitatively from the observations. This site is the shallowest and sees by far the strongest currents, which are unique among all records in that the increase of current amplitude above the bottom extends to the surface. The site is also inshore of predicted locations (approximately the 25- to 30-m isobaths [Edwards et al., 2004], Figure 10 in section 6.1) for the tidal mixing front. Therefore it is expected to have a different frictional regime, including a thicker log layer, which we speculate could account for the poor fits. [37] The most substantial failings of the frictional model, for all deployments other than at the North site, are in the upper water column. In most records the extent to which the observed mid-depth maximum ellipse size (item 2, section 5.1) exceeds ellipses at shallower depths is not captured well by the optimally fit model. While a mid-depth maximum is a 8of19

9 Figure 7. As in Figure 5, but for spring 2002 deployment (instrument at East site did not return adequate useful data). fundamental aspect of the model solution [e.g., Prandle, 1982a, Figure 5] (fit to FA01-C in Figure 5), in the model solutions its amplification relative to near-surface currents is weaker than observed. Near the surface, the model persistently underpredicts (overpredicts) ellipse size in the fall/winter (spring); in section 8 we present evidence linking such seasonal variation to the estuarine outflow. [38] Finally, the frictional model also cannot account for the observed nearly linear increases in orientation angle and Greenwich phase lag as the surface is approached (item 3, section 5.1). A more pronounced example of the phase lag is seen in a spring 2001 record (Figure 11 in section 6.2). We speculate this may be associated with the basic far-field forcing of the tidal currents, which is uniform spatially in the unbounded domain of the model configuration but may be impacted by the configuration of the coastline, estuarine outflow, and/or spatially varying large-scale tidal response at the field site Observed Seasonal Variations in Tidal Current Ellipses [39] Overlaid vertical profiles of measured ellipse axes from the three seasons (where available) at each of the five sites in the central array (Figure 9) make clear that substantial seasonal variations occur in tidal ellipses. First consider sites other than North, which is taken up below: the fall and 9of19

10 Figure 8. As in Figure 5, but for the three far-field deployments: Long Island, Deep, and Block Island (see Figure 1a for sites). winter records are generally indistinguishable from each other, while the spring records show marked differences from them. The primary spring modifications are (1) enhancement of ellipse size at mid-depth, particularly at the West, Central, and South sites, and (2) reduction in ellipse size near the surface. The mid-depth enhancement is seen, to a lesser extent, at the Central and West sites in fall as well as during spring. At the South site, the spring near-surface reduction of ellipse size does not extend as far vertically away from the surface as it appears to at the Central and East sites, and the mid-depth enhancement is seen through the entire deeper water column. [40] Owing to inherent operational limitations at sea during deployments, instrument locations at a given site were not exactly identical from season to season. As a result, in some cases the profiles being compared are from slightly different locations and therefore different depths (horizontal lines, Figure 9). This is most severe at the North site, where the winter deployment was about 1 km south of the fall and spring deployments; it is therefore in deeper water and has substantially weaker currents due to the abrupt offshore amplitude decay at this inshore location (section 4). Horizontal variability in tidal amplitudes near the North site thus limits conclusions about seasonal variations there. 6. Observed Seasonal Estuarine Outflow: Currents and Stratification [41] The magnitude and vertical structure of seasonal changes in tidal ellipses cannot be explained by seasonal variation in astronomical forcing, which prompts investigation of other aspects of the system that may be responsible. In this context, we now describe seasonally averaged mean flow dominated by a spring estuarine outflow, contrast spring and fall stratification measured by moored CTD profilers, and interpret Richardson number profiles in terms of the implied seasonal changes to the frictional regime Observed Seasonal Variations in Mean Flow [42] Record-mean currents (Figure 10) are calculated as averages over intervals from 45 to 117 days long (Table 1) from the fall 2001, winter 2002, and spring 2002 deployments. In each season, shallow flow is generally southward and westward away from the southern opening of BIS between Montauk Point and Block Island. This pattern is referred to as estuarine outflow and has qualitative characteristics [e.g., Garvine, 1987] of relatively fresh near-surface water exiting the estuaries and moving westward along the south side of Long Island as deflected by the Coriolis force. Peak current strengths of the estuarine outflow reach from 10 to 25 cm/s. Measured estuarine outflows in fall and winter deviate relatively little from each other, while that of Table 2. Frictional Models Optimally Fit to the Measured Tidal Current Ellipses Case Eddy Viscosity Profile Bottom b.c. Optimized Parameters 1 constant no-slip K 2 constant free-slip K, r b 3 above-bottom maximum (equation (B1)) no-slip K max,h K 4 above-bottom maximum (equation (B1)) free-slip K max,h K, r b 5 linear (equation (B2)) free-slip K, K 0, r b 10 of 19

11 Figure 9. Seasonal variation in vertical profiles of tidal currents. Overlaid semi-major and semi-minor axis profiles during fall 2001 (green, Figure 5), winter 2002 (blue, Figure 6), and spring 2002 (red, Figure 7). At the West, Central, and South sites the springtime ellipses are (1) larger at mid-depth (2) smaller near the surface. See color version of this figure at back of this issue. spring is substantially changed. Peak spring currents are up to 2 times stronger. The offshore spatial extent in spring is at least 5 km larger: In fall/winter the influence of the estuarine outflow is seen throughout the array except at the South site, to which it clearly extends in spring Current Ellipses, Stratification, and Mean Flow: Spring 2001 Versus Fall 2001 [43] Seasonal changes in tidal current ellipses (Figure 9) may be associated with the seasonal cycle in stratification, which strengthens in the late spring and summer [see Ullman and Codiga, 2004, Figure 10] due to a combination of solar heating and the freshening influence of the estuarine outflow. To explore this possibility we use two ADCP records, one from spring 2001 and one from fall 2001 (SP01 and FA01-S, Table 1), because a colocated moored CTD profiler collected density profiles concurrently for each. The two records are from sites within about 1 km of each other (Figure 1b). [44] Current ellipses are presented together with both the average density profile and the record-mean velocity vectors (Figure 11). Differences between spring and fall (Figure 11, top and bottom, respectively) ellipses are qualitatively similar to those seen above (spring 2002 versus fall 2001, South site, Figure 9). The fall ellipses are nearly uniform with depth in the upper water column. In spring the nearsurface ellipses are smaller by roughly a factor of 2 relative to those deeper in the profile. On a vertical-mean basis ellipses are larger in spring than fall, which can be understood to be due to horizontal variability alone (section 4) given the inshore location of the spring site relative to the fall site. The similarities of the near-surface spring 2001 and spring 2002 tidal ellipse characteristics to each other, as well as the similarities in their deviations from fall and winter, suggest that reduction in ellipse size occurs each spring. [45] The fall density profile consists of two relatively uniform layers separated by a stratified layer 5 10 m thick centered at 35 m deep. The spring density profile consists of a uniform lower layer extending farther off the bottom than in fall, but a nearly uniform density gradient throughout the shallowest 20 m. The depth penetration of stratification in spring matches that of the near-surface tidal ellipse modifications, as well as that of the mean flow. The spring nearsurface mean flow is strongly southwestward, consistent with the presence of estuarine outflow. In fall near-surface mean flow is opposite to that in spring and weaker, consistent with the estuarine outflow (Figure 10) not extending offshore far enough offshore to reach this site. [46] The possibility that the spring changes in tidal currents are due to internal tides is not considered likely. A reasonable expectation is that the first baroclinic mode would be most energetic, as tends to occur on continental shelves [Holloway, 1984]; this is at odds with observed mid-depth current enhancement and also with the nearly vertically uniform tidal density fluctuations (not shown) measured by the CTD profilers. Internal solitary waves, as seen on the nearby mid-shelf and outer shelf [e.g., Colosi et al., 2001], may 11 of 19

12 possibly be excited at our site, but since they persist for a fraction of an M 2 period and are not semidiurnal harmonics, their impact the present analysis is considered weak Richardson Number: Evidence for Reduced Deep Eddy Viscosity in Spring [47] The Richardson number (Ri) is nearly uniform vertically in fall but is on average lower (higher) shallower than (deeper than) 25 m in spring (Figure 12). Near the surface, spring estuarine outflow increases both stratification and shear, with the latter enhanced to a greater degree so Ri decreases slightly. At depth, Ri increases due to moderately increased springtime stratification with weaker shear. The spring change to Ri is strongest at depth, where it increases by a factor of 2 4. It is recognized that all the Ri values are well above the 0.25 criteria for shear instability, as expected given use of record-mean profiles, and therefore that the background conditions they represent do not alone cause instability. However, the background conditions contribute to the instantaneous flow field and can enhance likelihood of instability due to other sources of shear that are present year round, such as tidal flow; Sanders and Garvine [2001] estimated subtidal Richardson number similarly, also showing separate contributions due to background and tidal flows. Hence a plausible seasonal effect on tidal currents is reduced eddy viscosity at depth in association with springtime stratification. 12 of Larger Spring Mid-Depth Ellipses: Frictional Mechanism [48] We now demonstrate that the spring reduction in deep eddy viscosity implied by the Richardson number calculation, in the context of the frictional solutions discussed above, is a mechanism that could alone result in one of the observed seasonal changes to tidal current ellipses: mid-depth springtime enlargement. We focus on mid-depth enlargement, as distinct from the weak local maxima known to characterize frictional solutions [e.g., Prandle, 1982a, Figure 5]; by middepth we mean the shallower portion of the frictionally influenced deep flow. Vertical profiles of ellipse parameters from solutions to the Case 1 frictional model for different values of eddy viscosity can straightforwardly be overlaid (Figure 13a). For an eddy viscosity reduced by a factor of 2 4, which is plausible based on the above analysis, the thickness of the bottom frictional boundary layer (Appendix B) is times smaller. Relative to the original profile, this causes an increase in ellipse size at mid-depth (on the shallow side of the frictional influence, in this case m deep). In this mechanism the reduced eddy viscosity affects both the clockwise- and anticlockwise-rotating components, in effect simply reducing the overall frictional boundary layer thickness (both d + and d decrease by the same factor). Interpretations of other observations [e.g., Maas and van Haren, 1987; Visser et al., 1994; Souza and Simpson, 1996] use more complicated mechanisms in which reduced viscosity in a mid-depth pycnocline layer impacts one component only. Figure 10. Seasonal variation in mean currents: fall 2001, winter 2002, and spring 2002 record-mean flow (averaged over record duration, between 47 and 117 days; see Table 1). Vectors are averages across 10-m-depth intervals centered at 7, 17, 27, 37, and 47 m deep, indicated by increasingly lighter shading. The longest vector corresponds to a speed of 25 cm/s. Dark dashed lines are the 25 m and 30 m bathymetric contours, a proxy for the location of the tidal mixing front based on the h/u 3 criterion. In fall, estuarine outflow does not reach offshore to the South site; in spring it is about twice as strong and reaches the South site farther offshore.

13 Figure 11. Seasonal changes to tidal current ellipses, stratification profiles, and mean flow near the South site based on (top) spring 2001 and (bottom) fall 2001 deployments. Plots left of line show vertical structure of M 2 tidal ellipses and ellipse parameters. Plots right of line show vertical structure of recordmean current as plan view vectors, and 3-week average density profile based on moored CTD profiler. Scale for ellipses and mean currents is the same, shown in lower left. Tidal ellipses in spring appear to be modified by the stratification and/or estuarine outflow in the shallowest m. Figure 12. Comparison of fall 2001 and spring 2001 (same records as in Figure 11) Richardson number profiles based on record-mean velocity (u, v) and density anomaly (s t ) profiles. In spring, estuarine outflow affects both vertical shear and stratification. Near the surface both increase, shear increases more, and Ri decreases slightly. At depth, increased stratification and weakened shear cause Ri to increase by a factor of of 19

14 Figure 13. Frictional model solutions using parameters appropriate to the Central site. (a) Demonstration that the frictional model yields mid-depth enhancement of ellipse size when the deep eddy viscosity value is reduced by a factor of 2 4. (b) Demonstration that the frictional model with a depth-dependent eddy viscosity is relatively insensitive to even extreme changes in the shallow eddy viscosity, and therefore cannot account for the observed springtime reduction in near-surface ellipse sizes. [49] Section 5 showed two main seasonal changes to current ellipses that occur most strongly in spring: (1) enhancement of ellipse size at mid-depth and (2) reduction in ellipse size near the surface. Given that the first of these may be accounted for at least in part by the frictional model with reduced springtime eddy viscosity (Figure 13a), one might reasonably expect that the second (near-surface reduction) might also be captured by the frictional model with inclusion of a suitable vertically varying eddy viscosity profile. However, model current ellipse profiles are sensitive primarily to the deep eddy viscosity value; for cases in which K varies in depth, the K values near the surface have very little impact on the near-surface profiles (Figure 13b) because the no-stress surface boundary condition (Appendix B) suppresses gradients in ellipse properties near the surface. We conclude that near-surface eddy viscosity changes cannot account for ellipse sizes that sharply decrease with proximity to the surface as observed at selected sites (e.g., near the South site in spring 2001, Figures 9 and 11). Although relaxing the no-stress condition [Maas and van Haren, 1987] qualitatively yields reduced near-surface ellipse size, we consider an air-sea interaction mechanism unlikely to explain the seasonality of the measurements, and instead examine an inviscid mean-flow modification mechanism next. 8. Modification of Tidal Current Ellipses by Estuarine Outflow [50] The apparent inability of frictional effects to account for the near-surface seasonal variability in the tidal currents suggests they may result from interaction with the sheared mean currents of the estuarine outflow. In this section we present an inviscid mechanism, in the spirit of mean flow wave-modification dynamics [Lighthill, 1978], for current ellipse modifications by the ambient vorticity associated with a horizontally and vertically sheared background mean current chosen to represent estuarine outflow Mean-Flow Modification Model [51] Though inviscid, the mean-flow model shares the same coordinate system, configuration, and driving as the frictional models: a flat bottom, homogenous density, uniformly rotating fluid with no lateral boundaries is forced by a horizontally and vertically uniform, rotary oscillating horizontal pressure gradient, with vertical velocity and surface height displacements ignored and horizontal propagation disallowed. Tidal variables take the form, where in this section subscripts (x, y) denote partial derivatives, uz; ð t vz; ð t Þ ¼ Re f~uðþexp z ðiwtþg; Þ ¼ Re f~vðþexp z ðiwtþg; p x ðþ¼r t o Re f~p x expðiwtþg; p y ðþ¼r t o Re ~p y expðiwtþ ; for known complex constants ~p x and ~p y that characterize the oscillating pressure gradient driving the response and are unaffected by the presence or absence of the mean flow. To 14 of 19