Winter variability in the western Gulf of Maine

Dynamics of Atmospheres and Oceans 52 (2011) 224–249

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Winter variability in the western Gulf of Maine Part 1: Internal tides W.S. Brown ∗ School for Marine Science and Technology, University of Massachusetts Dartmouth, New Bedford, MA 02744, United States

a r t i c l e

i n f o

Available online 6 April 2011

Keywords: Semidiurnal internal tide Wilkinson Basin Winter Observations Gulf of Maine

a b s t r a c t During the winter 1997–1998, a field program was conducted in Wilkinson Basin–western Gulf of Maine–as part of a study of winter convective mixing. The field program consisted of (1) Wilkinson basin-scale hydrographic surveys, (2) a tight three-mooring array with ∼100 m separations measured temperature and conductivity at rates of 2–15 min and (3) a single pair of upward/downwardlooking pair acoustic Doppler current profiling (ADCP) instruments measured currents with 8 m vertical resolution over the 270 m water column in north-central Wilkinson basin at a rate of 10 min. The moored array measurements below the mixed layer (∼100 m depth) between 11 January and 6 February 1998 were dominated by a combination of the relatively strong semidiurnal external (depth-independent or barotropic) tide; upon which were superposed a weaker phase-locked semidiurnal internal tide and a very weak water column mean currents of about 1 cm/s southward or approximately across the local isobaths. The harmonic analysis of a vertical average of the relatively uniform ADCP velocities in the well-mixed upper 123 m of the water column, defined the external tidal currents which were dominated by a nearly rectilinear, acrossisobath (326◦ T) M2 semidiurnal tidal current of about 15 cm/s. The depth-dependent residual current field, which was created by subtracting the external tidal current, consisted of (1) clockwiserotating semidiurnal internal tidal currents of about 5 cm/s below the mixed layer; (2) clockwise-rotating inertial currents; and

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(3) a considerably less energetic subtidal current variability. The results from both frequency-domain empirical orthogonal function and tidal harmonic analyses of the of isotherm displacement series at each of the three moorings in the 100 m array mutually confirm an approximate east-northeastward phase propagation of the dominant M2 semidiurnal internal tide across Wilkinson Basin. Further investigation supports the idea that this winter internal tide is very likely generated by the interaction of the external tidal currents and the southwestern wall of Wilkinson Basin. The definitions of the local Wilkinson Basin external tide and phase-locked internal tides will enable us to analyze a less “noisy” set of measurements for the subtle atmospherically forced convective and wind-driven motions. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The geometry of the Gulf of Maine/Bay of Fundy system is the crucial factor in the amplified tidal response of the Gulf system. The characteristic or resonant period of the Gulf system is very near to the frequency of the semidiurnal tide that is forced by the tides in the North Atlantic (Garrett, 1972). Thus, the semidiurnal tidal response of the Gulf is amplified, while the diurnal tidal response is not. The M2 semidiurnal harmonic constituent amplitude in the Gulf is four times greater than the next largest semidiurnal constituent (i.e., N2 ). The near-standing semidiurnal tidal wave response of the Gulf system ranges from about 40 cm along the seaward edge of Georges Bank to about 15 m at the head of the Bay of Fundy. The amplitudes and phases of tidal currents associated with the Gulf surface or external tide (sometimes barotropic tide) tend to be depth-independent except in the lowest part of the water column where friction is important. Because of the complex Gulf bathymetry, there is considerable lateral spatial structure of external tidal currents (Brown, 1984). Throughout much of the interior Gulf, the tidal currents are relatively weak at ∼10 cm/s. However, in regions of steep bathymetry, such as the north flank of Georges Bank, the external tidal currents (∼50 cm/s) are relatively stronger and oriented across-isobath (Moody et al., 1984). Internal tidal currents (sometimes called baroclinic tidal currents) are generated by the interaction of external tidal currents and steep bathymetry in the presence of stratification. Loder et al. (1992) have documented the generation of the internal tide, internal solitary waves on each tide, and associated nonlinear packets of higher frequency internal waves over the north flank of Georges Bank. The internal tidal wave appears to be generated continuously at depth along the north flank of Georges Bank and propagates toward the interior Gulf. These waves have typical horizontal wave lengths of 20–30 km and phase speeds of 0.40–0.70 m/s, respectively. Internal wave packets, which exhibit surface texture changes associated with the internal solitary wave surface flow convergence (ripples) and divergence (slicks) patterns that can be seen from space (Sawyer, 1983), also appear to propagate away from Georges Bank. These internal tide-related patterns are highly variable due to the evolving stratification in the Gulf. The variability of density stratification in the Gulf of Maine is strongly influenced by the oceanography in this semi-enclosed marginal sea with the seasonally varying cyclonic gyres found in the three principal basins of the Gulf, including Wilkinson Basin (see Fig. 1). The basic density stratification of the Gulf is controlled by the stabilizing salinity gradient associated with the relatively fresh Maine Surface Water (MSW), Maine Intermediate Water (MIW), and the relatively salty Maine Bottom Water (MBW) (see Hopkins and Garfield, 1979; Brown and Irish, 1993). MIW, which is identified primarily by its minimum temperature at about 75 m depth, is a remnant of water from previous winter’s mixed layer that is produced by episodic convective and wind mixing. During an autumn episode, MSW cools, sinks, and mixes with the saltier, warmer MBW to form a mixed layer composed of “Winter Water.” During the winter, the mixed layer can penetrate to depths as great as 150 m in Wilkinson Basin. Spring warming, augmented by freshening, causes Winter Water layer to separate into MSW

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Fig. 1. (Left) Location map for the 1997–1998 Wilkinson Basin (WB) study. The Wilkinson Basin WB 1998 and Stellwagen Bank mooring U3 1991 sites, Cape Porpoise (CP), Jeffreys Basin and Ledge, 100 m (-·-) and 200 m (· · ·) isobaths are located. (Right) The tight mooring array, which was located at WB 1998, consisted of moorings A (ADCP/TC-chain), B (T-chain) and C (T-chain). There were temperature–conductivity sensor pairs on guard moorings D, E, and G, respectively.

and MIW. Summer solar warming produces a strong pycnocline at about 15 m depth throughout much of the gulf, particularly in Wilkinson Basin. A year-long 1986–1987 field program, described by Brown and Irish (1993), included hourly averaged measurements of temperature at 1 m and Sea Bird temperature and conductivity (TC) at depths of 15 m, 65 m, 115 m, 165 m respectively in Wilkinson Basin during winter 1987. These measurements documented a highly variable mixed layer with significant internal tidal variability at its base. In this paper, we report on observations of the internal tides in Wilkinson Basin of the western Gulf Maine from the winters of 1986–1987and 1998 (see Fig. 1 location map). The observations are described in Section 2. The external semidiurnal tide is described in Section 3; while the internal semidiurnal tide is described in Section 4. 2. Observations The 1997–1998 field program centered on an array of moored measurements with lateral separations of about 100 m, which were located in 270 m of water in north-central Wilkinson Basin during the winter of 1997–1998 (Fig. 1; Table 1). These moored ocean measurements were augmented by both operational and our research meteorological measurements as well as a set of seasonal shipboard hydrographic surveys of the broader Wilkinson Basin region (details in Brown, 2005; Miller et al., 1999, and Bub et al., 1998a,b,c, 1999a,b). A typical hydrographic station pattern, with nominal station separations of 16 km, consisted of tracks radiating from the Wilkinson Basin mooring array. A six-buoy moored array was deployed in north-central Wilkinson Basin (Fig. 1) at a location that was about 65 km east of Stellwagen Bank, about 45 km south of Jefferys Bank, and just south of the

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Table 1 Details of the Wilkinson Basin 1997–1998 moored measurement array, including meteorological (Met), ADCP currents, T-chain temperatures, temperature and conductivity (TC), and a late summer 1996 bottom pressure. Sensor types, depths, sample interval (t) and measurement durations are given. ID

North latitude (deg min)

West longitude (deg min)

Sensor type

t (min)

Depth (m)

Start date

End date

A

42◦ 42.10 (42.702)

69◦ 38.14 (69.636)

Met T/C ADCP ADCP

2 2 10 10

11 Jan 98 11 Jan 98 11 Jan 98 11 Jan 98

6 Feb 98 6 Feb 98 5 May 98 29 Apr 98

B

42◦ 42.14

69◦ 38.08

T-Chain

15

3 Oct 97

17 Mar 98

C

42◦ 42.09

69◦ 38.04

T-Chain

5

10 Jan 98

17 Mar 98

D

42◦ 42.11

69◦ 38.08

T/C T/C T/C na Paros

2 2 2 na 5

−2 4, 23, 38, 68, 98, 128 18–123 @ 8m 146–258 @ 8m 172 215 17–152 @ 15 m 21–156 @ 15 m 2 216 97 na 270

3 Oct 97

5 May 98

3 Oct 97 na 29 Aug 96

5 May 98 na 17 Oct 96

E G BP

◦



42 42.15 42◦ 42.11 42◦ 46.92 (42.782)

◦



69 38.12 69◦ 38.03 69◦ 44.88

location of our late summer 1996 moored current array (Fig. 2). The heavily instrumented mooring A was equipped with (1) a suite of meteorological sensors at the surface, (2) eight pairs of TC sensors that bracketed (3) a pair of upward- and downward-looking acoustic Doppler current profiling (ADCP) instruments (Fig. 2; Table 1). A pair of Aanderra temperature chains (buoys B and C) were located within about 100 m of mooring A. The main measurement array was protected from fishing hazard by a trio of surface guard buoys (buoys D, E and G in Fig. 1). Several Seabird Microcat TC sensors were attached to the guard buoy moorings (see Table 1 for details).

Fig. 2. Bathymetry along the transect from Cape Porpoise, ME (CP on Fig. 1) across Jeffreys Basin and Ledge to the Wilkinson Basin site of the 1996 (WB96) and 1998 (WB98) mooring sites; on which are indicated the sensor configurations (see Table 1 for details).

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Fig. 3. The Wilkinson Basin CTD temperature (upper) and sigma-theta (middle) profiles for (upper left) 21 January 1998, and (upper right) 31 January 1998, respectively. (Lower) The corresponding CTD-derived buoyancy frequency profiles on which are superposed (left) a 7-segment composite profile of the 13–23 January time mean of vertically averaged moored buoyancy frequency time series, and (right) the same for the 24 January–4 February time mean.

2.1. Water property measurements Weak stratification strength (i.e., low or even negative buoyancy frequency) during January–February 1998 is documented by CTD-derived density profiles and moored measurements in the winter Wilkinson Basin (see Fig. 3). Specifically, the January near-surface buoyancy frequency at the 40 m depth in January 1998 was about 2 cycles per hour (cph) versus 18 cph during late summer 1996 (Brown et al., 1999). Below nominal depth of the winter mixed layer (∼100 m) in January 1998, the buoyancy frequency is about a depth-independent 4 cph versus 8 cph in October. The temporal variability of the water property fields was measured with a trio of moorings; mooring A composed of Sea Bird TC sensors and mooring B and C–each an Aanderra model 2862 temperature

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Fig. 4. Temperature time-depth contour presentations for (upper) T-chain B, (middle) mooring A TC-chain, and (lower) mooring A augmented TC-chain time series (see text); which shows the improvement in the resolution of the internal tidal variability. The depths of the measurements are indicated. The contour interval (CI) is 0.2 ◦ C.

chain (T-chain) (see Table 1). The two T-chains were moored within about 100 m of mooring A (see Fig. 1; and Miller et al., 1999); each with a 10-sensor array between about 20 m and 155 m and buoyed vertically with a subsurface float with pressure sensor. T-chain B measured temperature every 15min between October 1997 and March 1998, while T-chain C measured temperatures every 5-min between 11 January and March 1998. The T-chain temperature sensors were calibrated via a linear regression between the measured bath temperatures and a reference Sea Bird Microcat. The typical misfit standard deviation (i.e., precision uncertainty) of a calibrated T-chain B temperature record was ±0.015 ◦ C and that for T-chain C temperature record was ±0.008 ◦ C (see Miller et al., 1999 for details). The pressure record, which was measured atop each T-chain by TR-7 Silicon Piezoresistive Bridge pressure sensors, shows that T-chain temperature sensors varied in depth by about ±2 m; presumably due to the (a) tidal sea level excursions and (b) tidal current- and storm current-induced drag on the array. To adjust for the mooring motion, the measured temperature/depth time series from both T-chains A and B were interpolated to produce the depth-constant temperature time series at 15 m intervals (see Miller et al., 1999; and see T-chain B in Fig. 4(top panel)). Besides the longer-term temperature variability due to surface air–sea heat fluxes and lateral advection of water, there is a distinctive internal tidal variability–most prominent at the base of the mixed layer. The taut-wire construction of mooring A resulted in a full set of TC measurements that were always at constant depth relative to the surface between 11 and 6 February 1998, when the measurements

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ended prematurely due an instrumentation malfunction. Most of the mooring A TC-chain measurements were obtained every 2 min at 6 levels in the upper 129 m. There were longer TC measurements at 172 m and 216 m on mooring A, as well as on mooring D at 22 m and 216 m; and mooring E at 97 m, respectively (see Table 1). Unfortunately, the TC records at 6 m, 70 m, and 129 m ended on 24 January. The missing data were inferred by employing cross-correlations between temperature and salinity measurements on the mooring (see Miller et al., 1999 for details). The visual similarity between the T-chain B and mooring A temperature records (see Fig. 4) is about what one would expect for measurements made about 100 m apart; except at semidiurnal tidal time scales. The objective was to infer isotherm displacement records via term-by-term interpolation of the temperature records–with a focus on the semidiurnal variability. The constant depth T-chain records with their 15 m vertical spacing were well suited for this process. However, comparison with T-chain B depth-time contoured temperature records in the upper 2 panels of Fig. 4 indicated that the mooring A-measured temperature poorly resolved the internal tidal variability at the base of the relatively well-mixed upper layer in the 70–130 m depth range. To deal with the spatial temperature resolution problem, the suite of mooring A temperature time series records was augmented with 85 m and 115 m temperature records derived via linear interpolation of the constant depth T-chain C records. This is justified on the basis of the results of a semidiurnal band frequency-domain empirical orthogonal function analysis of the ∼100 m temperature records on moorings A–C (see Section 4 below). As shown in the lowest panel of Fig. 4, the augmented set of mooring A temperature records better resolves the internal tidal temperature signature. The clusters of temperature records on each of the three moorings (A–C) were linearly interpolated to extract set of selected isotherm depth records–time step by time step. As shown in the lowest panel of Fig. 4, the augmented set of mooring A temperature records better resolves the internal tidal temperature signature. Then a set of selected isotherm depth records were constructed by linearly interpolating between each of the mooring A temperature time series at each time step. The same was done at T-chain moorings B and C. The M2 semidiurnal tidal harmonics for the isotherm depth series are presented in Table A2 of Appendix A. The salinity time series at 85 m and 115 m were estimated by combining the temperature time series and the instantaneous measured T–S relationships derived from the mooring A temperature and conductivity/salinity time series. Comparisons of T–S relationships derived from hydrography and the instantaneous TC-chain temperature and salinity measurements justify this process (see Miller et al., 1999). This augmented suite of mooring A temperature and salinity records was used to compute the corresponding density anomaly (sigma theta) records at the fixed depths of the measurements. The density anomaly isopleth records in Fig. 5 clearly reveal an internal tidal variability at depths below the upper mixed layer that hovers at about 100 m depth between 13 and 23 January and about 65 m between 24 January and 4 February (see Miller et al., 1999 for the detail). The winter 1998 moored Wilkinson Basin moored time series measurements provide excellent evidence of the episodic vertical mixing due to combined wind and convection, with mixed layers of (a) 0–50 m, 50–80 m, and 100–120 m respectively in the 21 January profile, and (2) 0–60 m, 80–100 m, and 115–130 m respectively in the 31 January profile. The temperature measurements in Fig. 4 and corresponding density anomaly time series in Fig. 5 reveal such processes at work. Pairs of these density time series were used to produce the layer-averaged buoyancy frequency time series that are contoured in Fig. 5–bottom panel. Though cooling-induced static instability is occurring throughout most of the study period, the associated convection penetrates much deeper during the earlier part of the series between 13 and 23 January than later. Both of the time-/space average buoyancy frequency profiles, which increase with depth, are inverted relative to those in summer. These measurements show that the upper mixed layer in Wilkinson Basin during January 1998 is unstable; both statically and dynamically (not shown). The basic static stability of the water column in Wilkinson Basin during winter, as in the rest of the Gulf, is usually dictated by salinity distributions. However, winter cooling of surface waters leads to vertical convection and associated static instability, which, in concert with mechanical stirring by winds, erodes the basic salinity stratification in the upper ocean.

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Fig. 5. (Upper) Sigma-theta anomaly depth/time contours are based on moored measurements at indicated depths (CI= 0.1). (Lower) Buoyancy frequency depth/time contours are based on moored measurements at the indicated depths (CI= 1 cph).

2.2. Current measurements A pair of upward-/downward-looking RD Instrument Inc. Workhorse ADCPs was deployed at a depth of about 135 m on mooring A in January 1998. The ADCP currents were measured every 10 min in 30, 8 m bins between depths of 11 m and 258 m between 11 January and 25 April 1998. The basic statistics of the currents measured between 11 January and 6 February 1998 (Table 2) show (a) water column average southward currents of 1 cm/s and (b) current variability ellipses, typically with ellipticities of about 2 and oriented across the local isobaths (330–150◦ T). The profile of current ellipse Table 2 Basic statistics of a representative subset of the ADCP 10-min current series in both the upper 123 m and lower 104 m of the water column during the 11 January and 6 February 1998 study period. The current variability ellipse is defined in terms of its major axis rms amplitude, orientation, and ellipticity ε = major axis/minor axis. Bin depth (m)

Mean eastward current (cm/s)

Mean northward current (cm/s)

Major axis rms Amp (cm/s)

Major axis direction (◦ T)

ε

Total current variance (cm/s)2

18 35 51 67 83 99 115 123 AVE upper–VA 146 162 178 194 210 226 242 AVE lower–VB AVE total

−2.5 −1.9 −0.4 0.4 0.4 0.1 −0.3 −0.4 −0.6 0.5 0.7 0.5 0.8 −0.3 −0.6 1.1 0.4 −0.1

−1.8 −1.9 −2.1 −2.4 −2.3 −2.0 −2.0 −2.1 −2.1 −1.3 −1.0 −0.1 1.0 1.2 1.0 0.9 0.2 −1.0

15.3 14.7 13.4 12.8 12.7 12.8 12.1 11.5 13.1 9.9 9.3 9.5 10.4 10.9 11.4 11.7 10.4 11.8

329 324 328 332 334 331 329 328 331 326 339 352 354 348 343 343 344 337

1.38 1.47 1.56 1.80 1.95 1.91 1.83 1.77 1.71 1.55 1.37 1.44 1.92 2.18 2.40 2.49 1.91 1.80

357 316 253 214 204 209 190 174 230 139 133 134 138 142 153 159 138 182

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amplitudes decreases from 15.3 cm/s at the surface to a minimum of 9.3 cm/s at a depth of 162 m and then increases to about 11 cm/s near the bottom. 3. The external semidiurnal tide The external (or barotropic) tide is reflected clearly in the variability of sea level, which we infer from bottom pressure measurements. Isopycnal (and isotherm) vertical displacement records, which can be derived from moored temperature and salinity measurements, tend to be dominated by the internal (or baroclinic) tide. Semidiurnal current variability consists of contributions from both the external and the internal tides, which are produced through the interaction of the external tidal currents and bathymetry. When the current–bathymetry interactions are within a few 10 s of kilometers, the internal tidal current component tends to be phase-locked with the external tidal currents. The local presence of phase-locked internal tidal currents makes it difficult to distinguish between the internal or the external tidal currents. Fortunately, we were able to estimate the external tidal currents because the upper 100 m of the water column, with exceeding weak stratification (see Fig. 3) and hence internal tidal variability, had relatively uniform tidal currents during the study period (see Table 2). The currents measured in the upper 123 m between 11 January and 9 February 1998 (29 days) were averaged (VA in Table 2). The VA harmonic analysis results (Table 3) define the depth-independent, external tidal currents for this Wilkinson Basin measurement site. The M2 constituent clearly dominates (∼85% of the variance) the external tidal current (Note: The M2 harmonic constants for a representative set of both the 29-day and the longer 104-day current records, which are very similar, appear in Tables A4a and A4b, respectively in Appendix A). The near-standing wave dynamics of the external semidiurnal M2 tide dominate the Wilkinson Basin region (Brown, 1984). Specifically, the highly polarized, generally across-isobath external M2 tidal currents in the Wilkinson Basin lag the low stand of M2 Wilkinson Basin sea level (i.e., bottom pressure BP) wave by about 90◦ (see Fig. 6, Table 3; and Table A1). Relatively smaller phase differences are found between Wilkinson Basin M2 external tidal currents and others in the region. For example, Wilkinson M2 external tidal currents lag those in Jeffreys’ Basin (at JB 1997 in Fig. 6; Brown, 2005) by 20◦ and lead those on Cashes Ledge (CL 1975–Vermersch et al., 1979) by 10◦ ; those at U3 1991 atop Stellwagen Bank by 10◦ ; and those at U2 1991 and U6 1991 in Massachusetts Bay by 18◦ and 33◦ respectively (Irish and Signell, 1992; Geyer et al., 1992). Wilkinson M2 external tidal currents are also consistent with those from an M2 barotropic tidal circulation model run (see WB 1996 ellipse in Fig. 6; Brown and Yu, in preparation) in that they lag by 10◦ . These western Gulf of Maine M2 external tidal currents are deflected vertically by major regional bathymetric features (see Fig. 2); to the northwest by Jeffreys Ledge and to the southwest by a combination of Stellwagen Bank at shallower depths and the sides of Wilkinson Basin below 100 m. Such current/bathymetry interactions are known to generate internal tides, with intermittent nonlinear internal solitons and associated internal wave packets. Such processes are generally very sensitive to the regional stratification, with large seasonal differences. In what follows, we explore the Wilkinson Basin internal tidal waves processes during the winter. The Wilkinson Basin internal tide is treated by a companion paper by Brown and Yu (in preparation). 4. The semidiurnal internal tide: winter 1998 The details of the winter semidiurnal internal tide in Wilkinson Basin are determined in terms of the measured ADCP currents and vertical displacements and vertical velocities derived from measured water property variability. 4.1. Water property signatures A set of isotherm depth time series in the 100 m to 120 m depth range were derived via a time step by time step linear interpolation of the fixed-depth temperature records from T-chains B and C as well as from mooring A (see Figs. 4 and 7). A tidal harmonic analysis of these series documents

Bin depth (m)

Total Var. (cm/s)2

East Amp (cm/s)

East phase (G◦ )

North Amp (cm/s)

North phase (G◦ )

Major axis Amp (cm/s)

Major axis Dir (◦ T)

ε

Vmax phase (G◦ )

M2 N2 S2 O1 K1 Total SD Var M2 MODEL M2 BP

96 11 3 0 2 110 84

7.7 1.9 1.8 0.4 0.3

187 142 235 309 347

11.5 4.3 1.5 0.3 1.1

8 355 35 73 69

13.8 4.6 2.3 0.4 1.1

326 339 309 302 2

691 −4.8 5.7 2.0 4.0

8 170 47 112 69

6.2 1.20 m

193 108

11.4

355

12.8

332

8.0

0

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Table 3 The harmonic constants for the five principal constituents of the vertically averaged current record for the upper 123 m of the Wilkinson Basin ADCP 8 m-bin averaged currents between 12 January and 9 February 1998; in terms of component amplitude and phases. Tidal current ellipses are given in terms of major axis amplitude and orientation, ellipticity (ε = major/minor; with a positive major axis amplitude indicating an anti-clockwise-rotating current vector), and maximum current Vmax Greenwich phase (in which by convention lower values lead higher values). The M2 harmonic constants are also presented for the Wilkinson Basin bottom pressure (BP ∼ sea level) and the Brown and Yu (in preparation) barotropic model external tidal current constants (MODEL).

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Fig. 6. The external (or barotropic) M2 tidal current ellipse major and minor axes with Greenwich epoch phases of the maximum current (lower values lead) for winter measurements in: Wilkinson Basin (WB 1998); Jeffreys Basin (JB 1997); Massachusetts Bay entrance (U2 1991); Stellwagen Bank (U3 1991); Stellwagen Basin (U6 1991); Cashes Ledge (CL 1975); and barotropic model-derived WB 1996 (see text).

both the dominant contributions of the M2 tides and the relatively large uncertainties of the harmonic constants for the 6.3 ◦ C, 6.5 ◦ C, and 7.8 ◦ C isotherms in particular (see Table A2). The large isotherm depth uncertainties reflect the problems of inferring isotherm depths (a) from measurements located near the base of the mixed layer, where temperature gradients are very time-variable, and (b) where they go deeper than the T-chain coverage (∼150 m). Thus, only the 6.9 ◦ C, 7.0 ◦ C, 7.2 ◦ C, 7.4 ◦ C, and 7.6 ◦ C isotherm depth or displacement (relative to mean depth) series were used for the following statistical analyses. These records were high pass filtered with a cutoff frequency of [36 h]−1 in order to focus on the tidal frequency band variability of interest. Representative T-chain B isotherm depth time series (6.9 ◦ C and 7.6 ◦ C) in Fig. 7 clearly illustrate the dominant semidiurnal variability at these levels. Both time-domain empirical orthogonal function (TEOF) and frequency-domain EOF (FEOF) analyses were conducted on a 3-mooring, 15 series set of the 6.9–7.6 ◦ C isotherm displacement series. For TEOFs, we consider a spatial array of discrete time series (with time step t) at M locations ujn , where j = 1, 2 . . . M indicates station number, and n = 1, 2 . . . N indicates time step number, where (N − 1) t = T or the length of series. The zero-lag cross-covariance for the jth and kth elements of the square, symmetric, real M × M matrix is given by Rjk =

1 N

N  n=1

(ujn − uj )(ukn − uk ),

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Fig. 7. The high-pass filtered (10 min) isotherm depth records for 6.9 ◦ C and 7.6 ◦ C at T-chain B.

where the overbar indicates the respective series mean values. R is diagonalized to obtain the M modes; each consisting of an M-component eigenvector of amplitudes with corresponding time series amplitude functions. For FEOFs, we first compute the complex Fourier coefficients uˆ j , uˆ k for the jth and kth discrete time series for a set of specified frequency bands. Then we form a complex M × M cross-spectral energy density matrix for each frequency band given by S = Sjk ≡ uˆ ∗j uˆ k , where the asterisk means complex conjugate. S is diagonalized to obtain its M complex eigenvectors or modes; each expressed in terms of amplitude and phase structures. A TEOF analysis of the filtered sets of isotherm displacement records was used to identify the most energetic frequency band. The mode-1 TEOF, explaining about 71% of the total set variance of the 15record set of isotherm displacement series, was characterized by relatively uniform rms amplitudes of about 4.1 m throughout the array. As expected most of the isotherm displacement energy was concentrated in the semidiurnal frequency band (∼0.08 cph); as evidenced by Fig. 8 auto-spectrum of the mode-1 TEOF amplitude series. A [12.7 h]−1 frequency band FEOF analysis of unfiltered ∼100 m depth temperature records; one each from moorings A–C, was used to obtain relative phase information. The mode-1 FEOF of the trio of temperatures (explaining 93.4% of the variance) showed high coherence and phases that indicated mooring A temperature led that at mooring B by 27◦ and C by 10◦ . That statistically significant result prompted the following. 4.1.1. Vertical displacement–horizontal structure An FEOF analysis of the unfiltered sets of isotherm displacement records focused on the [12.7 h]−1 frequency band; with a period range 13.33 h to 12.17 h that contains the M2 12.42 h period. The robust mode-1 FEOF of the 15 isopycnal displacement records (explaining 94.7% of the variance; Table 4) consisted of an average rms isotherm displacement amplitude structure of 2.56 ± 0.11 m with an average phase structure in which mooring A lead those at moorings B and C (located about 92 m to the east; see Fig. 1) by a statistically significant 20 ± 10◦ . These FEOF results are consistent with the M2 harmonic

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Fig. 8. The auto-spectrum of the mode-1 TEOF amplitude series of the 15-series set of high-pass filtered 6.9–7.6 ◦ C isotherm vertical displacement time series from moorings A, B and C. The 95% confidence intervals (8 DOF) are indicated.

analysis results (see Table A2); particularly in the statistically significant 20◦ phase lead of isotherms at mooring A relative to those at moorings B and C. Thus the isotherms indicate that the semidiurnal internal tidal wave arrives at mooring A between 0.35 and 1.05 h before the near simultaneous arrival at moorings B and C (see Fig. 9). Thus, these results are consistent with the idea of an M2 internal tidal wave that is generated to the west on the Wilkinson Basin side of Stellwagen Bank and propagates at about 58◦ T across Wilkinson Basin. However, the horizontal phase propagation speed estimates in the range between 0.03 and 0.08 m/s is much too slow for any of the low order internal modes that we expect in this situation. Perhaps this result is indicating a standing M2 internal tide in Wilkinson Basin. We will return to this issue below. Isotherm vertical velocity estimates were derived by taking central first-differences of the unfiltered isotherm displacement time series. The [12.7 h]−1 FEOF of the T-chain vertical velocity estimates Table 4 The semidiurnal-band [12.7 h]−1 mode-1 FEOF structure of the 3-mooring, 15-series composite isotherm displacement records (explaining 94.3% of the variance) is given in terms of rms amplitudes and phases relative to the 0◦ phase of a highly attenuated predicted Wilkinson Basin bottom pressure series (REF BP). The average response at each mooring (AVE) is indicated. Isotherm (◦ C)

6.9 7.0 7.2 7.4 7.6 AVE REF BP

T-chain C

T-chain B ◦

“T-chain” A ◦

Depth (m)

Amp (m)

Phase ( )

Depth (m)

Amp (m)

Phase ( )

Depth (m)

Amp (m)

Phase (◦ )

98 103 108 113 119

2.95 2.80 2.41 2.15 1.88 2.44 ± 0.44 1.2 m

109 118 112 109 107 111 ± 4 000

97 100 106 112 117

2.81 2.82 2.68 2.50 2.29 2.62 ± 0.23 1.2 m

105 112 114 109 106 109 ± 4 000

99 103 110 116 125

2.91 2.87 2.69 2.61 2.08 2.63 ± 0.33 1.2 m

123 129 135 133 131 130 ± 5 000

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Fig. 9. The [12.7 h]−1 FEOF isotherm displacement phases at moorings A, B, and C indicate a northeastward phase propagation of the semidiurnal band internal tide in the 100–125 m depth range.

were all very similar at about 0.35 mm/s (see Table 5). The mooring A minus T-chain B and C phase differences were the same as for the isotherm displacements themselves.

4.1.2. Vertical displacement–vertical structure A well-defined set of isopycnal depth time series were derived from those mooring A density anomaly series that spanned the water column between depths of 100 m and 200 m (Fig. 10). These isopycnal depth series were corrected for the external tidal “heaving “(Kelly et al., 2010) using depthrated contributions based on the bottom pressure time series. The structure of the [12.7 h]−1 frequency band FEOF of the isopycnal displacement series (Fig. 11; Table 6) is characterized by decreasing amplitude and increasing phase between depths of 108 m and 170 m to an amplitude minima; and then the converse between 170 m and 196 m. These amplitudes and phases are consistent with those of the isotherm-derived vertical velocities between 100 m and 130 m depth.

Table 5 The semidiurnal-band [12.7 h]−1 mode-1 FEOF of the 3-mooring, 15-series composite of the unfiltered isotherm-derived vertical velocities W (mm/s) (explaining 94.4% of the total variance) is given in terms of rms amplitude and phases (positive phases lead) relative to the 0◦ phase of a highly attenuated predicted Wilkinson Basin bottom pressure series (REF BP; with which it is highly coherent). The average response at each mooring (AVE) is indicated. Isotherm (◦ C)

6.9 7.0 7.2 7.4 7.6 AVE

AVE depth (m)

98 102 108 113 120

W: T-chain C

W: T-chain B

W: “T-chain” A

Amp (mm/s)

Phase (◦ )

Amp (mm/s)

Phase (◦ )

Amp (mm/s)

Phase (◦ )

0.40 0.38 0.33 0.29 0.26 0.33

199 208 203 199 197 201

0.38 0.38 0.36 0.34 0.31 0.35

195 202 204 199 196 199

0.39 0.39 0.36 0.35 0.27 0.35

213 349 225 223 221 220

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Fig. 10. A subset of the 15 corrected isopycnal depth records at mooring A.

4.2. Current structure The O (10 cm/s) external (depth-independent or barotropic) tidal current amplitudes can mask the less energetic internal tidal currents. The weak stratification and current shear in the upper water column above 123 m prompted us to harmonically analyze the vertically averaged ADCP current VA (see Table 2); assuming that the result would be a reasonable approximation of the true external tidal current. We then subtracted this estimated external tidal current from the total measured current series at each depth to produce a set of residual currents. The rotary spectra of a representative set of both the residual and total current series (Fig. 12) help to distinguish the internal and external tides. In particular the spectral peaks reveal (a) the dominant semidiurnal external tidal currents Table 6 The semidiurnal-band [12.7 h]−1 mode-1 FEOF of the mooring A (a) corrected isopycnal displacements ID (explaining 81.4% variance) and (b) isopycnal-derived vertical velocities W (explaining 77.3% variance) are given in terms of rms amplitude and phases relative to the 0◦ phase of a highly attenuated predicted Wilkinson Basin bottom pressure series (REF BP). Isopycnal

Depth (m)

ID Amp (m)

ID phase (◦ )

W Amp (mm/s)

W phase (◦ )

25.75 25.80 25.85 25.90 25.95 26.00 26.05 26.10 26.15 26.20 26.25 26.30 26.35 26.40 26.45 REF BP

108 116 124 130 135 141 147 152 158 164 170 176 182 189 196

2.37 2.47 2.25 1.91 1.80 1.76 1.70 1.62 1.52 1.44 1.39 1.42 1.48 1.47 1.40 –

141 145 151 154 156 160 166 174 183 193 201 204 202 197 191 000

0.32 0.34 0.31 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.19 0.19 0.20 0.20 0.19

231 235 241 244 247 251 256 264 273 283 292 294 292 287 282 000

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Fig. 11. The separate mode-1 semidiurnal ([12.7 h]−1 ) FEOFs, which are given in terms of (left) amplitudes and (right) phases that are referenced to the 0◦ phase of a highly attenuated Wilkinson Basin bottom pressure record, explain (top) 75.8% of the total variance of the heave-corrected isopycnal displacement series; (middle) 81.5% of the CW rotary internal tidal horizontal current variance; and (bottom) 76.2% of the isopycnal vertical velocity variance.

(dashed), which are nearly rectilinear as indicated by with their equally energetic clockwise (CW) and anticlockwise (ACW) rotary components; (b) the less energetic, less-polarized semidiurnal baroclinic tidal currents; (c) the moderately energetic CW-rotary inertial currents; and (d) the weak diurnal tidal currents. We define the internal tidal currents in terms of a tidal harmonic analysis of the residual currents; i.e., those from which the external tidal currents have been removed. As indicated in Table A4, the only statistically significant internal tidal currents are found at depths greater than 115 m. The most energetic of these internal tidal currents, all of which rotated CW throughout the water column) are found in the depth range between 175 m and 195 m. The dominant M2 internal tidal current ellipses in Fig. 13 are less polarized than those for the corresponding external tidal current (for details see Table A4a). The harmonic analysis results are corroborated by the very small CW rotary current

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Fig. 12. The rotary spectra of both total currents (dotted) and de-barotropic-tided currents (dashed) at a depth of: 35 m in the upper layer; 115 m–near the base of the upper layer; and 194 m–11 January–6 February 1998; (right) clockwise-rotating (CW); (left) anticlockwise (ACW). The semidiurnal and the inertial frequencies are indicated along with the 95% confidence interval.

contributions to the upper water column of the mode-1 semidiurnal band [12.7 h]−1 CW rotary FEOF (Fig. 11). 4.3. Semidiurnal internal tidal structure The dominant mode-1 semidiurnal band [12.7 h]−1 FEOF of the CW-rotary horizontal currents features an amplitude maximum at about 200 m depth (see Fig. 11); which coincides with a broad (160–250 m) phase minimum of 180◦ . The amplitude structure of the dominant mode-1 semidiurnal band [12.7 h]−1 FEOF of the isopycnal vertical velocity is the converse of the horizontal current FEOF structure. Specifically, it exhibits (1) a strong amplitude maximum in the depth range of the horizontal current minimum near 115 m (see Fig. 11), and (2) a broad minimum that coincides with the

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Fig. 13. A sampling of the clockwise-rotating M2 internal tidal current ellipses below the mixed layer-at 146 m (blk -), 178 m (r -), 194 m (gr -), 210 m (blu -), and 242 m (cy -) respectively- tend to be oriented along 190◦ T–10◦ T. They contrast with the less energetic internal tidal currents at 123 m (gr . . .), 115 (r . . .) and 67 (blk . . .), which tend to be oriented along the 58◦ T estimated propagation direction (solid line) of the isotherm-based semidiurnal internal tide. The more energetic nearrectilinear ellipse is that of the local M2 external tidal current (blk . . .). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

horizontal current maximum between 150 m and 200 m Similarly, the phase structure of the mode-1 vertical velocity FEOF is the converse of that for the horizontal current. So how do the kinematical parts in the Wilkinson Basin semidiurnal internal tide fit together? To address this question, we computed a single FEOF for a suite of 15 series - the IT FEOF - that was composed of 3-series clusters of the isopycnal displacement, vertical current, and 58◦ T horizontal current that was appropriate for each of the depths below the mixed layer; namely 107 m, 123 m, 146 m, 170 m, and 194 m. A time series depiction of the winter Wilkinson Basin semidiurnal internal tide, as defined by the amplitude/phase structure of the IT FEOF, is given in terms of the 12.7 h period sinusoidal time series in Fig. 14. The FEOF-derived time series have the general structure of a classic low mode internal tide in a constant-N ocean; namely downwardly decreasing vertical displacement amplitudes that accompany increasing horizontal current amplitudes. However, this winter internal tide in Wilkinson Basin differs from the classic case in that the variabilities of the different fields are not vertically simultaneous. For example, at 107 m and 123 m depth in Fig. 14, the vertical displacement lags the 58◦ T-current by about 90◦ ; like in a standing wave environment. However, at the deeper levels, the vertical displacement is more closely in phase with the 58◦ T-current; as in a progressive wave environment. This structural complexity in the semidiurnal internal tide in the center of Wilkinson Basin probably reflects the superposition of one or more higher order internal modes on a dominant low mode standing internal tide that is trapped by the surrounding bathymetry. The results of a simple internal tide modal analysis of a constant-N (@2 cph), flat bottom ocean of 270 m suggest properties of such a set of modes. For example, a few repetitions of the mode 1-with a 0.42 m/s phase speed and 18.9 km wavelength-could resonate with a 60 to 80 km wide basin (depending on orientation. A progressive wave form of the analysis mode 6-with a 0.07 m/s phase speed and a 3 km wavelength-could explain our finding the very low horizontal phase speeds associated with the isotherm displacements in the 100 m to 130 m depth range. A more definitive explanation of these results awaits an ongoing numerical modeling study of the situation.

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Fig. 14. The internal tidal kinematics in terms of mode-1 semidiurnal [12.7 h]−1 FEOF of the identified isopycnal vertical displacements D, vertical velocities W, and 58◦ T-ward velocities X respectively at five depths.

4.4 Semidiurnal internal tidal energetics The wave-averaged mechanical energy Ewa (z) of internal wave motion at each depth in the water column can be approximated by Ewa (z) =

1 2 (z)}, {u2wa (z) + v2wa (z) + N 2 (z)wa 2

(1)

where u and v are the horizontal velocity components, N is the buoyancy frequency,  vertical displacement,  is the depth-averaged water density, and the subscript wa indicates the temporal mean values–presumably over many wavelengths. The sum of the first two terms on the right-hand-side (RHS) of the Eq. (1) represents the wave-averaged the internal wave kinetic energy per unit volume (KE). The relatively small vertical velocity contribution can be neglected). The third RHS term is the wave-averaged internal wave potential energy per unit volume (PE). The profile of the winter Wilkinson Basin semidiurnal internal tidal energies in Table 7 are based on the semidiurnal mode-1 FEOF of clusters of rotated horizontal velocity component current components (X = 58◦ T-current, Y = 328◦ T-current) and N x heave-corrected isopycnal displacement series at 108 m, 123 m, 146 m, 170 m and 194 m, respectively. While the PE term dominates the energy in Eq (1) at the base of the upper “mixed” layer (108 m), the KE term dominates increasingly so at the deeper depths

Isopyc ID

Depth (m)

X Amp (cm/s)

X Ph(◦ )

X Var (cm/s)2

Y Amp (cm/s)

Y Ph(◦ )

Y Var (cm/s)2

N  (cm/s)

N  Ph(◦ )

N  Var (cm/s)

Ewa / × 10−4 (cm2 /s2 )

25.75 25.85 26.05 26.25 26.45

108 124 147 170 196

0.5 1.2 2.4 3.2 3.4

269 208 192 183 201

0.25 1.44 5.52 10.18 11.76 0.83

0.1 1.0 2.6 3.2 3.6

27 278 267 248 269

0.01 0.98 6.55 10.37 12.67 6.12

0.9 0.8 0.5 0.3 0.4

145 154 165 214 190

0.77 0.64 0.23 0.10 0.14

0.50 1.53 6.27 10.36 12.19

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Table 7 The semidiurnal-band [12.7 h]−1 mode-1 FEOF (explaining 83.5% variance) of a subset of the mooring A X (58◦ T) and Y (328◦ T) horizontal velocity components, and a vertically-averaged buoyancy frequency N-weighted isopycnal displacements; in terms of rms amplitudes and phases relative to that (000◦ ) of a highly-attenuated predicted Wilkinson Basin bottom pressure series. The variances and energy according to Eq. (1) with an assumed depth-constant N = 3.5 × 10-3 s−1 (= 2 cph) are also presented.

243

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Fig. 15. The January 1998 internal tide ray path estimates along the Stellwagen Bank to Wilkinson Basin transect with the (left) 26-day average moored buoyancy frequency profile; and (right) early January average buoyancy frequency profile. The site of the deep Wilkinson Basin mooring (Wilk98) and the shallow 1991 Stellwagen Bank mooring (U3) are indicated.

The structure of the observed kinematics indicates some complexity that should not be a surprise because the proximity to steep bathymetry and an internal tidal generation zones. We explore possible generation sites by looking “backward” along our estimated the internal tidal phase propagation pathway toward Stellwagen Bank. The internal tidal wave energy ray pathway geometry shown in Fig. 15 was estimated using the time-averaged, moored buoyancy frequency profiles (e.g., Fig. 3). The pathway geometry is consistent with a buoyancy frequency profile that increases with depth below the 100 m layer of relatively well-mixed water. Fig. 15(left) depicts internal tidal energy pathways using a buoyancy frequency profile that was averaged for the entire study period. Fig. 15(right) depicts internal tidal energy pathways in early January with the consistently 100 m deep mixed layer. Both scenarios direct internal energy toward the lower water column, where the observed internal tidal kinetic energy is greatest. This result suggests that the generation sites are probably on the steeper slopes between 85 m and 150 m depths on the flank of Stellwagen Bank. 5. Summary and conclusions Internal or baroclinic tidal currents are generated by the interaction of the barotropic tidal currents and steep bathymetry in the presence of stratification. Because the semidiurnal external or barotropic

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tide dominates throughout the Gulf of Maine, semidiurnal internal tidal waves are commonly observed in Wilkinson Basin in the western Gulf of Maine. This was so even during our winter of 1998 field program, which consisted of (1) a tight array of three temperature chain moorings with 100 m lateral separations, (2) a TC chain with an upward and downward-looking pair of ADCP current profilers, and (3) Wilkinson basin-scale hydrographic surveys. The ADCP currents were measured in 30, 8 m bins between 11 m and 256 m depths at a rate of 6/h starting in January 1998 for 4 months. The suite of high frequency (5 and 15-min sample rates) isotherm vertical displacement series between about 100 m and 120 m in Wilkinson Basin (derived through interpolation of a trio of T-chains records about 100 m apart laterally) resolved the winter internal tide during January 1998. The vertical structure of the internal tide between 100 m and 220 m was defined in terms of a suite of high frequency (2-min sample rate) isopycnal vertical displacement time series (and associated vertical velocities) that were derived via interpolation from the array of TC measurements; The main results of this research are that: • The total measured ADCP current variability (variance ∼182 cm2 /s2 ) was partitioned into: 1. M2 external (or barotropic) tidal currents ∼15 cm; in a semidiurnal current environment with a variance of about 110 cm2 /s2 with 96 cm2 /s2 in M2 ; 2. Semidiurnal internal tidal currents ∼5 cm/s (M2 variance ∼12 cm2 /s2 ); 3. Clockwise-rotating inertial currents; most intense in the upper 100 m; • The external tidal current–defined from a harmonic analysis of average ADCP currents in the wellmixed upper 123 m of the water column–is dominated by a nearly rectilinear, across-isobath (326◦ T) M2 semidiurnal tidal current of about 15 cm/s; • A set of clockwise-rotating elliptical semidiurnal internal tidal currents–extracted from the residual currents (external tidal currents removed) by way of a harmonic analysis–consisted of a mixture of 5 cm/s amplitude M2, N2 , and S2 currents that were concentrated between 100 m and 200 m depth; • Isotherm displacement records at a trio of moorings with 100 m separations indicate the propagation of the semidiurnal internal tide east-northeastward (∼58◦ T) through the north-central Wilkinson Basin measurement at a horizontal rate of about 4 cm/s. • A statistical analysis of the an integrated internal tidal set of isopycnal displacement, vertical velocity, and horizontal velocity time series was used to define the internal tidal structure which features: 1. Maximum vertical displacement (and vertical velocity) at the base of the nixed layer (∼100 m); 2. Maximum horizontal velocity near the minimum of the vertical displacement (and vertical velocity) at depths of ∼170 m; 3. The observed vertical structure of the relative phasing of the different dynamical components in the Wilkinson Basin semidiurnal internal tide, has characteristics of a mixture of standing and progressive waves. • An internal tide energy propagation ray analysis suggests that the winter semidiurnal internal tide is most likely generated on the southwestern wall in Wilkinson basin between depths of 85 m and 150 m; Acknowledgements This research has benefited significantly through my collaboration with Zhitao Yu on our ongoing work on Gulf of Maine internal tides. The data used in this paper were obtained and processed through the efforts of a great many people under the leadership of one or the original co-PIs Frank Bub and support by the Ocean Sciences Division of the National Science Foundation under grant OCE-9530249. Appendix A. Tidal harmonic constants for Wilkinson Basin A.1. Bottom pressure The tidal harmonic constants for a Wilkinson Basin bottom pressure record (Brown and Irish, 1992) are presented in Table A1. The tidal harmonic constants are given for the five primary (with estimated

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Table A1 Wilkinson Basin bottom pressure tidal harmonic constants (with estimated uncertainties) of the five principal tidal constituents for a 49-day record from 28 August to 16 October 1996 in terms of amplitude and Greenwich epoch phases. Con

H (db)

M2 N2 S2 O1 K1

1.202 0.273 0.177 0.112 0.079

G (◦ ) ± ± ± ± ±

0.019 0.019 0.019 0.019 0.018

108.4 77.7 138.9 189.5 225.3

± ± ± ± ±

0.8 3.5 5.4 9.2 13.3

Table A2a The M2 tidal harmonic constants for a suite of isotherm displacement time series from moorings B, C and A–based on the 12 January to 5 February 1998 (26 days) records–in terms of amplitude and phase in Greenwich epoch degrees; with estimated uncertainties. The 6.9–7.6 ◦ C isotherm displacement averages and the bottom pressure (BP) constants are given for reference. Note: By convention, the lower Greenwich phases lead the higher ones. Isotherm ID (◦ C) 6.3 6.5 6.7 6.9 7.0 7.2 7.4 7.6 7.8 6.9–7.6 AVE REF BP

T-chain C Depth (m)

T-chain B Phase (G◦ )

Amp (m)

1.94 ± 1.50 13 ± 46 2.65 ± 1.83 329 ± 41 3.28 ± 0.78350 ± 13 3.38 ± 0.51 4±8 3.90 ± 0.60 357 ± 8 1±5 3.42 ± 0.34 3±6 3.15 ± 0.36 5±9 2.66 ± 0.44 2.06 ± 1.93297 ± 59 3.30 ± 0.46 3±7

98 102 107 113 118

“T-chain” A Phase (G◦ )

Amp (m)

1.75 ± 1.10 16 ± 37 2.92 ± 1.69 341 ± 33 3.00 ± 0.85 352 ± 15 3.34 ± 0.58 8±9 3.71 ± 0.54 2±7 3.90 ± 0.36 2±5 3.70 ± 0.40 6±5 8±8 3.33 ± 0.50 3.17 ± 2.12 328 ± 40 3.60 ± 0.48 5±7 1.20 + 0.02 108 ± 0.8

Amp (m) 2.01 ± 1.54 3.11 ± 1.95 3.03 ± 1.11 3.21 ± 0.64 3.57 ± 0.61 3.53 ± 0.42 3.91 ± 0.55 2.64 ± 0.78 1.77 ± 0.69 3.37 ± 0.61

Phase (G◦ ) 15 ± 45 323 ± 37 353 ± 20 353 ± 11 349 ± 9 341 ± 6 339 ± 7 344 ± 16 334 ± 22 345 ± 10

uncertainty limits) and important nonlinear tidal constituents in terms of (a) amplitude (sinusoidal) (b) Greenwich epoch G and (c) local epoch . A.2. Isotherm vertical displacement The tidal harmonic constants for the selected set of Wilkinson Basin isotherm displacements in Table A2a were based on the analysis of 26-day records. The relatively large uncertainties for the tidal harmonic constants for the 6.3 ◦ C and 6.5 ◦ C isotherms reflect the difficulties of inferring isotherm depths from estimated temperature gradients in the region at the base of the mixed layer; while those for the 7.8 ◦ C isotherm are related to excursions deeper than the T-chain coverage (∼150 m). Thus, only the 6.9 ◦ C, 7.0 ◦ C, 7.2 ◦ C, 7.4 ◦ C, and 7.6 ◦ C isotherm displacement series were used for the semidiurnal Table A2b The semidiurnal-band [12.7 h]−1 mode-1 FEOF structure of the 3-mooring, 15-series composite of isotherm displacement records (explaining 94.7% of the total variance) is given in terms of equivalent amplitude and phases relative to a highly attenuated predicted Wilkinson Basin bottom pressure series (where positive phases lead the REF BP). The average response at each mooring (AVE) is indicated. Isotherm (◦ C)

6.9 7.0 7.2 7.4 7.6 AVE REF BP

T-chain C

T-chain B ◦

“T-chain” A ◦

Depth (m)

Amp (m)

Phase ( )

Depth (m)

Amp (m)

Phase ( )

Depth (m)

Amp (m)

Phase (◦ )

98 103 108 113 119

3.49 3.58 3.05 2.77 2.46 3.07

108 115 110 107 104 109

97 100 106 112 117

3.24 3.38 3.28 2.10 2.88 3.18 –

105 110 111 105 102 107 000

99 103 110 116 125

3.48 3.58 3.41 3.45 2.64 3.31

121 125 131 131 127 127

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Table A3 The harmonic constants for the M2 , N2 , and S “heave-corrected” (see text) semidiurnal internal tidal isopycnal displacement records (26 days) from mooring A; in terms of amplitude and phase in Greenwich epoch degrees (records with lower phases lead). Estimated uncertainties and the reference bottom pressure (BP) harmonic constants are also given. Isopyc ID

Dep. (m)

M2 Disp. Amp (m)

M2 Disp. phase (G◦ )

N2 Disp. Amp (m)

25.75 25.80 25.85 25.90 25.95 26.00 26.05 26.10 26.15 26.20 26.25 26.30 26.35 26.40 26.45 BP

108 116 124 130 135 141 147 152 158 164 170 176 182 189 196 270

2.65 ± 0.47 2.60 ± 0.51 2.38 ± 0.60 2.07 ± 0.65 1.90 ± 0.63 1.78 ± 0.62 1.61 ± 0.59 1.42 ± 0.55 1.26 ± 0.48 1.15 ± 0.43 1.13 ± 0.38 1.22 ± 0.35 1.44 ± 0.34 1.62 ± 0.32 1.74 ± 0.32 1.20

345 ± 10 327 ± 11 323 ± 14 324 ± 17 326 ± 18 326 ± 19 324 ± 20 319 ± 21 310 ± 21 298 ± 21 286 ± 19 283 ± 16 283 ± 13 287 ± 11 291 ± 10 108

0.87 ± 0.47 1.03 ± 0.51 1.00 ± 0.60 0.92 ± 0.60 1.05 ± 0.61 1.28 ± 0.59 1.46 ± 0.51 1.61 ± 0.56 1.71 ± 0.47 1.73 ± 0.41 1.69 ± 0.37 1.74 ± 0.36 1.71 ± 0.34 1.62 ± 0.32 1.44 ± 0.31 0.27

N2 Disp. phase (G◦ ) 312 ± 30 287 ± 29 265 ± 14 246 ± 39 228 ± 33 219 ± 26 212 ± 22 205 ± 19 199 ± 15 194 ± 13 191 ± 12 189 ± 11 186 ± 11 184 ± 11 182 ± 12 78

S2 Disp. Amp (m)

S2 Disp. phase (G◦ )

1.50 ± 0.48 1.58 ± 0.53 1.40 ± 0.60 0.98 ± 0.60 0.78 ± 0.58 0.63 ± 0.53 0.46 ± 0.47 0.30 ± 0.36 0.33 ± 0.36 0.57 ± 0.38 0.74 ± 0.36 0.77 ± 0.35 0.70 ± 0.33 0.56 ± 0.32 0.39 ± 0.30 0.18

347 ± 18 349 ± 19 351± 24 359 ± 37 10 ± 44 13 ± 52 9 ± 64 346 ± 79 286 ± 71 262 ± 40 251 ± 28 246 ± 26 243 ± 27 248 ± 32 257 ± 45 139

frequency [12.7 h]−1 frequency domain empirical orthogonal function analysis (FEOF); with results shown in Table A2b. A.3. Isopycnal vertical displacement The semidiurnal tidal harmonic constants for the mooring A isopycnal displacement records in Table A3 were based on the analysis of 26-day records.

Table A4a The M2 tidal harmonic constants for the total eastward and northward current components measured at the indicated depths in Wilkinson Basin between 11 January and 9 February 1998 (29 days); in terms of amplitude and phase in Greenwich epochs. The ellipse major axis amplitude, orientation, ellipticity (ε = major axis/minor; with negative values indicating clockwise-rotating current vector), and Greenwich epoch of the maximum current are also given. The harmonic constants for the upper water column average are also given. Note: By convention lower Greenwich phases lead the higher ones. Bin depth (m)

18 35 51 67 83 99 115 123 Upper 123 m AVE 146 162 178 194 210 226 242

Phase (G◦ )

ε

East Amp (cm/s)

East phase (G◦ )

North Amp North (cm/s) phase (G◦ )

Major axis Major axis Amp (cm/s) Dir (◦ T)

92 106 98 96 100 96 85 81 96

7.4 8.1 8.0 8.0 7.8 7.6 7.3 7.2 7.7

181 181 185 188 187 190 195 200 187

11.4 12.1 11.5 11.3 11.8 11.6 10.8 10.5 11.5

10 11 10 9 7 6 2 1 8

13.6 14.5 14.0 13.8 14.1 13.9 13.0 12.6 13.8

327 326 325 325 327 327 327 326 326

−14 −12 −25 −345 705 29 10 7 691

7 8 9 9 7 7 7 7 8

57 53 58 76 82 88 92

6.2 5.3 4.7 4.2 5.3 6.5 6.6

211 225 224 207 197 196 195

8.7 8.8 9.7 11.6 11.6 11.6 11.8

353 341 338 341 348 354 355

10.2 9.2 9.9 12.0 12.6 13.2 13.4

328 340 346 345 338 332 332

3 2 2 4 5 6 7

5 171 165 165 172 179 180

Total M2 Var (cm/s)2

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Table A4b The M2 tidal harmonic constants for the total eastward and northward current components measured in Wilkinson Basin between 11 January and 25 April 1998 (104 days) records; in terms of amplitude and phase in Greenwich epochs with estimated uncertainties. The ellipse major axis amplitude, orientation, ellipticity (ε = major axis/minor axis), and Greenwich epoch of the maximum current are also given. Note: By convention lower Greenwich phases lead the higher ones. Bin depth (m) 18 35 51 67 83 99 115 123 146 162 178 194 210 226 242

Total M2 Var (cm/s)2 105 113 108 107 108 108 103 96 67 66 73 86 93 98 98

East Amp (cm/s)

Phase (G◦ )

North Amp (cm/s)

Phase (G◦ )

Major axis Major axis Amp (cm/s) Dir (◦ T)

ε

Phase (G◦ )

8.2 8.5 8.3 8.3 8.2 8.3 8.3 8.0 6.6 5.5 4.7 4.6 4.9 5.4 5.4

191 191 192 192 192 193 196 199 206 213 211 204 200 199 197

11.9 12.4 12.1 12.0 12.2 12.1 11.7 11.3 9.5 10.1 11.1 12.3 12.7 12.9 12.9

10 10 9 9 9 8 7 5 355 345 342 342 344 347 348

14.4 15.0 14.7 14.6 14.7 14.6 14.2 13.8 11.2 10.8 11.6 12.8 13.4 13.7 13.8

144.0 150.0 49.0 36.5 36.8 24.3 12.9 8.6 3.9 2.8 3.4 4.3 5.0 5.1 5.5

10 11 10 10 10 10 10 10 5 174 168 166 168 171 172

326 326 326 326 326 326 325 325 327 337 343 343 342 339 339

A.4. Horizontal currents The tidal harmonic constants for Wilkinson Basin currents based on an analysis of the 11 January through 9 February 1998 (29 days) currents (Table A4a) are very similar to those obtained in an analysis of 104-day (11 January–15 April) current records in Table A4b. The anticlockwise-rotating M2 tidal current ellipses in the lower half of the water column are slightly weaker (∼12 cm/s), less polarized, and oriented a little more north-south (335–155◦ T). The slight differences between the structure of the upper and lower water column tidal currents are related to the differences in stratification strength (see Fig. 3). The M2 tidal harmonic constants from a harmonic analysis of the 11 January through 9 Table A4c The M2 tidal harmonic constants for the detided (external tide removed) eastward and northward current components measured in Wilkinson Basin between 11 January and 9 February 1998 (29 days) in terms of amplitude and phase in Greenwich epochs with estimated uncertainties. The ellipse major axis amplitude, orientation, ellipticity (ε = major axis/minor; with negative values indicating clockwise-rotating current vector), and Greenwich epoch of the maximum current are also given. Note: By convention lower Greenwich phases lead the higher ones. The statistically significant non-zero M2 internal tidal current harmonic constants are highlighted. Bin depth (m)

Total M2 Var (cm/s)2

East Amp (cm/s)

18 35 51 67 83 99 115 123 146 162 178 194 210 226 242

1 1 0 0 0 0 1 3 10 22 24 23 12 5 5

0.9 1.0 0.4 0.3 0.1 0.4 1.1 1.7 3.2 4.7 4.8 4.0 2.6 1.5 1.5

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.8 0.8 0.6 0.4 0.1 0.5 0.6 0.6 0.5 0.6 0.4 0.5 0.4 0.5 0.4

Phase (G◦ )

North Amp (cm/s)

73 ± 118 ± 142 ± 212 ± 173 ± 294 ± 305 ± 300 ± 317 ± 325 ± 331 ± 347 ± 347 ± 330 ± 335 ±

0.4 0.9 0.5 0.2 0.3 0.4 1.3 1.6 3.7 5.4 5.6 5.4 4.1 2.8 2.7

57 50 83 92 105 90 33 18 9 6 4 7 7 18 14

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.6 0.8 0.6 0.3 0.4 0.5 0.6 0.6 0.5 0.7 0.4 0.6 0.5 0.4 0.4

Phase (G◦ )

100 60 96 128 349 299 246 237 224 236 246 268 272 276 280

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

93 53 76 102 84 75 29 22 7 7 3 6 6 8 8

Major axis Major axis Amp (cm/s) Dir (◦ T) 1.0 1.2 0.6 0.3 0.3 0.6 1.4 2.0 3.7 5.4 5.7 5.5 4.2 3.0 2.9

67 45 43 79 348 39 37 47 349 5 14 14 15 21 23

ε

−5.8 −1.8 −2.3 −1.4 −83.3 28.0 −1.8 −1.6 −1.7 −1.1 −1.2 −1.4 −1.7 −2.5 −2.8

Phase (G◦ )

78 89 118 24 169 117 88 91 34 61 79 97 101 105 109

W.S. Brown / Dynamics of Atmospheres and Oceans 52 (2011) 224–249

249

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