Internal Tides in the Western Gulf of Maine

Transcription

1 SMAST Technical Report SMAST Internal Tides in the Western ulf of Maine W. S. Brown School for Marine Science and Technology University of Massachusetts Dartmouth New Bedford, MA Abstract Internal or baroclinic tidal currents are generated by the interaction of the barotropic tidal currents and steep bathymetry in the presence of stratification. This interaction usually generates internal tidal waves, as well as highly nonlinear internal solitary wave under the right circumstances. In the ulf of Maine the semidiurnal external or barotropic tide dominates so semidiurnal internal tidal waves are commonly observed throughout the ulf including Wilkinson Basin in the western ulf of Maine. This was so even during the winter of field program consisting of (1) a tight array of three mooring (100m separations) in Wilkinson Basin consisting of a T/C chain with an upward/downward-looking pair of ADCPs and a surface met package and two temperature chains; and (2) 5 Wilkinson basin-scale hydrographic surveys. The ADCP horizontal (and vertical currents) were measured at a rate of 6/hr starting in January 1998 for 4 months in 30, 8m bins in the depth range - 11 m to 256 m. The series mean currents were small ~ 2 cm/s and generally southward. The total velocities were partitioned into the (1) nearlyrectilinear, across-isobath (320 T) semidiurnal external (or barotropic) tidal currents ~ 15cm/s; (2) clockwise rotating semidiurnal internal tidal currents ~ 5cm/s concentrated below the mixed layer; and (3) clockwise-rotating inertial currents. The internal tidal was found to propagate from southwest to northeast across Wilkinson Basin during the study period. The strongest winter internal tide is very likely generated through the interaction of the external tidal currents and the south western wall of Wilkinson Basin. 1. INTRODUCTION The geometry of the ulf of Maine/Bay of Fundy system is the crucial factor in the amplified tidal response of the ulf system. The characteristic or resonant period of the ulf system is very near to the frequency of the semidiurnal tide that is forced by the tides in the North Atlantic. Thus the semidiurnal tidal response of the ulf is amplified, while the diurnal tidal response is not. The M 2 semidiurnal harmonic constituent amplitude in the ulf is four times greater than the next largest semidiurnal constituent (i.e. N 2 ). The near-standing semidiurnal tidal wave response of the ulf system ranges from about 40 cm along the seaward edge of eorges Bank to about 15 meters at the head of the Bay of Fundy. The amplitudes and phases of tidal currents associated with the ulf surface tide tend to be depthindependent (i.e. barotropic) except in the lowest part of the water column where friction is important. There is considerable lateral spatial structure of barotropic tidal currents because of the complex bathymetry of the ulf (see Brown, 1984). Throughout much of the interior ulf, the tidal currents are a relatively week (~10 cm/s). However, in regions of steep bathymetry, such as the north flank of eorges Bank, relatively stronger barotropic tidal currents (~50 cm/s) are oriented across-isobath (Moody et al., 1984). Tidal currents in the Bay of Fundy are even stronger. 1

2 Figure 1: Location map for the Wilkinson Basin study. The tight mooring array (blue/red dot; see inset) sits at the center of the 29January -2 February 1998 hydrographic survey map. Operational NOS sea level stations (circles) and NDBC (triangle)/nws (squares) meteorological measurement sites are located. The 100m and 200m isobaths are shown. Figure 2. The bathymetry along a north-south transect from Cape Porpoise, ME on the left through Jeffreys Basin to northern Wilkinson Basin marked by the location of the moorings on the right Internal or baroclinic tidal currents are generated by the interaction of the barotropic tidal currents and steep bathymetry in the presence of stratification. This interaction generates both a highly nonlinear internal solitary wave once every tidal cycle as well as a more regular internal tidal wave. The internal tidal wave appears to be generated continuously at depth along the north flank of eorges Bank and propagates toward the interior ulf. Apparently, the internal solitary waves are generated as a lee wave 2

3 associated with the incoming (i.e., flood) barotropic tidal current over the north flank of eorges Bank (Loder et al., 1992). When the flood tidal current begins to ebb, a solitary wave propagates toward the bank. As the solitary wave of isopycnal depression (or elevation) propagates away from a generation region, it can evolve into a packet of multiple depressions. Internal wave packets also appear to propagate away from eorges Bank, as seen from space by the sea surface texture changes associated with the internal solitary wave surface flow convergence (ripples) and divergence (slicks) patterns (Sawyer, 1983). Internal tides have been on the north flank of eorges Bank with moored current meters located at depths of 30, 40, and 75 meters in about 200 m of water. He found that 98% of the current spectral energy density in the semidiurnal frequency band was contained in the mode in which the across-isobath component was largest. Phase differences in the currents at adjacent levels indicated a downward energy propagation at the mooring site; consistent with the rays pattern emanating from the top of the slope. Horizontal wave length and phase speed were estimated to be 20 to 30 km and 0.40 to 0.70 m/s, respectively The variability of density stratification in the ulf 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 ulf, including Wilkinson Basin. The basic density stratification of the ulf 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 arfield, 1979; Brown and Irish, 1993). Maine Intermediate Water (MIW), which is identified primarily by its minimum temperature at about 75m depth, is a remnant of the 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 150m in Wilkinson Basin. Spring warming, augmented by freshening, causes Winter Water layer to separate into MSW and MIW. Summer solar warming produces a strong pycnocline at about 15m depth throughout much of the gulf, particularly in Wilkinson Basin. In this paper, we report on observations of the internal tides in Wilkinson Basin of the western ulf Maine from the winters of and 1998 (see Figure 1 location map). 2. OBSERVATIONS The field program consisted of seven seasonal shipboard hydrographic surveys of the Wilkinson Basin region between January 1997 and May 1998, moored ocean measurements, and research and operational meteorological measurements. (see Brown et al. 2005; and Bub et al. 1998; 1999; & 2000 for more details). The typical hydrographic station pattern consisted of tracks radiating from the central Wilkinson Basin mooring array (located in Figure 1), each with nominal station separations of 16 km. A small-scale array of moored measurements, with O(100m) separations, was made during the winter of (Brown et al. 2005; Table 1). The heavily instrumented mooring A was equipped with (1) a suite of meteorological sensors at the surface, (2) eight pairs of Sea Bird temperature and conductivity (TC) sensors that bracketed (3) a pair of upward/downward-looking RD Acoustic Doppler Current Profiling (ADCP) instruments (See Figure 2 and Table 1). The year-long field program included hourly average measurements of temperature at 1m and Sea Bird temperature and conductivity (TC) at depths of 15m, 65m, 115m, 165m respectively in Wilkinson Basin during winter 1987 (Brown and Irish, 1993). These measurements documented a highly variable mixed layer with significant internal tidal variability at its base. The moored time series observations were augmented with a ulf-wide survey of shipboard hydrography between 5 and 15 February, bracketing the intense 9-10 February storm. The hydrography before the storm showed that the upper 115m of the central Wilkinson Basin consisted of a relatively fresher (and colder) homogeneous layer of Winter Water floating on a deeper saltier, warmer Maine Bottom Water layer. The combination of measurements and model results showed that a fresher, colder upper water layer was advected into Wilkinson Basin during and after the storm, thus creating a shallower mixed layer observed after the storm. 3

4 Table 1 Wilkinson Basin Moored Measurement Information: Meteorological, ADCP currents, T-Chains, TC Sensors, Sample Interval ( t), and Duration. ID North Latitude (deg min) A ( ) West Longitude (deg min) ( ) Sensor Type Met T/C ADCP ADCP T/C T/C t (min) Depth -2 4, 23, 38, 68, 98, 128 8m 8m Start Date 11 Jan Jan Jan Jan 1998 End Date 6 Feb Feb May April 1998 B T-Chain 15 3 Oct Mar 1998 C T-Chain 5 10 Jan Mar 1998 D T/C Oct May 1998 T/C E T/C Oct May na na na na na A. Water Property Measurements 1. Hydrography CTD-derived density profiles (see Figure 3) were obtained at the Wilkinson Basin mooring in early and late January 1998, respectively. There is evidence of the episodic vertical mixing due to combined wind and convection, with mixed layers of (1) 0-40m and m respectively in the 12 January profile, and (2) 0-60m and m in the 31 January profile. Consequently the strength of the near-surface stratification during the winter is much reduced from that in October. Quantitatively the buoyancy frequency at 40m depth is about 3 cph in January versus 18cph in October 1996 (Brown and Yu, 2005). However throughout the rest of the lower water column the differences, with a more or less depth-independent 4 cph prevailing in January versus 8 cph in October. Figure 3 CTDderived density anomaly (sigmatheta) and buoyancy frequency profiles in Wilkinson Basin; (left) 12 January 1998; (right) 31 January

5 2. Moored Time Series Water Properties : The temporal variability of the water property fields was measured extensively with moored array (A) of Sea Bird temperature/conductivity (TC) sensors and The Aanderra Model 2862 temperature (T) chains during the study period (see Table 1. The two T- chains moored within about 100m of mooring A (see Figure 1 inset; and Brown et al. 2005); each with a 10-sensor array between about 20m and 155m and buoyed vertically with a subsurface float with pressure sensor. T-chain B measured temperature every 15-minutes between October 1997-March 1998, while T-chain C measured temperatures every 5-minutes between 11 January and March 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 ± C and that for T-chain C temperature record was ± C. (See Miller et al. 1999b for details). The pressure measured atop each T-chain by TR-7 Silicon Piezoresistive Bridge pressure showed that the actual depths of the T-chain temperature sensors varied about ±2m from their nominal depths due to the (a) tidal sea level excursions and (b) tidal and storm current drag on the array. To obtain depth-constant time series (i.e. compensate for the mooring motion), the measured temperature/depth time series were interpolated to the depth-constant temperature time series at 15m intervals as shown for T-chain B in the top panel of Figure 4 (see Miller et al. 1999). 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. Figure 4. Temperature time-depth contour presentations for (top) T-chain B, (middle) T/C-chain A, and (bottom) the augmented TC-chain A time series (see text). Note the improvement in the resolution of the internal tidal variability. The contour interval is 0.2 o C. 5

6 The mooring A TC measurements were obtained every 2-minutes (a) at 6 levels in the upper 129m on between 11 January and 6 February 1998 (before a storm-induced surface buoy data logger failure ended them); (b) for longer periods at 172m and 216m on mooring A; and (c) on mooring D at 22m and 216m; and mooring E at 97m respectively (see Table 1). The taut-wire mooring construction of mooring A resulted in a full set of temperature/conductivity measurements that were always at constant depth relative to the surface between 11 and 24 January Most of the measurement records extended to 6 February before they ended prematurely due an instrumentation malfunction. Our interest in performing tidal analyses on 28-day density time series motivated us to extend those temperature and salinity records at 6m, 70m, and 129m respectively that ended even before 6 February. We inferred the missing data by employing cross-correlations between temperature and salinity measurements on the mooring (for the details see Brown et al., 2005; and Miller et al., 1999). The visual similarity between the T-chain B and mooring A temperature records (upper and middle panels of Figure 4) is about what one would expect for measurements made about 100m apart except at internal tidal time scales. The mooring A temperature measurements just do not resolve the obvious internal tidal variability in the 70m-130m depth range very well. To address the problem, we constructed representative estimates of the 85m and 115m temperature time series by interpolating the 5-minute T-chain C temperatures records. With these extra temperature records, the augmented mooring A temperature measurement suite better resolves the internal tidal temperature signature (see lowest panel Figure 4). The task of estimating the corresponding mooring A salinity time series at 85m and 115m was accomplished 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 Brown et al. 2005). The suite of temperature and salinity time series between 6 and 216m was used to compute sigma theta (density anomaly) at the depths of the measurements. The internal tide is most clearly revealed in the temperature and density anomaly isopleth variability fields (Figure 5) below a variable mixed layer at about 100m depth (see Brown et al., 2005 for the detail). A suite isopycnal depth time series were derived from these measurements for further analysis. The tidal harmonic analysis results for a selected suite of isotherm displacement series are presented in Appendix A. Figure 5 Temperature and density anomaly (sigma-theta) contours based on measurements at indicated depths. 6

7 3. Water Column Stability Static Stability: The moored Wilkinson Basin temperature and density measurements (see Figure 5; Brown et al., 2005) reveal a mixed layer that first deepened to a depth of about 100 m during the January period of strong cooling. (Water density in Wilkinson basin is primarily determined by salinity, except near the surface). Then around 25 January, the base of the mixed layer began shallowing to about 40m, as a fresher (and colder) surface water mass was advected into the site. The negative (blue) Brunt- Vaisala frequency (i.e. N 2 = static stability) in the upper depth-time map of Figure 6 show that the unstable regions of convective motions penetrate to depths of ~ 100m before the 25 January advection event. Mupparapu and Brown (2002) and Brown et al. (in prep) show that the convection derives from surface temperature-induced instabilities. Dynamic Stability: The Richardson Number (i.e. Ri = N 2 /Sh 2, where Sh is the vertical current shear ) is a measure of the dynamic stability of the water column, where stratification is stabilizing and current shear is destabilizing. The lower depth-time map of Figure 6 shows that supercritical regions (i.e. 4xRi < 1) are (1) confined to the upper water column where static stability is weaker and (2) associated with wind-induced high inertial motion-related shear events. These data help to resolve the 4-D picture of the convectioninduced and the shear-induced mixing that both play a role in forming Winter Water in Wilkinson basin during the winter. Figure 6 Wilkinson Basin time-depth distributions of the evolution of water column (top) static stability (Brunt Vaisala Frequency) and (bottom) dynamic stability (4x Richardson No.; i.e. critical Ri=1) as it relates to atmospheric surface forcing between 13 and 17 January

8 B. Currents A pair of RD Instrument Inc. Workhorse Acoustic Doppler Current Profilers (ADCP) were deployed at a depth of about 135m in an upward-/downward-looking configuration on mooring A in January The 3-component ADCP currents were measured every 10 minutes in 15 (8m) bins between 11m and 123m (ADCP-up) and 15 (8m) bins between 146m and 258m (ADCP-down), respectively between 11 January and 25 April 1998 (104 days). The basic statistics of the currents measured between 11 January and 6 February 1998 (Table 2) show (a) 1 to 2 cm/s mean currents tending southward and (b) current variability ellipses (ellipticity ~ 2) that are oriented across local isobaths (~ o T) and with amplitudes that decrease from their 15.3 cm/s surface maximum to a minimum of 9.3 cm/s at 162m depth and the increase to about 11cm/s near the bottom. The current variability is strongly influenced by the highly-polarized (high ε), across-isobath M 2 tidal currents, as shown by the tidal harmonic analysis results of the full 104- day ADCP current records (see Appendix A). Currents in the semidiurnal frequency band consist of contributions from both the external (or barotropic) tide and the internal (or baroclinic) tide. When the internal tide is being generated locally through the interaction of the external tidal currents and nearby bathymetry, it tends to be phase-locked with the external tide. However, the internal and external tides have radically different physical characteristics, leading to confusion in interpretation of measurements. Specifically, the presence of phase-locked internal tidal currents confuses our ability to determine the harmonic characteristics of both internal and external tidal currents. To isolate the internal tidal variability, the external tidal signature must be determined and removed from the data. Since the internal tidal variability is strongest in the more stratified lower water column of the winter Wilkinson Basin, we focus on the more well-mixed upper water column to obtain better estimates of the external tide as discussed next. Table 2. Basic statistics of a representative subset of the ADCP measurements of total current for the 11 January and 6 February 1998 study period. The variability ellipse is defined in terms of its major axis amplitude, orientation, and ellipticity ε = major axis/minor axis. Bin Depth Mean Eastward Current Mean Northward Current Total Current Variance Major Axis Major Axis Direction ( o T) AVE-Upper AVE-Lower 143 AVE Total 188 ε 8

9 3. The External M 2 Semidiurnal Tide in the Western ulf of Maine The external M 2 tidal currents were estimated from the 1998 Wilkinson Basin ADCP current measurements through a harmonic analysis of the vertically-averaged upper 123m ADCP currents. The similarity of the harmonic analysis results (Table 3) and the total current statistics (Table 2) clearly shows that the M 2 tidal currents dominate the total Wilkinson Basin current field currents during the 12 January-6 February study period. In particular, the M 2 tidal current ellipses in the upper 123m of the water column are nearly rectilinear along 326 o T-146 o T, with a vertically-averaged amplitude of 14.6 cm/s. The anticlockwiserotating M 2 tidal current ellipses in the lower half of the water column (see Appendix A) are slightly weaker (~12 cm/s), less polarized, and oriented a little more north-south (335 o T-155 o 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 Figure 3). The Wilkinson Basin external tidal currents (see Figure 7; Appendix B) are consistent with the harmonic analysis results of a barotropic circulation model run by Brown and Yu (2005) for a nearby Wilkinson basin site (WB 1996; see Appendix C). Regional external M 2 tidal currents were also estimated from measurements at other sites (Figure 7; Appendix D) including Cashes Ledge (CL 1975; Vermersch et al., 1979), Jeffreys Basin (JB 1997; Brown, 2005a), and Massachusetts Bay (U2 1991, U3 1991, and U6 1991; eyer et al. 1992; Irish and Signell, 1992; Wallinga and Brown, 2005). Note the similarity of the reenwich phases of the maximum currents in Figure 7. The Figure 7 summary documents a regional external M 2 tidal current consists of (a) highly polarized across-isobath oscillations that the external M 2 tidal currents are (1) nearly in phase at all of these sites (leading Wilkinson Basin bottom pressure by a quarter tidal cycle consistent with the standing waves dynamics of the region (see Appendix A; Brown, 1984). Table 3 The M 2 tidal harmonic constants for the upper 123m of the Wilkinson Basin ADCP (8m) currents between 0000 MT 12 January to 0000 MT 6 February 1998; in terms of component amplitude and phase in reenwich and local epochs. The M 2 tidal current ellipses are given in terms of major axis amplitude and orientation, ellipticity (ε=major/minor, and reenwich phase of the maximum current; with a positive major axis amplitude indicating an anticlockwise rotating current vector. The harmonic constants for the five principal and 2 nonlinear tidal constituents of the vertically-averaged current records from the upper 123m are also given. Bin Depth Total Variance 2 Eastward Northward Major Axis Major Dir ( o T) AVE M N S O K M M ε 9

10 Figure 7. The external (barotropic) M 2 tidal current ellipse major/minor axes derived from winter measurements in Wilkinson Basin (WB 1998); Jeffreys Basin (JB 1997); in the entrance to Massachusetts Bay (U2 1991); on top of Stellwagen Bank (U3 1991); in Stellwagen Basin (U6 1991); and on Cashes Ledge (CL 1975). The M 2 tidal current ellipse at WB 1996 is from a barotropic model calculation for the ulf of Maine (see text). The reenwich phases (lower leads higher) of the maximum ellipse currents are given. Of particular relevance to us is the finding that these external M 2 tidal currents are continuously interacting with the major regional bathymetric features, including Jeffreys Ledge - the northwestern wall of Wilkinson Basin (see Figure 2)- and the combination of the southwestern wall of Wilkinson Basin (below 100m) and Stellwagen Bank at shallower depths. These current/bathymetry interactions, combined with the appropriate stratification, create highly favorable conditions for the generation of internal semidiurnal tides, internal solitons and the internal wave packets that evolve from these highly non-linear waves. In what follows we explore internal tidal waves processes in Wilkinson Basin during the winter. 4. The Semidiurnal Internal Tide in Wilkinson Basin: Winter 1998 Water Property Signatures: The external tidal sea level amplitudes are O(1m) and thus do not compete with internal water property tidal signatures, which can exhibit depth changes of 10s of meters at the semidiurnal frequencies (e.g. Figures 5). A suite of 5 of the 8 isotherm displacement time series that were derived from the array of fixed depth temperature records from mooring A, T-chain B and T-chain C respectively, proved particularly useful in exploring the internal tide characteristics in Wilkinson Basin. To emphasize the tidal frequency band variability, all of the records were high pass filtered with a cutoff frequency of [36hr] -1. The 7.6 o C isotherm displacement series from T-chain C in Figure 8 clearly illustrates the dominance of the semidiurnal variability with O(10m) amplitudes. Mooring A provided density anomaly time series that were used similarly to estimate the suite of isopycnal displacement time series in Figure 9. Both of these products exhibit the internal tidal variability that we seek to understand better. The mode-1 time-domain empirical orthogonal function (TEOF) structure functions for all three of the arrays were similar (see Table 4) in that they (1) had a maximum of just about rms 7m for the isotherms at 70m depth and (2) explained about half of the total variance. Where was the energy? A spectral analysis of the amplitude time series showed that most of the TEOF mode-1 energy was in the spectral region of the semidiurnal frequency band (0.08cph) as shown in Figures

11 Table 4. The mode-1 TEOF structure functions of the selected isotherm displacement records on each of the indicated moorings. The mean depths of the individual isotherms for each of the moorings is given. Isotherm ( o C) T-Chain B [51.8%] T-Chain B Mean Depth T-Chain C [49.6%] T-Chain C Mean Depth T-Chain A [55.2%] AT Mean Depth The semidiurnal internal tides (primarily M 2 ) are found to propagate across the mooring array (see Figure 1) from southwest to northeast, as shown by the following statistical analyses. The structure of the isotherm variability was explored with a frequency domain empirical orthogonal function (FEOF) analysis of the semidiurnal frequency band variability of 6 isotherm displacement records from moorings A, B, and C. The mode-1 FEOF of the semidiurnal frequency band tri-mooring isotherm displacement series consists of statistically similar rms amplitudes of about 2.3m (Table 5), an average B minus C phase difference of 1 o (statistically the same), but an A minus B (or C) phase difference of a statistically significant 16 o. (The harmonic analysis results in Appendix A are consistent with result and include uncertainty estimates). These results show that the semidiurnal internal tidal wave arrives at mooring A about 33 minutes before arriving at both moorings B and C. This finding suggests a propagation direction of about 63 o T and given the relatively deep pycnocline - a Wilkinson Basin western wall generation site. Figure 8. The 10-min 7.6 o C isotherm depth time series derived from T-chain C for the 11 January and 6 February 1998 study period. 11

12 Figure 9. The 10-min isopycnal time series derived from mooring A sigma theta time series for the 11 January and 6 February 1998 study period. Figure 10 The spectrum of the mode-1 TEOF amplitude series for a composite of T-chain B and C isotherm depth time series; representing 47.5 % of the total variance. The semidiurnal frequency band is indicated along with the 95% confidence interval for 8 DOF. 12

13 Table 5 The mode-1 semidiurnal-band FEOF of the 15-series suite of isotherm displacement records from the moored temperature array explain 94.5% of the total variance. The computed rms amplitudes of each isotherm have been converted to equivalent amplitude (enabling easier comparison with our harmonic analysis results) and phases, that when positive lead the reference bottom pressure tidal series (REF BP ~ sea level) predicted for Wilkinson Basin. (Note: The REF BP series was highly attenuated so that it did not influence the modal calculation except as a phase reference). Isotherm ( o C) T-Chain B T-Chain B Phase T-Chain C T-Chain C Phase T-Chain A T-Chain Phase AVE REF BP Finally vertical velocities were estimated from the central first-differences of the terms in a suite of isotherm displacement time series. As expected, the vertical velocities were about an order of magnitude smaller than the horizontal velocities. However these vertical velocities are highly coherent with both isopycnal displacement and horizontal current series as we explore in the next section. Current Signatures: The external tidal current amplitudes are O10 cm/s and as discussed above can mask the less energetic internal tidal currents. To isolate the internal tidal currents, the predicted barotropic external tidal current was subtracted from each of the ADCP currents to produce a set of residual currents. Then the series were high-pass (HP) filtered (cutoff frequency = 1/36hr). Without the external tidal currents, the residual current ellipses (see Appendix E) are significantly less polarized than those with the external tide in Table 2. The distinctions between the internal and external tides (and ever-present inertial currents) are highlighted by the peaks in the rotary spectra of a representative set of both the HP residual and total current series in Figures 11. The spectra reveal several features of interest here, including (1) dominant semidiurnal external tidal currents with their equally energetic clockwise (CW) and anticlockwise (ACW) rotary components (consistent highly polarized currents); (2) considerably less energetic CW and ACW rotary semidiurnal baroclinic tidal currents; (3) modestly energetic CW rotary inertial currents; and (4) weak diurnal tidal currents. An M 2 harmonic analysis of the individual HP residual current series (Table 6) reveals a set of internal tidal current ellipses that are most energetic at depths below the bottom of the mixed layer at ~ 100m (see Figure 12) and much less polarized than the barotropic current ellipses (Figure 7; Table 3). Part of the structure of the overall semidiurnal internal tide is revealed in the mode-1 and mode-2 [12.7 hour] -1 FEOFs of the eastward residual current component (Figure 13). This mode-1 FEOF is clearly confined to the more stratified lower water column below about 80m and dominates (75.1%) the energy in this frequency band. The phase of the currents decreases from zero to 90 o between 80m and 185m the depth of the maximum amplitude. The structure of the overall semidiurnal internal tide is revealed in the mode-1 [12.7 hour] -1 FEOFs of clusters of isopycnal displacement series, vertical velocity series, and eastward residual current component (Appendix F). This mode-1 FEOF (Figure 14) shows the timing of the component of what is a mode of highly coherent components. 13

14 Figure 11 The rotary spectra of a representative set of high-pass filtered ADCP currents: Total currents (dotted) and residual currents (dashed -barotropic tide removed) in the mixed layer (35m); near t he base of the mixed layer (115m); and in the deep layer between 10 January and 6 February 1998; right panels) clockwise rotating components (csp); (left panels) anticlockwise components (asp). The semidiurnal frequency (long), inertial frequency (short) and 95% CI are indicated. Figure 12 The internal tidal current ellipses at 146m (blk), 178m (r), 194m (g), 210m (blue), 242m (cy). The external tidal ellipse is dotted and the estimated propagation direction of the internal tide (see below) is the northeastward line. 14

15 Table 6 The M 2 tidal harmonic constants for a selected set of the HP residual currents between 0000 MT 12 January to 0000 MT 6 February in terms of component The M 2 harmonic current component amplitude and reenwich epoch phases are given along with ellipse information, including major axis amplitude and orientation, ellipticity (ε=major/minor; with negative values indicating clockwise rotating current vector), and the reenwich phase of the maximum current. Bin Total M 2 Eastward Northward Major Axis Major ε Depth Variance M 2 M 2 M 2 Dir 2 ( o T) Figure 13 The 12.7 hr mode-1and mode-2 FEOFs of the HP residual currents during the study period. 15

16 Figure 14 The 12.7 hr mode-1 internal tidal kinematics at several levels in terms of a trio of panels for isopycnal vertical displacement, vertical velocity, and eastward velocity respectively at five depths. 5. Summary Internal or baroclinic tidal currents are generated by the interaction of the barotropic tidal currents and steep bathymetry in the presence of stratification. This interaction usually generates internal tidal waves, as well as highly nonlinear internal solitary wave under the right circumstances. In the ulf of Maine the semidiurnal external or barotropic tide dominates so semidiurnal internal tidal waves are commonly observed throughout the ulf including Wilkinson Basin in the western ulf of Maine. This was so even during the winter of field program consisting of (1) a tight array of three mooring (100m separations) in Wilkinson Basin consisting of a T/C chain with an upward/downward-looking pair of ADCPs and a surface met package and two temperature chains; and (2) 5 Wilkinson basin-scale hydrographic surveys. The ADCP horizontal (and vertical currents) were measured at a rate of 6/hr starting in January 1998 for 4 months in 30, 8m bins in the depth range - 11 m to 256 m. The series mean currents were small ~ 2 cm/s and generally southward. The total velocities were partitioned into the (1) nearlyrectilinear, across-isobath (320 T) semidiurnal external (or barotropic) tidal currents ~ 15cm/s; (2) clockwise rotating semidiurnal internal tidal currents ~ 5cm/s concentrated below the mixed layer; and (3) clockwise-rotating inertial currents. The internal tidal was found to propagate from southwest to northeast across Wilkinson Basin during the study period. The strongest winter internal tide is very likely generated through the interaction of the external tidal currents and the south western wall of Wilkinson Basin. 16

17 6. Appendices Appendix A. Tidal Harmonic Constants for Wilkinson Basin Measurements Here we present the results of tidal harmonic analyses for a variety of bottom pressure, isotherm displacement, and current measurements made in Wilkinson Basin. The tidal harmonic constants are given for the primary tidal constituents (and in some cases the nonlinear tidal constituents) in terms of (a) amplitude (sinusoidal) (b) reenwich epoch degrees and (c) local epoch κ degrees; each with uncertainty limits except for the higher harmonics. Table A.1 BOTTOM PRESSURE: The harmonic constants of the 25 principal tidal constituents based on the tidal harmonic analysis of a 28 August - 16 October 1996 bottom pressure record from Wilkinson Basin. Con H κ M ± ± ± 0.8 N ± ± ± 3.4 S ± ± ± 5.3 O ± ± ± 8.8 K ± ± ± 13.1 M M M S S

18 Table A.2 ISOTHERM DISPLACEMENT: The M 2 tidal harmonic constants for a suite of isotherm displacement time series from moorings B, C and A between 0000 MT 12 January to 0000 MT 5 February 1998; in terms of amplitude and phase in reenwich epochs with estimated uncertainties. (Note: By convention lower reenwich phases lead the higher ones).the relatively large uncertainties for both amplitudes and phases for the 6.3 o C, 6.5 o C, and 7.8 o C isotherms makes their interpretation problematic. The bottom pressure phases are given for reference. Isotherm ( o C) T-Chain B M 2 T-Chain B M 2 Phase T-Chain C M 2 T-Chain C M 2 Phase T-Chain A M 2 T-Chain A M 2 Phase ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 22 REF BP ± ± ±

19 Table A.3 CURRENTS: The M 2, N 2, S 2, O 1, and K 1 tidal current harmonic constants for a subset of the Wilkinson Basin ADCP 8m-bin currents at the depths indicated; between 0000 MT 12 January to 0000 MT 2 May A negative minor axis current indicates that the tidal constituent vector rotates clockwise rather that anti-clockwise (positive). Eastward Northward Ellipse H Phase Phase H Phase Phase Maj Min Phase Orien (mm/s) (κ o ) (mm/s) (κ o ) (mm/s) (mm/s) ( o T) 18m M(2) N(2) S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1) Eastward Northward Ellipse H Phase Phase H Phase Phase Maj Min Phase Orien (mm/s) (κ o ) (mm/s) (κ o ) (mm/s) (mm/s) ( o T) 51m M(2) N(2) S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1) m M(2) N(2)

20 S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1) Eastward Northward Ellipse H Phase Phase H Phase Phase Maj Min Phase Orien (mm/s) (κ o ) (mm/s) (κ o ) (mm/s) (mm/s) ( o T) 178m M(2) N(2) S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1) m M(2) N(2) S(2) O(1) K(1)

21 APPENDIX B. M 2 Harmonic Constants for Wilkinson Basin Currents The M 2 tidal harmonic constants for the Wilkinson Basin ADCP current components; based on the (1) 104- day measurements between 11 January and 25 April 1998; (2) 26-day measurements between 11 January and 6 February Besides the constants for the individual components, the ellipse major axis amplitude, orientation, ellipticity (ε = major axis/minor axis), and reenwich epoch of the maximum current are given. (1) Bin Depth Eastward M 2 Northward M 2 Major Axis M 2 Major M 2 Axis Dir ( o T) ε (2) Bin Depth Total M 2 Variance 2 Eastward M 2 Northward M 2 Major Axis M 2 Major M 2 Axis Dir ( o T) ε 21

22 APPENDIX C: M 2 Harmonic Constants for MODEL Wilkinson Basin Currents The Brown and Yu (2005) M 2 tidal harmonic constants for a barotropic model run of Wilkinson Basin currents between 2000 MT 28 August to 1450 MT 17 October 1996 (49 days). The ulf of Maine response was hindcasted with model was a uniform-density (or barotropic) version of the Dartmouth threedimensional, finite-element circulation model (QUODDY; Lynch et al., 1996; 1997) forced by M 2 tidal sea level on the lateral boundaries and realistic winds and atmospheric pressure on the surface. The results of the harmonic analysis of the model results at the WB 1996 mooring site are given in terms of component amplitude and phase in reenwich epoch degrees. The M 2 tidal current ellipses are given in terms of major axis amplitude and orientation, ellipticity (ε =major/minor, and reenwich phase of the maximum current; with the positive ellipticity values indicating an anticlockwise rotating current vector. We also present the corresponding M 2, M 4, and M 6 results of an average of the 80m, 150m and 220m current records. Eastward Northward Major Axis Major Dir ( o T) Depth MODEL AVE. M M M OBS. AVE. M ε APPENDIX D. Tidal Harmonic Constants for Other Regional Currents 1. Tidal Analysis of the Winter Cashes Ledge Currents The 57-day analysis was on series between 0100 MT 20 November 1974 to 1700 MT 16 January The harmonic constants are amplitude H and phase in reenwich and local epochs. The tidal current ellipses are given in terms of major and minor axis amplitudes, orientation of the major axis, and reenwich phase of the maximum current; with positive minor axis means counterclockwise rotating current vector. The tidal harmonic constants are given for the indicated constituents in (a) for each current records; and (b) for a vertically-averaged current record. a. Cashes Ledge Currents: M 2 Tidal Harmonic Constants Eastward Northward Ellipse H Phase H Phase Maj Min Phase Orien (mm/s) (κ o ) (mm/s) (κ o ) (mm/s) (mm/s) ( o T) 33m m m

23 b. Cashes Ledge Three-Record Average Current: M 2, N 2, S 2, O 1, K 1 Eastward Northward Ellipse H Phase H Phase Maj Min Phase Orien (mm/s) (κ o ) (mm/s) (κ o ) (mm/s) (mm/s) ( o T) M(2) N(2) S(2) O(1) K(1) Tidal Analysis of the Spring 1997 Jeffreys Basin ADCP (4m) Currents The 21-day analysis was on series between 0000 MT 19 May to 1000 MT 9 June The harmonic constants are amplitude H and phase in reenwich and local epochs. The tidal current ellipses are given in terms of major and minor axis amplitudes, orientation of the major axis, and reenwich phase of the maximum current; with positive minor axis means counterclockwise rotating current vector. The tidal harmonic constants are given for the indicated constituents in (1) for each current records; and (2) for a vertically-averaged current record. a. Jeffreys Basin Currents: M 2 Tidal Harmonic Constants Eastward Northward Ellipse H Phase H Phase Maj Min Phase Orien (mm/s) (κ o ) (mm/s) (κ o ) (mm/s) (mm/s) ( o T) 50m m m m b. Jeffreys Basin 52m-124m Average Current: M 2, N 2, S 2, O 1, K 1 Eastward Northward Ellipse H Phase H Phase Maj Min Phase Orien (mm/s) (κ o ) (mm/s) (κ o ) (mm/s) (mm/s) ( o T) M(2) N(2) S(2) O(1) K(1) Tidal Analysis of the Winter 1991 Massachusetts Bay Currents The 57-day analysis was on series records between 0000 MT 8 February and 0000 MT 8 April The harmonic constants are amplitude H and phase in reenwich and local epochs. The tidal current ellipses are given in terms of major and minor axis amplitudes, orientation of the major axis, and reenwich phase of the maximum current; with positive minor axis means counterclockwise rotating current vector. The tidal harmonic constants are given for the indicated constituents in (1) for each current records; and (2) for a vertically-averaged current record. a1. Massachusetts Bay U2 Currents: M 2 Tidal Harmonic Constants U2 Eastward U2 Northward U2 Ellipse H Phase H Phase Maj Min Phase Orien (mm/s) (κ o ) (mm/s) (κ o ) (mm/s) (mm/s) ( o T) 25m m