Baroclinic and Barotropic Tides in the Weddell Sea - Lamont-Doherty ...

Baroclinic and Barotropic Tides in the Weddell Sea

Robin Robertson Lamont-Doherty Earth Observatory Columbia University Palisades, New York 10964 USA Office (845) 365- 8527 fax (845) 365- 8157 [email protected]

For submission to Antarctic Science July 15, 2004

Robertson: Baroclinic and Barotropic Tides in the Weddell Sea

Abstract Barotropic and baroclinic tides were simulated for the Weddell Sea using ROMS. The model estimates for both tidal elevations and velocities showed good agreement with existing observations. The rms differences were 9 cm for elevations and 1.2-1.7 cm s-1 for the semidiurnal constituents and 6-8 cm and 4.5 cm s-1 for diurnal constituents. Most of the discrepancies occurred deep under the ice shelf for the semidiurnal tides and along the continental slope for the diurnal tides. Along the continental slope, the model overestimated the generation of diurnal continental shelf waves. The diurnal tides were barotropic throughout the basin. However, internal tides were generated at semidiurnal frequencies over rough topography. Over the continental slope, semidiurnal baroclinic tidal generation was enhanced by the existence of continental shelf waves, through their harmonics. Baroclinic tides generated over rough topography in the northern Weddell Sea incited inertial oscillations as they propagated south. These inertial oscillations varied with depth since they were incited at different depths at different times as the internal tide progressed. Both the baroclinic tides and inertial oscillations induced vertical shear in the water column and increased the divergence of the horizontal surface velocities.

Key Words: Tides, Weddell Sea, Internal tides

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1. Introduction Much of the Antarctic Bottom Water (AABW) for the global ocean is formed in the Scotia Sea through the mixing of Weddell Sea Deep Water (WSDW) flowing out of the Weddell Sea (Figure1) with other waters (Deacon, 1937). WSDW is formed in the Weddell Sea primarily through mixing of Warm Deep Water (WDW) either with Ice Shelf Water (ISW), which flows out of the Ronne-Filchner Ice Cavity or with shelf waters. Two shelf waters, High Salinity Shelf Water (HSSW) and Low Salinity Shelf Water (LSSW), exist in the Weddell Sea and they are formed on the continental shelves surrounding Antarctica through brine rejection associated with ice formation in the coastal polynyas. Tides are a source of deep water mixing (Munk and Wunsch, 1998; Garrett, 2003) and are believed to be one of the sources of the mixing for WSDW formation. Tides influence mixing by increasing boundary layer shear and by induction of shear instabilities, which are associated with baroclinic tides. Tides also influence the circulation in the Weddell Sea through retardation of the mean flow due to their additional friction, induction of a residual tidal velocities, and generation of continental shelf waves (CSW). These effects, in turn, affect the sea ice cover through increased divergence and convergence of surface velocities and their influence on the sea ice affects the ocean-atmosphere heat flux. To evaluate the tidal effects, the tidal elevation and velocity fields must be known. Some tidal observations have been made in the Weddell Sea (Figure 2) and a comprehensive list is given in Robertson et al. (1998). However, the data are sparse and not well distributed within the basin, particularly the elevations (Figure 2a). More complete coverage for the tidal fields can be provided through modeling. Smithson et al. (1996) modeled the barotropic tides for the region under the FilchnerRonne Ice Shelf with reasonable agreement with observations. Elevation and barotropic velocities for the entire Weddell Sea were generated by the two-dimensional tidal model of Robertson, Padman, and Egbert for the four major constituents and the model estimates showed good agreement with observations (hereafter referred to as RPE) (Robertson et al., 1998). Further simulations with this model encompassed the circumpolar region, including both the Ross and Weddell Seas. (CATS-99; CATS-2000, Laurie Padman, unpublished). More recently, elevation information on portions of the Weddell Sea was provided

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by Padman et al. (2002) with their two-dimensional inverse model. However, no information on the vertical structure or the baroclinic tides was provided by these models. Baroclinic tidal information has been provided along a two-dimensional transect over the continental shelf (Robertson, 2001a and 2001b) and on an extremely coarse grid (Pereora et al., 2002), which had grid cells with widths in longitude ranging from 10-120 km. But the first model did not cover the entire Weddell Sea and the grid was too coarse in the longitude direction in the second model to resolve most of the baroclinic tides or continental shelf waves. The goal of this project was to provide a description of the three-dimensional structure of the barotropic and baroclinic tides for the entire Weddell Sea for the four major tidal constituents, M2 , S2 , K1 , and O1 . For this study, the Regional Ocean Modeling System (ROMS), described in Section 2, was used. In Section 3, the model results are discussed and compared with existing observations. A summary is given in Section 4. 2. Model Description The ROMS model in this application is fully described elsewhere (ROMS: Haidvogel et al., 1991; Song and Haidvogel, 1993, 1994; Shchepetkin and McWilliams, 2002) (this application: Robertson et al. 2003). ROMS had been modified previously to include the presence of a floating ice shelf (Robertson et al. 2003), including both mechanical and thermodynamic effects following Robertson (1999; 2001a) and Hellmer & Olbers (1989), respectively. Here only the pertinent details and recent modifications will be discussed. Recently, improvements have been made in the vertical mixing parameterization for primitive equation models. Different vertical mixing parameterizations available in ROMS were evaluated using a sensitivity study at a site with extensive hydrographic, velocity, and turbulence observations (Robertson 2004a). For vertical mixing, the Generic Length Scale (GLS) parameterization of Umlauf & Burchard (2003) was found to best replicate the observed velocities and vertical diffusivities and was used for these simulations. Tidal forcing was implemented by setting elevations along all the open boundaries, with the coefficients taken from a global, two-dimensional inverse model (TPXO6.2 Egbert and Erofeeva 2002). Four major tidal constituents were used, two semi-diurnals, M2 and S2 and two diurnals, K1 and O1 .

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The model domain (Figure 1) covered the Weddell Sea with a grid spacing of 0.045o in latitude, 0.186o in longitude, and 24 vertical levels. The ice thickness and water column thickness, defined as the distance between the bottom and the ice shelf base (or ocean surface), were taken from BEDMAP (Lythe et al. 2000). In the northern region beyond the extent of BEDMAP, the water column thickness was taken from Smith & Sandwell (1997). No smoothing was performed on either the water column or the ice shelf thicknesses. The minimum water column thickness was set to 30 m, which entailed artificially deepening a small portion of the region under the ice shelf, particularly near the eastern grounding line. The barotropic and baroclinic mode time steps were 6 s and 180 s, respectively, and the simulations were run for 30 days, with hourly data from the last 15 days saved for analysis. The kinetic and potential energies stabilized after around 15 days, thus the first 15 days of simulated data was discarded. Initial potential temperature, ?, and salinity, S, fields were assembled from the World Ocean Circulation Experiment (WOCE) Hydrographic Programme Special Analysis Center (Gouretski & Janke 1999), except under the ice shelf. Here, the hydrography was essentially a four layer system based on a ? and S profile through the ice shelf at a single location (90/2) (Robinson and Makinson, 1992), in a similar manner as was done for the Ross Sea (Robertson, 2004b). The model elevation and velocities were initialized with the geostrophic velocities associated with the initial hydrography as determined from a simulation without tidal forcing. Elevation, ? , and depth-independent velocities, U2 and V2 , are produced by the two-dimensional (barotropic) mode of the model and ?, S, and depth-dependent velocities, U3 , V3 , and W3 , by the threedimensional (baroclinic) mode. The depth-dependent velocities fully represent the velocity at each grid cell and do not have the depth-independent velocity removed. Foreman’s tidal analysis routines were used to analyze these fields (Foreman 1977; 1978). 3. Results 3.1 Elevations and Depth-Independent Velocities 3.1.1 Semidiurnal constituents (M2 and S2 )

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The semidiurnal tides propagated westwards around the Antarctic continent, splitting into two portions at the continental slope ~30o W, with one portion following the continental slope and the other following the Antarctic continent under the Ronne-Filchner Ice Shelves. Two amphidromic points were formed for the semidiurnal constituents, one at ~ 0o W and one at the edge of the Ronne Ice Shelf, ~ 56o W (Figure 3a and 3b). These results are consistent with those of a barotropic model (RPE) (Robertson et al., 1998). In order to evaluate the performance of the model, the elevation amplitudes and phases were compared to existing elevation observations for the region, for the twenty-four locations shown in Figure 2a and given in Tables 1 and 2. The observations and their sources are discussed in Robertson et al. (1998) and a good summary is given in Smithson et al. (1996). It should be noted that sites 1-3, 5, and 9 were collected on the ice shelf using a tiltmeters, which have been shown to have errors (Doake, 1992). Thirteen of the twenty-four estimates for the M2 constituent and thirteen of the twenty-two estimates for the S2 constituent fell within the observational uncertainties (Table 1). The model generally underestimated the tidal amplitudes along the continental slope and at a site under the western portion of the Ronne Ice Shelf (site 9) for both semidiurnal constituents. The model phase estimates fell outside the uncertainties at five sites for each semidiurnal constituent. Most of the phase discrepancies occur in the ice shelf cavity in the vicinity of the amphidromic point, where small errors in the location of the amphidromic point result in large phase errors. The performance was similar to that of RPE (Tables1-3). Rms errors for the M2 and S2 elevation amplitudes and phases were 11.9 cm and 47o and 9.5 cm and 44o , respectively (Table 3). These are slightly larger than those of RPE, 8.9 cm and 38o for M2 , and 7.1 cm and 45o for S2 , respectively. For both models, much of the rms error was associated with site 9. Site 9 had a short record length, 9 days, and the observation is suspect. When site 9 was excluded, the rms errors werer reduced to 8.5 and 8.6 cm for Roms and 8.7 and 7.6 cm for RPE (Table 3). The two models agreed well, particularly considering differences in the boundary forcing, topography and hydrography and the two-dimensional dynamics of RPE versus the three-dimensional dynamics of ROMS.

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The depth-independent velocities for the semidiurnal constituents are small, < 5 m s-1 , in the deep basin, increasing over the continental slope and under the ice shelves (Figures 4a and 4b). Major axes > 10 cm s-1 are reached under the Ronne-Filchner Ice Shelf for M2 and at the front of the Ronne-Filchner Ice Shelf for S2 and at the back of the Larsen Ice Shelf and between some of the islands along the southeastern coast for both (Figures 4a and 4b). Again the topography was the primary controlling factor for the depth-independent velocities, as has been previously noted for a two-dimensional tidal model (Robertson et al. 1998) and in the Ross Sea (Robertson, 2004b). A slight increase in the semidiurnal major axes occurs due to continental shelf waves (CSWs). This can be seen by the small regions of larger major axes, > 10 cm s-1 , along the continental slope in Figures 4a and 4b, which are present when four tidal constituents were used for forcing. These regions are not present or are diminished when forced by only the semidiurnal constituent M2 (Figure 4e). At the shelf break, the diurnal constituents excite CSWs along the continental slope where WDW and shelf waters meet. Since the semidiurnal constituent frequencies are at or near the first harmonic of the diurnal constituents, interactions between the CSW and variations in topography transfer energy from the diurnal tides to their first harmonic, which is interpreted as semidiurnal tides in the analysis. The mechanism for the transfer is probably parametric subharmonic instability, with the diurnal CSWs modulating the hydrography through the position of the front between the WDW and shelf waters at roughly twice the inertial frequency and the semidiurnal tides picking up the energy at near inertial frequencies, since along the continental slope in the southern Weddell Sea, the inertial frequency is near the semidiurnal tidal frequency. The influence of the CSWs on the semidiurnal depth-independent velocities was also noted in the Ross Sea (Robertson, 2004b). 3.1.2 Diurnal Constituents (K1 and O1 ) The diurnal tides also propagated as a Kelvin wave westwards through the basin, but they did not split like the semidiurnal constituents and amphidromic points are not formed (Figures 3c and 3d). Along the continental slope, Continental Shelf Waves (CSW) are formed by both diurnal constituents resulting in patches of higher and lower elevation amplitudes and changes in the phase (Figures 3c and 3d). The

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model estimates showed reasonable agreement with the observations (Tables 1 and 2) with rms differences of 8.4 cm and 50o for K1 and 5.6 cm and 33o for O1 when site 9 is excluded (Table 3). Most of the discrepancies occur along the continental slope where the CSW’s are generated. And again, the model performance was equivalent to that of RPE. CSWs are excited by interactions of currents with topographic irregularities (Huthnance 1978; Brink 1991). Excellent summaries of their properties are given by Huthnance (1978) and Brink (1991). They are coastally trapped waves with sub-inertial frequencies (Huthnance 1978; Brink 1991). In the Weddell Sea, CSWs are excited by the diurnal tides, but not the semi-diurnal tides. In the southern hemisphere, CSWs phase propagates westwards, while the group velocity (energy) propagates eastwards (Huthnance 1978; Middleton et al., 1982; Brink 1991). In weak stratification, they are essentially barotropic (Huthnance 1978). Increasing stratification will increase the wave speed (Huthnance 1989) and induce the frequency to increase. The CSWs decay primarily through friction (Brink 1991). Realistic topography was found to concentrate the motion over the upper slope and shelf (Huthnance 1978). In the presence of mean alongshore flow, the properties of CSW change due to a combination of Doppler shift, changes in the background vorticity, and the growth of instabilities (Brink 1991). The behavior of the mode one CSWs present in the model results is consistent with this theoretical behavior, phase propagating westward, and having a concentration of motion over the upper slope and shelf. They appear to be tide to specific topography. The major axes of the tidal ellipses for the diurnal constituents were less than 10 cm s-1 except for along the continental slope, along the Ronne Ice Shelf edge, and near the South Orkney Islands and the tip of the Antarctic Peninsula (Figures 4c and 4d). The larger velocities along the continental slope and the ice shelf edge are clearly associated with CSW. The amplified response at the other locations is likely to be local CSWs, as has been observed at locations such as Fieberling Guyot (Brink, 1991). 3.2 Depth-Dependent Response 3.2.1 Semidiurnal Constituents (M2 and S2 )

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Internal tides were generated over regions of steep topography, particularly along the continental shelf/slope break in the south and over the complex topography in the north. This is apparent by the vertical variation in the major axes for the depth-dependent velocities along longitude transects (indicated by IT in Figure 5). The locations of internal tide generation match those predicted by linear internal wave theory using Baines criteria (Baines, 1974) (not shown). As predicted by linear internal wave, significant generation of M2 tides occurred in two regions: over the continental slope and over the rough topography in the northern Weddell Sea. The continental slope in the southern Weddell Sea is near the M2 critical latitude, 74o 28.8’ S (Figure 1b and dashed line in Figure 5). At the critical latitude the inertial frequency equals the tidal frequency, which affects both the generation and propagation of internal tides. Linear internal wave theory predicts that internal waves will not be generated nor propagate poleward of the critical latitude (A more extensive explanation of the relevant linear internal wave theory is given in Robertson (2001a).) The internal tides had wavelengths (~60-80 km) and propagated along internal wave rays in accordance to linear theory with shallower slopes for the wave ray characteristics nearer to the critical latitude and steeper slopes more distant from it. An example of internal wave rays for the region is shown in Figure 6. Some amplification of semidiurnal internal tide generation occurred where CSWs were generated, which did not occur when the model was forced with M2 only (not shown). In the Weddell Sea, the continental slope is near the M2 critical latitude and is the location for CSW generation and propagation. The conditions for parametric sub-harmonic instability according to Hibiya et al. (2002) are also met here. The CSWs modulate the stratification, the position of the WDW and shelf waters and the front between them. There changes affect both internal tide generation and propagation and cause energy to be transferred from the diurnal frequencies, which are roughly twice the inertial frequency to the semidiurnal frequencies, which are roughly the inertial frequency, particularly M2 . The propagation for the two primary regions of baroclinic tidal generation was quite different. Baroclinic tides propagated along wave characteristics, an example of which is shown in Figure 6 for a mode one M2 internal wave originating at 60 57’ S and traveling south along a north-south transect at 40o

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W. Of course, the internal waves do not always propagate directly south, so Figure 6 shows just a subset of the propagation. However, it shows several key elements of baroclinic propagation according to linear internal wave theory. First, wave rays are more horizontal in the upper ocean where the density gradients are stronger and more vertical in the deeper ocean and the mixed layer where the density gradients are weaker. Near the critical latitude, the internal wave rays flatten out and become more horizontal. Also propagation for M2 stops at its critical latitude. The crosses are equally spaced with the bold crosses separated roughly by one tidal period. The group speed is smaller nearer to the critical latitude, as seen by the closeness of the crosses. Baroclinic tides generated along the continental slope in the southern region propagate primarily northward since they are prevented from propagating south by the critical latitude (Figures 5 and 6). With the slower group speed, internal tides generated in the south do not propagate as far as those generated in the north, with larger group speeds. When the continental slope is more than a degree north of critical latitude (Figure 5b), a portion of the baroclinic tide propagated south until it was turned by the critical latitude. In the northern region, the baroclinic tides propagated both north and south, but the northward propagating waves were either reflected by the high ridge or quickly left the domain (Figure 5). To evaluate the performance of the model, the model estimates were compared to 143 velocity observations from 68 mooring sites (Figure 2b) (Table 4). Most of this data is discussed fully in Robertson et al. (1998), although data from recent programs has been added: CORC/Arches (Visbeck, personal communication) and Ropex (Nicholls, personal communication). Generally, the model estimates were slightly higher than the observations, but within the observational uncertainties (Table 4 and Figure 7). The model reproduced much of the vertical structure of the observations for M2 as seen in comparisons of the model estimates (diamonds) and the observations (crosses) (Figure 7). Figure 7 includes most of the mooring sites with multiple measurements, with nearby multiple mooring sites often shown together. The good agreement between the model estimates and observations is reflected in the low rms differences for the major axes: 1.7 cm s-1and 1.2 cm s-1 for the M2 and S2 constituents, respectively.

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The rms difference reflects only the errors in the major axes. A more comprehensive measure is the absolute error, which combines errors in the amplitude with those in phase. The absolute errors (EA ) for each constituent were calculated for both positive (anticlockwise) and negative (clockwise) components

?

?

according to E A ? L? 1 ? L D , with D ? 0.5 A2o ? A2m ? Ao Am cos?? o ? ?

m

? , where L is the number of

observations and Ao and Am and ? o and ? m are the amplitudes and phases, respectively, with the subscripts of o and m representing the observatio ns and model results, respectively (Cummins and Oey 1997). The absolute error is determined for each component for each constituent. The absolute errors in the positive components for M2 and S2 were 1.2 and 0.9 cm s-1 respectively (Table 5). In the Southern Hemisphere, most of the baroclinic response for the boundary layers should be associated with the positive rotating component. The negative rotating component is associated with the barotropic response in the Southern Hemisphere. The absolute errors in the negative components for M2 and S2 were smaller, 1.0 and 0.7 cm s-1 , respectively (Table 5). The larger absolute errors for the positive rotating component indicate that more error is associated with the baroclinic response than the barotropic response. Most of the locations where the model exceeded the observational uncertainties (sites 2, 5, 7, 8, 10, and 53) were along the ice shelf edge (sites 2-5) or along the continental slope (sites 7-14) (Table 4). There are several sources for the differences between the model estimates and the observations, but the primary ones are topography and observational errors. Even more than elevations, the velocities are very sensitive to topography and errors in the topography will result in errors in the velocity estimates. Neither the water depth nor the ice shelf draft are well known, leading to errors in the topography and, in turn, the model estimates. The ice shelf is also assumed to float, which is true at its front. However, between the grounding line and the hinge line, the ice shelf does not float and the model does not include the proper dynamics for the grounded ice shelf. Additionally, the observed water depths at the observation locations were often different than that used by the model. Many of the velocity measurements were taken in the benthic boundary layer. If the model bathymetry for a location has a different water depth than that used by the model, the model estimate at the corresponding depth will not be at the corresponding location

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with respect to the bottom and the boundary layer resulting in a difference. For example the bottom values at site 7 is in the boundary layer for the model but not the observation (Figure 7) and the bottom values at sites 8 and 10 are in the boundary layer for the observation, but not the model (Table 4). Observational errors exist and differences occur between observations at nearby locations for example at site 28 the observations at the depths 2066 m and 2069 m differ by more than a factor of two (Table 4). The same occurs for repeat measurements, for example site 32 (Table 4). Additionally for the instruments located near the critical latitude, observations may be contaminated by inertial oscillations, which are impossible to separate from the semidiurnal frequencies at these latitudes, especially for short records. With the exception of the aforementioned mismatches, the model replicates the vertical structure of the internal tides reasonably well in the various regions of generation: along the front of the Ronne Ice Shelf (sites 2-4 in Figure 7), along the continental slope (sites 6-13 in Figure 7), along the eastern continental shelf (sites 19-21, 26-28, 30-31 in Figure 7), over Maud Rise (site 48 in Figure 7) and over the rough topography of the northern Weddell Sea (sites 52 and 61 in Figure 7). Under the ice shelf at sites 2 and 5, the model underestimated the velocity in the upper layer and overestimated the velocity in the lower layer. This is probably related to the simplified hydrography used under the ice shelf. Unfortunately, the observational data is too sparse and the coverage is too incomplete to provide a robust verification of the model. Baroclinic velocities are important to the divergence of the surface velocities, which induce lead formation in the pack ice. This has been observed by Geiger et al. (1998). The baroclinic velocities introduce additional divergence at the surface (Figure 4e) compared to the depth-independent velocities (Figure 4a). Since surface velocity divergence affects lead formation in this region, the internal tides will generate more lead formation than that due to the barotropic tide alone. 3.2.2 Diurnal Constituents (K1 and O1 ) The diurnal tides behaved barotropically, with only slight depth dependence (Figure 8). This is the expected behavior for this region, since it is far poleward of the diurnal critical latitudes (28o and 30o ) and internal tide generation is not expected at their frequencies. Most of the depth-dependence was a

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boundary layer response (Figure 8). The slight mid-water column depth-dependence, which does occur outside the benthic boundary layer, coincides with locations of semi-diurnal internal tides. The diurnal major axes were much larger than those of the semidiurnal constituents, reaching 50 cm s1

compared to 10 cm s-1 . The largest major axes and most greater than 10 cm s -1 were associated with

diurnal CSWs over the continental shelf break near 73-75o S (denoted by CSW in Figure 8). The performance of the model in replicating the observations for the diurnal constituents was also evaluated (Table 4 and Figure 9). Generally, the model estimates for the depth-dependent major axes fell within the observational uncertainty, except for sites 2, 3, 5-14, 19, 21, 22, and 64. Most of the disagreement sites occurred along the continental slope (sites 6-14, 19-30) (Table 4 and Figure 9) where the model overestimated the generation of CSWs (Table 4). Overestimation of CSWs also occurred in the Ross Sea (Robertson, 2004b) and with a barotropic tidal model of the Weddell Sea (Robertson et al., 1998). There was also disagreement at several sites along the ice shelf front (sites 2, 3, and 5) where the model underestimated the velocities. A similar situation occurred for the diurnal tides in the Ross Sea (Robertson, 2004b). Rms differences between the model estimates and observations were 4.5 cm s-1 for K1 and O1 (Table 5). Absolute errors in the positive rotating component were 1.8 and 1.6 cm s-1 for K1 and O1 , respectively and ~0.9 cm s-1 for the negative rotating component for both diurnal constituents (Table 5). 3.3 Combined Tidal Response So far, the discussion has focused on the model performance and the individual constituents. Most of the tidal response by the pack ice, sediments, mixin g, etc. is to the combined elevation and/or velocities. To evaluate the combined tidal response, standard deviations were calculated for the surface elevations and both depth-independent and depth-dependent velocities. Standard deviations for the elevations exceeding 50 cm occurred under most of the ice shelves, including those west of 16o W (Figure 10a). Standard deviations greater than 50 cm also occurred over a region along the continental slope at ~52o W as a result of CSWs (Figure 10a). At the back of the Filchner-Ronne Ice Shelf, standard deviations were typically 1.0 m and reached 2.0 m at some locations near the grounding line (Figure 10a). Since the

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model assumes the ice shelf is floating, and in actuality the ice shelf is grounded at the continental edge and does not move, these high standard deviations are likely to be overestimates. High standard deviations, > 10 cm s-1 , in the depth-dependent surface velocities occurred along the continental slope where CSWs were generated, along the Ronne Ice Shelf edge, under the Filchner Ice Shelf, and northwest of the Antarctic Peninsula in an area of rapidly changing topography (Figure 10b). The high standard deviations along the continental slope and ice shelf edge result from CSW. The rough topography north of the Antarctic Peninsula generates internal tides in that region. In the depth-dependent velocity transects (Figure 11), the standard deviations of the velocity anomalies, defined as the difference between the depth-dependent and depth-independent velocities, were also high at the surface for these locations. But in addition, high standard deviations occurred within the water column coinciding with steep topography and the generation of internal tides. There are three prominent locations of mid-water column high standard deviations: along front of the ice shelves, along the continental slope, and south of the rough topography in the northern Weddell Sea. As seen in Figure 5, baroclinic tides are generated in these three regions. However, spectral analysis showed that much of the energy for the high standard deviations North of 70o S did not occur at a tidal frequency, but at or near the inertial frequency. Baroclinic tides propagating south along the internal wave ray characteristics (a typical example is shown in Figure 6) induced inertial oscillations as they propagated. These inertial oscillations had a depth dependency since they were induced at different depths at different times during propagation. In the pycnocline, stronger inertial oscillations were induced. Unfortunately, observations are insufficient to verify the existence and strength of these inertial oscillations. Vertical shears of the horizontal velocities are important since they have the potential to induce mixing in the water column in certain stratification conditions through the development of shear instabilities. The primary sources of vertical shear in the horizontal velocities were depth-varying inertial oscillations, boundary layers, and mid-water column baroclinic tides (Figure 12). Both the benthic boundary layer and the surface boundary layer under the ice are apparent in the shear estimates (Figure 12). Additionally, high mid-water column vertical shears coincide with the locations of internal tides

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(Figure 12) and the depth-varying inertial oscillations (Figure 11). Mid-water column vertical shears exceeding 1x10 -3 s-1 occurred along the continental slope where the CSW enhanced internal tide generation and under the ice (Figure 12). Estimates of the Richardson number by the model indicated an unstable water column in some of these regions (not shown). 4. Summary Simulations of the barotropic and baroclinic tides in the Weddell Sea basin and the cavity under the Filchner-Ronne and Larsen Ice Shelves were performed with combined forcing of four tidal constituents, M2 , S2 , K1 , and O1 , using ROMS. Comparison of the model results with tidal estimates showed good agreement for elevations for all constituents and for velocity estimates for the semidiurnal constituents, M2 and S2 . The agreements for velocity for the diurnal constituents, K1 and O1 , were not as good, particularly along the continental slope, where the model overestimated the tidal response in the form of continental shelf waves. The diurnal tides were essentially barotropic with vertical differences in their response associated with the benthic and surface boundary layers. The baroclinic response occurred at the semidiurnal frequencies. Semidiurnal baroclinic tides were generated along the continental shelf break and over regions of steep topography. The baroclinic tidal behavior was consistent with that for internal waves in a continuously stratified fluid and propagating along wave rays with wavelengths corresponding to the theoretical estimates for mode one internal waves. The semidiurnal baroclinic tides were significantly amplified by the diurnal continental shelf waves where they were present. The semidiurnal tides were found to induce inertial oscillations in the northern Weddell Sea. These inertial oscillations varied with depth, since they were incited at progressively later times at different depths as they propagated through the water column. Although the agreement between the model estimates and observations is good, the sparseness of the data set is insufficient to provide a definitive verification that the model is replicating the conditions in the Weddell Sea. Nevertheless, there is room for improvement in the model predictions. The model estimates will improve as knowledge of topography and bathymetry improves. The German ISPOL

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project is obtaining hydrographic and bathymetric data for the seldom visited western Weddell Sea and the velocity data will be available for tidal analysis (H. Hellmer, personal communication). Data from this sources will be incorporated into the initial conditions for the model in future efforts. Also, the problem of the overexcitation of diurnal continental shelf waves needs to be addressed. The overexcitation may be linked to the lack of alongshore mean currents in the model. Two improvements to the model that are presently in-progress are 1) addition of the wind-induced mean circulation and 2) coupling to the dynamic sea ice model of Tremblay & Mysak (1997). These improvements, along with improved hydrography, may alleviate the excessive continental shelf wave excitation. Inclusion of more of the forcing factors and dynamics will improve the model estimations. Furthermore, it is planned to delve into what the effects of tides are on the surface pack ice, heat transfer to the atmosphere, and mixing in future efforts. Acknowledgements: This study was funded by (Office of Polar Programs) OPP grant OPP-00-3425 of the National Science Foundation (NSF). This is Lamont publication ????. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

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References BAINES, P. G., 1974, The generation of internal tides over steep continental shelves, Philisophical Transactions of the Royal Society, London, 277, 27-58. BRINK , K. H., 1991, Coastal-trapped waves and wind-driven currents over the continental shelf, Annual Review of Fluid Mechanics, 23, 389-412. CUMMINS, P. F., L.-Y-. O EY , 1997, Simulation of barotropic and baroclinic tides off northern British Columbia, Journal of Physical Oceanography, 27, 762-781. DEACON , G. E. R., 1937. The hydrology of the Southern Ocean, Discovery Reports, 15, 1-124. DOAKE, C. S. M., 1992, Gravimetric tidal measurements on Filchner Ronne Ice Shelf, Filchner Ronne Ice Shelf Programme Report No. 6, 34-39. EGBERT, G. D., and S. Y. EROFEEVA , 2002, Efficient inverse modeling of barotropic ocean tides, Journal of Atmospheric and Oceanic Technology, 19, 22,475-22,502. EROFEEVA , S. Y., G. D. EGBERT, and L. P ADMAN , 2004, Assimilation of ship mounted ADCP data for barotropic tides in the Ross Sea, under review for Journal of Atmospheric and Oceanic Technology. FOREMAN, M. G. G., 1977, Manual for tidal height analysis and prediction, Pacific Marine Science Report No. 77-10, Institute of Ocean Sciences, Patricia Bay, Sidney, B.C., 58 pp. FOREMAN, M. G. G., 1978, Manual for tidal current analysis and prediction, Pacific Marine Science Report No. 78-6, Institute of Ocean Sciences, Patricia Bay, Sidney, B.C., 70 pp. GARRETT, C. 2003, Internal tides and ocean mixing, Science, 301, 1858-1859. GEIGER, C. A., S. F. ACKLEY, W. D. HIBLER III, 1998, Sea ice drift and deformation processes in the western Weddell Sea, Antarctic Sea Ice: Physical processes, interactions and variability, Antarctic Research Series, 74, 141-160. GOURETSKI , V. V., and K. JANCKE, 1999, A description and quality assessment of the historical hydrographic data for the South Pacific Ocean. Journal of Atmospheric and Oceanic Technology, 16, 1791-1815. HAIDVOGE L, D. B., J. L. WILKIN , and Y. YOUNG , 1991, A semispectral primitive equation circulation model using vertical sigma and orthogonal curvilinear horizontal coordinates, J. Comp. Phys., 94, 151-185. 17


HELLME R, H. H., and D. J. OLBERS, 1989, A two-dimensional model for the thermohaline circulation under an ice shelf, Antarctic Science, 4, 325-326. HIBIYA, T., M. NAGASAWA , and Y. NIWA, 2002, Nonlinear energy transfer within the oceanic internal wave spectrum at mid and high latitudes, Journal of Geophysical Research, 107, doi:10.1029/2001JC00120. HUTHNANCE , J. M, 1989, Internal tides and waves near the continental shelf edge, Geophsyical and Astrophysical. Fluid Dynamics, 48, 81-106. HUTHNANCE , J. M, 1978, On coastal trapped waves: Analysis and numerical calculation by inverse iteration, Journal of Physical Oceanography, 8, 74-92. LYTHE , M.B., VAUGHAN , D.G. and the BEDMAP CONSORTIUM , 2000, BEDMAP - bed topography of the Antarctic. 1:10,000,000 scale map. BAS (Misc) 9. Cambridge, British Antarctic Survey. MIDDLETON , J. H, T D. FOSTER, and A. FOLDVIK, 1982, Low-Frequency currents and continental shelf waves in the southern Weddell Sea, Journal of Physical Oceanography, 12, 618-634. MUNK , W. and C. W UNSCH , 1998, The moon and mixing: Abyssal recipies II, Deep-Sea Research, 45, 19772010. PADMAN , L, H. A. FRICKER, R. COLEMAN, S. HOWARD , and L. EROFEEVA , 2002, A new tide model for the Antarctic ice shelves and seas, Annals of Glaciology, 34, 247-254. PEREORA , A. F., A. BECKMANN , and H. H. H ELLMER, 2002, Tidal mixing in the southern Weddell Sea: Results from a three-dimensional model, Journal of Physical Oceanography, 32, 2151-2170. ROBERTSON, R, 2004a, Baroclinic tides at Fieberling Guyot: Evaluating the Ability to Simulate Velocities, in preparation for Journal of Atmospheric and Oceanic Technology . ROBERTSON, R., 2004b, Barotropic and baroclinic tides in the Ross Sea, accepted for Antarctic Science. ROBERTSON, R., 2001a, Internal tides and baroclinicity in the southern Weddell Sea: Part I: Model description, and comparison of model results to observations, Journal of Geophysical Research, 106, 27001-27016.

18


ROBERTSON, R., 2001b, Internal tides and baroclinicity in the southern Weddell Sea: Part II: Effects of the critical latitude and stratification, Journal of Geophysical. Research, 106, 27017-27034. ROBERTSON, R.. A. B ECKMANN , and H. HELLMER., 2003, M2 tidal dynamics in the Ross Sea, Antarctic Science, 15, 41-46. ROBERTSON, R., L. PADMAN , and G. D. EGBERT, 1998, Tides in the Weddell Sea, in Ocean, Ice, and Atmosphere: Interactions at the Antarctic Continental Margin , Antarctic Research Series, 75, 341369. ROBINSON , A. V., and K. MAKINSON , 1992, Prelimianry results from hot water drilling and oceanographic measurements under Ronne Ice Shelf, Filchner Ronne Ice Shelf Programme Report No. 6, 340-46. SHCHEPETKIN, A., F., J. C., MCWILLIAMS , 2002, A method for computing horizontal pressure gradient force in an ocean model with non-aligned vertical coordinate, accepted for Journal of Geophysical. Research. SMITH , W. H. F., and D. T. SANDWELL , 1997, Global seafloor topography from satellite altimetry and ship depth soundings, Science, 277, 1956-1962. SMITHSON, M. J., A. V., ROBINSON , an R. A FLATHER, 1996, Ocean tides under the Filchner-Ronne Ice Shelf, Antarctica, Annals of Glaciaology, 23, 217-225. SONG , Y. and D. B. HAIDVOGEL, 1993, Numerical simulations of CCS under the joint effect of coastal geometry and surface forcing, in Estuarine and Coastal Modeling, 3rd International Conference, ASCE, Chicago, ed. M. L. Spaulding et al., 216-243. SONG , Y. and D. B. HAIDVOGEL, 1994, A semi-implicit ocean circulation model using a generalized topography-following coordinate, Journal of Computational Physics, 115, 228-244. TREMBLAY , L.-B. and L. A. MYSAK , 1997, Modeling sea ice as a granular material, including the dilatancy effect, Journal of Physical Oceanography, 27, 2342-2360. UMLAUF, L., and H. BURCHARD , 2003, A generic length-scale equation for geophysical turbulence, Journal of Marine Research, 61, 235-265.

19


List of Figures

Figure 1. a) The location of the model domain with respect to Antarctica. b) The model domain with the water column thickness contoured at 100, 500, 1000, 2000, 3000, and 5000 m. The Filchner-Ronne and Larsen Ice Shelf edges are indicated by dashed lines in b.

Figure 2. The locations of tidal elevation observations are indicated by numbers in a) and those of velocity observations by numbers in b). The 1000 m isobath is shown.

Figure 3. The amplitude of the tidal elevation for the a) M2,, b) S2 , c) K1 , and d) O1 constituents in cm. The overlaid heavy dashed lines indicate the phase for the elevation, with the zero phase line indicated in a) and b).

Figure 4. The major axes of the tidal ellipses for the depth-independent velocities for the M2,, b) S2 , c) K1 , d) O1 constituents, in cm s-1 . e) The same for M2 with only M2 forcing and f) for M2 from the depthdependent surface velocities.

Figure 5. The major axes of the M2 tidal ellipses from the depth-dependent velocities along N-S transects at a) 60o W, b) 50o W, c) 40o W, d) 30o W, and e) 0o W. IT indicates locations of internal tidal generation. The location of the critical latitude is indicated by a dashed line.

Figure 6. Internal wave ray characteristics starting from 60 57’ S and propagating south for the hydrography and topography used in the model along 40o W according to linear internal wave theory without dissipation. The bold crosses are separated by one M2 tidal period.

20


Figure 7. Major axes of the M2 tidal ellipses from ROMS (crosses) compared against observational data (diamonds). The error bars indicate the observational uncertainty (1.7 cm s-1 ). The top row shows locations near the ice shelf edge. The second row shows locations along the eastern end of the transect across the Weddell Sea and the third and bottom rows for the deep, middle section and the western end, respectively.

Figure 8. The major axes of the K1 tidal ellipses from the depth-dependent velocities along N-S transects at a) 60o W, b) 50o W, c) 40o W, d) 30o W, and e) 0o W, in cm s-1 . CSW indicates continental shelf waves.

Figure 9. Major axes of the K 1 tidal ellipses from ROMS (crosses) compared against observational data (diamonds). The error bars indicate the observational uncertainty (1.7 cm s-1 ). The top row shows locations near the ice shelf edge. The second row shows locations along the eastern end of the transect across the Weddell Sea and the third and bottom rows for the deep, middle section and the weste rn end, respectively.

Figure 10. The a) standard deviation of the elevations (cm) and the b) combined standard deviations of the depth-dependent surface velocities (cm s-1 ).

Figure 11. The combined standard deviations in the depth-dependent velocity anomalies (difference between the depth-dependent and depth-independent velocities) over 15 days at a) 60o W, b) 50o W, c) 40o W, d) 30o W, and e) 0o W. The M2 critical latitude is indicated by a dashed white line.

Figure 12. Vertical shear in the depth-dependent velocities along N-S transects at a) 60o W, b) 50o W, c) 40o W, d) 30o W, and e) 0o W. The M2 critical latitude is indicated by a dashed white line.

21


List of Tables

Table 1. Elevation amplitudes from ROMS compared against observational data and a two-dimensional model (RPE) (Robertson et al., 1998). Underlined values exceed the observational uncertainties, ~ 2 cm (Robertson et al., 1998)

Table 2. Elevation phases from ROMS compared against observational data and a two-dimensional model (RPE) (Robertson et al., 1998). Underlined values exceed the observational uncertainties, ~ 2 cm (Robertson et al., 1998)

Table 3. Rms differences between the model estimates and observations for the elevation amplitude and phases for each constituent for the ROMS simulation and for the two-dimensional simulation of RPE (Robertson et al., 1998).

Table 4. Major axes of the tidal ellipses from the depth-dependent velocities at the observation locations for each constituent for ROMS along with the observed value and observational uncertainty.

Table 5. Rms differences for the major axes of the tidal ellipses and absolute errors for the positive and negative rotating components from the depth-dependent velocities at the observation locations for each constituent from ROMS.

22


Site

Latitude

Longitude

1

79o 44’ S 78o 37’S 78o 33’ S 77o 58’ S 77o 53’ S 77o 43’ S 77o 8’ S 77o 7’ S 76o 45’ S 74o 26’ S 74o 23’ S 72o 53’ S 71o 3’ S 70o 37’ S 70o 30’ S 70o 26’ S 70o 13’ S 63o 17’ S 62o 8’ S 61o 28’ S 60o 51’ S 60o 43’ S 60o 3’ S 60o 2’ S

67o 21’ W 55o 8’ W 82o 58’ W 37o 10’ W 52o 45’ W 41o 8’ W 50o 30’ W 49o 3’ W 64o 30’ W 39o 24’ W 37o 39’ W 19o 37’ W 11o 45’ W 8o 32’ W 2o 32’ W 8o 18’ W 2o 44’ W 56o 55’ W 60o 41’ W 61o 17’ W 54o 43’ W 44o 39’ W 47o 5’ W 47o 6’ W

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

M2 (cm)

S2 (cm)

K1 (cm)

O1 (cm)

Obs. 137? 12

RPE 141

ROMS 126

Obs. 81? 12

RPE 86

ROMS 87

Obs. 32? 12

RPE 37

ROMS 30

Obs. 34? 12

RPE 35

ROMS 30

35? 10

59

45

25? 10

34

29

15? 10

27

25

14? 10

27

24

165? 10

161

180

104? 10

100

126

50? 10

41

31

45? 10

39

35

62? 10

73

66

41? 10

48

50

38? 10

30

24

26? 10

30

26

23? 10

37

30

8? 10

20

19

16? 10

26

22

17? 10

25

23

44? 2

57

58

23? 4

38

44

41? 4

27

23

22? 8

27

25

27? 4

48

28

16? 4

34

22

20? 4

40

26

22? 4

43

27

49? 3

39

34

29? 2

26

27

29? 2

28

25

29? 2

27

26

93? 4

80

52

54? 4

48

34

41? 4

32

25

51? 4

32

26

53? 1

51

47

38? 1

36

35

32? 1

29

30

32? 1

30

20

58? 4

53

48

39? 4

37

37

36? 4

25

20

30? 4

31

28

57? 4

55

45

39? 4

38

34

29? 4

29

23

31? 4

28

25

47? 4

46

37

33? 4

32

29

27? 4

27

22

29? 5

26

25

39? 5

42

34

35? 5

29

27

25? 5

27

23

27? 5

26

25

33? 5

37

31

23? 5

27

25

25? 5

25

23

31? 5

25

26

41? 4

40

33

30? 4

28

26

27? 4

26

22

29? 4

26

24

35? 7

36

29

38? 7

26

24

36? 7

25

22

27? 7

25

24

63? 5

59

48

-

37

30

-

32

26

-

28

28

32? 3

30

32

17? 3

17

15

25? 3

23

21

24? 3

21

20

33? 3

30

33

15? 3

15

13

23? 3

21

19

22? 3

20

18

44? 4

43

43

22? 4

22

22

20? 4

18

17

20? 4

19

19

46? 5

41

40

-

22

22

-

15

14

-

18

18

42? 3

41

42

21? 3

21

21

15? 3

13

14

19? 3

16

17

42? 3

41

42

22? 3

21

21

15? 3

14

14

19? 3

17

17

Table 2. Elevation amplitudes from ROMS compared against observational data and a two-dimensional model (RPE) (Robertson et al., 1998). Underlined values exceed the observational uncertainties, ~ 2 cm (Robertson et al., 1998)

23


Site

Latitude

Longitude

1

79o 44’ S 78o 37’ S 78o 33’ S 77o 58’ S 77o 53’ S 77o 43’ S 77o 8’ S 77o 7’ S 76o 45’ S 74o 26’ S 74o 23’ S 72o 53’ S 71o 3’ S 70o 37’ S 70o 30’ S 70o 26’ S 70o 13’ S 63o 17’ S 62o 8’ S 61o 28’ S 60o 51’ S 60o 43’ S 60o 3’ S 60o 2’ S

67o 21’ W 55o 8’ W 82o 58’ W 37o 10’ W 52o 45’ W 41o 8’ W 50o 30’ W 49o 3’ W 64o 30’ W 39o 24’ W 37o 39’ W 19o 37’ W 11o 45’ W 8o 32’ W 2o 32’ W 8o 18’ W 2o 44’ W 56o 55’ W 60o 41’ W 61o 17’ W 54o 43’ W 44o 39’ W 47o 5’ W 47o 6’ W

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

M2 (cm)

S2 (cm)

K1 (cm)

O1 (cm)

Obs. 61? 25

RPE 55

ROMS 62

Obs. 89? 25

RPE 84

ROMS 90

Obs. 72? 5

RPE 49

ROMS 55

Obs. 58? 5

RPE 47

ROMS 47

159? 25

35

20

182? 25

62

42

215? 5

45

42

127? 5

43

33

72? 25

71

115

98? 25

100

150

55? 5

56

78

63? 5

53

59

275? 25

281

265

-

302

286

-

13

13

-

11

8

144? 25

15

348

245? 25

38

4

16? 5

45

40

17? 5

43

31

286? 25

280

269

320? 25

301

289

-

16

18

23? 5

15

11

224? 25

229

298

291? 25

258

312

264? 5

49

30

132? 5

40

21

280? 25

303

289

295? 25

320

307

23? 5

16

28

23? 5

16

19

92? 25

102

112

161? 25

133

143

147? 5

68

70

36? 5

64

61

233? 25

248

236

264? 25

271

268

6? 5

2

355

7? 5

7

16

242? 25

248

244

262? 25

271

267

17? 5

12

348

6? 5

7

24

220? 25

220

223

242? 25

244

228

5? 5

3

357

359? 5

358

353

201? 25

207

208

223? 25

230

217

358? 5

357

352

352? 5

354

349

163? 25

196

197

201? 25

219

201

2? 5

351

345

336? 5

348

343

169? 25

178

180

194? 25

202

201

345? 5

347

345

331? 5

345

343

189? 25

196

197

211? 25

219

217

352? 5

352

352

347? 5

349

349

174? 25

178

180

169? 25

202

201

359? 5

347

345

343? 5

345

343

276? 25

285

276

-

326

-

47

-

40

280? 25

290

275

351? 25

1

350

72? 5

71

68

54? 5

55

54

268? 25

283

270

342? 25

357

345

72? 5

73

70

51? 5

55

52

277? 25

281

273

323? 25

327

319

66? 5

62

65

49? 5

53

49

261? 25

270

268

-

301

298

-

64

70

-

49

53

268? 25

271

268

299? 25

302

299

67? 5

66

64

50? 5

50

50

268? 25

271

268

299? 25

303

299

67? 5

66

65

51? 5

50

50

Table 2. Elevation phases from ROMS compared against observational data and a two-dimensional model (RPE) (Robertson et al., 1998). Underlined values exceed the observational uncertainties, ~ 2 cm (Robertson et al., 1998)

24


All Sites

Excluding Site 9

M2 Amplitude Phase (cm) (o ) ROMS 11.9 47 RPE 8.9 38 (1998) ROMS 8.5 48 RPE 8.7 39 (1998)

Constituent S2 K1 O1 Amplitude Phase Amplitude Phase Amplitude Phase (cm) (o ) (cm) (o ) (cm) (o ) 9.5 44 8.5 57 7.7 33 7.1 45 8.0 58 7.4 29 8.6 7.2

44 46

8.4 8.0

50 52

5.6 5.7

33 29

Table 3. Rms differences between the model estimates and observations for the elevation amplitude and phases for each constituent for the ROMS simulation and for the two-dimensional simulation of RPE (Robertson et al., 1998).

25


M2 Latitude

Longitude

Mooring

78o 52.0’ S 77o 15’ S 77o 1.8’ S 77o 0’ S 76o 29’ S 75o 1.8’ S

71o 20.3’ W 48o 20’ W 49o 55.2’ W 49o 1.2’ W 53o 0’ W 33o 33’ W

75o 1.2’ S

S2

K1

O1

1

Water Depth (m) 485

Instr. Depth (m) 400

Meas. (cm s1 ) 7.6

ROMS (cm s1 ) 9.3

Meas. (cm s1 ) 6.1

ROMS (cm s1 ) 5.8

Meas. (cm s1 ) 1.3

ROMS (cm s1 ) 1.9

Meas. (cm s1 ) 1.3

ROMS (cm s1 ) 1.9

2

-

3

-

4

-

100 224 25 75 263

28.8 13.6 14.4 14.9 11.9

15.5 17.2 12.9 13.3 10.3

7.0

10.6 10.3 9.0 9.1 8.6

6.7 6.7 4.3

3.1 3.1 3.9 3.9 3.5

3.6

2.3 2.3 3.2 3.2 3.0

5

431

6

574

31o 46.2’ W

7

610

74o 40’ S 74o 26’ S 74o 24’ S 74o 23’ S 74o 8’ S 78o 6’ S 73o 43’ S 73o 37.6’ S

33o 56’ W 39o 24’ W 39o 6’ W 39o 39’ W 39o 19’ W 39o 22’ W 38o 36’ W 26o 7’ W

8

475

9

475

10

465

11

475

258 411 191 342 445 554 257 378 484 590 375 450 375 450 400 450 450

19.4 13.4 7.1 6.3 5.5 3.3 5.7 6.3 6.4 5.3 6.8 4.5 6.8 3.4 5.0 2.6 2.2

12.3 19.0 7.2 7.9 6.7 2.3 8.3 8.1 6.5 2.0 7.2 6.6 5.2 4.4 6.4 5.2 3.4

11.4 8.2 3.9 3.8 3.5 2.8 3.6 3.8 3.8 3.8 4.0 3.1 4.5 3.7 3.9 2.5 1.7

14.0 7.4 4.6 6.2 6.3 4.3 5.6 7.1 8.1 2.7 4.4 4.7 4.4 3.4 5.4 5.6 2.5

9.2 9.3 3.6 3.2 3.2 2.9 2.5 2.7 2.7 2.7 5.1 5.7 10.2 10.1 11.0 10.3 15.4

3.2 3.1 13.9 13.9 14.8 12.7 16.0 16.0 16.0 13.9 24.8 24.9 24.6 24.6 23.7 23.7 15.0

8.3 8.3 2.1 1.9 1.8 1.6 1.2 1.2 1.4 1.2 2.1 2.3 2.1 2.2 2.8 2.7 8.4

2.9 2.8 8.2 8.3 8.3 7.3 6.9 7.0 6.8 6.0 18.9 18.9 21.3 22.3 21.1 21.2 13.9

12

650

627

3.0

3.9

2.4

2.0

10.1

14.9

3.0

12.5

13

720

720

2.9

3.6

2.6

1.8

10.9

13.8

3.4

12.7

14

1915

15

3360

72o 52.8’ S 71o 7.7’ S 71o 5.8’ S

19o 37.5’ W 12o 11.9’ W 20o 47.1’ W

16

415

17

682

1815 1890 3197 3300 3350 280 380 255

1.3 0.8 1.2 0.7 0.8 2.7 2.1 3.4

2.3 2.3 2.4 2.4 2.4 2.5 2.8 3.2

1.1 1.0 0.9 0.6 0.7 1.5 1.2 2.3

0.7 0.7 1.9 1.9 1.9 2.5 2.3 2.7

3.7 3.8 0.2 0.2 0.2 0.4 0.4 1.6

4.8 4.8 1.0 1.0 1.0 0.6 0.6 1.1

1.2 1.0 0.3 0.2 0.2 0.5 0.5 2.1

3.7 3.7 1.0 1.0 1.0 0.9 0.8 1.3

18

4440

4277

1.1

1.9

0.8

1.8

0.6

0.9

0.6

1.0

71o 3.3’ S 71o 3.0’ S 71o 2.7’ S 71o 2.4’ S 70o 59.2’ S 70o 56.4’ S

11o 44.1’ W 11o 46.0’ W 11o 45.4’ W 11o 44.6’ W 11o 49.4’ W 11o 57.7’ W

19

380

20

467

4430 210 320 462

0.6 4.1 4.0 1.9

1.9 4.0 4.0 3.4

0.4 2.4 2.2 1.4

1.8 2.6 2.6 2.8

0.4 5.2 6.0 2.3

0.9 1.4 1.3 1.4

0.4 7.1 9.1 3.5

1.0 1.8 1.9 1.8

21

425

22

676

23

2364

24

1522

325 425 293 671 309 999 706 1517

3.8 2.4 3.6 1.5 1.6 0.8 3.1 1.4

3.9 3.5 3.9 2.2 3.6 2.8 2.3 3.3

3.7 1.6 2.4 1.4 1.0 0.7 1.8 1.4

2.7 2.8 2.7 2.8 2.6 2.4 2.1 2.3

5.7 3.1 3.2 1.3 0.8 0.5 1.1 1.1

1.3 1.4 1.4 1.5 1.4 1.3 1.3 1.4

8.5 4.4 5.0 2.2 1.0 0.7 1.2 1.0

1.8 1.9 1.8 1.9 1.7 1.8 1.6 1.6

26


70o 54.7’ S 70o 42.6’ S

11o 57.8’ W 12o 21.5’ W

25

1555

26

2123

70o 29.7’ S 70o 29.5’ S

13o 8.9’ W 13o 7.0’ W

27

2450

28

2364

70o 26.0’ S 70o 22.8’ S

8o 18.0’ W 13o 32.5’ W

29

468

30

2950

70o 19.1’ S

13o 39.6’ W

31

4330

69o 39.6’ S

15o 42.9’ W

32

4728

250 760 335 805 1550 2090 340 1090 856 2066 2069 2313 280 380 190 940 2850 270 1130 2360 4280 270

33

69o 24.9’ S 69o 19.0’ S 69o 6.8’ S 68o 49.7’ S 68o 27.7’ S 67o 50.2’ S 67o 40.1’ S 67o 37.7’ S 67o 3.6’ S 66o 59.4’ S 66o 59.2’ S 66o 48.7’ S 66o 48.5’ S 66o 37.4’ S

52o 10.3’ W 53o 37.8’ W 55o 46.1’ W 17o 54.5’ W 53o 8.9’ W 53o 18.4’ W 54o 43.0’ W 55o 18.8’ W 24o 52.1’ W 53o 11.4’ W 4o 59.4’ W 54o 26.9’ W 55o 1.0’ W 27o 7.1’ W

4.6 2.6 4.9 2.0 2.1 1.9 2.9 2.9 2.5 2.4 2.4 2.9 4.8 4.3 2.2 2.8 2.8 2.2 3.2 2.6 2.3 3.2

-

289 988 1010 2547 4617 200

1.6 2.0 3.0 3.1 2.8 1.9 2.3 2.3 2.8 1.3 2.7 1.4 3.0 2.9 2.2 2.6 1.8 2.2 2.2 2.5 1.9 1.5, 1.4, 1.1 1.8 1.8 1.8 0.9 1.2 1.9

2.2 2.1 2.5 1.6 1.7 1.7 1.9 2.3 2.1 2.3 2.3 2.4 3.2 3.1 2.0 1.7 2.3 2.2 1.8 1.5 2.0 1.7

3.2 2.7 2.7 1.5 2.7 1.5

1.0 1.3 1.9 1.8 1.8 1.3 1.8 1.5 2.3 0.6 2.1 0.8 2.0 1.9 1.9 1.8 1.1 1.1 1.4 1.8 1.3 1.1, 0.9, 0.8 1.3 1.3 1.2 0.7 0.7 3.9

1.4 1.4 1.3 1.2 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.9 1.8 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.1

1.8 1.8 1.8 1.6 1.4 1.3

1.1 1.0 1.5 1.2 1.2 1.1 1.2 1.1 1.4 0.5 1.3 0.6 1.2 1.4 1.2 1.2 0.9 1.1 1.3 1.4 1.1 0.9, 0.7, 0.5 1.0 0.8 1.0 0.6 0.6 2.5

1.5 1.5 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 2.2 2.2 1.3 1.3 1.4 1.3 1.3 1.3 1.3 1.1

1.1 1.1 1.1 1.0 1.0 1.1

1.0 1.0 1.5 1.2 1.3 1.3 1.2 1.0 1.4 0.6 1.3 0.6 1.2 1.3 1.2 1.1 1.0 1.2 1.3 1.5 0.9 0.9, 0.8, 0.6 1.1 0.9 1.0 0.6 0.6 1.0

34

2700

200

2.3

1.6

1.4

1.2

1.7

0.9

1.4

0.7

35

-

50

3.8

3.5

3.9

1.6

2.9

1.4

2.7

1.8

36

4740 2900

4240 4690 200

1.3 3.0 2.1

1.8 2.0 2.0

1.0 1.9 1.6

1.6 1.4 1.2

0.7 1.9 2.1

0.9 0.9 0.6

0.7 1.9 1.7

0.9 1.0 0.7

37 38

2900

200

2.8

2.2

1.6

1.4

1.2

0.3

1.9

0.5

39

-

200

2.3

2.1

1.2

1.9

2.2

0.3

3.4

0.9

40

-

50

3.5

4.1

-

3.0

1.9

0.4

-

1.3

41

4840 -

4340 4790 200

0.9 2.9 1.9

2.2 2.0 1.8

0.7 2.0 1.3

1.3 1.2 1.4

0.5 1.9 1.1

0.7 0.7 0.2

0.6 1.9 1.1

0.7 0.7 0.3

42 43

4158

959

2.0

2.0

1.0

1.5

0.8

1.2

0.9

1.2

44

-

200

1.7

1.7

2.8

1.7

0.6

0.5

0.9

0.4

45

-

50

3.0

3.6

3.2

2.1

1.7

0.6

1.1

0.6

46

4830

293

1.0, 1.3 0.4 0.3 1.3

1.4

0.7, 0.7 0.3 0.2 0.8

0.8

0.7, 0.8 0.3 0.2 0.6

0.7

0.7, 0.8 0.3 0.3 0.6

0.7

993 4725 4810

1.2 1.8 1.8

27

0.9 1.2 1.2

0.7 0.7 0.7

1.1 1.1 1.1 1.0 1.1 1.0

0.7 0.7 0.7


66o 26.3’ S 66o 16.6’ S

41o

2.6’ W 30o 17.8’ W

47

4590

4540

0.7

0.9

0.6

0.9

0.5

0.6

0.5

0.6

48

4750

66o 3.2’ S 65o 58.2’ S 65o 55.2’ S

0o 47.1’ W 33o 20.3’ W 35o 49.4’ W

49

4650

50

4800

220 960 2470 4700 1180 4600 4300

0.9 0.7 1.0 1.0 1.1 0.4 0.8

1.6 1.3 1.5 2.1 1.5 1.6 2.0

0.7 0.5 0.6 0.6 0.5 0.3 0.5

1.5 1.2 0.8 0.7 1.3 1.5 0.8

0.6 0.5 0.6 0.5 0.8 0.6 0.6

0.7 0.7 0.7 0.7 1.0 1.1 0.7

0.6 0.5 0.7 0.5 0.8 0.6 0.6

0.7 0.7 0.7 0.7 1.0 1.2 0.7

51

4770

4270

0.6

1.3

0.3

0.9

0.5

0.7

0.6

0.7

65o 39.9’ S

37o 42.5’ W

52

4710

65o 38.1’ S

36o 30.2’ W

53

4742

64o 58.6’ S 64o 48.9’ S 64o 25.1’ S 64o 24.5’ S 64o 1.2’ S 63o 57.0’ S 63o 56.6’ S

2o 0.2’ W 42o 29.3’ W 45o 51.0’ W 0o 22.2’ E 1o 20.8’ E 49o 9.2’ W 40o 54.0’ W

54

4331

230 990 2601 2840 4230 4631 4680 288 1037 4710 901

0.6 0.5 0.1 1.1 0.7 0.7 0.6 0.3 0.5 0.4 1.1

2.1 1.6 1.1 1.1 1.1 1.1 1.1 2.4 1.8 1.2 1.7

0.6 0.4 0.1 0.7 0.5 0.4 0.4 0.3 0.4 0.2 0.7

1.3 0.9 0.9 1.0 0.8 0.8 0.8 1.3 1.1 0.7 1.1

0.5 0.5 0.1 0.9 0.5 0.5 0.5 0.2 0.4 0.2 0.7

0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.8 0.6 0.7 0.8

0.5 0.6 0.1 0.8 0.4 0.5 0.5 0.3 0.4 0.1 0.6

0.7 0.7 0.6 0.7 0.6 0.6 0.6 0.7 0.6 0.7 0.9

55

4650

960

0.5

1.0

0.4

0.9

0.4

0.5

0.4

0.5

56

4390

57

5019

220 4340 1120

0.9 0.7 1.2

1.2 1.2 1.6

0.8 0.5 0.7

0.9 0.8 1.1

0.5 0.4 0.6

0.6 0.7 1.1

0.6 0.3 0.7

0.6 0.6 1.1

58

3721

1043

1.4

1.2

0.9

1.5

0.8

1.1

0.9

1.1

59

3480

60

4575

63o 45.1’ S

50o 54.3’ W

61

2460

2970 3430 4075 4525 4570 263 300 952 1010 2150 2162 2410

0.8 0.9 1.2 1.1 1.1 2.2 2.1 1.7 1.7 1.8 1.8 2.0

4580

63

4560

64

940

63o 10.7’ S 62o 37.1’ S

42o 46.0’ W 43o 12.7’ W

65

3855

66

3140

1.3 1.3 0.7 0.7 0.4 1.6 2.5 1.5 2.0 1.6 1.7 1.8, 1.7 0.6 0.5 0.2 0.0 7.5 7.6 3.8 7.5 0.3 0.3 0.3 0.5 1.4

1.6 1.6 0.5 0.6 0.6 2.8 2.8 2.8 2.8 2.8 2.8 2.8

62

1.5 1.5 0.7 0.8 0.3 1.9 2.9 1.8 2.3 1.9 1.9 2.0, 1.9 1.0 0.7 0.2 0.3 8.2 7.8 4.4 8.4 0.8 0.7 0.2 0.6 1.2

1.7 1.7 0.6 0.6 0.6 3.1 3.1 3.0 3.0 3.1 3.0 3.0

41o 45.9’ W 41o 47.2’ W 52o 6.3’ W

1.5 1.6 0.5 0.6 0.4 2.0 2.6 1.3 1.2 0.7 0.7 0.7, 0.8 0.8 0.8 0.1 0.1 3.5 3.3 2.0 4.2 0.8 0.9 0.3 0.3 0.8

1.6 1.6 0.9 0.9 0.9 2.0 1.9 2.1 2.2 2.4 2.4 2.2

63o 31.0’ S 63o 31.0’ S 63o 29.6’ S

1.5 1.5 1.0 0.8 0.4 1.8 2.3 1.2 1.1 1.7 1.6 1.7, 1.5 0.9 0.7 0.3 0.3 3.5 3.9 2.4 4.5 0.9 1.0 0.2 0.4 0.8

4080 4530 4091 4548 229 260 876 900 3355 3805 2510 2528 3130

1.1 1.4 1.2 1.4 2.9 3.2 3.3 3.3 1.2 0.9 1.2 1.2 1.2

28

1.0 1.1 1.0 1.2 4.0 4.0 3.5 3.5 0.8 0.7 0.8 0.8 0.8

0.6 0.6 0.6 0.6 11. 11. 10. 10. 0.4 0.5 1.2 1.2 1.2

0.5 0.5 0.5 0.5 9.3 9.2 8.2 8.2 0.3 0.3 0.8 0.8 0.8


62o 4.5’ S 60o 11.3’ S

40o 35.7’ W 38o 8.6’ W

67

3375

3365

1.1

1.6

1.1

0.9

0.7

1.7

1.0

1.4

68

2969

2959

1.3

1.5

1.4

1.0

1.2

1.2

1.1

1.1

Table 4. Major axes of the tidal ellipses from the depth-dependent velocities at the observation locations for each constituent for ROMS along with the measured value and observational uncertainty.

Rms Positive rotating component Absolute error (anticlockwise) Negative rotating component Absolute error (clockwise) No. of sites exceeding uncertainty

All Observations M2 S2 K1 O1 1.7 1.2 4.5 4.5 1.23 0.91 1.76 1.58 1.01 0.69 0.87 0.89 9

7

26

27

Table 5. Rms differences for the major axes of the tidal ellipses and absolute errors for the positive and negative rotating components from the depth-dependent velocities at the observation locations for each constituent from ROMS.

29


a.

LIS

-65

2

-70 AP

Latitude

Maud Rise

South Orkney Is.

M critical latitude

b. -60

-75 3

-80

Ronne Ice Shelf Filchner Ice Shelf

-80

-60

-40

-20

0

Longitude Figure 1. a) The location of the model domain with respect to Antarctica. b) The model domain with the water column thickness contoured at 100, 500, 1000, 2000, 3000, and 5000 m. The Filchner-Ronne and Larsen Ice Shelf edges are indicated by dashed lines in b.

30


a. -60

21

20 19

24 23 22

18

Latitude

-65 -70

16 17 15 13 14 12 1011

-75 9

-80

2

3

5

78

1

-80

-60

-40

b. -60

-20

0

65 64 63 62 61 60 58 59 54 55 51 52 504947 46 4540 44 441 3 41 39 38 37 36 3 433 32

-65 Latitude

6 4

-70

14 13 12 10 911 8 67

-75

15

56 57 53 48 42 35 31 329 05 28 27 26 217 24 23 22 18 21 20 19 16

5 4 23 1

-80

-80

-60

-40

-20

0

Longitude Figure 2. The locations of tidal elevation observations are indicated by numbers in a) and those of velocity observations by numbers in b). The 1000 m isobath is shown.

31


a. -60

0o M2

Latitude

-65 -70 -75 -80

0

100

o

50

-80

-60

-40

-20

0

Longitude -60 b.

25 10 5

S2

2

-65 Latitude

1

-70

0

-75

Land (cm) 0o

-80 -80

-60

-40

-20

0

Longitude Figure 3. The amplitude of the tidal elevation for the a) M2,, b) S2 , c) K1 , and d) O1 constituents in cm. The overlaid heavy dashed lines indicate the phase for the elevation, with the zero phase line indicated in a) and b).

32


c. -60

K1

Latitude

-65 -70 -75 100

-80

50

-80

-60

-40

-20

0

25

Longitude 10

-60 d.

5

O

1

2

Latitude

-65

1

-70

0

-75

Land (cm)

-80 -80

-60

-40

-20

Longitude Figure 3. (cont.)

33

0


Figure 4. The major axes of the tidal ellipses for the depth-independent velocities for the M2,, b) S2 , c) K1 , d) O1 constituents, in cm s-1 . e) The same for M2 with only M2 forcing and f) for M2 from the depthdependent surface velocities.

34


Figure 4. (cont.)

35


Figure 4. (cont.)

36


0 Depth (km)

a.

b.

IT

-1

IT 60o W

IT

-2

-4 0 Depth (km)

c.

50o W

critical latitude

Depth (km)

0

10.0 IT

5.0 -2

2.5

IT

-4

IT

40o W

1.0

0 Depth (km)

d.

0.0

-2 -4

Ice Shelf IT

30o W

IT

0 Depth (km)

e.

7.5

Bottom

(cm s -1 )

-2 -4 IT

o

-6 0 W -80

IT -75

-70 Latitude

-65

Figure 5. The major axes of the M2 tidal ellipses from the depth-dependent velocities along N-S transects at a) 60o W, b) 50o W, c) 40o W, d) 30o W, and e) 0o W. IT indicates locations of internal tidal generation. The location of the critical latitude is indicated by a dashed line.

37


0

Depth (m)

1000 2000 3000 4000 5000 -75

-70

-65 Latitude

Figure 6. Internal wave ray characteristics starting from 60 57’ S and propagating south for the hydrography and topography used in the model along 40o W according to linear internal wave theory without dissipation. The bold crosses are separated by one M2 tidal period.

38


Depth (m)

0

5

500 2, 3, 4

0

10 20 30 0

10

20 0

27, 28

26

0

Depth (m)

9, 10, 12, 13

7

250

750

5

10 0

5

10 0

30

5

10

5

10

31

1000 2000 3000 4000

19, 20, 21

0 0

Depth (m)

6, 8

5

32

10 0

5

10 0

36

5

10 0

10 0

5

52

48

46

1000 2000 3000 4000 5000 0

Depth (m)

2

4

53

0

0

2

4

0

2

4

61

60

0

2

4

0

2

4

2

4

66

64

1000 2000 3000 4000 5000 0

2

4

0

2

4

0

2

4

0

-1

Major Axis (cm s

5

10 0

)

Figure 7. Major axes of the M2 tidal ellipses from ROMS (crosses) compared against observational data (diamonds). The error bars indicate the observational uncertainty (1.7 cm s-1 ). The top row shows locations near the ice shelf edge. The second row shows locations along the eastern end of the transect across the Weddell Sea and the third and bottom rows for the deep, middle section and the western end, respectively.

39


0 Depth (km)

a.

-1 60o W

b. Depth (km)

0

-4 c.

CSW

-2

30 50o W

20

Depth (km)

0

10 CSW

-2 -4

5 2

40o W

1

0 Depth (km)

d.

-2 -4

0

CSW

Ice Shelf Bottom

30o W

0 Depth (km)

e.

(cm s -1 )

-2 -4 o -6 0 W -80

-75

-70 Latitude

-65

Figure 8. The major axes of the K1 tidal ellipses from the depth-dependent velocities along N-S transects at a) 60o W, b) 50o W, c) 40o W, d) 30o W, and e) 0o W, in cm s-1 . CSW indicates continental shelf waves.

40


Depth (m)

0

5

6, 8

7

9, 10, 12, 13

250 2, 3, 4

500 750 0

5

Depth (m)

5

26

0

10 0

10

27, 28

20

0

10

30

20 0 10 20 30 31

1000 2000 3000 4000

19, 20, 21

0 0

Depth (m)

10 0

32

4

8 0

2

36

4 0

2

4 0

2

4 0

2

4

2

4 0

2

4

2

4

48

46

52

1000 2000 3000 4000 5000 0

Depth (m)

0

53

2

4 0

2

60

4 0

2

4 0

61

66

64

1000 2000 3000 4000 5000 0

2

4 0

2

4 0

2

4 0

-1

Major Axis (cm s

5

10 0

)

Figure 9. Major axes of the K 1 tidal ellipses from ROMS (crosses) compared against observational data (diamonds). The error bars indicate the observational uncertainty (1.7 cm s-1 ). The top row shows locations near the ice shelf edge. The second row shows locations along the eastern end of the transect across the Weddell Sea and the third and bottom rows for the deep, middle section and the western end, respectively.

41


Figure 10. The a) standard deviation of the elevations (cm) and the b) combined standard deviations of the depth-dependent surface velocities (cm s-1 ).

42


0 Depth (km)

a.

60o W

0 Depth (km)

b.

-2

-4 0 Depth (km)

c.

20 10

50o W

5 4

-2

3 -4

40o W

2

0 Depth (km)

d.

-1

1

-2

0

-4

Ice Shelf Bottom

30o W

0 Depth (km)

e.

(cm s -1 )

-2 -4 o -6 0 W

-80

-75

-70 Latitude

-65

Figure 11. The combined standard deviations in the depth-dependent velocity anomalies (difference between the depth-dependent and depth-independent velocities) over 15 days at a) 60o W, b) 50o W, c) 40o W, d) 30o W, and e) 0o W. The M2 critical latitude is indicated by a dashed white line.

43


0 Depth (km)

a.

-1 60o W

b.

-4 0 Depth (km)

c.

2

50o W

critical latitude

-2 M

Depth (km)

0

1E-001 5E-002 1E-002

-2

5E-003 -4

40o W

1E-003

0 Depth (km)

d.

-2 -4

Ice Shelf 30o W

Bottom

0 Depth (km)

e.

(s -1 )

-2 -4 -6

0o W -80

-75

-70 Latitude

-65

Figure 12. Vertical shear in the depth-dependent velocities along N-S transects at a) 60o W, b) 50o W, c) 40o W, d) 30o W, and e) 0o W. The M2 critical latitude is indicated by a dashed white line.

44