M2 Baroclinic

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or collective redistirbutionor collective of this by of any article portion Th THE INDONESIAN SEAS published in been has is article

M2 Oceanography , Volume 4, a quarterly journal of Th 18, Number

BAROCLINIC or other means reposting, photocopy machine, is only w permitted TIDES in the Indonesian Seas

BY ROBIN ROBERTSON AND AMY FFIELD Society. Copyright e Oceanography 2005 by Th

Baroclinic, or internal, Ocean. We used a tidal model to simulate in depths less than 2000 m where the tides play a signiﬁ cant the barotropic and baroclinic tides in the internal tidal wavelength ranges from

role in mixing in the deep Indonesian seas to verify model perfor- ~20–50 km. Grid cells of 4–5 km or ith the approval of Th ocean and in shallow mance against observations and to pro- ﬁ ner are required to resolve the internal seas (Munk and Wunsch, 1998; Garrett, vide examples of baroclinic tidal activity. wavelengths in shallow water (Holloway,

2003). In a stratifi ed ocean, when the ver- Although internal tides have been ob- 2001). In a study for Fieberling Guyot Permission reserved. Society. All rights is e Oceanography gran tically uniform horizontal velocities of served in the Indonesian seas, the baro- (Robertson, submitted), a resolution of all correspondence to: Society. Send e Oceanography [email protected] or Th barotropic tides (tides in which surfaces clinic tidal fi elds are not well known. In 1 km was required to accurately predict of constant pressure are parallel to sur- particular, relatively few full-depth, long- mean currents and major axis ampli- faces of constant density) interact with period current observations suitable for tudes. In the Fieberling Guyot study, rough topography, disturbing isotherms accurately quantifying the baroclinic model performance improved with high- and isopycnals, they generate baroclinic tidal fi elds exist. More complete coverage er-resolution (< 1 km) bathymetry and tides, for which the velocities are not ver- has been provided by modeling stud- more vertical layers; however, a resolu- tically uniform. Currents, internal waves, ies; good replication of the barotropic tion of ~5 km was suffi cient for indicat- and heaving isotherms resulting from fi elds has been obtained by Mazzega and ing where baroclinic tides occur. baroclinic tides affect forces on structures Bergé (1994), Hatayama et al. (1996), In this study, our goal is to estimate ted in teaching to copy thisand research. for use Repu article and vessels. Vigorous internal tides have and Egbert and Erofeeva (2002) us- the baroclinic tidal fi elds for the Indo- been observed in the Indonesian seas ing two-dimensional simulations. For nesian seas to provide baroclinic tidal e Oceanography Society, PO Box 1931, Rockville, MD 20849-1931, USA. 1931, Rockville, Box PO Society, e Oceanography with isotherm excursions up to 90 m in the baroclinic tides, three-dimensional information for future observational the Ceram Sea during 14-hour yo-yo sta- simulation is required to include vertical programs and focused regional modeling tions (Ffi eld and Gordon, 1996). Tides variability. Schiller (2004) and Simmons studies. Computing limitations require also affect the generation of mean cur- et al. (2004) simulated the baroclinic a balance between geographic coverage rents and mixing. Mixing processes mod- tides in the Indonesian seas on coarse and model performance, which is reso- ify the ocean’s hydrography, or physical grids (~0.5° in latitude and longitude, or lution dependent. For our overview, we characteristics, leading to density-driven ~50 km) using a z-level model (Modular selected a resolution of 5 km in order to fl ows. In the Indonesian seas, mixing Ocean Model [MOM]) and an isopyc- include the entire Indonesian seas re- blication, systemmatic reproduction, transforms the Pacifi c infl ow waters into nal model, respectively. However, the gion, realizing that this would be a more Indonesian throughfl ow waters (Gordon, grid cell sizes of these simulations are qualitative estimate than an accurate this issue) before export to the Indian inadequate to resolve the internal tides quantitative estimate.

62 Oceanography Vol. 18, No. 4, Dec. 2005 ...our goal is to estimate the baroclinic tidal ﬁ elds for the Indonesian seas to provide baroclinic tidal information for future observational programs and focused regional modeling studies.

Oceanography Vol. 18, No. 4, Dec. 2005 63 TIDALLY INDUCED EFFECTS box in Figure 1a) covers much of the included in the domain and much of the Interactions of the tides with bottom to- Indonesian Seas with a horizontal resolu- region adjacent to the boundaries will be pography affect circulation and mixing, tion of 5 km (Figure 1b) and 24 vertical ignored, due to the infl uence of model both as mean and oscillating effects. Our levels. Realistic bathymetry was taken boundary effects. focus is the latter. In a stratifi ed ocean, from Smith and Sandwell (1997) using internal waves can be generated when the 0 m isobath as the coastline; water TIDAL OBSERVATIONS the tide interacts with topography and depths shallower than 50 m were deep- Model performance evaluation requires the tidal frequency [ω] falls between the ened to 50 m. Smoothing was applied us- observations of both elevation (i.e., sea inertial frequency [f] and the buoyancy ing repeated Gaussian weighting in areas level) and velocities at multiple depths. frequency [N] (i.e., equatorward of the that exceeded the steepness tolerance of Thirteen TOPEX/Poseidon (T/P) satel- critical latitude). The critical latitude is the model. Hydrographic fi elds, potential lite crossover observations of elevations defi ned as the location where the iner- temperature, and salinity for the domain (yellow crosses in Figure 1a and Table 1) tial frequency equals the tidal frequency: 28–30o latitude for the diurnal constitu- o ents and 74.5–86 latitude for the semidi- For more accurate quantitative estimates, higher urnals. According to linear internal wave theory, the strength of internal-wave gen- horizontal and vertical resolutions are required. eration is dependent on the stratifi cation characterized by the buoyancy frequency, the inertial frequency, and the steepness were optimally interpolated from obser- and four moorings with velocities ob- of the bathymetry with the strongest vational profi les in the region obtained servations at multiple depths (red stars generation, both in amount and magni- from the National Oceanographic Data in Figure 1) were used. The T/P cross- tude, occurring when the steepness of the Center. Tidal forcing focused on a single over points of elevation observations bathymetry is roughly equivalent to the constituent, the M2 tide with a period were provided as amplitudes and phase slope of the internal wave characteristics: of 12.42 hrs, and was implemented by lags from the PATHFINDER data base prescribing the M elevations along the (contact R. Ray, [email protected]. ω2 − 2 2 f open boundaries using TPXO6.2 results nasa.gov). Current-meter mooring data N 2 −ω2 (Egbert and Erofeeva, 2002). Flather ra- from the two Makassar moorings were In the Indonesian seas, this criterion diative boundary conditions were used analyzed for tides using the T_Tide soft- predicts internal tides generation by for the normal 2-D velocities, advective ware (Pawlowicz et al., 2002), which steep topography at both diurnal and conditions for the 2-D tangential veloci- also provided estimates of the observa- semidiurnal frequencies over much of ties, Martinsen and Engedahl (1987) fl ow tional uncertainty. the domain. relaxation over four cells for the 3-D velocities, and relaxation over four cells ELEVATIONS

TIDAL MODEL for the tracers. There were no surface or Model estimates of the M2 tidal eleva- We simulated tides using a primitive- bottom fl uxes of tracers and the volume tion amplitudes range from 20–50 cm equation, terrain-following coordinate was unconstrained. A fuller description model, the Regional Ocean Model System of the model, boundary conditions, and Robin Robertson ([email protected] (ROMS) (http://marine.rutgers.edu/po/ forcing can be found in Robertson et al. bia.edu) is Doherty Associate Research Sci- index.php?model=roms). This model has (2003). The model was run for fi ve days entist, Lamont-Doherty Earth Observatory, been used for simulating tides for various before data were saved for analysis, which Palisades, NY, USA. Amy Ffi eld is Senior regions (Robertson et al., 2003; Robert- was suffi cient for the energies to stabilize. Scientist, Earth & Space Research, Upper son, 2005a, 2005b). The domain (yellow The small portion of the Sulu Sea that is Grandview, NY, USA.

64 Oceanography Vol. 18, No. 4, Dec. 2005 Figure 1. (a) Th e bathymetry of the Indonesian Seas with some of the major features identiﬁ ed. Th e model domain is indicated by a yellow dashed box and the locations of TOPEX/Poseidon crossover elevation observations by yellow crosses. Current meter mooring locations in the Makassar Strait and Maluku and Halmahera Seas are marked with red stars. (b) Th e bathymetry over the model domain. Transect locations of Figure 4 are indicated by yellow dashed lines with a red cross at the origin.

Table 1. M2 elevation amplitude and phase lags comparison between T/P crossover observations and model estimates at the locations shown as yellow crosses in Figure 1a. Th e diﬀ erences and rms of the diﬀ erences are given for both the amplitudes and phase lags.

Site Latitude Longitude M2 Amplitude (cm) Phase Lag (o) Obs. ROMS Diﬀ . Obs. ROMS Diﬀ . 1 5° 56’ N 121° 53’E 59.6 66 +6 290 298 +8 2 2° 9’ N 120° 28’E 58.9 71 +12 290 300 +10 3 2° 2’ N 123°17’ E 57.2 65 +8 291 297 +6 4 2° 1’ N 128°58’ E 49.3 46 -3 288 279 -9 5 2° 3’ S 127° 33’E 25.6 21 -5 160 165 +5 6 2° 9’ S 119° 3’ E 46.4 46 0 277 298 +21 7 5° 54’ S 131° 49’E 58.5 51 -8 139 154 +15 8 5° 58’ S 114° 48’E 13.4 19 +6 140 126 -14 9 9° 45’ S 127° 33’ E 62.2 51 -11 120 125 +5 10 9° 45’ S 119° 3’ E 83.1 91 +8 54 66 +12 11 9° 46’ S 133° 13’E 43.5 101 +57 189 189 0 12 13° 30’S 126° 8’E 84.7 68 -15 62 34 -28 13 13° 31’S 120° 28’E 89.7 94 +4 56 66 +10 Rms differences: all sites 18 13 Rms differences: excluding site 11 8 13

Oceanography Vol. 18, No. 4, Dec. 2005 65 Figure 2. (a) Th e elevation amplitude for the M2 tidal constituent over the model domain. M2 elevations amplitudes ranged from 20–50 cm over most of the domain, with higher amplitudes reached in the Indian Ocean, Sulawesi Sea, and along the Australian coast. Lower amplitudes occurred in the Java and Ceram Seas.

(b) Th e phase lag for the M2 elevation over the model domain with the direction of propagation indicated by white arrows. Th e tide propagates from the Indian Ocean through the Timor Sea, where an amphidromic point forms. A portion of the tide also propagates from the Indian Ocean through Lombok Strait into the region south of Makassar Strait. In the Timor Sea, the tide splits with a portion going into the Arafura Sea and another into the Banda Seas. In the Banda Sea, the tide splits again with a portion going into the Flores Sea and another north into the Ceram Sea. South of Makassar Strait is a conﬂ uence region for the portions from Lombok Strait, the Flores Sea, and the weaker portion from the Paciﬁ c Ocean (thinner arrows) via Makassar Strait. From there, it exits via the Java Sea.

through most of the region (Figure 2a). a portion passes through Lombok Strait where the tide coming through Lom- Higher amplitudes occur in the Sulawesi into the region south of Makassar Strait. bok Strait meets the Paciﬁ c tide coming Sea, Indian Ocean, and shallow regions, In the Timor Sea, it splits with one por- through Makassar Strait. The tide exits including along the Australian coast tion progressing into the Banda Sea and this region through the Java Sea. In the where they exceed 150 cm. Lower am- another into the Arafura Sea. The speed, Java Sea, the water depth is very shallow, plitudes, < 20 cm, occur in the Java and c, of tidal progression is dependent on less than 70 m, and the tide progresses Ceram Seas, and near an amphidromic the water depth, H, ( c = gH , where g slowly, resulting in closely spaced phase point (low-amplitude point with phase is gravity, 9.8 m s-2). The tide progresses lag lines (Figure 2b). changing rapidly through 360°), which rapidly in the deep Banda Sea (with bot- These estimates reasonably match the forms in the Timor Sea. tom depths exceeding 7000 m in the 2-D inverse simulations of Mazzega and

The M2 tide enters this region of the Weber Basin), resulting in little change Bergé (1994) and Egbert and Erofeeva Indonesian seas both from the Indian in phase lag. In the Banda Sea, the tide (2002), and the 2-D simulations of Ha- Ocean and the Pacifi c, with stronger continues into the Ceram Sea, which is tayama et al. (1996) and Ray et al. (this tides from the Indian Ocean. As evi- a confl uence region, where the Indian issue). Our 3-D simulation, which is not denced by the phase lag (Figure 2b), the Ocean tide meets that of the Pacifi c, re- an inverse model, reasonably reproduces

M2 tide progresses from the Indian sulting in a reduction of the tidal ampli- the elevations when compared to the T/P Ocean through the Timor Sea, where an tudes. Another conﬂ uence region occurs satellite crossover elevation observations amphidromic point forms. Additionally, at the southern end of Makassar Strait, (yellow crosses in Figure 1a). Differences

66 Oceanography Vol. 18, No. 4, Dec. 2005 between the T/P observations and the jor axes reﬂ ects only the portion of the meet, reducing the tidal elevations (Fig- model estimates are generally small (< maximum velocities at the frequency of ure 2a). In contrast to the elevations,

10 cm and <15°) (Table 1). Phase-lag dif- the tidal constituent, here M2. However, both the barotropic (Figure 3b) and the ferences > 20° occur in areas of rapidly the velocity fi elds contain contributions baroclinic (Figure 4a) M2 tidal velocities changing phase (near the amphidromic at other frequencies and at the mean are high. A strong benthic baroclinic tide point in the Timor Sea and in Makassar and are comprised of geostrophic veloci- occurs on the western side and two baro- Strait), where small differences in loca- ties, tidal residual velocities, harmonic clinic tidal beams originate from the east- tion or bathymetry result in large phase responses, and tidal mixing-induced ern slope at 500 and 800 m water depth. differences. Rms differences between T/P density-driven velocities, along with the Along the transect in the Timor Sea crossover observations and the model es- barotropic and baroclinic tides and vari- and across Ombai Strait into the Banda timates were 18 cm for the amplitude and ous other oscillations. Sea (Figure 1b), baroclinic tides are gen- 13° for the phase lag with all 13 sites in- The barotropic or depth-independent erated primarily in three locations: over -1 cluded. The largest discrepancy (+57 cm) M2 major axes are small (< 2 cm s ) over the Australian slope, on the southern occurs at Site 11, which is both in shallow much of the region (Figure 3b) with shoulder of Timor Island propagating water and near the boundary. This site is higher velocities in shallow water. High offshore, and over the sill north of the within a few kilometers of very shallow major axes occurred in straits, where the Ombai Strait propagating both into the water (28 m), which can be problematic fl uid is forced through the narrow chan- strait and northwest into the Banda Sea for both T/P analysis and the model esti- nels, occasionally reaching major axes (Figure 4b). The strongest internal tides mates. Removing Site 11 reduces the rms of over 50 cm s-1. The magnitude of the occur in the Ombai Strait, with major values to 8 cm and 13°. These discrepan- barotropic major axes correlates with the axes > 50 cm s-1. Focusing on the Ombai cies may be associated with inaccuracies topography, with low major axes in deep Strait because it is a clear example, baro- in the bathymetry and the hydrography water and high values in shallow water clinic tides are evident in the temperature because neither is well known. and narrow straits. fi elds, with isotherm fl uctuations of 50–

The M2 major axes are strongly depth- 200 m (Figure 5a–c). These fl uctuations VELOCITIES dependent particularly in straits and propagate away from the sill into the The model provides two velocity fi elds: a near rough topography, indicating the strait in the three snapshots, which are depth-independent or barotropic veloc- generation and propagation of internal 6 hrs apart (~M2 tidal cycle). The hori- ity fi eld and a depth-dependent velocity tides. This is clearly seen in a selection zontal and vertical model resolutions are fi eld. Both are complete estimates of the of transects of the major axes (Figure 4), barely adequate to resolve these waves. velocity fi elds (i.e., the depth-indepen- with their locations indicated in Figure But, isotherm depths and temperature- dent velocity does NOT need to be add- 1b. Beams of large major axes radiate layer thicknesses are clearly modifi ed ed to the depth-dependent velocity). The from sills and ridges propagating to- with time as the internal tides propagate. depth-dependent velocities include the wards the surface (Figure 4b–e). Large In the transect along the Maluku Sea barotropic or depth-independent mo- baroclinic major axes occur in the Ma- (Figure 4c), internal tides generated over tion through the barotropic-baroclinic luku Sea and Ombai, Lifamatola, and rough topography propagate into the mode linkage in the model. Tidal cur- Makassar Straits (Figure 4a–c), which upper water column where the internal rents are described using a tidal ellipse, also have large barotropic tides (Figure wave rays become more horizontal due which is traced by the tip of the current 3a). The transects in Figure 4 show vari- to stronger stratifi cation. The major axes vector during one complete cycle. The ous baroclinic responses according to increase in the strongly stratifi ed layer. In tidal ellipse is specifi ed by the major and their conditions. the eastern basin, much of the response minor axes representing the maximum The Lifamatola Strait transect (Figure appears not to be locally generated, but and minimum tidal currents along with 1b) lies between the Maluku and Ceram generated nearby, propagating into the the inclination of the orbits and the Seas where the barotropic tide propagat- transect. This includes the surface re- phase (Figure 3a). Discussion of ma- ing from the Indian and Pacifi c Oceans sponse generated along the coast.

Oceanography Vol. 18, No. 4, Dec. 2005 67 The transect through the restriction tide at the eastern edge (Figure 4d). In the transect over Dewakang Sill at in Makassar Strait (Figure 1b) shows These peaks may not be generated by the southern end of Makassar Strait (Fig- a strong baroclinic tide originating at topographic features along the transect, ure 1b), undulations of the sill generate the western shoulder and propagating but by off-transect features with propa- baroclinic tides both over the northern across the strait and a bottom-trapped gation into the transect. hump and at the trough between the

Figure 3. (a) A tidal ellipse is defi ned by the major axis, the minor axis, and the inclination. A phase (not shown) is also used for replicating currents. (b) Ampli- tudes of the major axis of the M2 tidal ellipses from the depth-independent velocity. Th e major axes are small in the deep basin areas and large in the shallow Java, Timor and Arafura Seas. Th e largest barotropic major axes, > 50 cm s-1, occur in narrow straits. (c) Th e maximum depth-dependent major axes in the water column at each grid cell of the M2 tidal ellipses are higher than the depth-independent or barotropic major axes over much of the domain, including the Sulawe- si, Ceram, and Banda Seas and the Makassar Strait. (d) Th e maximum baroclinic anomaly for M2, with the baroclinic anomaly defi ned as the diff erence between the depth-independent and maximum depth-dependent major axes. Th e highest maximum baroclinic anomalies occur in the Sulawesi and Ceram Seas, in Om- bai Strait, and south of Lombok Strait.

68 Oceanography Vol. 18, No. 4, Dec. 2005 humps. These tides propagate in both directions (Figure 4e). Even small fl uctuations of the bathymetry generate internal tides here although some of the high values are attributable to off-transect generation. This region is noted for high baroclinic tides and mixing, with the tidal fi eld highly sensitive to the topographic undulations (Hatayama, 2004). Lee waves were generated in Hatayama’s non-hydrostatic model, but our simulation does not include these lee waves or internal solitons, because it is hydrostatic. To evaluate the model performance in replicating baroclinic tides, model estimates were compared to velocity observations from moorings with multiple instruments. For logistical reasons, these observations are diffi cult to obtain due to strong oscillating currents, fouling from high biological productivity, and high ship traffi c in the regions, particularly fi shing net operations. A persistent problem is strong tidal currents pushing the mooring downwards, with the shallower meters easily pushed as much as 200 to 300 m deeper at some locations during the peak of each tidal cycle (Su- santo and Gordon, 2005; Molcard et al.,

2001). In fact, estimation of the M2 barotropic, depth-independent, tidal currents are not attempted here, because none of the offshore current observations have

Figure 4. Transects of the major axes of the M2 tidal ellipses from the depth-dependent velocity for the (a) Lifamatola Strait, (b) Timor and Ombai Straits, (c) Maluku Strait, (d) Makassar Strait, and (e) over Dewakang Sill. Large baroclinic responses occur in all transects, although some of the baroclinic responses were generated nearby, propagating into the transects.

Oceanography Vol. 18, No. 4, Dec. 2005 69 Figure 5. Th e temperature for a section of the Ombai Strait transect is shown at (a) 6.5 days, (b) 6.75 days, and (c) 7.0 days. Th e (d) 7.5 day temperature diff erences, (e) vertical diff usivity for temperature estimate, KT, averaged over one day, and f) major axes of the M2 tidal ellipses for the same section of the Ombai Strait transect. Th e isotherms and temperature layer thicknesses fl uctuate with the tide in panels (a)–(c) with the isotherms fl uctuating ~50–200 m. High vertical diff usivities over the sill and along the left fl ank in panel (e) coincide with the large gradient in the major axes f). Additionally, the high vertical diff usivity over the sill (e) coincides with the large 7.5 day temperature diff erences in panel (d). It is believed that these diff erences result from mixing over the sill and advection of the mixed fl uid away from the sill in both directions.

sufﬁ cient depth and time resolution to plus one in the Maluku Sea (Luick and meter on the eastern Makassar mooring attain an unbiased depth-average. The Cresswell, 2001) and one in the Halma- (2) was near its target depth of 205 m current-meter mooring records used hera Sea (Cresswell and Luick, 2001). for 32% of the record and the next lower here (red stars in Figure 1a) were read- Unfortunately, all of these moorings current meter on that mooring was near ily available with published depth-de- were blown over by strong tidal cur- its target depth of 255 m for 85% of the pendent velocity statistical information, rents. The uppermost current meter on record (Susanto and Gordon, 2005). consisting of two moorings in Makas- the western Makassar mooring (1), was Consequently, the eastern Makassar sar Strait (Susanto and Gordon, 2005), near its target depth of 200 m for only mooring 2 is assumed to be more accu- which are < 20 km (four grid cells) apart 6% of the record, whereas the uppermost rate, particularly for the deeper estimates

70 Oceanography Vol. 18, No. 4, Dec. 2005 where mooring blowover is reduced. difference between the observations and ure 3c) are signiﬁ cantly larger than the -1 Comparison of the model estimates model estimates of 4.8 cm s for moor- depth-independent or barotropic M2 ma- -1 for the M2 major axes to the observed ing 2, compared to 5.3 cm s for moor- jor axes (Figure 3b) over much of the re- values at the moorings are inconclu- ing 1. For the Maluku and Halmahera gion. They are of similar magnitude only sive (Figure 6). Although the Makassar mooring, rms differences were 2.0 cm in shallow water. To isolate the baroclinic -1 -1 mooring observations are similar to the s and 3.0 cm s , respectively. Both ob- M2 major axes, the depth-independent model estimates (Figure 6a–b), with servational and model errors contribute M2 major axes were removed from the smaller differences for the more accurate to the discrepancies along with other maximum depth-dependent M2 major mooring 2, the observations are insuf- factors such as water-depth differences axes without consideration of phase lag

ﬁ cient to verify the patterns seen with between the model and the observations. to determine the maximum M2 baroclin- the model. The model overestimates the At the mooring locations, differences in ic anomaly. The maximum M2 baroclinic velocities with the differences exceed- the observed water depths and the model anomaly (Figure 3d) shows strong M2 ing the observational uncertainty as de- depth range from ~200–400 m. baroclinic tides (> 20 cm s-1) over rough termined by T_Tide (red error bars in topography in the Sulawesi and Ceram Figure 6a–b). Blowover at the moorings DISCUSSION: IMPLICATIONS Seas and many of the narrow straits. The resulted in a reduction of the major axes OF THE TIDAL VELOCITIES maximum M2 baroclinic anomaly is only -1 in the upper ocean for the observations As discussed earlier, M2 baroclinic tides low (< 2 cm s ) in the Java, Timor, and where the model indicates an increase. occur throughout the region. The maxi- Arafura Seas.

The higher accuracy of the Makassar mum depth-dependent M2 major axes in Baroclinic tides induce vertical mix- mooring 2 is reﬂ ected in a lower rms the water column at each grid cell (Fig- ing, which is characterized by the vertical

Figure 6. Th e M2 major axes at the Makassar Strait moorings (a) 1 and (b) 2, (c) the Maluku mooring and (d) the Halmahera mooring are indicated by a blue line with dots at the levels for the model estimates and red diamonds for the observations. Th e observational uncertainties as determined by T_Tide are indicated by error bars, when available.

Oceanography Vol. 18, No. 4, Dec. 2005 71 mixing coeffi cient for density, K . Be- 500 m, refl ecting an upper ocean heat entire domain. The maximum baroclinic cause in this application vertical diffusiv- transfer. The surface cooling is a result of tidal anomalies, defi ned as the difference ities for temperature, KT, and salinity, KS, lack of a surface radiative heat fl ux rep- between the maximum depth-dependent are the same, KT is equivalent to K . KT is resenting incoming solar radiation. This major axes within the water column and calculated in the model according to the application also ignores freshwater fl uxes the depth-independent major axes for stratifi cation and the vertical shear of the representing net evaporation/precipita- each grid cell, were > 5 cm s-1 through horizontal velocities using the dissipa- tion. Mixing over the sill and along the most of the domain and > 20 cm s-1 over rough topography in the Sulawesi and Ceram Seas and in many of the straits. Improved performance can also be obtained through These tides induced modifi cations of the thickness of the density layers and iso- more accurate bathymetry and hydrography. therm displacements of 50 m near the thermocline. Larger isotherm displacements, reaching 200 m, occurred in the tion-based version of the Generic Length fl anks in the regions of high KT (Figure weaker stratifi cation below the perma- Scale method. This method is based on 5e) may induce most of the temperature nent pycnocline. High vertical mixing the gradient Richardson number, Rig, differences with advection spreading coeffi cients and large temperature differ- which is a ratio of the stability of the them away from the sill. ences often accompanied the baroclinic water column to the vertical shear in the tides, occurring in the high shear zone water column. An example of the model SUMMARY adjacent to the internal tide beams. estimate for KT averaged over one day We used a 3-D, primitive equation, Of particular interest, strong baroclin- for the Ombai Strait is shown in Figure terrain-following coordinate model ic tides often coincided with important

5e. Model estimates of KT increase in the (ROMS) to simulate the M2 barotropic Indonesian throughfl ow choke points in shear zone below the internal tide beams and baroclinic tides in the Indonesian straits where measurements were needed in the Ombai Strait (Figure 5e–f). Active seas. Model estimates of elevation and to quantify the fl ow of Pacifi c water that mixing and KT increase as Rig decreases, major axes of the tidal ellipses agreed passes through the Indonesian seas into with values of Rig less than 0.2 indicating well with T/P crossover and current-me- the Indian Ocean (Sprintall et al., 2004). an unstable water column. In the upper ter mooring observations for the model For example, the Ombai Strait revealed water column, high stratifi cation associ- resolution (5 km). Rms differences be- the largest baroclinic tides, in excess of ated with the permanent thermocline tween the model estimates and observa- 50 cm/s, with mid-water column tidal results in high Rig values and low KT val- tions were 18 cm and 13° for the eleva- velocity maximums. The Ceram Sea was ues. Thus, high diffusivity values over the tion amplitudes and phases. Discrepan- also a region of interference when con- sill in Figure 5e are signifi cant. It could cies were attributed to the coarse resolu- sidering the barotropic tides alone, be- be argued that they are a benthic bound- tion and/or inaccuracies in bathymetry cause the tide originating from the north ary response, but high shear in the major and hydrography. (Pacifi c) in the Halmahera and Maluku axes results from a beam of baroclinic Strong, baroclinic M2 tides were gen- Seas met the tide originating in the In- tides, and not a boundary-layer effect, erated along the shelf slope break and dian Ocean, which propagated through indicating the baroclinic tide increases over rough topography, particularly in Makassar Strait and the Banda Sea. The the shear and KT. straits. The baroclinic tidal velocities different propagation paths resulted in Mixing is apparent in the temperature exceeded the barotropic velocities over different phases and the destructive in- differences over 7.5 days (Figure 5d). most of the domain, with the maximum terference causes low tidal elevations. In Generally, there is a loss of heat from the baroclinic tidal major axes within the addition, the Lombok Strait, possibly the upper 200 m and a gain between ~250– water column > 5 cm s-1 over nearly the location of a planned Directed Research

72 Oceanography Vol. 18, No. 4, Dec. 2005 Initiative by the Offi ce of Naval Research non-hydrostatic model. Both multiple- Martinsen, E.A., and H. Engedahl. 1987. Imple- (Characterization and Modeling of Ar- constituent simulations to evaluate the mentation and testing of a lateral boundary scheme as an open boundary condition in a chipelago Strait Dynamics), was one of transfer of energy between frequencies barotropic ocean model. Coastal Engineering the most baroclinic regions revealed by and fi ner-resolution simulations are 11:603-627. Mazzega, P., and M. Bergé. 1994. Ocean tides in the model, yet appeared to have a fairly presently in progress, but not non-hy- the Asian semi-enclosed seas from TOPEX/ smooth barotropic tide regime with drostatic simulations by these authors. POSEIDON. Journal of Geophysical Research little contrast in phase north of the strait In the future, we plan to focus on high- 99:24,867–24,881. Molcard, R., M. Fieux, and F. Syamsudin. 2001. The versus south of the strait in the Indian resolution simulations of the strait re- throughfl ow within Ombai Strait. Deep-Sea Ocean. Because internal tides induce ver- gions and to investigate the effects of the Research 48:1,237–1,253. tical mixing due to the increase in shear, seasonal changes in the hydrography on Munk, W., and C. Wunsch. 1998. The moon and mixing: Abyssal recipes II. Deep-Sea Research all these “choke point” straits also have a the baroclinic tidal fi elds. 45:1,977–2,010. highly depth-dependent mixing variabil- Pawlowicz, R., R. Beardsley, and S. Lentz. 2002. ity that will contribute to the consider- ACKNOWLEDGEMENTS Classical tidal harmonic analysis with error analysis in MATLAB using T_Tide. Computers able modifi cation of the Indonesian seas Funding for this work has been provid- and Geoscience 28:929–937. thermohaline characteristics before they ed by the U.S. Offi ce of Naval Research Robertson, R., A. Beckmann, and H. Hellmer. 2003. M tidal dynamics in the Ross Sea. Antarctic Sci- are exported to the Indian Ocean. through grant N00014-03-1-0423. We 2 ence 15:41–46. These coarse-resolution results are would also like to thank Richard Ray Robertson, R. 2005a. Barotropic and Baroclinic useful as a qualitative indicator for plan- and two anonymous reviewers for their tides in the Ross Sea. Antarctic Science 17:107– 120. ning observational or higher-resolution helpful comments. Lamont-Doherty Robertson, R. 2005b. Barotropic and baroclinic modeling studies. For more accurate Earth Observatory contribution number tides in the Weddell Sea. Antarctic Science. quantitative estimates, higher horizon- 6819. Robertson, R. Submitted. Modeling internal tides: Resolution, parameterization, and performance. tal and vertical resolutions are required. Ocean Dynamics. Improved performance can also be ob- REFERENCES Schiller, A. 2004. Effects of explicit tidal forcing in tained through more accurate bathym- Cresswell, G.R., and J.L. Luick. 2001. A note on cur- an OGCM on the water-mass structure and cir- rent measurement in the Halmahera Sea. Jour- culation in the Indonesian throughfl ow region. etry and hydrography. Only one semidi- nal of Geophysical Research 106:13,945-13,951. Ocean Modelling 6:31–49. urnal constituent was used for this study, Egbert, G.D., and S. Erofeeva. 2002. Effi cient in- Simmons, H.L., R.W. Hallberg, and B.K. Arbic. 2004. Internal wave generation in a global although multiple constituents interact. verse modeling of barotropic ocean tides. Journal of Atmospheric and Oceanic Technology baroclinic tide model. Deep-Sea Research II The tidal fi elds are affected not only 19:22,475-22,502. 51:3,043–3,068. through integration of the constituents, Ffi eld, A., and A.L. Gordon. 1996. Tidal mixing sig- Smith, W.H.F., and D.T. Sandwell. 1997. Global natures in the Indonesian seas. Journal of Physi- seafl oor topography from satellite altimetry and but also through fortnightly beating ef- cal Oceanography 26:1,924-1,935. ship depth soundings. Science 277:1,956–1,962. fects and harmonic transfer of energy Garrett, C. 2003. Internal tides and ocean mixing. Sprintall, J., S. Wijffels, A.L. Gordon, A. Ffi eld, R. between constituents. Observations Science 301:1,858-1,859. Molcard, R.D. Susanto, I. Soesilo, J. Sopahe- Hatayama, T. 2004. Transformation of the Indone- luwakan, Y. Surachman, and H.M. van Aken. have shown that fortnightly beating is sian throughfl ow water by vertical mixing and 2004. INSTANT: A new international array associated with very strong baroclinic its relation to tidally generated internal waves. to measure the Indonesian throughfl ow. Eos tides and high mixing (Hatayama, 2004; Journal of Oceanography 60:569-585. Transactions of the American Geophysical Union Hatayama, T., T. Awaji, and K. Akitomo. 1996. Tidal 85:369–376. Susanto et al., 2000; Ffi eld and Gordon, currents in the Indonesian seas and their effect Susanto, R.D., and A.L. Gordon. 2005. Velocity and 1996). Another limitation of the ROMS on transport and mixing. Journal of Geophysical transport of the Makassar Strait throughfl ow. Journal of Geophysical Research 110:C01005, model is its inability to simulate the lee Research 101:12,353-12,373. Holloway, P.E. 2001. A regional model of the semi- doi:10./1029/2004JC002425. waves generated by the interactions of diurnal internal tide on the Australian North Susanto, R.D., A.L. Gordon, J. Sprintall, and B. barotropic tides with topography. This West Shelf. Journal of Geophysical Research Herunadi. 2000. Intraseasonal variability and 106:189,625-19,638. tides in Makassar Strait. Geophysical Research limitation is inherent in the hydrostatic Luick, J.L., and G.R. Cresswell. 2001. Current mea- Letters 27:1,499–1,502. assumption and simulation of the lee surements in the Maluku Sea. Journal of Geo- waves would require switching to a physical Research 106:13,953-13,958.

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